. . A '2‘ "1 4004 This is to certify that the thesis entitled DESIGN CONSIDERATIONS FOR MICRO WAVE DISC ENGINES presented by MARCO VAGANI has been accepted towards fulfillment of the requirements for the MS. degree in Mechanical EngineerinL fl/zg Major Professor’s Signature /Z/0/0<39 Date MSU is an Affirmative Action/Equal Opportunity Employer PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 5/08 K:IProjIAcc&Pres/ClRC/Dateoua indd DESIGN CONSIDERATIONS FOR MICRO WAVE DISC ENGINES By Marco Vagani A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Mechanical Engineering 2008 ABSTRACT DESIGN CONSIDERATIONS FOR MICRO WAVE DISC ENGINES By Marco Vagani With the increasing trend towards technological miniaturization, the demand for micro-scale power generation has been growing steadily. However, the downscaling of internal combustion and gas turbine engines has been hindered by losses in cycle efficiency at smaller scales. This thesis presents two concept micro wave disc engines which are specifically designed for micro-scale power generation. A wave disc is an unsteady pressure exchange device that has a proven potential for gas turbine enhancement. It employs shockwaves within rotating micro-channels to directly transfer energy between two fluids. The first concept engine presented is the External Combustion Wave Disc Engine, which employs a wave disc to replace the low efficiency turbomachinery components in a micro gas turbine engine. The second concept engine is the Internal Combustion Wave Disc Engine, with combustion occurring within the micro-channels of the rotor. The first part of this work discusses the operation principles for both wave disc engine concepts and the wave patterns developed for them using gas dynamics relations. The second part describes the numerical Simulation of wave discs and the design methodology employed. For this purpose, an automated tool was developed to model and simulate wave disc operation using FLUENT. Finally, an approach for modeling and simulating the internal combustion wave disc engine is proposed. To my wife and my parents iii ACKNOWLEDGMENTS I would like to start by expressing my gratitude toward Dr. Norbert Miiller, whose vision and support have brought me to this point. I thank him for his faith in my talents, for his always helpfiil guidance, and for the freedom with which he allowed me to explore my work. I wish him all the best in his professional and personal life. I would also like to thank Dr. Abraham Engeda and Dr. Criag Somerton, for agreeing to participate in my thesis committee and for their comments that helped me improve this work. I am especially grateful to Dr. Engeda for his support over the years and for all the Opportunities he has allowed me to have in this field. I would like to acknowledge the importance Of Florin Iancu’S work in this field. This thesis is a continuation on the work he started in this lab. In addition, I would like to thank all my colleagues and friends who helped make these years memorable. Ludék Pohorelsky has made major contributions to this project; and with his help, knowledge, and motivation has improved the lab tenfold. I thank Pradeep Kumar, Kanishka Sharma and Pranav Sané, whose work has helped improve my own. I also thank Stephanie Bonner, who was always willing to put up with more work. Finally, I thank John Quackenbush, J ijo Joseph and Anirban Lahiri for their good spirits and perennial availability during the long hours in the lab. Inoltre, vorrei ringraziare la mia famiglia, che mi hanno dato una tremenda opportunita nel mandarmi a studiare negli Stati Uniti. Finally, a special thanks to my wife for her help and understanding. iv TABLE OF CONTENTS LIST OF TABLES VI LIST OF FIGURES VIII NOMENCLATURE XI CHAPTER 1: INTRODUCTION 1 CHAPTER 2: BACKGROUND 3 2.1 MICRO-SCALE POWER GENERATION ........................................................ 3 2.2 PRESSURE EXCHANGE WAVE ROTOR TECHNOLOGY ................................ 9 CHAPTER 3: WAVE DISC ENGINE CONCEPTS 18 3.1 EXTERNAL COMBUSTION WAVE DISC ENGINE ...................................... 18 3.2 INTERNAL COMBUSTION WAVE DISC ENGINE ....................................... 21 CHAPTER 4: WAVE PATTERNS AND l-D DESIGN CODE 25 4.1 SIMPLE WAVE PATTERN ........................................................................ 25 4.2 IMPROVED WAVE PATTERN ................................................................... 30 4.3 l-D DESIGN CODE FOR WAVE DISC ....................................................... 34 4.4 WAVE PATTERN FOR INTERNAL COMBUSTION WAVE DISC ENGINE ...... 36 CHAPTER 5: AUTOMATED WAVE DISC SIMULATION CODE 43 5.1 NUMERICAL SIMULATIONS OF WAVE DISCS .......................................... 43 5.2 GEOMETRY ............................................................................................ 45 5.3 MESH ..................................................................................................... 50 5.4 PRE-PROCESSING SETUP ........................................................................ 55 5.5 SIMULATION .......................................................................................... 59 5.6 POST-PROCESSING ................................................................................. 62 CHAPTER 6: DESIGN METHODOLOGY AND RESULTS 65 6.1 DESIGN METHODOLOGY ........................................................................ 65 6.2 NUMERICAL COMPARISON AND VALIDATION OF WAVE PATTERNS ....... 67 6.3 ENERGY CONSIDERATIONS .................................................................... 78 CHAPTER 7: SUGGESTIONS FOR FUTURE WORK 87 7.1 OPTIMIZATION FOR NUMERICAL SIMULATION CODE ............................. 87 7.2 CFD SIMULATIONS OF INTERNAL COMBUSTION WAVE DISC ENGINE 88 CHAPTER 8: CONCLUSIONS 93 APPENDIX 95 REFERENCES 100 LIST OF TABLES Table 1. Sample Operating points for 1-D design code, results Shown in Figure 19 ........ 35 Table 2. Sample Operating point for internal combustion wave disc engine, result shown in Figure 22 ......................................................................................................... 42 Table 3. Input variables necessary for generation Of porting geometry ............................ 47 Table 4. Input variables necessary for generation Of straight and curved channels .......... 49 Table 5. Input variables necessary for FLUENT pre-processing setup and simulation 59 Table 6. General geometry and Operation parameters for numerical comparison Of wave patterns ................................................................................................................ 67 Table 7. Porting angles calculated using simple wave pattern ......................................... 68 Table 8. Porting angles calculated using l-D design code and improved wave pattern... 72 Table 9. Porting angles determined for final wave pattern iteration ................................. 75 Table 10. Comparison Of velocity magnitudes at the inlets and outlets Of the inviscid and laminar models ................................................................................................... 76 Table 11. Values and resulting specific work for final porting design with straight channels and ports .............................................................................................. 79 Table 12. Inlet and outlet port angles for a straight channel rotor, shown in Figure 40 80 Table 13. Values and resulting Specific work for wave disc with straight channels and angled ports ......................................................................................................... 82 Table 14. Values and resulting Specific work for wave disc with curved channels .......... 85 Table 15. Geometric and Operating conditions for wave disc simulation Of simple wave pattern. Results shown in Figure 36. .................................................................. 95 Table 16. Geometric and Operating conditions for wave disc simulation of improved wave pattern. Results shown in Figure 37. ......................................................... 96 Table 17. Geometric and Operating conditions for wave disc simulation Of final iteration Of wave pattern. Results shown in Figure 38 and Figure 39. ............................. 97 Table 18. Geometric and Operating conditions for wave disc Simulation with angled porting. Results shown in Figure 40. .................................................................. 98 Table 19. Geometric and Operating conditions for wave disc Simulation with curved channels. Results shown in Figure 41. ............................................................... 99 vii LIST OF FIGURES Images in this thesis are presented in color Figure 1. Specific energy for hydrocarbons and several battery technologies [10] ............ 