An efficient stochastic chemistry approximation for the PDF transport equation

Kraft, Markus; Wagner, Wolfgang

doi:10.1515/mcma.2002.8.4.371

Cited by 4 publications

(4 citation statements)

References 21 publications

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“…The Partially Stirred Reactor (PaSR) model has been widely used to study the interaction of turbulence and chemistry. In particle methods this model has provided a sophisticated way for chemical and mixing schemes in the field of combustion [22,23]. This model assumes statistical homogeneity of the mixture in the reactor.…”

Section: Model Formulation 21 General Formulationmentioning

confidence: 99%

“…The dimension of the system ( 12) is high; a splitting technique is then used to decouple the effects of reaction and mixing (more details about the splitting technique are given in [22][23][24]). Note that the term H i in Equation (12) has been solved using CVode software package [28], which is very efficient deterministic approach for stiff problems.…”

Section: Simulation Proceduresmentioning

confidence: 99%

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A PDF method for HCCI combustion modeling : CPU time optimization through a restricted initial distribution

Pommier

Maroteaux

Sorine

2012

Mechanics & Industry

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Probability Density Function (PDF) is often selected to couple chemistry with turbulence for complex reactive flows since complex reactions can be treated without modeling assumptions. This paper describes an investigation into the use of the particles approximation of this transport equation approach applied to Homogeneous Charge Compression Ignition (HCCI) combustion. The model used here is an IEM (Interaction by Exchange with the Mean) model to describe the micromixing. Therefore, the fluid within the combustion chamber is represented by a number of computational particles. Each particle evolves function of the rate of change due to the chemical reaction term and the mixing term. The chemical reaction term is calculated using a reduced mechanism of n-heptane oxidation with 25 species and 25 reactions developed previously. The parametric study with a variation of the number of particles from 50 up to 10 4 has been investigated for three initial distributions. The numerical experiments have shown that the hat distribution is not appropriate and the normal and lognormal distributions give the same trends. As expected when the number of particles increases for homogenous mixture (i.e. high turbulence intensity), the in-cylinder pressure evolution tends towards the homogeneous curve. For both homogeneous and inhomogeneous (i.e. low turbulence intensity) cases, we have found that 200 particles are sufficient to model correctly the system, with a CPU time of a few minutes when a restriction of initial distribution is adopted.

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Section: Model Formulation 21 General Formulationmentioning

confidence: 99%

Section: Simulation Proceduresmentioning

confidence: 99%

A PDF method for HCCI combustion modeling : CPU time optimization through a restricted initial distribution

Pommier

Maroteaux

Sorine

2012

Mechanics & Industry

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“…In the context of PDF methods, it has been found [15] that treating the chemistry splitting step by stochastic direct simulation can be efficient under some circumstances. Most authors, though, model the chemistry step by a system of ODEs and solve it using an implicit numerical method.…”

Section: Introductionmentioning

confidence: 99%

Explicit stochastic ODE solution methods applied to high-temperature combustion

Mosbach

Kraft

2006

Monte Carlo Methods and Applications

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New stochastic algorithms for the numerical solution of systems of ordinary differential equations (ODEs) are proposed. Furthermore, a correspondence principle is established between these algorithms, which are based on the theory of Markov jump processes, and deterministic schemes. For one of the proposed stochastic algorithms, a detailed numerical study of some of its properties is carried out using examples from high-temperature homogeneous gasphase combustion. One deterministic method yielded by our correspondence principle is used to shed light on various aspects of the considered stochastic algorithm. In addition, we use the widespread stiff ODE-solver package DASSL for comparison. Advantages of our methods include among others their exceptional simplicity of implementation and negligible start-up costs. For a large system at moderate accuracy requirements, the proposed stochastic algorithms exhibit computational efficiency in the same order of magnitude as implicit solvers, assuming multiple runs. In view of the stiffness of the considered systems and the explicit nature of our algorithms, this is rather surprising. Limitations of our methods concerning the choice of system, initial conditions, and accuracy requirements are also addressed.

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“…The ensemble of N particles describes the mixture in the combustion chamber and each particle evolution is obtained by ordinary differential equations (Equation ( 2)). A splitting technique was used to decouple the effects of reaction and mixing process (details about the splitting technique are given in [25][26][27]) in order to reduce the dimension of the system (2).…”

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confidence: 99%

Optical and Numerical Investigations on Combustion and OH Radical Behavior Inside an Optical Engine Operating in LTC Combustion Mode

Maroteaux

Mancaruso²,

Vaglieco³

2023

Energies

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Low Temperature Combustion (LTC) is a relevant process for internal combustion engines (ICE). This combustion mode is based on premixed fuel/air and fuel lean in-cylinder mixture allowing reduction in NOx and PM emissions while maintaining higher thermal efficiency. In order to investigate the effect of engine operating conditions on the behavior of LTC mode, including OH radical evolution, optical measurements and numerical simulations were performed on a transparent CR diesel engine. The homogeneity of the engine charge was obtained by using very early injection timings. In this study, varying injection strategies were investigated for different engine speeds. In parallel to the experimentation, simulations of LTC mode for the same experimental operations were carried out. The model used in this study is based on a stochastic reactor model. This model includes a turbulence (k-ε) model based on a zero-dimensional energy cascade to calculate the turbulent time scale during the cycle. On the other hand, due to the stochastic approach and to reduce initial heterogeneities of the mixture, a confidence parameter was introduced in the global model to consider the real variation ranges of engine. This latter was modeled as a function of the Reynolds number allowing to initiate heterogeneities of temperature and of species mass. OH radicals were estimated with high spatial and temporal resolution using chemiluminescence measurements. Simulated in-cylinder pressure and the OH radical rate were compared to the experimental data. A good agreement was observed in terms of in-cylinder pressure trace and ignition delay times, meaning that the confidence coefficient model is accurate to describe the initial heterogeneities of the mixture. The simulated OH rate profile has the same shape as the measured OH trace and the main ignition occurs at the same time. This study corroborates that the OH radical is an appropriate tool to identify combustion stages.

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An efficient stochastic chemistry approximation for the PDF transport equation

Cited by 4 publications

References 21 publications

A PDF method for HCCI combustion modeling : CPU time optimization through a restricted initial distribution

A PDF method for HCCI combustion modeling : CPU time optimization through a restricted initial distribution

Explicit stochastic ODE solution methods applied to high-temperature combustion

Optical and Numerical Investigations on Combustion and OH Radical Behavior Inside an Optical Engine Operating in LTC Combustion Mode

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