Turbulent Combustion Model Research Articles

Investigation of deep learning methods for efficient high-fidelity simulations in turbulent combustion

Turbulent combustion modeling often faces a trade-off between the so-called flamelet-like models and PDF-like models. Flamelet-like models, are characterized by a choice of a limited set of prescribed moments, which are transported to represent the manifold of the composition space and its statistics. PDF-like approaches are designed to directly evaluate the closure terms associated with the nonlinear chemical source terms in the energy and species equations. They generate data on the fly, which can be used to accelerate the simulation of PDF-like based models. Establishing key ingredients for implementing acceleration schemes for PDF-like methods by constructing flamelet-like models on the fly can potentially result in computational saving while maintaining the ability to resolve closure terms. These ingredients are investigated in this study. They include a data-based dimensional reduction of the composition space to a low-dimensional manifold using principal component analysis (PCA). The principal components (PCs) serve as moments, which characterize the manifold; and conditional means of the thermo-chemical scalars are evaluated in terms of these PCs. A second ingredient involves adapting a novel deep learning framework, DeepONet, to construct joint PCs’ PDFs as alternative methods to presumed shapes common in flamelet-like approaches. We also investigate whether the rotation of the PCs into independent components (ICs) can improve their statistical independence. The combination of these ingredients is investigated using experimental data based on the Sydney turbulent nonpremixed flames with inhomogeneous inlets. The combination of constructed PDFs and conditional mean models are able to adequately reproduce unconditional statistics of thermo-chemical scalars, and establish acceptable statistical independence between the PCs, which simplify further the modeling of the joint PCs’ PDFs.

LES of Reacting Flow in a Hydrogen Jet into Supersonic Crossflow Combustor Using a New Turbulent Combustion Model

Modelling the complete flow physics and chemical kinetics of supersonic combustion is a particularly complex and daunting task that requires significant computational resources. To foster performance evaluation tools for future hypersonic vehicles, developing accurate yet computationally efficient solution methods is of great importance. In this work, a new subgrid combustion model for large eddy simulations is derived and used in a three-dimensional in-house flow solver to provide simulations of experimental scramjet ground tests. In particular, this paper introduces a hybrid model closure with the reaction-rate approach to close the filtered chemical source terms in the governing equations for species mass fractions and total energy. The model developed here makes use of a linear bridging function, depending on the segregation rate of the mixture fraction, between a resolved contribution issued from a perfectly stirred reactor (PSR) estimation, and a subgrid-scale (SGS) contribution where a closure that approximates the Lagrangian trajectory in the composition space is retained. The new model considers the effect of fluctuations of compositions and can be extended to take into account, for example, the fluctuations of temperature. The new approach is tested using a hydrogen-fueled scramjet combustor from circular injector into a Mach 2 vitiated airflow for total pressure and temperature of 0.40 MPa and 1695 K, respectively. The selected operating conditions are representative of the LAPCAT-II dual-mode ramjet/scramjet combustion. Chemistry is described using a four-step reduced mechanism. The results obtained with the present modelling proposal are compared to those issued from numerical simulations performed with the quasi-laminar chemistry or PSR approach. These results do show that, even for a highly resolved computational mesh, the effects of composition fluctuations remain significant, especially in the vicinity of the injection where the SGS fluctuations of the scalar field are non-negligible.

Modeling of Turbulent Premixed CH4/H2/Air Flames Including the Influence of Stretch and Heat Losses

Abstract This paper presents a Reynolds averaged Navier Stokes turbulent combustion model for CH4/H2/air mixtures which includes the effect of heat losses and flame stretch. This approach extends a previous model concept designed for methane/air mixtures and improves the prediction of flame stabilization when hydrogen is added to the fuel. Heat loss and stretch effects are modeled by tabulating the consumption speed of laminar counterflow flames in a fresh-to-burnt configuration with detailed chemistry at various heat loss and flame stretch values. These computed values are then introduced in the turbulent combustion model by means of a turbulent flame speed expression which is derived as a function of flame stretch, heat loss, and H2 addition. The model proposed in this paper is compared to existing models on experimental data of spherical expanding turbulent flame speeds. The performance of the model is further validated by comparing computational fluid dynamics predictions to experimental data of an atmospheric turbulent premixed bluff-body-stabilized flame fed with CH4/H2/air mixtures ranging from pure methane to pure hydrogen.

