CFD Simulation and Numerical Study on 3 KW Driven Inline Alpha Stirling Engine

Size: px

Start display at page:

Download "CFD Simulation and Numerical Study on 3 KW Driven Inline Alpha Stirling Engine"

Sara Fox
5 years ago
Views:

1 CFD Simulation and Numerical Study on 3 KW Driven Inline Alpha Stirling Engine Joseph A.M. Soliman, Youssef A. Attia Mechanical Power Engineering Department Faculty of Engineering-Mataria Helwan University Cairo- Egypt Mechanical Power Engineering Department Faculty of Engineering-Mataria Helwan University Cairo-Egypt Abstract- The Stirling engine uses external combustion; hence, it can be powered by any source of energy (combustion energy, solar energy, etc.) and causes less pollution than traditional engines. The power piston converts gas pressure into mechanical power, whereas the other piston is used to move the working gas between hot and cold working spaces. Stirling presents an excellent theoretical efficiency of the same order as the Carnot efficiency. On the other hand, the produced output power of several prototype engines remain very weak compared to the excellent theoretical yield. because of the extremely complex phenomena related to compressible fluid mechanics, thermodynamics, and heat transfer. An accurate description and understanding of these highly nonstationary phenomena is necessary so that different engine losses, optimal performance, and design parameters can be determined. [1] [2] [3] [4] This paper presents comparison between three methods of Stirling engine stability and performance investigation which are numerical study ideal case using Schmidt method, simulation CFD study using search package FLUENT-ANSYS 16 and experimental work. The results give the optimum value of both engine configurations and operating conditions. It is found that, the marge between the three studies results will achieve high efficiency and stability for Stirling engine. The 3KW Stirling engine was built and tested as prototype. The prototype test results are used as validation case for the CFD-study. The engine was tested with air, helium, Nitrogen and hydrogen by using an electrical furnace as heat source. Working characteristics of the engine were obtained within the range of heat source temperature 900K and range of charging intial pressure 10 bar. Maximum power output was obtained with helium. [5] Keywords- Stirling engine; Thermodynamics; Schmidt equations; CFD; heat transfer. A L P P s Q R r T V W Piston stroke Connect rod length Pressure Piston distance Heat energy Gas constant Crank radius temperature Volume Work Nomenclature Greek ε Φ Θ η Generator effectiveness Crank angle Two piston shift angle Thermal efficiency Subscript h hot piston l cold piston mr matrix material r Regenerator Page 1

