DEVELOPMENT OF METHODOLOGY FOR DESIGNING WAVE DISK ENGINE BASED ON WAVE DYNAMICS AND THERMODYNAMIC ANALYSIS By Dewashish Prashad A THESIS Submitted to Michigan State University i n partial fulfillment of the requirements for the degree of Mechanical Engineering -- Master of Science 201 4 ABSTRACT DEVELOPMENT OF METHODOLOGY FOR DESIGNING WAVE DISK ENGINE BASED ON WAVE DYNAMICS AND THERMODYNAMIC ANALYSIS By Dewashish Prashad Wave rotor technology is based on p ressure wave compression and expansion wave scavenging in a compressible fluid. This can be used to realize compression and exhaust strokes of an IC engine in a rotating disk, power extraction is governed by turbo - machinery principle and constant volume combustion is achieved which makes the wave disk engine a highly fuel efficient devise for power extraction. Wave disk engine primarily consists of a rotor mounted in housing with inlet and outlet ports carved to implement given port timings. As the rotor revolves each channel outlet faces the housing wall for a fraction of revolution until it gets exposed to the outlet port opening in the housing. At high rp m this event is equivalent to sudden opening of valve in a channel filled with pressurized gas es , which generates expansion waves . The ga s es coming out impart angular momentum to the rotor generating power very similar to a reaction turbine operation. As t he rotor passes the opening port it faces the housing wall, this event is equivalent to sudden closing of val ve which generates hammer shock compressing the air - fuel mixture. When both the ports are closed the spark ignition initiates constant volume combu stion resulting in a pressure gain combustion which provides better fuel efficiency. This work focuses on determining the port timings by detailed study of wave dynamics and related thermodynamics of the process. A Methodology is developed using simulation tools to find the desired design. iii This work is dedicated to my dear parents : Mr Kanta Prasad and Mrs. Roopwati Prasad, my lovely brothers Rohit and Shailesh and all wonderful friends who has supported me throughout the two years of my hard work in achieving this milestone iv A C KNOWLEDGEMENT S I would like to thank Dr. Norbert Mueller, my thesis adviser for his support and inspiration, worked with me on the wave disk project, there inputs have been critica l in every analysis done in this study. I am specially thankful to Dr. Rohitashwa Kiran, my fellow project - mate, who mentored me throughout my study on wave disk engine. Also I want to thank my family and friends (Abhisek Jain, Itishree Swain, Nanda Kumar Sasi, Jessica Mesaros and Anju Kurian) v TABLE OF CONTENTS LIST OF TABLES vii LIST OF FIGURES ix KEY TO SYMBOLS AND ABBREVIA TIONS x i i CHAPTER 1 Introduction CHAPTER 2 S traight Channel Analysis 4 2.1 Straight Channel 6 2.2 Comparison of different channel shapes 11 2. 3 Discussion CHAPTER 3 Analysis of curved rotor shapes 1 4 3.1 Analysis of Rotor A 14 3.1.a) Simulation of Design A of rotor 16 3.1.b) Post Processing of the simulation results 21 3.1.c) Port Timing Calculation 25 3.2 Analysis of Rotor B 2 8 3.2.a) Similar Methodology is applied to this rotor simulation results 29 3.2.b) Simulations for Rotor 33 3.3 Analysis of r otor C 3 6 3.3.a) Chron ological Summary of Simulation 3 9 3.4 Compa rison of Rotor A, B and C 4 1 3.4.a) Discussion 43 3.5 Modified Roto r A 45 3. 