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tao April 1, 2003 20:34

solving non-newtonian fluid

I want to solve the flow with non-newtonian fluid in a tube using numerical method. The carrau model is used as a constitute equation. mu=viscosity gamma=shear rate

(mu-mu_inf)/(mu_0 - mu_inf) = (1 + (lamuda*gamma)^2)^((n-1)/2)

The governing eq.

0=-dp/dz + 1/r * d(mu*r*dw/dr)/dr

I would like to solve this, but have no idea. For newtonian fluid, it's so simple to analyze this. The constitue eq. and governing eq. are coupled. How can I deal with this problem using numerical approach(tips or algorithm)? If anyone know how to solve this or some open sources availalbe on site or at ftp, please let me know. I would much appreciate your help.

Thanks in advance. Peace in God.

xueying April 2, 2003 13:37

Re: solving non-newtonian fluid
Your problem equations are: (1)constitutive equation; (2)momentum conservation equation; (3)mass conservation equation.

Solve these three equations by Newton method since they are non-linear. Your unknowns are pressure, velocity and viscosity. You don't need boundary codnition for your constitutive equation since it's a linear algebraic equation.

From mathematical view, this way should work. I don't know if it's practical or not in your case.

tao April 2, 2003 20:01

Re: solving non-newtonian fluid
I just want to know the solving procedure in numerical approach. Normally, I prefer interative method(SOR), not newton method.

Tom April 3, 2003 04:48

Re: solving non-newtonian fluid
Why not just solve it by iteration/quadrature:

(1) Guess w (w_g) and calculate mu

(2) update w (w_*) by integrating the momentum equation (it's a simple quadrature).

(3) obtain a new guess for w from w = (1-q)w_* + q*w_g

(4) repeat from 1 until converged.

In 3 q is a relaxation parameter used to stop the iteration oscillating (which it will do if q=1 ).

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