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Solanki et al., International Journal of Advanced Engineering Technology E-ISSN 0976-3945 Research Paper MODELING AND ANALYSIS OF PULSE TUBE 1Nishant Solanki, 2Nimesh Parmar

Address for Correspondence 1Student, M.E. (Thermal Engineering), Gandhinagar Institute of Technology, Gandhinagar, Gujarat, India 2Asst. Professor, Mechanical Engineering Department, Gandhinagar Institute of Technology, Gandhinagar, Gujarat, India ABSTRACT: comes from the Greek word “kryos”, which means very cold or freezing and “genes” means to produce. Cryogenics is the science and technology associated with the phenomena that occur at very low temperature, close to the lowest theoretically attainable temperature. In this research paper, three dimensional model of pulse tube refrigerator is developed in ANSYS CFX and compared it with experimental results. It shows good agreement with experimental results with ANSYS CFD results. KEYWORDS : Pulse tube refrigerator, ANSYS CFD INTRODUCTION: on the thermodynamic performance of The pulse tube (PTR) are capable of various components in a simple orifice and a double cooling to temperature below 123K. Unlike the inlet pulse tube cooler by combining a linearized ordinary cycles which utilize the vapour model with a thermodynamic analysis. The results compression cycle as described in classical reveal that the performance of the pulse tube cooler is , a PTR implements the theory of significantly affected when the reservoir to pulse tube oscillatory compression and expansion of the gas volume ratio is less than 5, which helps the design of within a closed volume to achieve desired a practical pulse tube cooler. refrigeration. Being oscillatory, a PTR is a non steady Y.L. He, C.F. Zhao [4], carried out the numerical system that requires time dependent solution. simulation of two dimensional viscous compressible However like many other periodic systems, PTRs oscillating flow for the uniform cross section and attain quasi-steady periodic state (steady-periodic tapered pulse tubes. They found that the tapered pulse mode). In a periodic steady state system, property of tube gives the improved performance than the the system at any point in a cycle will reach the same uniform cross section pulse tube, but when the taper state in the next cycle and so on. A Pulse tube angle becomes much larger than this optimum value, refrigerator is a closed system that uses an oscillating the cooling performance of pulse tube refrigerator (usually produced by an oscillating piston) at becomes weaker than that of circular tube. L. one end to generate an oscillating gas flow in the rest Mohanta and M.D. Atrey [5] has been carried out of the system. The gas flow can carry away from fundamental relationship between mass flow rates at a low temperature point (cold end of pulse tube) to the the hot and cold ends of the pulse tube and also the hot end if the power factor for the mass flow rate through the orifice and DI valve by phasor quantities is favourable. The amount of heat phasor analysis of PTR. They have been found that they can remove is limited by their size and power the refrigerating effect is directly proportional to the used to drive them. mass flow rate at the cold end and the amplitude of Experimental study has been done by the B.J. Huang dynamic pressure. Taekyung Ki and Sangkwon and G.J. Yu [1] they have concluded experimentally Jeong [6] provide the step-by-step design methodology that there exists an optimum operating frequency for efficient stirling type PTR. Dion Savio Antao, which increases with decreasing pulse tube volume. Bakhtier Farouk [7], have presented a numerical For a fixed pulse tube volume, increasing the pulse simulations of transport proves in a pulse tube tube diameter will improve the performance. The for find out the effects of taper angle. experimental results are used to derive a correlation They found that the taper angle of the pulse tube is for the performance of OPTR which correlates the shown to have significant effects on the secondary net cooling capacity with the operating conditions streaming patterns observed in the pulse tube. and the dimensions of the OPTR. Ya Ling He, Hing Tapering the pulse tube improved the performance of Huang [2] has carried out the first and second law the OPTR. M.Y. Xu [8] developed a pulse tube analysis of pulse tube refrigerator, and found that the refrigerator with the cooling capacity below 2 K by cooling performance coefficient has been improved using the 3He in