Highly exothermic reaction and grid adaption
 

I'm similuting a heterogeneous-catalyzed exothermic reaction in a much more complex system, but I'm looking at a simple tubular (2ddp-axisym) reactor case to explore some issues I have with the solution.

I know that if I use too coarse of a mesh, I will have drastic temperatures and a difficult energy balance to converge because the reaction will appear to be completed over the width of large cell, and the energy generation term will be excessively large. Thus, I know I need to use a finer mesh where the reaction rate is high. Of course, using a fine mesh increases the CPU needed for solution, and while in the 2d-case this isn't a problem, I'd like to be careful in the case of the more complex problem that this exothermic reaction is buried in.

Even with a reasonably fine mesh where the reaction does not appear to have significant completion over one cell, I still get an imbalance in the total heat transfer, typically around 1W (with inlet having ~20W capacity, so this is a significant value). I have found (obviously?) that making a finer mesh can reduce this value, but I don't quite get zero at any point.

I'm looking for a couple of pointers here in this direction. First, is there some way to determine what a good mesh size should be for these exothermic reactions in order to get a good energy balance from the start? Secondly, I know I can play with dynamic grid adaptation for such situations, but I know that with wrong adaptation parameters, I can make the problem worse than it is. I figured that the best way is to go dynamic adaption on the reaction rate curvature, but does anyone have any good rules-of-thumb for setting the various parameters? My meshes for both the simplified and the more complex problem are all quad or hex (or hex-wedge using trielement nodes for a tubular 3d case), so refinement of these grids should not be a big problem.

Re: Highly exothermic reaction and grid adaption
 

I never tried grid adaption strategies. I generally play on under-relaxation factors with the segregated solver:

1) I freeze the chemistry. Only heat transfer (and gas dynamics)

2) I freeze heat transfer and let the chemistry and species transport evolve (so it's a virtual adiabatic chemistry). Underrelax species mass fraction if you use laminar rate (and stiff chemical kinetics)

3) I enable again heat transfer. As the energy balance will be calculated with nearly-final species mass fraction, heat transfer is not too stiff.

The weak point is it needs user intervention during the calculation and follows a non-optimal (I suppose but it seems obvious) path to convergence. But If you're craving for convergence and on the edge of despair (or unemployment), it can be good... :))