Andre Weiner, Richard Semaan
TU Braunschweig, ISM, Flow Modeling and
Control Group
AIAA SciTech Jan. 7, 2022
Copyright © by Andre Weiner and Richard Semaan, TU Braunschweig. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.Contradictions in literature about:
Main issues:
Goal: workflow that is fully
Simulation approach in a nutshell:
Various views of the computational mesh.
Definition of data matrices:
$$ \mathbf{X} = \left[ \begin{array}{cccc} | & | & & | \\ \mathbf{x}_1 & \mathbf{x}_2 & ... & \mathbf{x}_{N-1} \\ | & | & & | \\ \end{array}\right],\quad \mathbf{X}^\prime = \left[ \begin{array}{cccc} | & | & & | \\ \mathbf{x}_2 & \mathbf{x}_3 & ... & \mathbf{x}_{N} \\ | & | & & | \\ \end{array}\right] $$
$\mathbf{x}_n$ - state vector snapshot at timestep $n$
DMD in a nutshell:
Key difference to previous studies:
$^*$ Rowley et al. 2004; $\gamma$ - adiabatic index, $a$ - local speed of sound, $u/v/w$ - velocity components
Practical DMD details:
Setup motivated by exp. investigations of McDevitt and Okuno 1985:
Pressure coefficient $c_p$ at pre-onset conditions, $\alpha = 2^\circ$.
Pressure coefficient $c_p$ at post-onset conditions, $\alpha = 4^\circ$.
Local Mach number $Ma$, 2D, $\alpha=4^\circ$.
Slice of local Mach number $Ma$, 3D, $\alpha=4^\circ$.
DMD spectrum for 2D and 3D datasets/simulations; $\bar{f}=2\pi c f/U_\infty$.
Real parts of DMD buffet mode and first harmonic; $u$ and $v$ are the velocity components.
DMD mode at approx. $20f_{buffet}$, $u$-component.
https://github.com/AndreWeiner/naca0012_shock_buffet
{a.weiner|r.semaan}@tu-braunschweig.de