Thermoacoustics - Essay Example

Thermoacoustics Introduction The Stirling engine were invented in 1816 by Robert Stirling [1] in Scotland, some 80 years before the invention of diesel engine, and enjoyed substantial commercial success up to the early 1900s. A Stirling cycle machine is a device, which operates on a closed regenerative thermodynamic cycle, with cyclic compression and expansion of the working fluid at different temperature levels. The flow is controlled by volume changes so that there is a net conversion of heat to work or vice versa. The Stirling engines are frequently called by other names, including hot-air or hot-gas engines, or one of a number of designations reserved for particular engine arrangement. In the beginning of 19th century, due to the rapid development of internal combustion engines and electrical machine, further development of Stirling engines was severely hampered. High heat efficiency, low noise operation and ability of Stirling engines to use many fuels meet the demand of the effective use of energy and environmental security [2]. Stirling engine-based units are considered best among the most effective low-power range solar thermal conversion units [3]. In order to analyze and to improve the performance of three main sub-systems of these units, namely the solar receiver, the thermodynamic gas circuit, and the drive mechanism, simulation codes are under development worldwide. In 1980, with fuel crises, Stirling engines become a viable proposition with rapid advances in material technology. This was the second stage of transformation for the Stirling engines. This report provides a literature review on Stirling engine technological development. Number of research works on the Stirling engine is discussed. The aim of this review is to find a feasible solution, which may lead to a preliminary conceptual design of a workable Stirling engine. Future needs of power plants and attractive properties of Stirling engine Future needs and trends Attractive Stirling properties 1. Depleting conventional fuels • Multi-fuel capability • Low fuel consumption 2. Increasing fossil fuel cost • High efficiency (utilization of non-fossil fuels) 3. Utilization of alternative fuels • Multi-fuel capability (utilisation of non-fossil fuels) 4. Demand for low noise and less air-polluting prime mover • Clean combustion • Low noise levels 5. Waste heat recovery [4] • Low temperature operation Thermodynamics of Stirling Cycle Engine Robert Stirling invented the closed cycle regenerative engine and the regenerative heat exchanger. He builds an engine working on the closed thermodynamic cycle and operated. The engine and engine cycle invented by Robert Stirling represented on PV and TS. The cycle consists of four processes namely isothermal compression and expansion and isentropic heat addition and rejection processes in the sequence. Consider a cylinder containing two opposed pistons with a regenerator between the pistons. The regenerator is like a thermal sponge alternatively absorbing and releasing heat, it is a matrix of finely divided metal in the form of wires or strips. The volume between regenerator and the right side piston is expansion volume and between regenerator and left side piston is compression volume. Expansion volume is maintained at high temperature and compression volume is maintained at low temperature. Actual Stirling Cycle Engine The ideal thermodynamics of the Stirling engine have been examined, but the practical realities like adiabatic and or isothermal, internal heat exchangers, cylinder wall heat transfer and the general situations have not been accounted. The effects of the various practical factors that cause the actual engine cycle to deviate from the ideal case are required to be considered separately in order to highlight their influence. The basic four-path cycle will be used as the datum for illustrating the effects of practical factors. The working gas temperature through out the engine will have a tendency to be influenced in an adiabatic rather than an isothermal manner and this will influence the form of the PV. The cylinder walls in fact will not provide a sufficient heat transfer medium to ensure that the cylinder gas temperature remains constant and even the use of tubular heat exchangers does not ensure that isothermal conditions prevail at the entry and exit area of regenerator. Kaushik and Kumar [19] have made thermodynamic evaluation of irreversible Ericsson and Stirling cycles. The analysis made for heat sink losses with engine power output on the basis of ideal gas and perfect regeneration. Shoureshi [20] has tried to optimize cooler, heater and regenerator based on Mach number, operating temperature ratio, and percentage of heat exchanger dead