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Collective behavior in public urban spaces: a dynamic approach for fire emergency

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Collective behavior in public urban spaces: a dynamic approach for fire emergency

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Content Collective Behavior in Public Urban Spaces: A Dynamic Approach for Fire Emergency by Angella M. Johnson A Thesis Presented to the FACULTY OF THE USC SCHOOL OF ARCHITECTURE UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF BUILDING SCIENCE December 2018 Copyright 2018 Angella M. Johnson ii SDG 3 Acknowledgements I would like to sincerely thank the following thesis committee members, without whom this work would not have been possible: Chair: G. Goetz Schierle Committee Member: Joon-Ho Choi Committee Member: Aiichiro Nakano I would first like to thank my thesis advisor Goetz Schierle for guiding and supporting me over the years. I would like to also thank Aiichiro Nakano. The door to your office was always open whenever I ran into a trouble spot or had a question. Your feedback, ideas and suggestions has been very valuable to me. Thank you, Joon-Ho Choi, for your enthusiasm and for steering me in the right the direction whenever you thought I needed it. I would like to thank my collaborators, friends and colleagues that I have conversed with and who have contributed in some way to this research. Thank you Size for your technical skill and collaboration. I especially want to thank my mentors, Darwin Whitman and Randolph Skeete. You are both an inspiration to me. Finally, I must express my very profound gratitude to my amazing family for providing me with unfailing support and devotion throughout my years of study. In particular, I would like to thank my parents, and my siblings. Words cannot express my appreciation for your words of encouragement throughout the process of researching and writing this thesis. This accomplishment would not have been possible without the love and support. Thanks, from the bottom of my heart. 4 “…I absolutely believe that architecture is a social activity that has to do with some sort of communication or places of interaction and that to change the environment is to change behavior.” Thom Mayne 5 Table of Contents Introduction…………………………………………………………………………………….……………………………13 Kinetic Architecture………………………………………………………………………………………..………….13 Biomimicry and Collective Behavior……………………..…………….……..……………………….…….16 Chapter 1………………………………………………………………………………………………………………………20 Physical/Social Force Based Modeling….……….………………..………………….….………..20 Flow Based Modeling….…….……………….………………..…………………………….…….………22 Molecular Dynamics………………………………………………………………………………….……..22 Chapter 2………………………………………………………………………………………………………………..……28 Crowd Modeling…..……………………………………………………………………..…………….…….28 Fire Modeling……….………………..…….…………………………………………………….….….…….32 Flame Chemistry….…………………………………………………………………………….……...…….34 Chapter 3…………………………………………………………………………………………………………….……….47 Discrete Molecular Dynamics Simulation…………….………………………….…………….…47 Chapter 4………………………………………………………………………………………………………………………49 Path to Exit Simulation…………….…..……..……………………………………………………………49 Chapter 5………………………………………………………………………………………………………………………55 Implications……………………….…………………………………………………………………..…………55 Chapter 6………………………………………………………………………………………………………………………57 Conclusion…………..……………………………………………………………………………………………57 Chapter 7………………………………………………………………………………………………………………………58 Future Work………….…….……………………………………………………………………………….…..58 Bibliography…………………………………………………………………………………………………………………59 6 Figures and Tables Figure 1: Al Bahar Towers…………………………………………………………….…14 Figure 2: Milwaukee Art Museum…………………………………………………….…15 Figure 3: Paenibacillus Dendritiformis Bacteria………..………………………….…….18 Figure 4: Lennard-Jones Potential………………………………………………………..24 Figure 5: Barkow Leibinger’s Kinetic Wall and Motors……………………………….…30 Figure 6: Barkow Leibinger’s Kinetic Wall (Top and Side View)……………………..…30 Figure 7: Firefighter Fatality in the US……………………………………………….…..33 Figure 8: Combustion Model…………………………………………………….…….…34 Figure 9: Complete and Incomplete Combustion……………………………….……….35 Figure 10: Zonal Model…………………………………………………………………..36 Figure 11: Flame Chemistry-Laminar and Turbulent Flow………..………………….…42 Figure 12: Fire Model Behavior…………………………………..…………………..….43 Figure 13: Discrete Molecular Dynamics………………………………..…………….…47 Figure 14: Simulation Configuration……………………………………………………..50 Figure 15: Escape Time for Different Configuration…………………………………….51 Figure 16: Obstacle Configuration……………………………………………………….52 Figure 17: Escape Time for Spherical Obstacles….………………………..…………….52 Figure 18: Spherical Obstacle with Shifting Distances………………………….……….53 Figure 19: Curved Egression Wall…………………………………………..………..….54 Figure 20: Evacuation Process at 240s……………………………………………………55 Figure 21: Number of People Trapped………………………………………………..….56 Table 1: Configuration Parameters……………………………………………………….50 7 Nomenclature A Arrhenius pre-expontial factor an Acceleration (d 2 rn/dt 2 ) B Body Forces in the xi direction Cp Specific Heat Capacity at Constant Pressure Cr Empirical Constants D Mass Diffusion Coefficient D Diffusion Conductance per Unit Area d 3 Vectors in the three dimensional space E Total Emissive Power Es Energy levels of the system e Boltzmann’s Factor f Mixture Fraction F Force Fn Force due to interacting atoms Gb Buoyancy Term Gk Shear Stress Term htotal Total Enthalpy H heat of Reaction Hc Classical Hamiltonian h 3N Dimensionless quantity I Radiant Intensity K Turbulent Kinetic Energy Ka Gas Absorption Coefficient kB Boltzmann’s factor Ks Scattering Coefficient m Mass 8 mn Mass of the atom N Total number of particles in a gas n Normalised Vector ni Number of particles occupying microstate p Pressure pi Particle Momenta P Probability q Heat Flux Due to Thermal Radiation R Ideal Gas Constant r Distance of separation between particles Re Reynolds Number Rfr Rate of Reaction s Stoichiometric Fuel to Oxidant Ratio Sa Source Term in the Chemical Species Conservation Equation T Temperature t Time u, v, w Gas Velocity in x- y- and z- direction respectively uchar Characteristic Velocity ui Gas Velocity in the xi direction V Intermolecular potential xi Particle positions x, y, z Characteristic Length Scale of Flow Ya Mole Fraction of Species alpha 9 Thermal Expansion Coefficient in the Turbulence Mode i Inverse Temperature Gf Turbulent Diffusivity for Scalar f d Kronecker’s Delta e Emissivity ew Well depth- bonding energy i Energy of a particle in a microstate l Heat Conductivity µ Dynamic Viscosity µc Chemical Potential r Density s Stefan Boltzmann Constant sd Distance st Turbulent Prandtl Number for Turbulent Kinetic Energy tij Stress Tensor β β 10 “The person who follows the crowd will usually go no further than the crowd. The person who walks alone is likely to find himself in places no one has ever seen before.” Albert Einstein 11 Hypothesis The objective of this research is to analyze kinetic architecture for the purposes of safe egression during fire emergency. Event-driven molecular dynamics was utilized to simulate the movement of agents. Kinetic architecture has been used for purposes of energy conservation and sustainability. It is postulated that the concept of kinetic or adaptive buildings, especially in critical areas, may assist in the movement of large crowds. This technique may be integrated within a conventional model for the understanding of crowd dynamics. 12 Abstract Crowd modeling incorporates the study of human behavior, mathematical modeling, molecular and fluid dynamics. It has contributed to the development of emergency planning and evacuation methods. Consideration of means of egressing is important in an emergency situation. Simulating the movement of individuals in a crowd has helped scientists, engineers and designers reduce the number of deaths in buildings and public structures. Kinetic architecture is gaining popularity because of its ability to enhance energy efficiency and sustainability. This research proposes the use of kinetic architecture, in particular, kinetic walls to improve safety and efficiency during emergency evacuation. Architectural design and modes of egressing are critical in emergency evacuation. Kinetic walls are simulated in order to evaluate design optimization as it relates to rates of egression. Additionally, the impact of emergency evacuation was explored for large numbers of occupants. The research shows that the adaptive technique proposed may improve safety measures and should therefore be integrated within a conventional framework. 13 Introduction Kinetic Architecture Kinetic architecture has emerged from a need for innovative designs that adapts to the environment and changing human need. The nature of structures to adjust to its environment forms an ecological system. It is ecological in the sense of the relation to living organism and the physical surroundings. In addition to improved aesthetics, kinetic structures play an important role in environmental sustainability. At the intersection of science and architecture is adaptability, creativity and interactivity. Kinetic architecture is symbiotic in nature. Originally, the concept of responsive structures encompassed energy efficiency by focusing on heating, cooling, light, sound and ventilation. Adaptive buildings do not require human assistance but respond naturally to the environment in impressive ways, reducing energy consumption. Architectural features include, but are not limited to, moveable fenestration and responsive facades. Primarily, these features serve the purpose of ventilation, shading and natural heating. The Al Bahar Towers, located in the city of Abu Dhabi, is known for its innovative and sustainable design. The shading device consist of series of transparent components which open and close in response to the sun’s trajectory. The two towers have more than 1000 individual solar protectors which are controlled by the building’s management system. The Al Bahar Towers was designed by Aedas Arquitectos Studio and meets the 2030 Development Plan for Abu Dhabi. The architectural design is suitable given the climate in Abu Dhabi which has very little rainfall and almost year-round sunshine. The climate in this region is sub-tropical and arid. In collaboration with Arup Engineers, Aedas Architects created large geometric patterns that formed this sustainable and engaging façade. The façade system provides an adaptive and dynamic solution to the climate in this region. 