Direct numerical simulation of transition control via local dynamic surface modification

Abstract

Direct numerical simulations were carried out in order to reproduce the generation and control of transition on a flat plate by means of local dynamic surface modification. The configuration and flow conditions are similar to those of an experimental arrangement that employed piezoelectrically driven actuators to impart small-amplitude local deformation of the plate surface. One actuator was located in the upstream plate region, and it was oscillated at the most unstable frequency of 250 Hz in order to generate small disturbances that amplified Tollmien–Schlichting instabilities. A second actuator, placed downstream, was then oscillated at the same frequency, but with an appropriate phase shift and amplitude in order to mitigate the disturbance growth and delay the transition process. Numerical solutions were obtained for the two-dimensional and three-dimensional compressible Navier–Stokes equations using a high-fidelity numerical scheme and an implicit time-marching approach. Local surface modification of the plate was enforced via grid deformation. An empirical process was developed for determining the optimal phase shift and amplitude of the controlling actuator. Results of the simulations are described, and features of the flowfields are elucidated.