4 Figure 2. MIT micro gas turbine engine generator [8] ....................................................... 7 Figure 3. Micro-turbine (left) and micro-compressor (right), produced by MIT, etched out Of a silicon wafer, with diameters Of 4 mm and 8 mm [7] .................. 8 Figure 4. Cutaway of the micro gas turbine engine assembly [7] ....................................... 8 Figure 5. Schematic model Of a through-flow wave rotor and porting ............................. 10 Figure 6. NASA four port wave rotor drum (left) and Comprex® rotor drum (right) ..... 11 Figure 7. Schematic for a wave rotor enhanced gas turbine engine in a) through—flow and b) reverse-flow configurations ........................................... 12 Figure 8. Temperature-Entropy diagram for a gas turbine engine with and without wave rotor topping ....................................................................................................... 13 Figure 9. Schematic for a wave rotor enhanced micro gas turbine engine design ............ 14 Figure 10. Micro-scale wave disc, the bottom showing a cutaway View Of the rotor channels .............................................................................................................. 1 6 Figure 1]. Schematic for a radial wave disc enhanced micro gas turbine engine design . 16 Figure 12. Temperature-Entropy diagram for an external combustion wave disc engine 19 Figure 13. External combustion wave disc engine configuration ..................................... 20 Figure 14. Wave disc engine with a reverse-flow, two combustion chamber configuratioznl Figure 15. Temperature-Entropy diagram for internal and external combustion wave disc engines ................................................................................................................ 22 Figure 16. Schematic for the internal combustion wave disc engine ................................ 23 Figure 17. Simple wave pattern for a through-flow wave rotor ........................................ 26 Figure 18. Improved wave pattern for a through-flow wave rotor ................................... 31 Viii Figure 19. Wave pattern outputs for two Operating points. Left — Fully scavenged rotor. Right — EGR Present. .......................................... 36 Figure 20. Wave diagram for a wave disc with internal combustion ............................... 37 Figure 21. Wave diagram for an internal combustion wave disc Shown in absolute reference frame ................................................................................................... 39 Figure 22. Wave pattern output for an internal combustion wave disc engine ................. 42 Figure 23. Schematic Of the input variables necessary for the porting geometry ............. 46 Figure 24. Schematic of the input variables necessary for a straight channel .................. 48 Figure 25. Schematic Of the input variables necessary for a curved channel ................... 49 Figure 26. Close-up Of inner gap for a structured grid, aligned with geometric features . 50 Figure 27. Close up Of inner gap for a semi-structured grid, with skewed mesh within gap ............................................................................................................................ 5 1 Figure 28. Close-up Of high pressure zone with a coarse mesh, with 270 radial mesh points and 50 tangential mesh points ............................... 52 Figure 29. Close-up Of high pressure zone with a fine mesh, with 540 radial mesh points and 100 tangential mesh points ............................. 53 Figure 30. Complete mesph for a 4-cycle wave disc with curved channels and angled porting ................................................................................................................. 54 Figure 31. Full model Of the 4-cycle wave disc with curved charmels and angled porting ............................................................................................................................ 55 Figure 32. Numerical error present in coupled solver during transient start-up ............... 57 Figure 33. Wave disc pressure contours during initialization, transient start-up, and steady-state Operation ......................................................................................... 61 Figure 34. Graphical user interface for FLUENT post-processing interface .................... 63 Figure 35. Flowchart Of design methodology ................................................................... 66 Figure 36. Pressure and temperature contours for a wave disc using the simple wave pattern ................................................................................................................. 69 Figure 37. Pressure and temperature contours for a wave disc using the improved wave pattern ................................................................................................................. 71 ix Figure 38. Pressure and temperature contours for a wave disc using final wave pattern iteration ............................................................................................................... 74 Figure 39. Pressure and temperature contours for final wave pattern iteration using a laminar solver ..................................................................................................... 77 Figure 40. Pressure and temperature contours for a wave disc with angled porting ........ 81 Figure 41. Pressure and temperature contours for a wave disc with curved channels ...... 84 Figure 42. Possible geometry and mesh for the channels Of an internal wave disc engine ............................................................................................................................ 90 Figure 43. Heat addition zone for internal combustion wave disc modeling ................... 91 601 662 gap Linner Lower r51 N N cycles N solution P Q Tturbine NOMENCLATURE Speed Of sound Number Of cycles per revolution Inlet absolute tangential velocity Outlet absolute tangential velocity Gap size Enthalpy Specific enthalpy Length Of channel Length Of inner porting Length Of outer porting Mass flow rate Rotational velocity Of rotor Number Of full cycles to be simulated Number Of iterations for a full solution Pressure Heat transfer Gas constant Radius Temperature Turbine inlet temperature Flow velocity Internal energy xi [In/s] dimensionless [m/s] [tn/s] [m] [U] _ [Id/kg] [m] [m] [m] [kg/s] [rpm] dimensionless dimensionless [Pa] [k1] [kl/kg'K] [m] [K] [K] [m/s] [kl] U I Inlet blade velocity [m/s] U 2 Outlet blade velocity [m/S] uhead Expansion wave head velocity [m/s] up Induced flow velocity [m/S] um“ Expansion wave tail velocity [In/s] V Volume [m3] w Shockwave velocity [m/S] W Work [kl] mep Compression Work [U] W Rate Of work [kJ/s] y Specific heat ratio dimensionless AR Channel length [m] At Simulation time step Size [S] A hymn-0n, Maximum iterations per time step dimensionless A W Specific work [kl/kg] A (D Channel unit Size [deg] 6 Angle [deg] 175 Pressure ratio across Shockwave dimensionless r Torque [Nm] (0 Channel thickness [deg] a) Rotational velocity Of rotor [rad/s] Subscripts 1 Air inlet conditions / Conditions in front Of wave 2 Air outlet conditions / Conditions behind wave xii inner open outer P r ref Acronyms Al A0 CC CFD EC EGR El E0 IC MAV MEMS Exhaust inlet conditions Exhaust outlet conditions Port closing Final conditions Initial conditions Inner radius Port opening Outer radius Product conditions Reactant conditions Reference conditions Air inlet Air outlet Combustion Chamber Computational Fluid Dynamics Expansion Wave External Combustion Exhaust Gas Recirculation Exhaust inlet Exhaust outlet Internal Combustion Micro Air Vehicles Micro Electrical Mechanical Systems xiii UAV WD WDE WR Pressure Wave Shockwave Unmanned Air Vehicles Wave Disc Wave Disc Engine Wave Rotor xiv CHAPTER 1: INTRODUCTION The development Of micro power generation engines employing Micro Electrical Mechanical Systems technology has been strongly intensified in recent years. However, the creation Of such devices has been largely hindered by losses in cycle efficiency at smaller scales. The scaling Of conventional engines such as internal combustion and gas turbine engines faces major difficulties with heat loss, component efficiencies, fi'iction, sealing, fabrication and assembly. This work proposes two concept engines, micro wave disc engines. They are a novel idea for micro-scale power generation. In such devices, external or internal combustion is used to generate shockwaves that can enhance combustion and allow for compression and expansion of the Operating gases. Chapter 2 is a review Of the benefits Of micro-scale power