Auto Exhaust Power Generation Unit from Waste Heat. Table of Contents

Transcription

1 Table of Contents 1) One Page Summary 2) Roles and Responsibilities 3) Customer Needs Assessment 4) Engineering Specifications 5) Subsystems a. Heat Transfer b. Structure c. Thermoelectric Modules and the Electrical System 6) Thermal System Model 7) Exhaust Flow System Model Page 1 of 45

2 Project # Project Name Project Track Project Family P08441 Auto Exhaust Power Generation Unit Sustainable Products, Systems, and Next Generation Thermo-Electric from Waste Heat Technologies Systems Start Term Team Guide Project Sponsor Doc. Revision RIT ME Department 3 Project Description Project Background: The motivation for this project stems from an increasing need for highly efficient power generation in the transportation sector. Thermoelectric power generation is seen as a possible step in gaining efficiency in an economical manner. Furthermore, motivation lies in the general understanding of the operation and feasibility of thermoelectric power recovery. P08441 will build upon two previous Senior Design projects by implementing integral testing equipment which has already been designed. Furthermore, the RIT Mechanical engineering department has the desire to build its competency and knowledge base with thermoelectric power generation. This project will ideally lead to a better understanding of thermoelectrics and their viability as a form of renewable energy. Problem Statement: This project s mission is to design an efficient thermoelectric module to attach to a test fixture realistically modeling a chosen vehicle s dynamics. Additionally the power generated is meant to make the vehicle more fuel efficient by running a subsystem. Objectives/Scope: 1. Realistically simulate an actual vehicle using the test stand. 2. Design an efficient thermoelectric module to maximize heat recovery and electrical output. 3. Power an important vehicle subsystem using electricity generated by the thermoelectric module. For example, run headlights or charge vehicle battery. Deliverables: Fully operational exhaust heat recovery unit. Heat recovery unit should be fully tested and characterized for a range of driving conditions. Heat recovery unit will power vehicle subsystem or charge the battery. Conference paper and technical poster describing project Expected Project Benefits: There will be a better understanding of thermoelectric operation and the feasibility of applying thermoelectric technology to an actual vehicle. There will be an increase in operating of efficiency of the chosen vehicle because the thermoelectric generator will run an important vehicle subsystem or charge the battery. There will be a thermoelectric heat recovery unit that can be used in future students labs and used for validation of models. Core Team Members: Stephen Byrne Mike Rheinheimer Erin Crowley Paul Gaylo Joel Nelson Frank Trotto Strategy & Approach Assumptions & Constraints: 1. Current thermoelectric generator technology is not very efficient, typically less than 5% efficient, and has specific temperature limitations that must be adhered to. 2. The limitations of the test stand will limit the complexity and realism of our model. 3. Creating an effective temperature drop across the thermoelectric will be very challenging. It will be difficult to adequately cool the cold side of the TEG to maximize performance. 4. The budget for the project will be $3,000. Issues & Risks: No team member has had extensive experience with finite element software for heat transfer aspects or CFD for fluid flow aspects of the project. Collecting critical data from an actual exhaust system may be difficult without becoming invasive. Current thermoelectric technology is not very efficient and has specific temperature properties which must be adhered to. Thermoelectric lead time is about 4-6 weeks. Page 2 of 45

3 Roles and Responsibilities Name Project Area of Responsibility Functional Area of Responsibility Hardware Area of Responsibility Role Phone Number Roberts Stevens Guide Mechanical Support General Customer Stephen Byrne Team Lead Flow Modeling Heat Exchanger Structure ME Support Mike Rheinheimer ME 1 Thermal modeling Heat Exchanger Heat Transfer ME Support mer5067@rit.edu Erin Crowley ME 2 Structural modeling Heat Exchanger Structure ME Support ecc2553@rit.edu Paul Gaylo ME 2 System/vehicle modeling System Model ME Support pjg6713@rit.edu Joel Nelson EE 1 Electrical support PCU/Thermoelectrics EE Support jrn2673@rit.edu Frank Trotto EE 2 Electrical support PCU/Thermoelectrics EE Support fmt0375@rit.edu Page 3 of 45

