W. M. Clearman, S. M. Ghiaasiaan, J. S. Cha, C. S. Kirkconnell 1, P. V. Desai

Transcription

1 LONGITUDINAL HYDRAULIC RESISTANCE PARAMETERS OF CRYOCOOLER AND STIRLING REGENERATORS IN STEADY FLOW W. M. Clearman, S. M. Ghiaasiaan, J. S. Cha, C. S. Kirkconnell 1, P. V. Desai G.W. Woodru School o Mechanical Engineering Georgia Institute o Technology, Atlanta, Ga., U.S.A. 1 Raytheon Space and Airborne Systems (SAS) El Segundo, CA , U.S.A. ABSTRACT The results o an ongoing research program aimed at the measurement and correlation o anisotropic hydrodynamic parameters o widely-used cryocooler regenerator illers are presented. The hydrodynamic parameters associated with steady, longitudinal low are addressed in this paper. An experimental apparatus consisting o a cylindrical test section packed with regenerator illers is used or the measurement o axial permeability and Forchheimer coeicients, with pure helium as the working luid. The regenerator illers that are tested include stainless steel 325 and 400-mesh screens with 69.69% porosity, stainless steel 400-mesh sintered mesh iller with 61.65% porosity, stainless steel oam metal with 55.47% porosity, and micro machined nickel disks with 26.8% porosity. The test section is subjected to a steady low o helium at one end, and is open to the atmosphere at the other end. The instrumentation includes pressure transducers and a high-precision low meter. For each iller material, the pressures at inlet to the regenerator are measured under steady low conditions over a wide range o low rates and a CFD assisted methodology is then used or the analysis and interpretation o the measured data. The viscous and inertial resistance parameter values, and the corresponding permeability and inertial coeicients, obtained using CFD are then compared with the corresponding values that are separately measured under steadyperiodic low conditions. KEYWORDS: Pulse tube, steady low, permeability, inertial coeicient, axial low, porous media 728

2 INTRODUCTION Improving the perormance o the various types o cryocoolers is o great interest. For pulse tube rerigerators, there are several sources o irreversibility [1] but the regenerator is typically the largest source o loss in cryocoolers [2]. Axial heat conduction, thermal saturation, and rictional losses all cause irreversibility. However, it is very diicult to accurately predict the impact o the solid-luid interactions within the porous media or periodic low. To simpliy the analysis o these periodic systems, isotropic hydrodynamic parameters associated with steady low have oten been used [3]. It has recently been shown that CFD tools can simulate the entire cryocooler devices under steady and steady-periodic conditions [11, 12, 13]. However, the accuracy o these CFD predictions depend strongly on the accuracy o the closure relations they use. In this investigation measured pressure drops across cylindrical test sections containing various regenerator iller structures that are subject to a steady low o helium are reported. These data were used as boundary conditions or CFD simulations o the test section. Through an iterative process, the axial viscous resistance, D, and the inertial resistance, C, were adjusted to match simulated results to the experimental data. Using these results, the permeability and Forchheimer s coeicients were then calculated. TEST APPARATUS The test apparatus (Figure 1) includes a helium tank, two high requency Paine Electronics pressure transducers (Series ), a Sierra Instruments hot plate mass low meter (Model 826 Toptrak), and test section containing the regenerator illers o interest. Details o the 3-piece aluminum test section are displayed in Figure 2. The regenerator test sections is a slight variation o the design used by Cha [4]. It is made o aluminum 6061 and consists o the regenerator housing containing a 5/16 (0.79 cm) diameter by 1.5 (3.81 cm) length open volume or the test samples as well as two end pieces to hold the regenerator material in place. A larger regenerator housing 0.59 (1.499 cm) in diameter and (3.139 cm) in length was used or the micro machined disk samples. The helium tank contains research grade He with a nominal purity o %. Experimental pressure drop data were recorded or the ive matrix samples or low rates between 0 g/s to 1.5 g/s. The porous structures tested included 325 mesh and 400 mesh stainless steel screens at 69.69% and 69.68% porosity, respectively, sintered 400 mesh stainless steel screens at 61.65% porosity, stainless steel oam metal at 55.47% porosity, and stacked, micro machined nickel disks at 26.8% porosity. The latter regenerator iller was made o disks that were provided by International Mezzo Technologies, Inc. Baton Rouges, Louisiana). The disks had holes with diameter in the range 36~40 µm, and could be stacked such that the holes would get completely aligned. 729

