Stability of pulsatile quasi-two-dimensional duct flows under a transverse magnetic field

The stability of a pulsatile quasi-two-dimensional duct flow was numerically investigated. Flow was driven, in concert, by a constant pressure gradient and by the synchronous oscillation of the lateral walls. This prototypical setup serves to aid understanding of unsteady magnetohydrodynamic flows in liquid metal coolant ducts subjected to transverse magnetic fields, motivated by the conditions expected in magnetic confinement fusion reactors. A wide range of wall oscillation frequencies and amplitudes, relative to the constant pressure gradient, were simulated. Focus was placed on the driving pulsation optimized for the greatest reduction in the critical Reynolds number for a range of friction parameters H (proportional to magnetic field strength). An almost 70% reduction in the critical Reynolds number, relative to that for the steady base flow, was obtained toward the hydrodynamic limit (H = 10(-7)), while just over a 90% reduction was obtained by H = 10. For all oscillation amplitudes, increasing H consistently led to an increasing percentage reduction in the critical Reynolds number. This is a promising result, given fusion relevant conditions of H >= 10(4). These reductions were obtained by selecting a frequency that both ensures prominent inflection points are maintained in the base flow and a growth in perturbation energy in phase with the deceleration of the base flow. Nonlinear simulations of perturbations driven at the optimized frequency and amplitude still satisfied the no net growth condition at the greatly reduced critical Reynolds numbers. However, two complications were introduced by nonlinearity. First, although the linear mode undergoes a symmetry-breaking process, turbulence was not triggered. Second, a streamwise invariant sheet of negative velocity formed, able to arrest the linear decay of the perturbation. Although the nonlinearly modulated base flow maintained a higher time-averaged energy, it also stabilized the flow, with exponential growth not observed at supercritical Reynolds numbers.