generation and its applications, focusing also on the MIT micro gas turbine project. It also contains a review Of wave rotor technology and the development Of the wave disc for micro gas turbine enhancement. Chapter 3 presents the concept Of a Wave Disc Engine, which uses wave disc technology to replace the steady-state turbomachinery components in micro gas turbines. Two separate concepts are developed, with external combustion and internal combustion. The External Combustion Wave Disc Engine uses a pressure-exchange wave disc to compress and expand the working fluids. The Internal Combustion Wave Disc Engine is a novel concept that includes combustion within the channels Of the wave disc. Chapter 4 explains the wave patterns developed for wave disc technologies. Two different patterns are presented for wave discs as pressure exchangers. The first pattern is greatly simplified to reduce calculation time. The second pattern is much more accurate than the first, introducing various gas dynamics principles that were not taken into account in the Simplified version. In order tO solve the improved wave pattern, a 1-D design code was developed. This chapter also explains the wave pattern and similar code developed for an internal combustion wave disc. Chapter 5 introduces the need for numerical simulations in order to validate and improve on the results of the 1-D design code. An automated Simulation tool was developed to perform these numerical analyses using FLUENT, a common computational fluid dynamics software. The tool’s geometric and meshing parameters are explained, along with the solver setup and simulation process. Chapter 6 first introduces the new design methodology for wave discs that was developed. This methodology would not be possible without the 1-D design tOOls described in Chapter 4 and the 2-D numerical simulation tool described in Chapter 5. This chapter then proceeds to apply this design methodology on a wave disc design. Both of the wave patterns developed in Chapter 4 are simulated, and their results are combined to produce a final, more effective wave disc design. Chapter 7 outlines directions for future work. This includes the possibility Of using optimization software to improve the results Of the numerical simulation code. It also provides a possible approach tO modeling and Simulating the Internal Combustion Wave Disc Engine. Finally, Chapter 8 summarizes the conclusions drawn form this work. CHAPTER 2: BACKGROUND 2.1 MICRO-SCALE POWER GENERATION Modern technological society has an increasing need for smaller power generation devices. With the developing trend towards the miniaturization Of electronic and mechanical devices, the demand for high efficiency power generation units is growing steadily. This demand is largely focused on finding a viable alternative to chemical batteries. The demand for smaller, lighter, highly efficient systems and devices requires the integration Of both electrical and mechanical systems in progressively smaller devices. This field, called Micro Electrical Mechanical Systems (MEMS), appeared towards the end of the 20‘h century through the creation Of integrated sensors and actuators. MEMS combines electrical and mechanical engineering concepts with micro-fabrication technology to create fully integrated systems on Silicon chips. Currently, the field has expanded to a variety Of applications, from audio-Visual implants tO complete fluid micro-systems, including power generation. The development Of MEMS has Spurred research in the energy field, directed towards reducing the scale of common power sources. This led to the design of rnicro- heat engines such as internal combustion engines, gas turbines, and steam turbines. This field iS called MEMS Power Systems, or Power MEMS [8]. The Objective Of this field is to create smaller, sub-centimeter scaled engines that produce 10 to 100 watts with power densities and performances comparable to their larger-scale counterparts. Power MEMS engines provide a huge advantage over common chemical batteries. The liquid fuels used in such engines have a much larger energy density than most batteries, as Shown in Figure 1. Even only at 5% efficiency, a small octane engine would have a comparable energy density to that of a battery [10]. This means that devices powered by a micro-scale engine can be lighter and smaller than an equivalent battery powered device. They could Operate for a longer period of time and may even be refueled. This even reduces the manufacturing and waste disposal costs associated with chemical batteries. "000 -I——* T“ Specific Energy (Whlkg) Figure 1. Specific energy for hydrocarbons and several battery technologies [10] The most anticipated application for Power MEMS engines is the creation of portable power generation. With small, efficient power sources, it would be possible to replace or enhance batteries in most common applications. This includes laptop computers, cell phones, and other common electronic devices. Micro-engines built into these devices could provide a constant source Of power that could outlast the common batteries used. Alternatively, they could be used to recharge the battery when its charge is tOO low, running only for short periods Of time. [25,38] The largest field Of applications for Power MEMS engines is in the defense industry. Unmanned air vehicles (UAV) and micro air vehicles (MAV) are being developed Of increasingly smaller Sizes [13,30]. Three important factors in the development Of these vehicles are the size, weight and range Of the design. Micro-scale engines would be able to improve on these three issues while still providing the power necessary [37]. The small size and lightweight materials used in micro-heat engines provide a big improvement over traditional power sources, and their high efficiency and energy density will allow the vehicle to have a much larger range than one powered by battery cells. An additional electric flight concept includes micro-engines within the aircraft wings creating both electrical power and additional lift [22]. Furthermore, the increasingly high-tech devices used by soldiers and reconnaissance vehicles require them to carry bulky, heavy battery packs around for portable power [14,12]. The light weight of a micro-engine would provide a vast improvement for soldier packs, making them smaller and lighter. Also, the higher energy density Of liquid fuels would allow them tO carry smaller fuel reservoirs rather than large batteries. Currently most MEMS devices draw power from macroscopic power supplies such as external batteries. This limits their fimctionality in many applications [20]. Integrating MEMS micro sensors and actuators with micro-heat engines will improve the scope and application range Of such devices. Bulky and inefficient energy storage devices may be eliminated. Additionally, a power-independent MEMS device does not require electrical connections to external power sources, giving it improved mobility and autonomy. Another benefit Of micro-scale power includes the possibility Of having multiple backup power sources when the main source fails. This would be ideal for applications where certain components must retain functionality afier a power shortage. Multiple small or micro-scale engines could power these components, making them independent Of the main power generator or grid. The promise for flexible, energy-independent, multiple-application devices has led micro-scale power generation tO become a forefiont research topic in the energy industry. There have been significant recent attempts to miniaturize conventional combustion engines for small-scale application, using MEMS or other fabrication methods, to create micro-scale power generation devices. Well publicized among these are the MIT micro gas turbine engine [7,8], the UC Berkeley mini rotary engine [11,31], and the Georgia Tech and Honeywell-U. Minnesota fi‘ee-piston engines [1]. The MIT Micro Gas Turbine Engine Project was begun in 1995 with the Objective Of using it for power generation and small aerial vehicle propulsion. A cross-section schematic Of the engine is Shown in Figure 2. The basic design is composed Of a supersonic, radial compressor and turbine, with an annular ring combustion chamber. The compressor includes diffuser vanes, and the turbine includes swirl vanes. They are connected by a hollow shafl. The high rotational speeds Of the rotor required gas film bearings in order tO reduce fiiction. The previously existing MEMS dry-friction bearings would not have an acceptable Operating life at the required speeds [5]. The final design included a journal and thrust gas film bearings. Hydrogen gas is the fuel used, injected directly after the compressor vanes. A