NUMERICAL ANALYSIS of PULSE TUBE CRYOCOOLER

Transcription

1 International Journal o Innovative Research in Science, Engineering and Technology NUMERICAL ANALYSIS o PULSE TUBE CRYOCOOLER Pravin Mane 1, Ashutosh Dasare 2, Ganesh Deshmukh 3, Pratik Bhuyar 4, Kshiteej Deshmukh 5, Aditya Barve 6 Assistant Proessor, Mechanical Engineering Dept, Walchand College o Engineering, Sangli, Maharashtra, India 1 Final year B.Tech Student, Mechanical Engineering Dept, Walchand College o Engineering, Sangli, Maharashtra, India 2 Final year B.Tech Student, Mechanical Engineering Dept, Walchand College o Engineering, Sangli, Maharashtra, India 3 Final year B.Tech Student, Mechanical Engineering Dept, Walchand College o Engineering, Sangli, Maharashtra, India 4 Final year B.Tech Student, Mechanical Engineering Dept, Walchand College o Engineering, Sangli, Maharashtra, India 5 Final year B.Tech Student, Mechanical Engineering Dept, Walchand College o Engineering, Sangli, Maharashtra, India 6 Abstract: A commercial computational luid dynamics (CFD) package is used or numerical analysis o the oscillating luid low in a pulse tube cryocooler. This model uses helium as a working medium to achieve temperatures in cryogenic range by employing two pulse tubes with 180⁰ phase dierence in the mass low rate and the pressure at the cold end heat exchanger. The cryocooler comprises o compressor, ater cooler, regenerator, pulse tube with cold and hot heat exchanger and the inertance tube. A two-dimensional axis symmetric model was used or simulation. This simulation demonstrates the variation in temperature and pressure with respect to time at the cold heat exchanger. Keywords: pulse tube, cryocooler, CFD, phase dierence. NOMENCLATURE: D p Mean diameter o particles [m]. 2 T Temperature [K]. h Enthalpy [. k Thermal Conductivity [ 2 p Pressure [. & c Resistance coeicients 1 J kg ] Porosity [dimensionless]. W. m. K Nm ]. t Time [s]. Nm. ]. 1 1 ]. 2 Stress tensor [ SUBSCRIPTS: Fluid Velocity [ Molecular Viscosity [ Fluid Density [ 1 ms ]. r Radial direction. 1 1 kg. m s ]. s Solid. 3 kg. m ]. x Axial coordinate. I.INTRODUCTION Cryogenics is the branch o physics that deals with the production and study o eects at very low temperatures. Cryogenic Engineering is concerned with temperatures in the range o 0 to 123 K. Copyright to IJIRSET 1

2 International Journal o Innovative Research in Science, Engineering and Technology The rerigerating machines which are able to achieve and to maintain cryogenic temperature i.e. temperature below 123K are known as cryocoolers. These cryocoolers ind applications in space, military and low temperature research as well as in agriculture, transportation and security. An increased need o cryogenic temperatures in research and huge technological growth during last decade caused a rapid development o cryocoolers. All these applications mostly require eiciency and reliability o the rerigerators along with low cost and long lie time. Stirling rerigerators which are primarily used or these cryogenic applications satisy the above requirements. But the basic problem o these rerigerators is that they have a mean ailure time o 4000 hours. This is the reason why they can t be used in satellites and most o the commercial applications. That is why most o the developments in Stirling rerigerators are concentrated towards the techniques that can improve their reliability. This reliability problem can be overcome by research and development o Pulse Tube Rerigerators which are having potential or improved reliability, simplicity and low cost. II.SIMULATED SYSTEM The proposed model is the modiication o Gawali et.al model in which the oriice is replaced with an inertance tube, as shown in igure. It is called as Inertance Pulse Tube Rerigerator (IPTR). This enables us to eliminate the oriice required in basic Oriice pulse tube rerigerator (OPTR). Fig. 1 Simulated Inertance Pulse Tube Rerigerator (IPTR) In each rerigerator, the volume o gas in pulse tube can be divided into three parts: 1. Cold part: This is the letmost part o the pulse tube. Here the gas lows rom regenerator and expands to give out work. 2. Hot part: This is the rightmost part o the pulse tube. Here the gas lows rom the inertance tube and absorbs work. 3. Middle part: The gas at the centre o the pulse tube never lows out o the pulse tube and is similar to a displacer in a Stirling rerigerator. The solid displacer o the Stirling cycle is replaced by gas displacer. Each rerigerator consists o two heat exchangers namely CHX i.e. cold heat exchanger through which cooling eect is utilized, and HHX i.e. hot heat exchanger or rejection o heat to cooling media. Copyright to IJIRSET 591

3 International Journal o Innovative Research in Science, Engineering and Technology A. DIMENSIONS OF THE SIMULATED SYSTEM TABLE I. Component Radius(mm) Length(mm) A (Compressor) B (Transer line) C (Regenerator) D ( Cold heat (varying) 10 exchanger) E (Pulse tube) F ( Hot heat exchanger) G (Inertance Tube) H ( Reservoir) TABLE IIIII Parameter Unit Value Compressor swept volume cm Operating requency Hz 12 Transer line length mm 35 Regenerator ID mm 48 Regenerator length mm 40 Cold heat exchanger mm 10 (CHX) length Pulse tube ID mm 19 Pulse tube length mm 100 Hot heat exchanger (WHX) cm volume Inertance tube ID mm 3 Inertance tube length mm 1500 Reservoir volume m Copyright to IJIRSET 592

