Laser Doppler Velocimetry Measurements in Turbulent Gaseous Mixing Induced by the Richtmyer–Meshkov Instability: Statistical Convergence Issues and Turbulence Quantification

Abstract

A statistical characterization of the turbulent flow produced in a vertical shock tube dedicated to the study of the Richtmyer–Meshkov instability (RMI) is carried out using laser Doppler velocimetry (LDV), time-resolved Schlieren images, and pressure histories. The time evolution of the phase-averaged velocity field and the fluctuating velocity levels produced behind the shock wave (SW) are first investigated for different configurations of a pure air homogeneous medium. This allows us to determine the background turbulence of the experimental apparatus. Second, the RMI-induced turbulent air/sulfur hexafluoride (SF6) mixing zone (TMZ) is studied both in its early stage of development and after its interaction with a reflected shock wave (RSW) (reshock phenomenon). Here, the gaseous interface is initially produced by a thin nitrocellulosic membrane trapped between two grids. One of the most consistent issues regarding such a process is the generation of a large number of fragments when the incident SW crosses the interface. These fragments are likely to corrupt the optical measurements and to interact with the flow. This work seeks to clarify the influence of these fragments on the statistical determination of the velocity field. In particular, it is shown that statistical convergence cannot be achieved when the fragments are crossing the LDV measurement volume, even if a significant number of identical experiments are superimposed. Some specific locations for the LDV measurements are, however, identified to be more favorable than others in the air/SF6 mixing configuration. This finally allows us to quantify the surplus of turbulence induced by the reshock phenomenon.