Article

Simple-II: A new numerical thermal model for predicting thermal performance of Stirling engines

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... Because it only incorporates imperfect regeneration and tends to ignore major thermal and power losses, which are illustrated in Figure 13. In order to overcome this issue studies, 40,44,46 dedicated to encompassing these losses in the original adiabatic model were made to enhance the practicability of the model. Consequently, the basic ordinary differential equations of simple analysis were altered and improved to include the shuttle effect and mass leakages of the gas. ...
... These losses were incorporated in the model by subtracting their quantitative values from the total power output of the modified simple model. The following expression was obtained after including the shuttle effect in the energy equation of simple analysis in Equation (23), After including the shuttle effect in the previous energy equation given in Equation (23), the following expression was obtained 40 : ...
... For detailed derivation of the equations refer to previous works. 40,44,46 ...
Article
Modeling with optimization has become a ubiquitous practice in the field of Stirling engine. A plethora of studies in the literature is dedicated in developing a feasible optimized model that can precisely predict the performance of Stirling engine. Hence, the purpose of this article is to compile and expansively review the thermodynamic models and optimization efforts made in pursuit of performance enhancement of the Stirling engine. An extensive range of models available in the literature is painstakingly discussed. Likewise, a wide variety of available optimization techniques spanning from conventional experimental and univariate methods to more complex multiobjective optimization approach are critically reviewed. A comparative analysis of the models is carried out based on the accuracy of their predictability of the performance of Stirling engines. Results obtained from the models are validated through the experimental data of the GPU‐3 Stirling engine prototype. Several optimization techniques are investigated based on the effective and efficient optimization of operating and geometric parameters of the Stirling engine. The review concluded that the Comprehensive Polytropic Model of Stirling engine (CPMS) demonstrated better accuracy in comparison with other models. In addition, the multiobjective particle swarm optimization (MOPSO) technique was found to be effective and computationally efficient.
... Researchers are studying how to find a replacement for these engines that can provide simple utilization of renewable energy and have more scientific and economic justification. In this regard, the Stirling engine has received much attention recently (Babaelahi and Sayyaadi, 2014;Martini, 1983;Toghyani et al., 2014;Duan et al., 2014;Bayón et al., 2002;Bayon and Suarez, 2000;Boubaker et al., 2013;Motsa and Shateyi, 2012;Finkelstein, 0000;Deac, 1994;Tlili et al., 2008;Ahmadi et al., 2017;Abuelyamen et al., 2017;Almajri et al., 2017;Xiao et al., 2017a;Cheng and Yu, 2011;S et al., 2007;S. Scollo et al., 2013;Liao and Lin, 2015;Hooshang et al., 2015). ...
... Babaelahi and Sayyadi considered mechanical friction and heat loss and introduced a new numerical thermal model called Simple-II. This model, which was examined by the Lewis Research Center, was found to be more similar to the actual model (Babaelahi and Sayyaadi, 2014;Martini, 1983). Some researchers have modeled the engine with CFD models and achieved good results (Abuelyamen et al., 2017;Almajri et al., 2017;Xiao et al., 2017a). ...
... Assuming the isothermally of the Schmidt theory and that there is no dead volume in any of the engine compartments including the recovery and also in the connecting tubes, the pressure can be obtained as a function of the rotation of the crank angle (β) as follows (Babaelahi and Sayyaadi, 2014): (Egas and Clucas, 2018). ...
Article
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Nowadays, attractions are focused on Stirling engines because of their low noise, external combustion, and the possibility of employing solar energy. These engines can be designed and applied in cases of low or high-temperature differences, as needed. Evidently, the cylinder’s layouts and how they are arranged and the used movement mechanism can affect the engine performance. Experts and Engineers are always looking to increase efficiency and also increase the output work of the Stirling engines. In this study, the dimensional synthesis of the kinematic chain using in the Stirling engine will be discussed. For this purpose, kinematic relationships of different layouts of Stirling are extracted, and by optimizing the mechanism based on the maximum output work, the optimal values of the geometrical parameters of the mechanism and the lengths of its links are obtained. Evolutionary optimization Algorithms, including genetic algorithm, particle swarm optimization, and imperialist competition algorithm methods are employed to optimize the problem, and their obtained results are compared. The problem is solved for four different layouts of the Stirling engine. Based on the results, the output work can be increased 9 to 14 times by varying the geometrical parameters of the Stirling engine mechanism without considering changes in thermodynamic parameters, high-temperature, and low-temperature values. Moreover, average improvement (between three optimization algorithms) for output work is about 13.05, 9.14, 10.71 and 14.36 times for α type with slider-crank, β type with slider-crank, γ type with slider-crank and α type with Ross-Yoke, respectively. Therefore, the α type Stirling engine has better advance than β and γ types, for maximizing the output work based on changing the geometrical parameters.
... Hosseinzadeh and Sayyadi (Hosseinzade and Sayyaadi, 2015) offered the CAFS model (Combined Adiabatic-Finite Speed) and expressed that the power output and efficiency of the CAFS model had good agreement with the empirical results of the GPU-3 engine. Babaelahi and Sayyaadi (2014) developed the Simple analysis (Urieli and Berchowitz's work (Urieli and Berchowitz, 1984)) and for the first time added the effects of thermal losses of shuttle and gas leakages to the adiabatic equations. Therefore, the adiabatic differential equations of Urieli and Berchowitz (1984) were modified and the model of Simple ІІ was presented. ...
... Then, the frictional losses including the pressure drop of fluid in the heat exchangers, the mechanical friction between the cylinder and piston and the effect of finite speed thermodynamics of piston have been added. Furthermore, the heat conduction loss between Table 2 Input parameters for analysis of TPES and TCO 2 ER (Chahartaghi and Alizadeh-Kharkeshi, 2018;Chahartaghi and Sheykhi, 2017 Table 4 The operational parameters of the GPU-3 Stirling engine (Urieli and Berchowitz, 1984;Ziabasharhagh and Mahmoodi, 2012 Table 3 The geometrical parameters of the GPU-3 Stirling engine (Urieli and Berchowitz, 1984;Ahmadi et al., 2016;Timoumi et al., 2008;Hosseinzade and Sayyaadi, 2015;Babaelahi and Sayyaadi, 2014;Chahartaghi and Sheykhi, 2018 the cooler and heater, the thermal losses including the non-ideal recovery of the regenerator, and the effect of shuttle are added to the numerical code and the gas temperatures inside the cooler and heater have been corrected through Eqs. (39) and (40). ...
... In addition, because the frictional losses such as mechanical friction between the cylinder surface and piston and effect of finite speed thermodynamics are considered in the current study, to evaluate the thermal efficiency, the thermal efficiency of the current study (non-ideal adiabatic model) is closer to the experimental results compared to the ISAM model (Fig. 9). This non-ideal adiabatic model at lower engine rotational speeds (less than 1500 rpm) has better performance than the Simple ІІ model (Babaelahi and Sayyaadi, 2014), but at higher rotational speeds, the results of the Simple ІІ model is closer to the experimental data than non-ideal adiabatic model. ...
... Over the past decade, efforts have been made to improve the accuracy of the second-order models. This is achieved by better characterization of the engine irreversibilities and losses [5,[10][11][12][13][14]. In this regard, the dynamic model was developed by Timoumi et al. [10] taking various losses into account. ...
... In this regard, the dynamic model was developed by Timoumi et al. [10] taking various losses into account. Later Babaelahi and Sayyaadi [11] developed the Simple II model, a modification to the original Simple analysis, by implementing additional types of losses. In another research, Babaelahi and Sayyaadi [5] presented a new second-order model, called PSVL (polytropic analysis of Stirling engine with various losses). ...
... This relative velocity is applied in zones that are deformed due to the movement of piston and displacer. Here, it is worth mentioning that the effect of viscous dissipation term on the temperature in Eq. (11) can be ignored compared with the effect of heat transfer and compression during the cycle [32]. Also, the turbulent viscosity, μ t , is defined according to the eddy-viscosity models being used. ...
Article
A three-dimensional Computational Fluid Dynamics (CFD) simulation for the GPU-3 Stirling engine is performed. Firstly, the performance of six different eddy-viscosity models are assessed to identify the most appropriate model for the engine simulation. Secondly, a comprehensive characterization of the thermal and fluid flow fields during the cycle is presented. The effects of the unsteady behaviors of both thermodynamics and fluid dynamics on the heat transfer phenomena are also investigated. Results show that the realizable k-ε-enhanced wall treatment model produced the most accurate predictions for engine power with a robust convergence and a reasonable computational time. The average deviation in the CFD results with this model compared with the experimental ones is about 4%. Within the compression and expansion spaces, the dominant heat transfer rates occur during the expansion strokes due to the significant impinging effect of the tumble vortices generated from the flow jetting. Furthermore, the jetting and ejecting processes into the regenerator is characterized by a significant temperature gradient and large matrix temperature oscillation. Also, the temperature profile through the regenerator is almost logarithmic.
... Therefore, the actual power generated by the expansion process is reduced and the actual power consumed in the compression process is increased. As a result, the net power generated by the engine is less than the corresponding power predicted by the classical thermodynamic analysis [41]. ...
... Limited number of researchers [39][40][41][42] took this type of loss into consideration. They used a simple formula to calculate this pressure loss and combined it with the total pressure drop produced within the heat exchangers. ...
... Also, the pressure loss in the cooler tubes and its end-connection represents a considerable value. These results, about the heater and cooler tubes, conflict with the results of Babaelahi and Sayyaadi [41] and Tlili et al., [51]. The pumping loss can be calculated according the following equation ...
Article
Full-text available
A comprehensive characterization of the GPU-3 Stirling engine losses with the aid of the CFD approach is presented. Firstly, a detailed description of the losses-related phenomena along with the method of calculating each type of loss are addressed. Secondly, an energy analysis of the engine is carried out in order to specify the impact of each type of losses on the performance. Finally, the design effectiveness of each component of the engine is investigated using an exergy analysis. The results reveal that the hysteresis loss occurs mainly within the working spaces due to the flow jetting during the first part of the expansion strokes. Additionally, the pressure difference between the working spaces is the main driver for the flow leakage through the appendix gap. The exposure of the displacer top wall to the jet of hot gas flowing into the expansion space during expansion stroke essentially increases the shuttle heat loss. A new definition for the regenerator effectiveness is presented to assess the quality of the heat storage and recovery processes. The energy analysis shows that regenerator thermal loss and pumping power represent the largest part of the engine losses by about 9.2% and 7.5% of the heat input, respectively. The exergy losses within regenerator and cold space are the highest values among the components, consequently, they need to be redesigned
... Hoseyn Sayyadi and Mojtaba [19], presented a new thermal model basing it on the modification of the simple analysis called the Simple-II. They incorporated gas leakage and shuttle effect of the displacer in the basic differential equations. ...
... The efficiency based on output power and thermal were predicted with 20.7% and 7.1% errors, respectively. Summary of the equation set based on the Simple-II method is given in Table 2.1 [19]. Hadi and Hoseyn Sayyadi [20], presented a novel model based on the unification of adiabatic analysis and finite speed thermodynamics known as CAFS (combined adiabatic-finite speed). ...
