An Integrated Computational Enviroment for the FSI ... · • MD Nastran 2010 ... Torino 6-7...

An Integrated Computational Enviroment forthe FSI Nonlinear Analysis – Applicationsand Assessment for a Fixed-Wing Case

Coppola, F., Linari, M., Mastroddi, F., Nardecchia, F., Stella, F. [email protected]@uniroma1.it

MSC Italian Users ConferenceTorino 6-7 October 2010

Objectives and motivations

Validation of a multidisciplinary nonlinear FluidStructure Interaction (FSI) computational( ) penvironment for aeronautical applicationsOvercoming of the current linear aeroelasticOvercoming of the current linear aeroelasticmodeling limits (e.g., MD NASTRAN solvers144, 145, 146)

Capability to deals with other physical FSIproblems

Estimate of the computational capabilityand efficiency in terms of benefits vs

p

and efficiency in terms of benefits vscomputational costs

2An integrated Computational Enviroment for the FSI Nonlinear Analysis – Application and assessment for a Fixed-Wing Case

MSC Italian Users Conference Torino 6-7 Ottobre 2010

Summary of presentation

Capability and limits of the linear aeroelasticmodels and n me ical tools (a ailable in MDmodels and numerical tools (available in MDNASTRAN for fixed-wing only)

Numerical ApplicationsBuffle in a ductBuffle in a duct

Structural and Aerodinamic nonlinearities

Wi fl tt i t i flWing flutter in transonic flowAerodynamic nonlinearities

Comparison with linear analysis and experimental

An Integrated Computational Environment for the FSI Nonlinear Analysis-Application and Assessment for a Fixed-Wing Case

3MSC Italian Users Conference Torino 6-7 Ottobre 2010

Summary of presentation

N li FSI d li b iNonlinear FSI modeling by using:

• Structure modeling:• MD Nastran 2010 - Sol400 solver with OpenFSI

• Flow modeling:• Flow modeling:• Fluent 6.3.26

f d l• Interface modeling:• MPCCI 4.0.1 (Mesh-based parallel Code Coupling Interface)



odel

s Linear-aeroelastic modeling

STRUTTURES: linearly-elastic modelingfor solids

AERODINAMICS n iscid attached e ternalMat

hm

o

Structures

AERODINAMICS: unviscid attached externalflow (ideally-perfect gas)P

DE

Aerodynamics

SPACE DISCRETIZATION (fluid+solids) FEMLifting Surface (DLM)

Integro-differential Equation in time domainTranscendental system transfer function in Laplace domain

c St

abili

ty Flutter: dynamic instability characterized by the imaginary axis crossing of a couple of conjugated eigenvalues driven by flight parameters

An Integrated Computational Environment for the FSI Nonlinear Analysis Application and Assessment for a Fixed Wing CaseA

eroe

last

ic

Divergence: static instability characterized by the imaginary axis crossing of a real eigenvalue driven by flight parameters

Analysis-Application and Assessment for a Fixed-Wing Case

5

A y g p



Linear-aeroelastic modeling

Use of modal coordinates qn is a specific issue in linear aeroelasticity

An Integrated Computational Environment for the FSI Nonlinear Analysis Application and Assessment for a Fixed Wing CaseAnalysis-Application and Assessment for a Fixed-Wing Case

6An Integrated Computational Environment for the FSI Nonlinear Analysis-Application and Assessment for a Fixed-Wing Case


R bl (MDNASTRAN SOL 144/146)


Laplace/Fourier domainResponse problems (MDNASTRAN SOLs 144/146)

Aeroelastic Transfer-Function Matrix

NB: Aeroelastic Frequency-Response Matrix for

Time domainTime domain

where is the inverse L-transform of



(Gl b l )S bili bl ( SC S SO 1 )


(Global )Stability problems (MSC.NASTRAN SOL 145)Global stability for integro‐differential systems

‐ System asymptotically stable iff all the eigenvalues (namely, transfer functin poles) are on the left part of the complex plane

‐ System symply stable iff there are not eigenvalues (poles) on the right hand side of the l l ( l i l i l h i i i bl )complex plane (multiple eigenvalues on the imaginary axis not acceptable)

Not standad eigenvalues problemiterative procedures (as P k or k method in SOL145) necessaryiterative procedures (as P-k or k-method in SOL145) necessary

