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Applied Thermal Engineering 86 (2015) 161e167

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research paper

Thermal performance of a Stirling engine powered by a solar simulator € € o € ren a, Fatih Aksoy a, Halit Karabulut b, Can Çınar b, Hamit Solmaz b, *, Yasar Onder Ozg Ahmet Uyumaz c a b c

Department of Automotive Engineering, Faculty of Technology, Afyon Kocatepe University, 03200 Afyonkarahisar, Turkey Department of Automotive Engineering, Faculty of Technology, Gazi University, 06500 Teknikokullar, Ankara, Turkey Automotive Technologies, Vocational High School of Technical Sciences, Mehmet Akif Ersoy University, 15100 Burdur, Turkey

h i g h l i g h t s The performance of a beta type Stirling engine was investigated. 400 and 1000 W halogen lamps were used as a solar simulator in the experiments. Cavity temperature was measured 623 and 873 K for 400 and 1000 W lamps. 1000 W halogen lamp provided better engine performance and thermal efﬁciency. Experimental results of efﬁciency were compared with nodal analysis results.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 15 January 2015 Accepted 13 April 2015 Available online 26 April 2015

In this study, the performance of a beta type Stirling engine which works at relatively lower temperatures was investigated using 400 W and 1000 W halogen lamps as a heat source and helium as the working ﬂuid. The working ﬂuid was charged into the engine block and the pressure of the working ﬂuid was ranged from 1 to 5 bars with 1 bar increments. The halogen lamps were placed into a cavity adjacent to the hot end of the displacer cylinder, which is made of aluminum alloy. In the experiments conducted with 400 W halogen lamp, the temperature of the cavity was 623 ± 10 K. The power, torque and thermal efﬁciency of the engine were determined to be 37.08 W, 1.68 Nm and 9.27%, at 5 bar charge pressure. For the 1000 W halogen lamp, the temperature of the cavity was determined to be 873 ± 10 K. The power, torque and thermal efﬁciency of the engine were determined to be 127.17 W, 3.4 Nm and 12.85%, at the same charge pressure. The experimental thermal efﬁciencies of the engine were also compared with thermodynamic nodal analysis. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Stirling engine Solar energy Beta type Halogen lamp Solar simulator

1. Introduction The demand for energy around the world is escalating day by day. However, existing energy sources and energy diversiﬁcation is still not sufﬁcient to satisfy energy demand [1]. In addition, the cost of the existing energy sources is increasing steadily [2]. A large proportion of the world's energy requirements are currently generated by fossil-based fuels. Focusing on new energy sources is

* Corresponding author. Tel.: þ903122028653; fax: þ903122028649. E-mail addresses: [email protected] (F. Aksoy), [email protected] (H. Karabulut), [email protected] (C. Çınar), [email protected] (H. Solmaz), € € o €ren), [email protected] (Y.O. Ozg [email protected] (A. Uyumaz). http://dx.doi.org/10.1016/j.applthermaleng.2015.04.047 1359-4311/© 2015 Elsevier Ltd. All rights reserved.

mandatory because of the risk of petroleum depletion and the negative effects of fossil fuels on the environment and human health [3]. Many researchers exert a great effort in order to develop different renewable energy sources [4]. Solar energy is one of the most attractive alternative renewable energy sources. In addition, solar energy is the most abundant and inexhaustible energy source [5]. The reduction of air pollutant and greenhouse gases, the promotion of national energy independency and the protection of water resources are the main advantages of solar energy [6]. Today solar energy is mainly used for the production of electricity. There are several ways to convert solar energy into electricity, such as with photovoltaic cells [7], parabolic trough collectors [8], solar towers [9] and parabolic dish collectors [10].