place of 4He and achieved the from 0.091 to 0.108 of the double inlet type PTR and lowest temperature below 2 K is 1.87 K. Liang et corresponding exergy efficiency improved from al. [9] idealized the pulse tube refrigeration process by 25.04 % to 29.95% respectively. Alos they found that simplifying the practical conditions without losing the most of the exergy losses take place in to the the main characteristics of pulse tube refrigeration. orifice and regenerator so the improvements for these Based on this idealization, the thermodynamic two components are highly needed in order to further nonsymmetry effect of the gas element working at improve the performance of PTR. A pulse tube cooler the cold end of the pulse tube has been described. has the advantages of long life and low vibration over The gas elements enter the cold end of the pulse tube conventional vryocoolers such as G-M and stirling at the wall temperature of the cold end heat coolers because of the absence of moving parts at low exchanger but return to the cold end of the pulse tube temperature. In order to make the pulse tube cooler at much lower temperatures. They termed it compact for practical applications, the volume of thermodynamic non-symmetry in entering and reservoir should be minimized. X.B. Zhang and leaving the pulse tube during one cycle. This effect L.M. Qiu [3] analyzes the effects of the reservoir has been conveniently used to explain the IJAET/Vol. IV/ Issue II/April-June, 2013/90-95 Solanki et al., International Journal of Advanced Engineering Technology E-ISSN 0976-3945 refrigeration mechanism of the basic, orifice and As the regenerator plays very significant role in the double inlet pulse tubes. In their second paper, Liang performance of any cryocooler, the regenerator is et al. [10 ] developed the compound pulse tube model modelled as a porous media, for which some basic based on the earlier analysis and incorporated the parameters like porosity, viscous resistance factor thermal and viscous influence of the pulse tube wall and inertial resistance factor are required as input and proposed a thermal viscous layer in the pulse parameters for CFD analysis. tube. Wei et al. [11] have done theoretical calculation for inertance tube without a reservoir and showed that this device provides a rather large phase-leading effect. Thus phasor diagram is used to analyze the relationship between phase-leading requirement and the pulse tube geometry. They noticed that a larger void volume of pulse tube would require a larger Fig 1 woven wire mesh screens phase-leading effect. W. R. Smith [12] introduced a The geometrical parameters used in the description of new mathematical model to describe heat and mass screen regenerators are the porosity and area density. transfer in PTRs. De Boer [13] carried out a Porosity( ): The porosity is defined as the ratio of experiment on maximum attainable performance of the volume occupied by the fluid to the total volume. pulse tube refrigerator and found that the It could also be defined as the ratio of void volume to nondimensional rate of refrigeration of pulse tube is the total volume. It is expressed as, shown to have a maximum attainable value of 1/4. At maximum rate of refrigeration, the coefficient of performance equals one-half the temperature ratio Area density ( ): The area density is defined as a [14] across the regenerator. J. Jung presents the ratio of void surface area to the total volume of the expansion efficiency of the pulse tube refrigerator matrix. It is expressed as and concluded that the time needed for optimal design of the pulse tube refrigerator can be greatly reduced with simple calculation process of the expansion efficiency. A. Razani et al [15] was For the perfect stacking of square mesh screens in developed a thermodynamic model based on exergy which the weaving causes no inclination of the wires flow through the pulse tube refrigerators and they and the screen layers are not separated. These have proposed an exergetic efficiency parameter idealization lead to a matrix packing where the screen representing the losses in the pulse tube itself. Amir thickness t s is equal to 2d w and the porosity is given R Ghahremani, R.M. Saidi [16] has been analysed by, and optimized the performance of high capacity pulse tube refrigerator. As a result of their optimization they proposed a new configuration of high capacity Where, pulse tube refrigerator which provides 335 W at 80 K cold end temperature with a frequency of 50 Hz and Where m is mesh per inch and