A Numerical Study of the Hampson-Type Joule- Thomson Cooler

Transcription

1 Purdue University Purdue e-pubs International Rerigeration and Air Conditioning Conerence School o Mechanical Engineering 004 A Numerical Study o the Hampson-Type Joule- Thomson Cooler Hui Tong Chua National University o Singapore Xiao Lin Wang National University o Singapore Hwee Yean Teo National University o Singapore Kim Choon Ng National University o Singapore Follow this and additional works at: Chua, Hui Tong; Wang, Xiao Lin; Teo, Hwee Yean; and Ng, Kim Choon, "A Numerical Study o the Hampson-Type Joule-Thomson Cooler" (004). International Rerigeration and Air Conditioning Conerence. Paper This document has been made available through Purdue e-pubs, a service o the Purdue University Libraries. Please contact epubs@purdue.edu or additional inormation. Complete proceedings may be acquired in print and on CD-ROM directly rom the Ray W. Herrick Laboratories at Herrick/Events/orderlit.html

2 R149, Page 1 A NUMERICAL STUDY OF THE HAMPSON-TYPE JOULE-THOMSON COOLER Hui Tong CHUA 1+, Xiaolin WANG 1*, Hwee Yean TEO and Kim Choon NG Department o Mechanical Engineering, National University o Singapore, 10 Kent Ridge Crescent, Singapore 11960, Singapore. Tel no.: (65) , Fax no.: (65) , id: + mpecht@nus.edu.sg, * mpewx@nus.edu.sg, ++ mpengkc@nus.edu.sg Oice o Estate & Development, National University o Singapore, Estate Oice Drive, Singapore , id: oedthy@nus.edu.sg ABSTRACT Miniature Joule-Thomson (J-T) cooler is widely used in the electronic industry or thermal management o power intensive electronic components due to its special eatures o having a short cool-down time, simple coniguration and having no moving parts. In this paper, the sophisticated geometry o the Hampson-type J-T cooler is analyzed and incorporated into the simulation, so that the model is a useul design tool. The governing equations o the cryogen, helical tube and s, and shield are coupled and solved numerically under the steady state conditions, and yield agreements with experiment data to within 3%. The characteristics o low within the capillary tube and external return gas are accurately predicted. The temperature versus entropy, cooling capacity versus load temperature, and cooling capacity versus input pressure charts are plotted and discussed. The conventional way o simulating a Hampson-type J-T cooler, which is accompanied by a host o empirical correction actors, especially vis-à-vis the heat exchanger geometry could now be superseded. The eort and time spent in designing a Hampsontype J-T crycooler could be greatly reduced. 1. INTRODUCTION The miniature Joule-Thomson (J-T) cryocooler has been a popular technology in the electronic industry. It is widely used or rapid cooling o inrared sensors and electronics devices due to its special eatures o having a short cooldown time, simple coniguration and having no moving parts (Aubon, 1988, Joo et al. 1995, Levenduski et al. 1996). Fig.1 shows a typical Hampson-type cryocooler. The cooling power is generated by the isenthalpic expansion o a high pressure gas through a throttling (capillary) device, or namely the Joule-Thomson (J-T) eect. The perormance o this cooler is ampliied and improved by using the recuperative eect o the expanded gas to precool the incoming stream inside the capillary tube in a counter-low heat exchanging arrangement. Fig.1a A Hampson-type J-T cryocooler (Xue, 001) Fig.1b A picture o the Hampson-type J-T cryocooler International Rerigeration and Air Conditioning Conerence at Purdue, July 1-15, 004

