Inner-Scale Effects of Heat Release in Reacting Turbulent Shear Flows

Comparisons are presented from the first inner-scaled measurements of velocity gradient quantities in reacting and nonreacting versions of otherwise identical turbulent shear flows. Distributions of gradient quantities are obtained for outer-scale Reynolds numbers $Re_{\delta} \equiv u_{c} \delta / \nu$ from 7,200 to 200,000. The local outer length scale $\delta$ and velocity scale $u_c$ and associated inner scaling $\overline{ \left( \partial u_{i} / \partial x_{j} \right) ^{n} } \sim \left( \nu / \lambda^{2}_{\nu} \right)^n$ are used to identify the dominant physical mechanisms that produce heat release effects on the inner scales. In the nonreacting cases, classical inner scaling with the viscosity $\nu$ and inner (viscous) length scale $ \lambda_{\nu} \sim \delta \cdot Re_{\delta}$ removes most differences in distributions measured at different $Re_{\delta}$, with remaining differences being due to incomplete resolution of $\lambda_{\nu}$ with increasing $Re_{\delta}$. Inertial and dissipation range spectra allow the measurement resolution scale $\Delta^{*}$ and the proper resolution-corrected inner scaling to be determined, with the resulting scaling verifying near-perfect similarity for all $Re_{\delta}$. In the reacting cases, departures from this similarity reveal the true inner-scale changes due to heat release. Results clearly show that when inertial and body force effects on $\delta$ and $u_c$ are accounted for via the equivalent density, and viscous effects are accounted for via the mixture-fraction-averaged viscosity, the resolution-corrected inner scaling reveals remaining effects of heat release on turbulent shear flows to be remarkably small.