5.a) Simulation Summary 47 3.5.b) Chronological Summary of Simulation 49 3.5.c ) Comparison of Rotor A vs Modified Rotor A 51 CHAPTER 4 Conclusion and Future Work 5 2 REFERENCES 5 3 vi LIST OF TABLES Table 1 Quantitative results for the cycle 25 Table 2 RPM 26 Table 3 Time History of the Cycle 26 Table 4 Angular History of the Cycle 26 Table 5 Cycle Summary from Simulations 31 Table 6 Quantitative results for the cycle 31 Table 7 RPM 32 Table 8 Time History of the Cycle 32 Table 9 Angular History of the Cycle 32 Table 10 Quantitative results for the cycle 33 Table 11 Cycle S ummary from Simulations 33 Table 12 RPM 34 Table 13 Time History of the Cycle 34 Table 14 Angular History of the Cycle 34 Table 15 Cycle Summary from Simulations 39 vii Table 16 Quantitative results for the cycle 39 Table 17 RPM 40 Table 18 Time History of the Cycle a 40 Table 19 Angular History of the Cycle 40 Table 20 Comparison of the three rotors 41 Table 21 Cycle Summary from Simulations 49 Table 22 Quantitative results for the cycle 49 Table 23 RPM 50 Table 24 Time History of the Cycle 50 Table 25 Angu lar History of the Cycle 50 viii LIST OF FIGURES Figure 0 : Schematic for Wave disc Engine 1 Figure 1 : Sample image depicting simulation initialization 5 Figure 2 : Schematic of Straight Channel at 7 bar pressure (graph depicts pressure distribution in the channel) 6 Figure 3 : Representation of the Cycle 8 Figure 4 : Diverging Straight Channel 9 Figure 5 : Converging Straight Channel 10 Figure 6 : P - v diagram and T - s diagram 11 Figure 7 : P - v diagram for straight, diverging and converging channel shape 12 Figure 8 : Rotor of WDE, the right side of the figure represent top view. 14 Figure 9 : 2D model of single channel of rotor with outer turbine connected with Vane passage, right hand side depicts just the rotor channel meshed for simulations 15 Figure 10 : Simulation Initialization 16 Figure 11 : EVO : Burnt mixture is rushed out (time =0 ) 18 Figure 1 2 : Intermidiate Step of the EVO mode (time =.05ms) 18 Figure 13 : The pressure at inlet fa lls below atmospheric pressure, the inlet port is opened now: IVO (time =.164 ms) 19 ix Figure 14 : The air - fuel mixture is sucked into the channel, the pressure inside the channel rises up slightly (time = .193 ms ) 19 Figure 15 : The outlet port is closed : EVC (time = .455 ms) 20 Figure 16 : The Shockwave reaches the inlet port resulting in precompression (time=.650 ms) 20 Figure 1 7 : P vs Specific Volume 23 Figure 1 8 : Torque History 24 Figure 1 9 : Depiction of Inlet and Outlet angles 27 Figure 20 : 3D view for Rotor B 28 Figure 21 : 2D Projection for a rotor channel 28 Figure 22 : Sample image durung intermediate time step after exhaust port is opened 29 Figure 23 : P - v diagram and the Torque History 30 Figure 24 : Sample image right before exhaust port is opened 36 Figure 2 5 : P - v and T - s Diagram 37 Figure 2 6 : Torque History 38 Figure 27 : Comparison of Rotor A, B and C 41 Figure 2 8 : Comparison of P - v diagram 42 Figure 2 9 : Torque - History of all three rotors 43 Figure 30 : Mass - flow - rate at the outlet of the rotors. 44 x Figure 3 1 : 3D view of Rotor A - with external row of turbine 45 Figure 3 2 : Modified Rotor Channel with external channel 46 Figure 3 3 : Sample image from simulations, depicting pressure contour after the outlet port is opened 47 Figure 3 4 : P - v ans T - s Diagram 48 Figure 3 5 : Torque History 48 Figure 3 6 : Comparitive P - v diagram 51 xi KEY TO SYMBOLS AND ABBREVATIONS WDE Wave Disc Engine EVO Exhaust Valve Open IVO Inlet Valve Open EVC Exhaust Valve Closed L Length of channel H Height of Channel P Pressure V Specific Volume T Temperature S Specific entopy We Work done during expansion Ws Work done during suction of fuel Q Heat transfer during one cycle Cycle efficiency Wc Work done during compression t1 (EVO) Time period during EVO t2 (IVO) Time period during IVO t3 (EVC) Time period during EVC t4 (IVC) Time period during IVC T Total Cycle Time 1 Angle WDE traverse during EVO xii 2 Angle WDE traverse during IVO 3 Angle WDE traverse during EVC 4 Angle WDE traverse during precompression step e Exhaust Angle for WDE i Inlet Angle of WDE Angular speed of WDE 1 CHAPTER 1 Introduction Figure 0 : Schematic for Wave disc Engine Wave disk engine is a novel internal combustion engine [2] which stands apart in terms of fuel efficiency and power to weight ratio in the domain of small scale power output devices. Wave 2 disk engine utilizes work extraction by reaction turbine mechanism via a rotor revolving in a housing. This