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Nomenclature Ai Cp CV Ei [c [h hp/2 hd hi [d [m [r [p mt mi

nodal values of heat transfer surface (m2) speciﬁc heat at constant pressure (J/kg K) speciﬁc heat at constant volume (J/kg K) enthalpy ﬂow in and out the nodal volumes (J) length of cold volume (m) length of hot volume (m) distance between piston top and piston pin (m) displacer length (m) nodal values of convective heat transfer coefﬁcient (W/ m2K) length of displacer rod (m) distance between ﬁxing pin and crank pin (m) length of displacer rod (m) length of piston rod (m) total mass of working ﬂuid (kg) nodal values of working ﬂuid mass (kg)

Generally, in most solar energy applications, solar radiation is converted to heat in order to obtain superheated steam. While the superheated steam expands in a turbine, an electricity generator working with the turbine simultaneously produces electricity. On the other hand, solar radiation can be used to run a heat engine, such as a Stirling engine. The parabolic dish collector focuses the solar radiation on a receiver mounted on the heat engine. The receiver converts the solar radiation to heat and transfers this heat to a working ﬂuid that runs the heat engine. Thus mechanical energy produced by the heat engine is converted to electricity via an electricity generator [11]. The efﬁciencies of the parabolic trough collectors, the solar energy towers and the dish/heat engines are approximately 21%, 23% and 29% [12]. The photovoltaic cells convert the solar radiation into electricity with peak efﬁciencies in the range of 5e24% [13]. Xing et al. reported a 5% experimental efﬁciency for thermoelectric elements [14]. It is seen that dish/heat engine solar energy systems are capable of providing high conversion efﬁciency. Stirling engines have a wide range of research and application ﬁelds. The Stirling engines are attractive because they can be operated with any heat sources including solar radiation, geothermal energy, fossil fuels, coal, wood and radioisotope [15]. The ﬁrst idea of solar energy conversion using Stirling engine was investigated by Malik and Parker in 1962 [16]. Many of the dish/ Stirling solar energy conversion systems were built with a free piston Stirling engine (FPS). However, kinematic Stirling engines were also used in solar energy applications [17]. Fujita et al. performed a study to compare performance characteristics of three different solar energy systems. In their study, a dish/Stirling engine, a gas turbine operated with a Brayton cycle and a gas turbine operated with a BraytoneRankine cycle solar energy conversion systems were investigated. It was determined that the gas turbine systems using Brayton and BraytoneRankine combined cycles had advantages at high temperatures. However, the performance of the dish/Stirling engine solar energy system was higher than the gas turbine applications at temperatures below 950 C. Therefore, for small-scale solar energy conversion, it was determined that the dish/Stirling engine solar energy conversion system is more appropriate [18]. Advanco Corparation developed a 25 kW dish/Stirling engine solar energy system called the Vanguard System as a result of a three-year study conducted between 1982 and 1985. In the

Dmi Rg R SL hc Ti Tc Th Tw,i t Dt Vi 4

bp bd g q

variation of nodal mass within a time frame (kg) gas constant (J/kg K) radius of crankshaft (m) length of lever arm connected to displacer rod (m) length from cylinder top to the center of the ﬁxing pin (m) nodal values of working ﬂuid temperature (K) cold end temperature of displacer cylinder (K) hot end temperature of displacer cylinder (K) nodal values of heat transfer surface temperature (K) time (s) change in time (s) nodal values of volume (m3) angle between the lever arms (rad) angle made by piston rod with vertical (rad) angle made by displacer rod with vertical (rad) angle made by slotted arm of lever with vertical (rad) crankshaft rotation (rad)

