Numerical Study and Analysis of Inertance-Type Pulse Tube Refrigerator

Transcription

1 Numerical Stud and Analsis o Inertance-Tpe Pulse Tube Rerigerator SACHINDRA KUMAR ROUT, BALAJI KUMAR CHOUDHURY, RANJIT KUMAR. SAHOO, SUNIL KUMAR.SARANGI Department o Mechanical Engineering National Institute o Technolog Rourkela , Odisha INDIA Sachindra106@gmail.com Abstract:-This research article illustrates a numerical stud o single stage coaxial as well as inline Inertance- Tpe Pulse Tube Rerigerator (ITPTR), which perormance is mostl depending upon a regenerator. Regenerator is the signiicant component o a pulse tube rerigerator which has a great importance o producing cooling eect. In this present work a computational luid dnamic (CFD) solution approach has been chosen or numerical purpose. The detail analsis o cool down behaviour, heat transer at the cold end and pressure variation inside the whole sstem has been carried out b using the computational luid dnamic sotware package FLUENT. A number o cases have been solved b changing the porosit o the regenerator rom 0.5 to 0.9 and rest o parameter are remains unchanged. The operating requenc or all case is 34 Hz, pulse tube diameter 5mm and length is 125mm not changed or all cases. The result shows that porosit value o 0.6 produce a better cooling eect on the cold end o pulse tube rerigerator. The variation o pressure inside the pulse tube rerigerator during the process also analsed. To get an optimum parameter experimentall is a ver tedious job or iterance tube pulse tube rerigerator. So the CFD approach gives a better solution which is the main purpose o the present work. Ke-Words: -Pulse tube, Rerigerator, ITPTR, Regenerator, Porosit 1. Introduction In the histor o crogenics the invention o Pulse tube rerigerator was b Giord and Logesworth [1] in the ear o 1964S at Sracuse Universit. It was known as a Basic Pulse Tube Rerigerator (BPTR). Pulse tube rerigerator is used or helium liqueaction, magnetic resonance and aerospace. Pulse tube Rerigerator has the advantages o other tpe o crocoolers due to its high reliabilit, no moving part at cold end region, low price, and low magnet intererence. Mikulin [2] was the modiier who brought a modiication to the BPTR b adding a small oriice valve in 1984, which is responsible or increase in eicienc. It is due to addition o small oriice causes improve in phase between velocit and temperature as a result more enthalp low near hot heat exchanger. Such tpes o Rerigerator are known as Oriice Tpe Pulse Tube Rerigerator (OPTR). And then ater dierent researcher brought various new tpe o constructional modiication to enhance the cooling capacit and cool down behaviour. Zhu [3] introduce Double inlet Oriice Pulse Tube Rerigerator (DIOPTR) in which a bpass is directl connected to reservoir inlet rom the compressor outlet through which the surplus amount o luid passes to compressor and decreases the regenerator losses. Minimum temperature o nearl 3.5K was achieved with Multi stage pulse tube rerigerator [4-6]. Beside rom BPTR, OPTR and DIOPTR coniguration discussed, variegated alternative coniguration have been proposed. For a sample Zhu et al. [7] proposed an active-buer pulse tube rerigerator in which more than one reservoir was E-ISSN: Volume 9, 2014

2 attached. 80 K temperature was achieved with 11% o Carnot eicienc. Pan et al. [8] experimentall studied a 4 valve pulse tube rerigerator and archived a 57 K temperature at 100 W with an input power o 7 kw. The most recent tpe developed Pulse tube rerigerator is the Inertance-Tpe Pulse Tube Rerigerator (ITPTR). A long inertance tube is replaced instead o the small oriice in between the cold end and reservoir. The addition o inertance tube causes a batter phase relation between mass low rate and pressure than oriice tpe. Cha et al. [9] irst time gave a computational luid dnamics approach to solve the single stage iterance pulse tube rerigerator using well CFD solution sotware FLUENT and studied the multidimensional low eects. One major assumption o this CFD analsis using FLUENT package is the regenerator eicienc is 100 %. This is studied b Ashwin et al. [10] b considering a thermall non equilibrium medium o porous region inside the Regenerator. However there are so man ascinating investigations on mathematical as well as numerical analsis had been done b dierent researchers to stud the multidimensional low eect, nonlinear process, thermodnamic process and oscillator low.the main objective o this present paper is to stud the pressure luctuation as well as the cool down behavior at cold end due to varing in porosit inside the porous region. It is reported b the use o CFD simulation o the governing equation with the help o FLUENT sotware package I Fig.1. Schematic diagram o computational domain o ITPTR: 1 - compressor, 2 transer line, 3 - ater cooler,4 regenerator, 5 cold heat exchanger, 6 pulse tube, 7 hot heat exchanger, 8 - inertance tube, 9 - reservoir. Table 1. Dimensions o the ITPTR considered or the present analsis constituent part Diameter (m) Length (m) Boundar condition (1) Compressor Adiabatic (2) Transer line Adiabatic (3) Ater cooler K (4) Regenerator Adiabatic (5) Cold heat exchanger Adiabatic (6) Pulse tube Adiabatic (7) Hot heat exchanger (8) Inertance tube (9) Reservoir K Adiabatic Adiabatic 9 2. Description o Problem Geometr Fig. 1.shows the line diagram o Inertance-Tpe Pulse Tube Rerigerator (ITPTR) model along with its individual associated components. The whole sstem consists o a compressor which produces the luctuating pressure or the sstem and it is connected to a heat exchanger through a transer line known as ater cooler or extracting the heat to E-ISSN: Volume 9, 2014

