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(1) To address issues such as a low compression ratio and severe leakage in uniform wall thickness vortex compressors, this paper adopts a new scroll compressor model with a variable diameter double arc combined profile, which has a larger pressure ratio and smaller leakage than the scroll compressor with equal wall thickness that can bring new ideas and methods to the research in the field of scroll compressors. (2) This paper determines the theoretical equation of the variable diameter dual circular arc vortex profile and the combined profile, and infers mathematical models for the leakage line length, working chamber volume, and gas leakage per unit rotation angle of the vortex compressor, followed by simulation. (3) The results show that compared to the uniform wall thickness involute profile, the variable diameter dual circular arc combined profile model reduces the leakage line length by 25%, increases the average total pressure at the working chamber outlet by 2.38%, and decreases the leakage amount by 3.2%, consistent with theoretical analysis. (4) The tangential leakage caused by the radial gap in the variable diameter dual circular arc combined profile model has a significant impact on the uneven distribution of temperature and velocity fields in the working chamber of the vortex compressor, but a smaller impact on the pressure field.

Tangential leakage loss is the primary factor that significantly affects the output performance of oil-free scroll expanders. A scroll expander can function under different operating conditions, and the flow of tangential leakage and generation mechanism is different. This study employed computational fluid dynamics to investigate the unsteady flow characteristics of the tangential leakage flow of a scroll expander with air as the working fluid. Consequently, the effects of different radial gap sizes, rotational speeds, inlet pressures, and temperatures on the tangential leakage were discussed. The tangential leakage decreased with increases in the scroll expander rotational speed, inlet pressure, and temperature, and decreased with decrease in radial clearance. With an equal-proportional increase in radial clearance, the flow form of the gas in the first expansion and back-pressure chambers became more complicated; when the radial clearance increased from 0.2 to 0.5 mm, the volumetric efficiency of the scroll expander decreased by approximately 5.0521%. Moreover, because of the large radial clearance, the tangential leakage flow maintained a subsonic flow. Further, the tangential leakage decreased with increase in rotational speed, and when the rotational speed increased from 2000 to 5000 r/min, the volumetric efficiency increased by approximately 8.7565%.