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1 Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2013 Parametric Study of Graphite Foam Fins and Application in Heat Exchangers Michael Collins Follow this and additional works at the FSU Digital Library. For more information, please contact

2 THE FLORIDA STATE UNIVERSITY COLLEGE OF ENGINEERING PARAMETRIC STUDY OF GRAPHITE FOAM FINS AND APPLICATION IN HEAT EXCHANGERS By MICHAEL COLLINS A Thesis Submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Master of Science Degree Awarded: Spring Semester, 2013

3 Michael Collins defended this thesis on March 6 th, The members of the supervisory committee were: Chiang Shih Professor Directing Thesis William Oates Committee Member Juan Ordonez Committee Member The Graduate School has verified and approved the above-named committee members, and certifies that the thesis has been approved in accordance with university requirements. ii

4 This thesis is dedicated to: My father Mark, my mother Penny and my sister Kelly iii

5 ACKNOWLEDGEMENTS I would like to thank all of the members of my thesis committee, Dr. Chiang Shih, Dr. William Oates and Dr. Juan Ordonez. During our discussions, their patience and constructive criticisms helped to make this an excellent learning experience which greatly enhanced my writing and communication skills! Thanks to their help, I was able to overcome many disadvantages and obstacles which would have been difficult to solve on my own. I would also like to thank my research advisor Dr. James Klett from Oak Ridge National Laboratories for helping me understand and utilize the experimental tools used in this research as well as helping me to understand how to use the simulation software. With James help, I was taught how to diagnose and fix errors in my simulations as well as effectively use each experimental setup. Finally, I would like to acknowledge and give thanks to Scott Maurer and John Nagurny. They were the sponsors from Lockheed Martin which oversaw my research and helped to guide me. They gave me insight into the overall OTEC project and allowed me to discuss my research with them which gave me a much increased understanding of the overall project. Thanks to Scott, I was able to interpret and present my data in a more professional way for Lockheed Martin. He helped me to understand some of the underlying phenomena of the system and always updated me on the current progress of the project overall. iv

6 TABLE OF CONTENTS LIST OF TABLES... vii LIST OF FIGURES... viii LIST OF EQUATIONS... xi NOMENCLATURE... xiii ABSTRACT... xvi 1. INTRODUCTION Motivation OTEC Graphite Foam Material Chapter Organization LITERATURE REVIEW PHYSICS MODELING Porous Media Modeling Graphite Foam Fin Modeling Modeling Graphite Foam Fins in Air Flow Air Channel Simulation Analysis Subscale Condenser Modeling Simulating Baffles within Condenser Subscale Condenser Analysis EXPERIMENTAL EQUIPMENT AND PROCEDURE Overview v

7 4.2 Air Channel Equipment Overview Air Channel Instrumentation Air Channel Equipment Procedure Subscale Condenser Equipment Overview Subscale System Instrumentation Subscale System Test Procedure RESULTS AND DISCUSSION Graphite Foam Fin Simulations Air Channel Experiments Subscale Condenser Simulations Subscale Condenser Experiments CONCLUSION FUTURE RESEARCH APPENDICES A TEMPERATURE PLOTS OF SIMULATED FINS B SUPPLEMENTARY PLOTS REFERENCES BIOGRAPHICAL SKETCH vi

8 LIST OF TABLES 1. Physics models used for single-phase fluid flow and heat transfer Graphite foam fin parameters Mesh specifications Graphite foam properties Boundary conditions for graphite fin models Foam parameters Vapor region parameters Water region parameters Physics models used in subscale simulations HFE 7000 properties Air channel equipment Subscale system component list Fin Angle 5, inch Fin Thickness, inch Fin Spacing Open Flow Ratio classification Data set for experiment Calculated thermal resistances for air channel tests Subscale simulation results vii

9 LIST OF FIGURES 1. A simple Rankine cycle Atomic plane of graphene Straight Fins and Cross-Cut Fins Diagram illustrating velocity profile within porous media Visualization of each fin design parameter Air channel dimensions Surface mesh of air channel and graphite foam fins Plane section intersecting air channel Comparison of two plane sections at different heights Plot of Velocity vs. Modified Pressure Drop Basic subscale system Surface mesh for subscale system Sample plot of residuals Visualization of Baffle Type I and Baffle Type II Baffle Bar Type I and Baffle Bar Type II Three Baffles Experimental air channel Schematic of air channel showing important components Simplified 1-D thermal resistance concept Subscale condenser (Baffle Bar Type I) Control Model Heat Transfer Comparison viii

10 22. Velocity plot for graphite foam straight fins Temperature plot for graphite foam straight fins Velocity plot for aluminum straight fins Temperature plot for aluminum straight fins Pressure drop and heat transfer comparisons for each fin spacing Local velocity vectors of two different spacings Pressure drop and heat transfer for each fin angle Temperature plots for each fin angle test Vorticity plots for 5 and 15 degree fin angle Pressure drop and heat transfer for each fin thickness Velocity comparison between 0.25 and Thickness Temperature plots for each fin thickness Calculation of open flow area D surface of pressure drop for each fin design Comparison of heat transfer to open flow ratio Engineering dimensions of each air channel fin design Heat transfer of each fin type tested in air channel Pressure drop vs. Reynolds number Comparison of two fin designs to show differences using thermal resistance Contact resistance vs. Reynolds number Outlet air temperature comparison using calculated resistance Heat transfer comparison with calculated resistance Temperature plot for No Baffle Condenser ix

11 45. Side view comparison of pathlines between Baffle Type I and II Overhead view of pathlines in Baffle Type I Side view comparison of pathlines between Baffle Bar Type I and II Overhead view of pathlines in Baffle Bar Type I Temperature plot for Three Baffle System Overhead view of temperature pathlines for Three Baffle System Heat Transfer Coefficient vs. HFE Inlet Temperature Temperature: 0.25 Thickness Spacing Temperature: 0.25 Thickness 0.25 Spacing Temperature 0.25 Thickness Spacing Thickness Spacing Thickness Spacing Thickness Spacing Thickness Spacing Thickness 0.25 Spacing Thickness Spacing Comparison of pressure plots before and after interpolation Heat Transfer Surface for each fin design Pressure Drop for each fin design, classified by open flow percent Heat Transfer Coefficient vs. Reynolds Number x

12 LIST OF EQUATIONS. ar y s Law ar y or hheimer relation ontinuity equation Momentum equation Porosity equation nergy equation for porous me ia Time epen ent heat iffusion for soli material Simplifie first law of thermo ynami s Simplifie ar y or hheimer relation y rauli iameter Reynol s num er le tri power verage temperature for simulation raphite fin thermal resistan e Overall thermal resistan e for experiment om ine resistan e of experiment verage temperature for experiment Thermal onta t resistan e Spe ifi thermal onta t resistan e Logarithmi mean temperature ifferen e xi

13 . eat transfer oeffi ient Simplifie first law of thermo ynami s with phase hange Mass flow rate xii

14 NOMENCLATURE µ Dynamic Viscosity [kg/m s] K Intrinsic Permeability Tensor [m 2 ] U Mean Fluid Velocity [m/s] C f Forchheimer Coefficient [-] v Velocity Vector [m/s] g y Gravity Vector [m/s 2 ] P Fluid Pressure [Pa] T Temperature [ C] α Thermal Diffusivity [m 2 /s] v a Volume averaged Velocity in Porous Media [m/s] σ Heat Capacity Ratio [-] θ Porosity [-] q Internal Heat Generation [W/m 3 ] k Thermal Conductivity [W/m K] ρ f Fluid Density [kg/m 3 ] ρ s Solid Density [kg/m 3 ] c P Solid Specific Heat [J/kg K] c Pf Fluid Specific Heat [J/kg K] Mass Flow Rate [kg/s] Rate of Work [W] Thermal Power [W] xiii

15 α Inertial Porous Resistance Tensor [kg/m 4 ] β Viscous Porous Resistance Tensor [kg/m 3 s] L h Latent Heat of Vaporization [kj/kg] D h Hydraulic Diameter [m] A c Inlet Surface Area [m 2 ] P i Perimeter [m] Re Reynolds Number [-] Nu Nusselt Number [-] e Electric Power [W] I Current [Amps] V Voltage [Volts] E Heat Transfer from experiments [W] S Heat Transfer from simulation [W] R F Convective resistance of fin design [ C/W] T H Heater Plate Temperature [ C] T avg,sim Average air temperature for simulation [ C] T avg,exp Average air temperature for experiments [ C] R E Convective resistance of fin in experiment [ C/W] R C Thermal contact resistance in experiment [ C/W] R A Specific thermal contact resistance [ C m 2 /W] T out Outlet Air Temperature [ C] A C Surface Area of Heater Plate [ C] LMTD Log Mean Temperature Difference [ C] xiv

16 U Overall Heat Transfer Coefficient [W/m 2 K] T HFE-Cond-In Inlet HFE Temperature [ C] T H2O-Cond-In Inlet Water Temperature [ C] T HFE-Cond-Out Outlet HFE Temperature [ C] T H2O-Cond-Out Outlet Water Temperature [ C] T HFE-Cond-In Inlet HFE Temperature [ C] A H Surface Area in Condenser for Heat Transfer [m 2 ] A flow Cross Sectional Area of Flow [m 2 ] xv

17 ABSTRACT This thesis focuses on the simulation and experimental studies of finned graphite foam extended surfaces to test their heat transfer characteristics and potential applications in condensers. Different fin designs were developed to conduct a parametric study on the thermal effectiveness with respect to thickness, spacing and fin offset angle. Each fin design was computationally simulated to estimate the heat transfer under specific conditions. Following these simulations, graphite foam fins were then experimentally tested using an air channel to compare their thermal performance. The results of the graphite foam fin simulations demonstrated that the most effective fin design utilized the thinnest fins (0.125 inch) and the minimum spacing ( inch) with a 10 degree fin offset angle. The simulations showed that this optimal fin configuration could conduct more than 297% the amount of thermal energy as compared to straight aluminum fins. Experimental air channel tests confirmed that the fin design with inch spacing outperformed the other designs. Utilizing these results allowed for the thermal contact resistance of the fin design to be estimated. The thermal contact resistance was then utilized in simulations to provide more accurate results when compared against experimental tests. Graphite foam fins were then implemented into a simulation of the condenser system. The condenser was simulated with six different orientations of baffles to examine the incoming vapor and resulting two-phase flow patterns. The simulations showed that using both horizontal and vertical baffling provided the configuration with the highest heat transfer and minimized the bypass regions where the vapor would circumvent the graphite foam. This baffle configuration increased the amount of vapor flow through the inner graphite fins and cold water pipes, which gave this configuration the highest heat transfer. The results from experimental tests using the condenser system confirmed that using three baffles will increase performance consistent with the simulation results. The experimental data showed that the condenser using graphite foam had five times the heat transfer compared to the condenser using only aluminum fins. Incorporating baffles into the condenser using graphite foam enabled this system to conduct nearly ten times more heat transfer than the condenser system which only had aluminum fins without baffles. Utilizing three baffles caused the vapor xvi

18 to have a longer passageway from the inlet to the outlet, thus interacting more effectively with the graphite foam. The results from this research indicate that graphite foam is a far superior material heat transfer enhancement material for heat transfer compared to aluminum used as an extended surface. The longitudinal and horizontal baffles incorporated into the condenser system greatly enhanced the heat transfer because of the increased interaction with the porous graphite foam fins. xvii

19 CHAPTER 1 INTRODUCTION In this day and age, the demand for electricity is continuously increasing. Conventional power plants rely on combusting hydrocarbon fuels to produce power. These methods are contributing to large scale warming of the planet, which is a problem that needs to be addressed within our generation. Various ways to generate energy are being developed which do not harm the planet. [1] One of these green energy techniques is called Ocean Thermal Energy Conversion. Ocean Thermal Energy Conversion (OTEC) is a type of power plant which is situated near the coastline and utilizes the temperature differences between warm surface water and cold water from the depths to produce power. Typically, these power plants are not thermally effective and their efficiencies are usually around 3%. [2] The reason these plants are so inefficient is because of the small temperature gradient available. To increase the efficiencies of these plants and make them more feasible for widespread use, a more effective way to utilize the thermal energy must be developed. New materials are continually being developed to help with this design problem and graphite foam is a new material which shows great promise for use in heat exchangers because of its thermal properties. 1.1 Motivation Research using graphite foam has increased in recent years and it is now being investigated for use within heat exchangers. Graphite foam is a porous matrix of graphite ligaments which are extremely thermally conductive e ause of the materials stru ture. It s thermal and mechanical properties are discussed in section 1.3. This research included designing fins made out of graphite foam and studying different design parameters to compare how performance will change under specific conditions. Graphite foam fins were then designed based on these tests and implemented into a condenser system which was built to emulate an 1

20 OTEC condenser. The condenser was then tested further by using different configurations of baffles to alter the vapor flow pattern in order to increase the heat transfer of each system. This research gave valuable insight into methods to potentially increase the effectiveness of a fullscale OTEC condenser. 1.2 OTEC In a closed cycle OTEC power plant, a working fluid is vaporized using the temperature difference between surface and deep ocean water. The working fluid typically used is ammonia, due to its low boiling point and low specific heat. Figure 1 illustrates the basic Rankine cycle of an OTEC plant. The ammonia flows into the evaporator, where warm water flows inside the central core of the heat exchanger, transferring thermal energy to the ammonia causing it to change phases. [3] The vaporized ammonia then passes through a turbine to drive a generator in order to produce electricity. This lower energy vapor then flows into the condenser unit. In the condenser, cold water is pumped from deep in the ocean and flows through the core of the condenser. The vapor condenses and is then pumped back through to the evaporator again. [4] This Rankine cycle is shown below in Figure 1. Figure 1. A simple Rankine cycle 2

21 OTEC Rankine cycles have been investigated many times in the past. Research into the idea of using the ocean to provide power goes a k to the late s with Ja ques rsene rsonval. is stu ent, Georges Claude, then went on to build the first working OTEC plant in Cuba in 1930 which used Jacques principles to boil a working fluid and extract energy from it using a low-pressure turbine. [5] Japan has also led the world in producing OTEC technology for commercial use. In 1970, the Tokyo Electric Power Company engineered and constructed a 100kW OTEC power plant which provided electrical energy to the local electrical grid. [6] This plant was an example of a closed-cycle type, which kept the working fluid contained within its own cycle. The plant became operational in 1981 and was able to produce 120 kw of power. Of this amount, 90 kw was used to power the plant and keep it operational and the remaining 30 kw was used to power a school and other local buildings. In 1974, the United States established the Natural Energy Laboratory of Hawaii Authority (NELHA). This installation investigates green energy techniques and is located on the coast of Kona in Hawaii. At this location, solar power, biofuel and OTEC are among the technologies being investigated. The warm surface water at this location provides a perfect setting for OTEC research. [7] This is the reason why Makai Water Engineering, partnered with Lockheed Martin, has continued OTEC research at this location. Today, Lockheed Martin is in the final phases of their OTEC project. Working alongside researchers at Oak Ridge National Laboratories, new graphite foam fin designs have been incorporated into the OTEC heat exchangers to increase their efficiency by facilitating more heat transfer per heat exchanger. Lockheed finished construction of their prototype OTEC condenser and evaporator and these components are being installed at Makai Ocean Engineering in Hawaii. The testing phase will be completed between 2012 and 2013 and will provide useful insight into the potential of this technology and the use of the new graphite foam material. [8] Increasing the heat transfer between the ammonia and water is one method to increase the systems overall efficiency. The small temperature difference between the warm and cold ocean water has to be utilized to its full potential. One of the most effective ways to increase this efficiency would be by introducing new materials within the heat exchangers which greatly increase the surface area available for heat transfer. That is why graphite foam extended surfaces have been looked at so extensively as a replacement for aluminum fins in the system. Since 3

22 graphite foam contains millions of pores, the material allows fluid to flow within the volume and provide extremely high surface area per volume of material. Overall, OTEC plants seek a green energy solution for energy consumption as the oceans will always retain their temperature gradients, and this energy can always be harnessed. Searching for more efficient ways to obtain this energy is an obstacle which will hopefully be surpassed with more research. 1.3 Graphite Foam Material ar on is one of nature s interesting materials. Having four valence electrons allows it to have very remarkable properties. In nature, it can be found in many different forms. It is commonly used in mechanical pencils as graphite and can have planes of atoms easily sheared from one another to provide a dark line of carbon on paper. It is also found in nature as diamonds, in which the carbon forms very strong covalent bonds with its neighboring atoms and which creates the hardest crystal lattice known to man. Graphene is another type of carbon found in nature, which is also the primary constituent of graphite. Graphene is simply a two dimensional carbon lattice in which the carbon atoms are bonded covalently to three neighboring carbon atoms to form a chicken-wire type appearance and also maintain high electrical and thermal conductivity. A single plane of graphene showing atomic dimensions is shown in Figure 2. Figure 2. Atomic plane of graphene 4