... By making, m, the subject in equation (19) and substituting it in equation (16) gives, p= p m ⋅√1-c 2 1-c⋅cos(α-δ) (20) ...
Method
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The aim of this project is to design and fabricate a Stirling engine for a display mechanism using solar energy as the heat input. The objective is to convert the heat energy received from the sun into mechanical energy which in turn be used to lift a display of some sort. A Gamma based Stirling engine was thus designed and fabricated based on the zeroth-order and first-order design methods, additionally, a slider-crank the transmission was used for the display mechanism. Two types of heat sources were used during the experimental process, a gas and an alcohol burner with Qin of 100W and 771W respectively. The engine was tested with no loads and with loads, a maximum rotation of 1100rpm was recorded for a temperature difference of 325 °C with the gas burner while a maximum of 502 rpm was recorded for the alcohol burner at the same temperature difference without loads. Subsequently, the transmission system was assembled and via a polyurethane round belt, the connection between the two systems was made. The load on the transmission system was varied, 16g, 38g and 54g and the effect of it on the speed was recorded. From the experiment, the engine could only take a load until 54g. A maximum power output of 0.4W, 0.85W and 0.6W was recorded for the 16g, 38g and 54g respectively in the transmission system. Furthermore, a duration test was also conducted to see how long the engine operated with and without a coolant source, the engine operated 15 minutes without a coolant source, while with the coolant source, it operated for 45 minutes before the seals wore off.
... To determine the output work of the engine, the losses calculated in the simple method should be subtracted from the output work evaluated in the ideal adiabatic analysis. Complete details of the simple analysis procedures and calculating the real performance of the engine are cited in [37,33]. The accuracy and validation of the simple method is verified and cited in [39,40]. ...
... System of ODEs in the ideal adiabatic analysis for the Stirling engine [33,37]. ...
... Mathematical relations derived from thermodynamic analysis for BF-MED configuration presented in Table 3b and Eqs. (25)- (33). This is due to feed water supplying arrangement being interlinked and nonlinear. ...
Article
To meet the raising demands for energy and potable water, integration of power plants and desalination systems for large-scale coproduction have been widely used in the world. However, in remote and rural locations with no infrastructures such as power grids, integration of large-scale systems is not financially viable. This paper presents a conceptual design and a methodology based on the GPU-3 Stirling engine in upstream as prime mover, coupled with three configurations of multi-effect evaporation desalination (MED) unit in downstream to address the power-water demands for areas with lower population. A multi-objective optimization technique is employed to find the optimal design parameters of the proposed hybrid system. Three objective functions namely maximizing power and water production and minimizing the cost of products are considered. Decision-making tools are implemented on the optimal points of each configuration to select the optimized configurations for each cogeneration system. The most effective system is then introduced by implementing Analytical Hierarchy Process (AHP) technique. It is found that the final selected system is capable of delivering 2.58 kW of electricity and 19.92 m³ fresh water per day with 2.07 $ ∙ hr⁻¹ cost of products which can be divided into 0.29 $ ∙ kWhr⁻¹ and 1.6 $ ∙ m³ for power and water, respectively.
... • The decoupled (second-order) analysis takes the outcomes of the ideal analysis and improves the result, considering a selected number of main losses [65,87,89,141,159]. ...
... The energy losses are assumed to be decoupled from one another in all second-order models. Several authors use this analysis [20,65,73,80,87,89,141,159]. ...
... The system of the above ideal adiabatic differential equations was modified by including the effects of gas leakage from working space to buffer space (crankcase) and shuttle heat losses by displacer from compression to expansion spaces. This is by adapting and modifying the engine models (simple model by [20] and Simple-II model by [89]) to the refrigeration machine through reversing the process. The main reasons for the inclusion of mass leakage and shuttle heat losses to the differential equation are because these losses can affect the overall working of the machine by changing the pressure and temperature of the working fluid. ...
Thesis
The Stirling cycle machine has many successful applications as a prime mover and cooling machine. The Stirling cycle heat engine has a good potential for use in the future because of some advantages like external combustion, and fuel flexibility. The Stirling machine is used in cryogenics but applications for domestic cooling are still underdeveloped. The main goal of this study is to develop a precise thermodynamic numerical model that could predict the performances and provide means for further optimization. Hence, this dissertation presents the numerical modeling, simulation, experimental validation, and parametric optimization of an air-filled Beta type Stirling refrigerator for domestic application.The research shows that a non-ideal second-order numerical model called the modified simple model has been developed. The model incorporates effects of shuttle heat loss and mass leakage loss to the buffer space directly to the differential equations of pressure change, rate of change of mass of gas in compression and expansion spaces, and mass flow rates across these working spaces. Moreover, other power losses and heat losses are included as independent losses to evaluate the cooling production and associated COP. The model is simulated using MATLAB code for Beta configuration FEMTO-60 Stirling engine operating as a refrigerator. The model is validated both with an experiment conducted in the FEMTO-ST laboratory in refrigerating mode and by reversing the model to work producing engine so that the validation could be made with different theoretical models developed by other scholars so far. The validation results confirm that the proposed numerical model could be used to design a Stirling cycle refrigerating machine with reasonable accuracy. The contribution of this study also includes investigation of the effect of different working fluids (air, nitrogen, hydrogen, and helium), effects of losses (shuttle heat and mass leakage) that have a direct effect on the operating condition of the cooling machine, and parametric optimization. Air and nitrogen showed better cooling performance than helium and hydrogen mainly due to the higher mass flow rate. The effects of incorporating shuttle heat loss in the differential equations on the temperature and pressure of working gas and the overall performance of the Stirling refrigerator are analyzed. Parametric optimization includes the effect of operating (rotational speed, charging pressure, and temperature) and geometrical (phase angle, regenerator length, porosity, displacer height, displacer gap, piston-cylinder clearance gap, swept volume ratio, and piston diameter to stroke ratio) parameters on the cooling performance as well as on share of different power and heat losses. Finally, we propose a set of parameters to optimize a refrigerating Stirling machine achieving a COP of 1.3 for a cooling power of 625 W at a temperature of -4 °C.
... For in- stance, Timoumi et al. [25] proposed a second order model that in- cluded five types of energy loses and optimized the various parameters of the engine and later tested the model using experimental data of GPU-3 Stirling engine prototype. Sayyadi et al. modified the simple model of Urieli [12] and developed simple II [26], CAFS [27], and PFST [28] models by combining the simple model with the finite speed thermodynamics principle and analyzing the heat transfer in the heater and compression/expansion processes on the basis of polytropic ana- lysis, after comparing the results of the models with the available ex- perimental data of GPU-3 Stirling engine, error ranging from 4 to 16% were found. Ni et al. [6] developed ISAM (Improved Simple Analytical Model) and compared the results with the GPU-3 Stirling engine and found the predicted efficiency of the model to be 2% less than the ex- perimental efficiency. ...
... The simple adiabatic model of Urieli et al. [12] only consists of imperfect transfer of heat and pressure drops in the heat exchangers hence, the basic ordinary differential equations of simple analysis were modified to include the shuttle effect and mass leakage of the working fluid (for detailed explanation refer to [26]). Other losses, i.e. (Con- duction losses, flow resistance loss, seal leakage loss and gas spring hysteresis loss) were calculated separately and their values were de- ducted from the net power which was obtained from the modified simple model. ...
... Other losses, i.e. (Con- duction losses, flow resistance loss, seal leakage loss and gas spring hysteresis loss) were calculated separately and their values were de- ducted from the net power which was obtained from the modified simple model. Table 1 Equation set of modified simple-model [26]. Heater heat input ...
... The works conducted by Timoumi et al. [6], Campos et al. [7], Ahmadi et al. [8], Cheng and Yang [9] Hosseinzade and Sayyaadi [10] are considered as a second-order model, which divides the engine into discretized elements and carry out the governing equations related to every component. In those models, the additional types of losses [11], finite-time thermodynamic [12] or irreversible finite speed thermodynamic and losses [8] are incorporated to study the engines, which leads to a high degree of accuracy in predicting the engine's performance [13]. ...
... This is due to the high rate of heat transfer at the two sides of the regenerator. Most of the investigations conducted with the second-and third-order models considered it as a sinusoidal variation [11,[44][45][46][47][48][49][50]. This result confirms and agrees with the conclusion of El-Ghafour's work [34]. ...
... Another important feature of the regenerator is the temperature distribution. Most of the researchers found that the temperature profile of the regenerator is linear along the axial direction [6,11,47]. Fig. 23 shows the temperature distribution of the solid matrix of the regenerator at the crank angle of 0 • . It should be noted, the vertical position is nondimensionalized. ...
Article
Full-text available
A 3D modeling of the fluid dynamics and heat transfer in an advanced free-piston Stirling engine was conducted. The transient and conjugate fluid dynamics and thermodynamics of the coupling fluid-solid domain over the working cycle were comprehensively investigated. The comparisons among different turbulent CFD models and Sage result of the engine were performed. Results indicate that the k-epsilon turbulence model with improved wall treatment yields reasonable accuracy and stable convergence. The CFD results of the pressure drop in the regenerator are nearly the same as engine Sage design code results, while the pressure drop inside cold heat exchanger has about 10.43% deviation compared to the Sage result. The flow diffuser guide flow more evenly distributed inside the regenerator, but it was found that it causes a vast turbulent dissipation rate. The instantaneous transport variables such as temperature, density and viscosity cannot be treated as uniform distribution due to the complicated interaction and coupling between the fluid-fluid and fluid-solid during the operation. The ejecting and injecting flows result in non-uniformly distributed temperature, pressure and density in the regenerator. The flow friction coefficient in the regenerator over one cycle cannot be simply correlated by typical empirical equations. The linearly distributed temperature profile in the regenerator solid matrix in the Stirling engine is confirmed by this CFD modeling. The optimization results of the diffuser and regenerator are also discussed.
... The solving time of the proposed fast response model can be significantly reduced compared to previous numerical models. Babaelahi and Sayyaadi (2014) proposed an alternative method to calculate the regeneration heat loss and pumping losses, which is more suitable for preliminary engine design and optimization, known as the Simple II model. Abbas (2014) considered the effects of non-ideal regeneration, shuttle loss and heat conduction losses based on the Simple model. ...
... Where s se is the speed of the engine, Hz. d. Energy losses due to internal conduction The temperature differs from the heater and cooler, heat losses from the heater to cooler exists due to internal conduction through the walls of the regenerator (Babaelahi and Sayyaadi, 2014). The internal conduction loss in a cycle can be obtained by: ...
... The proposed model improved errors (s se = 25 Hz, p = 4.14 MPa) on the thermal efficiency and output power and reduced these errors from 7.49% and 110.11% (as difference) obtained in simple II model (Babaelahi and Sayyaadi, 2014) to 2.49% and 1.56% (as difference), respectively. However, there is still some discrepancy between the simulation results of the proposed model and the experimental data. ...
