MOR for ANSYS in turbine dynamics - CADFEM...MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix...

MOR for ANSYS in turbine dynamics

Felix Lippold / Dr. Björn Hübner

Voith Hydro Holding

MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 2

Outline

1. Introduction and motivation

2. Modelling acoustic-structure coupling

3. Model order reduction

4. Applications

5. Summary


IntroductionRotor-Stator Interaction (RSI)

RSI generation in vaneless space

Pressure pulsation Vibration unsteady forces fatigue


Pressure distribution (unsteady CFD)

Rotating blades pass wake

of steady parts

Interacting pressure fields

Pressure pulsations

Harmonic analysis

MotivationRSI background


MotivationSimulation methods

Surrounding water influences structural dynamics (added-mass)

Acoustic-Structure coupling required

Harmonic response analysis with turbine in water

Highly resolved ( f = 1.0 Hz) frequency response analysis

High computational effort for large systems

Not applicable for product development or parameter studies

Reduce number of unknowns


Finite-Element model used in harmonic analysis

Linear-elastic SOLID elements for runner structure.

Acoustic FLUID elements for surrounding water.

Complex load vectors for rotating pressure fields.

ModellingAcoustic-structure coupling

//euro1/HDH/HYDRO/home/10/bjoern.huebner/Praesentationen/MOR4ANSYS/GMA_Workshop_2007/FT_runner_press.avi


runner structure water as acoustic fluid

RSI pressure mode

shapes imposed at

vaneless space

impedance boundary at the outled

to eliminate outgoing waves

fixed support at the

shaft connection

modeling of

gaps and seals

Harmonic response analysis of turbine runner in water


ModellingCoupled acoustic-structure equations

Equations of motion

)(A

S

A

SAS

A

S

ASA

Stq

b

b

p

u

K

KK

p

u

E

E

p

u

MM

M

Formally equivalent to

)(tqbxKxExM

But:

non-symmetric matrices

non-proportional damping matrix

fluid damping EA only for impedance boundaries


MOR TheoryStructural dynamics without damping

0)(δ T tqbxKxMx

εzVx

)(tqbxM xK

z

Vx

)(tqrbzrM z

rK

TTTVzx

0)(δ TTTT tqbVzKVVzMVVz

Original system

Approximated DOF vector

Reduced system


MOR TheoryFind subspace V

Natural mode shapes: Possible but computational costly and

often not the best choice for unsymmetric matrices or arbitrary load

shapes.

Krylov subspace via Arnoldi process: Easier to compute

(especially for unsymmetric matrices) and good approximation for

arbitrary load shapes.

Arnoldi process for calculating reduction vectors vi:

bKv1

1 i1

1i MvKv i1i yKv LUK

,...,,, 13

12

11 vAvAAvvspanV MKA1


MOR theory

Harmonic response analysis of the reduced system (with damping)

Solution in frequency domain:

Proportional damping definition at the reduced system level

Rayleigh damping:

Constant global damping ratio :

titi eei rrrr2 )(ˆ bzKEM

tiet )(ˆ)( zz

rrr KME

rr

2KE

tiettt ω)()()( rrrr bzKzEzM

Proportional damping

may be defined and varied

at the reduced system level

without loss of accuracy

since it does not influence

reduction vectors!


MOR for ANSYS(1)

Application and methodology

Linear PDEs,1st or 2nd order in time, discretized with ANSYS.

Linear structural dynamics, structure-acoustic coupling, heat

conduction, ...

Not applicable for non-linear systems (e.g. turbulent flow)

MORforANSYS reads ANSYS full-files and reduces large

scale systems (106 DOFs) to low order systems (100 DOFs).

Harmonic (or transient) analyses of the reduced order system

performed by functions written in Python.

DOF results back transferred to ANSYS for stress calculation

and post-processing (graphics, animations).

Limitations: changing load shapes, non-proportional damping.

(1) E.B. Rudnyi, J.G. Korvink: Model order reduction for large scale engineering

models developed in ANSYS, PARA 2004, LNCS 3732, pp. 349-356, 2006.


ApplicationFrancis turbine runner in water

Structure of the Francis turbine runner and monitoring points on trailing edge


Axial displacement@centre trailing edge – no damping

Amplitude spectrum (Dim=100) Deviation related to ANSYS results

ResultsNo damping


Pressure distribution on runner for f = 40 Hz

Ansys (90 000 DOFs) Reduced (Dim=100)

REAL part of pressure

solution

Deviation < 0.2%

IMAG part of pressure

solution

Deviation < 0.2%

ResultsVerification of reduced order method


Axial displacement for f = 40 Hz

Ansys (90 000 DOFs) Reduced (Dim=100)


solution

Deviation < 0.2%


solution

Deviation < 0.2%



Parameter studyDamping variation

Global damping in

reduced model:

no damping, 1%, 2%


Summary

Introduction to RSI in hydraulic machinery

Excitation of turbine structure

Modelling acoustic-structure coupling for

water-filled turbine runner

Model order reduction to reduce

computational effort

Successful application and verification

with Francis turbine runner

)(tqbxM xK


Non-Proportional Damping (local variation including acoustic FSI) with MORforANSYS

Local damping multiplier j or FSI with structural Rayleigh

damping and/or impedance boundary conditions

Non-proportional but constant damping matrix.

Reduction vectors depend on the damping properties.

Possible solution procedures on the next slide.

Local damping ratios j or FSI with structural DMPRAT

Non-proportional and frequency dependent damping matrix or

complex stiffness matrix.

Both not supported by MORforANSYS

Approximately use global damping ratio for reduced system.


Non-Proportional but Constant Damping Matrix E

Reduction vectors are

calculated without damping,

but original damping matrix

will be reduced, too.

Bad approximation!

Always working, but add.

damping of reduced syst.

and back transformation

to ANSYS not possible.

Not appropriate!

Works well for impedance

boundary conditions. At

the reduced system level,

a global damping ratio

may be defined in addition.

qbKxxExM


ResultsIncluding damping effects

2% global damping for reduced model

2% structural damping in ANSYS w/ and w/o Impedance bc

Amplitude spectrum (Dim=100) Deviation related to ANSYS results


Pressure distribution on runner for f = 40 Hz

Ansys (DMPR=1.0%) Reduced (Damping 1%)


solution

Deviation < 2.0%


solution

Deviation < 2.0%

ResultsIncluding damping effects


Axial displacement for f = 40 Hz

Ansys (DMPR=1.0%) Reduced (Damping 1%)


solution

Deviation < 2.2%


solution

Deviation < 2.2%


MOR for ANSYS in turbine dynamics - CADFEM...MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix...

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