Hi! I am modelling the combustion in a pf boiler and I confront convergence problems.

For my case I use unstructured grid (440K cells), k-e (standard) for turbulence, EBU for combustion interaction with turbulence, 1 chemical reaction and P1 model for radiation. I also inject in the continuous phase 19,000 particles every 25 iterations.

The problem is that it is impossible to meet the convergence criteria for energy and P1 (set at 1e-6), as the residuals decrease at about 5e-5 and then become flat. I also notice that the temperatures in the combustion chamber are about 200K greater than the correct. Notice that all the other residuals are below their corresponding criteria of convergence.

I have already tested the following with no result: --number of continuous phase solution before calculate the discrete phase --alteration of the relaxation factors --1ord and 2ord discretisation schemes

I confronted the same problem (with the same residuals) in another case I had dealed with, where the chemical equillibrium (pdf) model was selected for combustion modelling.

Does anybody have any suggestions?

Thanks in advance for your help.

Ilias

Is your objective to get the residuals below 1e-6 or is it to solve a problem using FLUENT?

If it is to lower the residuals, I'm guessing you tried the normal things, increase underrelaxation, try a different scheme, etc.

If you are looking to solve a problem, you would want to first address why the temperatures are higher than expected. Too much energy input, gas specific heats too low, incorrect boundary conditions, etc. What are you doing for wall emissivity, gas/particulate radiation properties?

When you are happy with the set-up, and the residuals flatten out, check to see if the heat fluxes to walls and the gas temperature at the outlet are also converged. In my experience with boiler models, these are better indicators of convergence than the somewhat arbitrary residuals.

First of all I would like to point out 2 more "signs" of problem in my solution (beyond the very high temperature profiles): --turbulent viscocity exceeds in a few cells the upper limit of 1e5 (although k and epsilon residuals are on the order of 1e-5) --temperature near inlets exceeds the minimum temperature of my case (which is the temperature of the preheated-dried fuel)

Now concerning the energy input; from the ultimate and proximate analyses of the fuel (lignite) I calculated the empirical formula of the volatiles, the heating value and the enthalpy of formation. In this first simple approach, I use a simple 1 reaction mechanism (vols->CO2). Can this cause such a high overestimation of the temperature profile? Would a 2 reaction mechanism (vols->CO+CO2 & CO->CO2) in combination with the Eddy Dissipation model make any difference?

About the specific heats, mixing law is selected for the mixture (vols+air), typical value for lignite vols=1500, and constant typical cp's for the other fluids (taken from FLUENT library). For the combusting lignite particle, I consider the (constant) typical value of 1680.

For wall temperatures, I have already decomposited each side at 3 zones; hopper zone, burners zone and over-burners zone, and applied at each one constant temperature condition.

The other boundary conditions are OK (velocities, k, epsilon, temperatures etc.)

Now concerning the emissivities; Typical values considered everywhere. For walls 0.5 and 0.6, for particle 0.85. The same for scattering.

As it is obvious my purpose was to converge at first a solution taking into consideration many simplifications and then to proceed with corrections of the accuracy of properties, bc's etc.

Thank you very much for your help. Your experience on boiler models is invaluable.

Best regards,

Ilias

Gas specific heats will almost double at typical boiler temperatures. Make sure to make gas Cp's a function of temperature (FLUENT data base values are suitable), if not already doing so.

H2O vapor Cp is higher than other combustion gases, as well. Coal volatiles will produce some H2O.

Are you including any type of reaction kinetics? Higher temperatures mean faster reactions which means more energy released and still higher temperatures. Sometimes you need to dampen things out to improve the solution.

You are right. Constant cp's prooved to be not only insufficient but completely inappropriate. After some iterations maximum temperature decreased by 200K !!! The minimum temperature, which was lower than the lowest temperature entered the domain, also corrected! I knew that polynomial cp's would increase the accuracy of the solution but not that could affect the the whole convergence.

I also calculated my fuel's cp (Merrick's correlation) and found a completely different value from the typical of lignite (1680). So it is remaining to test the solution with it (unfortunately by Monday).

Now concerning the kinetics; I use the eddy dissipation model (no Arrhenious rates calculation). Is it possible to incorporate reaction kinetics for lignite volatiles which are in empirical form (CxHyOz)? Or I should model them as a CH4 and CO mixture? I would appreciate your opinion on that.

Thank you very much again for you continuous help. There are no many people that work on large scale boilers' simulation and experience is becoming rare.

Best regards,

Ilias

Kinetics can be quite time consuming due to the lack of published data, getting the units correct, and applying them in a CFD model. I would just go with something simple, but representative.