german aerospace center (dlr)...german aerospace center (dlr) aerogust workshop 27 th- 28 april...

Funded by the European Union

German Aerospace Center (DLR)

AEROGUST Workshop27th - 28th April 2017, University of Liverpool

Presented by M. Ripepi / J. Nitzsche

With contributions of D. Friedewald1, S. Görtz2, R. Heinrich2, J. Nitzsche1, M. Ripepi2, and M. Widhalm2

1Institute of Aeroelasticity, Göttingen, Germany2Institute of Aerodynamics and Flow Technology, Braunschweig, Germany


Outlook

AEROGUST WORKSHOP

▪ Motivation

▪ Towards reduced order modeling for gust simulations based on high-fidelity simulations

➢ T2.1 - Non-linear Aerodynamics of Gust Using RANS

➢ T3.2 - DLM Updating with CFD Data

➢ T4.1.2 - Nonlinear unsteady LSQ-ROM approach

▪ Next steps

▪ Summary


MotivationFrom design to certification of an aircraft many aerodynamic data (surface pressure and shear stress distribution) are needed – for the entire flight envelope – from steady and unsteady simulations

Loads due to maneuvers and discrete/continuous gusts

✓ Coupled CFD/CSM/FM model ✓ High simulation costs

➢ Design engineers require faster simulations for many load cases

Barrier

Objective: break barrier using Reduced Order Models (ROMs) and correction methods for linear models

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gust amplitude

gust lenght

altitude

Mach number


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Towards reduced order modeling for gust simulations based on high-fidelity simulations

▪ WP 2 - Understanding Non-linearities in CFD Based Gust Simulations (lead by ULIV)

✓ Task T2.1 Non-linear Aerodynamics of Gust Using RANS

✓ Task T2.4 Non-linear Structural Response to Gusts

▪ WP 3 - Reduced reliance on wind tunnel data (lead by DLR)

✓ Task T3.2 Investigation of modifications to the gust load process

▪ WP 4 - Adapting the loads process for non-linear and innovative structures (lead by UCT)

✓ Task T4.1 New ROM developments for gusts (by INRIA, DLR, UNIVBRIS, Optimad and NUMECA)


AEROGUST WORKSHOP

1) Gust simulations with TAU full-order model (reference)

2) Comparison of highly accurate and simplified methods for gust simulations

3) Extension of Linear Frequency Domain (LFD) TAU solver for gusts

4) Global ROM of LFD solver for gusts

5) Nonlinear unsteady least-squares (LSQ) ROM approach for gusts

6) Nonlinear structural response to gusts

7) Assessment of Doublet Lattice Method (DLM) corrections methods

8) Updating of industry-type DLM gust load models with linearized CFD data

Towards reduced order modeling for gust simulations based on high-fidelity simulations


AEROGUST WORKSHOP

T2.1 - Non-linear Aerodynamics of Gust Using RANS

Approaches for modeling of atmospheric effects realized in TAU:

1) Resolved Atmosphere Approach (RAA)

▪ Gust are fed into the flow field via an unsteady boundary condition

▪ Allows simulation of mutual interaction

▪ High resolution required very expensive

2) Disturbance Velocity Approach (DVA)

▪ Allows the usage of standard meshes very efficient

▪ Captures influence of gust on aircraft but not vice versa

Discretized flowfield

Additional inflow velocity prescribed at the boundary

t=t0 t=tN

Subtask T2.1.1Comparison of highly accurate methods resolving gusts in the flow field and simplified field velocity approach on 2D and 3D test cases, for different gust wave lengths

Unsteady boundary condition


AEROGUST WORKSHOP

T2.1 - Non-linear Aerodynamics of Gust Using RANSSubtask T2.1.1Comparison of highly accurate methods resolving gusts in the flow field and simplified field velocity approach on 2D and 3D test cases, for different gust wave lengths

Approaches for modeling of atmospheric effects realized in TAU:

1) Resolved Atmosphere Approach (RAA)

▪ Gust are fed into the flow field via an unsteady boundary condition

▪ Allows simulation of mutual interaction

▪ High resolution required very expensive

2) Disturbance Velocity Approach (DVA)