d w is wire diameter of screen. [17] COP of 0.05. Ju et al developed an improved For woven screen regenerator it is necessary to numerical model for simulating the oscillating fluid specify an additional analytical parameter, to define flow and detail dynamic performance of the OPTR the ratio of the minimum free flow area to the frontal and DIPTR. The simulation model is useful for area. understanding the physical process occurring in the pulse tube refrigerator, and also for predicting the β effect of the orifice and double-inlet valve on the O refrigeration power and efficiency of pulse tube The areaT density is given by [18] refrigerator. J.Y. Hu numerically studied the influence of the double inlet valve on the cooling From the porosity equation (3.1) and density equation performance and characteristics of inertance tubes (3.4) the hydraulic radius can be expressed as, and provided numerical results. It is concluded that the inertance tube cannot provide the optimum impedance for those pulse tube refrigerators with The hydraulic diameter is expressed as following, small cooling power because of turbulent flow and suggested that the in such case the double inlet valve can help to provide a better impedance and further Viscous and Inertial Resistance factor for porous improve the cooling performance. On other hand the media inertance tube can provide the optimum impedance The porous media model can be used for a wide for those pulse tube refrigerators with large cooling variety of problems, including flows through packed power and the double inlet is not necessary in such a beds, filter papers, perforated plates, flow distributors case. Cha J.S. and S.M. Ghiaasiaan [19] has been and tube banks. Heat transfer through these medium studied the oscillatory flow in microporous media can be represented subject to the assumption of applied in pulse tube and Stirling cryocooler. The thermal equilibrium between the medium and the results shown that the oscillatory flow hydrodynamic fluid flow. The porous media model incorporates an parameters are different than steady flow parameters essence, the porous media model is nothing more representing similar flow conditions. than an added momentum source in the governing Modelling of PTR equations of the navier-stoke equation.

IJAET/Vol. IV/ Issue II/April-June, 2013/90-95 Solanki et al., International Journal of Advanced Engineering Technology E-ISSN 0976-3945 The viscous resistance factor (D) and inertial S = Source term resistance factor (C) are obtained as, The diffusion flux is only important in multi- ′ component flows in our case = 0. j α β assuming ideal gas behaviour ′ P = RT Where -1 Where, ’= Number of packed material per length (m ) R = Gas constant = Porosity Now aforementioned equations can be cast in = Opening area cylindrical polar co-ordinate systems as: l = Mesh distance (m) = Permeability (m 2) Continuity equation for polar co-ordinate system: ρ Table 3.2 Operational parameters of the porous media ρ ρ Where, r = Radial co-ordinate x = Axial co-ordiante Vr = Radial velocity Vx = Axial velocity Momentum equation in axial direction: ρ ρ ρ So for a given wire mesh the value of viscous and inertial resistance factor can be obtained analytically µ using equation (3.7) and (3.8). Table 3.2 lists the important operational parameters of the porous media µ for the CFD simulation. 3.7 Governing Equations Momentum equation in radial direction: Conservation of mass equation: ρ ρ ρ ρ ρ Where, µ = Gradient operator = Density of the gas µ = Velocity in vector form µ µ t = Time Conservation of momentum equation: Energy equation: ρ ρ τ ρ ρ ρ τ Where, Aforementioned mass, momentum and energy P = Static pressure conservation equations are applied to all the = Stress tensor components of the pulse tube refrigerator except = Gravity acceleration regenerator and heat exchangers owing both that = External body force or Source term (e.g. associated component modelled as a porous media. The porosity with porous media) of the porous media is taken in to consideration for Assuming that the working fluid is Newtonian, the solving the equation. relation for shear stress-strain is given as: Mass conservation equation for porous media: τ µ ρ ρ TP Where, Where = Fluid molecular viscosity is the porosity of the porous medium. I = Unit (Identity) tensor Momentum equation for porous media: TP = Transpose The porous media model in CFX assumes that there Conservation of Energy: is local thermodynamic equilibrium between the fluid ρ ρ and the solid structure. The