Vanguard System, the United Stirling 4-95 Mark II kinematic Stirling engine and a glass-faceted dish with a 10.5 m diameter were used. Although the lubrication, vibration, noise and hydrogen leakage problems, 29.5% net solar to electricity conversion efﬁciency was obtained which was the world record [19]. In 1984, two 50 kW dish/Stirling systems were built in Riyadh, Saudi Arabia, by Schlaich-Bergerimann und Partner (SBP) of Stutgart, Germany. United Stirling 4-275 kinematic Stirling engines with direct insolation receivers and 17 m diameter dishes that stretchedmembrane concentrators were used in the system [20]. In 1985, a dish-Stirling solar energy system was built in the Jet Propulsion Laboratory of the California Institute of Technology (JPL) on the behalf of US Department of Energy. The Stirling engine used in the solar energy system was United Stirling 4-95 Mark II, the same engine that was used in Vanguard System. The power output of the system reached 25 kW with a conversion efﬁciency of 35% [21]. In 1991, Cummins Power Generation started to develop two dish/ Stirling solar energy systems with 7 kW and 25 kW power [29]. Cummins used advanced technologies in its dish/Stirling solar systems [22]. However, in 1996, the Cummins Engine Company decided to refocus on diesel engine development which was its core research ﬁeld. As a result, the solar operations of Cummins Power Generation were sold to Kombassan Company in Turkey [20]. Under the Eurodish project, a 10 kW dish/Stirling solar energy system was developed by Deutsches Zentrum für Luft und Raumfahrt (DLR) and SBP. In this system, an alpha type Stirling engine was used. The conversion efﬁciency and power output of the system were 21.6% and 11.1 kW [23]. Kongtragol and Wongwises performed two investigations on a solar energy system using Stirling engine. In the ﬁrst study, a gamma type double piston LTD Stirling engine was tested at 399, 409, 419 and 436 K heater temperatures. They used a 1000 W halogen lamp as the heat source in the experiments. While maximum engine torque was obtained as 0.352 Nm at the engine speed of 23.2 rpm, the maximum engine power and thermal efﬁciency were 1.69 W and 0.645%, at the engine speed of 52.1 rpm [24]. In their other study, the performance of a gamma type LTD Stirling engine with four power pistons was investigated under atmospheric conditions at four different hot source temperatures using four halogen lamps as the solar simulator. The maximum engine power and thermal efﬁciency were 6.1 W and 0.44% at 20 rpm engine speed and 439 K hot source temperature [25].

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Tavakolpour et al. designed and manufactured a gamma type LTD Stirling engine. The LTD Stirling engine was tested using a ﬂat plate solar collector as the heat source. 0.27 W engine power was obtained at a collector temperature of 110 C and at an engine speed of 14 rpm. The engine reached 30 rpm engine speed under no-load conditions at a solar radiation intensity of 900 W/m2 [26]. In an experimental study performed by Karabulut et al., a small dish/Stirling solar energy system was built and tested. In the system, no solar receiver was used and the solar radiation was directly reﬂected to the outer surface of the displacer cylinder. The system was tested under 820 W/m2 solar radiation. The hot end temperature of the beta type engine reached to 156 C and 23.59 W power output was obtained [27]. Aksoy and Karabulut developed a microsolar energy conversion system with a beta type Stirling engine. They used a fresnel lens instead of a dish to focus the solar radiation on the receiver. It was determined that the material of the cavity affects the conversion efﬁciency. Total conversion efﬁciencies were obtained as 3% and 5.6% with copper and aluminium cavities [28]. Thermodynamic analyses are useful to predict engine performance before manufacturing process. There are several thermodynamic analysis method for Stirling engines [29]. One of these methods is Nodal analysis which was developed by Finkelstein in 1967. Finkelstein divided the total volume of the engine into 13 nodal volumes, which were expansion volume, heater volume, regenerator volume, cooler volume and cold volume. Instantaneous pressure and temperature variations were calculated in these nodal volumes [30]. Martini performed a ﬁve zone nodal analysis in 1978. He assumed that the temperature of the working ﬂuid was equal to wall temperature [31]. Karabulut et al. conducted a nodal analysis to predict performance characteristics of a gamma type Stirling engine. In that study, the power cylinder was concentrically placed into the displacer cylinder to increase speciﬁc power [32]. Aksoy and Cinar conducted a nodal analysis on a beta-type rhombic driven engine. They used 50 nodal volumes in the analysis. They reached 86.30 W engine power with a smooth displacer for a heat transfer coefﬁcient of 200 W/m2K [29]. Another nodal analysis on a lever-driven Stirling engine was performed by Solmaz and Karabulut. They compared the novel lever-driven arrangement with a rhombic-driven engine. In the study, the total volume of the engines was divided into 12 nodal volumes. They compared the performance of both engines at 500, 1000 and 1500 W/m2K heat transfer coefﬁcients [15]. The convective heat transfer coefﬁcient has a signiﬁcant effect on engine performance [33]. In the nodal analysis, it is required to make an assumption for the heat transfer coefﬁcient. However, it is difﬁcult to estimate the convective heat transfer coefﬁcient in advance. Because of this situation, the performance of the analyses is decreasing. In the present study, the convective heat transfer coefﬁcient was predicted by considering experimental results. In the experiments, 400 W and 1000 W halogen lamps were used to simulate solar energy. The halogen lamps were placed into the cavity. Thus, more stable operating conditions and temperature distribution were obtained compared to solar energy tests at atmospheric conditions. Nodal analysis was conducted with the predicted heat transfer coefﬁcient and results were compared with experimental results. 2. Experimental setup and procedure A schematic view of the experimental set-up is given in Fig. 1. The technical speciﬁcations of the test engine are given in Table 1. The design details of the engine are given in Refs. [17,28]. In order to apply the solar energy to the engine its displacer cylinder has been modiﬁed so as to capture the reﬂected sun rays. The displacer

