FLEXOP: Integrated Modelling Approach for Flexible … · · 2017-10-24• Unsteady Aerodynamics:...

> Flexop > Integrated Flexible Aircraft Modelling > T.Kier > DLR-SR > 19.09.2017DLR.de • Chart 1

FLEXOP: Integrated Modelling Approach for Flexible Aircraft DynamicsInternational Workshop on Robust Modelling, Design & Analysis18th and 19th September 2017, Bristol, UK

Thiemo Kier Manuel Pusch, Matthias Wüstenhagen, Martin Leitner

DLR OberpfaffenhofenInstitute of System Dynamics & Control

Overview


Aeroelastic model integration:

• Aeroelastic Model Building: The Aero-Servo-Elastic Tetrahedron

• Dynamic Aircraft Model Integration Process: DAMIP

• FEM concepts: Stiffness Model, Guyan reduction, Modal Analysis, EOM

• Aerodynamics: Potential Flow, Vortex Lattice Method, Aerodynamic InfluenceCoefficients, boundary conditions

• Unsteady Aerodynamics: Kelvin Thompson Theorem, Wagner Function, DoubletLattice Method, Rational Function Approximation

FLEXOP:

• Data sources and Preprocessing steps for the FLEXOP demonstrator

• Flutter Analysis Methods: PK, P and Eigenvalues of the integrated model

• Mass Sensitivity of Flutter Results

• CFD corrected AICs and interpolation of nonlinear effects

Aeroelastic Model

Model

AM

S

K

Aerodynamics Mass

StiffnessFlight Control System

Aerodynamicss

Stiffness

• Primary Flight Control Laws• Load Alleviation Functions• Active Flutter Suppression• Actuators• Sensors• Other Systems (Airbrake, Engine)


Different Models with Different Requirements forDifferent Purposes (but based on the same Data)

• Flight Mechanics• Control Design for Primary flight control laws (Baseline Controller)• Real time capable model for pilot training

• Structural Dynamics / Flutter / Loads• Flutter Analysis• Control Design for Active Flutter Suppression• Loads Analysis• Control Design for Loads Alleviation

• Hardware in the Loop Simulations• Seperate (Sub-)Models for each component (e.g. aero forces for test

bed)

• Validation Models• Not necessarily real time capable• Include „everything“ in nonlinear ODE based model


DLR Dynamic Aircraft Model Integration Process

Data Sourcesaircraft geometry

Aerodynamic databases

CFD data

Mass, weight & balance

Stiffness model

Systems architecture

Model IntegrationSelection of modelequations:

Nonlinear modelequations

Linear, frequency domainequations

Linear state space models

PreprocessingModal analysis

Potential Flow Aero (AICs)

Rational function approx.

Data correction, inter-polation and transformation

Selection of environmental model

Model ApplicationLoads Analysis

Flutter Analysis

Flight Dyn. Simulation

Flight control law design

Real-time Simulation

Model Implementation

Object-Oriented (Modelica)

Block Diagram (Simulink)

Software Algorithms (Fortran, Matlab)


> Flexop > Integrated Flexible Aircraft Modelling > T.Kier > DLR-SR > 19.09.2017

Partitioning the System Matrices (reference nodes remain in a-set):Assume no load on omitted grid points:

Neglecting inertial terms, yields the following transfromation:

This results in the overall reduced stiffness matrix, where we apply theaeroloads and put the masses

Stiffness and Mass Model PreparationGuyan Reduction

1. Global FEM Assembly

2. Static condensation to Condensation points on Load Reference Axes Kgg

3. Lump structural and nonstructural masses (OWE + Payload + Fuel) to those grid points Mgg

4. Kgg and Mgg are used for modal analysis

5. Rigidly connect rib end points for splining of Aero

6. Cut Load Integration points (between condensationpoints)

DLR.de • Chart 6

Normal Modes Analysis


Equation of motion:

Generalized Eigenvalue Problem:

Eigenvalues and Eigenvectors:

Generalized Mass and Stiffness:

Modeshapes and frequenciesare then compared to GVT data

Equations of Motion

• Linear (frequency domain)

• Non-linear (time domain)

• External Loads mainly from Propulsion and Aerodynamics


Aerodynamic Governing Equations

inviscid

Navier-StokesConservation of mass

momentum energy

Euler

Full Potential

irrotationalisentropic

cancel time derivatives

Prandtl Glauert

Laplace

Strip Theorystripwise multiplication with an empirical gradient coefficient

empirical

linearizedLinear Methods

Doublet Lattice Method(unsteady)Mean Lifting Surface Grid

Vortex Lattice Method(steady)Mean Lifting Surface Grid

3D Panel Methods(steady, unsteady)Surface Grid

Note: Steady Compressibility accountedfor by Prandtl – Glauert –GöthertTransformation

no boundary layerno turbulence

no strong shocks

no transonic effects

NonlinearMethods

Finite DifferenceFinite Volume Finite ElementVolume Grid

also:Field Panel MethodSurface grid + cartesianfield overset

steady compr. ORunsteady incompr.

no interactionSmall y and z disturbances no blunt bodies

TSD


• Linear relationship between local angle of attack at the control point and thesurface pressure distribution

• Accounting for roll/yaw/pitch rate as well as structural deformation isstraight forward

