# Séminaire de Mécanique d'Orsay

## Le Jeudi 25 avril à 14h00 - Salle de conférences du LIMSI

### "DNS, LES and reduced order modeling of controlled transition to turbulence
on a flat-plate boundary layer"

## Taraneh Sayadi

Ladhyx

Direct numerical simulations (DNS) of Klebanoff (K-) type and Herbert (H-)
type controlled transitions are performed for compressible (Ma = 0.2),
zero-pressure- gradient flat plate boundary layers. Each calculation is
carried out using approximately 1.1 billion grid points, required to
directly resolve the small scale turbulent structures in the near-wall
region of the flow. For H-type transition, the computational domain extends
from Re_theta = 210, where laminar blowing and suction excites the most
unstable fundamental wave and a pair of oblique waves, to fully turbulent
stage at Re_theta = 1250. The computational domain for K-type transition
extends to Re_theta = 1410. The evolutions of K-type and H-type
disturbances are compared and contrasted across the entire transition
process. In each case localized linear disturbance is amplified through
weak non-linear instability that grows into Lambda-shaped vortices with
harmonic wavelength. These two calculations serve as a benchmark to assess
the performance of models in predicting transition.
Several subgrid scale models are applied to these transitional scenarios.
We assess the capability of each model to predict the location of
transition and the skin friction throughout the transition process. The
constant coefficient models fail to detect transition, but the dynamic
procedure, by allowing for negligible turbulent viscosity in the early
transition region, result in correct prediction of the point of transition.
However, after secondary instabilities set in leading to the overshoot in
the skin friction profile, all models (in coarse LES calculations) fail to
produce sucient subgrid scale shear stress required for the correct
prediction of skin friction and the mean velocity profile. The same
underprediction of skin friction persists into the turbulent region.
Modes of dynamical importance in the transitional regime of the two
controlled cases are then extracted using dynamic mode decomposition (DMD).
The contribution of each mode to the total Reynolds shear stress is
estimated by employing the triple decomposition methodology. It is shown
that in both transitional cases a few modes provide a good estimate of the
Reynolds shear stress gradient within the transitional region. As subgrid
scale models fail to produce sufficient subgrid scale shear stress to
compensate for the lack of resolution, these modes can potentially be used
as a reduced order representation of the transitional regime.