Hello everybody,

I am simulating species transportation with the source term in one fluid zone. I only have the clear mass (kg/m3-s) parameter from experiments. I don't know exactly momentum source parameter, Renold stress parameters(UU, UV,..) either. So I only add the mass source term in my simulation. In the period of iteration, Reverse Flow appears. The results diverged. I am thinking that if the reason is the missing of momentum source term , TKE, Dissipation source term, and Renold stress source term.

Could anybody tell me that the way I add the source term is right or wrong? I have no experiences for adding source term. Must I add each source term usually or some specific source terms depending on different cases?

Thanks in advance for your time and kindness.

Have good weekend.

Zwdi

[subha_meter]

Hello All,

I'm carrying out multiphase eulerian simulation in porous media to estimate pressure drop and liquid hold up. Addition of momentum source terms in both the phases (gas & liquid) have been reported in literature which I've incorporated through UDF as well however my simulation diverges pretty fast.

Momentum source terms:

Liq phase: (l)

(1-alpha)/k_liq*(A*Rel/Gal + B*Rel^2/Gal)*rho_l*g

Gas phaseg)

alpha/k_gas*(A*Reg/Gag + B*Reg^2/Gag)*rho_g*g

where alpha = gas vol fraction, A & B = Ergun co-eff, Re = Reynolds no, Ga = Galileo no, rho = density, g = 9.81 m/sec2
k = relative permeability for liq & gas phase


Gas phase momentum transfer UDF for example:

DEFINE_SOURCE(gas_phase_xmom_source,c,t,dS,eqn)
{

real x_vel_l, y_vel_l, abs_U, rho_l, drv1_g, drv2_g, Fg,drv,
mu_l, x_vel_g, y_vel_g, rho_g, mu_g, void_g, Reg, Gag, E0, eps, sg, kg, source;

/* find phase velocities and properties*/

x_vel_g = C_U(c,t);
y_vel_g = C_V(c,t);
rho_g = C_R(c,t); /*Gas Density*/
mu_g = C_MU_L(c,t); /*Gas Viscosity*/
abs_U=sqrt(x_vel_g*x_vel_g + y_vel_g*y_vel_g);
void_g = C_VOF(c,t); /* gas vol frac*/
Reg = rho_g*abs_U*dp/(mu_g*(1-ep));
Gag = pow(rho_g,2)*g*pow(dp,3)*pow(ep,3)/(pow(mu_g,2)*pow(1-ep,3));
E0 = rho_l*g*pow(dp,2)*pow(ep,2)/(sigma * pow((1-ep),2)); /*Eotvos no*/
eps = 1.0/(20.0 + 0.9*E0);/*static liq hold up*/
sg = 1.0 - eps/ep;
kg = pow(sg,4.80);

/*Momentum source Term*/

Fg = (void_g*rho_g*g/kg)*(E1*Reg/Gag + E2*pow(Reg,2)/Gag);

drv1_g = E1*rho_g*dp/(mu_g*(1-ep));
drv = rho_g*dp/(mu_g*(1-ep));
drv2_g = E2*2*abs_U*pow(drv,2);
source = Fg;

/* derivative of source term w.r.t. x-velocity. */

dS[eqn] = void_g*rho_g*g/kg*(drv1_g*E1*Reg/Gag + drv2_g*E2*pow(Reg,2)/Gag);

return source;
}


Is there any suggestion to correct it? Any suggestion will be highly appreciated.

Regards,

SM

[abhik.banerjee]

Hii Subha

I am working on trickle bed reactor with porous media concept exactly similar to your work. It seems like you have used momentum source terms instead of viscous resistance values. Or have you used both? Can you tell me which drag law you have applied for gas and liquid phase and the boundary conditions? It will be of great help as I am running out of time.

[subha_meter]

Hello Avik,

Well, I've spent sometime to build up this model since this post however validation with experimental data is still pending. The porous media model can be built using both "viscous and inertial resistance" and "momentum source" (I strongly believe so).

In both case, you need closure equations from "Relative permeability model" of Saez and Carbonell (1985)-AICHE journal. You can either keep the porosity uniform or variable. If you want to vary it, then a radial porosity distribution function proposed by Mueller et al (1994) is suggested.

Hope it helps.

[subha_meter]

Forgot to mention that you need to calculate boundary conditions by solving "phenomenological models" - proposed any of those by Holub et al(1992,1993), Larachi et al (1990), Wammes et al (1990,1991), Ellman et al (1990).

For gas-liquid interaction term, you can do the followings

--> use none considering loss against solid phase is much more than gas-liquid interaction

--> Use Attou et al's (1999) fluid fluid interaction model

Hope it helps

SM

[abhik.banerjee]

Hii Subha

Thanks a lot for your reply.

Regarding the boundary conditions:

1. I have specified velocity inlet and pressure outlet for 2 phase Eulerian-Eulerian model.. I have given 0.4 volume fraction of liquid phase(phase 2) at the inlet. The problem here is that I have to specify backflow volume fraction at pressure outlet. How to specify this value?What value have you taken? Did you choose pressure outlet or outflow condition?
2. I have defined the fluid zone as porous media. I have to specify inertial and viscous resistance values for both the phases. Using the formula you have mentioned in other posts, the value comes out to be a single value. But if we use pressure drop vs velocity values from experimental data, we will have different values for both phases. How did you compute these values?
3. If I am using momentum source UDF as you have mentioned, is it necessary to specify inertial and viscous resistance coefficients?

Your guidance regarding these issues will be of great help.

[subha_meter]

Hello Abhik,

1. Using backflow volume fraction is tricky in FLUENT for E-E multiphase flow. I suggest to use "dispersed phase" i.e. secondary phase volume fraction to set "0" at outlet.

Outflow BC is used normally for unconfined flow and it never gives a good prediction of pressure drop. So a pressure outlet BC is always recommended.

2. For theoretical computation, if you use Ergun equation then you will get single value for resistances which is not correct. You need to calculate this resistances from Saez & Carbonell (1985) formulation which uses relative permeability for both phases and gives different resistances. And if you have experimental data for pressure drop then it's OK.

3. Modeling of porous media model using momentum source terms is another way if you do not use porous media module. It's mutually exclusive.

Hope it helps,

SM

[abhik.banerjee]

Hii Subha

The information in your reply is of great help.

If I am specifying momentum source UDF, then can I specify viscous coefficients as well along with this UDF or only one of these two should be used?