American Journal of Oil and Chemical Technologies: Volume 3. Issue 4. October 2015

Petrotex Library Archive

American Journal of Oil and Chemical Technologies Journal Website: http://www.petrotex.us/2013/02/17/317/

Laminar Flow Modelling and Analysis of Helium Fluid into the Two Dimensional Pipe from Regenerative to Head of Cylinder of a New

Alpha Type Stirling Engine (zero alpha) with a Internal Diameter of 22/6 mm and Length of 4000 mm by Fluent software

Yousef Hosseini

Industrial & Mining Research Center, Cycle Science And Industry Company, Tehran, Iran.

Abstract:

The Stirling engine is an external combustion engine that works with any heat source. Surrounded by heating with gas pressure to the piston displacement and cooling gas, the piston reaches the initial point. This paper explores the Laminar flow modelling for analysis and the results of its Laminar flow modelling, for use in the analysis of the temperature and pressure of the fluid input and output to a zero alpha Stirling engine for numerical solution and conceptual design, it can be used. zero Alpha engine models should be such that thermal drops and irreversibility consider thermal efficiency of the engine. The results of analytical model of zero alpha engine on the tables and graphs are presented and validation. In addition, due to the efficiency of heater, regenerative, cooler are emphasized. Following the introduction of this type Stirling engine by elementary two-dimensional simulation (zero alpha) in the form of concepts such as the used fluids type to analyze fluid motion into regenerative pipe to the engine cylinder head. finally the piece of regenerative pipe zero alpha engine by solidworks software designed and assembled, with the help of gambit software and Fluent subsequently be analyzed.

Keywords: Zero Alpha Stirling Engine, Heat Regenerative, Numerical Solution, Laminar Flow, Thermal Drop and Efficiency, Design & Analysis Softwares.

1. Introduction The stirling engine is a heat engine that is the big difference with internal combustion engines in automobiles and in 1816 was invented by Robert Stirling. The system is an engine converts thermal energy into mechanical energy, In which the chemical reaction does not occur. Since the invention of Robert Stirling’s engine by much research has been done about it. The first acceptable mathematical analysis to analyze Stirling, fifty years after its invention, was presented by Schmidt [6]. Schmidt analysis based on the theory of compression chamber and expansion chamber isotherm is presented. Using the assumption Schmidt, thermodynamic equations are in linear and preliminary calculations used to measure the efficiency and output of the engine is done easily. Schmidt analyzed the initial analysis Stirling engines are widely used today. Schmidt cycle, the compression and expansion processes assumes the isothermal. However, in practice, for engines with engine speed 1,000 rpm or

231

more, as proved Rankine, heating or cooling, exactly dos not happen at constant volume or constant temperature, and the compression and expansion processes in cylinders of Stirling engine more adiabatic are close. So should the assumptions used to determine the most appropriate thermodynamic modeling using these models to real engine efficiency could be achieved. In Schmidt cycle every effort towards the resolution of the isotherm model Stirling engine out, are not explicitly and the only form of differential equations are using numerical methods will be resolved. In adiabatic cycle, thermal efficiency becomes a function that not only depends on temperature but also swept volume ratio, phase angle, and the dead volume ratio will depend. The output power in the isothermal cycle and the adiabatic cycle will be function of all the parameters. In 1975, Finkellstein [8] Schmidt thermodynamic analysis improved and the adiabatic preliminary analysis are presented. In the equations on Adiabatic, the compression chamber and the expansion chamber, considered as adiabatic. By given assumption in adiabatic the equations in linear form are out there, and by numerical methods should be used to solve them. Since the presentation model by Finkellstein to now, thermodynamic analysis was carried out on the basis of various models (isothermal and adiabatic), using a variety of heat sources (combustion, solar and heat waste) and the various forms of the Stirling engine (engine type alpha, beta and gamma), That such as the research was carried out by Israel Urieli and Berchowitz [1,9,11,20] using the adiabatic thermodynamic model, to get more power and efficiency output of Stirling engine, It can be pointed out. Kongtragool and Wang Wises [11] the modeling and optimization of Stirling engine by using the isotherm model have conducted and Yousef Timoumi and it’s colleagues [10, 13, 15, 16, 17, 18, 19] with the modeling Stirling engine in adiabatic, pests and non-utilized return into it, were examined. In recent research conducted by Alexander Tlili and it’s colleagues [16], The Stirling engine using by solar energy as a heat source, is modeled. In research conducted by Thombare and Verma [15] available technologies and progress made on stirling engines analysis are collected, and finally on the use of these, the recommendations have been presented. Alireza Tavakolpour and it’s colleagues [14] so with using the theory of Schmidt, solving equations in isotherm and use on flat plates in the absorption the temperature of sun as a source of warm temperature, analysis of gamma type stirling engine have done. Gustanteh and Invernizi [6] after the modeling of Stirling engine, the effect of various gases on the engine output power and efficiency are investigated. Formosa and Despesse [9] the modeling by using isotherm model to study the dead volumes effects on the output power and efficiency of the engine have done [16.19]. So that need to good models for better analysis of Stirling engines (zero alpha) will defined and then we analyzed them. In the following to check more models and by presentation the geometric model of zero alpha engine, we will analyze on the structural technology of this type innovative new engine.

2. The governing equations and solution Publications equation is as follows: [16]

(1) the pressure equation:

(2) the mass equation: dmc = (pdVc + Vc dp/γ) / (RTck) mk = pVk/ (RTk)

mr = pVr/ (RTr) mh = pVh/ (RTh)

me = M – (mc + mk + mh + mr)

(3) equations for mass changes:

232

(4) the temperature equations: [16]

Boundary conditions at the junction cells [16]

Finally, the equations for the amount of work and given heat to heater and getted heat from cooler and also the exchanged heat in heat regenerative are obtained using the following formulas: (5) the energy equations: [16]

2-1- Stirling Engine Features

Figure 2-1 P -V charts and entropy performance in Stirling Cycle

In order to obtain an Analytical phrase of the engine pressure, usually applies the following assumptions: 1. The fluid is used in the engine tanks, remains the constant and invariable temperature. 2. The temperature of the fluid used in volumes Vh !Vk thermal exchanger are respectively TL and TU. 3. The temperature in the regenerative maybe is described by a linear development between TL and TU. 4. The regenerative behaviour is symmetrical. 5. The ideal gas law is applied. 6. The pressure considered for any position is in the same displacer and piston. 7. Harmonic motions to move the piston and displacer are there. The organ has shown that an equivalent sterling car is always there [17]. As a result, an alpha sterling equivalent car, beta or gamma with mechanical makeup of stirling engine, or by using the same an one-dimensional geometry model can be considered. So, we are here to develop our model of

233

such machines in equivalent sterling car, it has chosen to can expand expansion volume and compression [17].

)1(

Where (t) is the angular position and α phase angle. Piston swept volume ratio and displacer in k=Vp/Vd is written. The total mass of gas in within the various tanks in total mass of gas in each tank is defined in Figure 2 [19]. )2(

If we instead the mass phrase in (2) by the ideal gas law is replaced it, that has been achieved [13]: )3(

Where R is the gas constant, the gas constant per unit of mass and TR is the average temperature in regenerative is considered. The results of the analysis of Schmidt [6] here is a reminder:

)4(

)5(

In which

234

2-2- Input heat from the heater to the cylinder: Input heat from the heater to the cylinder: )6(

)7(

The output heat from the cylinder to the cooler: ]13[

)8(

The heat among the helium transporting pipes between cooler and heater ]13[

)9(

3. The working fluid in the stirling engine In the Stirling Cycle, the working fluid as an important sub-system of the stirling engine, takes heat and cold in a closed volume alternately, and it is the duty of transport energy and do act. Every fluid with the high specific heat capacity may be considered as the working fluid in the stirling engine. With a few exceptions, most of the stirling engines in the nineteenth century from the air as the working fluid have used. Most of them have operated close to atmospheric pressure. Air is cheap and readily available. The working fluid used in stirling engine Should be the thermodynamic characteristics, heat transferring and dynamical (gas dynamic) is the following [2]. 1. The high thermal conductivity 2. The high specific heat capacity 3. The low viscosity 4. The low

density In addition to above requirements for engine beter performance, ease of availability, good price, performance safety and easy storage, are important characteristics that can not be ignored. As mentioned, in the first of air as the working fluid in the stirling engine was used and why its initial name was "the air engines", but then because of the helium and the hydrogen is lighter than air, It (air) were replaced by these gas [2,3]. Lighter fluid of working fluid to reduce the size and weight of the engine on the one hand and the other hand small and lightweight molecules to reduce the losses that are in Table 3-1 performance specifications of the several fluids have been compared. At present, hydrogen is ideal working fluid for stirling engine in the thermodynamic and physical properties is considered. But because of the risks (risk of explosion) and security issues, has less practical use. So now of helium as the working fluid more used. According to Table 3-1, the air has a molecular weight of about 29. While the molecular weight of helium is 4. So the air about seven times Heavier (more massive) than helium. Where in figure 3-2 was compared the performance specifications between the helium and air as inner fluid and with the help of data from table 3-1 and with help of software Tecplot was drawn chart 3-1. So helium must receives about seven times less energy than air, will also produces a specified force. In general thermodynamic properties of helium alone are good, is light, and the other doesn’t have the dangers of hydrogen too.

235

Exotic Mat'l Simple Mat'l Exotic Mat'l Simple Mat'l Exotic Mat'l Simple Mat'l Exotic Mat'l Simple Mat'l

We

igh

ted

To

tal

Single-Cylinder Multi-Cylinder

Inner Fluid is Air Inner Fluid is Helium

Fin

al

Pressurized Fluid Atmospheric Pressure Pressurized Fluid Atmospheric Pressure

Figure 3-2 The comparison chart between air and helium gas as inner fluid [5]

Figure 3-1 Chart of performance specifications of helium and hydrogen [4]

Table 3-1 performance specifications of the several gases as working fluid [2,3]

3-1- Analysis the different effects of equipments on the ideal cycle We know big difference between the ideal conditions and the real conditions. Here we refer to some of these differences: In the air conditioner and heater, the processes rather than constant temperature are similar to adiabatic, because the walls of the cylinder, are not capable of sufficient heat transferring to keep the temperature constant, especially at high speeds. The regenerative efficiency of the stirling cycle, that it is assumed, ideally, practically not realized. In operation, fluid leaks out and this leakage occurs, effective in reducing the cycle efficiency and constantly need to be compensated. Furthermore, if the

The Type Of Gas

Noun Molar Mass

Gas Constant Specific Heat Capacity

Cv Cp

Specific Heat Ratio

Hydrogen 2 12/4 20/14 08/10 41/1

Helium 4 08/2 19/5 11/3 67/1

Neon 20 415/0 03/1 62/0 66/1

Nitrogen 28 297/0 04/1 74/0 4/1

Carbon monoxide

28 297/0 04/1 75/0 4/1 Weather 29 287/0 01/1 72/0 4/1

Oxygen 32 260/0 92/0 66/0 4/1

Argon 40 208/0 52/0 31/0 67/1

Carbon dioxide

44 189/0 85/0 66/0 28/1

236

hydrogen is used as the working fluid, due to the severe effects of explosion, leakage is very dangerous [2].

3-2- Mass effect of fluid The total mass of gas with medium pressure in equation (7) in the relationship. The proper relationship between power and medium pressure can be found in Figure 3 -3 -a. The mass effect of fluid on the efficiency varies with thymoma [16]. fluid optimization mass is m = 1.6 g (e.g. medium pressure = 6.89 MPa), that maximum efficiency of 54% can be deduced (see Figure 3 -3 -b) that two percentage points above the reference sample is shown in Figure 3 -3 by dash line as shown. At the same time, the power from 6.09 kW to 10 kW can be reached.

Figure 3-3 mass effect of fluid on output power and efficiency [13]

4. Heat Regenerative Perhaps one of the most important parts of the sterling engine, which has an important role in increasing efficiency, is heat regenerative. In terms of physical structure, heat regenerative in the form of mesh sheets or stainless steel rods are stacked, are made (Figure 4-2). Over half of the engine duty cycle, heat regenerative like a heat sponge to absorb the heat of the operating gas. In the other half cycle, the regenerative, return heat to gas, therefore less heat to remove the cause of the engine in the cold area, there will be and is in this case, a way to increase the efficiency of engine. Therefore using the regenerative in stirling engine to reduces heat losing and to increase the efficiency of engine finally. Figure 4-1 computer diagram show to manufacturing regenerative by mechanical desktop software.

4-1- Thermal conductivity Regenerative Led ingredients of regenerative matrix, have strong effects. The increasing thermal conductivity of regenerative matrix, resulting in decreased performance due to increased internal thermal conductivity losses will be in regenerative. For an amount close to the thermal conductivity of steel (kw = 40 watts per meter Kelvin), optimal efficiency is about 19% higher frequency of stainless steel is used for GPU-

237

3. For low conductivity materials such as Inconel ®625 (kw =9.8 watts per meter Kelvin), the efficiency can be increased to 57 percent [17]. 4-2- The combined effect of fluid mass and frequency For a given mass of gas, operating frequency can be used to improve performance and optimize it. The operating reference value of zero alpha, 43/6Hz achieved that close to optimum amount of pressure.

Figure 4-1 the computer diagram to manufacturing regenerative by mechanical desktop software [8]

4-3- The length effect of regenerative By changing the length of regenerative, practices accordingly amended. Additional dead volume and as well as increased pressure losing leads to achieve power in maximum amount. However, for a small length of regenerative less than 15 mm, power and efficiency rapidly decrease, as shown in figures 4-2.

Figure 4-2 the structure of the heat regenerative [2]

238

Table 4-1 geometrical parameters of zero alpha engine

40 no Small pipes +1 Global pipe

Number of pipes Heater

/3 02 mm Internal diameter of pipe

(3600+400) mm Length of pipe with pre-heater &

during the pipe to cylinder head

Length of pipe

70 88/ cm3 Dead volume

312 The number of pipes for each cylinder

Cooler (a set of homogeneous and smooth

pipes) 46 1/ mm Diameter pipes

46 1/ mm Length of pipe

/13 8cm3 Dead volume

22 6/ mm Diameter pipes Regenerative (pipe-shaped body is retrieved that has accumulated on the metal

wires)

22 6/ mm Length of pipe

45 µm diameter of wire

0/697

Porosity

8 Number per cylinder

15W/m K Thermal conductivity Factor

/50 55Cm3 Dead volume

Table View 4-3 alpha cells retrieved with zero porosity and different wire diameter

Diameter of regenerative wire

(mm)

Regenerative porosity factor

M

Zero Alpha Zero Alpha Model

0035/0 9122/0 M 1

0065/0 8359/0 M 2

007/0 7508/0 M 3

007/0 7221/0 M 4

004/0 6980/0 M 5

008/0 6655/0 M 6

008/0 6112/0 M 7

Table 4-2 alpha engine performance parameters zero

Zero Alpha Model

Helium Operating gas

K 1080 Temperature of heat source

(heater) K 290 temperature of cold source

(cooler) Kpa 070/4777 Medium pressure of

operating gas grm 0205/0 mass of operating gas

Hz 6/43 frequency of engine

performance

239

Table 4-4 Comparison the results by using of specification of zero alpha motor with published research

[4.12]

Zero Alpha

Masood Zia Basharhagh &

Mostafa Mahmoodi

Urieli Timoumi Data

116/78 113/76 119/43 124/06 Heat released by cooler Qk [J /

cycle] 435/33 304/17 318/5 327 Heat transfer by

heater Qh [J / cycle]

12560 7942/47 8300 8286/7 output power P [W]

83/33 62/6 62/5 62/06 Thermal efficiency [η]

5. Designing of the inlet and outlet helium fluid in zero-alpha type Stirling engine Designing of intake and exhaust pipes of fluid in the cylinder head are done by solidworks software.

Figure 5-2 outlet flow of the helium fluid in zero-

alpha type stirling engine [4]

Figure 5-1 inlet flow of the helium fluid in zero-

alpha type stirling engine [4]

5-1- Design and Mesh pipe Designing and Mesh imprint pipe by Gambit software is done. That in figure (5-3) can be seen.

Figure 5-3 two-dimensional view of pipe with dimensions (22/6 mm × 4000 mm)

240

6. The states of fluid velocity vectors in pipe analysis Velocity vectors in Fluent software according to velocity size are colored. In the forms of (6-1) and (6-2) in two states can be seen.

Figure 6-2 Second case the fluid velocity vectors

Figure 6-1The first case of the fluid velocity

vectors

7. Analysis with graphs and geometry specifications The axial velocity of the fluid in the form of (7-1) from a to c, the friction coefficient of shell & tube, the changing velocity profile in found area, shear stress in fluid and output velocity according to distance form centre of pipe, respectively in figures (7-2), (7-3), (7-4) and (7-5) is remarkable.

(c)

(b)

(a)

Figure 7-1 the axial velocity of the fluid

Figure 7-3 the changing velocity profile in found area

Figure 7-2 the friction coefficient of shell & tube

241

Figure 7-5 output velocity according to distance form centre of pipe

Figure 7-4 shear stress in fluid

8. Conclusions As a first step for the design and optimization the regenerative of zero alpha type stirling engine, an analytical model is used. To deal with the difference between the high theoretical efficiency of stirling and prototypes built, is considered a major heat losing. In addition, they are associated with the geometric parameters and physical design model.

In order to obtain a simple analytical model, assuming the isothermal is applied. Model efficiency of regenerative and conduction losses, pressure drop and efficient of additional heat exchangers will merge together. Therefore, the effect of operating parameters on the regenerative performance of zero alpha engine can be assessed. As a validation stage, we applied GPU-3 engine data parameters in the developed model. Despite the assuming the isothermal and heat simple transferring model, the results are close to the experimental data and in accordance with the classical models. This thermodynamic model for all types of regenerative of stirling engines, especially zero alpha applies. Optimization of these parameters using by real data of GPU-3 engine is done. The proof, to reduce losses and significant improvement energy in performance of zero alpha engine can be reached. In addition to the known effects of regenerative, the effect of effectiveness of cooler performance was emphasized [18]. As a result, a developed handheld model (helium fluid into the Two-dimensional pipe from regenerative to head of cylinder of a new zero alpha type Stirling engine), which can use for the first time in a design and optimization method with regard to a specific application.

9. Acknowledgments Special thanks to the efforts of Mr engineer Abbas Sadri that I helped in the design and analysis knowledge of this type of regenerative. Also in front of, I thank of the teachers and authors of the publication will help to improve its quality.

10. References [1] Gholami, Shahab and inspiration, MR and Vafaee trait, A., 1389, Two-cylinder Stirling engine pod dynamic analysis of solar type α the first Regional Conference on Mechanical Engineering, Tehran, Islamic Azad University, Tehran East. (With Persian reference) [2] Kamvar, M, Stirling cycle test article in thermodynamics, Faculty of Mechanical Engineering, University of Science and Technology, 1392. (With Persian reference) [3] Article hid training in sterling engines, catalogs and posters of Iranian Society of Mechanical Engineers Company, 1391) a car. With finite element. (With Persian reference) [4] Izadi, M., Faraji Esfangrh able, Abbas Sadri, paper, conceptual design and new high-efficiency thermodynamic Stirling Engine Assembly Fourth National Conference Papers process engineering,

242

petrochemical refining 7 Persian date June 1394, Tehran, Iran, sound and Conference Center TV host: Chemistry Seminar. (With Persian reference) [5] Chaugaonkar, S. (2014). Design and Fabrication of Regenerative Heat Exchanger for Alpha Stirling Engine. International Journal of Advanced Mechanical Engineering, 4(7), 829-837. [6] Christoph, M., Arnaud, G. ( 2007). Stirling engine. University of Gavle.

[7] Denno, J. Design & Analysis of Stirling Engines. [8] Finkellstein, T. (1975). Analogue Simulation of Stirling Engine. Simulation, (2).

[9] Formosa, F., & Despesse, G. (2010). Analytical model for Stirling cycle machine design. Energy Conversion and Management, 51(10), 1855-1863.

[10] Gostante, M., & Invernizzi, A. (2010). Stirling Engines using Working Fluids with Strong Real Gas Effects. Applied Thermal Engineering (Vol. 30, pp. 1703-1710).

[11] Kongtragool, B., & Wongwises, S. (2003). A review of solar-powered Stirling engines and low temperature differential Stirling engines. Renewable and Sustainable Energy Reviews, 7(2), 131-154.

[12] Mahmoodi, M., & Ziabasharhagh, M. (2012). Numerical solution of beta-type Stirling engine by optimizing heat regenerator for increasing output power and efficiency. J Basic Appl Sci Res, 2, 1395-1406. [13] Mohiuddin, R. Design & Simulation of an Alpha Type Stirling Engine. Department of Mechanical Engineering, Bangladesh University of Engineering and Technology. [14] Tavakolpour, A. R., Zomorodian, A., & Golneshan, A. A. (2008). Simulation, construction and testing of a two-cylinder solar Stirling engine powered by a flat-plate solar collector without regenerator. Renewable Energy, 33(1), 77-87.

[15] Thombare, D. G., & Verma, S. K. (2008). Technological development in the Stirling cycle engines. Renewable and Sustainable Energy Reviews, 12(1), 1-38.

[16] Timoumi, Y., Tlili, I., & Nasrallah, S. B. (2007). Reduction of energy losses in a Stirling engine. Heat and Thechnology, 25(1), 81-90.

[17] Timoumi, Y., Tlili, I., & Nasrallah, S. B. (2008). Design and performance optimization of GPU-3 Stirling engines. Energy, 33(7), 1100-1114.

[18] Tlili, I., Timoumi, Y., & Nasrallah, S. B. (2008). Analysis and design consideration of mean temperature differential Stirling engine for solar application. Renewable Energy, 33(8), 1911-1921.

[19] Tlili, I., Timoumi, Y., & Nasrallah, S. B. (2008). Thermodynamic analysis of the Stirling heat engine with regenerative losses and internal irreversibilities. International Journal of Engine Research, 9(1), 45-56. [20] Urieli, I., & Berchowitz, D. M. (1984). Stirling cycle analysis. Oxford University Press, Oxford, UK.