4 International Journal o Innovative Research in Science, Engineering and Technology B. BOUNDARY CONDITIONS The components are subjected to various boundary conditions as listed in the ollowing table. TABLE IVVVI Models Condition Compressor wall Transer-line wall 300 K Regenerator wall CHX wall Pulse tube wall WHX wall 300 K Reservoir ( Isothermal) Dynamic wall velocity (m/s) WHX thickness(m) Not considered Regenerator thickness (m) Not considered CHX thickness (m) Not considered Pulse tube thickness (m) Not considered Initial temperature(k) 300 K Working luid Helium Initial system pressure 8 bar CHX load ( W) 0 W CHX temperature 142 K Steady state reached No C. MATERIALS OF COMPONENTS We have used FLUENT as a solver or the analysis in which we have speciied the ollowing materials or the corresponding parts. TABLE IV Parts Material Compressor wall Transer-line wall Regenerator wall CHX wall Pulse tube wall WHX wall Reservoir wall Inertance tube Regenerator porous medium CHX porous medium WHX porous medium Copyright to IJIRSET 593

5 International Journal o Innovative Research in Science, Engineering and Technology III.CFD ANALYSIS A. MESHING IN GAMBIT The accuracy o analysis o thermo-luidic problem or system in CFD is strongly depending on the computational mesh structure applied. Meshing is one o the most time consuming processes in pre-processing. Gambit has dierent eatures o meshing. The meshing involves discretization o domain into sub domains or cells. These divided domains are used in the numerical solutions o the dierential conservation equations o the mathematical model. For meshing dierent elements and structures quadrilateral and triangular mesh structure is used. B. CFD MODELLING The CFD code FLUENT (6.3.26) is used or simulation. The IPTR system is simulated by assuming cylindrical and linear alignment, axis-symmetric, two-dimensional low, with working media helium as ideal gas. The transient analysis is done because the process is time dependant. Dierent algorithms, namely SIMPLE, SIMPLEC, PISO and COUPLED are incorporated in commercial CFD Sotware, and these algorithms are having their own advantages and disadvantages. PISO algorithm has been used in this analysis o the pulse tube rerigerator. PISO algorithm is recommended or unsteady calculations and may sometimes be preerred or steady-state ones. Compressor is modelled by using dynamic mesh eature o the FLUENT. The requency o the compressor is 12 Hz. The dynamic mesh model in luent is used to model lows where the shape o the domain is changing with time due to motion o the domain boundaries. The motion is prescribed motion by speciying the linear and angular velocities about the centre o gravity o solid body with time. In order to model compressor, a user deined unction with necessary modiication was developed in C programming to simulate the piston cylinder eect. Regenerator, Warm Heat Exchanger (WHX), and Cold Heat Exchanger (CHX) were modelled as porous media. Stainless steel wire mesh screens (mesh size 250) were selected as the regenerator packing material, since they oer high heat transer surace areas, high heat capacity, and low thermal conductivity. mesh (mesh size 150) is used or WHX and CHX. Quadrilateral and triangular mesh structure is used or meshing the IPTR system with dierent eatures o Gambit [19]. Total numbers o cells or the model with zero thickness are Continuum based conservation equation is applied in the system. The mass, momentum and energy equations solved by FLUENT are as ollows: 1 r v r v x 0 t r r x v vv p t... (1) (2) E. v E p. k T. v t Where 2 p v E h 2 All properties represent the properties o the working luid helium. The above equations apply to all components, except or CHX, WHX and the regenerator. The latter three components are modelled as porous media, assuming that within the volume containing the distributed resistance, there exists everywhere local balance between pressure and resistance orces [18]. (3) ( ) 1 [ r r ] ( x ) 0 t r r x (4) Copyright to IJIRSET 594

6 International Journal o Innovative Research in Science, Engineering and Technology ( ) (. ) t 1 P j c j j 2 1 [ ] [ ] [ E (1 ) Es ] [ ( E P)] t [ K (1 ) T (. ) (5) (6) All the simulations are carried out as transient processes, starting with an initial system temperature o 300 K. Simulations can be continued until steady-periodic state is obtained. The criterion or steady periodic condition is that the cycle-average temperature o the cold end heat exchanger (CHX) would reach a steady state. C. ASSUMPTION MADE FOR THE ANALYSIS 1. All components have circular cross-section and have linear alignment. 2. Axis-symmetric geometry is considered or the analysis. 3. Flow is two dimensional and compressible. 4. Helium gas obeys the ideal gas equation. On the basis o assumption made, the geometry is simpliied rom three- dimensional to two-dimensional axis symmetric. The property variation in the third direction is strongly dependant on the geometry or the present model and thus is negligible. This simpliication will lead to minimum number o cells or meshing and reduce computer time or calculation. IV.RESULTS AND DISCUSSION Temperature variation along axial direction is shown in Figure2. Temperature contour along axial direction is shown in Figure3. Signiicant temperature gradients are predicted in the regenerator and pulse tube. Fig. 2 Temperature variation in axial direction Copyright to IJIRSET 595

