University of Bristol · NASTRAN Little difference between corrected strip theory and VLM for the nonlinear results –large deformations do not change the lift distributions drastically

Funded by the European Union

University of Bristol

AEROGUST Workshop27th - 28th April 2017, University of Liverpool

Presented by Robbie Cook and Chris Wales


Overview• Theory

• Nonlinear structural solver coupled with unsteady aerodynamics

• Gust loads process for nonlinear aeroelastic systems

• Results• WP2 recap of M18 results

• WP3 Uncertainty Quantification initial results

• Conclusions and next steps

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Nonlinear Aeroelastic Framework

EOM

Strain-Curvature/Velocity

Relation

• Additional equation required to satisfy free-free conditions• Free-free velocity couples with second equation above

• Allows for arbitrarily large rigid body rotations

• Linear finite-elements are used to solve the structural EOM

• Positions and orientations are obtained by integrating strains/curvatures along the beam, or, velocities with time (parameterising rotations using quaternions)

• Free-free geometrically-exact nonlinear beam code based on Hodges’ intrinsic beam formulation• Linear strain-curvature/force-moment relationship

• Large beam deformations and rotations capture

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• Aerodynamics from modified unsteady strip theory• Leishman’s indicial response method for unsteady effects (compressibility effects ignored)• Spanwise lift distribution from VLM• Sectional AoA related to beam motion• Linear relationship between AoA and lift (no stall)

• Static coupled nonlinear structural and aerodynamics equations solved using Newton-Raphson method• Dynamic solution obtained using Newmark-β time-stepping solver

• Code verified against Nastran, other UoB codes, UCT, UMich

Gust Loads Process for NL Aeroelastics• Industrial gust loads process can no longer be used for NL

system

• Large deformations may lead to RTC gusts exceeding a purely vertical or lateral gust• RTC gusts cannot be calculated directly for NL system

Nonlinear Aeroelastic Framework

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Vertical gust vs. angled gust on free-flying aircraft

Θ=0o Θ=60o

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WP2

• Analysis carried out on UAV wing (test case 2)

• Baseline isn’t flexible enough for nonlinear effects to become important• Flexible variants created from the original

baseline wing• EI1,EI2,GJ reduced uniformly by a factor

(no mass changes)

• A number of flexibility variants are trimmed • Wing cannot support the aircraft much

below 15% of the baseline stiffness

• Flexibilities below 25% baseline show considerable difference compared to NASTRAN

Little difference between corrected strip theory and VLM for the nonlinear results – large

deformations do not change the lift distributions drastically

Overview of Deliverable 2.6 – Nonlinear structure with linear aerodynamics

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WP3

• Part of Task 3.3, addresses WP3 objectives• “To assess the impact of the underlying assumptions of the cuurent loads

process”• “To investigate methods to extend the applicability of the current process to

highly flexible and innovative structures”• “To develop methods to include the uncertainty present in both the

aerodynamic and structural models within the current loads process and investigate the impact on gust loads”

Work Package 3: Overview of Deliverable 3.10Effects of uncertainty on the gust loads process

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AEROGUST WORKSHOP WP3

• Need to define what system inputs are uncertain• Environmental uncertainties (air density, temperature, etc.)

• Aircraft property uncertainties (stiffness properties, mass properties, etc.)

• Gust inputs themselves are assumed to be the known, EASA/FAA regulation deterministic input gusts

• Need to define reasonable input PDFs for the uncertain variables• Little information found in literature for what values to use

• Initial results use a normal distribution with 3σ limits at ±10% of the mean values

• First set of results consider only an uncertain air density, with mean value defined in the test case document• Polynomial Chaos Expansion techniques are used to determine how input uncertainties propagate through to the output

loads uncertainties

• Static PCE results can be compared to a Monte Carlo simulation to obtain an ‘exact’ result

• MCS of dynamic results requires considerable computation

Uncertainty Quantification of Aeroelastic System


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UQ Analysis –Aeroelastic Trim Analysis (Static)

WP3


• MCS carried out with 1000 trim cases at different air densities

• MSC PDF histograms for AoA compared to PCE PDFs calculated with 5 trim cases and 4 shape functions

• Good agreement to MCS from PCE using fewer simulations

• Trim loads do not vary much with air density

1000 simulation

Monte Carlo ‘exact’

solution

Polynomial Chaos

emulation from subset

of results

WP3AEROGUST WORKSHOP


WP3

• Mean values calculated from PCE values match well with the values calculated with the mean air density values

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WP3

• Standard deviations appear to remain roughly constant for linear system regardless of flexibility

• Standard dev increases in nonlinear system

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WP3

• Skewness and kurtosis plots included as a first case indication of how normal the output distributions are

• Small amount of skewness is seen for linear and nonlinear, and excess kurtosis is low –fairly normal output PDFs

