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NS-fan June 28, 2005 17:02

Slip boundary conditions
 
Background: For a given Knudsen number range, the N-S equation viability can be extended into rarefied flows with the use of slip/jump conditions for velocity and temperature. With such, there's a finite difference between the gas particle velocity and temperature (T_s and u_s) adjacent to the wall and the wall itself (T_s and u_s).

How are normal gradients for temperature calculated from the first node next to the wall for these slip conditions? Is it T_grad = (Tnode - T_s)/x ? Or is it T_grad = (Tnode - T_wall)/x ? x is the normal outward coord. from the wall.

Also how is T_s obtained if we have an adiabatic wall?

Any sources would be appreciated.

NS-fan June 29, 2005 12:44

Re: Slip boundary conditions
 
My question put alternatively:

- Adiabatic wall - There's a thin Knudson layer along the wall with restricted communication of molecular energy between the wall and fluid above the Knudson layer - T_s taken at top of Knudson layer (is this so?)

Does the above mean T_s = T_wall??? I'm trying to look beyond the obvious in this esoteric physical situation...

Anton Lyaskin July 1, 2005 04:35

Re: Slip boundary conditions
 
No, T_s is not equal to T_wall. If you'll waight till 3rd of July I'll provide you a reference :)

NS-fan July 1, 2005 13:46

Re: Slip boundary conditions
 
thanks!

Anton Lyaskin July 5, 2005 06:42

Re: Slip boundary conditions
 
Sorry, I'm a bit late :)

The formulas are

Velocity U_s = ((2-s)/s)*lambda_u*(dU/dn)_w

Temperature T_s = T_w + ((2-alfa)/alfa)*lambda_t*(dT/dn)_w

lambda_u = 2*mu/(ro*c) - meen free path for momentum,

lambda_t = 2*k/(ro*c*c_v) - meen free path for energy,

c = sqrt(8*R*T/pi) - meen molecular speed,

s - accomodation coefficient for momentum,

alfa - accomodation coefficient for energy

I'm citing this from the following paper

M. Giangi, F. Paglia, F. Stella, A. Nanni, A CONTINUUM MODEL FOR THE STUDY OF A SLIP FLOW REGIME, 4st International Conference on Computational Heat and Mass Transfer

(I can send you a copy if you need), and the reference is to

Wang, W.L. and Boyd, I.D., 2003, Hybrid DSMC-CFD Simulations of Hypersonic Flow Over Sharp and Blunted Bodies, AIAA Paper 2003-3644, June.

NS-fan July 5, 2005 12:15

Re: Slip boundary conditions
 
Anton, you are a hero. Please send to motec383@yahoo.com and cc to STAGED@email.sae.org

cheers

ameerrona October 21, 2010 09:00

slip_velocity
 
dear Anton would u pls send me the paper

M. Giangi, F. Paglia, F. Stella, A. Nanni, A CONTINUUM MODEL FOR THE STUDY OF A SLIP FLOW REGIME, 4st International Conference on Computational Heat and Mass Transfer

on muaddi13@yahoo.com

thanx in advance


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