volume. Heat Transfer Phenomenon In Stirling Engine Operation of Stirling engine is caused by variety of heat transfer modes. Costea and Feidt [21] have shown that the heat transfer coefficient varies linearly with respect to local temperature difference of the hot engine components. The regenerator must be able to deal with 4–5 times the heat load of the heater and if it is not capable of doing this then extra load will be imposed on the other heat exchangers. The regenerator may be as near as perfect as possible if the engine is to attain good efficiency values and this means that the gas must be delivered from the regenerator to the cold side of the engine at the lowest temperature and to the hot side at the highest temperature. If this temperature does not prevail then the temperature and thus the pressure of the cold gas will be too high whilst the pressure and temperature of the hot gas will be too low. Because of the regenerator ineffectiveness the gas enters the compression phase of the cycle at state 1′ rather than state 1 and the expansion phase at state 3′ rather than state 3. Chen et al. [22] have developed a combine model for analysis of engine performance with heat losses and imperfect regeneration for a solar-powered engine. The optimum operating temperature for engine operation at maximum power is derived with effect of regenerator imperfection. Wu et al. [23] established a relationship between net power output and efficiency for the Stirling engine with heat transfer and imperfect regeneration . Heat Exchangers in Stirling Engine Heat exchangers are key components in the Stirling engine. There may be three or four heat exchangers in the Stirling engine system. These are illustrated in Fig. 1, which includes a heater, cooler, regenerator and pre-heater (may be optional). The heater transfers heat from external source to the engine working fluid contained within the engine working space. The cooler does just reverse, it absorbs heat from engine working fluid adjacent to compression space and rejects to atmosphere through coolant. The regenerator acts as a thermal sponge alternatively accepting heat from working fluid and rejecting heat back to working fluid. The heat flow in a Stirling engine is shown in Fig. 1. The Sankey plot for heat flow is first made by Zacharias [24] in 1971 and further work is done by Pertescu [25] which shows that the heat exchanger configuration is largely affected by amount of pumping losses [26]. Heater The heat transfer phenomenon in heater is as follows: Convective heat transfer from external heating medium to walls of heater tubes or fins. Conductive heat transfer through outer tube wall surface to inner surface or to root. Convective heat transfer from internal wall of tube to the working fluid. In the relatively simple case of steady turbulent flow analytical techniques are not available. The heat transfer coefficient must then be determined using the well-known Reynolds analogy in its original or in a modified form. This analogy relates heat transfer to fluid friction, using standard non-dimensional parameters. The heater is a difficult heat exchanger to design for the inner tube requirements and outer tube requirements. The design is also affected by the choice of heat source. The outer tube surface will usually experience a high temperature low-pressure steady flow environment. The inner tube surface will experience a high pressure, high temperature, very unsteady flow. The heat transfer coefficients will be significantly different at inside and outside and thus it will be almost evitable that surface area requirements will not be comparable with each other. There are two further constraints, one is the inner to outer diameter ratio will be determined by both pressure and thermal loading and second the optimum diameter ratio may not be in harmony with the surface area needs. All these factors may also be out of step with the frictional drag and dead space requirements. The two parameters, which are of prime importance for the internal heater surfaces are the heat transfer coefficient and the friction factor. With knowledge of these two factors performance of heat exchanger can be assessed and the optimum dimensions of a proposed design can be formulated for given thermodynamic specifications. The rate at which the tube inner wall heat flux can be transferred to the gas depends upon the inner tube film coefficient of heat transfer, the mass flow rate and the specific heat of the gas. The working fluid is mostly pressurized at high density and moving with high velocity so the internal heat transfer process is well developed. Similarly, most metals used for heater tube are good thermal conductors so a good heat transfer takes place by conductance with a