Extended flamelet model and improved interaction of chemistry and turbulence for modeling partially premixed combustion with a joint PDF method

Turbulent combustion is commonly categorized into premixed, non-premixed and partially premixed combustion. For nonpremixed combustion simulations the laminar flamelet concept proved to be very valuable while for the more complex case of partially premixed combustion this model shows considerable deficiencies. Here, the classical laminar flamelet approach is extended to the partially premixed combustion regime. For that, the joint statistics of mixture fraction, scalar dissipation rate and a progress variable, calculated with a joint probability density function (PDF) method, is used to get the statistics of the compositions and of the chemical energy source term from pre-processed flame tables. This approach can be compared with the unsteady flamelet concept; the main differences consists of the way the progress variable evolution is computed and in the pre-computed flame tables. The progress variable describes the point of time a fluid parcel is consumed by a flame front. The fluid parcels are represented by computational particles, which are used for PDF methods. The pre-computed flame tables are computed from steady solutions 2D stabilized flames propagating into an unburnt mixture with varying mixture fraction. The corresponding position of a fluid particle in such a 2D laminar flame is determined by its mixture fraction and a burning time; both to be modeled for each computational particle in the PDF simulation. Numerical experiments of turbulent diffusion jet flames demonstrate that this approach can be employed for challenging test cases. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling Intermediate Species in Partially Premixed Turbulent Combustion Based on the LES-FGM Method北大核心CSCD

The LES of partially premixed turbulent flame MRB in TU Darmstadt was conducted based on the flamelet-tabulated combustion model FGM, and effects of premixed and partially premixed tabulations on the modelling results were studied. The results show that, different methods of tabulation exhibit limited influences on the predictions of the flame structure, velocity, and major species, but using a partially premixed tabulation largely improves the reliability of modelling intermediate minor species CO and H2. The underlying reason lies in a better inclusion of the fuel-air mixing effects through the partially premixed tabulation, which is built based on laminar counter-flow flames. Adding extra transport equations for the intermediate species improves the predictions of intermediate species, especially given a premixed tabulation adopted; meanwhile, the stretch effects in this turbulent flame are ignorable. The results are significant to guide the high-fidelity simulation of partially premixed turbulent flames based on the flamelet-tabulated combustion model. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

An Approach to Model Partially Premixed Turbulent Combustion withProbability Density Function (PDF) Methods

In turbulent combustion one distinguishes between premixed, non-premixed and partially premixed combustion. While laminar flamelet models proved to be extremely valuable for a wide range of non-premixed flame simulations, similar approaches are more problematic in the partially premixed regime. Here the laminar flamelet concept for non-premixed turbulent combustion simulations is generalized for the partially premixed regime. Similar as in the unsteady flamelet approach, the joint statistics of a progress variable, mixture fraction and scalar dissipation rate is used to obtain the joint statistics of the compositions from pre-computed flame tables. The required distribution is computed with a joint PDF method and the main differences between the new approach and previous ones, are the pre-computed tables and the way the evolution of the progress variable is calculated. Instead of evolving 1D flamelets, steady 2D solutions of burning flamelets propagating into unburned mixtures with varying mixture fraction are considered. The location of a fluid particle in this 2D laminar flame is defined by its mixture fraction and a burning time, which are modeled for each computational particle used in the PDF method. Numerical experiments of a turbulent lifted diffusion flame and a premixed Bunsen flame demonstrate that this approach can be employed for a wide range of applications. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Lagrangian Joint PDF Approach for Turbulent Premixed Combustion

A model for premixed turbulent combustion based on a joint velocity probability density function (PDF) method and a progress variable is presented. Compared with other methods employing progress variables, the advantage here is that turbulent mixing of the progress variable requires no modeling. Moreover, by applying scale separation, the Lagrangian framework allows to account for the embedded, quasi laminar flame structure in a very natural way. The numerical results presented here are based on a simple closure of the progress variable source term and it is demonstrated that the new modeling approach is robust and shows the correct qualitative behavior. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Embedding quasi laminar 1D flame profiles to model turbulent premixed combustion with a joint PDF method