2 I. Introduction Stirling engine is driven with any heat source (combustion, solar, waste heat, etc.). On the other hand, fossil fuels consuming achieves the extreme pollution generated. It has led the world into a new area of using renewable energies. Using renewable energies, for example: solar energy, as heat source for the Stirling engines, will give clear power source instead of internal combustion engines. Stirling engines are expected to have high efficiency, equivalent to the related Carnot cycle. Also, it can be driven with the heat loss in furnaces, chimney, etc. which reduces thermal pollution, [6] [7]. It is clear that, the industry is looking forward to power source with low operating cost, high efficiency, low noise level and matched with environmental requirements. Stirling engine can achieve all of these requirements, [8]. Nowadays, there are trends to use biomass or the waste heat as heat sources for the engines, [10]. Stirling engines have huge size in comparison with the same power source. Stirling engine s development faces two strong challenges. The 1 st challenge is mechanical challenge as low compression ratio and the leakage of working fluid from the engine where, changing working fluid and charging it with high pressure is the classical way to increase the output power. The 2 nd challenge is thermo-mechanical challenge as selecting the working fluid with high specific heat, increasing the temperature difference between hot and cold sources, increasing the internal heat transfer coefficient and heat transfer surface. It improves the engine efficiency. It is found that hydrogen and helium as working fluid are proved to give higher power on increasing their charging pressure, [9]. The Stirling geometrical configuration and physical characteristics affect Stirling engine performance the power output and its efficiency. But the working fluid gas properties, regenerator efficiency and porosity, dead volume, swept volume, temperature of sources and pressure drop losses affect the engine performance. II. Numerical Study The numerical study depends on mathematical method of calculation. It is similar to the Schmidt method without the defination of the multiple parameter which are used for the analytical solution of the integrals. The numerical integration can be used with high accuracy. The numerical study has assumptions as the pressure losses in the engine are neglected, the engine is running limited speed, its power is limited the pressure is uniform throughout the engine. The effect of the regenerator temperature is used analytically when its average temperature calcualted. The ideal gas equation is: PV = MRT which is, for a first approximation, sufficient for the range of temperatures. The engine is divided into three volumes: the volume in which the power piston, the volume containing the 2 nd piston for alpha engine, and the volume of the regenerator. It is assumed that the gas in the hot and cold volume is maintained at constant temperature T l (low) and T h (high). Hence the name of isothermal analysis. The temperature of gas in the regenerator is equal to the effective average temperature: T mr=(t h-t l)/ln(t h/t l) This formula is calculated assuming that the temperature in the regenerator moves linearly from Tl to Th. The density of gas varies throughout the regenerator, if the space is divided into slices, the average temperature will be: T mr= (T 1*m 1+ T 2*m 2+..+T n*m n)/(t 1+T 2+ +T n) where m 1, m 2, et T 1, T 2, are the masses and temperatures of gas of successive slices. In passing to the limit (ie., taking n number of infinitely thin slices). The two sums are some integrals. By resolving them, the formula used to T mr is found. In reality, the average temperature of gas in the regenerator is higher when the gas moves from hot zone to the cold zone and vice versa. It is easy to understand that it is inherent in exchanger design. This difference in temperature which allows the heat to flow from the gas to the heat exchanger and vice versa is called Td. It depends on the design of the exchanger and on the nature of the gas. It possible to seize an estimated value of this temperature difference in the calculation for seen the effect. The volumes at low and high temperatures vary depending on the positions of pistons. If the rods sufficiently long compared to the stroke, their movements may be regarded as a sine function of the angle ϕ of the crankshaft. It is almost always the case. This angle ϕ is zero when the first engine piston at top dead center. The movement of the 2 nd piston for an alpha type is shifted of an angle θ compared to the power piston. This angle θ is negative for a back shift, and positive for a forward shift in comparison with the first piston. Forward shift is usual for a Stirling engine. I.e. that the 2 nd piston is above the power piston. I.e. that the 2 nd piston precedes the power piston. The volume at high temperature is: V h= (V d/2)*(1 - cos(ϕ + θ))+ V dead hot where V d is the 2 nd piston, V dead hot is the hot dead volume which contains the heater. The volume at cold temperature is: V l= (V m/2)*(1 cos (γ)) + V mortm Page 2