is very similar to a gas turbine but the crucial difference is the ability of WDE to achieve pressure gain combustion [3] . There is no external compressor involved for pre - compression but the hammer shock waves generated by sudden closing of outlet port provides pre - compress ion for the fresh air - fuel mixture. Cycle starts right after the combustion end s . The gas inside the rotor channel is at very high pressure and temperature. As the channel revolves to face the exhaust port opening in the stator, the gases starts to rush o ut generating expansion waves. During this transient channel emptying process , there will be a stage where the channel pressure goes below ambient pressure. At this particular time the inlet port opens up and the fresh air - fuel mixture is sucked in. The ga ses are still rushing out at the outlet of rotor channel, the order of velocity magnitude is typically 100 - 200 m/s. As the channel revolves to see the wall at the outlet, a hammer shock is generated as a result of this sudden closing. This compresses the a ir - fuel mixture. When the compression waves reaches the inlet port, the inlet port closes (channel revolves to face wall at inlet). At this point spark is ignited and combustion begins. This cycle is referred as Humphrey - Cycle for When the pre - compression pressure ratio is very low, then the cycle is referred as Lenoir cycle. The unique features of WDE are its constant volume combustion, compression achieved by shock waves hence no m oving element is required and simple physical design which reduces manufacturing cost. Although as the pre - compression is not high therefore WDE belongs to small scale power generation devices. 3 This work investigates design features for WDE by analyzing 3 different proposed design s of rotors. The heart of design is the estimation of port timing. A methodology is developed to obtain the port timings using numerical simulations using Ansys Fluent commercial package. The report begins with basic study of wav e propagation in straight channel, then based on the inferences three proposed designs are analyzed and optimized design is suggested. 4 CHAPTER 2 Straight Channel Analysis Propagation of waves in gases is widely researched phenomenon [1]. As mentioned before, wave dynamics critically affects the determination of port timings [7]. To begin with , propagation of waves in a straight channel is analyzed. Next step would be to investigate effect of change in area or curvature of the channel on t he wave propagation. This understanding will be helpful in optimizing channel shape to achieve pre - compression and desired scavenging. Fluent Simulation start - up details: - Density based solver is used with inviscid flow model. Roe - Fds scheme is used for di scretization with courant number as 1. Explicit formulation for time step is used. Hence the simulation is primarily a marching method in time. 5 Figure 1 : Sample image depicting simulation initialization 6 2 .1 Straight Channel Figure 2 : Schematic of Straight Channel at 7 bar pressure (graph depicts pressure distribution in the channel) 7 The figure 2 represent s the straight channel filled with the exhaust mixture (CO2, N2, H2O) at 7 bar. The as pect ratio of channel is . The exhaust port or outl e t port is opened to atmosphere untill pressure at the inlet port becomes sub - atmospheric, ne x t the inlet port is then opened to take the fresh air - fuel mixture in the channel. When the channel is almost filled the outlet port is closed generating hammer shock wave which compresses air fiel mixture. When the hammer shock reaches the inlet port the inlet port is closed and th e mixture is ready for ignition. 