Conditional filtering method for large-eddy simulation of turbulent nonpremixed combustion

The book Turbulent Combustion by Norbert Peters is a concise monograph on single-phase gaseous low Mach number turbulent combustion. It is compiled from the author's review papers on this topic plus some additional material. Norbert Peters characterizes turbulent combustion both by the way fuel and air are mixed and by the ratio of turbulent and chemical time scales. This approach leads naturally to detailed models, which are based on results of turbulence modelling and asymptotic flame theory. In both areas Norbert Peters has contributed significantly over the last two decades. The book has four sections. In chapter 1 he discusses briefly the state of the art of combustion models as they are used by different authors. Important turbulent and chemical scales are introduced, which are then used to introduce and explain the different combustion models. He distinguishes between premixed and non-premixed combustion and also between infinitely fast and finite rate chemistry. The current turbulent combustion models are described in order of their complexity and physical accuracy. He explains Eddy BreakUp and Eddy Dissipation Models, the fundamentals of the PDF transport equation, and the laminar flamelet concept applied to non-premixed and premixed turbulent combustion. Then, the Conditional Moment Closure, the Linear Eddy Model, and combustion models used in Large Eddy Simulations are described very briefly. Chapter 2 is devoted to premixed turbulent combustion. After introducing some characteristic dimensionless numbers Peters uses the level set approach and the flamelet concept to formulate a combustion model valid in the thin zone and corrugated reaction zone regimes. He shows parallels between this more fundamental model and standard models like the Bray-Moss-Libby model. He also presents models for the turbulent burning velocity, the Flame Surface Area Ratio, and discusses the effects of gas expansion. Very helpful for the reader's understanding is the presentation of three worked examples of a slot burner, a propagating spherical flame and an oscillating counter flow. Peters' model for premixed turbulent combustion is based on the equations for the mean and the variance of the $G$-equation, some closure relations as well as the flamelet equation for premixed combustion. A numerical example is used to discuss its accuracy. Non-premixed turbulent combustion is the subject matter of chapter 3. Peters uses the mixture fraction variable and asymptotic flame theory to explain the regimes of non-premixed turbulent combustion. Two worked examples of a counterflow diffusion flame and the one-dimensional unsteady laminar mixing layer help the reader to understand the theory. After discussing turbulent jet diffusion flames and introducing the flamelet equation he develops steady and unsteady flamelet models for non-premixed turbulent combustion. In particular, the Eulerian Particle Flamelet Model and the RIF (Representative Interactive Flamelet) Model are discussed. These models have been used to predict pollutant formation in a gas turbine and a direct injection Diesel engine, respectively. Finally, partially premixed combustion is discussed in chapter 4. Lifted turbulent diffusion flames are reviewed and the prediction of the lift-off height is identified as a key problem. This leads directly to the introduction of the concept of a triple flame. Different models for partially premixed combustion are then presented and the numerical simulation and the scaling of lift-off heights in turbulent jet flames are studied. There is no doubt that this book is well written and is an important contribution to combustion literature. Peters uses asymptotic theory and scale separation to develop combustion models from first principles. Also, the book contains a comprehensive review of the current literature on turbulent combustion. It is clearly a `must have' for experienced combustion modellers and experimentalists. The book has not been written for non-experts and beginners; these readers would probably have liked more worked examples and exercises, a list of symbols, some material on the mathematical techniques of asymptotic analysis, and a more detailed discussion of the standard combustion models that are often used in the literature. Also, the numerical aspects of turbulent combustion modelling are not discussed in the book. Nevertheless, the book will be a useful source for advanced courses on combustion. Markus Kraft

Machine learning tabulation of thermochemistry in turbulent combustion: An approach based on hybrid flamelet/random data and multiple multilayer perceptrons

