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Application of AD in Turbomachinery Design

19th European Workshop on Automatic Differentiation Jan Backhaus DLR Cologne

www.DLR.de • Chart 1

CFD based Optimization


Gradient-free optimization is possible, but expensive

CRISP 1 rig

CRISP 2 optimization result

Design Process


CAD parameters

blade generator

surfaces

mesh generator mesh deformation

mesh

TRACE

CFD solution

POST

Objectives

Bladegenerator • Forward Mode AD CodiPack

Mesh deformation • self-adjoint problem: manually adjoined

TRACE • Reverse Mode AD: ADOL-C, DCO, CodiPack

POST • Reverse Mode AD:ADOL-C, DCO, CodiPack

Bladegenerator


DLRs NURBS based turbomachinery geometry tool differentiated with CodiPack + tinyform in forwardMode (Reverse Mode in progress)

Bladegenerator forward AD sensitivities


NonLinear TRACE - finite volume method on structured and

unstructured meshes - compressible Navier-Stokes, real-gas model - upwind-scheme 2nd order accurate - implicit time integration scheme - hybrid parallelization (MPI/OpenMP/SSE)

- turbulence modelling

- Spalart-Allmaras - Wilcox k-ω - Menter SST k-ω - W&J EARSM k-ω (Hellsten) - RSTM Wilcox Stress-ω

- transition modelling

- non-local: MultiMode − γ−Reθ Model (Menter & Langtry) - LKE Model

DES computation of a mixer

TRACE Post-Processing

- Data reduction - Massively parallel - Flexible process chains - Topology independet - Based on VTK


• Coupling of the aerodynamic and propulsion analysis tools for aircraft design is a necessity in multi- disciplinary design analysis and optimization of new aircraft concepts with highly integrated engines.

• To the authors knowledge, currently no propulsion system analysis tool is capable of providing analytic derivatives for gradient based optimization.

• Refactoring of DLR‘s inhouse gas turbine performance code GTlab-Performance undertaken in order to employ automatic differentiation.

• Current status: • Incorporation of active datatypes for AD (using CodiPack) • Introduction of a polynomial gas model • Interpolation libraries provide analytic derivatives which are

interfaced to the AD datatypes (forward and reverse mode) • Testing, testing, testing...;)

Automatic Differentiation in Gas Turbine Performance

DLR.de • Chart 8

AD in TRACE

AD-adjoint TRACE

AD know-how

(TU-KL)

industrial application

(MTU)

simulation code (DLR)


Adjoint Method

Continuous Discrete

Manual implementation

(+ GMRES)

+Finite differences

+Selective forward AD

adjointTRACE

Reverse Mode AD

+Optimizations

AD-adjointTRACE

3 year BMWi project R&E-Turb (completed) 3 year EU project CleanSky 2 (running)

Motivation: • new simulation models • consistency

TRACE Software Development

- 20+ years of code history - ~20 core developers + external developers at MTU, Universities - Language: C - Philosophy: stable trunk

- Coding guidelines - Code reviews - Automated test and validation suite - Branches for substantial developments

Task Tool Version Management Subversion Continuous Integration Jenkins Automated testing and validation In-house Python tools Bug tracking Mantis IDE Eclipse

AD in TRACE (2)


• ADOL-C • DCO • CodiPack

AD-Tools implemented for TRACE

• Adjoint MPI • Adjoinable MPI

adjoint Parallelization

• reverse accumulation

• pre accumulation of Jacobians

Optimizations

Challenges

• C is not C++ • C is not too strict about types • communication / structs • printf (tip: tinyformat) • unions • designated initializers • TRACE is optimized for performance • no influence on primal performance • only moderate changes to primal code • developer acceptance • restarting/checkpointing • computational ressources

Implicit Solution Scheme


dq

dt= R(q) = 0

qn+1 = qn + ¢tRn+1

Rn+1 ¼ Rn +@R

@q¢q + O(¢t2)

µ1

¢t¡ @R

@q

¯̄¯̄n¶

¢q = Rn

qn+1 = G(qn); q¤ = G(q¤)

Ãn+1 = Gadj(q¤; Ãn)

Steady Solution:

Euler Forward:

Taylor Series:

Implicit pseudo- time stepping:

Fixed point iteration:

Reverse Accumulation:

Implicit Solution Scheme


dq

dt= R(q) = 0

qn+1 = qn + ¢tRn+1

Rn+1 ¼ Rn +@R

@q¢q + O(¢t2)

µ1

¢t¡ @R

@q

¯̄¯̄n¶

¢q = Rn

qn+1 = G(qn); q¤ = G(q¤)

Ãn+1 = Gadj(q¤; Ãn)

What if we keep³

1¢t¡ @R

@q

¯̄¯n´

constant inside Gadj?

Steady Solution:

Euler Forward:

Taylor Series:

Implicit pseudo- time stepping:

Fixed point iteration:

Reverse Accumulation:

Constant implicit matrix CRISP 2


Testcase CRISP 2


CAD parameters

blade generator

surfaces

mesh deformation

mesh

TRACE

CFD solution

POST

Objectives

Testcase CRISP 2


CAD parameters

blade generator

surfaces

mesh deformation

mesh

TRACE

CFD solution

POST

Objectives

24 parameter shape changes by deformed surfaces

Sensitivities


CAD Param Const implicit mat. Updated implicit mat. 0 -2.82085542e-05 -2.82085543e-05 1 -1.81798135e-04 -1.81798135e-04 2 -3.57947732e-04 -3.57947732e-04 3 -1.46026411e-04 -1.46026411e-04 4 4.38913667e-07 4.38913632e-07 5 5.20296047e-05 5.20296037e-05 6 2.09157619e-04 2.09157620e-04 7 8.86496439e-06 8.86496444e-06 8 4.20493924e-05 4.20493929e-05 9 -3.66017192e-04 -3.66017194e-04

10 -4.88746949e-04 -4.88746951e-04 11 -1.46196978e-05 -1.46196979e-05 12 -3.83111784e-05 -3.83111781e-05 13 -7.83842571e-05 -7.83842570e-05 14 -1.88390056e-04 -1.88390056e-04 15 -4.38789624e-05 -4.38789619e-05 16 1.45440904e-05 1.45440899e-05 17 3.64904762e-05 3.64904757e-05 18 6.95241023e-05 6.95241020e-05 19 6.28804897e-06 6.28804871e-06 20 -1.17077950e-05 -1.17077951e-05 21 -1.58782348e-04 -1.58782349e-04 22 -2.65836414e-04 -2.65836415e-04 23 -1.11831870e-04 -1.11831870e-04

after 1000 adjoint iterations


Testcase CRESCENDO: 1st stage LPT

1.8 Mio Cells Wilcox k-w Multi-Mode transition Model Testbed for joint optimizations among MTU and RR distributed onto 72 procs

Constant implicit matrix


Memory [GB] factor time / iteration factor mem

Primal 12,79 1 1

adjoint var impmatrix 219,97 2,62 17,19

adjoint const impmatrix 123,36 1,12 9,64

Thanks! www.DLR.de • Chart 20

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