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A passive solar heating system for the perimeter zone of office buildings

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A passive solar heating system for the perimeter zone of office buildings

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Content A PASSIVE SOLAR HEATING SYSTEM FOR THE PERIMETER ZONE OF OFFICE BUILDINGS by Janes M. Gutherz A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Dtegree MASTER OF BUILDING SCIENCE May 1988 Copyright 1988 James M. Gutherz UMI Number: EP41417 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Publishing UMI EP41417 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 UNIVERSITY OF SOUTHERN CALIFORNIA T H E G R AD UA TE SC HO O L U N IV E R S IT Y PARK LO S AN G ELES. C A L IF O R N IA 9 0 0 0 7 % Bu.S This thesis, written by under the direction of h.lSt.-.Thesis Committee, and approved by a ll its members, has been pre sented to and accepted by the Dean of The Graduate School, in partial fulfillm ent of the requirements fo r the degree of ... Bean Date. T THESIS JZX3MMITTI -c Chairman I. TABLE OF CONTENTS page number II. LIST OF FIGURES. iv III. LIST OF TABLES. viii 1. INTRODUCTION. 1 2. THE ELEMENTS AND MECHANICS OF PASSIVE 6 SOLAR HEATING. 2.1 Heat Absorption and the Availability 7 of Solar Radiation. 2.2 Heat Storage. 24 2.3 Heat Distribution. 27 3. PASSIVE SOLAR SYSTEMS. 31 3.1 Direct Gain Systems. 31 3.2 Isolated Gain Systems. 53 4. DEVELOPMENT OF A NEW PASSIVE SOLAR 58 HEATING SYSTEM. 4.1 The Passive Solar Office Building 60 System. (The P.S.O.B. System.) 4.2 The Mechanics of Sunlight and the 62 P.S.O.B System. 4.3 The Optimum Tilt Angle for the Light 66 Shelf. 4.4 Thermal Storage with Phase Change 69 Material. 5. MATHEMATICAL MODELLING FOR SOLAR COVERAGE 78 ON THE PHASE CHANGE PANEL. 5.1 Two Dimensional Development for the 79 Light Shelf Tilt Angle and the Resulting Solar Depth. 5.2 Three Dimesional Development for the 90 Solar Area and Shape on the Phase Change Panel. 5.3 Verification of Theoretical Results. 105 6. ANALYSIS OF THE P.S.O.B. SYSTEM. 108 6.1 Obtaining the Amount of Solar 111 Radiation Available for Storage. 6.2 Sizing the Phase Change Panel. 126 6.3 Conducting a Heat Balance of the 130 P.S.O.B. System. 7. THE COST EFFECTIVENESS OF THE 167 P.S.O.B. SYSTEM. 8. CONCLUSION. 172 9. ACKNOWLEDGEMENTS. 177 10. REFERENCES. 178 iv II. LIST OP FIGURES. page number 2 . 1 The change in length of atmosphere on a monthly basis. 10 2 . 2 The change in length of atmosphere on a diurnal basis. 11 2 . 3 Change in energy density due to orientation of the receiving surafce. 12 2 . 4 Change in direct normal intensity with respect to the incidence angle. 14 2 . 5 Solar intensity on a vertical surface vs. a horizontal surface. 15 2 . 6 Sun path diagram for 40° N.Lat. 16 2 . 7 The percentage of solar radiation on vertical walls for orientations away from true south. 17 2.8 Solar radiation spectrum. 18 2 . 9 Solar radiation transmission through a transparent medium. 20 2 . 10 Comparitive qualities of three types of glass. 21 2 . 11 Beneficial convective heat transfer. 29 2 . 12 Adverse convective heat transfer. 30 3.1 Direct gain to floor. 32 3.2 Direct gain to wall. 33 3 . 3 Sawtooth roof construction. 34 V 3.4 The Wallasey school direct gain system. 3 6 3.5 Typical masonry thermal storage wall. 39 3.6 Typical water thermal storage wall. 4 0 3.7 Time-lag and heat storing capabilities 41 of concrete vs. water. 3.8 Trombe wall design. 4 3 3.9 The creation of natural vents due to the 44 shape of the thermal storage unit. 3.10 The Doug Kelbaugh residence. 45 3.11 One side reflective, moveable 46 insulation improves system performance. 3.12 Passive heating and cooling with the 48 roof pond system. 3.13 Direct gain with a sunspace/buffer. 51 3.14 Indirect gain with a sunspace. 51 3.15 Sunspace with rockbed heat storage. 52 3.16 Convective cycle of an isolated gain 54 system. 3.17 The isolated gain system of the Mark 56 Jones residence. 4.1 The passive solar office building 63 system. 4.2 Using the light shelf to reflect solar 63 radiation to the perimeter of the ceiling. 4.3 Solar coverage on the phase change panel 64 for December 21st. in Montreal. 4.4 Size and intensity of solar coverage vs. 67 position on phase change panel vi 4.5 The Sun-1ite PCM solar pod. 77 5.1 Sun's position defined by profile angle. 79 5.2 Two dimensional analysis. 81 5.3 Variation of the solar depth and location with tilt angle rotation. 83 5.4 The point where the overhang begins to interfere with the solar coverage. 85 5.5 Two dimensional analysis with overhang effects. 86 5.6 Mathematical modelling of a specularly reflective surface. 91 5.7 Mathematical modelling of the tilting light shelf. 92 5.8 Matrix modelling for the P.S.O.B. system. 96 5.9 Determining the X coordinates. 100 5. 10 Determining the Y coordinates. 101 5.11 Solar coverage on the phase change panel. 103 5. 12 Heliodon test model. 105 5. 13 Theoretical vs. Experimental results for December 21st. in Los Angeles. 107 6.1 Three configurations of the P.S.O.B. system and the base case. 110 6.2 Deriving the k-factor. 115 6.3 Transmissivity of three types of glass as a function of the incidence angle. 119 v i i 6.4 Development of transmission/incidence 121 curve for double insulating glass 6.5 Insulated phase change panel. 129 6.6 Base case. 139 6.7 Case A configuration. 144 6.8 Case B configuration. 153 6.9 Case C configuration. 162 8.1 New light shelf-overhang assemblies 175 viii III. LIST OF TABLES. page number 2.1 Qualities of various surface coatings. 23 2.2 Thermal storage properties of various substances. 25 4 .1 Solid to liquid PCMs. 71 4.2 Hydration-dehydration PCMs. 72 4.3 Properties of some available PCMs. 74 6.1 Global solar radiation falling on a horizontal surface in Montreal. (MJ/m ) 112 6.2 Diffuse solar radiation falling on a horizontal surface in Montreal. (MJ/m ) 112 6.3 Computation of direct solar radiation falling on a horizontal surface for December in Montreal. (BTU/ft2) 113 6.4 Intensity of direct solar radiation on phase change panel. 117 6.5 Transmittance of double insulating glass for December in Montreal. 122 6.6 Reflectances of specular surface coatings. 123 6.7 Actual hourly direct solar radiation available for storage on the phase change panel for a December day in Montreal 124 6.8 Amount of heat energy available for storage. 125 ix 6.9 Mean daily temperature data for Montreal. 132 6.10 Mean hourly temperature in Montreal. (6 pm - 12 am) 133 6.11 Office set-back schedules. 135 6.12 Hourly internal gains of the perimeter space. 136 6.13 Sum of hourly temperature differences. 138 6.14 Heat balance results of base case. 140 6. 15 Results of case A.I. 147 6. 16 Results of case A.2. 149 6.17 Results of case A.3. 151 6.18 Results of case B.l. 155 6.19 Results of case B.2. 157 6.20 Results of case B.3. 159 6.21 Results of case C.l. 163 6.22 Results of case C.2. 164 6.23 Results of case C.3. 165 7.1 Cost analysis of the system. 169 1 1. INTRODUCTION. We have come to a point in history where the building industry has employed the practice of constructing hermetically sealed boxes. During times when the cost of energy was inexpensive the creation of an internal environment devoid of any external interaction would have been the logical solution. As the cost of energy begins to rise we must once again design buildings that embrace the resources of the environment instead of ignoring them. A passive solar system fufills this objective. The term "passive" implies that the system does not attempt to control or disregard the elements of nature. It will operate by natural processes where the building itself acts as the system. The term "solar" implies the use of the sun as the system's renewable energy source. Compared to smaller scale buildings the functional nature of the office building does not lend itsef to environmental design, much less the use of a passive solar system. Consequently, the purpose of this thesis is to develop a passive solar system that can be incorporated into office building design. 2 In order to achieve an acceptable degree of thermal comfort in cold climates an office building must be heated and cooled at the same time. The interior zone is cooled due to its excessive internal gains while the exterior zone is heated. Thus a considerable amount of energy is expended. It is also often overlooked that many modern day businesses function well after 5 p.m. and well into the evening. Hence, the passive solar system will be designed to heat the exterior zone (8'deep, 15'long, 9'high) of an office space during less occupied hours (6 pm.-12 pm.) instead of operating energy consuming perimeter heating. It is imperative that the system integrate with the form and construction of the building without sacrificing floor space, functional priorities and architectural aesthetics. The conceptual passive solar heating sytem is based on the combination of two separate elements of building science; daylighting (with the use of a light shelf - overhang) and the concept of heat storage. The light shelf is usually used primarily as a daylighting tool. Daylight is redirected to areas of 3 insufficient lighting within the space while protecting exposed occupants from direct sunlight. Furthermore, the extra daylight allows for a reduction of artificial lighting. It can also help to reduce the cooling load of the space. In this system, the top of the light shelf is coated with a specularly reflective film such that 80% to 92 % of the radiant energy (visible and solar) incident upon it will be reflected. Moreover, the light shelf is modeled to rotate about its axis parallel to the window's edge. The ability of mass to store heat is a common and essential characteristic of almost all passive solar systems. Panels of phase change material are used to maximize the heat storing capabilities of this system. The panels are supported along the perimeter of the ceiling of the office space and extend approximately 6 to 8 feet into the space. Theoretically, the passive solar system would function as follows: Direct sunlight striking the specular surface of the light shelf is reflected onto the phase change panels. The light shelf is tilted to an optimum angle in order to achieve a maximum amount of solar 4 coverage at a specified location on the panels for the hour of the day and month of the year. Solar energy in the form of sensible heat is absorbed by the phase change panels at a rate characteristic of the phase change material and its surface absorptivity. A two dimensional mathematical model is developed to determine the optimum tilt angle of the light shelf for any given solar position. A three dimensional mathematical model is developed using basic principles of matrix multiplication in order to calculate the area and shape of solar coverage on the phase change panels for any given solar position. The validity of the calculations is confirmed using physical models placed in a heliodon. Data supplied by the Atmospheric Service of Canada for the test city of Montreal is used to determine the amount of solar radiation available for passive storage. To simplify the analysis it is assumed that all solar radiation incident upon the phase change panels is absorbed and "held" until the temperature of the space drops below that of the panels (some time after 6 pm.). Three different construction configurations of three light shelf depths each are evaluated to determine the 5 system's adaptability and sensitivity to change relative to a base case configuration. By earlier definition, this system is not a true passive solar system because the office building itself does not act as the system. When additional elements are adopted into the building design then it becomes part of the system, just as the system becomes part of the building. Thus, the system must qualitatively enhance the architectural fabric of the building, and must serve quantitatively as a practical and cost effective element of the building's design. 6 2. THE ELEMENTS AND MECHANICS OF PASSIVE SOLAR HEATING. The theory of passive solar heating is based on two fundamental absolutes; the sun's perpetual generation of solar energy and the ability of a material to absorb radiant heat. The successful design of a passive solar heating system relies upon the proper synthesis of these absolutes with the orientation, form, materials and construction of a given building - system. When combined effectively they form a synergetic union such that the total effect is greater than the sum of its parts. Almost all passive solar systems are driven by the mechanism of heat storage, but the amount of radiant heat that can be stored, how long it can remain stored and how well it can be distributed later on is dependant on the level of synergy between the building and the system. The functions of a passive solar system can be divided into three distinct physical processes: 1. Heat Absorption. 3. Heat Distibution. 7 Each process, or phase, has many factors which affect its performance. Subsequently, the efficiency of a given phase will have a propagative effect on the phase which succeeds it. This is carried through to the point where the efficiency of the whole system is affected. The following sections of this chapter investigates the 'factors' which affect the performance of each phase. 2.1. Heat Absorption and the Availability of Solar Radiation. The available solar radiation on a receiving surface will be absorbed at a rate characteristic of the material's specific heat, density absorptivity and surface area. Therefore, it is essential to optimize the factors which affect the intensity of solar radiation before it reaches the receiving surface. The intensity of the energy radiated by the sun reaching the outer perimeter of the earth's atmosphere is 429.2 Btu's per square foot per hour (1.353 kW/m2) [1]. Approximately 35% - 40% is reflected back into space mostly off of clouds and atmospheric dust and 8 partially from the earth's surface. Another 10% - 15 % is absorbed by the ozone layer, water vapour and carbon dioxide in the earth's atmosphere. One third of the remaining solar radiation is diffused by dust particles and air molecules throughout the earth's atmosphere. This diffused portion of radiation is responsible for the blue color of a clear sky [2]. The term used to define the degree of diffusion and absorption is known as the atmospheric extinction coefficient. It is a relative measurement of the attenuation of solar radiation with respect to the length of atmosphere it has passed through. For a monochromatic wavelength Bouger's Law is expressed as follows; - dl-^(x) = I^(x) K^dx. (2.1) The above equation is integrated over the length of the earth's atmosphere to obtain an overall extincion coefficient which varies with the altitude angle of the sun [3]. Since the remaining direct solar radiation is more concentrated per unit area than its diffuse counterpart it is preferable to make the most use out 9 of its availability. Thus, the most critical factor controlling the intensity of the solar radiation reaching earth's surface is the length of atmosphere the radiation must travel through. The greater the length of the radiative transmission path, the greater the degree of absorption and scattering of radiation. Unfortunately, we are not in a position to control this situation. The intensity of solar radiation at the earth's surface is a function of the length of atmosphere the solar radiation passes through. The length of atmos phere the solar radiation passes through is a function of the earth's axial tilt, rotation about its own axis and its orbit about the sun. The effect of the earth's constant tilt of exactly 23.47° (from a vertical plane to a plane passing through its axis) causes a change in the length of atmosphere the solar radiation passes through on a seasonal basis. Figure 2.1 on the following page illustrates that for the same location on earth, the average daily length of atmosphere 'A' in December is longer than the average daily length of atmosphere 'B' in June. The incident angle of the incoming rays with the normal to 10 earth's surface is greater in the winter than in the summer. Therefore, the intensity at earth's surface is less in the wintertime than in the summertime. JUNE Fig. 2.1. The change in length of atmosphere on a monthly basis. For any point in the northern hemisphere it is colder in December than in June because ther is more solar radiation that will be absorbed and scattered, thus reducing the direct radiation component reaching earth's surface. On a diurnal basis the incoming solar radiation of the noon sun is more intense than that of the morning or afternoon sun simply because the length of the atmosphere is shortest at noon. This effect is illustrated in figure 2.2 on the following page. Line 'OA' at high noon is shorter than line 'OB' at four in the afternoon. 11 Fig. 2.2. The change in the length of atmosphere on a diurnal basis. In conclusion, the passive solar heating system must function within the limits prescribed by Earth's orbit about the sun, the rotation about its own axis, current atmospheric composition and weather condition. All the other factors which affect the intensity of solar radiation on a receiving surface are (design decisions) partially controlled by man and are disscussed in detail on the following pages of this section. 12 The Incident: Angle. The intensity of direct solar radiation on a surface is a function of the angle at which the incoming rays of the sun strike the surface. The angle which the incoming rays subtend with the perpendicular of the receiving surface is known as the incident angle. In figure 2.3 "n" units of solar energy strike surface #1 exactly normal to the plane of surface #1, L units long by W units deep (into the page) . The same "n" units of solar energy strike surface #2 at an angle 60° from the perpendicular of surface #2, 2L units long by W units deep (into the page). Thus, the energy density on surface #2 is half that on surface #1. SURFACE 1 SURFACE 2 surface area of #1 = LW surface area of #2 = 2LW 2L Energy density on surface #1 = n / LW for © = 0° Energy density on surface #2 = n / 2LW for © = 60° Fig. 2.3. Change in energy density due to orientation of receiving surface. 13 The energy density of solar radiation on a receiving surface is a function of the incident angle [5], such that: Xq I^n ® (2.2) 1 ^ is the intensity of solar radiation directly normal to the receiving surface. When the incident angle is 0° 100 % of the available solar energy is intercepted by the surface. If surface #1 of figure 2.3 was tilted 30° the incident angle is 60° and the energy density is defined as: IQ = (n/LW) cos 60° Figure 2.4, on the following page, illustates how the intensity of solar radiation varies with the angle of incidence. 