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Integrating membrane-assisted radiant cooling panels in building energy simulation Sheppard, Denon 2020

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Integrating Membrane-AssistedRadiant Cooling Panels in BuildingEnergy SimulationbyDenon SheppardB.A.Sc., Queen’s University at Kingston, 2018A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Mechanical Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)December 2020© Denon Sheppard 2020The following individuals certify that they have read, and recommend tothe Faculty of Graduate and Postdoctoral Studies for acceptance, the thesisentitled:Integrating Membrane-Assisted Radiant Cooling Panels in Build-ing Energy Simulationsubmitted by Denon Sheppard in partial fulfillment of the requirementsfor the degree of Master of Applied Science in Mechanical Engineer-ing.Examining Committee:Adam Rysanek, Assistant Professor, School of Architecture & LandscapeArchitecture, Affiliated faculty, Mechanical Engineering, UBCCo-supervisorSteven Rogak, Professor, Mechanical Engineering, UBCCo-supervisorForrest Meggers, Assistant Professor, Architecture, Assistant Professor, An-dlinger Center for Energy and the Environment, Affiliated faculty, Civil andEnvironmental Engineering, PrincetonAdditional ExaminerAbstractThe world is in critical need of technologies that will make a significant andimmediate impact in our fight against climate change. As global temper-atures rise, building cooling demands could rise by 72% by the year 2100,meaning that the development of energy efficient space cooling technologiesis becoming increasingly important. Radiant cooling panels have shown a lotof potential as an energy efficient method of supplying space cooling. How-ever, they need to operate alongside dehumidification in many environmentsso that air moisture does not condense on their chilled surfaces.This thesis focuses on the development of the membrane assisted radiantcooling panel, a technology used to provide energy-efficient space cooling inhot and humid climates without the need for mechanical dehumidification.A heat balance model is developed that estimates the operational membranetemperature and cooling capacity of a membrane assisted panel. The modelis then calibrated using data collected from a field experiment in Singapore.Additionally, a framework is developed that allows the heat transfer modelto operate within a TRNSYS environment. This allows for the energy sim-ulation of buildings that utilize membrane assisted panels for sensible spacecooling. The framework is then used to predict the potential energy savingsthat could be obtained by implementing this technology in both Singaporeand Vancouver.The membrane temperatures predicted by the calibrated heat transfermodel differ from those observed through experimentation by 0.21oC. Themodel is sufficiently accurate for condensation mitigation, however, concernsregarding the coefficients used to model natural convection, along with thedata used for calibration, need to be addressed before the model can beapplied to different panel geometries. While some aspects of the TRNSYSframework need to be further developed, it was found through simulationthat membrane assisted radiant cooling can provide significant energy sav-ings in both tropical and temperate climates.The framework developed in this study will bring membrane assistedradiant cooling closer to widespread implementation, as modelers will beable to optimize the design of a radiant system before its construction in abuilding.Lay SummaryRadiant cooling is an energy efficient technology that is used to cool indoorspaces. One of the problems facing the widespread implantation of thistechnology is that the panel can not be colder than the dew point of theambient air, as doing so will condense air moisture. To address this prob-lem, membrane assisted radiant cooling panels were developed which isolatethe chilled surface from humid air using a semi-transparent membrane. Toimplement this technology in buildings, the temperature of the membraneand the amount of cooling the panel supplies to a space must be known.This study presents a calibrated heat transfer model that can be usedto predict both the membrane temperature and the rate of heat transfer. Aframework that can be used to integrate the developed model in commonbuilding energy simulation tools is then proposed.PrefaceThis research has been conducted and prepared by the author, Denon Shep-pard, under the supervision of Dr. Adam Rysanek.Some of the content in chapter 3 has been accepted by the conferenceeSim 2021. The submission is titled “Validated Transient Model of a NovelRadiant Cooling Panel”.Some of the content in chapter 4 has been prepared for conference sub-mission.Table of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xviiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xxii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . 41.3 Research Outline . . . . . . . . . . . . . . . . . . . . . . . . . 62 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . 92.1 Background on Radiant Cooling Panels . . . . . . . . . . . . 92.1.1 Problems Facing Radiant Cooling . . . . . . . . . . . 112.1.2 Characteristics of Condensation . . . . . . . . . . . . 122.1.3 Ventilation Control Strategies for Mitigating Conden-sation Risk . . . . . . . . . . . . . . . . . . . . . . . . 132.1.4 Local Dehumidification Panel Designs . . . . . . . . . 142.1.5 Membrane Assisted Radiant Panels . . . . . . . . . . 152.2 Methods for Evaluating Radiant Ceiling Panel Performance . 162.2.1 Thermal Performance of Standard Ceiling Panels . . 162.2.2 Thermal Performance of Membrane Assisted Panels . 172.3 Modeling Building Performance Using Simulation Software . 192.4 Research Gap . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Heat Transfer Model of Membrane Assisted Radiant Panel 213.1 The Membrane Heat Transfer Model . . . . . . . . . . . . . 223.2 Convective Heat Transfer, Q4-5 . . . . . . . . . . . . . . . . . 253.2.1 External Convection, Q4 . . . . . . . . . . . . . . . . 283.2.2 Internal Convection, Q5 . . . . . . . . . . . . . . . . . 313.3 Radiant Heat Transfer, Q1-3 . . . . . . . . . . . . . . . . . . 343.3.1 Background Theory . . . . . . . . . . . . . . . . . . . 353.3.2 Membrane Emission, Q1 . . . . . . . . . . . . . . . . 423.3.3 Chilled Surface Emission, Q2 . . . . . . . . . . . . . . 443.3.4 Surrounding Surface Emission, Q3 . . . . . . . . . . . 453.3.5 Determining the Radiant Characteristics of the Mem-brane . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.4 Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.5 Modeling Heat Transfer Between the Panel and its Surround-ings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.5.1 Modeling Radiant Exchange with the Panel’s Surround-ings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.5.2 Modeling Convective Exchange with the Panel’s Sur-roundings . . . . . . . . . . . . . . . . . . . . . . . . . 523.5.3 Determining the Mean Radiant Temperature of thePanel . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.6 Model Creation using Python . . . . . . . . . . . . . . . . . 553.6.1 Determining Model Variables for Convection Scenar-ios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.6.2 Implementing Radiative Properties of the Membrane 563.7 Membrane Temperature Model Validation . . . . . . . . . . 573.7.1 Obtaining Reference Data . . . . . . . . . . . . . . . 573.7.2 Calibration Approach . . . . . . . . . . . . . . . . . . 603.8 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.9 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663.9.1 Model Performance . . . . . . . . . . . . . . . . . . . 663.9.2 Panel Development . . . . . . . . . . . . . . . . . . . 683.9.3 Comparison to Previous Literature . . . . . . . . . . 704 Building Energy Modeling in TRNSYS . . . . . . . . . . . . 734.1 Building Energy Modelling . . . . . . . . . . . . . . . . . . . 744.1.1 Walls, Floor, Roof . . . . . . . . . . . . . . . . . . . . 744.1.2 Windows and Shading . . . . . . . . . . . . . . . . . 754.1.3 Occupancy . . . . . . . . . . . . . . . . . . . . . . . . 764.1.4 Electrical Appliances and Lighting . . . . . . . . . . . 774.1.5 Infiltration . . . . . . . . . . . . . . . . . . . . . . . . 794.1.6 Modeling Radiant Panels . . . . . . . . . . . . . . . . 794.1.7 Modeling of Electrical Energy Consumption . . . . . 824.2 Simulated Scenarios . . . . . . . . . . . . . . . . . . . . . . . 854.2.1 Investigation of Singapore (hot and humid climate) . 864.2.2 Investigation of Vancouver (Mediterranean climate)under climate change . . . . . . . . . . . . . . . . . . 864.2.3 Mechanical System Configurations . . . . . . . . . . . 874.3 Methods for Assessing Thermal Comfort . . . . . . . . . . . 944.3.1 PMV-PPD . . . . . . . . . . . . . . . . . . . . . . . . 954.3.2 Adaptive Comfort Model . . . . . . . . . . . . . . . . 964.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 984.4.1 Singapore Energy Performance Results . . . . . . . . 984.4.2 Vancouver RCP 8.5 2080 Energy Performance Results 1024.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1044.5.1 Framework Performance . . . . . . . . . . . . . . . . 1044.5.2 Simulated Environments . . . . . . . . . . . . . . . . 1114.5.3 Future Development . . . . . . . . . . . . . . . . . . . 1135 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118AppendicesA Monte Carlo Optimization Results . . . . . . . . . . . . . . . 133B Bridging TRNSYS and Python . . . . . . . . . . . . . . . . . 136B.1 Human to Panel View Factor Calculations . . . . . . . . . . 136B.2 Determining the MRT of the Panel’s Surroundings . . . . . . 138B.3 Determining Chilled Surface Temp from Inlet Temp . . . . . 140B.4 Calculating Heat Exchange Between the Panel and the BuiltEnvironment . . . . . . . . . . . . . . . . . . . . . . . . . . . 142B.5 Determining the MRT Perceived by Occupants . . . . . . . . 142B.6 Determining Thermal Comfort . . . . . . . . . . . . . . . . . 143B.7 Updating Panel Temperature . . . . . . . . . . . . . . . . . . 143C Estimating Calibrated Vertical Panel Performance . . . . . 144List of Tables3.1 Sensitivity of Membrane Temperature Model to its Parameters. 633.2 Optimized Membrane Temperature Model Parameters. . . . . 654.1 Table displaying the COPs used for different mechanical con-figurations an climates. . . . . . . . . . . . . . . . . . . . . . . 854.2 Systems Parameters: Radiant Cooling + Natural Ventilation. 904.3 Systems Parameters - Dehumidification/Mechanical Ventila-tion + Radiant. . . . . . . . . . . . . . . . . . . . . . . . . . . 924.4 Systems Parameters: Split system air conditioning. . . . . . . 954.5 Table displaying key performance metrics in the SingaporeClimate. From left to right, the result columns correspondto radiant cooling + natural ventilation, radiant cooling +dehumidification, and air conditioning scenarios. . . . . . . . 994.6 Table displaying key performance metrics in the VancouverClimate. From left to right, the result columns correspondto radiant cooling + natural ventilation, radiant cooling +mechanical ventilation, and air conditioning scenarios. . . . . 103List of Figures1.1 Schematic of Cold Tube panel (above) and illustration of ra-diant heat transfer through the panel (below) [87] . . . . . . . 31.2 The Cold Tube pavilion [87] . . . . . . . . . . . . . . . . . . . 41.3 Flowchart illustrating the structure of the thesis . . . . . . . 82.1 A schematic of the novel panel proposed by Charara et al. [24] 152.2 A comparison of experimental vs calculated results. This fig-ure was obtained from a study conducted by Xing et al. [93] . 183.1 The modes of heat transfer affecting the membrane. . . . . . 243.2 (a) Radiation components of a gray opaque surface. (b) Ra-diation traveling through a semi transparent surface. . . . . . 383.3 Illustration of two surface emitting different amounts of radi-ant energy because of different surface temperatures. . . . . . 393.4 Path of the energy emitted by the membrane. . . . . . . . . . 433.5 Path of the energy emitted by the chilled surface. . . . . . . . 443.6 Path of the energy emitted by the surrounding surface. . . . . 463.7 Diagram illustrating the net radiative heat transfer betweenthe panel and its surroundings. . . . . . . . . . . . . . . . . . 503.8 Diagram illustrating the total radiant energy traveling awayfrom the panel. . . . . . . . . . . . . . . . . . . . . . . . . . . 543.9 Wind speed measurements within Cold Tube. This figure wastaken from a study conducted by Teitelbaum et al. [86]. Theaverage wind speed line was added for this study. . . . . . . . 593.10 Non-calibrated correlation between modeled and measuredmembrane temperatures. . . . . . . . . . . . . . . . . . . . . . 623.11 Frequency of temperature difference results produced duringthe Monte Carlo simulation. . . . . . . . . . . . . . . . . . . . 653.12 Calibrated correlation between modeled and measured mem-brane temperatures. . . . . . . . . . . . . . . . . . . . . . . . 663.13 Graph showing how membrane temperature changes with paneldepth. This figure was taken from a study conducted by Xinget al. [93] where they evaluated a different approach to mod-eling a membrane assisted panel. . . . . . . . . . . . . . . . . 694.1 Comparing the facade of a real office in Singapore to the model. 754.2 The daily schedule used to determine internal gains causedby occupants. . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.3 An illustration of the thermal gain locations in the officespace, as well as the radiant exchange between occupants andpanel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.4 The daily schedule used to determine internal gains causedby electrical equipment. . . . . . . . . . . . . . . . . . . . . . 784.5 The daily schedule used to determine internal gains causedby lighting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.6 Diagram showing the sub-tasks that allows the heat transfermodel to operate in TRNSYS . . . . . . . . . . . . . . . . . . 804.7 A plot showing how COP increases as lift decreases. It wastaken from a study conducted by Meggers et al. [59] . . . . . 834.8 A plot showing how COP of a chiller is correlated to thefraction of the design load it is experiencing. It was takenfrom a study conducted by Seshadri et al. [78]. . . . . . . . . 844.9 Mechanical system diagram of the radiant + natural ventila-tion configuration. . . . . . . . . . . . . . . . . . . . . . . . . 894.10 Mechanical system diagram of the radiant + dehumidificationconfiguration. . . . . . . . . . . . . . . . . . . . . . . . . . . . 914.11 Mechanical system diagram of the split system air condition-ing configuration. . . . . . . . . . . . . . . . . . . . . . . . . . 944.12 Dependence of PPD on PMV. This graph was taken from astudy by Enescu [30]. . . . . . . . . . . . . . . . . . . . . . . . 964.13 Graph showing the indoor operative temperatures that willresult in a comfortable environment as a function of outdooreffective temperature. This graph was taken from a study byDe Dear and Brager [26]. . . . . . . . . . . . . . . . . . . . . 974.14 A comparison of the annual energy consumption of the threemechanical systems being simulated using the Singapore cli-mate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1004.15 Diagram showing how the membrane temperature is main-tained above the dew point for the Singapore Radiant + Nat-ural Ventilation scenario. . . . . . . . . . . . . . . . . . . . . 1004.16 Diagram showing how the membrane temperature is main-tained above the dew point for the Singapore Radiant + De-humidification scenario. . . . . . . . . . . . . . . . . . . . . . 1014.17 Diagram showing that thermal comfort is maintained in theSingapore Radiant + Natural Ventilation scenario. . . . . . . 1014.18 Diagram showing that thermal comfort is maintained in theSingapore Radiant + Dehumidification scenario. . . . . . . . 1024.19 A comparison of the annual energy consumption of the threemechanical systems being simulated using the future Vancou-ver climate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1044.20 Diagram showing how the membrane temperature is main-tained above the dew point for the Vancouver Radiant +Natural Ventilation scenario. . . . . . . . . . . . . . . . . . . 1054.21 Diagram showing how the membrane temperature is main-tained above the dew point for the Vancouver Radiant + Me-chanical Ventilation scenario. . . . . . . . . . . . . . . . . . . 1064.22 Diagram showing that thermal comfort is maintained in theSingapore Radiant+Natural Ventilation scenario. . . . . . . . 1074.23 Diagram showing that thermal comfort is maintained in theVancouver Radiant+Mechanical Ventilation scenario. . . . . . 108B.1 Parameters to be used in Equation B.1 for a seated person [20].137B.2 Description of analyzed scenarios B.1 for a seated person [20]. 137B.3 Coordinates between a person and a surface [20] . . . . . . . 138B.4 Relationship between inlet and chilled surface temperatures. . 141C.1 Relationship between the internal horizontal/vertical convec-tive coefficient ratio and the temperature difference betweenthe membrane and chilled surface. . . . . . . . . . . . . . . . 145C.2 Relationship between the external horizontal/vertical convec-tive coefficient ratio and the temperature difference betweenthe membrane and chilled surface. . . . . . . . . . . . . . . . 146List of SymbolsConvective Heat Transferα : Thermal diffusivity of fluid [m2/s]β : Thermal expansion coefficient [1/K]〈Nul〉l : Average Nusselt number, vertical panel external convection〈NuS〉 : Average Nusselt number, vertical panel external convection〈NuS〉l : Average Nusselt number, vertical panel internal convection〈Nulc〉 : Average Nusselt number, horizontal panel external convectionν : Kinematic viscosity of fluid [m2/s]υ : Fluid velocity [m/s]AM : Surface area of membrane [m2]g : Gravity [m/s2]h : Convective heat transfer coefficient [W/m2/K]k : Thermal conductivity of the fluid [W/m/K]L : Characteristic length of flow scenario [m]l : Panel height [m]lc : Panel surface area/perimeter [m]n : Empirical parameterNu : Nusselt numberNuF : Forced convection Nusselt numberNuN : Natural convection Nusselt numberPr : Prandtl NumberQnet conv : Panel’s convective thermal exchange with its surroundingsQconv : Convective heat transfer [W]Ra : Rayleigh NumberRe : Reynolds NumberS : Distance between the panel’s chilled surface and membrane [m]Tf : Temperature of fluid [K]TM : Surface temperature of membrane [K]Tcs : Temperature of chilled surfaceGeneral SymbolsQ1 : Radiation emitted by the membrane [W]Q2 : Radiation emitted by the chilled surface [W]Q3 : Radiation emitted by the surrounding surfaces [W]Q4 : External natural convection [W]Q5 : Internal natural convection [W]Radiant Heat Transferαλ : Spectral absorption component [%/µm]λ : Wavelength being analyzed [µm]ρλ : Spectral reflection component [%/µm]]σ : Stefan-Boltzmann constant [W/m2/K4]τλ : Spectral transmission component [%/µm]]ε : Emissivity of surfaceελ : Spectral emissivityAs : Surface area [m2]C1 : 3.743(10)8 [W/(µm4/m2)]C2 : 1.439(10)4 [µm-K]E : Total emission [W/m2]Eλ : Spectral emission [W/m2/µm]Fnm : View factor from surface n to mGλ : Spectral irradiance [W/m2/µm]Jλ : Spectral radiosity [W/m2/µm]Jn : Total energy traveling away from surface n [W/m2]kλ : spectral absorption coefficientL : Membrane thickness [M]Qλ,absorbed : Energy absorbed by surface spectrally [W/µm]Qλ,reflected : Energy reflected off surface spectrally [W/µm]Qλ,transmitted : Energy transmitted through surface spectrally [W/µm]QMRT Total radiant energy traveling away from panelQnet rad Panel’s net radiant thermal exchange with its surroundingsT : Surface temperature [K]TMRT : Mean radiant temperature [K]CS: Chilled surfaceM: MembraneSS: Surrounding surfacesAcknowledgementsFirstly I would like to thank Dr. Adam Rysanek at the University of BritishColumbia for his constant guidance and for giving me the opportunity toresearch a topic that I’m extremely passionate about. You provided me withso many opportunities beyond my Master’s thesis. I knew I made a goodchoice the moment I read that one of your favorite hobbies is beer brewing.I express my sincere thanks to my committee members Dr. Steven Rogakand Dr. Forrest Meggers. You supported me with helpful advice and gave memany opportunities that helped me to develop into an independent engineer.I would also like to thank all my friends, family, and co-workers thatsupported me throughout my studies. You always provided me with lotsof encouragement and advice when I needed it most. Special thanks to myparents and Weeda Mamozai for the extra support they gave me during thefinal stages of my thesis.Chapter 1Introduction1.1 BackgroundThe world is in critical need of technologies that will make a significant andimmediate impact in our fight against global climate change. To achievethis goal, we must target the most demanding