23 Dr. James Klett from Oak Ridge National Laboratory discovered a new type of graphite foam while trying to prepare a new carbon composite material by carbonizing some carbon mesophase pitch. Dr. Klett was experimenting with a new way to fabricate carbon composites and stumbled across the new material. [9] "We had been making carbon-carbon composites, which are carbon fibers embedded in a carbon matrix," Dr. Klett explained. "Because of their heat transfer abilities, such composites show promise for making better brakes and heat shields. But we were trying to find a cheaper way to make the composites. We usually heat-treat a carbon material to very high temperatures to develop a graphite product," he said. "I took the carbon foam and heat treated it to make it graphite foam. I then noticed that it transferred heat remarkably fast. When I held the sample in the palm of one hand and pressed an ice cube in tweezers against the top, the heat from my hand caused the ice to melt quickly, cooling my han. [10] Due to the high pressures and temperatures, over 1000 C, the carbon mesophase pitch was baked and turned into carbon-foam. For this process, a very slow heating rate is applied, 0.2 Celsius/minute until the carbon mesophase pitch reaches 1000 C. This also has to be done under a vacuum with supplied nitrogen to prevent combustion. The reason for the slow heat treatment is to wholly convert the carbon mesophase pitch into carbon foam and to do so in a way as to retain the isotropy of the inner structure. This isotropic carbon foam must be further heated using an Argon gas purge. This process took place at atmospheric pressure, but air was replaced with Argon. For the graphitization process, the carbon foam must be heated at a rate of 1 Celsius/minute until the carbon foam reaches 2800 C. [11] This stage of heating and high pressure forces the atoms in the carbon foam to re-align and form high organized graphite ligaments which replaced the carbon foam ligaments. As a result of the graphitization process, only a porous material remains comprised solely of graphite. The graphite ligaments are comprised of layers of Graphene, which utilize the weak van Der Waals bond in-between layers. The graphite foam has an incredibly large inner specific surface area, as average samples contain 10,000 m 2 /m 3. The inner structure of the foam has an open porous characteristic which allows fluid or gases to flow within the foam itself to some degree. [12] The process for creating graphite foam is very time consuming, as it takes many hours to heat up the furnace to the appropriate temperature and pressurize it in order to ensure proper 5

24 graphitization. One also has to ensure that the inert gases remain in the furnace to keep out any air. As Dr. Klett has received a number of patents on his invented material, he has also contracted out two companies to produce it commercially; Poco-Graphite and Koppers. These two companies have utilized this technique, but on a massive scale, to reproduce graphite foam much faster and at a lower cost. As the companies industrialize their processes of production, this price will continue to drop until it is a viable material for use in every application imaginable. Each company uses the basic idea of carbon mesophase pitch being heated to carbon foam, and then further heated to graphite foam, but the initial mesophase pitch is different for each. This results in the foam having different porosities, densities and thermal/electrical properties. These properties can be controlled and tailored to meet certain needs, but overall the basic characteristics stay the same. The reason for so much excitement about graphite foam is its thermal, electrical and mechanical properties. The foam itself is comprised of millions of inner ligaments and pores. These allow the structure to have a bulk volume which is so porous that up to 80% of the visual volume is actually air pockets, while high thermally conducting graphite remains the rest of the volume. The material is also only one fifth the density of aluminum, with essential the same bulk thermal conductivity. [10] This obviously has huge implications for convective or conductive heat transfer; where surface area is important for the exchange of heat. Using a piece of graphite foam instead of aluminum or copper for a heat sink could become a viable alternative since the available surface area for heat transfer is magnitudes larger than a regular metal. This is ouple with the foam s strange thermal a ilities. It was is overe by Dr. Klett that the foam ligaments exhibited an extremely high thermal conductivity of over 1700 W/m K which is more than four times higher than copper and also maintained the regular electrical conductivity of graphite. Copper has a thermal conductivity of 400 W/m K. The ligaments are highly organized, so the electrons can freely flow through the graphite parallel to the graphene sheets. Since the volume of the graphite foam material is largely air, the bulk thermal conductivity is lower at around 150 W/m K. This is different than carbon foam, such that carbon foam is both an electrical and thermal insulator. [13] Not only oes the foam s ligaments maintain an incredible thermal conductivity, but the bulk thermal diffusivity has been experimentally determined to be 4.53 cm 2 /s compared to Aluminum 6061 having a thermal diffusivity of 0.81 cm 2 /s. This allows the foam to diffuse heat 6

25 and handle transient heat loads more than five times faster than a solid block of aluminum, a common heat sink material. The bulk foam material exhibits an averaged thermal conductivity of over 180 W/m K but ligaments by themselves are over 1700 W/m K. This is still within comparison of Aluminum [13] This is combined with its super low density of only g/cm 3 compared to Aluminum 6061 which has is 2.88 g/cm 3. This makes it a very light material which is easy to machine. The use of the foam in a heat sink also does not require extra circulating air or liquid to help the convection, since the material is permeable. It can be used in applications where weight and size are an issue. Another application which is currently in use is the foam being used on LED light lamps to reduce the temperature and increase the lifespan. Light ballasts are usually over 60 C and this can be severely detrimental to the life of the LEDs themselves and cause them to burn out prematurely. The foam s use re u es the temperature of the L s y over ten degrees Celsius and according to Dr. Klett, if one can reduce the temperature of an LED by ten degrees, its lifespan could be essentially doubled. [10] These abilities of graphite foam material give it huge promise in the world of heat transfer and heat exchangers. Further research has been conducted using the graphite foam to contain a phase change material to enhance its thermal energy transfer abilities even further. This phase change material would absorb all of the energy from the graphite foam needed to change the phase of a material like wax, from solid to liquid. [14] Having all these properties easily reveal how useful it could be in real life applications. 1.4 Chapter Organization This chapter provides a basic insight into the existing Ocean Thermal Energy Conversion technologies out there and a basic history of OTEC power plants. Graphite foam is discussed as being utilized as an extended heat transfer surface within the OTEC heat exchangers to increase surface area for heat transfer. Chapter 2 explains previous research into graphite foam and its properties. This chapter also talks about previous uses of graphite foam to transmit heat and utilizing fin structures. Chapter 3 explains the methods of using computational fluid dynamics simulations with graphite foam fins and the modeling of a subscale two-phase heat exchanger. Chapter 4 discusses the laboratory test equipment, methods and the procedure to test graphite 7

26 foam fins and the subscale condenser. Chapter 5 discusses and interprets the results from these tests. Chapter 6 discusses the conclusions based on the results from this research. 8

27 CHAPTER 2 LITERATURE REVIEW Since its conception, Graphite Foam has been the subject of much research into its different abilities. After it was accidentally discovered, during a process meant to create carbon composites, its remarkable thermal abilities were noticed. In 2000, Klett et al. discovered that the carbon mesophase pitch would form graphite foam in different porosities and densities depending on temperature and pressure. These changes affected the size of the pores due to the expansion of the gases within the mesophase pitch. As the bubbles expand within the mesophase pitch, they put forces onto the cross-linked mesophase pitch molecules which further evolve into graphite over time in the furnace. This newly created graphite is then aligned into ligaments due to the forces from the expanding bubbles. The material was found to have a thermal conductivity of 1700 W/m K in the individual ligaments of graphite, with a bulk material thermal conductivity of over 150 W/m K. Depending on the temperatures and pressures used, the porosity would vary from 0.5 to 0.9 and the specific surface area was between 5000 and 50,000 m 2 /m 3. [15] The process for creating mesophase pitch for the graphite foam was further simplified by Klett at ORNL. This new process allowed for more consistent properties of the graphite foam as well as a procedure to create different porosities and thermal conductivities depending on the crystal alignment. [16] Tee et al. confirmed that as the pore size within the foam increased, the convective heat transfer decreased. A mathematical model was developed to help understand how changes in the material, like porosity, would affect its thermal properties. It was also discovered that by using graphite foam as a heat sink, it performed excellently due to its extremely high specific surface area and its high thermal conductivity. [17] In 2006, Straatman utilized graphite foam fins in a test to determine their convective heat transfer coefficient in parallel flow. It was determined that the optimum thickness of a graphite foam fin was ~3mm to obtain the maximum convective heat transfer. Fins with a larger thickness had a much decreased fluid velocity within the pores due to a longer mean free path. This longer path causes the fluid within the foam to remain in the foam for a longer period of 9

28 time and reach thermal equilibrium with the foam which is detrimental to heat transfer in those regions. [19] The pressure drop of graphite foam was investigated by Straatman et al. in 2007 and concluded that due to the small pore size there is a very large hydrodynamic loss of energy as the fluid flows within the material. This pressure drop was further investigated by Leong et al. in an experiment testing different fin designs of the graphite foam in an air flow. These different designs proved that the pressure drop could be reduced significantly by allowing open flow channels within the structure for air to freely flow. The ifferent fin esigns use in Straatman s research are a single block of foam, a continuous corrugated fin, parallel free standing fins and parallel free standing fins with notches. The notches in the free standing fins allowed for air flow to pass through the fins, as well as in between them. This design had the highest heat transfer and also lowered the pressure drop by allowing free flow channels. The pressure drop across the fin design dictated the mass flow rate within the foam. The quantity of foam determined the flow speed within the foam. Dr. James Klett and Dr. Jim Conklin also investigated the pressure drops of graphite foam. Using an experimental air channel, samples of graphite foam were placed in a constant stream of air at specific velocities to find the pressure drop. This pressure drop was used to calculate the foams permeability and flow factors which could be implemented in computational fluid dynamics software to successfully model the foam. The equation dictating the flow through the foam is a mo ifie version of ar y s Law alle the ar y-forchheimer Relation. This relation is explained in more detail in the next chapter. This equation relates the pressure drop across a section of porous material and the dissipation due to inertial forces to the overall fluid mass flow rate within the porous material. [19] The simulation software, STAR-CCM+, used this equation combined with Navier Stokes flow equations and the energy equations to solve for the flow and heat transfer within the graphite material. From the data and simulations performed by Dr. Klett and Dr. Conklin, their research concluded that using CFD software with Darcy-Forchheimer and Navier Stokes allows for solutions which are within 5% accuracy to experimental values. This is an important finding because it allows graphite foam fin structures to be simulated computationally with high accuracy. [19] 10

29 To illustrate the abilities of graphite foam to be able to process transient heat loads very quickly, research was done by Klett et al. to use graphite foam as a heat sink. A Pentium 133 processor was tested five times. Two of the tests were simply graphite foam blocks of different thicknesses bonded to the processor. One test was simply the processor by itself. The last two tests were using a copper finned heat sink and graphite foam finned heat sink with the same dimensions. The temperature of the processor at 90% power was 76 C at steady state. The graphite foam blocks were able to maintain the processor at the same temperature as the copper heat sink, 37 C, but being far less massive. The graphite foam fins were able to reduce the processors temperature to 33 C while only being 1/5 of the weight of the copper fins. A similar experiment was conducted by Williams et al. to investigate using heat exchangers which incorporated graphite foam fins and copper fins to compare their performance. A channel was devised which included a finned heat sink made of either copper or graphite foam. The graphite foam was found to be superior to the copper fins due to the large thermal diffusivity of the graphite foam which allows it to respond much more quickly to transient heat loads. [20] Wamei Lin conducted research into using graphite foam as a component in a large heat exchanger for heavy vehicles. In the simulated heat exchangers, graphite foam was used in different fin designs to provide different ways for the flow to travel within the structure. These different designs comprised wavy, baffled, pin and staggered fins. The pin fins were found to have the highest heat transfer and also the lowest pressure drop. Once again, this was due to allowing free flow channels for the air to travel unimpeded between the structures. Forcing fluid flow within the porous media drastically increased pressure drop. Having free flow paths is important to keep pressure drop low. [21] This literature review discussed research into graphite foam to investigate various aspects of its material properties. First, it was experimented with to determine why it was so thermally conductive and what factors will affect this property. Next, the graphite foam was tested against copper and aluminum, showing that it is extremely effective as heat transfer and accomplished this with much less density than its metal counterparts. Other research detailed methods to successfully simulate graphite foam in CFD software using empirically determined properties. These simulations illustrated that compared to experimental values, using the equations for 11

30 porous media and the Darcy-Forchheimer modification allows for models of graphite foam which perform within 5% of the experimental equivalents. 12

31 CHAPTER 3 PHYSICS MODELING The software used for all simulations was a computational fluid dynamics (CFD) software package called STAR-CCM+ produced from CD-Adapco. This software package utilized various physics models to model many different phenomena. For each simulation conducted in this research, the applicable physics models were chosen in the software. These specific physics models are discussed in more detail in a later section for each type of simulation. All 3D CAD models were created in SolidWorks and imported into STAR-CCM+ to be surface and volume meshed. Upon meshing, boundary conditions and initial conditions were assigned. All of the physics equations were then solved for every node point in the model. These equations were iterated until the change between iterations reached a certain threshold value. The mo el woul e onsi ere stea y-state when ea h varia le i not hange more than 0.001% between iterations. 3.1 Porous Media Modeling Porous media, such as graphite foam, consists of a material which permits fluid to flow within its volume through interconnected pores. The flow geometry and heat transfer phenomena within the material is actually very difficult to predict accurately, as the distribution of pores is random. The velocity of the flow within the material is also difficult to calculate since pores of different sizes will have different choking velocities, which prohibit any effective acceleration effects. This being the case, it is more effective to analyze flow through porous media as the material s overall capability to permit fluid flow. By volume averaging the flow properties, relationships between pressure drop and velocity have been developed to accurately predict the flow within porous media. One of these well-known relationships was developed by Darcy, who concluded that the velocity is directly proportional to pressure drop. [22] mo ifi ation of ar y s law alle the ar y-forchheimer 13

32 relation is a more a urate version of ar y s law whi h takes into onsi eration larger pressure drops at higher Reynolds numbers due to higher viscous forces and shear stresses. [23] When first investigated, porous media was found to have a mathematical relationship between velocity and pressure drop. This relationship was calle ar y s Law. [22] ar y s Law is shown in Equation 1. For this equation, the pressure gradient along the x-direction is described by the relation between several variables. In this equation, µ is the dynamic viscosity of the fluid, K is the permeability tensor and U is the bulk fluid velocity. ar y s Law is use in three dimensions, but in equation 1, the one dimensional relation is shown. ar y s law was further mo ifie to take into consideration the larger pressure drop at very high velocities due to inertial forces. This set of equations was used by Klett et al [19] to model the flow properties within graphite foam. Their research verified that using the mathematical modeling, the flow and heat transfer within the graphite foam could be accurately determined within 5% of experimental values. Further research using the same equipment yielded the empirical coefficients which were used in the Darcy-Forchheimer relation. Those simulations verified that the mathematical model of the graphite foam can accurately simulate the flow characteristics within porous media. The Darcy-Forchheimer relation is shown in Equation 2. or equation, the original ar y s Law is mo ifie y in orporating a term to describe an increased pressure drop due to inertial forces at high velocities and C f is the Forchheimer coefficient. This relation is also used in three dimensions for each principal axis, so only the analysis used for one dimension is shown. - P x K (1) - P x K U K f U (2) STAR-CCM+ utilized the Navier-Stokes flow equation and energy equations which solved the fluid dynamics and heat transfer within the fluid and solid regions. For the porous regions, the Navier-Stokes equations were used with the Darcy-Forchheimer relation to determine the flow within the pores of the material in three dimensions. Modeling the flow 14

33 within individual pores would be too computationally demanding, so the software used these relations to describe the flow through the material as a bulk average, knowing the relationship between pressure drop and velocity. However, to ease the computational time needed to compute this solution, the Navier-Stokes equations used in the existing computational model were modified to time-average the Reynolds Number parameter in the flow (Reynolds Averaged Navier Stokes). Instead of using the local velocity, a mean time-averaged velocity was used coupled with a term which represents the fluctuations in velocity. For the fin simulations, the pressures and velocities of the air were relatively low, so compressibility effects can be neglected and the fluid can be assumed to be incompressible. The system was solved implicitly and as an unsteady system. This means that future iterations of the solution for every mesh-node are reliant on the previous time-iterated solutions. As each of the variables cease to change more than 0.001% per iteration, the simulation was considered at steady-state. The physics models used to solve for the fluid flow and energy transfer are listed in Table 1. These models were all used with the graphite foam fin models, however, with the Subscale Condenser; extra physics models concerning two-phase flow were also introduced. These are discussed in a later section. Table 1. Physics models used for single-phase fluid flow and heat transfer Reynolds averaged Navier-Stokes Implicit Unsteady Realizable K-Epsilon Turbulence Segregated Temperature All y+ Wall Treatment The turbulence was modeled using the Realizable K-Epsilon model. This turbulence model combined the conservation equations with two other transport equations which were solved to find the turbulent kinetic energy and the dissipation rate. The physics model which described the on itions at the wall was alle the ll Y Wall Treatment model. This model specifically calculated the fluid behavior on and directly beside the wall-fluid interface and calculated the boundary layer behavior of the flow. The ll y Wall Treatment makes no assumption about how well the viscous sub-layer is resolved. By using a blended wall law to 15

34 estimate shear stress, the result will be similar to the Low y+ wall treatment if the mesh is fine enough. If the mesh is coarse enough, the wall law is equivalent to a logarithmic profile. [ ] The turbulence modeling and boundary layer equations went beyond the scope of this research to discuss the individual equations, but were implemented within STAR-CCM+ to govern the flow of these simulations because of their higher accuracy. The basic governing Navier-Stokes equations have been reduced and are shown below. Equation 3 is the basic fluid governing continuity equation. Equation 4 is the momentum equation. The heat capacity ratio is calculated in Equation 5. This ratio takes into consideration the ratio of heat capacities of both the porous medium and the fluid inhabiting the pores of the material. Equation 6 calculates the energy within porous media. f t f t ( f ) (3) - P f g y (4) σ θ f Pf ( -θ) s Ps f Pf (5) σ T t T α T q f p K f pf (6) These equations were used to dictate the flow characteristics of fluid particles travelling through the foam. Since the individual pores could not be modeled, the foam regions were just prescribed with these relations in order to calculate the bulk velocity and pressure drop changes of flow within this material. By using this method, flow within the foam could be accurately described without having to model individual pores. The velocity within the graphite foam was calculated by using the pressure drop across the fins and the Darcy-Forchheimer relation. This equation was automatically employed by STAR-CCM+ as a region in the simulation was selected as a Porous Region within the software. For all calculations for porous media, the computational domain was the three dimensional volume of the graphite foam itself. The porosity was isotropic. The foam was 16