4 Customer Needs Assessment Need 1: System Model rank = Vehicle selection Typical exhaust dynamics: Heat, flow, materials Exhaust characteristics compatible with test fixture in TE lab 1.2 Develop power module to replicate real world conditions Need 2: Thermoelectric Selection rank = Performance High efficiency over a range of operating conditions 2.2 Proper material limitations Device can with stand temperatures applied Device can withstand vibrations and shocks 2.3 Adequate power generation Thermoelectrics can produce enough power to operate a vehicle subsystem 2.4 Optimal delta T for thermoelectric is within modeling range 2.5 Low cost thermoelectric devices Need 3: Thermoelectric heat transfer structure rank = Efficiently transfers enough heat to hot side 3.2 Effectively cools cold side 3.3 Material selection adequate Materials can easily handle operating temperatures Materials can handle vibrations/shocks (structurally sound) 3.4 Maintain effective pressure Pressure drop across unit has minimal impact on engine performance 3.5 Device should not exceed budgeted amount 3.6 Structure should maintain sufficient contact pressure on thermoelectrics 3.7 Easily manufactured 3.8 Optimal size Does not take up excessive space Does not add excessive weight Need 4: Power Generation/Use rank = Thermoelectric unit needs to run an important vehicle subsystem Unit will charge battery or Unit will run headlights 4.2 Power generated must greatly outweigh power drawn 4.3 Output voltage matches vehicle electrical system Need 5: Operation rank = Device is durable and can run continuously over a long period of time without complication Need 6: Safety rank = No one can be near unit while in operation Need 7: Testing rank = Device characteristics easily obtained from testing Temperature sensors in test model to monitor temperature Pressure sensors in model to monitor pressure changes Power output measurable Page 4 of 45

5 Engineering Specifications Metric # Need Metric Importance Units Marginal Value Ideal Value Appropriate exhaust temp. 7 Celsius Appropriate exhaust flow 7 kg/s Appropriate exhaust material: melting point 8 Celsius Temperature range for test fixture 7 Celsius Flow range for test fixture 7 kg/s High thermoelectric module efficiency 7 % Suitable thermoelectric max operating temperature 6 Celsius TE can withstand vibrations and shocks 3 1 Foot Drops Adequate power generation 9 W Thermoelectric is optimized for flow temperatures that we are able to model 7 Celsius Low cost for thermoelectrics 6 $/TE <200 < Hot side of Proper Temp. 6 Celsius Cold Side of TEG@ Proper Temp. 6 Celsius Flow reduction (Pa) 50 0 Appropriate exhaust material: pipe surface does not oxidize or corrode a Negligible Pressure Drop 5 Pa Low cost for mass a mass production unit 4 $ Maintain adequate contact pressure (set by supplier) 5 Mpa 70±25 70± Reasonable size, specifically height 4 m Run Vehicle Sub System 8 n/a battery head lights Verify efficiency increase of vehicle 8 % System output voltage 6 Volts 12±3 12± Durability of System 3 Years User protected from electrical and thermal components 9 Accidents <1 0 System parameters easily obtained from testing 6 Labview Compatible Mostly Yes Page 5 of 45

6 Subsystems Hot Exhaust Flow Test Fixture: Models vehicle exhaust, supplys heating, cooling, and flow. Thermoelectric Heat Exchanger: Transfers heat from structure to heat TE hot side. Also transfers heat from cold side for cooling. TEG Structure: Manipulates flow, supports TE's and supoorts heat transfer system Cooling: Use of air or liquid cooling to remove heat from cold side of TE. Heating: Manipulations of flow through the structure with geometry, turbulizers and fins Thermoelectrics: Energy Ideally the temperature difference will be maximized to obtain the highest power output Vehicle Subsystem: Run headlights or charge vehicle battery Page 6 of 45

