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© 2011 ANSYS, Inc. October 14, 20111
Mesh Morphing and the Adjoint Solver in
ANSYS R14.0
Simon Pereira
© 2011 ANSYS, Inc. October 14, 20112
• Fluent Morphing‐Optimization Feature
• RBF Morph with ANSYS DesignXplorer
• Adjoint Solver
• What does an adjoint solver do, and how do we use the results?
• Supporting technologies and challenges
• Current Functionality
• Examples
• Summary
Agenda
© 2011 ANSYS, Inc. October 14, 20114
FLUENT Morpher‐Optimization feature
•Allows users to optimize product design based on shape deformation to achieve design objective
•Based on Free‐Form Deformation tool coupled with various optimization methods
© 2011 ANSYS, Inc. October 14, 20115
Mesh MorphingApplies a geometric design change directly to the mesh in the solver
Uses a Bernstein polynomial‐based morphing scheme• Freeform mesh deformation defined on a matrix of control points leads to a smooth deformation
• Works on all mesh types (Tet/Prism, CutCell, HexaCore, Polyhedral)
User prescribes the scale and direction of deformations to control points distributed evenly through the rectilinear region.
© 2011 ANSYS, Inc. October 14, 20116
Region Defined
ExamplesSome Basic examples…
Optimization based morphing…
BaselineModified
© 2011 ANSYS, Inc. October 14, 20117
Process
ORWhat if? OptimizerSetup CaseSetup Case
RunRun
Setup MorphSetup Morph
EvaluateEvaluate
Choose “best” design
Choose “best” design
RegionsRegions
ParametersParameters
DeformationDeformation
Setup CaseSetup Case
RunRun
Setup OptimizerSetup
Optimizer
OptimizeOptimize
Optimal SolutionOptimal Solution
MorphMorph
OptimizerOptimizer Auto
© 2011 ANSYS, Inc. October 14, 20118
Objective Function
Baseline Design Optimized Design
• Objective Function: Equal flow rate• Objective Function: Equal flow rate
© 2011 ANSYS, Inc. October 14, 20119
Example – Simple Sedan
Sequential TabsSequential Tabs
• Define Control Region(s)• Define Control Region(s)
© 2011 ANSYS, Inc. October 14, 201110
Deformation Definition
• Define constraint(s) (if any)
• Select control points and prescribe the relative ranges of motion
• Define constraint(s) (if any)
• Select control points and prescribe the relative ranges of motion
© 2011 ANSYS, Inc. October 14, 201111
Optimizer Algorithms; Compass, Powell, Rosenbrock, Simplex, TorczonAlgorithms; Compass, Powell, Rosenbrock, Simplex, Torczon
Auto
• Optimize!• Optimize!
© 2011 ANSYS, Inc. October 14, 201112
ResultsIncompressible turbulent flow
Objective Function; Minimize Drag
Baseline Design Optimized Design
• Questions?
• Please contact ANSYS Tech support for help in applying this technology
• Questions?
• Please contact ANSYS Tech support for help in applying this technology
© 2011 ANSYS, Inc. October 14, 201115
How RBF‐Morph Works?• Once displacements are defined by the user at the source points, Radial Basis Function interpolation is used to derive the displacement at any location in the space, so it is also available at every grid node.
• The RBF problem definition is mesh independent, same set up can be applied to different meshes
© 2011 ANSYS, Inc. October 14, 201117
RBF‐Morph main features
• Fully integrated within FLUENT and Workbench• Easy to use• Parallel calculation allows to morph large size models
(many millions of cells) in a short time• Mesh independent solution works with all element types
(tetrahedral, hexahedral, polyhedral, etc.)• Superposition of multiple RBF-solutions makes the
FLUENT case truly parametric (only 1 mesh is stored)
– RBF-solution can also be applied on the CAD• Precision: exact nodal movement and exact feature
preservation.