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Fig. 1. A schematic view of the experimental set-up.

cylinder designed and manufactured for solar energy is consisted of two sections and mounted to each other by means of screwing. The lower section performs as cooler and regenerator and is made of non-brass ASTM steel. The upper section functions as a heater and is made of aluminum alloy. Fig. 2 illustrates details of both sections. The upper section comprises a cavity in which the solar rays would be focused when solar energy is applied to the engine. In the experiments prior to the solar application however, the engine is powered with halogen lamps placed into the cavity. The outer surface of the both sections of the displacer cylinder has been covered with an insulation material in order to minimize heat losses. The heat transfer area on the working ﬂuid side of the displacer cylinder was enlarged by means of growing span-wise slots with 3 mm depth and 2 mm width. The engine has been loaded using a prony type dynamometer, which operates based on friction principle. The dynamometer consists of a shaft on which there is a disc, two consoles holding the roller bearings of the shaft, a hydraulic device to accomplish loading of the engine by means of compressing the disc, a load cell and a torque arm which transfers the braking force to the load cell. The load cell used in the experiments is type ESIT BB20 and it has a total measurement error of 0.05%. Uncertainty of engine moment, power and thermal efﬁciency were determined as 0.395%, 0.442% and 0.667%. In order to measure the speed of the engine, a digital tachometer operating with magnetic pulse and having 1 rpm accuracy has been used. The charge pressure has been measured by a bourdon type pressure gauge, which can make measurements between 0 and 10 bar with 0.1 bar accuracy. A pressure regulation valve has been used in order to set the charge pressure to desired values. The working ﬂuid has been charged into the engine block. The pressure of the working ﬂuid charged into the engine block was increased up to 5.5 bar without any leakage problem. Before recording experimental results, the engine was operated under several operating conditions in order to ensure steadiness of the engine's operation. Test operation includes measurements of hot source temperature, cold source temperature, block pressure, engine speed and torque. As the engine torque and speed are related to each other, they were measured simultaneously. During the experiments, the pressure ranged from up to down with 1 bar

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Table 1 Technical speciﬁcations of the test engine.

Parameters

Speciﬁcations

Engine type Bore (mm) Displacer stroke (mm) Displacer diameter (mm) Displacer swept volume (cc) Power piston stroke (mm) Power piston swept volume (cc) Working ﬂuid Compression ratio Heating

Beta 69 79 295 70 60 230 Helium 1.65 Solar Simulator (400 and 1000 W halogen lamps) 127.17 W @ 405 rpm 3.4 Nm @192 rpm 12.85% @ 405 rpm

Maximum engine power Maximum engine torque Maximum engine efﬁciency

bp ¼ arcsin

R sin q [p

(1)

0:7071 þ sin q g ¼ arctan 2:5 þ cos q bd ¼ arcsin

s R cosðg 4Þ 0:7071 [d [d

(2)

Rð0:7071 þ sin qÞ sin g

[m ¼

[c ¼ [d cos bd SL sinðg 4Þ þ [r [m cos g [p cos bp decrements. In the experiments conducted with a 400 W lamp, the temperature of the aperture of cavity was measured as 623 ± 10 K using an infrared thermometer. Through the experiments conducted with a 1000 W lamp, the temperature of the same point was measured as 873 ± 10 K. The working ﬂuid was cooled by circulating water around the piston cylinder and cooling water temperature was kept about 300 K.