14 10 20 30 40 50 «0 70 60 90 AMO 11 OP IHCIWN6I , • Fig. 2.4. Change of the direct normal intensity with respect to angle of incidence. The degree of heat absorption by a receiving surface is partly a function of the orientation of the surface with respect to the sun's position. In figure 2.5, on the following page,the vertical surface will intercept 86.6 % of the incident solar radiation. For the same altitude angle of 3 0° the horizontal surface will only intercept 50 % of the incident solar radiation. Hence, it would be better to orient the heat absorbing thermal mass vertically for winter passive heating 15 since the sun's altitude is relatively low throughout the winter months. The orientation of a vertical receiving surface with respect to the sun's daily path across the sky has a considerable effect on the degree of insolation that surface receives. It further emphasizes the importance of effectively positioning the receiving surface to obtain the highest degree of solar radiation on that surface. For the 40° N.Lat. sun path diagram of figure 2.6 a south facing vertical.wall in June only receives about 7 1/2 hours of direct sunshine a day out of a total 14 1/2 hours (52 %) . In December the same south face receives about 9 hours of direct sunshine a day o Fig. 2.5. Solar intensity on a vertical surface vs. a horizontal surface. 16 out of a total 9 hours (100 %) . The movement of the winter sun can be viewed from the south all day long. Fig. 2.6. Sun path diagram for 40° N. Lat. [6]. The low solar altitudes of the winter months strike the vertical surface at angles closer to the perpendicular than in the summer months. In December the incidence angle on a vertical surface ranges from 8.27° at 8 am/4 pm to 27.0° at noon. From figure 2.4 this results in a solar radiation intensity of 99% to 89.1% respectively of the direct normal intensity. For the same hours in June the intensity ranges from 0% to 29.2% of the direct normal intensity. 17 According to figure 2.7 vertical surfaces of the 40° N. Lat. that are oriented up to 30° east or west of south receive almost the same amount of solar radiation as vertical surfaces facing true south [7]. 100 z o < s z < o s o < c > < u c c o. so s W A IL AZIM UTH (degrees dev.aoon from South* Fig. 2.7. The percentage of solar radiation on vertical walls for orientations away from true south. The Greenhouse Effect and Fenestration. 18 A portion of radiant heat between the wavelengths of 0.3-3 micrometers will be converted to sensible heat and absorbed by the thermal storage mass. The mass will reradiate the stored heat at wavelengths between 3 to 100 micrometers, as illustrated in figure 2.8, graph B, by virtue of a temperature differential between the space and the mass, the surface area and longwave emissivity of the mass. From figure 2.8, graph C, typical architectural glass will transmit 75% to 85% of the radiant heat spectrum incident upon its surface, but it can't transmit any longwave radiation greater than 4 micrometers. The synergetic combination of the two physical processes results in what is known as the "greenhouse effect". WAVCLCNCTM, ft i*<MICJ i O N S ) 51 2 ; s « « * m z 2 f & i « e « & o ~ * I ** 9 Fig. 2.8. Solar radiation spectrum [8]. 19 Most of the heat radiated by the thermal storage mass remains trapped in the space because glass is opaque to longwave radiation. Therefore, the quality of the glazing must be optimized as an element of the passive solar heating system. It is no surprise that a common characteristic of most passive solar heating systems is the presence of vertical south face glazing. The success of the passive solar system is synonymous with the effective interaction between fenestration and the heat storage unit of the system. The transmission of radiation through glass primarily depends on the angle of incidence of the incoming rays, the refractive index and the extinction coefficient of the glass. The index of refraction is a characteristic of the transparent medium. It is an indication of how fast radiation travels through a transparent medium, such as glass, relative to how fast it travels through a vacuum [9]. Since radiation travels at the speed of light, the index of refraction for any medium, n', is defined as follows: n' = Cq/C (2.3) where: CQ = the speed of light in a vacuum. C = the speed of light in a transparent medium. 20 The air/glass interface of figure 2.9 is expressed by Snell's Law: sin 9 = n^. (2.4) sin r nQ for air: nQ = 1.00 therefore; sin 8 = nr sin r Since the refractive index for any transparent medium is greater than 1.0, the angle of refraction is always smaller than the angle of incidence. Incoming ray incidanca angla air angla of rafractlon air v Fig. 2.9. Solar radiation transmission through a transparent medium. As the incident angle increases so does the angle of refraction. Likewise, the length, L, the transmitted radiation travels in the glass is increased as shown on the following page. 21 L = t/cos r (2.5) where: L = optical path length. t = thickness of the transparent material, r = angle of refraction. As the optical-path length becomes longer the degree of absorption within the glass increases due to the effect of the exctinction coefficient of the glass [10]. The relative absorptance, P* , can be defined by Bouger's law as follows: A = 1 - e“KL (2.6) To summarize; when the incident angle increases, the reflectance increases and the transmitance decreases. The overall effect of the incident angle on the transmittance, reflectance and absorptance of three types of glass is illustrated in figure 2.10, below. 1 . 0 . 1 .0 . 02 9 0 INCIDENT ANGIE, 0 60 90 30 90 60 INCI0ENT ANGLE, 9 90 Fig. 2.10 Comparitive qualities of three types of glass [11]. 22 Size of Fenestrating Area. As mentioned earlier, we are not in a position to control the elements which affect the intensity of solar radiation on a receiving surface because these elements are generated by natural processes. We are subject to the orbital and rotational movements of the earth, weather conditions, geography, etc., and can only react to the actions of these processes. Due to the factors previously disscussed in this section the energy density of solar radiation on a receiving surface is generally low. In order to obtain the amount of solar radiation required for passive solar heating one must increase the fenestrating area and the surface area of the heat storage material. The south facing all glass wall of passively solar heated homes is a direct response to the conditions. 23 Surface Characteristics of the Thermal Storage Unit. Solar radiation finally reaching the surface of the heat storage material will be reflected or absorbed. Opaque substances do not transmit radiation. The ideal surface condition for the thermal mass would be one that absorbs all the shortwave radiation between 0.3 to 3 micrometers and emit all longwave radiation from 3 to 100 micrometers. A relative indicator of the overall effectiveness of a material as a good thermal storage coating is the absorptance to emmittance ratio of the substance. The substances of table 2.1 below act as surface coatings for the actual heat storage material since the heat storage material itself usually has a grey surface with a low absorptance to emittance ratio. Short-wave Long-wave a Substance absorptance emittance t Grey paint 0.75 0.95 0.79 Red oil base paint 0.74 0.90 0.82 Asbestos, slate 0.81 0.96 0.84 Linoleum, red brown 0.84 0.92 0.91 Dry sand 0.82 0.90 0.91 Green roll roofing 0.88 0.91-0.97 0.93 Black cupric oxide on copper 0.91 0.96 0.95 Black tar paper 0.93 0.93 1.0 Black gloss paint 0.90 0.90 1.0 Black silk velvet 0.99 0.97 1.02 Alfalfa, dark green 0.97 0.95 1.02 Black paint, 0.017*, on aluminum 0.94-0.98 0.88 1.07-1.11 Lampblack 0.98 0.95 1.03 Table 2.1. Qualities of various surface coatings [12]. 24 2.2. Heat storage. All materials will absorb radiant heat at their surface characteristic of the suface's absorptance. Heat energy is imparted to the surface molecules which causes them to vibrate. The degree of vibrational movement of a molecule is defined by its temperature. The greater the degree of molecular activity, the higher the temperature of the material. The absorbed heat energy is transfered from hot, active surface molecules to cool sluggish molecules within the material. This process is known as conduction, and the thermal conductivity of a material, k, defines the ability of the material to disperse heat energy within itself or to other materials in contact with it [13]. Heat is transfered from areas of higher molecular activity (higher temperature) to areas of lower molecular activity (lower temperature) proportional to the temperature gradient over the area it conducts through times the thermal conductivity of the material [14]. In one direction, Fick's Law is defined as: q = - k [ Ax(dT/dx) ] (2.7) 25 Primarily, the material must act as an effective heat storage medium. It must be able to contain the absorbed thermal energy within itself. A material's capacity to store thermal energy is defined by its specific heat (under constant pressure), Cp, the amount of heat one unit mass of substance can hold when its temperature is raised one degree [15]. A true indicator of a material's ability to store heat is its heat capacity, the amount of heat one unit of volume can hold when its temperature is raised one degree. Table 2.2 compares the heat storing capabilities and thermal conductivities of various substances. Thermal Heat Substance Specific Heat Density Conductivity Capacity J/kg*°K B*nyib*°F kg/m3 lb/ft3 w/m.°x BTUh/ft-°F HJ m3 -°K BTUh ft *°F Aluminum (alloy 1100) 896 0.214 2740 171 221 12B 2.455 36.59 Asphalt 920 0.22 2110 132 0,74 0.43 1.941 29.04 Brick, building 300 0.2 1970 123 0.7 0.4 1.576 24.60 Cement (Portland clinker) 670 0.16 1920 120 0.029 0.017 1.286 19.20 Concrete (stone) 653(473) 0.156(392) 2300 144 0.93 0.54 1.502 22.46 Iron: cast 500(373) 0.12(212) 7210 450 47.7(327)27.6(129) Rubber: vulcanized, soft 2000 0.48 1100 68.6 0.1 o.oe 2.200 32.93 Sand 300 0.191 1520 94.6 0.33 0.19 1.216 18.07 Steel (mild) 500 0.12 7830 489 45.3 26.2 3.915 58.68 Stone (quarried) 300 0.2 1500 95 1.200 19.00 Tar: pitch 2500 0.59 1100 67 0.38 0.51 2.750 39.53 Wood: Oak, white 2390 0.570 750 47 0.176 0.102 1.793 26.79 Water 4130(293) 0.999(68) 998.2 62.32(68) 0.602 0.348 4.173 62.26 Table 2.2. Thermal storage properties of various substances [16]. 26 The equation for the amount of thermal energy stored for a specific time period is defined as: Qs = m Cp (Tj - T±) (2.8) where: m = mass of the storage material. Cp = specific heat of the material. T ^ = temperature of the material at the beginning of the time period. T-i = temperature of the material at the end of the time period. The positive sign convention indicates heat is absorbed and stored since Tj is greater than T^. A negative sign convention indicates heat is expended by the material. The amount of heat stored or the amount of heat released is usually calculated on an hourly basis. In conclusion, the amount of heat stored with respect to the thermal storage material used is a function of the material's specific heat, thermal conductivity, density and volume. Ideally, the volume of the material must be adequate to store the amount of heat required to warm the building over a break of cloudy days. Thus, the material itself must have the capacity for storing the required amount of heat and it must be sufficiently conductive in order to "spread" the absorbed heat uniformly throughout its own volume. 27 2.3. Heat Distribution. After the sun sets the temperature of the space will drop below the temperature of the heat storage material. The heat storing process is now reversed. The thermal storage material acts as the source of energy used to warm the space. The intensity of energy radiated from the surface of the thermal material by virtue of its absolute temperature and the emissivitty of its surface [17] is defined as: q = V e A T4 (2.9) where: Stefan Boltzmann constant. = 0.1714 * 10"8 Btuh/ft R ■ 5.67 * 10“8 W/m2K4 A = surface area of the material, e = emissivitty of the surface. T = temperature of the surface. Thus the net radiant heat transfer between the surface of the thermal material and the space is defined as: qr - S/Aje^T4- T4) (2.10) where: T^ = the absolute temperarure of the surface. T2 = the absolute temperature of the space. Since the space receives all the radiated heat, it acts like a surrounding black body. 28 Heat transfer takes place from hot to cold areas until a state of equilibrium is reached. Therefore, the rate of heat radiated is dynamically regulated by the temperature differential between the space and the thermal material. Meaning, that the thermal material only releases what is needed to maintain the space. The balance of heat remains stored. As the cool air of the space comes into contact with the warm surface of the thermal material heat energy will be conducted to the adjacent layer of cool air. As the temperature of the air increases, it expands and the density decreases. The warmed air molecules rise and are replaced by cooler air molecules, ready to be warmed. This process creates a cyclic movement of warm and cool air molecules within the space. The continuous movement is generated by the temperature differential. The mode of heat transfer is known as natural convection [18]. The effectiveness of natural convection as a heat distribution device is dependant on the orientation of the thermal material. The position of the thermal material must complement the rise of warm air in order to allow it to circulate throughout the space. 29 The highest degree of convection circulation occurs when the flow of air over the wanned surface runs parrallel to the flow of heat from that surface. Since the thermal material will radiate heat approximately perpendicular to its surface one obtains the convective circulation paths illustrated below. In both cases of figure 2.11 the radiant heat is permitted to circulate within the space. Natural con vection effectively moves the warm air throughout the volume of the space. In figure 2.12 on the following page the position of the warm surface impedes the circulation of warm air. Hence, a warm layer of air remains concentrated in an area of the space that does not affect the thermal comfort of the occupants. Fig. 2.11. Beneficial convective heat transfer 30 Fig. 2.12. Adverse convective heat transfer. The installation of fans along the ceiling greatly improves the level of heat distribution within the space. This circulatory heat transfer mode is known as forced convection. 31 3. PASSIVE SOLAR SYSTEMS. There are two basic methods for passively heating a space with solar energy. The difference between the methods lie in how each passive solar system responds to the physical factors disscussed in the previous chapter. Generally, they can be categorized into two main groups; direct gain and isolated gain systems. 3.1. Direct Gain Systems. When the Space Serves as the System. The simplest passive solar systems are those which use the space as the system itself. Direct, diffuse and reflected solar radiation extends into the space via fenestration. Heat is stored in the walls, floor and ceiling of the space. The success of the direct gain system depends mostly on the integrity of the fenestrating area. Its size, orientation and transmitting characteristics control the degree of solar radiation entering the space. 32 Thus, the fundamental objective of the south face glazing is to expose the inner space to as much solar radiation as possible to reduce the mechanical heating load of the space. Consequently, the area of south glazing must be sized in order to gain more heat during the daytime than it loses. The position of a window wall on the south face will designate which surface solar radiation strikes in the space. Hence, one must consider the orientation of the thermal mass relative to the window [19]. The floor adjacent to the window receives maximum exposure to direct solar radiation (as illustrated in figure 3.1). Moreover, the natural convective air flow will promote the distribution of heat throughout the space when the thermal mass radiates the stored heat. Fig. 3.1. Direct gain to floor. 33 Unfortunately, floor coverings and furniture intercept the incoming direct radiation. The furniture absorbs solar energy and heats up. In turn it will heat the air and the air will heat the walls. Thus, the walls act as an alternative thermal storage unit. They receive the reflected component of the direct radiation off of the floor and furniture as well as some degree of direct and diffuse radiation through the fenestration. By placing the window high along the top of the wall the low winter sunlight may reach the north wall of the space as illustrated in figure 3.2. The walls receive solar radiation of greater intensity than the floor due to the smaller incident angles of the incoming rays of the sun on the vertical wall. As Fig. 3.2. Direct gain to the wall. 34 As a final alternative, the thermal mass may occupy the ceiling which receives only the diffuse and reflected component of the incoming radiation. Furthermore, the convective currents work against heat transfer to the space. Instead of usiing the ceiling for thermal storage the roof may be used for solar access like a window. The sawtooth roof configuration of figure 3.3 allows low altitude winter sunlight into the space while blocking out high altitude summer sunlight [20]. A specific amount of solar radiation requires less storage area if it is in the form of direct radiation, as opposed to diffuse and reflected because it is more energy dense. Hence, it is preferable to obtain direct radiation with respect to heat storage. Unfortunately, 35 direct sunlight is a daylighter's nightmare. It is uncomfortable for the occupants of the space to be in and it produces glaring reflections. As a solution, translucent glazing will scatter the direct solar radiation producing a uniform distribution of daylight and radiation all through the space. All the surfaces are considered for thermal storage and receive a generally equal portion of solar radiation. The downside of this factor is that translucent glazing denys the occupant of a view of the exterior. Furthermore, too much thermal mass will increase the structural, construction and capital costs of the space while sacrificing valuable floor area [21]. Thus, a compromise must be made between all the design elements of the space as to what the system will actually entail. All the requirements for maintaining a satisfactory degree of comfort within the space must be met. Heating the space, passively or actively, is just one of them. The St. George's County secondary school of Wallasey, England is a classic example of a direct gain passive solar system [22]. See Figure 3.4 on the following page. 36 >.y y jr c jr .; .y - ! v V'r SECTION 1st. FI.: 4" screed + 6" concrete. 