[piu58]

Dear Foamers,

I have a rather complicated problem for which I need your help or at least your advice.

Introduction

What I try to simulate is the mass transfer to a reacting surface which is driven by 1) the natural convection due to the changes of mass density and 2) external flow. Because the differential equations are equal I simulate this as heat transport problem. I’ll speak here in “heat data”, but if you check the material properties keep in mind that my case is concentration driven in reality.

I used both buoyantBousinesqPimpleFoam and boussinesqPimpleFoam. The formulation of the material properties is different, but the results are similar. The case I give is the simpler buoyantBousinesqPimpleFoam.

In the first step I checked both methods against the theoretical solution from Simon Ostrach for heat flow at a plate: https://ntrs.nasa.gov/archive/nasa/c...9930092147.pdf
Depending how I set the case the results are nearly identical to quite close with both solvers. To check this against my material properties I programmed something which helps to guess the initial F’’ and H’ values.

Gravity against 'ceiling' without external flow

Problems occur if you have some kind of heated ceiling where to gravity force is directed against a wall. I simulated this with w heated cylinder, which has some “ceiling” parts. I enclosed the case. Please keep in mind that I set the gravity toward the left side (all loose things would fall to the left). I made this because of the cylinder mesh I had and because of my screen side ratio.
7
If I start with only temperature and no external flow I have a strange effect. The simulation starts very slowly. At my standard desktop computer it takes around 500s to calculate the first step (2.1e-5 s), and again similar long to the second (3.6e-5 s). I wrote the results for every time step at disk and saw a similar effect which happens with external flow, but do a much lesser degree: There is an unsteady point at an angle of 45 deg. Mass dissappears at this point. This is a low amount and may be thought as numerical effect in the region of rounding errors. Nevertheless, here it is:


The effect disappears, showing other interesting looking effects in between. Again, that may be the phase of stabilization at the start of the simulation:




Later it runs with normal speed an runs to 7 s simulated time in a few hours, where I stopped it. The unsteady region disappears. All in all the result is what I expect.

Free convection with external flow - no conservation of mass

Things became very strange if a add a tiny amount of external flow. The discontinuity at 45 deg rises dramatically and gets nonphysical:
1) The flow violates the law of conservation of mass. As you might see, I got a flow form all directions to one point, and no flow away from it. I changed several conditions, but this effect was always present.
2) The temperature came to nonphysical values. I set the temperature of zero in the field and to 1 (Kelvin) at the boundary. From this a temperature of 1.9 K cannot arise. I thought that temperatures around 0K might lead to errors because some effects with negative absolute temperatures somewhere in the calculation. I remade the calculation (with my original geometry) with 300K and 301K and got an identical result.
I stored this result in the case (7).
BTW: In contradiction to the case without external flow, the simulations starts fast (at normal calculation speed).







I stored the complete case somewhere. The case is complete, but please run blockMesh first. Before let it rerun you have to delete the '7' folder which contain the results with external velocity. The case is set with external velocity of 0.01 m/s.

I would appreciate every hint or help. At the moment I let the simulation run with finer mesh in the near of the cylinder. I add the results if they are finished.

[piu58]

If somebody already downloaded the case,please do it again. I changed the mesh slightly to remove an irregularity.

The old case contains the result folder 0.8 an 10, the new one only 7 (in accordance to the also changed text above).

[piu58]

Dear Foamers,

I experimented with buoyantPimpleFoam and buoyantBoussinesqPimpleFoam for a while. Both solvers contain an error, and both act very similar.

The solvers are designed to calculate flow from heated (or cooled) surfaces. In these cases there is a strong flow away from the boundary, because of the gravity effects. The solver calculates nonsense, if they are strong velocity in the near of walls which have an external reason (no temperature).

The easiest case I could establish is a vertical wall which is heated at the lower part and has average temperature in the upper part. The flow gets accelerated by the temperature effect in the lower part. In the upper part we have a free flow without temperature effect, which leads to strange effects just above the temperature boundary. I used a plate of 5 cm and a free flow region of 5 cm too.

Please look at the first image for the case. The case is 2D, but I have rotated it slightly for you can see the temperature limit at the wall.

I used the following theromphysical and material constants (given for buoyantBoussinesqPimpleFoam, for buoyantPimpleFoam ist has to formulated different).
Thermophysical:

    transport
    {
		mu 690e-6;
		Pr 230; 
    }

transport:

nu              nu [0 2 -1 0 0 0 0] 0.69e-06; 
beta            beta [0 0 0 -1 0 0 0] 0.002; 
TRef            TRef [0 0 0 1 0 0 0] 0;
Pr              Pr [0 0 0 0 0 0 0] 230; //  alpha = 3e-5
Prt             Prt [0 0 0 0 0 0 0] 0.85;

Initial temperature was 300 with except of the hot plate, where it was 301.

I used this instead of 0/1 because I had the idea that temperatures may be fall slightly below zero due to computational effects and that this may cause errors. But this is not the case. You may use 0K overall and 1K for the hot plate as well.

I give some images for the results.
1) My case, setting of temperature field.
2) Closer look at the case after 10s simulated time (results do not change anymore). You see that we get temperatures up to 307K from the hottest place being 301K. I switched on the mesh: The horizontal lines are 0.1 mm apart.
3) Overview for velocity. Strange high velocity at the end of the hot plate.
4) Closer look, with mesh, but not rotated anymore
5) Glyphs for the flow. I could have used surface LIC instead , but this gives no direction of the flow. What you see here: The flow moves through the wall (boundary condition is fixed (0 0 0) here) and disappears in Nirwana.

From such a strange effect you may get every amount of following effects. So I don't wonder anymore about the temperature rising above the hottest point in case.

~

What can we do until that will be corrected?

- Avoid boundaries between hot and cool walls in the near of places where you need the solution. It may be better to change the geometry and extend a hot component if that is possible
- If you need an additional external flow (which I need), calculate it separately with pimpleFoam, and add the velocities. I calculated examples if that is acceptable (it is). Calculate the final thermal field with scalarTransportFoam.