Different coordinate transformation matrixes were used to scale the coordinate of isentropic surface

and a series of two-dimensional curved compression surfaces with different curvature were obtained. The curved compression surfaces were studied using numerical simulation

and then compared with the curved compression surfaces with wall Mach number linear distribution and controllable law of pressure rise. The result shows that: the surface length can be shortened obviously due to coordinate transformation of isentropic surface

and the curved compression surface length scaled using x axis scaling factor of 0.7 can be reduced by 30% at the same total turning angle. The curved compression surfaces with different x axis scaling factors produce dispersed compression waves that will not be converged to one point

and the isentropic compression flow characteristics can be kept. Wall pressure distribution is improved to a certain extent and wall Mach number distribution tends to be linear with decreasing x axis scaling factor. The curved compression surfaces with x axis scaling factor of 0.5 and wall Mach number linear distribution have similarity in the flowfield structure

wall pressure

wall Mach number distribution

exit total pressure recovery coefficient and exit Mach number distribution.