Computational Discovery ofHypersonic Aerothermoelastic Scaling Laws

Dr. Daning Huang

APUS Lab, apus.psu.edu

Aerospace multi-Physical and Unconventional Systems

Prepared for AERSP Seminar, 10/30/2019

Hypersonic: ≥ Mach 5

A conceptual hypersonic commercial jet

Image source: Boeing 2018

Forget about 14 hours one-way trip.

Let’s do round trip in 4 hours!Image source:Google Maps2

•Maturing propulsion•Advanced materials•Supercomputers

Hypersonic flight: A historical view

3USAF SAB report “Why and Whither Hypersonic Research in the USAF”

Hypersonic Commercial Jet Image source: Boeing

SR-72Image source: Lockheed Martin

Res

earc

h e

ffo

rt

X-51 WaveriderImage source: Boeing

2020+

Modeling and Testing challenges from 1988 NASP report:Because of the uncertainties ... in aerodynamic

loads and heating, ... precision of computation and lack of ground test facilities to replicate thermal and structural flight loads, the current ability to meet the structural designers requirements are marginal to non existent.

A technical barrier: Aerothermoelasticity

4

Aerothermoelasticity

SR-72Image source: Lockheed Martin

Aerothermoelastic response of a 2D skin panel

To Understand Aerothermoelasticity

Hypersonic

Aerothermoelasticity

Analysis &

Design

Validate

Understand &

Validate

Modeling Testing?5

??

Modeling: Multi-Physics

6

Hypersonic

Aerothermodynamics

Heat

Conduction

Structural

Dynamics

Heat flux

Temperature Deformation

Pressure

Temperature

Deformation

• Real gas effect

• Viscous interaction

• Compressible turbulence

• Thermal management

• Material degradation

• Charring and ablation

• Flutter and buckling

• Fatigue and creep

• Reliability assessment

Modeling: Timescale disparity

HighModel FidelityLow

Brute force simulation:𝟏𝟎𝟔 steps × sec/step = Weeks

Flight-long simulation• Culler, McNamara, et al. 2010

Lead to erroneous results:❖ Huang, Rokita, Friedmann, 2018

Transient simulation using RANS, LES, DNS• Ostoich, Bodony, 2013• McNamara, Crowell, Shinde, et al.,

since 2013

Characteristic times

Flight 1000 s

Thermal 1 s

Structure 0.05 s

Fluid 0.001 s

Computationallyintractable!

7

Academic problems using simple analytical models

• Lamorte, Friedmann, 2013, 2014• Blades, 2013

Modeling: Accelerating simulationsBrute force simulation:𝟏𝟎𝟔 steps × sec/step = Weeks

Efficient coupling schemes to reduce number of time steps

Reduced order models (ROMs) to reduce cost per time step

Example:Multi-cycling scheme, Miller, McNamara, AIAAJ 2018

→ Unable to reduce the cost of fluid solver – the real bottleneck

Example:Kriging-based ROM, Falkiewics, Cesnik, McNamara, AIAAJ 2011

→ Can we do better?Arbitrary geometric scales, structural and thermal responses.

8

Testing: Flight test v. s. Wind tunnel test

9

Flight test: Full-size prototype

Pros:• Cheaper• More detailed measurement• Controlled environment• Testing without compromising safetyCons:• Is it possible?

Pros:• Full duplication of flight conditionsCons:• Expensive• Time-consuming• Limited measurement options• Failure may result in program cancellation

Image source: NASA

Wind tunnel test: Scaled-down replica

Image source: NASA

Scaling law

Model construction

Map back to full scale

Testing: Hypersonic Aerothermoelastic Scaling?

Most studies concentrated in 1960’s (Dugundji 1966) – analytical dimensional analysis

• Possible for high supersonic flow (M<3.5)• For hypersonic flow: Possible only for a

unity scale ratio.

10

Full-size prototype

Flight test: High cost/risk

??Scaled-down replica

Wind tunnel test

Image source: NASA Image source: NASA

Objectives

Modeling:

• Develop a computational framework for fast long-time-duration aerothermoelastic simulation of hypersonic structures.