3 surrounding generated b the compressor. The heart o the whole sstem is a regenerator, whose eectiveness is responsible or the cooling capacit o the pulse tube rerigerator. The cold heat exchanger is the cold region where the cooling load is supplied to the sstem. The heat is extracted rom the sstem with the hot heat exchanger. In between hot heat exchanger and cold heat exchanger there is present a pulse tube which is responsible or producing the phase dierence between mass low rate and luctuating pressure. The reservoirs store the working luid and acting as the buer. It is separated rom cold heat exchanger either b an inertance tube or ITPTR or b an oriice in OPTR. 3. Details o Modeling All The details modeling and meshing o the linear coaxial 2D axi-smmetric inertance pulse tube rerigerator model is done using the modeling sotware GAMBIT. The experimental nonlinear model is turned into equivalent present linier model. The dimensions o the whole sstem are shown in the Table 1. The numbers o grid points are varied rom 3643 t or the purpose o a grid independenc test.to operate the compressor piston head a suitable DEFINE_CG_MOTION user deine unction (UDF) chosen rom FLUNT user manual [13]. This UDF is written in C language, compiled and attached to the head o the piston. The two head piston oscillate about its center with the relation a = a 0* sin * (ωt). Where a is the piston displacement and a 0 = m is the amplitude with a time increment o s is assumed and the piston head velocit is related with the correlation v = a 0* ω * cos * (ωt). Where v is the piston head velocit. For regenerator porous media region the parameters are taken rom [10], inertial resistance m -1 and permeabilit m 2. Steel is chosen as the matrix material or regenerator. The working luid is chosen is helium and the various propert (thermal conductivit, viscosit, speciic heat) o the luid are taken as temperature dependent rom NIST data base. No wall thickness consider as the assumption or present analsis. 4. Mathematical Modeling The governing equations or the present 2D axismmetric transient model are continuit equation, Momentum equation in both axial as well as in radial direction and energ equation or solid matrix inside the porous region written with no swirl assumption. Two extra source term, both axial as well as in radial direction are considered or the porous region to calculate momentum losses. For the rest o porous medium these values are assumed to be zero and solid matrix inside porous region is considered as homogeneous. Continuit Equation 1 [ ξρ] + ξ rρ + ξρ v x = 0 t x (1) Momentum Equation For axial direction 1 1 [ ξρvx] + [ ξrvv x x] + ξ ρ vv x = t x ξ p 1 ξvx 2 + µ 2 ( ξ. v) x 3 1 ξv ξv x + µ + + Sx...(2) For radial direction 1 1 ξρ v + ξ rvxv + ξρ vv = t x p 1 vx xµ (. v) + r x x 3 v 1 2 (. v ) v x µ 2 µ (. v) + (. v) + S (3) Where S x and S are the two source term in the axial and radial direction which values is zero or nonporous zone. But or the porous zone the source term which is solved b the solver is given b the ollowing equation. µ 1 Sx = vx + Cρ vvx ψ 2 µ 1 S = v + Cρ vv ψ 2 E-ISSN: Volume 9, 2014

