Characterization of a turbulent flow with independent variation of Mach and Reynolds numbers

TL;DR

This study uses a novel experimental setup to independently vary Mach and Reynolds numbers in turbulent flows, revealing that certain turbulence characteristics remain invariant while others depend on compressibility effects.

Contribution

It introduces a method to independently control Mach and Reynolds numbers in turbulent flows, enabling detailed analysis of their separate influences on turbulence statistics.

Findings

Turbulence length scales and Kolmogorov constant are invariant with Mach and Reynolds numbers.

Higher Mach numbers slow down the spreading of turbulent jets.

Flow behavior is similar to classical turbulent jets despite compressibility effects.

Abstract

The Variable Density and Speed of Sound Vessel (VDSSV) produces subsonic turbulent flows that are both compressible and observable at all scales with existing instrumentation including hot wires and particle tracking. We realize this objective by looking at the flow of a heavy gas (sulfur hexafluoride $SF_6$), with a speed of sound almost three times lower than for air. By switching between air and $SF_6$, we isolate the influence of the turbulent Mach number (up to $M_t$ = 0.17) on turbulence statistics from the influences of changes in the Reynolds number (up to $R_{\lambda}$ = 1600), and boundary conditions, which we hold constant. A free shear flow is produced by a ducted fan, and we show that it behaves like a turbulent jet in that the mean velocity profiles approach self-similarity with increasing distance from the orifice (up to $x/D_f$ = 9). The jet responds like a compressible shear layer in that it spreads more slowly at higher Mach numbers (up to $M_j$ = 0.7) than at low Mach numbers. In contrast, the integral length scales and Kolmogorov constant of the turbulence are approximately invariant with respect to changes in either the Reynolds or Mach numbers. We briefly report on instrumentation under development that will extend the accessible Taylor-scale Reynolds and turbulent Mach numbers to 4000 and 0.3, respectively.