resistance of gas flow through the porous media is modelled by an Ψ τ additional momentum source term. This source term is consisting of two parts: first is viscous loss term Where, presents the pressure drop which is directly proportional to the velocity. The second term is ρ inertial loss term which is directly proportional to the velocity square. T Assuming homogeneous and isotropic solid matrix µ ρ T α µ Where, ρ α k = Gas thermal conductivity Where = Turbulence thermal conductivity = Dynamic viscosity of the fluid = Specific heat of the gas = Permeability T = Temperature of the gas C = Inertial resistance factor V = local velocity V = Velocity j = Diffusion flux of species IJAET/Vol. IV/ Issue II/April-June, 2013/90-95 Solanki et al., International Journal of Advanced Engineering Technology E-ISSN 0976-3945 The porous medium momentum equation can be programme for modelling fluid flow and heat transfer expressed in the vector form as: process in complex engineering problems. CFX offers the flexibility of meshing any complex ρ ρ geometry and solving complicated 2-dimensional and τ 3-dimensional problems. Transient flow and transport µ ρ phenomena in porous media, tow phase flow, and α volumetrically generating sources can all be Momentum equation in axial direction: modelled by CFX. CFX numerically solves the entire ρ ρ ρ continuum fluid and energy balance equations with no arbitrary assumptions. • Finite Volume Formulation The Finite Volume Method (FVM) is one of the most µ versatile discretization techniques used for solving governing equations for fluid flow and heat and mass µ transfer problems. The most compelling features of µ the FVM are that the resulting solution satisfies the ρ α conservation of quantities such as mass, momentum, Momentum equation in radial direction: energy and species. This is exactly satisfied for any as well as for the whole computation ρ ρ ρ domain. Even a coarse grid solution exhibits exact integral balances. Apart from this, it can be applied to any type of grids (structured or unstructured, µ Cartesian or body fitted), and especially complex geometries. Hence, it is the platform for most of the commercial packages like CFX, Star-CD, and Fluent µ etc. which are used to solve fluid flow and heat and µ µ µ ρ mass transfer problems. In the finite volume method, α the solution domain is subdivided into continuous Energy equation for the porous media: cells or control volumes where the variable of ρ ρ ρ interests is located at the centroid of the control volume forming a grid. The next step is to integrate τ the differential form of the governing equations over Where, K = Thermal conductivity of fluid each control volume. Interpolation profiles are then f assumed in order to describe the variation of the Ks = Thermal conductivity of solid medium Ef = Total fluid energy concerned variables between cell centroids. The Es = Total solid energy resulting equation is called the discretized or CFX Analysis discretization equation. In this manner the The equations of fluid mechanics which have been discretization equation expresses the conservation known for over a century are solvable only for a principle for the variable inside the control volume. limited no. of flows. The known solutions are These variables form a set of algebraic equations extremely useful in understanding fluid flow but which are solved simultaneously using special rarely used directly in engineering analysis or design. algorithm. CFD makes it possible to evaluate velocity, pressure, CFD Methodology:- temperature, and species concentration of fluid flow CFD may be used to determine the performance of a throughout a solution domain, allowing the design to component at the design stage, or it can be used to be optimized prior to the prototype phase. analyses difficulties with an existing component and Availability of fast and digital computer makes lead to its improved design. For example, the techniques popular among engineering community. pressure drop through a component may be Solutions of the equations of fluid mechanics on considered excessive: The first step is to identify the computer has become so important that it now region of interest: The geometry of the region of occupies the attention of a perhaps a third of all interest is then defined. If the geometry already exists researchers in fluid mechanics and the proportion is in CAD, it can be imported directly. The mesh is then still is increasing. This field is known as created. After importing the mesh into the pre- computational