© 2011 ANSYS, Inc. October 14, 201118
Ship hull: Series 60, CB=0.6
external hydrodynamics
multiphase flow (air & water)
ship advancing steadly in calm water
trim and sinkage fixed
displaced volume as constraint
resistance prediction
Objective:Optimization of the hull shapewith no displacement reduction
Reduction of the resistance
Test case description
Conducted by Pranzitelli & Caridi
© 2011 ANSYS, Inc. October 14, 201119
CAD
Mesh ICEM‐CFD
Baseline sim. Fluent
Workbench and RBF‐morph setup
DOE RUNS
Optimization
Final solution
operator
workben
ch
Process
grid cells
Coarse 331,652
Medium 692,984
Fine 1,274,742 CT ∆CT
Coarse 5.81x10-3 -2.52%
Medium 5.94x10-3 -0.34%
Fine 5.96x10-3 0%
Exp.* 5.96x10-3 -
© 2011 ANSYS, Inc. October 14, 201120
CAD
Mesh ICEM‐CFD
Baseline sim. Fluent
Workbench and RBF‐morph setup
DOE RUNS
Optimization
Final solution
operator
workben
ch
Process
Symmetry plane fixedMorphing domain definedEight cross sections specifiedSection deformation applied
© 2011 ANSYS, Inc. October 14, 201121
CAD
Mesh ICEM‐CFD
Baseline sim. Fluent
Workbench and RBF‐morph setup
DOE RUNS
Optimization
Final solution
operator
workben
ch
Process
DX builds a DOE and drives Fluent and RBF Morph
Parameters are defined and transferred to the parameter set bar for use with ANSYS DesignXplorer
© 2011 ANSYS, Inc. October 14, 201122
• Design of Experiments
• 45 Design Points
• Solved in Batch
• Design of Experiments
• 45 Design Points
• Solved in Batch
• Input parameters• Input parameters
• Output parameters• Output parameters
• DOE Settings• DOE Settings
ANSYS DesignXplorer• Results• Results
• Sensitivity analysis• Sensitivity analysis
• Response Surface• Response Surface
© 2011 ANSYS, Inc. October 14, 201123
baseline
optimized
baseline
optimized
• Optimize• OptimizeOptimize with ANSYS DesignXplorer
Baseline Optimized
Fx 6.83N 6.29N
• 7.9% resistance reduction
• No volume reduction
• 7.9% resistance reduction
• No volume reduction
© 2011 ANSYS, Inc. October 14, 201124 *one Intel® i7 quad‐core processor, 2.8GHz
Performance with RBF‐Morph in Workbench:• Mesh generation: 6 man‐hours• Fluent case setup: 1 man‐hours• Baseline simulation (coarse grid): 4 CPU*‐hours• Workbench and RBF‐Morph setup:1 man‐hours• DOE (45 simulations): 45 CPU*‐hours• Optimization: Minutes
8 man hrs
2 CPU days
8 man hrs
2 CPU days
Without Workbench & RBF‐Morph....?• Mesh generation (first mesh): 6 man‐hours• Geometry (CAD) and mesh modification for each case (considering mesh automation in ICEM‐CFD): 1x45 = 45 man‐hours• Cases management (Fluent): 1x46 = 46 man‐hours• Cases execution: 4+45 = 49 CPU*‐hours• use of other optimization tools: ??
~100 man hrs
2 CPU days (optimistically)
~100 man hrs
2 CPU days (optimistically)
© 2011 ANSYS, Inc. October 14, 201126
Preface
• Adjoint solver in ANSYS Fluent 14 is the culmination of several years of R&D effort.
• This project was risky, but the rewards are great for ANSYS clients.
• There were a number of false starts and dead‐ends.• Writing an adjoint solver that meets the needs of the engineering community is not a trivial task.
• We are pleased to have come so far, and look forward to going much further.
© 2011 ANSYS, Inc. October 14, 201127
An adjoint solver allows specific information about a fluid system to be computed that is very difficult to gather otherwise.
The adjoint solution itself is a set of derivatives.• They are not particularly useful in their raw form and must be post‐processed appropriately.