small temperature difference. But the combustion system at atmospheric temperature limits heat transfer process due to low density and low velocity of products of combustion. Hence more focus is required on improvement on heat transfer process between hot combustion gases and heater tube. Cooler In principle, the Stirling engines may be air-cooled or water-cooled as like as IC engines. To reduce temperature of working fluid the cooling system of engine required to handle cooling load almost twice than of cooling load of conventional IC engine. As the coolant temperature increases there is considerable fall in thermal efficiency, so it is desirable to have coolant temperature at minimum possible value. The flow conditions are as similar as heater but at the lower temperature. Almost all engine designers have adopted water-cooling and the outer cooler tubes experience the same flow conditions as in conventional engine. The semi-empirical heat transfer coefficients for this condition are better documented, following a large number of investigations and many correlations available in the heat transfer literature NASA Lewis [30]. Regenerator Some of the heat supplied by external source to working fluid is converted in to useful work and while flowing out hot expanded gases from expansion space to the cooler the rest of the heat is stored in a regenerator. After cooling in the cooler and compressing in compression space gases flows back to expansion space through regenerator. The stored heat in regenerator is given back to the working fluid during back-flow. This process is called as regeneration. And the efficiency of the Stirling cycle machine depends on the efficiency of the regeneration process or regenerator. The regenerator of practical engine operates with conditions far away from those assumed for the ideal case. The temperature of working fluid entering the regenerator is not constant because the pressure, density and velocity of working fluid vary over a wide range. The effectiveness of the regeneration process largely depends upon the thermal capacity of the material also. Engine Configuration The elements of Stirling engine include two volumes at different temperatures connected to each other through a regenerative heat exchanger and auxiliary heat exchangers. To fulfill thermodynamic, gas dynamic and heat transfer requirements of the engine, these volumes are required to change periodically. The primary role of the drive mechanism must therefore be to reproduce these volumetric changes as precisely as possible. These elements can be combined to fulfill above requirements by wide range of mechanical arrangements. A comprehensive listing of possibilities of engine arrangement is given by Walker [39]. The drive mechanism is required to be considered when selecting an engine configuration because all mechanisms are not compatible with every engine arrangement. The basic engine parameters are also important which comprises the Beale number [40] namely engine speed, pressure and displacement. Gary Wood [41] of Sun-Power Corp. listed following parameters, which are required to be considered while selecting proper engine configuration. Senft [42] also mentioned that the optimum engine geometry will be based on the following engine parameters: 1. Engine cylinder layout/arrangement 2. Engine mechanism 3. Burner/heater type 4. Displacer and piston construction 5. Type and size of regenerator 6. Crankcase construction The three levels of classifications are (A) Mode of operation  1. Single acting  2. Double acting  3. Single phase  4. Multiphase  5. Resonant  6. Non-resonant (B) Forms of cylinder coupling  1. Alfa coupling  2. Beta coupling  3. Gamma coupling (C) Forms of piston coupling  (I) Rigid coupling   1. Slider crank   2. Rhombic drive   3. Swash plate   4. Crank rocker   5. Ross rocker  (II) Gas coupling   1. Free piston   2. Free displacer   3. Free cylinder  (III) Liquid coupling   1. Jet stream   2. Rocking beam   3. Pressure feedback Working Fluids For Stirling Engine Any working fluid with high specific heat capacity may be used for Stirling cycle engine. With few exceptions the engines in 19th century used air as a working fluid. Most of them operated close to atmospheric pressure. Air was cheap, readily available. The working fluid in a Stirling engine should have following thermodynamic, heat transfer and gas dynamic properties. 