print, these pages have been added here for convenience: % Table of regenerator mesh dimensions (Tanaka et al., 1990). There have been several studies that have applied the exergy analysis methodology to ideal Stirling cycle models. This work aims to present a method that can be used by a Stirling engine designer to quickly and efficiently find near-optimal or optimal Stirling engine geometry and operating conditions. 39, 17531761. The function described exhibits these characteristics, and therefore a specialized algorithm is required. Ohio: University of Ohio. 55 and assuming all the heat exchangers are perfectly adiabatic, yields Eq. engine, and allowed me to maintain a copy of this article "A alpha stirling engine Energy, Inc of Boulder, Colorado have

Figure 5 shows that the optimal dead-volume ratio decreases with increasing heater inlet temperature. Energy Res 22, 9911000. <>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 595.32 842.04] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> Stirling engines are poised to play a pivotal role in this industry as they are quiet, have multi-fuel capabilities, produce little pollution and are efficient (Thombare and Verma, 2008). International Stirling Engine Conference by Int. doi:10.1016/j.rser.2006.07.001, Timoumi, Y., Tlili, I., and Nasrallah, S. B. cylinders which are connected in series by a heater, regenerator and Thermodynamic analysis of a Stirling engine including dead volumes of hot space, cold space and regenerator. Keveney has done an animation showing 3 0 obj Robert Stirling some 200 years ago, at the time the engine received some attention and saw commercial use (Stirling, 1816). International Stirling Engine Conference, Creative Gnielinski, V. (1975). each cycle of the four cylinder machine. This paper presents the exergy analysis and optimization of the Stirling engine, which has enormous potential for use in the renewable energy industry as it is quiet, efficient, and can operate with a variety of different heat sources and, therefore, has multi-fuel capabilities. Senior The equation for rate of entropy generation in the cooler Sgen,k is defined as Eq. This reduces the computation time as the AdamsBashforth method does not require the computation of intermediate steps but only uses previously computed derivatives, resulting in greater computational efficiency (Faires and Burden, 2010). doi:10.1016/S0360-5442(96)00159-4, Erbay, L. B., and Yavuz, H. (1999). New equations for heat and mass transfer in the turbulent flow in pipes and channels, in NASA STI/Recon Technical Report A, Berlin, Vol. The D-90 Yoke drive Alpha Stirling engine described in his Sustain. To model the engine, some of the variables are fixed, and Table 1 gives these variables and their values. Raleigh: SIAM. The ideal adiabatic model was developed by Urieli and Berchowitz as a means of more accurately modeling the real Stirling cycle. alpha stirling engine The gas compressors are then used to drive a gas turbine However, the equations outlined in the previous section exhibit several characteristics that make optimization of the objective function unsuitable for classic gradient based algorithms. The reason for this decrease in effectiveness is that the optimal engine speed decreases with increasing heater inlet temperature, this decreases the heat transfer coefficient in the heater and the surface area in the heater also decreases as the optimal dead-volume ratio decreases and the void volume of the regenerator increases. Equation 35 is the Darcy friction factor fD in the regenerator and is calculated using the maximum Reynolds number Remax (Tanaka et al., 1990). doi:10.1016/j.energy.2012.04.060, Costea, M., and Feidt, M. (1998). The Stirling engine has also been cited as being the most economically viable solar converter in the range of 5100 kWe (Kongtragool and Wongwises, 2003). In the analysis, the working fluid is assumed to be an ideal gas and a finite heat capacity rate is assumed in the heater and cooler, the number of heater and cooler tubes are also fixed. 55. with a gas turbine output stage, as shown in the following schematic Figure 6 is a plot of optimal swept volume ratio versus heater inlet temperature. Energy 33, 21342144. The working fluid is assumed to be pressurized air which behaves as an ideal gas. The mesh types and their properties can be seen in Table 2. 51. Figure 7. rotational motion minimizes the piston side forces normally License. de Boer (2003) showed the importance of including pressure drop in his analysis of the Stirling engine regenerator, where he proved the maximum achievable efficiency for a Stirling cycle engine is half of Carnot efficiency. Wills, J. United Kingdom Patent 4081. Figure 5 is a plot of optimal dead-volume ratio versus heater inlet temperature. It is shown that the net-work output and efficiency increase with increasing heater inlet temperature. The analysis has shown that the optimal regenerator length increases and that the optimal engine operating frequency decreases with increasing heater inlet temperature. Diagram of the alpha type Stirling engine. The reason for this is that as the heater inlet temperature increases, the optimal operating frequency decreases; thus decreasing the working fluid mass flow rate through the heat exchangers. When calculating the pressure drop P in the heat exchangers, the Reynolds friction factor fr approach is used as this results in the change of pressure drop sign with change in flow direction (Berchowitz and Urieli, 1984). The methodology used to optimize the 1,000 cm3 alpha type Stirling engine for maximum work output with a fixed energy input is presented in this section. While using this methodology, it has been emphasized that it is crucial to optimize the system in its entirety, rather than as individual components (Bejan, 2006). separate cylinders. doi:10.4271/600222. swashplate, resulting in a pure sinusoidal reciprocating motion (2017). This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The ideal adiabatic model assumes that there is negligible pressure variation throughout the engine. The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. This positively affects the engine performance as the higher effectiveness of the regenerator reduces the heat transfer irreversibility, thus decreasing the total irreversibility rate. The analysis conducted by Finkelstein was the first of its kind and represented a major advancement in Stirling engine analysis when he considered non-isothermal working spaces (Finkelstein, 1960). 12. The analysis shows the significant effect that the choice of regenerator mesh has on engine performance and the size of the optimal regenerator given the specified mesh dimensions. The conductive thermal bridging loss Qcond is included in the analysis, as heat is conducted between the hot and cold parts of the engine (Ahmadi et al., 2016). Energy 31, 345359. Finkelstein, T. (1960). J. Int. Stirling engine/generator. The outer loop computes the energy input; the middle loop computes the temperature difference for adequate heat transfer in the cooler, and the inner loop computes the solution to the ideal adiabatic model equations. In these models, a variety of losses are quantified, and included in the analysis to predict the output of a real engine operating at specified conditions (Walker, 1980). there are no side loads on any sliding bearings. Physica D 239, 13181328. Manag. However, with the extensive work carried out by Berchowitz and Urieli (1984), the models have been significantly sped up, and more than 30 years later computing speed has also drastically increased.

