## Fluids

#### Anisotropic Porous Medium (Time Step Size and Momentum Sinks)

• rkoomul
Subscriber

Hello,

I am trying to simulate flow through an anisotropic medium with very low permeability.  The flow domain consist of an inlet pipe, a porous region, and an outlet pipe.   The permeability of the porous medium along the axis of the pipe (z-axis) is 1.0E-14 m^2 and along the other two directions are 1.0E-18 m^2, and these numbers are coming from the published data on the medium.  I have three questions on how to do the simulation.

• 1)      I set the Viscous Resistance for the porous zone as the inverse of the permeability under Cell Zone Conditions, and set zero as Inertial Resistance. The diameter and the length of the porous medium are 10 cm, the inlet velocity is 0.001 m/s, the flow is assumed to be laminar.  The maximum time step that I could use without crashing the code is 1.0E-06 seconds.  I tried different numerical methods (SIMPLE, SIMPLEC, and PISO), and there is no change in the maximum time step that I could use.  I need to run the simulation for a total of 6 hrs (real time), this will result in 21600 million time steps.   Is there any way to increase the time step size?

• 2)      I changed the Porous Formulation from Superficial Velocity to Physical Velocity, but the time step size constraint is even bigger.  The maximum time step that I could use is 1.0E-09 seconds.  Is there any way to increase the time step size?

• 3)      In the real problem, the permeability is function of the spatial location.  The user’s manual suggest to use momentum source to handle this.  So, I tried to test it with the above described problem.  I created three UDFs to add momentum sinks in each direction. For the sink in x-direction, I added the following lines in the UDF.

mu = C_MU_L(c, t); /*laminar viscosity */

Dxx = 1.0E+18;

Dxy = 0.0;

Dxz = 0.0;

source  = -(Dxx*mu*C_U(c,t)+ Dxy*mu*C_V(c,t) + Dxz*mu*C_W(c,t));

dS[eqn] = -(Dxx*mu);

return source;

The value of Dxx is exactly the same value that I specified in Viscous Resistance explained above.  Similarly, I created other UDFs for y and z directions.  I added these UDFs as source terms for the porous zone and set the Viscous Resistance to a very small value (1.0E-06), but it is not predicting proper pressure jump across the porous medium.  How do I setup the problem to use the momentum sinks, rather than setting the viscous resistance in the Cell Zone Conditions?

Thank you,