2nd. FI.: 9" concrete. Walls: 9" brick faced with plaster. Roof: 7" concrete + insulation. Clear openable windows spaced along south face glass permit exterior view and natural ventilation. Fig. 3.4. The Wallasey school direct gain system. The direct gain system features a 230 ft. by 27 ft. double pane south face glass wall which transmits solar radiation to the thick, exposed walls, floors and ceiling of the two story structure. The exterior pane is clear glass and the interior pane is rippled to refract direct sunlight and spread it uniformly over all the interior surfaces. The masonry structure of the school stabilizes daily temperature swings to approximately 7 °F over the entire year. 37 The direct gain system supplies 50% of the school's daily heating requirements. The balance is supplied by the heat generated by incandescent lighting and students. The school is used only during the day and requires no night heating. Most direct gain systems are designed to satisfy only the daytime heating requirements of the space. This accounts for only 10% of the total heating load [23]. The heat absoption, storage and distribution cycle is shorter than other systems since the only heat storage medium in the space is the space itself: a one-sided- absorbtive-distributive heat transfer system. As a result, it is easier and less expensive to design than any other passive solar system. 38 Systems that act as additional elements of the space. Some direct gain passive solar systems employ thermal storage as a separate element of the space. It is positioned behind south facing glazing to receive the maximum amount of available solar radiation on its surface. The thermal mass, placed between the glass and in space to be heated absorbs the available solar radiation, converts it to heat and transfers the heat into the living space. There are three basic types of direct gain systems; thermal storage walls, which use masonry and water as the heat storage medium, thermal storage roofs, known as roof ponds, and indirect attached greenhouses, known as sunspaces. Masonry and Water Thermal Storage Walls. The south facing glass, characteristic of the wall storage system is used to prompt the "greenhouse effect" in the space between the glass and the thermal storage wall. This permits the exterior surface of the mass to reach high energy transferring temperatures. A dark colored coating is applied to the exterior surface of the thermal storage wall to improve its 39 absorptance. In figure 3.5, the absorbed solar radiation is converted to heat and conducted through 8" to 16" of masonry (concrete, brick, adobe, etc.) to the interior surface of the wall. Since masonry walls are not highly conductive it takes a considerable amount of time before the absorbed energy travels through the wall and begins to radiate into the space. As a result of this long time-lag, masonry thermal storage systems are designed for night heating . Fig. 3.5. Typical masonry thermal storage wall. Conversely, the heat transfer mechanism in water thermal storage walls is faster since it is mostly convective. In figure 3.6 on the following page, the exterior surface of the water wall heats up, inducing 40 the convective cycle shown. As long as the sun shines the heated water is continuously replaced by cooler water at the exterior surface. Hence, the temperature swing across the wall is minimal. The effect of a rapid convective heat transfer in the water walls results in a much shorter time-lag than that of its masonry counterpart. Consequently, waterwalls are designed primarily for daytime heating. Fig. 3.6. Typical water thermal storage wall. Figure 3.7 on the following page, illustrates the difference in time-lags between an 8" thick by a 32" long concrete wall and an 18" diameter water cylinder of equal height (and volume). 41 O © © © i __________. I ________ $ n i £ density = 144 lb/ft3, vol. = 1.77 cubic ft./ft. weight = 255 lbs/ft.ht. Cp - 0.156 Btu/lb.F heat storage capacity = 255 x 0.156 = 39.78 Btu/F.ft. WAT1N density = 62.32 lb/ft3, vol. = 1.77 cubic ft./ft. weight = 110 lbs/ft.ht. Cp = 1.000 Btu/lb.F heat storage capacity = 110 x 1.000 = 110.00 Btu/F.ft. Fig. 3.7. Time-lag and heat storing capabilities of concrete vs. water. The calculations demonstrate that water is much more efficient as a heat storage medium than concrete, or any other masonry materials. For equal volumes, water can store approximately 177% more heat per unit temperature than concrete. Since water is usually contained in steel drums or in cylinders of durable, translucent fibreglass and corrugated steel the water thermal storage system relies on the integrity of the container to aesthetically and practically interact with the space to be heated. On the other hand, it is easier to integrate the masonry thermal storage wall 42 with the overall design of the space as load bearing structural members. Windows may be added to permit views to the outside while allowing for direct solar gain into the space. Heat is transfered from the interior surface of the thermal mass to the space by radiation and, to a lesser degree, by natural convection. To enhance the heat distribution of the system air vents are set in the top and bottom of the masonry thermal storage wall. Cool air is drawn through the bottom vents and brought into contact with the warm exterior surface of the mass. The air is warmed, causing it to rise and flow out the top vent as illustrated in figure 3.8, on the following page. The masonry thermal wall that employs this heat distribution technique is known as a Trombe Wall [24]. The Trombe Wall is named after Felix Trombe who incorporated it in a house designed with Jacques Michel in 1967, in Odeillo, France. 43 Fig. 3.8. Trombe Wall design. The second convective current effectively makes use of the exterior side of the masonry thermal storage wall in order to reduce exterior surface temperatures of the thermal mass and to permit daytime heating of the living space. Backdraft dampers may be added to prevent air from circulating in the wrong direction. Since the containers of the water thermal storage units are usually cylindrical, natural air vents are created which permit convective currents to flow freely between each cylinder and into the space. Such is the case with the system illustrated in figure 3.9, on the following page. 44 Fig. 3.9. The creation of natural vents due to the shape of the thermal storage unit. A fine example of the use of a masonry thermal storage system is the Doug Kelbaugh residence, located in Princeton, New Jersey [25]. It employs south facing Trombe walls on the first and second floor of a standard wood frame construction. 600 square feet of 15 inch thick concrete walls are used to limit temperature fluctuations in the space from 3 °F to 6 °F over a 24 hour cycle. The system, which includes an attached greenhouse, reduces space heating costs by 84% . A crossection of the house in figure 3.10 on the following page, illustrates the mechanics of the system and points out its characteristic features. - Two sheets of double strength glass and a flat black layer of paint on thermal walls ensures maximum absorption. - Top and bottom vents induce convective air currents for daytime heating. - Dampers prevent reverse circulation. - Windows set into thermal mass permit view to outside and direct gain element. - Door at top of stairwell prevents warm air migration to second floor. -Interior fireplace provides added direct gain element to space. - Summer ventilation provided by top & north wall vents, equiped with fans and dampers. - Thermal wall ventilates space by "pulling" cool north air across living space. Fig. 3.10 The Doug Kelbaugh residence [25]. 46 From an energy conservation standpoint, the addition of moveable insulation or triple glazing will help to cut down night time heat losses considerably. The Steve Baer residence in Corrales, New Mexico uses a manually operated insulating shutter [26] as shown in figure 3.11. The aluminum interior surface of the shutter is specularly reflective. Thus, during the day the black-coated steel drums receive an additional reflected component of solar radiation. The south facade water thermal storage wall coupled with the interior adobe walls and concrete floor accomodate the semi-desert temperature fluctuations and maintain an interior temperature between 63 °F and 70 °F through most of the winter. Fig. 3.11. One side reflective, moveable, insulation improves system performance [26]. 47 Thermal storage Roofs. As the heading implies, the thermal mass of a roof pond system is located on the roof of the building. Water, contained in thin, transparent or balck plastic bags act as the solar collector, storage medium and heat dispenser of the system. The bags are supported on highly conductive metal decking which functions as the ceiling of the space. Using water as a thermal storage medium induces a shorter time lapse between heat absorption and heat distribution. Hence, the space is heated during the day. Since water can store more energy than any other common building material, roof ponds are designed to heat the space 24 hours (if necessary). The diurnal heating cycle can only be completed when night time insulation covers the outer surface of the roof pond. Less than half the heat transferred to the interior during the day is lost due the adverse direction of the heat tansfer taking place. Since the convection factor works against the system moveable insulation must be added to reduce the convective and evaporative heat losses through the roof pond. 48 Unlike other systems, roof ponds may be used throughout the year. See figure 3.12. During summer days, the roof pond is insulated from overhead solar radiation while the rising heat on the interior is absorbed by the roof pond. At night the roof insulation is removed and the roof pond discharges the stored heat via convection and radiation. Roof ponds are used mostly in climates which require equal amounts of heating and cooling throughout the year. c sum m er w in te r Fig. 3.12. Passive heating and cooling with the roof pond system [27] 49 In the northern latitudes roof ponds are sloped in order to trap solar radiation from the low altitude sun and prevent extensive build up of snow. An excellent example of the roof pond system is the John Hammond residence of Winters, California [28]. The roof pond covers one third the roof area and holds 13,200 pounds of water in a series of 6' by 8' by 12" deep, tar coated, galvanized steel pans. In the winter months the heating requirements of the house are completely supplied by the roof pond. During the hottest month of the summer the interior temperature of the space never exceeds 78 °F. Attached Greenhouses. Attached greenhouses, also known as sunspaces, extend the application of the greenhouse effect in passive solar design to its useful limit. As long as there is a positive radiant heat exchange between the sunspace and the external environment, sunspace generated solar heat gain can be used to passively heat the adjacent living space or the sunspace itself. In effect, the sunspace serves as its own direct gain system and as 50 the solar collector of an indirect gain system. Unfortunately, the sunspace undergoes large daily temperature fluctuations due to excessive night time heat losses. Subsequently, it is not relied upon to passively heat the adjacent living space during the evening. Instead it functions as a buffer zone that protects the interior space from outdoor weather conditions. The buffer zone created by the sunspace reduces the amount of heat the interior space loses compared to the amount of heat lost if the sunspace was not present at all. The heat transfer mechanism from the sunspace to the interior depends on the wall construction that separates the two spaces. In figure 3.13 on the following page the sunspace is placed in front of a double pane glass window to act primarily as a buffer. Essentially, this is a direct gain system since the solar radiation is absorbed by the interior surfaces while the space is instantaneously heated in the process [29]. In figure 3.14, also on the following page, a high level of solar radiation through the sunspace is ab sorbed by the masonry (water) thermal storage wall, 51 conducted (convected) across the wall and discharged into the space by radiation and convection for night time ( day time) heating. Vents are set in the top and bottom of the masonry wall to naturally circulate the overheated sunspace air to the adjacent space [30]. Fig.3.13. Direct gain with a sunspace/buffer. Fig. 3.14. Indirect gain with a sunspace. 52 If the temperature fluctuations in the sunspace can be stabilized and the heat losses minimized the sunspace can function as a useful, naturally heated greenhouse. In figure 3.15 heat collected in the sunspace is drawn by fans into a rockbed under the uninsulated floor slab of the interior space. The stored heat in the rockbed will radiate through the floor slab into the interior space while fans are required to extract heat from the rockbed and send it back into the cold sunspace. The greenhouse should be double or triple glazed to prevent overnight freezing in colder climates. Exhaust and intake vents located along the top and bottom edges of the sunspace respectively are used to naturally ventilate the sunspace during the summer months [31]. Fig. 3.15 Sunspace with rockbed heat storage. 53 Even though permanently attached sunspaces are one of the most expensive passive solar systems they readily adapt and integrate with the overall design of the space. 3.2. Isolated Gain Systems. One may look at the various types of passive solar systems as a spectrum. It begins with the simple direct gain band, followed by the "attached sunspace" that marks the start of the indirect gain band of the spectrum. Analogously, the opposite end of the spectrum would be occupied by the isolated gain band of passive solar systems. The system is characterized by a flat plate solar collector and thermal storage unit that are detached from one another and detached from the space to be heated. The most basic solar collector consists of a flat, highly conductive metal plate, such as aluminum, painted black for maximum absorptance and one or two panes of glass cover over the absorber plate. The width of the air space between the glazing and the plate should be approximately one twentieth the vertical length of the collector [32]. 54 The thermal storage unit relies on a natural convective cycle as the effective heat transfer mechanism between the two elements. Warmed air rises up out of the collector and over the cool rockbed as illustrated below in figure 3.16. As heat is transfered to the rocks for storage, the air is cooled and sinks through the rockbed down to the collector inlet to be warmed again. As the intensity of the solar radiation on the collector increases, the temperature of the collector rises. This effect induces a faster convective cycle through the system that considerably increases the amount and rate of heat storage. Once the sun disappears the convective cycle stops and the system shuts down [33]. Fig. 3.16. Convective cycle of an isolated gain system 55 The heat stored in the rockbed radiates through the floor slab or is vented directly into the space to be heated. Reverse convection is prevented by locating the heat storage unit above the solar collector and installing backdraft dampers as shown in figure 3.16. Flat plate collectors are used extensively for heating domestic hot water supply as described above, using water as the heat transfering medium [34]. The isolated gain solar heating system used for the Mark Jones residence in Santa Fe, New Mexico is illustrated in figure 3.17 on the following page [35]. On sunny winter days the collector outlet temperature surpasses 170 °F while the top layer of the rockbed reaches approximately 150 °F. Enough heat is stored in the rockbed during the day to comfortably heat the house throughout the evening. No auxiliary heat sources were required to heat the house during the winter of 78//79/. The temperature of the greenhouse remained in the range to support indoor plant growth. 56 supply air return air gr*«ntiou»« , e» i ____ . m * ■ . * * - 1 a . , Collector: 34 ft. long by 18 ft. wide. Collector cover: Single layer, fiber reinforced plastic. Absorber plate: 3 layers of 3/8" mesh wire lath on black galvanzed sheet metal. Storage unit: 30 tons, 1/2" to 3” diam. washed gravel fills a 4ft. deep rockbed. - Thermostat activated 1000 cfm fan suplies air entire 2650 sq. ft. house. - Greenhouse acts as return air plenum. Fig. 3.17. The isolated gain system of the Mark Jones residence [40]. The flat plate solar collector, or thermosiphoning collector, may be mounted and integrated as south face wall panels, to instantly heat the space behind it. This system which combines the elements of indirect and isolated gain functions just like the convective cycle of a trombe wall without the thermal storage. 57 The higher surface temperatures of the flat plate collector induces higher convective air flow rates. As a result, the thermosiphoning system responds much quicker to the space's daytime heating requirements. Its light mass and common construction make it the least expensive of all passive solar heating systems. Furthermore, they can be used as retrofits over existing exterior window walls [36]. Isolated gain systems have become direct gain systems and direct gain systems have become isolated gain systems. In retrospect, it is unrealistic to categorize passive solar systems by their relation with the space to be heated* All things may be categorized to help in understanding them, but this does not affect the analysis of their performance. Each system performs on its own merits as a cost efficient and practical alternative to mechanically heating a space. 58 4. THE DEVELOPMENT OF A NEW PASSIVE SOLAR HEATING SYSTEM. The passive solar systems previously described function in a small range of exterior conditions and building sizes. Besides a few successful exceptions the majority operates most effectively in locales with a high percentage of possible sunshine that do not require more than 5000 degree days of heating. Their operating capacity is limited to one and two story large single family residences. Furthermore, they are not easily adaptable to other types of buildings because their presence interrupts the functional and architectural elements of the building. In general, it is difficult to integrate them with the overall design of the building. At times they appear like an extra appendage attached to the south side of a building (in the form of isolated gain systems and sunspaces) . In the case of direct gain systems the obvious presence of massive heat storage components can create a claustrophobic effect on the occupants within the space. Often, the wall thermal storage units obstruct the occupants view of the exterior. 59 Conversely, too much of an exterior view is not good either. In direct gain space systems excessive south face glazing creates a fishbowl effect for the occupants. Moreover, the incoming direct solar radiation is too hot and uncomfortable for the occupants to work in. The objectives for the design of a new passive solar heating system are established by attempting to prevail over the shortcomings of past systems. In the author's opinion, they are listed as follows: - The system can not compromise the primary function of the building space. - The system can not be a source of physical or psychological discomfort to the occupants. - The system must integrate and conform with the overall design of the building. - The system must function as a cost effective alternative to mechanical fuel consuming, electrical heating systems. The theoretical passive solar heating system presented in the following pages attempts to fulfill these objectives for a multi-story office building located in Montreal, Canada. 