Numerical simulation of performance of a double-acting alpha-type stirling engine

SCIENCE & TECHNOLOGY DEVELOPMENT, Vol 18, No.K7- 2015 Numerical simulation of performance of a double-acting alpha-type stirling engine  Nguyen Truong  Chin-Hsiang Cheng  Yen-Fei Chen Department of Aeronautics and Astronautics, National Cheng Kung University,Tainan, Taiwan ROC. (Manuscript Received on July 13th, 2015; Manuscript Revised October 16th, 2015) ABSTRACT Computational Fluid Dynamics (CFD) expansion chamber of a cylinder to the analysis is one of the most important compression chamber of the next cylinder powerful processes in commercial engine with a channel, the pressure difference project, which is going to give the engineers between the expansion and compression the overall vision that a simulator may want chambers is increased and the power to know about. It could save lots of time and capacity of the engine is improved. In this costs before people actually manufacture the paper, the numerical module is built based engine. This paper deals with numerical on the frame of commercial CFD software simulation of a double acting alpha-type (FLUENT). The user-defined functions Stirling engine (DASE), which has four (UDFs) of the software are adapted so that cylinders with four pistons moving the movement of those pistons in those respectively. In the engine, double actions of cylinders can be simulated. Periodic the four pistons take place in two opposite changes in temperature, pressure and chambers in each of four cylinders. For each velocity fields in the engine are predicted and cycle, the piston alternately moves back- the power output of engine is obtained. and-forth in a cylinder by the connecting Key words: Double acting alpha-type Stirling engine, CFD, Stirling engine. 1. INTRODUCTION The idea of double acting alpha-type Stirling (BDC) point to create the swept volume in other engine which original created with four cylinders room. The four pistons can be driven by apply but in one cylinder have two chambers, any mechanism systems, whichever can make the expansion room (hot space) and compression sinusoidal motions of multi-pistons by the phase room (cold space). The adjacent cylinders would angle differences of adjacent pistons in the be connected to the behind cylinders after engine, for example the crankshaft system and throughout the regenerators. Each cylinder has swash-plate systemetc. only one piston which can move from the top The models are designed with the exact dead center (TDC) point to bottom dead center fluids occupied by the volumes inside the engine. Trang 14 TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K7- 2015 The primer design has 4 modules within hot Each module has the same structure and chamber (fluid in the expansion chamber), cold working principles but the phase angle is 90 chamber (fluid in the compression chamber), and degree difference between these modules (shown regenerator (fluid in the regenerator) and pipes on Figure 1), so that total volume of each module (fluid occupied in the pipes which connected hot is not the same at the start point. At the beginning, chamber and cold chamber to regenerator). two modules are at the smallest volume (pressing) and two other modules are at the biggest volume (stretching). a) Circular configuration of DASE a) Circular configuration of DASE b) Liner configuration of DASE Figure 1. The different configurations of DASE Trang 15 SCIENCE & TECHNOLOGY DEVELOPMENT, Vol 18, No.K7- 2015 2. METHODOLOGY V V V Sc 1  cos  t   (9) CI Cd    2.1. Piston displacement 2 For the determination of sinusoidal motion V 3   (10) V V Sc 1  cos  t  CII Cd    of those 4 pistons in simulation, the analysis 2 2   trajectories of those pistons are a necessary V V V Sc 1  cos  t (11) CIII Cd   process. The displacements of four pistons in 2 alternate cylinders can be seen in Figure 1, it can V    V V Sc 1  cos  t  (12) be written following as bellow: CIV C d    2 2   1r cos   (1) S rsin  L cos sin   ; 1 L   where, VH is expansion space volume variation, V is compression space volume 1r sin   (2) C S rcos  L cos sin   ; variation, V is expansion death volume, V 2 L   Hd Cd is compression death volume, VSh is swept 1 r cos   (3) S  rsin  L cos sin  ; volume of expansion space, VSc is swept 3 L     volume of compression space. 