energy end-use sectors, anddevelop technologies that will reduce their energy demands. In many devel-oped countries, buildings are the most demanding energy sector, accountingfor 40% of the total Primary Energy Requirement (PER) in the USA, 39%in the UK, and 37% in the EU [71]. As climate change increases the aver-age global temperature, heating demand in buildings could drop by up to34% by the year 2100, however, cooling demands could rise by 72% [47],meaning that the development of energy efficient space cooling technologiesis becoming increasingly important. The need for rapid development in thisfield led to the creation of the Global Cooling Prize, which incentivizes in-novation in affordable energy efficient cooling technologies [72]. They claimthat currently about 30% of the world’s population is exposed to potentiallydangerous heat conditions, and by 2100, about 75% could be at risk. Bythe year 2050, the world will see a massive increase in the number of airconditioning units in service around the world, with developing countriesexperiencing the largest increase in demand. Additionally, the global airconditioning industry has relied largely on market signals, which has not in-centivised them to develop low cost, energy efficient solutions. This has putthe burden on researchers to develop cooling technologies that can addressheightened cooling demands while mitigating runaway climate change.One space cooling technology with the potential to address these chal-lenges is the radiant cooling panel. This technology can provide coolingin many climates with significant energy savings when compared to con-ventional air conditioning systems [61, 67, 96]. Radiant cooling can alsoprovide increased thermal comfort to occupants, as it cools the human bodymore evenly [45]. However, the cooling output of a radiant cooling systemis limited by the dew point of the environment it is in. If the surface of theradiant cooling panel drops below the dew point temperature of its environ-ment, condensation will begin to form on its chilled surface. This diminishesthe system’s energy efficiency and poses health concerns to occupants. Ashumid environments are often hot environments, adequate cooling can notbe supplied to these spaces without additional interventions.Pairing radiant cooling with dehumidification is a common approachused to avoid condensation. However, researchers have begun to realize thepotential of membrane assisted radiant cooling, which was first proposed byMorse [62] in 1963. A modern version of this technology has been developedwith the purpose of providing radiant cooling to hot and humid climateswithout mechanical dehumidification. This technology has been named theCold Tube [83], and can be seen in Figure 1.1.The Cold Tube allows the temperature of its chilled surface to be belowFigure 1.1: Schematic of Cold Tube panel (above) and illustration of radiantheat transfer through the panel (below) [87]the dew point of the ambient air by isolating the surface from the air us-ing a semi-transparent membrane. The membrane traps dry air inside thepanel, meaning that the temperature of the chilled surface is always abovethe dew point of the air it is in contact with. The membrane is kept ata temperature higher than the dew point of the ambient air, and allowsradiant energy to pass between the panel and its surroundings due to themembrane’s transparency to infrared radiation. To demonstrate the ColdTube’s ability to provide cooling in hot and humid environments withoutthe need for dehumidification, the Cold Tube pavilion was developed. Thisoutdoor, radiantly cooled structure was built in Singapore and allows peoplethe experience of being radiantly cooled while being surrounded by hot andhumid air. The Cold Tube pavilion can be seen in Figure 1.2, and is a col-laboration between the ETA Lab (UBC), Singapore-ETH Center, CHAOSLab (Princeton University), Center for Built Environment (UC Berkeley),and the Chair of Architecture and Building Systems (ETH Zurich).Figure 1.2: The Cold Tube pavilion [87]The Cold Tube demonstrated that membrane assisted radiant coolingcan provide thermal comfort to occupants outdoors in Singapore while avoid-ing condensation [87].1.2 Research ObjectivesThis thesis will further develop membrane assisted radiant cooling technol-ogy by creating a model that can predict the membrane’s temperature underany environmental condition as well as the thermal energy that is exchangebetween the panel and its surroundings. A framework will then be devel-oped that integrates the developed heat transfer model within a TRNSYSenvironment. This will allow for the energy simulation of a building thatuses this technology. TRNSYS is a transient system simulation tool that iscommonly used to conduct building energy simulations [53]. It allows forthe modeling of very detailed mechanical systems, and can utilize modelsdeveloped in other programs such as Python or MATLAB. This TRNSYSframework will bring the technology closer to widespread implementation,as modelers will be able to optimize the design of a radiant system before itis constructed in a building.The 4 research objectives of this study are as follows:1. Identify research gaps through a literature review.2. Develop a heat transfer model that can predict the temperature ofthe membrane along with the cooling power the panel applies to itsenvironment.3. Calibrate the model using data obtained from the Cold Tube experi-ment in Singapore.4. Develop a TRNSYS framework that can use the heat transfer modelto predict energy performance in a space that utilizes a membraneassisted panel.The literature review will identify that at the time of writing, no in depthscience based heat transfer model of a membrane assisted radiant coolingpanel had been created or integrated into transient building energy simu-lation. To accomplish objective #2, a model is created that analyzes thevarious modes of heat transfer that affects the membrane. To accomplishobjective #3, a sensitivity analysis is used to determine the model’s mostsensitive parameters, which are then calibrated using data collected fromthe Cold Tube pavilion though a Monte Carlo optimization. The final ob-jective is accomplished by creating a TRNSYS framework that allows forthe operation of the heat transfer model within the TRNSYS environment.This is done by creating methods that convert environmental informationinto the inputs required by the heat transfer model. Information regardingthe panel’s cooling output is then returned to TRNSYS so it can be appliedto the simulated space.The following are the main contributions of this thesis:1. Presents a calibrated model of a membrane assisted radiant panel thatcan be integrated into building energy simulation.2. The developed framework will allow future researchers and buildingdevelopers to predict the potential energy savings of integrating mem-brane assisted cooling panels into their building’s energy system.3. Illustration of the energy saving potential of combining membrane as-sisted radiant panels with natural ventilation, and demonstration ofits relevance in both tropical and temperate climates.1.3 Research OutlineChapter 1 outlines the need for advancements in space cooling technologyand the history of the Cold Tube. It also lays out the objectives and structureof the thesis. Chapter 2 presents a literature review covering the history ofradiant cooling, the approaches used to model the cooling capacity of radiantcooling panels, and approaches used to simulate radiant cooling panels usingTRNSYS. Chapter 3 presents the methodology behind developing and cali-brating the heat transfer model that simulates both the panel’s effect on theroom and its membrane temperature during operation. Chapter 4 presentsthe framework that allows for the integration of the heat transfer modelwith a TRNSYS environment. Chapter 5 summarizes the key conclusionsof this research, and provides recommendations for the further developmentof this technology. A complete breakdown of the chapters of this thesis canbe seen in Figure 1.3.Figure 1.3: Flowchart illustrating the structure of the thesisChapter 2Literature ReviewThis chapter surveys the literature on radiant cooling panels, including abrief history of the technology, methods used to model their cooling capacity,and ways in which radiant panel models have been integrated in buildingenergy simulation.2.1 Background on Radiant Cooling PanelsRadiant panels have been used to control thermal comfort in the built en-vironment for thousands of years [11, 12, 14, 15, 48]. Credit is often givento the ancient Romans for giving life to these systems, but research into an-cient texts show that this technology was first developed in Asia thousandsof years prior [14]. The Korean Ondol and the Roman Hypocaust systemsburn coal or wood to create hot smoke. This smoke then travels throughchannels beneath the floor, where the heat is absorbed and radiated into theoccupied space above.Radiant cooling (RAC) systems have gained a lot of interest recentlydue to their ability to provide thermal comfort indoors using less energyrelative to commonly used air conditioning approaches [69, 97]. A prelim-inary assessment of radiant cooling for US markets by Feustel and Stetiu[33] states that a significant portion of the energy required to air conditionnon-residential buildings is due to the fan power required to transport suf-ficient thermal energy. It then states that a building that uses an all aircooling system has an electrical peak load breakdown of approximately 37%for operating the fans and 63% for running the chiller. If a radiant coolingsystem is used to separate the tasks of ventilation and thermal condition-ing, the electrical energy requirement for fans and pumps can be reduced byabout 25%. It also states that the large amount of space available for radiantcooling means that these radiant surfaces need only be slightly lower thanambient temperature, meaning that heat pumps with very high coefficientsof performance (COP) can be used. A study by Roulet et al. [74] states thatradiant panels can sufficiently maintain a comfortable environment at only aslight temperature difference from room temperature. The paper illustratesanother benefit of radiant cooling, stating that it is likely the best optionto use when minimizing vibrations and noise, and maximizing temperaturestability are top priorities. A paper published in 1999 by Imanari et al.[45] compares occupant comfort and energy performance of a convectionalradiant cooling and air conditioning systems in a Japanese office building.It states that a radiant system would use 10% less energy while providingbetter thermal comfort to occupants. This reduction in energy consumptionwas primarily due to the 20% reduction in air transport energy.Studies focusing on energy saving potential in hot and humid environ-ments predict even greater energy savings [51, 67]. Zhang and Niu [96]compares the energy performance of a conventional all air, all air with heatrecovery, chilled ceiling with air handling unit (AHU), and chilled ceilingwith desiccant cooling systems with Hong Kong weather conditions usingthe cooling load program ACCURACY. It states that the chilled ceilingwith AHU system achieves 47% primary energy reduction relative to theconventional all air system and the chilled ceiling with desiccant coolingsaves 30% to the conventional all air system. It then states that addingtotal heat recovery ventilators to the all air system achieves 9% energy sav-ings relative to the conventional all air system. Kim et al. [51] compares theenergy performance of an all air, conventional radiant cooling, and a hybridradiant cooling plus Airbox convector system to be used in Shanghai China.It states that the hybrid system can achieve 9.3% reduced energy consump-tion relative to the conventional radiant system due to the hybrid systemhaving a larger cooling impact ratio, the chiller having a higher coefficientof performance, and increased air movement in the room. In this study,the cooling impact ratio is defined as the ratio between the actual obtainedcooling output from supplied air to a room, Airbox convector, and suppliedwater to the ceiling panel and the total cooling input required to produceenergy.2.1.1 Problems Facing Radiant CoolingDespite the advantages, one of the main challenges that is preventing thewidespread adoption of this technology is that air moisture will condenseon the panel if the panel’s surface temperature drops below the dew pointtemperature of its local environment [50, 69, 96]. This makes adoption ofthis technology in hot and humid climates difficult. A CFD study conductedby Teodosiu et al. [88] states that when moist warm air is added to a smalloffice building, a radiant cooling system alone can not provide sufficientthermal comfort. Another important finding from this study is that whenuntreated air is being provided to a room, mixed ventilation results in bettercondensation control and thermal comfort when compared to displacementventilation. For climates where a high degree of condensation risk is present,coupling radiant cooling with dehumidification is the primary method usedto deal with this issue [73]. In a review of radiant heating and cooling ap-plications in mainland china [43], four major projects consisting of differentbuilding types in different climate zones were assessed, and each required adehumidification system.2.1.2 Characteristics of CondensationThe significant challenges presented by condensation risk has led to manyresearch studies investigating the parameters that cause condensation toform on radiant cooling panels. Tang and Liu [81] compared an aluminiumradiant cooling panel treated with a hydrophobic surface to a non-treatedpanel. It was observed that at a sub cooling degree of about 2.8oC, thetime between condensate nucleating and falling off a horizontal panel wasgreater than 10h for both panels, although nucleation fell about 0.5h laterfor the hydrophobic panel. This indicates that condensation is likely not aconcern when a room experiences an event that intermittently causes theradiant panel to fall below the dew point of the room. However, it does notprovide conclusive evidence that using a hydrophobic surface can sufficientlycontrol condensation when the panel is held significantly below the dew pointfor long periods of time. Another study by Tang et al. [82] looked at thecondensation risk of radiant cooling panels based on their position in a room.It concluded that the rate of condensation forming on a radiant ceiling is3.5 times higher than on a radiant floor, and 1.25 times greater than ona radiant wall. It states that the driving force of condensation is the airdensity difference between the ambient air and the saturated air close tothe panel. Despite the condensation advantages, membrane assisted paneltechnology can not be applied to radiant floors. Radiant cooling panels canoften experience uneven surface temperatures due to the temperature changeof the fluid traveling though the panel. This is not ideal as locations thatexperience low temperatures can cause condensation, even if the averagetemperature of the panel is above the dew point. Ning et al. [66] proposeda novel panel design where the metal layer that is in contact with the pipescarrying chilled water is distanced from the panel’s outer surface by a thinair gap. This air gap results in a uniform surface temperature, but reducesthe panel’s cooling capacity by 14.2%.2.1.3 Ventilation Control Strategies for MitigatingCondensation RiskThere have been many studies investigating ventilation strategies tailoredtowards controlling condensation [38, 39, 50, 58]. Ge et al. [35], Kim andLeibundgut [49] used neural network predictions to investigate the optimalpre-dehumidification time for condensation avoidance. Pre-dehumidificationis a ventilation strategy where the space is dehumidified before the chilledpanel is activated. The study found that if pre-dehumidification takes placetoo close to the activation of the panel, the space might not reach its targetrelative humidity fast enough and the panel could condense air moisture.Conversely, dehumidifying long before the panel is activated will waste en-ergy. It was concluded that a pre-dehumidification time of about 30 minutesis sufficient for a typical office building in Hong Kong with an air infiltra-tion rate of 0.1 air changer per hour. The study states that optimal pre-dehumidification time depends on air infiltration rate, as 45 minutes wererequired when the infiltration rate of was 0.3 air changes per hour. Zhangand Niu [96] also conducted an investigation into pre-dehumidification andventilation requirements specifically in hot and humid climates, and con-cluded that initiating dehumidification 1 hour in advance of cooling paneloperation is sufficient to avoid condensation problems, and that no advanceddehumidification is required if the air infiltration rate of the space is <0.05at night. Song et al. [79] proposes a radiant floor cooling system coupledwith dehumidification that controls condensation on floor surfaces while pro-viding thermal comfort.2.1.4 Local Dehumidification Panel DesignsSome novel radiant cooling panel designs have been proposed that provideboth cooling and dehumidification, meaning that just the air around thepanel is dehumidified which reduces the dehumidification load on the sys-tem. One research group proposed a panel that removes moisture from itssurroundings using a flowing aqueous salt solution [31, 32]. Another researchgroup has proposed a novel panel and control strategy that uses liquid-to-airmembrane energy exchangers (LAMEEs). These panels dehumidify the airsurrounding the panel, and transfers this dehumidified air and the liquiddesiccant leaving the panel to the room’s displacement ventilation systemto reduce the amount of humidity build-up at the occupant level [24, 76]. Aschematic of this panel can be seen in Figure 2.1.Figure 2.1: A schematic of the novel panel proposed by Charara et al. [24]2.1.5 Membrane Assisted Radiant PanelsAlthough significant energy savings have been demonstrated through opti-mized condensation control strategies, additional energy savings are believedto be obtainable if a radiant cooling panel could operate below the ambientdew point without the need for dehumidification. This was first proposedin 1963 in a study by Morse [62] where sub dew point cooling was achievedby designing a panel that separated the chilled surface from humid ambientair though the use of a semi-infrared transparent membrane. Dry air wastrapped in the cavity between the membrane and the chilled surface, allow-ing the chilled surface to be well below the dew point of the surroundingair. The membrane was mechanically heated, which was a source of systeminefficiency, but the concept of membrane assisted radiant cooling was born.This technology was further developed by a research team from Princetonmany years later. Their first study demonstrated that condensation couldbe controlled without mechanically heating the membrane [84]. The feasibil-ity of this technology was then demonstrated in Singapore, where the ColdTube pavilion was able to maintain a mean radiant temperature 14.3oC be-low ambient air temperature while avoiding moisture condensation [83, 85].2.2 Methods for Evaluating Radiant CeilingPanel PerformanceThere are many methods used to evaluate the thermal performance of ra-diant panels. This literature review will focus on radiant ceiling panels,as thermally active building structures (TABS) and radiant floor modelsgenerally have added complexity due to their thick concrete construction.2.2.1 Thermal Performance of Standard Ceiling PanelsIn 1990, Glueck [37] proposed a simple empirical correlation that accountsfor both the radiant and convective heat flux transferred from a radiantcooling panel. This equation can be seen below.q” = 8.92(Tair − TCP )1.1 (2.1)Studies have used this correlation to predict the total heat transfer be-tween a radiant panel and a room [38]. Causone et al. [22] evaluated genericheat transfer coefficients that could be used to quickly model the heating/-cooling capacity of a radiant panel.Modeling RadiationThe radiant cooling capacity is often modeled using basic equations of radia-tive heat transfer and the laws of conservation of energy. Su et al. [80] usesa typical gray surface radiant heat balance to predict the net heat exchangebetween the panel and the different surfaces in the room. Ardehali et al. [8]goes a step further and applies the radiosity/irradiation method (RIM) tomodel radiation affecting the panel, and utilizes a complex matrix approachfor determining the total radiosity leaving the panel.Modeling ConvectionThere have been several studies that focus on modeling convective heattransfer on building interior surfaces. Alamdari and Hammond [2] derivedimproved data correlations to model buoyancy