Boundary condition | Solid volume fraction
The issue of specifying the CORRECT solid volume fraction at the BC has troubled me a lot!
In my case, at the side bottom inlet (F_SL in the figure below) these are the following conditions:
- the gas flow rate is ~ 0.00320 m3/s
- The solid mass flow rate is ~ 9.26 kg/s
- The air density is 1.6 kg/m3 | the solid density is 2500 kg/m3
- The diameter of that side inlet is 0.23 m | cross-section area ~ 0.042 m2
How exactly should I specify my boundary condition at this end?
As of now this is how I specify:
However, the above does not give the correct mass flow-rate at the inlet.
The geometry of the riser is shown below:
There is no correct value for the solids volume fraction, as long as you are below max packing. This is an input, and the solids velocity will be computed to get the specified mass flow rate (mass flow rate = solids volume fraction times solids density times solids velocity times area).
What mass flow rate do you get compared with the 9.26 kg/s you specify?
Thanks again for the reply!
I get the mass flow rate at the inlet as 8.73 kg/s instead of 9.26 kg/s, which is incorrect.
In that case, do I just specify the mass flow rate for the ‘solid’ phase as 9.26 kg/s
and then specify the mass flow rate for the ‘fluid’ phase as 0.00098 kg/s or 0.00320 m3/s?
And in this case, what should I keep the volume fraction at the solid?
This shows the monitor for mass flow rate at the boundary inlet and as seen it is off by 5-6% [8.73 kg/s instead of 9.26 kg/s].
Is such a variation expected in MFIX or is it because I am following an incorrect way of inputting the data at the BCs
It is normal to see some fluctuations because parcels are injected discretely. The difference could be due to the cross section area of the mesh being a little smaller than the stl file.
Okay great. So in this case, the fluctuations are not due to incorrect BCs.
One last question for this thread is: That means the solid volume fraction at the BC is not the actual solid volume fraction for the gas-solid mixture at the boundary - rather it’s just a number to determine the velocity of both solids and gas at that boundary, right?
It is the actual value at the boundary. This value will likely change once parcels enter the fluid domain.
Got it. Thanks!
In that case, if I have to enforce a solid volume flow rate (V_s) and a gas flow rate (V_g): I will enter the combined mass flow rate (V_s + V_g) at the BC [Solid Section] and enter the solid volume frac (E): E = V_s/ (V_s + V_g).
This will be the correct way of specifying the BC, right?
No. First make sure you do not confuse volume flow rate and mass flow rate.
Say you want to specify volume flow rates, I will call q_g the gas flow rate and q_s the solids flow rate (expressed in cubic meters per second).
q_g = epg x Ug x A (Eq. 1)
q_s = eps x Us x A (Eq. 2)
where:
epg is the void fraction (epg = 1 - eps)
Ug is the gas velocity at the inlet
eps is the solids volume fraction
Us is the solids velocity at the inet
A is the cross section area at the inlet.
A is known from the geometry. q_g and q_s are the flow rates you want to impose (you should have numbers for these). You should also know what solids volume fraction solids enter the domain (is it packed, or dilute?). If you don’t know eps, then you have to guess, say you pick eps=0.2. Then in the solids tab, you enter the value for q_s and eps. In the fluid tab, you enter q_g and epg will be automatically set to 0.8.
If you don’t know eps but you know Us, than you can compute eps from (Eq. 2).