1. High thermal conductivity 2. High specific heat capacity 3. Low viscosity 4. Low density For better system performance in addition to above ease of availability, cost, safe operation, storage requirements are also important properties, which should not be neglected. The capability of working fluid in terms of specific heat capacity, thermal conductivity and density is defined by Martini [57] and Clarke [58] which is useful for preliminary selection of working fluid. To determine the best working fluid the whole system performance with different working fluids can be analyzed. The experimental investigation of suitability is difficult and also expensive. Empirical equations derived by Beale [59] do not exist for working fluid assessment, probably because of lack of sufficient experimental data to enable any meaningful correlation to be formed. A simple approach suggested by Walker based on original steady flow analysis is useful for selection of fluid. By using Reynoldss analogy, a relationship between heat transfer and frictional drag in a flowing stream through duct for a system in terms of heat transfer ratio and temperature limits is derived. It is required to simulate engine operation with different working fluids by the available equations so as to select best working fluid. Factors Governing Engine Performance The engine power output from engine specification can be derived by utilizing the Beale number and the West number. William Beale observed that in practice the maximum power output of well-developed engine is roughly proportional to pressure, volume and speed. One important factor that is not taken in to account by Beale correlation is the temperature at which the engine is operated. We have already discussed in Stirling engine simple analysis says that the increase in heater temperature will increase power for a fixed cooler temperature. Beales empirical relation do not contain any temperature effects because most of the engines examined by him had the heater temperature above 650 °C. Iwamoto [62] shows that Beale number is about 0.15 in case of high temperature differential Stirling engine whose heater wall temperature is about 650 °C. The effect of the temperature is considered by West [63]. It was found that West number is about 0.25 in case of 5–150 kW Stirling engines and is about 0.35 in case of smaller power engines. Patrescu [64] derived factor which affect engine performance based on first law of thermodynamics. The method used for the analysis is irreversible cycle with finite speed involves the direct integration of equations based on the first law for processes. A numerical program is written by Altman [65] is also useful for determining engine performance. Regenerator Effectiveness The regenerator effectiveness increases with increase in reduced length and decreases in reduced period. The regenerator design must be such that the heat transfer coefficient and area of matrix of regenerator should be kept maximum possible by maintaining lowest fluid flow rate. The flow in Stirling engine regenerator alternates in many rapid cycles so it is highly probable that only a portion of total gas charge passes through the matrix and some of the fluid may remain in the regenerator. This factor is called as regenerator hold-up. For reduced length less than 10, the effectiveness of regenerator is more for a regenerator with hold-up than the regenerator without hold-up. Regenerator Material Choice of the materials for the regenerator matrix is a matter of concern as it influences the performance of the engine considerably. The efficiency and power output of the engine are function of engine speed for metallic and ceramic regenerator materials. Due to lower permeation rate of ceramics than metals it is found that efficiency and power output of the engine with ceramic-coated materials of regenerator is higher than the metallic regenerator under all speeds of investigation. Working Fluid and Fluid Leakage In a practical engine some leakage of the working fluid-invariably a gas-is inevitable. The pressure within the space is usually higher than the idealized minimum cyclic pressure and this means that because of seal leakage paths the gas will flow out of the system at the high cyclic pressure but tend to flow back in to the system during the compression phase. Both effects reduce the work output of the cycle. The effect of pressure loss due to friction, finite speed and throttling process in the regenerator of the engine is presented by S. Pertescu [25]. Fluid Friction Fluid friction with regenerator mesh becomes more serious issue in Stirling cycle engine. The flow friction is mainly due to size, shape and density of wire mesh and properties of working fluid such as density and viscosity of working fluid. The flow friction consumes power from engine so net power output is reduced. The regenerator material required to selected and system should be designed such that it will cause minimum friction resistance. It is demonstrated that friction factor of simple stacked wire mesh become function of Reynolds number when the aperture size of wire mesh