7 Subsystem: Heat Transfer Concept Development Heat the hot side and cool the cold side. The goal of any applicable heat transfer system is to establish a significant change in temperature across the Thermoelectric ( T). The said change in temperature must also be consistent with the operating constraints of the thermoelectric. Additionally, any cooling or heating aid must be chosen with respect to the overall system and most importantly the overall efficiency of the already limited thermoelectric. A final thought would be to select methods that have a high cost to benefit ratio as illustrated in the accompanying Pugh diagrams. The automotive system Project P08441, thermoelectric heat recovery from an automotive exhaust, is a project closely associated with the design advantages and disadvantages of a contemporary automotive platform and vehicle system. A modern vehicle exhaust is not unlike any other device that emits heat losses; heat is energy, these losses can equate to energy gain and it would behoove the smart engineer to exploit this free energy source as much as practical. Practical is the key word here, as the current thermoelectric chip design allows for only about a 5% efficiency when operated at ideal conditions. Moreover, net vehicle cost is the significant factor to the overall attractiveness and ultimately the marketability of any supplementary system. The common denominator throughout this project is to supply appropriate operating conditions to the thermoelectric elements. Luckily, a wide range of temperature conditions exist in the average exhaust system. Once an area in the exhaust system is chosen that exhibits ideal or near ideal flow and temperature characteristics, the chief consideration is heat flow and the optimization of that transfer. Ideally, the highest heat flux across the thermoelectric is desired. To achieve this, the design must incorporate active heat gathering and heat dissipating mechanisms. The exhaust side of the thermoelectic will be referred to as the hot side and the opposite side as the cold side. The hot side will see a relatively steady flow of exhaust gases varying only with engine speed. Fortunately, the engine speed exhibited by the average vehicle at a cruise condition is close to constant. Page 7 of 45

8 It s possible and important to keep in mind that a simple, well placed, flat plate could be sufficient for the purposes of this project. However, there are a variety of means to sink more heat to the surface of the thermoelectric. A primary idea is to actively turbulize the flow. Another idea is an array of fins. Lastly, a combination of the former could be the optimum. Any given road vehicle has a variety of cooling systems and subsystems. Many of the systems are redundant. It s possible for a vehicle to have independent engine cooling, transmission cooling, oil cooling, and air-conditioning, and most importantly forward speed. The forward speed, or velocity, is better equated as air speed since that is the speed that is relative to this system, the air speed flowing though the radiator for example. Intuition most likely will eliminate all but the air speed and engine cooling as these are the largest, and most consistent items through all auto makes and models. Below is a brief description of possible systems, products, and conceptual ideas that will be associated with this project s needs. The concepts are separated by cold and hot side Hot Side Concepts Flat Plate: Page 8 of 45

9 Pictured is a flow over a flat plate. This is the simplest and most cost effective means to draw heat to the hot side of the thermoelectric. Only a portion of the heat passing over the plate will pass through to the thermoelectric. It s possible to locate the entire system in a very hot part of the exhaust, expecting only a percentage of the heat to be caught by the plate and conduct through to the thermoelectric. This project is constrained by the capabilities of the test stand designed by project P The test stand being crucial to the development of this project, will play a role in the concept selection. The Flow could be turbulized to increase the heat transfer. This will induce a pressure drop that will have some effect on the operating efficiency of the engine. This effect could, and most likely, will be so small that it is negligible. Page 9 of 45

10 Fins on the Hot Side A very basic fin system will do a lot to increase the heat transfer. Along with an increase in heat transfer, comes an increase in cost. This system will still be justified, but it s still a consideration. Fins can turbulize the flow. It s also possible to arrange a set of fins to induce turbulence. Since turbulence will equate to a pressure drop, a complementary increase in heat transfer should be expected, along with a complementary increase in exhaust restriction. Page 10 of 45

11 There are many fin systems commercially available. Above are a two promising examples. The exhaust stream of any internal combustion engine is highly hostile. It s to be expected that any selected product or design should comply with the material demands of a hot exhaust stream. Cold Side Alternative to the hot side, the cold side will require a much more active cooling system. Fins or liquid cooling will certainly be inorder. Given that the temperature difference between the maximum operating temperature of the thermoelectric and ambient air is only about 220 degrees Celsius, maximum efficiency in heat dissipation is in order. Optional to fin cooling, is a liquid cooling arrangement utilizing either vehicle coolant at about 100 degress Celsius or a stand-alone system at perhaps a temperature closer to ambient. Page 11 of 45

12 Fins: A fin system would be similar to the hot side but on a larger scale. A high-end passive CPU cooler could satisfy the requirements. Ether filled tubes act as heat pipes and direct the heat to the fin array which is greatly oversized to promote natural convection rather than forced convetion. The advantage of this design is the vaiable fin array, which can can be oriented in a variety of directions. Page 12 of 45