35 assigned the Viscous and Inertial Resistance tensors which were empirically found during tests with the foam. The Viscous Resistance tensor provided the scale of kinetic energy dissipation within the foam due to viscous forces and shear stress. The Inertial Resistance Tensor provided the scale at which kinetic energy is dissipated within the foam due to the diffusion of momentum through the pores. Aluminum was only governed by the energy equation because no fluid could flow within the material. The time dependent heat diffusion equation is shown in equation 7 below. T t α T (7) 3.2 Graphite Foam Fin Modeling Previous research into graphite foam fin designs concluded that the most effective thickness of straight graphite foam fins for convective heat transfer was inches (3 mm). This was due to the fact that having larger fins drastically reduced the velocity of flow within the foam as the fluid travels further into the material. As the velocity of the flow within the foam decreased, the temperature reached equilibrium with the foam, reducing or eliminating heat transfer in that region. [18] The first step in fin modeling was to establish a baseline of comparison between all mo els. This was omplete y first simulating a set of Straight luminum ins, Straight raphite oam ins an ross- ut raphite oam ins. The ross-cut fins used the same spacing and thickness of the straight Graphite Foam Fins, except the angle for the cross cut was 5, instead of 0, which correspond to the straight fins. The thickness of each fin type was inches and the spacing for each was inches. Figure 3 shows the design for the 3D cad for each. These tests were performed to confirm the increased heat transfer abilities of the graphite foam compared to the bulk aluminum. Further study into the abilities of the graphite cross cut fins discussed in this thesis include studying the changes of performance when altering the spacing, thickness and offset angle of the cross cuts. 17

36 Figure 3. Straight Fins and Cross-Cut Fins The cross cut fins consisted of a two inch by two inch block of foam which was 0.5 in hes tall. These fins were ut using a ross- ut esign, whi h is shown in above in figure 3. This previous research discussed how important it was to maintain free flow channels within the fin structure, which kept the pressure drop low, while maintaining a large convective heat transfer coefficient. [25] The cross-cut design was conceptualized because this design allows for the heat sink to incorporate free flow channels while also creating diamond shaped intersection points between the two layers of cross-cut fins. The cross-cut fin design maintained free flow channels in the structure. These free flow channels allowed the foam to have a larger wetted outer surface area besides the inner pores. This larger outer surface area increased the available area for convective heat transfer. The porous media did not utilize the no slip on ition on the walls, sin e the flow permeated the material. So the velocity at the wall was able to be normal to the surface. This velocity into the foam depended on the driving pressure behind the flow. The relationship between the drop in pressure across a given sample of foam or fins and the velocity within the material was explained using the Darcy-Forchheimer relation. As the pressure drop across a fin design increased, this signified a larger velocity of flow throughout the porous material. A figure describing the average velocity profile using porous media is shown below in Figure 4. In this figure, one boundary is a solid wall while the other boundary is porous media. Note how the velocity profile is parabolic but maintains a finite value within the porous material. The boundary layer on the foam wall was perturbed similar to the boundary layer on a golf ball, though the fluid is permitted to flow within the foam. This caused the boundary layer to maintain large amounts of vorticity and turbulence at the foam interface. By incorporating 18

37 angles into the fin structure, the flow was also forced to travel on a convoluted path which continually separated this turbulent boundary layer as the flow encountered an intersection point between cross-cuts. As the fin angle increased, this created more intersection areas between the two layers of cross cut fins which forced the fluid to flow around them. The increased pressure drop seen across each fin design causes more fluid to flow within the porous media. This is explained using the Darcy-Forchheimer relation. Also, decreasing the spacing between fins would increase the Reynolds number, also increasing the local velocity within the porous media. [22] This diagram helps to explain why the boundary on the porous material does not use a noslip condition, since there can be a non-zero tangential velocity as well as a non-zero velocity normal to the surface. Figure 4. Diagram illustrating velocity profile within porous media Three parameters of the cross cut fins were varied: the thickness of the fins, the spacing between fins and the angle of the fins measured off of the flow axis. Each parameter had three different test values. This equated to 27 different fin models. Upon the completion of these fin simulations, three other fin designs were also tested using a smaller spacing. However, due to the availability of the equipment needed to machine the fins, inches was the minimum test value for the spacing. Though, in real life circumstances, the spacing of these fins could be set at any value. This was because of the width of the blade used to cut these fins. The thickness of the fins would remain inches, but all the angles would be varied. 19

38 Each one of these thirty fin models was designed in SolidWorks as 3D CAD and imported into STAR-CCM+ for meshing and calculations. For each of the created graphite foam fin models, only one parameter was changed at a time. This allowed for the analysis of how each parameter varied the flow and energy characteristics of each design. The list of parameters tested is located in Table 2. Table 2. Graphite foam fin parameters Spacing (in) Thickness (in) Offset Angle ( ) As discussed in a previous section, the optimum thickness for convective heat transfer in graphite foam fins in parallel flow was 3mm (0.118 inch). This thickness was important because it was the optimum value to ensure that the flow within the foam did not become stagnated. If the flow within the foam had a velocity which decreased too far, the fluid would reach equilibrium with the foam material. If the temperatures of the foam and fluid are equal, then no heat transfer can take place. The previous research did not use the cross-cut design, so the fin thicknesses tested started at this optimum thickness (0.125 inch) and was increased to inches and 0.25 inches. The fin spacing parameter was varied from the smallest spacing to inches. The fin angle parameter was varied from 5 to 15 degrees measured off of the flow axis. A visualization showing how each of these parameters is measured for each fin design is shown in Figure 5 below. 20

39 Figure 5. Visualization of each fin design parameter For the simulations, the 3D designs of the fins were assigned as Porous Regions, with their characteristics set to the empirically determined properties of the graphite foam. These material properties were already provided based from previous research into the graphite foam conducted by Klett et al. [19] The porosity of the graphite foam was set at 80% (0.80) which corresponded to the average porosity of the type of foam being used for these simulations. The inertial and viscous resistance tensors, which describe the resistance of flow going into the porous media, were also empirically determined in previous research. 3.3 Modeling Graphite Foam Fins in Air Flow Each fin design model was simulated as being within an air channel. This channel received an initial air velocity which was always maintained above a Reynolds number of This signifies that the flow was in its transition regime at this initial air speed. This channel was created as a 6 inch long (15.24 cm) rectangular channel which was 0.5 inches tall (1.27 cm) in the Z-direction. The channel was 2 inches wide (5.08 cm), and each fin design covered an area in the middle of the air channel which was 2x2 inches (25.8 cm 2 ). Each fin design was the same 21

40 height as the channel, to eliminate any air flow which could bypass the fins. The ends of the channel were considered the inlet and outlet of the air channel which were assigned appropriate boundary conditions. Also, included in the model of the air channel, was another rectangular prism which was placed underneath the graphite foam fins. This was modeled as the aluminum heating plate which was assigned a specific temperature and the properties of aluminum. This plate was 0.20 inches tall (.508 cm) and covered the area of the fin design at 4 inch 2. This plate simulated a constant temperature source for the flow. The walls of the channel were programmed as adiabatic. The aluminum heater plate was set at a constant temperature of 45 C and the inlet flow was at 25 C. The temperature was set as a constant to compare the abilities of each design to increase to transmit thermal energy to the air flow without subscribing a thermal contact resistance. For these initial simulations, there was no thermal contact resistance applied between the heater plate and the foam fins. This resulted in a much larger transfer of thermal energy than one would expect from a real life case. The calculation of the thermal contact resistance was completed using the results from the experimental air channel tests. These results allowed for the verification of the simulations and are discussed more in depth in a later section. The basic layout of the air channel simulation is shown in Figure 6. Figure 6. Air channel dimensions The entire air channel model was surface meshed and volume meshed using the criteria listed below in Table 3. The mesh provided the 3D CAD with a finite number of mesh nodes, 22

41 which are coordinates in the volume where all of the equations for flow and energy are solved. or the mesh, the ase size was the maximum distance between mesh nodes. The base size used for all of the air channel simulations was 4mm. The relative minimum size was the minimum distance between nodes and this was % of the ase size. The relative target size was the distance between nodes which the program will try to achieve. The meshing process is nearly autonomous once the base size and criteria are input. The software will calculate all of the nodes and faces in the mesh given the specifications. The relative minimum size ensured that the mesh would not be refined smaller than 0.20 mm. This improved accuracy around corners or bends by using more node points at places with distinct geometry. Table 3. Mesh specifications Surface Mesh Type Volume Mesh Type Base Size Relative Minimum Size Relative Target Size Tetrahedral Polyhedral 4 mm 5% Base Size 100% Base Size The meshing process was straightforward, as STAR-CCM+ had a very accurate and efficient meshing algorithm. First, each fin design utilized the surface wrapper. This surface wrapper applied a coarse mesh to the entire surface area of the model. This surface wrapper is used to gauge where the volume mesh will be more intricate if the geometry gets complicated in a certain region. This surface wrapper used tetrahedral mesh cells of different sizes. The wrapper assigned the channel a coarse mesh while the foam had much smaller mesh cells. These extra cells increased the accuracy of the calculations near the foam at this region, since the node points for calculation are more concentrated. The volume mesh pipeline was then utilized to calculate polyhedral prisms which filled the inner volume of the channel with nodes to calculate the flow and heat transfer in 3-dimensions. Each fin design model had different amounts of mesh faces. On average, each air channel simulation consisted of approximately 1,500,000 faces for the volume mesh. Nearly 1,000,000 of these faces exist in just the foam fin regions. 23

42 The area between these nodes was interpolated, to give the 3D space a solution in every coordinate available. To help illustrate how this mesh is applied to the air channel, an example surface mesh of the air channel and foam fin designs is shown in Figure 7. The foam fins in the center of the air channel had much more complicated geometry than the rest of the channel. Figure 7 shows the exterior surface mesh of the air channel above which allows one to see how the mesh is refined in the region where the fins are located. Below the surface mesh of the air channel is the mesh of the graphite foam fins, showing the complicated geometry. Figure 7. Surface mesh of air channel and graphite foam fins Upon the completion of the mesh process, other parameters had to be specified in order to maintain consistency between tests. This included allowing the software to calculate the interfaces between air, aluminum and foam regions of the model to ensure that calculations were accurate at the interfaces. After the interface calculations, each region in the flow had to be designated as a specific flow regime corresponding to the type of calculations performed in each. The interior volume of the channel (besides the foam material) was programmed as a Fluid Region. This applied the regular Navier-Stokes and the Energy equation to this region, including the physics models for turbulence and boundary layers. The foam fins were 24

43 programmed as a Porous Region. This esignation ensured that in this computational domain, the Darcy-Forchheimer relation was used to calculate the flow based on the pressure. The aluminum heating plate was esignate as a Soli Region, whi h only used the energy equation to calculate the heat transfer through the material. On each respective boundary in the simulation, appropriate boundary conditions were assigned. or the plane esignate as the inlet, the oun ary on ition was Velo ity Inlet with a specific velocity assigned to the incoming air flow. The plane designated as the outlet was assigne a Pressure Outlet oun ary on ition, whi h simulated the end of the channel opening up into ambient pressure. The walls were set as ia ati Walls. This meant that the walls would not conduct any heat away from within the channel. The aluminum heating plate region was sele te an set as eat Sour e su s ri e with a onstant Temperature. The other options for the heating plate were onstant eat lux or un tion, whi h woul allow users to select a function to i tate heat transfer from the heat sour e. onstant temperature was used during these first tests because this method would test the ability of each fin design to transmit as much energy as possible to the flow. The outlet air temperature would increase to near the temperature of the heater plate depending on how effective the fin design was. Each air channel simulation comprised the respective graphite foam fin design and was modeled at five different velocities. The velocities ranged from 1-5 m/s ( ft/s). The parameters set for the foam included its porosity, inertial and viscous resistance tensors (XX,YY,ZZ), thermal conductivity, density and specific heat. The resistance properties of the foam were isotropic, as proven using experiments, so the resistance tensors were equivalent for each major direction within the material. The viscous and inertial resistance tensors provided the amount of resistance the foam gave to incoming flow on each principle direction. The properties of air were obtained using tabulated data which was included in the software when the fluid was selected as ir. The built in models included all of the properties and thermodynamic tables for air. The properties of aluminum were o taine y sele ting luminum to simulate the material for the solid aluminum heater plate region. The empirically determined properties of the graphite foam are shown in Table 4. 25

44 Table 4. Graphite foam properties Porosity 0.8 Porous Inertial Resistance (XX, YY, ZZ axis) kg/m 4 Porous Viscous Resistance (XX, YY, ZZ axis) kg/m 3 s Density 2200 kg/m 3 Solid Specific Heat 1020 J/kg K Solid Thermal Conductivity 1700 W/m K The parameters used for the inlet and outlet boundary conditions and the heater temperature are shown in Table 5. The parameters in quotations are the selections in the software for each designated plane section of the 3D CAD. The software took each of these boundary conditions into consideration as the differential equations are solved. The initial conditions of the air within the air channel were set to match the conditions of the air at the inlet boundary. Table 5. Boundary conditions for graphite fin models Inlet "Velocity Inlet" Inlet Velocity 1-5 m/s Inlet Pressure 0.0 Pa (atmospheric pressure) Static Temperature 25 C Walls ia ati Heat Source onstant Temperature Constant Temperature 45 C Outlet "Pressure Outlet" 3.4 Air Channel Simulation Analysis Each simulation of the various graphite foam fin designs offered valuable insight into their different thermal abilities. Out of the 30 different designs of graphite foam fins, each one had to be simulated at 5 different velocities to test their performance over a range of Reynolds 26

45 Numbers. After each simulation at each velocity completed its iterations, STAR-CCM+ offered many ways to analyze the provided data. For these air channel simulations, the rate of thermal power transfer was solved by doing an analysis of the system using the First Law of Thermodynamics. The conservation of energy equations for the fin models are shown below, which yielded the simplified First Law of Thermodynamics equation for the air flow. Since each fin simulation was iterated until the outlet temperature of the air did not vary, this signified that the system was at steady-state. The temperatures shown in Equation 8 represent the inlet and outlet air temperature. system t system t Q W m in h in i n m out h out i n Q W m h h pf T W Q m pf T Q m pf T -Q m pf (T -T ) (8) Other important solved parameters of the system, such as Pressure Drop or Velocity, were inherently solved by the physics models discussed earlier. Since the local changes of these 27

46 parameters were more important than the average values, plane sections were created which intersected the air channel. These allowed for the solutions of each variable to be plotted to visualize how these variables were locally affected by the fins. The plane sections which intersected the air channel varied depending on their height in the channel. A plane section is shown intersecting a fin design in Figure 8. Figure 9 shows two plane sections of the same fin design and how will differ depending on the intersection points. Figure 8. Plane section intersecting air channel Figure 9. Comparison of two plane sections at different heights 28

47 3.5 Subscale Condenser Modeling This section gives an in-depth overview of the modeling process for the subscale systems. After finding the graphite foam fin design which could permit the highest thermal energy transfer, a heat exchanger was simulated using these fins as extended heat transfer surfaces for the working fluid. The fin design used in this subscale condenser simulation was chosen because of its performance in the graphite foam fin modeling as well as from the results of the experimental tests. The experimental tests and equipment are discussed in the next section. The most effective fin design was chosen for use in the subscale test system. In order to ease calculation time, the individual fins of the chosen design were not modeled, but rather, a 3D rectangular prism represented the chosen fin design. This rectangular prism had its properties set to have the same characteristics as a fin design occupying the same dimensions. This was accomplished by obtaining a sample of foam which was cut into the correct cross-cut fin pattern. The pressure drop along a specific length and the respective velocities were recorded. Using a mathematical relation, one could yield the correct parameters to use with the foam model in STAR-CCM+. In Figure 10, an example plot is shown which was used to calculate the foam parameters. The plot shows the relationship between the Velocity (U) and Pressure Drop (dp/(l U)). To modify the pressure drop for use within this relation, the overall drop in pressure was divided by the length of the channel (L) multiplied by the free stream velocity (U). This yielded a nearly linear plot, the slope and intercept of which corresponded to the inertial and viscous resistance of the foam respectively. The reason for dividing pressure drop by the Length Velocity is because of the equation that STAR-CCM+ uses to calculate the flow within the porous media. The Darcy-Forchheimer relation is further simplified by STAR-CCM+ by replacing the terms which are coupled to velocity (U) and (U 2 ) with and. This simplification is shown below. The first equation used was the Darcy-Forchheimer relation. This equation was then simplifie y esignating α an β to represent the terms whi h are ouple to ea h velo ity term. The final form of this equation is shown in Equation 9. In this equation, α and β correspond to the viscous and inertial porous resistance tensors, respectively. 29

48 P x αu βu α K P x U P x β f K α β U U α β U (9) Alpha and Beta of P1 Foams in cross cut design dp/(l U) Velocity (U) Figure 10. Plot of Velocity vs. Modified Pressure Drop This method made the modeling process much faster, because one does not have to model the intricacies of each foam fin. The empirically determined properties for the specific fin design were assigned to the rectangular prism, so the equations solved within that region will reflect the performance of the fin design itself. The modeling process for the subscale condenser entailed creating a three dimensional model which uses the same dimensions as the subscale unit being tested experimentally. For 30

49 these tests the only parameter which changed was the positions of baffles and blocking bars. These are explained in more depth in a later section. Figure 11. Basic subscale system Once the model was created in Solidworks, it was uploaded to STAR-CCM+. The subscale condenser had each of its boundary conditions and computational domains selected individually. This basic system (No Baffles) is shown in Figure 11. In Figure 11, the gray outer shell (including the protruding pipes) was designated as an ia ati Wall oun ary. This ensured that the large cylinder would not lose any heat to the surroundings At the top and bottom of this cylinder were the water inlet and outlet respectively. The brown colored pipes running from the top to the bottom constituted the core pipes of the on enser. These were programme as Soli Regions an were assigne the material properties of aluminum. These pipes were the flow domain of the cold water. The cold water was pumped from the top to the bottom at a constant velocity. The cold water convectively cooled the aluminum pipes, which were directly exposed to a higher temperature vapor pumped into the system. The graphite foam regions were attached to the aluminum pipes, which extended their heat transfer surfaces exposed to the hot vapor flow. The inlet of the vapor was the protruding pipe on the top of the system in Figure 11. The graphite foam fins were the yellow rectangular prisms attached to the brown water pipes. These are programmed to have the same heat transfer properties, inertial and viscous resistances as the graphite foam fins. The graphite s properties remain the same. 31

