Steady State Numerial Analysis of a Joule-Tompson Cryoooler for Cryosurgial Probe R. V. Topkar 1 and M.. Atrey 1 1 epartment of Meanial Engineering, Indian Institute of Tenology Bombay, Mumbai 400076 Te Hampson-type Joule-Tomson ryooolers are preferred for ryosurgial probes due to teir small size and no moving parts. ue to substantial ange of pressure and temperature bot along bot te inlet and returning streams, property variations of te working fluid and pressure drop in te streams ave to be realistially aounted for. Numerial analysis is te key for su demanding design appliations. In te present work, steady state simulation of te eat exanger in te Joule- Tomson ryoooler is arried out numerially. Te model predits te pressure and temperature profiles of te ig pressure inlet and low pressure returning stream. Tese results are validated using various data available in literature. One validated, te steady state model is used for design of eat exanger for Joule-Tompson ryoooler to be used in ryosurgial probe. Various key parameters of te eat exanger tat affet its performane are identified and teir effet is studied. Key words: Joule-Tompson Cryoooler, Cryosurgial Probe, Heat Exanger, Steady- State Simulation, Temperature-dependent Properties INTROUCTION A Joule-Tomson ryoooler is a losed system onsisting of a eat exanger, evaporator and an expansion devie. A Joule- Tompson ryoooler is one of te most effetive metods of providing low temperature ooling due to its features of sort ool down time, ompat size and no moving parts. Te Hampson-type eat exanger is usually used for tis devie mainly due to its spae utilization. Te eat exanger onsists of a ially oiled ned tube in an annulus between te inner mandrel and outer sield. Te ig pressure inlet fluid passes troug te ned tube and is expanded by a Joule-Tompson expansion proess at te end. Te expanded fluid produes ooling effet and delivers te same in te evaporator. Tis old fluid at low pressure ten, passes over te ned tube in te annular spae preooling te inoming ig pressure fluid. Te working fluids normally used are nitrogen and argon. Te performane of te JT ryoooler is igly dependent on te effetiveness of te eat exanger. Also, tere is substantial ange of pressure and temperature in te fluid on bot sides of te eat exanger and ene, property variations need to be taken into aount wile simulating te eat exanger. Previous studies ave been limited due to te omplex geometry of te eat exanger.
Ng et al. [1] and Xue et al. [] reported te experimental and numerial study of te Joule-Tompson refrigerator for steady-state arateristis wit argon as te working fluid. Numerial studies for transient arateristis of te Joule-Tompson refrigerator wit nitrogen as working fluid using a one dimensional transient model are reported by Cien et al. [3] and Cou et al. [4]. Cua et al. [5] developed te geometry model of te Hampson-type ryoooler. Hong et al. [6] applied te effetiveness-ntu approa to predit te arateristis of a Joule- Tompson ryoooler for argon and nitrogen gas. Ardapurkar and Atrey [7] identified an area orretion fator to alulate te atual area of eat transfer on te old side. Fredrikson [8] as modeled te ryosurgial probe onsisting of a Joule-Tomson ryoooler and presented a study on te ie ball model. Te model aims at maximizing te size of te ie ball produed at te tip of te ryosurgial probe. In te present study, steady state numerial simulation of te eat exanger in te Joule- Tomson ryoooler is arried out. Te model predits te pressure and temperature profiles of te ig pressure and low pressure streams along te lengt of te eat exanger. Te steady state model is used for design of eat exanger for Joule- Tompson ryoooler for a ryosurgial probe. Te effet of various key parameters of te eat exanger are ten studied. area of te eat exanger is onsidered for alulation of perimeters and areas of eat transfer between different omponents of te eat exanger. Figure 1 sows te rosssetional area of te eat exanger. NUMERICAL MOEL Te one-dimensional model given by Ng et al. [1] is used for simulating te eat exanger. Te following assumptions are made for simulating te eat exanger: 1. Temperature varies only along te lengt of te pipe (x-diretion only.. Tere is no ondution in te fluid. 3. Te emissivity of te surfae of te sield is independent of temperature. For implementing te one-dimensional model, aurate alulation of te eat transfer surfae areas is required. Te ross-setional Figure 1. Cross-setional View of te Heat Exanger [7] Te flow area for te low pressure side is te area in te annular spae witout te ned tube and is given in Equation 1. A ( si mo ( Nt ( o ( o o / 4 (1
