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Performance Parameters Prediction for FPFD Miniature Stirling Cryocooler Considering Polytropic Processes

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Abstract

The performance of an actual free piston free displacer (FPFD) Stirling miniature cryocooler has been simulated based on the parameters affecting the performance of the cryocooler. The processes of compression and expansion in the cryocooler have been assumed to be polytropic with variable ratio of specific heats for the working fluid, i.e., helium. The effect of design parameters like piston spring stiffness, displacer spring stiffness, mass of the piston, displacer mass and frequency of operation on the cooling power of the cryocooler has been calculated. The parameters thus obtained with polytropic processes have been compared with the parameters obtained by assuming the compression and expansion processes to be isothermal. The amplitude of the piston and the displacer is not constant in the case of free piston free displacer cryocooler with linear motors. Linear motor drives have been used for eliminating the side forces on the cylinder walls and wear and tear of the reciprocating parts of the cryocoolers giving them a very long life. A computer program named CRYOJIN which was developed for the isothermal case has been modified for analyzing the real-time performance of the cryocooler for polytropic processes. The physical dimensions of Philips 1 W FPFD cryocooler have been taken for study and comparison.

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Abbreviations

A :

Area (m2)

A n a n :

Constants in the Fourier series of the current (A)

Bc :

Motor Constant (Wb Ω−1 m−1)

Bg :

Flux density in the gap (T)

B n, b n :

Constants in the Fourier series of the current (A)

Bs :

Motor constant (Wb2 m)

Bu :

Motor constant (Wb2 m Ω−1)

cc :

Mutual inductive coupling coefficient

C p :

Specific heat of the material (W m−1 K−1)

C m :

Stiffness constant (N m−1)

D :

Diameter (m)

E :

Impressed voltage (V)

E m :

Induced Voltage (V)

E 0 :

Amplitude of the Impressed voltage (V)

E s :

Amplitude of the Induced voltage (V)

f :

Frequency (Hz)

f re :

Reynold’s friction factor

F :

Flow loss coefficient (Ns m-3)

h :

Height (m)

i :

Current (A)

K :

Spring Stiffness (N m−1)

l :

Wire length (m)

L :

Effective coil inductance (H)

L R :

Length of the regenerator

M :

Mass (Kg)

MAX :

Constant

P ci :

Ideal thermodynamic power input to the Stirling cryocooler (W)

P i :

Power input to the linear motor (W)

P o :

Power output from the linear motor (W)

P :

Pressure (N m-2)

P av :

Mean Pressure (Nm-2)

P r :

Prandtl number

Q eo :

Refrigeration effect (W)

Q sh :

Shuttle heat transfer (W)

R L :

Coil quality factor

R P :

Power source resistance (Ω)

R T :

Total resistance (Ω)

R w :

Wire resistance (Ω)

S 1, S 2 :

Constants

T :

Temperature (K)

t :

Time (S)

u :

Axial velocity of the gap flow

V :

Volume (m3)

X :

Amplitude of displacement (m)

Z :

Pressure position coefficient (N m-3)

α :

Thermal diffusivity (k/ρc)

β :

Piston phase angle

γ :

Kinematic viscosity

ρ :

Gas density

σ :

Solidity ratio

θ :

Phase lead of the displacer over piston

\(\phi\) :

Motor phase shift

ψ :

Complex constant

ω :

Angular velocity (rad s−1)

τ :

Temperature ratio

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Authors and Affiliations

  1. Department of Mechanical Engineering, Chandigarh College of Engineering and Technology (Degree Wing), Sector 26, Chandigarh, India

    Radhey Sham

  2. Department of Aerospace Engineering, PEC University of Technology, Chandigarh, India

    Tejinder Kumar Jindal

  3. Department of Mechanical and Automation Engineering, Amity School of Engineering and Technology, 580, Palam Vihar Road, Bijwasan, New Delhi, India

    Rajesh Kumar Saluja

  4. Department of Automobile Engineering, Chandigarh University, Mohali, Punjab, India

    Vineet Kumar

Authors
  1. Radhey Sham
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  2. Tejinder Kumar Jindal
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  3. Rajesh Kumar Saluja
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  4. Vineet Kumar
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Correspondence to Rajesh Kumar Saluja.

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Sham, R., Jindal, T.K., Saluja, R.K. et al. Performance Parameters Prediction for FPFD Miniature Stirling Cryocooler Considering Polytropic Processes. J Low Temp Phys 199, 1211–1229 (2020). https://doi.org/10.1007/s10909-020-02413-6

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  • DOI: https://doi.org/10.1007/s10909-020-02413-6

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