14 Figure 1: Al Bahar Towers Innovative designers, architects, and others in the construction community utilize multiple software tools to reach sustainability goals of zero energy buildings. However, the concept of adaptive structures for safety has not been thoroughly explored. This concept is a departure from static forms of design. It is postulated in this research that kinetic architecture might be used for additional purposes other than energy efficiency. In particular, adaptive structures may incorporate safe egressing of large numbers of occupants. If implemented, adaptive kinetic architecture used in urban structures like museums and concert halls, may prove effect for mitigating crowd turbulence. With this concept in mind, a building may be designed in such a way that parts of the structure move without affecting the structural integrity. An example of this is the Milwaukee Art Museum designed by Santiago Calatrava, a Spanish architect, structural analyst engineer and artist. The museum was designed with the comfort of the museumgoers in mind. This structure took advantage of natural sunlight, ventilation and radiant heating which saved time and money. 15 Figure 2: Milwaukee Art Museum Throughout the history of architecture there has been a wide range of design principles. Design of culturally-specific, fixed or immobile structures comprise much of the built environment. With the advancement of technology and adaptive elements, safety should also be made a priority. Successfully navigating exit or entrance ways is crucial in emergency evacuation. This is visible in situations where individuals lose the ability to orient to their surroundings, panic and fail to act logically. Instead of responding independently, individuals rely on group action. In this situation, the crowd or collective whole group possess the knowledge of avoiding dangerous situations. As a result, cognitive abilities are individually lost. The result is group-think mentality. If the danger is heightened, assertive behaviors are exhibited, like pushing or shoving. This behavior is termed as non-adaptive crowd behavior. It is responsible for injury and death in herding disasters. Within complex systems found in nature one can find innovative solutions to problems. Biomimicry, or the patterning of nature, utilizes sustainable solutions for challenges faced by humanity. Flocking or herding describes certain collective behavior where species are brought together into and move as a cohesive group from place to place. Human behavior in panic situations is notably similar to herding and flocking. Interestingly enough, these movements are also similar to fluids and certain molecules. What is observed at the macroscopic scale is also observed at the microscopic scale. Collective behavior may be observed in the microscopic as well as the macroscopic environment. 16 The behavior of crowds in emergency situations can be challenging to analyze since an actual experiment involves exposing participants to possibly hazardous conditions. Drills, such as fire or earthquake, are effective but can hardly recreate panic situations. Computational tools are good alternatives since current simulations allow for human and social behavior. Crowd behavior has been studied for decades and evacuation methods have been developed with the aid of time-lapse films, observations and simulations. Motivated by the computer gaming industry, entertainment-movie industry, researchers use familiar techniques to model agents in architectural buildings. In a familiar environment, pedestrian show basic attributes. The most basic principle is the principle of least effort. This principle postulates that people or animals will naturally choose the path of least effort or resistance. The action of a pedestrian in a normal situation suddenly changes for an emergence situation. For example; the desired velocity increases as occupants attempt to leave a building as quickly as possible and this leads to a typical formation. Occupants who are not well acquainted with a building will tend to exit where entered, even though a closer exit might exist or be easier to reach. They might therefore lose the ability to orient themselves to their environment and exhibit flocking behavior. Biomimicry & Collective Behavior Biomimicry utilizes sustainable solutions to humanities challenges by patterning nature. Within complex systems found in nature one can find innovative cues to problems. The basic concept is that nature has solved many problems that we currently have or are grappling with. Herding is visible in emergency situations where individuals lose the ability to orient to the surroundings, panic and fail to act logically. They fail to act or respond independently but trust and expect that the crowd possess the knowledge of getting out of the dangerous areas or situations. A loss in cognitive abilities result in aggressive behavior like pushing or shoving. Collective behavior emphasizes a type of behavior in the area of sociology. Robert E. Park and Ernest W. Burgess, urban sociologist, in 1924 was the first to differentiate crowds into two categories; active and passive. 17 Herbert Blumer, a sociologist, main area of research was termed symbolic interactionism. He further made a distinction between crowds that were conventionally “expressive” and crowds acting aggressively. Blumer’s methodology was an extension of Robert E. Park and George Herbert Mead. Robert Park noted that during times of social instability crowds move more readily. He observed that under these circumstances, crowds resembled herds of animals. Social Contagion Theory analyzes conditions and events that make crowd behavior possible. The word contagion is usually associated with the communication of disease from one person to another through close contact, similar to the H1N1 flu. The word, however, can apply to the rapid spread of anything from one person to another. In the light of collective behavior, social contagion is a metaphor that describes the transmission of thoughts, behaviors or ideas from one individual to a large group of people. Contagion Theory is based on the idea that thoughts and moods can become contagious. Once an individual becomes infected, the behavior becomes irrational. Normal behavior is replaced with illogical thoughts or ideas. The infected individual becomes the carrier and under the correct conditions, infect other members. In order for this to be effective, the crowd must focus attention on the same event, object or person. Members of the group begin to influence other members and excitement grows. In this frenzied state, individuals cease to think before they act. At this critical state, the group members become highly suggestive where any idea or behavior offered by any member will most likely receive support from all other members. This reduced level of the crowd is referred to by Gustave Le Bon as the “lowest members.” Crowds are quick to act and can be powerful but do not take time to reason. Gustave Le Bon, a French polymath, contribution to the area of collective behavior is notable. In addition to interests in medicine, anthropology, psychology and physics, Le Bon had a keen interest in sociology. His crowd mind theory is seen in his 1895 work titled: “The Crowd: A Study of the Popular Mind” for which he is best known. Three researchers, Gustave Le Bon, Herbert Blumer and Robert Park, formulated a hypothesis on crowd behavior and control. The hypothesis states that crowds transform individuals, eliminating their ability to control their behavior. The pioneering work of these scientist led to further 18 characterization and analysis of collective behavior. Roger Brown, a social psychologist, characterized four types of audiences and mobs. During his time teaching at Harvard University, he categorized audiences as aggressive, acquisitive, escape and expressive. Social movement can be linked to collective problem-solving. In an emergency, the pressing problem to solve is ease of egress or finding the best path to safety. Nature offers inspiration and the ability to better understand patterns that one sees, especially in homo sapiens. The connection between nature and emerging models is sometimes referred to as biometrics. It can be observed that cells, animals, molecules when grouped together, move as a single unit. Their behavior is both intriguing and complex. The groups sensing capacity arises from the simple behavior of the individual agent. For example, large groups of fish, upon sensing a predator, move in highly coordinated motion. This might entail swimming more slowing in darker areas where it is difficult for their predators to see, and likewise, moving more quickly in areas where they are easily seen. A vertebrae of interest is the golden shiner (Notemigonus crysoleucas). The behavior of this cyprinid fish is being studied by scientist such as Ian Couzin and his team at Princeton University. The mechanism as to how this group can sense danger and gravitate to safety is an interesting point of research. Similar examples can be seen in nature like flocking of starlings, herds of wildebeest, colonies (ants, bees, etc..) and groups of cells forming tissues. Another interesting group exhibiting collective behavior is, a eusocial insect, honey bee. Eusocial animals possess high levels of organization with division of labor, cooperative brood care and overlapping generations within its colony. It is the flying insect with the genus Apis. Honeybees are of three distinct type; Queen, Drone and Worker. The queen is the only reproductive female in the colony. She also produces pheromone which brings stability to the hive and it is a way for her to communicate with her workers. The drones are the male bees. The main function of the drone is to fertilize a young queen bee. The worker bees, as their name suggest, do the work of maintaining and defending the hive. Every spring, honey bee queens and thousands of workers leave their hives to look for new homes. Once a location is found, the honey bees return and perform a complex dance that convey the new location. Within their intricate dance pattern is information about direction 19 and distance of the new location. Competition from rival bees is stiff and the colony will, in the