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Fluid Leakage across a Pressure Seal
Ruby R PGaurav KulkarniUdayan Kanade
Mathematical Model Simulation→
Simulation Mathematical Model→
Multi-Scale Modeling (Homogenization)
● Mathematical theory of coordination between phenomena happening at different scales
Gasket Seals
Gasket Seals
Leakage rate depends on:● Geometries● Materials● Surface characteristics● Clamping forces● Fluid pressure
Fluid Leakage
Fluid Leakage
Homogenization
P
q
Homogenization
P
q
q = a ∇P
Homogenization
P
q
q = a ∇P
a = a (S, P, |∇P|)
Homogenization
P
qq = a ∇P
a = a (S, P, |∇P|) S
S
P
q = a ∇P
a = a (S, P, |∇P|)
Geometry of microcaverns depends only on S – P
Geometric Result
P
q
S
S
P
Idealization
Mechanical Simulation
Fluid Domain
Fluid Flow
Correlation
For a givengeometry
● q / P |∇P| is constant
New Formula
● q = f (S – P) P |∇P|
For a given geometry● q / P |∇P| is constant
New PDE!!!
P
q
● q = f (S – P) P |∇P|
New PDE!!!
P
q
● q = f (S – P) P |∇P|
● ∇·q = 0
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
)
What we have achieved
P
q
q = a (S, P, |∇P|) ∇P
● q = f (S – P) P |∇P|
∇·q = 0
S
S
P
Thank you!
q = a (S, P, |∇P|) ∇P
● q = f (S – P) P |∇P|
∇·q = 0
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