Particle response analysis for particle image velocimetry in supersonic flows

We examine the effects of compressibility, slip, and fluid inertia on the frequency response of particle-based velocimetry techniques for supersonic and hypersonic flows by solving the quasi-steady drag equation for solid, spherical particles. We demonstrate that non-continuum and fluid inertial effects significantly affect the particle response under all typical supersonic flow conditions. In particular, the particle frequency response obtained from a shock response test depends on the strength of the shock, decreasing with shock strength as non-continuum effects become more prominent. For weak disturbances, such as those typical of turbulence, the actual particle frequency response can therefore be much lower than that obtained from a typical shock response. The greatest variability in the response was found to occur at low supersonic Mach numbers. The results were found to be typical of solid particles used for velocimetry under a wide range of wind tunnel conditions, and so, previous particle frequency response analyses based solely on shock response tests may well have overestimated the response to turbulence.