Topology Optimization for Liquid Cooled Heat Sink Design
Hao Li, Xiaohong Ding*, Dalei Jing, Min Xiong
Mechanical EngineeringUniversity of Shanghai for Science and Technology (USST)
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Passive cooling devices (natural convection)
TopOPt for heat sink design
Page 3H. LI, USST, ME, Struct. Anal. & Optim. LAB
TopOPt for heat sink designActive cooling devices (forced convection)
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TopOPt for heat sink design
Common in TopOPt for heat sink design:
• Thermo-fluidic problems• High nonlinear• Topology (layout) determines the response of structure
We need to find the OPTIMAL TOPOLOGY (LAYOUT) to enhance the heat transfer rate.
Our project use TOPOLOGY OPTIMIZATION to come up with the optimal cooling channel layout.
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Structural Topology Optimization
{ }1 2 min max
01
: , , ( 1)
:
. . :
TN
T T
Ne e
e
Find X x x x x x x
Min C F U U KU
s t V fV x v
F KU=
= ≤ ≤ =
= =
= =
=
∑
Design problem Discretized elements Optimal topology
Bendsoe (1989), Zhou and Rozvany (1991), Miejnek (1992)
Interpolation function:
0( )1
pe eE x x E
p=
>
𝑥𝑥
𝐸𝐸
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Topology optimization
Common in TopOPt:
• Objective function i.e. compliance, flow dissipation, sound pressure
• Design variable• Constraint
i.e. volume fraction
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Fluid problems
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Navier-Stokes equations
Incompressible Navier-Stokes equation for porous flow
( ) ( )( )1ReT
p α∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ⋅∇ = ∇ − + ∇ + ∇ − u u u u uI
0∗ ∗∇ ⋅ =uNon-fluid (solid) domain
Fluid domain
Interpolation function
( ) ( )max1q
xq
γα α
γ∗ ∗ −=
+
γ=0, α→∞, F→∞ u=0
γ=1, α→0, F→0 NS equation
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2D flow distribution problem
( )
in
*
[0,1]minimize ,
. . ,
, i=1,...,n,
1,i
T
f
i i in
in
d
s t d V Vol
d FR V
p u d
γα
γ
∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗
Ω
ΩΩ
∗
Γ
∗
Γ
∈ Φ = ∇ ⋅ ∇ +∇ + ⋅ Ω
Ω ≤ ⋅
⋅ Γ = ⋅
Γ =
∫∫∫∫
u u u u u
u n
FR1= FR16=1/2, FR2= FR14=1/3,FR3= FR15=1/6,FR4= FR5= FR12= FR13=1/4,FR6= FR7= FR9= FR10=1/5,FR8= FR10=1/10
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2D flow distribution problem
Iterative process (Vf=40%)
Optimal channel layout
Vf=40% Vf=60%
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Thermo-fluidic problems
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Navier-Stokes equations
Incompressible Navier-Stokes equation for porous flow
( ) ( )( )1ReT
p α∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ⋅∇ = ∇ − + ∇ + ∇ − u u u u uI
0∗ ∗∇ ⋅ =u
( ) 22
RePr (in fluid domains)
0 (in solid domains)
T T
T Q
∗ ∗ ∗ ∗ ∗
∗ ∗ ∗
⋅∇ = ∇
=∇ +
u ,
,
Energy equation
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2D heat exchange problem
in
[0,1]maximize (1 ) (1 ) ,
. . ,
1.
f
in
h T d
s t d V Vol
p u d
γγ
γ
∗ ∗
Ω
ΩΩ
∗ ∗
Γ
∈Φ = − − Ω
Ω ≤ ⋅
Γ =
∫∫∫
Page 14H. LI, USST, ME, Struct. Anal. & Optim. LAB
2D heat exchange problem
Iterative process (Vf=40%)
Optimal channel layout
Vf=40% Vf=60%
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Flow and Thermal Performance
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Experimental Verification
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Reference case
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Reference case
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Temp. distrib. (Exper. VS Numerical)
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Conclusions
• Presented industrial application of TO in fluids, thermo-fluidic problems
• We are at the verge of being able to send TO results to manufacturing
• 3D channels with 3DP technology• TO considering turbulent flow
Future works…
Thanks for your attention!
Q&A
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