Article
Cascade solar thermal systems provide a new direction for solar power generation. This paper focuses on the configuration optimization of a cascade solar system in which a Stirling engine array is applied. The array has multiple configurations. To find out the influence of the configuration on the performance of the engine array, five basic connection types were proposed. A Stirling engine model considering various losses and irreversibilities was developed. The model was evaluated by considering the prototype GPU-3 Stirling engine as a case study. Stirling engine array models were developed based on the Stirling engine model. Global efficiency and power of different connection types of Stirling engine arrays with the same hot and cold flows were evaluated. The effects of different factors on the performance of the Stirling engine arrays were considered. The result shows that flow order, the co-current flow or the counter-current flow, has little influence on the engine array performance. The maximum differences of thermal efficiency and output power of different flow orders are 0.39% and 0.70%, respectively. Serial flow connection type is the best for a Stirling engine array to obtain the best performance and adaptability for given heating and cooling fluids.
... Over the past decade, efforts have been made to improve the accuracy of the second-order models. This is achieved by better characterization of the engine irreversibilities and losses [4,[7][8][9][10][11]. The thirdorder model, sometimes named nodal model, is another type of Stirling engine analysis. ...
... The pressure difference between the compression and expansion spaces is the sum of pressure drops in the heater, regenerator, cooler and manifolds with respect to the direction of the flow. Whereas, the difference between the pressure in the compression space and on the piston wall is the pressure loss due to the finite piston speed [8]. In fact, the pressure waves that are generated due to the movement of piston cause the difference between the gas pressure over the moving piston and the bulk gas pressure inside the cylinder according to the flow direction. ...
... The instantaneous variations of average gas temperature within the compression space, expansion space, heater, cooler and regenerator versus the crank angle during the cycle are represented in Fig. 7. Apparently, the temperature variation in each volume is far from the harmonic distribution. This result contradicts with those predicted from the second-and third-order models for the GPU-3 engine [4,6,8,16]. which confirmed that the temperature distribution was significantly near the sinusoidal profile. ...
Article
A three-dimensional Computational Fluid Dynamics (CFD) simulation for the beta-type Stirling engine is performed. Firstly, a thorough characterization of the thermal and fluid flow fields during the cycle is presented. Secondly, a comprehensive energy analysis for the engine is conducted to accurately identify the sources and magnitudes of thermodynamic losses. Computational results show a close agreement with the experimental results with an accuracy of about 96%. Within the compression and expansion spaces, the dominant heat transfer rates occur during the expansion strokes due to the significant impinging effect of the tumble vortices generated from the flow jetting. Furthermore, the jetting and ejecting processes into the regenerator is characterized by a significant temperature gradient and a large matrix temperature oscillation. The pressure difference between the expansion and compression spaces is the main driver for the flow leakage through the appendix gap. From the energy analysis, the regenerator thermal loss and the pumping power represent the largest part of the Stirling engine losses by about 9.2% and 7.5%, respectively.
... In another work, the combined adiabatic finite speed (CAFS) model was presented [15]. Babaelahi and Sayyaadi [16] developed the Simple model of Urieli and Berchowitz [14] and added the effects of shuttle thermal losses and gas leakage to the adiabatic differential relations. Therefore, a modified Simple model (Simple ІІ) was proposed with consideration of heat exchanger pressure drop, conductive losses in the regenerator, and finite speed thermodynamics effects. ...
... According to Fig. 7, The Reynolds number for two models reaches to its maximum value (about 79) at crank angle of about 300 . In Fig. 8, the pressure drop due to fluid friction in the regenerator at various crank angles is presented for non-ideal adiabatic model [18], Simple [14], and Simple ІІ [16] models, according to the conditions mentioned in Fig. 7. It shows that the maximum pressure drop in the regenerator for these three models is about 0.16 MPa which happens at 300 of crank angle rotation. ...
... The power output of the GPU-3 engine versus rotational speed for hydrogen. than 1500 rpm, the non-ideal adiabatic model has better performance compared to the Simple ІІ model [16], but at the higher engine rotational speeds, the thermal efficiency of the Simple ІІ model [16] has more agreement with the experimental data. In Fig. 12, the power output for current study (non-ideal adiabatic model) is presented compared to the experimental results [48] and ISAM model [17] at different rotational speeds for hydrogen. ...
Article
In this study, with a comprehensive approach, energy, economic, and environmental evaluations of a combined cooling, heating and power (CCHP) generation system driven by Stirling engine with working gases of hydrogen and helium were performed. This system can be used for residential applications. The engine was analyzed using the non-ideal adiabatic model, and two beta type Stirling engines were suggested in the CCHP system. Also, the energy analysis of the absorption chiller was presented with utilizing the waste heat of the engine. Then, the impacts of important specifications of the Stirling engine including: temperature of heater, length of regenerator, engine rotational speed, and type of working gases on the COP of absorption chiller, CCHP efficiency, Trigeneration Primary Energy Saving (TPES), Operational Cost Reduction (CR), and Trigeneration CO2 Emission Reduction (TCO2ER) relative to conventional energy supply systems were studied. Finally, at the appropriate conditions, the values for parameters of electrical power: 15.24 kW, 22.52 kW, heating capacity: 19.65 kW, 21.65 kW, cooling capacity: 12.65 kW, 14.43 kW, COP: 0.644, 0.667, CCHP efficiency: 70%, 72.29%, TPES: 24.05%, 31.3%, TCO2ER: 31.06%, 38% and CR: 75.53%, 78.8% were obtained for helium and hydrogen, respectively.
... The purpose of this paper was to develop a realistic numerical model for designing an air-filled domestic Stirling cycle refrigerator. Therefore, a numerical model for the Beta-type Stirling cycle refrigerating machine is presented, which has been developed by adapting and modifying engine models (Babaelahi and Sayyaadi, 2014;Urieli and Berchowitz, 1984) for refrigerating purpose. The differential equations have been modified by incorporating mass leakage and shuttle heat loss. ...
... The system of ideal adiabatic differential equations was modified by including the effects of gas leakage from working space to buffer space (crankcase) and shuttle heat loss by displacer from compression to expansion spaces for the Stirling cycle refrigerator by adapting and modifying the Simple-II engine model developed by Babaelahi and Sayyaadi (2014). The main reason for the inclusion of mass leakage and shuttle heat loss to the differential equation is because these losses could affect the overall working condition of working fluid. ...
Article
A key issue in the optimal designing of a Stirling machine is to develop a precise thermodynamic numerical model that could predict the performances and provide means for further optimization. In this paper, a non-ideal second-order numerical model called modified simple analysis model has been presented for the Stirling cycle refrigerating machine. The model incorporates effects of shuttle heat loss to the expansion space and mass leakage to the crankcase in the differential equations of pressure change, rate of change of mass of gas in compression and expansion spaces, and mass flow rates across these working spaces. The model was simulated using MATLAB code for Beta configuration FEMTO 60 Stirling engine operating as a refrigerator and validated with an experiment. The validation of the numerical model with experimental work showed that the results of the simulation are consistent with the results of the experiment. Hence, the numerical model could be used to design a Stirling cycle refrigerating machine for moderate temperature applications with reasonable accuracy especially if optimization is performed further. The effects of incorporating shuttle heat loss in the differential equations on the temperature of working gas and the overall performance of the Stirling refrigerator have been analyzed. Lastly, parametric investigations have also been performed to evaluate the effect of operating parameters (temperature, pressure, and frequency) on the performances of the refrigerating machine. Better performance could be achieved at relatively lower frequency or higher pressure.
... Abbas et al. developed a simple model of Stirling engine in which non-ideal characteristics of regenerator, shuttle loss and heat conduction losses were considered [28]. In another approach, Babaelahi and Sayyaadi in 2014 developed a new thermal model called 'simple-II' model by considering the shuttle effect and gas leakage in original simple adiabatic model, which had better accuracy than the previous model [29]. Further, Hosseinzade and Sayyaadi modified the actual adiabatic model of Stirling cycle engine by considering the effect of finite speed of piston, pressure drop in heat exchangers and piston mechanical friction and developed another combined adiabatic finite speed thermal model (CAFS), which gives better results when simulated with GPU-3 Stirling engine [30]. ...
... Further, Babaelahi and Sayyaadi considered the effect of the type of working fluid and clearance volume of expansion/compression space on the polytropic index [29]. A methodology was presented by them to find out the polytropic indexes of expansion/compression space as a function of crank angle. ...
... where f Re is calculated by [32] ...
... Table 3 summarises the potential phase angles up to the ph 8 Franchot engine where the phases are uniformly distributed around the crankshaft. These phase angles can be mathematically described by Eq. (32), which is also used to calculate the phase shift, but only for even y. These phase angles are similar to the phase angles of the multi-cylinder single-acting Stirling engine [7]. ...
Article
The Franchot engine is a double acting Stirling engine that has a freely controllable phase angle and no shuttle and axial conduction losses but is inferior to the Siemens and free piston Stirling engines in terms of its ability to self-start. In addition, the Franchot engine is not widely used with the reliable slider crank mechanism due to vibrations. Here, the multi-cylinder Franchot engine is thermodynamically and techanically studied with the simple slider crank mechanism with the aim of improving the self-start capability and to reduce the vibrations. Both instantaneous power and engine arrangements are used to judge the mechanical performance for different engine parameters and configurations. The optimal phase shifts and phase angles are derived and it is shown that both are governed by the number of cylinders. The theoretical analysis shows that by increasing the number of cylinders, different engine vibrations are reduced and the engine becomes self-starting. Hence, the Franchot engine can be superior to the Siemens engine, particularly due to the ability to remove the rocking couples for engines with more than two phases. Thus, the engine operation is stabilised and the simple slider crank mechanism can be used with the multi-cylinder Franchot engine.
... The purpose of this paper was to develop a realistic numerical model for designing an air-filled domestic Stirling cycle refrigerator. Therefore, a new numerical model for the Beta-type Stirling cycle refrigerating machine called the modified simple model is presented, which has been developed by adapting and modifying engine models [18,19] for refrigerating purpose. The differential equations have been modified by incorporating mass leakage and shuttle heat loss. ...
... The system of ideal adiabatic differential equations was modified by including the effects of gas leakage from work- ing space to buffer space (crankcase) and shuttle heat loss by displacer from compression to expansion spaces for the Stirling cycle refrigerator by adapting and modifying the Simple-II engine model developed by [19]. The main reason for the inclusion of mass leakage and shuttle heat loss to the differential equation is because these losses could affect the overall working condition of working fluid. ...
... It can be seen that it is better than simple model prediction and very close to CAFS model where the error at higher speeds (3000-3500 rpm) were widely reported in all previous models. [9][10][11][12][13][14]21 However, comparing the prediction of heat input to the heater from the current model against experiment was exclusively carried out in this study and also found to be in a good agreement as depicted in Figure 4B. This gives confidence in the predicted results and analysis methodology. ...
