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Thermal behavior of atria: a comparative study between measured data and a computational fluid dynamics model

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Thermal behavior of atria: a comparative study between measured data and a computational fluid dynamics model

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Content THERMAL BEHAVIOR OF ATRIA A COMPARATIVE STUDY BETWEEN MEASURED DATA A N D A COMPUTATIONAL FLUID DYNAMICS MODEL by Amitabh Barthakur A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF BUILDING SCIENCE (Architecture) December 1996 Copyright 1996 Amitabh Barthakur Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UNIVERSITY OF SOUTHERN CALIFORNIA SCHOOL OF ARCHITECTURE UNIVERSITY PARK LOS ANGELES, CA 90089-0291 This thesis, written B y AMlTA&H foARTHAKUK_ _ _ _ _ _ _ _ _ _ _ _ _ under the direction o f his, Thesis Committee, and approved B y a d its mem6ers, has B een presented to and accepted B y the (Dean o f The SchooC o f Architecture in partialfulfillment o f the requirements fo r the degree o f l^>TEt-0MQtLPlN6 eClEHCF______________ i — V i ___________ < Dean (Date kJoQ ^ t» THESIS COMMITTEE / t (L rf, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I TABLE OF CONTENTS Page n LIST OF FIGURES AND TABLES v m ACKNOWLEDGEMENTS ix Chapter 1 INTRODUCTION 1 1.1 Issues 1 1.2 Need for Study 5 1.3 Hypothesis 6 1.4 Methodology 6 1.5 Speculative Conclusions 7 Chapter 2 ATRIA g 2.1 Emergence and Re-emergence 8 2.2 Typology 10 2.3 Energy and Atria 1 1 2.4 Available Analysis Tools 14 2.5 Existing Research 16 2.6 Limitations 21 Chapter 3 SELECTING A ‘MODEL’ ATRIUM: THE BRADBURY BUILDING 22 3.1 Selection Criteria 22 3.2 The Bradbury Building 23 ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.2.1 Location 3.2.2 Configuration 3.3.3 Construction and Maintenance 23 24 29 Chapter 4 DATA COLLECTION AND PREPARATION OF A BASF. - CASE 32 4.1 The Variables 32 4.2 Collection method 33 4.3 Data Collection 34 4.3.1 Data and Observations 36 4.4 Preparation of a Base-Case 62 Chapter 5 COMPUTATIONAL FLUID DYNAMICS SIMULATIONS 67 5.1 Computational Fluid Dynamics(CFD) 67 5.2 Selection Criteria for a CFD software 68 5.3 PHOENICS 69 5.3.1 Structure 70 5.3.2 Calculation Procedure 71 5.3.3 Input Techniques 77 5.4 Inputting the 2 Dimensional Model of the Bradbury Building Atrium 79 5.5 Simulations 81 5.5.1 Unventilated Model with Symmetrical Boundary Conditions 83 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.5.2 Unventilated Model with Asymmetrical Boundary Conditions 89 5.5.3 Naturally Ventilated KE Model with Symmetrical Boundary Conditions 95 5.5.4 Naturally Ventilated KE Model with Asymmetrical Boundary Conditions 103 5.5.5 Simulation of Night-Time Conditions with Symmetrical Boundary Conditions 110 Chapter 6 FINAL OBSERVATIONS. CONCLUSIONS AND BROAD RECOMMENDATIONS 115 6.1 Observations Based on Temperature Data Collected 115 6.2 Conclusions Drawn from the CFD Simulations 116 6.3 Broad Recommendations 117 BIBLIOGRAPHY 119 APPENDIX 120 iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. II LIST OF FIGURES AND TABLES 1.1 The Mediterranean City Page 1 1.2 The Roman Atrium 1 1.3 The 19th Century Conservatory 2 1.4 John Portman’s Atrium Hotels 2 1.5 The Green House Effect 3 1.6 Stack Effect 4 2.1 The Core Atrium 10 2.2 The Integrated Atrium 11 2.3 The Linear Atrium 11 2.4 The Attached Atrium 11 2.5 The Envelope Atrium 11 2.6 Heating 12 2.7 Cooling 13 2.8 Daylighting 13 3.1 The Bradbury Building: 1st Floor Plan 25 3.2 The Bradbury Building: Typical Floor Plan 26 3.3 View of the Bradbury Building from Broadway 27 3.4 Another View from Broadway 27 3.5 Interior View of the Atrium 28 3.6 View from the Stairway 28 3.7 View Along the Walkway 28 v Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.8 The ‘Floating’ Elevators 28 4.1 The Stowaway Temperature Data Logger 33 4.2 Position of the Data Loggers Inside the Atrium 35 4.3 Stratification on the North Face 37 4.4 Stratifications on the South Face 38 4.5 Typical Day 40 4.6 Vertical Profile (Max.) on a Typical Day 41 4.7 Vertical Profile (Min.) on a Typical Day 42 4.8 Hot Day 43 4.9 Vertical Profile (Max.) on a Hot Day 45 4.10 Vertical Profile (Min.) on a Hot Day 46 4.11 Cool Day 48 4.12 Vertical Profile (Max.) on a Cool Day 49 4.13 Vertical Profile (Minimum) on a Cool Day 50 4.14 Surface and Air Temperature (5th Floor) 52 4.15 Surface and Air Temperature (4th Floor) 53 4.16 Surface and Air Temperature (3rd Floor) 54 4.17 Surface and Air Temperature (2nd Floor) 55 4.18 Air Temperature (1st Floor) 56 4.19 Typical Day (5th Floor) 58 4.20 Typical Day (4th Floor) 59 4.21 Typical Day (3rd Floor) 60 4.22 Typical Day (2nd Floor) 61 v i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.23 Vertical Profile (Max.) 64 4.24 Vertical Profile (Minimum) 64 4.25 Projected Conditions 65 5.1 The Basic Structure of PHOENICS 71 5.2 PHOENICS Grid Geometry 73 5.3 Slab-wise Operations in PHOENICS 75 5.4 Cell Distribution for the Atrium of the Bradbury Building in PHOENICS 80 5.5.1 Temperature Contours in the Unventilated Model with Symmetrical 85 Boundary Conditions 5.5.2 Velocity Vectors in the Unventilated Model with Symmetrical 86 Boundary Conditions 5.5.3 Horizontal Direction Velocity Contours in the Unventilated Model 87 with Symmetrical Boundary Conditions 5.5.4 Vertical Direction Velocity Contours in the Unventilated Model with 88 Symmetrical Boundary Conditions 5.6.1 Temperature Contours in the Unventilated Model with Asymmetrical 91 Boundary Conditions 5.6.2 Velocity Vectors in the Unventilated Model with Asymmetrical 92 Boundary Conditions 5.6.3 Horizontal Direction Velocity Contours in the Unventilated Model 93 with Asymmetrical Boundary Conditions 5.6.4 Vertical Direction Velocity Contours in the Unventilated Model with 94 Asymmetrical Boundary Conditions 5.7.1 Temperature Contours in the Naturally Ventilated K-Epsilon Model 98 with Symmetrical Boundary Conditions 5.7.2 Velocity Vectors in the Naturally Ventilated K-Epsilon Model with 99 Symmetrical Boundary Conditions 5.7.3 Horizontal Direction Velocity Contours in the Naturally Ventilated K- 100 Epsilon Model with Symmetrical Boundary Conditions vii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.7.4 Vertical Direction Velocity Contours in the Naturally Ventilated K- Epsilon Model with Symmetrical Boundary Conditions 5.7.5 Kinetic Energy Distribution Contours in the Naturally Ventilated K- Epsilon Model with Symmetrical Boundary Conditions 5.8.1 Temperature Contours in the Naturally Ventilated K-Epsilon Model with Asymmetrical Boundary Conditions 5.8.2 Velocity Vectors in the Naturally Ventilated K-Epsilon Model with Asymmetrical Boundary Conditions 5.8.3~ Horizontal Direction Velocity Contours in the Naturally Ventilated K- Epsilon Model with Asymmetrical Boundary Conditions 5.8.4 Vertical Direction Velocity Contours in the Naturally Ventilated K- Epsilon Model with Asymmetrical Boundary Conditions 5.8.5 Energy Dissipation Contours in the Naturally Ventilated K-Epsilon Model with Asymmetrical Boundary Conditions 5.9.1 Temperature Contours in the Night Time Simulations 5.9.2 Horizontal Direction Velocity Contours in the Night Time Simulations 5.9.3 Vertical Direction Velocity Contours in the Night Time Simulations TABLE 4.1 Recorded and Projected Values of Surface and Air Temperature for Creating a Base Case (4/29/96 2:35PM) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 101 102 105 106 107 108 109 112 113 114 66 v iii m ACKNOWLEDGEMENTS I would like to thank Prof. Marc Schiler, Dr. Mark Spitzglas and Xudong Yang for their guidance, encouragement, and advice from the very conception till the realization of this thesis. I am also grateful to Prof. Pierre Koenig and Prof. Douglas Noble whose encouragement was a valuable part of the process. Among others I am indebted to Ms. Francine Lipsman at the Bradbury Building, without whose help this thesis would not have been possible, Prof. Robert Harris, for giving me the liberty of using his name as a reference when I first met Francine, Mr. John Gautrey at Arup Associates, for the crisp and clear direction he gave to this thesis when it needed it the most, Prof. Anne Grete Hestnes and Prof. 0yvind Ashchehoug at the Norweigian Institute of Technology, and Prof. Yair Etzion at the Ben Gurion University, for helping me establish the initial direction of this thesis, Kjell Kollsaker at SINTEF, Norway, and Michael Holdt at Boulder CO, for the valuable background information on the topic, Howard and Alex at the USC slide library, whose efforts in scanning an unbelievably large number of slides in an even more unbelievably short period of time, greatly helped in making this document presentable, Marie Tran without whose resourcefulness, the hundreds of megabytes of file transfers would not have succeeded, Ingrid Popper whose unfailing efforts kept academic bureacracy out of the way of interfering with this thesis, Valezra Earl and Carole Gustin who allowed a liberal use of the office resources, Ray Madani for letting me use his ‘million dollar’ copying machines at my own convenience and finally to my friends Ram, Archit and Shubhra for contributing each of their specific skills to make this document possible. Amitabh Barthakur ix Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 1 INTRODUCTION 1.1 Issues: Large, vertically dominant open spaces have played a major role in architecture since very early times. The reasons for such spaces to exisrmight have been varied but they have appeared in many cultures and regions. The history of such, Atrium spaces, goes back to more than two thousand years, since when it has functioned either as a commanding entrance or a focal courtyard or a covered semi public space. On the other hand, the open courtyard, which was an efficient functional element of Mediterranean and west-Asian architecture1 (Figure 1.1) in order to keep buildings cool in higher temperatures and allow for more surface area for re-radiation, made the atrium a very necessary and functional part of the local architecture. Figure 1.1 The Mediterranean city Figure 1.2 The Roman Atrium 1 See Saxon, Richard, The Atrium Comes of Age, Longman, Essex, England 1994. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Lack of space and increasing density of cities, resulting in vertical expansion, has made light and fresh air extremely valuable commodities. Atriums have become obvious solutions to provide for such needs. Glazed roofs providing a visual connection to the outside as well as bringing in natural light, atriums provide a great relief to the occupants of its surrounding workspaces. But unfortunately as most outcomes resulting from a search for an universal ‘International Style’ of architecture atriums are seen being ‘plugged’ into many a contemporary building without giving much thought to its appropriateness in terms of response to regional variations in the forces of nature. It seems as if it has been assumed by many a designer that, if one ends up with a chunky office building, one might just punch a hole through it, cover it with glass, and call it an atrium, hoping it would take care of the shortcomings of letting ‘nature in’ which the building might otherwise have had. This in most cases, leads the atrium to harm the functioning of the building rather than adding to its benefits. Figure 1.3 The 19th Century Conservatory Figure 1.4 John Portman’s Atrium Hotels Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. If an atrium’s form, orientation, roofing material and nature of openings complies with climate and prevalent external as well as internal conditions, it can be extremely beneficial to a building in terms of acting as a buffer to the external conditions. It could retain solar heat in cold climates or could funnel out heat in warmer climates. But this is an ideal situation and is less so the case mainly due to the reasons discussed in the preceding paragraph, and it has become an absolute necessity to study the behavior atria m order for them to become positive architectural elements both functionally and spatially in a varied set of conditions. Atria involve the following two natural phenomena2 ; 1) Greenhouse effect: Short wave radiation from the sun pass through glazing to warm interior surfaces. The re-radiated heat in the form of long wave radiation is not able to pass back through the glass. This results in the effect of solar heat to be positive in the winter and negative in the summer. Figure 1.5 The Greenhouse Effect See Hastings, S. R., Passive Solar Commercial and Institutional Buildings: a sourcebook of examples and design insights, IEA, J. Wiley , New York, 1994 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2) Stack effect: The stack effect is the result of the action of pressure differences with altitude; air will always move from a lower opening to a higher one in any enclosed volume. Wind movement over openings will enhance the suction effect. Combined with the buoyancy of air warmed by the greenhouse effect, there will be strong stratification of air by temperature in a tall closed volume. Based on the above, the behavior of atria is believed to be mainly accountable due to its vertical form and its position in the building i.e. the area of adjacent building surfaces and the area of exposed surfaces. Atria act as buffers for adjacent spaces3 and reduce heat loss in cold periods. Energy savings in adjacent spaces partially offset the atrium heating energy. It also contributes heat to adjacent spaces in milder climates. It is seen that core atria or linear atria have more adjacent spaces next to it and has a greater potential for it to act as a buffer to most of the building. With natural ventilation and night ventilation (convective cooling) an atrium can act as a funnel to channel heat out from its adjacent spaces. 3 See Saxon, Richard, The Atrium Comes of Age, Longman, Essex, England 1994 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. It has been seen that the behavior of an atrium in cold climates can be especially favorable. This has resulted in a considerable amount of research in that area. The positive effects of the atrium in cold climates is also mainly due to its ability to retain solar heat within it with the green house effect and hence the research is also directed more towards ‘solar distribution’ within the atrium. With the help of computer programs, the total amount of energy coming into an atrium can be calculated, this can then be distributed to the various surfaces and ‘light elements’ (air), and some fairly close thermal predictions can be made. Still there is a lack of clarity in predicting the following in atria: • Stratification of temperature • Natural ventilation effects • comfort (Radiation, air flow patterns, temperature stratification and humidity) Moreover it has been rarely seen to predict thermal conditions of atria in warmer temperatures. The main reason being that in warmer conditions, the behavior of an atrium depends to a large extent on the buoyant or convective flow of air. This in turn give rise to stratification patterns which become difficult to predict with most of the available analysis tools. 1.2 Need for study: The above observations demand that there is an urgent need to study atrium temperature in wanner temperatures, especially in the area of temperature stratification and air movement within. There is also a need to find out ways of predicting behavior of atriums with regards to the above issues, using computer 5 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. programs or otherwise. This means that one has to find not only a mathematical or empirical model to predict temperature stratification and air movement, but also compare the results with real observations to make sure such predictions are reliable. 1.3 Hypothesis: This thesis aims to study temperature stratification and air movement in an atrium by comparing measured data and computational fluid dynamics (CFD) model for the same atrium. 1.4 Methodology: • An appropriate building is selected to be the ‘model atrium’ for data collection and observation. It is important that the model atrium is close to the generic definition of an atrium, with respect to form, atrium-volume to building-volume ratio and in terms of its occupancy and usage. • An appropriate method to collect temperature data is to be determined. The efficiency of the data collectors will be determined by its size, ease of set up, ease of downloading information and ability to be synchronized in time. • Temperature data is to be collected through a period of time with variations in weather and temperature conditions. • This data has to be organized in various forms in order to understand the behavior of the building itself. Whether stratification happens? If yes, then how and when? What is its magnitude? This data is then further filtered to provide for certain specific base-cases and/or worst cases to be used in the CFD model. 6 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. • A basic understanding of CFD procedures and selection of a simplistic input and graphic output oriented CFD program. • Input the base-case and study outputs as to its compliance to the real conditions. • If the results are favorable then make consecutive runs for other conditions and make appropriate observations. • Draw conclusions based on the above. 1.5 Speculative Conclusions: The primary conclusions will be based on the temperature data collected. One has to see whether the atrium behaves more or less as expected. What is the degree of stratification? Observations have to be made with respect to atrium’s response over a period of time; daily or seasonally to the changing external conditions. The next set of conclusions would be based on the performance of the CFD model and its comparison to the ‘real’ situation. It will also be attempted to see whether the CFD model is appropriate to predict other conditions which cannot be necessarily verified with empirical data. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 2 ATRIA 2.1 Emergence and Re Emergence: Atria have been a design feature in architecture for centuries. Energy conservation might not be the primary reason for its use in most cases other than in the courtyards or open atriums in wanner climates, but its usage and popularity can be accounted for by the following reasons1 : • Dramatic entrances and semi public spaces inside buildings. • Allow for a naturally lit amenity for the building users. • Enable more surfaces in a building to open to ‘nature’. • Facilitate circulation. Until the advent o f the industrial revolution, atria were seen in Roman and Islamic architecture, where architects worked within the limits of masonry, wood and fabric to produce covered semi-open courts. These atria were not always enclosed, mainly due to their presence in a Mediterranean climate. These forms might have had very little resemblance to the conventional atrium of today. The Middle-Eastern city developed on introverted planning principles, with inward looking buildings opening into internal courtyards. These in turn were connected by narrow streets and bazaars covered with fabric to protect from the sun. The behavior and function of these covered streets were close to linear atria. During the early nineteenth century due to European contact with the Islamic world and also due to revived interest in Roman architecture, elements like 1 See Saxon, Richard, The Atrium Comes of Age, Longman, Essex, England 1994. 8 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. covered streets and large semi public interior spaces were appearing in the western architecture. The post industrial period brought about materials like steel and glass and the knowledge that glass was selectively permeable to wavelengths gave rise to an entirely new generation architecture. Greenhouses used this phenomenon and appeared around the early nineteenth century, appealing everyone by its ability to defy climatic conditions and yet come up with ‘open to sky’ spaces2 . These ‘greenhouses’ gradually began to attach themselves to conventional buildings as conservatories. Public buildings in the nineteenth century aspired to the grandeur associated with royalty, of course with more modest means available to them. The creation of monumental spaces became even more difficult with reduction of plot sizes and the need to layer more and more floors one above the other. As a result useful spaces in most of the buildings became gradually smaller in scale and more economical in structure. Some innovative architects like John Nash adopted materials like iron and glass to create grand and well lit interiors economically. The rise of modernism in the early twentieth century, with its emphasis on freestanding cubic form ‘eclipsed but never extinguished the atrium concept’3 . The atrium re-emerged in America around the 1960s, as environmentally controlled (mechanically) public and private spaces in a grand scale. John Portman’s first atrium hotels were soon followed by a lot of architects in the ‘70s and into the ‘80s. This somehow led the mainstream commercial 2 See Saxon, Richard, Atrium Buildings: Development and Design, Van Nostrand Reinhold, New York, 1987 3 Ibid. 9 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. development in North America to adopt the atrium concept universally and believe in its economic value and ‘feasibility’4 . Through the late 70s and early 80s this trend was beginning to be visible both in Europe as well as Japan. In the former case it was mainly due to lower downtown development densities leading to a re-acceptance of the courtyard form while in the latter case it was an outcome of high densities combined with innovations in architectural ideas. It was also around the same time that the Islamic states had more and more control over western prosperity, bringing about rapid development in the Middle Eastern countries. The political scenario and delicate cultural sensitivity in the middle east, led a lot of western architects as well as local architects to build in the Islamic tradition in that region, with shaded courts and in many cases, atria. 2.2 Typology: Atria are usually generally classified on the basis of their configuration and position in a building broadly in the following manner5 : • A Core Atrium is the classical atrium form providing a sheltered glazed courtyard in the center of the building. These atria have only one of its surfaces exposed to the exterior and that is the roof. They are surrounded by adjacent spaces on all sides. 