An Improved Analytical Model for Efficiency Estimation in Design Optimization Studies of a Refrigerator Compressor

The stack up of losses within a system gives an indication of its efficiency. In a refrigerator compressor, valves contribute to thermodynamic losses (pressure and cooling capacity) due to valve dynamics and mistiming. This paper proposes an improvement to an existing analytic closed form solution for efficiency estimation of such compressors by incorporating more detailed valve physics/ dynamics. For maximum energy efficiency ratio (EER), it is beneficial in certain variable capacity compressor architectures to drive the piston at a resonant frequency. In an oscillating system, this is typically determined by the mechanical spring-damper characteristics. This resonant frequency is usually a complex function of the geometry and operating conditions due to the gas-spring effect. A closed form solution for performance estimation of such a setup proposed earlier in literature (Choe & Kim) does not account for the effect of valve dynamics. However, the timing of valve operation influences the in-cylinder pressure build-up transients and thus modulates the gas-spring stiffness. While an accurate estimation of the resonant frequency requires a multi-physics simulation of the compressor, a detailed simulation of such complexity is time intensive especially when performing design optimization studies and hence analytical models would be preferred. The current work presents an improved equivalent analytic model for such optimization. Uncertainty analysis of the present approach is also discussed by comparing different performance parameters against full nonlinear model estimates, as relevant