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wall slip law for newtonian fluid

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Old   April 19, 2012, 12:13
Default wall slip law for newtonian fluid
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I am trying to input a wall slip law for a newtonian fluid in a pipeline.
The law has a yield stress limit \tau_0.
When the yield stress is less than \tau_0, there is adhesion of the fluid to the wall.
When the yield stress is greater than \tau_0, there is a slip velocity at the wall like :
u_{wall}=\mu*\frac{\partial u_z}{\partial r}

The udf is here :
#define Cf 1			/* friction coefficient */
#define TAU0 0.2			/* limit yield stress for slipping */

DEFINE_PROFILE(wall_velocity_x, thread, position)
	face_t f;
	Thread *t0;
	cell_t c0;
	double VC[ND_ND];
	double TAUxy, VC_MAG, vg, mu;
	double dudy;
	begin_f_loop(f, thread)
		t0 = THREAD_T0(thread);		/* adjacent cell thread to f */
		c0 = F_C0(f, thread); 
		dudy = C_DUDY(c0,t0);
		mu = C_MU_L(c0,t0);	
		VC[1]=0;				/* stress vector's y componant*/
		if (NV_MAG(VC)==0)		/* stress vector's magnitude */
			{VC_MAG = 0.00000001;}
		else {VC_MAG=NV_MAG(VC);}
		if ( VC_MAG < TAU0)
			F_PROFILE(f, thread, position)=0;
		else	{
			F_PROFILE(f, thread, position)=vg;
	end_f_loop(f, thread)
At first I run Fluent with a "wall" boundary condition. And after some steps, I change the wall to a "velocity inlet" boundary condition in order to put the udf as a component of the axial velocity.

But, the continuity residual goes to 10^{20}.

I think the reason is the fact that I use the derivative of the adjacent cell of the boundary to put it as the value of the face of the boundary. But I don't know how to make it in an other way.

Help me please !
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