Similarly, te perimeter of te outer area of ned tube is alulated and given in equation. P o ( Te ydrauli diameter is used for te alulation of parameters assoiated wit te return fluid stream. Te area orretion fator of 0.3 as given by Ardapurkar et al. [7] is applied to aount for te atual eat transfer area on te old side. Tis aounts for te non-uniform flow distribution over te surfae. Termopysial Properties Te MBWR equation of state given by Younglove [9] is utilized for getting te density given te pressure and temperature. Te equation is non-linear and te bisetion metod is used for solving te equation. Te termal ondutivity and visosity are funtions of density and temperature and are given by Hanley et al. [10]. Te deviations in te termopysial properties alulated using tese equations is around a maximum of 0.5% wi may lead to small errors in te alulated temperature and pressure profiles ompared to atual termopysial properties. Governing Equations Te governing equations used for te model are given below. Continuity Equation: dm ( 0 ( N( Momentum Equation: o Pit / (3 dp fg d(1/ G (4 Energy Equations for te ot fluid, old fluid, tube, mandrel, and sield [Equations 5-9] respetively: o (1 Nt dt m C p pi ( T Tw (5 dt m C p [ po ( T Tw psi( T Ts (6 p ( T T ] d T kwaw d T kmam d Ts k s As w m mo m p ( T T p ( T T (7 i w p ( T T (8 p mo si ( T s m T p r o o w ( T 4 s T 4 amb (9 Te Fanning frition fator f for flow in a ial oil is given by: f 0.184(1 3.5 i Re 0. Te onvetive eat transfer oeffiients for flow given by Flynn [11] are employed in te model. Tey are as follows: 0. / 3 i 0.03C pg Re Pr (1 3.5 0.6C p G Re 0.4 Pr / 3 Were is valid single pase turbulent flow wit Re>10 4 and is valid for turbulent flow witin te range of 000<Re<3.x10 4. Boundary Conditions Te adiabati boundary ondition are applied at te ends of te tube for te sield, mandrel and tube. Te inlet pressure and temperature for te ot fluid as well as for te old fluid, after te evaporator, are deed. Te governing equations [Equations 3-9] are solved along wit te boundary onditions by disretizing te lengt L of te eat exanger using te ite differene metod. Te disretized equations are solved using te iterative Gauss-Seidel metod. For tis, an initial guess for te temperature and pressure at te nodes is made and te ode is run till onvergene of tese parameters as
well as te properties. Te termopysial properties are updated at te start of ea iteration using te previous pressure and temperature at tat node. Validation of te Model Te non-dimensional temperature (Equation 10 profiles obtained from te numerial simulation are ompared wit te profiles given by Ng et al. [1] and are sown in Figures and 3. T( x / L T, in ( x / L (10 T T, in, in As an be seen from te figures, te temperature profiles an aurately predit te old end temperature to an error of 1%. Te drop in pressure along te lengt of te eat exanger is almost linear. Te pressure drop in te inlet stream ΔP is ompared wit te experimental data and te results along wit te temperature results at te old fluid outlet are presented in Table 1. As an be seen, te pressure drop in te ig pressure fluid is omparable to te experimental result. Tere is no experimental result available for te temperature profile in te eat exanger. Te error an be redued by using more aurate termopysial data. ESIGN FOR CRYOSURGICAL PROBE Figure. Temperature profiles (P, in=17.91 MPa Figure 3. Temperature profiles (P, in=14.047 MPa After te validation of te model, te design for using te eat exanger for a Joule- Tompson ryoooler to be used as a ryosurgial probe is arried out. Instead of a ned tube, a apillary witout s is used for ease of winding around te mandrel and onstrution. Nitrogen is used as te working fluid for te non-ned tube due to ease of availability. Te apillary is made from opper wile te mandrel and sield are made from stainless steel. Parameters like te supply pressure, eat exanger lengt, and ial diameter are onsidered. Te ig pressure fluid is expanded troug an ideal isentalpi proess. Te eat transfer oeffiients are alulated for different Reynolds number as given by Flynn [11]. Temperatures onsidered are in te range of 100-150 K as required for a ryosurgial probe. Table 1. Comparison of experimental and numerial data Inlet Conditions Ng et al. [1] Numerial Relative Ng et al. [1] Numerial P,in P,in T,in T,in Experimental T,out (K Error ΔP ΔP (MPa (MPa (K (K T,out (K % (MPa (MPa 17.91 0.177 91.49 110.36 8.57 8.95 0.134 10.96 10.3 16.968 0.1746 91.40 110.4 83.73 8.40-0.469-16.010 0.1636 9.5 109.90 84.77 8.18-0.910-14.966 0.1471 9.14 109.8 84.90 8.78-0.74-14.047 0.134 91.94 108.70 84.98 8.64-0.8 7.75 7.334
