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An investigation of pressure loss and dynamical model of reed-type valves in compressors based on Euler–Bernoulli beam theory

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Abstract

Reed-type valve is widely used in refrigeration compressor; its dynamic performance directly affects the energy efficiency of compressors. In order to reveal the motion law of the reed-type valve of refrigeration compressor, a dynamic model based on vibration theory is established. According to the actual movement characteristics of the reed valve, the motion process of the reed is divided into two stages (i.e. before the reed bending to the limiter and after the reed bending to the limiter). The one-degree-of-freedom system is used to model before the valve reed bending to the limiter, and the vibration theory of Euler–Bernoulli beam is used to model after the reed bending to the limiter. The fourth-order Runge–Kutta method is applied to solve the new model in the MATLAB environment. In order to verify the validity of the new model, dynamic performance experiments of discharge reed valve at various operating conditions were carried out. The predicted results of the new model, the basic valve theory model and the cantilever beam model are compared with the experimental results. The analysis of error band and root mean square error shows that the calculation results of the new model can more accurately reveal the motion law of reed valve than that of other two models. Then, the effects of valve lift, reed stiffness and compressor speed on the valve dynamics and pressure loss are analyzed. This research can provide a reference for optimizing the structure parameters of reed-type valve and improving the energy efficiency of compressors.

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Abbreviations

\(A_\mathrm{c}\) :

Cross-sectional area of discharge valve reed (\(\hbox {m}^{2}\))

\(A_\mathrm{vg}\) :

Cross-sectional area of valve gap (\(\hbox {m}^{2}\))

\(d_\mathrm{do}\) :

Discharge orifice diameter (m)

E :

Elastic modulus of valve material (Pa)

\(F_\mathrm{g}\) :

Gas force (N)

\(F_\mathrm{sp}\) :

Elastic force (N)

\(h_\mathrm{dv}\) :

Displacement of discharge reed (m)

J :

Second moment of the cross-sectional area of valve reed (m\(^{4}\))

k :

Specific heat ratio (–)

\(L_{1}\) :

Length of discharge reed (m)

\(m_\mathrm{dv}\) :

Effective working mass of reed (kg)

p :

Pressure inside the cylinder (Pa)

\(p_\mathrm{d}\) :

Discharge pressure (Pa)

q :

Gas force acting on valve reed of unit length (N)

R :

Radius of the limiter (m)

\(R_\mathrm{g}\) :

Gas constant (J \(\hbox {kg}^{-1}\,\hbox {K}^{-1}\))

t :

Time (s)

T :

Temperature (K)

\(T_\mathrm{d}\) :

Discharge temperature (K)

V :

Transient volume (\(\hbox {m}^{3}\))

\(V_\mathrm{s}\) :

Stroke volume of the piston (\(\hbox {m}^{3}\))

\(\alpha _\mathrm{vg}\) :

Valve flow coefficient (–)

\(\beta \) :

Valve push coefficient (–)

\(\Delta p\) :

Difference between the pressure in cylinder and discharge pressure (Pa)

\(\xi \) :

Relative clearance volume of the cylinder (–)

\(\theta \) :

Crank angle (\(^{\circ }\))

\(\rho \) :

Valve reed density (\(\hbox {kg m}^{-3}\))

\(\lambda \) :

Ratio of crank radius to the length of the connecting rod (–)

\(\psi \) :

Ratio of pressure in cylinder to discharge pressure (–)

\(\omega _\mathrm{c}\) :

Angular velocity of crankshaft (\(\hbox {rad s}^{-1}\))

d:

Discharge chamber

do:

Discharge orifice

dv:

Discharge reed valve

vc:

Valve channel

vg:

Valve gap

c:

Calculated value

m:

Measured value

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Research Project 51605067) and supported by Natural Science Foundation of Liaoning province (Research Project 20170540107, Project 20180550493 and JL201915).

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Authors and Affiliations

  1. Mechanical and Power Engineering College, Dalian Ocean University, 52 Heishijiao Street, Dalian, 116023, Liaoning, China

    Guangyu Mu

  2. College of Locomotive and Rolling Stock Engineering, Dalian Jiaotong University, 794 Huanghe Road, Dalian, 116028, Liaoning, China

    Feng Wang

  3. Nautical and Marine Engineering College, Dalian Ocean University, 52 Heishijiao Street, Dalian, 116023, China

    Guodong Gao

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  1. Guangyu Mu
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Correspondence to Guodong Gao.

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Mu, G., Wang, F. & Gao, G. An investigation of pressure loss and dynamical model of reed-type valves in compressors based on Euler–Bernoulli beam theory. Arch Appl Mech 90, 2465–2486 (2020). https://doi.org/10.1007/s00419-020-01732-0

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