Mathematical modeling of scroll compressors

Yu Chen, Purdue University

Abstract

This thesis presents the development of a comprehensive R-410A scroll compressor model. The model is based on a previously existing R-22 scroll compressor model. This comprehensive compressor model combines a detailed compression process model and an overall compressor model and was used to investigate the compressor's performance under different operating conditions and subject to design changes. The governing mass and energy conservation differential equations were developed for each chamber in the detailed compression process model. Models for the refrigerant flow in the suction process, discharge process as well as the flow due to the radial and flank leakage, models for heat transfer between the gas and scroll wraps, and models for solving the mechanical losses are coupled to the conservation equations. The state of the refrigerant changes with a period of 2π, and thousands of steps are used to solve the governing differential equations. Each step covers a small angle, such as 2π/1000 radians. It is assumed that in each step the compressor is in steady state. Iteration is applied until the convergence criteria that the refrigerant returns to the original state after a rotation of 2π is satisfied. In the overall model, compressor components are modeled in terms of six different elements. Steady-state energy balance equations were established using the lumped elements. In combination with the detailed compression process model, these equations were implemented into computer code and are solved iteratively. In this way, the temperature and pressure of the refrigerant in different compressor chambers, the temperature distributions in the scroll wraps, and the temperatures of the other compressor elements can be obtained. Thereafter, power consumption and efficiency of the compressor can be calculated. Overall and detailed compressor performance measurements were conducted using a hot-gas bypass compressor load stand. Based on the these measurements, validation of the compressor model was conducted. Using the simulation program of the compressor model, parametric studies of the scroll compressor were performed, and the effects of internal leakage and heat transfer losses, and external frictional losses were investigated. Results from these investigations were used to make recommendations for design improvements.

Degree

Ph.D.

Advisors

Braun, Purdue University.

Subject Area

Mechanical engineering

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