60 The following sections discuss the conditions under which the system must function. It details the charac teristics and mechanics of the system in light of the objectives set forth and the factors which affect its performance. 4.1. The Passive Solar Office Building System. (the P.S.O.B. system). Internal gains due to lighting, office machinery and a central mechanical core coupled with a large floor area per story will induce a large temperature differential between the interior zone and the perimeter zone of a typical floor in a multi-story office building. Even during the winter months the interior zone must be cooled while the perimeter zone must be heated due to transmission losses. The excessive energy demands of the multi-story office building could be significantly reduced when the perimeter zone is heated by a passive solar system. Unfortunately, one of the main priorities of office building design is to maintain as much floor area as possible. Rental and retail space can not be 61 sacrificed with thick thermal storage walls, sunspaces or other space consuming passive systems. Likewise, the addition of thermal storage walls and floors require added structural support that would raise capital costs and lower floor to ceiling clearances. In the past, typical office building HVAC systems operated in setback mode during the unoccupied hours of the evening. Because modern day businesses put in longer, later work days, office buildings remain partially occupied well into the late hours of the evening. HVAC systems must now operate to maintain an acceptable level of comfort within the office space for a portion of the evening. Therefore, the passive solar system is designed to heat the perimeter of the office space during the less occupied hours of 6 pm. to 12 midnight. 62 4.2. The Mechanics of Sunlight and the P.S.O.B. System A schematic diagram of the passive solar office building (P.S.O.B.) system is illustrated in figure 4.1 on the following page. Direct solar radiation incident upon the specularly reflective light shelf is relayed towards a black phase change panel which lies along the perimeter ceiling of the space. To aim the reflected solar radiation along the perimeter ceiling of the space the light shelf is designed to rotate about its axis parrallel to the window as shown in figure 4.2 on the following page. The tilt angle of the light shelf is coordinated with any position of the sun such that the incoming ray of sunlight striking the front edge of the light shelf is reflected to strike the front edge of the phase change panel. The highly absorptive phase change panel stores the reflected solar radiation in the form of sensible and latent heat energy to be discharged later on when it is required to heat the space. 63 Fig. 4.1. The passive solar office building system. ft .CB m *n«l« W MflMlkn h Fig. 4.2. Using the light shelf to reflect solar radiation to the perimeter of the ceiling. 64 Figure 4.3 represents the solar coverage on a 15' by 6'phase change panel reflected from a 3' deep 15' long light shelf oriented half inside-half outside the perimeter. NOON I I s i I pm lOai 2 p m • am 2 pm 4pm Fig. 4.3. Solar coverage on the phase change panel for December 21st. in Montreal. 65 The thick outlines represent the solar coverage on the ceiling panel when the light shelf is tilted to cause the reflected direct solar radiation to strike the front edge of the phase change panel. For a typical December day in Montreal the light shelf rotates counterclockwise from 23° at 8 am to 10° at noon and back to 23° at 4 pm. The thin outlines represent the solar coverage on the ceiling panel when the light shelf is tilted permanently at 10° for the entire day. Constantly rotating the light shelf- would necessitate the use of a computerized motor which would increase the system's capital costs considerably. The constantly rotating light shelf would function to aim the reflected direct solar radiation within a smaller perimeter zone than actually desired. Consequently, the phase change panel is used uneconomically since heat is stored only in the front half of the panel. If this was the case, it is most likely that the panel would not be able to absorb all the radiation incident upon it. By setting the tilt angle of the light shelf at a fixed monthly position the stored heat is distributed more evenly throughout the panel, thus allowing for a 66 wider perimeter zone to be heated passively. Most importantly, the requirement of one angle setting per winter month can be accomplished manually by the occupants or the superintendant of the building. 4.3. The Optimum Tilt Angle for the Light Shelf. The optimum tilt angle for the fixed overall monthly setting is determined from the tilt angle obtained at 12 noon when the front edge reflected direct solar radiation strikes the front edge of the phase change panel (as shown in figure 4.2). Setting the angle accordingly does not guarantee the largest possible solar area on the panel, but given the conditions of the system it is the best choice. In figure 4.4, on the page following, rotating the light shelf 5° counterclockwise, 0°, and 5° clockwise increases the solar area on the ceiling panel by 8 % and 27 % respectively, while the last case is reduced 46 % compared to the 10° solar area. Notably, the solar areas, or sunspots, are reflected farther and farther from the perimeter zone (at a lesser and lesser 67 degree of intensity) to the point where the interior zone receives radiation (ie. See last case.)* tilt an«l« m I' tilt Mflt • I ' m Fig. 4.4. Size and intensity of solar coverage vs. position on phase change panel. 68 Therefore, a trade-off must be made between the amount of available solar radiation that can be provided for heat storage, the intensity of the reflected solar radiation due to the change in incident angle and the area and location within the space where the stored heat is eventually discharged. The analysis of the system is conducted under the premise that the light shelf tilt angle is set in a fixed position each month according to the tilt angle made when the reflected solar radiation strikes the front edge of the phase change panel at noon for a given winter month. 69 4.4. Thermal Storage with Phase Change Material. Since the system must conform with office building design the heavy weight, large volume and surface area associated with sensible heat storage is not acceptable as a thermal storage unit for office buildings. By locating the thermal storage unit in the ceiling plenum and reflecting the direct solar radiation on it we do not forfeit any floor space while maintaining the required surface area and volume for heat absorption and storage. Unfortunately, con vective currents impede the heat distribution to the space. The poor distributive effects of ceiling storage can be resolved by installing low cost fans along the perimeter/storage unit of the ceiling. Phase change materials (PCMs) are used as the thermal storage medium to enhance the heat storage capacity of the system. Heat is absorbed and stored characteristic of a material's specific heat and latent heat of fusion. The temperature of the material rises as sensible heat is stored until the material's melting point is reached. At this instant, the material will begin to store heat by virtue of its changing phase. 70 (As it begins to melt to liquid.) The latent heat of fusion of a material is a property used to describe its ability to store heat while it changes phase. It is defined as the amount of heat required to change the phase of one unit of mass of a substance. At any time, the heat storage capacity is defined as: Heat Storage = specific * total mass * (Tmelt - Tamb.) +... Cap. heat ...+ latent heat * mass of melted portion of fusion Solid to liquid phase change materials such as parrafin waxes Eicosane and Octadene are used as a heat storage medium for passive solar heating. They are non-corrosive and retain their initial high heat of fusion after repeated freeze thaw cycling. As raw materials they are considered expensive (0.2-1.5 ^/Btu circa 1986) and generally have low density and thermal conductivity [37]. Table 4.1 on the following page lists various types of solid to liquid PCMs. 71 Substance Melting point Heat of fusion C °F kJ/kg BTU/lb Aluminum bromide 97 207 42 18 Anthracine 96 203 105 45 Arsenic tribromide 32 89 37 16 Beeswax 62 143 177 76 Boron hydride 99 . 211 267 115 Metaphosphoric acid 43 109 107 46 Naphthalene 80 176 149 64 Naphthol 95 203 163 70 Paraffin 74 166 230 99 Phosphoric acid 70 158 156 67 Sodium 98 208 114 49 Tallow 76 169 198 85 Table 4.1. Solid to liquid PCMs [38]. A second phase change process involves the chemical reaction of hydration-dehydration [39] When hydrated materials absorb energy they "release bound molecular water" and wholly or partly dissolve in that water. The typical chemical hydration reaction for sodium sulphate decahydrate is: Na2S04 + 10 H20 ----> Na2S04 * 10 H20 + 108 Btu/lb. (241 KJ/Kg) and it occurs at a temperature of approximately 90°F (3 2°C) . Table 4.2 lists various low temperature hydration-dehydration processes. Salt hydrates have higher heats of fusion at lower transition temperatures ("melting points") and are less expensive (0.1^/Btu, circa 1986) than solid to liquid PCMs. 72 Substance Melting point °C °F Heat of fusion kJ/kg BTU/lb NH4C1 * NaS04 * 10H2O 11 52 163 70 NaCl * NH4C1 * 2NaS04 * 20H2O 13 55 181 78 NaCl * Na2S04 * 10H20 18 65 186 80 CaCl2 * 6H20 30 86 168 72 Na2C03 * IOHjjO 33 92 267 115 Na2HPQ4 * 12H20 40 104 279 120 Table 4.2 Hydration-dehydration PCMs [40]. Even though salt hydrates are better than waxes as heat storage elements they are subject to phase separation and supercooling. The salt hydrates will separate into solid and liquid phase from repeated freeze thaw cycling and, as a result, lose their high thermal storage properties. Proper packaging and chemical additives such as nucleating agents and eutectics have controlled these problems and lowered transition temperatures considerably [41]. The combined sensible and latent heat storing capabilities provide a potentially excellent dense energy storage unit within a somewhat restrictive volume of space. 73 A PCM that serves as a good heat storage unit for the system requires: - A well defined melting point slightly higher than the comfort range of the space to induce daytime storage and nightime discharge. - A high latent heat of fusion. (High energy of phase change). - A negligible degree of corrosion and expansion. - Good repeatability w.r.t. freeze thaw cycling. - High thermal diffusivity and conductivity. On the following page table 4.3 lists some types of PCMs available since 1980. Using the PCM with the highest degree of qualities listed above does not guarantee an excellent heat storage unit. Consequently, the protective envelope or container which holds the PCM must not hinder its overall performance. The type and shape of the container must take into account the poor heat transfer properties of the PCM, possible corrosion, leakage, expansion and any chemical friction that may occur between the PCM and the container. As a result, suitable packaging of PCMs have raised its overall cost significantly (up to 1 - 2 /Btu circa 1986) 142) . 74 Principal constituent and variant 1. Sodium sulfate Decahydrate U. of Delaware (borax nucl., thki M.l.T. (borax nucl.,thkr.,NaCl) Boardman 89 (proprietary) Boardman 74 (proprietary) 2. Calcium chloride hexahydrate DOW Bisol II (BaOH nucl.) Chi iarolithe (SrCl nucl.,thkr.) Suntek (BaCl nucl.) SunteX comfort (BaCl nucl., Nad) 3. Paraffin wax Sunoco P-116 Eicosane Octadecane Halt Heat of Heat point. fusion capacity °C (liquid) kJ/kg kJ/kg*°C 32 225 (init.) 3.3 > 100 - ISO 2i - 25 77 (stable value) 197 (unverified) 23 167 (unverified) 27 190 2.13 150 2.0 20 - 24* 47 209 2.5 Th. con. cost 1960 37 28 1330 1560 1520 770 2.25 4 -8 1.09 7-11 0.70 0.14 30 - 40 1. low cost, high initial heat of fusion, wide range of melt point ad justment, corrosive, requires nucleating agent, phase separation degrades heat of fusion. 2. Inexpensive, corrosive, requires nucleating agent, not as susceptible to phase separation as 1. 3. Noncorrosive, Doesn't supercool, retain initial high heat of fusion, fire resistive, low density, high conductivity, high cost. * smeared Values of variants are listed only when known to differ significantly. Table 4.3 Properties of some available PCMs [48] PCMs can be encapsulated in thick exposed containers and work best when heat is transfered through the PCM. PCM can also be encased in building materials by filling hollow concrete blocks or casting tile around flat pouches of PCM [43]. Perhaps the most effective method of "containing" PCM in a thermal storage unit is by impregnating the interior architectural surfaces with it. Studies show that a flat plate with a large surface area perpendicular to the flow of heat is the most effective shape for PCMs. The minimal thickness 75 (1/2” - 2 1/2”) of the panel eliminates the effects of thermal resistance within the material itself. Its familiar shape applies to normal building techniques, adaptable for new construction and retrofits. Moreover, the cost of PCM impregnated walls and ceilings lies mostly in the cost of the raw PCM itself [44]. Experimentation with PCM impregnated drywall has proven to be successfull. At the Centre for Building Studies of Concordia University in Montreal two types of PCMs were diffused into regular 1/2” gypsum wallboard [45]. The first solution; 45 mole percent capric acid and 55 mole percent lauric acid diluted 10% with two flame retardents melts at 63°F (17°C) and can store approximately 31 Btu/ft2 (349 KJ/m2) for a 130F (7°C) temperature increase. The second solution; 49 % butyl stearate and 48 % butyl palmitate also melts at 63°F (17°C) and can store up to 34 Btu/ft2 (382 KJ/m2) for a 13°F (7°C) temperature increase. As long as the PCM content is kept below 25 % by weight "the high surface tension of these mixtures prevents weeping of the liquid at temperatures above their melting range, so no protective envelope, which might 76 impede heat transfer, is required." Furthermore, the gypsum matrix increases the heat transfer abilities of the PCM. The initial freezing points of the PCMs are 70°F (21°C) and 69°F (20°) respectively. Thus, the PCM wallboard will either melt and absorb or freeze and emit heat depending on wether the temperature of the room is above or below the PCM temperature. If used properly and combined with minor energy conservation adjustments one can 100 % passively heat a 1184 ft2 (110 m2) house in Montreal with 3230 ft2 of PCM/wallboard. Incorporating the PCM impregnated wallboard as the thermal storage unit for the office building perimeter heating is favorable provided that it can absorb and store all the solar radiation incident upon it until about 6 pm. in the evening. Unlike the waxes used in the PCM impregnated wallboard the commercially available sun-1ite solar pod uses a proprietary salt hydrate PCM as its thermal storage medium. Its heat of fusion is 82 Btu/lb (191 KJ/kg) and "melts" at 81°F (27°C). The PCM is contained in 48" or 24" long by 16" wide rectangular fibreglass pods tapered from 2" thick at the center to 0.15" at 77 the edges as shown in figure 4.5 below. The PCM has a heat storage capacity of 400 Btu/ft2, hence the 16" by 24" pod can store up to 1200 Btus (1266 KJ) and the 16" by 48" pod can store up to 2400 Btus (2532 KJ) . The flat black coated pods are slipped into aluminum support channels and hung along the perimeter plenum similar to the way suspended ceilings are installed [46]. Fig. 4.5. The Sun-lite PCM solar pod [46]. 78 5. MATHEMATICAL MODELLING FOR SOLAR COVERAGE ON THE PHASE CHANGE PANEL. The folowing chapters deal with theoretically determining the effectiveness of the system as a passive solar space heater. Before any analysis of the system can be conducted the degree of solar coverage on the phase change panel must be determined. Hence, a two dimensional mathematical model is developed to find the proper light shelf tilt angle and the reflected solar depth into the space for any given sun position and north latitude location. A three dimensional mathematical model is developed to determine the area and shape of the reflected solar radiation on the phase change panel. Actual experimentation with a physical model placed in a heliodon is conducted to validate theoretical results. 79 5.1. Two Dimensional Development for the Light Shelf Tilt Angle and the Resulting Solar Depth. 1. The position of the sun is defined in space by its altitude angle, IX (angle AOB in figure 5.1.), and its azimuth angle, ft (angle BOD) . In order to determine the solar depth and the corresponding light shelf tilt angle, 6 , the sun's position must be resolved from three dimensional space to two dimensional space. In two dimensional space the position of the sun is defined by its profile angle $ (angle COD), which lies in a plane perpendicular to the vertical surface shown in figure 5.1. It is determined on the following page. Fig. 5.1. Sun's position defined by profile angle. 80 TAN>V = AB AB = OB TAN A (5.1) OB COS/3 — OD OD = OB COS/3 (5.2) OB TAN'S = CD CD = OD TANS (5.3) OD From figure 5.1: CD = AB Therefore equation 5.1 and 5.3 are equal. OB TANA = OD TAN& TAN2I = OB TANA Substituting equation 5.2 for OD. . . OD TAN i S = OB TAN A* = TANA OB COS/8 COS/3 Thus, the profile angle is defined as: ' f c = arcTAN/TAN A’ X I COS ft } 2. In figure 5.2 below, the incoming ray of sunlight (with its position defined by profile angle, $ ) strikes the front edge of the light shelf. The surface of the light shelf is specularly reflective such that the angle of incidence equals the angle of reflection. Based on this law the light shelf is tilted as shown so that the reflected ray of sunlight (line AB) strikes the front edge of the phase change panel. 81 R«ln R o o » 0 Where: 0 = Tilt angle of light shelf. (Uses +ve sign convention for counterclockwise rotation) "6 ss Profile angle of the sun. R = "Radius" of light shelf. Length from edge to pivot point. H = Height of light shelf. Length from pivot point to ceiling. Ssc = Distance to the start of solar coverage on phase change panel. Esc = Distance to the end of solar coverage on phase change panel. D = Depth of solar coverage. Fig. 5.2. Two dimensional analysis. 