Effet of Supply Pressure Te effet of supply pressure is studied. Return line inlet pressure is kept onstant at 1.5 bar and te lengt of eat exanger is kept as 500 mm. Figure 4 sows te ideal ooling apaity at supply pressures from 60 to 100 bar. Te low pressure fluid outlet pressure is kept onstant at 1 bar. As te eat exanger lengt inreases, te pressure drop along te lengt and te eat transfer area bot inrease. Also, te return stream inlet pressure also inreases. ue to tis, te ideal ooling apaity goes troug a maximum as an be seen in Figure 5. Effet of mass flow rate Te effet of mass flow rate on te ideal ooling apaity is studied for eat exanger lengt of 500 mm and 750 mm. Te study results are presented in Figure 6. Figure 4. Ideal ooling apaity at different supply pressures It an be seen tat te inrease in te supply pressure inreases te ideal ooling apaity available at any temperature. A supply pressure of 100 bar results in a ooling apaity of 11 W at 100 K wile wit a supply pressure of 60 bar te lowest temperature aieved is around 110K. Effet of eat exanger lengt Te eat exanger lengt is varied for a onstant mass flow rate and te results are sown in Figure 5. Figure 5. Effet of eat exanger lengt on ooling apaity Figure 6. Effet of mass flow rate on ooling apaity Te pressure drop inreases almost exponentially wit an inrease in mass flow rate. Tis results in an optimum ooling apaity for a given mass flow rate. Te maximum ooling apaity ours at lower mass flow rates for iger eat exanger lengts. Cryosurgial Probe Te above work is extended to design a ryosurgial probe for laboratory experimentation. Te performane of te ryoooler is optimized to give suffiient ooling apaity at a low temperature. Te design is arried out to yield a ooling apaity of 10 W at 15 K. Te maximum supply pressure is kept fixed at 10 MPa as a onsideration for safety. Te ial diameter and te eat exanger
lengt are varied parametrially for minimum spae utilization to lead to an optimum design. Finally, te mass flow rate is optimized for te above onditions. Te ooling apaity at different temperatures for tese optimized parameters is sown in Figure 8. Te semati of a ryosurgial probe is sown in Figure 9. Figure 8. Ideal Cooling Capaity at different temperatures Inlet Fluid Figure 9. Semati of Cryosurgial Probe CONCLUSION Probe Tip Outlet Fluid Joule-Tomson Expansion In te present work, te design for a ryosurgial probe is arried out using a numerial model tat uses first-order disretization of te governing ordinary differential equations. Te model takes into aount te anges in termo-pysial properties and te pressure drop. Te variation of key parameters is studied and an optimized design is made. Te fabriation of te probe is urrently being arried out. REFERENCES 1. Ng, K. C., Xue, H., and Wang, J. B., Experimental and numerial study on a miniature Joule-Tomson ooler for steadystate arateristis, Int. J. of Heat and Mass Transfer, Vol. 45, pp. 609 618. (00. Xue, H., Ng, K.C., and Wang, J.B., Performane evaluation of te reuperative eat exanger in a miniature Joule-Tomson ooler, Applied Termal Engineering, Vol. 1, pp.189-1844. (001 3. Cien, S. B., Cen, L. T., and Cou, F. C., A study on te transient arateristis of a selfregulating Joule-Tomson ryoooler, Cryogenis, Vol. 36, pp. 979-984. (1996 4. Cou, F. C., Pai, C. F., Cien, S. B., and Cen, J. S., Preliminary experimental and numerial study of transient arateristis for a Joule-Tomson ryoooler, Cryogenis, Vol. 35, pp. 311-316. (1995 5. Cua, H. T., Wang, X., and Teo, H. Y., A Numerial study of te Hampson-type miniature Joule-Tomson ryoooler, Int. J. of Heat and Mass Transfer, vol. 49, pp. 58-593. (006 6. Hong, Y. J., Park, S. J., and Coi, Y.., A Numerial study on te performane of te miniature Joule-Tompson refrigerator, AIP Conf. Pro. 118, 103 (010 7. Ardapurkar, P.M., and M.. Atrey., "Performane Optimization of a Miniature Joule Tomson Cryoooler Using Numerial Model." Cryogenis, vol.63, pp.94-101. (014 8. Fredrikson, Kylie L. Optimization of ryosurgial probes for aner treatment. iss. University of Wisonsin - Madison, 004. 9. Younglove, B., Erratum: Termopysial Properties of Fluids. I. Argon, Etylene, Paraydrogen, Nitrogen, Nitrogen Trifluoride, and Oxygen. J. Pys. Cem. Ref. ata, 14(, p.619. (1985 10. Hanley, H., MCarty, R. and Haynes, W., Te Visosity and Termal Condutivity Coeffiients for ense Gaseous and Liquid Argon, Krypton, Xenon, Nitrogen, and Oxygen. J. Pys. Cem. Ref. ata, 3(4, p.979. (1974 11. Flynn, T. M., Cryogeni engineering. New York: Marel ekker.(1997