VISION

Nonlinear Transonic Aeroelastic Analysis of a Cropped Delta Wing using Fluid-Structure Interaction and Dynamic Mode Decomposition

Langa Sheila C. F. & Takahashi Yusuke

Space Transportation System Lab.

Hokkaido University, Japan

CONFERENCE

24/10/2023

2

Outline

Background & Objective

2

FSI Model Analysis & Setup

3

Results & Comparison

Dynamic Mode Decomposition

3

2

Background & Objective

4

Aeroelasticity

Dowell, E. H., A Modern Course in Aeroelasticity, 6^th edition, 2022

Wright, Jan R., Cooper, Jonathan E., Introduction to Aircraft Aerolasticity and Loads, 2^nd Edition, John Wiley and Sons, 2015

5

Transonic Flutter

Self-excited

Vibration

Failure

Bendiksen, Oddvar O., Review of Unsteady Transonic Aerodynamics: Theory and Applications, Progress in Aerospace Series, 47(2):135-167,2011

Dowell, E. H., A Modern Course in Aeroelasticity, 6^th edition, 2022

https://www.youtube.com/watch?v=qpJBvQXQC2M&t=55s

6

Research Motivation

Most commercial aircraft fly in the transonic region, thus research on the range is essential

The primary sources of nonlinearities that cause the LCO are a current topic of debate

Recent configurations call for high flexibility and maneuverability and may be sensible to nonlinearities

7

Research Objective

8

2

FSI Model Analysis and Setup

9

Coupling Library

Communication

Data-mapping

Coupling Schemes

Time-interpolation

Bungartz, HJ., et al., preCICE – A fully parallel library for multi-physics surface coupling, 2016

10

Coupling Method

Bungartz, HJ., et al., preCICE – A fully parallel library for multi-physics surface coupling, 2016

11

FSI Analysis Setup – OSS

V2.15 & 2.20

V6.0.0 & 7.5.0

V1.61 & 2.5.0

12

Cropped Delta Wing Model

Attar, P.J., Gordnier R.E., Aeroelastic prediction of the limit cycle oscillations of a cropped delta wing, Structural Dynamics & Materials Conference, 18-21 April 2005.

Cui, P., Han, J., Numerical Investigation of the effects of structural geometrics and material nonlinearities on limit-cycle oscillation of a cropped delta wing, 2011

• The cropped delta wing was chosen to provide validation of the present analysis model through comparison with the experiment and other computed results.
• While Attar and Peng use structured and unstructured meshes with both Euler and N-S, the current simulation uses fully-unstructured and Compressible N-S equations.

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Schairer, E.T., Hand, L.A., Measurements of unsteady aeroelastic model deformation by stereo photogrammetry, Journal of Aircraft, 1999.

13

Solid Meshes - Overview

Coarse Mesh 122,626 nodes

Refined Mesh 270,762 nodes

14

Fluid Meshes - Overview

15

Computational Conditions

In order to match the experimental Reynolds number, SU2’s constant viscosity model =1.4E-5 was used.

in kPa: 20.54, 21.72, 22.96, 23.79, 26.75

Schairer, E.T., Hand, L.A., Measurements of unsteady aeroelastic model deformation by stereo photogrammetry, Journal of Aircraft, 1999.

Coarse

Refined

16

2

Results and Comparison

17

Eigenfrequency Analysis

Schairer, E.T., Hand, L.A., Measurements of unsteady aeroelastic model deformation by stereo photogrammetry, Journal of Aircraft, 1999.

18

Eigenfrequency Analysis

First Bending

First Torsion

Second Bending

Upper : Coarse Mesh

Lower : Refined Mesh

19

FSI Results – LCO and Flow Distribution

Refined mesh at 3.33 psi, 22.96 kPa

Coarse mesh at 3.33 psi, 22.96 kPa

20

FSI Results at 3.33 psi – Mach and Cp

• Difference in Reynolds number from about 2.88E6 and 3.56E6.

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• Leading motion of the wing is the bending motion.

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• We observe a vortex breakdown in the Refined model.

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• Fluid mesh refinement technique seems to play an important role on the FSI analysis.

Upper : Coarse Mesh

Lower : Refined Mesh

3.33 psi = 22.96 kPa

21

FSI Results – 2.98 - 3.33 psi

Cost for the Coarse Mesh Model: about 10 – 12 hours

Cost for the Refined Mesh Model: about 5-10 days

50.8 Hz

46.9 Hz

50.8 Hz

54.9 Hz

50.8 Hz

54.9 Hz

22

FSI Results - Comparison

Attar, P.J., Gordnier R.E., Aeroelastic prediction of the limit cycle oscillations of a cropped delta wing, Structural Dynamics & Materials Conference, 18-21 April 2005.