3 Mass Flow Meter Pressure Transducer 2 Regenerator Test Section Pressure Transducer 1 Pressure Regulator Valve 2 Valve 1 Ampliier 2 Ampliier 1 Compressed Helium Multimeter 3 Multimeter 2 M ultimeter 1 FIGURE 1. Axial pressure drop test apparatus. FIGURE 2. Detailed test section (dimensions in cm). RESULTS OF EXPERIMENTS Multiple pressure drop tests were conducted or each o the ive porous structures o interest. Figures 3 and 4 show the steady low axial pressure drop as a unction o the measured mass low rate. 90 Steady Flow Axial Pressure Drop 325 and 400 Mesh % Porosity 120 Steady Flow Axial Pressure Drop Metal Foam % Porosity Mesh Mesh (a) (b) FIGURE 3. Steady low axial pressure drop data or (a) 325 mesh and 400 mesh (b) metal oam 730

4 250 Steady Flow Axial Pressure Drop Sintered 400 Mesh % Porosity 12 Steady Flow Axial Pressure Drop Micro Machined Nickel Disk % Porosity Run 1, P_supply = 2068 kpa Run 2, P_supply = 2413 kpa Run 3, P_supply = 2757 kpa Run 4, P_supply = 3447 kpa (a) (b) FIGURE 4. Steady low axial pressure drop data metal oam (a) sintered 400 mesh (b) machined nickel disks. For the sintered 400 mesh sample, the 300 psia (2068 kpa) supply pressure, or regulator pressure, was insuicient to achieve a gas low o 1.5 gm/s. Thereore, our series o runs representing supply pressures covering the range 2068 kpa to 3447 kpa were perormed or this iller (Figure 4a). CFD MODEL Using Fluent [14], the entire regenerator test section and its vicinity were modeled and used along with the empirically measured boundary conditions (inlet pressure and mass low rate) and user deined values o the relevant hydrodynamic parameters. The simulated outlet pressure, and thus the simulated pressure drop across the porous medium could then be adjusted to match the actual pressure drop by varying the assigned values o the viscous and inertial resistances. For the open region o the test section model, Fluent solves the ollowing continuum based mass, momentum, and energy conservation equations: where v 0 (1) t v vv P g F (2) t E ve P h j J j S h t (3) j v v T 2 v I (4) 3 731

5 For the porous regions o the model, the ollowing volume-average governing equations are solved assuming isotropic porosity, : v 0 (5) t v vv P g F (6) t E 1 s Es v E P (7) t h ke T hi Ji v S i where the external body orce term o the momentum equation is modeled as F i 3 Dij j1 3 1 v j Cij vmagv j (8) j1 2 The regenerator is axi-symmetric, and its axial direction is a principle direction or the porous medium. Thereore, when low in the axial direction is considered the coeicients in the last two terms o Eq. (8) can be represented as Darcy permeability, Kx and Forchheimer s inertial coeicient, c, by the ollowing relationship [7]:, x K x C 2 x x c, x (9) 3 Dx 2 K RESULTS AND DISCUSSION Figure 5 shows the CFD model nodalization scheme consisting o 2200 total nodes that was used or all the iller structures except or the perorated disks. For the perorated disks, the dimensions o the test section were slightly dierent and the total number o nodes was FIGURE 5. Nodalization o test section and vicinity. 732

