Simulation and Design ofGas Turbine Components

B.L.Lapworth, S.Shahpar, D.C.RadfordRolls-Royce PLC, Derby.

M.B.GilesUniversity of Oxford.

Contents

l 2020 targetsl The role of simulationl The HYDRA CFD solverl The role of ADl The SOPHY design suitel Applications

The ACARE* Environmental Goals for 2020

lBackground:– In 2000, the European Union Commissioner Philippe Busquin

asked a distinguished group of representatives from theEuropean aviation industries to set out their vision for thefuture of aviation in the medium and long term.

– ACARE was set up with the objective of realising the goals.– In 2002 the Strategic Research Agenda was published which

set out four goals aimed at meeting the environmentalchallenge for 2020.

l The Goals– To reduce fuel consumption and CO2 emissions by 50 per

cent,– To reduce perceived external noise by 50 per cent,– To reduce NOx by 80 per cent,– To make substantial progress in reducing the environmental

impact of the manufacture, maintenance and disposal ofaircraft and related products.

* Advisory Council for Aeronautical Research in Europe

Rolls-Royce status*

lSteady progress since 1998 Datum– Trent 895 - Boeing 777-200 and -300 (EIS 2000),– Trent 556 - Airbus A340-600 Ultra long range (EIS 2002)– Trent 900 - Airbus A380 Super Jumbo (EIS 2006)– Trent 1000 - Boeing 787 Dreamliner (EIS 2008)

lSimulation has been and is the key to achieving targets

* Rolls-Royce Environmental Report 2003

The role of SimulationlSimulation is used:

– To reliably predict behaviour of engine components:- Aero-dynamic, aero-thermal, mechanical, vibration, aero-elastic,

aero-acoustic, impact, combustion, etc => virtual engine– To meet ever more stringent design requirements– To reduce reliance on expensive rig tests– To form basis of design optimisation systems– To understand physical behaviour

l Implications for simulation software– Validation is crucial,– Development tends to be incremental in order to preserve the

validation database.– At the same time we want leading edge capabilities to

achieve competitive advantage,– Maintaining a large industrial code in a quality assured

manner is a major undertaking- Benefits from AD are obvious and significant.

Typical Aerodynamic Simulation

2.1

2.2

2.3

2.4

2.5

2.6

2.7

0 20 40 60 80 100%Height

Tota

l Pre

s C

oeff

TestHYDRA

Prediction of the flow through a 4 stage low speed compressor

Suction Surface - 49.9% Cax

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

NGV Passing Events

Pres

sure

Flu

ctua

tion

(kPa

* 10

) HYDRAExpt

Modelling Unsteady Flows

Unsteady rotor-stator interaction

Unsteady votexshedding

The HYDRA CFD SolverlBackground:

– First version developed by Giles and co-workers at OUCLwith funding and technical assistance from RR

– Developed from outset to be a suite of non-linear, linear andadjoint CFD solvers

- Linearised unsteady and adjoint versions were hand coded– Since 2000 has been developed collaboratively by RR and a

number of university collaborators including OUCL.– Central code in Rolls-Royce corporate CFD strategy

lCurrent Status– HYDRA used on a wide range of gas turbine projects in both

the aerospace and non-aerospace sectors.– HYDRA is the basis of a large number of industry-university

collaborations involving RR.– The HYDRA collaborative network is one of the code’s major

strengths and the network is continuing to grow.

HYDRA Development Network

Cambridge CFD Lab(Dawes, Cant)

Surrey(Chew, Hills)

Loughborough(McGuirk, Page)

RR-Indianapolis(Neerarambam)

RR-UK Derby(Lapworth)

Oxford CFD UTC(Giles)

Cambridge Whittle Lab(Giacche, Naylor)

DLR(Nuernberger)

Design UTP(Keane)

Oxford Osney Lab(Atkins, Thomas)Imperial College

(Di Mare)

HYDRA Sample Applications

Fans

Turbines

Installations

NoiseExhausts

Full aircraft

Energy

Compressors

Air Systems

HYDRA Framework

Non-LinearSolver

Linearised Unsteady Solver

Steady Adjoint Solver

Harmonic Adjoint Solver

Common i/o, parallel, multigrid,visualisation libraries

Steady CFDUnsteady CFD

Steady design sensitivites:Loss, Flow rate etc.

Fixed frequencyunsteadiness:Flutter,Forced Response,Tone Noise.

Unsteady design sensitivites:Work sum,Acoustic energy,etc.

The Role of Automatic Differentiation

lCode maintenance:– Features are added to the non-linear code more rapidly than

the linear and adjoint versions.– Inconsistencies between versions affect stability and

accuracy of the linear and adjoint sensitivities.– Expertise needed to maintain hand-coded versions.

lAutomatic Differentiation– Allows consistent non-linear, linear and adjoint versions of

the code to be maintained with minimal effort.– More quality assured because scope for hand-coding bugs in

linear and adjoint versions is removed.- Less validation of new versions needed.

