Ray tracing simulation of aero-optical effect using multiple gradient-index layer

摘要

We present a new ray tracing simulation of aero-optical effect through anisotropic inhomogeneous media as supersonic flow field surrounds a projectile. The new method uses multiple gradient-index (GRIN) layers for construction of the anisotropic inhomogeneous media and ray tracing simulation. The cone-shaped projectile studied has 19° semi-vertical angle; a sapphire window is parallel to the cone angle; and an optical system of the projectile was assumed via paraxial optics and infrared image detector. The condition for the steady-state solver conducted through computational fluid dynamics (CFD) included Mach numbers 4 and 6 in speed, 25 km altitude, and 0° angle of attack (AoA). The grid refractive index of the flow field via CFD analysis and Gladstone-Dale relation was discretized into equally spaced layers which are parallel with the projectile's window. Each layer was modeled as a form of 2D polynomial by fitting the refractive index distribution. The light source of ray set generated 3,228 rays for varying line of sight (LOS) from 10° to 40°. Ray tracing simulation adopted the Snell's law in 3D to compute the paths of skew rays in the GRIN layers. The results show that optical path difference (OPD) and boresight error (BSE) decreases exponentially as LOS increases. The variation of refractive index decreases, as the speed of flow field increases the OPD and its rate of decay at Mach number 6 in speed has somewhat larger value than at Mach number 4 in speed. Compared with the ray equation method, at Mach number 4 and 10° LOS, the new method shows good agreement, generated 0.33% of relative root-mean-square (RMS) OPD difference and 0.22% of relative BSE difference. Moreover, the simulation time of the new method was more than 20,000 times faster than the conventional ray equation method. The technical detail of the new method and simulation is presented with results and implication.