• Examine the aerothermoelastic behavior of hypersonic skin panels.

Testing:

• Develop a two-pronged approach to generating refined hypersonic aerothermoelastic scaling laws.

• Develop scaled models for composite skin panels in hypersonic flow suitable for testing under realistic wind tunnel conditions.

11

I. IntroductionII. Modeling: The HYPATE FrameworkIII. Testing: Numerical Scaling LawsIV. ApplicationsV. Summary and Outlook

Python wrapper

Structural Solver

(C++)

Python wrapper

Thermal Solver

(C++)

HYPersonic AeroThermoElasticsimulation environment

pyJenny library for nonlinear finite element analysis

Huang, Rokita, Friedmann, AIAAJ 2018

Python wrapper

Low-Fidelity (Python)

ROM (C++)

CFD (Fortran)

Fluid Solver

ADflow from UM-MDOLab – Now open-sourced at github.com/mdolab/adflowc.f. publication in JCP 2019.

Data transfer

Coupling Schemes

• Loosely-coupled for transient response

• Tightly-coupled for quasi-steady response

13

Python wrapper

Linearized Stability

Analysis (C++)

ROM-based

Aerodynamic

Solver

Accelerating the aerodynamic solver by 𝟏𝟎𝟒

Structural

Solver

Thermal

Solver

Body temperature

Surface deformation

Surface temperature

Pressure distribution

Heat flux distribution

Output:• Pressure distribution• Heat flux distribution

Input:• Surface deformation• Surface temperature

Precomputed CFD-based sample solutions

Interpolation:Gaussian process

regressionDimension reduction:

Proper orthogonal decomposition

14Falkiewics, Cesnik, McNamara, AIAAJ 2011; Crowell, McNamara, AIAAJ 2012Huang, Rokita, Friedmann, SciTech 2017

CFD-based

Aerodynamic

Solver

ROM: Reduced-Order Model

Extrapolation of an interpolative ROM

𝑹𝑶𝑴𝒓𝒆𝒇

Reference states:• Fixed flight conditions• Fixed geometric scale

𝑹𝑶𝑴𝒄𝒐𝒓

New states:• Arbitrary flight conditions• Arbitrary geometric scale

=𝒇𝒄𝒐𝒓

Correction factor

*

Conventional ROM is not suitable for analysis and design:

➢ROM for a fixed state: geometry + flight conditions

➢ROM for all the possible states → Heavy offline computational burden

Geometric scale

Alt

itu

de

15Huang, Friedmann, Rokita, AIAAJ 2019

𝑓𝑐𝑜𝑟 =𝑅𝑂𝑀𝑐𝑜𝑟

𝑅𝑂𝑀𝑟𝑒𝑓

A: Analytical low-fidelity model

≈𝐴𝑐𝑜𝑟(𝑁𝑒𝑤 𝑆𝑡𝑎𝑡𝑒𝑠)

𝐴𝑟𝑒𝑓(𝑅𝑒𝑓 𝑆𝑡𝑎𝑡𝑒𝑠)

Cutting down number of steps by 𝟏𝟎𝟑

Loosely-coupled (Conventional)

Time step size: Fluid time ~ 0.001s

Tightly-coupled

Time step size: Thermal time ~ 1s

16Miller, McNamara, AIAAJ 2015Huang, Friedmann, SciTech 2016 Huang, Friedmann, Rokita, AIAAJ 2019

Tightly-coupled scheme would not work for unstable responses

Full response (based on ROM)

AT 𝐂 ሶ𝐓 + 𝐐𝐈(𝐓) = 𝐐𝐓 (𝐮, 𝐓)

AE 𝐌 ሷ𝐮 + 𝐂 ሶ𝐮 + 𝐅𝐈(𝐮, 𝐓) = 𝐅𝐒(𝐮, ሶ𝐮)

