# University of Minnesota

Aerospace Engineering and Mechanics

**Spring 2001 Seminar Series**

*Control of Turbulence in Fluid Flows: Suppression and Enhancement*

*Abstract*

### Due to the dimensionality and nonlinearity of Navier-Stokes equations,
fluid flows have received minimal attention in the area of control theory.
Fluid flow problems dominate the area of aerospace engineering, but are also
present in many applications in mechanical, chemical, nuclear and
bioengineering. In many cases the objective is to make the flow more steady (to
stabilize it), but in some cases the objective is exactly the opposite - to
make the flow more turbulent. We present progress towards solving both
problems. We consider the flow in a channel with actuators (for blowing and
suction) and sensors (pressure or shear stress) only on the walls of the
channel. Using the Lyapunov method, we design feedback controllers that,
depending on the gain choice, can either stabilize the flow or make it more
turbulent. We prove that the Navier-Stokes equations with our feedback laws as
boundary conditions are well posed. What is surprising here is that the control
propagates its effect throughout the flow even though it acts only from the
walls. This is achieved by exploiting viscosity in the flow, not as a means of
dissipativity but as a means of controllability. Computational and
visualization results, produced on a supercomputer, show vigorous flows being
tamed, and conversely, tame flows being made very agitated by a control effort
that is almost negligible relative to the levels of fluctuations in the
uncontrolled flow. This is due to a judicious use of measurements and model
structure in generating control inputs, i.e., due to the use of feedback.

### Friday, March 23, 2001

209 Akerman
Hall

2:30-3:30 p.m.

### Refreshments served after the seminar in
227 Akerman Hall.

Disability accomodations provided upon request.

Contact Kristal Belisle, Senior
Secretary, 625-8000.