4 In the above equation the irst term is called Darc term and the second term is called the Forchheimer term which are responsible or the pressure drop inside the porous zone. Energ Equation: ( ξρe + ( 1 ξ ) ρses) +.( v( ρ E + p) ) t =. k T + τ. v (4) ( ) 6. Numerical solution procedure The most important actor in simulation that suitable numerical scheme. Axismmetric, unstead, cell based second order implicit time; phsical velocit with segregated solver is taken or analsis. PISO algorithm with a PRESTO (Pressure Staggered Option) scheme or the pressure velocit coupling is used or the pressure correction equation. The PRESTO scheme uses the discrete continuit balance or a "staggered'' control volume about the ace to compute the "staggered'' (i.e., ace) pressure. This procedure is similar in spirit to the staggeredgrid schemes used with structured meshes. Note that or triangular, tetrahedral, hbrid, and polhedral where ( 1 ξ) k = ξk + k E = h p + v 2 / ρ /2 s 5. Initial and Boundar Conditions The governing equations or 2D model as described above are solved b Fluent. The suitable boundar condition or the present case is shown in Table 1. The mean charge pressure is 30bar at which the total sstem operate. The sinusoidal pressure variation inside the whole sstem is due to the compressor head motion which is operated with a UDF as stated above. For an ideal condition o operation, simulation started with 300K operating temperature. The working luid is helium, assumed or simulation with temperature dependent viscosit. The wall temperature o both the cold and hot heat exchanger is maintained at 300 K while the rest component walls are operated with adiabatic. For better solution convergence 40 inner steps with the time step or iteration o s is needed. It will take a more than 15das to reach a periodic state with the CPU coniguration o 8GB o RAM and 3.1 GHz processor. Fig. 2. Validation plot between present model and Cha et al. [9] model meshes, comparable accurac is obtained using a similar algorithm. The PRESTO scheme or pressure interpolation is available or all meshes in Fluent. PISO (Pressure Implicit with Splitting o Operators) algorithm is used or better convergence. For unstead problems it is an eicient method to solve the Navier-Stokes equations.suitable Under relaxation actors or momentum, pressure and or energ had been used or the better convergence. Quad lateral as well as triangular cells were used or the computational domain. For all equation Convergence o the discretized equations are said to have been achieved when the whole ield residual was kept at Model validation A model validation test is carried out against preceding published crogenic journal b Cha et al. [9] model to igure out the accurac o the model and solution method. It is noticeable rom the Fig. 2 that the stead state temperature is reached ater 120s or both the case ater which there no change in temperature with respect to time. The Cha et al. model reporting a temperature o 87 K using 4200 number o cell where in the present case it is ound a 86 K using 3900 cell. 8. Result and Discussion 8.1 Cool down behavior E-ISSN: Volume 9, 2014

5 The computational simulation werecontinuous till a stead periodic saturated state is achieved. In this condition the Facate Average (FA) temperature o the cold end achieves a stead state. Ater this stead state there no change in cold end temperature. In the present model it reach a temperature o 46 K with the supplied dimension, which is shown in Fig 3. Fig.3. Axial temperature plot varing rom compressor to Inertance tube ater stead state temperature o 46K at cold heat exchanger The whole sstem wall temperature is ploted here. The compressor temperature is above the operating temperature due to compression and expainsion o luid inside it. This extra tepmerature generated inside the compressor is extracted to sorroundig through the atercooler. Inside the regenerator due to presence o extra source term causes momentum loss. In source term the presence o two term such as Darc andforchheimer terms in which pressure drop is directl popertional to velocit inside the porous zone. The temperature drop contour inside the regenaror is shown in the Fig 4. It is observed rom the contures that the temperature at cold end is 46.5 K. Fig.4. Temperature Contours showing the temperature variation inside pulse tube. 8.2 Varing pressure during the simulation The Fig [5-9] shows the pressure variation during the simulation inside the whole sstem. The Area Weighted Average pressure variation inside the cold heat exchanger is shown in the Fig 5. which is sinusoidal in nature. The pressure variation inside the cold heat exchanger rom 35.5 bar upto 28.5 bar which can be clear rom the igure. Fig 6.shows the axial pressure variation inside the total sstem rom compressor to reservoir when the piston is presence near to the BDC o clinder. At that position the compressor pressure is 36 bar and the pulse tube pressure is 35 bar, where reservoir pressure is 32 bar. Fig7. shows the axial pressure inside the total sstem rom compressor to reservoir when the piston is presence at middle position during expansion. At that position the compressor pressure is 26.5 bar and the pulse tube pressure is 31.5 bar, where reservoir pressure is 32.5 bar. When piston reaches to its top position during expansion process, the sstem axial pressure variation is shown in ig 8. It shows that the maximum pressure is inside the reservoir and minimum pressure inside the compressor and pulse tube pressure is 28.5 bar. During compression process rom TDC to BDC a pressure variation plot is shown in Fig 9. From the pressure luctuation analsis during one complete ccle it can be concluded that when there is maximum pressure at one end at the same time the other end o sstem has the minimum pressure. This was the main purpose o the stud that to analze the pressure variation through the whole sstem during a complete ccle. Fig. 5. Area Weighted Average Pressure inside cold heat exchanger vs. iteration curves. E-ISSN: Volume 9, 2014