3 R149, Page Numerical studies on the J-T coolers have hitherto been ocusing on the prediction o cool-down rates albeit with an extensive use o empirical correction actors or the heat exchanging geometry. There are limited experimental and theoretical works reported on the prediction o the low characteristics or the Hampson-type Joule-Thomson (J-T) cooler. Maytal (1994) analyzed the perormance o an ideal low regulated Hampson-type Joule-Thomson (J-T) cooler. The prediction was not realistic because the heat-and-mass transers among the cryogen, tube wall, Dewar and mandrel were not considered. Chou et al. (1993, 1995) perormed experiments and preliminary numerical predictions on the transient characteristics o a Hampson-type Joule-Thomson (J-T) cooler. A one-dimensional model incorporating momentum and energy transport equations was presented. However, secondary low, torsion eect caused by the helical capillary tube and s, and the choking o low were not considered. Idealized heat transer coeicients o the tube wall, Dewar and mandrel were used in the simulation. This is not true as the heat transer coeicient varies signiicantly with the temperature. Chien et al. (1996) simulated the transient characteristics o a sel-regulating Hampson-type Joule-Thomson (J-T) cooler. However, this paper concentrated primarily on the development o the sel-regulating Hampson-type Joule-Thomson (J-T) cooler by bellows control mechanism. The simulation approach was similar to that o Chou et al. (1995). Recently, Ng et al. (00) simulated the perormance o a Hampson-type Joule-Thomson (J-T) cooler on its eectiveness, low characteristics, heat conduction and liqueied yield raction. Again, the torsion, secondary low eect, and the choking o low were not considered. Straight tube and straight s were used in the simulation despite the act that it was a Hampson-type heat exchanger. Furthermore, their ormulation exhibits signiicant thermodynamic inconsistency. In this paper, the sophisticated geometry o the Hampson-type heat exchanger is analyzed and incorporated into the model. The characteristics o high pressure gas, return gas, the mandrel, capillary tubes and s are numerically simulated. The choking o low in the capillary tube is also considered. The perormance o the Hampson-type Joule-Thomson (J-T) cooler in steady state condition is accurately predicted. The conventional way o simulating the Hampson-type Joule-Thomson cooler, which is accompanied by a host o empirical correction actors, especially vis-à-vis the heat exchanger geometry could now be superseded. The eort and time spent in designing a Hampsontype Joule-Thomson (J-T) cooler could be greatly reduced. Since we have totally avoided the use o empirical geometric correction actors, the model is a very helpul design tool.. THERMODYNAMIC MODEL The perormance o a Hampson-type Joule-Thomson (J-T) cooler could be determined i the amount o energy transer among the high pressure gas, tube wall, s and return gas at any instant is evaluated. The helical geometry o the capillary tube and s are analyzed and solved together with the governing equations. The governing equations or the energy balance, conservation o mass, the thermal conduction and radiation are discretized, coupled and simulated numerically. These governing equations are listed in the ollowing sections..1. High Pressure Gas in the Helical Capillary Tube Since the capillary tube diameter is much smaller compared to the capillary tube length, approximately 1 to 1840, one-dimension steady state low is assumed. The conservation o mass o the high pressure gas inside the helical capillary tube could be expressed as, dm& = 0 (1) The pressure inside the capillary tube drops rapidly due to the high velocity o the low and viscosity o the gas. The one-dimensional pressure drop along the natural helical direction (or the s-direction) o the capillary tube is given by, dp ρ u d( ρ u ) = () D mi is the Fanning riction actor o the high pressure gas. Timmerhaus and Flynn (1989) suggested an empirical expression or or the gas low in a helical tube as, D = (3) mi 0. ( p,t ) 0.184( )Re( p,t ) DHx International Rerigeration and Air Conditioning Conerence at Purdue, July 1-15, 004

