Skip to main content

Advertisement

SpringerLink
Log in

Optimal Design of Orifice Pulse Tube Refrigerator Based on Response Surface and Genetic Algorithm

  • Research Article - Mechanical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

The modeling and optimization of a pulse tube refrigerator is a complicated task, due to its complexity of geometry and nature. The present work aims to optimize the orifice type pulse tube refrigerator (OPTR) using the response surface methodology (RSM). The influence of operating condition like frequency, charging pressure, orifice opening, and geometrical dimensions of pulse tube and regenerator on cold end temperature and input compressor power in the OPTR is investigated. For a fixed reservoir volume and regenerator size and porosity, the optimized value of the above parameters suggested by the response surface methodology has been solved using available one-dimensional code. It is reported that the cold head temperature varies due to variation in dimension of the pulse tube and regenerator in between 44 and 160 K, and compressor work varies from 265 to 1288 W. Using the results from the simulation, RSM is conducted to analyze the effect of the independent variables on the responses. To check the accuracy of the model, the analysis of variance method has been conducted. A quadratic model for cold end temperature and compressor input power has been developed. Based on the proposed mathematical RSM models, a novel multi-objective optimization study, using the non-dominated sorting genetic algorithm, has been performed to optimize the responses by generating the pareto frontiers. To avoid subjectiveness and imprecision, maximum deviation theory is used to rank the pareto frontiers based on composite scores.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

A :

Cross sectional gas flow area (m2)

A s :

Cross sectional solid area (m2)

A L :

Heat transfer area per meter (m2)

C p :

Specific gas constant at constant pressure (J/kg K)

C v :

Specific gas constant at constant volume (J/kg K)

C s :

Specific heat of matrix

D h :

Hydro diameter (m)

df :

Degree of freedom

p :

Pressure (N/m2)

PVavg :

Volume averaged pressure (bar)

T :

Temperature of gas (K)

T s :

Temperature of solid matrix (K)

t :

Time (s)

u :

Velocity (m/s)

F value:

Fisher value

P value:

Significant probability value

R 2 :

Coefficient of determination (dimensionless)

x i :

Coded value of independent variable i

X i :

Natural value of independent variable i

Y :

Response (%)

\({\phi}\) :

Porosity

\({\rho}\) :

Density (kg/m3)

h :

Heat transfer coefficient

S:

Solid

f:

Fluid

W comp :

Compressor input power (W)

T cold :

Cold head temperature (K)

ANOVA:

Analysis of variance

DIPTR:

Double inlet pulse tube refrigerator

DOE:

Deign of experiment

Freq:

Frequency

ITPTR:

Inertance tube pulse tube refrigerator

OPTR:

Orifice pulse tube refrigerator

PD:

Pulse tube diameter

PL:

Pulse tube length

P charge :

Charging pressure

RD:

Regenerator diameter

RL:

Regenerator length

RSM:

Response surface methodology

NSGA:

Non-sorted genetic algorithm

References

  1. Dang H.Z., Ju Y.L., Liang J.T., Cai J.H., Zhao M.G., Zhou Y.: Performance of stirling-type non-magnetic and non-metallic co-axial pulse tube cryocoolers for high-Tc SQUIDs operation. Cryogenics 45(3), 213–223 (2005). doi:10.1016/j.cryogenics.2004.10.004

    Article  Google Scholar 

  2. Radebaugh R.: Pulse tube cryocoolers for cooling infrared sensors. Proceedings of SPIE, The International Society for Optical Engineering, Infrared Technology and Applications 4130(XXVI), 363–379 (2000)

    Google Scholar 

  3. Martin, J.L.; Corey, J.A.; Martin, C.M. : A pulse tube cryocooler for telecommunications applications. In: Ross, R.G. Jr.. (ed.) Cry ocoolers, vol. 10, pp. 181–189. Springer, Berlin (2005)

  4. Tate, G.S.: Linear-drive cryocoolers for the Department of Defense standard advanced dewar assembly (SADA). In: 2005, pp. 138–144

