Virtual Experiments of Light and Shock Wave Interaction Using Nonlinear Ray Tracing and Photon Mapping

Abstract

Light impinging on an aircraft wing surface interacts with the shock waves that form around it due to the high-speed flow and produces an oscillatory optical phenomenon composed of image distortions or shadow patterns, visible from the airborne perspective under particular observer, vehicle operation and illumination conditions. Analogously to traditional experimental techniques of shock wave visualization, the phenomenon can in principle be replicated computationally in its entirety, although the exact conditions that make it visible are still unknown. From a virtual experiment, it remains to be established what can be inferred about the shock wave and the trans-super sonic flow itself from the observed visual artifacts. This paper develops a three-dimensional nonlinear ray equation solver to predict the light propagation from the sun, through the refractive inhomogeneous density field acquired from a two-dimensional computational fluid dynamics (CFD) simulation and assembled as a pseudo-three-dimensional flow domain, to the physically-based reflective wing surface. Employing the traditional linear ray tracing algorithm, the photon mapping rendering technique and a simplified viewing system implementation, this computational tool is then used to assess the differences in the scene illumination caused by the shock wave. The contrast between the reflected radiance values, represented as a color triplet in the RGB space, considering the aerodynamic inhomogeneous flow field and a fictitious homogeneous optical medium demonstrates that the shock wave indeed induces radiometric disturbances. A strategically positioned and oriented recording film is able to capture magnified deflections of light rays and samples of the density of photons result in the reproduction of the shock wave’s shadow formation. Visualized as in the shadowgraphy experiment or observed from a perspective around the aircraft wing, the characteristics of the shadow pattern depend on the number of photons and the direction that they are emitted from the light source.