Separation
of flow is responsible for most of the form drag on airplanes, stall in
turbine blades and vortex shedding and vortex induced vibration of objects
placed in fluid flow. Controlled separation, however, has practical
applications and is used, for example,to enhance the mixing efficiency
in combustion chambers. Although criteria for steady separation were known
since Prandtl's article (1904), it took a century long for the unsteady
counterpart to be discovered. George Haller (JFM 2004) gave
dynamical-systems based rigorous criteria for flow separation in unsteady
flows.
Separation is in charge of most of the drag on flying objects like
airplanes and gulf balls
We developed, for the first time, a general (Reynolds independent)
analytical closed-loop algorithm for controlling the location of unsteady
separation and reattachment in two-dimensional Navier-Stokes flows. Our
controller enforces the Haller's exact kinematic separation criteria and
hence creates wall-based unstable manifolds at prescribed locations. The
underlying control algorithm is based on the exact wall-shear evolution
equation, a one-dimensional nonlinear partial differential equation (PDE)
defined on the wall between two discrete actuators. Performance of the
controller is studied numerically by implementation over a full
Navier-Stokes fluid.
Schematic
of the problem configuration. An unsteady flow enters the domain of
interest from the left. Two counter propagating wall jets are
connected to the controller and have to force a distinct separation
at a desired point. The wall (0<x<L) is carpeted with skin friction
sensors.
Numerical
simulation of effectiveness of our analytical feedback control for
controlling the point of separation in an unsteady flow. Red lines show
instantaneous streamlines (note that instantaneous separation point denoted
by the red triangle is a moving all the time). The blue curves are
streaklines (i.e. I am injecting dye particles at four points on the wall).
Black triangle points out the desired separation point. Eventually the
streaklines will point out the right separation point and show that our
controller indeed works.
References: - Alam, M.-R., Liu, W and Haller, G. "Closed
Loop Separation Control: An Analytic
Approach", Physics of Fluids, 18
(4): Art. No. 043601 APR 2006. (PDF)