13 It s possible to create a ram-air funnel (nozzle) to utilize air speed and direct higher velocity air over the fins at the expense of vehicle drag. The increase in drag would most likely be negligible. Page 13 of 45

14 Another method would force air over fins with some type of fan device, either electrical or mechanical. This system would require energy, impacting the overall system efficiency. Above are CPU coolers fitted with fans to force air across the fins. Note the compact size of these devices compared to the passive cooling fins. Page 14 of 45

15 Liquid cooling: A promising concept would be the use of engine coolant as a liquid to cool the cold side via a cold-plate style heat exchanger. Perhaps a pre cooler could be fitted to the incoming coolant line from the engine to Page 15 of 45

16 bring the temperature down from 100 degrees Celsius. Coolant will boil at 130 degrees Celsius, limiting this design. The most complex and expensive concept idea in termers of lost efficiency and overall cost would be a stand-alone liquid cooling system. This system would require a dedicated radiator and pump. The advantage is near-ideal operating temperature. This system could also be manipulated to a higher extent than a system piggy-backed onto the engine cooling system. This system was utilized as an experiment by project P Page 16 of 45

17 Heating Subsystem Options A B C D Turbulized Over Straight Flat Plate Fins Flow Over Flat Plate Angled Fins Turbulized Selection Criteria Rating Rating Rating Rating Heat Transfer to TE Cost Pressure Drop Potential TE Damage Total (+)'s Total (-)'s Total (0)'s Net Score Rank A Flow Over Flat Plate B Turbulized Over Flat Plate Selection Criteria Weight Rating Weighted Score Rating Weighted Score Rating Weighted Score Rating Weighted Score Heat Transfer to TE 40% Cost 10% Pressure Drop 10% Potential TE Damage 40% Total Score Rank Continue No Yes Yes Yes C Straight Fins D Angled Fins Turbulized Page 17 of 45

18 Cooling Subsystem Options A B C D Stand-Alone Forced Engine Coolant Air Fins Liquid Air Fins Selection Criteria Rating Rating Rating Rating Cooling Effectiveness Size Cost Manufacturing Overall System Efficiency Total (+)'s Total (-)'s Total (0)'s Net Score Rank A B C D Engine Coolant Air Fins Stand-Alone Liquid Forced Air Fins Selection Criteria Weight Rating Weighted Score Rating Weighted Score Rating Weighted Score Rating Weighted Score Cooling Effectiveness 40% Size 20% Cost Manufacturing 10% Overall System Efficiency 30% Total Score Rank Continue Yes Yes No No Page 18 of 45

19 Subsystem: Structure Concept Development Page 19 of 45

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22 Structure Subsystem Options A B C D E Large Box Large Flat/Diffused Hexagonal Small Box (Benchmark) Round Selection Criteria Rating Rating Rating Rating Rating Fabrication Thermoelectrics/Length Heat Transfer Flow (Pressure Drop) Cooling Feasibility Size/Weight Cost Total (+)'s Total (-)'s Total (0)'s Net Score Rank A B C D Flat/Diffused Small Box Hexagonal Large Box Selection Criteria Weight Rating Weighted Score Rating Weighted Score Rating Weighted Score Rating Weighted Score Fabrication 10% Thermoelectrics/Length 15% Heat Transfer 20% Flow (Pressure Drop) 20% Cooling Feasibility 20% Size/Weight 5% Cost 10% Total Score Rank Continue Yes Yes No No Page 22 of 45

23 Subsystem: Thermoelectric Modules and the Electrical System Figure 1 shows the high level block diagram of the electrical system. The TE modules produce power, which varies slightly as the temperature difference between its hot plate and cold plate changes. The voltages generated are added in series and delivered to the PCU (DC-DC buck converter). This will output a steady 12 V, which is needed to power the headlights. Figure 1. Electrical System Block Diagram When looking for an effective TEG, important features to look for are: efficiency, operating temperature, cost, and power output. These were considered when deciding on what type of thermoelectric to choose for the design. The following pugh diagrams, figures 2 and 3 compare and rank these important features of various models. In order to take the generated voltage from the thermoelectric modules and condition it to a useable form, a DC-DC converter is used. More specifically, a buck converter which is used to convert a Page 23 of 45

