Skip to main content

A numerical approach for optimization of the working fluid of a standing-wave thermo-acoustic refrigerator

Abstract

The development of refrigeration systems using thermo-acoustic technology is a novel solution for achieving environmentally friendly refrigerators. A full transient CFD method is introduced here that can resemble the whole thermo-acoustic phenomena along with its different governing physics as a whole. The working fluid contributes critically to the thermo-acoustic refrigerators’ cooling performance. In this paper, unlike previous researches, all different possible combinations of noble gases are considered and the performance of the refrigerator from both aspects of cooling temperature and \({\mathrm{COP}}_{\mathrm{R}}\) are investigated to determine the optimized gas mixture among all combinations. For this purpose, the effect of the sound intensity and the fluid’s Prandtl number as two key factors are investigated on the refrigeration performance. By considering a 2D-axisymmetric computational geometry resembling the real model, it is tried to attain results as reliable as possible. COMSOL software is used to perform the simulations. It is concluded that from the aspect of the cooling temperature, a sample with the highest sound intensity (pure He sample in this research) is the best. But, from the aspect of a higher \({\mathrm{COP}}_{\mathrm{R}}\) (relative coefficient of performance), a sample with the lowest Pr number (72%He–28%Xe sample in this research) would be the best. The lowest cooling temperature which is achieved by the pure He sample was about 273 K and the highest \({\mathrm{COP}}_{\mathrm{R}}\) which belongs to 72%He–28%Xe sample was approximately 0.335.

Graphical abstract

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Availability of data and material

If requested all data can be provided.

Notes

  1. Shipboard Electronics Thermoacoustic Chiller.

  2. Thermoacoustically Driven Thermoacoustic Refrigerator.

  3. Relative coefficient of performance.

Abbreviations

A :

Total cross-section area of the resonator, m2

A solid :

Cross-section area of solid walls, m2

a :

Adiabatic sound speed, m s1

BR:

Blockage ratio

C ij :

Coefficient defined by Lindsay and Bromley

C P :

Heat capacity at constant pressure, J kg 1 K1

COP:

Coefficient of performance

COPCarnot :

Coefficient of performance of the Carnot system

COPR :

Relative coefficient of performance

D h :

Hydraulic diameter, m

DR:

Drive ratio

d :

Distance between two stack plates, m

f :

Frequency, s1

H :

Amount of heat transfer along the stack plate, J

h :

Coefficient of convection heat transfer, W m2 K1

I :

Sound intensity, W m1

k :

Coefficient of thermal conductivity, W m1 K1

k 1 :

Wavenumber, m1

Lcupper :

Length of cupper tube, m

Lstack :

Length of stack plate, m

M :

Molar mass, kg mole1

m :

Mass, kg

n :

Mole number, mole

P :

Pressure, N m2

P 1 :

Amplitude of pressure oscillations, N m2

P A :

Amplitude of pressure oscillation at the pressure anti-node, N m2

P m :

Mean pressure, N m2

Pr:

Prandtl number

PD:

Particle displacement, m

Q C :

Heat taken from cold heat exchanger, J

Q H :

Heat given to hot heat exchanger, J

q :

Heat generation rate per unit volume, J s1 m3

R :

Gas constant, J kg1 K1

Re:

Reynolds number

S :

Sutherland’s constant, K

t :

Time, s1

throd :

Thickness of rod, m

thstack :

Thickness of stack plates, m

T :

Temperature, K

Τ :

Time period of one acoustical oscillation, s

T 0 :

Initial temperature, K

T 1 :

Amplitude of temperature oscillations, K

T m :

Mean temperature, K

T :

Outside temperature, K

u :

Velocity in z-direction, m s–1

u 1 :

Amplitude of velocity in z-direction oscillations, m s–1

W :

Amount of work given to the system, J

x :

Mole fraction

y :

Mass fraction

z, r, θ :

Cylindrical coordinate, m

α f :

Thermal diffusivity, m2 s1

δ k :

