Mathematical modeling of scroll compressors—part I: compression process modeling

Abstract

This paper presents a detailed model for the compression process of a scroll compressor, which is used for investigating a compressor's performance under different operating conditions and subject to design changes. Upon defining the compressor chambers as suction chambers, compression chambers and discharge chambers, a geometry study was conducted and the governing mass and energy conservation equations were developed for each chamber. Models for the refrigerant flow in the suction and discharge processes, radial and flank leakage, and heat transfer between the gas and scroll wraps were combined with the conservation equations. The state of the refrigerant changes with a period of angle 2 π, and thousands of step are used to solve the governing differential equations during each period. It is assumed that in each step the compressor is in steady state. Since the differential equations for the different chambers are coupled, all these equations are solved simultaneously using a nonlinear equation solver. A description of the corresponding computer code and some results are included in this paper. Verification of the compression process model can be referred to that of the overall model, which is described in Chen et al. [Chen Y, Halm N, Braun J, Groll E. Mathematical modeling of scroll compressors—part II: overall scroll compressor modeling. International Journal of Refrigeration 2002;25(6):751–764.].