PERFORMANCE INVESTIGATIONS OF SINGLE STAGE STIRLING TYPE PULSE TUBE CRYOCOOLER WITH INERTANCE TUBE USING CFD SIMULATIONS

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1 December 12-14, 2013, NIT Hamirpur, Himachal Pradesh, India Paper ID FMFP PERFORMANCE INVESTIGATIONS OF SINGLE STAGE STIRLING TYPE PULSE TUBE CRYOCOOLER WITH INERTANCE TUBE USING CFD SIMULATIONS Bhavin Shah Deep Gudhka Udeet Rangwala V.J.T.I. V.J.T.I. V.J.T.I. Mumbai, Maharashtra, India Mumbai, Maharashtra, India Mumbai, Maharashtra, India Mandar Tendolkar V.J.T.I. Mumbai, Maharashtra, India Arvind Deshpande V.J.T.I. Mumbai, Maharashtra, India ABSTRACT The present work reports about the performance evaluation and parametric studies of a Single Stage Stirling Type Inertance Tube Pulse Tube Cryocooler, using the CFD package FLUENT. Parametric studies are conducted with different ranges of frequencies and pressures. These results are analyzed to predict the performance of PTC, and thereby arrive at optimum operating parameters. A novel approach is used by replacing the compressor with a UDF. The variation of thermo-physical properties of working medium with temperature is taken into account using a separate UDF. Appreciable agreement is found between CFD simulations and experimental data. Significant multi-dimensional flow effects are observed at the vicinity of component-tocomponent junctions. Keywords: CFD Simulation, Inertance Tube Pulse Tube Cryocooler, User Defined Functions (UDF), Frequency Optimization, Pressure Optimization. 763

2 INTRODUCTION In the recent past, the pulse tube cryocooler (PTC) system has become one of the most important topics for investigations in the field of cryogenics engineering. The inherent advantages of this system include attainment of low temperature in a short duration of time and absence of moving parts in the low temperature region, along with simplicity and enhanced reliability. Pulse tube cryocoolers have several applications such as cooling of infrared sensors, night vision equipment, cryopumping etc. Pulse tube cryocooler units operate as closed systems where no mass is exchanged between the cryocooler and its environment. In order to accurately predict and improve the performance of the PTC system, a reasonably thorough understanding of the complicated thermo-fluidic process in the system is required. The recent availability of powerful computational fluid dynamics (CFD) software that is capable of rigorously modelling the transient and multidimensional flow, along with heat transfer processes in complex geometries, provides a good opportunity for analysis of PTC s. It demands for considerable amount of time and cost for the experimental investigations to evaluate the optimum parameters of PTC. On the other hand, developing a specialized computer code for such analysis is equally complex. Thus, numerical simulation using CFD software is a suitable option. Banjare, 2009 has reported the use of FLUENT for modelling the PTC, and showed that the performance of ITPTC is superior compared to an Orifice-PTC, for same geometrical and operating parameters. Simulations are also performed on G-M type DIPTC to find the optimum valve openings. Cha, 2004 has reported for 2 models of ITPTC systems, operating under a variety of thermal boundary conditions. The simulation results show that onedimensional modelling of PTC is appropriate only when all the components of the PTC have very large aspect ratios (i.e. L/D >>1). Ghiaasiaan et al., 2011 studied the effects of boundary layer on miniaturization of the pulse tube cryocoolers. The results indicate that the predicted boundary layer loss increases as the boundary layer thickness increases relative to the pulse tube diameter. Ashwin, 2010 has reported for performance evaluation and parametric studies of an ITPTC using CFD for different aspect ratios. The wall thickness of components and the local thermal non-equilibrium of the gas and the matrix for modelling of porous zones is taken into consideration in these investigations. GEOMETRY DESIGN A two-dimensional, schematic of the modelled ITPTC system is shown in Fig. 1. Figure 2 shows the complete meshing of the 2D geometry of the simulated system. The detailed dimensions of the ITPTC system are tabulated in Table 1. DETAILS OF MODELLING For the present study, Gambit is used as a preprocessor for modelling the geometry and generating meshes. The models are created in Gambit and exported to Fluent (solver). Helium is chosen as the working fluid for the system. Component material used for regenerator is Steel (SS304) and Copper (OFHC) for all the heat exchangers. The boundary and initial conditions are tabulated in Table 1. A sinusoidal oscillating pressure pulse is given by a UDF. It is coupled to the inlet of the aftercooler, thereby eliminating the need of modelling a compressor. Separate UDFs are developed to account for suitable thermo-physical properties and their variations with the temperature. The regenerator and all heat exchangers are modelled as porous zones with theoretically calculated values for porosity, viscous resistance, and inertial resistance. SIMPLE scheme with a PRESTO option is used for pressure velocity coupling to correct the pressure equation. Suitable Under relaxation factors for all parameters are used for better convergence, up to the least of 10e