Quasi-steady response, 𝑡𝐴𝑇 ∼ 1𝑠

AT 𝐂 ሶ𝐓qs + 𝐐𝐈(𝐓qs) = 𝐐𝐓 (𝐮

qs, 𝐓qs)

AE 𝐅𝐈(𝐮qs, 𝐓qs) = 𝐅𝐒(𝐮

qs, 𝟎)

Transient response (AE only), 𝑡𝐴𝐸 ∼ 0.01𝑠

𝐌 ሷ𝐮uns + 𝐂 ሶ𝐮uns + 𝐅𝐈(𝐮uns, 𝐓qs) = 𝐅𝐒(𝐮

uns, ሶ𝐮uns)

Tight coupling works for stable response

𝐊 =𝛛𝐅𝐈

𝛛𝐮, 𝐊𝐴 =

𝛛𝐅𝐒

𝛛𝐮; Neglect damping

Linearized stability analysis:Generalized eigenvalue problem

𝐊 − 𝐊𝐴 ഥ𝐮 = 𝜆𝑔𝐌ഥ𝐮

𝐓 = 𝐓qs + 𝐓uns, 𝐓uns ≈ 𝟎𝐮 = 𝐮qs + 𝐮uns

Tikhonov’s Theorem (singular perturbation analysis)• When stable, full response ≈ quasi-steady response→ Tightly-coupled scheme.• Stability of full response = Stability of transient response → Linearized stability analysis.

AT: AerothermalAE: Aeroelastic

Error∼ 𝑂𝑡𝐴𝐸

𝑡𝐴𝑇= 𝑂(10−2)

17

Real-Time aerothermoelastic simulation

1

2

4

8

16

32

64

CFD Conventional ROM Extrapolative ROM

Days

Hours

Minutes

Online simulation

Offline computation

CFD

Brute force

Conventional ROM

+ loose-coupling

10 days

2 hours

50 hours

30 min

1 hour

18

Computational cost of a 30-min flight-long simulation

Extrapolative ROM

+ tight-coupling

* On a computer cluster

* On a workstation using 5 Intel Xeon X5650 processors

I. IntroductionII. Modeling: The HYPATE Framework

III. Testing: Numerical Scaling LawsIV. ApplicationsV. Summary and Outlook

• Extrapolative ROM: Cost per step, Minutes → milliseconds

• Efficient coupling: Number of steps, 106 → 103

• Enabled fast high-fidelity flight-long simulation

I. IntroductionII. Modeling: The HYPATE FrameworkIII. Testing: Numerical Scaling LawsIV. ApplicationsV. Summary and Outlook

Example of Analytical scaling law

Subsonic

aerodynamics

Model construction

Map back to full scale

PrototypeFlight conditions[𝑝∞, 𝑀∞, 𝑇∞]

Scaled modelWind tunnel conditions

[𝑝𝑤𝑡 , 𝑀𝑤𝑡 , 𝑇𝑤𝑡]

Satisfy all similarity parameters

𝑅𝑒𝑝𝑟𝑜𝑡𝑜𝑡𝑦𝑝𝑒 = 𝑅𝑒𝑚𝑜𝑑𝑒𝑙

𝑀𝑎𝑝𝑟𝑜𝑡𝑜𝑡𝑦𝑝𝑒 = 𝑀𝑎𝑚𝑜𝑑𝑒𝑙

21

Image source: NARAImage source: Airbus

Analytical scaling law for aerothermoelasticity

22

Geometryℎ

𝐿, തℎ

Thermal characteristic time

𝐹𝑜 =𝑘𝑠𝑡

ො𝜌𝑠 Ƹ𝑐𝑝𝑠 𝐿2

Structural properties

𝑁𝑇𝑥 𝐿2

𝐷𝑥𝑥

Reference temperatures

𝑇𝑇𝑇𝑆,𝑇0𝑇𝑆,𝑇𝐹𝑇𝑆

ND dynamic pressure

𝜆𝐹 =𝛾𝑝∞𝑀∞

𝐿3

𝐷𝑥𝑥

Reynolds number 𝑅𝑒0 =𝜌0 𝑉𝐿

𝜇0

ND heat flux parameter

𝐵𝑖𝐹 =𝑘𝑓

𝑘𝑠𝑅𝑒0𝑃𝑟0

𝑉2

Ƹ𝑐𝑝𝑓 𝑇𝑇

ND: Nondimensional

Flight conditions [𝑝∞, 𝑀∞, 𝑇∞] for aerothermal similarity

Flight conditions [𝑝∞, 𝑀∞, 𝑇∞] for aeroelastic similarity

Principal barrier to complete

aerothermoelastic similarity:

