Turbulent boundary layer control utilizing the Lorentz force

Direct numerical simulations (DNS) of a turbulent channel flow at low Reynolds number $({\mathrm{Re}}_{\tau }\text{=100,200,400,}$ where ${\mathrm{Re}}_{\tau }$ is the Reynolds number based on the wall-shear velocity and channel half-width) are carried out to examine the effectiveness of using the Lorentz force to reduce skin friction. The Lorentz force is created by embedding electrodes and permanent magnets in the flat surface over which the flow passes. Both open-loop and closed-loop control schemes are examined. For open-loop control, both temporally and spatially oscillating Lorentz forces in the near-wall region are tested. It is found that skin-friction drag can be reduced by approximately 40% if a temporally oscillating spanwise Lorentz force is applied to a ${\mathrm{Re}}_{\tau }\text{=100}$ channel flow. However, the power to generate the required Lorentz force is an order of magnitude larger than the power saved due to the reduced drag. Simulations were carried out at higher Reynolds numbers $({\mathrm{Re}}_{\tau }\text{=200,400)}$ to determine whether efficiency, defined as the ratio of the power saved to the power used, improves with increasing Reynolds number. We found that the efficiency decreases with increasing Reynolds number. An idealized wall–normal Lorentz force is effected by detecting the near-wall turbulent events responsible for high-skin friction. It is found that the drag can be significantly reduced with a greater efficiency than that produced by the spanwise open-loop control approach. This result suggests that, when employed with a closed-loop control scheme, the Lorentz force might result in a net decrease of power required to propel objects through viscous conducting fluids.