Particle relaxation and its influence on the particle image velocimetry cross-correlation function

A study of some aspects of tracer particle responses to step changes in fluid velocity is presented. The effect of size distribution within a seed material on measured relaxation time is examined, with polydisperse particles of the same median diameter shown to possess a significantly higher relaxation time than their monodisperse counterparts when measured via a particle image velocimetry algorithm. The influence of a shock wave-induced velocity gradient within a PIV interrogation window on the correlation function is also examined using the noiseless cross-correlation function of Soria (Turbulence and coherent structures in fluids, plasmas and nonlinear media. World Scientific, Singapore, 2006). The presence of a shock is shown to introduce an artificial fluctuation into the measurement of velocity. This fluctuation is a function of the shock position, shock strength, spatial ratio and particle distribution. When the shock is located at the middle of the window, the magnitude of the fluctuation increases monotonically with increasing spatial ratio, increases asymptotically with shock strength, and decreases for increasing particle polydispersity. When the shock is located at the left-hand edge of the window, the magnitude of the artificial fluctuation is highest for intermediate spatial ratios, going to zero at infinitely high and low values. In this instance, particle polydispersity acts to increase the magnitude of fluctuations in measured velocity. In both cases, particle polydispersity serves to broaden the PDF of measured velocity. For the cases presented herein, with a shock located within the interrogation window, the root mean square of the artificial velocity fluctuations reaches values in excess of 30% of the freestream velocity.