– Generation of linear and adjoint code becomes a transientoperation controlled by the Makefile:

- Only the non-linear code and executables need to be retained,- Less reliance on specialist hand-coding expertise.

The Influence of Coding Inconsistencies

Comparison of Hand-Coded and AD-Derived Sensitivities For Inviscid Compressor Case

0.80

0.90

1.00

1.10

1.20

Mass Flow Rate Total PressureLoss (%)

Squared AngleDeviation

Axial Force Tangential Force

Objective Function

Rat

io R

elat

ive

to F

inite

Diff

eren

ces Hand-Coded

AD

Inconsistency in periodicboundary condition leads

to divergence

Inconsistency in flux evaluations leadsto larger errors in adjoint sensitivities

Makefile Implementation

lAD (Tapenade) automatically run by Makefile whenlinear or adjoint object file needed to build anexecutable.l Intermediate (AD generated) files are transientlSample Makefile*:

flux.o: routines.F${CPP} -E -C -P routines.F > routines.f;${TPN} -forward \

-head flux \-output flux \-vars “q res” \-outvars “q res” \routines.f;

${FC} ${FFLAGS} -c flux_d.f;/bin/rm -f routines.f flux_d.f *.msg

* Giles et. al, Post SAROD Workshop 2005

Rolls-Royce Experience with AD

lAcknowledgement– RR experience has been gathered through research

programmes with Oxford (Giles et al.), Cambridge (Radford)and Cranfield (Forth)

lRR perspective:– Reference hand-coded versions essential to demonstrations:

- Provided validation and performance database,- Provided infrastructure so that AD can be applied at a

subroutine level.– Application of AD via Makefile essential to deployment

- RR doesn’t want to maintain an expertise in AD, just as itdoesn’t have experts in compiler technology.

lOutlook– AD is essential to maintaining a large industrial code, HYDRA.– RR will use Tapenade for AD.– RR will continue to look to collaborators for recommendations.

Linearised Unsteady Method

l Assume temporal variation of the form eiwt :

l Introduce pseudo time and solve with standard time marching for q’– Multigrid, preconditioning, local time-stepping etc.

l Flutter– Select ω based on blade vibration– Use unsteady pressures and structural mode shape to assess aerodynamic

dampingl Forced Response

– Select ω based on relative rotational speed of adjacent blade row– Decompose incoming wake/potential field into Fourier harmonics– Use linear superposition for multiple Fourier harmonics

l Tone Noise– Blade passing frequency

q(x,t) = q(x) + q’(x)eiωt

Adjoint Design Sensitivities

Navier-Stokes residual, RFlow field, UObjective function, IDesign parameter, α

Design sensitivity:

0 0=∂α∂R

+∂α∂U

∂U∂R

⇒=dαdR

+∂U∂I

=dαdI

∂α∂U

∂α∂I

+−=dαdI

∂U∂I

−1

∂U∂R

∂α∂R

∂α∂I

=vT

∂U∂I

−1

∂U∂R

−=dαdI

∂α∂R

vT +∂α∂I

=v∂U∂I

∂U∂R

T

T

Adjoint equation:

Adjoint variable, ν:

Independent of flow, U

Sensitivity depends on flow, U

Depends on objective fn, I

Optimiser

Adjoint Design/Optimisation

PADRAM

PerturbedMesh

Base Design

Steady HYDRA

ObjectiveFunction

Adjoint HYDRA

Adjoint Variables

PrecursorCalculation

DesignParameters

ComputeHYDRA

Residuals

EvaluateObjective Fn

I = vT.R

Costs less thanone iteration of HYDRA solver

Virtuallyinstantaneous

Adjoint Design - Bypass OGV design

2D OGV design to reduce static pressure variation

Integrated Automatic Design Optimisation SystemSOPHY: SOFT-PADRAM-HYDRA

Basedesign

SOFT

HYDRA

PADRAM

Costconstraints

jm56

jm52

DesignReview

OK?

Newdesign

Yes

No

Optimumdesign

Convergencehistory

Design parameters

Optimizer

Additionaldesign

parameters/cost

Automation Flowchartl Geometry created & meshed parametricallyl CFD boundary conditions and mesh pre-processedin batchl Costs and constraints extracted in batchlLibrary of optimisers available

Designing for Reduced Noise

Cost Function (Pa)

Optimiser Iterations

Dynamic HillClimber

Noise cost function is the amplitude of the 1st

radial harmonic in 1BPF (Blade PassingFrequency) 1 chord upstream of the blade.

Design space covers axial and circumferentialmovement (lean and sweep) of the bladesections over the outer 20% of blade span (4design parameters).

Fan mesh of ~1.7M nodes.Each iteration takes ~2 hours onPC cluster (using 60 processors).