82 From triangle ABC: TAN OS +20) = BC = H + R SIN 9______ AC S - (R - R COS 9) SC Rearanging the terms... Ssc = H + R SIN 9 + R(1 - COS 9) (TAN'S + 29) (5.4) From triangle DEF: TAN Of + 20) = EF = H - R SIN 9______ DF E_ - (R - R COS 0) sc Rearranging the terms... EgC = H - R SIN 9 + R(1 + COS 9) (TANtf + 20) (5.5) Since D = Egc - Ssc , substistute equations 5.4 and 5.5 accordingly. D = H - R SIN 9 + R(1 + COS 9) - H + R SIN 9 + R(1 - COS 0) TAN(U + 20) TAN(5 + 29) D = 2R COS 0 - SIN 9_____ (5.6) TAN(S + 29) By tilting the light shelf one can position the reflected solar radiation anywhere along the ceiling but the depth of the solar coverage will vary as illustrated in figure 5.3 on the following page. As the light shelf rotates counterclockwise from the horizontal position the location of the solar coverage shifts towards the perimeter of the space. The solar depth decreases as the intensity of the solar radiation increases. As the light shelf rotates clockwise from the horizontal position the location of the solar coverage shifts towards the interior of the 83 space. The solar depth increases as the intensity of the solar radiation decreases to a point where the incoming solar radiation is reflected downwards until the light shelf tilt angle equals the profile angle. I i I Fig. 5.3. Variation of solar depth and location with tilt angle rotation. Even though the depth of the solar coverage in figure 5.3 decreases with a counterclockwise (positive) rotation, the change in the angle of incidence due to this rotation induces a much greater degree of intensity on the panel. Thus, more heat may be stored per unit area compared to the heat stored with the 84 greater solar coverage (which is induced by a clock wise rotating light shelf). This effect is analysed in detail in the following chapter. 3. The previous equations were derived without considering the effect of an overhang extending the width of the light shelf. If the ceiling to pivot point length, H, is inappropriate to accomodate high profile angles no direct sunlight will be transmitted to the back edge of the light shelf. As a result equations 5.5 and 5.6 are not applicable. Therefore, the profile angle at which the overhang begins to diminish the degree of solar coverage on the light shelf (and subsequently, the phase change panel) must be determined. The limiting angle, 0 , of figure 5.4 is a function of the profile angle, the tilt angle, H and R and is defined on the following page. 85 H - Rslnd Fig. 5.4. The point where the overhang begins to interfere with the solar coverage. TANgf = H - R SIN 9 d - arcTAN / H - R SIN 8 \ (5.7) R + R COS 9 I R + R COS 0 I If the limiting angle, 0 , is less than the profile angle the overhang will interfere with the solar coverage on the phase change panel. If the limiting angle, 0, is greater than or equal to the profile angle, the overhang will not interfere with the solar coverage on the phase change panel. 86 4. When the profile angle is greater than the limiting angle the overhang interferes with the degree of solar coverage on the phase change panel. The following derivations determine the new equations for Esc and D. Rain* tan(B-*«•••» Fig. 5.5. Two dimensional analysis with overhang effects. 87 By inspection: Y = H - R SIN 9 - R(1 - COS 9) TAN'S (5.8) Using the sine law on triangle ABC... R - X = Y NOTE; SIN(90*-)5 ) = COS'S SIN (90* -IS ) SIN (75 - 9) Rearranging the terms... R - X = Y COS &_____ (5.9) SIN ("6 - 0) From triangle BGH: TAN("6 - 20) = GH = H - R SIN 9_______ BH SgC - R(1 - COS 9) Rearranging the terms... Ssc = H - R SIN 9 + R(1 - COS 0) TAN($ - 29) (5.10) From triangle DEF: TAN(75 - 20) = EF = H - X SIN 9_______ DF EgC - (R - X COS 0) Rearranging the terms... E* = H - X SIN 9 + (R - X COS 0) TAN ("5 - 20) (5.11) Since D' = E' - S' , substitute equations 5.10 and 5.11 sc sc ' ^ accordingly. D* * H - X SIN 9 + (R - X COS 0) - H - R SIN 8 + R(1 - COS 0) TAN ("5 - 20) TAN ("5 - 20) D' = H - H - X SIN 0 + R SIN 0 + R - R - X COS 0 + R COS 0 TAN OS - 20) D' = (R - X) SIN 0 + (R - X) COS 0 TAN ("6 - 20) D' = (R - X) / SIN 0_____ + COS 0^ Substitue equation 5.9. V . TAN OS - 20) / D' = Y/ COS" 6_______SIN 0_____ + COS 0) Substitute equation 5.8. VSINOS - 0) /VTANOS - 20) / D' = (H—RSIN0—R( 1-COS0)TAN6 ) / COSS \ / SIN 0 + COS 0^ VSINOS -0)/ItAN(Y - 20) / (5.12) 88 In order to give the analysis more clarity it was conducted assuming a clockwise rotation to be positive even though the sign convention previously dictated a counterclockwise rotation to be positive. Changing the sign of the light shelf tilt angle in equations 5.10, 5.11, 5.12 prompts the following equations: S4C = H + R SIN 8 + R(1 - COS 9) Same as equation 5.4. TAN(b + 29) EgC = H + X SIN 9 + (R - X COS 9) (5.13) TAN ("5 + 29) D* = (H + R SIN 9 - R(1 - COS 9)TAN"& ) * . . . (5.14) 89 The tilt angle of the light shelf is determined by choosing a specific value for Ssc. Meaning, one chooses precisely where the front edge of the phase change panel is located and determines the corresponding tilt angle by trial and error. This is simply accomplished with the use of an iterative computer program run on a hand held calculator. The program, "SUNCOVE", also takes into account overhang effects. It will indicate when the overhang interferes with the solar depth and calculates the adjusted value for it (equation 5.14) when necessary. 90 5.2. Three Dimensional Development for the Solar Area and Shape on the Phase Change Panel. The following analysis is conducted by considreing rays of sunlight to act like three dimension directional unit vectors. The effects of solar radiation striking the tilted light shelf and reflecting onto the phase change panel can be modelled using matrix multiplication methods. 1. Determination of the "Bounce" Matrix. The bounce matrix is used to model the specular reflection of solar radiation incident on a horizontal surface as illustrated in figure 5.6 on the following page. The incoming ray of sunlight is defined as a vector in three dimensions such that for a right- handed coordinate system... [ I ] - [ C0SP<C0SjS COSAr SIH/3 - S IN A ] The reflected outgoing ray of sunlight is defined as a vector in three dimensions such that for a right- handed coordinate system... _[ R ] = [ cosA COS/3, cos A sin/3, S IN A ]___________________ 91 The bounce matrix is defined as [ b ], such that: MAY Fig. 5.6. Mathematical modelling of specularly reflective surface. Therefore: CCOSA CO S/3 COSA SIN/? -SINAI 0 -1 CCOSA COS/3 COSA SIN/3 The bounce matrix is: -lJ 2. Determination of the "Transformation" Matrix. The transformation matrix is used to model the tilt of the light shelf about one of its centroidal axes. The transformation matrix is defined as [ T ], such that : [ T ] X X' Y 5= Y' Z Z' j i expresses a vector defined in universe X-Y-Z in terms of universe X'-Y'-Z'. Fig. 5.7. Mathematical modelling of the tilting light shelf. 93 Point A, in figure 5.7 is defined in the X-Z universe as a point (X,Z) and is represented in terms of the X#-Z# universe as: X = X' COS 9 - Z' SIN 8 (5.15) Z = X* SIN 0 + Z* COS 0 (5.16) Now, one must define point A in the X'-Z' universe as a point (X/,Z/) and define it in terms of the X-Z universe... Rearranging equation 5.15... X' = X + Z* SIN 0 (5.17) COS 0 and substitute into equation 5.16. Z = X + Z’ SIN 9 SIN 0 + Z’ COS 0 COS 0 Z = X SIN 0 + Z' SIN20 + Z' COS 0 NOTE: SIN20 COS 0 COS 0 = 1 - cos20 Z = X SIN 0 + Z'(1 - COS20) + Z’ COS 0 COS 0 COS 0 Z = X SIN 0 + Z' - Z’ COS 0 + Z' COS 0 COS 0 COS 0 Rearranging the terms... Z' = Z COS 0 - X SIN 9 (5.18) Substitute equation 5.18 into equation 5.17 to obtain • • • X' = X + SIN 0 (Z COS 0 - X SIN 0) COS 0 COS 0 X' = X + Z COS 0 SIN 0 - X SIN20 COS 0 COS 0. COS 0 2 2 Substituting 1 - COS 9 for SIN 0 and breaking up last term... 94 x' = X + Z COS 6 SIN 9 - X + X COS 9 COS 0 COS 9 COS 0 COS 9 X* = x ~ x + Z SIN 0 + x cos 0 COS 0 X' = X COS 0 + Z SIN 0 (5.19) To summarize: X' = X COS 0 + Z SIN 9 Z' = - X SIN 9 + Z COS 9 Equations 5.19 and 5.18 are put into matrix form... ‘ COS© SIN0" [X1 X'- .-SIN0 COS0. L ,Z'. Any point in the X-Z universe may be defined in the X'-Z* universe. In three dimensions... COS0 0 SIN0 0 1 0 ‘x X* Y = Y’ .Z. .Z’ . The transformation matrix is: ' COS0 0 SIN0' ' COS0 0 -SIN0' [T] - 0 1 0 tT]'1 = 0 1 0 .-SIN0 0 COS9. . SIN0 0 C0S9. ...transforms vectors from the X-Y-Z universe to the X'-Y'-Z' universe. To transform a vector from the X'-Y'-Z' universe to the X-Y-Z universe one multiplies by the inverse of the transformation matrix shown 95 3. Matrix Modelling for the Solar Coverage on the Phase Change Panel. In figure 5.8 on the following page the light shelf is tilted in the counterclockwise direction (positive rotation) by degrees so that the reflected ray of sunlight will always strike the front edge of the phase change panel (fixed in space of universe X-Y-Z). Therefore, points Za2 and Zj^ are constant and equal to the vertical distance from the pivot point to the ceiling, H. The following steps explain how the solar shape and area of sun coverage on the phase change panel is determined using the previously developed matrix models. 96 ( N 5 + Fig. 5.8. Matrix modelling for the P.S.O.B. system 97 3a. The incoming ray of sunlight defined as the direction vector [ I ], in universe X-Y-Z, strikes the light shelf. The light shelf is tilted by degrees counterclockwise, which implies that it is laying flat in the X'-Y' plane of the X'-Y'-Z' universe. Thus, the incoming ray vector must be transformed to a vector defined in the X'-Y'-Z' universe. Thus, [ T ] [!]=[!'] COS 9 0 0 1 ■SIN9 0 SIN9 0 COS9J COS A COS/S COS> SIN£ -SIN A- . COS A- COSJ0 COS 9 - SIN* SIN9 COS* SIN/3 .-COS* COS(S SINS - SIN* COS9 3b. The new incoming ray vector, defined in universe X'-Y'-Z' as [ I'], reflects off the specular surface of the light shelf. Thus, [ I'] must be multiplied by the bounce matrix to determine the reflected outgoing ray vector. Thus, [ b ] [ I'] = [ R'] '1 0 o' ■ 0 1 0 ,0 0 -1. COS* COS£ COS9 - SINA- SINS COS* SIN/3 COS* COS/S COS9 - SIN* SIN9" COS* SIN/3 , COS* COS/3 SIN9 + SIN* COS9. 98 3c. The reflected ray vector, defined in the X'-Y'-Z' universe as [ R'], will strike the phase change panel. Since the phase change panel lies in the X-Y-Z universe the reflected ray vector must be transformed from the X'-Y'-Z' universe back to the X-Y-Z universe. Therefore the reflected ray vector must be multiplied by the inverse transformation matrix. Thus, [ T ]-1 [ R'] = [ R ] COS© 0 -SIN0" ‘ COSA COS/3 COS0 - SINA- SIN0' 0 1 0 COSA SIN = . SIN© 0 COS0. .COSA COS/3 SIN0 + SINA COS©. 2 o COSA COS/3 COS 0 - SINA SIN0 COS0 - COSA CO S/3 SIN^0 - . . . . . - SINA COS©.. SIN© COSA- SIN/3 COSA COS,S COS0 SIN0 - SINA SIN20 + COSA COS/8 SIN0 COS0 + . . . . . . + SINA COS2© . COSA COS/S (COS20 - SIN20) - 2 SINA SIN0 COS0' COSA SIN/3 .2 COSA COS/3 COS0 SIN0 + SINA (COS20 - SIN20) . ‘COSA COS/3 COS20 - SINA SIN29' COSA SIN/S .COSA COS/8 SIN20 + SINA COS20. This matrix is the unit directional vector for the reflected ray defined in the X-Y-Z universe. It will be referred to as the "unit vector**. 99 The unit vector is the vector sum of . . . X comp. • l = COS COS COS 2 - SIN SIN2 Y comp. j = COS SIN Z comp. z = COS COS SIN2 + SIN COS 2 3d. Points A2 and B2 on the phase change panel are determined from the unit vector as follows: COSA COS/3 COS29 - SINA SIN29 COSA SIN/3 COSA COS/S SIN29 + SINA COS29 ("A" scalar) xa2 - Xai X*2 " *al LZa2 ~ Zal ...is used to define point A2 on the phase change panel. The unit vector matrix is multiplied by a scalar quantity, "A", in order to give the reflected ray vector from the front edge of the light shelf a scaled magnitude defined by the value na2 - nal. COSA COS0 COS 2 9 - SINA SIN29 ("B" scalar) [Xb2 - xbl‘ COSA SIN/3 = Yb2 ’ Ybl .COSA COS/3 SIN29 + SINA COS20, ,h>2 ' Zbl. ...is used to define point B2 on the phase change panel. The unit vector matrix is multiplied by a scalar quantity, HBW, to give the reflected ray vector from the back edge of the light shelf a scaled magnitude defined by nb2 ~ nbl* 100 3e. Coordinates on the Phase Change Panel due to a Ray Reflected from the Front Edge of the Light Shelf. rCOSA COS* SIN29 + SINA-COS20] ("A" scalar)- = Z&2 “ zai Where; Za2 - Zal = H - (- R SIN 0) = H + R SIN 0 From figure 5.10. ("A" scalar) = H + R SIN 0_________ = H + R SIN 0 COS/V COS/3 SIN29 + SINA- COS20 Z comp For the X coordinates... Xa2 “ Xal = (COSA COS/3 COS20 - SINA- SIN20) Where Xa^ = - R COS 0 From figure 5.9 Z nco«e Fig. 5.9. Determining the X coordinates 101 For the Y coordinates__ a2 al Z comp. From figure 5.10. TAN/3 R(1 - COS 0) G = R(1 - COS 8) TAN(3 Rearranging the terms... According to the coordinate system of figure 5.9 Y al where W represents the half-length of the light shelf. Thus; al = R(1 - COS 0) TAN(3 - W and Z comp. Fig. 5.10. Determining the Y coordinates 102 3f. Coordinates on the Phase Change Panel due to a Ray Reflected from the Back Edge of the Light Shelf. [COSA COS/3 SIN29 + SINA C0S29J ("B" scalar) = Zfa2 - Zfcl Where; Zfa2 - Zbl = H - (R SIN 9) = H - R SIN 9 From figure 5.10 ("B" scalar) = H - R SIN 9_________ = H - R SIN 9 COSA COS/3 SIN29 + SINA COS29 Z comp. For the X coordinates... Xfa2 - Xfc,! = (COSA COS/3 COS29 - SISASIN29) I * H - R SIN 91 Z comp. J Where; = R COS 9 From figure 5.9. Therefore; Xb2 = (X comp.) I " H - R SIN 91 - R COS 9 L Z comp. J For the Y coordinates... Y 2 " Ybl = (COSA SIN/3 ) I " H - R SIN 91 [ Z comp. J From figure 5.10. TAN/3 - GJ__ _ R(1 + COS 9) Rearranging the terms... G' = R(1 + COS 9) T2UJ/5 According to the coordinate system of figure 5.9 Ybl = G' - W where W represents the half-length of the light shelf. Thus; Ybl = R(1 + COS 9) TAN/3 - W and Yb2 = (Y comp.) I " H - R SIN 91+ W - R(1 + COS 9) TAN/3 L Z comp. J 103 A computer program, "SUNAREA", was written for use with a hand held calculator which accomplishes two, otherwise arduous tasks, quite easily. Firstly, it calculates the coordinates of points A2 and B2 on the phase change panel for the inputted altitude, azimuth and tilt angles, light shelf dimensions, R and W, and the distance from the pivot point to the ceiling, H. The values of the four extreme coordinates are displayed on the screen so that the shape of the solar area may be plotted as shown in figure 5.11 below. Secondly, it calculates the reflected solar surface area on the phase change panel given the aforementioned input values. \ A2 tVub ■<c O' • Vails O IN IR A L D IR IC TIO N OR INCOMING RAYS Fig. 5.11. Solar coverage on phase change panel. 104 "SUNAREA" coupled with "SUNCOVE" provide an excellent and extensive perspective on the degree of solar access for any given light shelf/phase change panel size and configuration in any city located in the northern latitude. The concept of using directional unit vectors and matrix multiplication to theoretically model the natural and un-natural transmission paths of the sun provides an excellent passive and active solar system preliminary design aid. Before committing oneself to physical full scale testing a theoretical analysis can be conducted using the concepts presented in this chapter. The designer can determine the degree of solar radiation available on the collector surface of their own theoretical passive or active solar system. The concepts discussed previously incorporated with other feasibility studies can give the designer a clear perspective on the capabilities of the preliminary design long before the results of physical tests can be made available. 105 5.3. Verification of Theoretical Results. A scale model, 1/50 th the actual size was constructed for testing in University of Southern California, school of Architecture's heliodon. The dimensions and configuration of the P.S.O.B. system are illustrated in figure 5.12 below. The heliodon was set for a typical December day in Los Angeles, California (34° N. Lat.) for the hours of 9 am (3 pm), 10 am (2 pm), 11 am (1 pm) and 12 noon. 1 3’ i . . . . . .—isgy • » n C Fig. 5.12. Heliodon test model. The incandescent ’ ‘sunlight" reflected off of the south face tilted light shelf casts a sunspot on the translucent flimsy covered plexiglass which serves as 106 the phase change panel of the P.S.O.B. system. The tilt of the light shelf (ie. glass mirror) is set by inspection since one can actually see the reflected "sunlight" on the sidewalls of the model. The light shelf is adjusted until the reflected sunlight reaches the front edge of the plexiglass. Theoretically, "SUNCOVE" was used to determine the corresponding december tilt angles in Los Angeles. "SUNAREA" was used to find the solar coordinates on the phase change panel and the shape of the solar coverage was plotted as illustrated in figure 5.13 on the following page. The experimental results obtained are displayed alongside the theoretical output . Comparatively, there are no pathological differences between the crude experimental and theoretical results. Their resemblance is similar enough that the experimental results corroborate the theory. 107 x ^ ? * ^ ~ * - -***- > » * ■ * *< v ,vs/^ * ^ ?y -' j f - * L ^ -sK^ %AJ"' Vs * ^ ^ S f r g " ^jv^X « " 3 , ^ - - ' . ; ■ » -ilE'or^ * i.flSV*, ; j^r. *. -». ■xL j \ 4 . ■ Fig. 5.13. Theoretical vs. experimental results for December 21st. in Los Angeles. 108 6. ANALYSIS 07 THE P.S.O.B. SYSTEM. A heat balance of the perimeter zone is conducted to determine the amount of lost heat that can be recovered when the P.S.O.B. system is incorporated into the perimeter zone of the office building. To simplify the analysis it is assumed that the phase change panel is capable of absorbing all the solar radiation incident upon it and retaining the energy, in the form of sensible and latent heat, until 6 pm. in the evening. At this time the mechanical heating system will be set back. When the temperature of the space drops below that of the phase change panel it will begin to discharge the stored heat. It is also assumed that since the volume of the heat storage unit is so small the panels will discharge all of the stored heat between the hours of 6 pm. and 12 am. The heat balance equation compares the total amount of heat lost to the total amount of heat gained from 6 pm. to 12 midnight. The losses consist of transmission and ventilation losses and the internal gains consist of lighting, machinery, people and the contribution of the discharged heat from the phase change panel. 109 A base case heat balance is conducted in order to determine the relative effectiveness of the system. Its performance is investigated for the winter months from October through to March. The adaptability and sensitivity of the system is examined by modifying the location of the light shelf with respect to the perimeter edge of the building and the position of the phase change panel on the ceiling. Figure 6.1, on the following page, illustrates the three configurations of the P.S.O.B. system and the base case. Furthermore, the sensitivity of each configuration case is studied by changing the depth of the light shelf (2R) and the pivot point to ceiling height (H) of the system. 110 case A case B case C base case Fig. 6.1. Three configurations of the P.S.O.B. system and the base case. Ill 6.1 Obtaining the Amount of Solar Radiation Available for Storage. Solar radiation data is supplied by the Atmospheric Environment Service of Canada. Tables 6.1 and 6.2 contain the hourly global solar radiation and the hourly diffuse sky radiation falling on a horizontal surface for each month of the year and averaged over each available period of record. The radiation station located at Jean Brebeuf College in Montreal, Quebec (45.3° N.Lat., 73.37° W.Long.) has been recording global and diffuse radiation used in this analysis from 1964 to 1980. The hourly direct solar radiation falling on a horizontal surface (for a typical day of a given month) is computed by subtracting the diffuse component of solar radiation from the corresponding global solar radiation and converted to standard english units (Btu/ft2). (See table 6.3.) Since the recorded solar radiation is an average hourly value taken over 15 years it automatically takes into account an average degree of cloudiness for every hour of a typical day of each month. Therefore, it is not necessary to multiply the direct solar radiation by a sun cover reduction coefficient. 