Flight parameters to study stability in linear case:

Pagina 8MSC Users ConferenceTorino 6-7 October 2010



FLOWS PHYSICAL MODELS MATERIALS & STRUCTURES PHYSICAL MODELS

Nonlinear-FSI modeling

Eulerian flows

FLOWS PHYSICAL MODELS MATERIALS & STRUCTURES PHYSICAL MODELSMulti-physics charcterization

Large displacements & rotations

Stok

esav

ier-

SN

Simulation capabilities available Simulation capabilities available in MDNASTRAN SOL 400p

in several CFD codes

CONSEQUENCE OF NONLINEARITIES FOR COUPLED SYSTEMS (FSI)

MDNASTRAN SOL 400

FOR COUPLED SYSTEMS (FSI)LOCAL STABILITYBifurcation of equilibriumLimit Cycle Oscillation (LCO)

NB: Modal Coordinatescan not be used


9

y ( )MSC Italian Users Conference Torino 6-7 Ottobre 2010

U d t ti l i t

Nonlinear-FSI modeling StructuresMDNASTRAN Sol400

Sol400 undergoes the structural analysis taking for inputs the forces

Used computational environment: STRUCTURES: MDNastran (Sol400) Aerodynamics

Fluent Euler model

Sol400 undergoes the structural analysis taking for inputs the forces acting on the “wet surfaces” and gives as output the displacementsStructure is coupled with the fluidynamic field by the designation of the “wet surfaces” interfaces built choosing the free element faces of

This is possible by means of the Simulation Component Architecture (SCA) framework in MDNASTRAN

“wet surfaces” interfaces built choosing the free element faces of the solid body (they are carried out as a “load” case in SOL400).

Architecture (SCA) framework in MDNASTRAN.

->It allows the MD nonlinear solver to communicate with an external CFD or other external code, commercial or home built.CFD or other external code, commercial or home built.

The capabilities of the SCA framework are all embedded in the

Mpcci provides a service ad hoc to implement Nastran OpenFSI called up as an addition to the SCA service library. The capabilities of the SCA framework are all embedded in the SOL400 solver by means of which is possible to perform linear or non linear structural analysis, static or transient.



U d t ti l i t

Nonlinear-FSI modeling StructuresMDNASTRAN Sol400

Used computational environment: FLOW MODELING: FLUENT Aerodynamics

Fluent Euler model

Fluent carries out the CFD analysis given as input the fluid/structure interface motion (wet surfaces) and returns as output the pressurefield on the body.The wet surfaces undergo the displacements dictated by the Mpcci and given by the MDNASTRAN analysis. And give the pressure forces to the SOL400 in the meanwhile.The fluid-dynamic mesh is updated with two different concurrent strategies:

In the smoothing method, the nodes are moved as if connected by springs. In this process, node connectivity remains unchanged.

B hi Fl t l t h ll d k it fBy remeshing, Fluent evaluates each cell and marks it for remeshing if it does not meet one or more users-specified criteria on faces or cell quality.



U d t ti l i t

Nonlinear-FSI modeling

The analysis is performed by a time marching based algorithm:

Used computational environment: INTERFACE MODELING: MpCCI by Fraunhofer

The analysis is performed by a time-marching based algorithm:

for each time step the computations are carried out via a serial couplingalgorithmgDisplacements and forces are exchanged between two different meshes with a method based on shape functions workings in two steps:

Association For each node of one grid the “partners’” on the otherAssociation. For each node of one grid the partners on the other grid are found. This is also called neighborhood search.

Interpolation. The data transferred must be adapted to the target p p gmesh, while, for example, conserving the sum of forces.

(MDNASTRAN)

(FLUENT)



Numerical Example #1: baffle in a duct

A polypropylene baffle, with rectangular section, in closed duct is subject to aclosed duct is subject to a

viscous (Re=1.8 106), laminar, low-subsonic air flow

The upstream condition are 10m/s of air speed at atmospheric total pressure.

MDNASTRAN modelFLUENT model



Numerical example #1: baffle in a duct

The baffle is 1 m high, 0.1 m wide, 0.02 m thick.

The duct is 1.5 m high and 1.8 m wide, with the baffle symmetrically placed in the middle section in width.

