Experimental investigation of the turbulent Schmidt number in supersonic film cooling with shock interaction

TL;DR

This study experimentally investigates how shock interactions affect the turbulent Schmidt number in supersonic helium film cooling flows, revealing significant variations that challenge the common assumption of a constant Schmidt number.

Contribution

It provides the first experimental validation showing the turbulent Schmidt number varies drastically near shock interactions in supersonic film cooling, contrasting with prior assumptions of constancy.

Findings

Turbulent Schmidt number ranges from 0.5 to 1.5 without shock interaction.

Shock interaction causes drastic variation in the turbulent Schmidt number.

Experimental results align qualitatively with large-eddy simulation data.

Abstract

The interaction of an impinging shock and a supersonic helium cooling film is investigated experimentally by high-speed particle-image velocimetry. A laminar helium jet is tangentially injected into a turbulent air freestream at a freestream Mach number $Ma_\infty=2.45$. The helium cooling film is injected at a Mach number $Ma_i=1.30$ at a total temperature ratio $T_{0,i}/T_{0,\infty}=0.75$. A deflection $\beta=8\deg$ generates a shock that impinges upon the cooling film. A shock interaction case and a reference case without shock interaction are considered. The helium mass fraction fluctuations are measured and the turbulent mass flux as well as the turbulent Schmidt number are determined qualitatively. For comparison, large-eddy simulation (LES) results of a comparable flow configuration are used. The streamwise and wall-normal turbulent mass fluxes are in qualitative agreement with the LES data. The turbulent Schmidt number differs significantly from unity. Without shock interaction, the turbulent Schmidt number is in the range $0.5 \leq Sc_t \leq 1.5$ which is in agreement with the literature. With shock interaction, the turbulent Schmidt number varies drastically in the vicinity of the shock interaction. Thus, the experimental results confirm the numerical data showing a massively varying turbulent Schmidt number in supersonic film cooling flows, i.e., the standard assumption of a constant turbulent Schmidt number is valid neither without nor with shock interaction.