Simple specie diffusion problem with Fundamental solution of Laplace Equation

mohibanwar · September 20, 2020, 22:56

Hello Everybody

First of all, dear members, I would like to thank you for spending your precious time in reading my problem and giving usual suggestions hopefully.
I am simulating a very fundamental droplet evaporation problem to solve the steady state Laplace equation to calculate the concentration field around the droplet.
The boundary conditions are fundamental dirichlet and Neumann boundary conditions at four walls as shown in the figure. I have used the 1 mm axis symmetric hemisphere droplet and the far field conditions are achieved at 200 times of the Radius. I have achieved the grid independent and used already very fine grid near the droplet at nearly 1um or even below that. So far field boundary and grid resolution is not the problem.
I have used both the FVM solver ANSYS Fluent and FEM solver MATLAB PDE tool box. However, both give me incorrect results at the same extent.
The problem is that the concertation field calculated by both Fluent and matlab is not according the already published data. I have attached the comparison results between the results from the paper (International Journal of Thermal Sciences 84 (2014) 300e308). For your reference you can look at the concentration iso line at 4mm location in three of the figures. Similarly, the concentration gradient on the surface of the droplet is also not same to this paper.
Therefore, I kindly request you what is the possible answer to this numerical dilemma being a very simple problem of solving the Laplace equation. I am extremely thankful from the core of my heart for your kind suggestions explanation.
Note: I am just repeating this paper so every condition is same. Also I cross checked this paper results to be correct with other literature.
Regards,
Khan

arjun · September 20, 2020, 23:48

The top and right shall have fixed values of the variable but they do not have that in both images you posted from fluent and matlab. Are you sure the boundary conditions are properly applied?

mohibanwar · September 21, 2020, 00:19

Hello dear Arjun,
First of all thank you so much for your reply and reading my wordy post.
The top and right boundary has fixed value. In matlab i give exact value in g/m3 and in fluent i give mass fraction which is correct as humidity is calculated by fluent is correctly.
I have given the boundary condition correctly as very simple in nature.
I am not sure why it cannot replicate this paper.
What else is responsible?

mohibanwar · September 21, 2020, 00:22

The Figurs i have given from matlab and fluent is just a snapshot of the full domain as domain is very big to give understanding. And this paper also did the same.

arjun · September 21, 2020, 00:28

Quote:

Originally Posted by mohibanwar

The Figurs i have given from matlab and fluent is just a snapshot of the full domain as domain is very big to give understanding. And this paper also did the same.

That explains.

If that is the case then I would try everything again but this time all quantities in SI units. I think this might be messing up for you.

mohibanwar · September 21, 2020, 04:53

Dear Arjun,

Yeah infact i have given the try in the SI units. There is no big difference i guess. I am worried if FEM and FVM both give similar answer i guess there is nothing wrong with numerics.
Anyhow thank you so much for your kind response.

September 20, 2020, 22:56	Simple specie diffusion problem with Fundamental solution of Laplace Equation	#1
mohibanwar Member Mochibaru Join Date: Jan 2015 Location: Japan Posts: 41 Rep Power: 11	Hello Everybody First of all, dear members, I would like to thank you for spending your precious time in reading my problem and giving usual suggestions hopefully. I am simulating a very fundamental droplet evaporation problem to solve the steady state Laplace equation to calculate the concentration field around the droplet. The boundary conditions are fundamental dirichlet and Neumann boundary conditions at four walls as shown in the figure. I have used the 1 mm axis symmetric hemisphere droplet and the far field conditions are achieved at 200 times of the Radius. I have achieved the grid independent and used already very fine grid near the droplet at nearly 1um or even below that. So far field boundary and grid resolution is not the problem. I have used both the FVM solver ANSYS Fluent and FEM solver MATLAB PDE tool box. However, both give me incorrect results at the same extent. The problem is that the concertation field calculated by both Fluent and matlab is not according the already published data. I have attached the comparison results between the results from the paper (International Journal of Thermal Sciences 84 (2014) 300e308). For your reference you can look at the concentration iso line at 4mm location in three of the figures. Similarly, the concentration gradient on the surface of the droplet is also not same to this paper. Therefore, I kindly request you what is the possible answer to this numerical dilemma being a very simple problem of solving the Laplace equation. I am extremely thankful from the core of my heart for your kind suggestions explanation. Note: I am just repeating this paper so every condition is same. Also I cross checked this paper results to be correct with other literature. Regards, Khan Last edited by mohibanwar; September 23, 2020 at 08:18.

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September 20, 2020, 23:48		#2
arjun Senior Member Arjun Join Date: Mar 2009 Location: Nurenberg, Germany Posts: 1,283 Rep Power: 34	The top and right shall have fixed values of the variable but they do not have that in both images you posted from fluent and matlab. Are you sure the boundary conditions are properly applied?

September 21, 2020, 00:19		#3
mohibanwar Member Mochibaru Join Date: Jan 2015 Location: Japan Posts: 41 Rep Power: 11	Hello dear Arjun, First of all thank you so much for your reply and reading my wordy post. The top and right boundary has fixed value. In matlab i give exact value in g/m3 and in fluent i give mass fraction which is correct as humidity is calculated by fluent is correctly. I have given the boundary condition correctly as very simple in nature. I am not sure why it cannot replicate this paper. What else is responsible?

September 21, 2020, 00:22		#4
mohibanwar Member Mochibaru Join Date: Jan 2015 Location: Japan Posts: 41 Rep Power: 11	The Figurs i have given from matlab and fluent is just a snapshot of the full domain as domain is very big to give understanding. And this paper also did the same.

September 21, 2020, 04:53		#6
mohibanwar Member Mochibaru Join Date: Jan 2015 Location: Japan Posts: 41 Rep Power: 11	Dear Arjun, Yeah infact i have given the try in the SI units. There is no big difference i guess. I am worried if FEM and FVM both give similar answer i guess there is nothing wrong with numerics. Anyhow thank you so much for your kind response.