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Abstract- In this paper, numerical solution of beta-type Stirling engine was presented considering its non-ideal regenerator. To this end, the second-order model including thermal and hydraulic losses of regenerator was used and their effect on the output power and efficiency of the engine was obtained. Then, a numerical code was used for calculating dimensional and functional optimum values of regenerator. To confirm the obtained result, the functional and geometrical parameters of the engine made by General Motors Corporation called GPU-3 were used. According to the obtained results, the values of hydraulic and thermal losses in the regenerator were considerable and led to the decrease in the engine power and efficiency by 23% and 8%, respectively. Using the obtained results and numerical code, the amounts of porosity, frequency and length of the regenerator were suggested as less than 0.7, 35 Hz and 24 mm, respectively, in the optimum physical and geometrical conditions of the engine.

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A differential thermal model for simulation of Stirling engines was presented. In the new model polytropic expansion/compression processes were substituted to traditional isothermal or adiabatic models of previous studies. In addition, the developed polytropic model was corrected for various loss mechanisms of real engines. In this regard, the effect of non-ideal operation as well as heat recovery in the regenerator was considered. In addition, non-ideal heat transfer of heater and cooler were implemented into the model. In pressure analysis and evaluating work produced or consumed in cylinders, the effect of finite speed motion of piston was considered based the concept of finite speed thermodynamics. Moreover, the effects of heat leakage in regenerator, leakage effect and shuttle effect were evaluated. Finally, new differential polytropic model were employed on a benchmark Stirling engine so-called GPU-3 and accuracy of models was validated through comparing with experimental results as well as previous models. As thermal performance of Stirling engines are significantly affected by thermohydraulic performance of regenerator in one hand and there are various thermohydraulic models for regenerator, three famous thermohydraulic models of regenerator was integrated into models and through comparison with experimental performance of GPU-3 engine, a more accurate thermohydraulic model was introduced.

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A Stirling engine cycle combined with a SI engine cycle to recover the SI engine exhaust gas waste heat. One dimensional combustion simulation code is prepared for Spark Ignition type engine (M355G) simulation. The accuracy of numerical simulated results has been validated with M355G experimentally. The experimental generated power and exhaust gas temperature vary in the range of 84.1- 176.7 kW and 610-710 , respectively. The 1D code estimates the generated power with maximum 5.9% error and average exhaust gas temperature with 3.8% error in the operating range of the engine. The thermal analysis is done, and the results show that about 25% the part of input energy transfers by the exhaust gas as a waste. The results indicate that by installing a Stirling engine heater on the exhaust pipe of the SI engine can recover about 8.4kW of the waste heat at the best condition. The simulation of Alpha-type Stirling engine is done by GT-Suit program and the Solo V161 experimental results is used for the validation. According to 9% error in generated power calculation for validation, the new Stirling engine is suggested for installing in exhaust pipe. The generated power and thermal efficiency is estimated for Stirling engine in various exhaust gas temperature which occurred in various SI engine working condition. The coupled engines heat balance showed that the thermal efficiency is about 2-3% more than the ordinary one.

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Many variant configurations for Stirling engines have been presented. In Beta and Gamma type configurations, a displacer moves the working fluid between hot and cold sources. Whereas in the Alpha type there is no such a part and it has much simpler structure than the Beta and Gamma type. Therefore in this study, a novel configuration is introduced for Stirling engine the displacer is replaced by two pistons and cylinders. With this replacement, the new configuration can be called 3-Cylinders Gamma configuration for Stirling engine. Similar to Alpha type engine, this configuration has simpler structure and manufacturing process. For evaluation of new configuration, a simulation model of fabricated Gamma Stirling engine is prepared based on new configuration and geometry of ST-500 engine. The modeling is developed in GT-Suit software which is an industry-leading simulation tool. Maximum error between the experimental results and simulation of the new engine is about 20 percent for heat consumption and 14.7 percent for power. Thermodynamic analysis of performance parameters is done after the validation. The thermodynamic analysis results indicate that the increment of engine speed does not have appropriate effect on the performance and it led engine efficiency reduction. On the other hand by increasing the pressure and hot source temperature the engine performance improves and led higher thermal efficiency.