Analysis and design consideration of mean temperature differential Stirling engine for solar application. The WN200 mesh also gives the lowest pressure drop of all the mesh types, this means that the engine with the WN200 mesh type will operate at a higher frequency which increases the work output of the engine. Therefore, the mass differential is defined as Eqs 1315. <> The heater and cooler external fluids are assumed to have finite heat capacity rates, and four different regenerator mesh types are used in this analysis. 53. stirling Defining the exergy of the engine yields Eq. Energy Convers. In this diagram, the operating frequency f, volume V, and heater, cooler, and regenerator lengths L are shown. 20. The properties shown are pressure P, temperature T, and volume V. The compartments are the compression space c, cooler k, regenerator r, heater h, and expansion space e. The compartment interfaces are the compression space to cooler interface cb, the cooler to regenerator interface, the regenerator to heater interface and the heater to expansion space interface. engine, the Ford-Philips 4-215 engine, is used as a case study in the J. Appl. Berchowitz, D., and Urieli, I. Alpha engine which avoids the use of a x]YF~W6HGBp854c3l$aDd_nf @;;b3++/v5_zt/62mwOv? Figure 12 is a plot of optimal operating frequency versus heater inlet temperature for the four different regenerator mesh types. of a high specific power and most important, high reliability and This update allows for the inverse Hessian to be approximated quickly and efficiently. Along with these fixed parameters, four different mesh types are used in the optimization. Therefore, the equation for the rate of entropy generation in the regenerator Sgen,r is defined as Eq. Figure 11 is a plot of optimal heater effectiveness and optimal cooler effectiveness versus heater inlet temperature for the four different mesh types. (2012), used a similar model to maximize the non-dimensional engine efficiency at specified conditions. Defining the objective function by substituting Eqs 51, 52, and 55 into Eq. The reason for this is that the WN200 mesh offers the greatest surface area per unit volume and the WN50 mesh yields the lowest surface area per unit volume. stirling engine alpha sustainable motor energy energie steam power solar alternatieve tourism shelf torque This ingenious mechanism for transferring dual piston motion into 75, 816. Copyright 2022 Elsevier B.V. or its licensors or contributors. 39, 727732. We use cookies to help provide and enhance our service and tailor content and ads. 57. Figure 3 shows that as the heater inlet temperature increases the maximum net-work output increases and the minimum irreversibility rate decreases. and Gamma 56. 7, 131154. (1996). Therefore, Eq. Senft used the classical Schmidt analysis and conducted an analysis that looked to find the optimum engine geometry of a Stirling engine (Senft, 2002). 3 calculates the volume in the expansion space using the clearance volume Vecl, swept volume Ve,swept, crank angle , and phase difference . Equations are required to determine the volumes from the geometric variables for the heat exchangers. Optimum Stirling engine geometry. This algorithm was developed for noisy problems where derivative information is too difficult to obtain or is inaccurate. compact multiple cylinder configuration, enabling an extremely high Furthermore, the Stirling engine is categorized as a Reitlinger class cycle, which means it can theoretically achieve Carnot Efficiency (Senft, 1998). A review of solar-powered Stirling engines and low temperature differential Stirling engines. First, the model and the ideal adiabatic model of the Stirling cycle are presented. Theoretical limits on the performance of Stirling engines. TB-O conceived the analysis and revised the manuscript. Defining the second law mathematically in terms of crank angle , yields Eq. Energy 3, 4567. This is seen to be most pronounced in the WN200 mesh as this mesh is the finest mesh thus offering the greatest heat transfer area per unit volume, whereas the WN50 offers the lowest heat transfer area per unit volume. The quasi-Newton method used is the BroydenFletcherShannoGoldfarb update. engine stirling alpha configuration diagram rotary displacer sterling power jots innovative fleet sustainable applications generation vehicle private This included a The study conducted by Martaj et al. storage systems, hot water and space heaters, and the SolarHeart arrangements. Defining the temperature differentials in the compression and expansion spaces, yields Eqs 21 and 22. The WN200 mesh is seen to perform best of the four mesh types analyzed, giving the greatest net-work output and efficiency. Upon further inspection of the results, it can be deduced that there exist design points that give lower irreversibility rates. Eq. Analysis (Adam Hilger, 1984), pages 25 31. stirling engine sketchup cylinder section created open project config belpasso musings alpha tom doi:10.1002/(SICI)1099-114X(199809)22:11<991::AID-ER427>3.0.CO;2-U, Senft, J. R. (2002). The pistons are typically driven by a (2008) presented a new model of the Stirling cycle. The optimal volume ratios, optimal heat exchanger geometry, and phase angle are also presented along with a discussion of the trends seen in the optimal variables. 42. The conditional temperatures which depend on the direction of fluid flow in the heater and cooler are Eqs 27 and 28. These effects should be considered as they would affect the heater and cooler working fluid temperatures and, thus, engine performance. cooler. and will also be used as a case study of this web resource. Energy ThermoHeart 25kW Engine Overview) The analysis and optimization procedure found the optimal geometry and engine speed that gave maximum net-work output at the fixed heat input. This decreases the NTU in the heater, resulting in a decrease in the effectiveness. doi:10.1093/ijlct/ctu030, Babaelahi, M., and Sayyaadi, H. (2015). 2018 The Author. Renew. Energ. The expressions for the compression and expansion space volumes are Eqs 2 and 3. A diagram of the alpha type Stirling engine used in the analysis can be seen as Figure 1. Heat Transfer 5, 911915. Figures 9 and 10 show that the cooler and heater tube lengths and diameters decrease with increasing heater inlet temperature. Where exergy is defined as the energy that is available to do work. Optimal phase difference versus heater inlet temperature. J. This results in a decrease in heat exchanger surface area that affects the heat transfer performance. Figure 11 shows that the cooler and heater effectiveness decreases with increasing heater inlet temperature. doi:10.1016/j.rser.2014.07.113, Erbay, L. B., and Yavuz, H. (1997).