fluid dynamics(CFD). At the core of processor, other elements of the simulation including the CFD modelling is a three-dimensional flow solver the boundary conditions (inlets, outlets, etc.) and that is powerful, efficient, and easily extended to fluid properties are defined. The flow solver is run to custom engineering applications. In designing a new produce a file of results which contain the variation mixing device, injection grid or just a simple gas of velocity, pressure and any other variables diverter or a distribution device, design engineers throughout the region of interest. need to ensure adequate geometry, pressure loss, and The results can be visualized and can provide the residence time would be available. More importantly, engineer an understanding of the behavior of the fluid to run the plant efficiently and economically, throughout the region of interest. This can lead to operators and plant engineers need to know and be design modifications which can be tested by able to set the optimum parameters. changing the geometry of the CFD model and seeing As a result CFD tools, both for commercial and the effect. research purposes are now available. One of the most The process of performing a single CFD simulation is respected CFD code is CFX. CFX is a computer split into four components:

IJAET/Vol. IV/ Issue II/April-June, 2013/90-95 Solanki et al., International Journal of Advanced Engineering Technology E-ISSN 0976-3945 1. Geometry/Mesh 2. Physics Definition 3. Solver 4. Post-processor Geometry creation The first task in to CFD simulation is to create geometry. To model heat and fluid flow in pulse tube refrigeration system using CFX, first a proper geometry is to be created using a separate model/ Fig. 4 Meshed Model of Regenerator, Pulse Tube and mesh generation package, or pre-processor. For the Heat Exchanger present simulation solidworks is used as a pre- In general a finite element model is defined by a processor for modelling the geometry. mesh network, which is made up of the geometric arrangement of elements and nodes. Nodes represent points at which features such as displacements are calculated. Elements are bounded by set of nodes, and define localized mass and stiffness properties of the model. Elements are also defined by the number of mesh, which allowed reference to be made to corresponding deflections, stresses, , temperatures at specific model location. The traditional method of mesh generation is block Fig. 2 Geometry of the ITPTR structure (multi-block) mesh generation. The block Once the dimensions of all components of pulse tube structure approach is simple and efficient technique refrigerator are known, the geometry is entered in to of mesh generation. solid works to create the faces or volumes of different components depending on the 2-D or 3-D simulations. For ITPTR the 3-D model is used for the volume creation. The components after cooler and cold heat exchanger are eliminated for the simulation of the case 1 to case 3 as shown in fig. 5.1 due to proper validation of the simulation results with the experimental results.

• Dimensions of the ITPTR Fig. 5 Meshed Model of Heat Exchanger, Inner turns Table: Fixed dimensions of the component Tube and Reservoir CONCLUSION The study focuses on CFD investigation to optimize the pulse tube refrigerator dimensions, mesh size and operating frequency so that we get the possible lowest temperature at the cold end of pulse tube. The number cases were study in present .

Table: Geometry of the inertance tube is varying as • For case- 1 the lowest temperature 215.42 K achieved at 1.4 mm diameter of inertance tube with 0.7/0.5 valve opening/closing time at 50 cycle/min pulse rate. • The case- 2 were carried out for 1 meter and 0.37 meter length of inertance tube with Meshing different pulse rate with valve opening/closing Mesh generation (gridding) is the process of time, for which the lowest temperature 215.85 subdividing a region to be modelled in to a set of K achieved for 1 meter length with 0.7/0.5 small control volumes. Associated with each control valve opening/closing time at 50 cycle/min. volume there will be one or more values of dependent • Case-3 were simulated for 1.4 mm diameter flow variable (e.g. velocity, pressure, temperature and length of 1 meter of inertance tube with etc.). Usually these represent some type of locally reservoir and 7 meter for without reservoir for averaged values. Numerical algorithms representing fixed pulse rate 60 cycle/min at different valve approximation to the conservation law of mass, opening/closing time. The lowest temperature momentum and energy are then used to compute 212.41 K at 0.6/0.4 valve opening/closing these variables in each control volume. time. Meshing is the method to define and brake up the • Case 4 were focused on the effect of the mesh model into small elements. size of the regenerator material with different porosity on the cold end temperature it is concluded that cold end temperature decrease with increase in porosity of the regenerator material and increase with decrease in porosity. The best result achieved was 211.3 K at 300 mesh size. • Case 5 were focused on the optimization of the