50 a h region in the su s ale mo el was assigne as either porous, flui, or soli. The fluid region already has preprogrammed characteristics for the working fluid being used (HFE 7000). The solid region, aluminum, had built in characteristics as well. The graphite foam fins were modeled in STAR- M as porous me ia. This was a omplishe y sele ting porous me ia for the sele te yellow regions in igure 1. In STAR- M, porous me ia programs the mesh in that region to apply the Darcy-Forchheimer relation. This onfiguration was referen e as No Baffles in analysis. Other onfigurations utilize impermeable baffles which manipulate the flow of vapor and are discussed in the next section. The interior of the pipes in the right of the figure were esignate as lui Regions with water as the fluid. The interior volume inside the large gray cylinder on the left in Figure 11, except for the pipes and foam blocks, was onsi ere a lui Region as well. This region was the domain occupied with HFE7000. HFE7000 was a fluid with nearly the same thermal properties as ammonia, but non-toxic. This was used in place of ammonia because for the experimental tests, HFE7000 was utilized as the working fluid. This fluid is discussed in more depth in a later section. Each of these regions had its own parameters and boundary conditions. The inlet and outlet conditions for the water and vapor region were specified. For the vapor inlet, the vapor was always set at 3 m/s coming in to the system and the water inlet was set at 0.5 m/s. The large velocity of the incoming vapor and the slow velocity of the water were simulated as close as possible to the equipment used in the laboratory to simulate a condenser with the same dimensions. The vapor velocity will suddenly drop as the momentum of the flow is diffused throughout the volume. Since the graphite foam can allow HFE7000 to condense within its pores, the graphite foam must be enabled as an Energy Source within the program. The liquid and vapor phases of HFE7000 include their mathematical functions to calculate the phase change of this working fluid. These chosen parameters and functions for the foam are shown in Table 6. All others parameters stay as the default setting in the program, such as Turbulent Intensity. These parameters would only be varied for very specific cases or more complicated problems. For these cross-cut fins, the porous inertial and porous viscous resistance tensors were empirically determined to be 1000 times less than the bulk foam s properties. To determine 32

51 these properties, air was passed through a sample of the cross-cut fins using the relation discussed earlier. Due to the free flow channels, the pressure drop was much lower, thereby yielding a much lower resistance to flow. Table 6. Foam parameters Energy Source Yes Phase Sources: Composite HFE-L LiquidSourceGraphite HFE-V VaporSourceGraphiteCondense Porosity 0.80 Porous Inertial Resistance (XX, YY, ZZ axis) 12 kg/m 4 Porous Viscous Resistance (XX, YY, ZZ axis) 20 kg/m 3 s Density 2200 kg/m 3 Solid Specific Heat 1020 J/kg K Solid Thermal Conductivity 1700 W/m K The Vapor and Water regions also needed to have certain conditions specified before the model could be initiated. The mass flow rate of the cold water running through the Water Region and the vapor velocity always stayed constant. The Energy Source Option is selected because this programmed the flow to be multi-phase and contain both liquid and fluid particles. The phase sources for the HFE-Liquid and HFE-Vapor were selected from preprogrammed field functions within STAR-CCM which included all of the thermodynamic properties of this fluid. The other parameters of the vapor and water regions are shown in Table 7 and Table 8. These parameters include the type of inlet and outlet used for these regions, which are selected within the software and have the ability of setting appropriate boundary conditions. These conditions stayed constant for each simulated condenser system, in order to directly compare their performance. These boundary conditions are also listed in Table 7 and 8. 33

52 Table 7. Vapor region parameters Energy Source Phase Sources: HFE-L HFE-V Inlet Inlet Velocity Inlet Pressure Static Temperature Volume Fraction In Outlet Yes Composite LiquidSourceFluid VaporSourceFluid "Velocity Inlet" 3.0 m/s 0.0 Pa 35 C 100% Vapor "Pressure Outlet" Table 8. Water region parameters Inlet Inlet Velocity Inlet Pressure Static Temperature Outlet "Velocity Inlet" 0.5 m/s 0.0 Pa (gauge pressure) 10 C "Pressure Outlet" All of the subscale models were solved using these parameters to ensure consistency between the tested systems. Various orientations of baffles and blocking bars were the only factor which was changed between condenser simulations. The systems which were modeled each had the same flow characteristics as well as the same physics continua. This ensured that the only difference in performance arose from differences in baffle orientation. Sets of physics models were then selected for use in the condenser simulation and these are listed in Table 9. All of these sets of equations were solved for every node in the volume and surface mesh. The process for meshing is the same as with the graphite foam fins, discussed earlier. The number of cells for the subscale condenser is roughly the same as the air channel simulations. This is because the condenser does not contain any complicated or intricate geometries like the fin designs. For the subscale condenser, the base size for the mesh was set at 5mm. This is larger than the base size of the fin designs, which used 4mm. Figure 12 shows the 34

53 intricacy of the mesh for the exterior boundary of the subscale system as well as the interior surfaces. Table 9. Physics models used in subscale simulations Eulerian Multiphase Lagrangian Multiphase Multiphase Mixture Segregated Flow Segregated Multi-Phase Temperature Figure 12. Surface mesh for subscale system These physics models were utilized because they enabled a two-phase flow. The normal flow and energy equations used with the air channel simulations were also used to dictate the basic fluid mechanics and energy properties of the system. The new physics models utilized include both the Langrangian and Eulerian Multiphase equations. The Eulerian Multiphase 35

54 equation was used to represent the inner volume where the HFE vapor was condensing as a continuous phase whose equations are represented in Eulerian form. The condensed droplets were simulated using the Langrangian Multiphase equations which tracked the phase changes and characteristics with each in ivi ual flui parti le. The system was implicitly solved and unsteady. This required the equations to be iterated until they had converged to a realistic solution. After a few thousand iterations of these implicit equations, this solution converged to a solution which did not vary more than 0.001% with any extra computational time. As the solution converged, the residuals also started to level out. Residuals are the differences in variables as the set of equations are solved. A sample plot of the residuals for a simulation iterated to completion is shown below in Figure 13. Figure 13. Sample plot of residuals The plot of residuals shows how the system gradually becomes stable over time. As the simulation was iterated, each of the major equations of the system began to converge. The residuals track the convergence of the Continuity, the X-Y-Z Momentum, the Energy and the Turbulent Kinetic Energy and Turbulent Dissipation Rate. 36

55 First, the subscale system was tested by itself without any baffles in place. This system was solved to provide a baseline value by which alterations in the system could be compared. Next, two baffles were put into place and tested in forward and backward configuration. Following these baffle tests, longitudinal blocking bars were put into place as well. These blocked the horizontal bypass of the vapor around the core water pipes. Finally, a third baffle was also added, directly under the inlet, to direct the vapor into the graphite foam fins while it still maintained a high velocity from the inlet. Figures showing these orientations are explained in depth in the next section. The working fluid used for the condenser simulations and experiments was an engineered liquid from 3M called HFE It had properties very similar to that of ammonia, but it is nontoxic and non-corrosive. This provided a realistic analog to compare how the system would perform when it uses ammonia. The properties of HFE 7000 are listed in Table 10. Table 10. HFE 7000 properties Molecular Weight 200 g/mol Freeze Point C Saturation Temperature 24 C Liquid Density 1400 kg/m 3 Latent Heat of Vaporization 142 kj/kg Specific Heat 1300 J/kg K Thermal Conductivity W/m K The results from these models gave a very good indication of how the baffles will alter the performance in real life. Upon completion, the model gave insight into performance by offering the outlet temperature of the working fluid and water, the heat transfer across the waterpipe interface and the liquid fraction of the outlet. 3.6 Simulating Baffles within Condenser The next stage of study included modifying the design of the condenser. This modification involved testing various styles of horizontal and longitudinal baffles which changed the flow pattern of the vapor. Testing different styles of baffles altered the flow patterns of the 37

56 vapor flowing into the system. The performance of the system depended on the local Reynolds number of the vapor passing over the finned surfaces and the cold water pipes. Maintaining a large velocity and Reynolds number was important in order to maximize the convective heat transfer coefficient. If the flow bypassed the area with the graphite foam fins or aluminum pipes, there was a lower convective heat transfer coefficient due to the lower local Reynolds number over those surfaces. A high velocity ensures the largest temperature gradient between the vapor and cold water pipes. This temperature difference is the driving force behind the heat transfer to the cold water. At a low velocity, the layer of vapor nearest to the wall approaches the temperature of the cold water pipes, greatly reducing the amount of heat transfer from those surfaces. The focus was to direct the HFE vapor flow directly into the graphite foam and main pipes in the center of the condenser volume. In that case, the local Reynolds number was much larger travelling through the fins. As discussed before, a larger Reynolds number ensures a higher convective heat transfer coefficient and also led to a larger mass flow rate within the porous material as described by the Darcy-Forchheimer relation. As the velocity within the material increased, the viscous forces began to contribute more to the pressure drop due to much larger fluid shear stresses near small openings of pores. This was also shown with the Darcy- Forchheimer relation for a porous material. As the kinetic energy of the vapor was decreased and its temperature dropped, it reached the saturation temperature of 34 C which started the condensation process. When this temperature was reached, the vapor started condensing within the pores of the foam and on the outside of the aluminum pipes. As the volume of condensed HFE increased within the pores, eventually each pore became filled and the fluid exited the foam to collect at the bottom of the condenser. This reduced the subcooling of the fluid. Subcooling of a fluid occurs when the fluid is lowered past its condensation point. By using a porous material, this ensured that once enough HFE condensed within the foam, the pores would fill up and the liquid HFE would leak out. Each version of the condenser with different orientations of baffles shared the same dimensions and physics parameters as the version without baffles. These condensers also shared the same dimensions as their real life experimental systems which will be discussed in a later section. 38

57 The first performance test used the condenser with no horizontal or longitudinal baffles. This was to establish a baseline performance for the system in order to gauge the effects of adding in new structures. This no baffled system design is shown above in Figure 12. Since the inner structures of the condenser presented a large pressure drop to the flow, the majority of pathlines were expected to avoid this area and attempt to bypass it. These pathlines formed eddies which transported the vapor downward towards the outlet with a low overall heat transfer coefficient for the condenser Baffle Type I and Baffle Type II For the next subscale test, baffles were added to the system. These baffles were modeled as 0.25 inch (0.64 cm) thick, half circular plates which sealed against the outer shell of the condenser. These baffles prevented any downward bypass of the vapor unless the particles went around or through the inner pipes. The inlet pipe was placed 8 inches above the first baffle and the second baffle was on the opposite side of the system 8 inches above the outlet. This configuration is shown in Figure 14 below. Baffle Type II was essentially Baffle Type I turned upside down. In this configuration, the vapor coming in to the system from the inlet pipe would not encounter any baffles as it circulated downward in the condenser. Essentially, the top baffle in this configuration created a region of less vapor flow. In order for the vapor to circulate in the region above the top baffle, the vapor would have to pass through the inner pipes. Since these inner pipes offer a flow resistance and pressure drop, the majority of the vapor avoided this section and simply dropped downward to the lower baffle, since this path has less pressure drop. The region above the top baffle in Baffle Type II, did have vapor flow, but this vapor lost its momentum quickly, due to the loss of pressure needed to circumvent the inner pipes. The majority of particles in this arrangement simply maintained their momentum and circulated downward. By doing this, the vapor lost a majority of its velocity before encountering the heat transfer surfaces of the inner pipes and foam fins. The arrangement of the reversed baffle setup is also illustrated in Figure

58 Figure 14. Visualization of Baffle Type I and Baffle Type II Baffle Bar Type I and Baffle Bar Type II The next stage of testing consisted of implementing longitudinal baffles which forbid the flow from circumventing the inner core pipes. These baffles ran from the top header to the bottom header and were from the outer shell to the foam fin surface. These vertical baffles were impermeable and restricted the flow path of the vapor. Using these vertical baffles with horizontal baffles created a flow path which forced the vapor to come into contact with the inner pipes and graphite foam fins. The bars were also modeled as being 0.25 inches (0.64 cm) thick. The other dimensions and baffle orientations were the same as the original Baffle Type I test. As shown in Figure 15 below, these longitudinal baffles did not allow any vapor to simply flow around the inner pipes. This ensured that the local Reynolds is maintained at its maximum as the fluid passes over the inner pipes and graphite foam fins. This large local Reynolds number increased the local heat transfer coefficient of the foam material which increased the overall convective heat transfer from these surfaces. The longitudinal blocking bars were an important addition to the system since the most important factor to increase heat transfer in these condensers was to ensure the highest contact 40

59 velocities between the vapor and the foam. Without the bars, the vapor lost momentum and pressure as it would flow around the core water pipes. As the velocity of the vapor decreased, this lowered the heat transfer coefficient of the graphite foam and decreased the overall heat transfer to the cold water. Figure 15. Baffle Bar Type I and Baffle Bar Type II Baffle Bar Type II was set up the same was as Baffle Bar Type I, but for this model, the baffles were reversed (same arrangement as Baffle Type II but with longitudinal baffles). This arrangement is shown above in Figure 15. This arrangement created a region opposite of the inlet like Baffle Type II. This region was open to flow, but since only small openings allowed flow into this region, the pressure drop was much higher. It was expected that hardly any heat transfer could take place in this region since there would be minimal circulation of vapor. Since the path to the lower baffle is unimpeded, the vapor pathlines are expected to show the flow travelling downwards. 41

60 3.6.3 Three Baffles Using the results from the baffle bar tests, it was determined that adding a third baffle might further increase efficiency. This baffle was modeled and located approximately 4 cm below the inlet. The other horizontal and longitudinal baffles remained in the standard Baffle Bar II setup. Having the baffle directly under the inlet also would maintain the vapor at the largest velocity as it was forced to flow through the pipes. This system was expected to have higher heat transfer than all of the other systems tested, using the same initial and boundary conditions. Figure 16 displays the orientation of the third baffle. Figure 16. Three Baffles 3.7 Subscale Condenser Analysis The simulation results from the subscale condenser simulations provided a way to note the various flow characteristics and performance changes in each system as the baffle orientations were altered. The rate of thermal energy transfer for each system was calculated 42

61 using the same simplified First Law of Thermodynamics which was shown above in Equation 7. This allowed the various systems to be compared by judging the rate at which heat could be transferred away from the vapor to the cold water. The systems overall heat transfer coefficient was also calculated. This is discussed more in depth in the section discussing the subscale condenser experiment which describes the method of calculating the log mean temperature difference and using this to find the overall heat transfer coefficient of the system. These results were not expected to numerically reflect the real life system. The subscale condenser in the laboratory was coupled to a subscale evaporator. The only variables able to be changed for both systems were the temperature of the cold and hot water baths. These baths provided the hot and cold water to the inner pipes of each heat exchanger. Because of this, the inlet temperature of the vapor and its velocity were not directly controllable. To keep consistency, the simulations all were completed using the same initial and boundary conditions. The most important aspect of these simulations was to visualize the flow of vapor to notice if the baffles acted accordingly to direct the vapor through the graphite foam fins. The temperature, pressure drop and fluid velocity were all visualized by the solved equations in STAR-CCM. These provided an insight into how each performed. 43

62 CHAPTER 4 EXPERIMENTAL EQUIPMENT AND PROCEDURE This chapter explains the equipment used for the experimental laboratory tests and the procedures by which each experiment was conducted. The first test setup utilized was the experimental air channel to test the performance of the graphite foam fin designs. The second test setup involved an evaporator and condenser which used HFE 7000 in a closed cycle in a simulated OTEC environment. 4.1 Overview The air channel experiment involved a fiberglass constructed air channel, with an opening in the center. This opening was where the graphite foam fin design was secured for testing. The fin designs tested matched their counterparts in the simulation work. The air channel experiments were necessary to calculate the discrepancies between the simulated air channel and experimental air channel. From the results of the graphite fin simulations and experiments, the fin design best suited for heat transfer was utilized in a subscale condenser. The condenser received cold water through its inner pipes, as the evaporated HFE7000 flowed into the volume and condensed. The various baffle arrangements were tested to compare the thermal abilities of each. 4.2 Air Channel Equipment Overview The first stage in the experimental process was to select the fin designs to be tested and create engineering drawings for each. The fin designs selected were able to conduct the most heat in the simulations due to their parameters. The results of the simulations, the fin choices and the engineering drawings are discussed in the Results section. The engineering drawings 44

63 included the spacing, angle, thickness and height of the foam block, the depth of the cut, the length and the width of the foam fins. A photograph of the wind tunnel is shown in Figure 17. This picture shows the air channel and the air hoses, pressure gauges and thermocouples associated with it. On the left is the inlet tube for air, which enters into the left side of the red channel by the means of a 0.5 inch (1.27 cm) aluminum pipe. The air which was used by the system is obtained from an air hose. This air hose received its supply of air from the pumping systems outside of the building which pulled air in and filtered it to be delivered to different labs. The air is cleaned and filtered before reaching the experimental equipment. The flow rate can be altered depending on a screw valve down range from the air channel system. The inlet air temperature could not be altered, since the source of the air was in a separate area than the laboratory. However, the inlet air temperature only fluctuated between 18.0 C and 20.6 C. In Figure 17, the red section is the fiberglass air channel. An opening to the air channel is seen in the center of this fiberglass air channel. This air channel was 2 inches (5.08 cm) wide, 0.5 inch tall (1.27 cm) and was 24 inches (61 cm) long from inlet to outlet. Pressure Transducer Inlet Outlet Figure 17. Experimental air channel 45