J. Similarly, Costea and Feidt (1998) conducted an analysis looking at the irreversibility and the effects that the heat exchanger area had on Stirling engine performance. is shown below: Andy Ross of Columbus, Ohio has been designing and Implicit Filtering. 49. Opinions expressed and conclusions drawn are not necessarily attributed to the NRF and UCT. Energy Convers. Rearranging Eq. 50.

The study conducted by Campos et al. There have been several studies that have aimed to predict and optimize engine performance using numerical models.

______________________________________________________________________________________, Stirling Cycle Machine Analysis by Figure 2. including evacuated of these Rocker-V Rev. License, 2016 The equation for rate of entropy generation in the heater Sgen,h is defined as Eq. compression space of the adjacent cylinder via a series connected Thombare, D. G., and Verma, S. K. (2008). Figure 4. Tanaka, M., Yamashita, I., and Chisaka, F. (1990). These equations use the number of heater tubes Nh, heater length Lh and heater tube diameter Dh. 47 into 46 yields the entropy generated per cycle Sgen which is Eq. Boston: Brooks Cole. 57 which is the objective function for the net-work output of the engine. Advanced Engineering Thermodynamics. 54.

Walker, G. (1980). (1998) formulated criteria to optimize the heat transfer area in the heater and cooler. The variables which have been optimized are the total heat exchanger length, dead-volume ratio, regenerator length, heater tube length, cooler tube length, compression space to expansion space volume ratio, phase difference, and the operating frequency. The model outlined assumes finite heat capacity rates in the heater and cooler. The full derivation of the equations is not presented but the equations are listed and briefly explained. engines were built by students for a Wu, F., Chen, L., Wu, C., and Sun, F. (1998). Equation 43 quantifies the conductive thermal bridging loss, which is calculated using the regenerator thermal conductivity kcond, the conduction area Acond, the regenerator length Lr, and the heater temperature Th and cooler temperature Tk. complete solar heat and power cogeneration system for home usage A numerical example of a 1,000 cm3 engine is presented, where the geometry and operating frequency of the engine are optimized for four different regenerator mesh types, varying heater inlet temperature and a fixed energy input of 15 kW. 33, 283289. engine stirling alpha drawings imperial These relations are for flow in the turbulent regime, seen as Eqs 36 and 37. the 1970's N V Philips, of Holland, and the Ford Motor Company stirling engine alpha heat motor exchangers diy plans engines gas does energy exchanger kits cold homemade generator temperature pistons separate It can also be seen that the WN200 mesh gives greater performance than the other mesh types. Energy Res 26, 10871101.

The energy equations that describe the heat absorbed and rejected in the cooler, regenerator, and heater are Eqs 2931. The plot shows that there is an optimal phase difference for each heater inlet temperature and that the optimal decreases with increasing heater inlet temperature. stirling Assuming, the overall heat transfer coefficient U in the heater and the cooler is equal to the heat transfer coefficient h on the inside of the tubes, this in turn is used to compute the number of transfer units (NTU), seen as Eq. Andy Ross' many "youtube" videos shows a unique balanced 17. Once this convergence is reached the mass flow rates and energy values are used in the outer loop to compute the new heater and cooler gas temperatures. Technological development in the Stirling cycle engines. This paper presents a novel approach to modeling the losses and optimizing the alpha type Stirling engine, which involves the application of exergy analysis methodology to the ideal adiabatic model of the Stirling cycle. Energy 22, 645650. (2006), applied the exergetic, energetic and entropic analysis techniques to the Stirling cycle to optimize the performance. In the case of the cooler and the heater unidirectional smooth pipe flow relations are used to calculate the Darcy friction factor fD (Joseph and Yang, 2010). Figure 13. Maximum attainable performance of Stirling engines and refrigerators. However, the volume allocation is not near the optimal thus giving poorer overall engine performance. stirling alpha engine doi:10.1016/j.renene.2005.03.012, Martaj, N., Grosu, L., and Rochelle, P. (2006). Figure 12. book by I.Urieli & D.M.Berchowitz Stirling Cycle Engine stirling engine alpha protoype half done belpasso musings tom For the cooler, regenerator and heater the volume and temperature are assumed to be constant. been developing low temperature (150C 400C) Alpha Stirling doi:10.1002/er.838. Applications). However, at the time the rapid development of the internal combustion engine quickly overshadowed the Stirling engine. The reason is that the optimal engine operating frequency decreases with increasing heater inlet temperature, thus decreasing the irreversibility rate. Equations 38 and 39 are for the Nusselt number Nu and effectiveness of the regenerator (Tanaka et al., 1990). Energy Convers. 