motor-generator is built within the engine in order to start the rotor and produce electrical power. The built-in motor provides the advantage of reducing the number of parts and bearings necessary. The engine is designed to produce 20 kW of electrical power when using pre-compressed inlet air [8]. Starter! Generator Flame Fuel Fuel Com motor Holders Manifold Injectors Dim“: Rotor G“ Vans and” Inlet Path Vance Blade. maln- Figure 2. MIT micro gas turbine engine generator [8] Initially, the material chosen for micro-fabrication was silicon, but later research proved that a layer of silicon carbide would strengthen the material and allow it to withstand higher temperatures. The turbine and compressor were designed radially to ease the micro-fabrication process, which prefers structures with an extruded 2-D cross- Section. Two examples of micro-fabricated rotors produced by MIT on a silicon wafer are shown in Figure 3. The entire engine assembly consists of nine micro-fabricated wafers (layers), bonded together. A cutaway of the bonded assembly is Shown in Figure 4. Figure 3. Micro-turbine (left) and micro-compressor (right), produced by MIT, etched out of a silicon wafer, With diameters 0” mm and 8 mm [7] Figure 4. Cutaway of the micro gas turbine engine assembly [7] The MIT engine attempts to scale the compressor, combustor, and turbine of a conventional gas turbine engine using micro-fabrication methods. The functional principle and thermodynamic cycle are the same as conventional gas turbines. Turbo- component performance, however, suffers due to the downsizing effect. It was shown that the polytropic efficiency of conventional steady-state turbomachinery decreases with size [7]. The increased influence of wall effects decreases the turbo-component’s efficiency, since flow velocities remain similar while the channel dimensions are reduced. The continuous flow combustor suffers from increased heat loss at micro-scale, where the rate of heat loss is larger than the rate Of heat production through combustion. With lower component efficiencies, the overall thermal efficiency of the micro turbine engine is significantly decreased. One possibility for enhancing this engine is the addition Of a micro wave rotor [16,17]. 2.2 PRESSURE EXCHANGE WAVE ROTOR TECHNOLOGY A wave rotor is an unsteady flow device that utilizes the concept Of direct pressure transfer between fluids through waves. It is used as a pressure exchanger, employing shockwaves to transfer energy fiom a high energy fluid tO a low energy fluid. In most applications it is utilized to increase the pressure Of a low temperature, low pressure gas (the driven gas, usually air) using the energy provided by a high temperature, high pressure gas (the driver gas, usually exhaust gas). A wave rotor typically consists of a rotating drum with straight channels throughout the length Of the rotor. It lies between two fixed endplates, which are used to seal the channels from the manifold. The fixed plates contain ports, which allow the channels tO be periodically exposed to the driver and driven gases. The sudden exposure to these gases initiates shockwaves or expansion waves within the channels. A schematic Of a wave rotor is presented in Figure 5. The channels are exposed to a high pressure, high temperature gas at the Exhaust Inlet port (E1) and to low pressure, low temperature air at the Air Inlet (AI) port at the inlet side Of the rotor. After the energy exchange within the rotor is complete, the outlet side Of the channels is opened to release the pressurized, low temperature air at the Air Outlet (A0) port, and the expanded, high temperature gas, at the Exhaust Outlet (EO) port. End Plates Channels Ports Figure 5. Schematic model of a through-flow wave rotor and porting The Operating principle of the wave rotor allows it to compress the inlet air while expanding the exhaust gas. In this manner, the wave rotor acts as both an air compressor and a gas turbine, but Within a single rotating part This is achieved using lower flow velocities and a smaller rotational Speed than traditional turbomachines. The periodic exposure to hot gas and cool air allows the rotor to maintain lower Operating temperatures, having a “self—cooling” effect. Multiple applications have been found for wave rotor technology. Figure 6 Shows two wave rotors, the first of which was produced and tested by NASA as a performance enhancer to a gas turbine engine [35]. The second wave rotor depicted was produced by Brown Boveri Corporation. This wave rotor, named the Comprex®, has been used commercially in the Mazda 626 Capella as a supercharger for the internal combustion engine, which sold more that 150,000 units [21]. A wave rotor may be used to enhance the performance Of a gas turbine engine. The rotor would Operate in parallel to the combustion chamber, using the pro-compressed air from the traditional compressor as its inlet air, its driven gas. This air would be compressed further and sent to the combustion chamber. The combustion chamber exhaust would be the driver gas, and the rotor would then supply pro-expanded exhaust to the turbine. The wave rotor may be driven by an external motor or may be designed to be self- driven, using the momentum Of the flow to rotate the rotor. The Operation principle is analogous to the Operation of a supercharger or turbocharger in an automotive engine. The wave rotor increases the pressure Of air entering the combustion chamber and expands the exhaust gas leaving it. This has the effect Of increasing the total work output Of the engine. Figure 7. Schematic for a wave rotor enhanced gas turbine engine in a) through-flow and b) reverse-flow configurations Figure 7 depicts the cycle schematics for two possible configurations of the wave rotor for gas turbine engine topping. In the through-flow configuration, the two flows travel the length Of the rotor in the same direction, so that the rotor has an inlet side and an outlet side. In the reverse flow configuration, the two flows exit fi‘om the same side that they enter. This results in a hot side and a cold side. In both configurations shown above, the inlet air (0) is initially compressed by the compressor. It then reaches the air inlet (AI/ 1) port on the wave rotor, where it is ingested into the rotor channels. Once it comes in contact with the hot exhaust gas (El/3), a Shockwave is created which further compresses the flesh air. This air is then evacuated from the channel and is sent to the combustion chamber (AO/2). Finally, the exhaust gas is evacuated by means Of the expansion waves created by the sudden closing Of the channel’s inlet ports (BO/4). This exhaust gas, which loses some pressure in the process, is then supplied to the turbine for work extraction (5). 12 A g l0 - 1B - 4B - 53 baseline engine 15 0 —1A—2A— 3A-4A- 5A topped engine 0 3 g- A 0 .— ITUBBINE ____________ . .7 4B_ _ _ .x/ \ \ \ J increase of 18:1A / 5'3 Ioutputwork 5 A 0 Entropy, Figure 8. Temperature-Entropy diagram for a gas turbine engine with and without wave rotor topping The advantage provided by the wave rotor is apparent when comparing a wave rotor enhanced cycle with a baseline cycle. The two cycles, Shown in Figure 8, are compared for equivalent compressor pressure ratios and turbine inlet temperatures. The amount Of heat addition in the combustor is the same for both cycles, and the combustion pressure loss is Shown for both. The pressure increase provided by the wave rotor allows combustion to occur at a higher pressure than for the baseline engine. After the pro-expansion Of the exhaust gas in the wave rotor, the exhaust enters the turbine at a higher pressure than for the baseline cycle. In fact, the pressure increase provided by the wave rotor allows the turbine inlet pressure to be higher than the pressure at the outlet Of the compressor. The larger pressure ratio across the turbine results in added work extracted from the flow. The work output increases while the input work to the compressor remains the same. This improves the 13 cycle’s thermal efficiency. The wave rotor topped gas turbine engine extracts more work and is more efficient than the baseline engine. The potential improvement of the gas turbine engine cycle provided by the implementation Of a wave rotor makes it an ideal candidate for micro-scale power generation. For micro-scale applications, it is necessary to achieve high thermal efficiency. With a higher efficiency, the wave rotor topped engine can output more power while taking up the same space and weight. The following two designs were proposed to enhance a micro gas turbine engine similar to the MIT Micro Gas Turbine Engine [17]. The first design uses a conventional wave rotor configuration, as a rotating