Turbulence-chemistry Interaction Model Research Articles

Reynolds-average Navier-Stokes turbulence models assessment: A case study of CH4/H2/N2-air reacting jet

Computational Fluid Dynamics has become a very powerful tool for developing engineering combustion devices, such as burners and furnaces. However, there are a wide variety of turbulence models, and some of them have proven to be more effective for some turbulent flow configurations than others. A reacting turbulent jet is a common flow configuration found in combustion engineering devices like burners. The present work assesses Reynolds-Average Navier-Stokes turbulence models, being tested on a CH4/H2/N2-Air reacting jet. Eight two-equation eddy-viscosity and three five-equation turbulence models were tested in the studied turbulent flow. Computational results were compared against experimental measurements in terms of flow field variables, mean mixture fraction, temperature, and species mass fraction. The findings suggest a strong influence of the turbulence model perforce on the mean mixture fraction as well as on the turbulence-chemistry interaction model. The modified version of the standard k-ε model proves to be the more reliable choice for this reactive flow configurations. Specially, where the flow patterns of the jet dictate the general flow physics. Near the fuel nozzle, both the Reynolds stress model with stress baseline k-ω (RSM-SBSL) and the standard k-ω model exhibit better agreement with experimental data than the conventional modified k-ε model. Moreover, findings from the standard modified k-ε model indicate a significant underestimation of spreading rates for radial samples in regions where jet spreading intensifies.

LES Modeling of the DLR Generic Single-Cup Spray Combustor: Validation and the Impact of Combustion Chemistry

AbstractTurbulent spray combustion in a generic kerosene-fueled single-cup combustor at typical idle and cruise conditions of an aeroengine are studied with Large Eddy Simulations (LES) using Lagrangian spray and finite-rate chemistry combustion modeling. Three reaction mechanisms of varying complexity are used to model the combustion chemistry. The choice of turbulence-chemistry interaction model is shown to affect the results significantly. The impact of the choice of chemical reaction mechanism and the difference in operating conditions are gauged in terms of time-averaged flow, spray, and combustion characteristics as well as unsteady behavior. Good agreement between LES predictions and experimental results are generally observed but with a notable dependence on the choice of chemical reaction mechanism. The mechanism specifically targeting Jet A displays the best agreement. The choice of reaction mechanism is further demonstrated to influence the flow and thermoacoustics in the combustor, resulting in different thermoacoustic modes dominating. The spray cone is found to be too narrow and thin, an inaccuracy which could be remedied by either making the injection method more empirical or by introducing additional models.

CFD study of flameless combustion in a real industrial reheating furnace considering different H[formula omitted]/NG blends as fuel

On the path towards decarbonisation of the steel industry, the use of H2/NG blends in furnaces, where high temperatures are needed, is one of the alternatives that needs to be carefully studied. The present paper shows the CFD study carried out for a full-scale reheating furnace burner case. The real operating conditions as well as experimental measurements provided by the furnace operator were used to validate the results and reduce simulation uncertainties. The burner under consideration (2.5 MW) works in flameless mode with natural gas and preheated air (813 K). Starting from this point, another three fuel blends with volumetric percentages of 23% (also known as G222), 50% and 75% of H2 in natural gas were considered. For this purpose, the open source CFD code OpenFOAM was used, where the novel NE-EDC turbulence-chemistry interaction model was implemented, which has already been successfully validated specifically for flameless combustion in a furnace. The implementation incorporated an enhanced approach for calculating the chemical time-scale, coupled with a specific post-processing solver to predict NOx emissions. The study analyses the relative impact of the considered fuel blends on NOx formation and flameless regime. The modelling results demonstrated the burner’s capability to operate efficiently with high concentrations of hydrogen, maintaining flameless regime in all cases. This condition ensured uniform temperature distributions and low levels of NOx emissions, reaching a maximum value of 86 mg/m3. These results indicated the proper functionality of the existing natural gas-based burner with H2/NG blends, which was the primary requirement for the conversion process.