4 See Saxon, Richard, Atrium Buildings: Development and Design, Van Nostrand Reinhold, New York, 1987 5 See Hastings, S. R., Passive Solar Commercial and Institutional Buildings: a sourcebook of examples and design insights, IEA, J. Wiley , New York, 1994 10 Figare2.1 The Core Atrium Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure23 The Linear Atrium Figure2.5 The Envelope Atrium Figure2.2 The Integrated Atrium • An Integrated atrium is positioned in a building in a manner in which only one of its vertical surfaces are exposed to the exterior. Usually they cover a courtyard form created by an ‘U’ shaped building. • A Linear Atrium covers a void between two building blocks. They usually provide sheltered circulation and a semi public open to sky space between the two blocks. • An Attached Atrium is a glazed space a added to one of the external walls of a building. They tend to have two or more of their vertical surfaces exposed to the outside. • An Envelope Atrium encloses the building inside it, more like a building within a building. Sometimes the external envelope may include parts of the building facade but usually the atrium is more like a glazed double wall to the building. Figure2.4 The Attached Atrium 2.3 Energy and A tria: The greenhouse effect is a very positive property that encourages the use of atria in cold climates, especially in conditions where solar radiation is a valuable commodity 11 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. and heating is the dominant load. As it has been mentioned earlier, energy was less of a concern in resorting to the atrium as an architectural element, more so it was due to its spatial character that combined the ‘inside’ and the ‘outside’. After the popularity of the atrium increased in American commercial architecture in the late seventies and early eighties, the emphasis on conservation decreased due to cheaper fuel prices6 . Though this attitude could survive for only about a decade, when energy consciousness and the evils of active environmental controls made itself a significant issue among professionals and clients alike by the late eighties and nineties. It was then that the possibilities that new as well as existing atria could offer in terms of energy savings by natural heating, cooling or daylighting, began to be looked into more closely. As a result most of the energy related research on atria have been carried out only during the past ten years or so. The three primary energy strategies that can be incorporated in atria can be enumerated as follows7 : • Heating: An atrium is a buffer between its adjacent spaces and the outside environment. It could reduce transmission losses from adjacent spaces and could also provide additional heat to them. An atrium displaces auxiliary heating by solar gain transfer from atrium to the adjacent spaces. These effects can be optimized if the predominant orientation of the atrium is to the south and glazing is vertical (to reduce overheating in summer). Collected solar radiation must be stored in the internal 6 See Saxon, Richard, The Atrium Comes of Age, Longman, Essex, England 1994. 7 See Hastings, S. R., Passive Solar Commercial and Institutional Buildings: a sourcebook of examples and design insights, IEA, J. Wiley , New York, 1994 12 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. mass of the building components exposed directly to the sun, especially in the winter. A reduction in night-time losses can be achieved by the use of efficient thermal materials in the envelope glazing, walls and the windows separating the atrium from the rest of the building. • Cooling: Excess and undesirable solar gains can be avoided to an extent in an atrium by inducing natural ventilation. This is a result of the vertical ‘stack effect’ and can be achieved by proper placement of air inlets and outlets. Generically speaking, it is seen that cooling by ventilation is most effective when inlets are placed at the bottom of the atrium, and sufficient exhaust outlets are located at the top. Night-time convective cooling o f building mass structure can be achieved by cross ventilation, with air passing from ambient through the adjacent spaces and out via the atrium. • Daylighting: Atria can be extremely effective in providing additional daylight to the adjacent spaces and reduce lighting loads. Taking an example in colder climates, the window area in the intermediate boundary between the atrium and adjacent spaces, can be increased considerably, without being penalized by heating loads, due to the buffer effect of the atrium itself. This is sometimes necessary as the atrium glazing might sometimes reduce the available daylight inside otherwise. The amount of daylight available in the adjacent spaces is also greatly dependent on the 13 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. H i! * Figure2.8 Daylighting configuration, dimensions, and the size of aperture of the atrium as well as the properties of the walls and windows separating them. 2.4 Available Analysis Tools: Very few of the available computer simulation tools are actually appropriate for modeling atria. The main reason for this is the inability of most of the programs to simulate the movement of air. Most of the tools take stratification into account by dividing the space into zones and distributing radiative, conductive and Infra-red gains within them by means of inter-zonal transfer based on a series of assumptions. Some of the more widely used tools are the following8 : DOE2.1E: This is an energy simulation developed by the Lawrence Berkeley Labs at Berkeley CA with funding from the US Dept, of Energy. It uses a multi zone model, accounting inter zone heat transfers coupled with a weather file to simulate external conditions. The main purpose of the program is to calculate energy performance and hence all zonal temperatures have to be specified. The program cannot account for intra-zonal air movement patterns, hence stratification is difficult to account for. The only way temperature stratification can be simulated is by dividing a large space into layers of zones and assigning a different temperature for each. This is helpful for getting energy performance results of the space provided we already know the stratification patterns. BLAST: The Building Loads Analysis and System Thermodynamics or BLAST, program is used for energy simulations coupled with determination of comfort See Hastings, S. R., Passive Solar Commercial and Institutional Buildings: a sourcebook of examples and design insights, IEA, J. Wiley , New York, 1994 14 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. conditions. It is a multi-zone program that allows each zone to be analyzed separately as a thermal zone with a conductive coupling between the zones. It allows for user control of inter-zonal air flow, but cannot account of inter-zonal stratification. It relates the results with some available comfort indices and determines the comfort conditions within the zones. PI-M ODEL: This program is used mainly for fast energy analysis of large spaces like atriar It analyzes mainly with respect to solar gains, internal loads, infiltration, inter zone air exchanges and conductive transfers. There is no consideration of intra-zonal stratification o f temperature. FRES: The Flexible Room and Environment Simulator or FRES, is a program to calculate energy use and internal climate of buildings. The program allows for a multi zone system and accounts for air temperature differences within one single space, but these variations have to be input by the user. Otherwise it is pretty similar in function to the tools described above. TRNSYS: This program is used to calculate energy performance in large spaces due to it’s ability to make calculations and accommodate for assumptions in distribution of solar gains within a zone and it’s adjoining spaces provided the properties of the partition walls are specified. In order to calculate solar gains distribution in atria, the space has to be divided into zones vertically, and the user has to specify the percentage of solar gain penetrating into each zone from the top along other aspects like air exchanges, infiltration etc. TRNSYS then calculates the solar gain distribution in each zone according to a surface-ratio rule. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. MODPAS: This is a program developed by Sorane SA, which uses a nodal solver method to calculate energy performance of large spaces. First the total energy coming into the atrium is calculated by using a solar distribution program and distributed on the surfaces and other light elements like air. For each hour of the day a new solar distribution is used. MODPAS uses a mesh of 40 temperature nodes. These nodes can be air, surface or any element temperature of the building. Each node is then coupled with some other nodes by symmetrical connections (conduction, convection, Infra-Red radiative exchanges) or by non-symmetrical connections (short wave or solar heat gains) or by connections to the exterior. 2.5 Existing Research: Most of the research related to atria are with respect to cold climates. It is obvious from the above strategies that it is a much simpler task to harness the energy advantages of atria in colder climates. Following are two examples of current research regarding atria. The University of Trondheim in Norway, has been working with thermal conditions and energy consumption for atria for the last 20 years. “Norway is located at the same latitude as Alaska. Thus, climatic conditions are somewhat different than Southern Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. California”9 , says Prof. Per Olaf Tjelflaat from Trondheim. But in spite of a cold climate, solar irradiation is extensive in summer months and there is still a need for cooling -which is accomplished by opening hatches at walls in the lower part and in the ceiling to let the stack-effect do the job with removing hot air and supplying colder air from outside. (Outdoor air temperature is seldom above 75 F in Norway). The thermal stratification, or vertical temperature gradient, is actually a help in that process. Most of this research is based on empirical calculations As a part of the International Energy Agency (IEA) Solar Heating and Cooling Program Task XI, “Passive and Hybrid Solar Commercial Building”, a paper was presented by a team from the Norwegian Institute of Technology (NTH), in the form of an Advanced Case Study in I9901 0 . The study involved extensive comparison of measured data, computer simulation and occupant response of the atrium of the ELA building which is an extension of the Electrical Engineering building at the NTH. The simulations of the atrium were done using a program called TARP. Though there is no information in the paper as to the exact functioning of TARP other than the fact that it is a single zone, energy simulation tool. The conclusions of the paper state that the energy usage of the building is fairly low compared to buildings of the same category and generation. It is interesting to note that the energy consumption of the building measured and the values from simulations are extremely close. The authors suspect that the agreement may be purely coincidental and one cannot confirm this unless 9 As per personal correspondence between the author and Prof. Tjelflaat 1 0 See Aschehoug, 0 ., Hestnes, A. G., Thyholt, M., Jacobsen, T„ Norwegian Institute of Technology, Extension to the Dept, of Electrical Engineering and Computer Science, An Advanced Case Study for 17 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. further studies are conducted. The findings also suggest that the daylighting calculations are fairly close to the measured data but during sunny periods, when the atrium temperatures show strong temperature stratification, could not be modeled properly with the single zone simulation tool. This is a clear suggestion that understanding of temperature stratification behavior in atria remains to be one of the major issues that still needs to be tackled. In another study conducted by Aiulfi and Chuard (Sorane SA)n, attempts are made to model temperature stratification in an atrium using some available analysis tools. The building chosen for a case study is once again the ELA building in Trondheim, Norway. Simulations are carried out by dividing the atrium space into zones, assuming that temperature within each zone is homogenous. The simulation program used in this case is TRNSYS type 56 (A multi-zone simulation program). The problem faced in simulating a multi-zone atrium space with the TRNSYS program is that each zone is to be separated with a wall, and infrared radiative exchanges do not take place correctly between these walls. Interception of solar radiation is considered for each interzonal separation and the intercepted solar radiation is then distributed on the surfaces following a surface ratio rule. Air temperature data inside the atrium is collected over a period of time. Standard solar gains distribution are calculated next using TRNSYS in the first method and the the IEA Solar Heating and Cooling - Task XI (Passive and Hybrid Solar Commercial Buildings), SINTEF, Trondheim, 1990. 1 1 See Aiulfi, D., Chuard, D., Some Ways to Model the Temperature Stratification in an Atrium, ASHRAE Conference, San Diego, 1995 18 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. calculation procedure is deactivated and a more sophisticated solar gains distribution calculation is done for the second method. The comparison of results between the calculated and measured temperatures in the three zones show that the calculated temperatures (which are one for each zone) are approximately the average between the measured temperatures at two levels within the same zone, except for in the topmost zone, where calculated temperature is too high. The modified (second) method first calculates the total amount of solar gain coming into the whole atrium. It then calculates the solar gain distribution (obtained with a separate program). The sun penetration into the space and both the specular and diffuse reflections are calculated correctly, which in turn leads to a heat (power) distribution on the surfaces of the atrium. Both the diffuse and direct radiation are added and are introduced as radiative gain in TRNSYS, which in turn are distributed according to the surface ratios of the TRNSYS program. With this method the calculated temperatures are higher than the measured temperatures except in the topmost zone. According to the authors this is a discrepancy in the measured temperatures ,and with another set of data collected on another day they got fairly close results. The same technique is used for an open vent condition, but in addition to that field air flow conditions are taken into consideration. The results are fairly close to measured data. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The second part of the study uses the atrium of the University of Neuchatel. The procedure used here is a “Nodal Solver” method. The computer program used for this case is called MODPAS. The program uses a mesh of 40 nodes. Which can be air, surface or element temperature at different locations. Each node is in turn coupled with some other nodes by symmetrical connections like, conduction, convection, Infra red radiative exchanges or by non-symmetrical connections like short-wave radiative exchanges or solar heat gains or are provided with connections to the exterior. The total amount of energy coming into the atrium is calculated and then distributed on the different surfaces and light elements (air) according to a solar distribution program. Simulations are carried out for two kinds of air movements within the MODPAS program • Natural ventilation • Mixing due to buoyancy While the former assumes a “piston flow”, the latter assumes a convection flow due to the temperature difference between the zones. The resultant comparisons with the measured data and the calculated values are reasonably close. Though a certain lag difference is exhibited (due to the assumption of a homogenous temperature in each zone in the calculations) the temperature curves are extremely synchronous. Through modelling, calculation and examination of real data, the authors come to the conclusion that temperature stratification makes sense mainly from the comfort point 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. of view, but is not so relevant in the total energy consumption of the building and spaces adjacent to the atrium. Though it must be kept in mind that these conclusions are based on the study of one specific case, other geometries, orientations and external as well as climatic conditions might make significant differences. It is also important to note that the results and conclusions are based on a rough division of the atria into three sections and a series of assumptions and adjustments made in the process of distributing solar gains. The purpose of the study is to compare simulated and calculated energy consumption in atria, but does not elaborate on the patterns of temperature stratification and movement of air within them. 2.6 Limitations: • Most of the existing simulation programs are incapable of accounting for prediction of air flow rates in multi-zone models. They also do not account for interaction between mechanical and natural ventilation / infiltration as well as dependence on height and pressure gradients in space. • They do not account for spatial distribution of surface and air temperatures in a single space and hence are unable to consider temperature gradients. • Proper accounting for solar gains distribution is required to determine, surface temperature, air flow profiles, convection coefficients of surfaces, interior air temperature distributions and radiative exchange. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 3 SELECTING A ‘MODEL’ ATRIUM; THE BRADBURY B U T T PTNC 3.1 Selection Criteria: The primary criteria for selection of a model atrium is that the form and proportions of the selected case be closest to the more or less generic atrium. In order for the internal loads of the atrium to remain well within normal conditions, the usage and equipment inside the space has to be taken into account It is also important for the case study building to be easily accessible and within reach for frequent data collection over a period of time. In order to collect valuable research information and to offer validation of the hypothesis in a more concrete manner, during the initial stages o f research a list of possible case study buildings were made on the basis of their form, geometry, usage and uniqueness. • The Bradbury Building in downtown Los Angeles is a perfect example of a classical atrium space. It is a building not only of architectural grandeur, with its freely floating elevators and ornate wrought iron work but also one of the few unconditioned core atriums in the Los Angeles area. The primary usage of the building is offices which also represents a generic usage of an atrium space. • The Los Angeles Bonaventure Hotel, is on the other hand an example of a partially conditioned atrium. Being one of the landmarks o f downtown Los Angeles, the building offers itself as a lucrative case study. The building is also representative of a modem day application of an atrium space. The atrium is 22 with permission of the copyright owner. Further reproduction prohibited without permission. unique in its geometry as it surrounds a built space as well as being enclosed by one. As it I a renowned hotel it might be possible to get accurate energy consumption data over a period of time, which could be helpful in later analysis. • The Crystal Cathedral, in Anaheim CA, is not exactly an example of an atrium but presents an unique architectural form in terms of glazed spaces. It is also of interest to researchers due to the fact that the building behaves quite well in terms of comfort conditions inside, contrary to predictions by many critics earlier. It would be valuable to observe and quantify thermal data of the building and compare it with comfort conditions. Limitations of time forced this list to be cut down to a single building. Considering the issues governing the study, the most obvious choice of a model atrium from this list appears to be the Bradbury building. The building represents a classical atrium space both in terms of form and function and is also easily accessible to carry out a long term study with ease. The other two buildings, though very interesting in nature, represent two extreme examples of atrium usage, and would not be appropriate to carry out a more generic study. 3.2 The Bradbury Building: 3.2.1 Location The Bradbury building is located in downtown Los Angeles, at the intersection of Broadway and 3rd St. The building was designed by an Architect named George Wyman and completed in 1893. Wyman envisioned the building in terms of late 19th century views of science-fiction and futurism. Though the building from the exterior resembled any other building contemporary to the time only a little more intricate, and 23 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. on the lines of architects like Louis Sullivan, the interior transports a visitor to almost another world. Even though the entrance is immediately open to the busy Broadway street, once inside, the openness and the quality of filtering light is overpowering. The warm textures of the building, with terra-cotta tiles, ceramic mosaic and dark marble are enhanced by reflected sunlight The hydraulic elevators with wrought iron cars almost appear to be freely floating in air. The building can be entered from two directions. 3rd Street on the north and Broadway on the west. 3.2.2 Configuration In terms of configuration the building has five levels with a central core atrium. The atrium is narrower in the lowermost floor and widens in the upper floors. The atrium has walkways going all around at all levels providing access to the adjoining offices. The atrium is oriented lengthwise along the east-west direction, with the longer side facing north and south. Some of the dimensional and volumetric relationships between the atrium and the surrounding spaces are as follows1 : • Building floor area (approx.) 168 ft X 110 ft = 18480 ft2 • A trium area (approx.) 113 ft X 46 ft = 5198 ft2 The atrium is approximately 28% of the floor area of the building (considering typical floors for both cases) • Total volume (approx.) 