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WP3


UQ Analysis – Aeroelastic Gust Analysis (Dynamic)

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WP2

Overview of Deliverable 3.10 - Effects of uncertainty on the gust loads process

• Wing is subjected to a family of vertical 1-cosine gusts, with gust intensity and lengths defined by FAA/EASA certifications• Nonlinear aeroelastic code compared to linearised code about

underformed and trim geometries• Incremental loads about undeformed geometry

• 1g loads added afterwards under linear assumptions

• Nonlinear results obtained from the deformed trim geometry

• Loads time histories post-processed on linear and nonlinear results to look at trends

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WP3

• RTC gust direction calculated from linear system about trim geometry

• Even for stiff wings, the worst case gust is orientated away from purely vertical• Can lead to loads

increases ~10%

• May be exacerbated by fixed-root assumptions

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WP3

Baseline stiffness 15% baseline stiffness

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WP3

• Linear system over-predicts shear, torsion and bending moments on stiffer wing

• Trend reversed for torque at lower stiffness

• Axial and in-plane shear/bending are almost zero in linear

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WP3

• Standard deviation of the linear system output PDFs remains fairly constant for different flexibilities

• Standard dev reduces significantly for root shear, torque and bending moment as aircraft gets more flexible

• Opposite trend as seen in trim AoA

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WP3

• Low skewness and excess kurtosis for almost all cases – seems to be a fairly normal output PDF

• One exception on 25% flexibility where the skewness is relatively large

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Conclusions• PCE used to recreate the PDFs of quantities of interest of an aeroelastic system s.t. air density

uncertainties

• Comparison of linear to nonlinear systems

• Trim angle of attack uncertainty (std dev) increases in nonlinear system as it becomes more flexible, but remains fairly constant in linear

• Incremental gust loads uncertainty reduces in nonlinear system as it becomes more flexible, but remains fairly constant in linear

Next steps• Include more sources of uncertainties in the analysis

• Structural properties EI/GJ

• Mass properties

• Structural damping

• Drag?


WP2

• Part of Task 2.1, Non-linear Aerodynamics of Gust Using RANS• “Investigation of predicted non-linear behaviour using Field and Split Velocity

Methods”

Work Package 2: Understanding Non-linearities in CFD Based Gust Simulations

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• Gust velocity is prescribed throughout domain

• Moving grid code modified

• The grid velocity set to minus the gust

• No grid displacement

• Solves for the total velocity minus the gust

• Gust not dissipated by large cells

• Does not include the interaction with the body

• Correct if: no body in domain; steady state

change to uniform flow throughout the domain

Field Velocity Method

0

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22

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ˆ̂ˆ̂

vuEp

vup

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yvvxuu

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tt

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• Gust velocity component is split from total

• Gust component prescribed

• Follow split through equations

• Pressure not a function of gust component

• Moving grid code modified

• As FVM except Additional source terms

• Includes the interaction with the body

Split Velocity Method

34

vvvuuu ˆ̂~ˆ̂~

22

21

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ˆ̂ˆ̂ˆ̂~ˆ̂~ˆ̂,ˆ̂ˆ̂~ˆ̂~



Split Velocity Methods

Change in velocity due to gust Change in pressure due to gust

Prescribed velocity approach includes interaction of the gust with the body“1-cosine” gust, transonic 2D aerofoil case

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M=0.8 w=0.5c Δα=0.5°



• Case H

- 29995ft, Mach 0.86

• Maximum take off mass case

Case H

Gust Length(m)

Gust velocity(m/s)

Equivalent AoA(degrees)

18.29 11.24 2.47

91.44 14.70 3.23

213.36 16.94 3.72

Gust test case definition

0

2

4

6

8

10

12

14

16

18

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Gu

st v

elo

city

(m

/s)

Time (s)



30ft 350ft150ft

WP2

NCRM case H results - rigid

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30ft 350ft150ft

WP2

NCRM case H results - flexible

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Comparison between FVM and SVM surface pressures

FVM SVM

Case H gust length 30ft



Difference in surface pressures between SVM and FVM

30ft gust 350ft gust

Case H



WP3

Work Package 3: Reduced reliance on wind tunnel data

“The recreation of the industrial gust loads process, using CFD in place of experimental data”

“Investigation of the underlying assumptions of the current industrial gust loads process”