drum with channels running along its length, as shown in Figure 9. The wave rotor drum is attached to the outer radius of the rotating compressor/turbine assembly. The combustion chamber continues to be an annulus, on the outside edge Of the micro-engine. Being a through-flow design, the fresh air from the compressor enters the wave rotor channels and travels through the rotor to the turbine Side of the engine. The compressed air is then ducted into the combustion chamber, mixed with fuel and ignited. The combustion gas re-enters the rotor, is expanded, and exhausts to the turbine. Compraaaor Wave Rotor Ru til-u": DISK Air Intake End ”at” Combusbor 4 cycle! revolution (18 port wave rotor) Figure 9. Schematic for a wave rotor enhanced micro gas turbine engine design In this configuration, the wave rotor produces the desired pressure boost for the engine, but also has a few more advantages. With the wave rotor attached to the end of the rotating turbine/compressor disc, there is no need for a separate drive for the wave rotor itself. Additionally, the self-cooling characteristic Of the wave rotor helps isolate the rotating parts in the center Of the engine fiom the heat produced by the combustion chamber. However, the drawbacks of this design include the fact that it requires a small increase in diameter in order to accommodate for the wave rotor. Furthermore, the wave rotor configuration is not ideal for micro-fabrication. Its surface to height ratio is very small, having a very narrow 2-D surface that is extruded for a long length. This requires much more complicated micro-fabrication methods in order to ensure accurate sizes and straight channels. The difficulty in creating a wave rotor using micro-fabrication processes led to the creation Of the radial-flow wave rotor, otherwise called a wave disc [27]. The wave disc has channels that are located radially along a rotating disc. In this configuration, the porting is placed on the inner and outer radii Of the rotor. The large surface area and short height Of the rotor made it ideal for the micro-fabrication process. TWO halves Of the rotor would be fabricated from two wafers and bonded together. One more added benefit Of the wave disc over the wave rotor is the radial configuration allows the design to take advantage Of the centrifugal forces present in the channels. These forces allow the rotor to be scavenged more thoroughly if the exhaust outlet port is placed on the outer radius of the rotor. One possible configuration for a micro wave disc is shown in Figure 10. 15 Figure 10. Micro-scale wave disc, the bottom showing a cutaway view of the rotor channels The second topped micro gas turbine engine design includes the implementation of the wave disc, as is shown in Figure 11. It is located above the combustion chamber, on the compressor side of the engine. The inlet air is fed directly fiom the compressor, and travels through the disc to the combustion chamber. After combustion, the exhaust gas is again expanded through the rotor and ported to the turbine. Wave Rotor Routing Disk End Plates / . Compressor A A" Inltake / Combusbor 541/ I l—. '1! {M 5" .c .4 Im- —— ‘ Turbine Figure 11. Schematic for a radial wave disc enhanced micro gas tInbine engine design In this configuration, the wave disc provides a few advantages over the wave rotor. While still producing the same pressure boost, the disc is much Simpler to 16 manufacture in micro-scale. The radial Shape Of the wave disc allows the micro—engine to occupy the same diameter as the baseline engine. The disc does not have to be attached to the main shaft, and can be self-driven by using the momentum Of the flow through it. The improved scavenging provided by the centrifugal forces in the disc allows it to attain a lower average temperature than the wave rotor, where exhaust gas recirculation has been shown to create concentrated, hi gh-temperature areas that negatively affect its performance [23]. Another added benefit Of the radial wave disc is the possibility Of using it to extract energy from the flow. In gas turbine engine topping applications, it is sufficient for the wave disc to extract enough energy from the flow to become self-driven. However, by using angled porting, the rotor may be capable of extracting more energy than is needed to drive it. This energy could be harnessed to generate power. Modifying the channels so that they are curved, rather than the traditional straight channel design could improve the energy extraction of the wave disc even firrther. 17 CHAPTER 3: WAVE DISC ENGINE CONCEPTS The possibility Of extracting energy from the flOW using only a wave disc has Opened a promising new research area, Wave Disc Engines (WDE). The following sections present two different WDE concepts. The first replaces the turbine and compressor with a wave disc. The combustion chamber remains separate from the rotor; therefore it is designated as an External Combustion (EC) Wave Disc Engine. The second concept engine requires combustion to occur within the channels Of the wave disc. This concept is named the Internal Combustion (IC) Wave Disc Engine. 3.1 EXTERNAL COMBUSTION WAVE DISC ENGINE The wave disc enhanced gas turbine engines presented in the previous chapter effectively combine traditional, steady-state turbomachinery with unsteady, Shockwave compression. This leads to a higher thermal efficiency compared to the baseline MIT gas turbine engine. However, the low efficiency Of the compressor and turbine at the micro- scale is a limiting factor to the engine’s overall efficiency. The basic concept behind External Combustion Wave Disc Engines is to simply replace the turbomachinery components with a single pressure exchange wave disc [26]. The thermodynamic cycle remains the same as that Of traditional gas turbine engines, as shown in Figure 12. The wave disc alone provides the compression and expansion needed for the cycle to be completed. It also is designed to produce torque on its own, SO not even the turbine is required. The wave disc itself acts as a compression, decompression and torque generation unit, but all in a single rotating part. 18 The efficiency Of Shock wave compression is not as affected at micro-scale as that Of traditional steady-state turbomachinery components [15]. Therefore, the wave disc has a higher efficiency for the compression process, reducing the work requirement. Another added benefit Of the wave disc is its self-cooling feature. The channels are periodically cooled by the fresh inlet air, so the rotor remains at a lower temperature than a gas turbine engine with an equivalent compressor pressure ratio. The wave disc can therefore handle a much higher peak temperature from the combustion chamber. Both of these effects can be seen in the thermodynamic cycle Shown below. The overall efficiency Of the wave disc engine is higher than that of the gas turbine engine. A MaximumWPE Tsmreraturs ........ 35c 1—250-35c—45c: Wave Disc Engine with External Combustion ITLlRBlNE. _____ . _______ ,.-" Temperature 1‘ Wave Engine Net Work 2594!. ‘ Turbo Engine ' Net Work increased compression efficiency 250. T WCOMP L 1 1-2—3—4: Brayton Cycle Gas Turbine Engine V Entropy Figure 12. Temperature-Entropy diagram for an external combustion wave disc engine The wave disc engine uses only one rotating part. Using an external drive would increase the overall size of the engine and introduce losses. Instead, a generator-starter is integrated within the engine itself, following the conceptual design developed by MIT [7,9]. This completely eliminates the mechanical losses associated with shaft 19 transmission. Additionally, the wave disc engine rotates at much lower smds than a comparable compressor-turbine unit. This greatly reduces fiictional losses and simplifies the bearing and the electric generator design. Fuel tank Combustion chamber \/ Exhaust gases Wave disk : compression — decompression, torque generator unit Figure 13. External combustion wave disc engine configuration The EC wave disc engine shown in Figure 13 contains all of the features mentioned previously. Fresh air enters the center of the engine and is ported into the wave rotor channels. Shockwaves compress the air and send it to the combustion chamber, placed parallel to the disc. The hot exhaust gas is then redirected to the wave disc. After expansion, they are released through the bottom of the engine. Figure 14 is a better representation of the flow within the rotor. In the case depicted, the wave disc uses a reverse-flow configuration. This disc contains two cycles per revolution. The combustion chamber is split in half, using a separate combustion chamber for each cycle in the rotor. 