Stability of the cylindrical flame front in an annular combustion chamber

Using small perturbations, within the framework of phenomenological theory of mixture combustion we study stability of the cylindrical front of deflagration combustion in an annular combustion chamber. The flame front is described as a discontinuity of gasdynamic parameters. It is discovered that the flame front is unstable for some types of small perturbations of the mainstream flow of the fuel mixture and the flame front. The mechanics of instability is examined using both numerical and analytical methods. The cases are presented of evolution of the instabilities rotating in the annular channel.     

泄爆诱导的湍流、旋涡和外部爆炸

基于k-ε湍流模型和Eddy-dissipation燃烧模型,采用同位网格SIMPLE算法,对充满甲烷-氧气预混气的带导管柱形泄爆容器向空气中泄爆的情形进行了数值模拟．根据计算结果,分析了泄爆后外流场中可燃云团、火焰和压力的变化过程．结果表明,外部爆炸是因射流火焰点燃高压区中的可燃云团,从而引起的剧烈湍流燃烧所致．同时还讨论了外流场湍流和涡量的分布特征．射流火焰进入外部可燃云团后,湍流主要分布在平均动能梯度较大的区域,而不在火焰阵面上．涡量分布主要受斜压效应的影响,在压力和密度梯度斜交区域,其值较大．     

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.     

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)     

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)     

Quantifying bushfires

Bushfires are quantified by their flame characteristics or by calculations of the rate that energy is released from the fire front. These calculations require careful definition and measurement of available fuel. Researchers need to recognise that combustion proceeds at a variable rate across the combustion zone. This will influence the relationship between Byram's fireline intensity and flame characteristics or fire effects. Byram's fireline intensity should not be used to compare fires in fuel types which are structurally very different.     

Asymptotic Analysis in a Gas-Solid Combustion Model with Pattern Formation

The authors consider a free interface problem which stems from a gas-solid model in combustion with pattern formation. A third-order, fully nonlinear, self-consistent equation for the flame front is derived. Asymptotic methods reveal that the interface approaches a solution to the Kuramoto-Sivashinsky equation. Numerical results which illustrate the dynamics are presented.     

Stability of a flame front in a divergent flow

We study the evolution of perturbations on the surface of a stationary plane flame front in a divergent flow of a combustible mixture incident on a plane wall perpendicular to the flow. The flow and its perturbations are assumed to be two-dimensional; i.e., the velocity has two Cartesian components. It is also assumed that the front velocity relative to the gas is small; therefore, the fluid can be considered incompressible on both sides of the front; in addition, it is assumed that in the presence of perturbations the front velocity relative to the gas ahead of it is a linear function of the front curvature. It is shown that due to the dependence (in the unperturbed flow) of the tangential component of the gas velocity on the combustion front on the coordinate along the front, the amplitude of the flame front perturbation does not increase infinitely with time, but the initial growth of perturbations stops and then begins to decline. We evaluate the coefficient of the maximum growth of perturbations, which may be large, depending on the problem parameters. It is taken into account that the characteristic spatial scale of the initial perturbations may be much greater than the wavelengths of the most rapidly growing perturbations, whose length is comparable with the flame front thickness. The maximum growth of perturbations is estimated as a function of the characteristic spatial scale of the initial perturbations.     

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.     

Dynamics of coal dust flame acceleration: A feedback control model for unsteady flow

Several modeling concepts borrowed from control theory are employed to develop an algebraic and ordinary differential equations model for the dynamics of unsteady coal dust flame acceleration in a constant area duct closed at one end, e.g., in a coal mine tunnel. We are particularly concerned with modeling the feedback mechanisms which cause a coal dust flame to accelerate, leading to detonation. Previous experimental studies have been conducted on both coal dust flame propagation and on individual coal particle combustion. Based on the results, a physical model is proposed in which coal dust flame acceleration is entirely controlled, in a feedback fashion, by volatiles emission and their reaction. A control system model is developed that employs five well-stirred reactor subsystems with three feedback interaction mechanisms. The model consists of a leading shock wave, followed by a variable length volatiles emission region ahead of the flame, a fixed length burning region immediately behind the flame front, and a variable length exhaust region extending back to the closed end of the duct. The feedback mechanisms incorporated into the model include heat transfer and pressurization from the burning region to the volatiles emission region, and pressurization from the volatiles emission region to the turbulent mixing region behind the shock wave. Each well-stirred reactor is described by a system of algebraic and ordinary differential equations for the rate of change of conditions inside the reactor. Numerical simulation results reveal that, despite far-reaching simplifications (ordinary instead of partial differential equations, ideal gases insteady of two-phase flow, separation of volatiles emission and combustion, neglection of char burning), the model exhibits the fundamental dynamic properties of the flame propagation process. The model agrees with qualitative photographic experimental results and is applicable to both the case where the flame accelerates to detonation and to the case where the combustion process dies out.     

Kuramoto-Sivashinsky Equation and Free-Interface Models in Combustion Theory

In combustion theory, a thin flame zone is usually replaced by a free interface. A very challenging problem is the derivation of a self-consistent equation for the flame front which yields a reduction of the dimensionality of the system. A paradigm is the Kuramoto-Sivashinsky (K-S) equation, which models cellular instabilities and turbulence phenomena. In this survey paper, we browse through a series of models in which one reaches a fully nonlinear parabolic equation for the free interface, involving pseudo-differential operators. The K-S equation appears to be asymptotically the lowest order of approximation near the threshold of stability.     