6 Fig.6. Axial Pressure inside the ITPTR, when piston is near the BDC Fig.7. Axial Pressure inside the ITPTR, when piston is in middle position during compression Fig.8. Axial Pressure inside the ITPTR, when piston is near the TDC Fig.9. Axial Pressure inside the ITPTR, when piston is in middle position during expansion E-ISSN: Volume 9, 2014

7 8.3 Varing Porosit during the simulation The most important part o the pulse tube rerigerator is a regenerator. The pulse tube rerigerator perormance is depending upon the eectiveness o regenerator. In the present work a number o case studies have been carried out to investigate or which value o porosit it will give a better cooling temperature at the cold end. From the result o simulation it was ound that at the porosit value o 0.6 the optimum result ound relative to other value which is shown in the Fig 10. Fig.10. Cool down temperature vs. time or dierent porosit inside regenerator. 4 Conclusion A numerical approach is presented in this work to stud the multidimensional low characteristic o a pulse tube rerigerator. The results obtained b numerical analsis and previousl published paper work have been compared. It can be concluded that numerical method provides reasonabl accurate estimation o responses. Thereore, the method can be adopted to predict the responses beore going or actual experiment. It ma save time and cost o experimentation. The pressure variation inside the Inertance tpe pulse tube rerigerator plas a vital role which is discussed in above. The porosit value 0.6 at which it gives a better result. The proposed model can be used or selecting ideal process states to improve the perormance o PTR. Reerences [1] W Giord, and R.LongsworthPulse-tube rerigeration.trans ASME, J EngInd (series B) 1964, 86, pp [2] E. Mikulin, A. Tarasov, and M. Shrebonock.Low-temperature expansion pulse tubes, Advances in Crogenics Engineering 1984, 29, pp [3]Z. Shaowei, W. Peii and C.Zhonggi,.Double inlet pulse tube rerigerator: an important improvement, Crogenics 1990, 30, pp [4]Y. Matsubara, and J.L. Gao, Multi-stage Pulse Tube Rerigerator or Temperature below 4K. Proceeding o 8th Crocooler Conerence, 1994, pp [5]S. Zhu, Active-buer Pulse Tube Rerigerator. Proceedings o 16th International Crogenic Engineering Conerence / International Crogenics Materials Conerence, 1996, pp [6]C. Wang, S. Q. Wang., J. H. Caiand Z. Yuan, Experimental stud o multi-bpass pulse-tube rerigerator. Crogenics, (9),pp [7]S. Zhu, Y. Kakimi, and Y. Matsubara, Investigation o active-buer pulse tube rerigerator. Crogenics, (8),pp [8]H. Pan, A. Homann, and L. Oellrich, Singlestage 4-valve and active buer pulse tube rerigerators. Crogenics, (4),pp [9]JS Cha andsm Ghiaasiaan.Multi-dimensional low eects in pulse tube rerigerators. Crogenics 2006, 46, pp [10]TR Ashwin,GSVL Narasimham, S. Jacob.CFD analsis o high requenc miniature pulse tube rerigerators or space applications with thermal non- equilibrium model.crogenics 2010, 30, pp [11]L. Chen, Y. Zhang, E. Luo, T Li and X Wei.CFD analsis o thermodnamic ccles in a pulse tube rerigerator, Crogenics 2010, 50, pp E-ISSN: Volume 9, 2014

8 [12]S. K. Rout, D. P. Mishra, D.N. Thatoi and AK Mishra, Numerical Analsis o Mixed Convection through an Internall Finned Tube, Advances in Mechanical Engineering. Advances in Mechanical Engineering. 2012(ID ), pp. 10 pages, [13]Fluent 6.3 User s Guide, Fluent Inc. [14]S. K. Rout, D.N. Thatoi, A. K Mishra, andd. P. Mishra, CFD Supported Perormance Estimation o an Internall Finned Tube Heat Exchanger Under Mixed Convection Flow. Procedia Engineering, (0), pp E-ISSN: Volume 9, 2014