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Heat transfer simulation in cavity of twin screw compressor under coupling of clearance leakage-heat by utilizing fuzzy beamlet finite element model

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Abstract

In order to optimize structure of twin screw compressor, and improve the working efficiency of twin screw refrigeration compressor, the heat transfer rules of cavity in twin screw refrigeration should be obtained correctly. Because the coupling of clearance leakage flow and heat transfer has a significant effect on heat transfer of cavity medium of twin screw refrigeration compressor, the heat transfer model of cavity medium under clearance leakage-heat coupling is constructed. To promote the computation accuracy and efficiency, the fuzzy beamlet finite element model is constructed by considering fuzzy affecting parameters and taking beamlet transform as interpolating function of element. The heat transfer laws of medium in cavity are obtained based on the theoretical an experimental analysis. Based on the simulation results, the computation error of fuzzy beamlet finite element method has least computation error and diversity than the other two methods for comparison, and the running time of fuzzy beamlet finite element method is least. Heat transfer analysis of medium in cavity under three conditions is carried out, and results show that temperature of cavity medium of twin screw refrigeration compressor is highest when the clearance leakage-heat coupling is considered and agrees better with reality; therefore, the proposed method has higher computing precision and efficiency than selected numerical methods according to computing results and running time. The impact of different clearances on heat transfer of medium in cavity is analyzed based on fuzzy beamlet finite element method, results show that the temperature of cavity medium increases accordingly as tooth top clearance, clearance between teeth, suction end clearance and exhaust end clearance increase, and the suction end clearance and exhaust end clearance have less effect on temperature of cavity medium.

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Abbreviations

b :

beamlet in position and orientation at a certain scale

\(B_{{{\text{n}},\updelta}}\) :

Collection of beamlet basis on all scales

c p :

Specific heat capacity of medium in clearance (J kg−1 K−1)

c T :

Specific heat capacity (J kg−1 K−1)

\(\vec{c}\) :

Beamlet coefficient vector

dl:

Straight line infinitesimal

e :

Beamlet finite element

f(x(l)):

Physical quantity function on curvilinear infinitesimal

\(\tilde{h}_{\text{c}}\) :

Given convective heat transfer coefficient on third boundary condition \(\varGamma_{3}\)

H :

Heat capacity matrix

i, j :

x, y, and z coordinate

k :

Thermal conductivity (W m−1 K−1)

K :

Heat conduction matrix

n x, n y and n z :

Outward cosines of first boundary condition

p :

Pressure of medium in clearance of twin screw compressor (MPa)

\(\bar{p}\) :

Pressure after filtering processing (MPa)

q j :

Sub-grid thermal flux (J s−1)

\(\tilde{q}_{\text{f}} (t)\) :

Given heat flux density on second boundary condition \(\varGamma_{2}\) (J m−2 s−1)

\(Q = Q(x,y,z,t)\) :

Internal heat source of medium in cavity (W m−3)

R :

Temperature load vector (K)

S :

Surface of beamlet finite element (m2)

\(\bar{S}_{\text{ij}}\) :

Velocity deformation rate tensor on solvable scale

t :

Time (s)

T :

Temperature of medium in clearance of twin screw compressor (K)

T b(t):

Given temperature on first boundary condition \(\varGamma_{ 1}\) (K)

\(\vec{u}\) :

Velocity vector (m s−1)

u :

Velocity in the x direction (m s−1)

\(\bar{u}_{\text{i}}\) :

Velocity after filtering processing in the i coordinate direction (m s−1)

\(\bar{u}_{\text{j}}\) :

Velocity after filtering processing in the j coordinate direction (m s−1)

v :

Velocity in the y direction (m s−1)

V :

Volume of beamlet finite element (m3)

\(\Delta V\) :

Sub-grid volume (m3)

w :

Velocity in z direction (m s−1)

\(\alpha\) :

Constraint level of each variable

\(\rho\) :

Density of medium in clearance of twin screw compressor (kg m−3)

\(\bar{\rho }\) :

Density of medium after filtering processing (kg m−3)

\(\mu\) :

Kinetic viscosity of medium in clearance (Pa s)

\(\lambda\) :

Thermal conductivity of medium in clearance (W m−1 K−1)

\(\tau_{\text{ij}}\) :

Sub-grid scale stress

Superscript “−”:

Lower boundary of each variable

Superscript “+”:

Upper boundary of each variable

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Acknowledgements

The research is supported by “Scientific Research Funding Project form the Educational Department of Liaoning Province (L2019022).”

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Authors and Affiliations

  1. School of Mechanical Engineering, Liaoning Shihua University, Fushun, 113001, Liaoning, China

    Bin Zhao, Hao Chen, Diankui Gao, Lizhi Xu & Yuanyuan Zhang

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  1. Bin Zhao
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  2. Hao Chen
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  3. Diankui Gao
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  4. Lizhi Xu
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Correspondence to Bin Zhao.

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Zhao, B., Chen, H., Gao, D. et al. Heat transfer simulation in cavity of twin screw compressor under coupling of clearance leakage-heat by utilizing fuzzy beamlet finite element model. J Therm Anal Calorim 143, 3221–3232 (2021). https://doi.org/10.1007/s10973-020-09531-z

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