end, choose the most danced-for location. Their complex behavior is the particular study of melittologist or apiologist, a branch of entomology. Honey bees are interesting to study when investigating and analyzing social systems and collective behavior. Bacteria displaying interesting collective behavior is the Paenibacillus dendritiformis bacteria. Depending on the growth conditions, it can switch between two distinct growth patterns, as seen below: Figure 3: Paenibacillus Dendritiformis Bacteria The main image shows the result of bacteria grown on soft surfaces. This surface allows greater motion and allows Paenibacillus dendritiformis cells to move in long, slightly curved thin lines which produce colonies curvy branches that curve in the same direction. The opposite is true for cells grown on hard surfaces where nutrient is limited. The result is tip splitting where there are rounder cells that move in whirls which can be seen in the inset image above. The benefit of studying smaller organisms like cells and bacteria is the ease of tracking three-dimensional space over time and the behavior is similar to starlings, golden shiners and even pedestrian dynamics. Within the bacteria swarm are more cells than pedestrians on earth, lanes, etc. 20 Chapter 1 Physical/Social Force Based Modeling In 1995 Helbring and Molnar proposed the social force model. Human behavior is complex and can be seen as chaotic with an increase in individuals. Each agent (α) is affected by four factors: • Agents wants to reach a particular destination • Agents keeps a certain distance from obstacles and borders • Agents keeps a certain distance from other people (repulsion) • Agents can be attracted by other people (attraction) The total effect is given by the equation: 𝐹 " (t) = 𝐹 " # (𝑣 " ,𝑣 " # 𝑒 " ) + ∑ 𝐹 ") ) (𝑒 " ,𝑟 " −𝑟 , ,𝑡) + ∑ 𝐹 ") ) (𝑒 " ,𝑟 " −𝑟 / " ) + ∑ 𝐹 ", , (𝑒 " ,𝑟 " −𝑟 , ,𝑡) The total effect of the four factors on agent α is on the left-hand side of the equation. For crowd movement planning social force model is one of the most commonly used models. The core concept of the model is based on attractive or repulsive forces produced by pedestrians or obstacles. FDS+ EVAC is simulation software based on the concept of social-force model. The model has had several extensions over the years to include modeling of grouping behavior which is slightly adjusted from the original model. The original model was introduced in 1995 by Helbing and Molnar. The equation has three types of forces acting on the agent with mass mi, with instantaneous velocity and position, vi(t) and ri(t), respectively. The first two terms express repulsion of agents from walls. The third term, which is negative, explores interaction with walls. The original equation is: m i 01 02 =𝒇𝑖+ 𝛴𝒇𝑖𝑗 +𝛴𝒇𝑖𝑤 The first term is the restoring force that steers an agent towards the velocity at a rate determined by the time: 21 fi = -mi 1,;1< =, In this regard, the velocity v o is defined as: Vo = (1-p)(Vo ei(t) + p<vj> (1-p) is the weight given to the velocity, ei is a vector pointing to the exit and Vo is the desired speed. The second term is the repulsive, fij, where i and j represent the psychological tendency of agent who are too close to move away from one another. The sum of radii of two agents is 𝑅 ,? = 𝑅 ,@ 𝑅 ? , the notation 𝑑 ,? is the distance between the two agents and is written as 𝑑 ,? =|𝑟 , −𝑟 ? |. The term is the vector pointing from agents i to j: 𝑛 ,? =D𝑛 ,? E ,𝑛 ,? F G =(𝑟 , −𝑟 ? )/𝑑 ,? fij is defined as: fij = {A𝑒 I,?;0,? )// +𝑘𝜂(𝑅 ,? − 𝑑 ,? )}𝑛 ,? + 𝜅𝜂(𝑅 ,? − 𝑑 ,? )𝛥𝑣 ?, 2 𝑡 ,? In the equation above the range η(x) is as follows: η(𝑥) =Q 𝑥, 𝑥 ≥0 0, 𝑥 <0 Two important terms express a realistic panicking crowd. These are a sliding friction term, 𝑘𝜂(𝑅 ,? − 𝑑 ,? )n VW , and a counteracting body compression term 𝜅𝜂(𝑅 ,? − 𝑑 ,? )𝛥𝑣 ?, 2 𝑡 ,? . The tangential velocity difference is Δ𝑣 ?, 2 𝑡 ,? and the tangential direction is 𝑡 ,? =(−𝑛 ,? F ,𝑛 ,? E ). The final force considered mimics the observation that pedestrian tend to move faster near walls in a crowded situation so, is the normal vector of the wall: 𝑓 ,Y ={𝐴 , 𝑒 (I \ −𝑑 ,Y )/𝐵 2 + 𝜅𝜂(𝑅 , −𝑑 ,^ )}𝑛 ,^ − 𝜅𝜂(𝑟 , −𝑑 ,^ )(𝑣 , ∗𝑡 ,^ )𝑡 ,^ Where, 𝑡 ,^ is the tangent vector of the wall and 𝑛 ,^ is the normal vector. The first two terms repel agent from a wall that is 𝑑 ,^ away. The third term mimics what is observed that people move faster near walls in a crowd. 22 Flow Based Modeling In computational fluid dynamics, agents are treated as a fluid since the model uses a continuum approach. Macroscopic models utilize a continuum approach for studying crowd behavior because their movement exhibit similar attributes like a fluid. For such a model, individual actions are overlooked. The characteristic of the model are functions of time (t) and 2D space (x,y). Therefore, parameters considered are average speed v, flow rate f (ρ), and concentration density ρ. The mathematical approach for this model is accomplished by using hyperbolic partial differential equations. Molecular Dynamics Scientists, Alder and Wainwright, simulated elastic collision between hard spheres during the mid-50s. They used an IBM computer to simulate the elastic collision and by doing so are noted in the early history of molecular dynamics. Their success followed their earlier success of Monte Carlo simulation. Following this, in the 1960s, J.B. Gibson, A.N. Goland, M. Milgram and G.H. Vineyard, published a journal article entitled: Dynamics of Radiation Damage, which helped to pave the way for more dynamic simulation. Similarly, Rahman simulated liquid argon using Lennard Jones potential in the 1960s. This was considered novel at the time and may be thought of as seminal for molecular simulation. Molecular Dynamics gained popularity in material science and has since been utilized in biophysics, chemistry and proteomics. Molecular dynamics is based on simulation techniques that involve interacting atoms, their equations of motion and time evolution. Theoretically, it follows the laws of classical mechanics, Newton’s Law of Motion: Fn = mnan where, Fn represents the force due to interacting atoms mn is the mass of the atom an = d 2 rn/dt 2 The N-body problem is insoluble for three or more bodies and originated in the study of the solar system. In the above equation, each n in system constitute N atoms. The 23 nonquantum form behavior of matter can be mostly understood by classical terms. At the microscopic level, classical N-body problems of matter can be understood. Various modeling techniques have been developed for molecular level research that includes, in addition to molecular modeling, Monte Carlo methods, Cellular Automata, Lattice-Boltzmann method, molecular dynamics with electron density function theory and quantum-based techniques to name a few. Quantum mechanics is based on a measure of uncertainty-uncertainty principle. On the other hand, molecular dynamics requires the momentum and position at all times. Molecular dynamics is deterministic. A deterministic system is one in which there is no randomness. In principle, given a set of initial conditions (position and/or velocity), the time evolution can be determined. This model produces the same output given the same initial state. Time evolution is the process by which time passes where there is an internal change of state. In a continuous model the variables change in a continuous way but not in a predictable way. In this way it is not possible to exactly predict what will happen. Equations of motion are solved numerically. The Lennard-Jones Potential was proposed by Sir John Edward Lennard-Jones. This potential describes interaction between molecules and non-bonding atoms. The equation accounts for the attractive and repulsive forces and takes into consideration the distance of separation. Attractive forces may be dipole-dipole, London interactions or dipole-induced dipole interaction. The 12-6 Lennard-Jones potential model consist of two parts; a repulsive term ( ` a ) b and an attractive term ( ` a ) EF V(r) = 4e[( ` a ) EF − ( ` a ) b ] where, V is the intermolecular potential r is the distance of separation between particles ew is the well depth-bonding energy sd is the distance 24 The simplified form: V(r) = d a ef − / a g Where; A= 4es and B=4es Figure 4: Lennard-Jones Potential The Lennard-Jones equation is a function of distance between the centers of both particles. The distance between the centers of the particle are bound so their centers decrease until the particles reach equilibrium. If the particles are pressed further together, repulsion occurs. In this case, the bound particles are so close that the electrons orbiting their shell are forced to occupy the other particle’s shell. The potential energy becomes increasingly positive as the separation distance decreases below equilibrium. The opposite is true for negative potential energy due to the long separation distances. At these long distances, the pair of molecules experiences a stabilizing force. Molecular dynamics is a statistical mechanics method based on the partition function. Partition function is a function of temperature and other parameters which describes the statistical properties in thermal equilibrium. Each type of partition function corresponds to different types of statistical ensemble. The grand canonical partition function applies to a canonical ensemble in which the system exchanges both particles and heat with the environment. This is accomplished with a fixed volume, temperature and chemical potential. Variables of the thermodynamic system like entropy, free energy, and pressure 25 may be expressed in terms of the partition function. For the canonical partition function, the system is allowed to exchange heat with the environment at fixed volume, number of particles and temperature. The canonical partition function is expressed as: 𝑍 = ∑ 𝑒 ;) i j k 𝛽 (𝑖𝑛𝑣𝑒𝑟𝑠𝑒 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒)≡ E s t u 𝑘 / 𝑖𝑠 𝑡ℎ𝑒 𝐵𝑜𝑙𝑡𝑧𝑚𝑎𝑛𝑛 z 𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑒 ;) i j 𝑖𝑠 𝑡ℎ𝑒 𝐵𝑜𝑙𝑡𝑧𝑚𝑎𝑛𝑛’𝑠 𝑓𝑎𝑐𝑡𝑜𝑟 Es energy levels of the system In classical statistical mechanics, the momentum and position of a particle can continuously vary (as such the microstate is uncountable). It is best to describe it using an integral and not sum as shown below. The partition function of a gas of N identical particles: Z = E } ! ∫exp[−𝛽𝐻(𝑝 E …𝑝 } ,𝑥 E ….