Adjoint Solver Workshop Why is an Adjoint Solver useful? Design and - PowerPoint PPT Presentation

Adjoint Solver Workshop

Why is an Adjoint Solver useful? • Design and manufacture for better performance: e.g. airfoil, combustor, rotor blade, ducts, body shape, etc. by optimising a certain characteristic • CFD has the capability to explore the design space • Sensitivity analysis may be used to provide insight into how best to optimise the design

How can we explore a design space? • STAR-CCM+ already used for sensitivity and optimisation using DOE approaches with surface response and optimum search – Coupled with ISIGHT, modeFRONTIER, Heeds, Optimus, and Optimate – Pros: Straightforward generation of information by solving multiple design points to find optimal set of parameters for given objectives – Cons: Prohibitively expensive when the number of parameters goes up • i.e. for CCD: 1p-> 5 dp / 2p-> 9 dp / 5p-> 27 dp / 20 -> 553 dp • STAR-CCM+ adjoint method provides a more efficient approach to sensitivity analysis where cost is independent of the number of design parameters – Gradient method based on differentiating the “primal” equation – Can be used in shape optimisation, flow field insight, uncertainty quantification, and inverse problems

What is the Adjoint Method? • Helps understand influence of parameter variations on the solution – Examples • If I change the shape of my duct, what happens to the pressure drop? • If I change my inlet conditions, will flow uniformity improve at the outlet? • If I change my airfoil shape will it produce more lift? • How sensitive is my flow to changes due to manufacturing tolerances • The pressure loss of my system is too high, what are the main drivers of this?

Traditional Analysis Workflow • How do I know the effect on solution if… – Geometry changes? – Mesh changes? – Boundary/physics variation? • Traditional answer ends up in running many cases – N configurations = N Cases – Effects of parameter changes only understood after multiple iterations of analysis cycle Setup Setup Run flow Run flow Analyze Analyze geometry, geometry, solver solver results results physics physics Setup Setup Run flow Run flow Analyze Analyze geometry, geometry, solver solver results results physics physics Setup Setup Run flow Run flow Analyze Analyze geometry, geometry, solver solver results results physics physics

Adjoint Method Workflow • Adjoint provides design insight – Offers guidance towards improving system’s performance – Gives insight into relative influence of variables on objective • Adjoint is effective for problems with many design variables – Far fewer design iterations needed – Faster route to optimised design Setup Run Run flow Analyze Set Cost Analyze Update Run flow Analyze geometry, adjoint solver results Functions results model solver results physics solver STAR-CCM+ Adjoint Solver

What the Adjoint Method Provides Input User Data Choose how to modify our simulation Initial geometry, Surface/volume mesh Deform shape, change boundaries etc Physical conditions (boundaries, flow models) Run Flow Solver Solve Adjoint Flow & Mesh Provides output data for given inputs – Take flow solution and provide sensitivity of Pressures, Velocities, Forces, Drag, objectives to flow & geometry parameters Pressure Drop Choose Simulation Objectives Objectives become adjoint cost Reduce pressure drop, maximize lift, functions velocity uniformity etc

Examples of typical uses • Shape optimisation – Part design • Determine best design based on shape modifications • Drive the parametric changes – Leverage external optimisation code • Coupled with gradient-based optimisation method • Examples 1. Car-body shape analysis to improve external aerodynamics behavior 2. Optimise the geometry of three-way catalyst pipes • optimisation for satisfying (A) Velocity uniformity in front of catalyst and (B) Velocity value at the specific point conditions – Maximizing A, B, A and B – Maximizing A and minimizing B – Maximizing B and minimizing A

STAR-CCM+ Adjoint Solver • Available in STAR-CCM+ v8.04 onwards • Delivered as a standard feature – No additional license • Aggressive development schedule – lots of new features …

Compatibility with Primal Flow Solution • Adjoint solver provides sensitivities based on the following models: – Coupled implicit flow and fluid energy solvers – Steady State – Moving Reference Frame – Multi-region – Inviscid, laminar and frozen turbulence – Single component gas and liquid – Ideal gas (compressible) or constant density (incompressible) – Constant material properties • Use of the double precision version of STAR-CCM+ is recommended