Cui, P., Han, J., Numerical Investigation of the effects of structural geometrics and material nonlinearities on limit-cycle oscillation of a cropped delta wing, 2011

Schairer, E.T., Hand, L.A., Measurements of unsteady aeroelastic model deformation by stereo photogrammetry, Journal of Aircraft, 1999.

23

2

Dynamic Mode Decomposition

24

DMD – Parameters and Setup

• The DMD is performed on the coarse mesh case to understand if the frequency from the FSI analysis can be captured and if the range remains constant.
• DMD analysis performed using Revun V0.80 written by Prof. Yusuke Takahashi.

25

DMD – Frequency oscillation

FSI Frequency at 2.98 is 50.8 Hz

FSI Frequency at 3.15 is 54.9 Hz

FSI Frequency at 3.33 is 54.9 Hz

• The modes are detected using the Greedy Algorithm-based mode-sensing approach.

26

DMD – Displacement and Reconstruction

Though DMD was able to capture the FSI Frequency ranges, it was not able to capture the LCO trend nor displacement.

27

DMD – Spatial Modes at 2.98 psi

Mode 10, F=50.75 Hz

Mode 20, F=118.36 Hz

Mode 22, F=49.05 Hz

FSI Frequency at 2.98 psi (20.54 kPa) is 50.8 Hz

Modes 10 & 20 resemble 1 and 3 from the eigenfrequency analysis : Bending.

Imaginary

Real

28

DMD – Spatial Modes at 3.15 psi

Mode 13, F=54.75 Hz

Mode 11, F=109.22 Hz

Mode 18, F=50.64 Hz

FSI Frequency at 3.15 psi (21.72 kPa) is 54.9 Hz

Modes 13 & 18 resemble 1 and 3 from the eigenfrequency analysis : Bending.

Imaginary

Real

29

DMD – Spatial Modes at 3.33 psi

Mode 16, F=55.41 Hz

Mode 13, F=110.68 Hz

Mode 18, F=49.73 Hz

Modes 16 & 18 resemble 1 and 3 from the eigenfrequency analysis : Bending.

FSI Frequency at 3.33 psi (22.96 kPa) is 54.9 Hz

Imaginary

Real

30

2

Summary & Future Work

31

Summary

• An aeroelastic model for a cropped delta wing was analyzed and compared to experimental data as well as numerical studies

​

• Fluid mesh refinement techniques proved to affect the LCO results more than the solid mesh and vortex breakdown around the leading edge was observed

​

• The Refined mesh model using constant viscosity approach yielded displacement results that are close to Attar’s model

​

• A DMD study was performed on the coarse mesh model. Bending motion was confirmed, and the DMD analysis showed a difference in frequency stagnation

32

Future Work

• Studying the phenomena that maintains a constant frequency between 3.15 to 3.45 psi

​

• With the recent change to the use of supercomputers, the simulation will be rerun with different iterations and timesteps

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• Understanding the impact of timesteps and total simulation time in the FSI analysis & Implementing different refined meshes for the fluid case to understand the vortex breakdown phenomena

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• Continue to analyze the displacement data through DMD and perform a DMD analysis for the Refined model as well.

33

2

Thank you for your attention!

Questions and/or Comments?

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2

Ongoing Optimization Techniques

35

Optimization Techniques – Grid Study

Same Fluid mesh, different Solid mesh

Same Solid mesh, different Fluid mesh

• Grid study confirmed that the fluid mesh has a greater impact on the LCO analysis.

Solid Grid Study

Fluid Grid Study

36

Optimization Techniques – Timestep

1E-4, LCO Frequency = 52 Hz

• Changing the timestep size alone showed no difference in the LCO amplitude and a slight difference in the LCO Frequency.

5E-4, LCO Frequency = 51.9 Hz

5E-5, LCO Frequency = 52 Hz

37

Optimization Techniques – Total Time

LCO Frequency = 53.9 Hz

• Changing the maximum simulation time slightly reduced the LCO Frequency. LCO occurrence is seen in 0.175s case though not as fully developed.

LCO Frequency = 51.9 Hz

LCO Frequency = 51.3 Hz

38

Optimization Techniques – Iterations

50 inner iterations, no LCO reached

100 inner iterations, LCO occurs

• Inner Iteration study when applied to different timesteps revealed a difference in LCO occurrence.

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Optimization Techniques – Refinement

40

Optimization Techniques – Reconstruction

Full reconstruction at 3.15 psi

Full reconstruction at 3.33 psi