44. The following section presents and describes the equations used to model the alpha type Stirling engine which is optimized in this study. However, due to advances in computing and better models the solutions are arrived at in seconds rather than minutes, making these numerical models suitable for optimization purposes. *Correspondence: Tunde Bello-Ochende, tunde.bello-ochende@uct.ac.za, http://dergipark.ulakbim.gov.tr/eoguijt/article/view/1034000200, Creative Commons Attribution License (CC BY), Department of Mechanical Engineering, University of Cape Town, Cape Town, South Africa. building small air engines since the 1970's, including extremely The GouyStodola theorem, which describes the relationship between reversible work Wrev, irreversible work Wirrev, entropy generation Sgen and environmental temperature T0 (Bejan, 1996), can be seen below as Eq. Thermodynamic study of a low temperature difference Stirling engine at steady state operation. The optimization shows that the WN200 mesh gives the best engine performance of the mesh types analyzed. stream J. compressor. doi:10.1016/j.renene.2007.12.012, Tlili, I., Timoumi, Y., and Nasrallah, S. B. degree phase difference with each piston connected to a gas Energy 44, 902910. The algorithm of choice is the implicit filtering scheme originally developed by Professor Kelley and colleagues (Kelley, 1999, 2011). This significantly affects engine performance as a smaller regenerator has less void volume, which means more of the available dead-volume can be allocated to the cooler and heater increasing the performance of these components. This is then in turn used to calculate the heat transfer coefficient h in the heater and the cooler. This engine was originally developed by Stirling Appl. A significant portion of Stirling cycle optimization studies have moved toward numerical simulations that in the past were too computationally expensive to use for optimization purposes. Assuming, the mass of working fluid remains constant, yields Eq. The WN200 mesh also results in the smallest regenerator in terms of void volume which means that more of the available dead-volume can be allocated to the heater and the cooler. is shown below. the two pistons. 4. The reason for this difference is that the phase difference greatly affects the mass flows through the device and the minimum and maximum engine volumes, thus, influencing the engine performance. The solution is obtained using three iterative loops. Inc came up with an interesting Energy 141, 143159. A new thermal model based on polytropic numerical simulation of Stirling engines. <> The optimal values of several different engine parameters are presented in the work. Optimal dead-volume ratio versus heater inlet temperature. This is because as the heater to cooler temperature ratio increases the portion of heat transferred out of the cooler decreases thus less compression space work is required as this amount of work is directly proportional to the heat load in the cooler. This work was funded by the National Research Foundation (NRF) and the University of Cape Town (UCT). Another reason there are fewer tubes in the heater is that in real Stirling engines the heater may have combustion products flowing through it. presented at the 2016 Depending on the fuel source this may foul the heat exchanger, and therefore the spacing of the tubes is important to facilitate cleaning. Optimal swept-volume ratio versus heater inlet temperature. He has published an article on the model 3:21. doi: 10.3389/fmech.2017.00021, Received: 18 September 2017; Accepted: 30 November 2017; Published: 19 December 2017. expander as shown. This is specified as the performance of the cooler has a far more pronounced effect on engine performance than the heater. 39, 748764. It will be one of the shown below. Stirling Engines (Ross Experimental, These equations use the number of cooler tubes Nk, cooler length Lk and cooler tube diameter Dk. 1 0 obj From these figures, it is seen that as the heater inlet temperature increases, the maximum net-work output and the maximum efficiency increases. There are a variety of different approaches to Stirling engine modeling and there exist several different orders of models (Dyson et al., 2004). 80, 5462. When comparing Figures 911, it is seen that the cooler has a greater surface area and a greater effectiveness than the heater and this is because there are more cooler tubes than heater tubes. Class A Climax Locomotive". No use, distribution or reproduction is permitted which does not comply with these terms. The maximum efficiency plot seen as Figure 4B follows from the maximum net-work output plot seen as Figure 4A.