20 Fresh air inlet Exhaust gas outlet from combustion chamber A exhaust gases! Combustion 5» chamber A —— Compressed air —- Fresh alr Wave disk electric generator / High pressure and high temperature port Figure 14. Wave disc engine with a reverse-flow, two combustion chamber configmation 3.2 INTERNAL COMBUSTION WAVE DISC ENGINE The External Combustion Wave Disc Engine uses a typical Open combustion chamber, where combustion occurs at a nearly constant pressure. However, the constant pressure combustion used for gas turbine engines and the wave disc engine is much less efficient than the confined combustion that occurs in Internal Combustion (IC) engines. This is a constant volume process, where both the temperature and pressure increase. The IC wave disc engine takes advantage Of the confined combustion process by using the closed space within the rotor channels as a combustion chamber. During combustion, both ends Of the channel are closed, so the process occurs at constant volume. 21 ‘ l/ ," volume = constant pressure = constant / .MéximumWPETsmyeraiurs.-. f3,10 .. ...,._. ._..._,....".. 3150... _,. Temperature IMRBJNE _____ .__ _ 1‘2lC"3lC—4IC: Wave Disc Engine with Internal Combustion V 450 1-25c—35c—45c: Wave Disc Engine with External Combustion 1—2-3—4: Brayton Cycle Gas Turbine Engine w Entropy Figure 15. Temperature-Entropy diagram for internal and external combustion wave disc engines Constant volume combustion provides a huge thermodynamic advantage. Figure 15 compares the cycles for the two types Of wave disc engines. For the same peak temperature and compression ratio, the pressure after combustion is much higher for the IC wave disc engine. AS a result, the pressure ratio during the expansion process is much larger, producing a significant increase in the extracted work by the engine. The Operation Of the IC wave disc engine is very different from that Of the EC wave disc engine. For this engine, only two ports are necessary. The inlet port intakes fresh air/fuel mixture, while the outlet port releases the burnt gas produced by the combustion. A schematic showing the Operation principle Of this engine is shown in Figure 16. 22 Scavenging Q Compression “Jet Propulsion” F\\ R Expansion /,,_ ESE Constant Volume Combustion Figure 16. Schematic for the internal combustion wave disc engine The channel begins with a fresh firel/air mixture. It is closed on both ends, is rotating with the disc, and the fluid within it is at rest. The fuel/air mixture is then ignited, and the combustion process occurs at constant volume. This produces a large temperature and pressure rise within the channel. After combustion is complete, the channel reaches the exhaust outlet port. The sudden opening of the boundary creates two effects. The high pressure within the channel, when suddenly released, has a “jet propulsion” effect which generates extra torque for the rotor. It also creates an expansion wave, which will travel the length of the channel and expand the exhaust gas within it. The expansion wave will force the exhaust gas out of the rotor. When the expansion wave reaches the inlet side Of the channel, the inlet port is Opened. The flow created by the expansion wave will ingest fresh firel/air mixture Item that port. At this point, both ends of the channel are open, so the loading of flesh mixture 23 and scavenging Of exhaust gas is taking place. Additionally, the centrifugal forces within the channel aid the scavenging and loading process. The last step in the process is the compression Of the fresh air/fuel mixture. Once the channel is fully scavenged, the exhaust port is closed. The sudden deceleration Of the flow creates a Shockwave that travels into the channel. The Shockwave compresses the firel/air mixture, preparing it for ignition. It also brings the fluid within the channel to rest. The closing of the inlet port is timed for when the Shockwave reaches it. The channel is then completely closed again and is filled with flesh, compressed mixture. The cycle is complete and the channel is ready to be ignited tO begin once again. A few Options are available for the compression process. The strength Of the Shockwave created by the sudden closing Of the outlet port is dependant on the velocity of the flow through the channel at the moment it is closed. AS explained above, it is possible tO wait until the entire channel is scavenged before closing the exhaust outlet. However, if a stronger Shockwave is required, it is possible to close the channel earlier in the cycle. This will create a stronger Shockwave, but some exhaust gas will remain in the channel. This is called Exhaust Gas Recirculation (EGR). This may be beneficial to the combustion process, using the EGR gas to increase the temperature Of the firel/air mixture before ignition and limiting combustion to a smaller portion of the channel [34]. The Internal Combustion Wave Disc Engine takes advantage of the high efficiency Of confined combustion, while having the high power density and low maintenance characteristics Of continuous flow machines. It is physically Simple and compact, using only one rotating part with a simple extruded 2D geometry. This will lead to a much lower unit cost compared to other competitive technologies. 24 CHAPTER 4: WAVE PATTERNS AND l-D DESIGN CODE 4.1 SIMPLE WAVE PATTERN The wave rotor and wave disc Operate by transferring energy between two fluids using a set Of shockwaves and expansion waves. These waves are created within the channels by the Opening and closing Of the inlet and outlet ports. These events are timed to ensure the correct wave pattern is formed within the rotor. The design of wave rotors and wave discs consists of determining the timing for each port based on their thermodynamic conditions. From the pressure and temperature conditions at each port, it is possible to develop a wave pattern for the flow within the channels. From this pattern, it iS then possible to determine the timing Of each port and design the porting for the device. Multiple wave patterns have been developed for both trough-flow and reverse- flow wave rotors. The wave pattern presented in Figure 17 is based on the pattern developed by NASA for a four port, thorough-flow wave rotor [36]. The horizontal axis represents the position within the channel, and the vertical axis represents time. This pattern may be applied to both axial wave rotors and radial wave discs. Since the pattern depends only on the length of the channel and the timing Of the ports, it provides a good initial design. However, the pattern does not take into account the added centrifugal forces that are present within the wave disc. 25 —> Shockwave —>- Expansion wave ——> Direction of flow ------ Gas/Air Interface Low Pressure Air High Pressure Air 2 1; Low Pressure Gas E0 (4) - High Pressure Gas LP part HP part Figure 17. Simple wave pattern for a through-flow wave rotor The porting for the through-flow wave pattern is clearly divided into an inlet side and an outlet side. In addition, the wave pattern is also divided into a high pressure (HP) part, and a low pressure (LP) part. The exhaust inlet port (El) supplies high pressure, high temperature exhaust gas, while the air inlet port (AI) supplies low pressure, low temperature air. The air outlet port (A0) will be supplied with air at a higher pressure than the E1 port, but only a Slightly higher temperature than the AI port. The exhaust outlet port (E0) will be supplied with exhaust gas that is at a pressure between the AI and EI ports. The temperature at the E0 port will be slightly lower than that of the El port. The pressure exchange process, as shown above, begins with a moving channel, filled with low pressure, low temperature air (Zone I). At this point, the through-flow velocity of the channel is zero. Once the E1 port is Opened, the pressure difference between the channel air and the port gas creates a Shockwave (SI), which propagates 26 towards the outlet Side, into the channel. As S. moves into the channel, it compresses the air within it to same pressure as the El port, with only a slight raise in temperature (Zone Hair). The shockwave also induces a flow behind it, causing hot exhaust gas from the E1 port tO enter the channel (Zone Ilgas). The velocity induced by the Shockwave is less than the velocity Of the Shockwave itself, producing a clear division between the gas and air in Zone 11. This is called the gas/air interface. The first Shockwave reaches the end of the channel and reflects, creating a second Shockwave (S2). The Opening of the AO port is timed to match this reflection. This new Shockwave moves back into the channel and compresses both the air and gas in Zone II to a higher pressure, the pressure Of the AO port, creating Zone Illa:r and Zone IIIgas. The