24 high input voltage that may be varying, and produce a smaller stable output voltage. Important features of this converter are: input voltage range, output voltage range, efficiency, maximum power output, and cost. Figures 4 and 5 compare and rank these features of various converters in pugh diagrams. Thermoelectric Generator To generate large amounts of power, the thermoelectric modules need to have many thermocouples, and be rated for higher currents. The dependency on the temperature is key, as efficiency and performance change drastically when the hot side temperature and cold side temperature change. There are not many thermoelectric modules on the market that are designed to be used as power generators. The majority are used as coolers (TEC), where a voltage and current are applied to each side of the device, causing a temperature difference. Reversing this process is highly inefficient (approximately 3-4%). Hi-Z, Custom Thermoelectric, Tellurex, Ferrotec, Melcor, and Termo-Gen AB are various companies that produce thermoelectric modules. Only three produces TEG s, Hi-Z, Tellurex, and Termo- Gen AB. In terms of power generation and maximum temperatures, Hi-Z appears to be the best option, as seen in the pugh diagrams. Page 24 of 45

25 Figure 6. HZ-20 Dimensions Figure 7. HZ-20 Performance Graphs The HZ-20 cost $ each. Additional costs could be: Heat Transfer Grease (20 grams $45.00 each) Ceramic, Electrically Insulating Wafers ($5.00 each) Silicone, thermally conductive pads Page 25 of 45

26 These would all increase the performance of the TEG s. To run a car s headlights 100W is needed. Table 1 shows 4 different scenarios. It shows the impact that the temperature on the cold side of the TEG has on our design, as well as on our budget. The temperature we heat the hot side at is restricted by the TEG devices, as they start to break down when heated continually at 300 o C. Table 1. Tc Effect on Design and Cost to Achieve 100W from HZ-20 Page 26 of 45

27 Figure 8 shows the performance graphs of the HZ-14 TEG. Figure 8. HZ-14 Performance Graphs The HZ-14 cost $ each. Table 2 shows 4 different scenarios. It shows the impact that the temperature on the cold side of the TEG has on our design, as well as on our budget. The temperature we heat the hot side at is restricted by the TEG devices, as they start to break down when heated continually at 300 o C. Table 2. Tc Effect on Design and Cost to Achieve 100W from HZ-14 Thus, HZ-20 would be a better fit for this design. The cost and power produced are superior to the HZ-14 as well as any other TEG s. Page 27 of 45

28 Power Conditioning Unit Figure 9. Example of a Buck Converter Connected to Load and Input Power Page 28 of 45

29 Figure 10. Example of a Buck Converter Integrated into the System (Here the load are Headlights) Page 29 of 45

30 Overall System Model Diagram The diagram below illustrates the general layout of the proposed system. As the design process progresses finite values will be attached to the various subsystems to give the viewer a good idea of the inputs and outputs of the system. Page 30 of 45

31 TEG Subsystem Options A B C D FerroTec Termo-Gen AB TEP1- Custom Hi-Z HZ Thermoelectric Selection Criteria Rating Rating Rating Rating Efficiency Operating Temperature Cost Power Output Total (+)'s Total (-)'s Total (0)'s Net Score Rank A B C D Hi-Z HZ-20 FerroTec 9501 Termo-Gen AB TEP Custom Thermoelectric Selection Criteria Weight Rating Weighted Rating Weighted Rating Score Score Weighted Score Rating Weighted Score Efficiency Operating Temperature Cost Power Output Total Score Rank Page 31 of 45

32 Zahn Electronics DCDC48/12/160 PCU Subsystem Options A B C D E Hi-Z HZ-12- Wall Industries MPQ Calex HEW 24 Series Series Vicor VI- J00 Selection Criteria Rating Rating Rating Rating Rating Input Voltage Range Output Voltage Range Efficiency Maximum Power Output Cost Total (+)'s Total (-)'s Total (0)'s Net Score Rank DCDC48/12/160 Selection Criteria Weight Rating Weighted Rating Weighted Rating Weighted Score Rating Weighted Score Score Score Rating Input Voltage Range Output Voltage Range Efficiency Maximum Power Output Cost Total Score Rank A Zahn Electronics B Hi-Z HZ C D E Wall Industries MPQ Series Calex HEW Series Vicor VI-J Weighted Score Page 32 of 45

