Active open-loop control of elastic turbulence

Abstract

Abstract We demonstrate through numerical solutions of the Oldroyd-B model in a two-dimensional Taylor–Couette geometry that the onset of elastic turbulence in a viscoelastic fluid can be controlled by imposed shear-rate modulations, one form of active open-loop control. Slow modulations display rich and complex behavior where elastic turbulence is still present, while it vanishes for fast modulations and a laminar response with the Taylor–Couette base flow is recovered. We find that the transition from the laminar to the turbulent state is supercritical and occurs at a critical Deborah number. In the state diagram of both control parameters, Weissenberg versus Deborah number, we identify the region of elastic turbulence. We also quantify the transition by the flow resistance, for which we derive an analytic expression in the laminar regime within the linear Oldroyd-B model. Finally, we provide an approximation for the transition line in the state diagram introducing an effective critical Weissenberg number in comparison to constant shear. Deviations from the numerical result indicate that the physics behind the observed laminar-to-turbulent transition is more complex under time-modulated shear flow.

Abstract We demonstrate through numerical solutions of the Oldroyd-B model in a two-dimensional Taylor–Couette geometry that the onset of elastic turbulence in a viscoelastic fluid can be controlled by imposed shear-rate modulations, one form of active open-loop control. Slow modulations display rich and complex behavior where elastic turbulence is still present, while it vanishes for fast modulations and a laminar response with the Taylor–Couette base flow is recovered. We find that the transition from the laminar to the turbulent state is supercritical and occurs at a critical Deborah number. In the state diagram of both control parameters, Weissenberg versus Deborah number, we identify the region of elastic turbulence. We also quantify the transition by the flow resistance, for which we derive an analytic expression in the laminar regime within the linear Oldroyd-B model. Finally, we provide an approximation for the transition line in the state diagram introducing an effective critical Weissenberg number in comparison to constant shear. Deviations from the numerical result indicate that the physics behind the observed laminar-to-turbulent transition is more complex under time-modulated shear flow.