computational discovery of hypersonic ... - apus lab
TRANSCRIPT
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: [email protected] website: apus.psu.edu/join-usPersonal blog: smanist.github.io
Advertisement:
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)