[h ¼ hc [d cos bd þ SL sinðg 4Þ [r hd

3. Kinematic and thermodynamic relations of the engine

p¼V

hp 2 (5) (6)

The ﬂow loss was disregarded, and the pressure was calculated

Tc

Fig. 2. A schematic view of both sections of the engine.

(4)

by,

c

The mechanical arrangement of the test engine, which is shown in Fig. 3, was developed by Karabulut et al. [34]. In this mechanism, a slotted lever provides interconnected movement of the piston, displacer and crankshaft. The angle between the lever arms is 70 and the lever is ﬁxed with a bearing at the junction points of the arms. While the crank pin is sliding in the slotted arm of the lever, the other lever arm moves the displacer connecting rod. Therefore the required movement synchronization of the mechanism for the Stirling cycle is provided. A detailed explanation about the arrangement can be seen in the study conducted by Karabulut et al. [34]. In the nodal analysis the space occupied by working ﬂuid is to be divided to a number of nodal volumes. In the present study, 51 nodal volumes were used. The 49 nodal volumes were in the regenerator and these volumes had constant magnitudes. The ﬁrst nodal volume was hot volume and the last nodal volume was cold volume. The cold and hot volume variations were calculated using kinematic relations below;

(3)

þ

Vh Th

mt Rg P VRi þ n2 i¼3 TRi

(7)

Time dependent temperature changes in nodal volumes were calculated using the ﬁrst law of thermodynamics for an open system,

Fig. 3. Schematic illustration of the test engine.

F. Aksoy et al. / Applied Thermal Engineering 86 (2015) 161e167

DTi ¼

hi Ai Tw;i Ti Dt Dmi cv Ti þ Ei pDVi þ DTi U mi cv þ U

(8)

where U is an arbitrary constant and Ei is the enthalpy ﬂow of the nodal volume. If U is taken as zero, the numerical solution of the equations does not converge and cannot be solved. Therefore U is chosen, preferably as 1. Instantaneous values for mass (mi) can be calculated using the ideal gas equation. The enthalpy ﬂow in or out of the nodal volume can be calculated by,

Ti þ Tiþ1 ðDmiþ1 þ Dmiþ2 þ / þ Dmn Þ 2 T þ Ti ðDm1 þ Dm2 þ / þ Dmi1 Þ cp i1 2

Ei ¼ cp

(9)

4. Results and discussion Fig. 4 illustrates the variations of engine torque versus engine speed for 400 W and 1000 W halogen lamps. When the 400 W halogen lamp was used, at the charge pressures of 4 and 5 bar, the engine torques were obtained as 1.65 Nm at 191 rpm and 1.68 Nm at 197 rpm. The maximum engine torques were obtained as 3.05 Nm at 181 rpm and 3.4 Nm at 192 rpm, at 4 and 5 bar charge pressures with 1000 W halogen lamp. At low engine speeds, higher torque values were obtained. Similar speed-torque behaviors were obtained by other researchers Karabulut et al. [17], Tavakolpour et al. [26] and Kongtragool et al. [35]. Higher engine torques were obtained at low engine speeds because the ﬂow losses decreased and the prolonged heat exchange time enabled a better thermodynamic cycle. Also this torque behavior of the engine indicates inadequate heat transfer surface area in the expansion volume at higher speeds [15]. In order to obtain the same level of the engine torque at higher engine speeds, some applications may be performed for increasing the heat transfer at the hot end, such as increasing the heater temperature, providing a higher heat transfer coefﬁcient in the expansion volume and trying to enlarge the inner surface area. In Figs. 5 and 6, the engine shaft power and thermal efﬁciency variations are seen. For both halogen lamps, the maximum engine powers were obtained at 5 bar charge pressure. The maximum engine powers were obtained with 400 W and 1000 W halogen lamps as 37.08 W and 127.17 W. In addition, the corresponding

Fig. 4. The variations of engine torque versus engine speed.