Numerical simulation of turbulent premixed flames with the conditional source-term estimation model using Bernstein polynomial expansion

Conditional Source-term Estimation (CSE) is a turbulence-chemistry interaction model similar to CMC, except that the conditional scalars are calculated from unconditional ones using an integral equation. This problem is inherently ill-posed and should be regularised. Recently, an efficient regularisation approach based on Bernstein polynomial expansion was proposed by Mahdipour and Salehi (Combust. Flame, 2022) in an a priori analysis using DNS data. This work implements this approach in a reacting flow solver, and two laboratory-scale turbulent premixed flames are simulated in the Reynolds-Averaged Navier-Stokes (RANS) context. The turbulent intensity in the first flame is low, and the results show that, unlike the conventional CSE approach, the new approach can accurately predict the flamelet conditional averages. Furthermore, the predicted averaged velocity field and major and minor species mass fractions compare favourably with the experimental measurements. The turbulent intensity in the second flame is relatively higher, and the predicted conditional averages should deviate from an unstrained laminar flame solution. The new approach can correctly predict this trend as well as the flame height in this flame. The computational cost of the new CSE approach is also substantially reduced compared to the regular CSE approach.

Numerical Modeling and Analysis of Energy-Assisted Compression Ignition of Varying Cetane Number Jet Fuels for High-Altitude Operation

Abstract Computational fluid dynamics (CFD) simulations are performed to study the potential of energy-assisted compression ignition (EACI) strategy for enabling ignition and enhancing combustion of different cetane number jet fuels during high-altitude operation. EACI employs an ignition assistant (IA), which is an advanced glow-plug design with the ability to sustain higher temperatures for prolonged periods, to provide the necessary ignition energy for precise ignition control and enhanced combustion. In the numerical simulations, the combustion chemistry solver is coupled with a multicomponent wide distillation fuel mechanism, energy source modeling, and a turbulence-chemistry interaction model to accurately capture the ignition assisted-combustion. The simulation is first validated against optical engine measurements for cetane number (CN) 48 jet fuel and then transferred to another single-cylinder test engine to study the ignition and combustion characteristics of EACI with CN 35 jet fuel at varying IA temperatures. Simulation results show that EACI significantly improves fuel ignitability. Ignition delay reductions for CN 48 fuel of 57% and CN 35 fuel of 25% are noted at IA temperatures of 1550 K and 1405 K compared to when the IA is switched off. Furthermore, EACI improved the combustion efficiency to 99.7% compared to the 90% estimated for the IA off case in the optical engine.

On the Importance of Model Selection for CFD Analysis of High Temperature Gas-Solid Reactive Flow; Case Study: Post Combustion Chamber of HIsarna Off-Gas System

In this paper a CFD analysis of HIsarna off-gas system for post combustion of CO-H2-carbon particle mixture is presented to evaluate the effect of different sub-models and parameters on the accuracy of predictions and simulation time. The effects of different mesh type, mesh grid size, radiation models, turbulent models, kinetic mechanism, turbulence chemistry interaction models, including and excluding gas-solid reactions, number of reactive solid particles are investigated in detail. Based on the accuracy of the predictions and agreement with counterpart measured values, the best combination is selected and conclusions are derived. It was found that radiation and turbulence chemistry interaction model have a major effect on the temperature and composition profile prediction along the studied off-gas system, compared to the variations in other models. The effect of these two models becomes even more evident when the temperature and fuel content of the flue gas are high.

CFD modeling of petcoke co-combustion in a real cement kiln: The effect of the turbulence-chemistry interaction model applied with K-ϵ variations

Abstract Using alternative fuels (AF) in industry high consuming energy where fossil fuels are largely consumed may be a great solution to decrease CO2 emission and cost production. Or, when using these alternative fuels, the combustion may be difficult to control regarding the different components of AFs compared to fossil fuels. In this case, the use of the computational fluid dynamics CFD tools is a great solution to predict the AFs combustion behavior. This paper represents a computational study of petcoke and olive pomace (OP) co-combustion in a cement rotary kiln burner, established on the commercial CFD software ANSYS FLUENT. This study presents a useful key to choose an adequate simulation model that well predicts co-combustion problems. The performance of the K-ϵ turbulence models varieties (standard, Realizable, and Re-Normalization Group) combined with the hybrid finite rate/eddy dissipation model and the simple eddy dissipation model for predicting the co-combustion characteristics was investigated. The particle phase solutions are obtained using the Lagrangian approach. The performance of the mentioned model was evaluated based on the mesh accuracy, convergence time, temperature shape, and important chemical elements concentration. The predicted values of species concentrations and temperature are compared to the results obtained from the real case study and available literature. The standard K-ϵ model combined with the hybrid finite rate/eddy dissipation model gives the best results and the lower computational resources required for the 2-D model realized.