Article
This work aims to compare beta‐type Stirling engine performance (GPU‐3 [ground power unit]) driven by rhombic and crank mechanisms. A modified non‐ideal adiabatic model accounting for different frictional and thermal losses was adopted in this study. After validating the current model with engine experimental data, different scenarios of operating conditions including heater temperature, cooler temperature, charge pressure and engine speed were investigated. The results revealed that rhombic drive mechanism generates 32% more power and provides 20% more efficiency than crank mechanism at normal operating conditions. However, at low hot end temperature (300°C) and high charge pressure (50 bar) crank drive mechanism tends to slightly generate power more than rhombic drive mechanism at lower engine speeds. At low hot end temperature (300°C) and charge pressure (10 bar) both mechanisms cannot deliver any positive power. Higher power loss is recognized in crank drive mechanism at higher speeds due to increased pumping and gas spring hysteresis losses. This study highlights a wide analysis opportunity for designers and researchers of GPU‐3 Stirling engine for further optimization. This study highlights a wide analysis opportunity for designers and researchers of GPU‐3 Stirling engine for further optimization and compares thermodynamically the performance of the engine with rhombic and crank drive mechanisms. The results revealed that rhombic drive mechanism generates 32% more power and provides 20% more efficiency than crank mechanism at normal operating conditions.
... where m leak denotes mass leakage to crank case due to the clearance. The mass leakage to the crank case was calculated based on [3,7,9] using equation (2): ...
Conference Paper
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In this paper, a parametric investigation of domestic regenerative Stirling refrigerating machines is conducted using a modified simple model. The model is adapted from an ideal adiabatic engine model and different losses have been included at different stage based on their effect. The model is validated experimentally using the Beta type FEMTO 60 Stirling engine as a case study. The simulation and experimental results show that the coefficient of performance of the Stirling cycle refrigerator at a charging pressure of 17.5 bar, frequency of 12.1 Hz, cold end temperature of -22oC and using nitrogen as a working fluid are found as 38.2% and 35% respectively. Furthermore, the effects of phase angle, working fluid type, operating pressure, and operating frequency
... In particular, the non-ideal adiabatic model proposed by Urieli [8] is a quasisteady flow (QSF) model that predicts heat transfer characteristics by assuming the flow in the heat exchanger as a steady-state flow. It is combined with various loss models [9][10][11] for reasonable performance predictions. It is widely used in optimization research due to its advantages of accuracy and fast analysis speeds. ...
Article
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This paper presents the design optimization of a heat exchanger for a free-piston Stirling engine (FPSE) through an improved quasi-steady flow (iQSF) model and a central composite design. To optimize the tubular hot heat exchanger (HHX) design, a design set of central composite designs for the design factors of the HHX was constructed and the brake power and efficiency were predicted through the iQSF model. The iQSF model is improved because it adds various heat and power losses based on the QSF model and applies a heat transfer model that simulates the oscillating flow condition of an actual Stirling engine. Based on experimental results from the RE-1000, an FPSE developed by Sunpower, the iQSF model significantly improves the prediction error of the indicated power from 66.9 to 24.9% compared to the existing QSF model. For design optimization of the HHX, the inner diameter and the number of tubes with the highest brake power and efficiency were determined using a regression model, and the tube length was determined using the iQSF model. Finally, the brake output and efficiency of FPSE with the optimized HHX were predicted to be 7.4 kW and 36.4%, respectively, through the iQSF analysis results.
... However, a large amount of this research is focused on performance, prediction and optimization. Most analyses in steady or dynamic state draw from mathematical models derived from the ideal gas equation, differentiated by system considerations such as dead volume, compressibility factor, adiabatic sections, and the use of different design variables [12][13][14][15]. ...
Article
This paper presents a study to determine the influence of design variable interactions on the performance of a Stirling engine, as well as a new methodology to identify and quantify such influence. An Alpha-type 2 kW Stirling engine was assessed using a second order model where the engine, heater, regenerator and cooler variables were simultaneously analyzed in pairs. The study includes 240 interactions corresponding to the 16 selected design variables. It was observed that the piston stroke and cylinder diameter variables have more significant interactions with the rest of the parameters due to their strong influence over mass flow. The piston crown length does not show significant interactions; however, it reduces individual thermal losses in the expansion zone. The cycle achieves its maximum net power at angles less than 90° due to pressure, heat losses, and the ratio between mass flow rates and swept volume. Finally, this work presents recommendations for the analyzed interactions. The global interactions scheme provides a qualitative and quantitative identification of the variables that affect the system, synthesized into a hierarchy of variables that indicates a critical path for their exploration for system design and optimization purposes.
... A w : mean wetted area (m 2 ) seal leakage power loss (W) [33,34] W leak = q leak · C p · T leak q mleak = ρπD c As for the positive cycle, power losses directly affect the engine power whilst heat losses affect its ability to absorb heat directly, impacting the working gas temperature of the compression/expansion space and the cycle efficiency of the engine. However, for the reverse cycle, the power losses directly affect the input power, with heat losses affecting the actual cooling power of a cold head. ...
Article
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There are two kinds of working mechanisms for the Stirling cycle, i.e., the positive and the reverse cycles, and a Stirling engine (SE) can be operated as a Stirling refrigerator (SR). This indicates that a probable practical method for evaluating the performance of a Stirling engine is to run it as a refrigerator, which is much easier to operate. For this purpose, an improved Simple model for both the positive and the reverse Stirling cycles, considering the various loss mechanisms and actual operating conditions, is proposed and verified by a self-designed Stirling engine. As to the positive cycle with helium and nitrogen at 2.8 MPa, the model errors range from 5.4–11.3% for the indicated power, and 1–10.2% for the cycle efficiency. As to the reverse cycle with helium and nitrogen, the errors of the predicted input power range from 7.9–15.3% and from 2.5–10.9%, respectively. The experimental cooling temperatures can reach −92.2 and −53.6 °C, respectively, for the reverse cycle with the helium and nitrogen at 2.8 MPa. This Stirling-cycle analysis model shows a good adaptability for both the positive and the reverse cycles. In addition, the p-V maps of the positive and reverse cycles are compared in terms of “pressure ratio” and “curve shape”. The pressure ratio of the reverse cycle is significantly higher than that of the positive one at the same mean pressure. A method is proposed to predict the indicated work of the positive Stirling cycles using the reverse ones. A mathematical model to predict the indicated power of the positive Stirling cycles based on the reverse ones is proposed: Wheat2−Wcool1=A·(Tge2−Tgc2Tgc1−Tge1)B. The most critical issue with this method is to establish an associated model of the temperatures of the expansion and the compression space. This model shows a good adaptability for both the positive and the reverse cycles and can provide detailed information for deep discussion between the positive and the reverse cycles.
... A few years later, Urieli [9] proposed the adiabatic model of the Stirling engine, which to this day remains the benchmark of the various second and thirdorder models. Sayadi et al.'s team, by incorporating the finite speed of piston and polytropic expansion and compression processes, improved Urieli's model and developed Simple II [16], CAFS [17], PFST [18], PSVL [19,20] models. They validated their models by the General motor's GPU-3 Stirling prototype. ...
Article
In this article, a novel numerical model of the Stirling engine encompassing a potent loss mechanism coupled with the NSGA-II algorithm is proposed. Multi-objective optimization of GPU-3 Stirling engine was performed using a class of genetic algorithms, namely NSGA-II, with five decision variables to minimize the losses and increase the power output and efficiency of the GPU-3 engine. Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and Combinative Distance-based Assessment (CODAS) decision-making approaches were used to obtain the optimum solution from Pareto optimal space. Furthermore, the optimization results were compared with the experimental results of the GPU-3 Stirling engine. Results from the multi-objective optimization effort indicate that output power increases by approx. 500 W and efficiency enhances by approx. 5%, whereas losses decrease by 516 W. Later, to demonstrate the model's design capability, the developed model and optimization approach, i.e. (NSGA-II), is utilized to develop an optimal design of a beta-type free piston Stirling engine (FPSE) with an indicated power of 10 kW. After optimizing a combination of twelve operating and geometric parameters, the Stirling engine that yields a net power output of about 7.95 kW with a thermal efficiency of about 30% is developed. This work presents a novel and powerful numerical method for the optimal design of Stirling engine.
... Li et al. [8] developed a Polytropic Stirling Model with Losses (PSML) and studied a g-type Stirling engine finding that hydrogen is more suitable for high rotary speed engine compared with helium. Based on the Simple model (proposed by Urieli and Berchowitz [2]), Sayyaadi et al. presented a series of models named as, Simple-II [9], CPMS [10] and modified CPMS [11], by considering the piston shuttle effect, the longitudinal heat conduction loss and the finite speed thermodynamics, where the expansion/compression was regarded as a polytropic process. Udeh et al. [12] deployed a second-order model by coupling the effect of gas leakage through the displacer gap and into the crankcase and the shuttle heat loss to simulate the GPU-3, and found a minimum dimensionless gap for each given operating pressure below which the impact of the displacer gap on the engine performance was not significant. ...
Article
Stirling engine is a promising prime mover for distributed energy systems, and a reliable analysis model is essential to design different engines with various applications. In this paper, a third-order model for the Stirling engine is developed, considering the effects of pressure gradient of oscillating flow and main losses of heat and power. For the GPU-3 with hydrogen, the average relative errors between the simulated results and the experimental data are 10.76% and 5.86% for the indicated power and the indicated efficiency, respectively. The proposed model can provide transient information of pressure, temperature, Reynolds and Nusselt numbers, which are key parameters in the Stirling engine. The transient characteristics and the spatial distributions of Stirling cycles are investigated based on a 100-W prototype. The results show that the pressure drop on the regenerator is more than 95% of the total pressure drop, and increases almost linearly with the rotary speed. Limited amplitude change and nearly axial distribution are observed on the gas temperature of the regenerator. The pressure-volume diagrams predicted by the proposed model are close to the experimental data, indicating that the presented model predicts the transient performance of Stirling engines with reasonable accuracy.
... On the other hand, this model is unable to predict the effects of the relationship between fluid temperature and chamber heat transfer. Babaelahi and Sayyaadi [9] proposed a new numerical model called Simple-II, which can consider various engine losses, including mechanical friction, heat loss, and reduced gas mass. Their model can predict the engine's thermal performance better than previous models, but neither of these models is able to predict heat and fluid flow in a Stirling engine accurately. ...
Article
As an external combustion engine, the Stirling engine has low noise and can also easily use renewable and modern energies, such as solar energy. In this study, the dynamic synthesis of the alpha-type Stirling engine will be discussed. By combining the Stirling engine's thermodynamic and dynamic models, it is possible to predict the thermal efficiency, output power, and output velocity of the engine. It can be seen that the output angular velocity of the engine has some undesirable fluctuations. The main goal here is to reduce or eliminate the oscillatory behavior of the output angular velocity by optimizing the links’ lengths and their mass distribution in the engine's mechanism. Three optimization methods, namely the Genetic algorithm, the Particle swarm optimization, and the Imperialist competition algorithm, are used for searching the optimum design based on minimizing the output velocity fluctuations. Results show that if the flywheel’s mass moment of inertia is fixed, the angular velocity fluctuations have decreased by 24.18%, 19.20%, and 24.48% using GA, PSO, ICA, respectively. Moreover, at the same time, the efficiency has been improved by 38% approximately. For the best design in this case, which was extracted from Imperialist competition algorithm, the fluctuation has reduced to 133.72 rpm, while the average output velocity is 2620 rpm. Furthermore, as a second case, increasing the flywheel’s mass moment of inertia directly affects reducing the velocity fluctuations.