Thermal penetration depth, m

λ :

Wavelength, m

μ :

Dynamic viscosity, Pa s

ρ :

Density, kg m–3

ω :

Angular frequency, s–1

0:

Initial value

1:

Amplitude of oscillation

∞:

Ambient (outside) value

A :

Amplitude of oscillation at the anti-node

C:

Cold

H:

Hot

h:

Hydraulic

i, j :

Indicate each component in a mixture

m :

Mean value

R :

Relative

z, r, θ :

Indicate value in different cylindrical coordinates

References

  1. Rott N (1980) Thermoacoustics. Adv Appl Mech 20:135–175

    MATH  Article  Google Scholar 

  2. Swift GW (1988) Thermoacoustic engines. J Acoust Soc Am 84(4):1145–1180

    Article  Google Scholar 

  3. Rott N (1975) Thermally driven acoustic oscillations, part III: Second-order heat flux. Zeitschrift für angewandte Mathematik und Physik ZAMP 26(1):43–49

    Article  Google Scholar 

  4. Jin T et al (2015) Thermoacoustic prime movers and refrigerators: thermally powered engines without moving components. Energy 93:828–853

    Article  Google Scholar 

  5. Wheatley J et al (1983) An intrinsically irreversible thermoacoustic heat engine. J Acoust Soc Am 74(1):153–170

    Article  Google Scholar 

  6. Garrett SL, Adeff JA, Hofler TJ (1993) Thermoacoustic refrigerator for space applications. J Thermophys Heat Transfer 7(4):595–599

    Article  Google Scholar 

  7. Ballister SC, McKelvey DJ (1995) Shipboard electronics thermoacoustic cooler. Naval Postgraduate School Monterey CA.

  8. Adeff JA, Hofler TJ (2000) Design and construction of a solar-powdered, thermoacoustically driven, thermoacoustic refrigerator. J Acoust Soc Am 107(6):L37–L42

    Article  Google Scholar 

  9. Berson A et al (2011) Nonlinear temperature field near the stack ends of a standing-wave thermoacoustic refrigerator. Int J Heat Mass Transf 54(21):4730–4735

    MATH  Article  Google Scholar 

  10. Yahya SG, Mao X, Jaworski AJ (2017) Experimental investigation of thermal performance of random stack materials for use in standing wave thermoacoustic refrigerators. Int J Refrig 75:52–63

    Article  Google Scholar 

  11. Raut AS, Wankhede US, Ramteke S (2019) Experimental study on the performance of standing wave thermoacoustic refrigeration system. Smart technologies for energy, environment and sustainable development. Springer, pp 635–641

    Chapter  Google Scholar 

  12. Alamir MA (2019) Experimental study of the stack geometric parameters effect on the resonance frequency of a standing wave thermoacoustic refrigerator. Int J Green Energy 16(8):639–651

    Article  Google Scholar 

  13. Wetzel M, Herman C (1997) Design optimization of thermoacoustic refrigerators. Int J Refrig 20(1):3–21

    Article  Google Scholar 

  14. Herman C, Lavin C, Trávníček ZK (2008) Performance of thermoacoustic refrigerators: cooling load and coefficient of performance. In: ASME 2008 Heat Transfer Summer Conference collocated with the Fluids Engineering, Energy Sustainability, and 3rd Energy Nanotechnology Conferences. American Society of Mechanical Engineers

  15. Marx D, Blanc-Benon P (2004) Numerical simulation of stack-heat exchangers coupling in a thermoacoustic refrigerator. AIAA J 42(7):1338

    MATH  Article  Google Scholar 

  16. Marx D, Blanc-Benon P (2005) Computation of the temperature distortion in the stack of a standing-wave thermoacoustic refrigerator. J Acoust Soc Am 118(5):2993–2999

    Article  Google Scholar 

  17. Jin T et al (2016) Acoustic field characteristics and performance analysis of a looped travelling-wave thermoacoustic refrigerator. Energy Convers Manage 123:243–251