This thesis describes the latest developments in the Multiple Mapping Conditioning (MMC) framework and its application for non-premixed and premixed turbulent combustion. Turbulent combustion is considered a paradigm for multi-scale problems and of interest from a physical, computational and applied mathematical perspective. The practical roots of this interest stem from the global reliance on fossil fuels and associated concerns on sustainability, environmental impacts and efficiency. As fossil fuels are forecast to remain dominant in the fuel mix for the foreseeable future, maximising the efficiency of combustion systems and minimising the emission of pollutants are compelling endeavours. Although important, experimental investigations of turbulent reacting flows can be complex and expensive. A complementary approach, which permits analysis of a full scale combustor and reduces risk, is to model these systems. In general, modelling approaches are categorised as being based exclusively on, or a combination of, either mixture fraction based methods or the joint Probability Density Function (PDF) methods. Models belonging to the former category have had significant success for non-premixed combustion due to their low dimensionality. The attraction the PDF method, is the inherent closure of source terms and its flexibility in simulating the regimes of turbulent combustion. The major difficulty of the PDF method relates to the closure of molecular diffusion terms via an appropriate mixing model and the computational cost invoked by deploying millions of reacting, mixing particles. While the mixture fraction-based and PDF categories were conventionally viewed as distinct and incompatible areas, research in recent years has been marked by the development of the MMC model --- a universal and flexible framework that combines the useful features of the aforementioned categories. MMC unifies several turbulent combustion models under a single framework. Both deterministic and stochastic formulations of MMC are possible, as shown in the original derivation in 2003. Deterministic MMC combines Conditional Moment Closure (CMC), for the evaluation of reactive scalars, and generalised mapping closure, for the consistent modelling of conditional scalar dissipation and the PDF of conditioning variables. The great advantage of MMC is that mixing is localised within an independent reference space which, if selected appropriately, enforces mixing to be local within the chemical composition space. Localness of mixing is physically realistic and is therefore an essential criteria of a high-quality mixing model. In original MMC, reference variables are modelled as Markov processes and conditioning occurs on the entire set of variables. When recast into stochastic form for numerical efficiency, MMC can be understood as a full scale PDF model which differentiates fluctuations in the composition space into major and minor groups. The most obvious reference variable for non-premixed combustion is the mixture fraction, which enforces a CMC-type closure on the joint PDF mixing model. Generalised MMC concepts were later proposed in 2005, to expand the purpose of reference variables beyond conditioning or localisation, and can be applied within Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES), with the replacement of the Markovian reference variables with Lagrangian variables traced within an Eulerian field. The quality of MMC mixing has enabled the deployment of sparse-Lagrangian simulations, which have permitted significant reductions in computational expense. In this thesis, LES is first conducted for a non-premixed hydrogen lifted flame. Lifted flames are very sensitive to the proper matching of reaction rates as well as mixing and present an extreme test of the ability of sparse-Lagrangian MMC to model complex physics. Under sparse conditions, it is found that MMC has sufficient flexibility to deal with such sensitivity; the radical pool and hence the lift-off height are correctly predicted provided the correct level of localisation is selected. Parametric studies of coflow temperatures and a localisation parameter are also performed. Results indicate that caution is required when applying a sparse-Lagrangian simulation to such an ill-posed problem. Significant, novel advances are made on the fundamental modelling of turbulent premixed flames with MMC. For premixed cases, PDF methods are known to work well for distributed regimes but have difficulties in reproducing flamesheets of high Damkohler and low Karlovitz numbers. A stochastic formulation of original MMC with mixing conditioned on a simulated reference variable resembling position or implied position, is first implemented in the context of a Monte-Carlo simulation of a Partially-Stirred Reactor (PaSR). The ability of MMC to enforce thin, flamelet-like conditions is most notably demonstrated through the MMC-PaSR. The notion of conditioning mixing based on position is then extended to introduce a more general framework for the simulation of premixed turbulent flames. Reference variables based on the level-set, shadow position and progress variable are discussed, along with the concept of a second level of conditioning to introduce a hierarchy of MMC modelling which combines generality with computational efficiency.

Large-eddy simulations (LES) have been coupled with a conditional moment closure (CMC) method for the computation of a series of turbulent spray flames. An earlier study by Ukai et al. (Proc. Combust. Inst. 34(1),1643–1650, 2013) gave reasonable results for the prediction of temperature and velocity profiles, but some limitations of the method became apparent. These limitations are primarily related to the upper limit in mixture fraction space. In order to enhance the applicability of the LES-CMC model, this paper proposes a two-conditional moment approach to account for the existence of pre-evaporated fuel by introducing two sets of conditional moments based on different mixture fractions. The two-conditional moment approach is first tested for a non-reacting test case. The results indicate that the spray evaporation induces relatively large conditional fluctuations within a CMC cell, and one set of conditional moments might not be sufficient. The upper limit of the mixture fraction space is dynamically selected for the solution of the second set of conditional moments, and the corresponding CMC solution in a CFD cell is estimated by interpolation between the two conditional moments weighted by the amount of vapour emitted within the domain. The cell-filtered value is given by integration of the conditional moment across mixture fraction space using a bounded β-FDF for the distribution of the scalar. As a result, the fuel concentration profiles given by LES and the two-conditional moment approach are shown to agree well. Then, the two-conditional moment approach is applied to four different flame configurations. The comparison of LES cell quantities and conditionally averaged moments indicates that the two sets of conditional moments are necessary for accurate predictions in zones where gas phase mixture fraction is significantly increased by droplet evaporation within the computational domain. The unconditional temperature profiles clearly show that the new approach improves the predictions of mean temperature especially along the centerline. Also, the better predictions of the temperature field improve the accuracy of the predicted mean axial droplet velocities. Overall, good agreement with the experimental results is found for all four cases, and the methodology is shown to be applicable to flames with a relatively wide range of fuel vapour concentrations.