... Under optimal conditions, the power output and thermal efficiency improved by 15 and 20%, respectively. Babaelahi and Sayyaadi [9] disclosed that the working gas friction in the heat exchangers of a beta-type Stirling engine (GPU-3) includes more than 70% of the total friction losses of the engine. Besides, they added that increasing the porosity of the regenerator can have negative and positive impacts on the thermal efficiency of the engine, and at a porosity of 0.8, the maximum amount of the engine's thermal efficiency can be achieved. ...
Article
In this study, for the first time, the effects of various parameters including engine rotational speed, engine pressure, heater temperature, and piston stroke on technical (energy and exergy) and economic (cost savings and payback period) performance of a Ford-Philips 4-215 engine is investigated. Considering the different engine losses, a thermodynamic model of the engine is employed and validated with available experimental data. The results reveal that the increase in engine pressure and heater temperature, augments the capacity and efficiency of the engine, respectively, and increasing the engine rotational speed and piston stroke first shortens the payback period and thereafter makes it longer. Moreover, the engine parameters are designed from six different technical and economic standpoints, and the optimal parameters are selected using two well-known decision methods, namely, the linear programming technique for multidimensional analysis of preference (LINMAP) and the technique for order preference by similarity to ideal solution (TOPSIS). In one of the cases, from energy and economic viewpoints, engine parameters have been designed and the maximum electric power and minimum payback period have been gauged at 260.46 kW and 6.10 years, respectively. In another case, from the exergy perspective, the maximum exergy efficiency and minimum exergy destruction are 65.17 % and 6.81 kW, respectively. Finally, by performing a three-objective optimization (energy, exergy, and economic), the maximum output power and exergy efficiency are evaluated 258 kW and 44.5%, respectively at a 5-year payback period.
... Babaelahi and Sayyaadi [14] developed a polytrophic thermodynamic model by modifying the adiabatic model of Urieli and Berchowitz [9]. The modification involves the performance decrease of Stirling engines due to shuttle heat, the mass leakage between working volume and buffer space of the engine, power loss due to finite speed of piston, mechanical frictions and conduction heat loss through the regenerator wall. ...
... Ni et al. [11] established an improved simple analytical model (ISAM) to further improve the accuracy of the adiabatic model, which considered the gas leakage loss, gas spring hysteresis loss and piston friction loss. Babaelahi and Sayyaadi [12] developed the Simple II model by considering the gas leakage loss, the shuttle effect of the displacer, frictional loss and the axis-direction heat conduction between heater and cooler through the regenerator wall, which was a modification of the original Simple model. However, a large number of steady-state flow empirical formulas were used in the model, which made the output power be predicted with +20.7% error. ...
Article
A combined heating and power (CHP) system with a Stirling engine for building applications has been proposed in the present work. The use of these systems in building applications will be more common if they have significant advantages from the viewpoints of the pollution emission and operational cost in comparison with the other similar systems. The Stirling engine was modeled with consideration of different losses of its components. In addition, the effect of Stirling engine speed on efficiency, carbon dioxide emission, annual tax on carbon dioxide emissions and operational cost was analyzed. The results showed that the CHP system at low rotational speeds had better performance than other rotational speeds. Furthermore, the CHP system could achieve 900 $ reduction in annual costs of CO2 tax compared to the conventional system during operation.
Article
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In this paper, comprehensive governing differential equations of Stirling engines have been developed by coupling the effect of gas leakage through the displacer gap, gas leakage into the crank case and the shuttle heat loss into the traditional model. Instantaneous pressures and temperatures of the working fluid in the engine were evaluated at same time step. The present model was deployed for the thermal simulation of the GPU-3 Stirling engine and the obtained results were robustly compared to experimental data as well as results from previous numerical models. Then, parametric studies were conducted to assess the impact of geometrical and operating parameters on the performance of Stirling engines working with helium or hydrogen. Results suggest that the modifications made in this model led to better accuracy and consistency in predicting the experimental data of the prototype engine at all speeds, compared with most previous models. It was found that there exists a minimum dimensionless gap number, for every engine pressure below which mass leakage into the compression volume may not impact the brake power and energetic efficiency of the engine. In addition, an optimum mean effective pressure was found for maximum energetic efficiency of the engine. This optimum value is higher for helium gas than for hydrogen gas. Further results indicated that the brake power and energetic efficiency of the prototype Stirling engine can be significantly improved by 30% and 18%, respectively, provided that the heater temperature is raised to 850 °C while the cooler temperature is reduced to 0 °C.
Article
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In this paper, a novel design philosophy of free piston Stirling engines based on passivity based-control technique incorporating genetic algorithm is presented. First, the design problem of an FPSE is expressed as a physical nonlinear servo control system with unknown parameters. Accordingly, the desired motions of power piston and displacer (i.e. design objectives) are regarded as the reference trajectories of the control loop. Then, the unknown design parameters of the nonlinear control system including cross sectional-area of the displacer rod, mass and spring stiffness of the power piston and displacer, phase difference, hot gas temperature, and control coefficients are found using a GA along with an error-based objective function. Next, the estimated values of unknown parameters are used to simulate the control system performance. Subsequently, the simulated control system response is compared to the desired trajectories. It is found that the simulated displacements and velocities for both pistons as well as the corresponding limit cycles are close to the desired references of the control system. Finally, simulated performance of the FPSE is verified through experimental results. The outcomes of this research clearly reveal the effectiveness of the proposed nonlinear control-based design technique of the free piston Stirling engine (SUTECH-SR-1).
Article
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In this paper a beta type Stirling engine for cogeneration of heat and electricity is proposed. The Stirling engines have advantages such as flexibility of fuels and heat sources, low noise level, and higher thermal efficiency than internal combustion engines. In these engines, in power production process, some heat is released to the environment, which can be recovered, and therefore the Stirling engine has a good potential to be used in combined heat and power systems. In this research, the non-ideal adiabatic analysis has been used for the Stirling engine and for enhance the accuracy of the model, the frictional and thermal losses have been considered. Non-ideal adiabatic analysis, was performed using a numerical code developed in MATLAB software. To validate of the model, the geometrical and operational specification of the GPU-3 Stirling engine was used and the results were compared with experimental results and other previous models. Then a beta type Stirling engine was proposed for the combined heat and power system in residential applications. Also, the effect of engine rotational speed, regenerator length and temperature of heat source on electrical and CHP efficiency were investigated and the appropriate amounts of operating parameters were selected. Finally, the electrical power and thermal power were obtained 11263 W and 21653 W, respectively with electrical efficiency of 27.78% and CHP efficiency of 81.19% efficiency for this cogeneration system.
Article
Geleneksel gama tipi Stirling motorlarında iki silindir mevcut olup silindirlerden birisi aracılığı ile çalışma gazının sıkıştırılması ve genişletilmesi işlemleri, diğeri aracılığı ile çalışma gazının sabit hacimde ısıtılması ve soğutulması işlemleri gerçekleştirilmektedir. Geleneksel gama tipi motorlarda soğuk ve sıcak hacimlerin aynı silindirde bulunması nedeni ile sıcak uçtan soğuk uca iletimle önemli bir miktarda ısı kaybı olmaktadır. Ayrıca dispileyser’ in yapımı oldukça külfetli bir iştir. Bu problemleri yok etmek için, son zamanlarda sıcak ve soğuk hacimleri ayrı ayrı silindirlerde bulunan üç silindirli gama tipi bir motor modeli tanıtılmıştır. Bu motorlarda bulunan silindirlerden birisi sıcak hacim olarak bir diğeri soğuk hacim olarak üçüncüsü de güç silindiri olarak görev yapmaktadır. Bu motorların termodinamik süreçleri geleneksel gama tipi motorunkine çok benzediği için bunlara üç silindirli gama tipi motor adı verilmiştir. Her üç silindirin içerisinde alışılmış tipten pistonlar çalışmaktadır. Bu araştırmada geleneksel gama tipi bir motorun ve üç silindirli gama tipi bir motorun nodal termodinamik analizleri yapılarak performansları kıyaslanmıştır. Motorların çevrimlik işlerinin ve verimlerinin birbirine çok yakın olduğu görülmektedir. Yüksek hızlarda ve yüksek basınçlarında geleneksel gama tipi motorun, yüksek sıkıştırma oranında ise üç silindirli gama tipi motorun az miktarda avantajlı olduğu görülmektedir.
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Parallel‐plate regenerators (PPR), with flow resistance lower than traditional wire‐mesh regenerators, can improve the thermal efficiency of Stirling engines (SEs). However, as working frequency or plate thickness increase, the heat cannot penetrate into the plate effectively, resulting only the surface part of the plates to have substantial temperature variation, while the internal part fails to store and exchange heat energy. In order to obtain high performance of PPR, the heat storage efficiency and the heat transfer coefficient, as well as their influential factors, are theoretically studied. Three parameters are found to play an important role, which are working frequency, plate thickness, and thermal diffusivity of materials. Their roles can be represented by a dimensionless parameter as a whole, which is the relative thickness, e. By the critical value of relative thickness, ecr = 2.4, two distinct working conditions can be divided, thermally penetrated condition as e < ecr and thermally non‐penetrated condition as e > ecr. Under thermally penetrated condition, the heat storage efficiency is high, and the heat transfer coefficient is high enough when e > 1.6, while under thermally non‐penetrated condition, the heat storage efficiency is low. In conclusion, by comprehensively considering the heat storage efficiency and heat transfer coefficient, it is recommended that the relative thickness e should be chosen within the range [1.6, 2.4]. And the optimal working frequency, plate thickness, and suitable material can be determined accordingly. Envelopes of temperature distributions within the plate at different frequencies. A, ERCu plate, h = 2 mm; B, SS plate, h = 2 mm. Variation of heat storage efficiency, η, with frequency under some specific plate thicknesses. Variation of heat transfer coefficient K with plate thickness h. A, ERCu plate; B, SS plate.
Conference Paper
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Uma importante medida para se reduzir a emissão excessiva de gases do efeito estufa decorrentes da atividade humana é a ampliação da participação das fontes renováveis na matriz energética mundial. Esta ampliação se dá através da utilização de novas tecnologias, tais como a energia solar térmica concentrada com sistemas Dish Stirling. Com o objetivo de estabelecer um método simples para o dimensionamento do concentrador parabólico usado em sistemas Dish Stirling, a análise isotérmica de Schmidt é aplicada neste trabalho para a simulação de um motor Stirling e é desenvolvido um modelo térmico do sistema. Os dados experimentais de um motor Stirling GPU-3 são utilizados para o dimensionamento de um concentrador parabólico adequado às condições estabelecidas para a operação deste motor. Quando comparado com os valores experimentais do motor Stirling GPU-3, os resultados da simulação realizada com o modelo proposto demonstram um desvio entorno de 97% na estimativa da potência gerada, e um desvio entorno de 101% na estimativa da eficiência do motor. Entretanto, os resultados da simulação demonstram um desvio entorno de 2% na estimativa da potência consumida, variável que é utilizada para o dimensionamento de um concentrador. Com os resultados obtidos pela simulação, dimensiona-se um concentrador com o diâmetro necessário para atender a demanda do motor simulado. Apesar de o modelo do motor Stirling baseado na análise isotérmica de Schmidt apresentar resultados discrepantes quando comparado com outros modelos presentes na literatura, o método proposto pode ser utilizado como um estimador na realização de análises preliminares, devido à sua facilidade de aplicação. Palavras-Chaves: modelo isotérmico de Schmidt, motor Stirling, sistema Dish Stirling, energia solar, energia heliotérmica.