Differing requirements for aeroelastic

and aerothermal similarity.

Assume all satisfied

Two-pronged approach for scaling

23

Given

prototype

Design

scaled model

Friedmann, JFS 2004; Huang, Friedmann, SciTech 2019

Maximizes the similarity

in aerothermoelastic

response

Two-pronged approach

Classical approachAnalytical derivation of aerothermoelasticsimilarity parameters

Obtain refinedaerothermoelastic

scaling laws

“Modern” approachNumerical aerothermoelastic

simulations (prototype/scaled)

• Contains ad hoc assumptions that ignores:o Turbulence and real gas effect in fluid problemo Geometric nonlinearity in structural problemo Temperature-dependent material properties

• Provides scaling info., but inaccurate.

Refining scaling laws by Optimization

• Objectives: 𝑱(𝒅) = [𝐽𝑢(𝒅), 𝐽𝑇(𝒅)]

• Error in structural response: 𝐽𝑢 𝒅 = σ𝑖 Τ𝒖𝑖𝑚(𝒅) ො𝑢𝑚 − Τ𝒖𝑖

𝑝ො𝑢𝑝

2 1/2

• Error in thermal response: 𝐽𝑇 𝒅 = σ𝑖 Τ𝑻𝑖𝑚(𝒅) 𝑇𝑚 − Τ𝑻𝑖

𝑝 𝑇𝑝2 1/2

• Ideal aerothermoelastic scaling: 𝐽𝑢 = 0, 𝐽𝑇 = 0

• Design variables: 𝒅• Flow conditions, geometry, materials…

• External loading and heating

• Constraints• 𝒄𝐼 𝒅 ≤ 0: Wind tunnel and manufacturing limitations

• 𝒄𝐸 𝒅 = 0: Matching a partial set of similarity parameters

• Incomplete testing• Parameter relaxation

ND model response

ND prototype response

24Huang, Friedmann, SciTech 2019

Special strategies:

Bayesian optimization for Black-box objectives

• Bayesian optimization:o Expensive black-box objective functionso A limited computational budgeto “Global” optimum for nonconvex problemo AKA efficient global optimization (EGO)

➢ Surrogate:o Gaussian process regressiono Prediction + Uncertainty

➢ Acquisition function:o Lower confidence boundo Exploitation & Exploration

Uncertainty of prediction

25

𝑱 𝒅 = [𝐽𝑢 𝒅 , 𝐽𝑇(𝒅)]𝒄𝐼 𝒅 ≤ 0𝒄𝐸 𝒅 = 0

Objectives:Subject to:Example: Scalar optimization

Pareto front for Multiple objectives

𝐽𝑢

𝐽𝑇

Pareto Front

Pareto Optimal

solutions

Design

Point

26

𝑱 𝒅 = [𝐽𝑢 𝒅 , 𝐽𝑇(𝒅)]𝒄𝐼 𝒅 ≤ 0𝒄𝐸 𝒅 = 0

Objectives:Subject to:

Indirect approach:• Generate Pareto front and select

the design point.• Suitable for exploring the solution

distribution.