driven convective heat trans-fer on internal surfaces of naturally ventilated buildings. Fisher and Peder-sen [34] builds upon these correlations to take mixed convection into account.2.2.2 Thermal Performance of Membrane Assisted PanelsAlthough no literature was found at the time of conducting the research forthis thesis, a paper published in April of 2020 outlines a method of modelingthe heat transfer of a membrane assisted radiant cooling panel [93].A radiative network derived from a study by Dai et al. [25] was used tomodel an opaque closed system containing a transparent surface. Internaland external convective heat transfer rates were integrated into this network,allowing for the determination of membrane temperature and the net heattransfer rate between the panel and its surroundings. The heat transfermodel was validated using data obtained from a study conducted by Wang[90]. This study developed an experimental setup that simulates a membraneassisted radiant panel. The temperature observed during this experimentas well as the panel’s cooling capacity was compared to the results obtainedfrom the theoretical model. It was found that the experimental results agreewith the calculated results, as seen in Figure 2.2.Figure 2.2: A comparison of experimental vs calculated results. This figurewas obtained from a study conducted by Xing et al. [93]Xing et al. investigated various panel properties. It was found that thepanel depth that causes the transition from pure conduction to natural con-vection results in the highest membrane temperature when analyzing paneldepths between 0-50 mm. However, it is unclear if a panel depth greater than50 mm will results in an increased membrane temperature. Xing et al. statesthat the cooling capacity of a membrane assisted panel is highly sensitiveto the emissivity and transmissivity of the membrane, while the temper-ature of the membrane is not sensitive to these parameters. Finally, thepanel was simulated using various theoretical membrane materials. Thiswas to determine the membrane properties that allows a membrane assistedpanel to outperform a standard radiant panel under different environmentalconditions.2.3 Modeling Building Performance UsingSimulation SoftwareThough the primary computer-based methods used to simulate a buildingthat uses radiant cooling panels are TRNSYS, Energy Plus, ACCURACY,RADCOOL, and CFD [73], this review focuses on studies that use TRNSYSas it is the program used in this thesis. Miriel et al. [61] developed a novelapproach of modeled a suspended radiant panel in TRNSYS. The panel isrepresented in TRNSYS as the surface that separates two air zones whichallows convection and radiation on both sides of the panel to be modelled.Both Saelens et al. [75] and Memon et al. [60] used the active layer modelincluded in TRNSYS to model the panel’s interaction with a room. Zakulaet al. [95] uses matlab and TRNSYS to simulate a raadint panel, and employsthe usage of low-lift heat pump COP values to estimate system energy usage.Several other TRNSYS studies were reviewed [40, 56, 58], however none ofthe studies referenced in this section present simulation methods that areapplicable to membrane assisted radiant cooling. The active layer modelintegrated in TRNSYS is commonly used to model radiant panels. However,it is not used in this thesis as it can not model all the characteristics of amembrane assisted cooling panel.2.4 Research GapThere are few computational models that look at membrane assisted panels,however there is not yet evidence of work that develops a model with thecomplete functionality required for integration into building energy simula-tion software. Additionally, there is no framework currently developed thatallows for the integration of such a model.Chapter 3Heat Transfer Model ofMembrane Assisted RadiantPanelThis chapter explains the equations and calculations required to predictthe membrane temperature of a membrane assisted radiant panel, as wellas the heat transfer that occurs between the panel and its surroundings.The topics covered are as follows: The heat balance equation that governsthe membrane’s equilibrium temperature. The methods used to model theconvection heat transfer that occurs both internal and external to the panel.Radiant heat transfer, which includes the relevant background theory, howthe radiant heat balance equations are developed, and how the emission fromeach surface is analyzed. The reasoning behind conduction not appearing inthe heat transfer model. An analysis of how to determine the rate of heattransfer between the panel and its surroundings. An overview of how themodel is implemented in Python, followed by the methods used to validatethe model. This chapter finishes with a results and discussion section.3.1 The Membrane Heat Transfer ModelKnowing the temperature of the panel’s membrane is critical to the conden-sation free operating of the panel. The panel avoids condensing moisture onthe chilled surface by trapping extremely dry air inside the panel. A semitransparent membrane which is highly transparent to radiant thermal energycontains this dry air. When the panel is operating, the chilled surface con-tinuously cools the membrane, and as the membrane’s temperature lowers,it absorbs more convective energy from the ambient air, and more radiantenergy from the surfaces surrounding the panel. The membrane reaches itsequilibrium temperature when the amount of energy it losses to the chilledsurface is equal to the amount of energy it absorbs from the panels surround-ings. This means that even though the temperature of the chilled surfacecan be well below the dew point of the ambient air, a sufficiently low chilledsurface temperature can cause the temperature of the membrane to dropbelow this dew point. Accurately predicting the membrane temperature,and in turn the chilled surface temperature that will cause condensation onthe membrane, is critically important to the condensation free operation ofthe panel, especially in humid climates.Equation 3.1 is used to determine the equilibrium membrane tempera-ture by modeling each instance of heat transfer (Q) that affects the mem-brane. The membrane temperature of the panel is the value that causes thesum of the heat transfer terms on the left side of Equation 3.1 to equal zero.Q1 +Q2 +Q3 +Q4 +Q5 = 0 (3.1)Q1 : Radiation emitted by the membrane [W]Q2 : Radiation emitted by the chilled surface [W]Q3 : Radiation emitted by the surrounding surfaces [W]Q4 : External natural convection [W]Q5 : Internal natural convection [W]As seen in Equation 3.1, there are five instances of heat transfer thatmake up the total heat transfer affecting the membrane at any given time,three being radiant and two being convective. These modes of heat transferare illustrated in Figure 3.1.The radiant heat emitted by each surface is analyzed separately to de-termine how it affects the membrane. Internal natural convection exchangesheat between the chilled surface and the membrane, while external mixedconvection exchanges heat between the membrane and the air surroundingthe panel. Technically, conduction takes place through the membrane, butgiven its small width, it is assumed that both sides of the membrane are thesame temperature. This simplifying assumption, along with the uniformwall temperature assumption (UWT), are made in a similar study by Xinget al. [93].Figure 3.1 shows that the radiant energy impinging on the chilled sur-face is reflected back towards the membrane, while radiant energy impingingon the surrounding surfaces does not reflect. This is because the temper-ature used to determine the energy leaving the surrounding surfaces is themean radiant temperature (MRT). This is not the surface temperature ofthe surfaces, but the temperature that the surfaces need to be if they hadFigure 3.1: The modes of heat transfer affecting the membrane.an emissivity of 1. An emissivity of 1 means the radiant energy that im-pinges on the surface gets completely absorbed. MRT is used because thetemperature of building surfaces are often determined using MRT sensors.It also increases modeling simplicity as reflections are not modeled off ofthese surfaces.It is important to note that this heat transfer model is only concernedwith heat transfer that affects the temperature of the membrane. For exam-ple, some energy gets transferred between the chilled surface and the wall itis attached too, but as the temperature of the chilled surface is assumed tobe controlled, it is not necessary to take this instance of heat transfer intoaccount when estimating the membrane’s temperature.Finally, Even though Figure 3.1, shows a vertical panel, the model canbe applied to a horizontal panel, as this is how they will often be installedin buildings. The following sections explain the equations that allow for themodelling of each of the five modes of heat transfer.3.2 Convective Heat Transfer, Q4-5During the panel’s operation, convection is continuously transferring ther-mal energy from the air surrounding the panel to the panel’s membrane,while simultaneously transferring energy from the membrane to the chilledsurface. The convection that occurs within the panel will always be naturalas it is isolated from the ambient air, while convection that occurs betweenthe membrane and the surrounding air can be natural or mixed dependingon the panel’s local environment. All the equations used in this section arefrom the convective heat transfer textbook by Ghiaasiaan [36].In any convective heat transfer scenario, be it natural, forced, or mixed,the steady-state heat transfer rate between a solid and a fluid is calculatedusing equation 3.2.Qconv = hAM (Tf − TM ) (3.2)h : Convective heat transfer coefficient [W/m2/K]AM : Surface area of membrane [m2]TM : Surface temperature of membrane [K]Tf : Temperature of fluid [K]This is the general form of the terms Q4 and Q5 in Equation 3.1. Thearea of the membrane and the temperature of the participating fluids can bemeasured or set. The convective heat transfer coefficient, which is the rateat which heat transfer will take place given a defined temperature differenceand surface area, can not be measured, and it changes depending on thescenario where the convection takes place. This means that other equationsmust be used to determine h before Qconv can be solved.To derive the convective heat transfer coefficient for a given scenario, onemust first determine the Nusselt number (Nu) for said scenario. The Nusseltnumber is dimensionless and represents the ratio of convective to conductiveheat transfer that occurs at a solid/fluid interface. In other words, it’s theratio of the heat transfer that is due to a fluid transferring heat as it travelsacross a solid to the heat that would be transferred if the fluid was stationary(pure conduction). This relationship can be seen in Equation 3.3.NuL =convective heat transferconductive heat transfer=hLk(3.3)L : Characteristic length of flow scenario [m]k : Thermal conductivity of the fluid [W/m/K]The thermal conductivity of the fluid can be determined using the knownair temperature and the characteristic length changes depending on the sce-nario, but is readily available. The convective heat transfer coefficient is stillunknown, however many empirical correlation have been developed for dif-ferent heat transfer scenarios that allows for the calculation of the Nusseltnumber using geometry and air properties [18, 36, 89]. There are 4 con-vection scenarios that need to be included in this model, each requiring adifferent correlation. These are the internal natural convection scenarios andthe external natural/mixed convection scenarios that occur for a horizontaland vertical panel.The empirical correlations used to determine Nusselt numbers generallydepend on the Rayleigh Number (Ra) for natural convection scenarios andthe Reynolds Number (Re) for forced convection scenarios. The PrandtlNumber (Pr) is used in both.RaL =gβL3(TM − Tf )να(3.4)ReL =υLν(3.5)Pr =να(3.6)g : Gravity [m/s2]β : Thermal expansion coefficient [1/K]υ : Fluid velocity [m/s]ν : Kinematic viscosity of fluid [m2/s]α : Thermal diffusivity of fluid [m2/s]The Rayleigh Number describes the fluid flow regime for buoyancy drivenflows. It represents the ratio of the time scale for thermal transport via con-vection and diffusion. The Reynolds number describes the ratio of inertialto viscous forces taking place in a forced convection scenario, but it alsopredicts the transition between laminar and turbulent flow. The Prandtlnumber represents the ratio of momentum diffusivity to thermal diffusivity.There are three different characteristic lengths used in this model. Thecharacteristic length depends on the flow scenario. The symbol l representsthe height of the panel, lc is the ratio of the panel’s surface area to thepanel’s perimeter, and S is the distance between the panel’s chilled sur-face and membrane. The subscript of the Nusselt number indicates whichcharacteristic length is being used. Additionally if the Nusselt number issurrounded by angled brackets, such as 〈Nul〉l, 〈Nulc〉, 〈NuS〉l, or 〈NuS〉,the average Nusselt number for the entire surface is being represented, ratherthan a specific point on said surface.3.2.1 External Convection, Q4This section models the heat transfer that occurs between the membraneand the air surrounding the panel. As the panel can be either vertical orhorizontal, different correlations are needed for both orientations. Addi-tionally, as the panel could be exposed to high velocity ambient air eitheroutdoors or within an occupied space, the effects of forced convection mustbe taken into account.Vertical Panel External Natural ConvectionWhen modeling a vertical panel, there are only two widely used empiricalcorrelations for natural convection on vertical flat surfaces that assume auniform wall temperature boundary condition (UWT) [36]. One is consid-ered slightly more accurate but is only applicable when Ral < 109. Undernatural convection scenarios, the Ral at the panel consistently between 109and 1010. The second correlation, Equation 3.7, can be applied to any Ralvalue and produces a stronger model correlation to the experimental datarelative to the previously mentioned correlation. This second correlation isused in the model.〈Nul〉l =0.825 + 0.387Ra16l[1 + (0.492/Pr)916 ]8272(3.7)Horizontal Panel External Natural ConvectionWhen modeling a horizontal panel, the Nu correlation must represent ahorizontal surface that is cooling the air that is below said surface. TheNu correlation changes if the panel is heating the air, or if the panel isinteracting with the air above the panel, so it is important to ensure thatto correct correlation is chosen. Experimental data is not yet available forcalibrating a horizontal panel, as the data collected in Singapore is from avertical panel, meaning that horizontal correlations can not be compared.The Nu correlations available for natural convection on a horizontal panelcan be seen in Equations 3.8 and 3.9. Both equation are integrated into themodel and the one used depends on the flow’s Rayleigh number.〈Nulc〉 = 0.54Ra14lcfor 105 ≤ Ralc ≤ 107 (3.8)〈Nulc〉 = 0.15Ra13lcfor 107 ≤ Ralc ≤ 1011 (3.9)External Forced and Mixed ConvectionAs the panel’s membrane is exposed to its surrounding environment, it is im-portant that the model can incorporate the effects of forced convection whenestimating the heat transfer between the membrane and it’s surroundings.To determine the effects of forced convection, first the Reynolds number isestimated using Equation 3.5, which then allows the Nusselt number to beestimated using Equation 3.10.〈Nul〉l =0.825 + 0.387Ra16l[1 + (0.492/Pr)916 ]8272(3.10)To determine the combined effect of natural and forced convection, Equa-tion 3.11 is used.Nun = NunF ±NunN (3.11)Nu : Nusselt numberNuF : Purely forced Nusselt numberNuN : Purely natural Nusselt numbern : Empirical parameterIn this case the empirical parameter is 3 [36]. However, Equation 3.11 isnot used if the flow is determined to be Purely forced or Purely Natural.Pure forced convection occurs when0.99 <∣∣∣∣ NuNuF∣∣∣∣ < 1.01 (3.12)Pure natural convection occurs when0.99 <∣∣∣∣ NuNuN∣∣∣∣ < 1.01 (3.13)If the flow is identified as being purely forced convection, the effects ofnatural convection are insignificant compared to the effects of forced con-vection. The overall Nusselt number is then equal to the Nusselt numberdetermined using Equation 3.10. The reverse is true if the flow is purelynatural convection, and the overall Nusselt number is equal to the Nusseltnumber determined using Equations 3.7, 3.8, or 3.9.Once the final Nusselt number for the external convection scenario isdetermined, the Q4 term in Equation 3.1 can be determined using equation3.14.Q4 = AMkLNu(Tf − TM ) (3.14)3.2.2 Internal Convection, Q5In this section, the heat transfer between the membrane and the panel’schilled surface is modelled. Different correlations are again needed for ver-tical and horizontal panel orientations.Vertical Panel Internal Natural ConvectionThere are four empirical correlations that can be applied to a vertical panel[36]. The parameters that determine which equation should be used are thePrandtl number, the ratio of the panel’s height to depth, and the Rayleighnumber. The 4 relevant equations are as follows.For: 2 <lS< 10, P r < 10, RaS < 1010〈Nus〉l = 0.22(lS)−1/4 [ Pr0.2 + PrRas]0.28(3.15)For: 1 <lS< 2, 10−3 < Pr < 105,RaSPr0.2 + Pr< 103〈Nus〉l = 0.18[Pr0.2 + PrRas]0.29(3.16)For: 10 <lS< 40, 1 < Pr < 2(104), 104 < RaS < 107〈Nus〉l = 0.42Ra0.25s Pr0.012(lS)−0.3 (3.17)For: 10 <lS< 40, 1 < Pr < 20, 106 < RaS < 109〈Nus〉l = 0.046Ra0.33s (3.18)The parameters of the Cold Tube panel are used to determine whichcorrelation should be included in the model. The height to depth ratio( lS ) of the Cold Tube is 11.65, the Prandtl number varies between 0.75and 1, and the Rayleigh number varies, but is generally close to 3(10)6.Equations 3.15, 3.17, and 3.18 all have parameter ranges that are similar tothe Cold Tube’s parameters, although none of them match perfectly. Thecorrelation that best reflects the Cold Tube Panel was chosen by testingeach correlation in the model to determine which most accurately predictsthe membrane temperatures observed during the Cold Tube experiment.The method used to solve the heat transfer model and an overview of thedata collected during the Cold Tube experiment will be further discussedlater in this chapter. Equation 3.17 was identified as the best performingcorrelation, however, the model will switch from Equation 3.17 to 3.18 if theRayleigh number exceeds 107.It is important to note that for all internal natural convection equations,the temperature difference in Equations 3.2 and 3.4 is the difference betweenthe chilled surface and membrane temperature. Equations 3.19 shows howthe Rayleigh number is calculated in these scenarios.RaS =gβS3(Tcs − TM )να(3.19)S : Distance between chilled surface and membrane [m]Tcs : Temperature of chilled surfaceThe temperature of the air inside the panel does not need to be measured,and is assumed to be the average of the two surface temperatures for thepurpose of estimating air properties.Horizontal Panel Internal Natural ConvectionThere are two correlations that can be used to model natural convectionwithin a vertical panel. One equation is valid for any horizontal rectangularenclosure where the Rayleigh number is within the range of 1708 < Ras <108, while the other applies when the temperature of the bottom surface ishigher than the top surface and the Rayleigh number falls within the rangeof 3(10)5 < Ras < 7(10)9. The latter correlation is used as it more closelymatches the flow scenario being modelled, and can be seen in Equation 3.20.