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stitched VLM

components

rapid &

robust

unsteady

VLM

Loads DatabaseCFD or

experiment

Target

High T-tail

Prop wash

Strut

braced

universal

correction

process /

matrices

Rapid Loads evaluation



Steady state CFDNASTRAN Corrected

DLMSOL 144/145

Post process ResultsLoads

Envelope/Correlated Loads

Generate correction Matrices

Wkk/F2jg

Strip wise lift moments extracted

Correction matrices generated to match strip wise lift and moment

Run different gust and mass at corrected flight condition

Loads extracted from NASTRAN monitor points

Recreating the current industrial loads process



Mesh Deformation

Start

initialize Mesh Deformation -IC

TAU Solve Steady

TAU Solve

Unsteady

initializeTime

getWettedNodeForces

finalizeTime

terminate

End

MSC

NA

STR

AN

tim

e st

eps

iter

ati

on

st

eps

MSC Nastran1

DLR Tau

Spline Method

Nastran FE Solve

1 MSC Software Development Kit 2014 User's Guide. 2014.

putWettedNodeDisplacements

The coupling matrix 𝐇 is created using NASTRAN and exported using DMAP

𝐟𝑠𝑡𝑟 = 𝐇𝑠𝑎𝐟𝑎𝑒𝑟𝑜

𝐮𝑎𝑒𝑟𝑜 = 𝐇𝑎𝑠𝐮𝑠𝑡𝑟

Tau modified to allow variable time stepping. Speeds up simulation by using large time steps to convect gust to close to aircraft

Updated to allow rigid body motion as well

Coupling NASTAN to Tau



UVLM code• 3 Parts

• Vortex ring elements on body

• Layer of buffer panels in the wake

• Vortex particles in the wake

• Rigid body motions

• Deformations

• Gust interactions



UVLM correction process𝐶0 + 𝐶𝑤𝑤𝑏 + 𝑤𝑤 = 𝐴Γ∆𝑃 = 𝑆𝑍𝐴−1𝑤𝐶

Map CFD loads on to UVLM mesh

Iterate correction matrices

calculation due to interaction with wake

WP3

0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

6.00E-01

7.00E-01

8.00E-01

9.00E-01

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Cl

Angle of attack (deg)

DLM DLM_corrected UVLM UVLM_corrected CFD

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FEM condensed mass and stiffness from FERMAT structural modelDLM Mesh for wing and tailCFD mesh from 4th Drag Prediction WorkshopOnly wing coupled

Nasa Common Research Model



30ft350ft150ft

Corrected DLM and UVLM for rigid geometry

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30ft

350ft

Corrected DLM loads for flexible wing

Root shear Root bending Root torque



➢ Aeroelastic frequency response analysis in modal coordinates formulation:

➢ In the gust response analysis available in the Nastran solver these contributions are linearly added to obtain the total aerodynamic loads.

➢ From this the idea that it is possible to correct once to match the rigid gust loads and the other to generate the aerodynamic load obtained from a mode shape deformation.

Mode Deformation Rigid Gust

AIC Unsteady Correction



The aim of this correction approach is to match the integrated aerodynamic loads acting on the structural nodes computed from the CFD code:

where the right hand side term can be specialized for the corrected Doublet Lattice Method , as follow:

The downwash contribution is a matrix defined as follow

Defining the generalized aerodynamic influence coefficient matrix relating the downwash to the aerodynamic loads on the monitor points, corresponding to the CFD strip being mentioned:

AIC Unsteady Correction – Rigid Gust

A post multiplication correction approach



AIC Unsteady Correction FrameworkThe time domain CFD gust response loads has been evaluated for different reduced frequency.

For each of them the time history of the integrated loads of the ten strips along the wing has been computed.

The input signal has been chosen long enough to reach a stationary harmonic response.

At this point a reference period has been selected, and an equivalent periodic signal has been reconstructed.

To obtain comparable results to the ones computed by the DLM the Fourier Series has been used to obtain the frequency domain loads.

The correction factors have been used to update the AICs matricescomputed in the gust response analysis.



“1-COS” Gust Response Analysis

12.29 13.72 2.81 0.08

16.07 2.74 3.67 0.36

18.51 1.17 4.22 0.85

Mach number = 0.85

short

medium

largeThe main goal is to focus on the gust response analysis of interest in a design process:

With a design gust velocity given by :



“1-COS” Gust Response: M=0.85, “Short” Gust Length

AEROGUST WORKSHOP WP3


“1-COS” Gust Response: M=0.85, “Medium” Gust Length



“1-COS” Gust Response: M=0.85, “Long” Gust Length



Conclusions

Next steps

• For gust lengths required for certifying “1-cosine” gust loads the FVM and SVM produce the same results• DLM and UVLM both over predict gust loads when corrected with purely steady data• Using unsteady data the accuracy of the corrected DLM can be greatly improved

• Apply improved DLM correction method to NCRM test case• Test corrected UVLM coupled to NASTRAN• Use unsteady data to improve UVLM correction

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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.

Documents

University of Bristol · NASTRAN Little difference between corrected strip theory and VLM for the nonlinear results –large deformations do not change the lift distributions drastically