# Single-Component Mutiple-Phase flow with large density ratio

Hi,

Recnely, I study the SCMP at large density ratio with lattice Boltzmann method. My study base on Peng Yuan and Laura Schaefer’s work: Equations of state in a lattice Boltzmann model, the body force model is in accordance with A.L.Kupershtokh’s work. I use Carnahan-Starling EOS and the same parameters in Peng Yuan’s article. Now I have a problem with the initial density of vapor phase. For a flat inteface in my program, when the density ratio is close to 10^3, the initial density of vapor phase can’t be setted to the steady density directly, the difference between the initial and the steady is more than 10 times. The program has to iterate more times to the steady.

For example, the critical temperature is 0.09433306467862. When I set temperature T=0.055, the steady density of vapor and liquid is 2.14E-04 and 0.41407 respectively, the density ratio is 1935. But the initial density of vapor phase is limited to be 2E-03, it can’t be smaller and the initial density of liquid phase is 0.41407. In the simulation of a droplet in vapor, the steady density of vapor and liquid is 4E-04 and 0.41995 respectively with T=0.053 because of the surface tension. In this case, I can set the initial density of vapor phase to be 3.2E-04 directly but have a upper limitation with the radius of the droplet.

I don’t know this phenomenon is caused by my fault or the model? Anyone use this model or encounter this phenomenon?

Kind regards,
Skying

Hi Skying,

I had the same problem during my simulations, basically you can’t go down with the vapour phase density. That’s why I recommend to use the Shan-Chen model to simulate droplets but not bubbles. That means if you can’t initialize density you have to calculate the surface tension numerically and then plug into your real calculations.

Cheers,
Alex

## Alex Wrote:

Hi Skying,

I had the same problem during my simulations,
basically you can’t go down with the vapour phase
density. That’s why I recommend to use the
Shan-Chen model to simulate droplets but not
bubbles. That means if you can’t initialize
density you have to calculate the surface tension
numerically and then plug into your real
calculations.

Cheers,
Alex

Hi Alex,

I appreciate your answer and helping to my problem. I will try to calculate the surface tension numerically, or maybe I have to use another model. My advisor asks me to have a study about Mutiple-Component Mutiple-Phase flow with large density ratio. The SCMP flow with large density ratio is the base.

Sincerely,
Skying

Hi Alex,

I have plugged the surface tension into my real calculations numerically, but it has no help to the problem I meet. It makes the difference is I can change the density ratio in constant temperature by changing the surface tension parameter.

Sincerely,
Skying

Hi Skying,

I have plugged the surface tension into my real calculations numerically, but it has no help to the problem I meet. It makes the difference is I can change the density ratio in constant temperature by changing the surface tension parameter.

Sorry if I don’t understand it right. What I suggested is when you calculate the surface tension numerically then you probably will obtain the agreed parameters with the EOS, but not vice versa - like you want to have the certain surface tension you plug it into EOS and obtain gas and liquid densities. Try to do it vice versa to obtain surface tension and to see whether it makes sense.

Cheers,
Alex