33 Thermal System Model A thermoelectric generator functions on the Seebeck effect that electrical power can be produced if two dissimilar conductors are held at different temperatures. A portion of the heat flow entering one side of the thermoelectric is converted to electrical power. On the other side of the generator the heat flow leaves, minus the fraction that was converted. In order to maximize the power produced by the generators in our system, a thermal model was created. A schematic showing the heat entering and leaving the TE, q h - q c is the thermal energy converted to electrical energy. Page 33 of 45

34 The model describing the heat transfer concerning a single thermoelectric is as follows: System of Equations: T T 1 q = I R + α T I h e, TE m 1 RTh, TE 2 T T 1 q = + I R + α T I I c e, TE m 2 RTh, TE 2 m 1 2 e, TE 1 h h Th, h 2 c c Th, c h c T R T = T q R T = T + q R T T T T = α T = T = h, o h, i c, o c, i + T h, i h, o 2 + T c, i c, o 2 T + R = T m = T + m L qh c dot, h p, h qc c dot, c p, c α Seebeck Coefficient R R R R R T T q q m e, TE Th, TE Th, h Th, c L h, i c, i h c 1 2 Electrical Resistance of TE Thermal Resistance of TE Thermal Resistance, hot side Thermal Resistance, cold side Electrical Resistance, external load Exhaust Temperature Coolant Temperature Unknown Variables: I Electrical current T Temp. of TE, hot side T T h T Average temp of exhaust at cold side of TE T T c h, o c, o Heat flow into hot side Heat flow out of cold side Temp. of TE, cold side Average temp of exhaust at hot side of TE Temp. of exhaust leaving Temp. of cooling fluid leaving Design Parameters: Page 34 of 45

35 The Seebeck coefficient is the constant of proportionality between the voltage output and the temperature difference. It varies with thermoelectric, as well as the thermal resistance of the TE and the electrical resistance of the TE. There is a wide range of temperatures available along the exhaust pipe of a vehicle so we can effectively control Th by the placement of the TE. The temperature of the cooling fluid, be it coolant in a heat exchanger or outside air, is another design variable. The heat transfer can be modeled by a simple thermal circuit with three resistances in series: To maximize the temperature gradient, T1 to T2, R Th,h and R Th,c must be kept relatively small compared to R Th,TE. Since the TE thermal resistance is on the order of 1 K/W, achieving the appropriate hot and cold thermal resistances poses a significant challenge. Possible hot side design configurations include a straight fin design, effectively forcing the exhaust through channels to harness and redirect the heat toward the TE device, fins that are staggered to increase the turbulence of the flow, the use of a simple turbulizer to achieve a similar effect, and a simple plate design. On the cold side, a simple straight fin, heat exchanger cooled with engine coolant flow, stand-alone heat exchanger, and a forced air/fin design were considered. Page 35 of 45

36 Straight channel design Heat exchanger cold plate Staggered fin design Turbulizer Page 36 of 45

37 A number of assumptions have been made in order to maintain a steady ground for comparison and to simplify the calculations. exhaust temperature has been set to 550K any fins are assumed to be pure aluminum the mass flow rate is assumed to be 0.04 kg/s the temperature of the exhaust gas after exposure to the TE is assumed to be equal to T h (see above formulas) flow rate through cold plates = 1.5 gal/min single TE device used (HZ-20 Bismuth Semiconductors) RL = Re,TE Assuming a vehicle moving at 40mph The thermal resistance of each of these systems depends on a number of factors, and optimization has yet to be completed but the models have been constructed in Excell and preliminary results are as follows: Hot Side Design R TH Cold Side Design R TH Finned 0.54 K/W Finned 0.09 K/W Plate Flow 1.2 K/W Finned-Forced Convection 0.07 K/W Turbulizer??? K/W Cold Plate-Engine Exhaust 0.01 K/W Staggered Fin??? K/W Cold Plate-Stand Alone 0.01 K/W Hot Side Finned vs. Cold Side Cold Plate (engine coolant) Page 37 of 45

