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1
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!
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