▪ Allows the usage of standard meshes very efficient

▪ Captures influence of gust on aircraft but not vice versa

𝑑

𝑑𝑡න

𝑉(𝑡)

𝜌 𝑑𝑉 + ර

𝑆(𝑡)

𝜌 Ԧ𝑣 − Ԧ𝑣𝐵 − Ԧ𝑣𝐷 ∙ 𝑑 Ԧ𝑆 = 0

Additional disturbance velocity induced by e.g. gusts/wake vortices, which can be prescribed as function in space and time


Analyze the behavior of DVA compared to RAA for 3D configuration, for vertical gusts (“1-cos”)

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Set up and run 3D test case

▪ Aircraft configuration with forward swept wing from a national research project (LamAiR)

▪ Size and mission comparable to A320

▪ Ma = 0.78

▪ Flight level h = 11km

▪ Vertical gust

➢ Lgust / croot = 1, . . ., 4

➢ vgust / vinfinity = 0.1


tO

uinf

t1

uinf

t2

Grid setup of 3D test case

▪ 3 chimera grid blocks

1) “Nearfield grid” for aircraft

2) Gust transport grid (100 cells in x-direction to resolve gust sufficiently)

▪ Moves with gust through the flowfield

3) Background grid

▪ Resolution in x-direction much smaller compared to gust transport grid

▪ 24.6 x 106 nodes (half configuration)

Unsteady boundary condition in case of RAA

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Results of 3D test case

▪ Ma = 0.78

▪ Flight level h = 11km

▪ Vertical gust

▪ Lgust / cref = 1, . . ., 4

▪ vgust / vinfinity = 0.1

t [s]

C-l

ift

0.2 0.3 0.4 0.5 0.6

0.5

0.55

0.6

0.65

0.7

0.75

0.8

RGADVA

Solid:Dashed:

gust

/ cref

= 4

gust

/ cref

= 1

gust

/ cref

= 2

Solid: RAADashed: DVA

AEROGUST WORKSHOP


Lgust / cref Error CL, max

1 1.42 %

2 1.28 %

3 0.42 %𝑒𝑟𝑟𝐶𝐿, 𝑚𝑎𝑥

=𝑒𝑟𝑟𝐶𝐿,𝑚𝑎𝑥,𝑅𝐴𝐴

− 𝑒𝑟𝑟𝐶𝐿,𝑚𝑎𝑥,𝐷𝑉𝐴

𝑒𝑟𝑟𝐶𝐿,𝑚𝑎𝑥,𝑅𝐴𝐴

The simplified DVA is sufficient to capture maximum loads induced by vertical gusts of realistic wavelength


Gust condition

Half Gust Length (ft)

Amplitude (ft/s) (EAS)

30 37.18

50 40.49

70 42.82

100 45.45

150 48.62

200 51.01

250 52.95

300 54.58

350 56.00

Flow condition

CaseAltitude

(ft)Mach

numberAmplitude

scaling

I 35000 0.86 0.74662

Load alleviation factor Fg = 1.0

✓ Aerodynamic model only✓ Disturbance velocity approach (DVA)✓ Gust response about the (vertical)

trim condition of AoA = 9.45 deg(𝐶𝐿,trim = 0.08191) ➢ air density: 𝜌∞ = 0.37968 kg/m3

➢ airspeed: 𝑉∞ = 255.00 m/s (836.60 ft/s)

▪ Mass: 𝑀 = 824.8 kg▪ Reference chord: 𝑐ref = 8 m

𝐶𝐿,trim =𝑀𝑔

12𝜌∞𝑉∞

2𝑐ref cos 𝛼

𝑉∞

Weight

Lift

DragMoment

2D Test Case: FFAST crank airfoil

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Grid (62272 nodes) Steady state @ Mach 0.86, AoA 9.45 deg

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Lift Coefficient Moment Coefficient (@ 31% chord)

Next step:Perform ROM predictions of the FFAST crank airfoil



Full CFD gust response results:

T3.2 – DLM Updating with CFD Data

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forces:

• aerodynamic

• Inertial-rbm

• gravitational

• Inertial-elastic

• structural

Full CFD gust response results:


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• Assumptions:

• CFD-URANS, 107 grid points (rather coarse, grid convergence expected at 108 grid points)

• Physical simulation period: 10 seconds (safely assess peak loads and damping)

• Time step: 10-3 s (10-Hz-oscillation with 100 steps per period)

• 100 inner iterations per time step (TAU specific)

• 105 simulations per design loop

• 50 flight points (Mach number, flight level)

• 100 mass configurations

• 10 gust gradients

• maneuvers, failure cases, …

• Today: 1.2×10-5 s / inner iteration / grid point(non-aero disciplines neglected)

• Size of HPC cluster: 104 Cores (DLR C2A2S2E)

• Result:

• How long it takes: 38,1 years

• What industry wants: 1 week

• Gap today: factor 2000

So

urc

e: A

irb

us, 2

01

1


AEROGUST WORKSHOP


So

urc

e:

G. L

isen

sky,

Bel

oit

Co

llege


• Moore‘s Law: computing power roughly doubles every 18 months

AEROGUST WORKSHOP



• Moore‘s Law: computing power roughly doubles every 18 months

factor 2000

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Computational FluidDynamics (CFD)

Doublet-Lattice-Method (DLM)


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• Taylor expansion of a Low- and a High-fidelity-funktion of the parameter k around k0 = 0 :

𝐿 𝑘 = 𝐿 0 +𝑑𝐿

𝑑𝑘0 ∙ 𝑘 + 𝐿𝐻𝑂𝑇

𝐻 𝑘 = 𝐻 0 +𝑑𝐻

𝑑𝑘0 ∙ 𝑘 + 𝐻𝐻𝑂𝑇

• Succesive replacement of the series terms allows „blending“:

𝐿∗𝑘 = 𝐻 0 +

𝑑𝐿


𝐿∗∗

𝑘 = 𝐻 0 +𝑑𝐻


• Explicit Taylor expansion of low-fi code not necessary:

𝐿∗∗

𝑘 = 𝐿 𝑘 − 𝐿 0 + 𝐻 0 −𝑑𝐿

𝑑𝑘0 ∙ 𝑘 +

𝑑𝐻

𝑑𝑘0 ∙ 𝑘

DLM correction: generic idea

AEROGUST WORKSHOP


• Principle of DLM: 𝐴𝐼𝐶𝐷𝐿𝑀(𝑘) ∙ ∆𝑐𝑝𝐷𝐿𝑀(𝑘) = 𝑤(𝑘)

• What would be nice: 𝐴𝐼𝐶𝐶𝐹𝐷(𝑘) ∙ ∆𝑐𝑝𝐶𝐹𝐷(𝑘) = 𝑤(𝑘)

• Educated guess: 𝐴𝐼𝐶𝐶𝐹𝐷 0 = 𝐶0 ∙ 𝐴𝐼𝐶𝐷𝐿𝑀 0 and

𝜕𝐴𝐼𝐶𝐶𝐹𝐷

𝜕𝑘0 = 𝐶1 ∙

𝜕𝐴𝐼𝐶𝐷𝐿𝑀

𝜕𝑘0

• Improved AICs: 𝐴𝐼𝐶∗𝑘 = 𝐴𝐼𝐶𝐷𝐿𝑀 𝑘 + 𝐶0 − 𝐼 𝐴𝐼𝐶𝐷𝐿𝑀 0

𝐴𝐼𝐶∗∗

𝑘 = 𝐴𝐼𝐶𝐷𝐿𝑀 𝑘 + 𝐶0 − 𝐼 𝐴𝐼𝐶𝐷𝐿𝑀 0 + 𝐶1− 𝐼𝜕𝐴𝐼𝐶𝐷𝐿𝑀

𝜕𝑘0 ∙ 𝑘

• ∂/∂k realised via finite differences

• Correction matrices C0, C1 to be derived from steady/unsteady CFD samples (ideally linearised RANS)

DLM correction: specific idea

AEROGUST WORKSHOP


LANN wing: forced pitching oscillations LANN:

AEROGUST WORKSHOP


X

Y

0 0.2 0.4 0.6

0

0.2

0.4

0.6

0.8

1

delta cp 7

0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0

-0.05

DLM 19 May 2014

X

Y

0 0.2 0.4 0.6

0

0.2

0.4

0.6

0.8

1

delta cp 7

0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0

-0.05

CREAM-0 AIC Correction 19 May 2014

LANN wing: forced pitching oscillations LANN:

AEROGUST WORKSHOP


LANN wing: forced pitching oscillations

7.5

6.0

195

Reduced Frequency

4.50.8

180

165

150

10 0.2 0.4 0.6

0.8 10 0.2 0.4 0.6

Reduced Frequency k

Mag (

CL,a

)P

hase (

CL,a

) [d

eg]

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Harmonic heave motion

Harmonic gust


AEROGUST WORKSHOP


Aerostabil generic wing model

Steady Lift PolarDLM grid: 20x26 boxes

CFD mesh: 2.4Mio nodes


AEROGUST WORKSHOP


Aerodynamic Gust Responses AoA 0°1-cos Gust with max. 5m/sTime Domain

• Gust Induced AoA

• Delta(C-Lift)

Improved maximum

load with CREAM-0.


AEROGUST WORKSHOP


Aerodynamic Gust Responses AoA 0°1-cos Gust with max. 5m/sFrequency Domain

CREAM-0 improvesmagnitude of TFsignificantly.

Transfer Function:𝑑𝐶𝐿

𝑑α𝐺


AEROGUST WORKSHOP


Aerodynamic Gust Responses AoA 8°1-cos Gust with max. 1e-6 m/sTime Domain

• Gust Induced AoA

• Delta(C-Lift)

Oscillating response

even with CREAM-0!


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Aerodynamic Gust Responses AoA 8°1-cos Gust with max. 1e-6 m/sFrequency Domain

Aerodynamic resonance peakcaptured with CREAM-0!

Transfer Function:𝑑𝐶𝐿

𝑑α𝐺


AEROGUST WORKSHOP


Frequency domain Time domain

Aero(GAF matrices A(s) from

CREAM, Pulse, LFD, …)

Structure

S(s)=[K+s2M]-1

f

force

q

displ

+qgust


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Large-scale demonstration incl. fluid-structure coupling:

Parameter Value

Mass 198 450 kg

Inertia of Rotation 2.01E7 kg*m^2

Eigenfrequency 07 1.0003 Hz

mode 03 mode 05 mode 07

3 structural

DOFs!


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Elastic Aircraft!

Fluid-structure

coupled solution!

Reference: Nonlinear FSIGAF 03

GAF 05

GAF 07


AEROGUST WORKSHOP


Elastic Aircraft!

Fluid-structure

coupled solution!

mode 03

mode 05

mode 07

Reference: Nonlinear FSI


Way forward: CRM/FERMAT config

WP 3

Mapped ∆cp

DLM model

CFD solutionT3.2 – DLM Updating with CFD Data

AEROGUST WORKSHOP


AEROGUST WORKSHOP

T4.1.2 - Nonlinear unsteady LSQ-ROM approach

Search for an approximated solution 𝐰 = [ρ, ρ𝐯, ρ𝐸𝑡, 𝜈𝑡] ∈ ℝ𝑁

▪ in the POD subspace 𝐔𝑟 ∈ ℝ𝑁 x 𝑟 , 𝑟 ≪ 𝑁

▪ minimizing a subset of the unsteady residual in the L2 norm

▪ greedy missing point estimation (MPE) procedure to select the subset

𝐰 ≈

𝑖=1

𝑟

𝑎𝑖𝐔𝑖 +𝐰 = 𝐔𝑟𝐚 + 𝐰

𝐰: mean of the snapshots set

𝐚: vector of the unknown coefficients 𝑎𝑖

▪ N: order of CFD model (variables x nodes)

▪ r: order of the ROM (i.e. number of POD modes)

𝐑 ≝ 𝐑 𝐰 t + 𝛀𝜕𝐰 t

𝜕t= 𝟎 ∈ ℝ𝑁 𝛀: cell volumes

Semi-discrete Navier-Stokes Eqs.

min𝐚

∥ 𝐑∗ 𝐔𝑟𝐚 + 𝐰 ∥L22

nonlinear least squares problem

𝐏

mask matrix

𝐑

𝐑∗

𝐏T 𝐑


ONLINE

OFFLINE

time

𝐂L Training outputTraining input

timeAn

gle

of

Att

ack

/G

ust

inte

nsi

tyvg

Global POD+ MPE

Collecting snapshots coming from an unsteady simulation variation in the local effective angle of attack

▪ Boundary conditions disturbances

▪ Motion (forced or induced)

▪ Gust perturbations frozen formulation, rigid aircraft, no motion

Building the POD subspace

⋯ ⋯

𝐰 ti 𝐰 tj

⋯

Flow field output time history

(Lg, Ag)X

ROM prediction

Flow field output time history!

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ROM prediction assessment

𝑽∞ = 246 𝑚/𝑠

𝒘𝑔 = 10 𝑚/𝑠

∆𝛼 ≅ 2.3°

AEROGUST WORKSHOP

▪ ROMs used instead of TAU for many queries predictions

▪ TAU unsteady RANS equations with SA-neg

▪ V∞ = 246 m/s, Mach = 0.83, Re = 6.5 106

▪ Forced motion 3.8 Mln nodes

Airbus XRF-1

Online: many ROM predictions possibleOffline: one training maneuver

Aero coefficients and loads for(1-cos) gust–like pitching oscillation

Chirp pitching oscillationup to reduced frequency k=3


AEROGUST WORKSHOP

Time step @ max C-lift


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Time step @ max |C-my|


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Time step @ max C-my


AEROGUST WORKSHOP

Improvement of the acceleratedgreedy MPE procedure

Using an (additional) rank-1 SVD update within the iterative greedy step, to further accelerate the selection of the grid nodes

Computational cost

• Alg. Ref. [1]: 𝓞 𝐍𝐫𝟐𝐬 + 𝐫 𝐬𝟑

• Rank-1 SVD update: 𝓞 𝐍𝐫𝟐𝐬 + 𝐫𝟑𝐬

▪ N: order of CFD model (variables x nodes)▪ r: order of the ROM (i.e. number of POD modes)▪ s (> r): number of MPE selected nodes

[1] R. Zimmermann and K. Willcox. An accelerated greedy missing point estimation procedure. SIAM Journal on Scientific Computing, 38(5), A2827–A2850. DOI:10.1137/15M1042899

𝐑

𝐑∗𝐏T 𝐑

LANN wing test case

• 0.47 Mi grid nodes

• 23 POD modes

• 6 cores


Mean of the snapshots set

AEROGUST WORKSHOP

Accelerated greedy MPE procedure𝐑

𝐑∗𝐏T 𝐑

Greedy MPEN° nodes: 0.38 Mi (10% of total nodes)

The selected greedy nodes are maximising the „information content“ of the POD subspace (i.e. they cumulate where there are high values and gradients)

GridN° nodes: 3.8 Mi

Next step:Perform ROM predictions of the XRF-1 with the accelerated greedy MPE


Next steps

▪ Compute high-fidelity (vertical and lateral) gust simulations for the NASA CRM full aircraft

▪ Apply DLM correction CREAM-n to NASA CRM at off-design flight points

▪ Recompute the ROM predictions using Numpy/Scipy with Intel® Math Kernel Library (MKL) compiler

▪ Apply the nonlinear LSQ-ROM approach to discrete gusts for the FFAST crank airfoil and the NASA CRM full aircraft

▪ Include the greedy MPE selection in the ROM prediction

AEROGUST WORKSHOP


Summary

AEROGUST WORKSHOP

▪ The simplified disturbance velocity approach (DVA) is sufficient to capture maximum loads induced by vertical gusts of realistic wavelength

▪ CFD-based DLM correction has the potential to accelerate the gust loads process but needs careful testing

▪ The nonlinear unsteady least-squares (LSQ) ROM shows good capability in predicting aerodynamic coefficients and loads for (1-cos) gust–like pitching oscillation


The research leading to this work has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement number 636053.

german aerospace center (dlr)...german aerospace center (dlr) aerogust workshop 27 th- 28 april...

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