38 Design Parameters m dot,h 0.2 kg/s R L (Ω): Ω c p,h 1000 J/kg-K R e,te (Ω): Ω m dot,c kg/s R Th,h : 0.54 K/W c p,c 4000 J/kg-K R Th,c : 0.01 K/W R TH,TE K/W T h,i (K): 550 K α m V/K T c,i (K): 353 K Unknown Variables q h (W): W q c (W): W I (A): A T h (K): K T h,o (K): K Tc (K) : K T c,o (K): K T 1 (K): K T 2 (K): K Power Generated W Hot Side Finned vs. Cold Side Finned Design Parameters m dot,h 0.2 kg/s R L (Ω): Ω c p,h 1000 J/kg-K R e,te (Ω): Ω m dot,c 0.2 kg/s R Th,h : 0.54 K/W c p,c 4000 J/kg-K R Th,c : K/W R TH,TE K/W T h,i (K): 575 K α m V/K T c,i (K): 310 K Dependent Variables T 1 (K): K T 2 (K): K q h (W): W q c (W): W I (A): A T h (K): 575 K T h,o (K): K Tc (K) : 310 K Power Generated W Page 38 of 45

39 Exhaust Flow System Model The main concern with the TEG structure is the additional resistance to flow that it would add to the exhaust system. With an increase in flow resistance comes a greater pressure drop, which in turn creates more back pressure on the vehicle engine. With an increase in back pressure in the exhaust system the vehicle engine would have to work harder to expel its spent gases and there by lose operating efficiency. Therefore, it becomes important to ensure that the design of the TEG structure does not excessively increase back pressure with in the exhaust system. To begin, it must be determined whether the flow is laminar or turbulent. Ideally the flow will be turbulent so that the boundary layer will be reduced and heat can more easily be transferred to the hot side of the thermoelectric. Other TEG systems have run into issues with heat transfer due to boundary layer issues caused by the flow conditions. The ρvd Reynolds = number is obtained from: µ ρ= density of air (assumed for exhaust gas) µ = viscosity of air The velocity is obtained from the fact that the mass flow rate within the exhaust is. constant. m = V1 A1 = V2 where : V A structure 2 = V tube A A tube structure The Reynolds number should be verified both in the exhaust pipe and within the structure to see if there may be any transitional flow. The next step involves calculating the frictional losses within the structure. To do so the following equation should be used, assuming the flow is turbulent. Page 39 of 45

40 h = l f D L structure V 2 structure 2 Where f is the Moody factor and determined from the Moody diagram depending upon the material roughness, diameter and Reynolds number. Additionally, to incorporate the frictional losses that exist if a diffuser and nozzle were used, one must take an average velocity between the structure and exhaust pipe and calculate the head loss for the combined length of diffuser and nozzle. Upon calculating the major head loss it is time to calculate the minor losses caused by the expansion or contraction of the geometries involved. The calculation for the loss coefficient, K, is heavily dependent upon the geometry of the diffuser or nozzle. Flat/ Diffused: K entrance where D β = D = tube structure θ sin ( 1 β ) θ 2 0.8sin ( 1 β ) 2 4 β structure Small Box (Rectangular Expansion/Contraction): There are also loss coefficients from tables for sudden expansions and contractions. When the loss coefficients are calculated one can determine the minor head loss: K exit = where D β = D tube 2 4 β 2 h lm = 2 V K 2 tube The overall equation for the drop in pressure across the structure is given by: LV V P = ρ f + K 2Dstructure structure tube Another aspect that needs to be taken into consideration when looking into the pressure drop of a system is the change in temperature. There should be a considerable Page 40 of 45