was selected as the representative length scale. Also friction and Nusselt number of porous media are similar to those of simple stacked wire mesh. This result suggests that friction factor decreases gradually with increases in value of Reynolds number. Isshiki [37] and Muralidhar [38] study shows that the there is considerable effect of flow resistance and heat transfer of regenerator wire meshes of Stirling engines in oscillatory flow. Uses, Attractiveness, Obstacles and Opportunities Among the main advantages presented by Stirling engines • Global efficiency of about 30%, which makes them competitive against other small capacity generation technologies. According to Carlsen et al. (1996) for a 40 kW Stirling engine, an increase in the heating gas temperature from 360 °C to 700 °C corresponds to a rise of 25% in efficiency;[67] • high efficiencies during partial load operation • low NOx and CO emissions; • safe operation and low level of noise; • low maintenance cost. It was estimated to range about 0.008 US$/kW h, much lower than typical values for internal combustion engines (0.020 US$/kW h) • the possibility of using a wide variety of fuels; • expected useful life of about 25 000 h • possibility of cogeneration implementation. The disadvantages that can be mentioned are: • Capital costs of Stirling engines are relatively high, mainly because they are currently manufactured in very low quantities. Developers are working to lower costs through a combination of design refinement and material substitution; • few fuels have been tested. Problems may occur when residual fuels are used. Among them we can highlight: rust, tar and particles, which may reduce the efficiency of the heat exchanger. Tests have shown this type of difficulty with LPG and liquid fuels • only small power engines have been tested (9–75 kWe). In the future, engines with 150–300 kWe must be designed and tested [68, 69]; • data regarding reliability and useful life are scarce. Despite the air pre-heating for combustion, the emission level is very low presenting only a few mg/m3 of NOx and CO (NOx emission depends on the maximum temperature and not on pre-heated temperature). The possibility of using biomass as fuel makes Stirling engines attractive for isolated regions where this resource is available and where the electricity supply through the grid is completely unfeasible. If they are compared with other energy alternatives that are commonly used in isolated areas (solar and wind energy, internal combustion engines) and other promising technologies (micro turbines, and fuel cells), biomass fuelled Stirling engines are still more attractive: they have a continuous and stable service, do not need other auxiliary generating sources and eliminate high costs associated with consumption and transport of fossil fuels. Coupling the engine with a biomass furnace or a biomass gasifier is also an option. In the first case the engine will use the energy from the hot combustion gases. A pilot plant designed and tested by the Technical University of Denmark showed an electrical and overall efficiency of 19% and 87%, respectively, when burning 40% moisture biomass [67]. A Stirling engine/biomass updraft gasifier pilot plant was tested in Denmark, showing and efficiency of 0.153%, and its great advantage is a low intensity of ash deposition in the heat-transfer surface of the engine.[68] The use of biomass for electricity generation may perform a very important role in the near future because of the advantages granted by the clean development mechanism (CDM), which is a necessary contribution towards the reduction of CO2 emission levels established by the Kyoto Protocol. Approximately between 8% and 12% of the investments in CDM are forecast to be channelled to Latin America representing 3.670 billion tons of reduced CO2 in the period between 2008 and 2012. This will take place due to the fact that industrialized countries are unable to reduce their carbon emissions in the short term and the less industrialized countries need to develop. Stirling engines are beginning to stage a comeback to the market since the development of the modern ‘free piston’ Stirling engines. [71] The technology is not fully developed yet, and it is not widely used; however, it has good potential because of its ability to attain high efficiency, fuel flexibility, low emissions, low noise/vibration levels and good performance at partial load. [70] Unlike reciprocating internal combustion engines, the heat supply is from external sources, allowing the use of a wide range of energy sources including fossil fuels such as oil or gas, and renewable energy sources like solar or biomass. Since the combustion process takes place outside the engine, it is a well-controlled continuous