• The derivative of an engineering quantity with respect to all of the inputs for the system can be computed in a single calculation.– Example: Sensitivity of the drag on an airfoil to its shape.
There are 4 main ways in which these derivatives can be used:
1. Qualitative guidance on what can influence the performance of a system strongly.
2. Quantitative guidance on the anticipated effect of specific design changes.
3. Guidance on important factors in solver numerics.
4. Gradient‐based design optimization.
What is an adjoint solution and how do we use those results?
© 2011 ANSYS, Inc. October 14, 201128
GOAL: Identify features of a system design that are most influential in the performance of the system.
EXAMPLE:– Sensitivity of the Drag on a NACA 0012 airfoil to changes in the shape of the airfoil.
– The shape sensitivity field is extracted from the adjoint solution in a post‐processing step.
How to use the results ‐ Qualitative
High sensitivity – changes to shape have a big effect on drag
Low sensitivity – changes to shape have a small effect on drag
© 2011 ANSYS, Inc. October 14, 201129
GOAL: Identify specific system design changes that benefit the performance and quantify the improvement in performance that is anticipated.
EXAMPLE:– Design modifications to turning vanes in a 90 degree elbow to reduce the total pressure drop.
– The optimal adjustment that is made to the shape is defined by the shape sensitivity field (steepest descent algorithm).
– Effect of each change can be computed in advance based on linear extrapolation.
How to use the results ‐ Quantitative
Original P = ‐232.8 PaExpected change computed using the adjointand linear extrapolation = 10.0 PaMake the change and recompute the solution.Actual change = 9.0 Pa
BaselineModified
© 2011 ANSYS, Inc. October 14, 201130
GOAL: Identify aspects of the solver numerics and computational mesh that have a strong influence on quantities that are being computed that are of engineering interest.
EXAMPLE:– Use the adjoint solution to identify parts of the mesh where mesh adaption will benefit the computed drag by reducing the influence of discretization errors.
How to use the results – Solver Numerics
Baseline Mesh Adapted Mesh
Adapted MeshDetail
© 2011 ANSYS, Inc. October 14, 201131
GOAL: Perform a sequence of automated design modifications to improve a specific performance measure for a system
EXAMPLE:– Gradient‐based optimization of the total pressure drop in a pipe.– Flow solution is recomputed and the adjoint recomputed at each design iteration.
How to use the results – Optimization
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30p t
ot[Pa]
Iteration
Initial design
Final design30% reduction in total pressure drop after 30 design iterations
© 2011 ANSYS, Inc. October 14, 201132
Standard CFD Workflow elements– Define a flow problem.– Create a geometric representation of the problem and create a computational mesh.– Setup and solve the flow problem.– Post‐process the results.
If the design is not meeting performance requirements– Use insight, experience and intuition to decide how to select design changes that will improve
the performance of the system
orAdjoint workflow elements
– Use the results to improve the design systematically using one of the 4 strategies outlined– Pick an observation that is of engineering interest.
• Lift, drag, total pressure drop?
– Set up and solve the adjoint problem for this observation for the specific computed flow field• Define adjoint solution advancement controls• Set adjoint convergence criteria• Initialize the adjoint solution field• Iterate to convergence• Post process
How does an adjoint analysis fit into the familiar CFD workflow?
© 2011 ANSYS, Inc. October 14, 201133
– Mesh morphing– Mesh morphing & Adjoint Data– Mesh Morphing, Adjoint Data & Constraints
Supporting Technologies
© 2011 ANSYS, Inc. October 14, 201134
Once a desired change to the geometry of the system has been selected, how is that change to be made?
• Mesh morphing provides a convenient and powerful means of changing the geometry and the computational mesh.– Use Bernstein polynomial‐based morphing scheme discussed earlier
Mesh Morphing
© 2011 ANSYS, Inc. October 14, 201135
• Example: Sensitivity of lift to surface shape
• Select portions of the geometry to be modified
• Adjoint to deformation operation• Surface shape sensitivity becomes control point sensitivity (chain rule for differentiation)
• Benefit of this approach is two‐fold• Smooths the surface sensitivity field• Provides a smooth interior and boundary mesh deformation
Mesh Morphing & Adjoint Data
Flow
© 2011 ANSYS, Inc. October 14, 201136
The adjoint solution is determined based on the specific flow physics of the problem in hand.