Error in structural response

Erro

r in

th

erm

al r

esp

on

se

I. IntroductionII. Modeling: The HYPATE FrameworkIII. Testing: Numerical Scaling Laws

IV. ApplicationsV. Summary and Outlook

• Two-pronged approach: Dimensional analysis + Numerical simulation

• Scaling strategies: Incomplete testing + Parameter relaxation

• Multi-Objective Bayesian Optimization

I. IntroductionII. Modeling: The HYPATE FrameworkIII. Testing: Numerical Scaling LawsIV. Applications

V. Summary and Outlook

• Aerothermoelastic analysis of hypersonic skin panels

➢ Boundary layer thickness and aspect ratio

➢ Flow orientation angle and material orthotropicity

• Refined scaling laws using two-pronged approach

Case I: Aeroelastic scaling – Sanity check

Material 𝑀∞ 𝑝∞ Δ𝑇 Side Thick

PrototypeInconel

7186.0 104𝑃𝑎 1𝐾 1𝑚 2𝑚𝑚

Scaled model

Ti 6242 ?? ?? ?? ?? ??

Aeroelastic response with uniform thermal stress in inviscid flowReproduce aeroelastic response on scaled models

Problem:

Objective:

29

Analytical scaling v.s. Numerical scaling

Objective: Minimize the error in aeroelastic responses

𝐽𝑢 𝒅 = 𝑖

Τ𝒖𝑖𝑚(𝒅) ො𝑢𝑚 − Τ𝒖𝑖

𝑝ො𝑢𝑝

21/2

Design variables:

Constraints: ND time step size

Δ𝑡𝑚 =1

𝜉2

𝐷𝑥𝑥𝑝 መ𝐼m

𝐷𝑥𝑥𝑚 መ𝐼p

Δ𝑡𝑝

ℎ (mm) [0.2, 1.2]

𝑝∞ (kPa) [3.0, 11.0]

Δ𝑇 (K) [0.5, 4.5]

Thickness-length ratio

ℎ

𝐿ℎ𝑚 =

1

𝜉ℎ𝑝

ND pressure ҧ𝜆𝐹 =𝛾𝑀∞

𝐿2

𝐷𝑥𝑥𝑝∞𝑚 = 𝜉3

𝐷𝑥𝑥𝑚

𝐷𝑥𝑥𝑝 𝑝∞

𝑝

ND thermal stress

Δ𝑇 𝑁′TxL2

DxxΔ𝑇𝑚 = 𝜉2

𝐷𝑥𝑥𝑚 𝑁′Tx

p

𝐷𝑥𝑥𝑝 𝑁′Tx

mΔ𝑇𝑝

Characteristic time

𝐷𝑥𝑥መ𝐼 𝐿4

Ƹ𝑡 Ƹ𝑡𝑚 =1

𝜉2

𝐷𝑥𝑥𝑝 መ𝐼m

𝐷𝑥𝑥𝑚 መ𝐼p

Ƹ𝑡𝑝

𝜉 =𝐿𝑝

𝐿𝑚𝑚: Model𝑝: Prototype

Assuming same gas (𝛾) and 𝑀∞:

30

Dowell, 1975

Aeroelastic scaling law is recovered

Parametersℎ

𝐿, 10−3 ҧ𝜆𝐹

Δ𝑇 𝑁′TxL2

Dxx

Prototype 2.000 566.1 47.88

𝜉 = 2 2.008 (0.38%) 566.9 (0.14%) 47.58 (0.63%)

𝜉 = 3 2.003 (0.17%) 561.4 (0.83%) 47.76 (0.26%)

𝜉 = 4 2.003 (0.17%) 566.7 (0.11%) 47.67 (0.44%)

Aeroelastic similarity parameters are satisfied with errors < 1%!

31

Case II: Aerothermoelastic scaling

𝑀∞ Altitude Side

5.0-7.0 20-30 km 1.0 m

Component Material Thickness

Upper Sheet

Inconel 718

1 mm

Honeycomb Core 16 mm

Lower Sheet 1 mm

Component Material Thickness

Sheet Ti 6242 ??

𝑀∞ 𝑝∞ 𝑇∞ Side

?? ?? ?? ??