6 Assuming steady, 1-D low o helium, and neglecting axial body orces and enthalpy sources, the pressure drop and mass low data determined rom experimentation could be used along with user deined values o D and C to close and numerically solve the governing system o equations. Ater iteratively adjusting the magnitudes o the hydrodynamic parameters to reduce the average percent dierence between simulated and experimental pressure drop, the values o the viscous and inertial resistances resulting in the most accurate simulations were recorded in Table 1. These values o D and C can now be compared directly to the periodic hydrodynamic parameters determined by Cha [4] or identical porous structures. Data indicates that there can be a dierence between the steady and periodic low viscous resistance o as much as 42.6% while there can be a dierence between the steady and periodic low inertial resistance o as much as 57.7%. Using steady low hydrodynamic parameters to predict behavior o periodic low through porous media can thus lead to substantial inaccuracies. This data can also be compared with the directional radial hydrodynamic parameters [5]. For the stacked 325 mesh screens at 69% porosity, the axial viscous resistance was 350% higher and the inertial resistance was 50% lower than the same parameters in the radial direction. TABLE 1. Steady low axial hydrodynamic parameters [7]. Regenerator Porosity D C K c Material (%) (1/m^2) (1/m) (m^2) ( - ) 400 Mesh E E Mesh E E Sintered (2068 kpa) E E Sintered (2413 kpa) E E Sintered (2757 kpa) E E Sintered (3447 kpa) E E Metal Foam E E Machined Disk E E All the experimental measurements were perormed with a supply pressure (i.e., pressure upstream Valve 1 in Figure 1) o 2068 kpa, except or the sintered 400 mesh iller. For this iller, a series o experiments were perormed with back pressures o 2068 kpa, 2413 kpa, 2757 kpa, and 3447 kpa (300, 350, 400, and 500 psia), in order to examine the eect o pressure on the hydrodynamic parameters. Figure 6a shows that using the hydrodynamic parameters associated with a supply pressure o P supply = 2757 kpa to simulate low at other supply pressures leads to systematic discrepancies between data and CFD predictions. To correct or the eect o pressure on the hydrodynamic parameters, the ollowing correlation was proposed: P av D D0 P cr P av C C0 P cr n1 n2 (10) (11) 733

7 where P av is the average pressure in the porous test section, and P cr is the luid critical pressure. The constants D 0 = 6.650E+10 m -2, n 1 = -8, C 0 = m -1, and n 2 = were iteratively determined by seeking the minimum average error between the adjusted hydrodynamic parameters as calculated by Eq. 10 and Eq. 11 and the actual parameters determined through simulations it to the experimental data or each individual supply pressure Axial Pressure Drop -- Sintered 400 Mesh % Porosity (D = 5.35E+10, C = ) Run 1, P_supply = 2068 kpa Simulation 1, P_supply = 2068 kpa Run 2, P_supply = 2413 kpa Simulation 2, P_supply = 2413 kpa Run 3, P_supply = 2757 kpa Simulation 3, P_supply = 2757 kpa Run 4, P_supply = 3447 kpa Simulation 4, P_supply = 3447 kpa Axial Pressure Drop -- Sintered 400 Mesh % Porosity 250 Run 1, P_supply = 2068 kpa Simulation 1, P_supply = 2068 kpa 200 Run 2, P_supply = 2413 kpa Simulation 2, P_supply = 2413 kpa Run 3, P_supply = 2757 kpa 150 Simulation 3, P_supply = 2757 kpa Run 4, P_supply = 3447 kpa Simulation 4, P_supply = 3447 kpa (a) (b) FIGURE 6. Simulation vs. experimental pressure drop using (a) constant hydrodynamic parameters and (b) using pressure dependant hydrodynamic parameters. CONCLUSIONS In this investigation, experiments were perormed or the measurement and correlation o axial viscous and inertial resistance parameters associated with some common cryocooler regenerator structures. The data analysis was perormed using a CFD-assisted method. The structures studied included stacked 325 mesh screens, stacked 400 mesh screens, sintered 400 mesh screens, metal oam, and stacked micro machined disks. The steady low and periodic low viscous and inertial resistances were compared or identical porous structures, and were ound to be dierent. Thus, it was concluded that the behavior o periodic low within the porous cryocooler regenerator cannot be accurately predicted based on steady low hydrodynamic parameters. Likewise, the anisotropic parameters or a single porous sample were reported. The experimental data showed that the viscous and inertial resistances, and thus the permeability and Forchheimer coeicient, are unctions o pressure. The dependence o both parameters on pressure was empirically correlated or the sintered 400 mesh structure. ACKNOWLEDGEMENTS This research is supported by Raytheon Company. We would like to thank Dr. Carl S. Kirkconnell and Jeesung Cha or technical assistance. 734