Review of Lagrangian stochastic models for turbulent combustion

Review of Lagrangian stochastic models for turbulent combustion

FlameFoam: An open source CFD solver for turbulent premixed combustion

Severe accidents in nuclear power plants may cause significant and long-lasting harm to the environment in the case of containment integrity loss. Numerical simulation of phenomena threatening containment integrity, e.g., hydrogen combustion and explosion, is essential for the effective severe accident management.International research projects and benchmarks are organized in order to promote improvement of simulation codes adequacy and accuracy in the severe accident relevant conditions. Results of the most recent benchmarks show that current state-of-the-art simulations were able to mostly reproduce the observable flame speed at the considered conditions, but there are still inadequacies in estimating velocity and its maximum value.Addressing a need for an accessible open source turbulent premixed combustion simulation tool, a new solver is being developed. An OpenFOAM version 7 based combustion solver called flameFoam has been built by implementing a progress variable approach and turbulent flame closure model for premixed combustion simulation. Turbulent flame speed is defined as a function of laminar flame speed and turbulence parameters, and is evaluated using one of three different correlations. Laminar flame speed can be set as a constant or calculated using a laminar flame speed correlation. The basis for the solver are standard compressible OpenFOAM solvers rhoPimpleFoam, buoyantPimpleFoam and chtMultiRegionFoam.The article presents initial public flameFoam version 0.8 and provides examples of its validation. Initial validation and verification of general solver features are represented by the simulations of shock tube and backward facing step cases. Solver capabilities in relation to the current turbulent premixed combustion modeling state-of-the-art are demonstrated with the simulations of ETSON-MITHYGENE benchmark experiments.It is shown that flameFoam version 0.8 is capable of adequate simulation of general flow features, turbulent compressible flow phenomena and turbulent premixed combustion of lean hydrogen-air mixtures at the considered conditions. Solver code is publicly hosted and being developed further.

The thickened flame approach for non-premixed combustion: Principles and implications for turbulent combustion modeling

Modeling turbulent non-premixed combustion remains a challenge in the context of Large Eddy Simulation (LES) in complex geometries and for realistic conditions, taking into account all physical phenomena impacting the flame such as heat loss, dilution, or liquid fuel atomization and evaporation. In this work, the Thickened Flame concept, which allows to resolve the flame front on the LES grid while preserving the consumption speed, and initially derived for premixed combustion, is adapted to diffusion flames. It is demonstrated that the concept holds for these flames, with however, a different formulation of the model due to but their specific nature and properties. In particular, in the high-Damköhler regime, the thickening factor is applied only to the diffusion coefficients. The behavior of thickened diffusion flames is illustrated on laminar steady strained flames for both simple and complex chemistry, showing how the Thickened Flame concept applies. Based on these results, an expression for the thickening factor related to mesh coarsening is derived. For a complete turbulent combustion model, the thickening factor should also describe the sub-grid scale flame-turbulence interaction, which is left for future work.

Revisiting the relation between premixed flame brush thickness and turbulent burning velocities from Ken Bray’s notes

Applying the Bray-Moss-Libby (BML) bi-modal asymptotic limit to a progress variable signal in a premixed turbulent flame, a relation is established between the variation rate of the mean turbulent flame brush thickness, the flame surface wrinkling and the turbulent burning velocity. This scaling suggests that the link between the amplification of the flame surface by turbulence and the increase of the turbulent burning velocity may need to be modulated by a corrective term proportional to the rate of variation of the turbulent flame brush thickness. This correction is expected to be driven by a short relaxation time scale, which is representative of the turbulent flame brush adjusting to its continuously varying turbulence environment. The analysis is grounded on the usual exact expressions for the various characteristic displacements and consumption speeds, widely used in turbulent combustion modeling. Prior to this analysis, the validity of the implication on these characteristic speeds of the thin flamelet framework, introduced to perform the derivation of the relation between the turbulent flame brush dynamics and the turbulent burning velocity, is evaluated from direct numerical simulation (DNS) of a turbulent premixed jet-flame.