7 International Journal o Innovative Research in Science, Engineering and Technology Fig. 3 Temperature (K) contour along axial direction A. COOL DOWN CHARACTERISTICS The variation in cycle average temperature at CHX with time is shown in Figure 4.Temperature (cycle average) o K is attained ater sec. Fig. 4 Cool down characteristics B. PHASE SHIFT The variation in pressure and mass low rate with crank angle at CHX is shown Figure 5. The phase dierence in pressure and mass low rate o 40 0 is observed. The mass low rate is lagging the pressure wave. Copyright to IJIRSET 596

8 International Journal o Innovative Research in Science, Engineering and Technology Fig. 5 Phase shit at CHX C. CYCLIC PROPERTY VARIATION Fig. 6 Cyclic pressure variations with crank angle at CHX Copyright to IJIRSET 597

9 International Journal o Innovative Research in Science, Engineering and Technology Fig. 7 Cyclic temperature variations with crank angle at CHX The trends are predicted with the help o CFD tool luent i.e. igure 2, 3, 4, 5, 6, 7. V.CONCLUSION The entire IPTR system operating in periodic state under the given boundary conditions is numerically simulated using CFD code. From present analysis, the lowest temperature at the cold heat exchanger obtained is 132 K in 172 seconds by using helium as the working luid. The phase shit between the mass low rate and pressure variation at the cold heat exchanger is observed to be This indicates the easibility o the use o commercial CFD sotware packages or analysing the complex luid low and heat transer phenomena that occur in a pulse tube cryocooler. REFERENCES [1] Giord W. E. and Longsworth, Pulse tube rerigeration progress. Advances in Cryogenic Engineering, Vol. 10, pp , (1963). [2] Giord W. E. and Longsworth R. C., Pulse tube rerigeration. ASME paper, No. 63-WA 290, (1963). [3] Mikulin E. I., Tarasov A. A. and Shkrebyonock, Low temperature expansion Pulse Tube. Advances in Cryogenic Engineering, Vol. 29, pp , Plenum press, New York, (1984). [4] Zhu S.W and Chan Z.Q, Isothermal model o pulse tube rerigerator, Cryogenics (1994) Vol.34 PP [5] Atrey M.D and Narayankhedkar K.G, Development o second order isothermal model o oriice type pulse tube rerigerator (OPTR) with linear compressor, proc, ICEC-18, PP (2000). [6] Gawali B.S., Atrey M.D. and Narayankhedkar K.G. Perormance Prediction and Experimental Investigation o Oriices Pulse Tube Rerigerator ICEC 19, 2003,pp [7] M.E. Will, A.T.A.M. de Waele. Analytical treatment o counter low pulse tube rerigerators Cryogenics 46 (2006) pp [8] Barrett Flake and ArsalanRazani Modeling Pulse Tube Cryocoolers With CFD, Advance Cryogenic Engineering Vol.49 (2004). [9] J.S. Cha, S.M. Ghiaasiaan, P.V. Desai, J.P. Harvey, C.S. Kirkonnell Multi-dimensional Flow Eects in Pulse Tube Rerigerator Cryogenics 46 (2006) pp [10] Narayankhedkar K.G. and Gawali B.S. Design and Development o an Oriice/ Inertance Pulse Tube Cryocooler using a Linear Compressor CEC 49, pp [11] Gawali B.S. and Narayankhedkar K.G. Perormance Prediction and Experimental Investigation to Study the Eect o Hot End Heat Exchanger Volume on Oriice Pulse Tube Cyocooler ICEC 19, 2003, pp [12] Lothar O. Schunk, John M. Potenhauer, Gregory F. Nellis, Ray Radebaugh, E. Luo. Inertance Tube Optimization or KW- Class Pulse Tubes Cryogenics 46 pp [13] Xiao-bin Zhang, Zhi-huaGan, Li-min Qiu, Hua-xiang Liu. Computational Fluid Dynamics Simulation o an Inter-phasing Pulse Tube Cooler Journal o Zhejiang University Science A (1) pp [14] Gawali B.S., Khare S.B., Theoretical Prediction and Experimental Investigation o Counter Flow Pulse Tube Rerigerator Indian Journal o Cryogenics Vol. (32) pp (2007). [15] Biredar S.B., Gawali B.S., Analysis o Inertance Pulse Tube Cryocooler using Computational Fluid Dynamics Indian Journal o Cryogenics Vol. (32) pp (2007). [16] Anarase R.N. and Gawali B.S. Analysis o counter low heat exchanger used in pulse tube rerigerator IJC 2008, pp [17] Gawali B.S. and Mane P.A. CFD study o oriice pulse tube cryocoolers IJC 2010, pp [18] Fluent Users guide, Fluent. Inc. [19] Gambit Users guide. Copyright to IJIRSET 598