64 Each fin design was machined and then bonded to an aluminum heater plate, of the same dimensions listed in the modeling section. The aluminum plate was 0.25 inches thick (0.64 cm) with 2x2 inch surface area. The graphite foam fins were 0.5 inches (1.27 cm) tall and had the same footprint as the aluminum plate. The bonding agent used was Aremco 568, which is aluminum based thermal adhesive. This material has high thermal conductivity and was applied in very thin layers to ensure that its effect on the thermal abilities of each fin design was minimized. [26] As seen in Figure 17, the large circular opening which exposed the air channel is where the fin design is placed. The fin design is secured to a circular gasket which seals around that circular hole and contains the heater plate. Thermal grease is applied to the aluminum plate so the contact between the plate and the electric heater is maximized. Four screws secure the fin design in place on the heater plate. The gasket surrounding the electric heater completely seals the fin design into the air channel. The gasket contains the wire to the power supply, which supplied the heater plate with electrical energy. There were also two spots for two thermocouples; one to get the heater plate temperature, one to obtain the temperature of the interface between the foam and the heater. This gasket is shown in more detail in the schematic in Figure 18. The air s inlet temperature was re or e y the thermo ouple uilt into the inlet flow pipe. The air hose delivering the air flow to the inlet flow pipe was made out of an insulated rubber hosing. The thermal loss from the aluminum inlet was very small and negligible for the necessary calculations. A thermocouple was also located at the end of the channel recording the outlet temperature also located in the aluminum outlet pipe at the end of the channel which led to the outlet air hose. Two more thermocouples were also used, one of which was bound to the top of the heater plate, and the second was pushed through the metal heater plate into the foam to get the local temperature of the interface. Before and after the foam fin design in the air channel, there were two pressure hoses which attached to a pressure transducer. These are seen in Figure 17 above as two black hoses on either side of the circular housing for the foam fins. These two hoses connected to the pressure transducer which was located out of the picture in a metal housing which displayed the overall pressure drop on a small LED screen. This instrument was pre-calibrated and recorded the pressure in (PSI) as the built in unit. 46

65 Figure 18. Schematic of air channel showing important components An illustration of the wind tunnel is shown in Figure 18, which more clearly illustrates the method by which the graphite foam fin is secured within the air channel. In order to ensure accurate measurements of these flow parameters, the flow had to have its turbulent velocity profile developed fully before this flow reached the graphite foam fin structures. To first determine if the flow was laminar or turbulent, one had to calculate the flow s Reynolds number. First, the hydraulic diameter of the system was calculated using the relation in Equation 10 using the wetted perimeter of the air channel and its flow area. h P (10) Using this hydraulic diameter, the density of air, the maximum free stream velocity of the flow and the dynamic viscosity of air, the Reynolds number was calculated using equation 11. For air at 20 C, the dynamic viscosity was 1.786x10-5 kg/m s. The density of air at one atmosphere and 20 C was kg/m 3. For this calculation, the free stream velocity used was the maximum velocity used during wind tunnel testing. During the test, the minimum free stream velocity is 2.37 m/s. The hydraulic diameter of the channel was solved to be 0.02 m. 47

66 Re f h (11) The hydraulic diameter for this system was 0.8 inches (0.02 m) which then corresponded to a Reynolds number of This indicated that the flow was in the transition region which progressed to turbulent flow. This type of flow would be expected to obtain a well-defined velocity profile inside the channel at 10 times the hydraulic diameter. Using this relation, the velocity profile would be fully developed at 8 inches (20 cm) inches into the channel. The first pressure gauge was located 9 inches (23 cm) downstream from the inlet to ensure that this flow was fully developed when the pressure reading was taken. As discussed before, the hydrodynamic entry length for turbulent flow was 10D h, which was 8 inches (20 cm). The fin designs were located 11 inches (28 cm) downstream from the inlet. The outlet thermocouple was located in the outlet pipe, 11 inches (28 cm) away from the end of the fin design, to ensure that the flow has enough length to fully develop and mix completely before the temperature data was recorded. 4.3 Air Channel Instrumentation The measurement devices for pressure, temperature are all located starting at 9 inches inside the channel. At this distance within the channel, the velocity profile of the flow was developed as discussed in the previous section. The inlet and outlet thermocouples were located within the aluminum diffusers which delivered the air flow and this flow was also fully developed thermally. This produced accurate temperature readings which reflected the bulk fluid flow temperature. Each fin design was tested in the wind tunnel so the flow of air passed over the fins parallel to the flow. The power supply was only able to subscribe a specific power to the heating plate. Keeping the plate isothermal was not a possibility, as the power supply was not computer controlled but rather controlled by a manual dial. This dial was very sensitive and the slightest movement would cause the current or voltage to rise or fall significantly causing the temperature of the heater to be unpredictably changed. An ammeter and voltmeter were used to calculate the 48

67 electric power using the Equation 12 below. In this equation, I is the current and V is the voltage measured from the power supply. Q e I V (12) The power supply and other components are listed in Table 11. Table 11. Air channel equipment Main Air Channel Custom-Fiberglass Power Supply Variac W5MT3 Autotransformer Thermocouples Omega KQXL-116U-12 Pressure Gauges Omega DPG5500B-15G Flow Meter Micro-Flow FTB 3220 Pipe Fittings and Valves Swagelock Data Reader DAQPRO-5300 Attempting to maintain the heater plate temperature as one varied the flow turned out impossible to achieve manually. Due to this, the same amount of electric power, Q e was used for each fin design. Each of the designs were able to transmit a specific amount of heat transfer for a given power level. Keeping the power level constant allowed for each fin design to be directly compared noting which design could transmit the highest amount of power. The differences in each fin design changed the way the heat was conducted through the graphite foam fins and then transmitted to the air flow. Using a constant electric power source ensured that all tests would be given the same initial amount of energy and only their individual designs would play a part in how much energy could be transferred. The temperature data of the system was recorded in a DAQPRO This piece of equipment could handle all four thermocouples at the same time. As the temperatures of each stopped fluctuating and no temperature varied more than 0.2 C over the course of 30 seconds, the system was at steady state. The error for the thermocouples was +/-0.1 C. This error was taken into analysis during the calculations of the overall convective resistance between the heater plate and the air flow, but the discrepancy in heat transfer due to this fluctuation was so small that the error was negligible. 49

68 4.4 Air Channel Equipment Procedure The air channel tests allowed each fin design to be subjected to a constant heat flux surface to test their individual abilities to transmit thermal energy. The first step involved unfastening the 8 bolts around the circular gasket which was secured into the circular opening on the top of the air channel. This circular gasket housed the heater plate and thermocouples for the foam and heater plate. Once this gasket was removed, the fin design to be tested was applied with thermal grease and then fastened to the heater plate. This secured the aluminum base of the fin design to the heater plate and the thermal grease ensured good thermal contact. Four screws were then put in place to hold the fin design firmly. The next step of testing each fin design consisted of replacing the gasket back onto the circular opening by applying vacuum grease to the outside of it which provided a perfect seal against pressure leaks. The 8 bolts were refastened and air was pumped through the system to ensure no air leaks were present. Once the gasket was in place and there were no leaks, the thermocouples were put into place. The first thermocouple was secured to the top of the heater plate with thermal tape. This provided the temperature of the heater plate at its maximum. The next thermocouple was installed into the fin design via a small hole in the center of the aluminum plate which the graphite foam was bonded to. This provided the temperature of the heater plate and graphite foam interface. Next, the air flow was began and measured to ensure that it matched the appropriate flow speed for the test. After the air flow was initiated, the power supply had to be subscribed with the appropriate power input. This was accomplished by using the manual dial on the power supply and adjusting the power until it reached the value which was used for all the tests. This power was calculated by utilizing a voltmeter and ammeter to get the current and voltage and using the Equation 12 to calculate power. With the fin design in place and the heater plate providing energy to the foam, the system was monitored as the temperatures fluctuated until all of the temperatures were stable. Stability was judged by watching each temperature for changes and noting when no temperature varied more than 0.2 C over the course of 30 seconds. Once the system was at steady-state, the temperatures were recorded and the flow speed was increased. This process was iterated for each tested velocity with all the temperatures recorded. The heat transfer for each fin design was calculated by utilizing the same simplified 50

69 First Law of Thermodynamics as was used for the simulations. After this fin design was finished testing, the heater was turned off and the air supply was choked. The fin design was removed and cleaned and the next one was installed Air Channel Experiment Limitations The air channel experiment provided an efficient way to test the abilities of each fin design, but the system had its limitations. Since this system utilized a power supply which was manually controlled, it was not possible to regulate the temperature of the heater plate with an accuracy which could match the simulated fins. Since the velocity of the air flow was controllable, this affected the temperature of the heater plate. Because of this, manual adjustments had to be made to try and match the temperature for each data point. This proved to be nearly impossible as the power supply only controlled the amount of electric energy being transmitted into the heater plate. Therefore, for this experiment with the air channel, the power to the heater plate was set constant and only the velocity of the air was varied. By using this method, the velocity increased, allowing the air to absorb more heat from the heater plate, lowering its temperature. Next, the thermocouples reading the temperatures for the system were very sensitive, but still maintained an error of +/-0.1 C. Since the trials conducted with the air channel experiments dealt with larger temperature changes, this error is negligible. Other limitations to this experiment include the heat lost from the heater plate before it was transferred to the air channel. This heat was lost due to the poor contact between the graphite foam and the adhesive, conduction into the walls of the air channel, convection into the air above the heater plate, etc. Though the inlet/outlet pipes and heater plate were insulated, there exists no perfect insulator, so heat was lost. The next section details the method used to estimate the amount of heat lost to the environment, by using a thermal resistor concept to estimate the thermal contact resistance between the heater plate and the foam fins. 51

70 4.4.2 Estimating Thermal Contact Resistance for Fin Design While comparing the air channel experiment to the simulated results, there are substantial discrepancies and this section is dedicated to examine these differences. One major discrepancy identified is the fact that contact resistance in the experimental setup was not taken into account. There is an interface of adhesive between the fin design and the heater plate which decreased the overall heat transfer. In the simulations, an idealized boundary condition was used for this interface resulting in much higher heat transfer into the channel. In order to factor in this constraint, we decided to estimate the contact resistance of the graphite fins and the contact interface between the fins and the heater plate. This estimation includes the assumption that the majority of discrepancies occurred from this idealized boundary condition. Of course, this is a much idealized assumption, but this estimation can provide a better understanding of the process so the simulated results could be better utilized to compare with the experimental data. To achieve this goal, we start our analysis by using a simplified 1-D heat transfer/thermal resistance model. A figure which illustrates this 1-D thermal resistance concept for the fins is shown in Figure 19 below. Figure 19. Simplified 1-D thermal resistance concept By simplifying the analysis to this 1-D thermal resistance network, all of the discrepancies in heat transfer are assumed to be from the thermal resistance of the fin design and the contact resistance due to the adhesive. To begin, simulations were performed using the same boundary conditions as the experimental data set for the fin design. The parameters include the inlet air stream temperature, 52

71 the inlet velocity of the air stream and the heater plate temperature measured by the thermocouple. The air stream profile is specified by designating the inlet of the simulation with a maximum velocity in a channel flow. At the wall interface, the no-slip condition and turbulence models predicted the growth of the boundary layer. The air channel experiments used a constant power source, but not a constant temperature source, so the heater plate temperature for each data point varied. In the first set of simulations, there is no contact resistance applied at the interface between the heater plate and the fins. By setting the contact resistance (R C ) to zero in the simulation, the entirety of the heat transfer occurs according to the thermal resistance of the graphite fin (R F. Therefore, the fin esign s on u tion an its surface convection are considered the only mechanisms contributing to the thermal resistance in the simulations. All of the boundaries on the heater plate were adiabatic, except for the interface between the heater plate and the air channel. Using the simulated results, the overall thermal resistance of the fin design can be estimated. The estimation of the overall thermal resistance takes into consideration the conduction into the graphite fins as well as the surface convection. To estimate the overall thermal resistance of the graphite fins, the temperature difference between the heater plate and the average air temperature is used. The average air temperature was utilized in calculation in order to simplify the convective heat transfer calculations for the fin design. In reality, the air temperature would be varying as the air particles passed through the fins and absorbed thermal energy from the fins. This increasing air temperature would also decrease the rate of heat transfer. By using the average air stream temperature, the rate of heat transfer across the fin design is assumed to be a constant value at steady state. The calculation for the average air temperature in the simulations is shown below in Equation 13. T av,sim T in T out,sim (13) To estimate the overall thermal resistance of the graphite fins, the temperature difference between T avg,sim and the temperature of the heater plate (T H ) is divided by the amount of heat transfer to the air from the fin design, Q. This relation is described in Equation 14. The overall thermal resistance for the fins in the simulation was R F. 53

72 R T - T avg,sim Q (14) In order to estimate the contact resistance encountered in the experiment, the combination of the contact resistance, R C, and the overall thermal resistance of the fin design, R F, were assumed to constitute the thermal resistance network. Using the experimental data, this overall combined thermal resistance could be estimated, allowing for the estimation of the contact resistan e at the interfa e y eliminating the graphite fin s omponent to the thermal resistan e. By taking into account the heat transfer of the experiment (Q ) and the temperature difference between the heater plate and the average air temperature, R E can be estimated. This concept is shown in equation 15. R E takes into consideration the heater plate contact resistance as well as the overall thermal resistance of the graphite fins. R T - T avg,exp Q (15) R R R (16) The average air stream temperature for the experiment (T avg,exp ) was solved the same as above, but using the outlet air temperature of the experiment instead of the simulation. T avg,exp T in T out,exp (17) By combining and rearranging equations 15 and 16, the contact resistance can be estimated. The contact resistance is solved for in Equation 18. To obtain the specific thermal contact resistance using the area of the heater plate, one must multiply R C by the surface area of the interface on the heater plate, A H, as seen in Equation 19. R R T - T avg,exp Q 54

73 R T - T avg,exp Q - R (18) R R (19) For each experimental data point, the contact resistance is estimated. This is not realistic however, as the contact resistance of the interface is a constant. To find a specific contact resistance to use in the simulations, the calculated contact resistances are plotted against Reynolds number. As the Reynolds number increases, the contact resistances will approach a steady value. These results are discussed later in the air-channel experiment results. 4.5 Subscale Condenser Equipment Overview The next phase of experimental research involved testing the graphite foam fins on a heat exchanger to verify the performance increases compared to using only aluminum. The system to be tested was a condenser which was used in conjunction with an evaporator of the same outer dimensions which provided the inlet vapor flow. The subscale condenser system matched the condenser model used in STAR-CCM+ with the same engineering dimensions. The subscale system consisted of many components which worked together. The whole system was comprised of an evaporator and a condenser system in order to simulate a smallscale version of the entire OTEC plant. This research only dealt with the condenser portion of this subscale system. The condenser system consisted of three rectangular pipes which were 24 inches long and connected the top and bottom headers. The interior dimensions of this subscale condenser system were proprietary, so the actual dimensions of the pipes cannot be disclosed. [32] However, for all calculations in this analysis, the known surface area for heat transfer is known. photograph of the Baffle Bar Type I system is shown below in Figure 20. The entire system is sealed for pressure, to ensure that no air can enter the system and no evaporated HFE can exit the system. Before each test was conducted, the system was purged of air, by boiling HFE and releasing the valve at the top near the inlet pipe. HFE is much heavier 55

74 than air, so by boiling the HFE, the vapor stays near the level of the liquid, while the air is purged out of the system. Before the system had HFE fluid introduced, the system was ensured to be water-free, so the only liquid within the condenser was HFE Figure 20. Subscale condenser (Baffle Bar Type I) The HFE 7000 flowed from the evaporator to the condenser via an insulated rubber hose which was locked into place using hose clamps. The outlet of the evaporator was near the top and the HFE flowed into the condenser via the inlet pipe 1 inch (2.5cm) under the header. The condensed HFE flowed out through the outlet of the condenser 1 inch (2.5 cm) above the bottom header via another insulated hose. The condensed HFE then flowed from the outlet pipe at the bottom into a reservoir which had markings to show levels of fluid. The reservoir drained into an insulated hose which ran to the pump. The pump was powered by a power supply which was set at 110 volts. The pump pushed the condensed HFE through the flow meter and then traveled back into the bottom of the 56

75 evaporator to be vaporized again. The manufacturers and component identifications are listed in Table 12. Table 12. Subscale system component list Subscale System Equipment Used Hot Water Bath Lauda RE120-A08043 Cold Water Bath Lauda M Power Supply Variac W5MT3 Autotransformer Thermocouples Omega KQXL-116U-12 Data Acquisition DAQ-PRO 5300 Pump March Pressure Gauges Omega DPG5500B-15G Flow Meter Micro-Flow FTB 3220 Pipe Fittings Swagelock 4.6 Subscale System Instrumentation The level on the reservoir was regulated by a valve directly before the flow meter which allowed the flow to be changed in order to maintain a constant level in the reservoir. The system was to get to steady state before any temperature readings were taken and when the reservoir was at a constant level. As long as the level in the reservoir was constant, the flow rate was then in equilibrium. Since the level remained the same, the amount of fluid entering the reservoir was equal to the amount draining from the condenser after changing phase to a liquid. This flow rate was used to calculate power based on the various temperatures of the system taken at the inlet and outlet of both the HFE and water side of the system. The hot and cold water was supplied by separate heating and chiller units which cycled the hot and cold water in separate loops. The temperature of each water bath was manually controlled with dials and pumped from within the heater and chiller. The temperature was displayed on an LCD screen. The evaporator was set at 50 C, which provided water to the evaporator at a temperature ranging from C. This range was caused by the hot water bath 57