  5. Kirichek O., Down R.B.E., Kouzmenko G., Keeping J., Bunce D., Wotherspoon R., Bowden Z.A.: Operation of superconducting magnet with dilution refrigerator insert in zero boil-off regime. Cryogenics 50(10), 666–669 (2010). doi:10.1016/j.cryogenics.2010.06.011

    Article  Google Scholar 

  6. Swift, G.W.: Thermoacoustic natural gas liquefier. In: DOE Natural Gas Conference, Houston, TX (1997)

  7. Dreyer, J.G.; Hertrich, T.; Drury, O.B.; Hohne, J.; Friedrich, S.: A Liquid-Cryogen-Free Cryostat for Ultrahigh Resolution Gamma-Ray Spectrometers (2008)

  8. Marquardt E.D., Radebaugh R.: A pulse tube oxygen liquefier. Adv. Cryo. Eng. 4130, 363–379 (2000)

    Google Scholar 

  9. Gifford, W.E.; Longsworth, R.C.: Pulse-tube refrigeration. Trans. ASME, 264–268 (1964)

  10. Mikulin E., Tarasov A.M.S.: Low-temperature expansion pulse tubes. Adv. Cryo. Eng. 29, 629–637 (1984)

    Article  Google Scholar 

  11. Zhu, S.; Wu, P.; Chen, Z.: A single stage double inlet pulse tube refrigerator capable of reaching 42 K. ICEC 13 Proc Cryo 30(256–261) (1990)

  12. Zhu S., Matsubara Y.: Numerical method of inertance tube pulse tube refrigerator. Cryogenics 44(9), 649–660 (2004). doi:10.1016/j.cryogenics.2004.03.006

    Article  Google Scholar 

  13. Kaiser G., Brehm H., Thürk M., Seidel P.: Thermodynamic analysis of an ideal four-valve pulse tube refrigerator. Cryogenics 36(7), 527–533 (1996). doi:10.1016/0011-2275(96)00017-3

    Article  Google Scholar 

  14. Zhu S., Kakimi Y., Matsubara Y.: Investigation of active-buffer pulse tube refrigerator. Cryogenics 37(8), 461–471 (1997). doi:10.1016/s0011-2275(97)00080-5

    Article  Google Scholar 

  15. Wang K., Zheng Q.R., Zhang C., Lin W.S., Lu X.S., Gu A.Z.: The experimental investigation of a pulse tube refrigerator with a ‘L’ type pulse tube and two orifice valves. Cryogenics 46(9), 643–647 (2006). doi:10.1016/j.cryogenics.2006.01.019

    Article  Google Scholar 

  16. de Waele A.T.A.M., Tanaeva I.A., Ju Y.L.: Multistage pulse tubes. Cryogenics 40(7), 459–464 (2000). doi:10.1016/S0011-2275(00)00065-5

    Article  Google Scholar 

  17. Ju Y.L., Wang C., Zhou Y.: Dynamic experimental investigation of a multi-bypass pulse tube refrigerator. Cryogenics 37(7), 357–361 (1997). doi:10.1016/S0011-2275(97)00027-1

    Article  Google Scholar 

  18. Wang C., Wang S.Q., Cai J.H., Yuan Z.: Experimental study of multi-bypass pulse-tube refrigerator. Cryogenics 35(9), 555–558 (1995). doi:10.1016/0011-2275(95)91253-h

    Article  Google Scholar 

  19. Ki T., Jeong S.: Design and analysis of compact work-recovery phase shifter for pulse tube refrigerator. Cryogenics 52(2–3), 105–110 (2012). doi:10.1016/j.cryogenics.2012.01.007

    Article  Google Scholar 

  20. Chen G., Qiu L., Zheng J., Yan P., Gan Z., Bai X., Huang Z.: Experimental study on a double-orifice two-stage pulse tube refrigerator. Cryogenics 37(5), 271–273 (1997). doi:10.1016/S0011-2275(97)00006-4

    Article  Google Scholar 

  21. Shiraishi M., Murakami M.: Visualization of oscillating flow in a double-inlet pulse tube refrigerator with a diaphragm inserted in a bypass-tube. Cryogenics 52(7–9), 410–415 (2012). doi:10.1016/j.cryogenics.2012.04.001