112 O o o o M b © M o o o o o o o b © b © o » « o o b o o o o b o N O b o <0 m o o o o b o b b o e o o o o < o Table 6.1. Global solar radiation falling on a horizontal surface in Montreal. (MJ/m ) Table 6.2. Diffuse solar radiation falling on a horizontal surface in Montreal. (MJ/m2) 113 Time Global Diffuse Radiation Radiation Direct Radiation MJ/m2 Btu/ft 8 am 9 am 10 am 11 am 12 pm 1 pm 2 pm 3 pm 4 pm 5 pm 0.01 0.16 0.40 0.63 0.75 0.74 0.61 0.42 0.17 0.02 0.01 0.11 0.25 0.37 0.43 0.41 0. 35 0.25 0.11 0.01 0.00 0.05 0.15 0.26 0.32 0.33 0.26 0.17 0.06 0.01 0.00 4.41 13.22 22.91 28.20 29.08 22 .91 14.98 5.29 0.88 Table 6.3. Computation of direct solar radiation falling on a horizontal surface for December 21st in Montreal. The data recorded is for the intensity of solar radiation falling on the horizontal surface of an Eppley/Kipp Pyranometer. It takes into account the effect the angle of incidence has on the intensity of the incoming solar energy. Consequently, the intensity of the solar radiation on the phase change panel requires some adjustment because the incidence angle between the reflected direct radiation and the normal of the panel is altered by the tilted light shelf. Thus, one must consider the effect of the change in the intensity of the available solar radiation incident on the phase change panel. As discussed earlier, a counterclockwise rotation of the light 114 shelf induces a smaller angle of incidence between the reflected solar radiation rays and the normal of the horizontal panel. As a result, the intensity of the incident solar radiation increases. A clockwise rotation of the light shelf induces a greater angle of incidence between the reflected solar radiation rays and the normal of the horizontal panel. The following calculations derive the correlation between the direct solar radiation data of table 6.3 and the P.S.O.B. system. From figure 6.2, on the following page, the incident angle of the incoming solar radiation falling on a horizontal surface is defined as i^, such that: i1 = 90° - 3 The incident angle of the reflected solar radiation from the light shelf striking the phase change panel is defined as i2, such that: i2 = 90° -3-29 The intensity of the incoming direct solar radiation falling on a flat surface as a function of its incident angle is defined by the cosine factor as: T1 " xdn COS(90° - $) (6.1) 115 M INCOMING RAY Fig. 6.2. Deriving the k-factor. The intensity of the reflected direct solar radiation striking the flat surface of the phase change panel as a function of its incident angle is defined by the cosine factor as: X2 = Jdn COS (90° - IS - 20) (6.2) Since the hourly value of 1^ is determined using the Canadian Climate Normals, vol. 1 (solar radiation), I2 will be defined as a function of 1^ . . . 116 from eqn. 6.1 : Idn = IC0S(90o - 75 ) from eqn. 6.2 : Idn = I2/ C0S(90o - t- 2G) therefore: i0 = COS(90° -75 -_2©) I-j COS(90° - $ ) I2 = k I1 such that: k = C0S(90o -■$- 2©) COS (90° -t ) Where "k" is a function of the profile angle and the tilt angle of the light shelf and will be refered to as the k-factor. The above equation can be simplified: COS (90°- c - 2©) » COS(90°-75 ) COS (20) + COS(75)SIN(2 ) and COS (90° -T5 ) = SIN7$ SIN(90° -■$ ) - COS^S Using these trigonometric identities one obtains: COS (90°— 7S - 2©) - SIN (75) COS (2©) + COS fff) SIN (2©) = SIN(7$ + 26) Therefore: k = SIN(TS + 26) (6.3) SlN (75) Equation 6.3 is applied for the "best" fixed light shelf tilt angle of 10° and the corresponding profile angles of a typical December day. The light shelf is 3' by 15" and is oriented half inside/half outside the perimeter of the space (Case B.l. R = 1.5', H = 1.5'). 117 The resulting k-factors and radiation intensities are calculated below... Time Profile angle k-factor Radiation intensity outside BTU/ft Radiation intensity on panel BTO/ft2 9 am 12 .17 2.53 * 4.41 zs 11.16 10 am 17.55 2.02 * 13.22 ss 26.70 11 am 20.25 1.87 * 22.91 = 42.84 12 pm 21.20 1.82 * 28.20 = 51.32 1 pm 20.25 1.87 * 29.08 = 54.38 2 pm 17.55 2.02 * 22.91 = 46.28 3 pm 12.17 2.53 * 14.98 = 37.90 4 pm 1.86 11.47 * 5.29 = 60.68 Table 6.4. Intensity of direct solar radiation on phase change panel. A positive counterclockwise rotation (the tilt angle is greater than zero) will induce k-factors greater than 1.00. For example, a k-factor of 1.82 at 12 pm (see above) implies that the intensity of the direct solar radiation incident on the phase change panel is 1.82 (82%) times greater than the direct solar radiation falling on a horizontal surface outside. Conversely, a negative clockwise rotation will induce k-factors less than 1.00, which implies that the intensity of the direct solar radiation incident on the phase change panel is k times lesser than the 118 intensity of the direct solar radiation falling on a horizontal surface outside. A k-factor of 1.00 implies the light shelf is horizontal and the intensities are equal. The data obtained from the Atmospheric Environment Service's Canadian Climate Normals for the intensity of the solar radiation on a horizontal surface is an ideal value. Realistically, there are several factors which affect the intensity of the solar radiation. These factors serve as series "resistances" or reduction coefficients which diminish the intensity of the solar radiation on the phase change panel. Before the incoming direct solar radiation strikes the reflective surface of the light shelf it must be transmitted through two panes of clear 3/32" thick glass with a 1/4" air space. In a cold temperate climate such as Montreal it is common practice to use double insulating glass for the window glazing. Figure 6.3 on the following page illustrates the variation of the transmittance with the incidence angle for double strength sheet (A) , 1/4" clear (B) and 1/4" heat absorbing (C) glass. 119 None of these curves represent the transmissive effects of double insulating glass therefore a curve must be developed. Since the curves of the DSA (A) and clear (B) glass are practically parallel for incidence angles between 0° and 60° it is reasonable to assume that the transmission/incidence curve for the double insulating glass would be similarly parallel and adjusted for its solar transmittance directly normal to the surface. The Libbey, Owens, Ford Glass Company manufactures a clear double insulating glass that transmits 77 % of the direct normal solar radiation. 0j--1 --1 — - r 1 ‘ T. ' V A \\ ■ \ \V 2 — 0 , . J__ L ,,X— c-\ i __i __i _3 INC10CNT ANGLE. 0 Fig. 6.3. Transmissivity of three types of glass as a function of the incidence angle [8]. 120 In an attempt to find a simple and conservative linear equation which reasonably defines the transmission effects through double insulating glass, parallel line DE of FG of glass A or B is transferred down to the 77% direct normal transmittance value of the glass. This is illustrated in figure 6.4 on the following page. The linear equation of line JK for angles of incidence between 0° and 60° is defined as: 't ■ 77% - ( 8%/60°)© ... where 0 is the angle of incidence and it is defined as: 6 = arcCOS ( COSA; COS/3 ) The linear equation of line KL, for incidence angles between 61° and 70° is similarly determined and defined as: - 69% - (14%/10°)(© - 60°) 121 0.8 0.6 < 0.4 C C i — 0.2 60 90 30 0 INCIDENT ANGLE, 0 Fig. 6.4. Development of transmission/ incidence curve for double insulating glass. Thus, the degree of transmitted solar radiation is a function of the type of glazing unit used and the altitude and azimuth angles of the sun. Table 6.5 calculates the hourly transmittance for a typical December day from the equations on the previous page. 122 Time Altitude Azimuth Incidence Transmittance angle angle angle percentage 8am/4pm 1.09 54.11 54.11 69.79% 9am/3pm 8.99 42.79 43.54 70.79% 10am/2pm 15.27 17.55 35.59 72.52% 11am/1pm 19.47 16.56 25.35 73.62% 12 noon 21.20 0.00 21.20 74.17% Table 6.5. Transmittance of double insulating glass for December in Montreal. The percentage of solar radiation reflected off of the light shelf depends on the reflectivity of the specular surface. Table 6.6 [47], on the following page, lists the specular reflectances of various reflective materials. In this analysis the light shelf is assumed to reflect 90% of the incident solar radiation. A dirt depreciation factor of 95% is combined with the reflectance to account for possible dust and dirt particle build up on the light shelf. The effective reflectance of the light shelf is: (0.90 * 0.95) 100% = 85.50% 123 Substance Reflectance Silver (unstable as front surface mirror) 0.94 ±0.02 Gold 0.76 t 0.03 Aluminized acrylic, second surface 0.86 Anodized aluminum 0.82 ± 0.05 Various aluminum surfaces - range 0.82 -0.92 Copper 0.75 Back-silvered water-white glass 0.88 Aluminized type-C Mylar (from Mylar side) 0.76 Table 6.6 Reflectances of specular surface coatings. The surface absorptance of the phase change panel is greatly improved when it is coated with a layer of flat black paint. In this analysis the surface of the phase change panel is assumed to absorb 95% of the solar radiation incident upon it. Incidentally, the Sunlite solar storage pod is manufactured with a black coating for maximum absorptance. The combined surface "resistance" for the light shelf's reflectance and the phase change panel's absorptance is: (0.8550 * 0.95) 100% = 81.23% (a constant value) To obtain the actual intensity of the direct solar radiation available for storage, the hourly intensity of direct radiation in table 6.4 is multiplied by the corresponding transmittance of table 6.5 and the 124 effective surface "resistance" of the system. The actual intensity of direct solar radiation on the phase change panel is calculated and tabulated in table 6.7 below. Time Ideal Direct Transmittance R. Actual Direct Solar * Solar Radiation Surface R. Radiation (Btu/ft ) (%) (Btu/ft2) 9 am 4.41 57.50 6.43 10 am 13.22 58.91 15.74 11 am 22.91 59.80 25. 62 12 pm 28.20 60.25 30.92 1 pm 29.08 59.80 32.52 2 pm 22.91 58.91 27.27 3 pm 14.98 57.50 21.78 4 pm 5.29 56.69 34.41 Table 6.7. Actual hourly direct solar radiation available for storage on the phase change panel for a December day in Montreal. The amount of heat available for storage is calculated simply by multiplying the hourly intensity of the actual direct solar radiation by its corresponding solar area. The reflected solar area on the phase change panel for any sun position is calculated using the equations developed in the previous chapter. "SUNCOVE" and "SUNAREA" are used to determine the “best" tilt angle (set at a fixed monthly position) 125 and solar area for each light shelf depth (R) of each configuration case for each winter month. For example: a light shelf, 3' deep (R=1.5'and H=l.5') by 15' long (W=7.5/) that is oriented half inside and half outside the building perimeter (Case B) will generate the following coordinates and solar areas for the "best" fixed light shelf tilt angle of 10° in table 6.8. The shape of the solar area for each daylight hour of the December day is illustrated in figure 4.3. Time <fi?) (& ? > 9 am 1.32 -4.49 3.45 10 am 0.81 -5.88 3.09 11 am 0.60 -6.73 2.94 12 pm 0.53 -7.50 2.89 1 pm 0.60 6.73 2.94 2 pm 0.81 5.88 3.09 3 pm 1.32 4.49 3.45 4 pm 2.91 0.94 4.57 Solar Amount of Area (ft2) Heat Ener< (Btus) -2.64 23.52 151.14 -4.63 29.03 456.80 -6.08 32.53 833.38 -7.50 35.39 1093.82 6. 08 32.53 1057.86 4.63 29.03 791.66 2.64 23.52 512.35 -1.21 12.19 TOTAL 419.46 5318.47 Note: The origin of the X-Y-Z axis is located at the centroid of the light shelf and follows the sign convention posed in figure 5.8. Table 6.8. Amount of heat energy available for storage 126 6.2. Sizing The Phase Change Panel. The size of the phase change panel is governed by three factors and the stipulation that all the available solar radiation incident on the phase change panel will be absorbed and stored. The sizing factors are: The amount of heat enegy that the panel can store, the placement of the solar coverage on the phase change panel and the effective thermal conductivity of the panel. A total o/ 5318.47 BTUs of solar radiation is available for storage over a typical December day in Montreal. Since the depth of the reflected direct solar radiation extends, at the most, 4.57 ft. into the space (In table 6.8, Xb2 - 4.57' at 4 pm.) it would seem logical to have a phase change panel that is 4.57' deep by 15' long. A 1/2H thick piece of gypsum wallboard impregnated with Butyl Palmitate- Stearate PCM can store up to 34 BTU/ft2. Therefore, the 4.57' by 15' phase change panel can store as much as 2331 BTUs of the 5318.47 BTUs (44%) available for storage. 127 When increasing the depth of the phase change panel to store more heat we rely on the thermal conductivity of the PCM/wallboard panel to uniformly spread the received solar radiation (mostly located in the first 3 ft. of the panel) throughout the whole panel. Theoretically, a thermally conductive panel which extends 8.0' into the space (7.5' deep) can store up to 3825.00 BTUs of heat energy. The overall thermal conductivity of the Butyl Palmitate-Stearate impregnated wallboard ranges from 0.1196 BTUh/ft.°F in the solid phase to 0.1277 BTUh/ft.°F in the liquid phase. These values are far too low to assume that the thermal conductivity of the PCM/wallboard phase change panel will conduct the absorbed heat initially concentrated in one area throughout the whole PCM/wallboard panel. It is not within the scope of the thesis to determine the inherent conductive characteristics of the phase change panel. It was determined that in February, a P.S.O.B. system with the same size and configuration as that of table 6.8 must store a maximum of 7151 BTUs over a solar depth which extends 4.13' into the space. 128 Assuming that the heat storage capacity with respect to the wallboard thickness of the phase change panel is linearly proportional, one can say that since a 1/2” thick Butyl Palmitate - Stearate impregnated wallboard can store 34 BTU/ft2 then a 2” thick sample can store four times as much available heat energy (136 BTU/ft2). Therefore, a 2" thick PCM/wallboard panel can store: 4 * 34 BTU/ft2 * 3.63' * 15' = 7405.20 BTUs which accomodates all of the available solar radiation for a typical February day in Montreal. Note that the solar depth is 4.13' long but the phase change panel is only 3.63'long (4.13' - 0.5'). In conclusion, the size of the phase change panel is set at 5.5' deep by 15' long. 6" of space between the perimeter edge of the space and the phase change panel is reserved for construction clearance and is insulated to prevent heat loss between the panel and the exterior. Moreover, the top of the phase change panel is also insulated to prevent heat transfer to the ceiling plenum as shown in figure 6.5, on the following page. 129 Fig. 6.5. Insulated phase change panel. The thickness of the phase change panel will depend on the amount of solar radiation available for storage on a typical day in Montreal which generates the greatest amount of heat energy over all the other winter months. If the thickness becomes prohibitive, other materials, such as the sunlight storage pod, would have to be considered. 130 6.3. Conducting a Heat Balance of the P.S.O.B. System. The following heat balance is conducted for the south face of the office building perimeter zone. A zone increment is defined as a space 8 ft. deep by 15 ft. long by 9 ft. high. The heat losses and heat gains are calculated from 6 pm. to 12 midnight for the winter months of October through to March for the following light shelf to perimeter zone orientations: Configuration Case A: Light shelf is oriented all out side perimeter edge of space. Case Al: R = 1.5', H - 1.5' Case A2: R = 1.0'f H = 1.0' Case A3: R = 0.5', H - 0.5' Configuration Case B: Light shelf is oriented half in side/half outside perimeter edge of space. Case Bis R = 1.5', H = 1.5' Case B2: R = 1.0'# H = 1.0' Case B3: R = 0.5', H = 0.5' Configuration Case C: Light shelf is oriented all in side perimeter edge of space. Case CIS R = 1.5', H - 1.5' Case C2: R = 1.0', H - 1.0' Case C3: R - 0.5', H = 0.5' 131 Many general assumptions must be made in order to conduct a realistic heat balance of the space. The trend for any assumptions made in this thesis tends to lean towards a conservative, worst case scenario. Therefore, the results obtained are induced by minimum values for internal gains, maximum values for heat losses and maintaining a simple and inexpensive building envelope and light shelf construction (to keep capital and construction costs to a minimum). The analysis is broken down as follows; a. Mean daily temperature history for Montreal. Used to determine interior - exterior temperature differentials. b. Calculation of internal gains for heat balance of the P.S.O.B. system. c. Calculations of heat losses for heat balance of the P.S.O.B. system. d. Development of base case heat balance to use as a relative measurement of the system's performance. e. Calculation of the thermal resistance for light shelf-overhang assembly. f. Heat balance of case A configurations. g. Heat balance of case B configurations. h. Heat balance of case C configurations. 132 6.3a. Mean Dally Temperature History of Montreal, Que. Mean daily outdoor temperature data is supplied by the Atmospheric Environment Service of Canada in degrees Celsius and converted to degrees Fahrenheit. The data presented below in table 6.8 are the arithmetic averages taken over a period of record of 20 to 24 years. Mean Daily Mean Daily Mean Daily Mean Daily Max. Temp. Min. Temp. Temp. Temp. Swincr °c °F °c °F °C °F °C F Jan. -6.1 21.02 -13 .4 7.88 -9.8 14.45 7.3 13.14 Feb. -5.3 22.46 -12.4 9.68 -8.9 16.07 7.1 12.78 Mar. 1.4 34.52 -5.7 21.74 -2.2 28.13 7.1 12.78 Oct. 12.4 54.32 5.4 41.72 8.9 48.02 7.0 12.60 Nov. 5.0 41.00 -0.6 30.92 2.2 35.96 5.6 10.08 Dec. -3.3 26.06 -9.8 14.36 -6.6 20.21 6.5 11.70 Table 6.9. Mean daily temperature data for Montreal, Quebec. Hourly temperature data is determined by fitting the mean daily temperature variations to a sine wave such that one cycle is equal to one diurnal cycle. It is assumed that the maximum temperature occurs at 2 pm. (14 hrs) in the afternoon and the minimum temperature occurs at 2 am. (2 hrs) . 133 Hence, the hourly outdoor temperature as a function of time is; T(t) - Tme + AT/2 [27T (t - 8 hrs.)/24 hrs.] (6.4) where; TmeaQ = Mean daily temperature AT = Mean daily temperature swing, t = Time of the day in hours. Thus, one obtains the following hourly mean temperatures tabulated in table 6.10 below. Time Jan. Feb. Mar. Oct. Nov. Dec. °F °F °F °F °F °F 6 pm/18 hrs 17.74 19.27 31.33 51.17 38.48 23.14 7 pm/19 hrs 16.15 17.72 29.78 49.65 37.26 21.72 8 pm/20 hrs 14.45 16.07 28.13 48.05 35.96 20.21 9 pm/ 21 hrs 12.75 14.42 26.48 46.39 34.66 18.70 10 pm/2 2 hrs 11.17 12.88 24.94 44.87 33.44 17.29 11 pm/2 3 hrs 9.80 11.55 23.61 43.57 32.40 16.07 12 am/2 4 hrs 8.76 10.54 22.60 42.56 31.60 15.14 Table 6.10. Mean Hourly Temperature in Montreal. (6 pm. - 12 am.) 134 6.3b. Calculation of Internal Gains. Perimeter zone of office space: 8* * 15' * 9' Lighting gains = 1.8 Watts/ft2 * 3.41 BTUh/Watt * 8’ * 15' = 736.56 BTUh Machinery gains = 0.8 Watts/ft2 * 3.41 BTUh/Watt * 8' * 15' = 327.36 BTUh Therefore, Lighting + Machinery gains = 1063.92 BTUh Occupancy gains = (81 * 151) * 255 BTUh/occ.