    Article  Google Scholar 

  18. Gholamrezaei M, Ghorbanian K (2016) Thermal analysis of shell-and-tube thermoacoustic heat exchangers. Entropy 18(8):301

    Article  Google Scholar 

  19. Mergen S, Yıldırım E, Turkoglu H (2019) Numerical study on effects of computational domain length on flow field in standing wave thermoacoustic couple. Cryogenics 98:139–147

    Article  Google Scholar 

  20. Rahpeima R, Ebrahimi R (2019) Numerical investigation of the effect of stack geometrical parameters and thermo-physical properties on performance of a standing wave thermoacoustic refrigerator. Appl Therm Eng 149:1203–1214

    Article  Google Scholar 

  21. Alamir MA, Elamer AA (2020) A compromise between the temperature difference and performance in a standing wave thermoacoustic refrigerator. Int J Ambient Energy 41(13):1441–1453

    Article  Google Scholar 

  22. Miled O, Dhahri H, Mhimid A (2020) Numerical investigation of porous stack for a solar-powered thermoacoustic refrigerator. Adv Mech Eng 12(6):1–14

    Article  Google Scholar 

  23. Abbaszadeh M, Dehghan M (2020) Simulation flows with multiple phases and components via the radial basis functions-finite difference (RBF-FD) procedure: Shan-Chen model. Eng Anal Boundary Elem 119:151–161

    MathSciNet  MATH  Article  Google Scholar 

  24. Mohammadi V, Dehghan M (2020) A meshless technique based on generalized moving least squares combined with the second-order semi-implicit backward differential formula for numerically solving time-dependent phase field models on the spheres. Appl Numer Math 153:248–275

    MathSciNet  MATH  Article  Google Scholar 

  25. Abbaszadeh M, Dehghan M (2020) Direct meshless local Petrov-Galerkin method to investigate anisotropic potential and plane elastostatic equations of anisotropic functionally graded materials problems. Eng Anal Boundary Elem 118:188–201

    MathSciNet  MATH  Article  Google Scholar 

  26. Tasnim SH (2011) Porous Media Thermoacoustic Stacks: Measurements and Models. Dissertation, University of Waterloo. http://hdl.handle.net/10012/6296

  27. Ward WC, Swift GW (1994) Design environment for low-amplitude thermoacoustic engines. J Acoust Soc Am 95(6):3671–3672

    Article  Google Scholar 

  28. Watanabe M, Prosperetti A, Yuan H (1997) A simplified model for linear and nonlinear processes in thermoacoustic prime movers. Part I. Model and linear theory. J Acoust Soc Am 102(6):3484–3496

    Article  Google Scholar 

  29. Yuan H, Karpov S, Prosperetti A (1997) A simplified model for linear and nonlinear processes in thermoacoustic prime movers. Part II. Nonlinear oscillations. J Acoust Soc Am 102(6):3497–3506

    Article  Google Scholar 

  30. Salih A (2011) Conservation equations of fluid dynamics. Department of Aerospace Engineering Indian Institute of Space Science and Technology, Thiruvananthapuram

  31. Dalton J (1802) On the expansion of elastic fluids by heat. J Nat Philos Chemis Arts 3:130–134

    Google Scholar 

  32. Silberberg M (2018) Chemistry: the molecular nature of matter and change with advanced topics. McGraw-Hill, New York

    Google Scholar 

  33. Davidson TA (1993) A simple and accurate method for calculating viscosity of gaseous mixtures. US Department of the Interior, Bureau of Mines

  34. Gray P, Wright P (1961) The thermal conductivity of mixtures of nitrogen, ammonia and hydrogen. Proc R Soc Lond Series A 263(1313):161–188

