Modeling and numerical simulation of the thermal and fluid dynamic behavior of hermetic reciprocating compressors -: Part 1:: Theoretical basis

A detailed numerical simulation of the thermal and fluid dynamic behavior of reciprocating compressors, commonly used in household refrigerators and freezers, has been developed. The model is based on the integration of the transient fluid conservation equations (continuity, momentum, and energy) in the whole, compressor domain (compression chamber, valves, manifolds, mufflers, shell, piston, connecting tubes, parallel paths, etc.) using instantaneous local mean values for different variables. Effective flow areas are evaluated considering a multidimensional model based on modal analysis of fluid interaction in the valve. In order to evaluate the instantaneous compression chamber volume, force balances in the crankshaft connecting rod mechanical system are simultaneously solved at each time-step. The thermal analysis of the solid elements is based on global energy balances at each macro-volume considered (shell, muffler, tubes, cylinder head, crankcase, motor, etc.). The resulting governing equations (fluid flow, valve dynamics, conductive heat transfer in solids, etc.) are discretized by means of a fully implicit control volume formulation. The complete set of algebraic equations is coupled using the segregated pressure-based algorithm Semi-Implicit Method for Pressure-Linked Equations (SIMPLEC) extended to compressible flow. A detailed numerical analysis is presented with the aim of verging the quality of the numerical solution. A comparison between numerical simulation results and experimental data is presented in the companion paper (Part 2).