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engine speeds with the maximum engine powers for 400 W and 1000 W lamps were recorded as 221 rpm and 405 rpm. The engine power varies dependent on the engine torque and the engine speed. With the increase of the engine speed, the engine power increases as well up to a certain value of engine speed and then starts to decrease. The heat exchange time is shortened at high engine speeds. Therefore, it can be clearly said that the heat transferred into the working ﬂuid becomes insufﬁcient. Also the mechanical losses increase with the increase of engine speed. Therefore, the engine power decreases at higher engine speeds. It was also obtained that thermal efﬁciencies were 9.26% and 12.85% with 400 and 1000 W halogen lamps at 5 bar charge pressure. The thermal efﬁciency of a cycle depends on the maximum and minimum temperatures of the cycle [28]. When the 1000 W halogen lamp was used, a higher thermal efﬁciency was obtained because of increasing temperature difference between hot and cold volumes. For both halogen lamps, the variations of maximum engine power, engine torque and thermal efﬁciency versus charge pressure are seen in Fig. 7. It can be concluded that maximum engine powers, engine torque and thermal efﬁciencies increased as the charge pressure and the heat input increased. Heating performance of the lever driven beta-type Stirling engines is better than some other Stirling engine drive mechanisms [15]. Therefore with increasing charge pressure, the heating performance did not decreased immediately, and thermal efﬁciency, engine power and engine torque increased. On the other hand, the increase of charge pressure caused sealing problems. For this reason, the engine could not be operated at higher charge pressures. It is expected that the engine performance may have decreased after a certain level of the charge pressure because of the inadequate inner surface area like the other studies in the literature [14,15,36,37]. It can be also concluded from Fig. 6 that the maximum curves are beyond the applied range of the charge pressure. This implies that at higher charge pressures applied in this testing, the engine would give higher power outputs and thermal efﬁciency. A detailed thermodynamic nodal analysis of the test engine was already presented previously by Karabulut et al. [34]. In the previous study, the working ﬂuid space of the engine was divided 51 nodal volumes consisting of cold, hot and regenerator volumes. In the present study, experimental results were compared with the nodal analysis results using the same analysis method. In this experimental study, the maximum engine power was obtained as 127.17 W at 405 rpm for the 1000 W halogen lamp. In these conditions, the cyclic work was calculated as 18.84 J. The test was

Fig. 5. The variations of engine power versus engine speed.

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Fig. 6. The variations of thermal efﬁciency versus engine speed.

Fig. 7. The variations of maximum engine power, engine torque and thermal efﬁciency versus charge pressure.

Fig. 9. The comparison of the predicted and experimental thermal efﬁciencies of the engine.

carried out at 300 K cold source and 873 K hot source temperatures, 405 rpm engine speed, 170 cc regenerator volume, 1800 cc heat transfer surface, 0.177 g working ﬂuid mass. The thermodynamic nodal analysis was performed using the experimental test conditions. Using of nodal analysis, the convective heat transfer coefﬁcient was estimated as 148.3 W/m2K for the same cyclic work generation of the both experimental and numerical study. peV diagrams of the engine for both isothermal and estimated heat transfer coefﬁcient are shown in Fig. 8. In the isothermal analysis, it is assumed that the heat transfer performances of the heating and cooling processes were perfect. Therefore the heat transfer coefﬁcient converged to inﬁnity. However, because of the thermal and mechanical losses, it is not possible to provide inﬁnite heat transfer coefﬁcient in Stirling engines. As seen in Fig. 8, net cyclic work area of the peV diagram of the estimated heat transfer coefﬁcient is less than the isothermal condition. Fig. 9 shows the comparison of the experimental and the predicted thermal efﬁciencies of the engine for 1000 W halogen lamp. Both the experimental and the theoretical results were obtained at 5 bar charge pressure, 300 K cold source temperature and 873 K hot source temperature. For the same cold and hot source temperatures, Carnot efﬁciency was calculated as 65.64%. The predicted efﬁciencies were obtained via the nodal analysis presented by Karabulut [34]. When the maximum thermal efﬁciency was predicted as 25.38% at 237 rpm, the maximum experimental efﬁciency was obtained as 12.717% at 405 rpm. The difference between the experimental and theoretical efﬁciency was quite large at low engine speeds. This difference decreased with increasing engine speed. This is because of the worsening heating performance due to an insufﬁcient heat transfer time at higher engine speeds. Also it may be resulted from the decreasing leakages, which affects engine performance positively, in the experimental study at higher engine speeds. 5. Conclusion

Fig. 8. The comparison of peV diagrams obtained in nodal and isothermal conditions at the 5 bar charge pressure.