8 NOMENCLATURE A area o low tube (m 2 ) c Forchheimer coeicient C ij inertial resistance matrix (m -1 ) D ij viscous resistance matrix (m -2 ) E total speciic energy (kj/kg) F external body orce vector (N/m 3 ) g gravitational acceleration (m/s 2 ) I unit tensor J i diusion lux o species i (kg/m 2 s) k thermal conductivity (W/m-K) K permeability (m 2 ) m mass low rate o working luid (kg/s or g/s) P luid pressure (Pa) h S enthalpy source (W/m 3 ) T temperature (K) T bulk luid temperature (K) t time (s) v physical velocity vector (m/s) V x volumetric low rate (m 3 /s) axial coordinate (m) Greek letters porosity µ luid dynamic viscosity (N-s/m 3 ) density (kg/m 3 ) viscous stress tensor (Pa) Subscripts and Symbols av average cr critical e eective luid s solid Del operator (m -1 ) REFERENCES 1 Giord, W.E., Longsworth, R.C., Pulse Tube Rerigeration Progress. Advances in Cryogenic Engineering, Vol. 10. Plenum Press, New York, pp Radebaugh, R., Lewis, M., Luo, E., Potenhauer, J.M., Nellis, G.F., Schunk, L.A., Inertance Tube Optimization or Pulse Tube Cryocoolers. Advances in Cryogenic Engineering: Transactions o the Cryogenic Engineering Conerence, Vol. 51, pp Harvey, J.P., Oscillatory Compressible Flow and Heat Transer in Porous Media Application to Cryocooler Regenerators. PHD Dissertation, Georgia Institute o Technology, Atlanta, GA Cha, J.S., Measurement And Correlation O Anisotropic Hydrodynamic Parameters In Porous Media Under Steady And Oscillating Flow: Application To Cryocooler Regenerator. PHD Dissertation, Georgia Institute o Technology, Atlanta, GA Cha, J.S., Ghiaasiaan, S.M., Desai, P.V., Measurement o Anisotropic Hydrodynamic Parameters o Pulse Tube or Stirling Regenerators. Advances in Cryogenic Engineering: Transactions o the Cryogenic Engineering Conerence, Vol. 51, pp Vaai, K., Editor. Handbook o Porous Media. 2 nd Edition. Taylor and Francis Group, Clearman, W.M., Measurement and Correlation o Directional Permeability and Forchheimer s Inertial Coeicient o Micro Porous Structures Used in Pulse-Tube Cryocoolers, Master s Thesis, Georgia Institute o Technology, Atlanta, GA Cha, J.S., CFD Simulation o Multi-Dimensional Eects in Inertance Tube Pulse Tube Cryocoolers, Master s Thesis, Georgia Institute o Technology, Atlanta, GA Nam, K., Jeong, S., Measurement o Cryogenic Regenerator Characteristics under Oscillating Flow and Pulsating Pressure. Cryogenics 43, Elsevier, pp Jeong, Nam, Jung, Regenerator Characterization under Oscillating Flow and Pulsating Pressure. Cryocoolers 12, Kluwer Academic, New York, pp Hozumi, Y., and Shiraishi, M., Simulation o Thermodynamics Aspects About Pulse Tube Rerigerator, Proc. Int. Cryo. Eng. Con., Sept 2003, pp Flakes, B., and Razani, A., Modeling Pulse Tube Cryocoolers with CFD, Proc. Int. Cryo. Eng. Con., September 2003, pp Cha, J.S., Ghiaasiaan, S.M., Desai, P.V., Harvey, J.P., and Kirkconnel, C.S., Multi-dimensional Flow Eects in Pulse Tube Rerigerators, Cryogenics, Vol. 46 (2006), pp Fluent 6.2 User s Guide. January, Chapters 7 &