__Andre Weiner,__ Richard Semaan

TU Braunschweig, Institute of Fluid
Mechanics

- Investigating shock buffets on airfoils
- Simulation approach and sampling
- Dynamic mode decomposition overview
- Test of state vectors and DMD variants
- Selected results

Slice of local Mach number $Ma$; $Re_\infty=10^7$, $Ma_\infty=0.75$, $\alpha=4^\circ$.

Unsteady flow and interaction phenomena at high speed stall conditions

Improved understanding and prediction of flight envelop via:

- experiments: iPSP, PIV, Schlieren, ...
- simulations: LES, RANS, hybrid RANS/LES
- analysis and modeling: modal decomposition, ROMs

Modal decomp. = spatial structures + temp. behavior

spatial mode

temporal coefficient

Common issues/questions in DMD analyses:

- How to construct the state vector?
- Which DMD variant to use?
- How much data is needed?
- How to set the
**rank**parameter? - How sensitive to noise is the analysis?

$\rightarrow$ (partial) answers in this presentation

Simulation approach in a nutshell:

- OpenFOAM-v2012
- rhoCentralFoam
- IDDES turbulence modeling
- Spalart-Allmaras closure
- 2D and 3D simulations

Various views of the computational mesh.

Degrees of freedom in DMD analysis:

- State vector definition
- Data pre-processing
- Operator approximation
- Mode amplitude computation
- Mode selection

DMD as a five-step analysis - part I.

DMD as a five-step analysis - part II.

Abbreviations:

- TDMD - total least squares DMD
- UDMD - unitary DMD operator
- opt. - optimal mode coefficients $\mathbf{b}$
- int. - integral importance measure
- amp. - classical DMD amplitude $|b_i|$

opt. TDMD, int. $\rightarrow$ total least-squares DMD with optimal amplitudes and integral mode selection.

Test 0: variance of state vector norms

Test 1: rank sensitivity of buffet frequency

Assumption: **top mode = buffet mode**

Test 2: sensitivity to the sampling rate

Test 3: rank sensitivity of the full spectrum

**Winning configuration:**

- physics-based, weighted state vector
- no additional pre-processing
- standard operator def.
- optimized amplitudes
- integral selection criterion

Temporal mean, std., and probe locations.

PSD based on speed at probe locations.

DMD spectrum obtained from slice data.

Characteristic DMD modes: shock motion and vortex shedding/acoustic waves.

Mode with vortex shedding and acoustic waves.

Comparable modes and spectra for volume, slice, and surface data.

- OpenFOAM wiki (overview)
- Github (resource aggregation)
- Upcoming meeting: Sep 2022