〈Nus〉 = 0.069Ra1/3s Pr0.074 (3.20)Similar to the external convection scenarios, once the final Nusselt num-ber for either internal natural convection scenario is determined, the Q5term in Equation 3.1 can be determined using equation 3.21.Q5 = AMkSNu(Tcs − TM ) (3.21)3.3 Radiant Heat Transfer, Q1-3To model the membrane’s radiant heat transfer exchange with its surround-ings, the energy emitted from each of the three surfaces is determined. Theeffects of absorption, reflection, and transmission are then applied to theemitted energy, and finally the amount of energy that gets absorbed by themembrane is estimated.All radiant interactions are handled spectrally, meaning that when ra-diant energy is emitted by or impinges on a surface, the way in which thatsurface affects each individual wavelength is considered. This allows for amore detailed analysis of the radiant heat transfer taking place. The humanbody absorbs and emits radiant energy primarily over the range of 8-14 µm[44], meaning that it is important to know if the membrane is transparentto these specific wavelengths. If a variable in this section refers to a specificwavelength, the λ subscript is used. The absence of this subscript meansthat the variable represents a total or average value that includes the ef-fect of each wavelength. For example, the variable Eλ represents the energyemitted by a surface at a specific wavelength, and has the units [W/m2/µm],while E represents the total energy emitted by a surface, and has the units[W/m2]. In this section, a background on radiant heat transfer will be givenbefore the model is explained in detail. All the equations used in the sectionare from the textbooks by Bergman et al. [18], Thirumaleshwar [89] andHowell et al. [42].3.3.1 Background TheorySurface CharacteristicsSome important terms that describes how radiation interacts with surfacesneeds to be discussed. The first is a black body, which means that the surfacewill absorb 100% of the energy that impinges on it and will emit 100% ofthe theoretical maximum energy a surface can emit at a given temperatureaccording to the Planck distribution [89]. A black body is a surface with anemissivity of 1, meaning it is a perfect emitter and absorber. If a surface iscalled a gray body, it is not considered to be a perfect emitter or absorber,but the surface’s spectral emissions still follows the Planck distribution, andemits energy at a fraction of what a black body would emit. For example, ifa grey surface has an emissivity of 0.5, that means that at each wavelength,the energy emitted is half of what a black body would emit. The final typeof surface is known as a real surface, where the radiative properties of thesurface at individual wavelengths do not follow the Planck’s distribution.The terms that describe radiation leaving or impinging on a surface arelisted below.Eλ : Spectral emissionGλ : Spectral irradianceJλ : Spectral radiosityThese three values all have units of [W/m2/µm]. Spectral emission,otherwise known as spectral emissive power, is the energy being emitted bya surface in all directions at a specific wavelength. Spectral irradiance isthe energy impinging on a surface, and spectral radiosity is the total energyleaving a surface, which is the combination of emission and the reflectedportion of irradiance. When radiant energy impinges on a surface, threethings can happen to that energy. It can be absorbed by the surface, it canbe transmitted through the surface, and it can be reflected off the surface.The symbols that represent each of these interactions are listed below.αλ : Spectral absorption componentτλ : Spectral transmission componentρλ : Spectral reflection componentAt any given wavelength, a portion of the energy that impinges on asurface will do one of these three things, meaning that the sum of thesecomponents must equal 1, as seen in Equation 3.22.αλ + τλ + ρλ = 1 (3.22)These surface interactions can be visualized using Figure 3.2 which wascreated to reflect a figure found in Bergman et al. [18]. Figure 3.2 (a)illustrates an opaque non-black surface, where a portion of the incoming ir-radiance (GsAs) is reflected (ρsGsAs) and absorbed (αsGsAs), and the totalenergy leaving the surface (radiosity) is the combination of energy emittedby the surface (EsAs) and the energy reflected by the surface. Figure 3.2(b)illustrates how radiation can travel through a semi-transparent membrane.As the objective of this heat transfer model is to determine the equilib-rium temperature of the membrane by calculating the amount of heat that itabsorbs and emits, it is important to isolate the amount energy that affectsthe internal energy of the membrane (energy absorbed and emitted), fromthe energy that does not (energy reflected and transmitted). However, itis important to take reflected and transmitted energy into account, as thisenergy my return to the membrane after it interacts with other surfaces.Figure 3.2: (a) Radiation components of a gray opaque surface. (b) Radi-ation traveling through a semi transparent surface.Determining Net Heat Transfer Between SurfacesFigure 3.3 shows surfaces i and j exchanging radiant energy with one another.Surface j is emitting more energy because it is at a higher temperature inthis instance. This means that surface i will experience a net increase inits internal energy because it is absorbing more energy from surface j thanit is emitting. In contrast, surface j will experience a net decrease as it isemitting more energy than it is absorbing.Equation 3.23 is used to calculate the total emissive power of a grey orblack surface.E = σεT 4 (3.23)E : Total emission [W/m2]σ : Stefan-Boltzmann constant [W/m2/K4]ε : Emissivity of surfaceFigure 3.3: Illustration of two surface emitting different amounts of radiantenergy because of different surface temperatures.T : Surface temperature [K]This equation can only be used to model the emissive power of ideal blackor gray bodies that follows the Planck distribution, and can not be used todetermine the energy emitted at individual wavelengths. To calculate theenergy emitted at individual wavelengths, the emissivity of each wavelength,otherwise known as the spectral emissivity, of the surface must be known.ελ : spectral emissivityThe spectral emissivity of a surface is equal to the spectral absorptivityof the surface, as seen in Equation 3.24 [42].ελ = αλ (3.24)Once the spectral emissivity of a surface is known, Equation 3.25 is usedto calculate the spectral emissive power [W/m2/µm] of a surface.Eλ =[C1λ5[exp(C2λT )]]ελ (3.25)C1 : 3.743(10)8 [W/(µm4/m2)]C2 : 1.439(10)4 [µm-K]λ : Wavelength being analyzed [µm]The section in square brackets represents the emissive power at a specificwavelength for a black body, and ελ is the emissivity of the material at thatwavelength. Integrating the spectral emissive powers over the wavelengthspectrum being considered will give the total emissive power of a surface(W/m2), as seen in Equation 3.26.E =∫ λ2λ1Eλ dλ (3.26)When determining the net heat transfer between two surfaces, the area ofonly one of the surfaces is needed, along with the view factor from that sur-face too the second surface. This is because the total heat transfer betweentwo surfaces is the difference between the heat traveling in either direction,as seen in Equation 3.27. The reciprocity theorem shown in Equation 3.28indicates that Equation 3.27 can be simplified by cancelled out either A1F12or A2F21, as seen in Equation 3.29.Qnet = A1F12J1 −A2F21J2 (3.27)A1F12 = A2F21 (3.28)Qnet = A1F12(J1 − J2) (3.29)An : Area of surface n [m2]Fnm : View factor from surface n to mJn : Total energy traveling away from surface n [W/m2]Equation 3.30 is used to determine the portion of the energy emitted bya surface that impinges on a second surface.Gλ,2 = F12Eλ,1 (3.30)To calculate the portion of the irradiance (Gλ) that is absorbed, trans-mitted, or reflected, the irradiance is factored by the absorption, transmis-sion, and reflection components for the wavelength being analyzed. Thiscan be seen in Equations 3.31 through 3.32.Qλ,absorbed = αGλ (3.31)Qλ,transmitted = τGλ (3.32)Qλ,reflected = ρGλ (3.33)3.3.2 Membrane Emission, Q1This section models the radiation that is emitted from the membrane withthe goal of deriving an equation for the Q1 term in Equation 3.1. Energyis emitted by the membrane in both directions. It is assumed that theview factor between the membrane and the chilled surface is equal to 1because the walls that make up the interior of the panel are assumed to beperfectly reflective. This would imply that all the radiant energy emittedby the membrane will reach the chilled surface. The view factor betweenthe membrane and its surroundings is also equal to 1. This means thatthe energy emitted by a surface is equal to the irradiance on the receivingsurface as long as the area of the membrane is used to calculate the emittedenergy.Three subscripts will be used throughout this chapter to indicate thesurface being analyzed. M indicates the membrane, CS indicates the chilledsurface, and SS indicates the surrounding surfaces. For example, EM indi-cates the energy emitted by the membrane, while ρCS indicates the reflec-tivity of the chilled surface.The energy emitted towards the chilled surface gets partially reflected,and then returns back to the membrane and gets partially absorbed. Asstated earlier, reflections off the surrounding surfaces are not considered.This is illustrated in Figure 3.4.Equation 3.34 represents the net effect of the energy emitted by theFigure 3.4: Path of the energy emitted by the membrane.membrane, on the internal energy of the membrane.Q1 = AM (αλ,MG1 − E1−1 − E1−2) (3.34)Equation 3.25 is used to calculate the energy emitted by the membraneat each wavelength, and 3.26 is used to determine the total energy emittedby the membrane. The equation for determining E1−1 and E1−2 can be seenbelow.E1−1 = E1−2 =∫ λ2λ1[C1λ5[exp( C2λTM )]]ελ,M dλ (3.35)G1 is equal to the reflected portion of E1−1, which is then partiallyabsorbed by the membrane. The αλ,MG1 term in Equation 3.34 is calculatedusing Equation 3.36.αMG1 =∫ λ2λ1[C1λ5[exp( C2λTM )]]ελ,M ∗ ρλ,CS ∗ αλ,M dλ (3.36)Equations 3.35 and 3.36 can be inserted into Equation 3.34 to solve theQ1 term in Equation 3.1.3.3.3 Chilled Surface Emission, Q2This section models the radiation that is emitted from the chilled surfacewith the goal of deriving an equation for the Q2 term in Equation 3.1. Theapproach used to derive this equation is similar to the approach used tomodel membrane emission. As the internal energy of the membrane is beingmodeled, only the energy that ends up being absorbed by the membrane istaken into account when determining Q2. The path of the radiation beingemitted by the chilled surface is illustrated in Figure 3.5.Figure 3.5: Path of the energy emitted by the chilled surface.This is the simplest source of radiant energy to model, as radiant energydoes not reflect off the surrounding surfaces and reflections off the membraneare not modeled. This is because the membrane and the chilled surface areboth 5% reflective, meaning that only 0.2% of the energy emitted by thechilled surface will end up impinging on the membrane after being reflectedby the membrane, and an even smaller amount will be absorbed. The as-sumption is made that this interaction can be ignored due to the insignificantamount of energy that would be absorbed. Energy is emitted by the chilledsurface and is partially absorbed as it travels through the membrane. Thetotal heat transfer at the membrane due to energy emitted by the chilledsurface is determined using Equation 3.37Q2 = AM (αMG2) (3.37)The amount of energy absorbed by the membrane can be calculatedusing Equations 3.25, 3.26, and 3.31, as seen in Equation 3.38.αMG2 =∫ λ2λ1[C1λ5[exp( C2λTcs )]]ελ,CS ∗ αλ,M dλ (3.38)3.3.4 Surrounding Surface Emission, Q3This section looks at the energy that is emitted from the surrounding sur-faces and ultimately gets absorbed by the membrane. It is similar to theprevious section, but reflections off the chilled surface are taken into account.This can be seen in Figure 3.6.Energy is emitted from the surrounding surface, and is then partiallyFigure 3.6: Path of the energy emitted by the surrounding surface.absorbed as it travels through the membrane. The remaining energy ispartially reflected off the chilled surface, and is again partially absorbed bythe membrane. The equation used to model heat transfer at the membranedue to energy emitted by the surrounding surface is seen in Equation 3.39.Q3 = AM (αMG3 + αMG4) (3.39)The equation used to model the energy first absorbed by the membraneis identical in structure to that of Equation 3.38, and can be seen in Equation3.39αMG3 =∫ λ2λ1[C1λ5[exp( C2λTSS )]]ελ,SS ∗ αλ,M dλ (3.40)The energy that is transmitted through the membrane is then partiallyreflected and absorbed by the membrane. This is shown in Equation 3.41αMG4 =∫ λ2λ1[C1λ5[exp( C2λTSS )]]ελ,SS ∗ τλ,M ∗ ρλ,CS ∗ αλ,M dλ (3.41)Equations 3.40 and3.41 are inserted into Equation 3.39 to solve for theQ3 term in Equation 3.1.3.3.5 Determining the Radiant Characteristics of theMembraneOne function of the model is to allow for the evaluation of panel performanceusing any number of membrane materials and thicknesses. This is done byusing Fourier-transform Infrared Spectroscopy (FTIR) data for the materialsthat are being analyzed. This data contains the transmission and reflectioncharacteristics of the membrane at individual wavelengths, and Equation3.22 can be used to infer the absorption at each wavelength. The materialbeing analyzed can be varied by changing the FTIR data set being used,and changes in membrane thickness can be simulated using Beer’s law [18].Beer’s law states that the spectral absorption of a semitransparent solidis a function of the solid’s absorption coefficient and thickness. This is shownin Equation 3.42.τλ = e−kλ∗L (3.42)kλ : Absorption coefficientL : Membrane thickness [M]The spectral transmissivity at a specific thickness can be used to deter-mine the materials absorption coefficient at that wavelength. Once Equation3.42 has been used to determine kλ, it can be used again to determine τλat any thickness by changing the value of L. This in turn allows for thedetermination of the absorptivity of the membrane at any thickness, whichis accomplished by inserting Equation 3.42 into Equation 3.22, as seen inEquation 3.43.αλ = 1− ρλ − e−kλ∗L (3.43)3.4 ConductionConduction was not included in the membrane’s heat balance equation asit does not directly affect the membrane temperature, nor the radiationpassing through the membrane. Heat is transferred via conduction throughthe back of the panel into the chilled surface. Allowing more heat to travelthis way leads to an increase in the energy required to maintain a specificsurface temperature. However, it is assumed that the inlet and outlet of thechilled surface is monitored, so at any given time the temperature of thesurface is known. This means that heat traveling through the back of thepanel does not impact the modelled membrane temperature.Thermal conduction can also occur through the side walls of the panel. Itis assumed that the side walls will not significantly affect the membrane viaconduction, as the surface area of the interface is minuscule (5.39(10)−3m2)and polyethylene has a low thermal conductivity of only 0.33 W/m/K. Theheat being conducted through the side walls could affect the air inside thepanel. However, it is assumed that insulation can be added to the sides ofthe panel so that conduction through the sides is insignificant. This alsoapplies to the rear of the panel. This assumption can be re-evaluated in thefuture, however, the fact that the model can accurately predict membranetemperatures, as will be seen in this chapter, suggests that it is a validassumption at this stage of work.3.5 Modeling Heat Transfer Between the Paneland its SurroundingsThe equations that determine the rate at which heat is transferred betweenthe panel and its surroundings are similar to those that determine the mem-brane’s temperature. The panel interacts with its environment both radia-tively and convectively, and calculating these heat exchanges separately iscritical to modeling the panel’s performance inside a building. This sectionwill outline the methodology behind modeling various modes of heat trans-fer by referring to the heat transfer equations discussed previously in thischapter.3.5.1 Modeling Radiant Exchange with the Panel’sSurroundingsModeling the radiant heat exchange between the panel and its surroundingsshares many similarities with the approaches used to model the radiantheat transfer that affects the membrane. The emissions of each of the threesurfaces is determined and the ways in which the energy interacts withits surroundings is analyzed. The objective is to determine the amountof radiant energy generated by the panel that escapes the panel, and theamount of radiant energy emitted by the panel’s surrounding surfaces thatenters and remains inside the panel.The path of each source of emitted radiation is illustrated by the follow-ing Figure 3.7.Figure 3.7: Diagram illustrating the net radiative heat transfer between thepanel and its surroundings.Equation 3.44 is used to calculate the total heat transfer that occursbetween the panel and its surroundings.Qnet rad = Q3−2 −Q2−2 −Q1−2 (3.44)Where Q1−2 is the energy emitted by the membrane that ultimatelyleaves the panel, Q2−2 is the energy emitted by the chilled surface that istransmitted through the membrane, and Q3−2 is the energy emitted by thesurfaces surrounding the panel that remains within the panel after trans-mitting through the membrane.The approach used to determining Q1−2 is identical to the approachused to determine Q1 in section 3.3.2, except that the energy that is trans-mitted through the membrane after being reflected off the chilled surface isdetermined, rather than the amount reabsorbed by the membrane.Q1−2 can be calculated using the Equation 3.45.Q1−2 = AM (τMG1−2 + EM ) (3.45)Equation 3.35 is used to determine the value of EM , while equation 3.46is used to determine the value of τMG1−2.τMG1−2 =∫ λ2λ1[C1λ5[exp( C2λTM )]]ελ,M ∗ ρλ,CS ∗ τλ,M dλ (3.46)The value of Q2−2 can be calculated used Equation 3.47.Q2−2 = AM (τMG2−2) (3.47)Where the energy transmitted through the membrane (τMG2−2) is cal-culated using Equation 3.48.τMG2−2 =∫ λ2λ1[C1λ5[exp( C2λTCS )]]ελ,CS ∗ τλ,M dλ (3.48)The value of Q3−2 can be calculated used Equation 3.49.Q3−2 = AM (τMG3−2 − τMG4−2) (3.49)Where the energy transmitted through the membrane (τMG3−2) is calcu-lated using Equation 3.50, and the energy that is re-transmitted through themembrane after reflecting off the chilled surface is calculated using Equation3.51.τMG3−2 =∫ λ2λ1[C1λ5[exp( C2λTSS )]]ελ,SS ∗ τλ,M dλ (3.50)τMG4−2 =∫ λ2λ1[C1λ5[exp( C2λTSS )]]ελ,SS ∗ τλ,M ∗ ρλ,CS ∗ τλ,M dλ (3.51)3.5.2 Modeling Convective Exchange with the Panel’sSurroundingsModeling convective heat transfer between the panel and its surroundingsis done by using the equations derived previously to model heat transferbetween the membrane and the air surrounding the panel, the general formof which can be seen in Equation 3.52Qnet conv = Q4 = AklNu(Tf − TM ) (3.52)3.5.3 Determining the Mean Radiant Temperature of thePanelTo determine if an occupant of a space feels thermally comfortable, themean radiant temperature (MRT) of the occupant’s surroundings must bedetermined. To achieve this, the mean radiant temperature of the panel, asperceived by the occupant, must be determined. This is done by calculatingthe total energy that is traveling away from the panel, and determiningthe MRT that corresponds to this quantity of energy. The methods usedto determine the amount of energy traveling away from the panel is verysimilar to the method used to calculate the net heat transfer between thepanel and it’s surroundings.Figure 3.8 illustrate the radiant interactions that must be considered.Equation 3.53 is used to determine the total radiant energy travelingaway from the panel.QMRT = Q1−2 +Q2−2 +Q3−3 (3.53)The quantities Q1−2 and Q2−2 are identical to the those described insection 3.5.1 and are determined using Equations 3.45 and 3.47 respectively.The quantity Q3−3 is the total energy emitted by the surrounding sur-faces that is reflected of the membrane or transmitted through the mem-Figure 3.8: Diagram illustrating the total radiant energy traveling awayfrom the panel.brane, reflected off the chilled surface, and re-transmitted though the mem-brane. The value of Q3−3 can be calculated using Equation 3.54.Q3−3 = AM (ρMG1−3 + τMG2−3) (3.54)The energy reflected off the membrane (ρMG1−3) is calculated usingEquation 3.55 while the value of τMG2−3 uses Equation 3.51 which wasdeveloped in section 3.5.1.