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