Focused laser differential interferometer response to shock waves

The focused laser differential interferometer (FLDI) can be used to measure rapid density fluctuations non-intrusively in high-speed flow applications. Being a non-imaging shearing interferometer, FLDI response can be accurately modeled using a paraxial ray-tracing scheme. We present the details of a new numerical implementation of this scheme, capable of accepting flow-field input from analytical models, computational fluid dynamics (CFD) results, and experimental data. This implementation has previously been validated for static (laminar jet) and dynamic (ultrasound-generated) changes in index of refraction by Lawson et al. In this work, we examine the FLDI response to shock waves propagating at up to Mach 10, in Caltech's hypervelocity expansion tube. While the timescale and approximate form of the signal can be recovered using a simple inviscid, planar shock model, it is found that the inclusion of viscous shock effects allows an accurate simulation of both the magnitude and detailed shape of the experimental response. This is a further analytical validation of the FLDI model that extends beyond the results of the existing dynamic validation case. The model implementation is then coupled to a CFD code, and predictions reproduce experimental FLDI response to a complex shock-dominated flow-field.