3 Figure 1. 2-D Axisymmetric view of Model Figure 2. Mesh Diagrams for ITPTC Model Component Table 1. Details of Design Parameters and Boundary Conditions Diameter ( mm ) Length ( mm ) Boundary Condition Wall Fluid Regenerator Adiabatic Porous, Laminar Cold End 28 to 12.2 ( Taper ) 18 Adiabatic Porous, Laminar Pulse Tube Adiabatic Turbulent Hot End Isothermal, T= 293K Porous, Laminar Inertance Tube Adiabatic Turbulent GOVERNING EQUATIONS The general governing equations (differential form) used by the CFD Software are: (1) (2) Where, E= (4) h = (5) -porous zones S = (6) (3) 765

4 RESULTS AND DISCUSSIONS 1. Validation of Model with Cha, 2004 In order to validate for the accuracy of the algorithm and the method of solution, the results from simulation of the present model are validated with Cha, Table 2 shows the input parameters for both the models. Table 2. Input Parameters for Validation Parameters Cha, 2004 Model Present Model Pressure 31 bar 31 bar Frequency 34 Hz. 34 Hz. Steady State Temperature 87K 85.4K The Cooldown curves of Cha, 2004 and present model compared for a simulation time of 75 seconds and are shown in Figure 3. The estimated error of around 7 % is attributed to the use of a coarse mesh for present model. 2. Frequency and Pressure Optimization & Validation with Experimental Data Simulations are carried out by varying the parameters like frequency of operation and charge pressure. The results are compared to find the optimum conditions. Geometrical parameters are kept constant during the simulation processes. The simulations are carried out for no-load condition. The optimum frequency and pressure are found to be 54 Hz and 18 bar, respectively, which yield a minimum temperature of 46.4 K. The CFD simulation results are compared with experimental results reported in Tendolkar, Figure 4 shows that there is a good agreement between CFD results and experimental data. The nature of both the curves is almost same. The discrepancy between the CFD simulation and experimental results is due to the unaccounted losses including heat conduction through the wall, axial conduction, etc. Figure 3. Validation of Model with Cha, Figure 4. Comparison of Results of CFD Simulation with Experimental Data 766

5 3. Results for Optimum Operating Parameters i. Mass Balance Table 3 shows the mass balance or the Flux Report of the entire PTC at a particular instant. Mass balance is perfectly satisfied indicating a closed system without any spurious numerical leaks. The nomenclature or zones shown in Table 3 are generated by FLUENT software. In Table 3, the Default interior regions are the control volumes or the faces of the geometry where the mass inflow and outflow takes place whereas the rest of the regions are the boundaries of the geometry. Table 3. Mass Balance across the PTC Mass Flow Rate (kg/s) After cooler 0 Cold end heat exchanger 0 Default-interior Default - interior : Default - interior : Default - interior : Default - interior : Default - interior : Default - interior : Default - interior : Default - interior : Default - interior : Default - interior : Default - interior : Default - interior : Hot end heat exchanger 0 Inertance tube 0 Pulse tube 0 Regenerator 0 Surge volume 0 NET 0 ii. Pressure Variation Figure 5 shows the pressure variation along the axis of the PTC during expansion stroke. It can be observed from the figure that there is very small pressure drop across the pulse tube. Major of the pressure drop occurs across the porous media like cold end, hot end and regenerator. Hence, the design of porous zones is critical for achieving proper performance of the PTC. Figure 5. Pressure Variation along PTC Figure 6 shows the variation of the pressure at different locations of the PTC system. It can be observed that the pressure variation at the cold end and the hot end of the pulse tube is negligible. The pressure in the reservoir is almost constant, as the pressure variations at cold end and hot end gets damped in the reservoir, which is required for better performance of system. 767