8 Figu re 3 : Representation of the Cycle Exhaust_open Sub - atmospheric P achieved Fuel In Exhaust Port Closed Pre - Compressed mixture 9 Similar methodology is repeated for a converging channel and a diverging channel. The notion of converging or diverging channel is used with respect to the hamme r shock wave motion. Figure 4 : Diverging Straight Channel 10 Figure 5 : Converging Straight Channel At each time step, the properties of fluid in the chamber : Pressure, Temperature, Density and Entropy is saved. This data is post processed to generate P - v diagrams for the whole cycle. Using these diagrams comparat ive study is done between various channel shapes simulated. 11 2.2 Comparision of different channel shapes Figure 6 : P - v diagram and T - s diagram 12 Figure 7 : P - v diagram for straight, diverging and converging channel shape 13 2.3 Discussion From the straight channel analysis it is clear that compression waves are stronger when they see a converging cross - section, hence the rotor should be designed to utilize this fact. But at the same time a converging cross - section can decrease the strength of expansion waves which can result in low torque output. Hence from this point of view the rotor design is subject to optimization. This will be investigated in later part of this study. 14 Chapter 3 : Analysis of curved rotor shapes Keeping the results of straight channel in consideration, this chapter will analyse the curved channels and and corresponding rotor efficiency. 3 .1 Analysis of Rotor A Figure 8 : Rotor of WDE, the right side of the figure represent top view. 15 Figure 9 : 2D model of single channel of rotor with outer turbine connected with Vane passage, right hand side depicts just the rotor channel meshed for simulations 16 3.1 a) Simulations for Design A of rotor : Figure 10 : Simulation Initialization The figure above is the depiction of how the simulation is initialized. Inviscid, density based model in Ansys Fluent is used to simulate the wave phenomenon in the channel. ROE - FDS Explicit [1]. Scheme is used with explicit transiient formulation. Mesh size i s ΒΌ mm. 17 The channel is initialized with 7 bar pressure and 2000K temperature which is chosen to emulate post combustion properties of system. Simulation has three broad divisions : 1) EVO 2) IVO (inlet valve closed) : Inlet port is opened to get the fuel in. inlet boundary condition is f air - fuel mixture pressure and 300K temperature. The Exhaust port is still open. 3) EVC (exhaust valve closes) : The exhaust port or outlet port is closed while the inlet port is still opened. As the solution is intialized and it marches in time, depending on the pressure of the channel the boundary conditions are changed manually to switch EVO mode to IVO and finally into EVC . The idea is when solution starts in EVO mode ie when the outlet po rt opens and expansion waves decreases the pressure of the channel, the inlet port should be opened when the pressure goes sub atmospheric level. This result in suction of fuel which is at higher pressure(1.2 bar, assuming turbocharging or supercharging). Contours of CH4 are tracked to monitor how much fuel has entered, when the channel is almost filled the outlet port is closed ie the outlet boundary shock wave whic h compresses the incoming air - fuel charge. When the shock wave reaches inlet 18 of the channel, the simulation is stopped. The pre - combustion stage is achieved. This methodology is represented in the following contour diagrams and pressure plots. The left image is the pressure plot and the right image is pressure contour. Figure 11 EVO : Burnt mixture is rushed out (time =0 ) Figure 12 Intermidiate Step of the EVO mode (time =.05 ms) 19 Figure 1 3 The pressure at inlet falls below atmospheric pressure, the inlet port is opened now : IVO (time =.164 ms) Right hand side of image below represents the mole fraction contours of methane, the blue color represents burnt gases. Figure 1 4 The air - fuel mixture is sucked into the channel, the pressure inside the channel rises up slightly (time = .193 ms ) 20 Figure 1 5 The outlet port is closed : EVC (time = .455 ms) Figure 1 6 The Shockwave reaches the inlet port resulting in precompression (time=.650 ms) 21 3. 