76 being unable to heat the water up effectively. The temperature of the hot water bath was methodically increased. The condenser cooled down the vapor at different rates, depending on the baffle orientation, and as the condensed vapor reduced its temperature, this put strain on the evaporator forcing it to conduct more heat to the liquid to evaporate it again. Since the power level on the hot water bath was set at a constant, the temperature of the sub-cooled HFE reflected on the maximum temperature the HFE could reach from absorbing energy from the hot water. The pressure of the condenser/evaporator system was monitored by two pressure gauges located in the liquid and vapor region of the evaporator. Since both systems were connected with an insulated hose, the vapor pressure in the evaporator was taken as the vapor pressure in the condenser as well. 4.7 Subscale System Test Procedure To begin the subscale condenser experiments, the appropriate system had to be installed. The main condenser consisted of the aluminum pipes with fins bonded to them running from the top to the bottom, each different system just had different orientations of baffles to be tested. This was accomplished by unfastening all of the bolts holding up the condenser on the aluminum frame which housed both the evaporator and condenser. Once the system was taken down, the appropriate core was installed and secured in place. The headers were bolted back on after having vacuum grease applied. The pressure was then tested through the system to ensure that no leaks were present. Next, the HFE working fluid was put into the system by a graduated cylinder placed above the evaporator with a hose which was installed to the outlet pipe of the evaporator. By pulling a vacuum on the system, this pulled the HFE into its volume. By powering them on and applying temperatures to each, it allowed the built in units to control the temperature until the entire bath reached the temperature which was prescribed. Usually this took anywhere from minutes. Once the fluid was at uniform temperature, valves were opened to allow the hot and cold water to flow within the hot and cold water pipes respectively. Since the HFE had a low specific heat, boiling was evident within a few minutes of the hot water flowing through the evaporator pipes. To eliminate any air in the system as the HFE was boiling for the first time before each test, a vacuum was pulled in order to remove the lighter 58

77 air from the dense HFE vapor. As the HFE started to evaporate, vapor would flow into the condenser and begin to drip off of the foam fins and collect in the bottom of the system. The thermocouples at each location were monitored to ensure that they became stable. Once all of the temperatures stopped fluctuating, the data was recorded. Upon each data point being recorded at steady state, the hot water bath was slightly increased in temperature. This provided a larger flow rate of vapor to the condenser as well as rising its temperature. At the end of the data point acquisition, the hot and cold water baths were powered off and the HFE was left to cool until all of it had condensed back into liquid Subscale Condenser Limitations The subscale condenser allowed the differences in performance caused by the baffle orientations to be analyzed. However, this system had limitations which made it difficult to verify using simulations. The main limitation was the fact that the condenser was coupled to the evaporator in a closed loop. Due to this, the inlet vapor temperature and flow rate depended also on how efficient the evaporator was at providing energy to the HFE to vaporize it. Each baffle orientation changed the performance of the condenser. For some of the tests, the condenser was effective at condensing HFE. This caused the vapor to be cooled lower than its condensation point, which then required the evaporator to provide more thermal energy to evaporate it again. The only two variables able to be altered in these systems were the temperatures of the hot water and cold water bath which provided the energy sources to evaporate and condense the working fluid. Both of these were kept relatively constant in order to provide a good comparison for each system to perform at the same conditions. For the tests, data was acquired as the temperature of the hot water bath was increased. This gave the condenser a range of vapor inlet temperatures for which data was acquired. The error on each thermocouple was +/-0.1 C, which is negligible for the calculations and comparisons performed herein. There was also an inherent error for determining the flow rate of the condensed fluid exiting the condenser. The HFE was permitted to flow into a reservoir where it was then pumped back to the evaporator. To determine the flow rate, the flow valve was altered until the level in the reservoir stayed constant. This signified that the 59

78 condensed HFE leaving the reservoir was the same flow rate as the HFE entering the reservoir. Though this method is relatively accurate, there is an inherent error in this method due to human intuition to when the level is stable. There was no sure way to determine if the flow rates were precisely equal, though for these analyses and the flow rates encountered, this error is negligible Subscale Condenser Analysis The overall heat transfer coefficient of the subscale system was calculated by the equations shown below. The log-mean temperature difference was first calculated. This utilized the equation to calculate the log mean temperature difference of a counter-flow heat exchanger. [27] This method to find the log mean temperature difference is shown in Equation 20. The heat transfer coefficient gauged the performance of each system by comparing the heat flux of the system by how much of a driving temperature gradient was present. The overall heat transfer coefficient for the system was calculated by dividing the overall heat transfer of the system by the log mean temperature difference and the surface area exposed for heat transfer. This result is shown in Equation 21. In equation 21, A HT corresponds to the overall surface area within the condenser exposed for heat transfer; LMTD is the log-mean temperature difference and is the heat transfer rate. A higher overall heat transfer coefficient signifies that a system can transfer more heat per surface area, using a given temperature gradient as the driving force behind the heat transfer. T in T on in T O on Out T out T on Out T O on In LMT ( T in - T out ) ln T in T out (20) U LMT Q T (21) 60

79 The heat transfer for this system also utilized the simplified First Law of Thermodynamics shown below in Equation 22. In Equation 22, L h is the latent heat of vaporization and c pf is the specific heat of the fluid. Solving this equation gives the absolute heat rate from the vapor to the cold water. -Q m pf (T out -T in ) L h m (22) 61

80 CHAPTER 5 RESULTS AND DISCUSSION 5.1 Graphite Foam Fin Simulations The modeling results for the different fin designs helped to visualize how each attribute would affect performance. The data collected from these simulations consisted of temperature outlet, heat flux, pressure drop and also plane sections of the fin models showing plots of temperature, pressure and velocity. Table 13 is an example set of data values from one model, at each specific velocity. Each simulation had to be solved using five different velocities. For each velocity, the simulation had to fully iterate and this process took between four and eight hours for each model to converge to a realistic solution. The computational time needed for each simulation was one of the limiting variables with using simulations. Table 13 shows the results from one of the graphite foam fin simulations. Notice how the velocity increases from 1-5 m/s, but the Temp Out has almost no change. This is because in these simulations, there was no Thermal onta t Resistan e applie to the oun ary etween the heater plate and the foam fins in the simulation. Table 13. Fin Angle 5, inch Fin Thickness, inch Fin Spacing Vel Inlet (m/s) Temp Out (Deg C) Flux (W/m^2) Flow Rate (kg/s) Heat Transfer (W) Pressure Drop (Pa)

81 In real life tests, the contact between the heat source and graphite foam is not perfect and the heater source will leak heat to the environment. To take all of these losses into account, an overall convective thermal resistance was calculated for each design. Without a thermal contact resistance, each fin design approached the heater plate temperature very closely. This would be the ideal case if all the heat from the heater plate was able to be transmitted to the flow. However, each simulated fin design did yield different outlet temperatures. This allowed them to be relatively compared to each other Control Model Results This section will describe the results from the control model simulations. The three fin designs simulated for this test were Aluminum Straight Fins, Graphite Foam Straight Fins and Graphite Foam Cross-Cut fins. Though in both fin types, porous media was used, the cross cut fins enabled more heat transfer by introducing more vorticity to the flow. The cross-cut design forced air flow to follow a convoluted path throughout the fin structure, leading to a higher pressure drop and also more flow within the foam. The larger flow within the foam increased the inner convective heat transfer coefficient allowing the same fin dimensions to transmit more energy by simply using cross cut geometry instead of straight fins. A plot of these results is shown below in Figure 21. As seen by this plot, the cross-cut graphite foam fins were able to transmit the most heat energy to the air flow. Both sets of graphite foam fins were extremely superior to using bulk aluminum. The aluminum straight fins only allowe for onve tive heat transfer on the fin s exterior surfa e area. Since the straight fins allowed for turbulent boundary layers to grow on the surface without interruption, the heat transfer decreased along the length of the fin design due to the temperature difference decreasing as the air temperature increased. With cross cut fins, the boundary layers developing on the fins were interrupted periodically by the intersections between cross cuts. Allowing the flow to permeate the fin material allowed for much more surface area for convective heat transfer. 63

82 Figure 21. Control Model Heat Transfer Comparison The results from these control models confirmed that the graphite foam straight fins could conduct more than 3.5 times the heat than using the bulk aluminum as the fin material. The graphite foam cross-cut fins were four times more effective than the aluminum straight fins. The graphite straight fins transmitted 5% less energy than the graphite foam straight fins. Each of these simulations was iterated using no thermal contact resistance subscribed to the interface between the heater plate and the fins. Without a resistance at the interface, the outlet temperature of the air did not change much as mass flow rate increased. In the range of Reynolds tested for each fin design, the outlet temperatures only varied slightly, though each simulation had distinctly different outlet temperatures. Since each fin design had an outlet temperature which did not vary much as mass flow rate increased, this resulted in a plot which looked nearly linear. In fact, each fin design in the plot has a concave downward profile because of the decreasing outlet temperature as the mass flow rate increases. Figure 22, shown below, displays the results of the velocity plot for the Graphite Foam straight fins and the ability for them to allow flow within the material. Between each of the graphite fins, the fluid velocity increased because of the lower available cross sectional area for free flow. This is explained by Equation 23, which calculates the mass flow rate. By keeping the mass flow rate the same and decreasing the flow area, the local velocity increases 64

83 proportionally. This increased the local Reynolds number between the fins, depending on the spacing. m f V flow (23) As the Reynolds number increased between the fins, this created more shear stress on the fluid, in turn increasing the pressure drop. This larger pressure drop forced more air within the material, increasing its heat transfer. This is explained by the Darcy-Forchheimer relation. As one increased the distance into the foam fins, the fluid velocity decreased. As shown in Figure 22, one will note that the velocity within the fins is low but not 0. The graphite foam had a very high thermal conductivity which ensured that fluid flowing within its pores reached thermal equilibrium quickly. As the temperature of the fluid approached the graphite temperature, there was less heat transfer. Since the temperature difference in this region is near 0, there was no driving force for heat transfer to occur. Figure 22. Velocity plot for graphite foam straight fins The temperature of the graphite foam fins varied with the length into the channel, since the air flow first entering the foam fins at the beginning of the fin structure absorbed the most heat energy from the fins. This was because this entry region maintained the largest temperature difference between the fluid and the foam. As the fluid began to heat up, heat was transferred to 65

84 the air at a lower rate, until the air temperature matched the foam temperature and heat transfer is absent. The temperature of the graphite foam fins is shown below in Figure 23. Figure 23. Temperature plot for graphite foam straight fins Figure 24. Velocity plot for aluminum straight fins The aluminum fins performed much differently. As seen in Figure 24 above, showing the velocity plot of the aluminum fins, there was no velocity within the aluminum. This was because fluid cannot flow into the material. As the air passed between the fins, the local velocity increased sharply, since the mass flow rate of air had to flow through a smaller cross sectional area. 66

85 The heat transfer to the air from the aluminum fins depended on the local Reynolds number over the fin surfaces, dependent on the spacing between the aluminum fins. The convective heat transfer in this region was dictated by the Reynolds number, temperature difference between the air and aluminum and the surface area exposed to fluid flow as seen below in Figure 25. Figure 25. Temperature plot for aluminum straight fins Noted in the temperature plot of the aluminum fins is a small area on the right of the plots showing fluctuations in temperature and pressure. These were due to the fact that the aluminum fin on the right side of the simulation was actually against the wall. This provided a barrier for the flow, which created a high pressure region in front of this fin which created eddies and increased the local temperature. This fluctuation was very small and does not affect the overall characteristics of the flow, but it was important to explain this phenomenon. Also noted on the velocity plots of both types of fins is the turbulent boundary layer on the wall and the no-slip condition Effects of Fin Spacing on Performance The cross-cut fin design simulations had three main fin spacings which were tested. These spacings were discussed earlier; inches, 0.25 inches and inches. Of the three 67

86 parameters tested, the fin spacing altered the characteristics of the flow the most. This is because of the dependence of heat transfer on the local Reynolds number between the fins as the fluid travels through the structure. Using a decreased fin spacing related to these fins being closer together. With a smaller free-flow area for the fluid to travel, the mass flow rate of the air entering the fins must be the same as the flow rate of the air leaving the fins. Due to this, since there was less cross-sectional area for the fluid to flow at a specific flow rate, this increased the local velocities and Reynolds numbers between these fins. On the contrary, as the spacing got larger, the local fluid velocity between these fins decreased. This reduced the overall heat transfer from the region as the shear stress on the air decreased, decreasing the pressure drop. This decreased pressure drop also decreased the flow velocity within the porous media which caused the air temperature in the foam to rapidly increase to the foam temperature while the air was still slowly flowing through. Plots were generated to visualize the differences in performance for each spacing test. The differences in pressure drop and heat transfer are shown in Figure 26. In order to quantify the differences between fin parameters, the fin designs plotted only had one of their parameters changed. In this case, it was the spacing of the fins. The other two parameters remained constant at 0.25 inch Thickness, and 5 Fin angle. The spacing varied from 0.125, 0.25 and inches. Figure 26. Pressure drop and heat transfer comparisons for each fin spacing 68

87 Figure 26 demonstrated how much the spacing was reflected in the performance of each fin design. As seen above, the fins with the smallest spacing (0.125 inch) had an increase of 78% in heat transfer compared to the largest spacing (0.375 inch). The pressure drop of the smallest spacing fin design (0.125 inch) was five times higher than the largest spacing. As the spacing was decreased, the shear stress on the flow was increased. This increase in shear stress was the cause of the reduction in pressure of the air. However, this pressure drop also corresponded to a higher velocity of flow within the foam as it was forced through. This also explained the much higher heat transfer abilities of the fins. Figure 27. Local velocity vectors of two different spacings. As shown in Figure 27 above, velocity plots are shown which directly compare the effects of fin spacing. As seen on the left of Figure 27, this shows velocity vectors which describe the air flow between the fins which have a spacing of inches. On the right of Figure 27, this shows the effect of doubling the fin spacing, resulting in 0.25 inch spacing. As clearly seen, the local air velocity between these sets of fins drastically decreases as the spacing is increased. This also corresponded to a lower velocity permeating the porous material as spacing is increased. Since convective heat transfer is directly related to local Reynolds number, larger spacings are detrimental to heat transfer. The fin spacings of 0.125, 0.25 and inches had outlet air temperatures of 44.7 C, 41.2 C and 36.2 C respectively. The smallest spacing tested maintained the highest heat transfer. 69

88 5.1.3 Effects of Fin Offset Angle on Performance The next set of tests sought to compare the differences in performance between the three different fin angles to be used. For these three models, the other two parameters stayed constant as only the fin angle was varied. These fins maintained a thickness of 0.25 inches with a spacing of 0.25 inches also. The fin angles were varied from 5, 10 and 15. Plots of the pressure drop and heat transfer for each of these designs is shown in Figure 28. Figure 28. Pressure drop and heat transfer for each fin angle As evident by the plots above, changing the fin angle altered the flow in a different way than changing the spacings. As seen in the plot of pressure drop, the fins with 5 fin angles had a pressure drop which was only 62% of the pressure drop of the fins with 15 fin angles. The increased fin angle caused the incoming air flow to suddenly change directions upon encountering the fins of a steeper angle. This separated the turbulent boundary layer from the fins and also increased turbulence and vorticity in between the fins, which dissipated the kinetic energy of the flow. This increase in pressure drop due to increasing the fin angle did not significantly affect the heat transfer of the fins. The local velocities between the fins did not change drastically as the fin angle changed because the angle change did not affect the spacing between the fins. 70

89 The heat transfer of the fin designs is dependent on the flow velocity between the fins. This is in order to increase their heat transfer coefficient and drive more flow within the foam. In this case, the flow within the foam stayed relatively the same. Though, as seen in Figure 28 above, the design using 5 transferred 11% less energy to the air flow compared to the 15 fin angle design. Figure 29. Temperature plots for each fin angle test As displayed above in Figure 29, one can see how the temperature is varied as the fin angle is increased. The spacing and thickness remained the same and only the fin angle was varied. Due to this, the thermal entry lengths between the fins remained similar. However, as the flow traveled through the fins, the flow path encountered more intersections between crosscuts because of the increased fin angle. This increased turbulence of the flow slightly enhanced the convective abilities of the fins by causing the air molecules to circulate more, which more effectively wicked heat away from the foam and transferred this energy to the air flow. Increasing the angle of the fins also increased the vorticity of the fluid as it passed over intersections of cross cuts. This increased vorticity and constant mixing of the fluid from the created turbulence increased the convective heat transfer coefficient of the outer surface area of the fins slightly. This is the reason why angles increased heat transfer. However, due to the large amount of kinetic energy dissipated from the high vorticity, the flow also lost much more pressure. Since the pressure drop was caused by vorticity dissipating momentum throughout the 71

90 fluid, not much more fluid flowed within the porous media. A comparison showing the contour plot of vorticity from the 5 and 15 angled fins is shown below in Figure 30. As seen on the left of Figure 30, the 5 fin offset angle maintains some regions of low vorticity (1 s -1 ). As the angle is increased to 15, the plot of vorticity shows that the flow between the fins maintains a much higher vorticity on average ( s -1 ). Figure 30. Vorticity plots for 5 and 15 degree fin angle Effects of Fin Thickness on Performance In these tests, the only parameter changed was the fin thickness and each other parameter remained constant. The fin thicknesses were inches, inches and 0.25 inches. The three fin designs all had spacings of 0.25 inches and a fin angle of 5. Plots of pressure drop and heat transfer for each different fin thickness are shown below in Figure 31. As seen in Figure 31, the pressure drop is altered significantly as the fin thickness increases. The fins with the smallest thickness, inches, only had a pressure drop 57% that of the largest thickness 0.25 inches. However, the lowest thickness of maintained 90% the heat transfer of the 0.25 inch thickness. This illustrated that the increasing the thickness of the fins increased the volume of foam in the system which simply provided a larger flow resistance. 72

91 Figure 31. Pressure drop and heat transfer for each fin thickness The larger volume of foam used for the thicker designs did slightly increase heat transfer, but the low velocity within these fins caused the air and foam to reach thermal equilibrium. Using fins with the smaller thickness (0.125 inch) allowed for the flow within the foam to have a higher velocity allowing nearly the same heat transfer as the thicker fins, with only a fraction of the pressure drop. As the fins had increased thicknesses, this provided a larger volume of graphite foam for the flow to travel through. Thicker fins also decreased the overall open flow area for the air. This decreased open flow area increased the local velocity of the flow between the fins, which in turn increased the flow within the foam. However, using thicker fins makes it more difficult for the air flow to penetrate deep into the foam while still maintaining a large velocity. Due to this, the velocity within these thicker fins is decreased as the depth into the material increases. The pressure drop increases as thickness increases, but as thickness of the fins increases, the overall velocity of the flow within the foam is much lower. This low velocity causes the air temperature to reach the foam temperature in a shorter amount of time. This is evident in the plots, as the pressure drop increased steadily as the thickness increased, but heat transfer only increased slightly. Figure 32 below shows a velocity comparison between the inch thickness fin design and the 0.25 thickness fin design. As this clearly shows, the thicker fins reduced the amount of free flow area and there was a higher air velocity between the fins. However, the fins with the smaller thickness had a higher percentage of flow within the porous media. Once the 73