combustion process, and the products of combustion do not enter the engine. As a result of the continuous combustion process, two power pulses per revolution, and fewer moving parts compared to reciprocating internal combustion engines, Stirling engines have low wear and long maintenance free operating periods, and are quieter and smoother than reciprocating internal combustion engines. [70] The possibility of trading carbon credits (carbon emissions that were avoided by using clean technologies)—today estimated in the range of US$ 3.40 and US$ 7.50 per ton of carbon dioxide in the future—must greatly contribute towards the feasibility of these kinds of project. In relation to biomass, the only commercial technologies available are the steam cycle and the steam engine characterized by their low efficiency. The gasification technology using biomass gasifier/diesel engines sets has not been greatly spread because of operational difficulties and high investment costs. Technologies including micro turbines and fuel cells using biomass gasification are undergoing their initial phase of development. Thus, the Stirling engine presents itself as a promising technology as far as the use of biomass is concerned. Conclusions The Stirling cycle engines have proven its multi-fuel capability to operate with any possible fuel source-liquid, gaseous or solid fuels with wide temperature range. This is an important feature of the engine that it can use abundant heat source from solar radiation, waste heat from industry, heat produced from agricultural waste and so many other low-temperature sources. This particular feature of the engine has keep Stirling engine in focus for design and development for better system efficiency where there is large scope. Stirling engine system is most complicated thermo-mechanical system because of complications in mechanical arrangement caused by phase difference required between compression and expansion spaces and presence of heat exchangers like-heater, cooler, regenerator and auxiliary heat exchangers along with a complicated power control system. The reliable and efficient operation of the engine is depends upon the dynamic behavior of engine mechanism and performance of all heat exchangers, which is interdependent. This difficult task to design a system where thermal, fluid and mechanical design considerations are required to be taken in to account jointly with system optimization. The numerous investigations made by scientists and engineers since from invention of the engine have made a good base line information for designing engine system, but a more insight is essential to design systems together for thermo-fluid-mechanical approach. It is seen that for successful operation of such system a careful selection of drive mechanism and engine configuration is essential. An additional development is needed to produce a practical engine by selection of suitable configuration; adoption of good working fluid and development of better seal may make Stirling engine a real practical alternative for power generation. The study indicates that a Stirling cycle engine working with relatively low temperature with air of helium as working fluid is potentially attractive engines of the future, especially solar-powered low-temperature differential Stirling engines with vertical, double acting, gamma configuration. Works Cited 1. Robert Stirling, Patent no. 4081, Stirling air engine and the heat regenerator, 1816. 2. S. Pertescu, M. Coastea, C. Harman and T. Florea, Application of the direct method to irreversible Stirling cycle with finite speed, Energy Convers Conserv Environ Impact (2002), pp. 589–609. 3. T. Mancini and P. Heller, Dish Stirling systems: an overview of development and status, Trans ASME 125 (2003), pp. 135–151. 4. Shoureshi R, Paynter HM. Low temperature Stirling engine for waste heat recovery. Seventeenth intersociety energy conversion engineering conference, vol. 829284; 1982. p. 1716–20. 5. Schmidt G. Classical analysis of operation of Stirling engine. A report published in German Engineering Union (Original German), vol. XV; 1871. p. 1–12. 6. Urieli and D.M. Berchowitz, Stirling cycle engine analysis, Adam Hilger Ltd, UK (1984). 7. J.R. Senft, A mathematical model for ringbom engine operation, J Eng Gas Turbine Power 107 (1985), pp. 590–595. 8. Rallis CJ. A new constant volume external heat supply regenerative cycle. Proceedings of the 12th IECEC, September 1977. p. 1534–37. 9. Rankine WJM. Thermodynamics. Trans Roy Soc Londan, Part I. 144: 140–6. 10. Finkelstein T. Generalized thermodynamic analysis of Stirling cycle engines. SAE paper no. 118A, 1960. 11. Walker G, Khan MI. Theoretical performance of Stirling cycle engine, paper no. 949A. Proceedings of SAE International Automotive Congress, Detroit, 1965. 