Ruby R P Gaurav Kulkarni Udayan Kanade · Ruby R P Gaurav Kulkarni Udayan Kanade. Mathematical...
Transcript of Ruby R P Gaurav Kulkarni Udayan Kanade · Ruby R P Gaurav Kulkarni Udayan Kanade. Mathematical...
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Fluid Leakage across a Pressure Seal
Ruby R PGaurav KulkarniUdayan Kanade
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Mathematical Model Simulation→
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Simulation Mathematical Model→
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Multi-Scale Modeling (Homogenization)
● Mathematical theory of coordination between phenomena happening at different scales
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Gasket Seals
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Gasket Seals
Leakage rate depends on:● Geometries● Materials● Surface characteristics● Clamping forces● Fluid pressure
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Fluid Leakage
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Fluid Leakage
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Homogenization
P
q
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Homogenization
P
q
q = a ∇P
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Homogenization
P
q
q = a ∇P
a = a (S, P, |∇P|)
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Homogenization
P
qq = a ∇P
a = a (S, P, |∇P|) S
S
P
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q = a ∇P
a = a (S, P, |∇P|)
Geometry of microcaverns depends only on S – P
Geometric Result
P
q
S
S
P
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Idealization
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Mechanical Simulation
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Fluid Domain
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Fluid Flow
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Correlation
For a givengeometry
● q / P |∇P| is constant
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New Formula
● q = f (S – P) P |∇P|
For a given geometry● q / P |∇P| is constant
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New PDE!!!
P
q
● q = f (S – P) P |∇P|
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New PDE!!!
P
q
● q = f (S – P) P |∇P|
● ∇·q = 0
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q = f (S – P) P |∇P|
0 5000 10000 15000 20000 25000 300000.00E+000
2.00E-021
4.00E-021
6.00E-021
8.00E-021
1.00E-020
1.20E-020
1.40E-020
1.60E-020
1.80E-020
Conductance parameter f as a function of S-P
S - P (Pa)
f (kg
/s‧
Pa²
)
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What we have achieved
P
q
q = a (S, P, |∇P|) ∇P
● q = f (S – P) P |∇P|
∇·q = 0
S
S
P
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Thank you!
q = a (S, P, |∇P|) ∇P
● q = f (S – P) P |∇P|
∇·q = 0