How do I know that my natural convection model is good?
 

Hello, I need your help please. I did my thesis and I am not sure of the results, since my tutor does not tell me anything or if they are ok or not. And with the time that has passed it is generating insecurity in them. I think they are fine, but in the end I am only a student, and it is not me who decides if it is fine or not.

My thesis was a numerical simulation of natural convection and surface radiation in closed three-dimensional rooms with different aspect ratios.

I did a transient simulation in Ansys Fluent for the Rayleigh number range from 10e4 to 9e5 and H/L aspect ratio from 1 to 10 for two emissivity values ​​e = 0.05 and 0.10. First use two different geometries with different lengths, in order to evaluate the Rayleigh number range you wanted, one length of L = 0.02764 m for 10e4 <Ra < 9e4 and another length of L = 0.05995 m for 10e5 <Ra <9e5. Use a structured mesh in each geometry (attached image https://prnt.sc/s7eyea). This is the first question that arises for me, since I did the sensitivity analysis for the low Rayleigh number values ​​(10e4 for L = 0,02765m and 10e5 for L = 0,05995m), I had an error in this regard and I I know, I know I had to do them for the higher Rayleigh since they are the most unfavorable situation. However, I did it for various reasons: 1.- The convection regime is laminar and therefore does not need such a refined mesh to capture the movement of the fluid and the formation of the boundary layers, 2.- In previous studies of years Recent also used the least Rayleigh number to do the sensitivity analysis, and 3.- I did a numerical model validation, and in that case I had to do a validation of the physical model of the study with which I was comparing my numerical model, and in that case, for a Ra = 10e6, the difference between a 250,000 element mesh and another 1,000,000 element mesh was 0.90% in the comparison value, and since this Rayleigh number was higher than the study I did, consider that it was not necessary to do a sensitivity analysis for higher Rayleigh numbers from my study, since they carry a considerable computational cost, and only simulating a mesh of 1,000,000 elements for Ra = 10e6 was quite heavy .

So the question is, the meshes I selected for the models in my study were approximately 230,000 elements, and for example, for the model with L = 0.05995, the Nusselt number (parameter of interest in the study) for Ra = 9e5, H / L = 10 and a mesh of 230,000 elements was Nu = 5,30147, and perform a simulation for the same model but with a mesh of 1,000,000 elements, and the Nusselt number was Nu = 5, 3158, with a relative error of 0.27% between the two values ​​and the difference between simulation time is quite considerable. My question is: Are the ones I made okay? Are the reasons enough to say that the numerical model you built is fine? Do I need to perform a simulation for the other configurations and with their highest Rayleigh number, or is it okay, with that one case, to check that the meshes I chose are sufficient for the study?

The second question I have is regarding the passage of time I used (the simulation was transitory), in this case use a different passage of time for each Rayleigh number, Ansys fluent recommends the following equation DeltaT = (L) / (4sqrt (g * B * DT * L)), where L is the length, g the gravity, B the coefficient of volumetric expansion and DT the temperature difference in the room. As the Rayleigh number increases, that passage of time becomes less. So, is it okay that you have chosen a different time step for each Ra? Or did I have to use the time step of the greater Rayleigh number for the entire Rayleigh number range? I never had stability problems, I always reach convergence, but I have read that although there are no stability problems, the results may not be accurate. So I have doubts about it.

Now, it should be noted that, as I mentioned earlier, I did a validation study, the same procedure that I explained before I did in that validation. Compare the numerical model with an experimental study and the relative error percentage with respect to its results was less than 3% in the entire Rayleigh number range evaluated. I enclose a graph of the Nusselt number with my results and the experimental ones https://prnt.sc/s7eylu. The other study with which compares the numerical model and a Benchmark solution, presenting error percentages of less than 1.3% with its results. The percentage of error in the values ​​can be seen in the table https://prnt.sc/s7f034. So is my numerical model good? Comparing with these two cases, before I was sure that this validation was enough, but now not so much

Please, I need your help with this. I would be very grateful for your response