# Modeling natural convection in water tank with heat exchanger

Hello! I'm modeling natural convection in water tank. Geometry is simple, big water tank with heat exchanger (represented by 5 toruses). I'm using 2D axisymmetric model. BC are:

inlet: water, temp. 12.5 C, mass flow inlet 0.17 kg/s

outlet: mass flow outlet 0.17 kg/s

wall heat exchanger: temp 80 C (constant temp.)

all other walls are heat flux = 0 W/m2

I included energy equation.

Gravity is turned on, 9.81 m/s in negative X direction.

Simulation time is STEADY!

I'm using boussinesq aproximation for modeling natural convection but there is a problem because my residuals are not converging and total heat fluxes are not zero (they are around 3 kW which is big error).

I'm using coupled scheme with PRESTO pressure and all 2nd Order Upwind spatial discretization.

Turbulence model is k-epsilon RNG

I tried changing everything, including models and schemes, changing controls and everything but nothing helps.

I will provide pictures of mesh and geometry: https://imgur.com/a/ulEHLHY

## Answers

We can't open the attachment as we're not allowed, please post images.

For the results, how much heat is transferred from the coils? How well resolved is the mesh (y+ AND streamwise)?

Here are the pictures. I think the mesh is fine, I also tried with quadrillateral cells but the results are not better. Around 20 kW is transferred through the coils (but I dont think that is the exact value because the results are not correct, but its around that value +/-).

That looks OK. How do the residuals & flow field look?

Residuals do not converge. They look something like this

My total heat flux is not zero. So for example, this is what it looks like:

Why is the net result so big?

Here are velocity and temperature contours:

Create a few monitors and run the model on, you're looking to see how stable the temperature on the outlet is and possibly velocity on a few points in the domain. You may also need to review the solver settings, have a look at the tutorials to see what they suggest regarding UnderRelaxation factors etc.

I googled everything, I read every document I could find. The problem lies somewhere around boussinesq approximation for water. When I use air, it works, when I use constant density it also works but then there is no buoyancy and there are no layers of fluid at different temperature (hotter is above colder). Also, when I do transient calculation it works fine, but my task is to do a steady state simulation. Net heat flux is never zero, it is always around 10-30% wrong (it's always like in a picture I posted). Is it possible that it's impossible to find a steady solution, that I need to do it transient? I tried everything with boussinesq parameters and nothing helps.

Also, this is for Mr Rob. I tried to monitor temperature on the outlet and it varies because the net heat flux varies. So for example: net heat flux is 5000 W and outlet temp is 40 C, but after few iterations, net heat flux is -10000 W and outlet temp is 30 C. It never stabilize.

Tidied up some SPAM - @Bejrut you're not imaging things re the Google comment.

Your solution is entirely dependent on the flow: higher flow velocity will influence the temperature & heat transfer rate which changes the density etc. Check the water expansion coefficient and manually plot the water pseudo density against temperature. You may find it's changing a lot more than you expect.

Now, look at the underrelaxation factors, and more critically the Courant Number. Reduce the latter to around 25 and see what happens.