Hello my name is Chris Hill I‘m the

chief

technologist for the fluids business unit

here at Ansys my

collaborator in this work is doctor Min Xu

who is a

senior

R&D engineer also in the fluids business

I'm going to talk today about adjoint methods in

optimization technology

First of all I'll give you an overview of the

adjoint method how it applies to CFD and

shape optimization

what kind of things can be optimized what

physics is

supported how an adjoint solution is

computed and how

we apply constraints to the changes in the

design and

apply morphing

I move on to give some optimization examples

and then

close with a description of data informed

turbulence modeling which

is an emerging new area

So the adjoint method for CFD involves

problems with

a large design space if you only have a few

parameters then adjoints probably are not for

you

So it's a tool to provide detailed

sensitivity data and

the classic example here is shown in the

upper right

figure where you see the sensitivity of the

lift on

an airfoil to the shape of the airfoil and it

shows the classic trend of increasing camber

and increasing lift

increasing camber and increasing angle of

attack to generate

more lift

So the adjointmethod gives you the

derivatives of some

engineering quantity of interest with respect

to all of the

inputs to the problem this includes the flow

boundary conditions

the geometry the materials and even the model

parameters used

to define the modeling in the calculation

And of course you can use these derivatives

in many

ways shape and topology modification are a

very good example

mesh adaption

What if studies for geometry or boundary

condition variations robust

design and robust optimization

Now whereas the airfoil problem is perhaps

rather obvious

and classical the

example shown in the lower right over heat

exchanger is

not so obvious here we're trying to reduce

the pressure

drop and increase the heat transfer rate and

so we

have two objectives they may be competing but

we can

go through an optimization procedure in an

attempt to improve

both of them and in this case we're able to

do that and it produces rather a non obvious

change

to the design to achieve that goal

So the shape optimization procedure

involves an optimization loop

and the elements of that loop are CFD

analysis where

you first compute the CFD solution in a

classical traditional manner

And then proceed to run the adjoints solver

to compute

derivative information for some quantities

From there you can get the shape sensitivity

and apply design constraints that may limit

the application of

that sensitivity using the design tool you

can update the

geometry using a morpher and proceed around

the loop again

with your new updated geometry and as you do

so

the performance of the system improves until

eventually you get

to a local optimum

Then you can export the revised geometry as

an STL

file

All of this is controlled by our gradient

based optimizer

that you can see on the left as the main

panel for the optimizer

So what can be optimized are generally

quantities of interest

include things like lift and drag and

pressure drop those

are common goals for an optimization process

but there can

be many others for example flow uniformity

you may want

to perform a minimization or maximization of

some surface or

volume integral like the mean temperature in

your domain and

the many other options that are available

within the adjoints

solver for you to define the quantity that most

matters to you

Rarely is it a single objective that matters

usually you're

interested either in one objective at

different operating conditions or

multiple objectives or multiple objectives at

different operating conditions all

of these are supported in fluent adjoint

So for example the multiple operating point

scenario is shown in this multi point fan

optimization

We're interested in increasing the efficiency

of the fan with multiple

mass flow rates it would not simply be useful

to

optimize at one flow rate and find that the

efficiency

has deteriorated at others so we want a broad

spectrum

of improvement

Likewise on the lower right figure you see

the maximization

of lift and minimization of drag for a

geometric shape

When it comes to supported physics we're

looking at steady

single phase flows with constant property

fluid and a compressible

ideal gas so the example here is shown for

transonic

flow over an airfoil or wing of an aircraft

is

a classic aerodynamic design problem

We can also handle thermal problems including

and

conjugate heat transfer we're going to have

fluid solid porous

and MRF zones so we can do fan problems you

can handle all kinds of meshes and most kinds

of

boundary conditions We also have the adjoint

the GEKO turbulence

model available it's not something that is

necessarily a good

idea for all problems but there are

problems where

solving the adjoint to the turbulence is

valuable

When it comes to computing in a joint

solution

there is a computational cost you're getting

a large block

of interesting information about your

solution

And it involves an iterative solution

advancement procedure that minimizes

some adjoint residuals and typically we're

looking at about the

same computational time and memory as for a

single flow

solution so it's kind of doubles your time

compared to

the original flow solution but you end up

with a vast

array of interesting sensitivity information

Robustness of adjoint solutions has

traditionally been a challenge over

the last 10 years as we've developed the

adjoint solver

we have been able to overcome these

issues

to a large extent we have some modern schemes