13,43,051 ft3 • A trium volume (approx.) 3,51,560 ft3 The atrium occupies approximately 26% of the total building volume 1 The building dimensions have been measured from rough building plans made available by Ms. Francine Lipsman, Manager of the Bradbury Building 24 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner Further reproduction prohibited without permission Figure 3 .1 T h e Bradbury Building: 1 s t Floor Plan Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3 .2 T he Bradbury Building: 'typical Floor Plan Figure 3.3 View of the Bradbury from Broadway Figure 3.4 Another View from Broadway Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.5 Intenor View of the Atnum Figure 3.6 View from the Stairway Figure 3.7 View Along the Walkway Figure 3.8 The 'Floating' Elevators 28 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.2.3 Construction and Maintenance The building construction is mainly unreinforced brick masonry, clad with terra-cotta and at places stone tiles. The floors of the walkway along the atrium have intricate ceramic mosaic, while the stairways on both sides o f the atrium have a wrought iron frame with marble floors for the risers and landings. A large part of the building envelope is in the form of glazed windows, facing both the exterior as well as the interior, facing the atrium. The windows are at present completely sealed off to reduce infiltration into the office suites and minimize air conditioning loads. All windows are single glazed and in most places the original glazing is still being used. The doors separating the suites are wooden with about 35% - 40% glazed area. The doors are raised about 2ins. off the floor, and this is the only source of ventilation from the office suites into the atrium. Though there are pivoted shutters above the doors for ventilation, they are sealed now. The top of the atrium has a series of clear-storey windows on all sides. During the winter months these windows are kept shut and they are opened during the summer months. Some of the windows are jammed due to mechanical defects and as a result only about 40% of the clear-storey windows are can be left open. The atrium glazing is also single glazed, and a collection of dust on the exterior of the glazing make it behave in a diffusive manner. The only major source of air inlets at the bottom of the atrium are the two doorways on the west (Broadway) and the north (3rd Street). The doors usually remain shut and are opened only by individuals passing through them (the frequency of this is considerably low; about 5 or 6 times an hour at an average). 29 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The HVAC system for the office suites is in the form of a Heat Pump system2 , with more or less centralized controls. The ambient temperatures are set universally by a central control system, but thermostats within each suite allows for certain desired variations within a certain range. The atrium is not conditioned. One can summarize the physical and other characteristics of the Bradbury Building into die following points : • It is a mid size office building with about 50% occupancy • The construction materials, size and proportions suggest that the building should have a relatively high thermal mass • There is very little scope for ventilation/infiltration from the adjoining spaces into the atrium • The atrium itself has a potential for relatively good natural ventilation with the presence o f a fairly large number of clear-storey windows at the top, but there is a lack of openings for air inflow at the bottom. • The atrium glazing is unshaded and single glazed, and has a potential for contributing to large solar gains. • The internal loads in the atrium are fairly low due to moderate or low occupancy, resulting in a relatively low frequency o f elevator-usage. Also the primary use of the atrium is for circulation, primarily on the walkways, for people to get from the entrance points to their respective suites. There seems to be very little or no recreational or other usage of the atrium by the occupants. There is some 2 Referred from an interview with Ms. Francine Lipsman, Manager of the Bradbury Building by the author 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. contribution to internal loads at the lower levels by occasional groups of visiting tourists. • The building has extreme historical and architectural importance to the city of Los Angeles, being one of the few of its kind and hence a technological insight in terms of its behavior is lucrative. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 4 DATA COLLECTION AND PREPARATION OF A BASE-CASE 4.1 The variables: In order to study stratification of temperature and air movement in a space, one has to look at a range of variables. These can be enumerated as follows • Air temperature • Surface temperature • Air velocity • Solar radiation • Air pressure variations • Variations in external climatic conditions The methods that can be used to measure each one of these is unique in its own way. Both limitations of time and resources would allow one to look at only some of the above variables. Measurement of air temperature across a vertical cross section of an atrium is the probably the most concrete method of realizing temperature stratification in the space. Air temperature recorded at various points, synchronously over a period of time would reveal the patterns of stratification in the atrium with respect to time. Air velocity and air flow patterns would further demonstrate the nature of stratification with respect to internal air movement. This is where one is going to apply the Computational Fluid Dynamics method. The CFD analysis should give an idea of the air movement patterns in the space, which is otherwise extremely difficult to measure as well as predict. For analysis and computer simulation of the stratification process using a Computational Fluid Dynamics model, one has to record the surface temperatures of the surfaces adjoining the atrium at different strata. 32 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Moreover, a comparison of the surface and air temperature variation over time is bound give an idea of the atrium behavior in terms of thermal mass and time lag. In view of the above requirements, two basic data groups are determined: 1 Air temperature collected at different heights vertically 2 Corresponding surface temperature Data'is collected in several sets with a combination of the above two variables. Of course, the corresponding external temperature variation has to be recorded at all times. 4.2 Collection method: Ten Stowaway XTI temperature data loggers were used to collect the temperature data1 . The compact (about 2” X 2”) data loggers are extremely convenient for the purpose, as they can be launched with a time delay beforehand and all the units can be synchronized to be active at the same time. Moreover during the actual process of recording data the sensors do not need any external power source as they are powered by an internal lithium battery. A software called LogBook allows communication with the data loggers, in order to download as well as launch each unit. Each data logger is capable of 1 The Stowaway XTI Data Loggers are manufactured by the Onset Computer Corporation, Pocasset. MA 33 Figure 4.1 The Stowaway Temperature Data Logger Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. collecting approximately 8000 data points, the intervals between which can be set in a range of allowable values. Once the data is recorded in the data logger, it can be downloaded using the LogBook software in a spreadsheet format and formatted or reorganized in any desired manner. The effective temperature range for the data logger is from -40°C to 75°C. 4.3 Data Collection: Temperature data was collected in several sets between the months of February and May. There were ten data loggers positioned strategically inside the building ( Figure 4.2) in order to collect data at different strata of the atrium. The first few data sets were primarily to understand the temperature profiles and confirm the existence of stratification. Nine data loggers were positioned inside the atrium: One on the ground level and four each on the north and south side o f the atrium on each floor. The tenth data logger was placed on the exterior north face of the building, with proper shading to synchronously record external temperature. After the establishment of the existence of stratification and identifying the ideal position of the data loggers, the final data sets were collected which were collected between the 29th of February and the 14* of March and between the 26* of April to the 3rd of May. The first of these data sets were to record the air temperature variations only on both sides of the atrium vertically, with reference to the variations in external conditions. The second of these data sets was to record variations of air temperature along with corresponding surface temperatures and of course, external temperatures. It is also essential to record surface temperatures in order to construct a Computational Fluid Dynamics model which is based on primarily the boundary conditions of a space. 34 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ~ \ ; •y^sg- vtv*!* 4 > © 0 o o « c u 0 1 ) 35 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.3.1 Data and Observations: As mentioned in the preceding section, only the last two sets of collected data is being discussed here due to their immediate relevance. The first set of air temperature data is collected between the 29th of February and 14th of March, collecting only air temperatures in the atrium and the exterior (Figure 4.3-4.4). By plotting floor wise temperatures over the entire length of time, one can see a very clear pattern of internal temperature stratification. The temperature differential shows an increase (between consecutive floors) as one goes up. The temperature differential between the lower floors, starting from the ground level (Is * floor) to the fourth floor is considerably moderate, with a sharp increase on the top. Comparing the stratification profiles in the north and south faces of the atrium interior, one sees very little difference in the stratification pattern among both the faces (Note: The interior north face of the atrium actually faces the south). The north face records slightly higher temperatures in the lower floors with a sharper increase with respect to the south face on the top floor. The high air temperatures on the top floors is due to the high direct solar gain through the roof glazing and clerestorey windows and also due to a collection of hot air on the top due to buoyant movement. Observing the relationship between the external temperature variations with the internal temperatures, one sees that the internal temperature curves almost synchronously follow the external temperature curve. While during the day the internal temperatures in the upper floors shoot up even higher than the external temperatures, but they do not fall below a certain level during the night, even though 36 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. STRATIFICATION NORTH FROM 2/29/96 TO 3/14/96 / DAYS I Temperature (*F) Ground Temperature (*F)2nd Temperature (*F)3rd Temperature (*F)4th Temperature (*F)5th Temperature (*F)EXT Figure 4.3 Stratification on the North Face Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. STRATIFICATION SOUTH FROM 2/29/96 TO 3/14/96 95 85 « ui D C 75 6 5 55 45 ft DAYS Tem perature (*F) Ground Tem perature (’F)2nd T em perature (*F)3rd T em perature fF )4 th T em perature CF)5th Tem perature (*F)EXT Figure 4.4 Stratification on the South Face U J o o l the external temperatures fall considerably. This results in an increase of temperature differential among the vertical strata during the day and a decrease at night. In order to observe the specific patterns of internal temperature, three cases have been selected to be observed closely, namely, a typical, a cool day and a hot day. The classification is based in relative terms of the range of data collected in that specific period. Each of these cases is a 24 hour cycle beginning 4:00AM in the morning, till 3:55AM the next morning. Typical Day, 3/6/96 4:00 AM to 3/7/96 3:55 AM (Figure 4.5-4.7): Within the range of data collected in the month of March, a typical day is chosen as a day with a maximum temperature of about 70°F (71.36°F) and a minimum temperature of about 50°F (49.87°F). The day was mosdy clear and sunny with a little amount of high clouds. Between 4:00AM and 6:00AM when the external temperature within 50°F, one observes that the temperature differential between the floors is very little, in the range of about 3°F, but the internal temperature, even at the ground level is about 10°F higher than the external temperature (Ground = 60.7°F while Ext. = 49.87°F). There is a sharp increase in the external temperature after 6:00AM (after sunrise) and this increase is reflected about an hour later in the internal profile, first on the top floor and by 8:00AM the increase in temperature outside filters down to the ground level. It is important to note that the rate of increase in temperature is higher as one moves vertically up the floors i.e. the ground level temperature increases with a very small gradient while the top floor temperature increases very sharply. The top floor 39 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. STRATIFICATION NORTH FROM 3/6/96 4:00 AM TO 3/7/96 3:5§ AM 85 80 75 u. U i 7 0 a 65 60 55 50 5 < 5 < o o o o 5 a. 5 a. o o o o o o o o o 00 o o C O C O C T ) C O O) C O C O o > C O C O a > C O C O o > C O C O C O C O C O -Temperature (*F) Ground -Temperature (*F) -Temperature (*F) Temperature (*F) -Temperature (*F) -Temperature (*F)EXT TIME Figure 4.5 Typical Day - P * o Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. NORTH AND SOUTH STRATIFICATION ON 3/6/96 AT 2:00 PM (TYR. DAY) 85 -Temperature (*F) NORTH -Temperature (*F) SOUTH Temperature (*F)EXT. 80 L L m 75 cc g 70 65 . 6 0 1st Floor 2nd Floor 3rd Floor FLOORS 4th Floor 5th Floor Figure 4.6 Vertical Profile (Max.) on a Typical Day I I Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. I NORTH AND SOUTH STRATIFICATION ON 3/6/96 AT 5:00 AM (TYP., NIGHT) 6 4 Temperature (*F) NORTH Temperature (*F) SOUTH Temperature (*F)EXT. 62 60 & 5 8 56 54 52 50 — 1st Floor _ 1 ------- 2nd Floor 3rd Floor 4th Floor 5th Floor Figure 4.7 Vertical Profile (Min. nr i g u i c t , f FLOORS Typical Day ■ i * ro temperature curve almost synchronously follows the external temperature curve. The external temperature peaks at 2:00PM (71.36°F) and the top floor temperature peaks at the same time, only recording a temperature 12.34°F higher than the external temperature at 83.7°F. The temperature differential across the floors also steadily increases and around the vicinity of 2:00PM, the temperature differential between the ground and the top is 19.22°F (Ground = 64.48°F and Top = 83.7°F). As the external temperature starts dropping after 2:00PM, the top floor temperature starts dropping as well. One might note that the ground to the fourth floors exhibit a slight time lag (with respect to the exterior). Though interestingly the time lag is reverse of what is expected; the lower floors peak at around 11:00-12:00PM, about 2 to 2.5 hours before the exterior. This might be due to a cut off of direct solar gain in the area where the data loggers were positioned. The falling temperature gradient is slightly more gradual than the rising temperature gradient. At around 5:00PM, the external temperature drops even below the ground level temperature, while the internal temperatures stabilize quite a bit. By 8:00PM the internal temperature differential between the ground and the top is 3.87°F. Throughout the rest of the night, the external temperature moves within 55.63°F and 57.53°F while the minimum internal temperature does not fall below 60.7°F. Hot Day, 3/8/96 4:00AM to 3/9/96 3:55AM (Figure 4.8*4.10): The hottest day within the range of data collected, was when the external temperature peaked at 84.86°F. The day was sunny with slight haze and no cloud cover. The synchronous movement of the internal temperature curves with respect to the external temperature 43 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. STRATIFICATION NORTH FROM 3/8/96 4:00 AM TO 3/9/96 3:5? am 95 90 85 u. * 1 1 1 DC 80 75 a. 70 65 A _ _ 6 0 55 I 1 2 ° < 9 . o O 1- — I - - s C l — 2 Q . o 2 < o 2 < o o o o o o o o o o o > C O O ) C O C O p > (O C T ) (O o > (O O ) (O C D C O o > O ) C D C D C O •Temperature (*F) Ground •Temperature (*F) Temperature (*F) Temperature (*F) •Temperature (*F) Temperature (*F)EXT TIME Figure 4.8 Hot Day £ Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. NORTH AND SOUTH STRATIFICATION ON 3/8/96 AT 14:15 (HOT/DAY) 1st Floor 100 — Temperature (*F) NORTH • —Temperature (*F) SOUTH ■ A —Temperature (*F)EXT. 95 90 75 70 65 2nd Floor 3rd Floor FLOORS 4th Floor 5th Floor Figure 4.9 Vertical Profile (Max.) on a Hot day tn Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. I NORTH AND SOUTH STRATIFICATION ON 3/8/96 AT 4:30 AM (HOTt NIGHT) 68 ♦ —Temperature (*F) NORTH ■ —Temperature (*F) SOUTH ♦ —Temperature (*F)EXT. 66 64 u. « Q . 60 58 56 ------ 1st Floor 2nd Floor 3rd Floor 4th Floor 5th Floor FLOORS Figure 4.10 Vertical Profile (Min.) on a Hot day is similar to the patterns exhibited during a typical day, only in this case the peak external temperature is considerably lower than the peak temperature on the top floor. Internal temperature differentials are much higher, at 2:15PM the ground (95.93°F) and the top floor (69.51°F) is 26.42°F and the temperature differential between the top and the external temperature (84.06°F) is 11.07°F. It is interesting to note that during the hottest part of the day the lower floors is 12.84°F while the temperature differential between the top two floors is 13.58. Convective gains from the heated roof glazing might account for this. Throughout the day the temperature on the ground level fluctuates within a range of 5.66°F while the top floor temperature moves within a range of 29.47°F. Due to high external temperatures, the internal temperatures take a little longer to fall, but by 10:00PM, the internal temperature differential reduces to 5.12°F across the floors. Rainy/Cool Day, 3/4/96 4:00AM to 3/5/96 3:55AM (Figure 4.11-4.13): The cool day’ chosen from the data set is one with a maximum external temperature of 60.06°F, with a diurnal range of 5.06°F. The was heavily overcast with occasional showers and drizzles throughout. The temperature curves, both internal and external, in this case are comparable to the night-time temperature patterns during a typical day. The internal temperature stratification is minimal, 5.13°F (at 2:15PM) at the maximum. The lower floors do not show any drastic variations of temperature throughout the day, but the top floor still shows a more or less clear rise and fall of temperature, even though the external temperature curve lacks that clarity. Slight stratification between the top three floors is exhibited at 8:00AM and 4:00PM, reaching a peak at 2:15PM. 47 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission. STRATIFICATION NORTH FROM 3/4/96 4:00 AM TO 3/5/96 3:55 AM1 69 67 65 u. ♦ U J A C g 63 i _ / l j 59 57 u u 55 5 < 2 < 2 o < 9. o o S 2 Q - CL O O O O C O C O C O 00 C O C O C O C O C O C O C O C O C O C O C O C O C O C O C O -Temperature (*F) Ground -Temperature (*F) Temperature (*F) Temperature (*F) -Temperature (*F) Temperature (*F)EXT 0 0 TIME Figure 4.11 Cool Day i Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission. NORTH AND SOUTH STRATIFICATION ON 3/4/96 AT 2:15 PM (COOJ. DAY) 68 ♦ —Temperature (*F) NORTH • —Temperature (*F) SOUTH ■ A — Temperature ('F)EXT. 67 66 65 62 60 59 1st Floor 2nd Floor 1 0 3rd Floor FLOORS 4th Floor 5th Floor Figure 4.12 Vertical Profile (Max.) on a Cool Day l Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission. I NORTH AND SOUTH STRATIFICATION ON 3/5/96 AT 3:50 AM (COOL,( NIGHT) 65 ♦-Temperature (*F) NORTH •-Temperature (*F) SOUTH ■*— Temperature (*F)EXT. 64 63 62 u. « U i 61 § c l 60 59 58 57 56 —- 1st Floor 2nd Floor 3rd Floor 41h Floor 5th Floor Figure 4.13 Vertical Profile (Min.) on FLOORS a c °o 1 Day There is negligible or no difference between the north and south side of the atrium, mainly due to the lack of direct solar gain. The second set of data was collected in a period of seven days from 12:00PM 4/26/96 to 12:00PM 5/3/96. The primary reason for collecting this data set was to help construct a Computational Fluid Dynamics Model using PHOENICS. PHOENICS models CFD scenarios based on surface conditions, hence it is required for one to know surface temperatures of the atrium across it’s height with corresponding air temperatures. For this, two data loggers were placed on each of the top four floors, one measuring the surface temperature that floor and the second measuring air temperature for the same floor, one data logger was placed on the ground measuring only air temperature (assuming that there would be less variation between the air and surface temperatures at the lower floors) and the last data logger was placed on the outer north face of the building to measure external temperatures. All the internal sensors were placed on the south wall of the atrium (the one that actually faces north). The initial observations suggest that the surface temperature moves within a smaller range compared to the external and air temperatures (Figure 4.14-4.18). Though the temperature curves move almost synchronously, there exists a slight time lag between the air and the surface temperatures. In the top floor both the surface and air temperatures are higher than the external temperature almost at any given time. To understand these curves better, a typical day is chosen and examined more closely. 