Mathematical Modelling of Turbulent Combustion of Two-Phase Mixtures of Gas and Solid Particles with a Eulerian–Eulerian Approach: The Case of Hydrogen Combustion in the Presence of Graphite Particles

The numerical modelling of turbulent combustion of H2–air mixtures with solid graphite particles is a challenging and key issue in many industrial problems including nuclear safety. This study presents a Eulerian–Eulerian model based on the resolution of the Navier–Stokes equations via large eddy simulation (LES) coupled with a system of ordinary differential equations (ODEs) of the detailed chemical kinetics to simulate the combustion of mixtures of gases and particles. The model was applied to predict the transient evolution of turbulent combustion sequences of mixtures of hydrogen, air and graphite particles under low concentration conditions. When applied to simulate lab-scale combustion experiments, the results showed a good agreement between experimental and numerical data using a detailed chemical kinetic model. Moreover, the model was able to predict some key experimental tendencies and revealed that the presence of a low concentration of graphite particles (~96 g/m3) in the scenario influenced the hydrogen combustion dynamics for mixtures of 20% (in volume) of hydrogen in air. Under these conditions, pressure levels reached at the walls of the sphere were increased and the combustion time was shortened. The results also showed the viability of using this kind of a model for obtaining global combustion parameters such as wall pressure evolution with time.

Effect of sub-grid wrinkling factor modelling on the large eddy simulation of turbulent stratified combustion

Different flame efficiency function (wrinkling factor) models are compared and tested for the Cambridge stratified flame using Large Eddy Simulations (LES) with an artificially thickened flame approach. Different numerical discretisations and definitions of the outer cut-off length are tested, as different practices exist that can have a strong impact on the results. The Cambridge experiment is chosen since it exhibits a Reynolds number of more than 11,500 and the stratified flame is strongly wrinkled further downstream, making it a challenging configuration for the turbulent (stratified) combustion modelling. The sub-grid level physics have been modelled by four wrinkling factor closures, which rely explicitly on algebraic functions of resolved variables, to analyse the influence of wrinkling factor modelling on the predictions of LES. Many such models have been proposed and were tested successfully – but typically for perfectly premixed flames, using specific discretisations and definitions of the cut-off length or filter width. The present paper shows that the models tested perform well even for stratified combustion, provided that the correct definition for the cut-off length is used, and to a lesser extent, suitable discretisation methodologies are employed.

A Data-Driven Methodology for the Simulation of Turbulent Flame Speed across Engine-Relevant Combustion Regimes

Turbulent combustion modelling in internal combustion engines (ICEs) is a challenging task. It is commonly synthetized by incorporating the interaction between chemical reactions and turbulent eddies into a unique term, namely turbulent flame speed sT. The task is very complex considering the variety of turbulent and chemical scales resulting from engine load/speed variations. In this scenario, advanced turbulent combustion models are asked to predict accurate burn rates under a wide range of turbulence–flame interaction regimes. The framework is further complicated by the difficulty in unambiguously evaluating in-cylinder turbulence and by the poor coherence of turbulent flame speed (sT) measurements in the literature. Finally, the simulated sT from combustion models is found to be rarely assessed in a rigorous manner. A methodology is presented to objectively measure the simulated sT by a generic combustion model over a range of engine-relevant combustion regimes, from Da = 0.5 to Da = 75 (i.e., from the thin reaction regime to wrinkled flamelets). A test case is proposed to assess steady-state burn rates under specified turbulence in a RANS modelling framework. The methodology is applied to a widely adopted combustion model (ECFM-3Z) and the comparison of the simulated sT with experimental datasets allows to identify modelling improvement areas. Dynamic functions are proposed based on turbulence intensity and Damköhler number. Finally, simulations using the improved flame speed are carried out and a satisfactory agreement of the simulation results with the experimental/theoretical correlations is found. This confirms the effectiveness and the general applicability of the methodology to any model. The use of grid/time resolution typical of ICE combustion simulations strengthens the relevance of the proposed dynamic functions. The presented analysis allows to improve the adherence of the simulated burn rate to that of literature turbulent flames, and it unfolds the innovative possibility to objectively test combustion models under any prescribed turbulence/flame interaction regime. The solid data-driven representation of turbulent combustion physics is expected to reduce the tuning effort in ICE combustion simulations, providing modelling robustness in a very critical area for virtual design of innovative combustion systems.