1r sin   S  rcos  L cos sin  ; (4) Thermodynamic of this model calculated by 4 L     the consideration on three main spaces are hot where, α is the phase angle; r is the radius; chamber (CV-hot), cold chamber (CV-cold) and L is the length of connecting rod; S1 , S 2 , S 3 , S 4 regenerator space [1]. The volumes of hot are the straight trajectory of these 4 pistons. chamber and cold chamber are not stationary; its 2.2. Volume variation variable due to piston’s displacements all the time but the volume of regenerator is constant. In a DASE model there are 4 modules, one module consisting of compression chamber, 2.3. A control volume of DASE expansion chamber and regenerator. Those In the Figure 2 shows a control volume theoretical thermodynamics model of each (CV) in a DASE which called one module. The module are the same as sinusoidal variation so CV design includes hot chamber (fluid in the that in this section, theoretical study of one unit expansion chamber), cold chamber (fluid in the module analytical studied model as others. These compression chamber), and regenerator (fluid in total expansions space and total compressions the regenerator) and pipes (fluid occupied in the space can be calculated as equations below: pipes which connected hot chamber and cold chamber to regenerator), which are the exact V V V Sh 1  cos  t  fluids occupied by the volumes inside the engine. HI Hd 2 (5) 2.4. Working condition V    V V Sh 1  cos  t  The operation of Stirling engine [2] can be HII Hd    (6) 2 2   controlled by the different levels of heat sources from both of expansion room and compression VSh VH V Hd 1  cos  t    (7) room. The net work done can be adjusted by III 2 many ways such as initial pressure in charge, V 3   variation of volume including dead volume in V V Sh 1  cos  t  (8) HIV Hd    2 2   each room, variation of temperature of heat sources, etc. Trang 16 TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K7- 2015 Figure 2. A control volume in a DASE Table 1. Dimensional design of base-line case Expansion cylinder & piston Bore 70 mm Stroke 50 mm Swept volume 192 cm 3 Compression cylinder & piston Bore 70 mm Stroke 50 mm Swept volume 192 cm 3 Regenerator Diameter 20 mm length 50 mm Volume filling up in fact 14 cm 3 Connected Pipe Diameter 8 mm Total length 210 mm Volume filling up in fact 10 cm 3 Table 2. Working conditions of DASE Regenerator P T T D S Ω H L e, c Porosity (atm) (mm) (rpm) (K) (K) (mm) (%) 1-3-5 1200 300 70 0.9 50 750-1500-3000 Trang 17 SCIENCE & TECHNOLOGY DEVELOPMENT, Vol 18, No.K7- 2015 500 Case 1 P=1atm 11 450 Module IV Module I Module I Module II Module III Module IV Module III Module II 9 400 ] ] m t c c a [ 350 [ 7 e e r m u u s l s 300 o e r 5 V P 250 3 200 1 150 90 180 270 360 90 180 270 360 Crank Angle [deg] Crank angle [deg] Figure 3. Volume variations of 4 modules in cycle Figure 4. Pressure variations of 4 modules in cycle 22 500 36 P=5atm Work done per cycle P=3atm 20 P=1atm Power output 34 18 450 32 16 ] m 14 30 t 400 a [ ] ] J e 12 [ W r [ 28 u W s P s 10 e 350 r 26 P 8 6 24 300 4 22 2 250 20 100 150 200 250 300 350 400 450 0 1 2 3 4 5 6 Volume [cc] P [atm] Figure 5. PV diagrams of each module in different Figure 6. Work done per cycle and power charged pressures in a cycle output at different charged pressures Besides, the working fluid used inside those 3. RESULT AND DISCUSSION chambers is considered as air, hydrogen and In this paper, the results obtained at primer nitrogen; they have almost the same design which can be seen in Table 1. The design thermodynamic proprieties [3] so that the of engine cylinder diameter and stroke are fixed. performance in a Stirling cycle [4] also must be We do investigate the effects of power output and similar. The advantages of nitrogen is reduces the energy to improve the performance of engine. The work done per cycle can be calculated as the explosion factor under working and the hydrogen following formula: can creates high engine’s efficiency but the main W PdV  PdV  PdV  PdV  PdV purpose that we had used air as working fluid  1 1  2 2  3 3  4 4 because it is likely as the normal environment and c c c c c 4  PdV during the time life cycle of engine it is not only  1 1 reduce the maintenance fee but also can make the c (13) longer life time for the engine. Trang 18 TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K7- 2015 At high charged pressure and low rotation will create the higher result of power output and speed of engine, the performance of engine is work done. increased as the difference in pressure between To know about the performances of engine, the lowest and the highest point in the PV the investigation effect of speed engine is diagram is larger. Morever, the area enclosed by necessary, in this paper the performance of PV diagram also becomes bigger. The effect of engine bases on the affection of speeds engine charged pressure also influences to obtain better have shown on. The best performance of this indicated work. By the ideal gas equation engine given at rotation