ρMG1−3 =∫ λ2λ1[C1λ5[exp( C2λTSS )]]ελ,SS ∗ ρλ,M dλ (3.55)Once the total energy traveling away from the panel is determined, Equa-tion 3.56 is used to determine the MRT of the panel as perceived by anoccupant.TMRT =4√QMRTσ(3.56)3.6 Model Creation using PythonTo determine the membrane temperature that satisfies Equation 3.1, theequations discussed in this chapter are coded in Python. Python was usedas it allows for rapid modifications to the methods used in this chapter asthey were developed. There also exist several Python libraries that are use-ful for analyzing data, such as SALib [63] for conducting sensitivity analysisand CoolProp for determining air properties [17]. Like many heat trans-fer models, this model is solved numerically by iterating though potentialmembrane temperatures and determining which value causes the sum of theterms in Equation 3.1 to be closest to zero. As the membrane temperature isalways between the chilled surface and highest environmental temperature(either MRT or air temperature) the value is iterated over this range.3.6.1 Determining Model Variables for ConvectionScenariosThe Nusselt number correlations are solved through the use of several tem-perature dependant air variables and panel dimensional variables. All airvariables, except thermal diffusivity, are determined using the Python plu-gin CoolProp which determines these variables using known air tempera-ture, pressure and relative humidity values. Thermal diffusivity can not becalculated using CoolProp, and is determined by inserting internal air tem-perature into a 4th-degree polynomial correlation which was created usingdata provided by Engineering Toolbox.3.6.2 Implementing Radiative Properties of the MembraneTo specify the properties of the membrane material being used, spreadsheetsspecifying the spectral transmissivity and reflectivity of the membrane arerequired. The Python model reads this data, and uses Equation 3.22 todetermine the membrane’s spectral absorptivity. Depending on the FTIRmachine being used to obtain this spectral data, it is likely that the datawill need to be extrapolated to include a wider range of wavelengths so thatmore radiant energy can be taken into account. The FTIR data used inthis analysis only includes wavelengths over the range of 2.5 and 14.8 mi-crometers, which accounts for 53.6% of the emissive power for a surface at20oC. To account for this deficiency, the spectral data was extrapolated toinclude wavelengths from 2.5 to 130 micrometers. This was done by usingthe average transmission and reflection data present in the original measure-ments and applying this average to the wavelengths that were not explicitlymeasured. This is the same approach used in the membrane assisted radiantcooling study conducted by Teitelbaum et al. [84].3.7 Membrane Temperature Model Validation3.7.1 Obtaining Reference DataTo validate the model’s performance, data points were collected during theCold Tube experiment that was conducted from December 2018 to January2019. All information regarding the setup of the experiment and the meth-ods behind data collection are from the following paper by Teitelbaum et al.[85]. These data points, consisting of the panel’s chilled surface temperatureand the temperature and humidity of the air surrounding the panel, are usedto determine how accurately the model can predict the membrane temper-ature observations that were conducted during this experiments. The tem-perature of the membrane was determined by slowly decreasing the chilledsurface temperature of the panel and observing when condensation startedto form on the membrane. By knowing the relative humidity within theCold Tube pavilion (measured using the ThermCondSys5500 measurementsystem), the dew point temperature of the air around the panel could be cal-culated. When condensation is initiated on the membrane, it can be inferredthat the temperature of the membrane is equal to the dew point tempera-ture of the air. Nine membrane temperature measurements were taken overthe course of the Cold Tube experiment, which were accompanied by thechilled surface temperature and air property measurements at the time ofcondensation. However, neither MRT or wind speed measurements weretaken at the same time as membrane temperature observations.The temperature of the chilled surface was assumed to be the averagetemperature of the water entering and exiting the panel. The temperatureof the air inside the Cold Tube pavilion was measured using Pt-100 ther-mistors (±0.1oC) that were shielded from radiation using a reflective silvercone. The mean radiant temperature inside the panel was measured using6 pyrgeometers (Apogee, SL–510–SS; 0.12 mV per Wm−2; 1% measurementrepeatability), which were arranged orthogonally on a small wooden cube,along with a pyranometer (SP–510; 0.057 mV per Wm2; 1% measurementrepeatability) which was manually directed in all six caridnal directions.Pyrgeometers measure MRT using a highly accurate thermistor that con-tinuously measures the device’s internal temperature (Tpyrg), while beingisolated from convection and conduction. The device simultaneously createsa voltage output that is proportional to the radaint flux (Qrad) it is receivingfrom a 150o field of view. Knowing the radiant flux and the device’s tem-perature allows for the MRT calculation of the sensor’s surroundings usingEquation 3.57.Qrad = σ(T4pyrg − T 4avg) (3.57)Pyranometers function similarly to Pyrgeometers, but measure the short-wave radiation rather than the long wave. The cumulative radiant flux(Qrad,tot) measured over the short and long wave is used in Equation 3.58to determine the final MRT measurement.TMRT =4√Qrad,totσ− 273.15 (3.58)Unfortunately, even though many MRT data points were taken over thecourse of the experiment, MRT data was not collected when membranetemperatures were measured. However, many MRT data points were takenalongside chilled surface temperature measurements, meaning a correlationcould be derived that estimates the MRT inside the panel based on thechilled surfaces temperatures within the pavilion. This correlation can beseen in Equation 3.59.TMRT = 0.6766Tcs + 13.557 (3.59)Additionally, air speed data was not measured at the time membranetemperature measurements were taken, so an average air speed of 0.3 m/swas used, as seen in Figure 3.9.Figure 3.9: Wind speed measurements within Cold Tube. This figure wastaken from a study conducted by Teitelbaum et al. [86]. The average windspeed line was added for this study.3.7.2 Calibration ApproachTo determine how accurately the Python model predicts membrane temper-ature, the environmental measurements that were taken during each of thefilm temperature observations are used to predict the observed film tempera-tures. The differences between the predicted temperatures and the observedtemperatures are determined, and the mean of the nine differences is usedto determine the accuracy of the model. The objective of the calibrationprocess is to reduce the average difference between measured and predictedtemperatures by scaling the uncertain parameters used in the model. For ex-ample, if it is determined that multiplying the internal convection coefficientby 1.1 results in improved model performance, the model will be calibratedby scaling the external convection coefficient calculated in each simulationby 1.1. The value used to scale a parameter will be referred to as the errorfactor for the rest of this chapter.To save time during the calibration process, the sensitivity of each ofthe model parameters is determined. Each additional parameter includedin the calibration significantly increases the time required to produce de-tailed results, meaning that only highly sensitive model parameters shouldbe included. Determining the sensitivity of model parameters is done by con-ducting a sensitivity analysis using the Morris Method [19]. This method isparticularly useful when the number of uncertain factors is high and whenthe model is computationally expensive, both of which are the case in thisstudy. The model functions by computing several incremental ratios, orelementary effects, for each parameter, from which basic statistics are com-puted to determine sensitivity.Once the sensitivity of each model parameter is determined, the 6 mostsensitive parameters are included in a Monte Carlo optimization. However,parameters that are model inputs are not included in the optimization. Thisincludes air and chilled surface temperatures, as these are accurately mea-sured and are not uncertain. The MRT of the surrounding surfaces can beincluded because these measurements were not taken at the time of filmtemperature measurements, meaning that the values were determined usingthe correlation seen in Equation 3.59 and are uncertain. The Python code isupdated so that each of the six parameters can be scaled by an error factor.For example, while the uncalibrated Python model determines the externalconvective coefficient (hext) using Equation 3.60, the calibrated model canscale the coefficient using equation 3.61hext = NuextkL(3.60)hext = EFhext(NuextkL)(3.61)EFhext : External convection coefficent error factorNuext : Nusselt number of external convectionEach of the six error factors is assigned a random value using Python’srandom.uniform command which produces a random value within a speci-fied range of potential values. These randomly generated error factors areapplied to the model. The model uses these error factors to determine differ-ence between the predicted membrane temperatures and the ones observed.This process is repeated 8000 times to produce a large collection of errorfactor combinations and the average difference values.To determine the error factor values that should be used to calibrate themodel, the top 5% of error factor combinations are collected. The meanvalue for each error factor contained in this collection is used to calibratethe model.3.8 ResultsThe correlation between the membrane temperatures predicted by the non-calibrated model and those measured can be seen in Figure 3.10.Figure 3.10: Non-calibrated correlation between modeled and measuredmembrane temperatures.The average predicted membrane temperature is about 1.3oC lower thanwhat was measured in the pavilion. However, there are many sources of errorthat could have contributed this temperature difference, namely the MRTmeasurements, wind speed, and convection correlations. It is reasonable toincrease the performance of the model by scaling uncertain model parame-ters. The results of the Morris Method sensitivity analysis used to determinethe most sensitive parameters can be seen in Table 3.1.Table 3.1: Sensitivity of Membrane Temperature Model to its Parameters.Parameter µ∗ µ σExterior Convective Coefficient 3.195 3.195 1.539Ambient Air Temperature 2.056 2.056 0.966Temperature of Chilled Surface 1.251 1.251 0.449Interior Convective Coefficient 1.159 -1.159 0.540MRT of Surrounding Surfaces 0.908 0.908 0.444Transmissivity of Membrane 0.781 0.739 0.537Air Thermal Conductivity External 0.563 0.563 0.264Air Thermal Conductivity Internal 0.225 -0.225 0.172Air Thermal Diffusivity 0.185 -0.185 0.115Air Thermal Expansion Coefficient 0.103 0.100 0.070Emissivity of Chilled Surface 0.101 -0.029 0.130Air Speed 0.050 0.050 0.040Air Dynamic Viscosity 0.047 -0.041 0.057Air Density 0.046 0.038 0.055µ and σ represent the mean and variance of the parameter’s elementaryeffects. There are qualitative measurement, meaning that the numbers inTable 3.1 don’t quantify the exact influence of each parameter relative toeach other, but they can be used to reliably separate sensitive from non-sensitive variables. µ∗ is the value that best reflects the model’s sensitivityto each parameter.It is clear that the internal and external heat transfer coefficients, alongwith the air temperature around the panel and the chilled surface temper-ature, are the most influential variables by a significant margin. However,as mentioned previously, the chilled surface and air temperatures are notcalibrated as they are non-uncertain model inputs.The variables included in the calibration are the internal and externalheat transfer coefficients, as well as the four next most sensitive parameters,these being internal and external thermal conductivity, the transmissivityof the membrane, and the MRT of the panel’s surroundings. While ther-mal conductivity is derived from the air temperature being used, the methodused to determining these values may have faults. Although the transmissiv-ity of the membrane was measured using a highly accurate FTIR machine, inpractice, dust and other matter can gather on its surface, thereby changingthe properties of the membrane.The histogram showing the average temperature differences obtainedduring the Monte Carlo optimization are shown in Figure 3.11.It should be mentioned that a few smaller Monte Carlo optimizationswere conducted prior to this final simulation to decrease the range over whichthe parameters were varied. This is likely why the histogram is skewed sofar to the left. Appendix A shows the histograms containing the top 5% ofsamples for each variable. The error factors used to calibrate each modelparameter were determined by taking the mean value that appears in thisdata. The standard deviation was also calculated as it indicates whetherthe data is fairly consistent around the mean, or if it is spread out. A lowstandard deviation is ideal because it indicates that the values that cause astrong model fit generally agree with each other. If the standard deviationFigure 3.11: Frequency of temperature difference results produced duringthe Monte Carlo simulation.is high, determining an error factor value is difficult, as the values vary by asignificant amount. The resulting mean and standard deviation values canbe seen in Table 3.2.Table 3.2: Optimized Membrane Temperature Model Parameters.Error Factor Mean Standard DeviationInterior Convective Coefficient 0.6047 0.0974Exterior Convective Coefficient 1.497 0.1352Transmissivity of Membrane 0.8993 0.0322MRT of Surrounding Surfaces 1.018 0.0298Air Thermal Conductivity Internal 0.9925 0.0994Air Thermal Conductivity External 1.160 0.1060After applying the error factors to the model parameters, the modelpredicts an average temperature difference of only 0.21oC. The results ofthe calibrated model can be seen in Figure 3.12.Figure 3.12: Calibrated correlation between modeled and measured mem-brane temperatures.3.9 Discussion3.9.1 Model PerformanceThe results indicate that the Python based heat transfer model developed inthis chapter can accurately predict the operational membrane temperatureof a membrane assisted radiant panel. In a building, it is likely that themembrane temperature would be maintained at least 2oC above the dewpoint of the ambient air. As the model has an accuracy of 0.21oC with amaximum error of 0.6oC, it can predict the membrane temperature suffi-ciently accurately as to avoid condensation. However, further research isrequired to address the uncertainties affecting both the model and the re-sults. While this thesis implements the developed model in TRNSYS, themodel is not designed for any specific energy simulation tool, and can beimplemented in any tool that allows for the integration of python scripts.It is speculated that the Nusselt number correlations used to determineconvective heat transfer rates may not accurately model the air flows af-fecting the panel due to the panel’s large size. This concern was validatedas a study by Alamdari and Hammond [2] proposes correlations that moreaccurately model natural convection within occupied spaces. Additionally,the results of the Monte Carlo optimization suggest that the internal con-vection coefficient should be reduced by 40% while the external convectioncoefficient should be increased by 50%. These error factors also suggest thatthe convection coefficients are not being derived accurately, and that themethods used to determine Nusselt number correlations should be furtherdeveloped.The absence of MRT measurements alongside membrane temperatureobservations is another significant source of error affecting the model results.While using a correlation to predict the MRT of the panel’s surroundings atthe time of the membrane temperature observations was the best methodavailable, this deficiency introduces a level of uncertainty regarding the re-sults of the heat transfer model. However, the inclusion of MRT in themodel calibration is an attempt to address this error in the short term, andthe fact that the Error factor is 1.01 is an indicator that the correlation usedto predict MRT may be accurate.When determining the cooling capacity of a membrane assisted radiantcooling panel, the temperature of the membrane is the greatest unknown.The assumption was made that if the calibrated model is accurately predict-ing the membrane temperature, the accuracy of the calculated heat transferrates should be of the same magnitude. The net heat transfer model couldnot be validated using the available data, and further research is neededto confirm its accuracy. The same discussion applies to the model used tocalculate the MRT of the panel.It should be noted in Table 3.1 that the air temperature surroundingthe panel and the temperature of the chilled surface are the second andthird most sensitive model parameters. This implies that it is highly impor-tant that these parameters are accurately measured, as small deviations inmeasurement could lead to significant errors in temperature prediction.3.9.2 Panel DevelopmentThe depth of the panel has a large influences on the amount of heat beingtransferred by means of internal convection. It was assumed initially thatthe main form of condensation control would be varying the panel depth, asincreasing the distance between the chilled surface and the membrane willincrease the operating temperature of the membrane. This is because as thedistance increases, the amount of energy that can be transferred betweenthe membrane and the chilled surface is lowered relative to the other modesof heat transfer. If less energy is leaving the membrane through convection,the temperature of the membrane must increase so that the temperature dif-ference between the membrane and its surroundings is smaller, decreasingthe amount of energy that can be absorbed and satisfying the heat balanceequation. However, it has been observed from the model, along with otherliterature ([93]), that at a certain panel depth, further increasing the depthwill no longer significantly affect the membrane temperature. When imple-menting the panel in a building, it is important to determine the optimalpanel depth, where further increasing the depth has no significant impact onthe panel’s membrane temperature and is just wasting materials and space.Further, it was stated in the literature review that their is critical paneldepth at which the heat transfer within the panel changes from pure con-duction through the air to natural convection [93]. As seen in Figure 3.13,Having a panel depth that is just slightly shorter than this critical lengthresulted in the highest membrane temperature when looking at panel depthsthat are less than 5cm.Figure 3.13: Graph showing how membrane temperature changes withpanel depth. This figure was taken from a study conducted by Xing et al.