1 b) Post Processing of the simulation results The work done by the gasses coming out from the channel is governed by unsteady flow physics. To calculate the work done in each mode (EVO, IVO,EVC) the first law of thermodynamics is used as applied to a control volume considering all transient t erms. This equation is integrated over time to find the workdone during exhaust stroke, compression stroke and the fuel suction stroke. This is work done by the gases hence the positive sign of W will indicate work output and negative sign will indicate work input. 22 Wc, We, and Ws represent the work done during compression (EVC), exhaust(EVO) and fuel suction(IVO) stages. To use above equations we need the properties of the flow at each time step. Therefore pressure, density, entropy, temperature, mass flow rate, enthalpy, and total energy of the gases inside the channel is averaged over entire volume and at required surface area s of control volum e at each time step. This data is then used estimate the work done by the gases and constructing cycle diagrams. 23 Figure 1 7 : P vs Specific Volume 24 Figure 1 8 : Torque History 25 The P - (specific volume) is constructed by using average pressure and density values of channel at each time step. Similarly torque history is recorded at each time step. As clear from the graph the the torque output is an impulse acting over the channel. The peak of the impulse is goverened by the channel shape and port timings. The quantitative results for the cycle are summarized below : Table 1: Quantitative results for the cycle Wc - 79.34 J We 379.65 J Ws 24.56 J Q 949.2 J 34.25 % 3. 1 c) Port Timing Calculation The port timing can be calculated if the rotational velocity of rotor is known. calculate dusing the energy balance for complete cycle. Wnet is the net work output of the cycle. This value must be equal to the expression : - = work done during one cycle over time interval T or, Wnet = 26 can be calculated as the torque Table 2 : RPM 17000 rpm 1780.24 rad/s Table 3 : Time History of the Cycle t1 (EVO) 1.5 ms 7bar to below 1bar t2 (IVO) 0.9 ms fuel in t3 (EVC) 0.85 ms pre compression t4 (IVC) 3.53 ms C ombustion T 7 ms time period Table 4 : Angular History of the Cycle 1 153 deg Exhaust Angle e = 1 + 2 = 244.8 deg 2 91.8 deg 3 86.7 deg Inlet Angle i = 2 + 3 = 178.5 deg 4 360 deg 27 The angular sizing of the ports is determined on the basis of the time intervals t1, t2, t3, and t4 which are governed by the result of numerical simulations. These values implicitly depends on the aspect ratio chosen for the given channel. For rotor A aspect ratio Length / width = 5. With radial length of the channel is 5 cm. Because of very high rpm requirement owing to low torque output, the combustion should be timed such that ignition should start in next cycle, this implies there is 1 power stroke in 2 revolution, one complete revolution is used for combustion. Hence using the described approach rpm and exact required size of the rotor can be determined. Inlet Angle Exhaust Angle Figure 1 9 : Depiction of Inlet and Outlet angles 28 3. 2 Analysis of Rotor B Figure 20 : 3D view for Rotor B Figure 21 : 2 D Projection for a rotor channel 29 3.2 a) Similar Methodology is Applied to this rotor simulation results Figure 22 : Sample image durung intermediate time step after exhaust port is opened 30 Figure 23 : P - v diagram and the Torque History 31 3.2 b) Ch ronological Summary of Simulation Table 5 : Cycle Summary from simulations Mode (port - setting) Time Iteration number Average P and T Intialization 0 0 7 bar, 2000K EVO 0 0 7 bar, 2000K IVO .91 ms 12204 .9 bar, 1200 K EVC 1.65 ms 212204 1.2 bar, 481.7 K Ignition 1.87 ms 23991 1.55 bar, 471 K Table 6 : Quantitative results for the cycle Wc 17.55 J We 587.54 J Ws 3.35 J Q 1.108 kJ 54.45 % 32 As calculated above the rotational speed is determinjed as : - Table 7 : RPM 10,963 rpm 1148 rad/s Table 8 : Time History of the Cycle t1 (EVO) .91 ms 7bar to below 1bar t2 (IVO) .74 ms fuel in t3 (EVC) .20 ms pre compression t4 (IVC) 3.62 ms C ombustion Time T (1.85 + 3.62) = 5.47 ms time period Table 9 : Angular History of the Cycle 1 59.86 deg Exhaust Angle e = 1 + 2 = 108.53 deg 2 48.68 deg 3 13.20 deg Inlet Angle i = 2 + 3 = 61.83 deg 4 238.32 deg 33 3. 