    Article  Google Scholar 

  35. Wassiljewa A (1904) Heat conduction in gas mixtures. Physikalische Zeitschrift 5(22):737–742

    MATH  Google Scholar 

  36. Mason E, Saxena S (1958) Approximate formula for the thermal conductivity of gas mixtures. Phys fluids 1(5):361–369

    MathSciNet  Article  Google Scholar 

  37. Sutherland W (1893) LII. The viscosity of gases and molecular force. Lond Edinburgh Dublin Philos Mag J Sci 36(223):507–531

    MATH  Article  Google Scholar 

  38. Russell DA, Weibull P (2002) Tabletop thermoacoustic refrigerator for demonstrations. Am J Phys 70(12):1231–1233

    Article  Google Scholar 

  39. Pedagopu VM, Pattapu K (2013) A novel approach to design and fabrication of thermo-acoustic refrigerator using high amplitude sound waves. IOSR J Mech Civ Eng 8: 15–24

  40. Belcher JR et al (1999) Working gases in thermoacoustic engines. J Acoust Soc Am 105(5):2677–2684

    Article  Google Scholar 

  41. Tijani M, Zeegers J, De Waele A (2002) Prandtl number and thermoacoustic refrigerators. J Acoust Soc Am 112(1):134–143

    Article  Google Scholar 

  42. Engineering ToolBox (2003) Solids, Liquids and Gases - Thermal Conductivities. [online] Available at: https://www.engineeringtoolbox.com/thermal-conductivity-d_429.html

  43. Hilsenrath J (1955) Tables of thermal properties of gases: comprising tables of thermodynamic and transport properties of air, argon, carbon dioxide, carbon monoxide, hydrogen, nitrogen, oxygen, and steam. 564. US Govt. Print. Off.

  44. Yaws CL (1995) Handbook of transport property data: viscosity, thermal conductivity, and diffusion coefficients of liquids and gases.: Inst of Chemical Engineers.

  45. Reid RC, JM Prausnitz and BE Poling (1987) The properties of gases and liquids, 4th edition, McGraw-Hill

  46. Hirota K (1944) The quantum mechanical treatment of viscosity by use of the rigid elastic sphere model. II. The Sutherland constant. Bull Chem Soc Jpn 19(5):109–113

    Article  Google Scholar 

  47. Tan Z (2014) Air pollution and greenhouse gases: from basic concepts to engineering applications for air emission control. Springer, New York

    Book  Google Scholar 

  48. Dua S et al (1994) Gravitational transport of particles in pure gases and gas mixtures. Aerosol Sci Technol 21(2):170–178

    Article  Google Scholar 

  49. Kim J (2014) Architectural Acoustics. Sejin Co

  50. Films DT (2003) Mylar polyester film physical-thermal properties. DuPont Teijin Films, Hopewell

    Google Scholar 

  51. Shah V (1998) Handbook of plastics testing technology, 2nd edn, John Wiley & Sons. https://www.osti.gov/biblio/6174437

  52. Valencia  JJ & Quested PN (2013) Thermophysical properties, ASM Handbook, vol 15. Casting ASM Handbook Committee, pp 468–481. https://doi.org/10.1361/asmhba0005240

  53. Fox RW, McDonald AT, Mitchell JW (2020) Fox and McDonald’s introduction to fluid mechanics. John Wiley & Sons, Hoboken

    Google Scholar 

  54. Convective heat transfer coefficients table chart. Available from: https://www.engineersedge.com/heat_transfer/convective_heat_transfer_coefficients__13378.htm. Accessed 2000

  55. Ishikawa H, Mee DJ (2002) Numerical investigations of flow and energy fields near a thermoacoustic couple. J Acoust Soc Am 111(2):831–839

    Article  Google Scholar 

Download references

Funding

Not applicable.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. Ebrahimi.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Rahpeima, R., Ebrahimi, R. A numerical approach for optimization of the working fluid of a standing-wave thermo-acoustic refrigerator. Engineering with Computers (2022). https://doi.org/10.1007/s00366-022-01646-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00366-022-01646-1

Keywords

  • Refrigerator
  • Thermo-acoustic
  • Working fluid
  • Standing-wave
  • Numerical simulation