3 where V m is the volume swept by the power piston, V deadcold the cold dead volume which contains the cooler. The constant volume of the regenerator is V r. At any time, the total volume: V= V h + V l + V r and the total mass of gas is: m = m h + m l + m r The indices h, c and r indicate volume at hot temperature or cold temperature and the one of the regenerator. With the ideal gas law, the volumes are: P*V h = m h*r*t h P*V c = m c*r*t c P*V r = m r*r*(t mr + dt) where dt is the temperature difference in the regenerator compared to the theoretical average. The three masses are: m h = P*V h / (R*T h) m l = P*V l / (R*T l) m r = P*V r / (R*(T mr + dt)) for, respectively, the cold volume, the hot volume and the regenerator volume. The total mass of gas is: m + P o*v max / (R*T o) where P o, V max and T o are the pressure, the volume and the temperature at the moment of the filling with. During this filling, the internal volume is maximal. Vmax is calculated with: V = V h + V l +V r By replacing the values of masses of gas in the above equations, it is found that: P o * V max / T o = P*(V h/t h + V l/t l + V r/(t mr + dt)) which give the pressure value: P = (P o*v max/t o) / (V h/t h + V l/t l + V r/(t mr + dt)) The pressure is independent of R for a filling pressure. By integrating on a complete cycle P*dV, the engine work is got. For convenience, P*dV is integrated numerically by computing V each 5 o for example. dv is the difference between two successive steps and P is the average between two steps. III. CFD set up In the current study, the main objective is to obtain maximum output power and maximum performance efficiency. The predication is developed using search package FLUENT in ANSYS 16.2, CFD-program, to generate performance variations comparing different parts characteristics and conditions via its thermodynamics analysis. The validation case is taken from actual inline alpha Stirling engine type in the lab. It produces 3Kw with 35% efficiency. The inline alpha Stirling engine type is more efficient compared to other types. Table 1 shows the engine s specifications. ANSYS has many tools. One of these tools is the geometry tool that gives the ability to build the engine configuration with its required design in simulation program. The engine design and configuration with section view are shown in Figure1 and Figure 2. In ANSYS program, the working fluid field is the focus of study, see figure 3. It is clear from the piston motion, the mesh cells will be demolished in piston and will be created in another one. The ANSYS dynamic mesh is suitable for this case study investigation. The structured mesh provides the best performance and results in ANSYS dynamic mesh. Number of nodes is and number of elements is The constructed working fluid mesh is shown in figure 4. The mesh program tool is used to resize all elements to obtain accurate solution. This program has the ability to change the working fluid type and the operating conditions. A finite volume CFD solver ANSYS FLUENT is used in this work, that implements Reynolds averaged Naviere -Stokes equations. The fluid has been assumed to be compressible. In addition, same study performed for the maximum number of iteration as the calculation performed using 720 and 1440 maximum number of iteration relative to the crank shaft rotation. Two turbulence models have been checked in this step of work, Realizable k-ε and the SST k-w. These two models are recommended by the CFD worker for the dynamic mesh. The Realizable k-ε model has been adopted for this study. The dynamic mesh tool is activated. The hot piston motion is defined by activation of in-cylinder window where the cold piston motion is defined by using UDF. Using C++ programming language to describe the piston motion, shown in figure 5, according to the following equation: Ps=L+ A (1 cos Φ) (L 2 A2 sin 2 Φ) Page 3

International Journal Of Advancement In Engineering Technology, Management and Applied Science TABLE I ENGINE SPECIFICATIONS Denomination Value / Type Engine type Inline

600rpm Over pressure up to 30bar Piston diameter 90mm Stroke length 210 mm General dimensions 716 mm x 770 mm x 240 mm phase delay between cooling and 90 o power pistons

4 International Journal Of Advancement In Engineering Technology, Management and Applied Science TABLE I ENGINE SPECIFICATIONS Denomination Value / Type Engine type Inline Alpha Swept volume 522 CC x 2 Lubrication No Working fluid N2, He, H2&air Cooling system Water cooled Operating temperature 1000K Maximum engine power >3 kw Engine speed 600rpm Over pressure up to 30bar Piston diameter 90mm Stroke length 210 mm General dimensions 716 mm x 770 mm x 240 mm phase delay between cooling and 90 o power pistons heat exchange surface Hot cylinder head, cold cylinder Fig. 1 Schematic illustration of the predicated engine. Fig. 2 The predicated engine section view. Page 4

3 The engine fluid view contained in ANSYS. Fig. 4.

5 International Journal Of Advancement In Engineering Technology, Management and Applied Science Fig. 3 The engine fluid view contained in ANSYS. Fig. 4. Prediction engine mesh. L r Φ P s A Fig. 5 Piston motion description. Page 5

