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Adjoint Shape Optimization Example #1 using OpenFOAM

- Target Velocity Profile at Outlet -

Fumiya Nozaki

Last Updated: 11 August 2014

English

Keywords： • Continuous Adjoint • Shape Optimization • OpenFOAM

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Optimization objective

Inlet

Outlet

Fixed velocity: Parabolic profile

Fixed pressure

Target velocity profile @ outlet：

Parabolic profile

Change shape to obtain the target velocity profile @ outlet

• Laminar flow • Air @ 20℃

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Objective function

𝐼 = 𝑐

2𝒖 − 𝒖𝑡𝑎𝑟𝑔𝑒𝑡

2 𝑑𝛤

𝑜𝑢𝑡𝑙𝑒𝑡

Difference between the calculated velocity and target velocity profile

Calculated by simpleFoam

Target velocity profile

Repeat shape modifications to get smaller value of 𝐼

Adjoint method gives this information

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Sensitivity map

Positive sensitivity area ⇒ Inward surface displacement improves the objective

Sensitivity distribution

Negative sensitivity area ⇒ Outward surface displacement improves the objective

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Shape comparison between baseline and modified geometry

baseline modified

Shape modifications

20 times

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Outlet velocity distribution

baseline modified

Improved by 64%

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Thank You!