𝑥 } )]𝑑 𝑝 E …𝑑 𝑝 } 𝑑 𝑥 E …𝑑 𝑥 } where, 𝑝 , 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑚𝑜𝑚𝑒𝑛𝑡𝑎 𝑥 , 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛𝑠 ℎ } 𝑎𝑙𝑙𝑜𝑤𝑠 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦 (ℎ−𝑢𝑛𝑖𝑡 𝑜𝑓 𝑎𝑐𝑡𝑖𝑜𝑛) 𝑑 𝑟𝑒𝑚𝑖𝑛𝑑𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑝 , 𝑎𝑛𝑑 𝑥 , 𝑣𝑒𝑐𝑡𝑜𝑟𝑠 𝑖𝑛 𝑡ℎ𝑟𝑒𝑒 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑎𝑙 𝑠𝑝𝑎𝑐𝑒 𝐻 𝑐𝑙𝑎𝑠𝑠𝑖𝑐𝑎𝑙 𝐻𝑎𝑚𝑖𝑙𝑡𝑜𝑛𝑖𝑎𝑛 𝛽 𝑖𝑛𝑣𝑒𝑟𝑠𝑒 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 Grand canonical function A system that exchanges particles and heat with the environment at a constant chemical potential and temperature for a grand canonical ensemble. It deals in a simple way to the quantum system of spin statistics of particles 𝑍 = ∑ ∑ ∏ 𝑒 ;) \ ( \ ;) , { \ } } # 26 𝑁 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠 𝑖𝑛 𝑎 𝑔𝑎𝑠 𝑛 , 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠 𝑜𝑐𝑐𝑢𝑝𝑦𝑖𝑛𝑔 𝑚𝑖𝑐𝑟𝑜𝑠𝑡𝑎𝑡𝑒 𝑖 𝑎𝑛𝑑 𝜖 , 𝜇 𝑐ℎ𝑒𝑚𝑖𝑐𝑎𝑙 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝜖 , 𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑓 𝑎 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑖𝑛 𝑎 𝑚𝑖𝑐𝑟𝑜𝑠𝑡𝑎𝑡𝑒 for N=3 ∏ 𝑒 ;) \ ( \ ;) , = 𝑒 ;) ( e ;) 𝑒 ;F) ( ;) Central to statistical mechanics is the dependence on microscopic variables. Understanding the system and the microstate energies, one may obtain the partition function which allows the calculation of all other thermodynamic properties of a particular system. Statistical mechanics provides a formal description of a system in thermal equilibrium. Given the modeling ability of molecular dynamics, there are a variety of techniques and applications that have emerged. Below is a list, albeit not an exhaustive one, of the areas of research where molecular dynamic simulation is used: Collective behavior- orientational order, coupling of rotational and translational motion, decay of space and time correlation function, spectroscopic measurement and vibration. Material science- grain boundaries, epitaxial growth, defect formation and migration (vacancies and interstitials), fracture, friction, and shock waves, etc.. Polymers- rings, chains and branched molecules, transport processes and equilibrium conformation Biomolecular- protein folding, nucleic acids (DNA, RNA) membranes, structure and dynamics of protein, drug design. Complex fluids- liquid crystal, molecular liquids, ionic liquids, structure and dynamics of glasses, films and monolayers. Fluid dynamics- boundary layers, unstable flow, laminar flow, transport phenomena. 27 Electronic and dynamic properties- Car-Parrinello method refers to a method used in molecular dynamics. It is a method that utilizes density functional theory, periodic boundary conditions, and planewave basis sets. This method includes the electrons as active degrees of freedom through dynamical fictitious variables. Density functional theory is a quantum mechanical method used in chemistry, physics and material science. It is used in order to investigate the electronic structure of a many body system. Molecular dynamic simulation is can be applied to real world problems in various categories. Molecular problems are classified into various categories: Pairs of particles or multiparticle Long range or short-range interaction Isolated or open to outside influence Continuous potential function or step potential Structureless atoms or complex molecules (rigid or flexible) Thermally or mechanically isolated or open Molecular dynamics is a powerful technique but possess challenges. The foremost limitation is the foundation of Newton’s law. It is used to analyze atoms but at the atomistic level, quantum laws dominate. Classical approximation is poor for light systems (H2, He, etc.) and at low temperatures. Inhomogeneities might be challenging in small systems like gradients of temperature or density. Size and time simulation restrictions may also present a challenge since some systems may contain millions of atoms and the time to run such simulations might be expensive. 28 Chapter 2 Crowd Modeling The current global population of 7+ billion continues to grow. This exponential growth is nowhere more clearly seen than in large cities. As a result, more people attempt to move into cities than can offer job opportunities and exposure. Naturally, urban public structures experience more foot traffic which may also contribute to a greater risk of crowd related disasters. The increase in population density makes crowd simulation and modeling an important area of research. Crowd modeling is the study of human behavior, mathematical modeling, molecular and fluid dynamics. It has contributed to the development of emergency planning and evacuation methods. There are three levels of crowd behavior: group, interactions among the agents or individuals and the individual. A crowd is made up of a collection of agents. In normal and in emergency situation, the behavior of the agent drives the behavior of crowds. It is instinctive to want to egress as quickly as possible. Following instinct, however, does not require conscious thought. One’s options may not be thoroughly evaluated. Instead a phenomenon called faster-is-slower can be observed where quick uncoordinated movements may cause a crowd to move slower. This experience can have both positive and negative effects since an agent is heavily relied on in an emergency. The presence of an experienced authority figure to calmly guide others to utilize all exits of a building would be ideal but not practical. Instead, it is important to explore ways to improve evacuation times by re-evaluating architectural layout. Most individuals, it has been observed, tend to exit buildings along a route that is familiar. Individuals tend to exit the same egression location entered. In high-density crowds, each agent is physically restricted and does not have enough room to behave as one normally does. Decisions are rather based on a crowd than the individual. When this phenomenon occurs, the entire crowd’s movement is similar to a fluid or group of molecules. For example, an agent is forced forward by the pressure of other agents moving forward. This is common for cases of more than 6 people per square meter and one starts to lose freedom of movement. The transition stage, where it is observed that crowds obey the laws of molecular dynamics and social force model. 29 A critical stage for crowd density is more than 8+ people per meters squared. At this stage, it becomes extremely difficult for an agent to move and the probability of injury or death becomes highly likely or probable. In a crowd crush an extremely large and high-density crowd move in one direction in a confined space, like a hallway. The problem occurs when the crowd hits a choke point. This point can be caused by a block entrance (similar to the Station Nightclub fire in 2003). In this case, a single open doorway, a sharp turn, or an opposing high-density crowd moving in the opposite direction is critical. Survivors of crowd crush have described the experience, of lack of control, as being carried by a river of people. Agents are not able to stop or move in another direction. If the choke point is too narrow for the crowd to pass through it is highly likely that the agents in the front are crushed by the force of the crowd behind, creating what is commonly called, a shock front. Crowd pressure occurs at densities of about 12+ people per meters squared, fatalities are common in this case due to compressive asphyxiation, suffocation by crushing. The sheer force of all the weight of bodies stacked up and around may cause agents to suffocate. Crowd pressure have been known to bend steel guard rails and collapse walls, to give a few examples. Human behavior in panic situations is notably similar to ordinary fluids and molecules. Agents or “thinking fluids” are supported by observations and has been refined as knowledge expands and modeling techniques improve. What is observed at the macroscopic scale is also observed at the microscopic scale. Human reaction to emergency, like a fire, is modeled in order to analyze design methodology. For public structures like museums, kinetic fire walls are proposed for faster evacuation times. The kinetic wall would be made of fire retardant material with a dynamic seamless aesthetic. The wall proposed would be controlled by sensors and building management. Its main function and purpose being ease of egression during an emergency. An example of the proposed wall is Barkow Leibinger’s kinetic wall. It was showcased at Rem Koolhaas’ Elements Exhibition during the Venice Architecture Biennale in 2014. It was created by German architects Frank Barkow and Regine Leibinger. The shape-shifting wall rhythmically expands and contracts by a programmed grid of motorized nodes. It is an example of a wall that is both materially and spatially dynamic. 30 Figure 5: Barkow Leibinger’s Kinetic Wall and Motors Figure 6: Barkow Leibinger’s Kinetic Wall (Side and Top View) 31 The distribution of occupants is important in the model in addition to door widths and placement, lighting, human psychology and position of obstacles. Studying the behavior of crowds in emergency situations is challenging since an actual experiment involves exposing participants to possibly hazardous conditions. Computational tools are good alternatives since it allows the simulation of agent dynamics, motion, and evacuation behavior. 32 Fire Modeling The first fire brigades were created in France around the 18 th century. Until the 17 th century firefighting was rudimentary. The city of London suffered five great fires. The most notable fire being the Great Fire of 1666 in which two square miles of the city was consumed and left tens of thousands homeless. After this incidence a fire protection system was organized. A conglomeration of insurance companies formed private fire brigades to protect their clients’ interest. Brigades would only fight fires of buildings identified as fire insurance marks. A major breakthrough in firefighting commenced with the first fire engine. Hans Hautsch, a German Inventor, created the first suction and force pump and Jan Van der Heyden, a Dutch artist and inventor, developed the fire hose. It consisted of flexible leather coupled with brass fittings. Dutch inventor, John Lofting, further developed the fire engine and patented his invention, “Sucking Worm Engine” in 1690. In 1725, Richard Newsham developed a similar engine and patented it in the United States and as a result he had a monopoly on the market in America. The first American fire engine company went into service on January 27, 1678. Fifty-eight years later in 1736 Benjamin Franklin of Philadelphia established the Union Fire Company. George Washington was a volunteer firefighter and a member of the Friendship Veterans Fire Engine Company. In 1774 he bought and gifted a new fire engine for the town of Alexandria, Virginia. In the United States government-run fire departments was not instituted until the American Civil War. Currently as of 2010, seventy percent of firefighters were volunteers. An average of one hundred firefighters die in the line of duty every year. The National Institute for Occupational Safety and Health, NIOSH, conducts investigations of incidents of fallen fire fighters. Below is a map of fire fatality deaths in the United States. 