A new model for turbulent premixed combustion is presented which is based on a joint velocity composition probability density function (JPDF) method. The key idea is a scale separation approach. The method combines the model by Bray, Moss and Libby [1] (BML) for premixed combustion with the flamelet approach for nonpremixed combustion. Here, a Lagrangian formulation of the BML model is considered. The progress variable used by the BML model becomes a computational particle property and its value is triggered by the arrival of the flame front at the particle's position. Similar as in the flamelet approach we assume that the smallest eddies are not small enough to disturb the reactive diffusive flame structure. To resolve the (embedded) quasi laminar flame structure, a flame residence time is introduced. With that residence time, the evolution of the particle composition, including enthalpy, can be determined from precomputed laminar 1D flames. The main challenge with this approach is to model the probability that an embedded flamefront arrives at the particle location, which is necessary to close the chemical source term. Numerical experiments of a turbulent premixed flame show good agreement with experimental data. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Re.ned Modeling of the pressure redistribution/scrambling under consistent consideration of scalar turbulence effects in turbulent combustion

In practical turbulent flow problems of engineering importance the coupling between velocity and scalar turbulence along with the variable density plays a non negligible role. For computations using second moment closure approach, the pressure redistribution/scrambling is the most critical term to be modeled as well known. Almost all existing models consist in rescating models derived on a constant density basis in a density weighted form. With regard to turbulent premixed combustion in fact, the application of such models to a range of transient one‐dimensional and two‐dimensional premixed flames in the flamelet regime has been found to yield unsatisfactory results, see [1]. As pointed out by Sadiki [2], the use of the Favre method must be consistently considered as far as open thermodynamic systems are concerned. Furthermore, the need for maintaining certain invariance properties, physical and mathematical realizability conditions in formulating turbulence models is well accepted. Because turbulent processes are irreversible, these efforts demand a carefull consideration of thermodynamic concepts. Based on the results in [1] and following [2], this work aims to derive a physically consistent formulation of the pressure redistribution/scrambling term under consideration of the variable density. Considering the case of premixed flames, the thermochemistry is included by means of a single reactive scalar ‐ the reaction progress variable. The accuracy of the model extensions proposed is demonstrated by comparing the numerical results with experimental data in opposed jet premixed flame configuration.     

A self-similar premixed turbulent flame model

This paper is devoted to premixed combustion modelling in turbulent flow. First, we derive a model for the turbulent flame velocity based on the observed self-similarity of the turbulent flame. The model uses the local flame brush width as a fundamental parameter and, therefore, we show how it can be retrieved for numerical implementation. The diffusive property of the brush width is treated in such a way as to theoretically let the brush have a clearly defined boundary propagating at finite velocity. The model, implemented in Star-CD CFD software through user programming, is then numerically tested on three configurations for which another model, the Turbulent Flame Closure model, is known to give very good agreement. Some effects of numerics are commented and results for both models are compared. While based on very different approaches the two models lead to substantially similar results. In this way, we have shown that the local brush width can effectively be used, giving an additional degree of freedom for premixed turbulent combustion modelling.     

Thermodynamically conditioned splitting schemes in combustion problems

Algorithms for solving the two-dimensional combustion problem for premixed flames are proposed and examined. The solution method is based on splitting into convective and diffusion parts according to the processes involved. A high-resolution explicit quasi-monotone scheme with flux correction is used for the hyperbolic part. For the parabolic part, the scheme is conservative and the source in the heat equation is set to be positive; i.e., the scheme ensures that the different thermodynamic consequences of the original equations hold; therefore, the scheme is thermodynamically conditioned. The applicability of the scheme to the full and purely gasdynamic problems is examined under various types of initial conditions and with various flux limiters. Numerical results are presented for one-and two-dimensional problems, including the Frank-Kamenetskii classical problem in two dimensions. The flame is shown to become turbulent in sufficiently wide pipes.     