12. Berchowitz DM. A new mathematical model for Stirling cycle machine. Proceedings of the 12th IECEC, September 1977. p. 1522–27. 13. K. Makhkamov and D.B. Ingham, Analysis of the working process and mechanical losses in a Stirling engine for a solar power unit, ASME J Sol Energy Eng 121 (1999) (2), pp. 121–127. 14. K. Mahkamov, An asymmetric computational fluid dynamic approach to the analysis of working process of solar Stirling engine, ASME J Sol Energy Eng 128 (2006), pp. 45–53. 15. Urieli and D.M. Berchowitz, Stirling cycle engine analysis, Adam Hilger Ltd, UK (1984). 16. A.J. Organ, Thermodynamics and gas dynamics of Stirling cycle machines, Cambridge University Press, Cambridge, UK (1992). 17. J.R. Senft, Theoretical limits on the performance of Stirling engines, Int J Energy Res 22 (1998), pp. 991–1000. 18. P.C.T. de Boer, Maximum obtainable performance of Stirling engine and refrigerators, ASME J Heat Transfer 125 (2003), pp. 911–915. 19. S.C. Kaushik and S. Kumar, Finite time thermodynamic analysis of endoreversible Stirling heat engine with regenerative losses, Energy 25 (2000) (10), pp. 989–1003. 20. Shoureshi R. General Method for Optimization of Stirling Engine. Seventeenth intersociety energy conversion engineering conference, vol. 829279; 1982. p. 1688–93. 21. M. Costea and M. Feidt, The effect of the overall heat transfer coefficient variation on the optimal distribution of the heat transfer surface conductance of area in a Stirling engine, J Energy Convers Manage 39 (1998) (16–18), pp. 1753–1761. 22. Chen Jincan, Yan Zijun, Chen Lixuan and Andersen Bjarne, Efficiency bond of solar driven Stirling heat engine system, Int J Energy Res 22 (1998), pp. 805–812. 23. Wu Feng, Chen Lingen, Wu Chih and Sun Fengrui, Optimum performance of irreversible Stirling engine with imperfect regeneration, J Energy Conserv Manage 39 (1998) (8), pp. 727–732. 24. Zacharias FA. Advanced development of external combustion Stirling engine. Proceedings of the second symposium on low pollution power system development, 1971. p. 371–8. 25. S. Pertescu, M. Coastea, C. Harman and T. Florea, Application of the direct method to irreversible Stirling cycle with finite speed, Energy Convers, Conserv Environ Impact (2002), pp. 589–609. 26. Organ AJ. Back to back test for determining the pumping losses in Stirling cycle machine. Proceedings of the 17th intersociety energy conversion engineering conference, 1982. p. 1856–61. 27. C. Bergmann and J. Alberto, Numerical prediction of the instantaneous regenerator and incylinder heat transfer of a Stirling engine, Int J Energy Res 15 (1991), pp. 623–635. 28. G. Walker, Stirling cycle machines, Clarendon Press, Oxford (1973) (p. 65–83). 29. Reader GT. The marine Stirling engine. Seventeenth intersociety energy conversion engineering conference, vol. 829287; 1982. p. 1732–37. 30. G. Reader and C. Hooper, Stirling engines, University Press (1983) (p. 29–35). 31. T.R. Knowles, Composite matrix regenerator for Stirling engines, Energy Science Laboratories, Lewis Research Center (2000). 32. Miyabe H, Takahashi S, Hamaguchi K. An approach to the design of Stirling engine regenerator matrix using pack of wire gauges. Seventeenth intersociety energy conversion engineering conference Philip, vol. 829306; 1982. p. 1839–44. 33. Hausen H. An approximate method of dimensioning regenerative heat exchangers. RAE Library Transactions, No. 98, 1931. 34. S. Isshiki and A. Sakano, Studies on flow resistance and heat transfer of regenerator wire meshes of Stirling engine in oscillatory flow, ISME Int J Ser B 40 (1997) (2), pp. 282–289. 35. O. Ercan Ataer, Numerical analysis of regenerator of free-piston type Stirling engines using Lagrangian formulation, Int J Refrig 25 (2002), pp. 640–652. 36. Fette P. About the efficiency of the regenerator in the Stirling engine and the function of volume ratio Vmax/Vmin. Proceedings of the seventh international conference on Stirling cycle machines 95, ICSC-95041; 1995. p. 271. 37. S. Isshiki, A. Sakano, I. Ushiyama and N. Isshiki, Studies of flow resistance and heat transfer of regenerator wire meshes of Stirling engines in oscillatory flow, JSME Int J Fluid Therm Eng, Series B 40 (1997) (2), pp. 281–289. 38. K. Muralidhar and K. Suzuki, Analysis of flow and heat transfer in a regenerator mesh using a non Darcy thermally non-equilibrium model, Int J Heat Mass Transfer 44 (2001), pp. 2493–2504. 39. M. Walker, Stirling cycle machines, Clarendon Press, Oxford (1973) (p. 65–83). 40. W.T. Beale, J.G. Wood and B.F. Chagnot, Stirling engine for developing countries, American Institute of Aeronautics and Astronautics 809399 (1980), pp. 1971–1975. 