Ignition of turbulent non-premixed flames

OpenFOAM based conditional moment closure (CMC) model for solving non-premixed turbulent combustion: Integration and validation

LES-CMC of a dilute acetone spray flame

The complex interactions among turbulence, combustion and spray in liquid-fuel burners are modeled and simulated via a new two-phase Lagrangian-Eulerian-Lagrangian large eddy simulation (LES) methodology. In this methodology, the spray is modeled with a Lagrangian mathematical/computational method which allows two-way mass, momentum and energy coupling between phases. The subgrid gas-liquid combustion is based on the two-phase filtered mass density function (FMDF) that has several advantages over “conventional” two-phase combustion models. The LES/FMDF is employed in conjunction with non-equilibrium reaction and droplet models. Simulations of turbulent combustion in a spray-controlled double-swirl burner are conducted via LES/FMDF. The generated results are used for better understanding of spray combustion in realistic turbulent flow configurations. The effects of spray angle, mass loading ratio, fuel type, droplet size distribution, wall and inflow/outflow conditions on the flow and combustion are investigated. The LES/FMDF predictions are shown to be consistent with the experimental results.

Large eddy simulation and finite-volume conditional moment closure modelling of a turbulent lifted H2/N2 flame

Higher-order, conditional moment closure approaches to modelling local extinction and reignition in turbulent, non-premixed combustion are investigated. This is done by studying closure strategies of the conditional source term itself. Feasibility studies are done using direct numerical simulation (DNS) experiments which exhibit varying degrees of local extinction. The higher-order conditional moments are taken directly from the DNS experiments as opposed to solving modelled transport equations for them. Results show that with moderate levels of extinction, the conditional probability density function (pdf) of the reduced temperature is unimodal, but skewed, and at least third-order terms in a series expansion of the nonlinear chemical source term conditional on the mixture fraction are required to predict the conditional means. With higher levels of local extinction, the conditional pdf shapes can be bimodal and third-order closure breaks-down. The success of a presumed beta pdf shape for conserved scalars is well known. A beta probability distribution for the conditional reactive scalar cannot describe either the unimodal or bimodal pdf shapes which result from the local extinction and reignition events. However, predictions of the conditional means are excellent with the beta pdf model incorporated into a conditional moment closure modelling framework. The modelling results show little sensitivity to the conditional variances.

Large-eddy simulations (LES) have been coupled with a conditional moment closure (CMC) method for the improved modelling of small scale turbulence-chemistry interactions in turbulent spray flames. Partial pre-evaporation of the liquid fuel prior to exiting the injection nozzle requires a modified treatment for the boundary conditions in mixture fraction space and mixture fraction subgrid distribution and conditionally averaged subgrid dissipation need to be known. Different modelling approaches for the subgrid distribution of mixture fraction have been assessed, but the modelling of subgrid scalar dissipation that is responsible for the subgrid fuel transport from the droplet surface towards the cell filtered mean has not been forthcoming. Instead, we introduce a new conditioning method based on two sets of conditional moments conditioned on two differently defined mixture fractions: the first mixture fraction is a fully conserved scalar, the second mixture fraction is based on the fluid mass originating from the liquid fuel stream and is strictly not conserved due to the evaporation process. The two-conditional moment approach is validated by comparison with measurements from a turbulent ethanol spray flame and predicted temperature and velocity profiles could significantly be improved when compared to conventional LES-CMC modelling.