51 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission. I i SURFACE AND AIR TEMP. 5TH FLOOR FROM 4/26/96 TO 5/3/j96 Temperature (*F)EXT. Temperature (*F)5TH.IN Temperature (*F)5TH.SURF 105 100 95 L L « O l s oc £ 8 5 8 0 9 0 75 70 \ / "T/ 65 6 0 o o c v i o o c v i o o c v i o o c v i o o o o U l M C O O) C O C V I C O o > C V I C O o > o o C V I C O o > o > C V J C O o > o C O TIME C O O ) C O C O 0) O J In Figure 4.14 Surface and Air temperature (5,h Floor) Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. I SURFACE AND AIR TEMP. 4TH FLOOR FROM 4/26/96 TO 5/3/06 Temperature (*F)EXT. ■Temperature (*F)4TH.IN -Temperature (*F)4TH.SURF 1 0 5 100 9 5 u. « O i 9 0 8 5 80 7 5 7 0 6 5 6 0 o o o o o o o o o o o o o o U 1 L U C O o> C O C V I C O o > C V I C O 0 > 0 0 c v i C O o> O ) C V I C O C D o C O TIME C O o > C O C O C D C V I to Figure 4.15 Surface and Air temperature (4,h Floor) Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. J l 'I SURFACE AND AIR TEMP. 3RD FLOOR FROM 4/26/96 TO 5/3/06 Temperature (*F)EXT. Temperature (*F)3RD.IN Temperature (*F)3RD.SURF 105 100 95 IL « a! s IS 90 85 80 75 70 65 T l. 60 o o o o o o o o o o o o o o 1 / 1 C O C D C O C V I C O C D f-. C V I C O C D — C O C V I C O C D O ) C V I ■ 5 " co C J > o C O TIME C O C D « > C O a > C M io Figure 4.16 Surface and Air temperature (3,d Floor) Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission. 'I • i SURFACE AND AIR TEMP. 2ND FLOOR FROM 4/26/96 TO 5 /3 ^ 6 Temperature (*F)EXT, — Temperature (*F)2ND.IN — Temperature (*F)2ND.SURF 105 100 95 u. * CL S oir U i 85 t- 80 90 75 70 65 60 o o o o o o o o o o o o o o 1 / 1 l/l < o C D C O Cvi C O C D N C v i C O O ) C O C M C O O) T O C M C O O) O C O TIME co o > co co C D C M in Figure 4.17 Surface and Air temperature (2n i 1 Floor) Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. AIR TEMP. 1ST FLOOR FROM 4/26/96 TO 5/3/96 — Temperature (*F)GROUND - Temperature (*F)EXT. 105 100 95 UL * - - CL | 85 80 90 75 70 65 60 o o o o o o o o o o o o o o U 1 < y > < o o > co O J C O o > C M C O o > 00 C M C O C D O) C M C O O) o C O TIME C O cn C O C O o > C M Figure 4.18 Air temperature (I" Floor) Typical Day, 28/4/96 4:00AM to 29/4/96 4:00AM (Figure 4.19-4.22): The recorded maximum external temperature on this day 82.89°F at 10:30AM, though it must be noted that this is not the actual maximum external air temperature, it is suspected that due to some error in positioning the data logger on external face some direct solar radiation must have penetrated into it, creating a spike on the temperature curve. The actual maximum occurs at 3:40PM, recording 81.59°F. The diurnal range of the external air temperature is 20.31°F. On the 5th floor the air temperature peaks at 2:35PM recording 98.66°F, which is 18.35°F higher than the external air temperature at the same time. The surface temperature on the 5th floor peaks at 2:20PM recording 87.68°F and this remains constant for a period of almost three and a half hours until the temperature begins to fall at 4:55PM. It is important to note that the surface temperature curves follow the external temperature curves more closely in terms of its gradient and the surface temperature curves tend to have flatter peaks even on the upper floors, as opposed to the air temperature curves which tend to have spiked peaks. After 5:00PM the air temperature starts dropping rapidly, even below the surface temperature, while the surface temperatures begin to stabilize. During the period between 5:00PM and 4:00AM the surface temperature drops by 11.07°F while the external temperature drops by 17.73°F and the air temperature by 14.92°F. The 4th floor exhibits a similar pattern but the range of diurnal surface temperature has reduced considerably to 3.86°F. The diurnal range of air temperature has also reduced to 9.63°F. By 5:00PM the external temperature starts dropping below the surface temperature and by 7:00PM the internal air temperature drops below the surface temperature, giving the building a chance to lose heat internally from then on. On the 2n d and 3rd floors the surface temperature curves tend to get flatter and flatter, with 57 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. i SURFACE AND AIR TEMPERATURE 5TH FLOOR BETWEEN 4/28/96 4:00AM AND 4/29/96 4:00A M 100 95 90 u. « U l cc g 80 < L 75 70 65 60 o o U l oo (0 (0 (0 (11(0(0 ® r o r o 0 ) 0 ) ® ( 0 ( D ( D ( 0 ( 0 ( D ( 0 ( 0 ( 0 cococococoeoJ5®5J5£?2J£55S* C M C M C M C M C M C M C O C O O O O O O O O O O O O O C O TIME C O C O O ) O ) oo co C M C M C O C O o> 0 > 00 00 C M C M C O co o > S > o> 00 C M C M ^ ■ M - T f 'M ' • M ' C O C O <5 O ) o> o > C O C O O , O) 0) O ) C M C M •Temperature (*F)EXT. •Temperature (*F)5TH.IN Temperature (*F)5TH.SURF Figure 4.19 Typical Day (S'" Floor) Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission. I SURFACE AND AIR TEMPERATURE 4TH FLOOR BETWEEN 4/28/96 4}00AM AND 4 /29/96 4:00AM 100 95 90 Li. U 85 O C 5 S 80 CL 75 70 65 60 o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o t i i j f f l N » 6 ) o r w n ^ i n ® N ( i t i 6 i o T - ' c j n 6 ^ N c o T f (D (O (O (O (O (O — — w » ^ * (0<0(0(0(0 fflfflfflfflfflffl(0(0(0(0(0(D«(D(0(0(0(0(0(00)<JIO)0)0) o o o o o o o o ( o o o 5 5 5 ! ®®5 ®5 1 ®v 5 ®5 ! 5 r o o 5 f f l o 5 a <M/M/\irkl< M /M 00o000o00O 00 00 0OflO0OflOeO0O0OCVJCVlcvJCVJ W N N W W N N N N N N N N N " " ~ - TIME K O CM CM CM CM CM CM ^ ^ •Temperature (*F)EXT. •Temperature (*F)4TH.IN •Temperature (*F)4TH.SURF Figure 4.20 Typical Day (4lh Floor) i Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission. I SURFACE AND AIR TEMPERATURE 3RD FLOOR BETWEEN 4/28/96,4p00AM AND 4 /29/96 4:00AM 100 95 90 Li. « U J cc 80 a. 75 70 65 "V - , . A 60 Temperature (*F)EXT. — Temperature (*F)3RD.IN — Temperature (*F)3RD.SURF o o O o o o O o O o o O o o o o o o O o o O O o o o o O o o o O o o o o o o o o o o o 9 o o o o O o • m- to C D K 00 6 ) o 1— C M C O v / i ti C O I V 00 C D o cvi 00 o T— cvi 00 ■ v l - 1— T — J— r — T “ T— 1— T— T — cvi C M C M C M (O (O C O C O C O C O co C D C O C O C O o> 00 o> v . oo o> 1 — 00 O) V , 00 0 ) * > » 00 0 ) v . oo C O C D C O o> C O O) C O O) C O O) co o> C O o> C O C D co C D C O C J) C O C D C O o> C O o> C O O) C D o> C D 0> C D cd 0 ) O) C D 0 ) C M ■ m- C M C M C M ■ M - C M C M vF 00 C M 00 C M oo C M 00 C M oo C M 00 C M oo C M oo C M 00 C M 00 C M oo C M 00 C M 00 C M 00 C M C M C M C M C M M " § • M " V? vF •vf ' J v f C T > O TIME Figure 4.21 Typical Day (3r d Floor) i Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. SURFACE AND AIR TEMPERATURE 2ND FLOOR BETWEEN 4/28/96,4:00AM TO 4/29/96 4:00AM 100 95 90 L L « UJ DC e 80 CL 75 70 65 60 o o o o o o O O O O O O iij cb o o o o o o o o o o o o o r- c\j pi \j" o o o o o o o o o o o o o O O O O O O O O O O O O O CO N 00 O) O T - ’ cvi CO O T - ' <N 00 00 •Temperature (*F)EXT. •Temperature (*F)2ND.IN ■Temperature (*F)2ND.SURF o > ffl (O (O ffl ID ID ® f f l Q O ) C I ) 0 ) ( D ( 0 ( D ( D ( D ( 0 ( 0 ( 0 ( 0 ( 0 ( D o o c o c o o o o o m 2! ® ® 5! ® 2! 5 5 9 5 5 ! N W W W J I f l O O O O C O W O O O O O O O O O O I O f f l CMCMCMCMCMCMCMCMCMCMCM TIME C O C O o> o> * ■ » . ■-* . 00 00 C M C M 'J C O C O O) 2? o > 00 CM CM ^ C O C O O) o> — cn O) CM CM ■ < fr ^ C O C O O) O) O ) O ) CM CM •M - ^ Figure 4.22 Typical Day (2n d Floor) i respect to the external and internal air temperature curves. It is also important to note that the internal air temperature begins to rise higher than the surface temperature in almost all the floors by 11:00AM, which means that the building cannot lose heat after that. This is an issue which needs closer examination. It seems that the internal air temperature, especially on the upper floors is driven by the external conditions and the proximity to the roof glazing. If the internal air temperature can be allowed to stay lower than the surface temperature for a longer time, it is possible that the building is able to lose heat for a longer period of time. 4.4 Preparation of a Base Case: In order to construct a Computational Fluid Dynamics (CFD) model, a base case is prepared based on the data that has been collected. The PHOENICS software uses boundary conditions of one instant to carry out further iterations, hence the base case data will be for an instant and not for over a period of time. In order to get slightly magnified results in terms of range, the base case selected is one with the ‘worst’ internal conditions, within the range of data collected. This means the ‘instant’ that would define the base case data, is the one with the highest internal air and surface temperatures, which is found out to be on 29/4/96 at 2:35PM, when the maximum internal air temperature on the top floor reaches 111.62°F and the maximum surface temperature on the top floor reaches 95.93°F. (Figure 4.23-4.25) Since the recorded temperatures are only for the south face of the atrium, assumptions have to be made to project temperatures for the north face of the atrium. For this purpose the previous data set with air temperatures of both the north and south face is 62 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. SECTIONAL PROFILE (HIGHEST) ON 4/29/96 14:35 111.62 - ♦ —Temperature (*F)ATRIUM - • —Temperature - ♦ —Temperature 105 100 u. « U l oc g 95.93 95 a. 90 1189.54 08.18 85 4.26 01.06 80 .42 75 ------ 1st Floor 2nd Floor 3rd Floor 4th Floor 5th Floor O l U ) FLOORS Figure 4.23 Vertical Profile (Max.) i i Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. I SECTIONAL PROFILE (LOWEST) ON 5/3/96 0:55 80 77.77 79.13 79.16 76.49 75 75.2 75.21 75.14 75.1 UL « ui D C i 70 U i 0. 73.28 — ♦ —Temperature (*F)ATRIUM — ■ —Temperature (*F)EXT. A -Temperature (*F)SURF. 65 1161.95 60 ------ 1st Floor 2nd Floor 3rd Floor 4th Floor 5th Floor FLOORS Figure 4.24 Vertical Profile (Min.) Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. i PROJECTED MAXIMUM CONDITIONS ON 4/29/96 AT 2:35 PM 50 48.12 45 44.23 40 39.4 P ui o c £ 35 32. CL 31.97 31,21 29.59 30 28.3 9.03 26.86 ■ 28.37 f 26.35 25.79 27.26 f 25.49 25.08 25 20 ----- 1st Floor 2nd Floor 3rd Floor 4th Floor 5th Floor -♦— Temperature (*C)ATRIUM SOUTH ■ Temperature (*C)EXT. A Temperature (*C)SURF.SOUTH ■Temperature (*C)ATRIUM NORTH (Projected) Temperature (*C)SURF.NORTH (Projected) or tn FLOORS Figure 4.25 Projected Conditions re examined. By taking average differences between north and south face air temperatures on each floor, certain values of air temperatures for the north face are arrived at. Again taking average differences of surface and air temperatures for the south face, surface temperatures for each floor on the north face are arrived at. FLOORS EXT. AIR TEMP. °F/°C SOUTH AIR TEMP. °F/°C SOUTH SRF. TEMP °F/°C NORTH AIR TEMP (Projected). °F/°C NORTH SRF. TEMP (Projected) °F/°C lw FLOOR 89.54 / 31.97 80.34 / 26.86 -/- 80.34 / 26.86 -/- 2^ FLOOR 89.54/31.97 82.19 / 27.88 77.14 / 25.07 82.94 / 28.3 77.89 / 25.49 3^ FLOOR 89.54 / 31,97 84.26 / 29.03 78.42 / 25.79 85.26 / 29.59 79.42 / 26.34 4ry FLOOR 89.54 / 31.97 88.18 / 31.21 81.06 / 27.25 90.18 / 32.32 83.06 / 28.36 5lk FLOOR 89.54/31.97 111.62 / 44.23 95.93 / 3552 118.62/48.12 102.93 / 39.40 Table 4.1 Recorded and Projected Values of Surface and Air Temperature for Creating a Base Case (4/29/96 2:35PM) The second ‘case’ extracted from this data set is a ‘night-time’ condition, which records the minimum internal conditions within the range of data collected. This happens on 5/3/96 at 12:55AM. This is important to simulate night-time stratification patterns, when the surface temperature is higher than the air temperature. All these data sets are converted to degrees Celsius from degrees Fahrenheit, since PHOENICS only uses a metric system with degrees Celsius as units of temperature. 66 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 5 COMPUTATIONAL FLUID DYNAMICS SIMULATIONS 5.1 Computational Fluid Dynamics (CFD): CFD is an advanced computer simulation tool that simulates fluid flows and non linear physical conditions associated with it, using physical principles, mathematical deductions and iterative processes. CFD procedures involve determining a numerical solution to the governing equations of fluid flow whilst advancing the solution through space or time to obtain a numerical description of the complete flow field of interest. The advantage of CFD procedures, especially for architectural purposes, is that these numerical descriptions of fluid flow can be easily converted into a graphical format, which makes it considerably easy to draw inferences from. As a developing science, Computational Fluid Dynamics has received extensive attention throughout the international community, especially in the fields of aerospace engineering and thermodynamics, but it’s applications to architecture have been realized fairly recently. The attraction of the subject is twofold 1 • Its ability to model physical fluid phenomena that cannot be easily simulated or measured with a physical experiment, for example weather systems or hypersonic aerospace vehicles. • Its ability to investigate physical fluid systems more cost effectively and more rapidly than with experimental procedures. 1 See The University of Cranfield WWW Page at http://www.cranfield.ac.uk/public/sme/cfd/david/pages/whatisCFD.html 67 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Though there has been considerable growth in the development and application of Computational Fluid Dynamics to almost all aspects of the engineering and CFD programs are now considered to be standard numerical tools, widely utilized within industry, its potential in the area of building technology and environmental controls is yet to be fully realized. The ability of CFD procedures to simulate flows of one or more fluids in space, is extremely useful in scenarios which cannot be experimentally determined, like spreading of fires and internal air contamination. In fact these are the areas through which this technology has gradually began to filter into the architectural profession. Besides predicting disaster scenarios, CFD models can also be applied for simulating internal air quality and air movement within large spaces. This makes it very appropriate to simulate stratification of air temperature inside a large space like an atrium. 5.2 Selection Criteria for a CFD Software: In spite of its wide application most CFD programs are considerably user unfriendly. Most CFD programs require a thorough knowledge of the equations and processes involved and often require alterations of the source code to adapt to individual needs. Due to the large number of iterations involved CFD programs often require heavy computing power and even then the large number of unknowns make these procedures very time consuming. Considering these conditions, for carrying out simplistic simulations one requires a CFD program that fulfills the following criteria: • Input method should be simplistic • Graphic outputs are absolutely essential 68 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. • The software and simulations should be supported by the available hardware (IBM Compatible Pentium PCs) • Computation time should not be very long 5 3 PHOENICS : PHOENICS is an acronym for Parabolic, Hyperbolic or Elliptic Numerical Integration Code-Series2 . It is manufactured and distributed by a UK based organization called Concentration, Heat and Momentum Limited. This series of computer code is capable of solving fluid heat-mass transfer problems in various scenarios ranging from one dimensional single phase steady flow to three dimensional multi phase transient flows. One of the salient features of this software is its application in a broad range of CFD procedures, ranging from aerospace to chemistry and its well designed user interface far overrides its relatively lower efficiency of utilization. PHOENICS is ideal for the use of architects as it almost completely complies with the conditions set in the preceding section. The input method in PHOENICS is in the form of a relatively simplistic input language called the PHOENICS input language (PEL). Unlike most other CFD software, the user is not required to know a lot about the source codes and does not need to change them unless absolutely necessary. Its graphic output engine PHOTON can graphically display the output in color. The software can be run on IBM compatible PCs and performs relatively well in terms computation time when a Pentium Processor is used. The relative simplicity of the PEL also means that one can leam the 2 See Rosten, H. I., Spalding, D. B., Shareware PHOENICS Beginner’ s Guide, CHAM, London, 1987 69 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. applications fast, without necessarily being familiar with all the numerical processes involved in a CFD procedure. As an application in architecture and to be used by architects, it is enough for one to know how to correctly input the necessary factors that would control the simulation process, how the CFD procedure and calculations are carried out at a conceptual level and most importantly how to make sense of the outputs. For this one has to have an understanding of the basic structure of PHOENICS and their functions in the procedure. 5.3.1 Structure PHOENICS consists of two essential computer codes - a pre-processor called SATELLITE and a processor called EARTH, and two auxiliary ones - a post processor called PHOTON and a separate self instruction program called POLIS. • SATELLITE is an interpreter that supplies the problem defining data which earth can understand and perform. • EARTH is the central equation solver. It incorporates coding sequences which represent the relevant laws of physics applied to elements of the material distributed in space and time. EARTH reads the data file provided by SATELLITE and executes the corresponding computations. It then creates an output file called ‘Result’, which the user can read and another file called ‘PHI’, which can be read by PHOTON to create a graphic output, or by EARTH itself when a new run is started. • PHOTON provides graphic display facilities for numerical predictions of phenomena involving fluid flow and heat transfer, which are got from EARTH. It 70 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. can display flow-field geometry representation, vector representation, vector field representation and scalar field representation. P H O E N I C S : S t r u c t u r e S A T E L L IT E Problem definition EARTH Equation solver PHOTON G raphic output R ESU LTS POUS Utilities an d help Figure 5.1 The Basic Structure of PHOENICS SATELLITE is a static program. It modifies or resets the default values before EARTH makes any move. EARTH acts in accordance with the information SATELLITE transmits, but it does not interact with SATELLITE. 5.3.2 Calculation Procedure3 1. Description of Physical Phenomena a) Dependent Variables: PHOENICS describes phenomenon involving the flow of heat or material in terms of distributions in time and space of temperature, velocity, pressure, concentration and other meaningful quantities. These are called ‘dependent variables’. 3 See Yang, Xudong, PHOENICS for Architects: An Instruction Manual to PHOENICS Shareware 1.4, Unpublished document. University of Southern California, Los Angeles, 1996 71 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. These distributions involve ascribing numerical values to the temperature, velocity etc. in an orderly array of locations, called ‘nodes’ or ‘mid-points’. If the process is time dependent, such distributions are calculated for each of a succession of instants of time. PHOENICS can handle either one or two inter-penetrating ‘phases’ or distinguishable fluids. The two-phase flows, however, seldom occur in building simulations except in the case of determining effects of contaminants in indoor air quality. The primary dependent variables in building simulation are as follows: Name Variable PI Pressure UI X-Direction Velocity V I Y-Direction Velocity W 1 Z-Direction Velocity KE Turbulent Kinetic Energy EP Dissipation Rate of Turbulent Kinetic Energy HI Specific Enthalpy (Temperature) C l Concentration Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. b) Description of Cells and the Grid: Before carrying out computations, the field must be divided into a two dimensional or three dimensional grid (Figure 5.2) consisting of various cells. Calculations are carried out for each cell considering the effects of the variables from its surrounding cells in an iterative manner. Cells are not necessarily of equal size, usually cells near the boundary, which specify the boundary conditions are relatively small to help the simulations to be carried out more accurately. In a 3 Dimensional model, for the sake of convenience, orientations of east-west (in the x direction), north-south (in the y direction) and low-high (in the z direction) are used for defining the location of cells. Dimensions are represented in x, y, z coordinate system. NX, NY and NZ are the symbols used to represent the total number of cells in the x, y and z direction, while IX, IY and IZ are indications of the direction of the cells. In a two dimensional model, NZ is taken to be 1. Temperature, pressure and concentration are evaluated by locations P, N, S, E and W (Figure 5.2) which lie within the cells, but variables like west-to-east velocity are evaluated for locations w and e and north-to-south velocities are evaluated for locations s and n. This is also known as the ‘staggered grid’ arrangement. 73 W « t North South UNIT CELL W ert X Eort low Figure 5.2 PHOENICS Grid Geometry Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2. The Equations Solved PHOENICS provides solutions to the discretized versions of sets of differential equations, which include continuity equations, momentum equations (for x , y and z directions), energy equations and concentration equations. For computing turbulent models PHOENICS also solves a set of turbulent kinetic energy (k), rate of dissipation of turbulent kinetic energy (e) equations (also known as the k-epsilon model). 3. Distribution of Dependent Variables For each dependent variable, there are as many equations as there are cells (NX*NY*NZ). Thus, the total number of equations is NX*NY*NZ*No. of Dependent Variables. In addition to being numerous, these sets of equations are often strongly coupled. PHOENICS therefore solves them in an iterative ‘guess and correct’ manner, the object of which is to reduce the imbalance between the left and right sides of every equation to a magnitude which is small enough to negligible. The iterative process is a complicated one, involving a multi-stage sequence of adjustments of values, repeated many times. Two of the important features of this iterative process are the definitions of ‘slabs’ and ‘sweeps’. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ‘Slabs’ are arrays of cells having the same value of ‘low-to-high’ coordinates. Many of the mathematical procedures conducted by PHOENICS operate over a single slab. Many cycles of adjustments can be performed for one slab before PHOENICS transfers its attention to the next slab. This is often referred to as ‘slab-wise solutions’. ‘Sweeps’ are a set of slab-wise operations, conducted in sequence from the lowest slab to the highest. Because the equations for values of one slab make reference to the values at the next higher slab, later adjustments made at the higher slab will invalidate, to some extent, the adjustments which have just been made at the lower one. For this reason, many sweeps must be made in succession. Ideally the process should be continued until all equations are in such perfect balance that further adjustments are unnecessary. Realistically this would result in an infinite number of sweeps. Hence the user has to specify either the number of sweeps to be carried out or a numerical value for the net imbalance (usually a very small number) at which the sweeps should be terminated. SLAB O F CELLS AT iX Figure S3 Slab-wise Operations in PHOENICS Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4. Geometric Input a) Types of Grids: PHOENICS can employ grids of three distinct kinds, namely; Cartesian, Cylindrical or Polar and Curvilinear or ‘Body Fitted Coordinates’ (BFC). For the purpose of this study only a 2 dimensional Cartesian grid system is applied. A Cartesian grid is composed of cells formed by the intersection of three sets of mutually perpendicular parallel planes (forming a box), on any one of which either x, y or z is a constant, these quantities being the distances in the three coordinate direction. The spacing between the planes can be arbitrary functions of those distances. b) Porosity and Blockage: PHOENICS is often required to simulate the flow in a field where parts of it are inaccessible to the fluid, because of partial or total obstruction by solid or porous material. This inaccessibility is represented by way of porosity factors assigned to each cell, which allow the extent of blockage of each cell face and cell volume be numerically expressed. For example if the porosity value of a cell is assigned to be zero it will imply that the cell is a completely solid obstruction. The porosity function is useful in architectural simulations to define internal walls, slabs, overhangs and other obstructions. 5. Boundary Conditions and Other Sources The most important input task in setting up a flow simulation model is the specification of boundary conditions. In particular, this involves specifying the convective and diffusive fluxes, specific enthalpy etc. at the surfaces bounding the 76 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. domain. This means, values have to be specified for each of the cells at the bounding edges of the domain. Other sources that need to be specified, include initial conditions of the fluid and inlet-outlet specifications of the domain if they exist. 5 3 3 Input Techniques: 1. Input Files: PHOENICS input files which are written in PIL are stored in a set of six ‘Libraries’ in the SATELLITE section of the program. Each library can contain many input files, but each one is identified with an unique identification number. The library files can be edited and updated. Another set of instructions have to be input by the user for each CFD procedure in the form of a Q1 file. This is also known as a ‘quick input file’. The Q1 file specifies the individual input file to be run with the help of the unique number and the nature of graphic output desired through PHOTON. 2. Input Data Structure: The data used in PHOENICS for each input file is organized in 24 groups. The order of appearance of the data items in these groups seems to conform well with the thought process which leads to the rational formulation of flow simulation computation. The groups are organized as follows: GROUP 1 Run identifiers and other preliminaries GROUP 2 Time dependence and related parameters GROUP 3 x direction grid specification GROUP 4 y direction grid specification GROUP 5 z direction grid specification GROUP 6 Body-fitting and other grid distortions GROUP 7 Variables (including porosities) named, stored and solved 77 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. GROUP 8 Terms (in differential equations) and devices GROUP 9 Properties of the medium GROUP 10 Inter-phase transfer processes and properties GROUP 11 Initialization of fields of variables, porosities etc. GROUP 12 Adjustments to fluxes of convection and diffusion GROUP 13 Boundary and internal conditions and special sources GROUP 14 Downstream pressure (for free parabolic flow) GROUP 15 Termination criteria for sweeps and outer iterations GROUP 16 Termination criteria for inner iterations GROUP 17 Under relaxation and related devices GROUP 18 Limits on variable values or increments to them GROUP 19 Data communicated by SATELLITE to GROUND GROUP 20 Control of preliminary printout GROUP 21 Frequency and extent of field printout GROUP 22 Location of spot value and frequency of residual printout GROUP 23 Variable by variable field printout and/or tabulation of spot values and residuals GROUP 24 Preparation for continuation of runs All units of variables input in the PEL as well as the outputs in PHOTON follow the metric system. Hence all dimensions are to be converted into meters and all values of temperature are to be converted into degrees Celsius. Since a discussion of the PHOENICS Input Language is not within the scope of this thesis, it is not being elaborated. It must be noted that the PIL is close to a full fledged ‘Language’ and 78 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. some insight into its structure and procedures is a must before starting to use the tool for simulations, even though this is a much simpler exercise than manipulating the source code as in the case of most other CFD programs. Quite a few of the input variables and case-specific constants, other than the ones that one is absolutely sure of, have to be based on judgment and experience related to CFD procedures. 5.4 Inputting the 2 Dimensional Model of the Bradbury Building Atrium: In order to input a two dimensional model of the Bradbury atrium, it is assumed that the ‘slice’ of the atrium being modeled lies somewhere in the center of the actual building, at the point where the temperature data was collected. Instead of making exact conversions of the building dimensions into metric units, assumptions are made by rounding off the figures in order to keep the grid dimensioning simple and yet be close to the true geometry of the building. with permission of the copyright owner. Further reproduction prohibited without permission. m m m in I Figure 5.4 Cell Distribution for the Atrium of the Bradbury Building in PHOENICS The following are the basic input dimensions: WIDTH 14.0m. The Ground level is a 4.0m wide cavity located centrally with respect to the rest of the atrium FLOOR TO FLOOR HEIGHTS GROUND 6.0m 2n d TO 4* 4.0m TOP 7.0m GLAZED ROOFING 3.5m high starting from 7.0m above the top floor slab WALKWAYS 2.25m wide. 0.10m thick Since the model is only two dimensional, absence of cells in the z direction, allows the mesh to be relatively fine without using much of computing time. No. of cells along the y axis: 42 No. of cells along the x axis: 56 Total No. of cells: 2352 80 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 9 179595 But some of the cells have been assigned a ‘porosity’ value of zero, in order to attain the internal geometry of the building. As a result The Total Effective No. o f Cells; 1720 There is a variation of cell sizes across the domain in the following manner General Space 1.0m X 0.25m Slab / Walkway 0. lm X 0.25m Gabled Roof 0.25m X 0.25m 5.5 Simulations: There are five sets of simulations carried out in all. The first two sets are unventilated models with symmetrical and asymmetrical boundary conditions. The next two sets are simulations considering natural ventilation, once again with symmetrical and asymmetrical boundary conditions. The fifth set is a simulation considering night time conditions with symmetrical boundary conditions. The graphical outputs requested after each simulation are: 1. Velocity Vectors 2. Temperature Contours 3. Horizontal direction velocity contours 4. Vertical direction velocity contours 5. Kinetic energy distribution contours (Only in the ventilated models) 6. Energy dissipation rate (Only in the ventilated model) 81 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. There are various assumptions and variations made in each of these simulations, considering the limitations in the nature of data at hand for the boundary conditions. These assumptions are summarized as follows: • Since temperature data was collected at only five points across the height of the atrium, there doesn’t exist a smooth gradation in the surface conditions across the vertical edges of the model. The surface temperatures measured are assigned to the edge-walls of each floor in the model, and the transition from one value to the other is demarcated by presence of the horizontal slabs or walkways. The bottom of each slab is assigned a surface temperature the same as the wall below it while the top is assigned a temperature the same as the wall above it. • Due to the lack of data collectors, surface temperatures at the ground level and of the roof glazing were not collected. Values are assigned to these surfaces based on calculated and logical judgment • For the ventilated modelsr assumptions are made in terms of air changes per hour and values of mass flux and inlet velocity are calculated • Inlet air temperatures and initial fluid temperatures are assumed in each case. 82 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.5.1 Unventilated Model with Symmetrical Boundary Conditions Input Values: FLOORS SURF. TEMPERATURE SURF. TEMPERATURE EAST WEST 1st FLOOR 24.4°C 24.4°C 2n d FLOOR 25.1°C 25.1°C ' 3r d FLOOR 25.8°C 25.8°C 4™ FLOOR 27.3°C 27.3°C 5™ FLOOR 35.5°C 35.5°C Surface Temperature of the Roof Glazing: 48.9°C (Same as the top floor air temp.) Initial Air Temperature: 25.0°C Air Changes: None Mass Flux: None Number of Sweeps: 100,000 Observations (Figure 5.5.1-5.5.4): The observed temperature contours exhibit a maximum internal temperature of 41.0°C as opposed to the corresponding recorded value of 44.23°C (considering only the south face air temperature corresponding to the input from Table 4.1), which is considerably close. Though the highest temperature is recorded in the simulated model, very close to the surface glazing. The net vertical temperature differential in the simulated model is 16.5°C (24.5°C to 41.0°C) which is quite comparable to the recorded value of 17.37°C. The temperature contours are displayed as strong, uniform and symmetrical 83 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. strata, the gradient of which increases as one moves from the bottom to the top. Even this observation compares strongly with the recorded data. By looking at the velocity vector distribution, one sees that the air movement lacks any distinct directionality and the maximum internal air velocity is close to 0.027m/s, which is a considerably small number. This suggests that the internal air is relatively still. The velocity vector plot clearly shows that whatever air movement exists, is concentrated on the top, dose to the glazing, while the lower part has close to zero air movement. This appears to be a representation of warmer internal air rising up and concentrating on the top. 84 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. m * ji si fi;; a si k « ti fi si ? » » J Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 5.5.1 Temperature Contours i n th e Unventilated Model w ith Symmetrical Boundary Conditions 86 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 5 .5 .2 Velocity Vectors i n th e Unvcntilntcd Model w ith Symmetrical Boundary Conditions fee Mo I! VCIDC Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. > C 1 t l j Reproduced with permission of the copyright owner. Further reproduction prohibited without permission 5.5.2 Unventilated Model with Asymmetrical Boundary Conditions Input Values: FLOORS SURF. TEMPERATURE SURF. TEMPERATURE EAST WEST 1 st FLOOR 24.4°C 24.4°C 2n d FLOOR 25.1°C 25.5°C - 3r d FLOOR 25.8°C 26.3°C 4™ FLOOR 27.3°C 28.4°C 5™ FLOOR 35.5°C 39.4°C Surface Temperature of the Roof Glazing: 48.9°C (Same as the top floor air temp.) Initial Air Temperature: 25.0°C Air Changes: None Mass Flux: None Number of Sweeps: 100,000 Observations (Figure 5.6.1-5.6.4) : The velocity vectors in this set of simulations exhibit more or less the same characteristics as the previous set. There is very little air movement, the maximum internal air velocity being 0.026m/s. The air flow patterns exhibit no directionality. The temperature contours are strongly stratified, exhibiting a net temperature differential of 19°C (Min. 25.3°C Max. 44.3°C). The maximum internal air temperature simulated, 44.3°C is considerably close to the actual recorded maximum of 48.12°C. 89 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Both these sets of simulations compare well with the recorded temperature conditions, and besides they provide further information in terms of air flow patterns and internal air velocities. Moreover, the field data was collected under conditions of minimum ventilation inside the atrium, though it would not be correct to say that the atrium was hermetically sealed, as in the case of the simulations, but the unventilated model seems to simulate the conditions with error margins which are well within the acceptable range. The validity of these first set of simulations involving the base case, which had known results to compare with, confirms the ability of the software to predict similar scenarios. This would enable one to go ahead and try to model conditions which do not necessarily have known results. Which is the next step, that is followed. The next two sets of simulations will model internal conditions considering natural or forced ventilation. with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 92 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.5.3 Naturally Ventilated Ke Model with Symmetrical Boundary Conditions: Input Values: FLOORS SURF. TEMPERATURE SURF. TEMPERATURE EAST WEST Ist FLOOR 24.4°C 24.4°C 2n d FLOOR 25.1°C 25.1°C 3r d FLOOR 25.8°C 25.8°C 4th FLOOR 27.3°C 27.3°C 5™ FLOOR 35.5°C 35.5°C Surface Temperature of the Roof Glazing: 100.0°C Initial Air Temperature: 25.0°C Air Changes: 2.8/Hr Mass Flux: 0.305 Kg/s Number of Sweeps: 100,000 Inlet Air Temperature: 20.0°C Two primary assumptions are made in this model. 1. By observing the previous simulations and the field data it is seen that the internal air temperatures on the upper part of the atrium is almost disproportionately higher than the lower parts. This leads us to believe that the convective gains and the radiative gains through the roof glazing plays an important role in this. But it was not possible to collect field data in terms of the surface temperature of the roof glazing or the air temperature in the areas very close to the roof. Hence, in order to get a more realistic idea in the simulations, the surface temperature of the roof glazing in this 95 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. case has been assumed to be 100.0°C. The large value of this number would account for the radiative and convective solar gains through the roof to the air close to it. It must be noted here that, radiative convective solar gains can also be simulated in PHOENICS by placing a ‘Heat Source’ on the roof, but this procedure has not been attempted here. 2. The second important assumption, is the air change rate of the model. The air change rate in this case, is assumed to 2.8 air changes/Hour. This is a relatively moderate number. Air changes in PHOENICS are simulated by means of a variable called ‘Mass-flux’, given in Kg/s. Mass-flux defines the mass of air escaping or entering the space per second. The following formula can be used to find Mass-flux : Mass-flux (Kg/s) = Air-Changes/Hour * Volume (m3) * p of Air (Kg/ m3i 3600 seconds (s) In this case: Air-Changes/Hour = 2.8 Volume = Sectional Area of the Atrium * 1 ( Since it is a 2 Dimensional Model) = 318.7m3 p of Air = 1.2 Kg/m3 Mass-flux = 2.8 *318.7* 1.2 Kg/s 3600 = 0.305 Kg/s An air inlet, 2m wide, is provided at the bottom floor of the atrium and two outlets, lm wide, are provided on each side at the top. Observations (Figure 5.7.1-5.7.5) : The obvious difference between the temperature of contours of this set of simulations and the previous sets is the absence of a clear stratification pattern. The temperature 96 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. patterns are governed by the air flow paths from the inlet to the outlets at the top. Though there is a internal temperature differential of 16.1°C, this is not distributed vertically across the atrium. The highest internal air temperature simulated is 39.9°C, which is considerably lower than the measured values as well as the previous simulations, in spite of assuming the glazing temperature on top to be 100.0°C. The velocity vectors also show strong directionality, with air movement patterns strongly following the inlet-to-outlet path. The maximum internal air velocity is relatively higher than the previous two cases at 0.65m/s. Though the boundary conditions inputted were symmetrical, the temperature contours and the vertical direction velocity contours exhibit a slight shift in one direction. This seems to be a result of the ‘slabwise-solution’ process of PHOENICS. Since PHOENICS carries out slabwise-solutions from the left to right, there might be some unbalanced or incomplete processes which give a slight shift to left. Two new dependent variables were considered in this set of simulations. They are, Kinetic Energy Distribution (K) and Energy Dissipation Rate (£), and this kind of a model is often referred to as a K- epsilon model. These two variables are useful in determining degrees of turbulence in the space. It is seen from the Kinetic Energy distribution contours that the maximum values of energy distribution patterns are fairly low. Hence turbulence is not an aspect to be concerned about. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 98 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. o o 4 > .4 ■)rlU V.-'i! MrtTUJttrf.I.V U7N7ILATK0 K K ttODn. p h o iw ic s Figure 5.7.3 Horizontal Direction Velocity Contours in the Naturally Ventilated K-Epsilon Model with Symmetrical Boundary Conditions 101 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 102 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 5 .7 .5 K inetic Energy Distribution Contours i n a Naturally V cSrtlatedTnilpsilm ^kx^^ 5.5.4 Naturally Ventilated Ke Model with Asymmetrical Boundary Conditions: Input Values: FLOORS SURF. TEMPERATURE SURF. TEMPERATURE EAST WEST 1 st FLOOR 24.4°C 24.4°C 2n d FLOOR 25.1°C 25.5°C 3r d FLOOR 25.8°C 26.3°C 4t h FLOOR 27.3°C 28.4°C 5t h FLOOR 35.5°C 39.4°C Surface Temperature of the Roof Glazing: 48.9°C Initial Air Temperature: 25.0°C Air Changes: 2.8/Hr Mass Flux: 0.305 Kg/s Number of Sweeps: 100,000 Inlet Air Temperature: 20.0°C Two changes are made in this set of simulations compared to the previous set. 1. The boundary conditions are set to be asymmetrical in this case 2. The roof glazing surface temperature is set back to 48.9°C as opposed to 100°C in the previous case. The rest of the input variables are same as the preceding case. Observations (Figure 5.8.1-5.8.5) : The temperature contours in this set of simulations demonstrate surprisingly low internal temperature differential and lack of stratification. The net internal temperature 103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. differential is only 0.72°C (Max. 20.72°C, Min. 20.0°C). These temperatures are very close to the inlet air temperature set at 20.0°C. The reduction of the glazing temperature has resulted in some significant changes in the scenario. This turns out to be one of the most crucial observations. The glazing surface temperature seems to be a major factor contributing towards the internal air temperature differential and stratification patterns. One of the primary conclusions that can be drawn from the temperature contours, is that with air change rates in the vicinity of 3.0 Air/Changes/Hour (2.8 Air-Changes/Hour simulated), and a low surface temperature of the roof glazing the internal stratification and temperature differential is almost negligible. The velocity vectors demonstrate strong directionality from the bottom to the top (Inlet-to-outlet), with a maximum internal air velocity of 0.71m/s, which is a relatively high number. Once again the Kinetic Energy Distribution and Dissipation Rate demonstrate very small values, confirming the absence of any internal turbulence. 104 with permission of the copyright owner. Further reproduction prohibited without permission. 105 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission Figure 5 .8 .2 Velocity Vectors i n th e Naturally Ventilated K-Epsilon Model w ith Asymmetrical Boundary Conditions : : 107 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 5.8.3 Horizontal Direction Vclocily Contours i n th e Naturally Ventilated K-Epsilon Model w ith Asymmetrical Boundary 7415 108 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission. f t . 6 8 1 9 f t . f t f t y / 6.tK4& ft.ftCW, e.W !?4 8.W!TI ft.cia? ft.B ill 8.0L 2S e.ei:te ASYWITKIGftL HAT. VEHT. K E MODEL P W O O llC S Figure 5.8.5 Energy Dissipation Contours in a Naturally Ventilated K-Epsilon Model with Asymmetrical Boundary Conditions 5.5.5 Simulation of Night-Time Conditions with Symmetrical Boundary Conditions: Input Values: FLOORS SURF. TEMPERATURE SURF. TEMPERATURE EAST WEST I st FLOOR 23.5 23.5 2n d FLOOR 24.7 24.7 3r d FLOOR 25.4 25.4 4™ FLOOR 26.2 26.2 5™ FLOOR 26.2 26.2 Surface Temperature of the Roof Glazing: 15.0°C Initial Air Temperature: 22.0°C Air Changes: None Mass Flux: None Number of Sweeps: 100,000 The primary difference between the night-time conditions and the previous ‘day-time’ conditions is that, during the night the external air temperatures are lower than the wall surface temperatures. This results in the temperature of the roof glazing to be much lower than the internal surface temperatures, hi this case the roof glazing temperature is assumed to be 15.0°C. Observations (Figure 5.9.1-5.9.3) ; The outputs of this set of simulations exhibit some interesting results. There is absence of any clear stratification, as the measured data suggests, and the net 110 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. internal temperature difference is only 1.38°C. But the temperature contour patterns are self explanatory in terms of the air flow patterns. The wanner internal air rises towards the roof, and when it comes in contact with the cool roof glazing, the air cools down and starts to sink back to the bottom. This results in the ‘swirling’ contour patterns at the top. The walkways help in obstructing internal air flow, which results in pockets of warm air being trapped in between them. The horizontal direction velocity contours show a strong air movement about the middle of the atrium towards the positive x direction and movement of air in the exactly in the opposite direction at the top, further explaining the ‘swirl’. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 112 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 113 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. o e e e b i » « o 114 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 6 FINAL OBSERVATIONS. CONCLUSIONS AND BROAD RECOMMENDATIONS 6.1 Observations Based on Temperature Data Collected: The primary observations based on examination of the temperature data collected can be enumerated as follows: • The atrium demonstrates strong vertical stratification of air temperature during the day. The temperature differential shows a gradual increase from the lower floors to the 4th floor and then increases sharply as one approaches the glazed roof. • The internal temperature fluctuations are almost always synchronous with the external temperature variation, with no or very little time lag. This observation leads to believe that the thermal mass of the building itself contributes very little towards the thermal behavior of the atrium. • The internal air temperature does not fall below a certain level even though the external air temperature decreases considerably at night. It is seen that with decreasing external temperature there is a decrease in the magnitude of temperature stratification. This can be a result of the ‘buffer effect’ of the atrium. Due to the greenhouse effect and lack of proper ventilation the atrium retains re radiated heat from the adjoining spaces and does not allow the internal air temperatures to drop. • The sharp increase in temperature differential on the topmost levels is an outcome of the ‘stack effect’, where wanner air rises up by buoyant behavior and what makes it worse is the lack of adequate ventilation on top. 115 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. • There is also an added rise in air temperature due to increased radiative gain on top. The surface temperature of the glazing on top increases to very high levels which also accounts for high convective gains to the air at the upper level. • The building itself is of considerably high thermal mass, but it is surprising how the atrium air and surface temperatures demonstrate negligible time lag in their diurnal patterns. By closely observing the floor-wise air and surface temperature curves, i r seems as if the building is not allowed to lose heat to its fullest extent in a diurnal cycle. In other words, the building might be still losing heat till later in the morning if the air temperatures inside the atrium are lower than the surface temperatures for a longer time (which is the case at night). But a sharp increase in the air temperatures earlier in the day, due to solar gains through the glazing and lack of ventilation, prevents this from happening. 6.2 Conclusions Drawn from the CFD Simulations : The conclusions drawn from the CFD simulations can be enumerated as follows: • The simulations done with an unventilated model are satisfactorily close to the measured stratification patterns. This might suggest that the real building itself faces extreme lack of ventilation. • The ventilated models show very little or no stratification with a moderate air change rate 2.8 Air-Changes/Hr. • The ventilated model with low roof glazing temperatures exhibits m inim al internal temperature differential compared to the one with high roof glazing temperatures. • The above observations lead one to believe that the governing issues resulting in strong internal stratification are: 116 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1) Ventilation 2) Surface temperature of the roof glazing • One still cannot confirm, on the basis of these observations, which one of these issues are dominant. In this specific case, stratification might be a result of both lack of ventilation and high temperatures on the roof surface. • No conclusions can be drawn on how a 2 Dimensional model in PHOENICS compares with a 3 Dimensional model. It is possible that with an absence of cells on the Z-axis the flow might be demonstrated as much more directional in the X-Y axes than it actually is. In reality the inlets and the outlets are distributed in all axes unlike in the 2 Dimensional model. 6.3 Broad Recommendations : 4. Comparison of a three dimensional model with the two dimensional model, with further variations in ventilation and surface conditions should lead to a better understanding of the process . 5. With reference to this specific atrium, the following steps should alleviate the present internal conditions • Increased ventilation on the upper levels to flush out hot air. This can be done by designing an efficient exhaust system. Further simulations of the atrium with a 3 Dimensional model, would greatly help determine strategic locations of outlets to effectively ventilate the atrium. • Proper shading of the glazed roof during the day, would greatly help to reduce the internal temperature differential. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6. The generic nature of PHOENICS and most other CFD tools in the market, demands that for architectural purposes they need to be coupled with other energy analysis software for convenience and accuracy in making fluid flow and predictions. 7. It would be beneficial if CFD simulation results done over several instants can be put together in an animated form to depict transient fluid flow 118 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. BIBLIOGRAPHY : Aiulfi, D., Chuard, D., Som e W ays to M odel the Tem perature Stratification in an A triu m , ASHRAE Conference, San Diego, 1995 Andersen, Karl T., N a tu ra l Ventilation in A tria, ASHRAE Atrium Symposium, San Diego 1995 Andersen, Karl T., T heoretical Considerations on N a tu ra l Ventilation by Therm al B uoyancy, A S H R A E L arge Enclosure Sym posium , San Diego, 1995 Aschehoug, 0 ., Hestnes, A. G., Thyholt, M., Jacobsen, T., N orw egian Institute o f ~ Technology, E xtension to the D ept, o f E lectrical E ngineering and C om puter Science, A n A d va n ced Case Study f o r the TEA S o la r H ea tin g and C ooling - Task X I (P assive a n d H ybrid Solar Com m ercial B uildings), SINTEF, Trondheim, 1990. Hastings, S. R., P assive S o la r C om m ercial and In stitutional B uildings: a sourcebook o f exam ples a n d design insights, IEA, J. Wiley , New York, 1994 Markatos, N. C., Numerical Simulation of Fluid Flow and Heat/Mass Transfer Processes, Springer-Verlag, New York, 1986 Murakami, S., Kato, S., Kobayashi, H., Hanyu, F., C urrent Status o f CFD A pplication to A ir-C onditioning E ngineering, Proceedings, Pan Pacific Symposium on Building and Urban Environmental Conditioning in Asia, Nagoya, Japan, March 1995 Rosten, H. I., Spalding, D. B., Shareware PH O EN IC S B e g in n e r's G uide, Concentration, Heat and Momentum Ltd. (CHAM), 1987 Saxon, Richard, The A trium C om es o f Age, Longman, Essex, England 1994 Saxon, Richard, A triu m Buildings: D evelopm ent and D esig n , Van Nostrand Reinhold, New York, 1987 Sullivan, Anne C., M odeling the Elem ents, ARCHIRECTURE, February 1996 Yang, Xudong, PHOENICS for Architects: An Instruction Manual to PHOENICS Shareware 1.4, Unpublished Report, University of Southern California, Los Angeles, 1996 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. NATURALLY VENTILATED K-EPSILON MODEL W ITH SYM M ETRICAL BOUNDARY CONDITIONS 2 7 4 . ****** x 0 LOAD CASE: TYPE LOAD(274) ****** GROUP 1. Run title and other preliminaries TEXT(NATURALLY VENTILATED K E MODEL) REAL(UIN,UOUT,TIN,TKEIN,EPSIN) UIN=0.305;UOUT=-0.305;TIN=20.0 GROUP 2 . Transience; time-step specification GROUP 3. X-direction grid specification ** Set a symmetrical grid, consisting of power-law grids (varying as IX**2.0), which start from each edge and meet in the middle. GRDPWR(X,5 6,14,1.0) GROUP 4. Y-direction grid specification ** Set a symmetrical grid as in GROUP 3 NY=42;YVLAST=1.0 YFRAC( I )=-10.0; YFRAC(2)=1.0 YFRAC(3)=1.0; YFRAC(4)=0.1 YFRAC(5)=4.0; YFRAC(6 )= 1.0 YFRAC(7)=1.0;YFRAC(8)=0.1 YFRAC(9)=4.0;YFRAC(10)= 1.0 YFRAC(11 )=1.0; YFRAC( 12)=0.1 YFRAC(13)=7.0; YFRAC( 14)= 1.0 YFRAC( 15)= 14.0; YFRAC( 16)=0.25 GROUP 7. Variables stored, solved & named SOLVE(P 1 ,U1, VI ,H1) TURMOD(KEMODL) GROUP 8 . Terms (in differential equations) & devices TERMS(H1,N,Y,Y,Y,Y,Y) GROUP 9. Properties of the medium (or media) ** Set the temperature as TMP1A+TMP1B*H1 ENUL= 1.45E-5 ;TMP 1=GRND2 ;TMP 1 A=0.0 ;TMP 1 B=1.0 ** Set the density as RHO1 A+RHO1 B*Temperature RH01=GRND4;RH01A=l.293;RH01B=-0.0044;PRNDTL(Hl)=l.0/1.3 GROUP 11. Initialization of variable or porosity fields TKEIN=0.25*UIN;TKEIN=TKEIN*UIN;TKEIN=TKEIN*0.018 EPSIN=TKEIN** 1,5;EPSIN=EPSIN*0.1643£ PSIN=EPSIN/3.429E-3 RESTRT(ALL) FIINIT(P 1 )=READH;FHNIT(U 1 )=READFI FIINIT(V 1 )=READFI;FIINIT(H1)=READFI FIINIT(EP)=READFI;FIINIT(KE)=READFI FIINIT(P1)=0.0;FIINIT(U1)=0.0;F1INIT(V1)=0.0;FIINIT(H1)=25.0 FIINIT(EP)=EPSINfIINIT(KE)=TKEIN Porosity Fields CONPOR(0.0,CELL, 1,20,1,6 ,1,1) CONPOR(0.0,CELL,37,56,1,6,1,1) CONPOR(0.0,CELL, 1,9,1 1,1 1,1,1) CONPOR(O.O.CELL,48,56,11,11,1,1) CONPOR(0.0,CELL, 1,9,16,16,1,1) CONPOR(0.0,CELL,48,56,16,16,1,1) CONPOR(0.0,CELL, 1,9,21,21,1,1) CONPOR(O.O.CELL,48,56,21,21,1,1) CONPOR(0.0,CELL, 1,1,29,42,1,1) CONPOR(O.O.CELL,2,3,30,42,1,1) 121 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CONPOR(O.O.CELL,4,5,31,42,1,1) CONPOR(O.O.CELL,6,7,32,42,1,1) CONPOR(O.O.CELL,8,9,33,42,1,1) CONPOR(0.0,CELL,10,11,34,42,1,1) CONPOR(0.0,CELL, 12,13,35,42,1,1) CONPOR(0.0,CELL,14,15,36,42,1,1) CONPOR(O.O.CELL, 16,17,37,42,1,1) CONPOR(O.O.CELL,18,19,38,42,1,1) CONPOR(0.0,CELL,20,21,39,42,1,1) CONPOR(0.0,CELL,22,23,40,42,1,1) CONPOR(0.0,CELL,24,25,41,42,1,1) CONPOR(0.0,CELL,26,27,42,42,1,1) CONPOR(0.0,CELL,30,31,42,42,1,1) CONPOR(O.O.CELL,32,33,41,42,1,1) CONPOR(0.0,CELL,34,35,40,42,1,1) CONPOR(0.0,CELL,36,37,39,42,1,1) CONPOR(0.0,CELL,38,39,38,42,1,1) CONPOR(0.0,CELL,40,41,37,42,1,1) CONPOR(O.O.CELL,42,43,36,42,1,1) CONPOR(0.0,CELL,44,45,35,42,1,1) CONPOR(0.0,CELL,46,47,34,42,1,1) CONPOR(0.0,CELL,48,49,33,42,1,1) CONPOR(0.0,CELL,50,51,32,42,1,1) CONPOR(O.O.CELL,52,53,31,42,1,1) CONPOR(0.0,CELL,54,55,30,42,1,1) CONPOR(0.0,CELL,56,56,29,42,1,1) GROUP 13. Boundary conditions and special sources ** Pressure relief PATCH(REFP,CELL, 15,19,1,1,1,1,1,100);COVAL(REFP,P1 .FIXP.O.O) ** Set the heat flux to be the prevailing value of HI in the cell COVAL(REFP,Hl,FDCVAL,SAME) ** Inlet PATCH(INLET,CELL,25,32,1,1,1,1,1,100) CO V AL(INLET,P 1 ,FIXFLU,UIN) COVAL(INLET,Hl ,ONLYMS,TIN) CO VAL(INLET, V1 ,ONL YMS ,0.102) COVAL(INLET,KE,ONLYMS,TKEIN) COVAL(INLET,EP,ONLYMS,EPSIN) ** Outlet PATCH(OUILETl .CELL, 1,1,28,28,1,1,1,100) CO V AL(OUTLETl ,P 1 ,FIXFLU,UOUT) COVAL(OUTLETl,Hl,ONLYMS,SAME) PATCH(OUTLET2,CELL,56,56,28,28,1,1,1,100) COVAL(OUTLET2,Pl .FIXFLU.UOUT) CO VAL(OUTLET2,H 1 .ONLYMS .SAME) ** west walll PATCH(WEST1, WWALL.21,21,1,6 ,1,1,1,100) COVAL(WEST1,V1,1.0,0.0) COVAL(WESTl ,H1,1 ./PRNDTL(H 1 ),24.4) COVALCWEST1 ,KE,GRND2,GRND2) COVAL(WESTl ,EP,GRND2,GRND2) ** west wall2 P ATCH(WEST2, WWALL, 1,1,7,10,1,1,1,100) CO V AL(WEST2, V1,1.0,0.0) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CO V AL(WEST2,H 1,1 ./PRNDTL(H1),25.1) COVAL(WEST2,KE,GRND2,GRND2) COVAL(WEST2,EP,GRND2,GRND2) ** west wal!3 PATCH(WEST3, WWALL, 1,1,12,15,1,1,1,100) COVAL(WEST3,V 1,1.0,0.0) COVAL(WEST3,H 1,17PRNDTL(H1),25.8) COVAL(WEST3,KE,GRND2,GRND2) COVAL(WEST3,EP,GRND2,GRND2) ** west wall4 PATCH(WEST4, WWALL,1,1,17,20,1,1,1,100) COV AL(WEST4,V 1,1.0,0.0) COVAL(WEST4,H 1,17PRNDTL(H1),27.3) COVAL(WEST4,KE,GRND2,GRND2) COVAL(WEST4,EP,GRND2,GRND2) ** west wallS PATCH(WEST5, WWALL,1,1,22,27,1,1,1,100) COVAL(WEST5,Vl, 1.0,0.0) CO VAL(WEST5,H 1,1 ./PRNDTL(H 1 ),35.5) COVAL(WEST5,KE,GRND2,GRND2) COVAL(WEST5,EP,GRND2,GRND2) ** east walll PATCH(EAST1 ,EWALL,36,36,1,6,1,1,1,100) COVAL(EAST1,V1,1.0,0.0) C0VAL(EAST1,H1,17PRNDTL(H1),24.4) COVAL(EASTl ,KE,GRND2,GRND2) COVAL(EASTl ,EP,GRND2,GRND2) ** east wa!1 2 PATCH(EAST2,EWALL,56,56,7,10,1,1,1,100) COVAL(EAST2, V1,1.0,0.0) C0VAL(EAST2,H1,17PRNDTL(H1),25.1) COVAL(EAST2,KE,GRND2,GRND2) COVAL(EAST2,EP,GRND2,GRND2) ** east wall3 PATCH(EAST3 ,EWALL,56,56,12,15,1,1,1,100) COVAL(EAST3,Vl, 1.0,0.0) C0VAL(EAST3,H1,17PRNDTL(H1),25.8) COVAL(EAST3,KE,GRND2,GRND2) COV AL(EAST3,EP,GRND2,GRND2) ♦♦ east W 31 1 4 PATCH(EAST4,EWALL,56,56,17,20,1,1,1,100) COVAL(EAST4,Vl, 1.0,0.0) COV AL(EAST4,H1,1./PRNDTL(H1),27.3) COVAL(EAST4,KE,GRND2,GRND2) COV AL(EAST4,EP,GRND2,GRND2) ** east wa ! 1 5 PATCH(EAST5,EWALL,56,56,22,27,1,1,1,100) COVAL(EAST5, VI, 1.0,0.0) COV AL(EAST5,H1,17PRNDTL(H1),35.5) COVAL(EAST5,KE,GRND2,GRND2) COVAL(EAST5,EP,GRND2,GRND2) ** ground PATCH(B ASE1 ,LWALL,22,24,1,1,1,1,1,100) CO VAL(B ASE1 ,H 1,1 ,/PRNDTL(H 1 ),24.4) COVAL(B ASE 1,KE,GRND2,GRND2) 123 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. COVAL(B ASE1 ,EP,GRND2,GRND2) PATCH(BASE2v LWALL,33,35, 1,1,1,1,1,100) COV AL(B ASE2,H 1,1 ./PRNDTL(H1),24.4) COVAL(BASE2,KE,GRND2,GRND2) COVAL(BASE2,EP,GRND2,GRND2) ** west slabl PATCH(WSLB 1 ,NWALL,2,20,7,7,1,1,1,100) COV AL(WSLB 1 ,U 1,1.0,0.0) COV AL(WSLB 1 ,H 1,17PRNDTL(H 1 ),25.1) COVAL(WSLB 1 ,KE,GRND2,GRND2) COVAL(WSLB 1 JEP,GRND2,GRND2) ** west slab2 PATCH(WSLB 1 ,NWALL,2,9,10,10,1,1,1,100) COVAL(WSLB 1,U1,1.0,0.0) COVAL(WSLB 1,H1,1 ./PRNDTL(H1),25.1) COVAL(WSLB 1,KE,GRND2,GRND2) COVAL(WSLB 1 3 P,GRND2,GRND2) ** west slab2A PATCH(WSLB 1A, WWALL,10,10,11,11,1,1,1,100) COVAL(WSLB 1A,U1,1.0,0.0) COVAL(WSLBlA,Hl,l./PRNDTL(Hl),25.1) COVAL(WSLB 1 A,KE,GRND2,GRND2) COVAL(WSLB 1A,EP,GRND2,GRND2) ** west slab2B PATCH(WSLB IB ,S WALL,2,9,12,12,1,1,1,100) COVAL(WSLB IB,Ul,1.0,0.0) COVAL(WSLBlB,Hl,l./PRNDTL(Hl),25.8) COVAL(WSLB 1B,KE,GRND2,GRND2) COVALCWSLB 1BV EP,GRND2,GRND2) COVAL(WSLB 1B3P,GRND2,GRND2) ♦♦ west slab3 PATCH(WSLB2,NWALL,2,9,15,15,1,1,1,100) COVAL(WSLB2,Ul, 1.0,0.0) COV AL(WSLB2,H1,1./PRNDTL(H1),25.8) COVAL(WSLB2,KE,GRND2,GRND2) COVAL(WSLB2,EP,GRND2,GRND2) ♦♦ west slsb3A PATCH(WSLB2A, WWALL, 10,10,16,16,1,1,1,100) COVAL(WSLB2A,XJl,1.0,0.0) COV AL(WSLB2A,H1,1./PRNDTL(H1),25.8) COVAL(WSLB2A,KE,GRND2,GRND2) COVAL(WSLB2A,EP,GRND2,GRND2) ** west slab3B PATCH(WSLB2B JLWALL,2,9,17,17,1,1,1,100) COVAL(WSLB2B,Ul, 1.0,0.0) COVAL(WSLB2B,Hl,l./PRNDTL(Hl),27.3) COVAL(WSLB2B,KE,GRND2,GRND2) COVAL(WSLB2BJEP,GRND2,GRND2) ** west slab4 PATCH(WSLB 3 ,NWALL,2,9,20,20,1,1,1,100) COVAL(WSLB3,U 1,1.0,0.0) C0VAL(WSLB3,H1,17PRNDTL(H1),27.3) COVAL(WSLB3,KE,GRND2,GRND2) COVAL(WSLB3,EP,GRND2,GRND2) ** west slab4A 124 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PATCH(WSLB3A,WWALL, 10,10,21,21,1,1, 1,100) C0VAL(WSLB3A,U1,1.0,0.0) COVAL(WSLB3 A,HI, 1 ./PRNDTL(H1),27.3) COV AL(WSLB3 A,KE,GRND2,GRND2) COVAL(WSLB3A,EP,GRND2,GRND2) ** west slab4B PATCH(WSLB3B JLWALL.2,9,22,22,1,1,1,100) COVAL(WSLB3B,Ul, 1.0,0.0) COV AL(WSLB3B,H1,1./PRNDTL(H1), 35.5) COVAL(WSLB3B ,KE,GRND2,GRND2) COVAL(WSLB3B,EP,GRND2,GRND2) ** east slabl PATCH(ESLB 1 ,NWALL,37,55,7,7,1,1,1,100) COVAL(ESLB 1 ,U1,1.0,0.0) CO VAL(ESLB 1 ,H 1,1 ./PRNDTL(H 1 ),25.1) COV AL(ESLB 1 ,KE,GRND2,GRND2) COVAL(ESLB 1,EP,GRND2,GRND2) ** east slab2 PATCH(ESLB2,NWALL,47,55,10,10,1,1,1,100) COVAL(ESLB2,U 1,1.0,0.0) C0VAL(ESLB2,H1, l./PRNDTL(Hl),25.1) COVAL(ESLB2,KE,GRND2,GRND2) COVAL(ESLB2,EP,GRND2,GRND2) ** east slab2A PATCH(ESLB2A,EWALL,46,46,11,11,1,1,1,100) CO VAL(ESLB2 A,U 1,1.0,0.0) COVAL(ESLB2A,Hl, l./PRNDTL(Hl),25.1) COVAL(ESLB2A,KE,GRND2,GRND2) COVAL(ESLB2AJEP,GRND2,GRND2) ** east slab2B PATCH(ESLB2B,LWALL,47,55,12,12,1,1,1,100) C0VAL(ESLB2B,U1,1.0,0.0) COVAL(ESLB2B,Hl,17PRNDTL(Hl),25.8) COVAL(ESLB2B,KE,GRND2,GRND2) COVAL(ESLB2BJEP,GRND2,GRND2) ** east slab3 PATCH(ESLB3,NWALL,47,55,15,15,1,1,1,100) COVAL(ESLB3,U1,1.0,0.0) C0VAL(ESLB3,H1,17PRNDTL(H1),25.8) COVAL(ESLB3,KE,GRND2,GRND2) COVAL(ESLB3,EP,GRND2,GRND2) ** east slab3A PATCH(ESLB3A3WALL,46,46,16,16,1,1,1,100) COVAL(ESLB3 A,U1,1.0,0.0) C0VAL(ESLB3A,H1,1./PRNDTL(H1),25.8) COVAL(ESLB3A,KE,GRND2,GRND2) COVAL(ESLB3A,EP,GRND2,GRND2) ** east slab3B PATCH(ESLB 3B ,LWALL,47,55,17,17,1,1,1,100) COVAL(ESLB3B,U1,1.0,0.0) COV AL(ESLB3B,H1,1VPRNDTL(H1), 27.3) COVAL(ESLB3B,KE,GRND2,GRND2) COVAL(ESLB3B^P,GRND2,GRND2) ** east slab4 PATCH(ESLB4,NWALL,47,55,20,20,1,1,1,100) 125 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. COV AL(ESLB4,U 1,1.0,0.0) CO VAL(ESLB4,H 1,1 ./PRNDTL(H 1 ),27.3) COVAL(ESLB4,KE,GRND2,GRND2) COVAL(ESLB4.EP,GRND2,GRND2) ** east slab4A PATCH(ESLB4A,EWALL,46,46,21,21,1,1,1,100) C0VAL(ESLB4A,U1,1.0,0.0) COV AL(ESLB4A,H 1,1 ./PRNDTL(H1),27.3) COVAL(ESLB4A,KE,GRND2,GRND2) COV AL(ESLB4A,EP,GRND2,GRND2) ** east slab4B PATCH(ESLB4B,LWALL,47,55,22,22,1,1,1,100) CO VAL(ESLB4B ,U1,1.0,0.0) CO VAL(ESLB4B ,H1,17PRNDTL(H 1 ),35.5) COVAL(ESLB4B,KE,GRND2,GRND2) COVAL(ESLB4BEP,GRND2,GRND2) ** topi from west PATCH(T1,NWALL,2,3,29,29,1,1,1,100) C0VAL(T1 ,U 1,1.0,0.0) C0VAL(T1,H1,1 ./PRNDTL(H1), 100) C0VAL(T1,KE,GRND2,GRND2) C0VAL(T1,EP,GRND2,GRND2) ** top2 from west PATCH(T2,NWALL,4,5,30,30,1,1,1,100) CO VAL(T2,U1,1.0,0.0) CO VAL(T2,H 1,1 ,/PRNDTL(H 1), 100) COVAL(T2,KE,GRND2,GRND2) COVAL(T2,EP,GRND2,GRND2) ** top3 from west PATCH(T3 ,NWALL,6,7,31,31,1,1,1,100) C0VAL(T3,U1,1.0,0.0) CO VAL(T3,H 1,1 ./PRNDTL(H 1), 100) COVAL(T3,KE,GRND2,GRND2) COVAL(T3,EP,GRND2,GRND2) ** top4 from west PATCH(T4,NWALL,8,9,32,32,1,1,1,100) COVAL(T4,Ul, 1.0,0.0) COVAL(T4,H 1,1 ,/PRNDTL(H 1), 100) COVAL(T4,KE,GRND2,GRND2) COVAL(T4,EP,GRND2,GRND2) ** top5 from west PATCH(T5,NWALL, 10,11,33,33,1,1,1,100) COVAL(T5,Ul, 1.0,0.0) COVAL(T5,H1,1./PRNDTL(H1),100) COVAL(T5,KE,GRND2,GRND2) COVAL(T5,EP,GRND2,GRND2) ** top6 from west PATCH(T6 ,NWALL, 12,13,34,34,1,1,1,100) COVAL(T6,U1,1.0,0.0) COVAL(T6 ,H 1,1 ./PRNDTL(H 1), 100) COVAL(T6,KE,GRND2,GRND2) COVAL(T6,EP,GRND2,GRND2) ** top7 from west PATCH(T7,NWALL, 14,15,35,35,1,1,1,100) CO VAL(T7,U 1,1.0,0.0) 126 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CO VAL(T7,H 1,1 ./PRNDTL(H 1), 100) COVAL(T7,KE,GRND2,GRND2) COVAL(T7,EP,GRND2,GRND2) ** top8 from west PATCH(T8,NWALL,16,17,36,36,1,1,1,100) C0VAL(T8,U1,1.0,0.0) C0VAL(T8,H1,1 ./PRNDTL(H1), 100) COVAL(T8,KE,GRND2,GRND2) COVAL(T8,EP,GRND2,GRND2) ** top9 from west PATCH(T9,NWALL, 18,19,37,37,1,1,1,100) CO VAL(T9,U1,1.0,0.0) C0VAL(T9,H1,17PRNDTL(H1), 100) COVAL(T9,KE,GRND2,GRND2) COVAL(T9,EP,GRND2,GRND2) ** toplO from west PATCH(T10,NWALL,20,21,38,38,1,1,1,100) COVAL(T10,U1,1.0,0.0) COVAL(T10,H1,1./PRNDTL(H1),100) COVAL(T10,KE,GRND2,GRND2) COVAL(T10,EP,GRND2,GRND2) ** topi 1 from west PATCH(T11 ,NWALL,22,23,39,39,1,1,1,100) COV AL(T 11,U l,1.0,0.0) COVAL(Tl 1 ,H1,1 ./PRNDTL(H1), 100) COVALCT11 ,KE,GRND2,GRND2) COVAL(Tl 1 ,EP,GRND2,GRND2) ** topl2 from west PATCH(T12,NWALL,24,25,40,40,1,1,1,100) COVAL(T12,U1,1.0,0.0) COVAL(T12,Hl,l./PRNDTL(Hl), 100) COVAL(T12,KE,GRND2,GRND2) COVAL(T12,EP,GRND2,GRND2) ** topl3 from west PATCH(T13,NWALL,26,27,41,41,1,1,1,100) COVAL(Tl 3,U 1,1.0,0.0) COVAL(T13,H1,1./PRNDTL(H1),100) COVAL(T13,KE,GRND2,GRND2) COVAL(Tl 3,EP,GRND2,GRND2) ** top 14 from west PATCH(T14,NWALL,28,29,42,42,1,1,1,100) COV AL(T14,U1,1.0,0.0) COVAL(T14,H1,1jTRNDTL(H1),100) COVAL(T14,KE,GRND2,GRND2) COVAL(T14,EP,GRND2,GRND2) ** top 15 from west PATCH(T15,NWALL,30,31,41,41,1,1,1,100) COV AL(T15,U 1,1.0,0.0) CO VAL(T15,H 1,1 VPRNDTL(H 1), 100) COVAL(T15,KE,GRND2,GRND2) COVAL(T15,EP,GRND2,GRND2) ** topl6 from west PATCH(T16,NWALL,32,33,40,40,1,1,1,100) CO VAL(T16,U 1,1.0,0.0) COVAL(T16,H 1,1 ,/PRNDTL(H 1), 100) 127 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. COVAL(T16,KE,GRND2,GRND2) COVAL(T16,EP,GRND2,GRND2) * * top 17 from west PATCH(T17,NWALL,34,35,39,39,1,1,1,100) COVAL(Tl 7,U1,1.0,0.0) CO VAL(T17,H 1,1 ./PRNDTL(H 1), 100) COVAL(T17,KE,GRND2,GRND2) COV AL(T17,EP,GRND2,GRND2) ** top 18 from west PATCH(T18,NWALL,36,37,38,38,1,1,1,100) COVAL(Tl 8,U1,1.0,0.0) COVAL(T18,H1,1./PRNDTL(H1),100) COVAL(T18,KE,GRND2,GRND2) COV AL(T18 ,EP,GRND2,GRND2) ** top 19 from west PATCH(T19,NWALL,38,39,37,37,1,1,1,100) COVAL(Tl 9,U1,1.0,0.0) CO VAL(T19,H 1,1 ./PRNDTL(H1), 100) COVAL(T19,KE,GRND2,GRND2) COVAL(Tl 9,EP,GRND2,GRND2) ** top20 from west PATCH(T20,NWALL,40,41,36,36,1,1,1,100) COVAL(T20,U1,1.0,0.0) COVAL(T20,H1,1./PRNDTL(H1),100) COVAL(T20,KE,GRND2,GRND2) COVAL(T20,EP,GRND2,GRND2) * * top21 from west PATCH(T21 W A L L ,42,43,35,35,1,1,1,100) COVAL(T21,U 1,1.0,0.0) COVAL(T21,H1,1./PRNDTL(H1),100) COVAL(T21 ,KE,GRND2,GRND2) CO VAL(T21 ,EP,GRND2,GRND2) ** top22 from west P ATCH(T22,NWALL,44,45,34,34,1,1,1,100) COVAL(T22,U1,1.0,0.0) COVAL(T22,Hl, l./PRNDTL(Hl), 100) COVAL(T22,KE,GRND2,GRND2) COVAL(T22,EP,GRND2,GRND2) ** top23 from west PATCH(T23,NWALL,46,47,33,33,1,1,1,100) C0VAL(T23,U1,1.0,0.0) COVAL(T23,H 1,1 ./PRNDTL(H1), 100) COVAL(T23,KE,GRND2,GRND2) COVAL(T23,EP,GRND2,GRND2) ** top24 from west PATCH(T24,NWALL,48,49,32,32,1,1,1,100) COV AL(T24,U 1,1.0,0.0) CO VAL(T24,H 1,1 ./PRNDTL(H1), 100) COVAL(T24,KE,GRND2,GRND2) COVAL(T24,EP,GRND2,GRND2) ** top25 from west PATCH(T25,NWALL,50,51,31,31,1,1,1,100) COV AL(T25,U 1,1.0,0.0) CO VAL(T25,H 1,1 ./PRNDTL(H 1), 100) COVAL(T25,KE,GRND2,GRND2) 128 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. COVAL(T25,EP,GRND2,GRND2) ** top26 from west PATCH(T26,NWALL,52,53,30,30,1,1,1,100) COV AL(T26,U 1,1.0,0.0) COVAL(T26,H 1,1 ./PRNDTL(Hl), 100) COVAL(T26,KE,GRND2,GRND2) COVAL(T26,EP,GRND2,GRND2) ** top27 from west PATCH(T27,NWALL,54,55,29,29,1,1,1,100) C0VAL(T27,U1,1.0,0.0) COVAL(T27,H 1,1 ./PRNDTL(Hl), 100) COVAL(T27,KE.GRND2,GRND2) COVAL(T27,EP,GRND2,GRND2) ** Buoyancy PATCH(BUO YANCY,PHASEM, 1,56,1,42,1,1,1,100) COVAL(BUOYANCY,Vl JTXFLU.