4 R149, Page 3 The temperature o the high pressure gas varies along the capillary tube due to the drop o pressure, rictional loss and heat transer between the gas and the tube wall. It is expressed as, dt ν dp d( u ) h (Tm T ) π Dmi = G A cp + ν T + (4) T the heat transer coeicient,, could be expressed as, h 0. 3 D h = 0.03cpG Re Pr ( D.. Helical Capillary Tube The energy balance equation in the helical capillary tube is, mo Hx ) (5) d Tm h (T T )( A ) h (T T )( A ) m m l m l ml T m m = (6) Am km Amk m Amk m k T m k (T T )( A km k = (7) k W + k H ).3. Helical Fins The energy balance equation or the helical s wound around the helical capillary tube can be expressed as, d T h l(t Tl )( Al ) kt (T Tm )( Am ) = (8) A k A k.4. Shield The energy balance equation or the shield could be written as, h r Tsh d h l(tsh Tl ) πd = dz Asiksh is the radiative heat transer coeicient given by, hr = 1 ε + ( A sh sh si 4 sh hrπdsi(t T A k σ A )(1 ε 1) r r si sh 4 amb ) (9) (10).5. Return Gas The conservation o mass and momentum equations o the return gas along the primary axial direction (or the z- direction) o the helical capillary tube and s could be expressed as, dm& l = 0 (11) dz l dpl lρlul d( ρlul ) = + (1) dz D dz is the Fanning riction actor o the return low pressure gas and it is written as, Hl 0. l ( pl,tl ) Re( pl,tl ) = (13) The energy balance equation o the return gas along the primary axial direction (or the z-direction) o the heat exchanger is given by, A A ml l dtl dν l dp + + = + l d(ul ) h l(tl Tm ) h l(tl T ) h l(tl Tsh ) π Dshi Gl Al cpl νl Tl + (14) dz dz dz dtl dz dz International Rerigeration and Air Conditioning Conerence at Purdue, July 1-15, 004

5 R149, Page 4 the heat transer coeicient, h l could be expressed as, The conversion actor between and dz is given by,.6. Spacers l p l h = 0.6c G Re Pr (15) ( Pitchm π ) + Rcurve = (16) dz Pitch / π Nylon strings, which possess an extremely low thermal conductivity, is used to wind round the helical capillary tube and s, so as to limit the cross-sectional area available to the returning low pressure gas and thereby enhancing its contact with the s and the primary helical capillary tube. In our model, we assume that the spacers play the sole role o limiting the heat exchange cross-sectional area..7. Entropy Generation or High Pressure Gas in the Helical Capillary Tube m The entropy generation equation is used to assess the choking position o the high pressure gas in the capillary tube and is expressed as, ds dt T d dp dp gen Tm T Am m c ρ = & p + + h (17) T dt T T m ρ ρ ρ.8. Thermo-physical Properties o the Cryogen and Materials In this context, argon is chosen as the cryogen due to its easy availability, low cost and being able to achieve relatively low cryogenic temperature. The thermo-physical properties o argon are obtained rom the sotware o NIST (001) which makes use o the Helmhotz energy equation, a modiied Benedic-Webb-Rubin equation (mbwr), and an extended corresponding states model (ECS). The viscosity and thermal conductivity values are determined with a luid speciic model and a variation o the ECS method. Temperature-dependent thermal conductivities o copper, monel, stainless steel and polycarbonate are used in the simulation. The polycarbonate could be readily substituted by the Dewar in actual applications. Copper is used or the s that are wound round the stainless steel capillary tube. The assembly is inserted into the shield, which is made o monel, and insulated with polycarbonate. The exterior o the polycarbonate is assumed to be perectly insulated in our model. The relevant empirical correlations are summarized in Table 1 (Perry et al., 1997 and Flynn, 1997). Table 1 Thermal conductivities o materials Materials Correlation Relative Errors (Perry,1997) Copper 0.413T T + 848,(60K T 100K ) (Fins) k = { 0.08T 1.55T + 608,(100K T 300K ) < 1.5% Monel (Shield) Stainless Steel (Capillary Tube) k sh k m = lnt 14.76,( 40K T 400K ) < 1.0% = lnt ,( 40K T 400K ) < 1.0%.9. Jet Impingement Boiling The jet impingement boiling correlation on the heated surace proposed by Brian (1991) is used to estimate the heat lux at the load. Q A = ( T) International Rerigeration and Air Conditioning Conerence at Purdue, July 1-15, 004