air and gas continue to move through the channel. The air, now at its desired pressure, is outlet through the AO port. Once the second Shockwave reaches the inlet side Of the rotor, the BI port is closed. This prevents further gas from entering the channels. In addition, the sudden closing Of the port creates an expansion wave (E) that moves into the channel. The expansion wave decreases the pressure Of the gas, but also Slows the flow down SO its velocity is zero. The A0 port is closed once the E. reaches the end Of the channel. With this timing, the velocity in the entire channel is zero, and the exhaust gas is partially expanded (Zone IV). The channel next reaches the low pressure part of the wave pattern. The flow is again initiated by the Opening Of the E0 port. This sudden Opening generates a new expansion wave (E2), which reduces the pressure Of the exhaust gas to its final state (Zone Vgas). E2 also increases the velocity Of the fluid, forcing it out Of the E0 port. 27 When the expansion wave reaches the inlet side Of the channel, the AI port is also opened. Due tO the induced velocity by the expansion wave, the air from the port moves into the channel (Zone Vair). The gas/air interface appears again, and moves towards the outlet side Of the channel, scavenging the exhaust gas from the rotor. Once the exhaust gas has been completely removed from the channel, the E0 port closes. Due to this sudden closing, a weak Shockwave (S3) is created. 83 increases the pressure of the inlet air, but also reduces its velocity to zero. Once the Shockwave reaches the inlet Side Of the rotor, the AI port is closed. This results in a channel full of flesh air with zero velocity (Zone I). The channel is now at the same initial conditions as the beginning of the wave pattern, and is ready to begin the cycle again. Once the wave pattern has been established, it is possible to calculate the port timings and other design variables. The port timings will largely be dependant on the time required for the shockwaves and expansion waves to travel across the rotor. The gas dynamics behind the operation Of the wave disc are governed by the following set Of equations [3]. Using these equations, it is possible to calculate the flow velocities and port timings for the wave pattern. Shockwave relations: P2 IT =—— 1 S PI () Lfl+ns I3- 7“ (2) TI _ ’5 y+1 1 ———-TIS y+l w=al\/fi1(nS—1)+I (3) 27 28 I 2_7 1 up =“7'(ns _1) —7+— (4) VHS—Fl: 7+1 Where: 1 — conditions in front of the Shock, 2 — conditions behind the shock, w — velocity Of the Shockwave, up — induced velocity Of the flow behind the wave. Expansion wave relations: Q=1+7-1u2—ul (5) a] _ 2 a] 2 T_2= Fl (6) TI 01 EL 52.: “—2 7" (7) Pl “I {ahead = “I i “l (8) “tail = “2 i “2 Where: 1 — conditions in front Of the wave, 2 — conditions behind the wave, w — velocity Of the Shockwave, uhead —velocity Of the head Of the wave, um“ — velocity Of the tail Of the wave. 29 4.2 IMPROVED WAVE PATTERN With the wave pattern presented in the previous section, the calculations involved are not tOO complex or time consuming, 80 they may be carried out by hand. However, in order to do this, that pattern has some major simplifications. A computer code was envisioned to solve for the wave pattern. This code reduces calculation time and is capable Of solving more complex equations. This enabled the production of an improved wave pattern. The new pattern is more accurate and uses fewer simplifications than its predecessor. The basic wave pattern calculated by the code is similar to the simple pattern presented in the previous section. The improved wave pattern is shown in Figure 18. It adds some significant changes to the gas/air interface and the low pressure portion Of the rotor. The first major enhancement consists Of the change of speed Of the shockwaves and expansion waves when they cross the gas/air interface. The waves move fi'om a low temperature medium to a high temperature medium, or Vice versa. Also, the exhaust gas has a different specific heat ratio, y, than the air. From the aforementioned gas dynamics equations, the Speed of the wave depends on both the temperature and the specific heat ratio Of the air. In general, the waves will move at a higher velocity in the exhaust gas than in the air. This can be noticed on the wave pattern by the change in slope Of the waves as they cross the gas/air boundary. The second improvement on the wave pattern is a more accurate calculation Of the position Of the gas/air boundary. The flow within the rotor is mainly dependant on the Shockwaves and expansion waves. Shockwaves induce the channel flow in the same 30 direction as they propagate. Expansion waves have the opposite effect. As a result, when any wave crosses the gas/air boundary, it should speed it up or slow it down. For example, when the second Shockwave crosses the gas/air interface, it slows it down, since it is moving in the opposite direction than the boundary itself. This can be again seen by the change in slope of the boundary in the wave pattern. When this is taken into account, it produces a much more accurate prediction of the position of the interface. P1 0 _|l_——_ 0.1. l_______ Figure 18. Improved wave pattern for a through-flow wave rotor Using this more accurate prediction for the gas/air interface, it is possible to notice that in a majority Of cases, the compressed air fails to frilly exit through the AO port before it is closed. Therefore, in zone IV, when the channel is at rest between the A0 31 and E0 ports, a portion Of the channel is still taken up by flesh air. This air then exits the rotor through the E0 port, in the low pressure section Of the rotor. A number of important changes were made to the wave pattern in the low pressure section Of the disc. For the Simplified pattern, all the reflected waves within the low pressure portion were ignored. When an expansion wave reaches a boundary, it may either reflect as an expansion or a pressure wave. In this pattern the reflections of the second expansion wave, E2, are taken into account in order to improve the porting design in the low pressure part. The enhanced pattern provides better scavenging Of the exhaust gas before the E0 port is closed. Due to the considerable dissimilarity between the two patterns, the improved wave pattern is again explained in detail, starting flom Zone IV, where the channel is at rest between the A0 port closing and E0 port opening. As before, when the E0 port Opens, a strong expansion wave (E2) is created, traveling to the inlet side Of the rotor. Because this is a strong wave, both the head and the tail Of the wave are taken into account. The AI port is not opened until the tail Of the expansion wave reaches the inlet Side of the channel. When E2 sees the closed boundary at the inlet Side, it is reflected as a weak expansion wave (E3). This wave expands the gas in the channel to a lower pressure, and also slows it down (Zone V). When E3 arrives to the E0 port, it is reflected as a pressure wave (PI). The pressure ratio across the E0 and AI ports is not large enough to create shockwaves. The first pressure wave travels across the channel, increasing the pressure Of both the exhaust gas and air (Zone VI). It also has the effect Of Slowing down the flow, Since it is moving in a direction Opposite to the flow. 32 This process is repeated one more time, creating expansion wave E4, pressure wave P2 and Zones VIII and IX. The closing Of the AI port is timed with the arrival Of the last pressure wave (P2) to the inlet side Of the rotor. This creates the final expansion wave (E5), which decelerates the flow in the channel to zero velocity (Zone X). When this final expansion wave reaches the outlet Side Of the rotor, the E0 port is closed and the charmel is completely at rest. This channel is then used at the beginning Of the next cycle. Multiple waves cross the gas/air interface in the low pressure portion. Each Of these waves has the effect of reducing the speed within the channel. As a result, the gas/air interface is repeatedly slowed down, and may not be able to reach the E0 port before it is closed. If this occurs, an amount of exhaust gas will remain in the channel after the wave pattern is complete, and the next cycle will not start with a clean channel firll Of flesh air. That is the final important enhancement for the new pattern. It allows for recirculation tO occur, if necessary. Therefore, the channel may begin the new cycle with the final portion taken up by exhaust gas. The exhaust gas then exits the rotor through the A0 port. Depending on the design, it may not be possible tO avoid this phenomenon, and some recirculation will occur regardless Of the Operating conditions chosen for the rotor. 