-9.81) GROUP 15. Termination of sweeps LS WEEP= 1 ;RESREF(P1 )=1 .E-4;RESREF(H 1 )= 1 .E-5 GROUP 16. Termination of iterations ENDIT(Pl)=l.E-7;ENDIT(Hl)=l£-7;ENDIT(Ul)=l.E-7 ENDIT(Vl)=l.E-7 GROUP 17. Under-relaxation devices RELAX(U1 ,FALSDT, 1.0) ;REL AX(V1 ,FALSDT, 1.0) RELAX(H 1 .FALSDT, 1.0);RELAX(P1,FALSDT, 1.0) RELAX(KE,FALSDT, 1.0);RELAX(EP,FALSDT, 1.0) GROUP 20. Preliminary print-out ECHO=F GROUP 21. Print-out of variables OUTPUT(P 1 ,Y,Y,Y,Y,Y,Y);OUTPUT(U 1, Y, Y, Y, Y, Y, Y) OUTPUT(Vl,Y,Y,Y,Y,Y,Y);OUTPUT(Hl,Y,Y,Y,Y,Y,Y) GROUP 22. Spot-value print-out IXMON= 1 ;IYMON=9 GROUP 23. Field print-out and plot control NTPRIN=5 ;NXPRIN= 1 ;NYPRIN=1 PATCH(CONT,CONTUR, 1,10,1,10,1,1,1,1000) PLOT(CONT,Hl ,0.0,10.0) PATCH(IYEQ5,PROFIL, 1,10,5,5,1,1,1,1000) PLOT(IYEQ5, VI ,-0.1,0.1 );PLOT(IYEQ5,H 1,0.0,1.0) PATCH(IYEQ9,PROFIL, 1,1,9,9,1,1,1,100) PLOT(IYEQ9,Hl ,0.0,1.0) STOP Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UNVENTILATED MODEL WITH SYMMETRICAL BOUNDARY CONDITIONS 340: ****** TO LOAD CASE: TYPE LOAD04O)****** GROUP 1. Run title and other preliminaries TEXT(SYMMETRICAL TEMPERATURE PROFILES) GROUP 2. Transience; time-step specification GROUP 3. X-direction grid specification ** Set a symmetrical grid, consisting of power-law grids (varying as IX**2.0), which start from each edge and meet in the middle. GRDPWR(X,56,14,1.0) GROUP 4. Y-direction grid specification ** Set a symmetrical grid as in GROUP 3 NY=42;YVLAST=1.0 YFRAC( 1 )=-10.0; YFRAC(2)= 1.0 YFRAC(3)=1,0;YFRAC(4)=0.1 YFRAC(5)=4.0;YFRAC(6)=1.0 YFRAC(7)=1.0;YFRAC(8)=0.1 YFRAC(9)=4.0;YFRAC(10)=1.0 YFRAC( 11 )=1.0; YFRAC( 12)=0.1 YFRAC( 13)=7.0; YFRAC( 14)=1.0 YFRAC( 15)=14.0; YFRAC( 16)=0.25 GROUP 7. Variables stored, solved & named SOLVE(Pl,Ul,Vl,Hl) GROUP 8. Terms (in differential equations) & devices TERMS(H1,N,Y,Y,Y,Y,Y) GROUP 9. Properties of the medium (or media) ** Set the temperature as TMP1A+TMP1B*H1 ENUL= 1.45E-5 ;TMP1=GRND2;TMP1A=0.0;TMP1B=1.0 ** Set the density as RH01A+RH01B*Temperature RHO1=GRND4;RHO 1 A=1.293 ;RHO 1 B=-0.0044;PRNDTL(H 1 )= 1.0/1.3 GROUP 11. Initialization of variable or porosity fields RESTRT(ALL) FHNIT(P 1 )=READFI;FHNIT (U1 )=READFI FIINIT(V 1 )=READFI;FIINIT(H 1 )=READFI FIINIT(P 1 )=0.0;FIINIT(U 1 )=0.0;FIINIT(V 1 )=0.0;FIINIT(H 1 )=25.0 Porosity Fields CONPOR(0.0,CELL, 1,20,1,6,1,1) CONPOR(0.0,CELL,37,56,1,6,1,1) CONPOR(0.0,CELL, 1,9,11,11,1,1) CONPOR(O.O.CELL,48,56,11,11,1,1) CONPOR(0.0,CELL, 1,9,16,16,1,1) CONPOR(0.0,CELL,48,56,16,16,1,1) CONPOR(0.0,CELL,1,9,21,21,1,1) CONPOR(0.0,CELL,48,56,21,21,1,1) CONPOR(0.0,CELL, 1,1,29,42,1,1) CONPOR(0.0,CELL,2,3,30,42,1,1) CONPOR(O.O.CELL,4,5,31,42,1,1) CONPOR(0.0,CELL,6,7,32,42,1,1) CONPOR(0.0,CELL,8,9,33,42,1,1) CONPOR(0.0,CELL, 10,11,34,42,1,1) CONPOR(0.0,CELL,12,13,35,42,1,1) CONPOR(O.O.CELL,14,15,36,42,1,1) CONPOR(0.0,CELL, 16,17,37,42,1,1) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CONPOR(0.0,CELL, 18,19,38,42,1,1) CONPOR(0.0,CELL,20,21,39,42,1,1) CONPOR(0.0, CELL,22,23,40,42,1,1) CONPOR(O.O.CELL,24,25,41,42,1,1) CONPOR(0.0,CELL,26,27,42,42,1,1) CONPOR(0.0,CELL,30,31,42,42,1,1) C0NPOR(0.0, CELL,32,33,41,42,1,1) CONPOR(0.0,CELL,34,35,40,42,1,1) CONPOR(0.0, CELL,36,37,39,42,1,1) CONPOR(0.0,CELL,38,39,38,42,1,1) CONPOR(0.0,CELL,40,41,37,42,1,1) CONPOR(0.0,CELL,42,43,36,42,1,1) CONPOR(O.O.CELL,44,45,35,42,1,1) CONPOR(0.0,CELL,46,47,34,42,1,1) CONPOR(0.0,CELL,48,49,33,42,1,1) CONPOR(0.0,CELL,50,51,32,42,1,1) CONPOR(0.0,CELL,52,53,31,42,1,1) CONPOR(0.0,CELL,54,55,30,42,1,1) CONPOR(0.0,CELL,56,56,29,42,1,1) GROUP 13. Boundary conditions and special sources ** Pressure relief PATCH(REFP,CELL,5,5,5,5,1,1,1,100) ;CO VAL(REFP,P 1 ,FEXP,0.0) ** Set the heat flux to be the prevailing value of HI in the cell COVAL(REFP,H 1 ,FIXVAL,S AME) ** west walll PATCHCWEST1,WWALL,21,21,1,6,1,1,1,100) COVAL(WESTl, V1,1.0,0.0) COVAL(WESTl ,H1,1 VPRNDTL(H 1 ),24.4) CO VAL(WEST1 ,KE,GRND2,GRND2) COVAL(WESTl JEP,GRND2,GRND2) ** west wall2 PATCH(WEST2, WWALL, 1,1,7,10,1,1,1,100) COVAL(WEST2, V1,1.0,0.0) COV AL(WEST2,H1,17PRNDTL(H1),25.1) COVAL(WEST2,KE,GRND2,GRND2) COVAL(WEST2,EP,GRND2,GRND2) ** west wall3 PATCH(WEST3,WWALL,1,1,12,15,1,1,1,100) COVAL(WEST3, V1,1.0,0.0) COVAL(WEST3,Hl, 1 ./PRNDTL(H1),25.8) COVAL(WEST3,KE,GRND2,GRND2) COVAL(WEST3,EP,GRND2,GRND2) ** west wal!4 PATCH(WEST4, WWALL, 1,1,17,20,1,1,1,100) COVAL(WEST4, V1,1.0,0.0) COVAL(WEST4,Hl,17PRNDTL(Hl),27.3) COVAL(WEST4,KE,GRND2,GRND2) COVAL(WEST4,EP,GRND2,GRND2) ** west wa!15 PATCH(WEST5, WWALL,1,1,22,28,1,1,1,100) COV AL(WEST5, V1,1.0,0.0) COVAL(WEST5,Hl, 1 ./PRNDTL(H1),35.5) COVAL(WEST5,KE,GRND2,GRND2) COV AL(WEST 5 ,EP,GRND2,GRND2) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6dSt W 3 1 1 X PATCH(EAST1 ,EWALL,36,36,1,6,1,1,1,100) C0VAL(EAST1, VI, 1.0,0.0) C0VAL(EAST1 ,H1,1VPRNDTL(H1),24.4) C0VAL(EAST1,KE,GRND2,GRND2) CO VAL(EAST1 ,EP,GRND2,GRND2) ** east wa!12 P ATCH(EAST2,EWALL,56,56,7,10,1,1,1,100) COVAL(EAST2, VI, 1.0,0.0) COV AL(EAST2,H 1,17PRNDTL(H 1 ),25.1) COVAL(EAST2,KE,GRND2,GRND2) COVAL(EAST2,EP,GRND2,GRND2) ** east wall3 PATCH(EAST3,EWALL,56,56,12,15,1,1,1,100) CO VAL(EAST3, V1,1.0,0.0) C0VAL(EAST3,H1,17PRNDTL(H1),25.8) CO VAL(EAST3 ,KE,GRND2,GRND2) COVAL(EAST3,EP,GRND2,GRND2) ** east wall4 PATCH(EAST4,EWALL,56,56,17,20,1,1,1,100) COV AL(EAST4, V1,1.0,0.0) C0VAL(EAST4,H1,17PRNDTL(H1),27.3) COVAL(EAST4,KE,GRND2,GRND2) COVAL(EAST4,EP,GRND2,GRND2) ♦ ♦ C 3 st w e1 1 5 PATCH(EAST5,EWALL,56,56,22,28,1,1,1,100) C0VAL(EAST5,V1,1.0,0.0) C0VAL(EAST5,H1,17PRNDTL(H1),35.5) COVAL(EAST5,KE,GRND2,GRND2) COVAL(EAST5,EP,GRND2,GRND2) ** ground PATCH(B ASE 1 J.WALL,22,35,1,1,1,1,1,100) C0VAL(BASE1,H1,17PRNDTL(H 1 ),24.4) COVAL(B ASE 1 ,U1,1.0,0.0) CO VAL(B ASE 1 ,KE,GRND2,GRND2) C0VAL(BASE1,EP,GRND2,GRND2) PATCH(BASE2,LWALL,33,35,1,1,1,1,1,100) COVAL(B ASE2,H1,17PRNDTL(H1),24.4) COVAL(BASE2,KE,GRND2,GRND2) COVAL(BASE2,EP,GRND2,GRND2) ** west slabl PATCH(WSLB 1.NWALL,2,20,7,7,1,1,1,100) COV AL(WSLB 1,U1,1.0,0.0) COVAL(WSLB 1 ,H 1,17PRNDTL(H 1 ),25.1) COVAL(WSLB 1 ,KE,GRND2,GRND2) COVAL(WSLB 1 ,EP,GRND2,GRND2) ** west slab2 PATCH(WSLB 1,NWALL,2,9,10,10,1,1,1,100) COVAL(WSLB 1,U1,1.0,0.0) COV AL(WSLB 1 ,H 1,1 ./PRNDTL(H 1 ),25.1) COVAL(WSLB 1 ,KE,GRND2,GRND2) COVAL(WSLB 1 ,EP,GRND2,GRND2) ** west slab2A PATCH(WSLB 1 A, WWALL, 10,10,11,11,1,1,1,100) COVAL(WSLB 1 A,V 1,1.0,0.0) 132 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CO V AL( WSLB1 A,H 1,1 ,/PRNDTL(H 1) ,25.1) COVALCWSLB1 A,KE,GRND2,GRND2) COVALfWSLB 1 A£P,GRND2,GRND2) * * west slab2B PATCH(WSLB IB ,S WALL,2,9,12,12,1,1,1,100) CO VAL(WSLB 1B ,U1,1.0,0.0) C0VAL(WSLB1B,H1,17PRNDTL(H1),25.8) COVAL(WSLB 1B,KE,GRND2,GRND2) COVAL(WSLB 1BV EP,GRND2,GRND2) * * west slab3 PATCH(WSLB2,NWALL,2,9,15,15,1,1,1,100) COV AL(WSLB2,U 1,1.0,0.0) COVAL(WSLB2,Hl, 17PRNDTL(H1),25.8) COVAL(WSLB2,KE,GRND2,GRND2) COVAL(WSLB2,EP,GRND2,GRND2) * * west slab3A PATCH(WSLB2A, WWALL, 10,10,16,16,1,1,1,100) COVAL(WSLB2A,V 1,1.0,0.0) COVAL(WSLB2A,Hl ,17PRNDTL(H1),25.8) COVAL(WSLB2A,KE,GRND2,GRND2) COVAL(WSLB2A,EP,GRND2,GRND2) ** west slab3B PATCH(WSLB2B ,L WALL,2,9,17,17,1,1,1,100) COVAL(WSLB2B ,U1,1.0,0.0) COVAL(WSLB2B JHl,17PRNDTL(H1), 27.3) COVAL(WSLB2B,KE,GRND2,GRND2) COVAL(WSLB2B ,EP,GRND2,GRND2) ** west slab4 PATCH(WSLB3,NWALL,2,9,20,20,1,1,1,100) COVAL(WSLB3,Ul, 1.0,0.0) COVAL(WSLB3,Hl, 17PRNDTL(H1),27.3) COV AL(WSLB3,KE,GRND2,GRND2) COVAL(WSLB3,EP,GRND2,GRND2) west PATCH(WSLB3A,WWALL, 10,10,21,21,1,1,1,100) COVAL(WSLB3 A,VI, 1.0,0.0) COVAL(WSLB3A,Hl, 1 ,/PRNDTL(H 1 ),27.3 ) COV AL(WSLB3A,KE,GRND2,GRND2) COVAL(WSLB3A,EP,GRND2,GRND2) ** west slab4B PATCH(WSLB3BiWALL,2,9,22,22,l,l,l,100) COVAL(WSLB3B,Ul, 1.0,0.0) COVAL(WSLB3B ,H1,17PRNDTL(H1),35.5) COVAL(WSLB3B,KE,GRND2,GRND2) COVAL(WSLB3B,EP,GRND2,GRND2) ** east slabl PATCH(ESLB 1,NWALL,37,55,7,7,1,1,1,100) COVAL(ESLB 1 ,U 1,1.0,0.0) COVAL(ESLB 1,H1,1./PRNDTL(H1),25.1) COV AL(ESLB 1 ,BCE,GRND2,GRND2) COVAL(ESLB 1 JEP,GRND2,GRND2) ** east slab2 PATCH(ESLB2,NWALL,47,55,10,10,1,1,1,100) COVAL(ESLB2,U 1,1.0,0.0) COVAL(ESLB2,H 1,1 JPRNDTL(H1 ),25.1) 133 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. COVAL(ESLB2,KE,GRND2,GRND2) COVAL(ESLB2,EP,GRND2,GRND2) ** east slab2A PATCH(ESLB2AtEWALL,46,46,11,11,1,1,1,100) COVAL(ESLB2 A, V1,1.0,0.0) CO VAL(ESLB2A,H 1,1 VPRNDTL(H 1 ),25.1) COVAL(ESLB2A,KE,GRND2,GRND2) COVAL(ESLB2AJEP,GRND2,GRND2) PATCH(ESLB2B,LWALL,47,55,12,12,1,1,1,100) CO VALCESLB2B ,U1,1.0,0.0) COVAL(ESLB2B,Hl,lJPRNDTL(Hl),25.8) COVAL(ESLB2B,KE,GRND2,GRND2) COVAL(ESLB2B,EP,GRND2,GRND2) ♦♦ © 3st slab3 PATCH(ESLB3,NWALL,47,55,15,15,1,1,1,100) COVAL(ESLB3,Ul ,1.0,0.0) COVAL(ESLB3,Hl, 17PRNDTL(H1 ),25.8) CO V AL(ESLB 3 ,KE.GRND2,GRND2) COVAL(ESLB3,EP,GRND2,GRND2) * * east slab3A PATCH(ESLB3 A JEWALL,46,46,16,16,1,1,1,100) COVAL(ESLB3A,Vl, 1.0,0.0) C0VAL(ESLB3A,H1,17PRNDTL(H1),25.8) COVAL(ESLB3A,KE,GRND2,GRND2) COVAL(ESLB3A,EP,GRND2,GRND2) ** east sIab3B PATCH(ESLB3B,LWALL,47,55,17,17,1,1,1,100) COVAL(ESLB3B,U1,1.0,0.0) COVAL(ESLB3B,H 1,17PRNDTL(H 1 ),27.3) COVAL(ESLB3B,KE,GRND2,GRND2) COVAL(ESLB3B,EP,GRND2,GRND2) ** east slab4 PATCH(ESLB4,NWALL,47,55,20,20,1,1,1,100) CO VAL(ESLB4,U 1,1.0,0.0) CO VAL(ESLB4,H1,1 ./PRNDTL(H 1 ),27.3) COVAL(ESLB4,KE,GRND2,GRND2) COVAL(ESLB4,EP,GRND2,GRND2) ** east slab4A PATCH(ESLB4A,EWALL,46,46,21,21,1,1,1,100) COV AL(ESLB4 A, V1,1.0,0.0) COV AL(ESLB4A,H 1,17PRNDTL(H 1 ),27.3) COVAL(ESLB4A,KE,GRND2,GRND2) COVAL(ESLB4A,EP,GRND2,GRND2) ** east slab4B PATCH(ESLB4B,LWALL,47,55,22,22,1,1,1,100) CO VAL(ESLB4B,U 1,1.0,0.0) COVAL(ESLB4B ,H 1,1 VPRNDTL(H 1 ),35.5) COVAL(ESLB4B,KE,GRND2,GRND2) COVAL(ESLB4B,EP,GRND2,GRND2) ** topi from west PATCH(T1 ,NWALL,2,3,29,29,1,1,1,100) COVAL(T1,U1,1.0,0.0) CO V AL(T 1 ,H 1,17PRNDTL(H 1 ),48.9) C0VAL(T1,KE,GRND2,GRND2) 134 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C0VAL(T1 ,EP,GRND2,GRND2) ** top2 from west PATCH(T2,NWALL,4,5,30,30,1,1,1,100) COVAL(T2,Ul, 1.0,0.0) COVAL(T2,Hl, 17PRNDTL(H1),48.9) COVAL(T2,KE,GRND2,GRND2) COVAL(T2,EP,GRND2,GRND2) ** top3 from west PATCH(T3,NWALL,6,7,31,31,1,1,1,100) COV AL(T3 ,U 1,1.0,0.0) COVAL(T3,H 1,1 ./PRNDTL(H1),48.9) COVAL(T3,KE,GRND2,GRND2) COVAL(T3,EP,GRND2,GRND2) * * top4 from west PATGH(T4,NWALL,8,9,32,32,1,1,1,100) C0VAL(T4,U1,1.0,0.0) COV AL(T4,H 1,1 VPRNDTL(H 1 ),48.9) COVAL(T4,KE,GRND2,GRND2) COVAL(T4,EP,GRND2,GRND2) ** top5 from west PATCH(T5, NWALL, 10,11,33,33,1,1,1,100) COV AL(T5 ,U 1,1.0,0.0) COVAL(T5,H 1,17PRNDTL(H1 ),48.9) COVAL(T5,KE,GRND2,GRND2) COVAL(T5,EP,GRND2,GRND2) ** top6 from west PATCH(T6,NWALL, 12,13,34,34,1,1,1,100) COVAL(T6,U 1,1.0,0.0) C0VAL(T6,H1,17PRNDTL(H1),48.9) COVAL(T6,KE,GRND2,GRND2) COVAL(T6,EP,GRND2,GRND2) ** top7 from west PATCH(T7,NWALL, 14,15,35,35,1,1,1,100) COV AL(T7,U 1,1.0,0.0) CO VAL(T7,H 1,17PRNDTL(H 1 ),48.9) COVAL(T7,KE,GRND2,GRND2) COVAL(T7,EP,GRND2,GRND2) ** top8 from west PATCH(T8,NWALL, 16,17,36,36,1,1,1,100) COVAL(T8,U1,1.0,0.0) COV AL(T8 ,H 1,17PRNDTL(H 1 ),48.9) COVAL(T8,KE,GRND2,GRND2) COVAL(T8,EP,GRND2,GRND2) ** top9 from west PATCH(T9,NWALL, 18,19,37,37,1,1,1,100) COV AL(T9 ,U 1,1.0,0.0) C0VAL(T9,H1,17PRNDTL(H1),48.9) COVAL(T9,KE,GRND2,GRND2) COVAL(T9JEP,GRND2,GRND2) ** toplO from west PATCH(T10,NWALL,20,21,38,38,1,1,1,100) COVAL(T10,U1,1.0,0.0) COVAL(T10,H1,17PRNDTL(H1),48.9) COVAL(T10,KE,GRND2,GRND2) COVAL(T10,EP,GRND2,GRND2) 135 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ** top 11 from west PATCH(T11 ,NWALL,22,23,39,39,1,1,1,100) COVAL(Tl 1 ,U1,1.0,0.0) COVAL(Tl 1 ,H 1,17PRNDTL(H1),48.9) COVALCT11,KE,GRND2,GRND2) COVAL(Tl 1 ,EP,GRND2,GRND2) * * top 12 from west P ATCH(T12,NWALL,24,25,40,40,1,1,1,100) COVAL(T12,Ul, 1.0,0.0) COV AL(T 12,H 1,1 ./PRNDTL(H 1 ),48.9) COVAL(T12,KE,GRND2,GRND2) COVAL(T12,EP,GRND2,GRND2) ** topl3 from west PATCH(T13,NWALL,26,27,41,41,1,1,1,100) COVAL(Tl 3,U1,1.0,0.0) C0VAL(T13,H1,1./PRNDTL(H1),48.9) COVAL(T13,KE,GRND2,GRND2) COVAL(T13,EP,GRND2,GRND2) ** topl4 from west PATCH(T14,NWALL,28,29,42,42,1,1,1,100) COVAL(T14,Ul, 1.0,0.0) CO VAL(T14,H 1,1 ./PRNDTL(H 1 ),48.9) COVAL(T14,KE,GRND2,GRND2) C0VAL(T14,EP,GRND2,GRND2) * * toplS from west PATCH(T15,NWALL,30,31,41,41,1,1,1,100) COVAL(T15,U1,1.0,0.0) C0VAL(T15,H1,17PRNDTL(H1),48.9) C0VAL(T15,KE,GRND2,GRND2) C0VAL(T15,EP,GRND2,GRND2) ** topl6 from west PATCH(T16,NWALL,32,33,40,40,1,1,1,100) COVAL(T16,Ul, 1.0,0.0) C0VAL(T16,H1,1./PRNDTL(H1),48.9) COVAL(T16,KE,GRND2,GRND2) COVAL(T16JEP,GRND2,GRND2) ** topl7 from west PATCH(T17,NWALL,34,35,39,39,1,1,1,100) COVAL(T17,U1,1.0,0.0) COVAL(T17,Hl,lVPRNDTL(Hl),48.9) COVAL(T17,KE,GRND2,GRND2) COVAL(T173P,GRND2,GRND2) * * topl8 from west PATCH(T18,NWALL,36,37,38,38,1,1,1,100) COVAL(T18,U1,1.0,0.0) COVAL(Tl 8,H 1,17PRNDTL(H 1 ),48.9) COVAL(T18,KE,GRND2,GRND2) COVAL(T18^P,GRND2,GRND2) ** topl9 from west PATCH(T19,NWALL,38,39,37,37,1,1,1,100) COV AL(T19 ,U 1,1.0,0.0) CO VAL(T19,H1,1 ./PRNDTL(H 1 ),48.9) COVAL(T19,KE,GRND2,GRND2) COVAL(T19,EP,GRND2,GRND2) ** top20 from west 136 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PATCH(T20,NWALL,40,41,36,36,1,1,1.100) COVAL(T20,U1,1.0,0.0) CO VAL(T20,H 1,1 ./PRNDTL(H 1 ),48.9) COVAL(T20,KE,GRND2,GRND2) COVAL(T20,EP,GRND2,GRND2) ** top21 from west PATCH(T21, NWALL,42,43,35,35,1,1,1,100) COVAL(T21,Ul,l.0,0.0) CO VAL(T21 ,H 1,17PRNDTLCHI ),48.9) COVAL(T21 ,KE,GRND2,GRND2) COVAL(T21 ,EP,GRND2,GRND2) ** top22 from west PATCH(T22,NWALL,44,45,34,34,1,1,1,100) C0VAL(T22,U1,1.0,0.0) CO VAL(T22,H 1,17PRNDTL(H 1 ),48.9) COVAL(T22,KE,GRND2,GRND2) COVAL(T22JEP,GRND2,GRND2) ** top23 from west PATCH(T23,NWALL,46,47,33,33,1,1,1,100) CO VAL(T23,U1,1.0,0.0) COVAL(T23 ,H 1,17PRNDTL(H 1 ),48.9) COVAL(T23,KE,GRND2,GRND2) COVAL(T23JEP,GRND2,GRND2) ** top24 from west PATCH(T24,NWALL,48,49,32,32,1,1,1,100) C0VAL(T24,U1,1.0,0.0) COVAL(T24,H 1,1 ./PRNDTL(H 1 ),48.9) COVAL(T24,KE,GRND2,GRND2) COVAL(T24,EP,GRND2,GRND2) ** top25 from west PATCH(T25,NWALL,50,51,31,31,1,1,1,100) COVAL(T25,U1,1.0,0.0) COVAL(T25,H 1,1 ,/PRNDTL(H 1 ),48.9) COVAL(T25,KE,GRND2,GRND2) COVAL(T25£P,GRND2,GRND2) ** top26 from west PATCH(T26,NWALL,52,53,30,30,1,1,1,100) C0VAL(T26,U1,1.0,0.0) COVAL(T26,H 1,1 VPRNDTL(H 1 ),48.9) COVAL(T26,KE,GRND2,GRND2) COVAL(T26,EP,GRND2,GRND2) ** top27 from west PATCH(T27,NWALL,54,55,29,29,1,1,1,100) COVAL(T27,U 1,1.0,0.0) CO VAL(T27,H 1,1 VPRNDTL(H 1 ),48.9) COVAL(T27,KE,GRND2,GRND2) COVAL(T27JEP,GRND2,GRND2) ** Buoyancy PATCH(BUOYANCY,PHASEM, 1,56,1,42,1,1,1,100) COVAL(BUOYANCY,Vl ,FIXFLU,-9.81) GROUP 15. Tennination of sweeps LSWEEP=l;RESREF(Pl)=l.E-4;RESREF(Hl)=l.E-5 GROUP 16. Tennination of iterations ENDIT(P 1 )= 1 .E-7 ;ENDIT(H 1 )= 1 .E-7 ;ENDIT(U 1 )= 1 .E-7 ENDIT(Vl)=l.E-7 137 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. GROUP 17. Under-relaxation devices RELAX(U 1 ,FALSDT, 1.0) ;RELAX(V 1 ,FALSDT, 1.0) REL AX(H 1 .FALSDT, 1.0) GROUP 20. Preliminary print-out ECHO=F GROUP 21. Print-out of variables OUTPUT(P1,Y,Y,Y,Y,Y,Y);OUTPUT(U1,Y,Y,Y,Y,Y,Y) OUTPUT(Vl,Y,Y,Y,Y,Y,Y) ;OUTPUT(H 1 ,Y,Y,Y,Y,Y,Y) GROUP 22. Spot-value print-out IXMON=l;IYMON=9 GROUP 23. Field print-out and plot control NTPRIN=5 ;NXPRIN= 1 ;NYPRIN=1 PATCH(CONT,CONTUR, 1,10,1,10,1,1,1,1000) PLOT(CONT,H 1,0.0,10.0) PATGH(IYEQ5,PROFIL, 1,10,5,5,1,1,1,1000) PLOT(IYEQ5, V1 ,-0.1,0. l);PLOT(IYEQ5,H 1,0.0,1.0) PATCH(IYEQ9,PROFIL, 1,1,9,9,1,1,1,100) PLOT(IYEQ9,H 1,0.0,1.0) STOP Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UNVENTILATED MODEL WITH ASYMMETRICAL BOUNDARY CONDITIONS 276: ****** TO LOAD CASE: TYPE LOAD(275) modified!****** GROUP 1. Run title and other preliminaries TEXT(ASYMMETRICAL TEMPERATURE PROFILES) A stationary fluid in a cavity is suddenly exposed to walls of unequal temperature. Flow is generated by buoyancy forces acting unequally on hot and cold parts of the fluid. Interesting variants include changes to: the aspect ratio of the cavity; and to the temperature difference between the hot and cold walls. GROUP 2. Transience; time-step specification GROUP 3. X-direction grid specification ** Set a symmetrical grid, consisting of power-law grids (varying as IX**2.0), which start from each edge and meet in the middle. GRDPWR(X,56,14,1.0) GROUP 4. Y-direction grid specification ** Set a symmetrical grid as in GROUP 3 NY=42; YVL AST= 1.0 YFRAC( 1 )=-10.0; YFRAC(2)= 1.0 YFRAC(3 )=1.0; YFRAC(4)=0.1 YFRAC(5)=4.0; YFRAC(6)= 1.0 YFRAC(7)=1.0;YFRAC(8)=0.1 YFRAC(9)=4.0; YFRAC( 10)= 1.0 YFRAC(1 l)=l.0;YFRAC(12)=0.1 YFRAC(13)=7.0;YFRAC(14)=1.0 YFRAC(15)= 14.0; YFRAC(16)=0.25 GROUP 7. Variables stored, solved & named SOLVE(Pl,Ul,Vl,Hl) GROUP 8. Terms (in differential equations) & devices TERMS(H1,N,Y,Y,Y,Y,Y) GROUP 9. Properties of the medium (or media) ** Set the temperature as TMP1A+TMP1B*H1 ENUL= 1.45E-5 ;TMP 1=GRND2;TMP 1 A=0.0;TMP 1 B=1.0 ** Set the density as RH01A+RH01B*Temperature RHO1 =GRND4;RHO 1 A=1.293;RHO 1B=-0.0044;PRNDTL(H 1 )= 1.0/1.3 GROUP 11. Initialization of variable or porosity fields RESTRT(ALL) FIINIT(P 1 )=READFI;FIINIT(U 1 )=READFI FIINIT(V 1 )=READFI;FIINIT(H 1 )=READFI FIINIT(P1 )=0.0;FHNIT(U1 )=0.0;FIINIT(V1 )=0.0;FIINIT(H1 )=25.0 Porosity Fields CONPOR(0.0,CELL, 1,20,1,6,1,1) CONPOR(0.0,CELL,37,56,1,6,1,1) CONPOR(0.0,CELL, 1,9,11,11,1,1) CONPOR(O.O.CELL,48,56,11,11,1,1) CONPOR(0.0,CELL, 1,9,16,16,1,1) CONPOR(O.O.CELL,48,56,16,16,1,1) CONPOR(0.0,CELL, 1,9,21,21,1,1) CONPOR(0.0,CELL,48,56,21,21,1,1) CONPOR(0.0,CELL, 1,1,29,42,1,1) CONPOR(0.0,CELL,2,3,30,42,1,1) CONPOR(0.0,CELL,4,5,31,42,1,1) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CONPOR(0.0,CELL,6,7,32,42,1,1) CONPOR(0.0,CELL,8,9,33,42,1,1) CONPOR(0.0,CELL, 10,11,34,42,1,1) CONPOR(O.O.CELL, 12,13,35,42,1,1) CONPOR(O.O.CELL,14,15,36,42,1,1) CONPOR(O.O.CELL,16,17,37,42,1,1) CONPOR(0.0,CELL, 18,19,38,42,1,1) CONPOR(0.0,CELL,20,21,39,42,1,1) CONPOR(O.O.CELL,22,23,40,42,1,1) CONPOR(0.0,CELL,24,25,41,42,1,1) CONPOR(O.O.CELL,26,27,42,42,1,1) CONPOR(0.0,CELL,30,31,42,42,1,1) CONPOR(0.0,CELL,32,33,41,42,1,1) CONPOR(0.0,CELL,34,35,40,42,1,1) CONFOR(0.0,CELL,36,37,39,42,1,1) CONPOR(0.0,CELL,38,39,38,42,1,1) CONPOR(0.0,CELL,40,41,37,42,1,1) CONPOR(0.0,CELL,42,43,36,42,1,1) CONPOR(O.O.CELL,44,45,35,42,1,1) CONPOR(0.0,CELL,46,47,34,42,1,1) CONPOR(0.0,CELL,48,49,33,42,1,1) CONPOR(O.O.CELL,50,51,32,42,1,1) CONPOR(0.0,CELL,52,53,31,42,1,1) CONPOR(0.0,CELL,54,55,30,42,1,1) CONPOR(0.0,CELL,56,56,29,42,1,1) GROUP 13. Boundary conditions and special sources ** Pressure relief PATCH(REFP,CELL,5,5,5,5,1,1,1,100) ;COVAL(REFP,Pl ,FIXP,0.0) ** Set the heat flux to be the prevailing value of HI in the cell CO VAL(REFP,H 1 ,FIXVAL,S AME) ** west walll PATCH(WEST1,WWALL,21,21,1,6,1,1,1,100) CO VAL(WEST1, V 1,1.0,0.0) COVAL(WESTl ,H1,1 ./PRNDTL(H1),24.4) COVAL(WESTl ,KE,GRND2,GRND2) COVAL(WESTl ,EP,GRND2,GRND2) ** west wal!2 PATCH(WEST2,WWALL, 1,1,7,10,1,1,1,100) COVAL(WEST2, V1,1.0,0.0) COVAL(WEST2,Hl, 17PRNDTL(H1),25.1) COVAL(WEST2,KE,GRND2,GRND2) COVAL(WEST2JEP,GRND2,GRND2) * * west wall3 PATCH(WEST3, WWALL, 1,1,12,15,1,1,1,100) CO VAL(WEST3, V1,1.0,0.0) CO VAL(WEST3,H 1,1 VPRNDTL(H 1 ),25.8) CO V AL(WEST3 ,KE,GRND2,GRND2) COVAL(WEST3,EP,GRND2,GRND2) ** west wall4 PATCH(WEST4, WWALL, 1,1,17,20,1,1,1,100) COV AL(WEST4, V1,1.0,0.0) CO VAL(WEST4,H 1,1 ./PRNDTL(H 1 ),27.3) COVAL(WEST4,KE,GRND2,GRND2) COVAL(WEST4,EP,GRND2,GRND2) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ** west waII5 PATCH(WEST5, WWALL, 1.1,22,28,1,1,1,100) COVAL(WEST5,V 1,1.0,0.0) COVAL(WEST5,Hl,17PRNDTL(Hl),35.5) COVAL(WEST5,KE,GRND2,GRND2) COVAL(WEST5,EP,GRND2,GRND2) ** east walll PATCH(EAST1 ,EWALL,36,36,1,6,1,1,1,100) C0VAL(EAST1, V1,1.0,0.0) C0VAL(EAST1 ,H1,1 ./PRNDTL(H1),24.4) C0VAL(EAST1 ,KE,GRND2,GRND2) C0VAL(EAST1 JEP,GRND2,GRND2) ** east wall2 PATCH(EAST2,EWALL,56,56,7,10,1,1,1,100) COVAL(EAST2,V1,1.0,0.0) CO VAL(EAST2,H 1,17PRNDTL(H 1 ),25.5) CO V AL(E AST2,KE,GRND2,GRND2) COVAL(EAST2JEP,GRND2,GRND2) ** east wall3 PATCH(EAST3,EWALL,56,56,12,15,1,1,1,100) COV AL(EAST3, V1,1.0,0.0) CO VAL(EAST3,H 1,1 ./PRNDTL(H1),26.3) COVAL(EAST3,KE,GRND2,GRND2) COVAL(EAST3,EP,GRND2,GRND2) ** east wall4 PATCH(EAST4,EWALL,56,56,17,20,1,1,1,100) COVAL(EAST4, V1,1.0,0.0) CO VAL(EAST4,H 1,1 VPRNDTL(H1 ),28.4) COVAL(EAST4,KE,GRND2,GRND2) COVAL(EAST4JEP,GRND2,GRND2) ** east wall5 PATCH(EAST5,EWALL,56,56,22,28,1,1,1,100) COVAL(EAST5, V1,1.0,0.0) C0VAL(EAST5,H1,1./PRNDTL(H1),39.4) COVAL(EAST5,KE,GRND2,GRND2) COVAL(EAST5,EP,GRND2,GRND2) ** ground PATCH(B ASE1 ,LWALL,22,35,1,1,1,1,1,100) COVAL(B ASE1 ,H 1,1 ./PRNDTL(H 1 ),24.4) COVAL(B ASE1 ,U 1,1.0,0.0) COVAL(B ASE 1 ,KE,GRND2,GRND2) C0VAL(BASE1,EP,GRND2,GRND2) PATCH(BASE2JLWALL,33,35,1,1,1,1,1,100) C0VAL(BASE2,H1,1./PRNDTL(H1),24.4) COVAL(BASE2,KE,GRND2,GRND2) COVAL(BASE2JEP,GRND2,GRND2) ** west slabl PATCH(WSLB 1,NW ALL,2,20,7,7,1,1,1,100) COVAL(WSLB 1 ,U 1,1.0,0.0) COVAL(WSLB 1,H1,17PRNDTL(H1),25.1) COVAL(WSLB 1 ,KE,GRND2,GRND2) COVAL(WSLB 1 ,EP,GRND2,GRND2) * * west slab2 PATCH(WSLB 1 ,NWALL,2,9,10,10,1,1,1,100) COV AL(WSLB 1 ,U 1,1.0,0.0) 141 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. COVAL(WSLB 1 ,H1,1 ./PRNDTL(H1),25.1) CO VAL(WSLB 1 ,KE.GRND2,GRND2) COVAL(WSLB 1 LP,GRND2,GRND2) ** west slab2A PATCH(WSLB1A,WWALL,10,10,11,11,1,1,1,100) COVAL(WSLB I A,VI ,1.0,0.0) COVAL(WSLB 1 A,HI, 1 ./PRNDTL(H1),25.1) COVAL(WSLB 1A,KE,GRND2,GRND2) COVAL(WSLB 1A,EP,GRND2,GRND2) ** west slab2B PATCH(WSLB IB ,SWALL,2,9,12,12,1,1,1,100) COVAL(WSLB 1B,U1,1.0,0.0) COV AL(WSLB 1B ,H 1,17PRNDTL(H 1 ),25.8) COVAL(WSLB 1B,KE,GRND2,GRND2) COVALCW SLB 1BV EP,GRND2,GRND2) ** west slab3 PATCH(WSLB2,NWALL,2,9,15,15,1,1,1,100) COVAL(WSLB2,Ul, 1.0,0.0) COV AL(WSLB2,H 1,17PRNDTL(H1),25.8) COVAL(WSLB2,KE,GRND2,GRND2) COVAL(WSLB2,EP,GRND2,GRND2) west sldbSA PATCH(WSLB2A, WWALL, 10,10,16,16,1,1,1,100) COVAL(WSLB2A,Vl, 1.0,0.0) COVAL(WSLB2A,Hl, 17PRNDTL(H1 ),25.8) COVAL(WSLB2A,KE,GRND2,GRND2) COVAL(WSLB2A3P,GRND2,GRND2) ** west slab3B PATCH(WSLB2B XWALL,2,9,17,17,1,1,1,100) CO VAL(WSLB2B ,U1,1.0,0.0) COVAL(WSLB2B ,H 1,17PRNDTL(H 1 ),27.3) COVAL(WSLB2B,KE,GRND2,GRND2) COVAL(WSLB2B,EP,GRND2,GRND2) * * west slab4 PATCH(WSLB3,NWALL,2,9,20,20,1,1,1,100) COVAL(WSLB3,Ul, 1.0,0.0) COVAL(WSLB3,Hl, 1 ./PRNDTL(H1),27.3) COVAL(WSLB3,KE,GRND2,GRND2) COVAL(WSLB3,EP,GRND2,GRND2) west slflb4A PATCH(WSLB3 A, WWALL, 10,10,21,21,1,1,1,100) COVAL(WSLB3 A, V1,1.0,0.0) C0VAL(WSLB3A,H1,1./PRNDTL(H1),27.3) COVAL(WSLB3A,KE,GRND2,GRND2) COVAL(WSLB3A,EP,GRND2,GRND2) ** west slab4B PATCH(WSLB3B X WALL,2,9,22,22,1,1,1,100) COVAL(WSLB3B ,U1,1.0,0.0) COVAL(WSLB3B,Hl, 17PRNDTL(H1),35.5) COVAL(WSLB3B,KE,GRND2,GRND2) COVAL(WSLB3BJEP,GRND2,GRND2) ** east slabl PATCH(ESLB 1 ,NWALL,37,55,7,7,1,1,1,100) COVAL(ESLB 1 ,U1,1.0,0.0) CO V AL(ESLB 1 ,H 1,1 VPRNDTL(H 1 ),25.5) 142 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. COVAL(ESLB 1,KE,GRND2,GRND2) COVAL(ESLB l.EP,GRND2,GRND2) ** east slab2 PATCH(ESLB2,NWALL,47,55,10,10,1,1,1,100) C0VAL(ESLB2,U1,1.0,0.0) COV AL(ESLB2,H1,1 ./PRNDTL(H1 ),25.5) COVAL(ESLB2,KE,GRND2,GRND2) COVAL(ESLB2,EP,GRND2,GRND2) ** east slab2A PATCH(ESLB2A,EWALL,46,46,11,11,1,1,1,100) C0VAL(ESLB2A,V1,1.0,0.0) COVAL(ESLB2A,H 1,1 ./PRNDTL(H1 ),25.5) COVAL(ESLB2A,KE,GRND2,GRND2) COVAL(ESLB2A,EP,GRND2,GRND2) ** east slab2B PATCH(ESLB2B,LWALL,47,55,12,12,1,1,1,100) CO VAL(ESLB2B ,U1,1.0,0.0) C0VAL(ESLB2B,H1,17PRNDTL(H1),26.3) COVAL(ESLB2B,KE,GRJND2,GRND2) COVAL(ESLB2B3P,GRND2,GRND2) ** east slab3 PATCH(ESLB3,NWALL,47,55,15,15,1,1,1,100) COVAL(ESLB3,Ul, 1.0,0.0) COVAL(ESLB3,HI, 1 ./PRNDTL(H1 ),26.3) COVAL(ESLB3,KE,GRND2,GRND2) COVAL(ESLB3JEP,GRND2,GRND2) ** east slab3A PATCH(ESLB3 A JEWALL,46,46,16,16,1,1,1,100) COVAL(ESLB3 A, V1,1.0,0.0) COV AL(ESLB3 A,H 1,1 ,/PRNDTL(H 1 ),26.3) COVAL(ESLB 3A,KE,GRND2,GRND2) COVAL(ESLB3A,EP,GRND2,GRND2) ** east slab3B PATCH(ESLB3B,LWALL,47,55,17,17,1,1,1,100) COVAL(ESLB3B,U1,1.0,0.0) COVAL(ESLB3B,Hl, 1 VPRNDTL(H1),28.4) COVAL(ESLB3B,KE,GRND2,GRND2) COVAL(ESLB3B3P,GRND2,GRND2) * * east slab4 PATCH(ESLB4,NWALL,47,55,20,20,1,1,1,100) CO VAL(ESLB4,U1,1.0,0.0) COVAL(ESLB4,H 1,1 ./PRNDTL(H 1 ),28.4) COVAL(ESLB4,KE,GRND2,GRND2) COVAL(ESLB4,EP,GRND2,GRND2) * * east slab4A PATCH(ESLB4A,EWALL,46,46,21,21,1,1,1,100) COV AL(ESLB4A,V 1,1.0,0.0) COV AL(ESLB4A,H1,1./PRNDTL(H1),28.4) COVAL(ESLB4A,KE,GRND2,GRND2) COVAL(ESLB4AvEP,GRND2,GRND2) ** east slab4B PATCH(ESLB4B ,LWALL,47,55,22,22,1,1,1,100) CO VAL(ESLB4B ,U1,1.0,0.0) COV AL(ESLB4B ,H 1,1 ,/PRNDH.