Aero-Optical Effect Similarity Law in Subsonic Flow over a Hemisphere-on-Cylinder Turret

All physics issues are expected to be solved with a concise expression, and the field of aero-optical effect is no exception. Due to the excessive influencing factors and coefficients that are difficult to determine, there are only a few available conclusions at present. Moreover, the validation of these conclusions is often inadequate due to their limited scope of applications. In this paper, the Reynolds averaged Navier–Stokes equations are used to simulate the flow field of a hemisphere-on-cylinder turret with various Mach numbers equal to 0.3, 0.4, and 0.5. The wavefront distortion of the beam is calculated using the ray-tracing method and Zernike fitting. The similarity law proposed by the predecessors is verified, and the variation trend of OPD_steady/[(ρ_∞/ρ_SL)M²D] with window angle is studied for the first time. It is found that the functional relation between OPD_steady/[(ρ_∞/ρ_SL)M²D] and the window angle is approximately quadratic. Based on the Prandtl–Glauert compressibility correction principle, the similarity law proposed by predecessors is improved.