2 c ) The simulations so far were carried out without considering the angular velocity. The simulations are carried out with respect to the frame of motion of the rotor channel itself. Hence it is worth while to investigate the role of centrifrugal forces in the overall thermodynamics of the cycle. To investi gate this a frame motion equivalent to 5000 rpm is given to the mesh. The result are summarised below Table 10 : Quantitative results for the cycle Wc 17.55 J We 587.54 J Ws 3.35 J Q 1.13 kJ 53.45 % Table 11 : Cycle Summary from simulations Mode (port - setting) Time Iteration number Average P and T Intialization 0 0 7 bar, 2000K EVO 0 0 7 bar, 2000K IVO .89 ms 12140 .9 bar, 1200 K EVC 1.54ms 20160 1.2 bar, 481.7 K Ignition 1.75 ms 24270 1.55 bar, 471 K 34 From the comparision of the work done and efficiency number it is concluded that the centrifugal forces doesnot affect the overall thermodynamic cycle of the engine. Table 12 : RPM 10,963 rpm or 1148 rad/s Table 13 : Time History of the Cycle t1 (EVO) .89 ms 7bar to below 1bar t2 (IVO) .65 ms fuel in t3 (EVC) .20 ms pre compression t4 (IVC) 3.73 ms Combustion Time T (1. 74 + 3. 73 ) = 5.47 ms time period Table 14 : Angular History of the Cycle 1 58.54 deg Exhaust Angle e = 1 + 2 = 101.3 deg 2 42.76 deg 3 13.20 deg Inlet Angle i = 2 + 3 = 55.9 deg 4 245.55 deg 35 But from the above tables it is infered that although the centrifugal force doesnot play a significant role in influencing the overall thermodynamic cycle, it affects the time interval during EVO, IVO, and EVC phases hence plays a role in influencing final angular shapes of the ports. Therefore it is concluded that to obtain the final port - timings for a rotor a second simulation with corr 36 3. 3 Analysis of Rotor C Figure 24 : Sample image right before exhaust port is opened 37 Figure 2 5 : P - v and T - s Diagram 38 Figure 2 6 : Torque History 39 3.3 a) Ch ronological Summary of Simulation Table 15 : Cycle Summary from simulations Mode (port - setting) Time Iteration number Average P and T Intialization 0 0 7 bar, 2000K EVO 0 0 7 bar, 2000K IVO .99 ms 13680 .9 bar, 1200 K EVC 1.52 ms 20680 1.2 bar, 481.7 K Ignition 1.87 ms 25959 1.55 bar, 471 K Table 16 : Quantitative results for the cycle Wc 0.0032 J We 1274 J Ws - 500.20 J Q 1.70 kJ 46.9 % 40 As calculated above the rotational speed is determinjed as : - Table 17 : RPM 87933 rpm or 920.83 rad/s Table 18 : Time History of the Cycle t1 (EVO) .99 ms 7bar to below 1bar t2 (IVO) .53 ms fuel in t3 (EVC) . 35 ms pre compression t4 (IVC) 4.95 ms Combustion Time T ( 1.87+4.95 ) =6.82 ms time period Table 19 : Angular History of the Cycle 1 52.2 deg Exhaust Angle e = 1 + 2 = 80.19 deg 2 28.0 deg 3 18.5 deg Inlet Angle i = 2 + 3 = 46.43 deg 4 261.3 deg 41 3. 4 Comparsion of Rotor A,B and C Rotor A Rotor B Rotor C Figure 27 : Comparison of Rotor A,B and C Table 20 : Comparison of the three rotors Rotor A Rotor B Rotor C Wc - 79.34 J 17.55 J .0032 J We 379.65 J 587.4 J 1274 J Ws 24.86 J 3.35 J - 500.2 J Wnet 325.13 J 608.3 J 773.8 J Q 949.26 J 1.108 kJ 1.7 kJ 34.26 % 54.45 % 46.9 % Power 37.81 kw 110.6 kw 113.5 kw 42 Figure 2 8 :Comparison of P - v diagram 43 3. 4 a) Discussion 1. Rotor A is least efficient and has least power output. This is owing to the fact that mass flow rate at outlet is not restricted hence lot of mass goes out at a higher total enthalpy without exchangin g energy. This is il l ustrated from following figures. 2. Rotor C has superior torque output owing to the convergig - diverging shape of outlet . Though the complicated channel shape results in alomost zero precompression 3. Rotor B is most efficient, although the power output is low comparative to rotor C but owing to lesser torque output it will result in more losses in real world operations. 