33 Figure 7: Fire Fighter Fatality According to the National Fire Protection Association an estimated 3% of all reported structure fires were in high-rise structures during the period of 2007-2011. Additionally, during this period, approximately 15,400 reported high-rise building fires per year resulted in associated losses of 530 civilian injuries, 46 civilian deaths and two hundred and nineteen million dollars in property damage per year. High-rise fires are classified by four property class. These include: hotels, offices, apartments and healthcare facilities. The risk of fire and fire loss is notably lower in high-rise structures than in other buildings of the same property loss but, the method of evacuation during a fire adds a level of complexity. 34 Flame Chemistry Flame chemistry and its propagation results from energy released in an exothermic reaction. The energy released may come about by various processes like exothermic decomposition, combustion or a combination of the two. Nonstationary flame involves a rather complex interaction between fluid dynamics and chemistry. Combustion is described as the oxidation of fuel and involves a sequence of single step reactions of atoms and radicals with high reaction rates. These occurrences involve a complex sequence of exothermic reactions between oxidant ad fuels. The final reaction product is primarily carbon dioxide and water vapor, which has no excess of oxygen or fuel. Fuel + Oxidant ® Products Figure 8: Combustion Model For example, below is a stoichiometric equation of hydrocarbon such as methane In Oxygen: CH4 + 2O2 ® CO2 + 2H2O Above fuel and oxygen are equivalent or proportional stoichiometrically. In Air: CH4 + 2O2 + 2(79/21) N2 ® CO2 + 2H2O + 2(79/21) N2 In combustion, the reaction may develop slowly or occur rapidly as there is an increase in the temperature. The latter is true for most chemical reactions. The burning or combustion 35 of practical fires is replete with complex reactions and by turbulence. j, Stoichiometric ratio expresses the concentration of fuel. On a molar basis it is a fraction of stoichiometric concentration that describes fuel mixtures. If j > 1, the mixture is rich and if j < 1, the mixture is lean. The closer j is to one or unity, the more rapid the combustion. Fuels like ethane (j ~1.5) exhibit easier ignition and faster burning. On the other hand, hydrogen and methane, which diffuses faster than oxygen, have a leaner composition. Figure 9: Complete & Incomplete Combustion As urban populations grow, safety has to some extent been taken for granted. A boom in city growth results in complex methods of preserving and protecting its populous. Efforts to predict and understand the course of a fire are greatly influenced by current scientific methods available. These methods include mathematical modeling and large-scale experiments and drills. Large-scale experiments, however, are expensive and labor intensive. Small-scaled experiments where the geometry is resized up to 1/3 of the true scale are beneficial. Using these models, hand calculation and mathematical models can be derived. The mathematical models describe fire-related phenomena using techniques that are numerical and analytical; predicts smoke spread, pressure and temperature fields, and the concentration of toxic gases. There are two types of fire modeling which include non- deterministic and deterministic. 36 Deterministic modeling is the most dominate of all the other methods. These models are based on physical and chemical relationships. Non-deterministic modeling uses statistics to include fire growth, barrier failures and fire frequencies. Computer simulation of fires uses CFD for field and zone modeling. Computational fluid dynamics, CFD, is the study of fluid systems that is changing in time and space. Fluid systems can be either dynamic or static. This branch of study is performed by a numeric method on high-speed computers. Zone models use a limited number of control or enclosed room (zones). Figure 10: Zonal Model Zone models, like the most common two-zone model, divides a room into two control volumes. The upper layer refers to the upper control volume near the ceiling containing burnt and entrained hot gases. The lower layer contains cooler fresh air. Equations for the plume model includes chemical species, momentum, mass and energy are solved separately for the upper and lower layers. Both layers are considered homogenous and represent average values over the control volumes. These models are developed in order to present approximate values of the smoke interface and the gas layer. In field modeling, a domain space is defined. The domain is divided into smaller volumes and the CFD technique is applied in order to solve differential equations from laws of nature. In real life most flows are complex so turbulence, soot model or fire-spread models, for example, has to be included for fire predictions. Mass continuity equation reflects a physics principle that matter can be neither created or destroyed so that the total mass is left the same or unchanged in an isolated system. The 37 rate of change of mass in the control volume or zone must equate to the rate of change or inflow across its faces. The mathematical expression can be written as such: 𝜕𝜌 𝜕𝑡 + 𝜕 𝜕𝜒 (𝜌𝜇) + 𝜕 𝜕𝑦 (𝜌𝜈) + 𝜕 𝜕𝑧 (𝜌𝑤) = 0 2 + (𝜌𝜇) = 0 (compact form) Above, the first part of the equation 2 is the mass per unit volume or change of density. The second part of the equation (𝜌𝜇) due to convection it is the rate of flow through the zone or control volume. Similar to mass, momentum is also conserved. According to a physics principle, Newton’s Law, the sum of all forces acting on an object Σ 𝐹 = 0 02 (𝑚𝜈) is equivalent to the time rate of change of momentum. Fire risk assessment is an important consideration for the urban landscape. In order to bring the risk into focus three factors are outlined below: 1. Potential of the fire hazard 2. Likelihood of risk occurrence 3. Likelihood of fire risk exposure These three elements combined define the risk factors. These factors led to the development of building codes and fire test methods. Fire risk consists of elements that weigh the probability of occurrence, the probability of exposure and potential for harm, not necessarily in that order. The risk of fire is multifaceted because of this the response to fire risk is also multifaceted. Outline of the response are below: 1. Building standards and codes- used to evaluate likelihood of risk 2. Fire tests- assesses the potential of harm 38 Building codes and standards is used to regulate construction for safety issues. For architects, engineer and designers a review of applicable or related codes and standards is required. In some cases, test procedures were developed, and requirements evaluated in product certification programs. This has contributed to changes or revisions in the development of installation standards and codes. Fire risk assessment address: sprinkler and detection, compartmentation, flashover and fire confinement. Some resolved problems of conflagration include; compartmentation to help control and contain fire to a single room, fire walls to keep fire confined to an area, and advance detection system and sprinkler. Most of the broader problems in conflagration have been addressed while the narrower problems remain. These that remain can be addressed through experiment while others are better addressed analytically. There are several approaches used in fire risk assessment methodology. Approaches are listed below: Simulation- laboratory situations can be created, simulated and observed based circumstances of risk methodology. Exposure fires and smoke spread can offer a challenge in simulated situations. Results from simulation can be used for conflagration experiments. Test Methodology- laboratory observations are formulated. Development of a test method to establish appropriate requirements for windows, doors, etc. Comparative Analysis- a determination of functionally similar products is developed to determine relative performance and materials given conditions of interest. Theoretical and experimental fire spread, and compartmental fire growth test have been a subject of investigation. Research is generally successful and has produced a quantitative understanding of phenomena involved. Methodologies include statistical modeling of test process utilizing regression analysis, statistical factor analysis, scale modeling, deterministic modeling and field equation methodology. Different approaches depend on the degree of knowledge of fire risk of physical processes. For some approaches there are no known factors of fire growth phenomenon. The other method assumes that certain parameters are known like the basic structure of the model. The deterministic modeling approaches is different in the that it requires a more detailed knowledge of component processes. Phase of fire growth is primarily described by equation and simulation. Mode 39 of the flame propagation is opposite the airflow direction or considered “creeping.” This model demonstrate flame spread and combustion: Flame Area-Af increases linearly with the total rate of production of heat. Ap is the ceiling pyrolysis are Af = c1Ap Pyrolysis Area-The subsequent pyrolysis areas are proportional to the initial. Ap,o is the initial pyrolyzing area Ap ~ Ap,o The equation for the rate of spread of Ap is inversely proportional to 𝛿𝑡, and the time necessary to increase the temperature of the surface at the tip of the flame, from the pyrolysis temperature (Tp) to the initial temperature (Ti). Combining equations from the results enumerated, it can be concluded that Ap is a driving force in the process. The rate of increase or change in Ap is proportional to the quantity Ap. Ap = d¡ ;d¢ £2 = ¤E;E £2 𝐴𝑝 In order to express the elementary heat conduction theory of a given thermally thick material, we need the equation for the quantity 𝛿𝑡. 