Adjoint Solver Capabilities • Flow and mesh adjoint solvers • Fully parallel • 1st or 2nd order spatial discretisation solution • Defect correction solver method • GMRES – Krylov solver method – Optional method for tough to converge cases • Arbitrary number of cost functions – Force (drag, lift), Moment – Pressure drop – Flow uniformity • Sensitivities of cost functions with respect to – Flow residuals • Momentum equations, continuity, etc – Design points • Gradients with respect to user defined design points • Mesh morphing based on design point relocation

Adjoint Cost Functions • Cost functions represent the engineering objectives of the simulation – An arbitrary number may be setup – It is possible to view the flow and mesh adjoints for each cost function – They may be created on physical boundaries or interfaces • Force (e.g. Lift, Drag) & Moment – Takes information from force or moment report with usual inputs • Pressure drop – Difference of mass flow averaged total pressure between two groups of boundary surfaces • Specify high and low pressure boundaries • Uniformity ratio • Deviation of local normal velocity from mass flow averaged value

Adjoint Outputs • Adjoint flow data – Sensitivity of cost functions with respect to x, y and z momentum • Allows us to understand how a change in the velocity field affects the cost function of interest • E.G. Will increasing inlet velocities of my duct harm the uniformity at the outlet? – Continuity • Sensitivity of cost functions to changes in the mass of the system • E.G. if I insert a boundary layer suction device will my drag change? – Energy • Effects of changing thermal properties on the cost function • E.G. How will energy affect my pressure drop as a result of changing my fluid’s density?

Adjoint Outputs • Adjoint mesh data – The adjoint mesh solver provides sensitivities with respect to mesh coordinates – This allows you to better understand the affect of mesh structure on the cost function of interest • E.G. Which areas of mesh have the greatest effect on my lift force and where should I pay attention to adequately capturing flow structures • Boundary parameter sensitivity reports – These reports return the gradient of the cost function with respect to changes in boundary inputs – Gradients are only returned for inputs for the boundary type specified – This allows you to better understand the influence of boundary conditions values on the cost function of interest • E.G. If I change the velocity on my inlet, how will my uniformity change?

Example Case

Front Wing optimisation • Goal: Increase the downforce on race car front wing • Case Details: – 100 kph – 700k polyhedra – Cost function based on force report on lower element

Solution Method • Unconstrained steepest decent method used • 524 design points created in a “net” around the wing – Gradients calculated at design points – Displacements calculated by scaling gradients by an alpha of 5e-5 Run Primal Flow Solution Run Adjoin Flow Solution Calculate Mesh Sensitivities Scale Gradients to Calculate Offset Positions Morph Mesh

Results – Wing Profile

Results - Downforce Front Wing Lower Element Downforce 480 475 470 465 Downforce [N] 460 455 10% Improvement in 450 Downforce Across 10 Design Iterations 445 440 435 430 1 2 3 4 5 6 7 8 9 10 Design Iteration

Using the STAR-CCM+ Adjoint Solver

Running an Adjoint Analysis • Run primal flow solution – Attention must be paid to convergence • Enable adjoint flow solver – Selection via physics continua model selector • Choose cost functions – Available via right click on “Adjoint cost functions” • Run adjoint flow solver – Right click on adjoint flow model to step or run • Run adjoint mesh solver – Right click on adjoint mesh “compute mesh sensitivity” to run • Visualize results – Scalars and vectors grouped under “Adjoint” then by cost function

Demonstration

Summary • Sensitivity analysis may be used to provide insight into how best to optimise a design • STAR-CCM+ provides an integrated adjoint solver – The solver provides both 1st and 2nd order adjoints for improved accuracy • Requires no additional licenses • Extensive documentation and tutorials • CD-adapco is actively involved with our partners to integrate adjoint with optimisation tools • Aggressive adjoint development schedule will be maintained, delivering new features

Thank You