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The usages of stirling engine in many industry such as aerospace, submarines and combined heat and power systems, requires more and detailed analysis in such engines. This type of engine is an external combustion which may use almost any type of fuel. In this article the Nusselt number and friction coefficient of a Stirling engine heat exchanger is investigated numerically. The geometry of this heat exchanger is an arc shape pipe with reciprocating flow. Various parameters such as angular frequencies, type of fluids, working gas pressures, flow regime and heater geometry impact on the Nusselt number and friction coefficient of the heater were investigated. By increasing the angular frequency and the working gas pressure the Nusselt number increases but the friction coefficient decreases. The influences of different working fluids indicated that the Carbon dioxide has the highest Nusselt number. The results also show that the friction coefficient is highly dependent on the flow regime. The comparison between the two different geometry type heaters show that the arc-type geometry led to higher Nusselt number. The friction coefficients of both geometries are almost similar to each other at high frequencies.

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In this paper the modeling of combined heat and power (CHP) system driven by Stirling engine has been discussed. The system consists of one beta type Stirling engine as the prime mover, heat recovery system, power generator and the auxiliary boiler. The analysis of the Stirling engine is a non-ideal adiabatic analysis. To increase the accuracy of modeling, the frictional and thermal losses of Stirling engine are considered in comparison of other previous studies and the non-ideal adiabatic analysis is performed using a developed numerical code in MATLAB software. For model validation, the operational and geometrical specification of the GPU-3 Stirling engine was used and the results were compared with experimental results and other previous models. Then, one beta-type Stirling engine was proposed as prime mover in cogeneration system for building applications. The use of the cogeneration systems in building applications becomes more common, which system from the perspective of the fuel consumption and pollution emission, have a significant advantage in comparison with the other conventional systems. For this purpose, the effects of engine frequency, regenerator length, and heat source temperature on fuel consumption and pollution emission of system were examined and proper engine design parameters were selected. Finally, the electric power and thermal power were achieved 11263 W and 21653 W, respectively, with reduction in fuel consumption and pollution emission of 37% and 42%, respectively.

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In this paper, optimization phase angle of alpha Stirling engine performed step by step method. After studying on the operation of various types of Stirling engines, the effect of the phase angle on the power and efficiency of Alpha Stirling engines was studied. The kinematic modeling of volumetric compression and expansion volumes has been done by ADAMS software. Then, the linearization of the thermodynamic equations was carried out on the basis of analysis of the isothermal and five-volume adiabatic stirling cycles to obtain the initial solution of its effective parameters on the power and efficiency. To optimize the phase angle between compression and expansion pistons, stepwise numerical solution of the stirling cycle was performed. Comparison of numerical solution with experimental data indicates an error rate of less than 5.3%. The simulation results show the optimum phase angle of 103 °. At this optimal angle, the results indicate an increase of 4.8% of the output power rather than the output power at a 90 ° pre-aligned angle. Simulation results indicate an improvement of 1.2% of the Alpha Stirling engine efficiency by adjusting this phase priority angle to the efficiency at 90 °.

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Today, with increasing consumption of non-renewable energy sources, scientists are looking for an alternative for these resources. The Stirling engine is one of the ideas that have recently attracted engineers' attention. The purpose of this study is to optimize the output power and stability of a beta type free-piston Stirling engine. In this regard, at first by deriving the thermodynamic and dynamic equations of the system and combining them, the governing equations are obtained including the nonlinear function of the pressure loss in heat exchangers. The governing nonlinear equations are solved and for the purpose of validation, simulation results obtained in this study are compared with experimental and simulation results presented in the literature. In free-piston Stirling engines, increasing the output power by keeping their stability is very important. Therefore, by performing parametric study, the parameters with more effects on the output power and stability are determined and considered as optimization variables. In order to perform multi-objective optimization of output power and stability of the free-piston Stirling engine, a proper objective function is selected and one of the methods in genetic algorithm is employed using optimization software Modefrontier. Finally, values of variables, before and after optimization and also, percentage of improvements in output power and stability of the free-piston Stirling engine are presented.

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This paper examines the design, manufacture, and analysis a Gamma-type Stirling engine using the solar parabolic collector. The calculation base for designing is so that the size of the solar parabolic collector needed to start the engine is not too large. After finishing the design and manufacturing of the parts, the assembled Stirling engine was initially initiated by a 550W electric heater tested in two non-insulated and insulated conditions for different input power. In the non-insulated state, the Stirling engine has a maximum power of about 68.69W with an output of 12.66%; and insulated mode of Stirling engine maximum watts with an output of 15.72% was obtained. Then we constructed a solar parabolic collector based on the power of the heater used. Designing the collector is such that it has the ability to reflect around 550W. Thus, the diameter of the collector is 1m and its depth is 12cm. This solar parabolic collector provides the power needed by the engine to work during the day. The maximum output power of the solar Stirling engine is about 30W.