Localized conditional source-term estimation model for turbulent combustion

A novel functional form for approximating the conditional scalars in turbulent reacting flows is introduced based on the Bernstein polynomial. Multi-scalar measurement data of turbulent premixed and non-premixed flames are used to demonstrate that the new functional form provides an excellent reduced-order model for the conditional scalars. This model order reduction technique can be used to improve the accuracy, reduce the computational cost and enhance the spatial localization of the Conditional Source-term Estimation (CSE) model. CSE is a turbulence-chemistry interaction model similar to the Conditional Moment Closure (CMC) model, except that the conditional scalars are estimated from the filtered field in an ensemble of LES cells using an integral equation. An a priori analysis using the DNS data of a series of statistically planar turbulent premixed flames shows that using Bernstein polynomials as the presumed functional form for the conditional scalars provides better regularization than the conventional CSE approach. Furthermore, the ensemble size – that was previously kept on the order of thousands of LES cells in the singly-conditioned CSE – can be reduced to as low as 16 LES cells. This enhanced localization approach reduces the modelling error and the computational cost compared to the conventional CSE approach for tabulated and reduced chemistry models.

Numerical Study of the Influence of Turbulence–Chemistry Interaction on URANS Simulations of Diesel Spray Flame Structures under Marine Engine-like Conditions

The present work performs unsteady Reynolds-averaged Navier-Stokes simulations to study the effect of turbulence-chemistry interaction (TCI) on diesel spray flames. Three nozzle diameters (d0) of 100, 180, and 363 μm are considered in the present study. The Eulerian stochastic fields (ESF) method (with the TCI effect) and well-stirred reactor (WSR) model (without the TCI effect) are considered in the present work. The model evaluation is carried out for ambient gas densities (ρam) of 30.0 and 58.5 kg/m3. The ESF method is demonstrated to be able to reproduce the ignition delay time (IDT) and lift-off length (LOL) with an improved accuracy than that from the WSR method. Furthermore, TCI has relatively more influence on LOL than on IDT. A normalized LOL (LOL*) is introduced, which considers the effect of d0, and its subsequent effect on the fuel-richness in the rich premixed core region is analyzed. The RO2 distribution is less influenced by the TCI effect as ambient density increases. The ESF model generally predicts a longer and wider CH2O distribution. The difference in the spatial distribution of CH2O between the ESF and WSR model diminishes as d0 increases. At ρam = 30.0 kg/m3, the ESF method results in a broader region of OH with lower peak OH values than in the WSR case. However, at ρam = 58.5 kg/m3, the variation of the peak OH value is less susceptible to the increase in d0 and the presence of the TCI model. Furthermore, the influence of TCI on the total OH mass decreases as d0 increases. The total NOx mass qualitatively follows the same trend as the total OH mass. This present work clearly shows that the influence of TCI on the global spray and combustion characteristics becomes less prominent when d0 increases. (Less)

Presumed Joint-PDF Modelling for Turbulent Stratified Flames

Turbulence–chemistry interaction models such as the conditional moment closure and various flamelet models require a presumed Probability Density Function (PDF) model of the conditioning variables. In turbulent stratified flames, a joint-PDF model for a reaction progress variable and the mixture fraction is required. The joint-PDF is often modelled by two beta functions using the first and second moments of the two conditioning variables. In this work, the performance of a joint-PDF model based on the flamelet PDF approach is compared to the double beta-PDF model. The conditional PDF of the reaction progress variable conditioned on mixture fraction is modelled with the flamelet PDF. Unlike the beta PDF, the flamelet functional form for the conditional PDF varies with the local mixture fraction. The two PDF models are coupled with a two-dimensional premixed flamelet-generated manifold chemistry model. Two stratified flames of the Cambridge–Sandia bluff-body burner are simulated using a Reynolds-Averaged Navier–Stokes (RANS) approach. The results indicate that the flamelet PDF model has a superior, albeit marginal, predictions of the temperature, major and minor species mass fractions.

Numerical investigation of cavity-induced enhanced supersonic mixing with inclined injection strategies

In this study, an inclined injection system with a cavity and grooves arranged in series is developed to enhance the supersonic mixing in a scramjet combustor. Three-dimensional steady Reynolds-averaged Navier–Stokes equations, the two-equation shear stress transport k-ω model, and the finite-rate/no turbulence-chemistry interaction model are used to simulate the flow field structures with and without grooves at different inclination angles. The numerical method used in the study has been verified using experimental data from the open literature, and the static wall pressure distribution of the numerical simulation is in good agreement with the experimental data. The numerical results reveal that the grooved configuration has a significant influence on the flow field structure. The downstream streamline of the structure with grooves is more turbulent and produces more streamwise vortices because the geometry of the grooves enhances the shear effect between the vortex and the high-speed incoming flow. In the case of the grooved configuration, the mixing coefficient at the fuel orifices is slightly lower, but the fuel mixing effect in the downstream is enhanced and gradually exceeds the grooveless configuration. Moreover, the grooved configuration can obtain the best mixing coefficient at a jet angle of 30°. The grooved configuration has a greater stagnation pressure loss than the grooveless configuration.

Impact of Chemistry–Turbulence Interaction Modeling Approach on the CFD Simulations of Entrained Flow Coal Gasification

This paper examines the impact of different chemistry–turbulence interaction approaches on the accuracy of simulations of coal gasification in entrained flow reactors. Infinitely fast chemistry is compared with the eddy dissipation concept considering the influence of turbulence on chemical reactions. Additionally, ideal plug flow reactor study and perfectly stirred reactor study are carried out to estimate the accuracy of chosen simplified chemical kinetic schemes in comparison with two detailed mechanisms. The most accurate global approach and the detailed one are further implemented in the computational fluid dynamics (CFD) code. Special attention is paid to the water–gas shift reaction, which is found to have the key impact on the final gas composition. Three different reactors are examined: a pilot-scale Mitsubishi Heavy Industries reactor, a laboratory-scale reactor at Brigham Young University and a Conoco-Philips E-gas reactor. The aim of this research was to assess the impact of gas phase reaction model accuracy on simulations of the entrained flow gasification process. The investigation covers the following issues: impact of the choice of gas phase kinetic reactions mechanism as well as influence of the turbulence–chemistry interaction model. The advanced turbulence–chemistry models with the complex kinetic mechanisms showed the best agreement with the experimental data.

Anchoring of turbulent premixed hydrogen/air flames at externally heated walls

A joint experimental and numerical investigation of turbulent flame anchoring at externally heated walls is presented. The phenomenon has primarily been studied for laminar flames and micro-combustion while this study focuses on large-scale applications and elevated Reynolds number flows. Therefore, a novel burner design is developed and examined for a diverse set of operating conditions. Hydroxyl radical chemiluminescence measurements are employed to validate the numerical method. The numerical investigation evaluates the performance of various hydrogen/air kinetics, Reynolds-averaged turbulence models and the eddy dissipation concept (EDC) as a turbulence-chemistry interaction model. Simulation results show minor differences between detailed chemical mechanisms but pronounced deviations for a reduced kinetic. The baseline k-ω turbulence model is assessed to most accurately predict flame front position and shape. Universal applicability of EDC modeling constants is contradicted. Conclusively, the flame anchoring concept is considered a promising approach for pilot flames in continuous combustion devices.

Mesh-Sequenced Realizations for Evaluation of Subgrid-Scale Models for Turbulent Combustion

This paper develops a new approach for analysis of subgrid closures for turbulent combustion as modeled using direct quadrature (finite-rate chemistry) techniques. The approach, termed multiresolution analysis through mesh-sequenced realizations (MRA-MSR), conducts simultaneous, constrained large-eddy simulations on a set of hierarchically coarsened meshes. The availability of underlying fine-mesh (subgrid) data corresponding to coarse-mesh locations allows a clearer assessment of the effects of unresolved fluctuations on apparent reactivity. A key to MRA-MSR is the correlation of eddy structures at coarser mesh levels, which is facilitated by the transfer of filtered fine-mesh velocity information. A seven-mesh MRA-MSR hierarchy using three resolution levels is applied to one of the Sydney bluff-body stabilized methane–hydrogen flames. Analysis of the simultaneously evolved data at different resolution levels reveals several interesting trends. First, at high Damköhler numbers, there is clear evidence of attenuation of apparent reactivity due to the effects of unresolved fluctuations. Secondly, single-point, single-time filtered density functions of a normalized subgrid Damköhler number show a characteristic beta probability density function (PDF) form and display evidence of scale similarity. Interrogation of the MRA-MSR database also shows that the recently-proposed least-squares minimization (LSM) turbulence–chemistry interaction model can account for the observed diminishment in reactivity at high Damköhler numbers but cannot reduce scatter significantly. A new form of the LSM model, which makes use of the normalized subgrid Damköhler number beta PDF distribution, performs slightly better than the original model, illustrating the potential of MRA-MSR both in assessing existing closure concepts and in developing new ones.