speed of engine around PV mRT , while the specific gas R is constant, point 1500rpm, even though the indicated work the initial volume and the initial temperature are done at this speed does not perfect. Its indicated the same;the change of initial pressure will work is smaller than the one created by the lower directly affect the quality of the initial mass. By of speed engine and higher speed engine. The that mean, the variation of pressure will change important issue has also explored is the negative the quality of initial mass so if the power output work will be created when the rotation speed of per unit mass fixed, more quality of initial mass engine increases too high. So that, to reach the charged which will create more power output of highest engine efficiency, the operation engine at Stirling engine. Figure 7 is the influence of this point is possible. charged pressure to work done and power output, which shows the greater of the charged pressure, 600 25 Work done Power output 500 20 400 15 ] ] J [ W [ 300 10 W P 200 5 100 0 0 -5 750 1500 2250 3000 Speed [rpm] Figure 7. Work done and power output in a cycle at different rotation speeds of engine Trang 19 SCIENCE & TECHNOLOGY DEVELOPMENT, Vol 18, No.K7- 2015 4. CONCLUSIONS conditions. The analyses are considered making The complete construction of three- heat transfer fluid inside the cylinder, ignoring dimensional computational fluid dynamics the heat conduction wall. Setting heat source simulation is based on solving the dynamic boundary conditions and assumptions are boundaries problem of the heat distribution and forwarded to low temperature working engines flow fields in the cylinder of double acting α-type [6]. The results such as average temperature, Stirling engine. The design, simulation and average pressure, and average mass continuity analysis processes were done by using the are written out with the match up to variation of numerical simulation model software volume at the differences of time, it is getting (FLUENT). Using one of the most advanced close to the real engine and improved the results. simulation software ANSYS FLUENT [5] has Acknowledgement: Financial support from brought much benefits and given us an useful the Ministry of Science and Technology, Taiwan, observation on setting the reliable working under grant MOST104-2622-E-006-011-CC2 is conditions, also verification the unreal working greatly appreciated. Mô phỏng số tính năng công suất của động cơ stirling tác động kép loại alpha  Nguyễn Trường  Chin-Hsiang Cheng  Yen-Fei Chen Khoa Hàng Không và Vũ Trụ, Trường ĐH Quốc Gia Cheng Kung University, Đài Loan TÓM TẮT Phần mềm tính toán CFD pháp mô phỏng số cho động cơ Stirling loại (Computational Fluid Dynamics) được biết alpha tác động kép (DASE), trong đó có bốn đến là một trong những công cụ mạnh và xy-lanh với bốn piston chuyển động tương hữu hiệu để hỗ trợ thiết kế các mẫu động cơ ứng. Trong mỗi động cơ, tác động kép của mới có tính thương mại, phần mềm này bốn piston diễn ra trong hai buồng đối diện thông qua các giả lập sẽ cung cấp cho các trong mỗi bốn xy-lanh. Đối với mỗi chu kỳ, kỹ sư tầm nhìn tổng thể trong quá trình thiết piston luân phiên di chuyển qua lại trong một kế. Nó có thể tiết kiệm rất nhiều thời gian và hình trụ thông qua các kết nối buồng giãn nở chi phí trước khi thực hiện chế tạo mẫu thực. của một xy-lanh tới buồng nén của hình trụ Công trình nghiên cứu này trình bày phương tiếp theo với một kênh, chênh lệch áp suất Trang 20 TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K7- 2015 giữa buồng giãn nở và buồng nén được tăng mềm được sửa đổi phù hợp để mô phỏng lên và cải thiện công suất của động cơ. chuyển động của các piston trong các xy- Trong bài báo này, các mô-đun số được xây lanh. Các thay đổi định kỳ của các trường dựng dựa trên khung của phần mềm CFD nhiệt độ, áp suất và vận tốc trong động cơ thương mại (FLUENT). Các chức năng được dự đoán và ghi nhận giá trị công suất người dùng định nghĩa (UDFs) của phần đầu ra của động cơ. Từ khóa: Động cơ Stirling loại alpha tác động kép, CFD, Động cơ Stirling. REFERENCES [1]. Campos, M., J. Vargas, and J. Ordonez, [5]. Fluent, A., 14.5, Theory Guide; ANSYS. Thermodynamic optimization of a Stirling Inc., Canonsburg, PA, 2012. engine, Energy, 44(1): p. 902-910, 2012. [6]. Alberti, F. and L. Crema, Design of a new [2]. Reader, G.T., Stirling engines, 1983. medium-temperature Stirling engine for [3]. Reid, R.C., J.M. Prausnitz, and B.E. Poling, distributed cogeneration applications, The properties of gases and liquids, 1987. Energy Procedia, Vol. 57, pp.321-330, 2014.. [4]. Urieli, I. and D.M. Berchowitz, Stirling cycle engine analysis, Taylor & Francis, 1984. Trang 21