Learning Forum

[can.sumeyye]

I am running a transient LES combustion case in ANSYS Fluent 2022 R2 and repeatedly receive the warning:

Maximum PDF table enthalpy exceeded in XXXXX cells

I would appreciate some guidance on whether this is mainly a PDF-table setup issue, a boundary-condition issue, or insufficient convergence within each time step.

My setup is:

• 3D transient LES, WALE SGS model

• Partially Premixed Combustion

• Flamelet Generated Manifold

• C-Equation

• Turbulence-Chemistry Interaction: Finite-Rate

• Premixed flamelets generated adiabatically

• CFD Energy Treatment: Non-Adiabatic

• No TFM, EDC, or finite-rate species chemistry in the 3D CFD domain

The physical configuration is a premixed CH4-air jet discharging into ambient air. In the Fluent FGM two-stream definition:

• (Z=1): premixed CH4-air mixture at (phi=0.8), 300 K

• (Z=0): air at 300 K

• Main inlet: (Z=1, c=0)

• Ambient pressure boundaries/backflow: (Z=0, c=0, T=300) K

The flame is ignited/stabilized using an annular pilot mass-flow inlet. For numerical simplicity, I prescribe the pilot as already-burnt products:

• (Z=1)

• (c=1)

• currently (T=2001) K

Initially I used 2230 K, but this produced stronger local temperature/enthalpy overshoots near the pilot, so I reduced it to approximately the adiabatic burnt temperature of the (phi=0.8) mixture.

The pilot mass flow was originally 13% of the main inlet flow. With hot burnt products, the pilot inlet velocity is about 3.91 m/s. I have also tested lower pilot flow rates.

The non-adiabatic PDF table display shows a maximum temperature of approximately 2425 K at the upper enthalpy range. During the CFD solution, the cells exceeding the maximum PDF-table enthalpy are mainly associated with the hot flame/pilot region. The maximum CFD temperature also occasionally approaches approximately 2425 K.

The warning count is sensitive to the transient convergence settings. For example, reducing maximum iterations per time step from 25 to 20 caused both residuals and the number of affected cells to increase substantially. 

Most residuals behave reasonably, although continuity remains relatively high compared with the other equations.

There is some reverse flow at the upper pressure outlet, but the magnitude is very small: approximately -0.004 m/s minimum velocity. Backflow temperature and composition are correctly specified as 300 K air.

My main questions are:

1. Is it correct to generate adiabatic FGM flamelets and then use Non-Adiabatic Energy Treatment in the CFD solution in this way?

2. Does Maximum PDF table enthalpy exceeded usually indicate that the PDF enthalpy range itself is insufficient, or can under-converged transient time steps create the same warning?

3. Could prescribing the pilot directly as hot burnt products ((c=1, Tapprox2000) K) cause this problem, even though its temperature is below the maximum temperature visible in the PDF table?

4. Is the relevant upper enthalpy limit dependent on local (Z) and (c), rather than simply on the global maximum temperature shown in Display PDF Table?

5. What is the recommended way in Fluent to identify exactly where and why the cells exceed the PDF-table enthalpy range?

6. Before rebuilding the PDF table with a larger enthalpy range, what settings or fields should I check first?

I would prefer to identify the root cause before simply extending the table range, since I do not want to hide a numerical or boundary-condition problem by increasing the table limits.

[skulkarn]

Hello,

Could you please share the images? Did you first run the lower equation models for turbulence and then switch to LES? Please run the two-equation turbulence models and once converged, proceed with LES. Once converged with LES, only then turn On the Species Transport (Relax to Chemical Equilibrium) and converge it. Once done, please use Partially Premixed Combustion and then radiation.

[can.sumeyye]

Hello,

Thank you very much for your reply and for suggesting a staged initialization procedure.

I think I couldn't upload the images because the forum's interface changed. The console shows "Maximum PDF table enthalpy exceeded in XXXXX cells" while residuals are scrolling. Or were you asking about the image of the flame?

To answer your first question directly, I did not first converge a two-equation RANS solution and then switch to LES. I developed the non-reacting flow directly with LES before activating combustion.

If I understood your recommendation correctly, you are suggesting the following sequence:

Two-equation RANS → LES → Species Transport with “Relax to Chemical Equilibrium” → Partially Premixed FGM → Radiation

Before restarting the calculation, I would like to clarify whether this sequence is being recommended specifically as a remedy for the Maximum PDF table enthalpy exceeded warning, or mainly as a general best-practice initialization procedure.