6 R149, Page 5 T is the temperature dierence between the surace and the measured bulk luid. 3. RESULTS AND DISCUSSION Our simulation is applied to a Hampson type J-T cooler which is shown in the igure 1b. The dimensions o the Hampson-type Joule-Thomson (J-T) cooler are listed in the table. Table : Typical dimensions o a Hampson-type Joule-Thomson (J-T) heat exchanger Items Inner diameter, mm Outer diameter, mm Capillary tube, helical pitch = 1.0 mm Mandrel.3.5 Shield Fins: height = 0.5 mm, thickness = 1.0 mm, secondary pitch = 0.5 mm Length o heat exchanger = 50.0 mm The simulation results are compared with the experimental data as shown in table 3. Only the relative errors o the outlet temperatures o the return gas are compared with the simulated results. This is due to the unavailability o tiny sensors to measure the pressure and temperature in the capillary tube. It is noted that the measured return gas outlet temperature is slightly higher than the simulated results. This could be due to: i. the use o the polycarbonate instead o a Dewar lask, which inevitably increases the heat gain during the experiment. ii. readings o the temperature sensor at the return gas outlet are aected by the ambient conditions, on account o the minuteness o the exit port. However, it is observed that the relative errors between the simulations and experiments all ell within 3%. Table 4. A comparison between the experimental data and simulation results Case Pressure (bar) Temperature (K) M v Temperature (T outlet, K) Relative p 1 p 3 T inlet T sat =(p 3 ) (SLPM) Experiment Simulation Error, % * *The originally reported experimental value ( SLPM) was erroneous. Since the experimental mass low rates behave essentially linearly with the input pressure, the present value is obtained by linear interpolation. Figure shows the Temperature-Entropy diagram o the cryogen in the Hampson-type Joule-Thomson (J-T) cooler. The trend is similar to a typical T-S chart in the literature. However, it is ound that the pressure drops much more rapidly due to the higher rictional loss and expansion process in the high pressure gas channel than that in the low pressure channel. This in turn increases the cooling capacity o the Hampson-type Joule-Thomson (J-T) cooler and demonstrates the eiciency o the recuperative method in improving the perormance o the Hampson-type Joule- Thomson (J-T) cooler substantially. Figure 3 presents the eect o the load temperature on the cooling capacity. With an increase in the cooling load temperature, the cooling capacity increases greatly. This corroborates with the basic theory commonly used in the traditional air-conditioning and rerigerant systems. It is noted that the cooling capacity is linearly proportional to the load temperature. International Rerigeration and Air Conditioning Conerence at Purdue, July 1-15, 004

7 R149, Page Input Pressure : bar Input Temperature : K 1 Isobar (1.77 bar) 5' Isobar (1.55 bar) 40 Temperature (K) Isobar (179.1 bar) Isobar (81.40 bar) Cooling Speciic Entropy (J/kgK) Fig. A typical simulated T-s diagram o the Hampson-type Joule-Thomson (J-T) cooler Input Pressure : bar Input Temperature : K Flow Rate : SLPM Cooling Capacity, W Load Temperature, K Fig.3 Eect o the load temperature on the cooling capacity The higher the input pressure, the higher the cooling capacity that could be achieved. This is evident rom the simulation results as shown in Fig 4. Within our simulated range, the cooling capacity increases as the input pressure increases. It is observed rom the chart that the cooling capacity increases gently at the lower range o pressures while it increases more rapidly at the higher range. International Rerigeration and Air Conditioning Conerence at Purdue, July 1-15, 004