    Article  Google Scholar 

  22. Richardson R.N., Evans B.E.: A review of pulse tube refrigeration. Int. J. Refrig. 20(5), 367–373 (1997). doi:10.1016/S0140-7007(97)00005-4

    Article  Google Scholar 

  23. Popescu G., Radcenco V., Gargalian E., Ramany Bala P.: A critical review of pulse tube cryogenerator research. Int. J. Refrig. 24(3), 230–237 (2001). doi:10.1016/S0140-7007(00)00023-2

    Article  Google Scholar 

  24. de Boer P.C.T.: Optimization of the orifice pulse tube. Cryogenics 40(11), 701–711 (2000). doi:10.1016/S0011-2275(01)00003-0

    Article  Google Scholar 

  25. de Waele A.T.A.M.: Optimization of pulse tubes. Cryogenics 39(1), 13–15 (1999). doi:10.1016/S0011-2275(98)00127-1

    Article  Google Scholar 

  26. Razani A., Roberts T., Flake B.: A thermodynamic model based on exergy flow for analysis and optimization of pulse tube refrigerators. Cryogenics 47(3), 166–173 (2007). doi:10.1016/j.cryogenics.2006.11.002

    Article  Google Scholar 

  27. Ki T., Jeong S.: Optimal design of the pulse tube refrigerator with slit-type heat exchangers. Cryogenics 50(9), 608–614 (2010). doi:10.1016/j.cryogenics.2010.02.017

    Article  Google Scholar 

  28. Ko J., Jeong S., Ki T.: Effect of pulse tube volume on dynamics of linear compressor and cooling performance in Stirling-type pulse tube refrigerator. Cryogenics 50(1), 1–7 (2010). doi:10.1016/j.cryogenics.2009.08.008

    Article  Google Scholar 

  29. Jafarian A., Saidi M.H., Hannani S.K.: Second law based modeling to optimum design of high capacity pulse tube refrigerators. Int. J. Refrig. 32(1), 58–69 (2009). doi:10.1016/j.ijrefrig.2008.07.005

    Article  Google Scholar 

  30. Ghahremani A.R., Saidi M.H., Jahanbakhshi R., Roshanghalb F.: Performance analysis and optimization of high capacity pulse tube refrigerator. Cryogenics 51(4), 173–179 (2011). doi:10.1016/j.cryogenics.2011.01.006

    Article  Google Scholar 

  31. Antao D.S., Farouk B.: Computational fluid dynamics simulations of an orifice type pulse tube refrigerator: effects of operating frequency. Cryogenics 51(4), 192–201 (2011). doi:10.1016/j.cryogenics.2011.02.001

    Article  Google Scholar 

  32. Antao D.S., Farouk B.: Numerical and experimental characterization of the inertance effect on pulse tube refrigerator performance. Int. J. Heat Mass Transf. 76, 33–44 (2014). doi:10.1016/j.ijheatmasstransfer.2014.04.006

    Article  Google Scholar 

  33. Jahanbakhshi R., Saidi M.H., Ghahremani A.R.: Numerical modeling of pulse tube refrigerator and sensitivity analysis of simulation. HVAC&R Res. 19(3), 242–256 (2013). doi:10.1080/10789669.2012.758549

    Google Scholar 

  34. Antao D.S., Farouk B.: Experimental and numerical investigations of an orifice type cryogenic pulse tube refrigerator. Appl. Therm. Eng. 50(1), 112–123 (2013). doi:10.1016/j.applthermaleng.2012.05.015

    Article  Google Scholar 

  35. Antao D.S., Farouk B.: Numerical simulations of transport processes in a pulse tube cryocooler: effects of taper angle. Int. J. Heat Mass Transf. 54(21–22), 4611–4620 (2011). doi:10.1016/j.ijheatmasstransfer.2011.06.016

    Article  MATH  Google Scholar 

  36. Farouk B., Antao D.S.: Numerical analysis of an OPTR: optimization for space applications. Cryogenics 52(4–6), 196–204 (2012). doi:10.1016/j.cryogenics.2012.01.005