The fluidynamic field is meshed in 529037 tetraedal cells withThe fluidynamic field is meshed in 529037 tetraedal cells, with 115278 nodes. Max face skewness is 0.68, max cell skewness 0.817. the surface of the baffle is meshed with an homogeneous interval size of 0 01 m along its edges The mesh is more refinedinterval size of 0.01 m along its edges. The mesh is more refined in the neighborhood of the baffle and gradually more coarse pulling away from it.

The cell minimum volume is 3.190848e-008 m3 the maximum volume 1.074925e-003 m3.

NB t t d h i d f lt f d i h i fl tNB: unstructured mesh is a default for dynamic mesh in fluent.



Numerical example #1: baffle in a duct

Mesh view Mesh section view



Example #1: baffle in a ductStructural mesh: structured mesh with hexahedral 8-node elements. The nodes of th b t i d ll th ithe base are constrained on all their degrees of freedom.The first 4 modes are bending modesg

4.164 Hz first bending mode20.563 Hz first transverse bending mode26 045 Hz second bending mode26.045 Hz second bending mode72.762 Hz third bending mode

Starting from a non equilibrium initial condition, the baffle vibrates until an equilibrium solutionthe baffle vibrates until an equilibrium solution with a damped harmonic oscillation mainly on the first bending mode.

A minor order oscillation on the first transverse bending mode producing a small oscillations in transverse direction.



Numerical example #1: baffle in a ductThe air flow rams the baffle bypassing it at his sides and above it. There is a recirculation zone downstream the obstacle with

id bl l l f ti it

p

considerable level of vorticity.

SIDE view TOP view17An Integrated Computational Environment for the FSI Nonlinear

Analysis-Application and Assessment for a Fixed-Wing CaseMSC Italian Users Conference Torino 6-7 Ottobre 2010

Flow wise tip displacement Transverse Flow wise tip displacement

Numerical example #1: baffle in a ductDisplacement in x direction of the tip of the baffle

0,03

0,035

0,04

Flow‐wise tip displacement Transverse Flow‐wise tip displacementspostamento in direzione y dell'estremità dell'ostacolo

0,0001

0,00015

0,01

0,015

0,02

0,025

Dis

plac

emen

t u(t)

[m]

0

0,00005

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Spos

tam

ento

u(t)

[m]

-0,01

-0,005

0

0,005

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Time [s]

Displacement in x direction of the tip of thebaffle

-0,00015

-0,0001

-0,00005

spostamento in direzione y dell'estremitàdell'ostacolo

Time [s]

-10

-50 10 20 30 40 50 60 70 80 90 100

-20

-150 10 20 30 40 50 60 70 80 90 100

Tempo [s]Time response Time response

CFD-basedresonance

-20

-15

Pxx

[dB

]

-30

-25

Pyy

[bB

]

-30

-25

f [Hz]

Power spectral density of x displacements

First natural frequency

Second natural frequency

third natural frequency

fourth natural frequency

-40

-35

f [Hz]

Power specral density of y direction displacements

First natural frequency

Second natural frequency

Third natural frequency

Fourth natural frequency

Frequency response (PSD of time signal) Frequency response (PSD of time signal)

18

Frequency response (PSD of time signal) Frequency response (PSD of time signal)



Numerical example #2: Agard 445.6 45° wing”

For assessment and validation of the nonlinear computations, it hasbeen chosen the case of a 45° sweptback wing to make a

i ith th i t l lt icomparison with the experimental results inE. C. Yates, “AGARD standard aeroelastic configurations for dynamic response. I – wing 445.6,” R 765, AGARD, 1985.




• Among the proposed configurations in Ref. [2] it has been made theg p p g [ ]choice of a wall mounted wing, denoted as “Solid 2” on which variousflutter tests have been performed in freon-12 flow for transonic flows.

Th h i f f fl tt di ll t bt i hi h M h• The choise of freon as flutter medium allows to obtain higher Machnumbers at same air speed comparing to air, as freon has a speed ofsound about 55% lower than air at the same temperature.

• The model has been tested in a wind tunnel with the root of the wingfixed to a solid plain wall, with no provisions to avoid boundary layer,in zero lift conditionin zero lift condition.

