Hi, I have a question. suppose there is a tube and I solve the flow and turbulent equations for the flow and adapt the grid till the pressure drop results do not change, i.e a grid independent solution( i am using a two layer model). now I solve for the heat transfer with constant properties. so I just solve the energy equation. BUT will the grid independent solution be grid independent for the heat transfer also. As in my case Pr is 7 so accordingly the thermal sublayer would be thinner then momentum sublayer. the momentum sublayer would be well resolved but for the heat transfer do I need to further refine the grid.

Thanks Ranjeet

(1). Follow your own intuition. And check your results.

Your grid might be good for the mean flow prediction, but not for heat transfer. I suggest to check the followings:

1)Plot velocity profiles in the log-scale(U+ via Y+). Make sure you have enough grids in the near-wall region.

2)Now you can do the same thing for the thermal field i.e T+ via Y+ [T+=qw/(rho cp Ut)]. Such plots will tell if you are accurately resolving the conduction dominated near-wall region.

3) Calculate the Nusselt number and refine your grid until it doesn't change with further grid refinment.

No and your reasoning is correct. The pressure drop is rarely a wise measure of grid indpendence if wall functions are used.

A knoweldge of WHY you are conducting the CFD simulation will provide you with the parameter to check for grid independence. If it's heat transfer you're after then Nusselt number will do. It's interesting to note that not all parameters become grid independet at the same rate.....

Robin.

No. A solution is either grid independent or it is not. A wise person will monitor a sensitive quantity (e.g. loss) and not just a quantity they happen to be interested in.

Having said that, if you are performing 3D engineering simulations then you will be dealing grid dependent solutions. For these solutions to be reliable the engineer needs to be fairly confident that the effects of the partially unresolved terms are not going to trip them up. This requires the engineer to have knowledge of what inadequate resolution is doing to the solution (well, probably, since it would be unwise to have absolute condfidence in the answers from unresolved nonlinear equations). Alternatively, they can simply believe (have trust in?) the solution and, perhaps, that will OK. In the real world this is often necessary but it is an inherently risky strategy. Education is the key to reducing this risk but that can be expensive.

Of course, the same goes for the modelling assumtions built into the governing equation (but in spades). And the, usually only partially known, boundary condtions.

However, I would fully endorse your first comment that an engineer has got to know what answers they want before starting a simulation.

You're right, it comes down to the concept of risk (rather trust and confidence). I still hold though that if the only parameter you are interested in achieves grid independency (i.e. a parameter such as a wall point temperature)then why bother to refine the mesh to resolve features that:

a) are not of concern b) do not affect the point temperature (this is assured because the point temperature does not vary with addition of grid)

There are some who maintain that the ONLY useful solution is a totally accurate solution. To quote a very wise man indeed:

"All models are wrong but some are useful"

Robin.