    Article  Google Scholar 

  37. Gu C., Zhou Y., Wang J., Ji W., Zhou Q.: CFD analysis of nonlinear processes in pulse tube refrigerators: streaming induced by vortices. Int. J. Heat Mass Transf. 55(25–26), 7410–7418 (2012). doi:10.1016/j.ijheatmasstransfer.2012.07.085

    Article  Google Scholar 

  38. Arablu M., Jafarian A., Deylami P.: Numerical simulation of a two-stage pulse tube cryocooler considering influence of abrupt expansion/contraction joints. Cryogenics 57(0), 150–157 (2013). doi:10.1016/j.cryogenics.2013.07.002

    Article  Google Scholar 

  39. Huang T., Caughley A.: Comparison of sage and CFD models of a diaphragm pressure wave generator. AIP Conf. Proc. 1434(1), 1217–1225 (2012). doi:10.1063/1.4707044

    Article  Google Scholar 

  40. Boroujerdi A.A., Ashrafizadeh A., Mousavi Naeenian S.M.: Numerical analysis of stirling type pulse tube cryocoolers. Cryogenics 51(9), 521–529 (2011). doi:10.1016/j.cryogenics.2011.06.008

    Article  Google Scholar 

  41. Ashwin T.R., Narasimham G.S.V.L., Jacob S.: CFD analysis of high frequency miniature pulse tube refrigerators for space applications with thermal non-equilibrium model. Appl. Therm. Eng. 30(2–3), 152–166 (2010). doi:10.1016/j.applthermaleng.2009.07.015

    Article  Google Scholar 

  42. Dietrich M., Thummes G.: Two-stage high frequency pulse tube cooler for refrigeration at 25K. Cryogenics 50(4), 281–286 (2010). doi:10.1016/j.cryogenics.2010.01.010

    Article  Google Scholar 

  43. Banjare Y.P., Sahoo R.K., Sarangi S.K.: CFD simulation and experimental validation of a GM type double inlet pulse tube refrigerator. Cryogenics 50(4), 271–280 (2010). doi:10.1016/j.cryogenics.2010.01.013

    Article  Google Scholar 

  44. Zhang X.-b., Gan Z.-h., Qiu L.-m., Liu H.-x.: Computational fluid dynamic simulation of an inter-phasing pulse tube cooler. J. Zhejiang Univ. Sci. A 9(1), 93–98 (2008). doi:10.1631/jzus.A071259

    Article  Google Scholar 

  45. Zhang X.B., Qiu L.M., Gan Z.H., He Y.L.: CFD study of a simple orifice pulse tube cooler. Cryogenics 47(5–6), 315–321 (2007). doi:10.1016/j.cryogenics.2007.03.005

    Article  Google Scholar 

  46. Paek I., Braun J.E., Mongeau L.: Evaluation of standing-wave thermoacoustic cycles for cooling applications. Int. J. Refrig. 30(6), 1059–1071 (2007). doi:10.1016/j.ijrefrig.2006.12.014

    Article  Google Scholar 

  47. Cha J.S., Ghiaasiaan S.M., Desai P.V., Harvey J.P., Kirkconnell C.S.: Multi-dimensional flow effects in pulse tube refrigerators. Cryogenics 46(9), 658–665 (2006). doi:10.1016/j.cryogenics.2006.03.001

    Article  Google Scholar 

  48. Dodson C., Razani A., Roberts T.: Numerical simulation of oscillating fluid flow in inertance tubes. Cryocooler 15, 261–269 (2009)

    Google Scholar 

  49. Cao, Q.; Gan, Z.; Liu, G.; Li, Z.; Wu, Y.; Qiu, L.: Theoretical and experiment study on a pulse tube cryocooler driven with a linear compressor. In: Cryocooler 2009, pp. 149–156

  50. Sobol S., Katz Y.a., Grossman G.: A study of a miniature in-line pulse tube cryocooler. Cryocoolers 16, 87–95 (2011)

    Google Scholar 

  51. Hofmann, A.: Numeric Code for the design of pulse tube coolers. In: Ross, R. Jr.. (ed.) Cryocoolers, vol. 13, pp. 323–332. Springer, Berlin (2005)