Article
In this study, a Stirling engine with a free-displacer and a kinematically controlled power piston was proposed and analyzed from thermodynamic and dynamic points of view. The analysis intended to reveal the dynamic behaviors of moving components of the engine as well as predicting global thermal performance of it. A dynamic-thermodynamic mathematical model of the engine involving the isothermal gas pressure equation and motion equations of the displacer, power piston and crankshaft was developed. For the solution of the dynamic-thermodynamic model equations, and simulation of the engine’s running, a computer program was prepared in FORTRAN language. By considering a hot-end temperature of 1,000 K and a cold-end temperature of 350 K, dimensions of mechanic, volumetric and thermal components of the engine were quantified interactively. Variations of engine speed, engine power, displacer stroke, and engine torque were examined with respect to the spring constant, displacer mass, displacer damping constant and external load and, results were graphically presented. In comparison with engines having free-piston and kinematically driven displacer, the thermodynamic performance of the free-displacer engine was found to be lower. The engine was found to be able to work at constant speed and power. The values of the displacer mass and spring constant were optimized as 1,500 g and 1,30,000 N/s, respectively and the global speed of the engine was determined to be 47.75 Hz for these values. The effective and the indicated work of the engine were determined to be 113 and 126 J, respectively.
Article
Stirling engines are constructed with different mechanical configurations namely Alpha, Beta, Gamma and all of them can be powered by any source of renewable energies including biomass, solar energy or even waste heat from industrial sectors. The question that arises is: how can we choose the right type of Stirling engine that best matches our renewable energy source? In the existing bibliography, there is a great lack of an in-depth approach that establishes an objective comparison between the different types of Stirling engine, which leads researchers to make an inappropriate choice of a given configuration for a specific application. Consequently, a decrease in engine output performance can be noted while increasing the engine operating price. In this context, this paper develops a solution to Stirling engine users that will help them choose the suitable configuration for a given energy source. To do this, a non-ideal adiabatic model which takes several thermal and mechanical losses into consideration has been proposed using MATLAB software. The results of the current model have been compared with experimental findings of NASA Lewis Research Center and previous models and the comparison results demonstrate the high accuracy of the present model. The same physical and geometrical parameters were used to analyze the different configurations of Stirling engine by using crank drive mechanism. The results of this work demonstrate that each Stirling engine type is more suitable for a particular application where it provides high performances. The findings show the ability of Alpha configuration to operate with high temperature difference which correspond to waste heat recovery in industrial sectors where the gas temperature reaches high values. Alpha engine can produce high power-volume ratio and efficiency thanks to its low dead volume in working spaces and the separation that exists between its hot and cold sources. Under the same operating conditions, the output power and efficiency of Alpha, Beta and Gamma were 4120 W, 2280 W, 2500 W and 40.19%, 32.13%, 32.95% respectively. Beta and Gamma types have been found to be more suitable for low and medium temperature difference such as biomass and solar energy. Within these temperature ranges, Beta and Gamma types can produce almost the same output power as Alpha machine with less engine pressure requirement since they contain only one power piston. Beta and Gamma types have efficiencies of 17.57% and 18.40% with only mean pressure of 2.6 MPa and 2.7 MPa respectively, while Alpha arrangement provides an efficiency of 20.95% at 3.5 MPa mean pressure. This contributes to a main advantage of Beta and Gamma Stirling engines in terms of sealing process which will decrease the engine construction cost of these types. In addition, the code developed in this work indicates, at its output, the appropriate type for any application based on the user’s input parameters including the temperature of the hot source. This contributes to a new decision support approach allowing the choice of the suitable configuration for a given energy source.
Chapter
Basic concepts of thermal modeling based on zero-dimensional thermodynamic analysis were given in Chapter 2. However, thermodynamic models are general and can be implemented on all similar systems; sometimes, they lack accuracy for modeling of real energy systems. The advanced thermal model is intended to be used for the augmentation of the accuracy of thermal models. In this regard, finite-time thermodynamics (FTT), finite-speed thermodynamics (FST), combined finite-time finite-speed analysis (FTT-FST), and quasi-steady thermodynamic models are presented in this chapter along with several case studies about IC and Stirling engines.
Article
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Stirling engines (SE) offer good part load performance and high heat sink temperatures which make it a suitable candidate to serve as a prime mover in micro-combined cooling, heating and power (μ-CCHP) applications. In this study, a novel μ-CCHP configuration hybridising a SE prime mover with an ORC to utilise the waste heat from the SE to produce additional power is proposed. Additional waste heat was recovered from the flue gas to dry the biomass feedstock, fire a thermal chiller and produce hot water. Further, a non-ideal thermal model was formulated and implemented in MATLAB to model the SE prime mover while the models of the other subsystems were implemented in Aspen plus®. Also, the control of the subsystems of the μ-CCHP was achieved in MATLAB by establishing a connection between the software and Aspen plus®. A detailed sensitivity analysis was conducted to study the influence of cooling and heating loads, rotational speed of the prime mover and quality of the biomass fuel on the energy utilisation factor, primary energy savings (PES), CO2 emissions reduction (CO2ER) and exergy efficiency of the μ-CCHP system. It was found that hybridising SE and ORC increased the power output and thermal efficiency of the standalone SE by 66% and 63.4%, respectively at its operating speed of 2500 rpm, and also improved the performance at high rotational speeds. Further, the deployment of hybrid prime movers in the design of the μ-CCHP yielded high PES and CO2ER of 55% and 43%, respectively when the system utilised woodchips fuel containing 10% moisture. The proposed energy system performs better than conventional energy systems producing only one energy vector over a wide range of engine frequencies, cooling ratios and woodchips compositions.
Article
This study involves performance examination of an alpha-type novel Stirling engine and performance comparison with a V-type alpha engine. The novel engine displays very different features from the conventional V-type alpha engine. In the conventional engine, the work calculated with nodal analysis (real work) is lesser than isothermal work. In the novel engine, however, the real work becomes larger than the isothermal work if the heat transfer in compression and expansion cylinders is poor. If performances of engines are compared for equal amount of working fluid mass, the real work of the novel engine is always larger than the real work of the conventional V-type alpha engine. If performance comparison is made for equal amount of charging pressure of the working fluid, the difference of works of engines becomes multiple. The thermal efficiency of the novel engine is also greater. At relatively lower speeds and lower charging pressures of the engine, the efficiency difference between novel engine and conventional engine becomes more than 25%. The mean gas pressure in the novel engine is about 40% lesser than that in the conventional engine. All of the properties of the novel engine were found to be advantageous except flow losses.
Article
Regenerators play an important role in Stirling engines, pin-array stack regenerators have low flow resistance, to verify their advantages in Stirling engines, the heat transfer performance was explored theoretically, and the equivalent heat transfer coefficient and its influencing factors were obtained. The results show that the magnitude of equivalent heat transfer coefficient of this kind of regenerator can be up to 10⁵W/m²·K, indicating that the pin-array stack generator is satisfactory when used in Stirling engines. Equivalent heat transfer coefficient is influenced by three factors: the working frequency, radius and thermal diffusivity of pins. With the increase of frequencies, the heat transfer performance increase monotonously, while with the increase of radius, there are two extreme points. Based on this, two typical working conditions are determined, the thermally penetrated condition and the thermally unpenetrated condition, and the heat transfer performance of the thermally penetrated condition is good, but the thermally unpenetrated condition should be avoided. Based on the equivalent heat transfer coefficient, the regenerator size optimization criterion was proposed according to the target parameter of specific volume heat transfer capacity, and the optimal parameters can be obtained by setting the relative radius to be 1.
Article
Nowadays, the Stirling engine is very important for its high efficiency, the usability of any types of the heat source, the quiet operation and the working fluid consistency within the engine. Hence, design engineers have always sought to improve the performance of this engine, using various processes and the optimization. In this article, the performance analysis of the Stirling engine has been performed by the non-ideal adiabatic thermodynamics model and was compared to the experimental results. In addition, the effect of coating on the regenerator and the influence of the coating type and the thickness were also investigated. Besides, a regression model was utilized for the sensitivity analysis. Ceramics coating included YSZ (Densed), YSZ (50% Porosity) and MgZrO 3, with 10 different thicknesses for each material. Obtained results showed that as the thickness of coating increased, the heat loss decreased and the efficiency enhanced. The results also indicated that by changing the coating type, the heat loss reduced and the efficiency enhanced due to decrease in the thermal conductivity coefficient in YSZ (50% Porosity) coating, as the optimum coating type. A good agreement was observed between theoretical and experimental results in the P–V curve and the relative error of the maximum power was observed 22.63%.
Article
This study presents a theoretical and numerical thermodynamic model for a β - type Stirling engine with a rhombic-drive mechanism. This study focuses on developing a thermal model that overcomes the poor performance of previous models at high engine speed (above 60 Hz). The developed model is a modified version of the recently developed simple II model. The inaccuracy of the simple II model especially at high speed is improved by considering the power loss due to inertial forces and the variations of the gas temperature inside the heater and cooler with engine speed. The effect of several geometric and operational parameters. The accuracy of the developed numerical model is evaluated against experimental data of the GPU-3 Stirling engine. The difference between the current model predictions and experimental measurements for the output power and efficiency are 4.3% and 3.26% (as a difference), respectively. Moreover, the current model shows superior performance at high speed compared to previous models. It maintains its accuracy at high speed.
Article
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This article presents the results of the development of a numerical - analytical method for solving the problem of thermal conductivity in a plate fuel element. An unsteady temperature field inside a fuel element is investigated for a given spatial distribution of heat sources. The heat release rate is given by the quadratic function of the coordinate. Modeling the temperature state of bodies with internal heat sources allows you to study the operation of equipment in transient modes, control heating/cooling modes of elements, determine temperature stresses, etc. It is shown in the work that regardless of the power of internal sources of heat, the temperature state is stabilized at a temperature level that depends on the Pomerantsev number.