𝛿𝑡 ~ s¤(u,¦;u<) f § ¨f where the variables are expressed below: Tig = ignition temperature Ta = ambient temperature 𝑞̇” = net heat flux from flame to ceiling k = product of thermal capacity and thermal conductivity k The heat flux equation 𝑞̇” can be expressed as: 40 𝑞̇” = h(Tf - Ta) In this case: Tf = flame temperature h = total heat transfer coefficient Therefore: 𝛿𝑡 ~ 𝑘𝜌𝑐(Tig-Ta) 2 /[ℎ(𝑇 ¡ −𝑇 « )] F and for nondimensionalized time at = h 2 t/k𝜌𝑐 the scaling parameter is: Âp ~ aAp Ap, the pyrolysis area in the regression model of ceiling flame spread and combustion can be written as: Ap = f (e at ) or written another way: Ap = 𝛼(e at -1) ß In the case above 𝛼 and 𝛽 are coefficients that are determined statistically. This expression is the basic equation for regression analysis. The rate of energy release (Qrt) from a room test used to validate the model is expressed as: Qce = ApQ” av Qce (ceiling combustion) is part of Qrt (rate of energy release) that is derived from ceiling combustion. There are basic flammability parameters that need to be considered when analyzing flame spread and fire ignition in a room or area. These parameters are (1) thermal 41 inertia (𝑘𝜌𝑐 ) (2) flame spread coefficient C (“creeping”) (3) Minimum radiant flux for flame spread and (4) Minimum radiant flux for ignition. For a description of rate of energy release parameters include (1) Heat of reaction ∆𝐻 (2) Heat of Vaporization L and (3) Stoichiometric oxygen to fuel ratio rox The equation below demonstrates scaling properties of the factor 𝑡 𝑘𝜌𝑐 ¯ . Equations for: U, 𝜏, 𝛾, s, 𝑞 " , are the basis for the determination of k𝜌c. 𝑡 =𝑈[ ´ j f §" + = µ f ln (Fk´ j @ =; √µ)(=@ µ ) (Fk´ j @ =@ √µ )(=; µ) – ´ j (=@Fk´ j ) µ§" therefore; U = F s¤ f 𝜏 = −( ¹ +4𝜎𝑇 « ) 𝛾 = (𝜏 F −4𝑞 ¼ " 𝑠) s = - F½ 𝜎𝑇 « F 𝑞 " = 𝑞 ¼ " 𝜖 ¯ = 𝑞 ¼ " + 𝜏𝜃 k +𝑠𝜃 k F 𝜖 absorptivity of surface 𝑞 ¼ " impressed flux The mass loss rate from a burning hot surface is formally written as: 𝑚 ¿ " = E À 𝑞 ¼2 " so that 𝑞 ¼2 " reflects the difference between heat (convective and radiative) to the loss heat flux to the fuel surface. The heat required to produce volatiles is defined as L. 42 Figure 11: Flame Chemistry-Laminar & Turbulent Flow Convection is defined by the mechanism where the gas layers gain or lose energy to an object like a wall. Closely associated with convection is conduction that measures heat gain or loss directly. Heat flow of convection is the transfer of energy across boundary layers. Heat flux term is written as 𝑄 ¤ = ℎ ¤ (𝑇 ¦ − 𝑇 Y )𝐴 Y The equation for the transfer coefficient is defined as ℎ ¤ = s Â 𝐶 1 (𝐺 a ∙ 𝑃 a ) e Aw = area of wall in contact with zone Gr (Grashof number) = 𝑔𝑙 ∥ 𝑇 ¦ − 𝑇 Y ∥/ 𝑣 F 𝑇 ¦ Pr (Prandtl number) = 0.7 k (thermal conductivity of the gas) = 6.5 x 10 -8 ( u È @ u É F ) 4/5 l (length scale) = 𝐴 Y Cv (coefficient depends on orientation) Nu = Nusselt number v = 7.18 x 10 -10 Ê u È @u É F Ë 7/4 43 A heat balance must be done which includes all objects that radiate to the zone in order to calculate the radiation absorbed. The calculation requires that some approximations are necessary, and assumptions are made in regard to layers and zones. Generally, it is usually assumed that all zones are similar. Radiation can travel from one layer to the next or by exiting vents or going to walls. It can also heat up an object or change the pyrolysis rate of the fuel source. Emission and absorption throughout a gas layer are constant with the stratified zone assumption. Most models assume that surfaces and zones radiate and also absorb with a certain emissivity, but radiative transfer can be done with some generality. Figure 12: Fire Model Behavior Walls of compartments or partition tend to be flat and rectangular. Fires, plumes, flames and bounding surfaces tend to have an average shape that can be analyzed. The equivalent radius of a gas layer L = 4V/A In addition, 𝑄 " in a formal sense is given by 𝑄 " = 𝜒 ∆𝐻𝑚 ¿ " = 𝜒 ∆𝐻 𝐿 𝑞 ¼2 " The degree of the completeness of combustion in the above equation is represented by 𝜒 B = ∆Í À 𝑟 <Î 𝑌 <,« 44 B represents the mass transfer number that has an important role in the theory of convection-controlled combustion. The above equation gives the engineering approximation to B where 𝑟 <Î is equal to the mass oxygen and fuel stoichiometric ratio. 𝑌 <,« is the ambient mass fraction of oxygen. Initial transient period can be written as below and is of interest for room fire growth process. 𝑄 " (𝑡) = 𝑄 Ð«Î " 𝑒 ;Ñ(2;2 Ò ) Also, written alternatively; 𝑄 " (𝑡) = 𝑄 # " +D𝑄 Ð«Î " − 𝑄 # " G𝑒 ;Ñ(2;2 Ò ) The values for 𝑄 Ð«Î " is to be taken directly from measurements and 𝜆 is the value for the corresponding regression. Fires generate plumes. This plume transports energy and mass to the upper layer so that mass and energy is entrained from the lower layer to the upper layer. The lower layer increases the upper zone’s internal energy while the upper layer has a cooling effect. The heat addition will be: 𝑄 ≅ 𝜒 ¼ 𝑚 ¡ 𝐻𝑐 mf = rate of consuming mass, 𝜒 I the exit radiation as fire and 𝜒 ¼ is the relative fraction of pyrolysate which participates in combustion. Across a vent flows are governed by the pressure difference: S = Smoke A = Air ij = Flow from compartment to i to j P = Floor pressure N = [Pj – Pi + (pli – pui)gZi]/(plj – pui) SAul(2)/ AS12 = 0.5 (Tlj/Tuj) ( } ;Õ \ } ) 45 Mass pyrolysis rate is specified, and the heat release rate is: 𝑄 ¡ = ℎ ¤ 𝑚 ¡ − 𝑐 ¢ D𝑇 Ö − 𝑇 ¡ G𝑚 ¡ − 𝑄 ¢ 𝑚 ¡ Mass loss rate 𝑚 1 and is related to the pyrolysis rate by 𝑚 1 − 𝑚 ¡ =(1−𝜒 ¡ )𝑚 1 All the volatiles are burned when the burning efficiency becomes 100%. Heat release goes into enthalpy flux and radiation. In the plume flow equation, the notation for the fire Qc is the driving term 𝑄 I (𝑓𝑖𝑟𝑒)= 𝜒 I 𝑄 ¡ 𝑄 ¤ (𝑓𝑖𝑟𝑒) =(1− 𝜒 I ) 𝑄 ¡ This can be applied to pool fire which is a turbulent diffusion fire burning above a “pool”. Horizontal pool consists of vaporizing fuel. It can reradiate from the compartment and the flame. Pool fires may be “running” or static (contained). Fuel-controlled are fires that burn in well-ventilated or open areas. Ventilation-controlled fires are fires that are within enclosures and become under-ventilated. Notations are as follow: Qflame = radiation from the flame back to the fuel QR = external radiation to the fuel source Qconv = enthalpy flux away from the fire Qcond = conductive heat loss from the fuel to the surroundings QRR = fuel surface reradiation 𝑄 ¡ = 𝑄 I (𝑒𝑥𝑡)+ 𝑄 ¡Â«Ð¼ − 𝑄 II + 𝑄 ¤<1 − 𝑄 ¤<0 Conduction is a transfer of internal energy through collision of particles or small-scale diffusion within a body. Much of the total heat loss from an area or zone occurs through the walls and through heating of object in the compartment. The equation below depicts heat propagation or transfer in solids: 46 u 2 = s ¤ ∇ F 𝑇 Variable that influence the growth of a room fire are categorized into five groups: 1. Room geometry- height, volume, depth, etc. 2. Ventilation- location and dimensions of fenestration 3. Fuel- wall linings, furnishings 4. Initial fire- location, size, etc. 5. Heating of ceiling and walls- radiation, conduction, and convection 47 Chapter 3 Discrete Molecular Dynamics Simulation Discrete molecular dynamics (DMD) simulation algorithm is an extremely fast alternative to traditional molecular dynamics. It was first introduced in 1959 by Alder and Wainwright for simulations of hard spheres. Later, it was used by Rapaport for simulation of polymer chains. It has since been adopted for simulations of protein-like polymers. Benefits of using DMD is that it is extremely fast and suitable for simulation of large systems on long time scales. During DMD simulation, potentials applied to particles are approximated by discontinuous step-functions of inter-particle distance 𝑟 (Figure 13). Figure 13: DMD Potential (a) hard sphere collision (b) attractive square well interaction (c) repulsive soft interaction (d) covalent bond and auxiliary bond interaction No force will be exerted on particles until their distance becomes equal to the point of a discontinuity on the potential. When particles encounter a potential discontinuity, this is called an “event.” Between events, particles move at constant velocities. Because the energy change during each event is known, the post-event velocities can be calculated by solving the conservation of momentum and the conservation of energy simultaneously. 48 Thus, the trajectory of a particle can be simulated discontinuously between events. The simulation code for DMD is significantly different than that for traditional molecular dynamics because the particles are moved discontinuously from one event to the next with known velocities. sDMD is a simulation package based on the DMD technique and a high- resolution all-atom molecular model. The package was written in the C language by Size Zheng and has since been optimized. Its modularized structure is highly expandable: new molecular groups can be introduced by simply adding new formatted connection and potential data files. The configurations are controlled by an easy-to-read configuration file and several command flags. 