41. Gary Wood J, Chagnot BJ, Penswick LB. Design of a low pressure air engine for third world use. Proceedings of the 17th intersociety energy conversion engineering. 42. JR. Senft, Optimum Stirling engine geometry, Int J Energy 1 (2001), pp. 1087–1101. 43. C. Bratt, Design characteristics and test results of the United Stirling P40 engine, American Institute of Aeronautics and Astronautics 809397 (1980), pp. 1964–1966. Ross A. Balanced crankshaft mechanism of the two piston Stirling engine. US Patent 4138897, 1979. 44. Philip NV. A report of Philip Stirling engine program. Eindhovan, 1987. 45. Meijer RJ. Hot gas reciprocating engine. US Patent no. 2828601, 1958. 46. Ross A. Balanced crankshaft mechanism of the two piston Stirling engine. US Patent 4138897, 1979. 47. W.T. Beale, J.G. Wood and B.F. Chagnot, Stirling engine for developing countries, American Institute of Aeronautics and Astronautics 809399 (1980), pp. 1971–1975. 48. S.T. Hsu, F.Y. Lin and J.S. Chiou, Heat-transfer aspects of Stirling power generation using incinerator waste energy, Int J Renew Energy 28 (2003) (1), pp. 59–69. 49. W. Rifkin, R. Vincent and O. Benson, Application of free piston Stirling engine, American Institute of Aeronautics and Astronautics 809401 (1980), pp. 1982–1986. 50. Shtrikman S, Urieli I. Linear moving magnet motor/generator for Stirling engine. Seventeenth intersociety energy conversion engineering conference, vol. 829310; 1982. p. 1862–66. 51. Berggren RW, Moyniham TM. Effect of displacer seal clearance on free-piston Stirling engine performance. Seventeenth intersociety energy conversion engineering conference, vol. 829313; 1982. p. 1885–90. 52. Shvangiradze G, Shvangiradze G. Cam mechanism for conversion of piston reciprocating motion in to drive shaft rotary motion. Twelfth international Stirling engine conference and technology exhibition; 2005. p. 325–30. 53. Shoureshi R. General method for optimization of Stirling engine. Seventeenth intersociety energy conversion engineering conference, vol. 829279; 1982. p. 1688–93. 54. Gary Wood J, Chagnot BJ, Penswick LB. Design of a low pressure air engine for third world use. Seventeenth intersociety Energy conversion engineering conference, vol. 829289; 1982. p. 1744–48. 55. J. Senft, Extended mechanical efficiency theorem for engines and heat pump, J energy (2000), pp. 679–693. 56. Martini WR. Stirling engine design manual. Martini Engineering Publication. 57. Clarke MA, Reader GT, Taylor DR. Experiences in the commissioning of a prototype 20 kW helium charged Stirling engine. Seventeenth intersociety energy conversion engineering conference, vol. 829298; 1982. p. 1796–1800. 58. W.T. Beale, J.G. Wood and B.F. Chagnot, Stirling engine for developing countries, American Institute of Aeronautics and Astronautics 809399 (1980), pp. 1971–1975. 59. Z. Gu, H. Sato and X. Feng, Using supercritical heat recovery process in Stirling engines for high thermal efficiency, J Appl Therm Eng 21 (2001) (6), pp. 1621–1630. 60. L. Berrin Erbay and H. Yavuz, Analysis of the Stirling heat engine at maximum power conditions, Int J Energy 22 (1997) (7), pp. 645–650. 61. S. Iwamoto, K. Hirata and F. Toda, Performance of Stirling engines, JSME Int J 44 (2001) (1), pp. 140–147. 62. C.D. West, A fluidyne Stirling engine, report no. AERE-R 6776, Harwell University (1981). 63. S. Patrescu, M. Costea, C. Harman and T. Florea, Application of the direct method to irreversible Stirling cycles with finite speed, Energy Convers, Conserv Environ (2002), pp. 586–609. 64. Altman A. SNAP-A Stirling numerical analysis program with user viewable and modifiable code. Thirty-sixth intersociety energy conversion engineering conference, 2001. 65. L. Berrin Erbay and H. Yavuz, Analysis of the Stirling heat engine at maximum power conditions, Energy 22 (1997) (7), pp. 645–650. 66. B. Kongtragool and S. Wongwises, A review of solar-powered Stirling engines and low temperature differential Stirling engines, Renew Sustain Energy Rev 7 (2003) (2), pp. 131–154. 67. H. Carlsen, N. Ammundsen, J. Traerup, , 1996. 40 kW Stirling engine for solid fuels. Proceedings of the European Stirling Forum 1996, vol. 1. Osnabrück, Germany, pp. 139–146. 68. H. Carlsen, J.K. Bovin, J. Werling, N. Jensen, J.F. Kittelmann, 2002. Results from tests of a Stirling engine and wood chips gasifier plant. Proceedings of the European Stirling Forum 2002, CD. Osnabrück, Germany. 69. J. Mc Kenna, , 2003. Game changer: Stirling engines at landfills, Landfill Methane Outreach Program. 6th Annual Conference and Project Expo. 70. CA. Frangopoulos EDUCOGEN, The European educational tools on cogeneration. European Commission. December 2001. 71. Energy Nexus Group. Technology characterization: fuel cells. USA: Environmental Protection Agency; 2002. Appendix Heat exchangers in stirling engine. (Muralidhar, 2001) Read More