Prototype: Composite skin panel

Scaled model: Isotropic panel

32

Hypersonic Cruise Vehicle (HCV)

Image source: Zuchowski, 2012

Aerothermoelastic response of hypersonic skin panelsMinimize errors in average temperature and center deflection of aerothermoelastic response

Problem:

Objective:

Design variables and constraints

Design Variables Constraints

Test conditions 𝑀∞, 𝑝0, 𝑇0 Wind tunnel

Side length 𝐿 (m) [0.1, 0.5]

Front panel length 𝐿𝑙𝑒 (m) [0.1, 2.0]

Thickness ℎ (mm) [1.0, 10.0]

Surface emissivity 𝜖 [0.5, 1.0]

Radiation temperature 𝑇𝑟𝑎𝑑 (K) [300, 2500]

Thermal characteristic time

𝐹𝑜 =𝑘𝑠𝑡

ො𝜌𝑠 Ƹ𝑐𝑝𝑠 𝐿2

Reference temperatures

𝑇𝑤𝑇𝑆,𝑇𝑇𝑇𝑆,𝑇0𝑇𝑆,𝑇𝐹𝑇𝑆

A partial set of similarity parameters for the parameter relaxation strategy

External radiant heating for the Incomplete testing strategy

33

Equality constraints:

Ideal wind tunnel conditions – I• Arbitrary flight conditions in wind tunnel

5.0 ≤ 𝑀∞ ≤ 7.0, 20 ≤ 𝐻 ≤ 30𝑘𝑚

• Prototype flight conditions:

𝑀∞ = 6.0, 𝐻 = 25km

• Four cases:

𝐿𝑚𝑜𝑑𝑒𝑙 =1

2,1

3,1

4,1

5(𝑚)

Design Variables Constraints

Ideal wind tunnel

conditions

𝑀∞ [5.0,7.0]

𝑝0 (MPa) [0.276,86.18]

𝑇0 (K) [416.5, 2500.0]

Front panel 𝐿𝑙𝑒 (m) [0.1, 2.0]

Thickness ℎ (mm) [1.0, 10.0]

𝜉 =𝐿𝑝𝑟𝑜𝑡𝑜𝑡𝑦𝑝𝑒

𝐿𝑚𝑜𝑑𝑒𝑙

Rapid increase in 𝐽𝑇

Rapid increase in 𝐽𝑢

Ideal scaling

34

Ideal wind tunnel conditions – IIVariables 𝜉 = 2 𝜉 = 3 𝜉 = 4 𝜉 = 5

𝑀∞ 6.841 5.653 5.407 6.250

𝑝0 (MPa) 64.76 39.16 38.58 73.30

𝑇0 (K) 2280. 1868. 2130. 2187.

𝐿𝑙𝑒 (m) 1.812 2.000 0.3516 0.1950

ℎ (mm) 10.00 5.971 4.317 4.150

35

𝜉 =𝐿𝑝𝑟𝑜𝑡𝑜𝑡𝑦𝑝𝑒

𝐿𝑚𝑜𝑑𝑒𝑙

Realistic wind tunnel conditions – I

• Prototype flight conditions:𝑀∞ = 6.0, 𝐻 = 25𝑘𝑚

• Realistic wind tunnel constraints:𝑀∞ = 5.0, 6.0, 7.0

• Two cases:

Design Variables Constraints

Test conditions 𝑝0, 𝑇0 WT5, WT6, WT7

Side length 𝐿 (m) [0.1, 0.5]

Front panel length 𝐿𝑙𝑒 (m) [0.1, 2.0]

Thickness ℎ (mm) [1.0, 10.0]

Surface emissivity 𝜖 [0.5, 1.0]

Radiation temperature 𝑇𝑟𝑎𝑑 (K) [300, 2500]

Case 1: Parameter relaxation only

Case 2: Parameter relaxation and incomplete testing

36

Hypersonic Tunnel Facility (HTF),NASA Glenn Research Center

𝑀∞ = 6

𝑀∞ = 5

𝑀∞ = 7

𝑀∞ = 6

𝑀∞ = 5

𝑀∞ = 7

Realistic wind tunnel conditions – II

Prototype: 𝑀∞ = 6.0Model: 𝑀∞ = 7.0

External heating

37

Case 1: Parameter

relaxation only

Case 2: Parameter relaxation

and incomplete testing

Aerothermoelastic scaling enabled!