Numerical Approximations of the Spectral Discretization of Flame Front Model

In this paper, we consider the numerical solution of the flame front equation, which is one of the most fundamental equations for modeling combustion theory. A schema combining a finite difference approach in the time direction and a spectral method for the space discretization is proposed. We give a detailed analysis for the proposed schema by providing some stability and error estimates in a particular case. For the general case, although we are unable to provide a rigorous proof for the stability, some numerical experiments are carried out to verify the efficiency of the schema. Our numerical results show that the stable solution manifolds have a simple structure when $\beta$ is small, while they become more complex as the bifurcation parameter $\beta$ increases. At last numerical experiments were performed to support the claim the solution of flame front equation preserves the same structure as K-S equation.     

Premixed Turbulent Combustion Modelling Using Level Set Approach

The paper deals with a level set approach application to SI engine combustion modelling, which is based on solving an additional transport equation to determine the flame front propagation. The presented work is an extension of the paper [6]. The influence of engine speed, air excess, swirl number, engine load as well as application of different turbulence model, in.uence of mesh coarseness and model fine-tuning constants are investigated and the results are presented. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparisons between thermodynamic and one-dimensional combustion models of spark-ignition engines

A one-dimensional combustion model, employing a constant eddy diffusivity and a one-step chemical reaction, has been developed and applied to study the flame propagation in a spark-ignition engine. Calculations have been made at 1600 and 4200 rev min⁻¹ under fuel rich conditions and compared with available engine pressure data. One- and two-zone thermodynamic models have also been developed and applied to study the combustion process in the engine. The thermodynamic models have been compared with the one-dimensional model results and comparisons include the average mixture temperature, the temperatures of the burned and unburned gases and the flame surface area. These comparisons indicate that the one-dimensional model predictions are very sensitive to the eddy diffusivity and reaction rate data. The two-zone thermodynamic model predicts, first, a monotonically increasing flame surface area with time and, then, a monotonically decreasing surface area, whereas the one-dimensional model always predicts a monotonically increasing flame surface area. The average mixture temperature predicted by the one-zone thermodynamic model is higher than those of the two-zone and one-dimensional models during the compression stroke, while that of the one-dimensional model is higher than the temperatures predicted by the one- and two-zone models during the expansion stroke. The one-dmensional model predicts an accelerating flame even when the front approaches the cold cylinder wall. This yields a faster fuel consumption rate than those predicted by the one- and two-zone thermodynamic models which predict smoother burned fuel mass profiles.     

Weakly supercritical dissipative structures on curved surfaces

Cellular, low amplitude structures appearing at cylindrical and spherical fronts of gaseous combustion and laser evaporation are described. In the case of a spherical front all these structures are found to be unstable. When the cylindrical front of gaseous combustion is expanded, we must expect the quasi one-dimensional structure homogeneous with respect to the ignorable coordinate to be replaced by a parquet-like pattern of rectangular cells, and later to reach a non-stationary regime. On the cylindrical front of laser evaporation the quasi one-dimensional structure of maximum amplitude is globally stable.

The best known hydrodynamic example of a kinetic problem connected with the formation of dissipative structures i.e. thermodynamically nonequilibrium stationary structures appearing as a result of the development of aperiodic instability in a spatially homogeneous state, are Benard cells /1,2/. New problems of this kind are connected with the instability of plane fronts of laser evaporation of condensed material, and of gaseous combustion /3–5/. The instability is aperiodic and appears at finite values of the wave number of the perturbation representing curvature of a plane front. The development of the instability leads to the formation of a stationary, periodically curved front /3/.

The purpose of this paper is to investigate such structures and their stability on cylindrical and spherical surfaces, and this corresponds to the problem of the propagation of a cylindrical or spherical flame through a gas, and of the laser evaporation of a spherical sample. Problems dealing with dissipative structures on curved surfaces are also of interest in biophysics, where a spherical surface models a cell membrane, while the cylindrical surface models the axon /6/.     

层焰系统奇点结构的研究

在一定的假设条件下,将气体燃烧的物理模型简化为层焰系统．借助于热力学理论和相关的守恒定律建立了层焰系统的数学模型并对其进行了深入地分析．利用常微分方程的定性理论和方法,结合燃烧的实际需要,对应于参数的不同取值,研究了位于瑞利线上奇点的个数和位置,确定了暴燃区和爆炸区内不同奇点的定性结构及其稳定性,给出了在反应速度-滞止焓平面及燃烧速度-滞止焓平面内层焰系统轨线的相图．     

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 numerical method for nonconvex multi-objective optimal control problems

A numerical method is proposed for constructing an approximation of the Pareto front of nonconvex multi-objective optimal control problems. First, a suitable scalarization technique is employed for the multi-objective optimal control problem. Then by using a grid of scalarization parameter values, i.e., a grid of weights, a sequence of single-objective optimal control problems are solved to obtain points which are spread over the Pareto front. The technique is illustrated on problems involving tumor anti-angiogenesis and a fed-batch bioreactor, which exhibit bang–bang, singular and boundary types of optimal control. We illustrate that the Bolza form, the traditional scalarization in optimal control, fails to represent all the compromise, i.e., Pareto optimal, solutions.     

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.     

Asymptotic analysis of stationary propagation of the front of a two-stage exothermic reaction in a gas : PMM vol. 37, n6, 1973, pp. 1049–1058

We construct an approximate solution of the problem concerning the propagation of a planar. front of a two-stage exothermic sequential chemical reaction in a gas, by the method of matched asymptotic expansions. As the parameter in the expansion we use the ratio of the adiabatic combustion temperature to the sum of the activation temperatures of both reactions. Depending on the values of the characteristic parameters of the problem, we consider several solutions, each with a different asymptotic behavior, corresponding to the various flame front propagation modes. The analytical results obtained are compared with numerical data available in the literature.