49 Chapter 4 Path to Exit Simulation For this study, discrete molecular dynamics (DMD) method was used to simulate an evacuation process. During the simulations, 400 people (modeled as spheres) move towards the exit door. The driving force is simulated as a potential well where the minimal locates near the exit. The random movements of the spheres follow Brownian motion. The room has dimensions of 40 x 16 (L x W) m 2 ; The exit door is 3 m wide. All the obstacles and walls presented in this research are impermeable and opaque to agents. Four configurations were simulated as shown below in Figure 14. The configurations are as follows: (a) reference configuration; nothing added in the room (b) kinetic contoured wall- the moveable wall strategically placed in the middle of the room (c) linear compression wall-the wall will compress towards the center (d) curved egression wall-kinetic wall located at an entrance/exit to aid in egressing occupants. For configurations (b), (c) and (d), seven different parameters were used. Also, for (b) and (d), different radii of curvature are used. In the case of (c) different compressing distances were used. Details can be found in the table below: 50 Figure 14: Simulation Configuration Table 1: Configuration Parameters Wall Types Distance / Radii (m) Compression Wall 4.050 4.725 5.400 6.075 6.750 7.425 8.100 Contour Wall 8.775 9.450 10.125 10.800 11.475 12.150 12.825 Curved Wall 8.775 9.450 10.125 10.800 11.475 12.150 12.825 Different configurations will have different effects on agents escaping where some cases may help, the others may not. In each configuration, we performed ten independent simulations in order to model the evacuation process for up to 420 s. The total evacuation time was recorded. Results are the averages of the ten independent simulations. This is shown in Figure 15 below: 51 Figure 15: Escape Time with Different Configuration In Figure 15, the red line represents the reference configuration, the grey line represents the kinetic contour wall, the blue line represents the linear compression wall, and the orange line represents the curvature wall. Analytical results show that compared with the reference configuration, the curved egression wall significantly reduced the evacuation time. The reduction in evacuation was up to 14 s. The linear compression wall showed some improvement, and in some cases, would even increase the time cost. The kinetic contour wall, however, performed disappointedly in every case. It would, in a real situation, prevent a crowd from escaping and in many cases increase the escape time. Analytical results showed that compared with the reference configuration, the curved egression wall significantly reduced the evacuation time. The reduction in evacuation was approximately 14s. Next, placement of obstacles was simulated and compared evacuation times with the curved egression wall. The proposed kinetic curved egression wall outperformed in the previous case. A single spherical and multiple offset (zigzag) obstacles were compared with the original parameters area of egress and number of agents simulated. For the single obstacle, a sphere was placed directly in front of the exit/entrance and after simulation the position was systemically offset in order to find the optimal position. Likewise, a zigzag pattern of spherical objects was analyzed. In this case, distances between obstacles were varied to find the prime position. These two configurations were compared to a reference model and the curved egression wall. This can be seen in the figure below: 8.775 9.45 10.125 10.8 11.475 12.15 12.825 240 242 244 246 248 250 252 254 256 258 260 262 4.05 4.725 5.4 6.075 6.75 7.425 8.1 Radius of Curvature / m Escaping time / s Compress Distance / m 52 Figure 16: Obstacle Configuration Below are graphs of the comparison: Figure 17: Escape Time for Spherical Obstacles 8.775 9.45 10.125 10.8 11.475 12.15 12.825 0 10 20 30 40 50 60 5.4 6.075 6.75 7.425 8.1 8.775 9.45 Radius of Curvature / m Escaping time / s Spherical Obstacle Shifting Distance / m SphShift Flow curve ref 53 Figure 18: Spherical Obstacle with Shifting Distances reference case (ref)-red line curved egression wall (curve)-brown line multiple offset obstacles (SphShift)-blue line single obstacle (Flow)-green line 8.775 9.45 10.125 10.8 11.475 12.15 12.825 0 10 20 30 40 50 60 5.4 6.075 6.75 7.425 8.1 8.775 9.45 Radius of Curvature / m Escaping time / s Spherical Obstacle Shifting Distance / m SphShift Flow curve ref 54 In comparing and analyzing the various configurations, the proposed kinetic wall (curved egression wall) performed well in all cases. Example of the proposed kinetic wall: Figure 19: Curved Egression Wall We compared the evacuation time; distribution of total distance and evacuation rate. It is postulated that an effective crowd simulation could converge to form a simulation metric that depict observable real-world data. 55 Chapter 5 Implications Based on the existing test case, if we set a fixed evacuation time at 240 s, we can also obtain the numbers of agents that would remain trapped in the respective rooms. The simulation snapshots are shown below. Calculated results are depicted in Figure 20: Figure 20: Evacuation Process at 240s for Different Configurations (a) reference (b) kinetic contour wall (c) linear compression wall (d) curved egression wall 56 Figure 21: Number of People Trapped After 240s Evacuation Time Figure 20 and Figure 21 show that with the reference situation (the red line), there would be approximately 7 people left in the room after 240 s. In the case of the compression wall (the blue line), it may save 1 or 2 more people. The curved egression wall construction, shows a reduction in the number of casualties (number 1 or 2). This would save as many as 6 people compared to the other cases. However, with the kinetic contour wall configuration, more people would remain trapped in the room increasing the total number of up to 12. This is almost double the number in the reference case. In this research, we analyzed the role of kinetic architecture in emergency evacuation. We were concerned with the simulation of crowds in the built environment and how dynamic walls and obstacles aid in safe egressing using discrete molecular dynamics. Braess’s paradox is a well- known proposed explanation that states that obstacles or additional network may improve flow, especially in the case of traffic flow. A well-positioned obstacle can decrease internal pressure of agents and break symmetries at the egress. This mechanism leads to faster outflow and safer egression. We found that the configuration that performed better than expected when compared to the other configurations was the curved egression wall. The “obstacle” was best positioned at the entrance of the area of egression. 8.775 9.45 10.125 10.8 11.475 12.15 12.825 0 2 4 6 8 10 12 14 4.05 4.725 5.4 6.075 6.75 7.425 8.1 Radius of Curvature / m Number of People Trapped Compress Distance / m 57 Chapter 6 Conclusion Crowd modeling is an important tool for evacuation planning. Events like the 9/11, various earthquakes and tsunami around the world have brought this area of research to the forefronts of emergency planning. In this research we outlined and compared, quantitatively, two crowd models using mathematical theory of fluids and physical forces. For this research we outlined and quantitatively compared various architectural layouts. We described the strong correlation between event-driven molecular dynamics and occupants’ movement. From the microscopic view of molecular dynamics, we found application to crowd simulation where agents are supported by observations and are refined in computer simulation. Discontinuous dynamic molecular modeling was utilized to optimize kinetic walls and occupants’ egression. Kinetic structures have been shown to improve modes of egression of building occupants. The evacuation time, distribution of total distance and kinetic wall configurations were compared. It is postulated that an effective crowd simulation could converge to form a simulation metric that depict observable real-world data. As knowledge expands and modeling techniques improve we will be able to learn more about social force, psychological and behavioral science of large crowds. The proposed kinetic contour wall may show an improvement over the other architectural configuration because curved geometrical spaces reduce shear stress vector. Additionally, the results depict a streamline pattern that is consistent with fluid flow through curved spaces. Fluid flow around curved geometries is encountered in much of nature from microscopic organism to the cosmological scale. Researchers Debus, Mendoza, Succi and Herrmann detail in their journal article “Energy Dissipation in Flows through Curved Spaces,” that energy dissipation plays a significant role in fluid dynamics in curved spaces. Curvature-induced viscous forces are shown to cause appreciable energy dissipation. In recent years major progress has been made in the theory of crowd modelling and pedestrian dynamics. Since this area of research is still growing there is much room for innovation. The results show promise for fire emergency and methods of mitigating fire safety risk. 58 Chapter 7 Future Work There is a need to understand the transition from behavior at the microscopic scale to the macroscopic scale. Understanding this transition and the nature of it is crucial to understanding the turbulence of flow behind an object as it relates to crowd panic. Theories such as this is based on continuum modeling. This research analyzed the strong similarities between event-driven dynamics and occupants’ movement using discrete modeling. The latter medium presents an added challenge because crowd movement have a thinking capacity which makes the problem more intriguing. Both are supported by observations and has been refined as knowledge expands and modeling techniques improve. These simulations, whether discrete or a continuum, have to also include complicated behavioral effects. Pedestrians is simulated according to a deterministic approach. Variables taken into consideration are: -entry point of an office building, concert hall, parking lot, etc. -unexpected attractions/distraction -pedestrians demand and intention There is still much to learn about the psychological and behavioral science of large crowds. As our understanding improves modifications are developed and accommodated in the present theory. The equations presented in this research are basic equations governing molecular dynamic modeling of agents. These equations are easily solved. Numerical simulation of crowds is useful when dealing with complicated geometry. There is a need to extend current theories in a probabilistic way to include pedestrian flows to low density flows. This would create an interface between current models of human flow. There is also a need to understand the transition from behavior at the microscopic scale to the macroscopic scale. Understanding this transition and the nature of it is crucial to understanding the turbulence of flow behind an object. Understanding the interface between an architect, engineering and behavioral scientist is important. 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Abstract (if available)

