Amplification mechanism of perturbation energy in controlled backward-facing step flow

A body force resembling the streamwise Lorentz force which decays exponentially in the wall-normalwise direction is applied in the primary and secondary separation bubbles to modify the base flow and thereby adjust the amplification rate of the perturbation energy. The amplification mechanisms are investigated numerically via analyzing the characteristics of the terms in the Reynolds-Orr equation which describes the growth rate of the perturbation energy. The results demonstrate that the main convective term always promotes the increase in the growth rate while the viscous terms usually play the reverse role. The contours of the product of the wall-normalwise and streamwise perturbation velocities distribute on both sides of the isoline, which represents the zero wall-normalwise gradient of the streamwise velocity in the base flow, due to the Kelvin-Helmholtz (KH) instability. For the case without control, the isoline downstream the reattachment point of the primary separation bubble is closer to the lower wall, and thus the viscous term near the lower wall might suppress the amplification rate. For the case in which the body force only acts on the secondary separation bubble, the secondary separation bubble is removed, and the magnitude of the negative wall-normalwise gradient of the base flow streamwise velocity decreases along the streamwise direction, and thus the growth rate of the perturbation energy is smaller than that for the case without control. For the case where the body force acts on both the separation bubbles, the secondary separation bubble is removed, the isoline stays in the central part of the channel, and thereby the viscous term has less effects on the amplification rate of which the peak value could be the maximum one for some control number.

Automated summary

The study investigated the effect of a streamwise Lorentz force applied in the primary and secondary separation bubbles on the base flow and the amplification rate of perturbation energy. The results showed that the convective term promotes the growth rate while the viscous term usually plays a suppressing role.