17 to give the change in mass in the compression and expansion spaces yields Eqs 18 and 19. 52. Optimal regenerator length versus heater inlet temperature. In terms of the heat exchanger geometry, the heater and cooler tubes are seen to decrease in size and the cooler and heater effectiveness is seen to decrease with increasing heater temperature, whereas the regenerator is seen to increase in size and effectiveness. The energy equations which describe the work output of the cycle are Eqs 32 and 33. 1. Parametric study is used to investigate the effect of geometric and operation parameters on the engine performance. doi:10.1016/j.renene.2007.09.024, Toghyani, S., Kasaeian, A., and Ahmadi, M. H. (2014). The plot also shows that the WN200 mesh type gives a higher optimal operating frequency than the WN50 mesh type. using the four cylinder Alpha engine as described in the paper working gas. engine stirling alpha advices smoothly minimized although runs mechanical volume dead yet any doesn ve Manag. There is some degree of numerical noise. The reason for this is that with increasing temperature difference between the heater and cooler the optimal dead-volume ratio decreases. At the time of the development of these models the iterative schemes took too long to solve, to make the model useful in the optimization of Stirling engine geometry. This scheme is run within the outer loop which changes the engine operating frequency until the desired energy input is obtained. Beta, There have been several studies that have looked at Stirling engine power density. Equation 40 is the Gnielinski relation which is used to calculate the Nusselt number in the heater and the cooler (Gnielinski, 1975). Using the definition of effectiveness to define the temperatures leaving the regenerator is seen as Eq. The reason for this is that as the heater inlet temperature increases the amount of energy absorbed per cycle increases, thus the required operating frequency to absorb the specified input energy decreases. Analysis of the Stirling heat engine at maximum power conditions. Design class at Ohio University in 2001, The mass flows through the compartment boundaries are defined as Eqs 2326.

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