Vortex/Doublet Lattice Methods for aeroelastic applications


Aerodynamic Influence Coefficient MatrixAIC

AIC matrix explained:Vortex Lattice Methodsteady: Q0

jj

Biot-Savart-Law

Kutta-Joukowsky

AIC Matrix

Aerodynamic load point (1/4 - chord)

Aerodynamic control point (3/4 chord)

bj

cjaj


Aerodynamic boundary conditions

Torsional deformation:

Heaving motion:


Unsteady Aerodynamicsexample: starting vortex

0dtd

Kelvin-Thompson Theorem:


Indicial Functions: Wagner and Küssner Fcn.Change of normal velocity at the

control point

Change of bound vortex circulation

Free vortex of same strength but opposite sign is shed at trailing edge

Free vortex also induces velocity at control point

Free vortex loses influence as it is washed downstream with freestream velocity


• Theodorsen and Sears are frequency domain equivalents of the Wagner andKüssner Function

Theodorsen and Sears Function> Flexop > Integrated Flexible Aircraft Modelling > T.Kier > DLR-SR > 19.09.2017DLR.de • Chart 15

• Same mean lifting surface grid as VLM• Doublet Line • Acceleration (pressure) potential • No Wake Model needed• Harmonic solution of lin. potential equations• at discrete reduced frequencies

• Equivalent to VLM at k = 0

Frequency Dependent AIC MatrixDoublet Lattice Methodunsteady: Qjj(k)

Doublet Line (1/4 -chord)

Aerodynamic control point (3/4 chord)

bj

cjaj


Folie 17 > IFASD 2007 > T. Kier

DLM Formulas

with


Rational Function ApproximationRoger‘s Method

• AIC matrices have to be transformed from frequency into time domain• Approximated as rational functions with Roger‘s Method (Least Squares Fit)

Generalized Aerodynamic Forces:


Equations of Motion

• Linear (frequency domain)

• Non-linear (time domain)

• External Loads mainly from Propulsion and Aerodynamics


Ma=0.78, h=37000ft, WVE at = 10 deg, = 486 m2/s


FLEXOP Model Preprocessing


Uncondensed FEM


Loads Reference Axes (Condensation Points)


RBE3 Elements / Static Guyan Reduction


Aero Interpolation Grid (Rigid Elements in Rib Direction)


Condensed Stiffness Model


Aerodynamic Model: Doublet Lattice Panels


Lumped Masses


> Flexop > Integrated Flexible Aircraft Modelling > T.Kier > DLR-SR > 19.09.2017DLR.de • Chart 29 > Flexop > Integrated Flexible Aircraft Modelling > T.Kier > DLR-SR > 19.09.2017DLR.de • Chart 29

PK-Method Flutter Analysis(Rodden et al., NASTRAN)


The GAF are expanded linearly along the imaginary axis and therefore include aerodynamic damping

+ 14 Im + 12 Re = 0• The eigenvalues become = = 1 +• The damping is recovered by = 2• The converged eigenvalues are determined iteratively until <• Flutter points are found by determining zero crossings of converged damping

wrt. the flight state

-> Not only the flutter points are exact, but the evolution of damping and frequency is approximately physical and can be used to e.g. assess how

quickly a flutter point approaches

• Instead of iterating k and for the tabulated GAFs, a Rational FunctionApproximation of the tabulated GAFs is used directly in the equations.

• The system matrix A then reads

with

• The eigenvalues can be determined directly

P-Method Flutter Analysis


• Instead of assembling the system matrix symbolically, the integrated model isnumerically linearized

• Additional effects (nonlinear EOM, nonlinear (control) systems, nonlinearsensor equations, flight state, etc) can be easily considered.

• The integrated model is set up as nonlinear state space system

• The aircraft is trimmed for horizontal flight and linearized about this state• The Eigenvalues are determined for increasing speeds until flutter occurs

Integrated Model P-Method Flutter Analysis


),(),(

uxgyuxfx

Flutter analysis results


• The actuator mass increased significantly to ~0.9 kg• Where should we place it and how does that affect flutter speeds and

mechanisms• 15 candidate positions were examined

Mass Sensitivity of Flutter


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Symmetrical Flutter Mechanism


- -

flutter mass/no actuator

no flutter mass/no actuator

Antisymmetrical flutter


- -

a

a

a

a

a

a

a

a

a

flutter mass/no actuatora

no flutter mass/no actuatora

Correction of AICs with CFD data (steady)


Correction of AICs with CFD d t (steady)with CFD data (

AIC Correction and AIC-ROM

• Aerodynamic Influence Coefficients (AIC-Matrix)relates local AoA at control points to panel pressures

• I.e. AIC Matrices contain linearized gradientinformation and therefore can easily account forfexibility of the structure

• Mapping of CFD mesh onto VLM/DLM/Panel MethodGrid

• AIC Correction of gradients and offsets with CFD data

• This is repeated for multiple linearization points(different AoA, flight shapes) resulting in multiple AIC-matrices

• POD of AIC-matrices allows nonlinear interpolation

• Advantage over POD of CFD pressures:

Correct only for AoA get flexibility, roll rates, etc. for free ===

DLM CFD


Evaluation of AIC-ROM(LANN wing example)


Thank you for yourattention !

Questions ?


FLEXOP: Integrated Modelling Approach for Flexible … · · 2017-10-24• Unsteady Aerodynamics:...

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