Improved pollutant predictions in large-eddy simulations of turbulent non-premixed combustion by considering scalar dissipation rate fluctuations

Opposed jet burner and Tsuji burner for representative laminar flamelet with differential molecular diffusion for non-premixed combustion modeling

Spray combustion under turbulent conditions occurs in many technical devices. Therefore, the proper prediction of the characteristics of turbulent spray flames is of vital importance for the design of new combustion technologies in view of efficiency and pollutant reduction, where the latter requires consideration of detailed chemical reaction mechanisms. Unfortunately, a direct inclusion of detailed chemical reactions dramatically increases the computational cost of the numerical simulations of technical combustion processes, and it is prohibitive in practical situations. Models based on the assumption that turbulent ames can be seen as an ensemble of laminar stretched flame structures, the so-called flamelet models, represent a very promising approach for the cost effective inclusion of detailed chemical reaction mechanisms in the simulation of turbulent spray flames. Several flamelet models are currently available in the literature for the simulation of pure non-premixed and pure premixed gas flames. Additionally, some two-regime flamelet formulations have been proposed in the last years for situations where nonpremixed and premixed gas combustion coexist and interact. These models, however, are not adequate for the simulation of turbulent spray combustion, since they do not take into account spray evaporation, which strongly affects the flame structure. Although a spray flamelet model has been proposed for the simulation of flames where non-premixed and evaporation-dominated combustion regimes coexist, most studies of turbulent spray flames use gas flamelet models, neglecting the effects of evaporation on the flame structure. In the present thesis, a common framework is developed in which the several single and two-regime flamelet models existing in the literature can be described and combined in order to advance the development of a comprehensive multi-regime spray flamelet model for turbulent spray flames. For this purpose, a set of multi-regime spray flamelet equations in terms of the mixture fraction and a reaction progress variable is derived, which describes all combustion regimes appearing in spray flames. The flamelet equations available in the literature for single and two-regime flames are retrieved from these multi-regime spray flamelet equations as special cases. Additionally, exact transport equations of the mixture fraction and its scalar dissipation rate are derived, which are then used to evaluate the validity of several assumptions commonly made in the literature during their derivation, such as the use of unity Lewis number and the negligence of spatial variations of the mean molecular weight of the mixture. These assumptions had not yet been tested for the calculation of the scalar dissipation rate of the mixture fraction in spray flames, and their validation is of vital importance for the formulation of any spray flamelet model. Numerical simulations of axi-symmetric laminar mono-disperse ethanol/air counterflow spray flames are carried out to analyze the influence of spray evaporation on the flame structure. Parametric studies of the influence of the initial droplet radius and strain rate are presented, which clearly illustrate the major importance of evaporation in the determination of the flame structure. Additionally, the relative importance of non-premixed and premixed combustion regimes in the previously analyzed counterflow spray flames is studied by means of the derived multi-regime spray flamelet equations. The results show that premixed effects can be neglected in this kind of flame with all fuel injected in liquid phase. Moreover, the derived transport equations of mixture fraction and its scalar dissipation rate are solved for the counterflow spray flames considered in this work considering and without considering the assumptions of unity Lewis number and spatially uniform mean molecular weight of the mixture. The results are compared, and it is found that the assumption of unity Lewis number may lead to non-physical values of the scalar dissipation rate of the mixture fraction, whereas the use of a mass-averaged diffusion coefficient of the mixture is an acceptable approximation. Effects associated with the spatial variation of the mean molecular weight of the mixture are found to be small at low strain rate and negligible at high strain rates. These results confirm the validity of the use of Fick's diffusion law in highly strained flames. Finally, a set of non-premixed spray amelet equation is obtained by neglecting premixed effects in the previously derived multi-regime spray flamelet equations. This set of equations, which is valid in situations where non-premixed and evaporation-dominated combustion regime coexist, is similar to the classical non-premixed gas flamelet equations, but it contains two additional terms for the description of evaporation effects. These equations are then used to evaluate the relative importance of the effects attributable to evaporation. The results show that they are always relevant and they should be always considered.

The Conditional Source-term Estimation (CSE) method was recently proposed to close the chemical source terms occurring in the spatially filtered transport equations of species and enthalpy for Large Eddy Simulation (LES) of nonpremixed reacting flows [W. K. Bushe and H. Steiner, Phys. Fluids 11, 1896 (1999)]. The model is based on the Conditional Moment Closure hypothesis, which provides fairly accurate predictions for the conditional averages of the chemical reaction rates as functions of the conditionally averaged composition vector and temperature with the mixture fraction being an appropriate conditioning variable. In CSE the conditionally averaged composition vector and temperature are obtained by mapping the corresponding spatially filtered scalar fields resolved by the LES into the conditioning (i.e., mixture fraction) space. After the conditional averages of the chemical reaction rates are approximated in mixture fraction space, these are mapped into the physical space to close the source terms in the LES transport equations for the reactive scalars. The present simulation of a turbulent reacting jet is the first test of this new closure in a self-sustained predictive LES. A two-step reduced chemical kinetic mechanism for methane–air flames was used. The results of the simulation, which are in reasonable agreement with available experimental data, prove the model’s predictive capabilities as well as its robustness and feasibility for LES.