I. IntroductionII. Modeling: The HYPATE FrameworkIII. Testing: Numerical Scaling LawsIV. ApplicationsV. Summary and Outlook

Key Novel Contributions

Testing: First ever hypersonic aerothermoelastic scaling implemented

➢A new, two-pronged approach to aerothermoelastic scaling

o The classical approach augmented with numerical simulations.

o Formulated as a multi-objective optimization problem and solved using a Bayesian approach.

o Applied to the scaling of a finite-dimension panel configuration.

➢Potential applications

o Map aerothermoelastic results from tests of scaled models to an actual vehicle.

o Potential for significant cost saving in hypersonic vehicle development.

40

→ Accelerate the advent of Era of hypersonic flight

Future works

• Joint efforts of the computational and experimental communitiesoComputation: Detailed design of scaled model for wind tunnel testing.

o Experiments: Measurement techniques for aerothermoelastic testing.

• Robust multidisciplinary design of hypersonic structureso Inclusion of epistemic uncertainties due to modeling, esp. fluid ROM.

o Exploitation of benign aerothermoelastic instabilities.

• Aerothermoelastic analysis with more complex physics and subsystemso Shock wave/boundary layer interaction, turbulent acoustic radiation, etc.

oCoupling with propulsion and control systems.

41

Coupling with complex physics

42

➢Coupling with shock-dominated flow

oChallenges: boundary layer transition,

turbulent acoustic radiation, localized

heating

oRequires: Large Eddy Simulation,

computational aeroacoustics, reduced-

order modeling

• Current collaborator: Dr. X.I.A. Yang

Shock Wave Boundary Layer Interaction on a 24 deg two-dimensional ramp at Mach 2.3 visualized trough Schlieren image.

Source: https://www.youtube.com/watch?v=aqudZCRiTbQ

Aero-thermo-servo-propulso-elasticity

43

➢Coupling with control system

o Time-dependent vehicle dynamics

o Spectrum overlapping of controller and

structural response

➢Coupling with propulsion system

o Integrated airframe-propulsion system

o Aerothermoelastic deformation → Offset from

engine design point

Kitson and Cesnik, 2016

Lamorte, Friedmann et al., 2014

Multi-physics Uncertainty Quantification

44

Uncertainty quantification

and propagation

Hypersonic

Aerothermoelasticity

Modeling Testing

Understand &

Validate

➢Identify knowledge gaps in modeling tools and

assess impact on analysis and design

oChallenges: Certification of hypersonic

vehicles, Design and optimization under

uncertainty

oRequires: Propagation of uncertainty in

high-dimensional dynamical system

• Current collaborator: Dr. Puneet Singla

Fluid

Solver

Structural

Solver

Thermal

Solver

Body temperature

Surface deformation

Surface temperature

Pressure distribution

Heat flux distribution

Rotary-wing/eVTOL Aircraft Applications

45

➢With the VLRCOE folks

• Example I: Aeromechanics/Aeroacoustics

o Reduced-order modeling for real-time applications

o Numerical scaling laws for eVTOL-class aircraft

• Example II: Rotorcraft Icing

o Modeling: Develop PSU’s own high-fidelity tools

o Testing: PSU-AERTS, NASA-IRT

Kreeger and Broeren, 2018

Gupta, Halloran, Sankar, Palacios, et al., 2018

Chia, 2017

Thank you!

Questions?

Contact: daning@psu.eduLab website: apus.psu.edu/join-usPersonal blog: smanist.github.io

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Spring 2020, AERSP 597:

Machine Learning in Aerospace Engineering

Topics (with applications!):

• Regression (least-squares, Gaussian process regression, multi-fidelity modeling)

• Reduced-order modeling (dimensional manipulation, projection-based models, esp. nonlinear systems)

• Neural networks * (networks for regression, recurrent networks)