[93] where they evaluated a different approach to modeling a membraneassisted panel.It can be interpreted from the graph that the membrane temperaturewould likely exceed this critical temperature at panel depths > 100mm.Further research of a panel designed around this critical depth is required,but it is predicted that designing a panel with a significantly larger depthwill result in better performance, and will be more reliable. This is due tosmall deviation away from the critical panel depth resulting in significantdecreases in membrane temperature, as seen in Figure 3.13.3.9.3 Comparison to Previous LiteratureWhile there are many similarities between the modeling methods used inthis thesis and those employed by Xing et al. [93], the objectives of bothstudies are very different. A comparison of both studies is given in thissection along with a discussion on how they will both benefit future work.The radiative network proposed by Xing et al. could prove to be a moreaccurate method of modeling radiant heat transfer. The use of a radiativenetwork means that the radiant energy that reflects off surfaces does notneed to be individually calculated. This thesis models each instance of re-flection, and makes the assumption that emitted radiation will only reflectoff of one surface as the amount of energy that is not absorbed after reflect-ing off of two surfaces is insignificant. Implementing the radiative networkapproach means that this assumption does not have to be made, however, itis predicted that this assumption does not significantly affect the modeledmembrane temperature.The methods employed by Xing et al. to determine convective heat trans-fer are similar to those employed in this thesis. Both studies determine theheat transfer within the panel’s air gab using Nusselt number correlationsfor horizontal enclosed spaces which are heated from below. Xing et al.obtained correlations from the textbook written by Holman [41], while thisthesis obtained correlations from Ghiaasiaan [36]. However, the correlationspresented in both texts differ, and those found in Holman [41] vary depend-ing on the Rayleigh number of the flow. This allows for the modelling of thetransition from pure conduction to mixed convection. This thesis modelsexternal natural convection on a horizontal plate heated from above usingcorrelation found in Ghiaasiaan [36], while the discussed paper used cor-relation presented by ASHRAE [5]. The model presented in this thesis isvery sensitive to convective coefficients. Future work should compare thecorrelations employed by both studies to determine which model membraneassisted panels most accurately.As discussed in the literature review, Xing et al. investigated variouspanel properties. This thesis does not investigate panel parameters as theuncertainties present in the data use to calibrate the model would lead touncertainty in the finding. Instead, this thesis looks to optimize a heat trans-fer model using the data available, and create a framework that allows forthe energy simulation of a building that utilizes membrane assisted panels.Although uncertainties are present in the building energy use estimations,the framework can be used to re-evaluate building energy usage once theuncertainties present in the heat transfer model are addressed. To devel-oped the framework, the heat transfer model includes many features thatare needed for the model to run within a TRNSYS environment. These fea-tures include the ability read spectral data for a specific membrane materialand the ability determine how the properties of the membrane will change atdifferent thicknesses. The modeling of both horizontal and vertical panels.The automatic determination of air properties both within and the aroundthe panel. A sensitivity analysis to determine the parameters that need tobe validated in future research, and a method of optimizing the performanceof the heat transfer model.The two studies being compared have different research objectives. Thestudy conducted by Xing et al. [93] looked to further our understandingof membrane assisted panels by investigate 3 specific design parameters.This thesis looks to develop a complete framework that allows for buildingenergy simulation. The different methods used to model the panel shouldbe evaluated and could result in a heat transfer model that is more accuratethan the two discussed in this section. Additionally, both studies presentdistinct findings that will come together in future research to further thedevelopment of this technology.Chapter 4Building Energy Modeling inTRNSYSIn this chapter, the heat transfer model developed in chapter 3 will be in-tegrated into a TRNSYS framework that allows for the energy performanceevaluation of an office space that uses membrane-assisted radiant panels.The topics covered are as follows: An overview of the energy modeling ap-proach, which will include the methods used to model the walls, floor, roof,windows and shading system. Simulating the thermal gains of occupants,electrical equipment and lighting. The method used to model infiltration,radiant panels, and electrical energy consumption. The scenarios that aresimulated, which will include the justification supporting the chosen climatesand mechanical systems. The methods used to evaluate thermal comfortwithin the space. This chapter finishes with the results generated duringthe simulations and a discussion addressing the validity of the framework aswell as the simulation results.4.1 Building Energy ModellingTRNSYS is used to simulate the energy usage of a building as it allows forthe transient, or time varying, simulation of very detailed mechanical sys-tems [53, 54, 75]. TRNBuild is a program that operates within TRNSYSand allows the modeller to specify building characteristics such as roomgeometry, construction types, ventilation types, and internal gains. Thissection gives an overview of the building simulation methodology, includ-ing the construction of the office space, the office’s internal gains, and theapproach used to predict the electricity demand of the various mechanicalcomponents. The objective is to create a space that reflects a relatively en-ergy efficient office floor in Singapore, as the membrane assisted panel wasdesigned for hot, humid, tropical climates.4.1.1 Walls, Floor, RoofFigure 4.1 illustrates how the simulated office shares similar dimensions withan office in Singapore. A 1000 m2 office floor is simulated by created a modelthat has a 250 m2 floor area with two walls being exposed to the local climate(wall shown in Figure 4.1), and two walls being adiabatic. A reduction ofthe floor area was necessary in order to comply with TRNSYS componentlimitations. The model has a floor to ceiling height of 3 m, and an exteriorwindow to wall ratio of 65%.The walls are modeled using the external wall construction profile sup-plied by the TRNSYS library. They have a thickness of 0.377 m and aU-value of 0.250 W/m2K. This is a reasonable U-value for a high perfor-Figure 4.1: Comparing the facade of a real office in Singapore to the model.mance office buildings in Singapore, as typical U-values in Singapore officesare generally higher and vary between 0.145 and 3.504 W/m2K [1].The floor and roof constructions are modeled using the constructionprofiles supplied by the TRNSYS library. However, they are modeled asbeing adiabatic, so the U-values of their constructions are not considered inthe simulation.4.1.2 Windows and ShadingThe windows have a U-value of 2.14 W/m2K and a G-value of 0.23. This isa typical U-value as double glazed office windows in Singapore tend to haveU-values between 1.64 and 3.23 W/m2K [1]. Windows generally have a G-value within range from 0.2-0.7, with solar control glazing having G-valuesless than 0.5.The window employs an automatic internal shade that blocks 70% of thesolar energy entering the room when it is closed. The shades switch fromopen to closed when the radiant energy incident on the window exceeds 140W/m2.4.1.3 OccupancyThe thermal load generated by occupants of a space are modeled using thestandard office profiles supplied by TRNBuild. This is done by defining amaximum thermal gain that the occupants can supply to the space, andscaling this gain throughout the day using a predetermined schedule. Theoccupants produce a maximum radiative gain of 9 kJ/hr/m2, which relatesto the floor area of the room. Additionally, they produce a maximum convec-tive gain of 9 kJ/hr/m2, and a maximum humidity gain of 0.0055 kg/hr/m2.These gains are scaled using the schedule shown in Figure 4.2.Figure 4.2: The daily schedule used to determine internal gains caused byoccupants.In TRNBuild, the location of a thermal gain within a room can be spec-ified. The occupants are modeled as being distributed evenly throughoutthe office space. To reflect this, a fifth of the total gains generated by theoccupants are located at each of the 5 seated occupants seen in Figure 4.3.This figure is intended to give a visual representation of how the office spaceis modeled and where the gains enter the room, and dose not reflect theTRNBuild interface.Figure 4.3: An illustration of the thermal gain locations in the office space,as well as the radiant exchange between occupants and panel.It is assumed that 15 people occupy this office, giving it an occupancydensity of 16.7 m2/person, which is similar to ASHRAE’s default office spacevalue of 18.6 m2/person [7]. This occupancy assumption is only used todetermine the fresh air rate that is supplied to the space.4.1.4 Electrical Appliances and LightingThe approach used to model electrical appliances and lighting is similar tothe approach used to model occupancy. TRNSYS defines the maximumthermal gains produced by electrical equipment to be 5.04 kJ/hr/m2 and20.16 kJ/hr/m2 for radiant and convective gains respectively. These gainsare scaled using the schedule displayed in Figure 4.4.Figure 4.4: The daily schedule used to determine internal gains caused byelectrical equipment.TRNSYS defines the maximum thermal gains produced by lighting tobe 40.07 kJ/hr/m2 and 17.17 kJ/hr/m2 for radiant and convective gainsrespectively. These gains are scaled using the schedule displayed in Figure4.5.The location of the electrical equipment gains are the same as the oc-cupant gains. The lighting gains are emitted from the 5 blue spheres alongthe ceiling in Figure 4.3. The reason the middle sphere is a different coloris explained in Section 4.1.6.Figure 4.5: The daily schedule used to determine internal gains caused bylighting.4.1.5 InfiltrationThe office space infiltration rate was modeled as 0.1 air changes per hour,which is similar to infiltration values modeled for a small office in a studyby Ng et al. [65].4.1.6 Modeling Radiant PanelsTo simulate a membrane assisted radiant panel in a TRNSYS environment,a novel framework was created. Although TRNBuild contains radiant panelsimulation tools, they do not reflect a membrane assisted panel due to thecomplexities introduced by the membrane and air gap. Figure 4.6 illustratesthe methods that allow a membrane assisted radiant panel to be simulatedin the TRNSYS environment.Figure 4.6: Diagram showing the sub-tasks that allows the heat transfermodel to operate in TRNSYSFirst, the view factors between the panel and each occupant needs to becalculated. The MRT of the panel’s surroundings is then calculated usingthe view factor weighted average of all the building and occupant surfacesthat interact radiantly with the panel. A function is created at each timestep that correlates the panel’s inlet temperature and average cold surfacetemperature. The heat transfer that occurs between the panel and the roomcan then be calculated. The thermal energy leaving the panel is used to de-termine the MRT of the panel, which is then combined with the MRT ofother surfaces in the room to determine to total MRT experienced by eachoccupant. This MRT value, along with other environmental factors is usedto calculate each person’s perceived thermal comfort. Finally, the thermalcomfort values are used to control the mechanical system that provides cool-ing to the space. Detailed methods for each of these steps is provided inAppendix B.To simulate the effects of the panel in TRNBuild, radiant heat transferoccurs at the dark blue dot in the center of the panel as seen in Figure4.3. The convective heat transfer is distributed across the five blue spheresalong the panel. This spreads out the effect of air cooling across the roomrather than having it localized directly above the center. The radiative andconvective heat transfer rates that take place at each location are calculatedat each time step using the heat transfer model and sent to TRNBuild.A major simplification was made in the modeling of the horizontal ceil-ing panels. While membrane temperature data was obtained for a verticalpanel which was used to calibrate the vertical panel model, no such data wasobtained for the horizontal panel, meaning that the horizontal panel modelcould not be calibrated. The three options available for overcoming thisobstacle are, 1) use the heat transfer balance for a horizontal panel withoutthe calibrations discussed in section 3.7, 2) use the calibrated heat transferbalance for a vertical panel and assume that the difference in convectioncoefficients would not be significant enough to meaningfully change the re-sults, and 3) use the heat transfer balance for a calibrated vertical panel,and apply a scaling factor that one would expect if the panel was madehorizontal. As no data was available to compare the accuracy of the threeapproaches, option three was chosen as it attempts to incorporate both cal-ibration and orientation, however there is no evidence that this is the mostaccurate method of simulating a horizontal panel. The functions used topredict vertical to horizontal scaling factors are presented and discussed inAppendix C.4.1.7 Modeling of Electrical Energy ConsumptionModelling the electricity consumption of the mechanical system configura-tions is done by combining the electricity usage of the heat pump, standardwater pumps, and fans.Heat PumpIncluding complex TRNSYS objects such as heat pumps in a simulationcan often cause convergence issues. Instead, the heat pump was modelledusing the Coefficient of Performance (COP) values that are expected in eachscenario. COP represents the amount of useful heating or cooling the heatpump provides for a given amount of electricity consumed. For example, if aheat pump has a cooling COP of 3, the heat pump will provide cooling equalto three times the amount of electrical energy it consumes. COP dependson the temperature difference or ’lift’ between the source of the heat andit’s destination. COP increases as lift decreases, meaning that the efficiencyof the system will increase as the heat pump provides higher temperaturewater to the HVAC system.In most buildings that use heat pumps for cooling, lift is the temperaturedifference between the outside air (the air surrounding the heat pump’scondenser) and the chilled water leaving the heat pump, with an additional 6degrees added to this temperature difference to include the effects of coolingsystem sub-processes that increase the work done by the cooling system[78]. COP of a typical heat pump can be determined by using an equationderived from figure 4.7 that correlates COP and lift. The other operationalcondition that effects COP is called the Part-Load fraction, and is definedas the load the chiller experiences divided by the load it was designed for[78]. Figure 4.8 illustrates how the COP of a chiller changes with Part-Loadfraction.Figure 4.7: A plot showing how COP increases as lift decreases. It wastaken from a study conducted by Meggers et al. [59]This study simplified COP calculations by assigning an average lift valuederived from the average daytime temperature for each scenario rather thana transient one that changes with the outdoor air temperature. It alsoignores the effect of Part-Load fractions. As the purpose of this study is tocompare the relative performance between different mechanical systems, it isexpected that changes in partial load and lift should happen at similar timesand with similar magnitudes across each scenarios and should largely canceleach other out. These factors would need to be included if the objective ofthis study was to create a model with the most detail possible, but as theFigure 4.8: A plot showing how COP of a chiller is correlated to the fractionof the design load it is experiencing. It was taken from a study conductedby Seshadri et al. [78].objective is to compare general scenarios, it is sufficient to employ a staticCOP value that reflects the average heat pump performance for a scenario.Table 4.1 displays the average outdoor air temperature, return watertemperature, COP, and lift used to model each mechanical system and ge-ographic location. The two mechanical systems that utilize a cooling coilrequire a heat pump supply water temperature of 6oC so that the air canbe cooled/dehumidify within a sufficiently small space. The radiant cool-ing and natural ventilation scenarios don’t use a cooling coil, and thereforthe supply water temperature from the heat pump can be higher. Theseheat pump values are represented in Figure 4.7 are and associated with highefficiency heat pumps.Singapore VancouverAverage Daytime Outdoor Temperature [C] 32 276oC Heat Pump Supply Temp COP [C] 5.0 6.013oC Heat Pump Supply Temp COP [C] 6.2 8.1Table 4.1: Table displaying the COPs used for different mechanical config-urations an climates.Pumps and FansThe fact that radiant systems can utilize liquid pumps to move thermalenergy around a building represents a significant portion of the system’senergy saving potential. The electricity usage of these pieces of equipmentare modeled using correlations that relate the amount of energy used to theamount of fluid being moved. ASHRAE 189 defines a pump power limitationof 0.1 W/l/hr [6], and ASHRAE 90.1 defines a specific fan power limit of0.482 W/m3/hr [3].4.2 Simulated ScenariosThis section outlines the characteristics of the scenarios being simulated.The objective of the simulations is to identify the incremental energy savingsthat can be obtained by replacing air conditioning with membrane assistedradiant cooling, and then integrating natural ventilation. This is achievedby initially simulating a standard air conditioning system. This is followedby a simulation that attempts to be identical to the air conditioned environ-ment, except that sensible cooling is supplied by radiant panels rather thanconditioned air. The final scenario removes all modes of air conditioningthat was present in the second scenario and implements a high air changerate to simulate a naturally ventilated environment. These three scenariosare modeled in both Singapore and Vancouver as membrane assisted radiantcooling has the potential to significantly improve the cooling systems usedin these locations.4.2.1 Investigation of Singapore (hot and humid climate)The Singapore climate is being simulated as it represents the hot and humidconditions that membrane assisted radiant panes were designed for. Addi-tionally, it is speculated that the performance of the panel in Singaporewill reflect its potential to provide energy efficient space cooling to otherlocations that have hot, humid, tropical climates. The model predicts theenergy usage of an entire year. As the climate in Singapore is fairly con-sistent throughout the year [91], the months of January and February weremodeled and the results were extrapolated so save modeling time.4.2.2 Investigation of Vancouver (Mediterranean climate)under climate changeVancouver was chosen because a large portion of the buildings in this citycurrently do not utilize space cooling. However, there is a growing con-cern that in the near future mechanical cooling will need to be adopted toaddress the higher temperatures caused by climate change [70]. Demonstrat-ing how membrane assisted radiant cooling can provide sufficient cooling atthe end of the century could convince the City of Vancouver to implementthis technology rather than adopting air conditioning. A RCP8.5 2080 fu-ture weather file is used to model Vancouver as it represents the worst caseglobal emissions scenario, and therefor the warmest climate [16, 23]. As theentire year does not require cooling, only the months of July and Augustwere modeled as they are the warmest.4.2.3 Mechanical System ConfigurationsThree mechanical systems are modeled in both the Singapore and Vancou-ver climates. A radiant cooling plus natural ventilation scenario will bemodeled in both climates. A radiant cooling system that does not utilizenatural ventilation is modeled, however it differs slightly between climates.A radiant cooling system that utilizes both mechanical dehumidification andfresh air ventilation is modeled in Singapore. A radiant cooling system thatutilizes mechanical fresh air ventilation is modeled in Vancouver as it wasdetermined that dehumidification is not necessary. Finally, an air condition-ing system with an ERV will be modelled in both climates as this is used asa benchmark to compare the performance of the radiant systems.Radiant Cooling + Natural VentilationTraditionally, if a building wants to utilize natural ventilation for space cool-ing, it needs to address 100% of the occupied space’s cooling load becauseit cannot operate at the same time as air conditioning. If the space requiresmore cooling than natural ventilation can provide, the space will need tobe sealed before switching to air conditioning as the loss of conditioned airto the outside would reducing the efficiency of the system. This is not thecase with radiant systems, as they can operate alongside natural ventilationbecause the panel does the majority of its cooling via radiant heat trans-fer. This means that a building can take advantage of natural ventilation,and can add radiant cooling when natural ventilation alone cannot addressthe building’s cooling requirements. Additionally, the removal of active airconditioning means that high efficiency heat pumps can be implemented,creating a true low exergy system. Low exergy radiant cooling systems havebeen previously developed for this type of application [78], however thissystem looks to further reduce energy consumption by combining radiantcooling with natural ventilation. A diagram of the radiant cooling systembeing simulated can be seen in figure 4.9.The system consists of a ceiling mounted radiant panel that sends ther-mal energy extracted from the room to a heat exchanger. The heat ex-changer transfers the thermal energy to the heat pump while controllingthe temperature of the water entering the panel. It does this by bypassinga fraction of the cold water it receives from the heat pump, thereby mod-ulating the amount of thermal energy that gets removed from the panel’swater loop. The heat pump removes heat from the system by transferringit to the air surrounding the building. For consistency between mechani-cal system, the flow rate through the heat exchangers, radiant panels, andcondenser coils are set to maintain an average temperature difference acrossthese pieces of equipment of 1oC.The indoor wind speed is modeled as 0.5 m/s as this is a fairly typicalvalue for naturally ventilated spaces [9]. Offices that utilize natural ventila-tion generally have an air change rate that varies between 1 - 6 AC/hr [68].Additionally, [10] claims that AC/hr values below 10 are relatively easy toFigure 4.9: Mechanical system diagram of the radiant + natural ventilationconfiguration.obtain using commonly available natural ventilation strategies, leading toan air change rate of 5 AC/hr being chosen for this model. A full list of thesystem’s components and parameters can be seen in table 4.2.The values used to model the heat exchanger were left at their defaultTRNSYS values as it is assumed that these reflect a generic piece of