6 Fig.6 C++ code of piston motion IV. Results and Discussion Figure 7 shows PV diagram of actual, numerical and CFD alpha Stirling engine cycle. It is clear, the net area in case of numerical cycle is larger than the case of actual and CFD cycle. So, the total work output in case of numerical is higher than the other cases as the area indicates the work. The numerical solution depends on adiabatic process as assumption which means there is no heat loss. It is found that the CFD cycle is closed to actual cycle. Figure 8 shows the indicated power output and the efficiency over the phase angle for different volume ratios. Looking at the indicated power in Figures 8 (a) and (b) it can be seen that, independent of the volume ratio the expansion piston to compression piston volume, the optimum phase angle is about 90 o. The optimum volume ratio of the expansion and compression space should be at unity. The difference between the actual, CFD and numerical solutions on the engine efficiency with the change of hot surface temperature and the regenerator effectiveness, see Figure 9. It shows that increasing hot surface temperature up to 900K approx. improves the thermal efficiency for different generator effectiveness values. The engine thermal efficiency is constant by increasing temperature above 900k, except in case of effectiveness value 0.8 or above the thermal efficiency will increase. The effect of changing the working fluid is shown in Figure 10. Nitrogen, Hydrogen and air require huge amount of heat to increase their operating temperature. On the other hand, Helium needs less heat energy to reach the same operating temperature because Helium has high thermal characteristics. Figure 10 shows that Helium consumes less heat as compared to Air, Hydrogen and Nitrogen. However, the specific heat of Hydrogen, Nitrogen and Helium is 10kJ/kg K, 1.04kJ/kg K and 3.1kJ/kg K, respectively. From this logic, Nitrogen should consume least amount of heat to reach a certain temperature but the density of Hydrogen, Nitrogen and Helium is kg/m 3, 1.251kg/m 3 and 1.225kg/m 3. Changing working fluid type will affect the total work and thermal efficiency due to different characteristics of working fluid, especially specific heat coefficient. At the same operating conditions using Helium as working fluid gives higher thermal efficiency compared to the others, see Figure 11. Thermal efficiency can be defined: η= W out / Q input Q 3-4+ Q 1-2 η i= Q3-4+(Q2-3+Q 4-1) In this ideal Stirling process it is supposed, the regenerator is of 100 % effectiveness; ε= 1. Then the isochoric heat supplied by the regenerator Q 2-3 at constant volume V min is equivalent to the isochoric heat Q 4-1 that is received by the regenerator at constant volume V max. So Q Q 4-1 = 0. and the external supplied heat for the ideal process is: Q input = Q 3-4. Now the ideal efficiency is: η i= Q 3-4+ Q 1-2 Q3-4 Page 6

7 Q reg = (1-ε) * Q 2-3 Q 3-4+ Q 1-2 η therm= Q3-4+(1 ε)q2-3) Q 3-4 = W ex = R M gas T ex ln (V max/v min) Q 1-2 = W c = R M gas T c ln (V min /V max) W c = - R M gas T c ln (V max/v min) The isochoric heat supplied at V min is: Q 2-3 = M gas C v ln (T ex /T c) R Mgas (Tex Tc) ln (Vmax/Vmin) η therm= R Mgas Tex ln (Vmax/Vmin)+(1 ε) Mgas Cv(Tex Tc) We make further substitutions: Carnot efficiency C = (T ex T c) / TE. The adiabatic exponent = C p/ C v and the gas constant: R = C p - C v leads to the term C v / R = 1 / (. We now get therm in the wanted form for computer calculations: 1 η therm = ε ηc 1 K ln( Vmax ) Vmin Thermal efficiency increases with decreasing cold temperature. The increasing effectiveness and using Helium as working fluid also improve this effect on thermal efficiency value. These changes are presented in Figures 12,13. In this study the thermal efficiency value of V-shape and inline alpha types are obtained at the same operating condition. It is found that the value of thermal efficiency can be obtained in inline type is less than the other one. In addition, thermal efficiency will increase. Increasing the initial working pressure needs more heat amount. However, the total work and thermal efficiency are increased, see Figures 14,15. Fig.7 PV diagrams. Page 7

8 International Journal Of Advancement In Engineering Technology, Management and Applied Science (a) (b) Fig.8 The indicated power output and the efficiency over the phase angle for different volume ratios Page 8

9 International Journal Of Advancement In Engineering Technology, Management and Applied Science Fig. 9 Effect of hot temperature and effectiveness on thermal efficiency. Fig. 10 Effect of hot temperature and working fluid types on heat energy required. Page 9

10 International Journal Of Advancement In Engineering Technology, Management and Applied Science Fig. 11 Effect of hot temperature and working fluid types on thermal efficiency. Fig. 12 Effect of cold temperature and effectiveness on thermal efficiency. Page 10

11 International Journal Of Advancement In Engineering Technology, Management and Applied Science Fig. 13 Effect of cold temperature and working fluid types on heat energy required. Fig. 14 Effect of initial pressure and effectiveness on heat energy required. Page 11