In this study, a beta type Stirling engine was tested using 400 W and 1000 W halogen lamps as the solar simulator. The experiments were conducted between the range of 1e5 bar charge pressure with 1 bar increments and 150e500 rpm engine speeds. Using 400 W halogen lamp, 37.08 W maximum power output, 1.68 Nm maximum torque and 9.27% maximum thermal efﬁciency were obtained at 5 bar charge pressure. The maximum torque and power

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were obtained corresponded to 197 and 221 rpm. The lamp with 1000 W power provided 127.17 W maximum power, 3.4 Nm maximum torque and 12.85% maximum thermal efﬁciency. The maximum torque and power of the engine corresponded to 192 and 405 rpm when tested with 1000 W lamp. Acknowledgements This study was supported by Gazi University Scientiﬁc Research Foundation in frame of the project code of TEF-07/2009-32. As researchers, we thank Scientiﬁc Research Foundation of Gazi University. References [1] J.A. Araoz, M. Salomon, L. Alejo, T.H. Fransson, Non-ideal Stirling engine thermodynamic model suitable for the integration into overall energy systems, Appl. Therm. Eng. 73 (1) (2014) 205e221. [2] A. Cacabelos, P. Eguia, J.L. Miguez, G. Rey, A. Elena, Development of an improved dynamic model of a Stirling engine and a performance analysis of a cogeneration plant, Appl. Therm. Eng. 73 (1) (2014) 608e621. [3] S. Aydın, C. Sayın, H. Aydın, Investigation of the usability of biodiesel obtained from residual frying oil in a diesel engine with thermal barrier coating, Appl. Therm. Eng. 80 (2015) 212e219. [4] T. Li, D. Tang, Z. Li, J. Du, T. Zhou, Y. Jia, Development and test of a Stirling engine driven by waste gases for the micro-CHP system, Appl. Therm. Eng. 33 (2012) 119e123. [5] W. Yaici, E. Entchev, Performance prediction of a solar thermal energy system using artiﬁcial neural networks, Appl. Therm. Eng. 73 (1) (2014) 1348e1359. [6] B. Parida, S. Iniyan, R. Goic, A review of solar photovoltaic technologies, Renew. Sustain. Energy Rev. 15 (3) (2011) 1625e1636. [7] M. Bortolini, M. Gamberi, A. Graziani, Technical and economic design of photovoltaic and battery energy storage system, Energy Convers. Manag. 86 (2014) 81e92. [8] Z.D. Cheng, Y.A. He, K. Wang, B.C. Du, F.Q. Cui, A detailed parameter study on the comprehensive characteristics and performance of a parabolic trough solar collector system, Appl. Therm. Eng. 63 (1) (2014) 278e289. [9] H. Zheng, X. Yu, Y. Su, S. Riffat, J. Xiong, Thermodynamic analysis of an idealized solar tower thermal power plant, Appl. Therm. Eng. 81 (2015) 271e278. [10] Z. Li, D. Tang, J. Du, T. Li, Study on the radiation ﬂux and temperature distributions of the concentrator-receiver system in a solar dish/Stirling power facility, Appl. Therm. Eng. 31 (10) (2011) 1780e1789. [11] A.D. Minassians, Stirling Engines for Low-temperature Solar-Thermal- Electric Power Generation, Ph.D, University of California, California, USA, 2007. [12] D.Y. Goswami, F. Kreith, Energy Conversion, CRS press, Florida, USA, 2008. [13] P.G. Charalambous, G.G. Maidment, S.A. Kalogirou, K. Yiakoumetti, Photovoltaic thermal (PV/T) collectors: a review, Appl. Therm. Eng. 27 (2007) 275e286. [14] X. Niu, J. Yu, S. Wang, Experimental study on low-temperature waste heat thermoelectric generator, J. Power Sources 188 (2009) 621e626. [15] H. Solmaz, H. Karabulut, Performance comparison of a novel conﬁguration of beta-type Stirling engines with rhombic drive engine, Energy Convers. Manag. 78 (2014) 627e633.

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