(sensible heat only) 100 sq.ft/occ. = 306.00 BTUh The values for lighting and machinery gains are abstracted from California title 24, building energy performance requirements. The value for the office occupancy gains derives from two sources. The heat gain rate per person for seated occupants doing light office work (ASHRAE fundamentals, 1981) generates 255 BTUh/occ. (sensible). The space requirement of 100 sq.ft. per occupant is abstracted from the office occupancy load for fire safety (U.B.C. 1985) The above values for the internal gains are adjusted according to the machinery, lighting and office occupancy Schedules listed in table 6.11 on the following page. 135 The schedules are abstracted from the California title 2 building energy requirements suggested for use in computer simulations of offices. Time am - 7 am 8 am am - 11 am 12 noon 1 pm 2 pm pm - 5 pm 6 pm pm - 9 pm Office Occupancy Schedule 0% 30% 100% 80% 40% 80% 100% 30% Time 1 am 8 9 am 11 am 1 3 . 10% 10 pm - 12 am 5% pm pm 5 6 7 8 9 10 11 pm - 7 am am - io am - 12 pm - 2 pm - 4 pm pm pm pm pm pm pm - 12 am Machinery Lighting Schedule 5% 80% 90% 95% 80% 90% 95% 80% 70% 60% 40% 30% 20% Table 6.11. Office set back schedules. The setback schedules generate the following values for the internal gains of the perimeter space from 6 pm to 12 midnight. (Table 6.12, next page). 136 Time Occupancy Lighting £ M Gains Gains BTUs BTUs 6 pm 91.80 851.14 7 pm 30.60 744.74 8 pm 30.60 638.35 9 pm 30.60 425.57 10 pm 15.30 319.18 11 pm 15.30 212.78 12 am 15.30 212.78 TOTAL 229.50 3404.54 Table 6.12. Hourly internal gains of the perimeter space. The sum of the individual hourly gain components is a constant value of 3634.64 BTUs for the time interval of 6 pm to 12 midnight. The calculation of the internal gains in the space are considered to be conservative since it applies to occupancy, lighting and machinery schedules that represent a lesser degree of evening activity than that posed in this thesis. Schedules which reflect the actual degree of activity could not be reasonably determined thus, the schedules posted in table 6.10 were used as a solid but conservative reference. It is most likely that the actual office occupancy schedule would deviate most from the schedules outlined in table 6.11. Fortunately the occupancy gains only account for 6.74% of the 137 total gains. Therefore its deviation with respect to the actual total gains would be minimal. 6.3c. Calculation of Heat Losses. The hourly transmission heat loss is defined as: q - U0A0(Ta - Tc) (6.5) Where: UQ = The overall design heat transfer coefficient of a given wall section. AQ = overall surface area of a given wall section. Ta = Interior ambient temperature. Assumed to be 70 °F. TQ = Outside temperature. The hourly ventilation heat loss is defined as: q - Cp^ V(Ta - Tq) (6.6) Where: Cp = Specific heat of air, 0.24 BTU/lb°F 5 = Density of air, 0.075 lb/ft3 V = Volumetric air change rate = 2.0 ACH (9'*15'*8") Note that the 2.0 air changes per hour derive from an office space requiring 8 air changes per hour, 1/4 of which is fresh air coming in at TQ that must be heated to Ta. 138 To simplify the heat balance analysis the indoor/outdoor total monthly temperature differential £(Ta- Tq) , is calculated and tabulated in table 6.13 below. Equations 6.5 and 6.6 can be combined as follows: Stotal = C uoAo + CP8^ ](Ta - T0) (6.7) where the first term will be referred to as the ••Total Loss Coefficient". Time Jan. Feb. Mar. Oct. NOV. Dec. °F °F °F °F °F °F 6 pm 52.26 50.73 38.67 18.83 31.52 46.86 7 pm 53.85 52.28 40.22 20.35 32.72 48.28 8 pm 55.55 53.98 41.87 21.98 34.04 49.79 9 pm 57.25 55.58 43.52 23.81 35.34 51.30 10 pm 58.83 57.12 45.06 25.13 36.56 52.71 11 pm 60.20 58.45 46.39 26.43 37.60 53.93 12 am 61.24 59.46 47.40 27.44 38.40 54.86 TOTAL 399.18 387.55 303.13 163.97 246.20 357.73 Table 6.13. Sum of hourly temperature differences. 139 6.3d. Base case development:. A BASE CASE configuration/building envelope must be established which serves as a relative yardstick to compare with the results of the P.S.O.B. system con figuration cases. From the Canadian climate normals supplied by the Atmospheric Environment Service of Canada: For Montreal: Degree days below 18 °C = Degree days below 65 °F = 4430.1 8006.2 9’ ASHRAE standard 90-7 5, "Energy Conservation in New Building Design", defines the suggested minimum overall heat transfer coefficient of the building envelope as a function of the number of degree days of heating. For type "B" buildings (non- res idential) over 3 stories high and 8000 degree days of heating specifies : UQ - 0.28 BTUh/ft2.°F Fig. 6.6. Base case 140 For this analysis, the building envelope of the wall section in figure 6.6 and all similar sections must maintain the required value of UQ. The total loss coefficient for the base case is calculated as follows: Therefore: = 0.‘ 28 BTUh/ft2'°F * 9’ *15’ = 37.80 BTUh/°F and Cpotf = (0.24 BTU/lb'°F) (0.075 lb/ft3).(2.0 air changes) * ... ... * (9’ * 15’ * 8') = 38.88 BTU/°F The total loss coefficient, (UqAq + Cp^V) = 37.80 + 38.88 =76.60 BTU/°F The total heat losses are defined as (UqAq + CpgV)(ZI(Ta - T0)) and are tabulated below . Note that'ZL(Ta - TQ) is the total value taken from table 6.12. Month Total Total percent Losses (BTUs) Gains(BTUs) recovery Jan. 76.60 * 399.18 S S 30609 3634.64 11.9% Feb. 76.60 * 387.55 = 29717 3634.64 12.2% Mar. 76.60 * 303.13 — 23244 3634.64 16% Oct. 76.60 * 163.97 S S 12573 3634.64 29% Nov. 76.60 * 246.20 as 18879 3634.64 19% Dec. 76.60 * 357.73 = 27431 3634.64 13% Table 6.14. Heat balance results of base case. 141 The data organized for each size of each configuration case will be tabulated in 7 columns: Month of the year, corresponding tilt angle, total losses, passive gains due to P.S.O.B. system, total gains, percent recovery of losses and percent improvement over the established base case. 6.3e. Thermal Resistance of the Light Shelf /Overhang Assembly. The Light shelf construction is supported by a lightweight aluminum frame approximately l" thick in total cross section. 1/2” Expanded plain polystyrene insulation fills the space in between the aluminum framing. Two sheets of 1/4" fibreglass are applied to the top and bottom surface of the light shelf. A specularly reflective film is applied to the top surface of the light shelf. In reality, the light shelf would most probably be thicker than 1" because the aluminum frame must be designed to span 15 ft. The top and bottom overhangs also use a lightweight aluminum frame approximately 2" thick in total cross- section. The space between the framing is filled with 142 1" of expanded plain polystyrene insulation board. 1/2" Gypsum board sheathing is applied to the interior surface of each overhang . The exterior surfaces are finished with a 1/2" layer of gypsum plaster. The thermal resistances of each component of the light shelf/overhang assembly is computed as follows: a. Light Shelf Resistance. - Inside air film. Since the inside surface of the light shelf is specularly reflective, its emmisivity is low. This induces a higher resistance. R = » 1.70 ft -F/BTUh - Fibreglass Sheathing. 1/4" Soda lime glass. k = 0.59 BTUh’ft/ft2-°F and L = 0.25V12, , /, - 0.0208' R = L/k For 2 layers: R = 0.0706 ft2-°F/BTUh - Insulation. 1/2" Expanded plain polystyrene (R4>. R = 2.00 ft2 *°F/BTUh - Inside air film, other side of light shelf. R = 0.68 ft2*°F/BTUh TOTAL: R = 4.4506 ft2-°F/BTUh 143 b. Top Overhang Resistance. - Inside air film. r = 0.61 ft2-°F/BTUh - Gypsum board. 1/2" thick. R = 0.45 ft2.0F/BTUh - Insulation. 1" Expanded plain polystyrene (R4) . R = 4.00 ft2-°F/BTUh - Gypsum plaster. 1/2” Lightweight aggregate. R = 0.32 ft2 *°F/BTUh - Outside air film. R = 0.17 ft2.°F/BTUh TOTAL: R = 5.55 ft2-°F/BTUh Bottom Overhang Resistance. - Inside air film. R = 0.92 ft2‘°F/BTUh - Gypsum board. 1/2" thick. R * 0.45 ft2*°F/BTUh - Insulation. Same as in b. R = 4.00 ft •°F/BTUh - Gypsum, plaster. Same as in b. R » 0.32 ft *°F/BTUh - Outside air film. R = 0.17 ft2*°F/BTUh TOTAL: R = 5.86 ft2*°F/BTUh d. Top Light Shelf Window. - Double insulating glass, 3/32” thick, 1/4" air space. Winter/nightime overall U = 0.58 BTUh/ft2-°F, U = 1/R R = 1.72 ft2 *°F/BTUh 144 6.3f. HEAT BALANCE OF CASE "A" CONFIGURATION. The light shelf is located entirely outside the perimeter of the building and balanced for light shelf sizes of 3', 2' and 1' depth. The overall thermal resistance of the light shelf/overhang assembly inside the boxed-in area of figure 6.7 must be determined. A weighted average of the thermal resistance of the top and bottom overhangs and the light shelf window is calculated and combined as resistors in parallel. The combined resistance is added to the resistance of the light shelf in series. Top overhang: R'= 5.55 ft2-°F/BTUh * 0.25 = 1.5 ft. * 15 ft 1/R' = 16.21 BTUh/°F Bottom overhang: R'= 5.86 ft2,°F/BTUh * 0.25 = 0.0651 <JF/BTUh 1.5 ft. * 15 ft. 1/R'= 15.36 BTUh/°F bottom overhang top overhang Fig. 6.7. case A config. 0.0617 °F/BTUh 145 Light Shelf Window; R'= 1.72 ft2•°F/BTUh * 0.50 = 0.0191 °F/BTUh 3 ft. * 15 ft. 1/R'= 52.33 BTUh/°F Total 1/R'= 83.89 BTUh/°F and R' = 0.0119 °F/BTUh Therefore; R = 0.0119 °F/BTUh * (3 ft. * 15 ft.) = 0.5364 ft2-°F/BTUh This value is added to the resistance of the light shelf. <ie. Resistors in series.) The overall resistance for the inner box is; RbOX * 4.4506 ft2 *°F/BTUh + 0.5364 ft2*°F/BTUh * 4.987 ft *°F/BTUh CASE A.1 : R = 1.5' and H = 1.5'. 0.5 1 . 5 3 The overall design heat transfer coefficient for the case A.1 wall section above is calculated using: 146 UoverallAoverall * uboxAbox + ^top overhangAtop overhang + * * * ^bottom overhangAbottom overhang + • * * uwindow/wallAwindow/wall (6.8) UboxAbox = ^-/^box * Abox = 3 ft. * 15 ft. = 9.018 BTUh/°F 4.99 ft2-°F/BTUh Utop overhangAtop overhang = l/Rtop overhang * Atop overhang = 1.5 ft. * 15 ft. = 4.054 BTUh/°F 5.55 ft2-°F/BTUh ubot. overhangAbot. overhang * l/^bot. overhang * Abot. overhang = 1-5 ft. *15 ft. = 3.840 BTUh/°F 5.86 ft2-*F/BTUh ^window/wallAwindow/wall = ^-/Window/wall * Window/wall * 6 ft. * 15 ft. » 25.210 BTUh/°F 3.57 ft2>°F/BTUh Therfore: Uovera2lAoverall ~ 42.122 BTUh/°F and A0verall = ft. (6 ft. + 1.5 ft. + 1.5 ft. + 3 ft.) - 180.00 ft2 The total loss coefficient is: 42.122 BTUh/°F + 38.88 BTUh/°F TLC * 81.00 BTU/°F for a 1 hr. interval. The TLC is multiplied by 21 (Ta“ To) ea°h month to determine the total losses for a typical day of the month (ie. apply equation 6.7). The results of the heat balance for case A.l are tabulated on the following page. 147 Total Passive Total Tilt losses gains gains % % Month angle BTUs BTUs BTUs rec. impr. Jan. -1 32334 4479.66 8114 25% 13% Feb. -7 31392 5177.23 8812 28% 16% Mar. -13 24554 4320.56 7955 32% 16% Oct. -7 13282 4255.14 7890 59% 30% Nov. -1 19942 3237.88 6873 34% 15% Dec. 1 28976 3187.20 6822 24% 11% Table 6.15. Results of case A.I. The light shelf assembly does not supply any additional thermal resistance to the building envelope. In fact, it tends to draw more heat out of the space because the overall heat transfer coefficient of the entire light shelf/ overhang assembly is higher than UQ of the window/wall. The TLC for the base case is 5.43% lower than the TLC for case A.I. The effect of these extreme losses derives from the reduced resistance of the light shelf assembly coupled with the extended surface area of the building facade. (180 ft2 instead of 135 ft2.) Furthermore, the negative clockwise tilt angles induce a greater area of solar coverage and a reduced solar intensity on the phase change panel which works against this configuration and the ones to follow. 148 CASE A.2 : R - 1.0' and H « 1.0' 0.5' 2 The overall design heat transfer coefficient for case A.2 is calculated using equation 6.8 as follows: For the boxed in wall section: uboxAbox = 2 ft. * 15 ft. =6.01 BTUh/°F 4.99 ft2-°F/BTUh For the top overhang: utop overhangAtop overhang = ^ = 2-70 BTUh/°F 5.55 ft *0F/BTUh For bottom overhang: ubottom overhangAbottom overhang = . 1-„° ft- * I?. = 2,56 BTUh/°F 5.86 ft^* F/BTUh For the window/wall: Uwindow/wall^indo.v/wall = 0.28 BTUh/ft^*°F * 7 ft. * 15 ft. = 29.40 BTUh/^F Therefore: Uoverall^verall = 40-67 BTUh/°F_________________ 149 The total loss coefficient is: 40.67 BTUh/°F + 38.88 BTUh/°F TLC » 79.55 BTU/°F for a 1 hr. interval. The results of the heat balance for case A.2 are tabulated below. Total Passive Total Tilt losses gains gains % % Month angle BTUs BTUS BTUs rec. impr Jan. -21 31755 2996.08 6631 21% 9% Feb. -8 30830 3624.71 7259 24% 12% Mar. -14 24114 3017.00 6652 28% 12% Oct. -8 13044 3023.86 6659 51% 22% Nov. -2 19585 2201.15 5836 30% 11% Dec. 0 28457 2127.01 5761 20% 7% Table 6.16. Results of case A.2. The addition of the light shelf still causes the building envelope to lose more heat than the base case. In this case, it loses 3.85% more heat than the base case while the system passively discharges 29% to 33% less heat than in case A.I. This is due to the reduced size of the light shelf and the greater tilt angles in the clockwise direction ("intensity reduction" direction). 150 CASE A.3 : R = 0.5' and H = 0.5' 0.5' 0.5’ -----2 wmmMrnim .4 " c 1 ----- 1 7 ----= ------ 0. 5 The overall design heat transfer coefficient for case A.3 is calculated using equation 6.8 as follows: For the boxed in wall section: UboxAbox = 1 ft. » 15 ft. =3.01 BTUh/°F 4.99 ft2*°F/BTUh For the top overhang: Otop overhangAtop overhang = 0.5 ft. * 15 ft. - 1.35 BTUh/°F 5.55 ft^.OF/BTUh For the bottom overhang: ^bottom overhangA^ttQjj, overhang = = i*28 BTUh/°P 5.86 ft • F/BTUh For the window/wall: ^indow/wall^indow/wall " 0*28 BTUh/ft ,0F * 8 ft. * 15 ft. =33.61 BTUh/°F Therefore: Uo g e r a l l A „ „ . r an ° 3 9 ' 2S B T O h / ° F _________________________________ 151 The total loss coefficient is: 39.25 BTUh/°F + 38.88 BTUh/°F TLC = 78.13 BTUh/°F for a 1 hr. interval. The results of the heat balance for case A. 3 are tabulated below. Total Passive Total Tilt losses gains gains % % Month angle BTUs BTUs BTUs rec. impr. Jan. -4 31188 1421.64 5056 16% 4% Feb. -9 30299 1931.02 5566 18% 6% Mar. -16 23684 1530.04 5165 22% 6% Oct. -9 12811 1622.45 5257 41% 12% Nov. -4 19236 1054.03 4689 24% 5% Dec. -2 27949 997.37 4632 17% 4% Table 6.17. Results of case A.3. The addition of the light shelf assembly continues to work against the thermal resistance of the building envelope. The reduced size of the light shelf and the greater "intensity reducing" tilt angles account for passive system gains 62% to 69% less than a light shelf three times as large (case A.l). 152 In conclusion, it would seem illogical to design a system that defeats its own purpose. Thus, the thermal resistance of the light shelf assembly should be redesigned to obtain a lower heat transfer coefficient than that used for the window/wall of the building envelope (ie. UQ .LE. 0.28 BTUh/ft2.°F). If this were the case, increasing the size of the light shelf reduces heat losses and increases passive gains. Moreover, the light shelf should be oriented with respect to the phase change panel in order to induce a counterclockwise light shelf rotation. Thus, one may obtain improved energy dense solar areas for a given light shelf size and configuration. 153 6.3g. HEAT BALANCE OF CASE "B" CONFIGURATION. In this case, the light shelf is located half inside and half outside the perimeter of the building. It is balanced for light shelf depths of 3', 2' and 1' respectively. The thermal resistance of the boxed-in light shelf assembly for case B configurations is the same as the thermal resistance of the boxed-in light shelf assembly for case A, Such that; Rbox = 4‘" ft2.°F Calculating the overall heat transfer coefficient for the following light shelf sizes combines R^x as a resistor in parallel with the thermal resistance of the window/wall. The equation is defined as: ^overall^overall - ^box^box + ^window/wall^window/wall (6.] "1 top overhang w indow ' bottom overhang ! o T Fig. 6.8. Case B config. light shelf 154 CASE B.l : R = 1.5' and H - 1.5' os' 1.5 The overall design heat transfer coefficient for case B.l is calculated using equation 6.10 as follows: UboxAbox = 3 ft. * 15 ft. =9.02 BTUh/°F 4.99 f t"* •'■'F/BTUh ^window/wall^indow/wall = 0.28 BTtJh/ft *°F * 6 ft. * 15 ft. = 25.20 BTUh/°F Therefore: UoverallAOVerall = 34’22 BTUh/°F The total loss coefficient is: 34.22 BTUh/°F + 38.88 BTUh/°F TLC = 73.10 BTU/°F for a 1 hr. interval. The results of the heat balance for case B.l are tabulated on the following page. 155 Total Passive Total Tilt losses gains gains % % Month angle BTUs BTUs BTUs rec. impr Jan. 8 29180 6571.43 10206 35% 23% Feb. 2 28330 7150.67 10785 38% 26% Mar. -5 22159 5757.66 9392 42% 26% Oct. 2 11986 6080.23 9715 81% 52% Nov. 8 17997 5208.50 8843 49% 30% Dec. 10 26150 5559.88 9195 35% 22% Table 6.18. Results of case B.l. 156 CASE B.2 : R = 1.0' and H = 1.0' o s ' The overall design heat transfer coefficient for case B.2 is calculated using equation 6.10 as follows: ' W W = 2 ft. ; 15 ft. =6.01 BTUh/°F 4.99 ft*"• wF/BTUh ^indow/wall^indow/wall = 1 3 *28 BTUh/ft^*°F * 7 ft. * 15 ft. = 29.40 BTUh/ F Therefore: UoverallAoverall = 35-41 BTUh/°F The total loss coefficient is: 35.41 BTUh/°F + 38.88 BTUh/°F TLC ■ 74.29 BTU/OF for a 1 hr. interval. The results of the heat balance for case B.2 are tabulated on the following page. 157 Total Passive Total Tilt losses gains gains % % Month angle BTUs BTUs BTUs rec. impr Jan. 6 29655 4261.35 7896 27% 15% Feb. 0 28791 4765.54 8400 29% 17% Mar. -7 22520 3877.94 7513 33% 17% Oct. 0 12181 4197.58 7832 64% 35% Nov. 6 18290 3428.95 7064 39% 20% Dec. 8 26576 3446.36 7081 27% 14% Table 6.19. Results of case B.2 158 CASE B.3 : R = 0.5' and H = 0.5' 0.5 0.5’ 0.5 0.5 The overall design heat transfer coefficient for case B.3 is calculated from equation 6.10 as follows: ^boxAbo> 1 ft. * 15 ft. =3.01 BTUh/°F 4.99 ft *°F/BTUh ^indow/wall^Srfindow/wall 0*28 BTUh/ft^*°F * 8 ft. * 15 ft. = 33.60 BTUh/°F Therefore: D0VerallA0verall = 36’61 BTUh/°F The total loss coefficient is: 36.61 BTUh/°F + 38.88 BTUh/°F TLC = 75.49 BTU/°F for a 1 hr. interval. The results of the heat balance for case B.3 are tabulated on the following page. 159 Total Passive Total Tilt losses gains gains % % Month angle BTUs BTUs BTUs rec. impr. Jan. 1 30134 1951.61 5586 19% 7% Feb. -5 29256 2321.03 5956 20% 8% Mar. -12 22883 1764.36 5399 24% 8% Oct. -5 12378 1987.50 5622 45% 16% Nov. 1 18586 1438.27 5073 27% 8% Dec. 3 27005 1405.05 5040 19% 6% Table 6.20. Results of case B.3. The TLC for each light shelf size of case B was lower than the TLC of the base case due to its improved thermal resistance, (ie. U-value for light shelf assembly was less than Uc of 0.28 BTUh/ft2,°F for the window/wall.) The improved thermal resistance is a result the reduced surface area of case B conf igurations. Consequently, the reduced light shelf size induces a lesser degree of solar coverage on the phase change panel compared to that obtained with case A con figurations. Fortunately, this does not adversely affect the system because the phase change panel is positioned closer to the light shelf in case B than in case A. In case A configurations the distance from the centroid of the light shelf to the front edge of the 160 phase change panel is 2.0', 1.5' and 1.0' respectively. In case B configurations the centroid to the front edge of the phase change panel distance is always 0.5'. Therefore, most case B configurations require positive counterclockwise light shelf tilt angles to ensure proper location of the solar coverage on the phase change panel. As a result, the intensity of the direct solar radiation increases and case B configurations absorb a great deal more heat energy than their case A counterparts. The greater centroid-to-edge in case A implies that the light shelf must rotate more in the clockwise direction than case B to ensure proper location of the solar coverage on the phase change panel. As mentioned previously in this text, a clockwise rotation produces larger areas of solar coverage. Unfortunately, it also produces a considerable decrease in the intensity of the direct solar radiation incident on the phase change panel. For this reason Case A configurations do not store a greater degree of solar radiation than its case B counterparts. 