6 Figure 6. Pressure Variation at different locations iii. Temperature and Density Variation Figures 7 and 8 display the temperature and density distributions respectively, along the length of the system. The temperature distribution shows that the temperature is nearly constant along the radial direction of trends are consistent with the ideal gas equation of state. Figure 8. Density Distribution along Axial Direction Figure 9 depicts the temperature contours under steady periodic conditions. It can be observed from the figure that the contours are consistent with Fig. 7. The distributions suggest that the profiles are approximately one-dimensional with little variations of temperature along the radial direction. Relatively significant lateral non-uniformity in temperature can be noticed in the pulse tube near the CHX, however. Figure 7. Temperature Distribution along Axial Direction Figure 9. Temperature Contours 768

7 Figure 10 shows the cooldown curve. It indicates that the cold end wall temperature gradually decreases with time till cyclic steady state condition is reached. A steady state temperature of 46.4 K is obtained after a simulation of 762 seconds. Figure 10. Cooldown Curve at Cyclic Steady State Figure 12. Five time steps for a cycle where Velocity Vector are plotted iv. Velocity Vector Plots Figure 11. Velocity Vector Plots at five time steps for a cycle Figure 11 shows the vector plots for the velocity distribution at the hot end. The results are obtained for five different time steps, as shown in Fig.12. The pulse tube and the inertance tube are at the left and right of the hot end, respectively. The oscillating flow, which reverses the direction in each cycle, can be seen from these vector plots. From the first time step vector plot, it can be observed that the velocity near the pulse tube is towards right, whereas that at the inertance tube is in the opposite direction. As the pressure starts developing, the velocity at the pulse tube end heads towards right. The velocity at the central core of the tube is larger than the velocity adjacent to the wall, because of the inertia effects. The velocity at the wall is zero; hence the adjacent layers reverse first. This can be observed from the first time step vector plot. The velocity vector near the wall is in the right direction (due to quick reversal), whereas the flow near the axis is heading towards the left. At the second time step, the flow is completely directed towards the right, and tends to develop the velocity near the axis. 769

8 After reaching the maximum value, pressure starts decreasing, which results in a decrease in the velocity, as shown in the third time step. At the fourth time step, as pressure goes below mean charging value, the direction of velocity near the pulse tube reverses, whereas in the inertance tube end the flow moves towards the right. This is attributed to the same situation, as discussed in the first case. As pressure decreases further, at the fifth time step, the flow reverses completely and flow develops. The pressure now goes on increasing till the maximum value. And, thus, the cycle goes on. Figure 13 shows the velocity vector plot at the junction between hot end and inertance tube. It can be seen that two-dimensional effects are more prominent at the junctions between the components. There are also swirl circulation patterns around the axis of symmetry as well. v. Induced Phase Difference Figure 14 shows pressure variations at the cold end, hot end and inlet. It can be observed from the figure that the pressure amplitude decreases due to the pressure drops across various components. The pressure wave of cold end and hot end is slightly shifted with respect to the compressor wave. This is attributed to the phase difference, and is measured to be approximately 18 degrees. CONCLUSIONS The results show that CFD simulations are capable of elucidating the complex periodic processes in PTCs very well. Significant multi-dimensional flow and temperature effects occur at the vicinity of junctions of different components. Different cases are simulated by varying the pressure and frequency independently to obtain the optimum parameters. The UDF developed for the oscillating flow in the compressor is also confirmed for proper working of the system. The Optimum results are obtained for 18 bar and 54 Hz with lowest temperature of 46.4 K at the cold end. Figure13. Velocity Vector Plots at the junction of Hot End and Inertance Tube Figure 14. Variation of Pressure at Inlet, Cold End and Hot End 770