The effect of other practical engineering constraints must also be taken into account.
Example:– Some walls within the control volume may be constrained not to move.– A minimal adjustment is made to the control‐point sensitivity field so that deformation of the fixed walls is eliminated.
Mesh Morphing, Adjoint Data & Constraints
Fixed wall
Fixed wall
Moveable walls
© 2011 ANSYS, Inc. October 14, 201137
Current Functionality
ANSYS‐Fluent flow solver has very broad scope
Adjoint is configured to compute solutions based on some assumptions– Steady, incompressible, laminar flow.– Steady, incompressible, turbulent flow with standard wall functions.– First‐order discretization in space.– Frozen turbulence.
The primary flow solution does NOT need to be run with these restrictions– Strong evidence that these assumptions do not undermine the utility of the adjointsolution data for engineering purposes.
Fully parallelized
Gradient algorithm for shape modification– Mesh morphing using control points.
Adjoint‐based solution adaption
© 2011 ANSYS, Inc. October 14, 201138
The adjoint solver is an addon that will be part of the Fluent 14 distribution.
Documentation is available– Theory– Usage– Tutorial– Case study
Training is available.
Functionality is activated by loading the adjoint solver addon module.
A new menu item is added at the top level.
Limitations include unsupported models (porous media, MRF etc.), convergence can be challenging for large cases (5‐10M+ cells) and cases that exhibit unsteady flow or strong shear flows– Stabilized solution advancement algorithm is in place
Current Functionality
© 2011 ANSYS, Inc. October 14, 201139
GUI• Follow as closely as possible the same design layout as Fluent solver– Specify observable– Adjoint solution advancement controls– Residual monitors– Initialization and iteration– Post‐processing: contours, vectors.– Results reporting– Mesh‐morphing with pre‐calculation of expected change in observable.
TUI
User‐Interface
/adjoint> controls morphing/ reporting/monitors/ observable/ run/
/adjoint> controls morphing/ reporting/monitors/ observable/ run/
© 2011 ANSYS, Inc. October 14, 201141
Full discrete adjoint for shape sensitivity
Frozen turbulence
Reduce total pressure drop, P, through system
Total Pressure Drop in a Bend
P = ‐232.8Expect change 10.0
Baseline1
Actual change 9.0P = ‐223.8Expect change 8.9
Actual change 6.9P = ‐216.9Expect change 7.0
2
Actual change 3.1P = ‐213.8
Total improvementof 8%
3
© 2011 ANSYS, Inc. October 14, 201142
Goal is to reduce the total pressure drop through the system
Set up and solve the adjoint system with a total pressure drop objective function
Total Pressure Drop in a Duct
Flow residuals
Adjoint residuals
Flow
Outflow
© 2011 ANSYS, Inc. October 14, 201143
Aggressive adjustment results in a 17% reduction in loss in just one design iteration
Total Pressure Drop in a DuctTotal Pressure Drop (Pa)
Geometry Predicted Result
Original ‐‐‐ ‐22.0
Modified ‐14.8 ‐18.3
© 2011 ANSYS, Inc. October 14, 201144
The adjoint solver will be released with R14
An adjoint solver computes sensitivity data that can be used to aid with design decisions in 4 main ways:
1.Qualitative identification of critical parts of the system of interest.2.Quantitative predictions of the optimal choice for a design change and a prediction of the effect of that change.
3. Aiding in the numerical analysis of the flow solution to improve solution quality.
4.Gradient‐based optimization.
Supporting technologies such as mesh morphing, and the application of design constraints, are seen as important.
The adjoint solver for the present release is limited to steady incompressible flows, with other restrictions on models.
Summary