Thermodynamic analysis of a modified 4-cylinder alpha type Stirling engine

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1 Thermodynamic analysis of a modified 4-cylinder alpha type Stirling engine Abdul Aowal 1, Kazi Afzalur Rahman 2, Md. Kamrul Islam 3 and Bodius Salam 4 1,2,3,4 Department of Mechanical Engineering Chittagong University of Engineering and Technology Chittagong-4349, Bangladesh 1 aowal_cuet@yahoo.com, 2 afzalur99@yahoo.com, 3 kamrul.cuetme@gmail.com, 4 bsalam@cuet.ac.bd Abstract Stirling Engine is an external combustion engine which operates on a thermodynamic cycle named Stirling Cycle invented by Robert Stirling. All forms of thermal energy source such as combustion heat of petrol, diesel, natural gas, coal, wood and leaf, solar energy and even by the waste heat from furnace can be used to operate Stirling engine. Energy crisis is the most affecting factor to all over the world. Generally power is being produced from fossil fuels, most of cases liquid or gaseous fuels, whereas the supply of these fuels are going to a critical position. Moreover, solid fuels are not being properly utilized. In this situation, Stirling Engine can be an effective alternative in power production by using solid fuel. In this paper, a modified assembly of a 4 cylinder alpha type Stirling Engine is proposed, whose output and efficiency are determined by using Schmidt Theory with the aid of MATLAB and SolidWorks, which includes fluid flow and heat transfer analysis of the engine to determine necessary parameters. The main outcome of this analysis is to find the available power developed by the engine. A comparative study of the performance of this engine with two different working fluids, Helium and Air, is also conducted. Keywords Stirling Engine; External combustion engine; Thermal Energy; Helium; Air I. INTRODUCTION The Stirling engine has many types i.e. displacer type, piston type, alpha, beta, gamma type. The different features of the engine can fulfill specific purpose. Providing the flexibility of using both renewable and nonrenewable energy, Stirling Engine can be used in various applications. In this paper thermodynamic analysis to find output power of the alpha type Stirling engine is discussed with a modification. The analysis provides comparison of the thermodynamic properties such as maximum/minimum pressure, indicated power, effective power, and thermal efficiency when it operates in two different working fluids. Helium and air are used as working fluid. The Stirling engine was the first invented regenerative cycle heat engine. Robert Stirling patented the Stirling engine in 1816 (patent no. 4081). Engines based upon his invention were built in many forms and sizes until the turn of the century. Those were small and the power produced from the engine was low (100 W to 4 kw) [1]. In 1853, John Ericsson built a large marine Stirling engine having four 4.2 m diameter pistons with a stroke of 1.5 m producing a brake power of 220 kw at 9 rpm [2]. The second era of the Stirling engine began around 1937, when the Stirling engine was brought to a high state of technological development by the Philips Research Laboratory in Eindhoven, Holland, and has progressed continuously since that time [1,3]. Intensive research by Philips and industrial laboratories led to the development of small Stirling engines with high efficiencies of 30% or more. In 1954, Philips developed an engine using hydrogen as a working fluid. Which produced 30 kw for a maximum cycle temperature of 977 K at 36% thermal efficiency and the efficiency of the same engine was later improved to 38%. Philips research team used new materials, such as stainless steel. The specific power of the small 102C engine of 1952 was 30 times that of the old Stirling engines [4]. Ghai and Khanna worked with an open cycle solar-powered Stirling engine using a parabolic collector in India [5,6]. The solar energy was focused on the metal engine head but they had problems with heat loss. Jordan and Ibele described the 100 W solar powered Stirling engine for water pumping [7]. Ghai pointed out the point of economy and technical simplicity of a solar powered device even though its competitor was the internal combustion engine [8]. Stirling Engine with two cylinders provides a positive turning moment at half revolution and negative turning moment at other half. To get a positive turning moment at full revolution, Stirling Engine of four cylinders has been introduced. In this paper, a modified 4-cylinder Stirling Engine with single heat source for expansion cylinders is described. The remainder of this paper is organized as follows. Section II gives the modeling including assembly components, notations and assumptions of necessary parameters, modeling of the regenerator and total assembly. Section III presents simulation of the model with two different working fluid. Section IV presents computations designed to investigate the comparison of the thermodynamic analyses. Finally, section V discusses the implications of the findings and direction to the future research. II. MODELLING AND SIMULATION A. Components of the assembly Choosing Aluminium 2024 as material, cylinder bore diameter is 15 cm and cylinder wall is 1 cm. The regenerator pipe is 1.5 cm diameter and 1.5 mm thick. The major components are, Component Name Quantity Piston 4 Cylinder 4 Connecting Rod 4 Crank Shaft 1 Flywheel 1 Support Structure 1

B) Parameters of the Engine The output of the engine is obtained by Schmidt Theory for Stirling Engines, which requires the value of the

expansion piston V SE 2650 cm 3 Swept volume of compression piston V SC 2650 cm 3 Dead volume of expansion space V DE 530 cm 3 Regenerator

5 cm 3 Dead volume of compression space V DC 530 cm 3 Expansion space gas temperature T H 723 K Phase angle dx 90 Deg Swept volume ratio V 1

and exposed to outside atmospheric air at 40 C. Hot air enters into pipe. The pipe is divided into elements of 1cm length.

and δl = 1cm Again, quantity of heat transferred from the element Qm ct T (2) From these equations, temperature at the next element, T 2 = T

pipe The fined sectionof regenerator surface consists of aluminum pipe of 1.5 cm inner diameter shown in Fig 2.

1: Final assembly of the engine To determine the final outputs using Schmidt Theory for Stirling Engines the temperature of compression

The regenerator consistss of plain pipe and finned pipe.

2 B) Parameters of the Engine The output of the engine is obtained by Schmidt Theory for Stirling Engines, which requires the value of the following parameters Name Symbol Value/Unit Stroke length L s 15 cm Bore diameter D 15 cm Mean engine pressure P m 1 MPa Swept volume of expansion piston V SE 2650 cm 3 Swept volume of compression piston V SC 2650 cm 3 Dead volume of expansion space V DE 530 cm 3 Regenerator volume V R cm 3 Dead volume of compression space V DC 530 cm 3 Expansion space gas temperature T H 723 K Phase angle dx 90 Deg Swept volume ratio V 1 Dead volume ratio X 1 Engine speed N 10 Hz C) Modelling The final assembly of the engine is shown below, This pipe contains hot fluid inner and exposed to outside atmospheric air at 40 C. Hot air enters into pipe. The pipe is divided into elements of 1cm length. The quantity of heat transferred from an element of the pipe to the surrounding, Q = h δa s ( T s T a ) (1) Here, surface area, δa s = π D δl and δl = 1cm Again, quantity of heat transferred from the element Qm ct T (2) From these equations, temperature at the next element, T 2 = T Q (3) The equation which govern the temperatures along the pipe in a finite number of point is, T (n+1) = T A T T (4) 2) Modelling of finned pipe The fined sectionof regenerator surface consists of aluminum pipe of 1.5 cm inner diameter shown in Fig 2.3, with circumferential aluminum fins. The fins are 1 mm thick and spaced two fins per centimeter. Fig 2.1: Final assembly of the engine To determine the final outputs using Schmidt Theory for Stirling Engines the temperature of compression cylinder has to be known which is attainable from the heat transfer analysis of the regenerator. The regenerator consistss of plain pipe and finned pipe. 1) Modelling of plain pipe The plain pipe section of regenerator surface is an aluminum pipe of 1.5 cm diameter shown in Fig 2.2. Fig 2.3: Circumferential Fin Characteristic properties of the fin: Length, L c = L t = = 2.05 cm Radius, r c = r 1 + L c = = 2.9 cm Area, A m = t (r 2 c r 2 1 ) = cm 2 r c / r 1 = 3.4 and / / = Fig 2.2: Divided Plain Pipe Section Fig 2.4: Effectiveness of Circumferential Fins [9]. From Fig 2.4, effectiveness of the fin, η f = 88 %

The amount of heat transferred from a fin is the summation of heat transferred from fin surface and pipe surface at base of fin.

h can be calculated from following Nusselt number equation [9], Nu 0.53Gr Pr 1/4 This equation also used for the vertical fins.

by, T n+1 = T n T T A T T (9) 3) Power Loss Due to Friction The pipe is assumed as smoth and the friction factor for the pipe is only depends on Reynolds number. Friction factor,.

3 The amount of heat transferred from a fin is the summation of heat transferred from fin surface and pipe surface at base of fin. Heat transferred from a fin surface is expressed as: q = η f 2π ( r 2 c r 2 1 ) h ( T w T ) (5) Heat transfer equation for pipe surface is Q = h A s ( T s T ) (6) Convection heat transfer coefficient h can be calculated from following Nusselt number equation [9], Nu 0.53Gr Pr 1/4 This equation also used for the vertical fins. Now, total heat transfer, Q = η f 2π ( r 2 c r 2 1 ) h ( T s T ) f -1 + h A s ( T s T ) (7) So, the temperature drop can be calculated as, Qm ct S T S (8) So, the temperature at any point is given by, T n+1 = T n T T A T T (9) 3) Power Loss Due to Friction The pipe is assumed as smoth and the friction factor for the pipe is only depends on Reynolds number. Friction factor,. f f = R (10) Friction head loss, L h f = (11) D Friction power loss, P loss = γ Q h ρ g Q h m g h (12) 4) Air in Hot Cylinder At maximum expansion of air the volume of air is divided into finite number of sections as shown in Fig 2.5. No heat transfer will occur between two points at same radial distance from the center axis of the cylinder. So heat transfer at any point will occur from points at different radial distance and points before and after the point along length. Fig 2.5: 3D Mesh grid of the volume of air Fig 2.6: 2D Mesh of air in hot cylinder. Creating the mesh to analyze the temperature distribution into the cylinder can be generated as Fig 2.6. Taking mesh lengths Δx = Δy = 3 cm Assuming the properties of the body are constant with the change of the temperature. The following equations are used for modeling. T, T, T, T, 4 T, 0 2 T, T, T, 4 2 BiT, 2 Bi T 0 Here, Biot number, Bi = III. SIMULATION OF THE MODEL A) Simulation with Air as Working Fluid To avoid the complexity of simulation, the regenerator is divided into four sections i.e. First, Second, Third and Fourth Section and also find some correlations with respect to temperature. Density of the air, ρ= ; Volu ume flow rate, Q = T Q R T Velocity of fluid, v = T T v T ; Reynolds number, Re = Nusselt number, Nu = D so, h = (13) For 0.5 < Pr <1.5 and 10 4 D < Re < 10 6 Nussle number equation, Nu = ( Re ) Pr 0.4 (14) Here, Q o = 2 V se f = m 3 / s ; v o = Q = 300 m/s A P = P mean = 1MPa ; D = 1.5 cm = m Initial temperature, T o = 450 C = 723 K For air, Ideal gas constant, R = 287 J/Kg.K So, heat transfer coefficient, N h = = = D. R. P... P. = μ Pr. k (15) Forming data table 1.2 and using curve fitting, obtain some simplified relation between heat transfer coefficient and temperature, Specific heat and Viscosity, Table 2.1: Properties of Air [9]. T ( K) µ (Kg/m.s) 10 5 k (W/m.K) C v (J/Kg.K) N Pr h (W/m 2.K)

So, the relation between temperature and heat transfer coefficient is, h = 7.263 10-7 T 3 0.001931 T 2 + 2.

3 Relation between Viscosity and Temperaturee µ = ( 1.7 10-9 T 3 4.7 10-6 + 0.007 T +0.

1) First Section of Regenerator The first section of regenerator surface is an aluminum pipe of 48 cm length shown in Fig 2.7.

the equation derived in modeling section.

This section consists of an aluminum pipe with circumferential aluminum fins.

A MATLAB program is formulated to find out the heat loss from each fin and temperatures after passing a fin using equations

3) Third Section of regenerator The third section of regenerator surface consists of two quarter bend and a finned tube of 40

11: Major Dimensions Total length of this section, L= 132.

4 So, the relation between temperature and heat transfer coefficient is, h = T T T Relation between specific heat and Temperature is, c = T T T Relation between Viscosity and Temperaturee µ = ( T T ) 10-5 The forth section of regenerator surface is a combination of straight and bend pipe shown in Fig 2.10 and ) First Section of Regenerator The first section of regenerator surface is an aluminum pipe of 48 cm length shown in Fig 2.7. This pipe contains hot fluid inner and exposed to outside atmospheric air at 40 C. Hot air enters into pipe at 450 C. Fig 2.10: Isometric View Fig 2.7: First Section A MATLAB program is formulated to calculate the temperature drop in each centimeter of the aluminum pipe using the equation derived in modeling section. 2) Second Section of Regenerator The second section of regenerator surface is a finned tube shown in Fig 2.9. This section consists of an aluminum pipe with circumferential aluminum fins. There are 61 fins of 1 mm thickness and spaced two fins per centimeter. Fig 2.8: Finned Tube. A MATLAB program is formulated to find out the heat loss from each fin and temperatures after passing a fin using equations derived in modeling section. 3) Third Section of regenerator The third section of regenerator surface consists of two quarter bend and a finned tube of 40 fins shown in Fig 2.9. Fig 2.9: Third Section of Heat Transfer Surface 4) Forth Section of Regenerator Fig 2.11: Major Dimensions Total length of this section, L= cm A MATLAB program is demonstrated using modeling equations to calculate the temperature drop in each centimeter of the aluminum pipe. 5) Power Loss Due to Friction The power loss in regenerator pipe are also calculated by formulating a MATLAB program using the modeling equations and physical parameters of each section. 6) Simulation withheliumr as Working Fluid For simulation with Helium, follow the same process as Air with the following correlations obtained from the data of table. Table 2.2: Properties of Helium [10,11]. T( K) µ k C (Kg/m.s) v h Pr 10 5 (W/m.K) (J/Kg.K) (W/m 2.K)

So, the relation between temperature and heat transfer coefficient is, h 1.5 10 T 0.00339 T 3.15T 2.

479) 10-5 The Results is discussed in Result and Discussion section. IV.

The design parameters of the engine is given in table below, Parameter Value Mechanical configuration Alpha Material Aluminum (2024)

25 cm Shaft speed 6000 rpm Mean pressure 10 bar Phase angle 90 Angle between two pairs 180 Heat source temperature 723K Heat sink

From the results the total temperature drop from 450 C to 94.4 C is shown in Fig 3.1 Fig 3.

3: Temperatures in hot air Compression end temperature of the engine varies with pressure and pressure varies with crank angle.

1 shows that the rate of change of temperature with respect to pipe length decreases with corresponding increase of length.

The rate is lowest in forth section, cause the temperature difference between hot air and ambient temperature is lower.

5 So, the relation between temperature and heat transfer coefficient is, h T T 3.15T The relation between viscosity and Temperature µ= ( T T T ) 10-5 The Results is discussed in Result and Discussion section. IV. RESULT AND DISCUSSION The results obtained from the simulation section are discussed in this section. The design parameters of the engine is given in table below, Parameter Value Mechanical configuration Alpha Material Aluminum (2024) Working fluid Air / Helium Cylinder diameter 15 cm Piston stroke 15 cm Connecting rod length cm Shaft speed 6000 rpm Mean pressure 10 bar Phase angle 90 Angle between two pairs 180 Heat source temperature 723K Heat sink temperature 313K Number of cylinder 4 (Two pair) A) Simulation result with Air In the simulation, Regenerator is divided into 4 sections. From the results the total temperature drop from 450 C to 94.4 C is shown in Fig 3.1 Fig 3.2: Sinusoidal volume variation The temperatures in hot cylinder are shown in Fig 3.3 Fig 3.3: Temperatures in hot air Compression end temperature of the engine varies with pressure and pressure varies with crank angle. The variation of temperature with length and crank angle is shown in Fig 3.4. Fig 3.1: Total Temperature Drop in the Regenerator Fig 3.1 shows that the rate of change of temperature with respect to pipe length decreases with corresponding increase of length. The rate is higher in second section due to performance of fin. The rate is lowest in forth section, cause the temperature difference between hot air and ambient temperature is lower. Sinusoidal variation of volume is a representation of summation of compression volume, expansion volume and regenerator volume. Fig 3.2 shows the sinusoidal volume variation of the engine for one complete cycle of operation. Fig 3.4: Surface plot of temperature variation The temperature of compression end of the engine is varying from 104 C to 85.8 C. The temperature is maximum at maximum pressure and minimum at minimum pressure. B) Simulation result with Helium From the result obtained from simulation of the engine using helium as working fluid, the total temperature drops in regenerator can be shown as,

At last of all, the following point can be said for a better output from a Stirling Engine, the specific gravity of working fluid should be as less as possible and the length of the regenerator

6 At last of all, the following point can be said for a better output from a Stirling Engine, the specific gravity of working fluid should be as less as possible and the length of the regenerator should be as short as possible. Fig 3.5: Total temperature drop in regenerator The system reached the lowest temperature of 55 C where, air system reached only 94.4 C. The cause of this variation of end temperature with air and helium is density. Air has a larger density than Helium. So, temperature drop of Air is lower than Helium by removing same amount of heat. C) Final output of the systems The main purpose of the analysis was to find the final output, the available output power of the engine for both system with Air and Helium. Here, the obtained outputs are, Parameter Maximum pressure Minimum pressure Indicated power Effective power Working Fluid Air 17.1 bar 5.9 bar 9.94 KW 1.9 KW Thermal efficiency 49 % Working Fluid Helium 17.2 bar 5.8 bar KW 9.3 KW 55 % The results show that working with Helium gas, the engine operates on higher output. Between these, the system with Helium has reached the minimum temperature of 55 C. Helium has a large expansion coefficient and lower density than air. So, for the same volume of each gas, Air needs more amount of heat to remove than Helium to cool down same amount. For a lower density Helium has a lower friction loss in regenerator, one-tenth of friction loss for Air. Hence the system working with helium gas has the lowest end temperature and friction lossthus maximum power output between these systems. Symbol A s T s T a h N Gr d Pr NOMENCLATURE Meaning Surface area Surface temperature Ambient temperature Convectionn heat transfer coefficient Nusselt number Grashof number Prandtl number REFERENCES [1] Senft JR. Ringbom Stirling engines New York: Oxford University Press, 1993 [2] Walker G. Stirling engines. Oxford: Clarendon Press, 1980 [3] Walpita SH. Development of the solar receiver for a small Stirling engine; In Special study project report no. ET Bangkok: Asian Institute of Technology; 1983 [4] West CD. A historical perspective on Stirling engine performance. In: Proceedings of the 23 rd Intersociety Energy Conversion Engineering Conference, Paper Denver: American Society of Mechanical Engineers; 1988 [5] Spencer LC. A comprehensivee review of small solar-powered heat engines: Part I.I. Research since 1950, Conventional engines up to 100 kw. Sol Energy 1989;43: [6] Daniels F. Direct use of the sun s energy. New Haven: Yale University Press, [7] Jordan RC, Ibele WE. Mechanical energy from solar energy. In: Proceedings of the World Symposium on Applied Solar Energy, Phoenix p [8] Ghai ML. Small solar power plants. In: Daneils F, Duffie JA, editors. Solar energy research. London: Thames and Hudson; p [Section 4] [9] Heat transfer (Ninth edition) by J P Holman [10] Robert D. McCarty, Thermodynamic properties of Helium 4, Cryogenic Division, Institute for Basic Standards, Boulder, Colorado [11] E. Bich, J. Millat and E. Vogel, The viscosity and thermal conductivity of pure monatomic gasses, University of Rostock, Fachbereich Cheme, Buchinderstrasse 9, D-O-2500, Germany V. CONCLUSION The main objective of the analysis was to find the final available outputs by simulating a 4-Cylinder Stirling Engine for Air and Helium as working fluid. The indicated power of the Stirling Engine depends on the temperature difference between the expansion cylinder and compression cylinder. Then available useful power depends on the indicated power and friction power loss in the regenerator. The friction power loss largely depends on the length of the regenerator, velocity and specific gravity of the fluid. The specific gravity of the Helium is much less than Air, about one tenth. So, Helium is better working fluid than Air. The results show that Helium provides a higher output than Air.

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