12 Fig. 15 Effect of initial pressure and working fluid types on heat energy required. V. Conclusion Real 3KW inline alpha Stirling engine is investigated by prediction work using ANSYS program and numerical method. Main parameters of the study are hot temperature, cold temperature, regenerator effectiveness. The study shows the optimal conditions for this engine such as it must be of 90 o phase angle. Using helium as working fluid fulfills better working characteristics compared to nitrogen or hydrogen due to higher specific heat coefficient. Therefore, engines which work with helium have higher efficiency. Increase in initial pressure leads to an increase in net work. Rising heating temperature improve the rate total work which means that thermal efficiency is improved also. Thermal efficiency depends on heat input, cooler temperature and regenerator effectiveness. Increasing the heat input rate and cooler temperature reduction with higher regenerator effectiveness will achieve optimum thermal efficiency. So, change the regenerator interior material with high porosity material, increasing heat transfer area and decreasing the heat sink temperature will increase the efficiency. References [1] Walker G. Stirling engines. Oxford: Clarendon Press; [2] Kolin, 1991 Kolin, I. (1991). Stirling motor: History theory practice, Inter Univ. Center, Dubrovnik. [3] Timoumi, Y., and Ben Nasrallah, S. (2002). Design and fabrication of a Stirling Ringbom engine running at a low temperature. Proc., TSS Int. Conf. Mechanical Engineering, ICAME, Hammamet-Tunisia. [4] Halit, K., Huseyin, S., and Atilla, K. (2000). Manufacturing and testing of a V-type Stirling engine. Turk. J. Engine. Environ. Sci., 24, [5] Chang, Z.-C., and Chent, P.-H. (1998). Flow channeling effect on a regenerator s thermal performance. Cryogenic., 38(2), Miyabe et al [6] Pålsson, M., Olsson, F., and Öberg, R. (2004). Demonstration Stirling engine based micro-chp with ultra-low emissions. Rapport SGC 144, Svenskt Gastekniskt Center, Sweden. [7] Sullivan, T. J. (1987). Calibration and comparison of NASA Lewis Research Center s performance code s pressure-drop model predictions to Stirling engine working-space flow test data. NASA, Lewis Research Center, Cleveland. [8] Thomas, B., and Pittman, D. (2000). Update on the evaluation of different correlations for the flow fiction factor and heat transfer of Stirling engine regenerators. Proc., 35th Intersociety Energy Conversion Engineering Conf., AIAA, Reston, VA, [9] Gedeon, D., and Wood, J. G. (1996). Oscillating-flow regenerator test rig: Hardware and theory with derived correlations for screens and felts. Rep , NASA, Lewis Research Center, Cleveland. Page 12

13 [10] Siegel, A. (2000). Experimental investigations on the heat transfer behaviour of wire mesh regenerators in an oscillating flow. Proc., Europe Stirling Forum, Stirling International Association, Ancona, Italy, [11] Andersen, S., Carlsen, H., and Thomsen, P. (2006). Numerical study on optimal Stirling engine regenerator matrix designs taking into account the effects of matrix temperature oscillations. Energy Convers. Manage., 47(7-8), [12] Rogdakis, E., Antonakos, G., and Koronaki, I. (2012). Thermodynamic analysis and performance investigation of an alpha-type Stirling engine. Proc., 11th Biennial Conf. Eng. Systems Des. Analysis Conf. ESDA 2012, Vol. 2, ASME, New York, [13] Rogdakis, E., Antonakos, G., Koronaki, I., and Dogkas, G. (2014). Numerical analysis of Stirling engines using advanced thermodynamic quasi-steady approaches. Proc., 16th Int. Stirling Engine Conf., Stirling International Association, Ancona, Italy. [14] Meijer, R. J. (1960). The Philips Stirling thermal engine Analysis of the rhombic drive mechanism & efficiency measurements. Ph.D. thesis, Technishe Hogeschool te Delft, Eindhoven, Netherlands. [15] Y. Timoumi, I. Tlili, and S. Ben Nasrallah, Performance optimization of Stirling engines, Renewable Energy, vol. 33, no. 9, pp , Page 13

Thermodynamics Fundamentals for Energy Conversion Systems Renewable Energy Applications

Thermodynamics Fundamentals for Energy Conversion Systems Renewable Energy Applications The study of the laws that govern the conversion of energy from one form to the other Energy Conversion Concerned