(H 1),39.4) COVAL(ESLB4B,KE,GRND2,GRND2) 143 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. COVAL(ESLB4B,EP,GRND2,GRND2) ** topi from west PATCH(T1 .NWALL,2,3,29,29,1,1,1,100) CO VAL(T1 ,U1,1.0,0.0) COVAL(Tl ,H1,17PRNDTL(H1),48.9) COVAL(Tl ,KE,GRND2,GRND2) COVAL(Tl 3P,GRND2,GRND2) ** top2 from west PATCH(T2,NWALL,4,5,30,30,1,1,1,100) CO VAL(T2,U 1,1.0,0.0) CO VAL(T2,H 1,1 VPRNDTL(H 1 ),48.9) COVAL(T2,KE,GRND2,GRND2) COVAL(T2,EP,GRND2,GRND2) ** top3 from west PATGH(T3,NWALL,6,7,31,31,1,1,1,100) COVAL(T3,U1,1.0,0.0) COVAL(T3,Hl,iyPRNDTL(Hl),48.9) COVAL(T3,KE,GRND2,GRND2) COVAL(T3,EP,GRND2,GRND2) ** top4 from west PATCH(T4,NWALL,8,9,32,32,1,1,1,100) COVAL(T4,U 1,1.0,0.0) COV AL(T4,H1,17PRNDTL(H1) ,48.9) COVAL(T4,KE,GRND2,GRND2) COVAL(T4,EP,GRND2,GRND2) ** top5 from west PATCH(T5,NWALL, 10,11,33,33,1,1,1,100) COV AL(T5,U 1,1.0,0.0) CO VAL(T5,H 1,17PRNDTL(H 1 ),48.9) COVAL(T5,KE,GRND2,GRND2) COVAL(T5,EP,GRND2,GRND2) ** top6 from west PATCH(T6,NWALL, 12,13,34,34,1,1,1,100) COVAL(T6,U 1,1.0,0.0) C0VAL(T6,H1,17PRNDTL(H1),48.9) COVAL(T6,KE,GRND2,GRND2) COVAL(T6^P,GRND2,GRND2) ** top7 from west PATCH(T7,NWALL, 14,15,35,35,1,1,1,100) COVAL(T7,U1,1.0,0.0) COVAL(T7JHl, l./PRNDTL(Hl),48.9) COV AL(T7 ,KE,GRND2,GRND2) COVAL(T7,EP,GRND2,GRND2) ** top8 from west PATCH(T8,NWALL, 16,17,36,36,1,1,1,100) COVAL(T8,Ul,l. 0,0.0) COVAL(T8,Hl, 17PRNDTL(H1),48.9) COVAL(T8,KE,GRND2,GRND2) COVAL(T8,EP,GRND2,GRND2) ** top9 from west PATCH(T9,NWALL, 18,19,37,37,1,1,1,100) COV AL(T9,U1,1.0,0.0) COVAL(T9,Hl, 1 ./PRNDTL(H1 ),48.9) COV AL(T9,KE,GRND2,GRND2) COVAL(T9,EP,GRND2,GRND2) 144 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ** toplO from west PATCH(T10, NWALL,20,21,38,38,1,1,1,100) COVAL(T10,U 1,1.0,0.0) COVAL(T10,H 1,1 ./PRNDTL(H 1 ),48.9) COVAL(T10,KE,GRND2,GRND2) COVAL(T10,EP,GRND2,GRND2) ** topll from west PATCH(T11,NWALL,22,23,39,39,1,1,1,100) COVAL(Tl 1 ,U1,1.0,0.0) COVAL(Tl 1 ,H 1,1 VPRNDTL(H 1 ),48.9) COVAL(Tl 1 ,KE,GRND2,GRND2) COVAL(Tl 1 ,EP,GRND2,GRND2) ** top 12 from west PATCH(T12,NWALL,24,25,40,40,1,1,1,100) COVAL(T12,Ul, 1.0,0.0) C0VAL(T12,H1,17PRNDTL(H1),48.9) COVAL(T12,KE,GRND2,GRND2) COVAL(Tl 2,EP,GRND2,GRND2) ** topl3 from west PATCH(T13,NWALL,26,27,41,41,1,1,1,100) COVAL(Tl 3,U1,1.0,0.0) COVAL(T13,H 1,1 ,/PRNDTL(H 1 ),48.9) COVAL(T13,KE,GRND2,GRND2) COVAL(T13,EP,GRND2,GRND2) ** topl4 from west PATCH(T14,NWALL,28,29,42,42,1,1,1,100) COVAL(T14,U 1,1.0,0.0) COVAL(T14,Hl, 1JPRNDTL(H1),48.9) COVAL(T14,KE,GRND2,GRND2) COVAL(T14,EP,GRND2,GRND2) ** topl5 from west PATCH(T15,NWALL,30,31,41,41,1,1,1,100) CO VAL(T15,U 1,1.0,0.0) COVAL(T15,Hl, 17PRNDTL(H1),48.9) COVAL(T15,KE,GRND2,GRND2) COVAL(T15,EP,GRND2,GRND2) * * topl6 from west PATCH(T16,NWALL,32,33,40,40,1,1,1,100) COVAL(Tl 6,U 1,1.0,0.0) COV AL(T16,H 1,1 VPRNDTL(H 1 ),48.9) COVAL(T16,KE,GRND2,GRND2) COVAL(T16,EP,GRND2,GRND2) ** topl7 from west PATCH(T17,NWALL,34,35,39,39,1,1,1,100) COVAL(T17,Ul, 1.0,0.0) CO VAL(T17,H 1,1 ./PRNDTL(H 1 ),48.9) COVAL(T17,KE,GRND2,GRND2) COVAL(T17,EP,GRND2,GRND2) ** topl8 from west PATCH(T18,NWALL,36,37,38,38,1,1,1,100) COVAL(Tl 8,U1,1.0,0.0) CO VAL(T 18,H 1,1 ./PRNDTL(H 1 ),48.9) COVAL(Tl 8,KE,GRND2,GRND2) COVAL(T18,EP,GRND2,GRND2) ** top!9 from west 145 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PATCH(T19,NWALL,38,39,37,37,1,1,1,100) CO VAL(T19,U 1,1.0,0.0) COVAL(T19,Hl,l 7PRNDTL(H1),48.9) COVAL(T19,KE,GRND2,GRND2) COVAL(T19,EP,GRND2,GRND2) ** top20 from west PATCH(T20,NWALL,40,41,36,36,1,1,1,100) COVAL(T20,U1,1.0,0.0) CO VAL(T20,H 1,1 ./PRNDTL(H 1 ),48.9) COVAL(T20,KE,GRND2,GRND2) COVAL(T203P,GRND2,GRND2) ** top21 from west PATCH(T21,NWALL,42,43,35,35,1,1,1,100) COVAL(T21,U1,1.0,0.0) CO VAL(T21 ,H 1,1VPRNDTL(H1 ),48.9) COVAL(T21 ,KE,GRND2,GRND2) COVAL(T21,EP,GRND2,GRND2) ** top22 from west P ATCH(T22,NWALL,44,45,34,34,1,1,1,100) CO VAL(T22,U 1,1.0,0.0) COVAL(T22,H 1,17PRNDTL(H 1 ),48.9) COVAL(T22,KE,GRND2,GRND2) COVAL(T22,EP,GRND2,GRND2) ** top23 from west PATCH(T23,NWALL,46,47,33,33,1,1,1,100) CO VAL(T23,U 1,1.0,0.0) CO VAL(T23,H 1,1 VPRNDTL(H1 ),48.9) COVAL(T23,KE,GRND2,GRND2) COVAL(T23,EP,GRND2,GRND2) ** top24 from west PATCH(T24,NWALL,48,49,32,32,1,1,1,100) CO VAL(T24,U 1,1.0,0.0) COV AL(T24,H 1,17PRNDTL(H 1 ),48.9) COVAL(T24,KE,GRND2,GRND2) COVAL(T24,EP,GRND2,GRND2) ** top25 from west PATCH(T25,NWALL,50,51,31,31,1,1,1,100) COVAL(T25,U1,1.0,0.0) COVAL(T25,Hl, 17PRNDTL(H1),48.9) COVAL(T25,KE,GRND2,GRND2) COVAL(T25JEP,GRND2,GRND2) ** top26 from west PATCH(T26,NWALL,52,53,30,30,1,1,1,100) CO VAL(T26,U 1,1.0,0.0) COVAL(T26,H 1,17PRNDTL(H1),48.9) COVAL(T26,BCE,GRND2,GRND2) COVAL(T26JEP,GRND2,GRND2) ** top27 from west PATCH(T27,NWALL,54,5S,29,29,1,1,1,100) COVAL(T27,U 1,1.0,0.0) COV AL(T27,H 1,1 ,/PRNDTL(H 1 ),48.9) COVAL(T27,KE,GRND2,GRND2) COVAL(T27,EP,GRND2,GRND2) * * Buoyancy PATCH(B UO YANC Y.PHASEM, 1,56,1,42,1,1,1,100) Reproduced with permission of the copyright owner. Further reproduction prohibited COVAL(BUOYANCY,V 1 ,FIXFLU,-9.81) GROUP 15. Termination of sweeps LS WEEP= 1 ;RESREF(P1 )= 1 .E-4;RESREF(H 1 )=1 £ - 5 GROUP 16. Termination of iterations ENDITCP1 )=1 .E-7;ENDIT(H 1 )= 1 .E-7 ;ENDIT(U 1 )= 1 .E-7 ENDIT(Vl)=l.E-7 GROUP 17. Under-relaxation devices RELAX(U1 .FALSDT, 1.0);RELAX(V1 .FALSDT, 1.0) RELAX(H 1 .FALSDT, 1.0) GROUP 20. Preliminary print-out ECHO=F GROUP 21. Print-out of variables OUTPUT(Pl,Y,Y,Y,Y,Y,Y);OUTPUT(Ul,Y,Y,Y,Y,Y,Y) OUTPUT(Vl,Y,Y,Y,Y,Y,Y);OUTPUT(Hl,Y,Y,Y,Y,Y,Y) GROUP 22. Spot-value print-out IXMON=l;IYMON=9 GROUP 23. Field print-out and plot control NTPRIN=5 ;NXPRIN= 1 ;NYPRIN=1 PATCH(CONT,CONTUR, 1,10,1,10,1,1,1,1000) PLOT(CONT,Hl,0.0,10.0) PATCH(IYEQ5,PROFIL, 1,10,5,5,1,1,1,1000) PLOT(IYEQ5,V 1 ,-0.1,0.1) ;PLOT(IYEQ5,Hl ,0.0,1.0) PATCH(IYEQ9,PROFIL, 1,1,9,9,1,1,1,100) PLOT(IYEQ9,Hl ,0.0,1.0) STOP Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. NATURALLY VENTILATED K-EPSILON MODEL WITH ASYMMETRICAL BOUNDARY CONDITIONS 275: ****** TO LOAD CASE: TYPE LOAD(277) ****** GROUP 1. Run title and other preliminaries TEXT(ASYMMETRICAL NAT. VENT. K E MODEL) REAL(UIN,UOUT,TIN,TKEIN,EPSIN) UIN=0.305;UOUT=-0.305;TIN=20.0 GROUP 2. Transience: time-step specification GROUP 3. X-direction grid specification ** Set a symmetrical grid, consisting of power-law grids (varying as IX**2.0), which start from each edge and meet in the middle. GRDPWR(X,56,14,1.0) GROUP 4. Y-direction grid specification ** Set a symmetrical grid as in GROUP 3 NY=42;YVLAST=1.0 YFRAC( 1 )=-10.0; YFRAC(2)= 1.0 YFRAC(3)=1.0;YFRAC(4)=0.1 YFRAC(5)=4.0;YFRAC(6)=1.0 YFRAC(7)= 1.0; YFRAC(8)=0.1 YFRAC(9)=4.0; YFRAC( 10)=1.0 YFRAC(11)=1.0;YFRAC(12)=0.1 YFRAC(13)=7.0;YFRAC(14)=1.0 YFRAC(15)=14.0;YFRAC(16)=0.25 GROUP 7. Variables stored, solved & named SOLVE(Pl,Ul,Vl,Hl) TURMOD(KEMODL) GROUP 8. Terms (in differential equations) & devices TERMS(H1,N,Y,Y,Y,Y,Y) GROUP 9. Properties of the medium (or media) ** Set the temperature as TMP1A+TMP1B*H1 ENUL= 1.45E-5 ;TMP 1 =GRND2;TMP1A=0.0 ;TMP 1 B=1.0 ** Set the density as RH01A+RHOlB*Temperature RH01=GRND4;RH01A=1.293;RH01B=-0.0044;PRNDTL(H1)=1.0/1.3 GROUP 11. Initialization of variable or porosity fields TKEIN=0.25 *UIN ;TKEIN=TKEIN*UIN ;TKEIN=TKEIN*0.018 EPSIN=TKEIN**1.5;EPSIN=EPSIN*0.1643;EPSIN=EPSIN/3.429E-3 RESTRT(ALL) FIINIT(P 1 )=READFI;FnNIT(U 1 )=READFI FIINIT(V 1 )=READFI;FUNIT(H 1 )=READFI FIINIT(EP)=EPSIN;FIINIT(KE)=TKEIN FnNIT(P 1 )=0.0;FnNIT(Ul )=0.0;FnNIT(Vl )=0.0;FIINIT(H1 )=25.0 FIINIT(EP)=READFI;FIINIT(BCE)=READFI Porosity Fields CONPOR(0.0,CELL, 1,20,1,6,1,1) CONPOR(O.O.CELL,37,56,1,6,1,1) CONPOR(0.0,CELL, 1,9,11,11,1,1) CONPOR(0.0,CELL,48,56,11,11,1,1) CONPOR(0.0,CELL, 1,9,16,16,1,1) CONPOR(0.0,CELL,48,56,16,16,1,1) CONPOR(0.0,CELL,1,9,21,21,1,1) CONPOR(0.0,CELL,48,56,21,21,1,1) CONPOR(0.0,CELL, 1,1,29,42,1,1) CONPOR(0.0,CELL,2,3,30,42,1,1) 148 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CONPOR(0.0,CELL,4,5,31,42,1,1) CONPOR(0.0,CELL,6,7,32,42,1,1) CONPOR(0.0,CELL,8,9,33,42,1,1) CONPOR(0.0,CELL, 10,11,34,42,1,1) CONPOR(0.0,CELL, 12,13,35,42,1,1) CONPOR(0.0,CELL, 14,15,36,42,1,1) CONPOR(O.O.CELL, 16,17,37,42,1,1) CONPOR(0.0,CELL, 18,19,38,42,1,1) CONPOR(0.0,CELL,20,21,39,42,1,1) CONPOR(0.0,CELL,22,23,40,42,1,1) CONPOR(0.0,CELL,24,25,41,42,1,1) CONPOR(0.0,CELL,26,27,42,42,1,1) CONPOR(0.0, CELL,30,31,42,42,1,1) CONPOR(0.0,CELL,32,33,41,42,1,1) CONPOR(0.0,CELL,34,35,40,42,1,1) CONPOR(O.O.CELL,36,37,39,42,1,1) CONPOR(0.0,CELL,38,39,38,42,1,1) CONPOR(0.0,CELL,40,41,37,42,1,1) CONPOR(0.0,CELL,42,43,36,42,1,1) CONPOR(0.0,CELL,44,45,35,42,1,1) CONPOR(0.0,CELL,46,47,34,42,1,1) CONPOR(0.0,CELL,48,49,33,42,1,1) CONPOR(0.0,CELL,50,51,32,42,1,1) CONPOR(0.0,CELL,52,53,31,42,1,1) CONPOR(O.O.CELL,54,55,30,42,1,1) CONPOR(0.0,CELL,56,56,29,42,1,1) GROUP 13. Boundary conditions and special sources ** Pressure relief PATCH(REFP,CELL,5,5,5,5,1,1,1,100);COVAL(REFP,Pl ,FIXP,0.0) ** Set the heat flux to be the prevailing value of HI in the cell COVAL(REFP,Hl ,FIXVAL,SAME) PATCH(INLET,CELL,25,32,1,1,1,1,1,100) CO VAL(INLET,P 1 ,FIXFLU,UIN) COV AL(INLET,H 1 .ONLYMS ,TIN) CO VAL(INLET, V1 .ONLYMS ,0.102) COVAL(INLET,KE,ONLYMS,TKEIN) COVAL(INLET,EP,ONLYMS,EPSIN) * * Outlet PATCH(OUTLETl,CELL,1,1,28,28,1,1,1,100) COVAL(OUTLETl,Pl,FIXFLU,UOUT) COVAL(OUTLETl ,H1,ONLYMS,SAME) P ATCH(OUTLET2,CELL,56,56,28,28,1,1,1,100) COVAL(OUTLET2,Pl,FIXFLU,UOUT) COVAL(OUTLET2,Hl,ONLYMS,SAME) ** west walll PATCH(WEST1 .WWALL,21,21,1,6,1,1,1,100) COVAL(WESTl ,V 1,1.0,0.0) CO VAL(WEST1 ,H 1,1 ,/PRNDTL(H 1 ),24.4) CO VAL(WEST1 ,KE,GRND2,GRND2) CO VAL(WEST1 ,EP,GRND2,GRND2) ** west wal!2 PATCH(WEST2, WWALL, 1,1,7,10,1,1,1,100) COVAL(WEST2, V1,1.0,0.0) COVAL(WEST2,H 1,1 ./PRNDTL(H1),25.1) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. COVAL(WEST2,KE,GRND2,GRND2) COVAL(WEST2,EP,GRND2,GRND2) ** west wall3 PATCH(WEST3, WWALL, 1,1,12,15,1,1,1,100) COVAL(WEST3, V1,1.0,0.0) COVALCWEST3 ,H1,17PRNDTL(H1),25.8) COVAL(WEST3,KE,GRND2,GRND2) COVAL(WEST3,EP,GRND2,GRND2) ** west wa!14 PATCH(WEST4, WWALL, 1,1,17,20,1,1,1,100) CO VAL(WEST4,V 1,1.0,0.0) COVAL(WEST4,Hl, 17PRNDTL(H1),27.3) COVAL(WEST4,KE,GRND2,GRND2) COVAL(WEST4,EP,GRND2,GRND2) ** west wa!15 PATCH(WEST5,WWALL,1,1,22,27,1,1,1,100) COVAL(WEST5,Vl, 1.0,0.0) CO VAL(WEST5,H 1,1 VPRNDTL(H 1 ),35.5) COVAL(WEST5,KE,GRND2,GRND2) COVAL(WEST5,EP,GRND2,GRND2) ** east walll P ATCH(EAST 1 ,EWALL,36,36,1,6,1,1,1,100) COVAL(EASTl, V1,1.0,0.0) CO VAL(EAST1 ,H1,1 ./PRNDTL(H1),24.4) COVAL(EASTl ,KE,GRND2,GRND2) COVAL(EASTl ,EP,GRND2,GRND2) ** east w a!12 PATCH(EAST2,EWALL,56,56,7,10,1,1,1,100) COVAL(EAST2, V1,1.0,0.0) CO VAL(EAST2,H 1,1 ./PRNDTL(H1),25.5) COVAL(EAST2,KE,GRND2,GRND2) COVAL(EAST2,EP,GRND2,GRND2) ** east wall3 PATCH(EAST3,EWALL,56,56,12,15,1,1,1,100) CO VAL(EAST3, V1,1.0,0.0) COVAL(EAST3,H 1,1 ./PRNDTL(H1),26.3) COVAL(EAST3,KE,GRND2,GRND2) COVAL(EAST3,EP,GRND2,GRND2) ** east wall4 PATCH(EAST4,EWALL,56,56,17,20,1,1,1,100) COVAL(EAST4, V1,1.0,0.0) COVAL(EAST4,H 1,1VPRNDTL(H1),28.4) COVAL(EAST4,KE,GRND2,GRND2) COVAL(EAST4,EP,GRND2,GRND2) ** east wallS PATCH(EAST5,EWALL,56,56,22,27,1,1,1,100) COVAL(EAST5,V 1,1.0,0.0) CO VAL(EAST5,H1,1 ./PRNDTL(H1),39.4) COVAL(EAST5 ,KE,GRND2,GRND2) COVAL(EAST5,EP,GRND2,GRND2) ** ground PATCH(B ASE 10-WALL,22,24,1,1,1,1,1,100) CO VAL(B ASE 1 ,H 1,1 ,/PRNDTL(H 1 ),24.4) COVAL(B ASE1 ,KE,GRND2,GRND2) COVAL(B ASE1 ,EP,GRND2,GRND2) 150 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PATCH(BASE2XWALL,33,35,1,1,1,1,1,100) COV AL(B ASE2,H1,1 ./PRNDTL(H1),24.4) COVAL(BASE2,KE,GRND2,GRND2) COVAL(BASE2,EP,GRND2,GRND2) ** west slabl PATCH(WSLB 1 JSTWALL,2,20,7,7,1,1,1,100) COVAL(WSLB 1 ,U 1,1.0,0.0) COV AL(WSLB 1 ,H 1,17PRNDTL(H1 ),25.1) CO VAL(WSLB 1 ,KE,GRND2,GRND2) COVALCWSLB1 ,EP,GRND2,GRND2) ** west slab2 PATCHCWSLB1, NWALL, 2,9,10,10,1,1,1,100) CO VAL(WSLB 1 ,U 1,1.0,0.0) COV AL(WSLB1,H1,1./PRNDTL(H1),25.1) COVAL(WSLB 1,KE,GRND2,GRND2) COVALCW SLB 1 ,EP,GRND2,GRND2) ** west slab2A PATCH(WSLB 1 A, WWALL, 10,10,11,11,1,1,1,100) COVAL(WSLB 1 A, V1,1.0,0.0) COVALCWSLB 1A,H 1,1 VPRNDTL(H 1), 25.1) COVALCW SLB 1 A,KE,GRND2,GRND2) COVALCWSLB 1 A,EP,GRND2,GRND2) ** west slab2B PATCHCW SLB IB,SWALL,2,9,12,12,1,1,1,100) COVALCWSLB 1B ,U1,1.0,0.0) COVALCWSLB IB JI1,1 ./PRNDTLCH1),25.8) COVALCW SLB IB ,KE,GRND2,GRND2) COVALCW SLB 1B,EP,GRND2,GRND2) ** west slab3 PATCHCWSLB2,NWALL,2,9,15,15,1,1,1,100) COVALCWSLB 2,U 1,1.0,0.0) COVALCWSLB2.H 1,1 ./PRNDTLCH1 ),25.8) COVALCWSLB2,KE,GRND2,GRND2) COVAL(WSLB2,EP,GRND2,GRND2) ** west slab3A PATCHCWSLB2A,WWALL, 10,10,16,16,1,1,1,100) COVALCWSLB2A, V1,1.0,0.0) COVALCWSLB2A.H 1,1 ./PRNDTLCH1 ),25.8) COVALCWSLB2A,KE,GRND2,GRND2) COVALCWSLB2A,EP,GRND2,GRND2) ** west slab3B PATCHCWSLB2B J-WALL,2,9,17,17,1,1,1,100) COVALCWSLB2B.U1,1.0,0.0) C0VAL(WSLB2B,H1,17PRNDTL(H1),27.3) COVALCWSLB2B,KE,GRND2,GRND2) COVALCWSLB2B£P,GRND2,GRND2) ** west slab4 PATCHCW SLB 3,NWALL,2,9,20,20,1,1,1,100) COVALCWSLB 3,U 1,1.0,0.0) CO VALCWSLB3.H 1,1 ./PRNDTLCH1 ),27.3) COVALCWSLB3,KE,GRND2,GRND2) COVALCWSLB3,EP,GRND2,GRND2) ** west slab4A PATCHCW SLB 3 A, WWALL, 10,10,21,21,1,1,1,100) COVALCWSLB 3A, V 1,1.0,0.0) 151 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. COVAL(WSLB3A,Hl, 1 ./PRNDTL(H1),27.3) COVAL(WSLB3A,KE,GRND2,GRND2) COVAL(WSLB3A,EP,GRND2,GRND2) ** west slab4B PATCH(WSLB 3B ,LWALL,2,9,22,22,1,1,1,100) C0VAL(WSLB3B,U1,1.0,0.0) COVAL(WSLB3B ,H 1,17PRNDTL(H 1 ),35.5) COVAL(WSLB3B,KE,GRND2,GRND2) COVAL(WSLB3B,EP,GRND2,GRND2) ** east slabl PATCH(ESLB 1,NWALL,37,55,7,7,1,1,1,100) COVAL(ESLB 1 ,U1,1.0,0.0) C0VAL(ESLB1,H1,17PRNDTL(H1),25.5) COVAL(ESLB 1,KE,GRND2,GRND2) CO VAL(ESLB 1 ,EP,GRND2,GRND2) ♦♦ cdst sldb2 PATCH(ESLB2, NWALL,47,55,10,10,1,1,1,100) COVAL(ESLB2,U 1,1.0,0.0) COVAL(ESLB2,H 1,1 ./PRNDTL(H1),25.5) COVAL(ESLB2,KE,GRND2,GRND2) COV AL(ESLB2,EP ,GRND2,GRND2) ** east slab2A PATCH(ESLB2A,EWALL,46,46,11,11,1,1,1,100) COVAL(ESLB2A, V1,1.0,0.0) COVAL(ESLB2A,H 1,17PRNDTL(H 1 ),25.5) COVAL(ESLB2A,KE,GRND2,GRND2) COVAL(ESLB2A^P,GRND2,GRND2) ** east slab2B PATCH(ESLB2B ,LWALL,47,55,12,12,1,1,1,100) CO VAL(ESLB2B ,U1,1.0,0.0) C0VAL(ESLB2B,H1,17PRNDTL(H1),26.3) COVAL(ESLB2B ,KE,GRND2,GRND2) COVAL(ESLB2B,EP,GRND2,GRND2) ♦♦ c3St slab3 PATCH(ESLB 3,NWALL,47,55,15,15,1,1,1,100) COVAL(ESLB3,Ul, 1.0,0.0) COVAL(ESLB3 ,H 1,1 VPRNDTL(H 1 ),26.3) COVAL(ESLB3,KE,GRND2,GRND2) COVAL(ESLB3,EP,GRND2,GRND2) ** east slab3A PATCH(ESLB3A,EWALL,46,46,16,16,1,1,1,100) C0VAL(ESLB3A,V1,1.0,0.0) C0VAL(ESLB3A,H1,17PRNDTL(H 1 ),26.3) COVAL(ESLB3A,KE,GRND2,GRND2) COVAL(ESLB3A,EP,GRND2,GRND2) ** east slab3B PATCH(ESLB3B,LWALL,47,55,17,17,1,1,1,100) COVAL(ESLB3B ,U1,1.0,0.0) C0VAL(ESLB3B,H1,17PRNDTL(H1),28.4) COVAL(ESLB3B ,KE,GRND2,GRND2) COVAL(ESLB3B£P,GRND2,GRND2) ♦♦ slab4 PATCH(ESLB4,NWALL,47,55,20,20,1,1,1,100) C0VAL(ESLB4,U1,1.0,0.0) COVAL(ESLB4,H 1,1 ,/PRNDTL(Hl),28.4) 152 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. COVAL(ESLB4,KE,GRND2,GRND2) COVAL(ESLB4,EP,GRND2,GRND2) ** east slab4A PATCH(ESLB4A,EWALL,46,46,21,21,1,1,1,100) CO VAL(ESLB4A, V1,1.0,0.0) COV AL(ESLB4A.H1,1./PRNDTL(H1),28.4) COVAL(ESLB4A,KE,GRND2,GRND2) COVAL(ESLB4A,EP,GRND2,GRND2) ** east slab4B PATCH(ESLB4B,LWALL,47,55,22,22,1,1,1,100) COVAL(ESLB4B,U1,1.0,0.0) COVAL(ESLB4B ,H 1,17PRNDTL(H 1 ),39.4) COVAL(ESLB4B ,KE,GRND2,GRND2) COVAL(ESLB4B,EP,GRND2,GRND2) ** topi from west PATCH(T 1,NWALL,2,3,29,29,1,1,1,100) COV AL(T1 ,U 1,1.0,0.0) CO VAL(T1 ,H 1,17PRNDTL(H 1 ),48.9) C0VAL(T1,KE,GRND2,GRND2) COVAL(Tl,EP,GRND2,GRND2) ** top2 from west PATCH(T2,NWALL,4,5,30,30,1,1,1,100) COVAL(T2,U 1,1.0,0.0) COVAL(T2,H 1,1 ./PRNDTL(H1 ),48.9) COVAL(T2,KE,GRND2,GRND2) COVAL(T2,EP,GRND2,GRND2) ** top3 from west PATCH(T3 .NWALL,6,7,31,31,1,1,1,100) COVAL(T3,Ul, 1.0,0.0) COVAL(T3,Hl, 17PRNDTL(H1),48.9) COVAL(T3,KE,GRND2,GRND2) COVAL(T3,EP,GRND2,GRND2) ** top4 from west PATCH(T4,NWALL,8,9,32,32,1,1,1,100) COVAL(T4,Ul, 1.0,0.0) CO VAL(T4,H 1,1 ./PRNDTL(H1 ),48.9) COVAL(T4,KE,GRND2,GRND2) COVAL(T4,EP,GRND2,GRND2) ** top5 from west PATCH(T5,NWALL, 10,11,33,33,1,1,1,100) COVAL(T5,U1,1.0,0.0) CO VAL(T5,H 1,17PRNDTL(H 1 ),48.9) COVAL(T5,KE,GRND2,GRND2) COV AL(T5,EP,GRND2,GRND2) ** top6 from west PATCH(T6, NWALL, 12,13,34,34,1,1,1,100) COVAL(T6,U1,1.0,0.0) COVAL(T6,Hl, 1 ./PRNDTL(H1),48.9) COVAL(T6,KE,GRND2,GRND2) COV AL(T6,EP,GRND2,GRND2) ** top7 from west PATCH(T7,NWALL, 14,15,35,35,1,1,1,100) COVAL(T7,U 1,1.0,0.0) COVAL(T7,H 1,17PRNDTL(H 1 ),48.9) COVAL(T7,KE,GRND2,GRND2) 153 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. COV AL(T7,EP,GRND2,GRND2) ** top8 from west PATCH(T8,NWALL, 16,17,36,36,1,1,1,100) COV AL(T8 ,U 1,1.0,0.0) COV AL(T8,H 1,1 VPRNDTL(H 1 ),48.9) COVAL(T8,KE,GRND2,GRND2) COV AL(T8 ,EP,GRND2,GRND2) ** top9 from west PATCH(T9,NWALL, 18,19,37,37,1,1,1,100) COVAL(T9,U1,1.0,0.0) C0VAL(T9,H1,1VPRNDTL(H1),48.9) COVAL(T9,KE,GRND2,GRND2) COVAL(T9,EP,GRND2,GRND2) ** toplO from west PATGH(T10,NWALL,20,21,38,38,1,1,1,100) COVAL(T10,U1,1.0,0.0) COV AL(T10,H1,1./PRNDTL(H1),48.9) COVAL(T10,KE,GRND2,GRND2) COVAL(T10,EP,GRND2,GRND2) ** topll from west PATCH(T11,NWALL,22,23,39,39,1,1,1,100) COVAL(Tl 1,171.1.0,0.0) C0VAL(T11,H1,1./PRNDTL(H1),48.9) COVAL(Tl 1 ,KE,GRND2,GRND2) COVAL(Tl 1,EP,GRND2,GRND2) ** top 12 from west PATCH(T12,NWALL,24,25,40,40,1,1,1,100) COVAL(T12,U1,1.0,0.0) C0VAL(T12,H1,1./PRNDTL(H1),48.9) COVAL(T12,KE,GRND2,GRND2) COVAL(T12,EP,GRND2,GRND2) ** topl3 from west PATCH(T13 ,NWALL,26,27,41,41,1,1,1,100) COVAL(T13,U 1,1.0,0.0) C0VAL(T13,H1,17PRNDTL(H1),48.9) COVAL(T13,KE,GRND2,GRND2) COVAL(T13,EP,GRND2,GRND2) * * top 14 from west PATCH(T14JMWALL,28,29,42,42,1,1,1,100) COVAL(T14,U1,1.0,0.0) COVAL(T14,Hl,lJPRNDTL(Hl),48.9) COVAL(T14,KE,GRND2,GRND2) COVAL(T14,EP,GRND2,GRND2) ** toplS from west PATCH(T15,NWALL,30,31,41,41,1,1,1,100) COVAL(T15,U1,1.0,0.0) COV AL(T15,H1,1VPRNDTL(H1),48.9) COVAL(T 15,KE,GRND2,GRND2) COVAL(T15,EP,GRND2,GRND2) ** topl6 from west PATCH(T16,NWALL.32,33,40,40,1,1,1,100) COVAL(T16,U1,1.0,0.0) COVAL(Tl 6,H 1,17PRNDTL(H 1 ),48.9) COV AL(T16,KE,GRND2,GRND2) COVAL(T16,EP,GRND2,GRND2) 154 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ** top 17 from west PATCH(T17,NWALL,34,35,39,39,1,1,1,100) CO VAL(T17,U 1,1.0,0.0) COVAL(T17,Hl, 1VPRNDTL(H1),48.9) COVAL(T17,KE,GRND2,GRND2) COVAL(T17,EP,GRND2,GRND2) ** top 18 from west PATCH(T18,NWALL,36,37,38,38,1,1,1,100) COVAL(Tl 8,U1,1.0,0.0) C0VAL(T18,H1,17PRNDTL(H1),48.9) COVAL(Tl 8 ,KE,GRND2,GRND2) COV AL(T 18 ,EP,GRND2,GRND2) ** topl9 from west PATCH(T19,NWALL,38,39,37,37,1,1,1,100) COVAL(T19,U1,1.0,0.0) C0VAL(T19,H1,17PRNDTL(H1),48.9) COVAL(T19,KE,GRND2,GRND2) CO VAL(T19,EP,GRND2,GRND2) ** top20 from west PATCH(T20,NWALL,40,41,36,36,1,1,1,100) CO VAL(T20,U 1,1.0,0.0) CO VAL(T20,H 1,17PRNDTL(H 1 ),48.9) COVAL(T20,KE,GRND2,GRND2) COVAL(T20,EP,GRND2,GRND2) ** top21 from west PATCH(T21,NWALL,42,43,35,35,1,1,1,100) CO VAL(T21 ,U1,1.0,0.0) COVAL(T21,H 1,1VPRNDTL(H1),48.9) COVAL(T21,KE,GRND2,GRND2) CO VAL(T21,EP,GRND2,GRND2) ** top22 from west PATCH(T22,NWALL,44,45,34,34,1,1,1,100) COV AL(T22,U1,1.0,0.0) CO VAL(T22,H 1,17PRNDTL(H 1 ),48.9) COVAL(T22,KE,GRND2,GRND2) COVAL(T22,EP,GRND2,GRND2) ** top23 from west PATCH(T23,NWALL,46,47,33,33,1,1,1,100) C0VAL(T23,U1,1.0,0.0) COV AL(T23 ,H 1,17PRNDTL(H1 ),48.9) COVAL(T23,KE,GRND2,GRND2) COVAL(T23,EP,GRND2,GRND2) ** top24 from west PATCH(T24,NWALL,48,49,32,32,1,1,1,100) COVAL(T24,U 1,1.0,0.0) COVAL(T24,H 1,1 ./PRNDTL(H 1 ),48.9) COVAL(T24,KE,GRND2,GRND2) COVAL(T24,EP,GRND2,GRND2) ** top25 from west PATCH(T25,NWALL,50,51,31,31,1,1,1,100) COV AL(T25,U 1,1.0,0.0) C0VAL(T25,H1,1./PRNDTL(H1),48.9) COVAL(T25,KE,GRND2,GRND2) COV AL(T25 ,EP,GRND2,GRND2) ** top26 from west 155 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PATCH(T26,NWALL,52,53,30,30,1,1,1,100) COVAL(T26,U 1,1.0,0.0) CO VAL(T26,H 1,1 ./PRNDTL(H 1 ),48.9) COVAL(T26,KE,GRND2,GRND2) COVAL(T26,EP,GRND2,GRND2) ** top27 from west PATCH(T27,NWALL,54,55,29,29,1,1,1,100) C0VAL(T27,U1,1.0,0.0) COVAL(T27,H 1,1 ./PRNDTL(H 1 ),48.9) COVAL(T27,KE,GRND2,GRND2) COV AL(T27 ,EP,GRND2,GRND2) ** Buoyancy PATCH(BUOYANCY,PHASEM,1,56,1,42,1,1,1,100) COV AL(BUOYANCY,V 1 ,FIXFLU,-9.81) GROUP 15. Tennination of sweeps LSWEEP=l;RESREF(Pl)=l.E-4;RESREF(Hl)=l.E-5 GROUP 16. Tennination of iterations ENDIT(Pl)=l.E-7;ENDIT(Hl)=l.E-7;ENDIT(Ul)=l.E-7 ENDIT(Vl)=l.E-7 GROUP 17. Under-relaxation devices RELAX(U1,FALSDT,1.0);RELAX(V1,FALSDT,1.0) RELAX(H 1 .FALSDT, 1.0) GROUP 20. Preliminary print-out ECHO=F GROUP 21. Print-out of variables OUTPUT(Pl,Y,Y,Y,Y,Y,Y);OUTPUT(Ul,Y,Y,Y,Y,Y,Y) OUTPUT(Vl,Y,Y,Y,Y,Y,Y);OUTPUT(Hl,Y,Y,Y,Y,Y,Y) GROUP 22. Spot-value print-out IXMON=l;IYMON=9 GROUP 23. Field print-out and plot control NTPRIN=5 ;NXPRIN= 1 ;NYPRIN= 1 PATCH(CONT,CONTUR, 1,10,1,10,1,1,1,1000) PLOT(CONT,Hl ,0.0,10.0) PATCH(IYEQ5,PROFIL, 1,10,5,5,1,1,1,1000) PLOT(IYEQ5, V1 ,-0.1,0.1 );PLOT(IYEQ5,H 1,0.0,1.0) PATCH(IYEQ9,PROFIL,1,1,9,9,1,1,1,100) PLOT(IYEQ9,Hl ,0.0,1.0) STOP 156 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type o f computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. 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Contact UMI directly to order. UMI A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor MI 48106-1346 USA 313/761-4700 800/521-0600 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 1383522 UMI Microform 1383522 Copyright 1997, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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Creator Barthakur, Amitabh (author)

Core Title Thermal behavior of atria: a comparative study between measured data and a computational fluid dynamics model

School School of Architecture

Degree Master of Building Science

Degree Program Architecture

Degree Conferral Date 1996-12

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag architecture,engineering, civil,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-7463

Unique identifier UC11341529

Identifier 1383522.pdf (filename),usctheses-c16-7463 (legacy record id)

Legacy Identifier 1383522.pdf

Dmrecord 7463

Document Type Thesis

Rights Barthakur, Amitabh

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA