Mesh Study Scalar Transport
 

Hello guys,

I am simulating a 2D gap flow of air. The simulation is steady state, incompressible and the flow is laminar. The domain is 0.1 m long (x-dir) and 0.001 m wide (y-dir). At x=0 there is the inlet with a block profile and at x=0.1 m there is the outlet with a zeroGradient BC. At y=0 there is a wall and at y=0.001 m there is a symmetry BC.

I am adding a passive scalar to the system of equations. This scalar should represent the temperature in the flow, so the diffusion coefficient is set to be the thermal diffusivity. The scalar enters with a block profile of 293.15 K (20 °C) and is set to be 283.15 K (10 °C) at the wall.

The mesh I am using has uniform cells. I started with 1000 cells in x-dir and 10 cells in y-dir. I refined the mesh by increasing the amount of cells in both directions.

I now compare the outlet temperature and the mean heat flux density at the wall between the different meshes. The outlet temperature I calculate as a phi (volume flow) weighted average at the outlet. For the heat flux density I take the gradient of the passive scalar T at the wall and multiply it with the thermal conductivity of air.

Neither the outlet temperature nor the mean heat flux density seem to converge to a "constant" value. I increased the amount of cells until I hit 160.000 (4000 x 40), which feels very fine to me. Residuals of the simulation are great (all <1e-9). I compared the mean heat flux density to correlations given in the VDI-Wärmeatlas and the absolute value seems to be fine (~ 1 % abbreviation).

Any ideas why the solution does not converge to a "constant" value? I also tried different things as using a finer mesh in y-dir compared to the x-dir and also set a fully developed flow profile and only calculated the passive scalar T. Nothing seems to change the said behavior. I have attached a plot where you can see the mean heat flux density in dependency of the amount of cells for the mesh with uniform cells.

Best,
Felix