Entropy production-based nonlinear optimal perturbation for subsonic flows around an airfoil

Abstract

The extraction and time evolution of optimal perturbation (OP) offers abundant physical insights in fluid dynamics. Nonlinear OP (NLOP) analysis provides an approach for obtaining the trajectory to induce the maximum changes in the flow field. In an extension into unsteady flow field, we tracked the changes of trajectory by an application of initial perturbation field in the compressible Navier–Stokes equation, and we focused on the entropy production (EP) to characterize the trajectory. We proposed entropy production-based NLOP (EP-NLOP) analysis for compressible flows and investigated the effect of evaluation function on the extracted Ops using the subsonic flow around an airfoil. Compared with the conventional disturbance energy (DE-) based NLOP (DE-NLOP) analysis, we demonstrated that the OPs with different spatial wavelength and concentration regions were successfully extracted due to the different spatial sensitivity of evaluation function. In the EP-NLOP analysis, the spatial distribution of OP extracted the larger energy dissipation upstream of the separation points for the short evaluation time. For the long evaluation time, EP-NLOP analysis extracted the transient-time evolution of interacting separation vortices, attributing the multiple wavelengths of OPs. These differences in the OPs offer promising insights into fluid dynamics.