KR419: How can we model forced diffusion in binary mixtures (single phase)? (Solution ID: 672)


ANALYSIS
J = J_ordinary + J_forced

J1_ordinary = -rho D12 Grad yi

J1_forced = -rho^2 * w1 * w2 * y1 * y2 * D12 * (F1 - F2) / (P * W * W)

where

w1 = mol wt 1
w2 = mol wt 2
y1 = mass fract 1
y2 = 1-y1
W = mol wt mixture
F1 = Force Vector on species 1 (N/kg)
F2 = Force Vector on species 2 (N/kg)
P = pressure

This is solved by UDF

species equation source is equal to

S = - DIV (J1_forced)

Problem is solved using UDS:
UDS(0) = y1
UDS(1) = xcomp of J1_forced
UDS(2) = y-comp of J1_forced
UDS(3) = z-comp of J1_forced

In Define Adjust function, we
* compute J_forced.
* compute grad of components of J_forced (nine terms stored in memory)(
* add appropriate components to get divergence: div J = d(J1x)/dx + D(J1y)/dy + d(J1z)/dz

Source term = Div J is stored in UDM(0)

For boundary condition, at a wall: J.n = 0

J = J_ord + J_forced,

thus

Flux(1) = J1_ord . n = - J_forced . n

Where J1_forced is evaluated at the wall

So far only wall boundary conditions are in the UDF. Others can be added as necessary.





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