Focused laser differential interferometer response to shock waves

Abstract

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.

Supersonic Freestream Density Fluctuations from Focused Laser Differential Interferometry and Pitot-Probe Measurements

“…Schmidt and Shepherd proposed a more accurate model of FLDI based on geometric ray tracing [16]. The validity of this model, and its associated numerical implementation, was demonstrated experimentally by Lawson et al [18] and Lawson and Austin [27]. The key applicable result of this validation is that we now have the capability to compute the FLDI temporal response, in terms of phase shift ΔΦt, to any arbitrary dynamic refractive index field nx; t, where x is some 3D space.…”

Combined Experimental and Numerical Investigation of a Hypersonic Turbulent Boundary Layer by Means of FLDI and Large-Eddy Simulations

“…A promising solution to counteract the drawbacks of the instrument is to compare the experimental FLDI data to the equivalent data gathered using computational FLDI (cFLDI; not to be confused with cylindrical-lens FLDI, referred to in the literature with a capital "C" as CFLDI) with spatially well-resolved CFD results. This has been explored with a laminar jet [45] and a complex dynamic flowfield containing shock waves [48]. In these works, computational FLDI was confirmed to be able to extract information from the numerical flowfield directly comparable with experiments.…”

“…The means to obtain this quantity on the LES is through computational FLDI (cFLDI). This algorithm is based on the ray-tracing model presented in [44], with further improvements detailed in [48]. A detailed description of the cFLDI algorithm used in the present work is presented in [49].…”

Multi-depth focused laser differential interferometer based on chromatic aberration

“…Focused-laser differential interferometry (FLDI) has recently become a valuable optical measurement technique for diagnostics of high-speed transitional [1][2][3] and turbulent flows [4,5]. The technique, discussed in detail by several authors [6][7][8][9], provides measurements of the index of refraction changes which are spatially filtered across the beam path by the focusing aspect of the beams. This filtering capability is especially valuable in high-speed aerospace testing in order to minimize the effects of turbulent boundary layers on the walls of the facility (or the jet shear layer in the case of a free-jet facility) in measurements.…”