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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.