The reason I am hesitant to restart immediately is the computational cost. This is a roughly 10-million-cell LES, and my available core-hour budget is limited. The present solution has already accumulated a considerable amount of computational time. If you strongly recommend restarting and using the Relax to Chemical Equilibrium stage, I can certainly do that. I am not trying to avoid restarting if it is technically necessary. My concern is simply that I do not want to spend a large part of my remaining core-hours either restarting unnecessarily or, conversely, continuing a solution that cannot properly recover.

The present solution has also improved considerably after adjusting the transient convergence settings. My current settings are approximately:

Time step: 5×10e−6s
Maximum iterations per time step: 55
Progress Variable URF: reduced from 0.9 to 0.8
Energy URF: 1.0
Momentum URF: 0.7

With these settings, the continuity residual generally decreases to approximately 7−8×10e−3
 within each physical time step. The number of cells reported by

Maximum PDF table enthalpy exceeded in XXXXX cells has also decreased substantially and is currently around 13,000 cells, although the decrease has now become quite slow.

This leaves me uncertain whether the present solution is still recovering and can eventually become acceptable, or whether I am spending computational time trying to recover a solution that should instead be restarted.

Could you please clarify the following points from my original question?

Can Maximum PDF table enthalpy exceeded be caused by insufficient convergence within a transient time step, even if the PDF table enthalpy range itself is adequate?
In my case, the warning count has shown a strong sensitivity to time-step size, maximum iterations per time step, and Progress Variable relaxation.
Is the relevant maximum PDF-table enthalpy a local limit depending on mixture fraction Z, progress variable c, and the local thermochemical state, rather than simply the global maximum temperature/enthalpy visible in Display PDF Table?
Could prescribing the pilot directly as hot burnt products, with approximately
Z=1, c=1, T=2001 K, still trigger the warning even though this temperature is approximately equal to the adiabatic burnt temperature at Z=1, c=1 and below the highest temperature visible in the non-adiabatic PDF table?
Is it correct in this Partially Premixed FGM formulation to generate adiabatic premixed flamelets and then use Non-Adiabatic Energy Treatment in the CFD calculation?

What is the recommended Fluent method to identify the exact cells responsible for Maximum PDF table enthalpy exceeded?

I can visualize PDF Table Heat Loss/Gain = 1, and this region appears mainly around the pilot/flame-base area. However, I do not know whether these are exactly the same cells that generate the console warning. At present, I therefore do not know the exact spatial location of the approximately 13,000 exceeded cells.

Before rebuilding or extending the PDF table, which specific fields or settings would you recommend checking to distinguish between:
insufficient PDF-table enthalpy range,
transient under-convergence,
a boundary-condition/pilot issue,
or an initialization/startup problem?
Regarding your recommendation to use Species Transport with “Relax to Chemical Equilibrium”, do you mean that this should be used only as an intermediate initialization/stabilization stage, and then disabled before activating Partially Premixed FGM?

Do you specifically recommend that I restart this existing calculation from the RANS stage, or is the RANS → LES → Relax to Chemical Equilibrium → FGM sequence mainly a best-practice recommendation for initializing new cases?

This is particularly important for me because of the computational cost. If I restart from the beginning using your proposed procedure, would you expect this to reach a reliable FGM solution faster than continuing to stabilize the present LES-FGM solution?

In other words, based on your experience, would you consider my current reacting solution still recoverable, or would you consider it unreliable because of the way combustion was initialized?

Finally, is there any practical acceptance criterion for the Maximum PDF table enthalpy exceeded warning?

In particular:

Does the number of exceeded cells necessarily need to reach zero?
Is there an acceptable fraction of the total cell count?
Does the location of the affected cells matter more than the absolute number?

I have seen discussions suggesting that a very small and highly localized region near a burner lip or flame-anchoring region may sometimes be tolerable, but I do not know whether this is an officially supported interpretation. Since I have not yet identified the exact warning cells, I also cannot currently determine whether my remaining ~13,000 cells are confined to such a region or distributed more broadly.

Radiation is intentionally neglected in the present study. Could you also please clarify whether the radiation step in your previous recommendation is necessary for the stabilization procedure, or whether it was only a general recommendation?

I am attaching the relevant images of the Solution Methods settings, residual behavior, PDF Table Heat Loss/Gain, temperature field, Courant number, and PDF-table display to provide more context.

I apologize for the number of detailed questions, but I am currently at a decision point where restarting the calculation or continuing the present solution both have a substantial computational cost, and I am quite concerned about making the wrong choice with the remaining core-hour allocation.

Thank you very much for your time and guidance. I genuinely appreciate your help with this issue.

Best regards,
Sümeyye Can