equip-ment. As the model is not meant to reflect a specific office building, genericmodels can be used to model building components as long as they are con-sidered reasonable.In Singapore, the control strategy for this system is simple. As there isPanel dimensions [m] 10 x 18panel depth [m] 0.2Heat Pump COP Sing/Van 6.2/8.1outlet temp [C] 13Heat Exchanger efficiency 0.95Indoor Environment wind speed [m/s] 0.5air changes per hour [ac/hr] 5Table 4.2: Systems Parameters: Radiant Cooling + Natural Ventilation.little risk of the system over-cooling the space, the model predicts the coldsurface temperature that will initiate condensation on the membrane, andinstructs the heat exchanger to supply water that is 2oC higher than thiscritical temperature. The radiant panel only operates during occupied hours(9am - 5pm), while natural ventilation occurs continuously. The controlstrategy had to be adapted for Vancouver as over-cooling was a concern. Thewater entering the panel was set to be 1oC below the dew point temperatureof the surrounding air, which resulted in a comfortable thermal environmentthroughout the simulation.Radiant Cooling + Dehumidification/Mechanical VentilationAs it is unlikely that a building would utilize a membrane assisted panelalongside dehumidification/mechanical ventilation, the purpose of this con-figuration is to isolate the energy reductions caused by the radiant panelfrom those caused by natural ventilation. This scenario shows the energysavings that could be obtained by replacing mechanical sensible air coolingwith radiant cooling, while keeping the other aspects of the system similarto a typical air conditioning approach. A diagram of this system can be seenin figure 4.10.Figure 4.10: Mechanical system diagram of the radiant + dehumidificationconfiguration.The interactions between the panel, heat exchanger, and heat pump areidentical to the radiant cooling + natural ventilation scenario. However, inthe Singapore environment, the heat pump also supplies chilled water to acondenser coil which dehumidifies the space by removing sensible and latentheat from the recirculated indoor air. As the system wants to minimizethe sensible cooling done on the air, a heat pipe transfers sensible heatfrom the air stream leaving the occupied space to the air stream enteringthe space, thereby diverting a portion of the sensible heat away from thecondenser coil. The fact that the chilled water supplied by the heat pumpis needed for dehumidification means that the supplied water must be at alower temperature relative to the natural ventilation scenario, which resultsin a lower heat pump COP. This will be explained in greater detail laterin this chapter. In the Vancouver environment, little dehumidification isintended, so the heat pump COP is the same as in the naturally ventilatedsystem. An energy recovery ventilator is used to precondition the outdoorair entering the space. A full list of the system’s components and parameterscan be seen in table 4.3.Panel dimensions [m] 10 x 18surface area [m2] [m] 180panel depth [m] 0.2Heat Pump COP Sing/Van 5.0/8.1outlet temp Sing/Van [C] 6/13Heat Exchanger efficiency 0.95Energy Recovery Ventilator sensible efficiency 0.6latent efficiency 0.4Fresh Air Circulation rate [l/s/person] 10Table 4.3: Systems Parameters - Dehumidification/Mechanical Ventilation+ Radiant.The performance of the cooling coil and heat pipe were modeled usingTRNSYS objects previously calibrated for a study in Singapore [77].In the Singapore climate, this system attempts to maintain a relativehumidity between 65-70%. While ASHRAE recommends a maximum rel-ative humidity of 65% in air conditioned spaces [7], the goal is to have arelative humidity as high as possible to reduce the amount of sensible cool-ing done on the air. Maintaining the thermal comfort of the space withinthe PMV comfort range is some indication that the space would be comfort-able despite the somewhat high humidity levels. Additionally, the SingaporeNational Environmental Agency states that 70% is the upper limit for ac-ceptable relative humidity in office spaces [46]. The system then attemptsto maintain a PMV value around 0.25 by modulating the water temperatureentering the panel. Again, the radiant panel only operates during occupiedhours (9am - 5pm), while full dehumidification starts at 8 am so that thespace achieves a comfortable level of relative humidity before occupants ar-rive. The dehumidification is set back between the hours of 5pm and 7am toa value that maintains a steady relative humidity level during these hours.The fresh air supply is also at its maximum during the hours of 8am - 5pm,and is set back to half outside these hours. In the Vancouver climate, thesystem is controlled the same way, however dehumidification is uncontrolled.Air ConditioningThe final mechanical system being modeled is a conventional mechanicalventilation-based air conditioning system. A diagram of this system can beseen in figure 4.11.The system consists of a heat pump that supplies chilled water to acooling coil that provides both sensible and latent cooling to the recircu-lated indoor air. Additionally, an energy recovery ventilator is present toprecondition the fresh air entering the space. A full list of systems compo-nents and parameters can be seen in table 4.4.This system is controlled simply by modulating the air flow over thecooling coil to maintain an air temperature of 23-24oC between the hoursof 8am-5pm. The flow rate is set back outside these hours to a value thatmaintains a steady temperature inside the space. Fresh air is controlled thesame way as in the previous mechanical system.Figure 4.11: Mechanical system diagram of the split system air conditioningconfiguration.4.3 Methods for Assessing Thermal ComfortWhen modeling thermal comfort inside a space, choosing the correct ap-proach to quantifying thermal comfort is important. This section gives anoverview of the thermal comfort models chosen for this study and why theyreflect the environments being modeled. All the information used in thissection comes from a review paper on thermal comfort models by Enescu[30] unless otherwise referenced.Heat Pump COP Sing/Van 5.0/6.0outlet temp [C] 6Energy Recovery Ventilator sensible efficiency 0.6latent efficiency 0.4Indoor Environment wind speed [m/s] 0.1target air temperature 23-24oCFresh Air Circulation rate [l/s/person] 10Table 4.4: Systems Parameters: Split system air conditioning.4.3.1 PMV-PPDThe Predicted Mean Vote (PMV) model is based on Fanger’s comfort equa-tion for human body heat exchange and is used to predict the averageperceived thermal comfort of large groups of people in steady-state air-conditioned environments. Four physical parameters (air temperature, airvelocity, humidity, mean radiant temperature) and 2 personal parameters(metabolic rate and clothing insulation) are taken into account. The PMVindex corresponds to a 7 point thermal scale consisting of hot(3), warm(2),slightly warm(1), neutral(0), slightly cool(-1), cool(-2) and cold(-3). Neutralis considered the most comfortable environment while the thermal comfortrange is between -0.5 and 0.5.The PMV index should only be applied to healthy adults and children, asdisabled and elderly people were not considered when creating this model.Furthermore, it should not be applied to naturally ventilated spaces, asthere is a large difference between the PMV predictions and thermal comfortanalyses [94] that have been conducted in these environments.The PPD (Predicted Percentage Dissatisfied) model computes the per-centage of persons dissatisfied with a given thermal environment. The PPDindex is directly correlated to the PMV index as seen in figure 4.12.Figure 4.12: Dependence of PPD on PMV. This graph was taken from astudy by Enescu [30].It is useful to know the number of occupants that will likely be dissatisfiedin their environment when evaluating thermal comfort. Staying within thePMV thermal comfort range of -0.5 to 0.5 keeps the percentage of dissatisfiedoccupants below 10%, while having a PMV beyond ± 1 will likely result inover a quarter of occupants being dissatisfied.4.3.2 Adaptive Comfort ModelThe adaptive model of thermal comfort is a method of predicting thermalcomfort that only takes the prevailing mean outdoor temperature into ac-count. The goal of the adaptive method is to consider the psychological andheat balance approaches to thermal comfort simultaneously. The generalphilosophy is that the occupant will dress according to the recent outdoorweather, and will attempt to adapt to their indoor environment by removinglayers of clothing. The result of the model is a range of indoor operative tem-peratures that will allow occupants to adapt and achieve thermal comfort.ASHRAE states that the 80% acceptability limit is for typical applications,while the 90% acceptability limit is used when higher standards of comfortare desired [4]. The adaptive approach is being used to predict the thermalcomfort of occupants in naturally ventilated spaces as it is considered to bemore accurate than the PMV method in these environments. The simulatedindoor environment is considered comfortable if the operative temperaturefalls within the 90% acceptability limit. Figure 4.13 illustrates how the theadaptive model relates thermal indoor comfort with outdoor temperatureand displays the acceptability limits.Figure 4.13: Graph showing the indoor operative temperatures that willresult in a comfortable environment as a function of outdoor effective tem-perature. This graph was taken from a study by De Dear and Brager [26].4.4 ResultsThe results section looks to compare the energy performance of the threemechanical systems across two climates, and consists of 6 sets of data. Itshould be noted that although parameters were manually adjusted with theobjective of achieving maximum energy performance for the radiant cool-ing scenarios, a proper model optimization was not conducted due to longsimulation times and scope of thesis. The objectives that drive these sim-ulations are to show that significant energy savings may be obtained byusing natural ventilation rather than dehumidification/mechanical ventila-tion alongside radiant cooling, and that sufficient cooling can be supplied tooccupants in these climates without condensing air moisture. An no datacould be used to confirm the performance of the model, results should beprimarily used to indicate the energy saving potently of these technologies.4.4.1 Singapore Energy Performance ResultsEach scenario was simulated from January 1st till March 1st. Full years werenot simulated due to long simulation times, and the fact that Singapore hasa consistent climate year round means that using a two month simulationyields a reasonable estimate for yearly cooling loads. Table 4.5 displays keymetrics obtained from the Singapore climate simulations. The AC scenarioproduced an energy usage estimate of 84.5 kWh/m2/yr, which is a reasonablebaseline for comparison. Singapore office buildings at the 3rd percentile ofenergy efficiency consumes about 143 kWh/m2/yr [13] in electricity, of whichabout 60% is used for space cooling [29], which results in a space coolingenergy consumption of 85.8 kWh/m2/yr. The radiant cooling and naturalventilation configuration achieved a 45% energy reduction from the AC onlyconfiguration, and a 23% reduction from the dehumidification scenario. Italso managed to achieving thermal comfort 99% of the time. The radiantcooling and dehumidification scenario also demonstrating significant energysavings, achieving an energy reduction of 29% relative to the AC scenario.Rad+Nat Rad+De ACTotal Electrical Load [kWh/m2/yr] 46.5 60.1 84.5Heat Pump Load [kWh/m2/yr] 20.8 26.7 36.6Auxiliary Load [kWh/m2/yr] 25.7 34.2 47.8Average Panel Rad Load [watts] 7378 5653 0Average Panel Conv Load [watts] 2627 1586 0Average Cooling Coil Load [watts] 0 2034 9885Comfortable Hours % 99.4% 100 100%Table 4.5: Table displaying key performance metrics in the Singapore Cli-mate. From left to right, the result columns correspond to radiant cooling +natural ventilation, radiant cooling + dehumidification, and air conditioningscenarios.A visual comparison of the yearly energy loads of each mechanical systemis displayed in Figure 4.14.It should be noted that the average cooling coil load includes power usedfor both cooling and dehumidification, and is the average power used duringoccupied hours. The figures in this section display one weeks of resultsas displaying the full simulation would produce figures that are too large.Figures 4.15 and 4.16 compare the chilled surface, membrane, air, and dewpoint temperatures for both radiant cooling scenario, and illustrates howthe chilled surface of the panel can reach temperatures well below the dewFigure 4.14: A comparison of the annual energy consumption of the threemechanical systems being simulated using the Singapore climatepoint of the air without allowing the membrane to reach the dew pointtemperature.Figure 4.15 illustrates how the membrane temperature is maintainedjust above the dew point temperature inside the room. It also illustratesthe degree to which the chilled surface temperature can be below the dewpoint temperature.Figure 4.15: Diagram showing how the membrane temperature is main-tained above the dew point for the Singapore Radiant + Natural Ventilationscenario.Figure 4.16 displays a similar scenario, but in this case the dew pointwithin the room is much lower because it is dehumidified, and the chilledsurface temperature is a few degrees higher than in the Figure 4.15 becausesome of the cooling is supplied by the cooling coil.Figure 4.16: Diagram showing how the membrane temperature is main-tained above the dew point for the Singapore Radiant + Dehumidificationscenario.Figures 4.17 and 4.18 shows that thermal comfort is maintained in bothSingapore radiant cooling scenarios.Figure 4.17: Diagram showing that thermal comfort is maintained in theSingapore Radiant + Natural Ventilation scenario.Figure 4.18: Diagram showing that thermal comfort is maintained in theSingapore Radiant + Dehumidification scenario.4.4.2 Vancouver RCP 8.5 2080 Energy Performance ResultsEach scenario was simulated during the summer months of July - August,and the results shown in this section are the total energy used during thesemonths rather than the yearly values used for the Singapore results. Table4.6 displays key metrics obtained from the Vancouver climate simulations.The AC scenario produced an energy usage estimate of 15.5 kWh/m2. Theradiant cooling and natural ventilation configuration achieved a 52% energyreduction from the AC only configuration, and a 19% reduction from thedehumidification scenario. The radiant cooling and mechanical ventilationscenario achieved 40% energy saving relative to the AC scenario.A visual comparison of the yearly energy loads of each mechanical systemis displayed in Figure 4.19.Figures 4.20 and 4.21 compare the chilled surface, membrane, air, anddew point temperatures for both radiant cooling scenario in the VancouverClimate.Rad+Nat Rad+Mech ACTotal Electrical Load [kWh/m2] 7.44 9.22 15.5Heat Pump Load [kWh/m2] 3.65 3.52 6.39Auxiliary Load [kWh/m2] 3.80 5.70 9.11Average Panel Rad Load [watts] 6159 6701 0Average Panel Conv Load [watts] 2160 2249 0Average Cooling Coil Load [watts] 0 0 8442Comfortable Hours % 99.0% 100 100%Table 4.6: Table displaying key performance metrics in the VancouverClimate. From left to right, the result columns correspond to radiant cooling+ natural ventilation, radiant cooling + mechanical ventilation, and airconditioning scenarios.It is clear in Figure 4.20 that the control strategy used to keep thechilled surface temperature just below the dew point is functioning properly.Additionally, there is lots of potential for additional cooling as the membranetemperature is well above the dew point temperature.Figure 4.21 suggests that one would not want to operate a radiant panelwithout natural ventilation in this climate, as the dew point within thespace is very close to, and occasionally exceeds the membrane temperature.This illustrates the benefits of natural ventilation, as it both reduces thesensible cooling required by the mechanical system while simultaneouslydehumidifying the space.Figures 4.22 and 4.23 shows that thermal comfort is maintained in bothVancouver radiant cooling scenarios.Figure 4.19: A comparison of the annual energy consumption of the threemechanical systems being simulated using the future Vancouver climate4.5 DiscussionThe first topic of discussion focuses on the performance of the frameworkused to simulate the python heat transfer model developed in Chapter 3within the TRNSYS environment. This will be followed by a discussionregarding the simulated environments and the results obtained from thesesimulations.4.5.1 Framework PerformanceThe primary objective of this chapter is to develop a framework that allowsfor the simulation of a membrane assisted radiant panel within the TRNSYSenvironment. The individual sub-tasks shown in Figure 4.6 function prop-erly, although there are aspects of each that should be further developed.Figure 4.20: Diagram showing how the membrane temperature is main-tained above the dew point for the Vancouver Radiant + Natural Ventilationscenario.Occupant View Factor CalculationThe method used to calculate view factors accounts for the geometry of ahuman body and can be applied to a seated or standing occupant. How-ever, the view factors are hard coded into the framework and have to bemanually calculated when the size of the panel, or the position of the panelor occupants are changed. View factor calculations should be automated toallow for quick modifications to occupant locations as well as panel locationand size, and to allow for the simulation of several panels spread out acrossthe room. The benefits of using ray tracing rather than the current methodused to determine view factors should be explored.MRT of the Panel’s SurroundingsWhen determining the MRT of the panel’s surroundings, Rhino/Grasshop-per is used to calculate view factors between the panel and the walls/floorFigure 4.21: Diagram showing how the membrane temperature is main-tained above the dew point for the Vancouver Radiant + Mechanical Ven-tilation scenario.of the simulated environment. Rhino allows for easy modifications to roomgeometry and contains a plugin named ladybug that can automatically de-termine the view factors between the panel and a surface [64]. A simplifyingassumption was made that the view factors between the panel and the build-ing surfaces are equal to the view factors from a differential surface at thecenter of the panel. As TRNSYS models radiant thermal gains as beingemitted from a signal point in space, it was presumed reasonable to modelthe view factors from the panel to the building surfaces in the same way.However, there are some issues related to modeling radiant gains this waywhich will be discussed shortly.Determining Chilled Surface TemperatureThe theory behind determining the chilled surface temperature based onthe panel’s inlet water temperature is validated though simulation, but aphysical experiment would aid in further confirming the accuracy of thisFigure 4.22: Diagram showing that thermal comfort is maintained in theSingapore Radiant+Natural Ventilation scenario.approach.Heat Exchange Between the Panel and its EnvironmentThe methods used estimating the heat transfer rate between the panel andits environment, as well as its shortcomings, are discussed is Chapter 3.However, the methods used to distribute this heat transfer spatially through-out the room can be discussed. TRNBuild’s internal gains tool is used tosimulate the panel’s affect on the room because the rate of heat transfercalculated using the python model can be inserted as a value. This meansthat the correct rate of heat transfer can be easily simulated. A shortcomingof this approach is that using a point source to model radiant heat transfermeans that all the surrounding surfaces are affected equally. This is to saythat while the simulation is removing the correct amount of energy from theroom, it is radiantly affecting the ceiling which does not accurately reflecta real panel. A solution is to modify the simulated space by modeling aFigure 4.23: Diagram showing that thermal comfort is maintained in theVancouver Radiant+Mechanical Ventilation scenario.section of the ceiling as a chilled surface. The python model would first de-termine the rate of heat transfer that occurs between the membrane assistedpanel and its surroundings, and then determine the temperature that thechilled surface in TRNBuild needs to be in order to transfer an equivalentamount of energy. This would ensure that the radiant exchange distribu-tion is being simulated properly, however, a chilled surface that transfers anequivalent amount of radiant energy will likely not transfer an equivalentamount of convective energy. Another