Abstract Crowd modeling incorporates the study of human behavior, mathematical modeling, molecular and fluid dynamics. It has contributed to the development of emergency planning and evacuation methods. Consideration of means of egressing is important in an emergency situation. Simulating the movement of individuals in a crowd has helped scientists, engineers and designers reduce the number of deaths in buildings and public structures. Kinetic architecture is gaining popularity because of its ability to enhance energy efficiency and sustainability. This research proposes the use of kinetic architecture, in particular, kinetic walls to improve safety and efficiency during emergency evacuation. Architectural design and modes of egressing are critical in emergency evacuation. Kinetic walls are simulated in order to evaluate design optimization as it relates to rates of egression. Additionally, the impact of emergency evacuation was explored for large numbers of occupants. The research shows that the adaptive technique proposed may improve safety measures and should therefore be integrated within a conventional framework.

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Development of data-driven user-centered building façade design guideline models: machine learning-based approaches to predict user preferences

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Acoustics simulation for stadium design using EASE: analyzing acoustics and providing retrofit options for the Los Angeles Memorial Coliseum

Asset Metadata

Creator Johnson, Angella M. (author)

Core Title Collective behavior in public urban spaces: a dynamic approach for fire emergency

School School of Architecture

Degree Master of Building Science

Degree Program Building Science

Publication Date 11/28/2018

Defense Date 11/28/2018

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

Tag collective behavior,evacuation,kinetic adaptive architecture,molecular dynamics,OAI-PMH Harvest

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Schierle, G. Goetz (committee chair), Choi, Joon-Ho (committee member), Nakano, Aiichiro (committee member)

Creator Email angelajo@usc.edu,angellaj@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-109799

Unique identifier UC11675520

Identifier etd-JohnsonAng-6984.pdf (filename),usctheses-c89-109799 (legacy record id)

Legacy Identifier etd-JohnsonAng-6984.pdf

Dmrecord 109799

Document Type Thesis

Format application/pdf (imt)

Rights Johnson, Angella 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 a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA