Air entrainment model setup for spillway
 

Hi!

I want to model a spillway weir with a vertical shaft and a tunnel system directly downstream. I expect including the air entrainment model in Flow-3D will cause an earlier backwater effect than without the model. My question is how to set up the parameters of the air entrainment model in Flow-3D for best possible results with no calibration data?!

In the basic air entrainment exercise (given by Flow Science) the following parameters are used (SI-units):
-Air entrainment rate coefficient = 0,5
-Surface tension coefficient = 0,073 N/m (water 20 degrees C)
-Drag coefficient = 0,95 (for buoyant spheres)
-Average particle radius = 0,0005 m (typical 0,5 mm - 2 mm)
-Richardson-Zaki coefficient multiplier = 1
-Viscosity of two-phase mix = 0,001 Ns/m^2 (assumed to be viscosity of continuous phase - water)
- Viscosity of water (phase 1) = 0,001 Ns/m^2
- Viscosity of air (phase 2) = 0,001 Ns/m^2 (assumed bubbles always separated by fluid film)
- Density of liquid = 1000 kg/m^3
- Volume fraction of air at inversion point = 1 (assumed bubbles always separated by fluid film for smaller volume fractions)
- Allow gas to escape at free surface = Yes
- Density of air = 1,2 kg/m^3

Does these parameters give reasonable results? Any better suggestions? I find it a bit weird to set the viscosity of air and the two phase mix to the one of water. I also wonder if there is any validation data to help me choose the air entrainment coefficient and or the drag coefficient?

I've also heard that the air entrainment model is really cell size sensitive. Any advice on setting the cell size for air entrainment (rule of thumb)? Will a cell size reduction study give better results (or convergence at all?)?

Is there any gain in also activating the adiabatic bubble model?

Any replies are welcome.

Some air entrainment experiences
 

Dear Olav,
please find some comments below..
General remarks
I can understand your concerns with the air and water viscosity issue from a physical point of view, from a purely CFD point of view it becomes a minor problem. However, please notice that eddy viscosities arising during the simulation will probably be bigger than the difference between both viscosities. Also, notice that you are setting an inversion point of 1, if I am correct, this means that you are not going to use the air properties over any concentration (as you set this maximum concentration to 1).
Concerning the adiabatic model, it is intended to be useful when you are able to "resolve" the bubbles. The User's manual recommends ~10 cells/diameter to correctly reproduce this bubbles. Probably, this will not be your case.
Mesh sensitivity
Even the most simple CFD model is cell sensitive. In this case, I think it is interesting to have a look to the input parameters of the air entrainment model. You will soon realize you are employing $k$, the TKE, as the main input. Let's say it in an informal way: Once the depths converge, and velocities converge, your TKE (which is dependant on the velocity gradient) will be able to converge also! Consequently, you will usually find that TKE is converging slower and I fear this is why the air entrianment model shows some higher dependence than you can usually appreciated. I studied TKE dependence in a stilling basin flow, althought there was no air entrainment modeled, in this Open Access paper.
For me, it seems logical to study mesh sensitivity for TKE without activating the air entrainment model (in a representative flow section) and then choose your cell resolution. More comments on a spillway flow mesh convergence can be found in here (which you can also find in my personal Research Gate profile). One easy and straight forward way to mesh convergence (or numerical uncertainty) can be found in the paper of Celik et al (2008), recommended by the ASME and found in the references of the Open Access paper above.
Calibration/Validation data
Having calibration/validation data would be fantastic! But you really need to know well the literature to find something comparable and/or profitable for your study. Some commonly accepted values on air concentrations in spillways can be found in this book of Prof. Chanson. Recently, the IAHR committee of Hydraulic Structures released a monograph which could be helpful.

All the best,
Daniel

Air entrainment first run
 

Thank you for your comments - they make sense and was helpful for me. As a part of my preparation I actually read your paper: "Calibration of an Air Entrainment Model for CFD Spillway Applications".

I ran the spillway simulation with the air entrainment model setup as shown above. The result was a calculated air entrainment ranging from 0 % of the total flow (tunnel system filled - confined flow) to 10 % of the total flow (tunnel system partly filled) transported through the tunnel system. This seems quite reasonable to me.

I also used the air entrainment model for a steep river (30-45 degree slope) with the same parameters. Here I got an air entrainment of ~90 % of the total flow, which seems to be too much by my opinion (expected 40 - 60 %). I tried reducing the air entrainment coefficient to 0.3, reducing the mesh sizes as much as possible and testing different roughness values. This had however very little effect on the result. I'm thinking this may have to do with the additional logic for adding turbulent energy to intersecting surfaces in the model, which may produce an artificially high air entrainment in all my shock waves along the river (due to change of flow direction). Any thoughts on how to improve the calculated air entrainment in this river model? Reduce the air entrainment coefficient even more?

Olav

I would suggest you to chose a mesh resolution and keep it constant for all the simulations you perform. This choice has to be reasoned, so I would suggest you again to choose it based on a sensitivity analysis focused in the TKE. For that purpose, you can follow Celik et al (2008), which makes it easy and understandable as well as it is a recommendation of ASME.

If you consider you have excessive aeration still (40 - 60 might be reasonable as you point out), you can keep on reducing the $C_{air}$ parameter. It is must happend that for $C_{air}$ = 0, the mean air concentration $\overline{C}$ should be similarly 0. Thus, it is only a matter to find the best $C_{air}$ value.

At this point, I will offer you some personal observation which might be as inaccurate as maybe useful. Not sure if it was just happening in my simulations but you can test it. Some time ago I noticed there was some "exponential" relation between $C_{air}$ and $\overline{C}$, which some how makes sense with the general idea of diffusion that is modelled, if we understand that $C_{air}$ is only affecting to the boundary condition (air entrained in the free surface). Then, if you have modelled with 2 - 3 different values of $C_{air}$, you might be able to fit a (1 - exp()) fit easily and then extract your desired $C_{air}$ value (see the sketch I quickly prepared).

Please keep me updated with any new on your ongoing study.

Regards,
Daniel

spillway model
 

hello very one
Dear friends I am trying to study pressue on spillway and I have some problems, my question are:
1- wich parameters shuld actived in physics part of flow 3d for messuring pressure on specific point on ogee spillway.
2- how can obtained result in the points by text or table.


best regard