• Experimental results presented as undimensional flutter-speedmargin point as function of Mach numberg p


20MSC Users ConferenceTorino 6-7 October 2010


• Geometry and materials. The material is laminated mahogany, whichcan be modeled as orthotropic.p

Wing span 0.762 mAspect ratio 1.6575Root chord 0.559 m

i h dTip chord 0.368 mWeight 2.1392 Kg

• Dynamic analysis

First bending mode 14.10 HzFirst torsional mode 50.70 HzSecond bending mode 69.30HzSecond torsional mode 127 10HzSecond torsional mode 127.10Hz

• Flutter analysis

Flutter point example: Mach 0 92Flutter point example: Mach 0.92Flow speed 141.458 m/sFreon density 1.7677 kg/m3

Flutter frequency 27.404 Hz




• Internal optimization tools of MDNASTRAN have been used to builti l fi it l t d l th t t l t th

Modal tuning of the structural model via SOL200

a numerical finite elements model that accurately represents thestructural dynamic behavior of the experimental model

• SOL200 has been exploited to perform the modal optimization.p p p

• The error function to be minimized was based on the quadratic erroron the numerical estimates of the first natural frequencies ofthe structure computed by normal modes analysis.p y y

• The chosen design variables chose are the elastic parameters oforthotropic wing material.

D it i k t t t t th l l l t d t bt i th t l• Density is kept constant at the value calculated to obtain the actualmeasured mass of the physical wing.

• A modal tracking allows to follow natural modes evaluated atdifferent iterations of the optimization process by means of the ModalAssurance Criterion, to assure the replica of experimental modalsequence.




Natural frequencytuning table

Experimentalvalue

F.e.m value Relative errortuning table value value

First bending mode natural frequency 14.10 Hz 14.45 Hz 2.42%natural frequency

First torsional mode t l f 50.70 Hz 51.15 Hz 0.88%natural frequency

Second bending mode 69 30 Hz 69 36 Hz 0 09%natural frequency 69.30 Hz 69.36 Hz 0.09%

Second torsional d t l 127 10 H 131 86 Hz 3 61%mode natural

frequency127.10 Hz 131.86 Hz 3.61%

Numerical updated natural frequencies23An Integrated Computational Environment for the FSI Nonlinear


u e ca updated atu a eque c es


Numerical updated natural modes24An Integrated Computational Environment for the FSI Nonlinear


u e ca updated atu a odes


• The fluid-dynamic domain is meshed withThe fluid dynamic domain is meshed with 161573 tetrahedron cells

• The wing surface is meshed with 20 mesh d i h d d 43 i lti iseeds in chord and 43 spanwise, resulting in

1518 tria faces for top and bottom of the and 18 faces for the wing tip surface.

• The boundaries of the domain make a tunnel with a mass flux inlet and a pressure outlet.

NB: In the experimental test no provision made to avoid boundary layer on the wall on which the wing is mounted so a no slip condition

d h b dis imposed on this boundary.



Numerical example #2: Agard 445.6 45° wing”Linear analysis v.s. experimental results

Reference linear aeroelastic stability analysis (SOL 145)

Linear analysis v.s. experimental results

• The linear analysis is conducted using the structurally tuned structure and linear potential aerodynamics as given by DLM. Namely, a CAERO1 card for defining the lifting surface. 30 panels y, g g pin chord and 55 spanwise are used for the lifting surface aerodynamics. A SPLINE1 links the lifting surface to the structure.

• The aeroelastic (iterative) stability analysis performed via the P-K method.

• Linear analysis overestimates flutter velocity with error• Linear analysis overestimates flutter velocity with error growing with the mach number increase.

Linear analysis is not conservativeLinear analysis is not conservative



Numerical example #2: Agard 445.6 45° wing”Linear analysis v.s. experimental results

0.9

Linear analysis v.s. experimental results

0.7

0.8

ficie

nt

0 4

0.5

0.6

spee

d co

eff

0 2

0.3

0.4

Flut

ter s

Experimental adimensional

0

0.1

0.2 pflutter speed dataLinear adimensional flutterspeed data

0.8 0.85 0.9 0.95 1 1.05Mach number




• Linear aeroelastic analysis shows that instability occurs asd i i t bilit i fl tt i l b th b ti f t

Linear analysis

dynamic instability, i.e. flutter, as is clear by the observation of rootlocus.

• The critical flutter mode is a bending/torsional mode at a

Root locus

9.00E+02

• The critical flutter mode is a bending/torsional mode at afrequency of 27,58Hz.