92 flow penetrated the foam it quickly lost its momentum. If the fins were too thick, the fluid velocity would be slightly above zero. If the fluid was stagnant within the foam, this made that volume of porous media useless for heat transfer as the fluid reached the foam temperature quickly. This is the most important factor when considering the ways fin thickness affected the flow. Figure 32. Velocity comparison between 0.25 and Thickness Figure 33, shown below, displays the temperature plots of each fin thickness. The temperature plots showed how there was not a very noticeable change in the outlet temperature of the air. The 0.125, and 0.25 inch thick fins had outlet temperatures of 40.6 C, 41.0 C and 41.2 C respectively. The change in thickness increased the local shear stress and pressure drop across each fin design due to the reduction of the open free flow area, but the increased volume of foam decreased the flow velocity within the material which decreased the heat transfer. This trade off resulted in the fins with the larger thickness only increasing pressure drop while not significantly improving heat transfer. Extra temperature plots of each fin design (at 10 fin angle) are shown in Appendix A. 74

93 Figure 33. Temperature plots for each fin thickness Open Flow Ratio Comparisons The previous results demonstrated that each parameter would alter the performance of each fin for different reasons. The most important factor is maximizing the flow velocity within the porous material. From the analysis of the changing of the fin angle, it was shown that increasing the fin angle from 5 to 15 would provide more intersection points between crosscuts. These intersection points offered an increased number of obstacles for the flow to pass through, increasing its pressure drop by introducing more vorticity into the flow. The increase in vorticity and slightly increased local heat transfer coefficient slightly increased the heat transfer of the fin designs with the large fin offset angle. To further understand the results from the 27 models simulated with each variation of the parameters, the models were also analyzed by their Open Flow Ratios. The Open Flow Ratio described each fin design by its inlet cross-sectional area and the percentage of this area which allowed for free air flow. Since the cross-cut design is very geometrically complex, the free air flow ratio will change throughout the length of the fin design in the channel. To compare all of the different combinations of thicknesses and spacings, a 2D Plane was projected through the 75

94 ross se tional area of the fin whi h woul e near the inlet. The plane s area was kept constant for every fin design to calculate the open flow ratio. The red areas signify free air flow areas, while the bright yellow indicates graphite foam fin material. To calculate the open flow ratio, one just calculated the area of graphite foam on the plane projection and subtracted it from the total. By taking this number and dividing it by the original area of the plane, one will get an open flow ratio corresponding to each fin design. Figure 34. Calculation of open flow area With all of the various thicknesses and spacings tested, there were no identical open flow ratios. The 10 fin angle simulations were used for this comparison, since 10 was the parameter chosen for the fin angle. Seen above in Figure 34 is an example to compare the open flow ratios of two different designs This calculation was completed for all models and a table was created to show how each combination of spacings and thicknesses corresponded to each fin designs own Open Flow Ratio. Table 14 lists these ratios and their respective designs. 76

95 Table 14. Open Flow Ratio classification Thickness (in) Spacing (in) Open Flow Ratio The lowest open flow ratio occurred using a fin design the thickest fins and the smallest spacing. To compare the pressure drops of all 27 models, a surface plot was created which plots the Open Flow Ratio against Reynolds number and Pressure Drop. Figure 35 gives a good representation of the overall pressure drop for all of the fin designs. As the available area for free flow decreases, the pressure drop increases steadily. This surface showed that the largest pressure drops occur with the smallest open flow ratios. The smallest open flow ratios provided the largest local Reynolds number between the foam fins, as well as the largest shear stress as discussed before. However, a larger pressure drop did not signify a larger increase in heat transfer necessarily. Using foam fins with increased thickness caused the heat transfer within these fins to decrease due to the overall lower velocity of flow within the material. This decrease in velocity caused the fluid to reach equilibrium with the foam temperature. This lead to a lower heat transfer overall. 77

96 Figure 35. 3D surface of pressure drop for each fin design This phenomenon is visualized better in Figure 36, which plotted the Open Flow Ratio against the heat transfer for every fin design. For this plot, the maximum heat transfer is marked as fin esign. This orrespon s to the esign with. in h spa ing an. in h thi kness. B orrespon s to. in h thi kness an. in h spa ing. orrespon s to 0.25 inch thickness and 0.25 inch spacing. Figure 36. Comparison of heat transfer to open flow ratio 78

97 As seen in Figure 36 below, a lower open flow ratio did not directly lead to higher heat transfer. In fact, the largest heat transfer occurred with the model with the smallest possible spacing ( inch). As the open flow ratio decreased further than esign %, the heat transfer actually decreased due to the thicker fins. The thicker fins could not maintain a high enough velo ity of flow throughout the foam to maximize the heat transfer in these regions. B an ha slightly less heat transfer than, ut also ha a lower pressure rop. The results from these plots show that using open flow ratios less than esign would require more foam material and also would increase pressure drop and decrease the heat transfer. Additional temperature and velocity plots for each spacing and thickness are shown in the appendix. (A.1 A.9) The pressure drop surface generated from the data of all the fin designs is also shown in the appendix since the data created a very coarse surface. These results were interpolated to make the surface more visually appealing, without altering any data points. This comparison is shown in A Air Channel Experiments The air channel experiments tested the performance of the three fin designs which were simulated as having the highest amount of heat transfer. The three fin designs previously listed as, B an were the hosen esigns. The reason these were hosen is e ause they ha the highest heat transfer an the lowest pressure rop. Though ha the highest heat transfer, the two other designs which were close to its performance had a much higher pressure drop. These two fins had a higher pressure drop due to their increased thickness. As discussed earlier, thicker fins reduce the overall flow area which increases pressure drop, but the flow penetrating the foam lost its momentum quickly. This loss in momentum slowed down the fluid until it reached the temperature of the foam and no heat transfer could occur. These fin designs which were chosen for experimental testing and their engineering specifications are shown below in Figure

98 Figure 37. Engineering dimensions of each air channel fin design These three fin designs were tested in parallel flow within the air channel to test their abilities at transferring heat. The heat source in the air channel was a heater plate which was subscribed with a constant power for each fin design. The performance of each design was gauged by the amount of thermal power transferred compared to the amount of electrical power input to the system. (Equation 11) The plot below in Figure 38 shows the heat transfer of each fin design in the air channel. The fin esign, with. inch spacing, was able to transmit the most power out of the three designs. This was followed by the inch spacing model which could transmit approximately % of heat that esign oul. The fin esign with. in h spa ing was only able to transmit about 65% of the heat. These results fall in line with what was expected from the simulations. 80

99 Figure 38. Heat transfer of each fin type tested in air channel As seen in this plot, as the Reynolds number increased, the efficiency of each fin design started to level off around Re= At this Reynolds number, the flow is fully turbulent and completely out of the transition regime. Between Reynolds numbers of 10, the efficiency of each fin design leveled out showing that this was the maximum efficiency the fin design would reach in the flow regime which was tested. This is due to the fact that in this flow regime, the fluid is fully turbulent and the transport of heat from the foam is only limited by the thermal diffusivity of the porous material. Since the thinner fins allowed fluid to flow more easily throughout the material, at high Reynolds numbers, these fins can more easily transmit heat from the heater plate to the flow. Figure 37 confirms that the inch spacing fin design will transmit the most thermal energy, which was also the conclusion derived from the simulations. Shown in Figure 39 is a plot of the pressure drops of these three fin designs. The pressure gauge used to obtain the pressure drop data was only accurate to +/- 6.9 Pa (0.001 psi) which equates to +/- 2% in the plot shown in Figure

100 Figure 39. Pressure drop vs. Reynolds number The pressure drop results from the air channel confirm that the inch spacing simulation will have the highest pressure drop, followed by the inch spacing and 0.25 inch spacing. Since the boundary conditions between the simulated and experimental air channel could not be matched exactly, due to equipment limitations, the comparison of the performance from each test is qualitative and not quantitative. Being so, the air channel pressure drop measurements met the expectations put forth by the results of the simulated air channel. The inch spacing design only had 62% the pressure drop of the inch spacing model, with the 0.25 inch spacing having only 48% of the pressure drop. From the air channel experiments, it was confirmed that the inch spacing, inch thickness fin design was able to transmit the largest amount of heat for given boundary conditions. This design also maintained the largest heat transfer for the given conditions in the simulated air channel. The smaller spacing correlates to a higher local Reynolds number between the graphite fins which increases their Nusselt number and the convective heat transfer from the surface. This fin design was chosen for machining and use in the subscale condenser system. 82

101 5.2.1 Discussion of Thermal Losses in Air Channel Experiments This section discusses the results from the air channel simulations using the estimated contact resistance. These estimations are discussed in detail in the air channel analysis section. In the air channel experiment, heat was lost to the surroundings and because of the interface between the heater plate and the fin design. These mechanisms acted together to decrease the overall heat transfer ability of the fins and were estimated to provide a way to help simulated results more accurate. In the simulations using no resistance, the only thermal resistance to heat transfer was the fin design itself. However, in the experiments, the various mechanisms for the decrease in heat transfer were simplified by assuming that there was only a thermal resistance of the fin design and a thermal contact resistance. Below, in Figure 40, a comparison shows the difference between a fin design simulated with no thermal contact resistance between the heater plate and the channel and also a fin design using the calculated thermal contact resistance applied at the interface between the channel and the heater plate. As this figure shows, applying a resistance at the interface between the heater plate and the fins reduces the rate of heat transfer from the heater plate to the base of the graphite fins. Figure 40. Comparison of two fin designs to show differences using thermal resistance 83

102 A table is shown below which includes the set of tests from the experiments and the respective inlet and outlet temperatures with the corresponding Reynolds numbers. The air outlet temperatures for the simulations are much higher than the experimental data points because there is no thermal contact resistance applied. Table 15. Data set for experiment Reynolds Air Inlet ( C) Heater ( C) Air Outlet Exp ( C) Air Outlet Sim ( C) Shown below are the tabulated results of the resistance calculations for each set of tests in the experiment using the spacing fins. R F corresponds to the overall thermal resistance estimated for the graphite foam fins using the simulation data with no contact resistance. R E corresponds to the thermal resistance of the fins using the set of experimental tests. R C is the calculated contact resistance of each experimental data point, solved by subtracting the simulated fin resistance from the experimental resistance. Multiplying the R C by the surface area of the heater plate gives the specific thermal resistance, R A, which can then be applied to the interface between the heater plate and the graphite foam in the simulations. As Table 16 shows, the estimated contact resistance R A decreases as the Reynolds number increased. This table shows the thermal resistance for the fins, the overall thermal resistance for the experiment, the estimated contact thermal resistance and the specific thermal contact resistance. As Reynolds increases, R A approaches a stable value. A plot of contact resistance against Reynolds number is shown in Figure

103 Table 16. Calculated thermal resistances for air channel tests R A Reynolds R F R E R C W W W m W E E E E E E E E E E E-04 Figure 41. Contact resistance vs. Reynolds number The above plot helps to shows how the estimated contact resistance seems to approach a stable value as Reynolds gets large. This is because as Reynolds increases the convective resistance of the graphite fins approaches 0, as the limiting factor is the heat conduction into the graphite from the heater plate. The contact resistance was estimated to be m 2 C/W. This value is actually in a realistic range, since most thermal resistances between different 85

104 materials is approximately m 2 C/W. This thermal contact resistance was then used as a boundary condition on the interface between the heater plate and the graphite fins in the simulation. The same sets of tests were performed, using the same boundary conditions. The results showed a much more accurate depiction of the experimental results. A plot of the outlet temperature against Reynolds is shown below in Figure 42. The experimental results and simulated results are comparable but the simplified analysis still yields a slight error. It is not possible to perfectly simulate an experimental case, because of many unpredictable variables. Figure 42. Outlet air temperature comparison using calculated resistance The discrepancy between the simulated results and the experimental results is most likely because of extra heat transfer from the heater plate to the air, in the regions where the heater plate was exposed to the air stream. In this estimation, the entire interface of the heater plate and fins had the same contact resistance. Realistically, this contact resistance would vary depending on location. The plot below, shown in Figure 43, compares the overall heat transfer of the fin design versus Reynolds number. This plot clearly shows that the calculated values used for the thermal contact resistance also correlated nicely with the experimental tests. By simplifying the 86

105 constraints of the air channel tests and estimating thermal and contact resistances, the simulations had their accuracy increased drastically. This allows the simulated results to be better utilized when comparing to the experimental data. Figure 43. Heat transfer comparison with calculated resistance By analyzing this air channel using a simplified thermal resistance concept, the resulting contact resistance applied to the simulations gave a much more accurate result overall. Using this contact resistance can allow for the same fin design to be tested at many other boundary conditions which may not be achievable in the laboratory setting. Since the other mechanisms for the discrepancy in heat transfer were assumed to originate from just the contact resistance, this value is most likely not the true value for the experimental system. However, this analysis does give a good estimate. The estimated contact resistance is also comparable to real life calculated resistances between different materials. Previous research into the contact resistance between materials shows that a value of K m 2 /W is a common thermal resistance value between ceramics. Between stainless steel surfaces, which have macroscopic bumps and ridges, the thermal contact value is averaged between K m 2 /W. Stainless steel surfaces which have been machined smooth can reach values lower than this at a range of K m 2 /W. [27] Since the estimated 87

106 contact resistance was K m 2 /W, it fits in to the normal range for contact resistances amongst other materials. Throughout this section, the analysis of the estimated contact resistance for the air channel was shown to improve the accuracy of the simulated results so they could be compared to the experimental results. 5.3 Subscale Condenser Simulations All of the subscale condenser simulations used the same boundary and initial conditions. The models were each run to between 1200 and 1800 seconds of virtual time. This iteration time depended on how well the residuals converged over time. The converging residuals ensured that variations in momentum, energy and continuity were negligible which signified steady state. Each simulated second included 20 inner iterations in order to make sure that each time step was accurate as each solution within each time step was averaged together. The addition of baffles to the flow improved the overall performance of each system, allowing each improvement to facilitate more heat transfer and condense more fluid. The main goal of these simulations was to investigate the flow patterns and characteristics as the baffle orientations were altered No-Baffles The first subscale condenser tested did not include baffles at all. This lack of baffles allowed the incoming vapor flow to bypass the inner core of cold water pipes. By bypassing the inner core, little heat was transferred from the vapor to the cold water. This maintained the outlet temperature of the condensed fluid at 21.2 C. This signified that the condenser without any baffles was able to condense fluid, but the outlet temperature was still higher than what was expected. As the vapor circulated through the system, much of the kinetic energy of the vapor particles was lost as they formed eddies and vortices within the volume. These mechanisms reduced the overall velocity of the vapor, which drastically reduced its convective heat transfer coefficient at the heat transfer surfaces. The temperature plot for the No Baffle system is shown in Figure

107 Figure 44. Temperature plot for No Baffle Condenser This temperature contour plot is representative of a Y-Z plane section taken from the condenser which displayed the local temperature values on the plane located directly in the middle of the condenser. This gave a better understanding of how the inner pipes were not reducing the temperature of the vapor significantly. This was because the vapor formed eddy currents and vortices which rotated from the top of the system down to the bottom, bypassing the inner pipes and foam. Due to these eddies, the vapor s momentum was issipate qui kly an the local Reynolds number of the flow passing through the graphite fins and cold water pipes was very low. As the particles had reduced velocities, the heat transfer rate was decreased drastically. Regions of the condenser remained much warmer than other regions due to recirculation of vapor due to these eddies. This was the main reason why the No Baffle system could not reduce the temperature of the vapor lower than 21.2 C. 89

108 5.3.2 Baffle Type I and Baffle Type II Next, the systems using horizontal baffles were tested. These system incorporated horizontal baffles in the orientation discussed in a previous section. Both orientations of baffles redirected the flow better and forced it to mix and interact more with the cooling pipes and foam. This is clearly shown in Figure 45. Figure 45 shows a side view of both horizontal baffle orientations to visualize the ways each manipulated the flow of vapor. Baffle Type I, on the left in Figure 45, illustrates how the vapor is forced to the opposite side of the system, since vertical bypass is prohibited. This forced a larger percentage of particles to come into contact with the aluminum pipes and graphite foam, increasing the heat transfer of the system. This increased the local Reynolds number between these fins, increasing their convective heat transfer coefficient, which in turn absorbed more heat energy from the vapor. The outlet temperature of the liquid dropped from 21.2 C using the No Baffle system to only 16.1 C with Baffle Type I. Figure 45. Side view comparison of pathlines between Baffle Type I and II The next simulation tested the two horizontal baffles in the opposite orientation as discussed earlier. On the right of Figure 45, it shows the Baffle Type II system with pathlines. These pathlines helped to visualize how the flow bypassed the core horizontally by 90