based

on dissipation and residual minimization that

now work extremely well

the residual minimization scheme does require

some extra memory

We've reached the point where many adjoint

problems can be

solved successfully with just a single mouse

click

Now inevitably there are design constraints

that are applied to

in design problems and we need to be able to

handle those and we can

So we can actually optimize problems in the

presence of

design constraints typical constraints

involve symmetry or invariants and conditions

of smoothness may also apply on the

deformations

We often find that limits on motion are

desirable so

you can introduce a bounding surface to

confine the motion

of your geometry and of course thick surfaces

are commonly

required in the design definition

So now you have the sensitivity data and

constraints and

you need to be able to reconcile these two to

come up with an optimal design change in the

presence

of the constraints Once you have that we

apply mesh

morphing to change the computational mesh and

the mesh morphing

technology is not represented very well by

that single item

line item on the slide there but there's a

considerable

amount of mesh morphing technology that comes

into play to

successfully modify the geometry and the mesh

without introducing poor

quality into the mesh

We must of course find pathways back to CAD

if

you can't get the new design back into the

CAD

system you can't build it so we need to be

able to get back to CAD and exporting of

modified

surfaces as STL files is one way that works

quite well

So here's the first optimization example this

is an internal

flow where we have two flow streams that are

mixing

one hot one cool and we would like to ensure

that the mixing is maximized but also

that the

variance of the velocity of those four

outflows is reduced

So we go through this optimization cycle of

30 design

iterations

And compute the adjoints for velocity

variance and temperature variance

and blend them together and you were able to

reduce

velocity variance by 35%

and the temperature variance by 80%

And you see on the left the temperature plots

on

the geometry between the original and the

optimized shape

and the change to the actual geometry is

rather subtle

here but it has a dramatic effect

And the adjoint gives us the strategic guidance

on how

to make that happen

Here's an example of an internal flow

Where we're trying to reduce the

pressure drop

And the mass flow variance or the velocity

profile variance

at the outlet

But at the same time we have a constraint

that

there is a limiting geometry as shown on the

left

side by the green boxes and our geometry must

not

pass through those limiting surfaces so this

is like a

packaging limitation

So we can go through a sequence of design

iterations

and we find the geometry changes the pressure

drop goes

down the form of the velocity at the outflow

improves

until eventually we have improved the

pressure drop by 91%

on the flow variance by 94 this is fully

automated

using the optimizer

And when you're done you have the picture on

the

right as compared to the picture on the left

when

you began and this is the total pressure on

the

surface of the geometry so you see those red

total

pressure

high total pressures are now gone in the

right hand

picture

This is a classic external aerodynamics

optimization problem for a

vehicle here we're interested in reducing the

drag on the

vehicle

And by sequence of design iterations and

modifications being made

to the hood of the vehicle and on the left

you see the initial and lower left the

optimized forms

So it introduces an interesting dimple on the

front of

the hood and also the form of the hood is

modified up against the windshield

The lower right figure you see a plot of the

high sensitivity regions on the vehicle and

so it picks

out the wing mirror and the a pillars and the

tires and other interesting regions of the

vehicle

If morphing is not sufficient then we need to

look

for dramatic design changes not achievable

with morphing and topology

optimization offers such an avenue so the

adjoint solutions provide

guidance on the sensitivity to the effect of

introducing new

solids or removing them indeed so here we

have an

example of a plenum with three inlets and a

single

outlet and we look for changes to the design

region

as shown such that will end up with greater

swirl

in the flow and spontaneously we end up with

this

solid that looks remarkably like a mixer

So this can lead to unusual or unexpected and

non

intuitive designs

Finally we have the subject of data informed

turbulence modeling

and in this scenario we have experimental

data available and

we notice that the computed and experimental

results are not

the same and so we use the adjoint compute

the derivative of that difference with

respect to the model

parameters for the turbulence model and then

make local optimal

adjustments to those parameters so that the

experimental data is

matched

Now a key step here is the generalization of

what

has been learned by this process and so a

human

expert in turbulence modeling can take good

advantage of this

to come up with a better turbulence model

Alternatively we

could look to machine learning to guide a

model modification

If you now apply this modified model to a

family

of problems you find that are distinct from

the original

problems you can find that you get improved

agreement with

experiment

So we've looked at the adjoint method giving

you an

overview and some optimization examples and

closed with a brief

discussion on data informed turbulence

modeling thank you for your

attention