5 00E+02

6.00E+02

7.00E+02

8.00E+02

part

2.00E+02

3.00E+02

4.00E+02

5.00E+02

Imag

inar

y p

Flutter point

0.00E+00

1.00E+02

-2.50E+02 -2.00E+02 -1.50E+02 -1.00E+02 -5.00E+01 0.00E+00 5.00E+01

Real part

Root loci and flutter point Flutter mode



Numerical example #2: Agard 445.6 45° wing”FSI simulation at flutter point

0.7

0.8

0.9

Mach 0.92R 0 76 106

0.4

0.5

0.6

spee

d co

effic

ientRe 0.76 106

Flow speed 141.458 m/sFreon density 1.7677 kg/m3

0.1

0.2

0.3

Flut

ter s

Experimental adimensionalflutter speed data

Linear adimensional flutterspeed data

00.8 0.85 0.9 0.95 1 1.05

Mach number

speed data

• Unstable solution found inUnstable solution found inthe experimental result point(CFD field)

• N.B.: LINEAR ANALYSISPREDICTS STABILITY!



Numerical example #2: Agard 445.6 45° wing”FSI simulation at flutter point

Different post processing tools are at disposal as given by the differentsoftwares building the computational environment.

FSI simulation at flutter point

PATRANStructures view

(flutter deformation)

MpCCIpInterface view



Numerical example #2: Agard 445.6 45° wing”FSI simulation at flutter pointFSI simulation at flutter point

Frequency content: comparison with exp. data

Time history of wing tip vertical displacement




FSI simulation at a stable point




The computations have been performed on a Intel core2 quad

Computational Issues

The computations have been performed on a Intel core2 quad64bit machine, with 8 Gb of RAM, running Fluent in parallel onthe four processors.

El d l i f h l d i l i i b 45 iElapsed real time of the coupled simulation is about 45 minutesfor 10 time steps, with 200 CFD iteration per time step. A 100 timestep simulation is adequate for detecting the insurgency ofinstability and perform a spectral analysis of the output takinginstability and perform a spectral analysis of the output, takingabout 6 hours. Multiple simulations are required for differentspeeds.

Elapsed real time of linear aeroelastic analysis for one machnumber at different air speeds is of order of minutes.



Concluding remarks

Estimated the capability of a multidisciplinary nonlinear fluidstructure interaction (FSI) computational environment( ) pcomposed by

• MD NASTRAN (SOL400 with OpenFSI)

• FLUENT

• MpCCIMpCCIOvercoming of the current linear aeroelastic modeling limitscomparing with linear tool available in the same environment(MDNASTRAN SOL145)

f h i l ffi i f b f

(MDNASTRAN SOL145)

Capability to deals with general FSI problems (not fixed wings only)

Estimate of the computational efficiency in terms of benefits v.s.computational costs: the distance of CPU cost between standardlinear analysis and nonlinear one is still considerable.



Bibliography

[1] Yates, E. Carson, Jr; Land, Norman S.; Foughter, Jerome T.,Jr.:M d d C l l t d S b i d T i Fl ttMesuredand Calculated Subsonic and Transonic FlutterCharacteristics of a 45°Sweptback Wing Planform in Air and in Freon-12 in the Langley Transonic Dynamics Tunnel. NASA TN D-1616,1963.

[2] Yates, E. Carson, Jr: AGARD Standard Aeroelastic configurationsfor Dynamic Response I.-Wing 445.6. AGARD report No 765, 1985.

[3] M CCI 4 0 1 3 D t ti P t I O i PDF i J l[3] MpCCI 4.0.1-3 Documentation Part I Overview PDF version July20, 2010

[4] MD Nastran R4 Release Guide, Revision 0. July 15, 2010MDNA 2010 Z Z Z DC RELMDNA:2010:Z:Z:Z:DC-REL

[5] MD Nastran R4 User Guide, Revision 0. July 8, 2010MDNA*V2010*Z*Z*Z*DC-QRG-VOL-1

[6] Rodden, W.P., Johnson, E.H., MSC/NASTRAN AeroelasticAnalysis, user's guide V68, The Macneal-Schwendler Corporation,1994.



An Integrated Computational Enviroment for the FSI ... · • MD Nastran 2010 ... Torino 6-7...

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