Article
Cement plants are one of the most energy consuming industries in which a large amount of heat energy is lost into the atmosphere causing the increase of environmental issues and leading to the rise of cement production energy cost. Recently, waste heat recovery systems such as steam and Rankine cycles have received much attention by researchers and industrial sectors for power production application to enhance the system efficiency. However, the existing waste heat recovery systems present different drawbacks. This paper proposes, for the first time, a new technique of recovering cement plants waste heat based on Stirling engine technology. The modelling of a Gamma type Stirling engine was conducted for recovering the waste heat released from the clinker cooling process. Furthermore, the non-ideal adiabatic model was used for engine designing in MATLAB software. For model validation step, the results obtained from the present study have been compared with experimental data of Lewis Research Center in the National Aeronautics and Space Administration and previous numerical models. The comparison findings have shown a high accuracy of the current model. The effect of several geometrical and physical specifications on Stirling engine performances was studied to obtain the best engine design. The results showed that maximum efficiency can be achieved by increasing the regenerator porosity up to 79 % and by decreasing the regenerator length to 0.015 m. A matrix wire diameter of 50 μm has been found as an optimum value regarding the high output power generated and acceptable heat input required. The parametric analysis of heat exchangers geometries has revealed that the increase of the heater and cooler tube lengths reduces the engine performances. However, the rise of heater and cooler tube inner diameters could enhance the power and efficiency. Furthermore, it was found that the variation of phase angle has an important influence on Stirling engine outputs, thus the consideration of 90 degree as phase angle is more suitable for engine design which will be able to produce 1641.36 W with a thermal efficiency of 21.29 %. Additionally, it was concluded that the augmentation of pressure and rotational speed increases the engine power. Finally, it was shown that the rise of working gas mass enhances the engine output power but increases the heat input requirement. This work demonstrates the potential of using Stirling engine technology for cement plants waste heat recovery applications and highlights its ability to produce high output performances.
Article
A Stirling cycle is a thermoelectric conversion method with high efficiency and reliability. The Stirling cycle applies to small- and medium-sized power space nuclear reactors or radioisotope heat sources. A high-precision and well-predicted Stirling cycle thermodynamic model is the key to optimizing and improving the Stirling engine for space. The present study modified the classical Simple model by incorporating the local pressure loss into the pressure loss. An improved second-order adiabatic model based on the Simple model, namely the Incorporated Pressure Drop-modified Simple Model (IPD-MSM), was proposed. The prediction of the IPD-MSM shows well with the changing tendency of the GPU-3 Stirling engine experimental data. Moreover, this model has better prediction accuracy at high-pressure and high-frequency conditions than other adiabatic models, such as CAFS and ISAM. The thermodynamic properties of He, H2, and Helium-Xenon mixtures in the Stirling cycle were also analyzed. Results show that the He-Xe mixture reaches the highest output power and thermal efficiency when the mole percentage of Xe is approximately 2%. The mechanism is as follows: the addition of Xe leading to the reduction in non-ideal heat transfer loss exceeds the increase in pressure loss. The addition of Xe leads the pressure loss to increase abruptly as the mole percentage of Xe exceeds 2%. The characteristics and application analysis of H2, He, and He-Xe mixture were discussed. The present study provided theoretical support for the Stirling cycle analysis for space missions and the selection of working fluids.
Article
The objective of this article is to develop a combined thermodynamic and dynamic model for alpha -type Stirling engine with Ross Yoke mechanism. Thermal, pumping, and regeneration loses are considered in developing the thermodynamic model. Two methods for solving the governing equations are proposed. In both solution schemes, the gas forces exerted in compression and expansion chamber are obtained from the instantaneous gas pressure determined from the thermodynamic model. The proposed model is validated against experimental available data. A model validation is carried out. A parametric study is used to investigate the effect of geometric and operation parameters on the engine performance. The effect of regenerator effectiveness, the dead volume ratio, and the heat source temperature, and the swept volume ratio at the maximum of the engine performance are evaluated. Furthermore, deriving and presenting the governing equations allows for rigorous optimization analysis in order to find the optimal combination of the major variables.
Article
Full-text available
This paper reports on the investigation of the simulation accuracy of a second order Stirling cycle simulation tool as developed by Urieli (2001) and improvements thereof against the known performance of the GPU-3 Stirling engine. The objective of this investigation is to establish a simulation tool to perform preliminary engine design and optimisation. The second order formulation under investigation simulates the engine based on the ideal adiabatic cycle, and parasitic losses are only accounted for afterwards. This approach differs from third order formulations that simulate the engine in a coupled manner incorporating non-idealities during cyclic simulation. While the second order approach is less accurate, it holds the advantage that the degradation of the ideal performance due to the various losses is more clearly defined and offers insight into improving engine performance. It is therefore particularly suitable for preliminary design of engines. Two methods to calculate the performance and efficiency of the data obtained from the ideal adiabatic cycle and the parasitic losses were applied, namely the method used by Urieli and a proposed alternative method. These two methods differ essentially in how the regenerator and pumping losses are accounted for. The overall accuracy of the simulations, especially using the proposed alternative method to calculate the different operational variables, proved to be satisfactory. Although significant inaccuracies occurred for some of the operational variables, the simulated trends in general followed the measurements and it is concluded that this second order Stirling cycle simulation tool using the proposed alternative method to calculate the different operational variables is suitable for preliminary engine design and optimisation.
Article
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Solar energy is one of the more attractive renewable energy sources; the conversion of the latter per thermal way into electricity is a major energy stake. The current systems are primarily based on technology known as ‘solar dish/Stirling’, which uses Stirling engines placed at the focal plan of a parabolic concentrator. The Stirling engine presents an excellent theoretical output equivalent to the output of Carnot one. It is with external combustion, less pollutant, silencer and request little maintenance. Thanks to these advantages which the Stirling engine is very interesting to study. The dish Stirling system studies consist on three parts; the thermal modelling of Stirling engine, optical study of parabolic concentrator and finally the thermal study of the receiver. The present study is dedicated only to a thermal modelling of the Stirling engine based on the decoupled method. We evaluate, starting from an ideal adiabatic analysis, the thermal and mechanical powers exchanged, that we correct then by calculating the various losses within the machine. This model led to the writing of important set of equations algebra - differentials. The calculation programme worked out under Fortran to solve this system, makes allow to calculate the performances of any types of the Stirling engines, according to the kinematics used, the types of regenerators, the exchangers, as well as the various working liquids used.
Article
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A Stirling engine configuration consisting of two cylinders, a regenerator and a sliding disc actuating mechanism (“swashplate”) is considered in this paper. A mathematical model, which combines fundamental and empirical correlations, and principles of classical thermodynamics, mass and heat transfer accounting for variable heat transfer coefficients, is developed. The proposed model is then utilized to simulate numerically the system transient and steady state response under different operating and design conditions. A system global optimization for maximum performance in the search for optimal parameters that lead to maximum cycle efficiency is performed with low computational time. Appropriate dimensionless groups are identified and the results presented in normalized charts for general application. The numerical results show that the two-way maximized system efficiency, ηmax,maxηmax,max, occurs when two system characteristic parameters, the ratio between the total swept volume during the expansion, and the total swept volume, φφ, and the ratio between the heat transfer area of the hot side heat exchanger and the total heat exchange area, y, are optimally selected, i.e., (φ,y)opt≅(0.5,0.4)(φ,y)opt≅(0.5,0.4). The two-way maximized cycle efficiency found with respect to the optimized parameters is sharp, in the sense that a 225% variation of the calculated efficiency values was observed within the range of tested configurations in this study, and “robust” (i.e., relatively insensitive) to the variation of several parameters, thus stressing the importance to be considered in actual design. It is also found that the twice-maximized cycle efficiency and the total engine work output increase monotonically with the temperature of the hot source, Th. As a result, the model is expected to be a useful tool for simulation, design, and optimization of Stirling engines.
Article
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This paper presents a preliminary design method based on dynamic similarity and quasistatic simulation. The proposal improves methods based on Beale and West correlations and provides the engine speeds corresponding to the maximum indicated powers and the achievement of indicated power maps. The dimensionless factor of indicated power losses provides a new viewpoint for engine analysis and design. In support of the method, experimental GPU-3 test results have been reanalysed, proving the accuracy of maximum indicated power predictions and providing values of the dimensionless factor of indicated power losses. Scaling factors corresponding to strict dynamic similarity are supplied for several typical cases. Similarity relaxation criteria are also recommended to be used when strict dynamic similarity leads to inadequate specifications for the derivative. Some numerical examples illustrate the method.
Article
Full-text available
Dimensional analysis is applied to both leakage and mechanical power losses in order to obtain the set of parameters that influence power performance of the kinematic Stirling engine. An empirical model of mechanical power losses is proposed to complete the indicated power model previously introduced by Prieto and co-workers. That approach is mainly based on the characteristic Stirling number and allows the performance of known prototypes to be analysed from the viewpoint of indicated power, brake power and mechanical efficiency. After showing that similarity criteria can be extended to brake power performance, scaling factors have been derived for typical scaling cases. Some examples show that quasi-static simulation and scaling techniques may be combined to support preliminary design procedures.
Article
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Previous work carried out for the last eight years resulted in the proposal of a complete system of dimensionless groups in order to represent the performance of different kinematic Stirling engine configurations. When looking for experimental support for the proposed model, some differences between the performances of several prototypes were observed. In this paper an equation is introduced to be applied to all known kinematic engines and to their whole range of performance. The coefficients appearing in this equation can be computed from temperature and geometrical dimensionless ratios and from experimental measurements at the maximum indicated power operating point. The meaning of those coefficients is interpreted and their usefulness to provide an engine performance overview is shown. The quasi-static simulation and the characteristic Mach number at the maximum indicated power operating point appear to be interesting criteria in order to evaluate the performance of prototypes.
Article
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To increase the performance of Stirling engines and analyze their operations, a second-order Stirling model, which includes thermal losses, has been developed and used to optimize the performance and design parameters of the engine. This model has been tested using the experimental data obtained from the General Motor GPU-3 Stirling engine prototype. The model has also been used to investigate the effect of the geometrical and physical parameters on Stirling engine performance and to determine the optimal parameters for acceptable operational gas pressure. When the optimal design parameters are introduced in the model, the engine efficiency increases from 39% to 51%; the engine power is enhanced by approximately 20%, whereas the engine average pressure increases slightly.
Article
Full-text available
In the current energy economy context, the use of renewable energies and the valuation of lost energies are the subject of many studies. From this point of view, the Stirling engine draws attention of the researchers for its many advantages. This paper presents a thermodynamic analysis of a low temperature Stirling engine at steady state operation; energy, entropy and exergy balances being presented at each main element of the engine. A zero dimensional numerical model describing the variables evolution (pressure, volumes, masses, exchanged energies, irreversibilities...) as function of the crankshaft angle is also presented. The calculated irreversibilities are due to imperfect regeneration and temperature differences between gas and wall in the hot and cold exchangers. A favourable comparison was made with experimental results obtained on an small size engine.
Article
A high performance model Stirling engine, in which the heater, regenerator and cooler as a whole is formed by hundreds of porous metal sheets, is identified for theoretical analysis to facilitate the future scale-up design. The reciprocating flow and heat transfer both in the heat exchanger and in the full engine is simulated by a dynamic mesh Computational Fluid Dynamics (CFD) method, and is validated by analytical solutions and experimental data. An optimization method is also developed to incorporate the entropy generation caused by flow friction and irreversible heat transfer. The results show that relatively high indicated power of 33.4 W is obtained, corresponding to a specific power of 1.88 W/cm3 and a thermal efficiency of 43.9%, which are attributable to the extremely small flow friction loss and excellent heat transfer characteristics in the regular shaped microchannels, as well as to the compact heat exchanger design that significantly reduces the dead volume. Given the same operating conditions, the optimized porous-sheets regenerator has a significantly lower total loss of available work while maintaining even higher thermal effectiveness in comparison with the optimized conventional wire mesh regenerator.
