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


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.

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Availability of data and material

If requested all data can be provided.


  1. Shipboard Electronics Thermoacoustic Chiller.

  2. Thermoacoustically Driven Thermoacoustic Refrigerator.

  3. Relative coefficient of performance.


A :

Total cross-section area of the resonator, m2

A solid :

Cross-section area of solid walls, m2

a :

Adiabatic sound speed, m s1


Blockage ratio

C ij :

Coefficient defined by Lindsay and Bromley

C P :

Heat capacity at constant pressure, J kg 1 K1


Coefficient of performance

COPCarnot :

Coefficient of performance of the Carnot system


Relative coefficient of performance

D h :

Hydraulic diameter, m


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


Prandtl number


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


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


Initial value


Amplitude of oscillation


Ambient (outside) value

A :

Amplitude of oscillation at the anti-node







i, j :

Indicate each component in a mixture

m :

Mean value

R :


z, r, θ :

Indicate value in different cylindrical coordinates


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Rahpeima, R., Ebrahimi, R. A numerical approach for optimization of the working fluid of a standing-wave thermo-acoustic refrigerator. Engineering with Computers (2022).

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