Mathematical modeling and parametric study of the limaçon rotary compressor

•A double-acting rotary compressor based on the limaçon of Pascal.•High capacity can be achieved within a small overall size.•The design can be described by simple mathematical models.•Clear geometric parameters control the machine performance.•Thermodynamic models are easily developed. In this paper, a class of rotary positive displacement compressors which is known as the limaçon compressor is introduced. The main feature of such a compressor is that profiles of its housing and rotor and the motion of its rotor are developed from a mathematical curve called the limaçon of Pascal. A mathematical model of the limaçon compressor, which incorporates the mass flow of the working fluid, the leakage loss, the dynamic response of the discharge valve, as well as the thermodynamic behaviors, is formulated, and the simulation of such a model has been performed to study the operational characteristics of the limaçon compressor. A parametric analysis is also conducted to investigate the effects of various parameters on the compressor performance. Based on the results, it is found that the machine performance deteriorates as the operating speed increases despite an initial rise in the volumetric efficiency. Additionally, the isentropic efficiency appears insensitive to the change of the pressure ratio, whereas a negative effect on the volumetric efficiency is noticed when the pressure ratio is increased. The effect of the valve diameter on the over-compression loss has also been studied, and the result indicates that a smaller valve diameter leads to a higher level of fluid over-compression.