Article
In the recent years, numerous studies have been done on Stirling cycle and Stirling engine which have been resulted in different output power and engine thermal efficiency analyses. Finite speed thermodynamic analysis is one of the most prominent ways which considers external irreversibilities. In the present study, output power and engine thermal efficiency are optimized and total pressure losses are minimized using NSGA algorithm and finite speed thermodynamic analysis. The results are successfully verified against experimental data.
Article
Friction pressure drop correlation equations are derived from a numerical study by characterizing the pressure drop phenomena through porous medium of both types namely stacked and wound woven wire matrices of a Stirling engine regenerator over a specified range of Reynolds number, diameter and porosity. First, a finite volume method (FVM) based numerical approach is used and validated against well known experimentally obtained empirical correlations for a misaligned stacked woven wire matrix, the most widely used due to fabrication issues, for Reynolds number up to 400. The friction pressure drop correlation equation derived from the numerical results corresponds well with the experimentally obtained correlations with less than 5% deviation. Once the numerical approach is validated, the study is further extended to characterize the pressure drop phenomena in a wound woven wire matrix model of a Stirling engine regenerator for a diameter range from 0.080 to 0.110 mm and a porosity range from 0.472 to 0.638 within the same Reynolds number range. Thus, the new correlation equations are derived from this numerical study for different flow configurations of the Stirling engine regenerator. The results indicate flow nature and complex geometry dependent friction pressure drop characteristics within the present Stirling engine regenerator system. It is believed that the developed correlations can be applied with confidence as a cost effective solution to characterize and hence to optimize stacked and woven Stirling engine efficiency in the above specified ranges.
Article
A full theoretical model of a low-temperature differential Stirling engine is developed in the current paper. The model, which starts from the first principles, gives a full differential description of the major components of the engine: the behaviour of the gas in the expansion and the compression spaces; the behaviour of the gas in the regenerator; the dynamic behaviour of the displacer; and the power piston/flywheel assembly. A small fully instrumented engine is used to validate the model. The theoretical model is in good agreement with the experimental data, and describes well all features exhibited by the engine.
Article
A mathematical model for the calculation of the Stirling cycle and of similar processes is presented. The model comprises a method to reproduce schematically any kind of process configuration, including free piston engines. The differential balance equations describing the process are solved by a stable integration algorithm. Heat transfer and pressure loss are calculated by using new correlations, which consider the special conditions of the periodic compression/expansion respectively of the oscillating flow. A comparison between experimental data achieved by means of a test apparatus and calculated data shows a good agreement.
Article
The thermodynamic analysis of a V-type Stirling-cycle refrigerator is performed. The Stirling-cycle refrigerator consists of expansion and compression spaces, cooler, heater and regenerator, and divided into 14 fixed control volumes subjected to a periodic mass flow. The conservation of mass and energy equation are written for each control volume. A computer program is prepared in FORTRAN, and the basic equations are solved iteratively. The mass, temperature and density of working fluid in each control volume are calculated for a given charge pressure, engine speed, and fixed heater and cooler surface temperatures, and the results are obtained from a PC. The heat transfer coefficients are assumed constant. The work, instantaneous pressure and COP of the Stirling-cycle refrigerator are also calculated. The steady cyclic conditions are obtained for temperature after few cycles and the results are given by diagrams.
Article
A mathematical model for the overall thermal efficiency of the solar-powered high temperature differential dish-Stirling engine with finite-rate heat transfer, regenerative heat losses, conductive thermal bridging losses and finite regeneration processes time is developed. The model takes into consideration the effect of the absorber temperature and the concentrating ratio on the thermal efficiency; radiation and convection heat transfer between the absorber and the working fluid as well as convection heat transfer between the heat sink and the working fluid. The results show that the optimized absorber temperature and concentrating ratio are at about 1100K and 1300, respectively. The thermal efficiency at optimized condition is about 34%, which is not far away from the corresponding Carnot efficiency at about 50%. Hence, the present analysis provides a new theoretical guidance for designing dish collectors and operating the Stirling heat engine system.
Article
In this study, a thermodynamic analysis of a gamma type Stirling engine is performed by using a quasi steady flow model based on Urieli and Berchowitz's works. The Stirling engine analysis is performed for five principal fields: compression room, expansion room, cooler, heater and regenerator. The conservation law of the mass and the energy equations are derived for the related sections. A FORTRAN code is developed to solve the derived equations for all process parameters like pressure, temperature, mass flow, dissipation and convection losses for the different spaces (compression space, cooler, regenerator, heater and expansion space) as a function of the crank angle. The developed model gave more precise results for the pressure profile than the models available in the literature.
Book
This third edition is an update of the second edition published in 1964. New data and more modern theoretical solutions for flow in the simple geometries are included, although this edition does not differ radically from the second edition. It contains basic test data for eleven new surface configurations, including some of the very compact ceramic matrices. Al dimensions are given in both the English and the Systeme International (SI) system of units.
Article
A technique for calculating the efficiency and power of Stirling machines is presented. This technique is based on the First Law of Thermodynamics for processes with finite speed and the Direct Method for closed systems. In order to apply the Direct Method to Stirling Cycles, a new and novel PV/Px diagram is presented that shows the effects of pressure losses due to friction, finite speed and throttling processes in the regenerator of the Stirling engine. The method used for the analysis of this irreversible cycle with finite speed involves the direct integration of equations based on the first law for processes with finite speed to obtain the cycle efficiency and power directly. This technique is termed the Direct Method. The results predicted by this analysis are in good agreement with the actual engine performance data of 12 different Stirling engines, over a range of output from economy to maximum power. This provides a solid verification that this analysis, based on the Direct Method, can accurately predict actual Stirling engine performance, particularly with regard to efficiency and output power. In addition to the powerful predictive capabilities of the Direct Method, the new PV/Px diagram for the Stirling cycle is both an effective and an intuitive tool for explaining the operation and design of Stirling machines. Copyright © 2002 John Wiley & Sons, Ltd.
Article
This paper presents a new design for high temperature fuel cell and bottoming thermal engine hybrid systems. Now, instead of the commonly used gas turbine engine, an externally fired – Stirling – piston engine is used, showing outstanding performance when compared to previous designs.Firstly, a comparison between three thermal cycles potentially usable for recovering waste heat from the cell is presented, concluding the interest of the Stirling engine against other solutions used in the past.Secondly, the interest shown in the previous section is confirmed when the complete hybrid system is analyzed. Advantages are not only related to pure thermal and electrochemical parameters like specific power or overall efficiency. Additionally, further benefits can be obtained from the atmospheric operation of the fuel cell and the possibility to disconnect the bottoming engine from the cell to operate the latter on stand alone mode. This analysis includes on design and off design operation.
Article
This paper provides a study on power output determination of a gamma-configuration, low temperature differential Stirling engine. The former works on the calculation of Stirling engine power output are discussed. Results from this study indicate that the mean pressure power formula is most appropriate for the calculation of a gamma-configuration, low temperature differential Stirling engine power output.
Article
This paper presents a global thermal model of the energy conversion of the 10 kWel Eurodish dish/Stirling unit erected at the CNRS-PROMES laboratory in Odeillo. Using optical measurements made by DLR, the losses by parabola reflectivity and spillage are calculated. A nodal method is used to calculate the heat losses in the cavity by conduction, convection, reflection and thermal radiation. A thermodynamic analysis of a SOLO Stirling 161 engine is made. The Stirling engine is divided in 32 control-volumes and equations of ideal gas, mass and energy conservation are written for each control-volume. The differential equation system is resolved by an iterative method developed using Matlab™ programming environment. Temperature, mass, density of working gas, heat transfers and the mechanical power are calculated for one Stirling engine cycle of 40 ms and for a constant direct normal irradiation (DNI). The model gives consistent results correctly fitting with experimental measurements.
Article
This article presents a technical innovation, study of solar power system based on the Stirling dish (SD) technology and design considerations to be taken in designing of a mean temperature differential Stirling engine for solar application. The target power source will be solar dish/Stirling with average concentration ratio, which will supply a constant source temperature of 320 °C. Hence, the system design is based on a temperature difference of 300 °C, assuming that the sink is kept at 20 °C. During the preliminary design stage, the critical parameters of the engine design are determined according to the dynamic model with losses energy and pressure drop in heat exchangers was used during the design optimisation stage in order to establish a complete analytical model for the engine. The heat exchangers are designed to be of high effectiveness and low pressure-drop. Upon optimisation, for given value of difference temperature, operating frequency and dead volume there is a definite optimal value of swept volume at which the power is a maximum. The optimal swept volume of 75 cm3 for operating frequency 75 Hz with the power is 250 W and the dead volume is of 370 cm3.
Article
The purpose of this study is to determine the effect of pressure losses and actual heat transfer on the performance of a solar Stirling engine. The model presented includes the effects of both internal and external irreversibilities of the cycle. The solar Stirling engine is analyzed using a mathematical model based on the first law of thermodynamics for processes with finite speed, with particular attention to the energy balance at the receiver. Pressure losses, due to fluid friction internal to the engine and mechanical friction between the moving parts, are estimated through extensive and rigorous use of the available experimental data. The results of this study show that the real cycle efficiency is approximately half the ideal cycle efficiency when the engine is operated at the optimum temperature.
Article
This manual is intended to serve both as an introduction to Stirling engine analysis methods and as a key to the open literature on Stirling engines. Over 800 references are listed and these are cross referenced by date of publication, author and subject. Engine analysis is treated starting from elementary principles and working through cycles analysis. Analysis methodologies are classified as first, second or third order depending upon degree of complexity and probable application; first order for preliminary engine studies, second order for performance prediction and engine optimization, and third order for detailed hardware evaluation and engine research. A few comparisons between theory and experiment are made. A second order design procedure is documented step by step with calculation sheets and a worked out example to follow. Current high power engines are briefly described and a directory of companies and individuals who are active in Stirling engine development is included. Much remains to be done. Some of the more complicated and potentially very useful design procedures are now only referred to. Future support will enable a more thorough job of comparing all available design procedures against experimental data which should soon be available.
development of thermodynamics with finite speed and direct method
  • S Petrescu
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Petrescu S, Costea M. development of thermodynamics with finite speed and direct method. Editura AGIR; 2011.
Principles and applications of Stirling engines
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West CD. Principles and applications of Stirling engines. New York: Van Nostrand Reinhold; 1986.
The regenerator and the Stirling engine
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Organ AJ. The regenerator and the Stirling engine. London: Mechanical Engineering Publications Ltd.; 1997.
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M. Babaelahi, H. Sayyaadi / Energy 69 (2014) 873e890