4. The p ower output can be increased if the gases exiting at outlet can further be expa n ded via external turbines. Figure 2 9 : Torque - History of all three rotors 44 Figure 30 : Mass - flow - rate at the outlet of the rotors. 45 3. 5 Modified Rotor A Figure 31 : 3D view of Rotor A - with external row of turbine To simulate the complete cycle for one given channel a simplified passage of rotor channel guide vane and turbine channel is meshed. The figure below depicts the simplified 2D mesh. 46 Figure 3 2 : Modified Rotor Channel with external channel 47 3. 5 a) Simula tion Summary Figure 33 : Sample image from simulations, depicting pressure contour after the outlet port is opened 48 Figure 3 4 : P - v ans T - s Diagram Figure 3 5 : Torque History 49 3.5 b) Ch ronological Summary of Simulation Table 21 : Cycle Summary from simulations Mode (port - setting) Time Iteration number Average P and T Intialization 0 0 7 bar, 2000K EVO 0 0 7 bar, 2000K IVO .532 ms 17500 .9 bar, 1200 K EVC 1.12 ms 28370 1.2 bar, 481.7 K Ignition 1.7 ms 38570 1.55 bar, 471 K Table 22 : Quantitative results for the cycle Wc - 97.60 J We 1223 J Ws - 701..02 J Q 950 kJ 37.31 % 50 In addition work done by external turbine = mass flow rate at outlet of rotor *(total enthalpy at rotor outlet - tot al enthalpy at turbine outlet) = 58.34 J. This gives net work output of 412.79 J . Hence the effective efficiency is 43.45 % As calculated above the rotational speed is determinjed as : - Table 23 : RPM 17000 rpm 1780.24 rad/s Table 24 : Time History of the Cycle t1 (EVO) .99 ms 7bar to below 1bar t2 (IVO) .53 ms fuel in t3 (EVC) .35 ms pre compression t4 (IVC) 3.53 ms Combustion Time T 3.53 ms time period Table 25 : Angular History of the Cycle 1 100.98 deg Exhaust Angle e = 1 + 2 = 155.04 2 54.1 deg 3 35.7 deg Inlet Angle i = 2 + 3 = 89.8 deg 4 360 deg 51 3. 5 c ) Compariso n of Rotor A vs Modified Rotor A Fi gure 3 6 : Comparitive P - v diagram 1. Rotor A when operated with an external turbine in tandem r esults in higher efficiency but the torque output is still low, hence the operating RPM is still high (17000). 2. Modified rotor A has better pre - compression ratio (1.5 against 1.33). Though the increa se in precompreesion is not significantly high 3. We conclude that because of the poor torque output of the rotor A, it is not a feasible design even if topped up with an external turbine. 4. Multiple rows of external turbine is required to enhance the torque o utput of Rotor A. 52 Chapter 4 : Conclusion and Future work Converging shape of rotor channel enhances thermal efficiency by creating stronger compression waves. Torque output is more when a C - D outlet shape is chosen, this weakens the compression wave. Therefore a rotor channel shape is a subject of optimization by balancing this two competing phenomena Current methodology is a handy tool in comparing different rotor shapes. The methodology can be further refined by including gradual valve opening limita tions, effect of viscosity, heat losses across non adiabatic wall, and integrating simulation with combustion models Practical Designs of wave rotor based machines are badly impacted by leakage. 53 REFERENCES 54 REFERENCES [1] Anderson, John, 1995, Computational Fluid Dynamics: the Basics with Applications, McGraw - Hill Science/Engineering/Math [2] ASME Journal of Engineering for Gas Turbines and Power, October 2006, Vol. 128, pp. 717 - 735. [3] - 4069, 2002. [4] Paxson D. E., 1996, "Numerical Simulation of Dynamic Wave Rotor performance," AIAA Journal of Propulsion and Power, Vol. 12, No. 5, pp.949 - 957, (also, NASA TM 106997). [5] Paxson D. E., AIAA Paper 95 - 2800. Also NASA TM - 106997. [6] of Recent Developments in Wave Rotor Combustion - 844, July August 2009. [7] - Micro Wave Rotor Research a t Michigan State University, second International Symposium on Innovative Aerial/Space Flyer Systems, The University of Tokyo, 2005, pp 65 70.