8 R149, Page Cooling Load Temperature : 110 K 7.0 Cooling Capacity, W Input Pressure, bar Fig.4 Eect o the input pressure on the cooling capacity CONCLUSION A simulation design tool or the Hampson-type Joule-Thomson (J-T) cooler has been developed according to the correct geometry o the helical capillary tube and s. The result shows that the numerical simulation agrees with the experimental data. The perormance characteristics o the Hampson-type Joule-Thomson (J-T) cooler are analyzed and discussed. Thereore, it could be concluded that this simulation is useul or the prediction, estimation and evaluation o the Hampson-type J-T cooler. It provides realistic design solutions or the manuacturers to design a J-T cooler and avoid most o the trial and error procedures commonly adopted. NOMENCLATURE A Contact area (m ) Superscripts & Subscripts c p Speciic heat capacity (J/kg K) amb Ambient D Tubes diameter (m) Rerigerant inside the tube Fanning riction coeicient Capillary s G Mass lux (kg/m.s) l Return rerigerant along the s h Heat transer coeicient (W/m K) m Capillary tube k Conductivity (W/m.K) man Mandrel m& Mass low rate (kg/s) mi Capillary tube interior p Pressure (Pa) min Minimum Pr Prandtl number = c p.µ / k mo Capillary tube exterior q Heat lux (W) out Outlet R, r Radius (m) sat Saturation situation R curve Radius o curvature o capillary tube sh Shield Re Reynol number si Shield interior S gen Entropy generation (J/K) Tot Total s J-T primary helical direction (capillary tube) Hx Hydraulic diameter T Temperature (K) u Bulk mean velocity o cryogen (m/s) W,H Eective width length and Height or (m) z J-T primary axial direction µ Viscosity (N s/m ) ρ Density (kg/m 3 ) σ Stean-Boltzmann constant (W/(m.K 4 )) International Rerigeration and Air Conditioning Conerence at Purdue, July 1-15, 004

9 R149, Page 8 REFERENCE Aubon, C.R., 1998, Joule-Thomson Cooling-An Overview, SPIE, vol. 915, p Brian, A., Sherman, S., Schwartz, H., 1991, Jet Impingement Boiling Using a J-T Cryostat, Cryogenic Heat Transer vol. 167, p Chien, S.B., Chen, L.T., Chou, F.C., 1996, A study on the Transient Characteristics o a Sel-regulating Joule- Thomson Cryocooler, Cryogenics, vol. 36, p Chou, F.C., Wu, S.M., Pai, C.F., 1993, Prediction o Final Temperature Following Joule-Thomson Expansion o Nitrogen Gas, Cryogenics, vol. 33, p Chou, F.C., Chien, S.B., 1995, Preliminary Experimental and Numerical Study o Transient Characteristics or a Joule-Thomson Cryocooler, Cryogenics, vol. 35, p Flynn, M.T., 1997, Cryogenic engineering, Marcel Dekker Inc., NewYork. Joo, Y., Dieu, K., Kim, C., 1995, Fabrication o Monolithic Microchannels or IC chip cooling, IEEE, p Lemmon, E.W., Peskin, A.P., McLinden, M.O., Friend, D.G., 000, Thermodynamic and transport properties o pure lui, NIST Standard Reerence Database 1, Version 5.0 Levenduski, R., Scarlotti, R., 1996, Joule-Thomson Cryocooler or Space Applications, Cryogenics, vol. 36, p Maytal, B.Z., 1994, Perormance o Ideal Flow Regulated Joule-Thomson Cryocooler, Cryogenics, vol. 34, p Ng, K.C., Xue, H., Wang, J.B., 00, Experimental and Numerical Study on a Miniature Joule-Thomson Cooler or Steady-state Characteristics, Int. J. Heat & Mass Trans., vol. 45, p Timmerhaus, K.D., Flynn, T.M., 1989, Cryogenic Process Engineering., Plenum Press, New York, USA. Xue. H., Ng, K.C., Wang, J.B., 001, Perormance Evaluation o the Recuperative Heat Exchanger in a Miniature Joule-Thomson Cooler, App. Thermal Eng., vol. 1, p ACKNOWLEDGEMENT We grateully acknowledge the generous support rom A*STAR SERC via the project number International Rerigeration and Air Conditioning Conerence at Purdue, July 1-15, 004