The effect of turbulence on mixing in prototype reaction‐diffusion systems

The effect of turbulence on mixing in prototype reaction‐diffusion systems is analyzed here in the special situation where the turbulence is modeled ideally with two separated scales consisting of a large‐scale mean flow plus a small‐scale spatiotemporal periodic flow. In the limit of fast reaction and slow diffusion, it is rigorously proved that the turbulence does not contribute to the location of the mixing zone in the limit and that this mixing zone location is determined solely by advection of the large‐scale velocity field. This surprising result contrasts strongly with earlier work of the authors that always yields a large‐scale propagation speed enhanced by small‐scale turbulence for propagating fronts. The mathematical reasons for these differences are pointed out. This main theorem rigorously justifies the limit equilibrium approximations utilized in non‐premixed turbulent diffusion flames and condensation‐evaporation modeling in cloud physics in the fast reaction limit. The subtle nature of this result is emphasized by explicit examples presented in the fast reaction and zero‐diffusion limit with a nontrivial effect of turbulence on mixing in the limit. The situation with slow reaction and slow diffusion is also studied in the present work. Here the strong stirring by turbulence before significant reaction occurs necessarily leads to a homogenized limit with the strong mixing effects of turbulence expressed by a rigorous turbulent diffusivity modifying the reaction‐diffusion equations. Physical examples from non‐premixed turbulent combustion and cloud microphysics modeling are utilized throughout the paper to motivate and interpret the mathematical results. © 2000 John Wiley & Sons, Inc.     

Multi‐Block Solution Algorithm for Joint PDF Methods

A multi‐block grid (MBG) based algorithm to solve the joint velocity‐frequency‐composition PDF transport equation for turbulent reactive flow is presented. The algorithm is based on a previously developed hybrid finite‐volume/particle approach which has significant advantages over stand alone particle PDF methods. It is demonstrated that the new solution method, due to the flexibility of MBGs, allows to perform simulation studies which involve very complex 3D geometries. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

RANS-simulation of premixed turbulent combustion using the level set approach

A model for premixed turbulent combustion is investigated using a RANS-approach. The evolution of the flame front is described with the help of the level set approach [1] which is used for tracking of propagating interfaces in free-surface flows, geodesics, grid generation and combustion. The fluid properties are conditioned on the flame front position using a burntunburnt probability function across the flame front. Computations are performed using the code FASTEST-3D which is a flow solver for a non-orthogonal, block-structured grid. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Multigrid Algorithm for Hybrid Joint PDF Simulations in Complex Geometries

In hybrid joint probability density function (joint PDF) algorithms for turbulent reactive flows the equations for the mean flow discretized with a classical grid based method (e.g. finite volume methods (FVM)) are solved together with a Monte Carlo (particle) method for the joint velocity composition PDF. When applied for complex geometries, the solution strategy for such methods which aims at obtaining a converged solution of the coupled problem on a sufficiently fine grid becomes very important. This paper describes one important aspect of this solution strategy, i.e. multigrid computing, which is well known to be very efficient for computing numerical solutions on fine grids. Two sets of grid based variables are involved: cell-centered variables from the FVM and node-centered variables, which denote the moments of the PDF extracted from the particle fields. Starting from a given multiblock grid environment first a new (refined or coarsened) grid is defined retaining the grid quality. The projection and prolongation operators are defined for the two sets of variables. In this new grid environment the particles are redistributed. The effectiveness of the multigrid algorithm is demonstrated. Compared to solely solving on the finest grid, convergence can be reached about one order of magnitude faster when using the multigrid algorithm in three stages. Computation time used for projection or prolongation is negligible. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evaluation of the approximated diffusion flamelet concept using fuels with different chemical complexity

The ability of flamelet models to reproduce turbulent combustion in devices such as diesel engines or gas turbines has enhanced the usage of these approaches in Computational Fluid Dynamics (CFD) simulations. The models based on turbulent look-up tables generated from counterflow laminar diffusion flames (DF model) permit drastic reduction of the computational cost of the CFD calculation. Nevertheless, for complex molecular fuels, such as n-heptane, the oxidation process involves hundreds of species and the calculation of the transport equations together with the ODE system that models the chemical kinetics for the DF solution becomes unaffordable for industrial devices where hundreds of flamelets are required. In this context, new hypotheses have to be introduced in order to reduce the computational cost maintaining the coherence of the combustion process. Recently, a new model known as Approximated Diffusion Flamelet (ADF) has been proposed with the aim of solving the turbulent combustion for complex fuels in a reduced time. However, the validity of this model is still an open question and has to be verified in order to justify subsequent CFD calculations. This work assesses the ADF model and its ability to reproduce accurately the combustion process and its main parameters for three fuels with different chemical complexity and boundary conditions by its comparison with the DF model. Results show that although some discrepancies arise, the ADF model has the ability to correctly describe the ignition delay and the combustion structure in the auto-ignition zone that is the most relevant one for industrial processes.     

An efficient PDF calculation of flame temperature and major species in turbulent non-premixed flames

In spite of recent developments in the PDF calculations of turbulent flames, the high computational time required to implement PDF simulations makes it intractable in practical applications. Therefore, it is important to design and select different parameters for PDF calculation of most important quantities, i.e. temperature and major species means, in an efficient manner. The ingredients of the present model are a standard k$k$–ε$\epsilon$ turbulence closure for modeling flow field and a joint composition PDF closure for the scalar fields. A modified Curl model is applied to consider molecular mixing in PDF transport equation and a simplified two-step mechanism which lowers the computational cost is incorporated to describe the chemistry. The flow field is solved numerically using an upwind discretization for the convective terms and a central discretization for the diffusion terms by coupling it with an Eulerian Monte Carlo algorithm to solve PDF transport equation. To show the superiority of the current PDF calculations over traditional moment-closure methods commonly used in practical applications, simulation is also performed by RANS method which shows large discrepancies, especially in prediction of maximum flame temperature (on the basis of present results, predicted flame temperature has 26%$26\%$ error via RANS method and 8%$8\%$ error via PDF method). Stoichiometric flame length predicted by RANS has 10%$10\%$ error while, by PDF method, this error is negligible and about 0.6%$0.6\%$. The effect of coefficient _CΦ$C_{\Phi }$ on the modified Curl model is also investigated and it is concluded that the commonly used value _CΦ=2.0$C_{\Phi }=2.0$ is the best choice for the case of study. The numerical results obtained reveal that Westbrook–Drier mechanism is working very well in fuel-lean (F<_Fst$F<F_{\mathit{st}}$) non-premixed combustion and also it predicts the total heat released in methane combustion in a very good agreement with the experiment.     

Application of a non-asymptotic approach to prediction of the propagation of a flame through a fuel and/or oxidant droplet cloud

The mathematical analysis of laminar premixed spray propagation has generally been based on exploiting the inverse of the large chemical activation energy as an appropriate parameter for asymptotic analysis. In the current work we apply a modification of a recently suggested non-asymptotic approach for gaseous flames which makes use of a different approximation. In it, only the Arrhenius exponential term in the reaction rate expression is approximated using a step function chosen so that the two functions are in proximity in an integral sense. Application of this approach is more amenable and is shown to yield a simple formula for the burning velocity of a flame propagating through a cloud of fuel and/or oxidant droplets, for the fuel rich off-stoichiometric case in which the only reactant present in the chemical reaction term is the deficient oxidant which appears linearly. Results computed with the new analytical solutions are presented and a comparison is made with the predictions using the usual large activation energy approach. In addition, a double spray is considered for the first time in which both liquid oxidant and liquid fuel feature as sprays of droplets in the unburned pre-mixture. Such a situation arises in rocket engines in which two initially separate spray streams mix in a turbulent shear flow so that locally one dimensionally propagating double spray premixed flames are created. The analysis leads to an analytical expression for the laminar burning velocity dependent on the spray- and gas-related parameters. Typical thermal and velocity maps in parametric space are presented.     

Simulation of methane turbulent swirling flame in the TECFLAM combustor

A presumed probability density function (PDF) model for temperature fluctuation is proposed and formulated in this paper. It incorporates the four-step reaction mechanism of methane combustion. A set of analytical expressions is derived for the time-averaged four-step reaction rates. The model is employed to numerically simulate methane turbulent swirling flame in the TECFLAM combustor. The calculated gas axial, radial and tangential velocities, species mass fractions, temperature, and temperature fluctuation are compared with the measured test data. Agreement is achieved between the calculation and the measurement.     

Large eddy simulation of an ethylene-air turbulent premixed V-flame

Large eddy simulation (LES) using a dynamic eddy viscosity subgrid scale stress model and a fast-chemistry combustion model without accounting for the finite-rate chemical kinetics is applied to study the ignition and propagation of a turbulent premixed V-flame. A progress variable c-equation is applied to describe the flame front propagation. The equations are solved two dimensionally by a projection-based fractional step method for low Mach number flows. The flow field with a stabilizing rod without reaction is first obtained as the initial field and ignition happens just upstream of the stabilizing rod. The shape of the flame is affected by the velocity field, and following the flame propagation, the vortices fade and move to locations along the flame front. The LES computed time-averaged velocity agrees well with data obtained from experiments.     

A mixing model providing statistics of the conditional scalar dissipation rate

Joint composition probability density function (PDF) methods are used for the numerical simulation of turbulent reactive flows. Here, other than in classical Reynolds averaged Navier–Stokes (RANS) or large eddy simulation (LES) approaches, the highly non-linear chemical source term appears in closed form. On the other hand, mixing models are required for the closure of the molecular diffusion term. In the present work, the joint statistics of the scalar and the scalar dissipation rate provided by the parameterized scalar profile (PSP) mixing model are validated. The goal is to combine the PDF method with a flamelet approach, where the scalar dissipation rate plays a crucial role in determining the contribution of the chemical source term. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical and numerical aspects of one-dimensional laminar flame simulation

The aim of this paper is to solve several mathematical and numerical questions related to the simulation of stationary and nonstationary premixed flat flames. Most of the results are obtained in the general context of complex chemical and diffusion mechanisms. The main mathematical results concern: (i) thea priori positivity of the mass fractions, and (ii) the sensitivity of the flame speed to the computational domain. The numerical method proposed for solving the stationary problem is a new combination of the pseudo-nonstationary approach, the Newton iterations, and the adaptive gridding. The computation of H₂-O₂-N₂ flames with various initial concentrations (including the chemical extinction zone) shows the efficiency of this method.     

Progress in the Self-Similar Turbulent Flame premixed combustion model

This paper is devoted to premixed combustion modeling in turbulent flow. First, we briefly remind the main features of the Self-Similar Turbulent Flame model that was more extensively developed in a former paper. Then, we carefully describe some improvements of the model. The determination of the turbulent flame velocity is based on the observed self-similarity of the turbulent flame and uses the local flame brush width as a fundamental parameter, which must be retrieved. With respect to the former version, we now derive more rigorously how the density variation has to be taken into account in the width retrieving function. We reformulate the diffusion term as a classical flux divergence term. We enforce the compatibility of the model for the limit of weak turbulence. We include a contracting effect of the source term, thus allowing to give a stationary mono-dimensional asymptotic solution with a finite width. We also include in a preliminary form, a stretch factor, which proves to be useful for controlling the flame behavior close to the flame holder and near the walls. The model implementation in the Star-CD CFD code is then tested on three different flame configurations. Finally, we shortly discuss the model improvements and the simulation results.