I am trying to implement Monte Carlo PDF(Probability Density Function) model into KIVA code for the combustion modeling. May I know if anyone knows about the implementation of PDF method and suitable references on this matter. Any help would be greatly appreciated.

Atsushi Yamada

(1). You can find more references by typing "monte carlo pdf method" into a web-search engine. Here is an example.

References Raju M.S.: Heat Transfer and Performance Characteristics of a Dual-Ignition Wankel Engine. SAE Paper 920303, SAE Tech. Lit. Abstr., 1992.

Shyy, W.; Correa, S.M.; and Braaten, M.E.: Computation of Flow in a Gas Turbine Combustor. Combust. Sci. Tech., vol. 58, 1988, pp. 97-117.

Hsu, A.T.; Tsai Y.-L.P.; and Raju M.S.: Probability Density Function Approach for Compressible Turbulent Reacting Flows. AIAA Journal, vol. 32, no. 7, pp. 1407-1415, 1994.

Hsu A.T.; Raju M.S.; and Norris A.T.: Application of a pdf Method to Compressible Turbulent Reacting Flows. AIAA Paper 94-0781, 1994.

Raju, M.S.: Coupled Monte-Carlo-PDF/SPRAY/CFD Computations of Swirl-Stabilized Flames. AIAA Paper 95-2442, 1995.

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Dear Chien, Thank you very much for the kind helps.

A good start point is a paper Stephen B. Pope "Pdf mehtods for turbulent reactive flows." Prog. Energy Combust. Sci, 1985, Vol. 11. pp. 119-192.

Depends on you situation, you should choose between Lagrangian and Eulerian methods and their coupling to the flow field. With KIVA, I assume you want to use the Eulerian method. Beware of the numerical diffusion. One key feature of the PDF mehtod is its ability to close turbulence-chemistry interaction. If the mixing part is too diffusive, then it defeats the purpose. Also integrating the reaction kinetic step in PDF is very computationally intensive. Simplification of the reaction kinetics is almost essential. Another good reference is Chapter 7 (by Cesar Dopazo) in the book "Turbulent reacting flows" by Libby and Williams, Academic Press, 1994.

Good luck.

Hi, Tsai Thank you for your post. I am trying to use PDF method for modeling of gasoline engine combustion.

Why do you suggest to use Eulerian method, is it implemented easier into kiva code? Could you cite any reference of the matter.As I know, IWR, Universitaet Heidelberg implemented PDF into kiva, they used Lagrangian particle technique.

"Simplification of the reaction kinetics is almost essential", I finally want to use detailed chemical mechanism. Is it really a problem with PDF? Before reading your message, in my image, PDF is able to treat the detailed chemical mechanism.

Thanks a lot for the helps.

Simplification is intended to accelerate the calculation. PDF methods are very computationally intensive. Unless your kinetics is already highly simplified and limited to a few species, otherwise, either a look-up table or a fast integration scheme is necessary to make the simulation usable. Lagrangian mehtods require great care about the statistical integrity in each cell. Artificial re-sampling is needed to achieve good results. Eulerian methods do not have the sampling problem, but is very numerically dissipative.

First, KIVA is an arbitrary Lagrangian-Eulerian (ALE) code, which means it can be run as an Eulerian code, a Lagrangian code, or neither (the grid moves but not following the fluid). Engine simuations are almost always neither, and your PDF model will have to be made consistent with this mode of operation.

Second, you should reconsider your plan to use detailed kinetics for gasoline for a variety of reasons. Gasoline is a complex mixture of species that varies from one batch to another. The most abundant species have 6 or more carbon atoms, and not all of them are alkanes. Therefore, in addition to not having a specific starting composition, you have the problems of needing to use well over a thousand species and many thousands of reactions, many of which have poorly known or unknown rates. Just developing these mechanisms independently of cfd codes is a research specialty.

To get an idea of the computational difficulty, consider that KIVA has an array containing the species densities in each zone. A 3d engine simulation is going to have at least 100,000 zones, and it will be run in double precision (8 bytes per word). For 1000 species, this one array will use a gigabyte of memory.

Unless I have misunderstood what you want to do, you will be forced to consider simplifications to either the chemistry or the cfd to make the problem tractable.

Gasoline composition does indeed vary a lot. However, Gasoline is often approximated to be mostly iso-octane and (few other species in some instances) for chemistry purposes. The larger hydrocarbons break down into smaller hydrocarbons before oxidation. You can get some clue as to what the smaller hydrocarbons are by looking at what the unburnt hydrocarbon emissions are. Typically, you find methane, propane & propene in the exhaust.

As Dean pointed out, your goals seems too ambitious if not intractable at this point. KIVA is not known to be a fast code. You would need to parallelize it before running it with additional time-consuming routines. Perhaps, running the code with methane as a fuel is a less simpler task. Methane is a good approximation for natural gas and there are engines running on it. Also, take a look at the ERC homepage at Wisconsin. These guys have done extensive engine research (including work on KIVA) and you may want to run your ideas by them.

Dean, Thanks for the suggestions. Simplification is necessary for engine combustion modeling by using pdf and detailed chemical mechanism. In the begining, I want to construct a frame that should allow further detailed mechanism implementation.

kalyan, Thanks for the message. Yau are right, my plan is really somewhat ambitious for modeling very complicated engine combustion.As your suggeations, I will try with simlified cases. However, it is very important for me to make a reasonable strategy and select stuitable models.I know Prof Rutland has implemented LES and PDF models in KIVA.

Mr./Mrs. Yamada,

I'm developing a Monte Carlo PDF code too.A hybrid algorithm is employed:Finite Volume on unstructured mesh and Monte Carlo with Lagrangian method.The test case is the turbulent reactive flow past a bluff-body.

As my point of view, thec omputation will be very huge if detail chemistry mechnism is used.In my work, the fuel is premixed propane/air.Now I use single-step reaction mechnism. There are 40 particles in every cell in average.I run the program on an AMD-1200M/512M RAM PC.The program evolves 5 steps every minute(~5*4.e-6s).I can't image how huge the computation cost is if detail chemistry mechnism is used.And to perform a new code is a hard work.simple chemistry mechnism and sim ple test case is a goodc hoice.PDFm ethods is very powerful to deal with the chemistry reaction. It's easy to adopt detail one in the future.I think your major work is to make the code run correctly,not to create a perfect,omnipotent tool.

I'm a student too.We can exchange experiment of work. Good luck! Hai-Wen Ge

Dear Hai-Wen, Thank you for your nice comments. I would like to share the experinces of PDF method with you.

I am just a beginner of PDF and trying to construct a code for combustion modeling. Although I have read some PDF papers, I am still always confused by the method, detailed treatment of implementation of the PDF. If there is a reference PDF file available, that would be of great helps.

Yours,