Comparing Global Spray Combustion Characteristics and Local Shot-to-Shot Variations in a Reacting n-Heptane Spray

Abstract In support of efforts to develop improved models of turbulent spray behavior and combustion in diesel engines, experimental data and analysis must be obtained for guidance and validation. For Reynolds-averaged Navier–Stokes (RANS)-based Computational fluid dynamics (CFD) modeling approaches, representative ensemble average experimental results are important. For high-fidelity models such as large eddy simulations (LES)-based CFD, precise individual experimental results are desirable. However, making comparisons between a given experiment and LES is a challenge since local parameters cannot be directly compared. In this work, an optically accessible constant pressure flow rig (CPFR) is utilized to acquire diesel-like fuel injection and reaction behavior simultaneously with three optical diagnostic techniques: rainbow Schlieren deflectometry (RSD), OH* chemiluminescence (OH*), and two-color pyrometry (2CP). The CPFR allows a large number of repeated injection experiments to be performed for statistical analysis and convergence using ensemble-averaging techniques, while maintaining highly repeatable test conditions. Even for stable test conditions, variations in local turbulent fuel–air mixing introduce variability, which manifests as significant differences in OH* and 2CP results. Experimental measurements of characteristic parameters including liquid and vapor jet penetration, liftoff length, soot temperature and concentration, and turbulent flame speed, along with the shot-to-shot variability of each dataset, are presented and discussed. A statistical method is utilized to analyze the extent of this variability, and to identify superlative injections within the dataset for discussion and analysis of shot-to-shot variations.

Publisher's Note: “Using approximate inertial manifold approach to model turbulent non-premixed combustion” [Phys. Fluids 33, 035125 (2021)

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Assessment of Turbulent Combustion Models for Simulating Prechamber Ignition in a Natural Gas Engine

Abstract Lean combustion is a promising strategy to increase thermal efficiency in an internal combustion engine, by exploiting a favorable specific heat ratio of the fresh mixture while simultaneously suppressing the heat losses to the cylinder wall. However, unstable ignition and slow flame propagation at fuel-lean conditions lead to large cycle-to-cycle variability and limit the high-efficiency engine operating range. Prechamber ignition is considered an effective concept to extend the lean operating limit, by providing spatially distributed ignition with multiple turbulent flame-jets and enabling a faster combustion rate compared to the conventional spark ignition approach. From a numerical modeling standpoint to date science base and available simulation tools are inadequate to properly understand and predict the combustion processes in prechamber ignited engines. In this paper, conceptually different Reynolds-averaged Navier–Stokes (RANS) combustion models widely adopted in the engine modeling community are used to simulate the ignition and combustion processes in a medium-duty natural gas engine with a prechamber spark-ignition system. A flamelet-based turbulent combustion model, i.e., G-equation, and a multizone well-stirred reactor model are employed for this modeling study. Simulation results are compared with experimental data in terms of in-cylinder pressure and heat release rate. Finally, the analysis of the performance of the two models is carried out to highlight the strengths and limitations of the two evaluated approaches.

A Strategy to Couple Thickened Flame Model and Adaptive Mesh Refinement for the LES of Turbulent Premixed Combustion

A trend towards the increasing use of Adaptive Mesh Refinement (AMR) algorithms to simulate combustion processes is observed in the recent literature. AMR is attractive as it enables the physical phenomena of interest to be tracked by the numerical mesh, reducing the computational cost drastically. It is particularly efficient for combustion as small computational cells are needed very locally to resolve the flame structure. However, the questions arising from the coupling between AMR and the turbulent flame propagation have rarely been investigated so far. Indeed, the incomplete cascading of turbulent structures from a relatively coarse mesh used to solve the flow to a finer mesh solving the flame has implications on the turbulent combustion model which must be considered. In the present paper, a strategy for coupling AMR with the Thickened Flame Model (TFM) is proposed. It is shown that, under conditions relevant to industrial cases, the standard TFM model strongly under-estimates the turbulent flame propagation when the effects of AMR is not taken into account. A new model, AMR-E, is introduced to take this effect into account. The behavior of the model is first analyzed on an a priori 1D-study and is consequently validated on a 3-D turbulent flame propagation in Homogeneous Isotropic Turbulence (HIT). In particular, it is shown that the presented model has a similar behavior for different AMR refinement levels in the flame front.

Modelling of a Bluff-Body Stabilised Premixed Flames Close to Blow-Off

As emission legislation becomes more stringent, the modelling of turbulent lean premixed combustion is becoming an essential tool for designing efficient and environmentally friendly combustion systems. However, to predict emissions, reliable predictive models are required. Among the promising methods capable of predicting pollutant emissions with a long chemical time scale, such as nitrogen oxides (NOx), is conditional moment closure (CMC). However, the practical application of this method to turbulent premixed flames depends on the precision of the conditional scalar dissipation rate,ζ ⟨Nc|ζ⟩, model. In this study, an alternative closure for this term is implemented in the RANS-CMC method. The method is validated against the velocity, temperature, and gas composition measurements of lean premixed flames close to blow-off, within the limit of computational fluid dynamic (CFD) capability. Acceptable agreement is achieved between the predicted and measured values near the burner, with an average error of 15%. The model reproduces the flame characteristics; some discrepancies are found within the recirculation region due to significant turbulence intensity.

Using approximate inertial manifold approach to model turbulent non-premixed combustion

The theory of inertial manifolds (IM) is used to develop reduced-order models of turbulent combustion. In this approach, the dynamics of the system are tracked in a low-dimensional manifold determined in situ without invoking laminar flame structures or statistical assumptions about the underlying turbulent flow. The primary concept in approximate IM (AIM) is that slow dominant dynamical behavior of the system is confined to a low-dimension manifold, and fast dynamics respond to the dynamics on the IM instantaneously. Decomposition of slow/fast dynamics and formulation of an AIM is accomplished by only exploiting the governing equations. Direct numerical simulation (DNS) of initially non-premixed fuel–air mixtures developing in forced isotropic turbulence have been carried out to investigate the proposed model. Reaction rate parameters are varied to allow for varying levels of extinction and reignition. The AIM performance in capturing different flame behaviors is assessed both a priori and a posteriori. It is shown that AIM captures the dynamics of the flames including extinction and reignition. Moreover, AIM provides scalar dissipation rate, mixing time for reactive scalars, and closures for nonlinear terms without any additional modeling. The AIM formulation is found promising and provides a new approach to modeling turbulent combustion.