Fig. 3 Meshed Model of Compressor, Transferline and frequency, it is concluded that there is an Regenerator optimum frequency for the better performance IJAET/Vol. IV/ Issue II/April-June, 2013/90-95 Solanki et al., International Journal of Advanced Engineering Technology E-ISSN 0976-3945 of the pulse tube refrigerator. The lowest temperature 209.5 K achieved at 1.8 Hz. • It is also noticed that the in the all above cases that the valve opening and closing time greatly affect the performance. It is concluded that the valve opening time should be more in the range of 0.2 to 0.3 sec than the valve closing time. • After simulate the all the cases the best performance obtained was 209.5 K at 1 meter length and 1.4 mm diameter at1.8 Hz operating frequency, 300 mesh size and 0.6/0.4 valve opening/closing time with 6 bar operating pressure. REFERENCES 1. B.J. Huang, G.J. Yu, Experimental study on the design of orifice pulse tube refrigerator, International journal of refrigeration 24 (2001), 400-408. 2. Ya-Ling He, Jing Huang, Chun-Feng Zhao, Ying-Wen Liu, First and second law analysis of pulse tube refrigerator, Applied thermal engineering 26 (2006), 2301-2307. 3. X.B. Zhang, L.M. Qiu, Z,H. Gan, Y.L. He, Effects of reserve oir volume on performance of pulse tube cooler, Internation journal of refrigeration 30 (2007) 11-18. 4. Y.L. He, C.F. Zhao, W.J. Ding, W.W. Yang, Two- dimensional numerical simulation and performance analysis of tapered pulse tube refrigerator, Applied thermal engineering 27 (2007) 1876-1882. 5. L. Mohanta, M.D. Atrey, Phasor analysis of pulse tube refrigerator, cryocooler 16 (2011) 299-308. 6. Taekyung Ki, Sangkwon Jeong, Step-by-step design methodology for efficient stirling type pulse tube refrigerator. International journal of refrigeration 35 (2012) 1166-1175. 7. Dion Savio Antao, Bakhtier Farouk, Numerical simulation of transport processes in a pulse tube cryocooler: Effects of taper angle. International journal of heat and mass transfer 54 (2011) 4611-4620. 8. M.Y. Xu, A.T.A.M. De Waele, Y.L. Ju, A pulses tube refrigerator below 2 K. Cryogenics 39 (1999) 865-869. 9. Liang, J., Ravex, A. and Rolland, P., Study on pulse tube refrigeration Part 1: Thermodynamic nonsymmetry effect .Cryogenics, 36(1996), pp. 87-93. 10. Liang, J., Ravex, A. and Rolland, P., Study on pulse tube refrigeration Part 2: Theoretical modeling, Cryogenics, 36(1996), pp. 95-99. 11. Wei Dai, Jianying Hu and Ercang Luo, Comparison of two different ways of using inertance tube in a pulse tube cooler, Cryogenics 46(2006), Pages 273-277. 12. W.R. Smith, One-dimensional models for heat and mass transfer in pulse tube refrigerators. Cryogenics 41 (2001) pp 573-582. 13. PCT de Boer, Maximum attainable performance of pulse tube refrigerators. Cryogenics 42 (2002), pp 123- 125. 14. Jeheon Jung, Sangkwon Jeong, Expansion efficiency of pulse tube in pulse tube refrigerator including shuttle heat transfer effect. Cryogenics 45 (2005) pp 386-396. 15. A. Razani, T. Roberts, B. Falke, A thermodynamic model based on exergy flow for analysis and optimization of pulse tube refrigerators. Cryogenics 47 (2007), pp 166-173. 16. Amir R Ghahremani, M.H. Saidi, R. Jahanbakshi, F. Roshanghalb, Performance analysis and optimization of high capacity pulse tube refrigerator. 17. Y.L. Ju, C. Wang and Y. Zhou, Numerical simulation and experimental verification of the oscillating flow in pulse tube refrigerator. Cryogenics 38 (1998) pp, 169- 176. 18. J.Y. Hu, J. Ren, E.C. Luo, W. Dai, Study on the inertance tube and double inlet phase shifting modes in pulse tube refrigerators. Energy conservation and management 52 (2011) pp 1077-1085. 19. J.S. Cha, S.M. Ghiaasiaan, C.S. Kirkconnell, Oscillatory flow in microporous media applied in pulse tube and cryocooler regenerators. Experimental Thermal and fluid Science 32 (2008) 1264-1278.

IJAET/Vol. IV/ Issue II/April-June, 2013/90-95