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)     

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)     

Mixing modeling for stochastic simulations of turbulent premixed flames

The use of probability density function (PDF) methods for turbulent combustion simulations is very attractive because arbitrary finite-rate chemistry can be exactly taken into account. However, many real flames involve a variety of mixing regimes (non-premixed, partially-premixed and premixed turbulent combustion), and the development of PDF methods for partiallypremixed and premixed turbulent combustion turned out to be a very challenging task. A promising way to extend the range of applicability of PDF methods to the fast flamelet chemistry of turbulent premixed flames is described here. Simulation results of three turbulent premixed flames demonstrate the suitability of this approach. (© 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.     

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)     

Examination of errors of table integration in flamelet/progress variable modeling of a turbulent non-premixed jet flame

A flamelet model implementation consists of two steps: the generation of a set of laminar flamelet solutions and the integration of the laminar flamelet solutions with presumed shape probability density functions (PDFs) to produce a flamelet table for turbulent flame simulations. Many studies have been done in the past to examine the effect of different flamelet modeling strategies including the effect of employing different laminar flamelet solutions for the modeling. However, little work has been done to examine the effect of different presumed PDF table integration approaches on different flamelet model predictions. This work aims at investigating the source of errors arising from the flamelet table integration. The flamelet/progress variable model is chosen as a representative flamelet model, and three different presumed PDF table integration approaches are compared to examine the effect of table integration on flamelet model predictions. A laboratory-scale turbulent non-premixed jet flame (Sandia flame D) is chosen as a test case for the examination. In general, some evident sensitivity of the modeling results to the different flamelet table integration approaches is observed. The underlying reasons for the performance difference of different approaches are explored, and it is found that a model that preserves the one-dimensional laminar flamelet structure during the presumed-PDF table integration can improve the model prediction accuracy. Different sources of errors involved in flamelet model implementation are investigated, including numerical integration errors, flamelet table errors, and the errors in the predictions of the flamelet independent variables.     

Laminar flamelet modeling of a turbulent CH4/H2/N2 jet diffusion flame using artificial neural networks

The laminar flamelet concept is used in the prediction of mean reactive scalars in a non-premixed turbulent CH₄/H₂/N₂ flame. First, a databank for temperature and species concentrations is developed from the solutions of counter-flow diffusion flames. The effects of flow field on flamelets are considered by using mixture fraction and scalar dissipation rate. Turbulence-chemistry interactions are taken into account by integrating different quantities based on a presumed probability density function (PDF), to calculate the Favre-averaged values of scalars. Flamelet library is then generated. To interpolate in the generated library, one artificial neural network (ANN) is trained where the mean and variance of mixture fraction and the scalar dissipation rate are used as inputs, and species mean mass fractions and temperature are selected as outputs. The weights and biases of this ANN are implemented in a CFD flow solver code, to estimate mean values of the scalars. Results reveal that ANN yields good predictions and the computational time has decreased as compared to numerical integration for the estimation of mean thermo-chemical variables in the CFD code. Predicted thermo-chemical quantities are close to those from experimental measurements but some discrepancies exist, which are mainly due to the assumption of non-unity Lewis number in the calculations.     

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 numerical algorithm for flame propagation in premixed gases

The propagation speed of a premixed laminar flame or a weak deflagration wave is not uniquely determined in the hyperbolic theory of reactive gas flow. In this paper, we take a hyperbolic system of conservation laws as a governing system of equations for reacting gases and propose an algorithm to determine a wave propagation speed uniquely. The wave speed and states around a flame are computed through solving a Riemann problem near a flame in the phase space. The Riemann problem can be solved by combining the information from the internal wave structure, which is ignored in the hyperbolic approximation, and characteristic information. Therefore, the wave speed comes to depend on the internal variables such as viscosity and diffusion. This method can be used to track a premixed laminar flame when combined with any front tracking method. Some computational results are also presented.     

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.     

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.     

A joint SSPDF–CMC method for simulating turbulent methane–air jet combustion

A joint single scalar probability density function and conditional moment closure (SSPDF–CMC) method is proposed for modeling a turbulent methane–air jet flame. In general, the probability density function (PDF) of passive scalar (such as mixture fraction) is non-Gaussian and not fully determined by the advecting velocity field, therefore the presumed shape of PDF of mixture fraction assumed as clipped Gaussian distribution or beta function in normal conditional moment closure (CMC) method is incorrect. In SSPDF–CMC method, the PDF of mixture fraction is obtained using a Monte-Carlo method to solve a PDF transport equation. An assumption that the averaged scalar advection is approximately equal to the averaged scalar dissipation in the wake of a grid-generated turbulence flow is adopted to model the averaged scalar dissipation. The predictions using the proposed method are compared with those using the conventional CMC method and the experimental data. It is seen that the predicted Favre conditional averaged statistics and Favre unconditional averaged statistics using the proposed method are in better agreement with the measurement data than those using the conventional CMC method. The predicted conditional or unconditional mean NO even using the SSPDF model is only in fair agreement with the experiments. It shows that the first-order closure for the conditional reaction rate of NO should be improved.     

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)     

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.     

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)     

Adaptive numerical simulation of pulsating planar flames for large Lewis and Zeldovich ranges

We study numerically the behaviour of pulsating planar flames in the thermo-diffusive approximation. The numerical scheme is based on a finite volume discretization with an adaptive multi-resolution technique for automatic grid adaption. This allows an accurate and efficient computation of pulsating flames even for very large activation energies. Depending on the Lewis number and the Zeldovich number, we observe different behaviours, like stable or pulsating flames, the latter being either damped, periodic, or a-periodic. A bifurcation diagram in the Lewis–Zeldovich plane is computed and our results are compared with previous computations [Rogg B. The effect of Lewis number greater than unity on an unsteady propagating flame with one-step chemistry. In: Peters N, Warnatz J, editors, Numerical methods in laminar flame propagation, Notes on numerical fluid mechanics, vol. 6. Vieweg; 1982. p. 38–48.] and theoretical predictions [Joulin G, Clavin P. Linear stability analysis of nonadiabatic flames: diffusional-thermal model. Combust Flame 1979;35:139–53]. For Lewis numbers larger than 6 we find that the stability limit is again increasing towards larger Zeldovich numbers and not monotonically decreasing as predicted by the asymptotic theory. A study of the flame velocities for different Zeldovich numbers shows that the amplitude of the pulsations strongly varies with the Lewis number. A Fourier analysis yields information on their frequency.     

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.     

Simulation of Premixed Turbulent Combustion in a Gas Engine using the Immersed Boundary Method and a Level Set Flame Model

An efficient simulation approach for turbulent flame brush propagation is a level set formulation closed by the turbulent flame speed. A formulation of the level set equation with the corresponding treatment of the turbulent mass burning rate that is compatible with standard Finite Volume discretization schemes available in computational fluid dynamics codes is employed. In order to simplify and to speed up the meshing process in complicated geometries (here in gas engines) the immersed boundary method in a continuous formulation, where the forces replacing the boundaries are introduced in the momentum conservation equations before discretization, is employed. In our contribution, aspects of the numerical implementation of the level set flame model combined with the immersed boundary formulation in OpenFOAM are presented. First representative simulation results of a homogeneous methane/air mixture combustion in a simplified engine geometry are shown. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application of Enthalpy Deficit Flamelet Model in Spray Combustion Simulation北大核心CSCD

An OpenFOAM-based solver for spray combustion simulation with the large eddy simulation (LES) and the flamelet generated manifold (FGM) method, was developed. A simple reduction of the temperature was employed to account for the evaporative heat loss. The solver was firstly validated against the Sydney piloted ethanol spray flame benchmark EtF7. The predicted mean gas temperature and droplet statistics correspond well with the experimental data and have similar accuracy to the spray flamelet model. The turbulence-chemistry interaction modeling may have a larger influence on the simulation accuracy. Then a realistic gas turbine slinger combustor was simulated with 2 sets of operating conditions. The simulation results reveal different flame characteristics of the 2 working conditions. The predicted total pressure losses are close to the measured values. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Wall effect on determination of laminar burning velocity in a constant volume bomb using a quasi-dimensional model

In experiment, two optical and pressure-based methods are frequently used to evaluate laminar burning velocity of a combustible mixture. In the currently reported work, the pressure-based method was utilized to find the laminar burning velocity using the measurement of pressure variations during the combustion process in a spherical bomb and analyzing them through a multi-zone quasi-dimensional model. To check the results of the method, isooctane–air mixtures were used at equivalence ratios of 0.85 and 1.0 and initial pressures of 95 and 150 kPa with 343 K initial temperature. The time history of the bomb pressure during the combustion event, initial pressure and temperature, fuel type, and equivalence ratio were applied as input to a Fortran program written by the author based on the multi-zone combustion model; and, flame radius-time, flame speed, and laminar burning velocity at different pressures and temperatures were evaluated assuming spherical flame growth. The obtained results were compared with those of some other researchers and a reasonable agreement was observed. The wall effect on the laminar burning velocity at the end of the combustion process was clearly highlighted and a reliable range of burning velocity was distinguished. The results showed that the evaluated laminar burning velocity was not reliable at the late part of the combustion process due to possible local contact of flame front and the bomb wall, the wall effect on the reacting species, flow to small crevices, and the boundary layer effect.