Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

In order to reduce the computational cost of flame simulations, several methods have been developed during the last decades, which simplify the description of the reaction kinetics. Most of these methods are based on partial-equilibrium and steady-state assumptions, assuming that most chemical processes have a much smaller time scale than the flow time scale. These assumptions, however, give poor approximations in the ‘colder’ regions of a flame, where transport processes are also important. The method presented here, can be considered as a combination of two approaches to simplify flame calculations, i.e. a flamelet and a manifold approach. The method, to which we will refer as the Flamelet-Generated Manifold (FGM) method, shares the idea with flamelet approaches that a multi-dimensional flame may be considered as an ensemble of one-dimensional flames. The implementation, however, is typical for manifold methods: a low-dimensional manifold in composition space is constructed, and the thermo-chemical vari...

Modelling of premixed laminar flames using flamelet-generated manifolds

The cost of including full kinetics in realistic computations remains extremely high. This has led many researchers to develop reduction techniques for the chemistry. These methods are generally valid only in a very limited range of equivalence ratio, pressure, or temperature and require extensive human time to develop the reduced schemes. Recently, an automatic method based on intrinsic low-dimensional manifolds (ILDM) has been proposed. Because of ILDM, the reduction of detailed reaction schemes is much simuplified, leading to the fast generation of look-up tables containing the information corresponding to the reduced chemical schemes. Nevertheless, the ILDM method is not well suited to describe the low-temperature domain, since the dimension and therefore the complexity of the databases increase tremendously in this zone. In this work, we propose a new version of the ILDM method, called flame prolongation of ILDM (FPI), which enables us to solve the problem at low temperatures. We used laminar premixed free flames to extend the manifolds generated with ILDM, thus leading to smooth and accurate evolutions of the species along all the flame front. In order to demonstrate the interest of FPI, we computed the response of a premixed flame to straining using the double-premixed counterflow flame configuration. We show that using FPI, the correct evolution is obtained for all species from almost unstrained flames up to flames near extinction. The computational times are tremendously reduced with FPI in comparison with full chemistry.

Liminar premixed hydrogen/air counterflow flame simulations using flame prolongation of ILDM with differential diffusion

The Extended Coherent Flame Model of Colin et al. (2003) developed to model combustion in perfectly or partially mixed mixtures is adapted to also account for unmixed combustion. The ECFM model is based on a flame surface density equation which takes into account the wrinkling of the flame front surface by turbulent eddies and a conditioning averaging technique which allows precise reconstruction of local properties in fresh and burned gases even in the case of high levels of local fuel stratification. This model has been used with success in gasoline engines (Duclos et al., 1996; Duclos and Zolver, 1998; Lafossas et al., 2002; Henriot et al., 2003; Kleemann et al., 2003). In order to adapt the model to unmixed combustion for Diesel application, a description of the mixing state has been added. It is represented by three mixing zones: a pure fuel zone, a pure air plus possible residual gases zone and a mixed zone in which the ECFM combustion model is applied. A mixing model is presented which allows progressive mixing of the initially unmixed fuel and air. This new combustion model, called ECFM3Z (3-Zones Extended Coherent Flame Model), can therefore be seen as a simplified CMC (Conditional Moment Closure) type model where the mixture fraction space would be discretized by only three points. The conditioning technique is extended to the three mixing zones and allows to reconstruct, like in the ECFM model, the gas properties in the unburned and burned gases of the mixed zone. Application of the model to internal combustion engine calculations implies the necessity of auto-ignition modelling coupled to premixed and diffusion flames description. Auto-ignition is modelled following (Colin et al., 2004), while the premixed turbulent flame description is given by the ECFM. The diffusion flame is now accounted for thanks to the three zones mixing structure which represents phenomenologically the diffusion of fuel and air towards the reactive layer, that is the mixed zone. The ECFM3Z combustion model has already been presented (Beard et al., 2003) in a comparative work between Diesel experiments and corresponding calculations covering different engine operating points. Here, the model is presented in all its details and its behavior is analysed when the relative duration of injection and auto-ignition delay are varied in a direct injection Diesel engine. It is shown that the model is able to reproduce the relative importance of auto-ignition and diffusion flame on the total heat release, depending on the engine operating point considered.

/pdf/the-3-zones-extended-coherent-flame-model-ecfm3z-for-xfe9a586nc.pdf

The 3-Zones Extended Coherent Flame Model (Ecfm3z) for Computing Premixed/Diffusion Combustion

Approximating the chemical structure of partially premixed and diffusion counterflow flames using FPI flamelet tabulation

Many models are now available to describe chemistry at a low CPU cost, but only a few of them can be used to describe correctly premixed, partially premixed and diffusion combustion. One of them is the FPI model that uses two coordinates: the mixture fraction Z and the progress variable c. In this paper, we introduce a new evolution of the FPI method that can now handle heat losses. After a short review of kinetic models used in turbulent combustion, the main features of the new three-dimensional FPI method, in which we introduce a third coordinate for enthalpy h, are presented. First, a one-dimensional radiative premixed flame validation case is presented for a large range of radiative heat losses. Second, we present the results of simulations of two laminar burners. Both the fully and the partially premixed burner simulations give a good estimation of all the flame features such as the flame stabilization (driven by heat losses), the flame structure and the profile of major and minor species.

Modelling non-adiabatic partially premixed flames using flame-prolongation of ILDM

https://hal.archives-ouvertes.fr/hal-00472611/document

A filtered tabulated chemistry model for LES of premixed combustion

Tabulated chemistry and presumed probability density function (PDF) approaches are combined to perform RANS modeling of premixed turbulent combustion. The chemistry is tabulated from premixed flamelets with three independent parameters: the equivalence ratio of the mixture, the progress of reaction, and the specific enthalpy, to account for heat losses at walls. Mean quantities are estimated from presumed PDFs. This approach is used to numerically predict a turbulent premixed flame diluted by hot burnt products at an equivalence ratio that differs from the main stream of reactants. The investigated flame, subjected to high velocity fluctuations, has a thickened-wrinkled structure. A recently proposed closure for scalar dissipation rate that includes an estimation of the coupling between flame wrinkling and micromixing is retained. Comparisons of simulations with experimental measurements of mean velocity, temperature, and reactants are performed.

Olivier Gicquel

Papers

Liminar premixed hydrogen/air counterflow flame simulations using flame prolongation of ILDM with differential diffusion

Approximating the chemical structure of partially premixed and diffusion counterflow flames using FPI flamelet tabulation

Modelling non-adiabatic partially premixed flames using flame-prolongation of ILDM

A filtered tabulated chemistry model for LES of premixed combustion

Premixed turbulent combustion modeling using tabulated detailed chemistry and PDF