Investigation of scalar–scalar-gradient filtered joint density function for large eddy simulation of turbulent combustion

The scalar–scalar-gradient filtered joint density function (FJDF) and its transport equation for large eddy simulation of turbulent combustion are studied experimentally. Measurements are performed in the fully developed region of an axisymmetric turbulent jet (with jet Reynolds number UjDj/ν=40 000) using an array consisting of three X-wires and three resistance-wire temperature probes. Filtering in the cross-stream and streamwise directions is realized by using the array and by invoking Taylor's hypothesis, respectively. The FJDF and the terms in the transport equation are analyzed using their means conditional on the filtered scalar and the subgrid-scale (SGS) scalar variance. The FJDF is unimodal when the SGS scalar variance is small compared to its mean value. The scalar gradient depends weakly on the SGS scalar. For large SGS variance, the FJDF is bimodal and the gradient depends strongly on the SGS scalar; therefore, the often-invoked independence assumption is not valid. The SGS scalar under such a condition contains a diffusion layer structure and the SGS mixing is similar to the early stages of binary mixing. The isoscalar surface in the diffusion layer has a lower surface-to-volume ratio than that in a well-mixed scalar. The conditionally filtered diffusion of the scalar gradient has an S-shaped dependence on the scalar gradient, which is expected to be qualitatively different from that of a reactive scalar under fast chemistry conditions. However, because modeling is performed at a higher level and because the scalar–scalar-gradient FJDF contains the information about the scalar dissipation and the surface-to-volume ratio, the FJDF approach is expected to be more accurate than scalar filtered density function approaches and has the potential to model turbulent combustion over a wide range of Damköhler numbers.

Numerical Investigation of Turbulent Premixed Combustion of Methane / Air in Low Swirl Burner under Elevated Pressures and Temperatures

Turbulent combustion modeling of lean premixed methane/air gas mixture in a low swirl burner is carried out using Large Eddy Simulation (LES). The operating conditions of the experiment as well as simulation are carried out at elevated pressure and temperature. The first case-simulation is a premixed combustion model based on C-equation formulation, the second one is based on species transport – Eddy Dissipation Concept (EDC) model. Numerical results for axial velocity and turbulence intensity along the centerline showed a good agreement against the experimental data. Quantitative results of OH mass fraction contour showing the flame structure are in a plausible agreement compared to the experimental measurement.

Minimization of Torque Deviation of Cylinder Deactivation Engine through 48V Mild-Hybrid Starter-Generator Control.

Cylinder deactivation (CDA) is an effective technique to improve fuel economy in spark ignition (SI) engines. This technique enhances volumetric efficiency and reduces throttling loss. However, practical implementation is restricted due to torque fluctuations between individual cylinders that cause noise, vibration, and harshness (NVH) issues. To ease torque deviation of the CDA, we propose an in-cylinder pressure based 48V mild-hybrid starter-generator (MHSG) control strategy. The target engine realizes CDA with a specialized engine configuration of separated intake manifolds to independently control the airflow into the cylinders. To handle the complexity of the combined CDA and mild-hybrid system, GT-POWER simulation environment was integrated with a SI turbulent combustion model and 48V MHSG model with actual part specifications. The combustion model is essential for in-cylinder pressure-based control; thus, it is calibrated with actual engine experimental data. The modeling results demonstrate the precise accuracy of the engine cylinder pressures and of quantities such as MAF, MAP, BMEP, and IMEP. The proposed control algorithm also showed remarkable control performance, achieved by instantaneous torque calculation and dynamic compensation, with a 99% maximum reduction rate of engine torque deviation under target CDA operations.

Measurements and Data Analysis Review of Laminar Burning Velocity and Flame Speed for Biofuel/Air Mixtures

Precise measurement and prediction of flame speed and laminar burning velocity are essential for premixed combustion properties characterization, turbulent combustion models validation, progress, and validation of chemical kinetic models. Besides, the problem of lack of fossil fuel, planet pollution, and production of several fuel alternatives led researchers to reexamine the process of combustion and optimize fuel consumption. So, it would be necessary to know the change of laminar burning velocity and flame speed with thermodynamic conditions to understand the impression of practical applications in all combustion systems as working pressures and temperatures are extensively higher than the atmospheric conditions. Several investigations work regarding flame speed and laminar burning velocity had been achieved. However, a detailed literature review of methods and techniques used to measure these two parameters and the effect of operating factors for different fuels focusing on biofuels is presented in this paper for ease of reviewing.