41 temperature drop across the TEG structure since heat is being drawn out of the exhaust gas and being transferred to the thermoelectrics. Analysis of Small Box Concept: Input Parameters at Cruising Speed Temperature Air Density Air Viscosity Mass Flow Rate Celsius kg/m^3 N*s/m^2 kg/s E Table 1: Input Parameters Table 1 defines the assumed input parameters at the typical cruising speed of a vehicle with a typical 4-cylinder engine. Table 2 calculated the Reynolds number for various geometries for comparison purposes. The structure geometry selected in the concept phase was the small box design. Reynolds Number Calculations Geometry Type Tube Diameter Structure Diameter A (Structure) A (Tube) Velocity (Structure) Re (Structure) m m m^2 m^2 m/s Exhaust Pipe Flat/Diffused Small Box Table 2: Reynolds Number Comparison Table 3 compares the frictional losses within the TEG structure. This calculation does not include the frictional losses within the geometries of the diffusers and nozzles used to fit the exhaust pipe to the TEG structure. Frictional Losses Re e/d Moody Factor Major Head Loss Geometry Type Structure Commercial Steel f Structure Only (m^2/s^2) Exhaust Pipe Flat/Diffused Small Box (square geometry, slight d increase) Table 3: Major Head Loss Comparison Page 41 of 45

42 The table below compares losses from the diffuser fitting between the exhaust pipe and the TEG structure. Sudden Expansion Gradual Expansion (20degrees) Geometry Type A1/A2 K Fig 8.14 Minor Head Loss K Minor Head Loss Exhaust Pipe Flat/Diffused Small Box (square geometry, slight d increase) Table 4: Head Loss from Expansion Table 5 outlines the minor losses resulting from the structure contraction with a reduction angle of 20 degrees. The loss coefficient equations were both obtained from the Fluid Flow Handbook. Gradual Contraction (20 degrees) Geometry Type K Minor Head Loss Exhaust Pipe 1 0 Flat/Diffused Small Box (Square) Table 5: Minor Head Loss from Contraction The final table compares the overall pressure drops for the two chosen structure designs due to frictional loss and fitting losses. P (Total) Geometry Pa Flat/Diffused Small Box (Square) Table 6: Total Pressure Drop From the frictional loss model one can say that the frictional losses are negligible, and the focus must be turned to the considerable pressure drop that fins would add. Page 42 of 45

43 Off Set Fins in Rectangular Structure: Off set fins provide excellent heat transfer from the exhaust gas to the hot side of the thermoelectric at the cost of an increased pressure drop. To determine the pressure drop that will be experienced the following equations are used. Furthermore there are some necessary correlations that have been developed: Colburn j-factor: Franning friction f- factor: Where: j=0.101re α β δ γ f=2.092re α β δ γ The equations that relate pressure drop and heat transfer coefficient to the Colburn and Franning factors respectively are as follows: Page 43 of 45

44 From the Franning fiction factor equation the pressure drop can be backed out. To do so, one must first define the variables with in the equation. The exact equation for the minimum free-low area and total air-side surface area are not yet known. The total air-side surface area should be significantly larger than the minimum free-low area for the air side. If the difference is large, as it should be, it will greatly effect the pressure drop across the TEG structure. Furthermore, as seen in the minor loss calculations, the entrance and exit loss coefficients will have a minimal effect on the overall system pressure drop. To continue, the Colburn factor can be used to determine the convective coefficient of the fin assembly, which can help greatly in maximizing the heat transfer to the hot side. It is important to note that the overall heat transfer coefficient and pressure drop decrease as the fin height and spacing increases. It is most important to maximize heat transfer, but it is necessary to verify that the pressure gradient is not excessive. h Fin Parameters (Meters) Number of Fins Across s Number of Fins per Length l d t Table 7: Off Set Fin Parameters Table 7 defines some test fin parameters. The table basically outlines how different parameters could be varied to test a resultant pressure drop. Page 44 of 45

45 Franning Friction Factor α β γ δ De Re E E E E E+03 Table 8: Franning Friction Factor Parameters The Franning Friction Factor Parameter table processes the fin parameters from table 7 into a workable form for the j and f factor correlations. The equation below incorporates the Franning Friction factor, and entrance and exit losses, to solve for the pressure drop. Issues and concerns: A o P = f + Kc A c ρv + Ke 2 The exact definitions of the areas used in the Franning friction equation are not precisely defined in the research paper referenced. Other papers point in one direction but do not seem to result in the correct pressure drop. There needs to be further investigation into the definition of the areas used, which most likely have a very large effect on the pressure drop. 2 The flow model needs further development to be able to change the variables more easily and obtain optimized flow conditions while transferring as much heat energy as possible. There needs to be more research into modeling different types of fins. Page 45 of 45