109 circumventing the inner pipes. These baffles sealed off a region opposite of the inlet which presented a larger pressure drop to the flow. Due to this, the vapor pathlines showed that only a fraction of the fluid particles traveled into this region, the remainder formed flowed downward as the momentum was dissipated. Baffle Type II was able to transmit more heat than No Baffle, but not as much as Baffle Type I. This was due to the region of low circulation above the top baffle, opposite of the inlet. In this region, there is little circulation of flow, which decreased the Reynolds number of the vapor particles travelling through the fins. The outlet temperature of the liquid slightly rose from 16.1 using the Baffle Type I system to. with Baffle Type II. Figure 46. Overhead view of pathlines in Baffle Type I In Figure 46, a top view of the Baffle Type I system is shown with pathlines to help identify the path of vapor. In this figure, the pathlines visibly bypassed most of the center structures by circumventing them. The only way to prevent this was by introducing longitudinal baffling which is discussed with the Baffle Bar Type I and Baffle Bar Type II simulations. When the vapor particles bypass the center cold water pipes and foam, their momentum is dissipated throughout the condenser volume. As their local velocity decreases, this decreases the Reynolds number of the particles travelling through the graphite foam, lowering the available heat transfer by lowering the Nusselt number. 91

110 5.3.3 Baffle Bar Type I and Baffle Bar Type II Baffle Bar Type I tested longitudinal baffles within the condenser. The horizontal baffles were identical to those in the Baffle Type I system, but the longitudinal baffles helped to eliminate bypass of the central pipes. These ran from the top to the bottom and completely eliminated the possibility of the vapor avoiding the inner pipes by flowing around them. Coupled with horizontal baffles, the longitudinal Baffle Bars forced the vapor through the inner core pipes while maintaining a large velocity. This translated to a much larger local Reynolds number encountered by the vapor travelling between the graphite fins. Due to this, the Baffle Bar Type I maintained a larger heat transfer coefficient on its cold surfaces which were able to more efficiently extract energy from the vapor. Below, in Figure 47, both systems incorporating longitudinal baffles are shown side by side to visualize the differences in the flow patterns. Figure 47. Side view comparison of pathlines between Baffle Bar Type I and II The pathlines for Baffle Bar Type I are seen as forming large eddies in front of the longitudinal baffles. However, in the systems without the longitudinal baffles, much less flow travelled between the cold water pipes. In this system, a large percentage of the fluid particles traveled directly between the cold water pipes and graphite fins, transferring their heat energy to 92

111 the ol water. This re u e the liqui s outlet temperature to only. C. This is a full 3 degrees less than the system which just used horizontal baffles and signified that longitudinal baffles were an important addition to the subscale system to increase performance. On the right of Figure 47, one can see the Baffle Bar Type II system. The longitudinal baffles in this condenser prohibited any type of bypass of the central pipes and because of this, the majority of vapor particles did not flow into the region opposite of the inlet. In order for fluid particles to enter this region, they would have to travel through the graphite fins and a large pressure drop. This is the reason why the pathlines show the vapor circulating downward without going through the central pipes. Also, the pathlines were only shown if the flui parti le s velo ity was a ove. m s. So the area where the pathlines end is where the flow becomes very slow and stagnated. The goal of these tests was to ensure that before the flow lost its momentum, it was able to come into contact with the graphite foam and aluminum pipes to maximize the heat transfer. This is seen clearly in Baffle Bar Type I, on the left, as all of the pathlines were forced to travel through the central pipes since bypass was prohibited. Figure 48. Overhead view of pathlines in Baffle Bar Type I 93

112 Figure 48, above, shows the top view of the pathlines in the Baffle Bar Type I system. As seen in the figure, no pathlines were able to circulate around the inner pipes as the longitudinal baffles provided impermeable barriers. This forced a much larger amount of vapor to travel directly through the graphite foam fins and contact the aluminum pipes. Since the vapor was forced through these pipes with a relatively high velocity, coming directly out of the inlet, the Reynolds number on the pipes and graphite foam was much higher than in previous systems. Therefore, the Baffle Bar Type I system was able to absorb much more heat from the vapor, lowering the flui s temperature to.. This is compared to Baffle Bar Type II, which had the reversed orientation of horizontal baffles, and was only able to lower the temperature of the fluid to 15.0 C. This was due to the region opposite of the inlet which was effectively blocked by the baffles from any type of flow. Vapor flowed into this region, but the velocity of the particles was very low, leading to a much lower heat transfer coefficient and making this region negligible for heat transfer Three Baffles The next system modeled was with a third baffle added to the Baffle Bar Type II system. This third baffle was placed about 2 inches under the inlet. This added baffle prohibited the vapor from simply dropping and losing energy. This forced the vapor through the piping system while it still had a high velocity and kinetic energy. This system caused the vapor to flow through the cold water pipes and foam at the highest Reynolds number, causing this system to be able to transmit more heat than any other. Shown in Figure 49 is the temperature plot of this system, complete with pathlines. Figure 50 shows the pathlines from an overhead view to more clearly show how the flow is directed. The hot vapor entering this system is shown to change temperature very quickly once entering. This temperature and pathline visualization was obtained once the system had gotten to steady state. Because of this, the high temperature vapor cools much faster since it enters the system which has a fluid with a much lower temperature. 94

113 Figure 49. Temperature plot for Three Baffle System Figure 50. Overhead view of temperature pathlines for Three Baffle System As shown by these figures, the vapor was forced to flow directly through the central piping system of the condenser. Nearly all of the flow pathlines show that the vapor particles travelled directly within the foam and cold water pipes. This was because the top baffle was placed directly below the inlet, allowing the vapor to travel into the cold water pipes at the highest speed possible without dissipating much momentum. This allowed the Three Baffle System to reduce the temperature to only 13.0 C. These simulation results clearly showed that by utilizing baffles, the heat transfer of the system can be increased simply by manipulating the flow of the vapor. 95

114 5.3.5 Subscale Condenser Simulation Summary Overall, the addition of baffles proved to successfully manipulate the path of vapor so it would encounter the graphite foam fins at a higher Reynolds number, to increase the heat transfer coefficient of the fins. As the simulations showed, the addition of baffles in Baffle Type I and Type II prohibited downward bypass of the vapor, which was seen in the system with No Baffles. With the addition of longitudinal baffles, the horizontal bypass of the inner core was eliminated. These baffles caused a much larger percentage of the flow to travel within the graphite foam fins. With the third baffle added, the vapor maintained the highest velocity possible as it encountered the graphite foam, which resulted in the most heat transfer. These results are summarized in the table below in Table 17. All of the systems were compared to the No Baffle system, by showing a percentage increase over what this system could achieve. By maximizing the vapor s velo ity as it travels own to the outlet, it maintains the highest lo al heat transfer coefficient in the graphite foam fins. Table 17. Subscale simulation results Temperature Out Heat Transfer (%) Heat Transfer Coefficient (%) ( C) ((Q/Q0)-1) 100 ((U/U0)-1) 100 No Baffle Baffle Type I Baffle Type II Baffle Bar Type I Baffle Bar Type II Three Baffle As shown in the table, the system using Three Baffles had an overall heat transfer coefficient which was 82.8% higher than No Baffles. The outlet temperature for Three Baffles also decreased the vapor to only 13.0 C compared to No Baffles, which could only reduce the temperature of the vapor to 21.2 C. 96

115 5.4 Subscale Condenser Experiments The subscale system consisting of an evaporator and condenser was tested to judge the performance differences between different types of baffles which were added to the condenser. These baffles are identical to the systems modeled. However, since the experimental system utilized an evaporator in conjunction with a condenser, the vapor velocity and temperature were dependent on the performance of the evaporator. In this case, the results from the experimental tests are to verify that the addition of baffles will increase the heat transfer of the system and should reflect the results of the simulations. Though, these results cannot be directly numerically compared to the simulations. This is because the boundary conditions are different since the condenser was modeled as its own system, given a constant flow of vapor with specific properties. In the simulations, the cold water velocity, vapor velocity and temperatures were chosen to closely match the experimental equipment. Nevertheless, some variables of the heat exchanger system remained uncontrollable. This included the temperature at which the condensed vapor re-enters the evaporator. If a condenser is very good at transferring heat, the system will lower the temperature of the vapor much lower. This was shown by the simulations. In the experimental equipment, a lower outlet temperature for the condensed HFE means that the evaporator has to work harder to re-heat this liquid HFE back to evaporation temperature. This meant that the results from the experimental tests had to be looked at qualitatively compared to numerically when comparing the results to the simulations. However, the results from the experimental tests showed that the baffles affected the flow in the same ways that the simulations showed they would. Each subscale condenser system used the same cold water temperatures and flow rates. The cold water bath remained at a constant power level, which provided cold water to the condenser at a specific flow rate, discussed previously. The hot water bath was changed from being set at 55 C to being set at 65 C. This enabled each condenser to be compared by looking at their respective heat transfer coefficient. 97

116 Figure 51. Heat Transfer Coefficient vs. HFE Inlet Temperature As shown above in Figure 51, the plot shows the heat transfer coefficient of each tested baffle orientation versus the temperature at which the HFE entered the system. The only variable changed was the hot water bath providing energy to vaporize the HFE. As the temperature in the hot water bath was increased, this would increase the overall temperature of the HFE coming into the condenser as well. For each of these systems, a range of HFE inlet temperatures were used, however, these were not directly controllable as only the hot water bath temperature was able to be varied. As this plot shows, the lowest performing system was the condenser using only aluminum and no graphite fins. This system could only achieve 10% of the overall heat transfer coefficient that the system with Three Baffles and Graphite Foam could achieve. This was an expected result, judging by the huge difference in performance explained in a previous section which tested aluminum fins versus graphite foam fins. The green data points reflect the No Baffle setup, which allowed the vapor to freely circulate within the volume. This made it difficult to condense HFE, especially at higher vapor temperatures, which is why this range is so much larger than the other tests. The heat transfer coefficient of the No Baffle system is approximately 50% that of the system with Three Baffles. 98

117 Performing slightly above and slightly below the No Baffle systems were the condensers which only utilized horizontal baffles and no longitudinal baffles. The Baffle Type I had a higher heat transfer coefficient because of the pathway created for the vapor which forced it to pass through the inner core of cold water pipes and graphite foam. The Baffle Type II had a slightly lower heat transfer coefficient due to the region opposite of the inlet, above the first baffle, which did not see much vapor circulation due to the vapor usually flowing in the direction of least resistance. Next, the longitudinal baffle systems are located above the horizontal baffle systems, indicating that the longitudinal baffles directly increased the performance of each. The Baffle Bar Type II system, which also maintains a region with low circulation, increased the overall heat transfer coefficient of the system to about 80% of the performance seen by the Three Baffle system. Using Baffle Bar Type I, which is the same as Baffle Type I, but just introduces longitudinal blocking bars, increased the heat transfer coefficient from 55% at Baffle Type I, to approximately 85% at Baffle Bar Type I. This showed that the longitudinal baffles stopped circulation of the vapor around the core and forced more energy to be absorbed from the vapor due to a higher Reynolds number passing through the inner pipes and graphite foam. The top performing system was the Three Baffle System which maintained the vapor at its highest velocity from the inlet as it was forced through the inner core. As the vapor passed through the graphite foam and cold water pipes, the vapor which did not condense still maintained a high enough velocity to continue to circulate efficiently without becoming stagnant (as seen with Baffle Type II and Baffle Bar Type II). As compared to the simulations, the experimental results showed the same trends as expected. Though the boundary conditions could not be kept identical, the performances of each experimental system reflected its simulation counterpart. The simulations showed that Baffle Type II and Baffle Bar Type II would be less efficient at transferring heat compared to Baffle Type I and Baffle Bar Type I, respectively. This was because of to the reversed style of the baffles, effectively restricting a region of the condenser from receiving maximum vapor flow. The vapor avoided these areas due to a higher pressure drop to flow into this region compared to simply bypassing it. These results were reflected in the experimental systems as well, as the Baffle Type II and Baffle Bar Type II systems also had a lower heat transfer coefficient compared to their counterparts. Another plot comparing the Reynolds number of the incoming 99

118 vapor to the overall heat transfer coefficient is shown in the appendix in A.15. The experimental results can also be compared to the simulated results since the 3-baffle orientation had the highest heat transfer as well. The simulations provided an excellent way to visualize the phenomena of the vapor path which could explain the higher heat transfer using this baffle orientation. Overall, using three baffles in a condenser system can enhance the heat transfer because this longer passageway for the vapor particles and larger velocity through the graphite extended surfaces allows for more heat transfer over a greater surface area of the system. 100

119 CHAPTER 6 CONCLUSION This research sought to study the parameters of cross-cut graphite foam fins. These cross cut fins were designed based on previous research and were shown to maintain a high heat transfer while keeping pressure drop at a minimum. The cross-cut fins accomplished this by incorporating free flow channels into the structure. Using the simulated tests, it was shown that the fin spacing had the largest effect on the flow, locally increasing the Reynolds number and shear stress between fins. This larger subsequent pressure drop forced more fluid within the material, increasing the fins overall heat transfer coefficient because of the increased Reynolds number over the larger surface area within the material. As the spacing between fins decreased, the shear stress of the fluid increased as the local velocity increased. This directly affected the amount of flow within the foam. Combining a small spacing with a fin that was not thick ensured that the flow was forced through the foam at the highest velocity and that the flow did not stagnate as much as it would with thicker fins. Increased fin thickness actually led to less heat transfer, since the fluid within the foam travelled at a lower velocity, reaching thermal equilibrium with the foam and ceasing the transfer of heat. As the fluid penetrated the foam, the momentum from the fluid diffused through the porous media. As the fluid slowed, the temperature difference between the foam and the fluid decreased until they were at thermal equilibrium. At thermal equilibrium, this region of porous media could not contribute to heat transfer since there did not exist any driving force behind transferring heat. Increasing fin angle did not substantially affect each fin design either. The increased fin angle did show to slightly increase heat transfer, but also greatly increased pressure drop. The reason for this is because the increased fin angle simply increased the vorticity of the flow which dissipated kinetic energy from the fluid and dissipated it as turbulence. By dissipating kinetic energy, the fluid retained a larger pressure drop. This pressure drop did not reflect on flow within the porous media, the dominating factor in the dissipation of kinetic energy was the vorticity and not shear stress at the walls of the fins. Since increasing fin angle did not increase 101

120 the flow within the foam, it only served to increase the local heat transfer coefficient on the outside surface area of the fins due to increased turbulence at these interfaces. The simulations clearly showed that the fin design with inch spacing and inch thicknesses would enable the largest amount of heat transfer to a gas flowing through the fin stru tures. This result was refle te in the experimental air hannel as the fin esign with inch spacing outperformed the other two fin designs by more than 15%. Estimating the thermal contact resistance on the heater plate in the simulations allowed for solutions to be much more accurate. This estimation led to simulated results which reflected on the results from the experimental tests. The estimated contact resistance enabled the solution of the simulated tests to approach the experimental data to within 12%. This clearly made the accuracy of the simulations reflect real life data and allowed accurate models of each fin design to be developed which could accurately depict their real life abilities. The subscale condenser research concluded that the use of baffles could manipulate the vapor flow in a way to increase heat transfer by a significant amount. By simulating the different baffle types and noting the flow characteristics and overall heat transfer abilities, it was concluded that the system with Three Baffles would out perform all others due to the extra baffle maintaining the vapor at a high velocity as it encountered heat transfer surfaces. The local Reynolds number of the flow over the cold water pipes and graphite foam was maximized by using the Three Baffle setup, which increased its local heat transfer coefficient on these fins and pipes, while increasing the systems overall heat transfer coefficient. The other systems showed that their flow tended to avoid the cold water pipes or circumvent them where baffles were not placed. The placement of these baffles and longitudinal blocking bars is very important to get the most heat transfer out of a given volume used for a condenser. This conclusion was also verified by experimental tests using the same condenser in the laboratory under slightly different conditions. The thermal performance of the system without baffles was significantly lower than the system using horizontal or vertical baffling. The systems using baffles condensed more fluid, at a faster rate, and also lowered its temperature lower. This research investigated the use of graphite foam as an extended use within a heat exchanger. It is apparent that graphite foam is a much better alternative than aluminum for heat transfer. Finned graphite surfaces can enhance the heat transfer of aluminum fins by over 250%. 102

121 By incorporating graphite foam finned surfaces into a heat exchanger, the usable energy from a temperature gradient is increased. Baffles added into condensers using graphite foam manipulate the vapor in a way to also increase the heat transfer. As graphite finned surfaces are investigated further, the potential for more efficient OTEC power plants grows. 103

122 CHAPTER 7 FUTURE RESEARCH In order to further the enhancement of heat exchangers using graphite foam, research could be conducted into the use of cross-cut graphite foam fins to further investigate the effects of the parameters on each fin designs performance. For this future research, the experimental tests would be conducted first. This would allow the simulations to follow, allowing the simulations to use the exact same boundary conditions as the experimental equipment. By following the same method to estimate the thermal losses and equating them to a contact resistance, these simulations could potentially give a more realistic idea of how the fins would perform in real life. This method could allow for different initial conditions to be tested which would not be possible in the lab to give more insight into the phenomena behind each. Further research could be conducted into the baffles within the subscale condenser, to see if different shaped baffles or spiral baffling could potentially increase the heat duty of each system as well. With more resources available, the testing of the baffles and boundary conditions for the systems could be varied on a larger range, allowing a more indepth insight into why each system performs differently than the others. The future research being conducted at Lockheed Martin for this OTEC project includes installation of the condenser and evaporator systems in Hawaii on the coast. Real life testing will begin this year to determine the optimum flow rates and other conditions to enable the most thermal power transfer. Hopefully, using this research, OTEC becomes a cheap, efficient way for coastal regions to provide their populations with abundant green energy for years! 104

123 APPENDIX A TEMPERATURE PLOTS OF SIMULATED FINS Extra plots for all 10 offset angle models with velocity = 5 m/s Figure 52. Temperature: 0.25 Thickness Spacing 10 Figure 53. Temperature: 0.25 Thickness 0.25 Spacing

124 Figure 54. Temperature 0.25 Thickness Spacing 10 Figure Thickness Spacing

125 Figure Thickness Spacing - 10 Figure Thickness Spacing

126 Figure Thickness Spacing 10 Figure Thickness 0.25 Spacing

127 Figure Thickness Spacing

128 APPENDIX B SUPPLEMENTARY PLOTS Figure 61. Comparison of pressure plots before and after interpolation Figure 62. Heat Transfer Surface for each fin design 110