topology optimization for liquid cooled heat sink designŽ... · 2019. 5. 17. · topology...
TRANSCRIPT
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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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Page 2H. LI, USST, ME, Struct. Anal. & Optim. LAB
Passive cooling devices (natural convection)
TopOPt for heat sink design
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Page 3H. LI, USST, ME, Struct. Anal. & Optim. LAB
TopOPt for heat sink designActive cooling devices (forced convection)
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Page 4H. LI, USST, ME, Struct. Anal. & Optim. LAB
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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Page 5H. LI, USST, ME, Struct. Anal. & Optim. LAB
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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Page 6H. LI, USST, ME, Struct. Anal. & Optim. LAB
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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Page 7H. LI, USST, ME, Struct. Anal. & Optim. LAB
Fluid problems
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Page 8H. LI, USST, ME, Struct. Anal. & Optim. LAB
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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Page 9H. LI, USST, ME, Struct. Anal. & Optim. LAB
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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Page 10H. LI, USST, ME, Struct. Anal. & Optim. LAB
2D flow distribution problem
Iterative process (Vf=40%)
Optimal channel layout
Vf=40% Vf=60%
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Page 11H. LI, USST, ME, Struct. Anal. & Optim. LAB
Thermo-fluidic problems
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Page 12H. LI, USST, ME, Struct. Anal. & Optim. LAB
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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Page 13H. LI, USST, ME, Struct. Anal. & Optim. LAB
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 =
∫∫∫
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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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Page 15H. LI, USST, ME, Struct. Anal. & Optim. LAB
Flow and Thermal Performance
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Page 16H. LI, USST, ME, Struct. Anal. & Optim. LAB
Experimental Verification
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Page 17H. LI, USST, ME, Struct. Anal. & Optim. LAB
Reference case
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Page 18H. LI, USST, ME, Struct. Anal. & Optim. LAB
Reference case
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Page 19H. LI, USST, ME, Struct. Anal. & Optim. LAB
Temp. distrib. (Exper. VS Numerical)
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Page 20H. LI, USST, ME, Struct. Anal. & Optim. LAB
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…
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Thanks for your attention!
Q&A
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