# University of Minnesota

Aerospace Engineering and Mechanics

**Fall 1997 Seminar Series**

*Genesis, dynamics and control of near-wall coherent structures
in a fully turbulent boundary layer*

*Abstract*

#### It is now well established that the enhanced drag and heat transfer of
turbulent boundary layers is dominated by slender longitudinal vortices
immediately near the wall. The geometry and dynamics of near-wall vortices are
not well understood and often controversial. We educe coherent structures (CS)
near the wall from a numerically simulated turbulent channel flow using a
conditional scheme which extracts the entire extent of locally dominant
vortical structures. Such structures are detected from the instantaneous flow
field using our newly developed vortex definition - a region of negative
lambda2 , the second largest eigenvalue of the tensor Sik Skj + omegaik omegajk
- which accurately captures the structure details, unlike velocity, vorticity
or pressure-based eduction schemes. Extensive testing shows that lambda2
correctly captures vortical structures, even in the presence of strong shear
occurring near the wall of a boundary layer. Our conceptual model of the CS
array reproduces experimentally observed important events reported in the
literature, such as VITA, gradient and counter-gradient Reynolds stress
distributions (Q1, Q2, Q3 and Q4 and their relative contributions), wall
pressure variation, elongated low-speed streaks, spanwise shear, etc. Notably,
the often heralded hairpin vortices, not to be confused with hairpin-shaped
vortex line bundles, are absent both in the instantaneous and ensemble-averaged
fields.

Further, we have discovered a new primary instability (of
low-speed "streaks"), responsible for near-wall CS formation in fully
turbulent boundary layers. A two-dimensional analytical base flow, containing
no x-dependence or streamwise vorticity - modeling the instantaneous flow
during quiescent phase- is considered. This flow is stable to varicose
instability but unstable to sinuous instability which is inviscid in nature and
resembles oblique mode instability in a mixing layer. The vortical structure
resulting from the nonlinear phase of this instability agrees with the CS
educed from DNS of fully turbulent flow.

Based on this discovery, we
have developed effective new control approaches for turbulent boundary layers,
via large-scale streak manipulation, which exploit the crucial role of streaks
in vortex generation and hence drag. Using control flows with no x variation, a
spanwise wavelength of 400 wall units, and an amplitude of only 5% of the
channel centerline velocity, we find a significant sustained drag reduction :
20% for imposed counterrotating streamwise swirls and 50% for colliding
spanwise wall jet-like forcing. These results suggest promising new drag
reduction strategies, e.g. passive vortex generators and spanwise jets from
x-aligned slots, involving large-scale (hence more durable) actuation and
requiring no wall sensors or feedback logic.

### Friday, October 10, 1997

209 Akerman Hall

2:30-3:30
p.m.

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

Disability accomodations provided upon request.

Contact
Audrey Stark-Evers, Senior Secretary,
625-8000.