161 In conclusion, case B configurations are clearly more effective than case A configurations due to their increased degree of available heat energy for storage and added thermal resistance of the building envelope. This raises the issue of the cost effectiveness of increased insulation versus increased insolation. Furthermore, the reduced overhang depths of case B systems do not truncate the use of the built-up area on the site as much as case A configurations. 162 6.3h. HEAT BALANCE FOR CASE "C" CONFIGURATIONS. The light shelf is located entirely within the perimeter of the building space. Thus, case C systems do not have any overhangs which impinge on the possible built-up area of the building. It is assumed that the light shelf does not offer any thermal resistance to the building envelope therefore the total losses for case C configurations are the same as the total lossses for the base case. - i - Fig. 6.9. Case C configuration. 163 CASE C.l : R = 1.5' and H - 1.5' 1.5* t = 2 t . ^----- u - 1 .....t 7 " Total Passive Total Tilt losses gains gains % % Month angle BTUs BTUs BTUs rec. impr Jan. 28 30609 8785.17 12420 41% 29% Feb. 23 29717 9734.94 13370 45% 33% Mar. 16 23244 8128.68 11763 51% 35% Oct. 23 12573 8742.94 12378 98% 70% Nov. 28 18879 7250.16 10885 58% 38% Dec. 30 27431 8517.59 12152 44% 31% Table 6.21. Results of case C.l. 164 CASE C.2 : R * 1.0' and H « 1.0' 0.5' » 2 Total Passive Total Tilt losses gains gains % % Month angle BTUs BTUs BTUs rec. impr Jan. 24 30609 5906.22 9541 31 19 Feb. 19 29717 6527.88 10163 34 22 Mar. 12 23244 5406.90 9042 39 23 Oct. 18 12573 5886.06 9521 76 47 Nov. 24 18879 5300.30 8935 47 28 Dec. 27 27431 5915.10 9550 35 22 Table 6.22. Results of case C.2. 165 CASE C.3 : R = 0.5' and H = 0.5' 0.5’ 0.5’ 0.5’ Month Tilt angle Total losses BTUs Passive gains BTUs Total gains BTUs rec. impr. Jan. 13 30609 2653.12 6288 21% 9% Feb. 7 29717 2753.30 6388 21% 9% Mar. 0 23244 2394.79 6029 26% 10% Oct. 7 12573 2657.24 6292 50% 21% Nov. 13 18879 2274.54 5909 31% 12% Dec. 16 27431 2467.98 6103 22% 9% Table 6.23. Results of case C.3. The light shelf must rotate counterclockwise from 16° to 30° in case C.l, from 12° to 27° in case C.2 and from 0° to 16° in case C.3 to ensure proper location of the solar coverage on the phase change panel. As a result the intensity of the solar radiation incident on the phase change panel available for storage is considerably greater than the solar energy available 166 in cases A and B even though the areas of solar coverage are smaller. For example, case C.l obtains a solar area of 30.75 ft2 at noon in December compared with a solar area of 43.16 ft2 for the corresponding case A. 1 configuration. Likewise, the case C.l has a k-factor of 2.73 compared with that of 1.09 for case A.I. Since the light shelf is constructed entirely within the space it would serve as an excellent retrofit P.S.O.B. system. Consequently, it does not impinge on the built up area of the site. Comparatively, the building envelope surface area is smaller and the degree of construction is less complex for case C configurations than cases A and B. Hence, the overall construction and capital costs will be considerably less than those for cases A and B. It is only unfortunate that the system does nothing to complement the architecture of the building facade. In conclusion, case C is the most effective P.S.O.B. configuration out of the three cases analysed. It produces the greatest amount of heat storage at the lowest cost. 167 7. THE COST EFFECTIVENESS OF THE P.S.O.B. SYSTEM. All the objectives set forth in chapter four have been fulfilled except the final one. . . Is the system a cost effective alternative compared to mechanical heating? The results from the heat balance of cases A, B and C indicate that the incorporation of the P.S.O.B. system into the perimeter space would recover an additional percentage of the heat lost (over the initial percent recovery due to internal gains) from as low as 4% (in case A.3, Jan.) to as high as 70% (in case C.l, Oct.). In reality, the percentage of recovered heat is only a relative indicator of how each configuration performs with respect to itself. Meaning, that if the cost of energy is extremely high, perhaps even a 4% recovery may render the system as a cost effective alternative to mechanical heating. An implementation study of the P.S.O.B. system is conducted based on the cost of mechanically heating the building using natural gas as the fuel source. 168 The cost of natural gas supplied by Gaz Metropolitain of Montreal is broken down as shown: The base cost of natural gas: $ .10725 per cubic meter consumed. The gas is imported from Alberta therefore, a transportation and distribution fee which is a function of the rate of consumption is added to the base cost accordingly: 0 to 1000 cubic meters consumed; $ .11788/m;? 1001 to 3200 cubic meters consumed; $ .11081/m3 3201 to 10000 cubic meters consumed; $ .10416/m3 The transporatation and distribution fee is divided into seven additional price tiers based on consunption rates from 10001 m3 to anything over 100000000 m3. An interim rate adjustment of $ .0339/m3 is charged over the top to cover capital and construction costs of various projects throughout the province. Thus, for the first 1000 cubic meters consumed the total cost of energy is $ .25552/m3, or 25.552 per cubic meter of consumption. There are 35301 BTUs of energy in one cubic meter. This equates to $ 7.24 per million BTUs. The amount of cash saved over the year by using the P.S.O.B. system is calculated in table 169 7.1, below, for the highest degree of available solar radiation on the phase change panel, case C.l: Equivalent Energy Month Monthly passive gains, BTUs Consumption M saved $ Jan. Feb. Mar. Oct. Nov. Dec. 8785.2 9734.9 8128.7 8742.9 7250.2 8517.6 * 31 = 272340 * 29 = 282313 * 31 = 251989 * 31 = 271031 * 30 = 217505 * 31 = 264045 7.71 8.00 7.14 7.68 6. 16 7. 48 1.97 2.04 1.82 1.96 1. 57 1.91 Totals 1559223 44.17 11.27 Table 7.1. Cost analysis of the system. Since this is the amount of heat delivered directly to the space the value of $ 11.27 is multiplied by an efficiency factor of 1.25, which is indicative of a mechanical system with an efficiency of 80% The highest degree of solar coverage on the phase change panel will save $ 14.09 worth of energy per half year (Oct. to Mar.) All other configurations will induce even a smaller amount of cost "savings". With respect to cost feasability, the P.S.O.B. system is completely ineffective as an alternative perimeter space heating source. 170 Why does the P.S.O.B. system perform so inadequately? The intensity of the average hourly direct solar radiation falling on a horizontal surface in Montreal is considered very low for passive solar heating. The data obtained are values which take into account the average hourly degree of cloudiness over the specified period of record. The reduced intensity due to the high average degree of cloudiness in Montreal is especially significant in December when the direct solar radiation is needed most. When first determining the potential cost savings of the system it was believed that the lack of available solar radiation was the sole reason for the exceedingly low results. To test if this was the case, the same size and configuration case was tested for the location of Boulder, Colorado. Boulder experiences a total average of 192 hours of December sunshine [48] compared with a total average of 78 hours in Montreal [49]. For December, one obtains a cost savings of only $ 18.88 in Boulder ($ 15.10 * 1.25) compared to $ 2.39 in Montreal ($ 1.91 * 1.25). Hence, even though the intensity of direct radiation falling on a horizontal 1 171 surface is very low in Montreal, the inherent problem lies primarily within the design and sizing of the system itself. The strict limitations set forth in attempting to comply with the office design parameters render the system inadequate to provide a worthwhile degree of passive heating. The PCM/wallboard research conducted by Shapiro et al [50] indicates that to passively heat 1184 square feet of floor area one requires approximately 273% (3230 sq.ft.) more surface area of PCM/wallboard within the space. Analogously, 328 square feet of 1/2" thick PCM/wallboard would be required to the office perimeter zone of 120 sq.ft. The present P.S.O.B. system utilizes only 82.5 sq. ft. of 2" thick PCM/wallboard. Incidentally, the volume of space occupied by each PCM/wallboard scheme is equal. This confirms the basic premise that a good passive solar design requires a large absorptive surface area (solar collector). In an attempt to fit the P.S.O.B. system within the prescribed zone this basic premise, for the most part, was forsaken. As a result, the required solar coverage was not achieved and the system's passive output is considered insignificant. 172 8. CONCLUSION. The passive solar office building system does not function on a cost effective basis in an office building scenario, although the concepts developed in this thesis, and the information obtained from them, prove to be quite interesting. The concept of using directional unit vectors and matrix multiplication to theoretically model the natural and modified transmission paths of the sun provides an excellent preliminary design aid for passive and active solar systems, determining shadow paths and designing buildings according to their solar envelope. The tool developed to evaluate this process remains a primary product of this research and may warrant further examination in the future. Consequently, the ideas presented in this thesis can be easily adapted to daylighting design fundamentals. Perhaps one can use the tilting light shelf to reflect sunlight to the otherwise dark areas of a deep interior space. The provision of additional daylight can replace a portion of the artificial lighting in a 173 space and serve to reduce the interior cooling load of that space as well. Moreover, it is likely that the presence of natural daylight in an otherwise unnatural setting can only benefit the occupants of the space. In retrospect, it appears that the constraints imposed upon the system may have been too severe to permit the required amount of solar coverage on the phase change panel. Thus, some of the limitations established in order to develop the concepts which were applied to the system may be slackened to induce a greater degree of energy storage in the phase change panel. The primary constraint imposed on the system is the limited size of the light shelf. Using a wider light shelf cuts down on vertical window viewing and horizontal floor space. For example, a 4 ft. case B light shelf reduces the built up area of the site by 2 ft. depth on its south side, cuts the window height down to approximately 3.5 to 2.5 ft. during the night and lowers the ceiling height to approximately 7 to 8 ft. within a 2 ft. perimeter depth of the space during the day. Thus, the following recommendations are made in order to increase the solar coverage on the panel without increasing the size of the light shelf. 174 The sidewalls included in the three dimensional mathematical modelling of the system's light shelf- overhang construction of case A and B may be removed to provide a greater degree of solar coverage on the phase change panel. Eliminating the sidewalls which flank the ends of the light shelf permits from 10% (at 11 am/1 pm) to, as much as, 66% (at 9 am/3 pm) more direct solar radiation on the phase change panel. The opaque top overhang of the light shelf-overhang assembly can be replaced and constructed with transparent material that permits the transmission of solar radiation as well as daylight. This alteration is most effective during the months of February, March and October. During these months the sun's position above the horizon is high enough to induce overhang interference of potential p.c. panel insolation. If the top overhang is transparent the resulting passive gains would be high enough to passively heat the space 100% (without any mechanical assistance) from 6 pm. to 12 am. This is provided that the phase change panel has the capacity to store all the solar energy incident upon it. 175 Incorporating the two recomendations into one entity renders a light shelf-overhang assembly such as those illustrated in figure 8.1, below. As an architectural element of the facade this proves to be quite interesting. Fig. 8.1. New light shelf-overhang assemblies, As noted, the system did not perform effectively on a quantitative basis, mostly due to its size and partly due to its location. Logically, incorporating a larger passive system in a space which complements its usage and is situated in a warmer and sunnier climate seems to be a valid recomendation. In this thesis, we have learned that the space should not be an office building located in Montreal (especially because of the high percentage of cloud cover). 176 On a qualitative basis, the benefits of this passive system remain unexplored. It is the author's opinion that a full scale testing model complete with office occupants would provide favourable information concerning the degree of human comfort in this space. In general, it is believed that the addition of the passive system to the perimeter zone of an office building would function to increase the mean radiant temperature of the space adjacent to the cool window surfaces. In effect, it would improve the degree of human comfort within the space. In closing, it is believed the concept of reflecting solar radiation towards properly located heat storage units (which may or may not incorporate PCMs) can still be successfully achieved, especially when making use of the recommendations discussed earlier. For now the relation between passive solar heating and solar mathematical modelling remains an untapped and innovative facet of building science which definitely warrants future research. 177 9. ACKNOWLEDGEMENTS. I would like to thank Prof. Marc Schiler for his timely input, patience and guidance throughout the course of this thesis. Without his assistance this thesis would have never materialized. I would also like to thank Prof. Ralph Knowles for the use of his heliodon . 178 11. REFERENCES. 1. ASHRAE Handbook of Fundamentals 1981, American Society of Heating, Refrigerating and Air Conditioning Engineers, Inc., Atlanta, Georgia, 1981, p. 27.2. 2. Mazria, E., The Passive Solar Energy Book, Rodale Press, Emmaus, Pa., 1979, pp. 8 - 10. 3. Kreith, F. and J.F. Kreider, Principles of Solar Engineering, McGraw-Hill Book Company, New York, 1978, p. 172. 4. Mazria, 1979, pp. 11 - 12. 5. Mazria, 1979, p. 14. 6. Anderson, B., et al., Passive Solar Design Hand book, Part One; Total Environmental Action, Inc., Van Nostrand Reinhold Company, New York, 1984, p. 18. 7. Anderson, 1984, p. 20. 8. ASHRAE Handbook of Fundamentals, 1981, p. 27.14, Fig. 11. 9. Kreith and Kreider, 1978, p. 170. 10. Kreith and Kreider, 1978, p. 173. 11. ASHRAE Handbook of Fundamentals, 1981, p. 27.14, Fig. 12. 12. Kreith and Kreider, 1978, pp. 699 - 700. 13. Mazria, 1979, p. 21. 14. Kreith, F. and W.Z. Black, Basic Heat Transfer, Harper & Row, Publishers, New York, 1980, p. 2. 15. Mazria, 1979, p. 26. 179 16. ASHRAE Handbook of Fundamentals, 1981, pp. 39.8, Table 2 and Table 3. 39.2 - 17. Kreith and Black, 1980, p. 19. 18. Mazria, 1979, p. 21. 19. Anderson, 1984, p. 23. 20. Mazria, 1979, p. 35. 21. Anderson, 1984, p. 23. 22 . Anderson, 1984, p. 30. 23. Anderson, 1984, p. 22. 24. Mazria, 1979, p. 45. 25. Mazria, 1979, pp. 47 - 50. 26 . Szokolay, S.V., Solar Energy and Building, Halstead Press, a division of John Wiley & Sons, Inc., New York, 1975, p. 104. 27. Mazria, 1979, pp. 55 - 58. 28. Anderson, 1984, p. 55. 29. Anderson, 1984, pp. 56, 60. 30. Mazria, 1979, p. 54. 31. Anderson, 1984, p. 62. 32. Anderson, 1984, p. 33. 33 . Mazria, 1979, p. 60. 34. Kreith and Kreider, 1978, p. 417. 35. Anderson, 1984, p. 39. 36. Anderson, 1984, pp. 36 - 37. 180 37. Neeper, D.A., "Opportunities for Thermal Storage Research in the Solar Buildings Program", Prepared for the Technical Program Integrator, Los Alamos National Laboratory, Los Alamos, New Mexico, 1986, pp. 10 - 11. 38. Kreith and Kreider, 1978, p. 324, Table 5.5. 39. Neeper, 1986, p. 10. 40. Kreith and Kreider, 1981, p. 325, Table 5.6. 41. Benton, C.C., "Off-Peak Cooling Using Phase Change Material", Thesis Paper for Master of Architecture in Advanced Studies at the Massachusetts Institute of Technology, 1979, p. 51. 42. Neeper, 1986, p. 11. 43. Swet, C.J., "Phase Change Storage in Passive Solar Architecture", Proc. Fifth National Passive Solar Conference ISES, University of Massachusetts at Amherst, Massachusetts, Oct. 19 - 26, 1980, Vol. 5.1, p. 282. 44. Neeper, 1986, p. 12. 45. Shapiro, M.M., D. Feldman, D. Hawes, D. Banu, "P.C.M. Thermal Storage Wallboard", Proc. 12th Passive Solar Conference Proceedings, ASES, Solar '87, Portland, Oregon, July 11 - 16, 1987, p. 48. 46. Sedrick, A.V., "Translucent Phase Change Material Thermal Storage System", Report for Solar Components Division of Kalwall Corporation, Manchester, New Hamshire, 1981. 47. Kreith and Kreider, 1978, p. 169. 48. Anderson, 1984, p. 206. 49. Canadian Climate Normals, Vol. 7, "Bright Sunshine", Atmospheric Environment Service of Canada, Ottawa, 1982. 50. Shapiro, et al., 1987, p. 57.

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Asset Metadata

Creator Gutherz, James M. (author)

Core Title A passive solar heating system for the perimeter zone of office buildings

Degree Master of Building Science

Degree Program Building Science

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

Tag engineering, architectural,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Schiler, Marc (committee chair), [illegible] (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c17-782982

Unique identifier UC11348011

Identifier EP41417.pdf (filename),usctheses-c17-782982 (legacy record id)

Legacy Identifier EP41417.pdf

Dmrecord 782982

Document Type Thesis

Rights Gutherz, James M.

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