  52. Mitchell, M.P.; Bauwens, L.: Modeling pulse tube coolers with the MS* 2 stirling cycle code. In: Cryocoolers, vol. 10, pp. 379–385. Springer, Berlin (2002)

  53. Roach, P.R.; Kashani, A.: A Simple modeling program for orifice pulse tube coolers. In: Cryocoolers, vol. 9, pp. 327–334. Springer, Berlin (1997)

  54. Mayers R., Montgomery D.: Response Surface Methodology. Wiley, New York (1995)

    Google Scholar 

  55. Chiang K.-T., Chou C.-C., Liu N.-M.: Application of response surface methodology in describing the thermal performances of a pin-fin heat sink. Int. J. Therm. Sci. 48(6), 1196–1205 (2009). doi:10.1016/j.ijthermalsci.2008.10.009

    Article  Google Scholar 

  56. Sun L., Zhang C.-L.: Evaluation of elliptical finned-tube heat exchanger performance using CFD and response surface methodology. Int. J. Therm. Sci. 75(0), 45–53 (2014). doi:10.1016/j.ijthermalsci.2013.07.021

    Article  Google Scholar 

  57. Hariharan N.M., Sivashanmugam P., Kasthurirengan S.: Optimization of thermoacoustic refrigerator using response surface methodology. J. Hydrodyn. Ser. B 25(1), 72–82 (2013). doi:10.1016/S1001-6058(13)60340-6

    Article  MATH  Google Scholar 

  58. Hariharan N.M., Sivashanmugam P., Kasthurirengan S.: Optimization of thermoacoustic primemover using response surface methodology. HVAC&R Res. 18(5), 890–903 (2012). doi:10.1080/10789669.2012.680646

    Google Scholar 

  59. Gedeon, D.: SAGE\({\circledR}\)-Stirling cycle model class reference guide, Gedeon Associates, Athens, OH, USA, April. (2006)

  60. Jafari S., Mohammadi B., Boroujerdi A.A.: Multi-objective optimization of a stirling-type pulse tube refrigerator. Cryogenics 55–56, 53–62 (2013). doi:10.1016/j.cryogenics.2013.02.004

    Article  Google Scholar 

  61. Mehrabi M., Sharifpur M., Meyer J.P.: Modelling and multi-objective optimisation of the convective heat transfer characteristics and pressure drop of low concentration TiO2–water nanofluids in the turbulent flow regime. Int. J. Heat Mass Transf. 67(0), 646–653 (2013). doi:10.1016/j.ijheatmasstransfer.2013.08.013

    Article  Google Scholar 

  62. Shafaghat R., Hosseinalipour S.M., Nouri N.M., Lashgari I.: Shape optimization of two-dimensional cavitators in supercavitating flows, using NSGA II algorithm. Appl. Ocean Res. 30(4), 305–310 (2008). doi:10.1016/j.apor.2009.02.005

    Article  Google Scholar 

  63. Deb K., Pratap A., Agarwal S., Meyarivan T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  64. Wang Y.M.: Using the method of maximizing deviations to make decision for multi-indices. Syst. Eng. Electron. 20(7), 24–26 (1998)

    Google Scholar 

  65. Radebaugh R., Lewis M., Luo E., Pfotenhauer J.M., Nellis G.F., Schunk L.A.: Inertance tube optimization for pulse tube refrigerators. AIP Conf. Proc. 823(1), 59–67 (2006). doi:10.1063/1.2202401

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, CV Raman College of Engineering, Bhubaneswar, India

    Sachindra Kumar Rout

  2. Department of Mechanical Engineering, National Institute of Technology, Rourkela, India

    Ranjit Kumar Sahoo

Authors
  1. Sachindra Kumar Rout
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ranjit Kumar Sahoo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sachindra Kumar Rout.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rout, S.K., Sahoo, R.K. Optimal Design of Orifice Pulse Tube Refrigerator Based on Response Surface and Genetic Algorithm. Arab J Sci Eng 41, 1735–1755 (2016). https://doi.org/10.1007/s13369-015-1875-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-015-1875-7

Keywords

Search

Navigation