33 4.3 l-D DESIGN CODE FOR WAVE DISC In order tO SOlve for the wave pattern and port timings, a 1-D design code was developed at the MSU Turbomachinery Lab [28,29]. This code was developed using MATLAB for a wave rotor used to enhance a gas turbine engine. It was then possible to modify it to apply for a pressure exchange wave disc. The 1-D design code requires a few inputs which need to be determined before it is executed. The inputs depend largely on the application for the wave rotor or wave disc that needs to be produced. The length Of the channel is an important input parameter. This will depend on the overall size Of the device. Also, the pressures and temperatures at the two inlets Of the rotor have to be supplied. The desired pressures at the two outlets must also be given. Among the outputs of the code, the most important are the port timings and the flow velocities along the inlet and outlet ports. The code also outputs mass flow rates and an ideal rotational speed for a wave rotor, but these results cannot be applied to the wave disc due tO their different geometries. The flow velocities, however, can be used tO determine the ideal angles for the inlet and outlet porting. The port timings are used to determine the porting geometry for the wave disc. The wave pattern in the disc remains the same, so the port timings also remain the same. From these timings, it is possible to calculate the porting angles for the wave disc separately. In order tO do this, a rotational speed must be assumed. In most cases, it is calculated flom the number Of cycles required for the disc. For example, if the disc has four cycles, all the porting angles must fit between 0° and 90°. Usually, though, it is best 34 to leave some space between different cycles on the disc, so the rotational speed is decreased slightly to allow this. Furthermore, the code creates a plot displaying the wave pattern and velocities at the inlet and outlet ports. This allows for a quick, visual analysis Of the results. Two sample operating points are given in Table l, with their outputs shown in Figure 19. The output on the left Shows a wave pattern without EGR, where the gas/air interface exits the rotor through the E0 port. The output on the right shows a wave pattern with EGR, where the rotor is not fully scavenged. The exhaust gas exits the channels at the A0 port at the beginning of the cycle instead. Table 1. Sample operating points for 1-D design code, results shown in Figure 19 Operating Operating Point 1 Point 2 L 0.093 m 0.093 m Pl 0.98 bar 0.99 bar P2 2.40 bar 1.88 bar P3 1.80 bar 1.50 bar P4 1.02 bar 1.01 bar T1 300 K 300 K T3 1100 K 1100 K 35 Wave Diagram l Wave Diagram ‘ Operating Point 1 Full Operating Point 2 2..) ' ' ' A, ..... _'Si:avenging2'5 ' ' l f K ) Traces of vii. _. flow 2 0 ' 2 0 / velocities F E g I 5 5 I 5 ” E 1'0 ‘Gas/Air Interface E" :5.) 1'0 ' I" [~- i I 0.5 « 0.5 0 0.02 0.04 0.06 0.08 0.10 0.12 0 0.02 0.04 0.06 0.08 0.10 0.12 Channel Length [m] Channel Length [m] Figure 19. Wave pattern outputs for two operating points. Left — Fully scavenged rotor. Right — EGR Present. The wave pattern and porting design created by the 1-D code are a good starting point for numerical modeling. This preliminary design provides a good approximation for the wave pattern in the rotor. However, it still does not take into account important effects such as centrifugal forces and leakage. The preliminary design produced by the 1- D code needs tO be simulated more accurately, improved, and validated. 4.4 WAVE PATTERN FOR INTERNAL COMBUSTION WAVE DISC ENGINE The external combustion wave disc engine uses a pressure exchange wave disc, which can be designed by the code mentioned in the previous section. The internal combustion wave disc engine uses a completely different wave pattern. It was necessary to develop a separate wave pattern and l—D code only to be used for an IC wave disc engine. 36 Only two ports are present in an IC wave disc engine: the air/fire] mixture inlet and the exhaust outlet. The wave pattern is designed to completely scavenge the rotor before a new cycle begins. No EGR should be present in the channel when combustion occurs. For the inlet, the mixing of the two fluids occurs before the inlet port, and is assumed to be Of even, constant concentration. This fiIel/air mixture is near atmospheric pressure. The exhaust outlet pressure is higher than the air inlet, but significantly lower than the combustion pressure. A me Tl Exhaust Inlet (Air + Fuel) Flow velocity —> Distance Figure 20. Wave diagram for a wave disc with internal combustion The wave pattern developed is shown in Figure 20 and Figure 21. The first is shown in a relative reference flame. The horizontal axis represents the position within the 37 channel, and the vertical axis represents time. The second figure uses an absolute reference flame. The same wave pattern is presented, but shown for a radial wave disc. In this case, the Shockwaves are curved, following the motion Of the rotating channels. The wave pattern begins after the combustion process. At this point, the rotor is filled with combusted gas with a through-flow velocity Of zero. Furthermore, the channel is now at the highest temperature and pressure in the cycle (Zone II). The outlet side Of the rotor is then Opened to the exhaust port, which is at a lower pressure than the channel. This creates a strong expansion wave (E), which travels into the channel. The expansion wave produces two effects. First, it expands the gas in the channel to a lower pressure. Second, it induces a fluid flow in the direction Opposite to that in which it is traveling. This forces the expanded combustion gas out of the channel (Zone 111). When the first expansion wave reaches the inlet Side of the rotor, it is reflected as another expansion wave (E2). At this time, the inlet port is Opened, allowing the flesh air/fuel mixture into the channels. E2 expands the exhaust gas to the same pressure as the inlet air. Both the expanded gas and the inlet air travel into the channel. The gas/air interface becomes visible in this area (Zone IV). When E2 reaches the open exhaust port, it is reflected as a pressure wave (Pl). This pressure wave compresses both the gas and mixture inside the channel, but also Slows it down (Zone V). The pressure wave then reflects as an expansion wave on the Open inlet side of the channel. This reflection process continues with the same effects until the exhaust gas is completely scavenged out Of the rotor. When the gas/air interface reaches the outlet side Of the rotor, the channel is entirely filled with flesh air/fire] mixture (Zone VII). At this point, the last pressure wave 38 (P2) is allowed to reach the inlet side of the channel. Once the pressure wave reaches the inlet and reflects as an expansion wave (E4), the inlet port is closed, preventing any flow flom entering the rotor. A low pressure area is created in the wake of the wave (Zone VIII). At this point, compression is necessary to pressurize the air/fuel mixture to the conditions necessary for combustion. The exhaust port is closed when the last expansion wave reaches the outlet side Of the channel. The sudden closure of the port forces the flow to come to a rest, which creates a strong Shockwave (SI). This Shockwave moves through the charmel, compressing the mixture and decelerating all the flow to a velocity of zero. The wave pattern is complete and the channel is at rest. It contains a compressed air/fuel mixture (Zone I). This mixture can then be ignited, increasing both the pressure and temperature of the channel (Zone II). This returns the channel to the conditions at which the wave pattern can begin again. Exhaust Inlet (Air + Fuel) I; Figure 21. Wave diagram for an internal combustion wave disc shown in absolute reference flame 39 The biggest challenge with modeling this wave pattern concerns how to model the combustion process accurately. Combustion occurs in a constant volume, confined channel. It provides not only a temperature increase, but also a pressure increase. The fuel chosen was hydrogen. The combustion process was modeled using a constant volume adiabatic flame temperature calculation. The flame temperature calculation assumes complete combustion of the reactants, and is capable Of calculating a flame temperature at rich, lean, or stoichiometric conditions. For the stoichiometric calculation, the following reaction balance is used: H2 + %(02 + 3.76N2) —> H20 +1.88N2 (9) The adiabatic flame temperature can be Obtained flom the first law of thermodynamics, simplified for an adiabatic, constant volume process. With no exchange of heat or work, the internal energy of the reactants must be equal to that Of the products. Q — W = AU (10) U.