calculation would be conducted thatcompares the convective exchange of the real radiant panel and the chilledsurface in TRBuild, and introduce convective gains/losses within the simu-lated space to balance out these effects. Additionally, a method would needto be implemented that insures that the simulated panel does not condenseair moisture, as that would affect the simulated environment.Determining the MRT Percived by OccupantsTo determine the MRT perceived by an occupant, The MRT of the panelis combined with the MRT of the surfaces surrounding the occupant. TheMRT of the panel is determined using the energy leaving the panel as dis-cussed in Chapter 3, and therefor is not affected by the previously discussedradiation distribution concern. However, the MRT of the surrounding sur-faces is affected and therefor the MRT perceived by the occupant is affectedas well. Developing the method used to distribute radiant energy through-out the space will in turn address the concerns related to determining theMRT perceived by occupants.Determining Thermal ComfortThe methods used to determine thermal comfort have been well establishedand no shortcomings regarding the implementation of these methods havebeen observed.Controlling Panel TemperatureThe final framework element to be discussed are the methods used to updatethe water temperature that gets supplied to the panel. While they succeedin maintaining a comfortable thermal environment within the space, they donot maintaining a specific level of thermal comfort very precisely. Increasingthe precision of the control strategies will allow for more detailed energyusage analysis. For example, it would be useful if the energy savings achievedby maintaining an indoor PMV of 0.3 rather than 0.0 could be compared.ConductionThere are two reasons why conduction between the rear of the panel andthe ceiling is not modelled. The first is that the rear of the panel can beinsulated to an extent that renders heat loss through conduction almostirrelevant. For example, a 50mm thick Kingspan OPTIM-R panel, which iscomprised of rigid vacuum insulated panels with a microporous core, has anR value of 60 [52]. If the temperature difference between the chilled surfaceand the ceiling is assumed to be a consistent 13oC, which is the averagechilled surface to air temperature difference seen in the Singapore naturalventilation scenario, 307 W of thermal energy would travel into the rear ofthe panel. This is only 3% of the total energy exchange between the paneland its surroundings.Additionally, as the panel can either be attached flush to the wall or sus-pended, it is difficult to determine which approach should be used to modelinsulation. A model that can accurately predict the conduction through therear of the panel should be developed, but the results of the simulations stillindicate the energy saving potential of this technology.Framework ApplicabilityAn experimental study evaluating the performance of the framework shouldbe conducted before it is used to design a radiant system in a real building.The magnitude to which the uncertainties affect the simulation results arenot yet quantified. However, the model likely under predicts energy savings.This is because a large portion of the simulated radiant cooling is applied tothe portion of the ceiling that is covered by the radiant panel, and therefordoes not contribute to a lower MRT. Installing the system in a really officefloor would give the opportunity to conduct a detailed study of model per-formance will supplying the office with an energy efficient cooling system.However, the result uncertainty means that more development is necessarybefore it is widely applicable. Once this is done, the framework can be ap-plied to any building type, as it was not designed specifically for an officespace.4.5.2 Simulated EnvironmentsThe purpose of membrane assisted radiant panels is to provide low exergycooling systems to buildings in humid climates [59]. By pairing membraneassisted panels with natural ventilation, a heat pump no longer needs toproduce the low water temperatures required for air conditioning and caninstead supply water at the temperature required by the radiant panel. Tocondition air, the air must be transferred over a condenser coil which con-tains chilled water supplied by a heat pump. Higher chilled water tem-peratures means that the condenser coil needs to be larger to allow moretime for the air to reach the system’s desired temperature. Chilled waterneeds to be supplied at around 5-6oC to allow for sufficient cooling whileusing a reasonably sized condenser coil. A radiant system does not requirechilled water at such a low temperature because the water that leaves theheat pump can be applied directly to the space. For example, if the radi-ant panel requires a 15oC surface temperature, the water leaving the heatpump can be at 14oC. This introduces significant energy saving potential,as the efficiency of a heat pump depends on the temperature of the chilledwater it supplies. The results presented in this chapter indicates that thetechnology can provides low exergy cooling to Singapore, and that a casecan be made that supports the implementation of this technology in moretemperate climates such as Vancouver.Singapore DiscussionThe results from this study indicate that sufficient cooling can be suppliedyear round in Singapore without any active dehumidification. This is signif-icant for many reasons. The results show that implementing natural venti-lation can reduce the load on the cooling system as it removes a significantportion of the thermal gains generated within the space. Additionally, inte-grating neutral ventilation can improve the indoor air quality within a spaceby removing the carbon dioxide that occupants exhale and has been shownto reduce the effects of sick building syndrome [57, 92]. In a post COVID-19world where indoor ventilation rates will likely be viewed as having a greaterimportance, this study shows that humid climates like Singapore can imple-ment an energy efficient cooling system while simultaneously achieving veryhigh indoor ventilation rates.Vancouver DiscussionIt is difficult to definitively state that if Vancouver follows the RCP 8.5global emissions pathway that a membrane assisted radiant panel would berequired to supply sufficient cooling when paired with natural ventilation.Figure 4.20 and Figure 4.23 indicates that maintaining a chilled surfacetemperature slightly below the dew point keeps the average operative tem-perature around the middle of the comfort range. However, implementinga standard radiant panel would supply cooling more efficiently, meaning itmay be possible to keep it above the dew point of the surrounding air. Thatbeing said, membrane assisted radiant cooling is the more reliable option asit insures that condensation will not be an issue. Additional research shouldbe conducted to conclude whether a standard or membrane assisted radiantpanel is the better choice for this climate.4.5.3 Future DevelopmentThere is a lot of potential for this system to increase its energy efficiency withfurther research and development. Developing a membrane that has a highertransparency to the wavelengths being exchanged between the panel and itssurroundings will further increase the efficiency of the system. There are alsomaterials being developed that insulate from conduction while being largelytransparent to infrared radiation that could allow for even higher degrees ofsub-dew point cooling [21, 27]. Seeing as there are no physical buildings thatcan be used to compare the results of the modeling done in this study, itcan not be stated that these results quantitatively reflect the energy savingsthat will occur if a membrane assisted radiant cooling system is installedalongside natural ventilation in these climates. However, the simulationswere designed to isolate the relative energy savings that could be obtained,which are very promising in both climates. These results reflect the needfor further research in this field to address the uncertainties present in theheat transfer model and confirm that the TRNSYS framework is producingan accurately prediction of building energy usage.Chapter 5ConclusionsMembrane assisted radiant cooling is a low exergy space cooling technologythat can be applied in various of climates. To bring this technology closer towidespread implementation, this study developed a method of predicting thecooling capacity and membrane temperature of a membrane assisted panel,and calibrated it against data obtained from the Cold Tube pavilion inSingapore. A framework was then developed that allows for the integrationof the heat transfer model within a TRNSYS environment. It is the firststudy to integrate membrane assisted cooling with energy modeling software,and will aid in the design and optimization of cooling systems that utilizethis technology.It was observed that the heat transfer model can predict, with sufficientaccuracy to prevent condensation, the membrane temperate of a membraneassisted panel. The calibration of the model has indicated key areas thatshould be focused on in further model development.The framework used to simulate membrane assisted panels within aTRNSYS environment has some shortcomings that need to be addressed,and the lack of real building data to confirm model performance means thatfurther research is required before the framework can be widely adopted.However, solutions to these shortcomings have been proposed and the corefunctions of the framework that allow for the integration of the heat transfermodel operate as designed.The simulated results suggest that operating radiant cooling alongsidenatural ventilation can obtain significant energy savings relative to both airconditioning and radiant cooling + dehumidification/mechanical ventilationsystems. This study indicates that both Singapore and Vancouver couldbenefit from the adoption of membrane assisted panels.5.1 Future WorkTo further this research, the heat transfer model used to predict membranetemperature should be evaluated using data that contains MRT measure-ments. The accuracy of the Nusselt number correlations should also beassessed.Real building data should be used to evaluate the energy usage resultsproduced by the TRNSYS framework. Various framework shortcomings arelisted below and should be addressed by implementing solutions presentedin section 4.5.1.• Automate human to surface view factor calculations and investigatethe benefits of implementing ray tracing.• Improve panel to building surface view factor calculations by account-ing for the surface area of the panel rather than calculating view factorsfrom a single point.• Further validate the model’s ability to predict chilled surface temper-ature from the panels inlet water temperature.• Improve the method by which TRNSYS simulates the panel’s radiantthermal exchange with the occupied space.• Refine the inlet water temperature control strategy so the level ofthermal comfort within the space can be maintained more precisely.• Implement a method of accurately predicting conduction through therear of the panel.Currently, the radiant heat transfer between the panel and its environ-ment is set to zero the moment water is no longer entering the panel. 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Ex-perimental study on the characteristics of non-steady state radiationheat transfer in the room with concrete ceiling radiant cooling panels.Building and Environment, 96:157–169, 2016.Appendix AMonte Carlo OptimizationResultsThis appendix contains histograms depicting the data used to determine theerrors factors used to calibrate the model. The histograms show the errorfactors present in the top 5% of best performing samples obtained from theMonte Carlo simulation.Appendix BBridging TRNSYS andPythonThis appendix explains the operations that are needed to facilitate the oper-ation of the Python heat transfer model within the TRNSYS environment.B.1 Human to Panel View Factor CalculationsA paper by Cannistraro et al. [20] was used to calculate the view factorsbetween a human and a rectangular surface. A seated human was used inthis study, but this method can be applied to a standing human as well.Equation B.1 is used to calculate the view factors.FP−A = Fsatmax(1− exp[−(a/c)/τ ])(1− exp[−(b/c)/γ]) (B.1)The parameters used in this equation are taken from Figure B.1.All parameters shown are for a seated human, and each row correspondsto a different subject orientation and surface location. A description of eachrow can be seen in Figure B.2. Rows SEU1 and SEU2 were used, as it wasFigure B.1: Parameters to be used in Equation B.1 for a seated person [20].Figure B.2: Description of analyzed scenarios B.1 for a seated person [20].assumed that the occupants can sit in any direction.Figure B.3 is used to determine the spacial dimensions affecting the viewfactor between a human and a surface.Figure B.3: Coordinates between a person and a surface [20]B.2 Determining the MRT of the Panel’sSurroundingsThe total Mean Radiant Temperature of the surroundings, as perceived froma point in space, is calculated using Equation B.2.T4r = T41Fp−1 + T42Fp−2 + T4NFp−N (B.2)T r : Average MRT of surroundingsTN : Surface temperature of surface NFp−N : View Factor from the measurement point to surface NThe view factor between the center of the panel and each building surfaceis calculated using a Grasshopper plugin named Ladybug and the tempera-ture of each building surface is supplied by TRNSYS.Two MRTs need to be calculated. The first is the MRT caused by justthe surrounding building surface (occupants ignored), and the second takesboth occupants and building surfaces into account. To calculate the MRTcaused by both occupants and surfaces, the view factor between the paneland the occupants is determined. This is done by taking the view factorsbetween occupants and the panel, and applying the reciprocity theoremwhich is described by Equation 3.28 in Chapter 3. An effective clothedhuman radiation area of 1.55m2 is determined using relations presented byCannistraro et al. [20] and an average male body surface area of 1.9m2. Thebody surface area is determined using Equation B.3 obtained from a paperby [28], and typical male height and weight of 170cm and 78.5kg respectively.The surface temperature of a clothed human is modeled as a constant 32oC.This value is determined using ranges presented in a study by Kwon andChoi [55]. The area of the panel in all simulated scenarios is 180m2.BSA = 71.84 ∗H .725 ∗W .425 (B.3)BSA : Body surface area [cm2]H : Stature height [cm]W : Body weight [kg]B.3 Determining Chilled Surface Temp fromInlet TempThe heat transfer model requires the average temperature of the chilledsurface to calculate heat transfer between the panel and its surroundings.However, TRNSYS supplies the heat transfer model with the panel’s inletwater temperature and flow rate. The panel’s chilled surface is determinedusing the outlet water temperature, which in turn depends on the heatbeing transferred from the panel. This is to say that the chilled surface ofthe panel, and therefor the heat being transferred by the panel, can not beimmediately calculated using the panel’s inlet water temperature.The relationship between the heat transfer provided by the panel andthe water temperature difference across the panel is shown in Equation B.4.Q = m˙Cp(Tout − Tin) (B.4)Q : Heat transfer supplied by panel [W]m˙ : Mass flow rate [kg/s]Cp : Specific heat capacity of water [kJ/Kg/oC]Tout : Temperature exciting the panelTin : Temperature entering the panelWhere (Tout + Tin)/2 is the average temperature of the chilled surface.To determine Tout, it was discovered that for a given environmental condi-tion, there exists a linear relationship between the temperature of the waterentering the panel and the chilled surface temperature, as seen in FigureFigure B.4: Relationship between inlet and chilled surface temperatures.B.4.To determine the linear relationship for a specific instance of environ-mental parameters, the heat transfer model is run twice. Both instancesassume a different chilled surface temperature (5 and 10 oC), and calculatesthe heat transfer the panel provides to the space. Then Equation B.4 isused to determine the temperature difference across the panel (Tout − Tin)in both cases. Since the average temperature chilled surface temperature isknow in both cases, the temperature difference across the panel can be usedto determine the panel’s inlet and outlet temperatures.Finally, as there exists a linear relationship between panel inlet and av-erage chilled surface temperature, the inlet and surface temperatures forthe two cases are used to create a linear relationship between the inlet tem-perature and the chilled surface temperature for the specific environmentalcondition being analyzed.B.4 Calculating Heat Exchange Between thePanel and the Built EnvironmentThe radiant heat that is transferred between the panel and its surroundingsmust be isolated from the radiant heat transferred between the panel and thebuilding’s occupants. This is because the heat that is transferred betweenthe panel and the occupants does not affect the room’s thermal environment,as the occupant’s surface temperature is assumed constant. To achieve this,the MRT of the panel’s surroundings that ignores occupants is used. Themethodology presented in Section 3.5 of this thesis uses this MRT value tocalculate the net heat transfer between the panel and the built environment,assuming no humans occupy the space. However, humans due occupy thespace, so the total heat transfer is scaled by the view factor between thepanel and its surroundings. For example, if the view factor is 0.9 from thepanel and the building surfaces and 0.1 from the panel and the occupants,the heat transfer value is be multiplied by 0.9.The total convective heat transfer between the panel and the space iscalculated using the methodology presented in Section 3.5.B.5 Determining the MRT Perceived byOccupantsWhile the panel’s effect on the simulated environment must be in the formof total heat transfer, most thermal comfort models incorporate radiant heattransfer by determining the MRT perceived by an occupant. To determinethis value, first the MRT of the panel is calculated using the methodologylaid out in Section 3.5. Equation B.2 uses the MRT of the panel, the temper-atures of the building surfaces, and the view factors between the occupantsto each surface (including the panel) to determine the MRT perceived byeach occupant.B.6 Determining Thermal ComfortOnce the MRT perceived by an occupant is determined, the thermal comfortmodels outlined in Section 4.3 are used to asses the thermal comfort percivedby each occupant. The minimum, maximum, and average thermal comfortof the occupants are then determined.B.7 Updating Panel TemperatureThe thermal comfort results are used to determine if the panel’s currentoperating conditions are providing a comfortable environment. The tem-perature of fluid entering the panel is incremented if a warmer or coolerenvironment is required.Appendix CEstimating CalibratedVertical Panel PerformanceTo model a horizontal panel, an assumption was made, based on no researchor data, that the amount by which the internal and external convection co-efficient change when an uncalibrated vertical panel is modeled as beinghorizontal, may also apply when a calibrated vertical panel is made hori-zontal. This is an attempt to apply a calibration to the horizontal panel.To determine the amount by which the calibrated internal convectioncoefficients should be scaled, the ratio of the uncalibrated horizontal/verticalconvection coefficients need to be determined. This is done by simulatingan uncalibrated horizontal and vertical panel 6 times, each with a differenttemperature difference between the chilled surface and the membrane. Atrend line is fitted to these data points to determine how the ratio changeswith the temperature difference within the panel. Figure C.1 displays theequation used to determine the convective ratio for a given temperaturedifference.This ratio is then applied to calibrated vertical panel internal convectioncoefficient to determine the horizontal internal convection coefficient used inFigure C.1: Relationship between the internal horizontal/vertical convectivecoefficient ratio and the temperature difference between the membrane andchilled surface.the model.The same approach is used to scale the calibrated external convectioncoefficient, however the ratio depends on the temperature difference betweenthe membrane and the air surrounding the panel. The equation used to carryout this calibration is shown in Figure C.2.Figure C.2: Relationship between the external horizontal/vertical convectivecoefficient ratio and the temperature difference between the membrane andchilled surface.

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