9 NOMENCLATURE Abbreviations CFD CHX DIPTC G-M HHX ITPTC OPTC UDF Symbols F Computational Fluid Dynamics Cold end Heat Exchanger Double Inlet Pulse Tube Cryocooler Gifford McMahon Hot end Heat Exchanger Inertance Tube Pulse Tube Cryocooler Orifice Pulse Tube Cryocooler User Defined Function Density (kg/m 3 ) Differential time Divergence / Gradient operator Differential Operator External body forces Generation of energy per unit volume of time G Gravity acceleration, [m/s 2 ] j Mass Flux Density (kg/m 2 s) P q S Cp Pressure (Pascal) Velocity (m/s) Volumetric flow rate (m 3 /s) Source Term Specific Gas Constant, (J/kg-k) k Subscripts j eff Thermal Conductivity (W/m-K) Unit vector along Y direction Effective ACKNOWLEDGEMENT The authors would like to show their greatest gratitude to their advisors Dr. M.V.Tendolkar and Prof. Arvind Deshpande at V.J.T.I. for their constant guidance, motivation and endless support during the entire course of this work. The Authors gratefully acknowledge the help and support of all the faculty members and non-teaching staff of Mechanical Engineering Department, V.J.T.I. REFERENCES Ashwin, T.R., CFD Studies of Pulse Tube Refrigerators, PhD Thesis, IISC, Bangalore, India. Ashwin, T.R., Narasimham, G.S.V.L., Jacob S., CFD analysis of high frequency miniature pulse tube refrigerators for space applications with thermal nonequilibrium model, International Journal of Applied Thermal Engineering, vol. 30, pp Antao D., Farouk B., Flow and Heat Transfer Processes in an Inertance Type Pulse Tube Refrigerator, 16th International Cryocooler Conference. Banjare Y.P., Sahoo R.K., Sarangi S. K., CFD Simulation of Inertance tube Pulse Tube Refrigerator, 19th National and 8th ISHMT-ASME Heat and Mass Transfer Conference JNTU College of Engineering Hyderabad, India. Paper No. EXM-7, PP

10 Banjare, Y.P., Theoretical and Experimental Studies on Pulse Tube Refrigerator, PhD Thesis, National Institute of Technology Rourkela, India. Cha, J.S., CFD Simulation of Multi- Dimensional Effects in Inertance Tube Pulse Tube Cryocoolers, Master Thesis, Georgia Institute of Technology, Atlanta. Cha J.S., Ghiaasiaan S.M., Desai P.V., Harvey J.P., and Kirkconnell C.S., Multidimensional Flow Effects in Pulse Tube Refrigerators, Cryogenics, vol. 46, pp Conrad T.J., Ghiaasiaan S.M., Kirkconnell C.S., Simulation of Boundary Layer Effects in the Pulse Tube of a Miniature Cryocooler, Cryocoolers 16, p Fluent INC. Fluent 12 User Manual, Mohanta L., Atrey M.D., Experimental Investigation on Single Stage Inline Stirling Type Pulse Tube Refrigerator, International Cryocooler Conference. Tendolkar, M.V., Narayankhedkar, K. and Atrey, M.D., Performance Comparison of Stirling Type configurations, Proceedings 15 th International Cryocooler Conference, pp Versteeg H.K. and Malalasekera. An Introduction to Computational fluid dynamics. Longman, England, Walker G. Cryocoolers Part-1: Fundamentals. Plenum Press,