Preventing transition to turbulence using streamwise traveling waves: direct numerical simulations

Abstract

We use direct numerical simulations of the nonlinear Navier-Stokes (NS) equations to examine the effectiveness of streamwise traveling waves for controlling the onset of turbulence in a channel flow. We highlight the effect of a base flow induced by the streamwise traveling waves on the dynamics of velocity fluctuations and on the net efficiency of control. It is shown that properly designed downstream traveling waves are capable of reducing the fluctuations' kinetic energy and maintaining the laminar flow. In contrast, our results demonstrate that upstream traveling waves promote turbulence even when the uncontrolled flow stays laminar. Our numerical simulations elucidate the predictive power of the theoretical framework developed in a companion paper [1] and suggest that the linearized NS equations with uncertainty serve as an effective control-oriented model for preventing transition.

Preventing transition to turbulence using streamwise traveling waves: theoretical analysis

“…Moreover, we show the existence of DTW parameters that result in a positive net efficiency compared to the uncontrolled flow that becomes turbulent. Our theoretical predictions are confirmed in [1], where we exhibit the predictive power of the proposed method by conducting high fidelity simulations of the nonlinear flow equations.…”

“…We note, however, that poorly designed traveling waves can promote turbulence even for background disturbances for which the uncontrolled flow stays laminar (see [1]). Fig.…”

“…3). For the uncontrolled flow that becomes turbulent, we have U B,u = 0.4066 which corresponds to the skin-friction drag coefficient C f = 0.0121 of the uncontrolled turbulent flow (see DNS results of [1]). Owing to the difference between U B,u and U B,0 , it is possible to obtain a positive net efficiency for sufficiently small value of α.…”

“…In the absence of the nominal body force,F ≡ 0, base velocity u b = (U, V, W ) represents the steady-state solution to (1) …”

“…In contrast, the downstream traveling waves with properly designed speed and frequency can significantly reduce sensitivity which makes them wellsuited for preventing transition. These theoretical predictions are facilitated by perturbation analysis (in the wave amplitude) of the linearized Navier-Stokes equations, and they are verified using full-scale simulations of the nonlinear flow dynamics in companion paper, [1].…”