New extended eddy dissipation concept model for flameless combustion in furnaces

Flameless combustion, also called MILD combustion (Moderate or Intense Low Oxygen Dilution), is a technology that reduces NOx emissions and improves combustion efficiency. Appropriate turbulence-chemistry interaction models are needed to address this combustion regime via computational modelling. Following a similar analysis to that used in the Extended EDC model (E-EDC), the purpose of the present work is to develop and test a Novel Extended Eddy Dissipation Concept model (NE-EDC) to be better able to predict flameless combustion. In the E-EDC and NE-EDC models, in order to consider the influence of the dilution on the reaction rate and temperature, the coefficients are considered to be space dependent as a function of the local Reynolds and Damköhler numbers. A comparative study of four models is carried out: the E-EDC and NE-EDC models, the EDC model with specific, fixed values of the model coefficients optimized for the current application, and the Flamelet Generated Manifold (FGM) model with pure fuel and air as boundary conditions for flamelet generation. The models are validated using experimental data of the Delft Lab Scale furnace (9 kW) burning Natural Gas (T = 446 K) and preheated air (T = 886 K) injected via separate jets, at an overall equivalence ratio of 0.8. among the considered models, the NE-EDC results show the best agreement with experimental data, with a slight improvement over the E-EDC model and a significant improvement over the EDC model with tuned constant coefficients and the FGM model.

Characteristic Chemical Time Scales for Reactive Flow Modeling

ABSTRACT The chemical time scale can be used to characterize a reactive system(’s behavior). In addition, various dimensionless numbers (e.g. Damköhler number) rely on a characteristic chemical time scale. The inverse eigenvalues of a system are regarded as the system’s time scales. This means, the number of time scales is equal the numbers of eigenvalues. A formulation for a single characteristic time scale is required for the system characterization and to calculate dimensionless numbers. Recently proposed modifications of the Eddy Dissipation Concept (a turbulence-chemistry interaction model) also incorporate the Damköhler number in their formulation. Besides accuracy, the numerical efficiency is important, since the chemical time scale needs to be computed in each cell at every time step. We present different chemical time scale definitions found in literature, evaluate them on simple test problems and use them for flame simulations in conjunction with the modified Eddy Dissipation Concept. For the simple test case, most formulations give satisfactory results. The complexity of the chemical reaction mechanism greatly impacts the calculated time scale values. Therefore, we suggest to use a simple global mechanism for the calculation of chemical time scales to ensure reproducibility and consistency of the results.

Large Eddy Simulation of Bluff-Body Flame Approaching Blow-Off: A Sensitivity Study

ABSTRACTAs almost all combustion processes of practical interest take place in the presence of turbulence, the development of the increasingly refined turbulence–chemistry interaction (TCI) models has led to highly sophisticated approaches. Nearly all of the studies comparing different models focus on stable premixed/non-premixed flame configurations. In this work, the focus is on well-documented, lean premixed bluff-body stabilized flames approaching blow-off and on the blow-off sequence itself. Large Eddy Simulations (LES) have been used to capture the time-dependent, three-dimensional flow-field using Transported Probability Density Function (TPDF), Partially Stirred Reactor Model (PaSR), and Implicit LES (ILES) models. Furthermore, the influence of finite-rate chemistry and different chemical mechanisms is evaluated to determine the limitation and capability of the different TCI approaches for modeling flames just prior to and during the transient blow-off process. While the average flow-fields do not reveal any significant differences between modeling approaches, detailed analysis of the flame reveals that there are differences in the predicted flame thickness and composition. The ability of the considered TCI models to predict local as well as full-flame extinction during the blow-off is investigated as well. It is demonstrated that such a blow-off sequence is not always governed by complex chemistry.

Influence of inlet boundary conditions in computations of turbulent jet flames

PurposeThis paper aims to assess the sensitivity of numerical simulation results of turbulent reactive flow to the formulation of inlet boundary conditions. The analysis concerns the profiles of the mean velocity the turbulence kinetic energy k and its dissipation rate ϵ. It is intended to provide guidance to the determination of inlet conditions when only global flow data are available. This situation can be met both in simple laboratory experiments and in industrial full-scale applications, when measurements are either incomplete or infeasible, resulting in lack of detailed inlet data.Design/methodology/approachTwo turbulence–chemistry interaction models were studied: eddy dissipation concept and partially stirred reactor. Three different velocity profiles and related turbulence statistics were applied to present feasible scenarios and their consequences. Simulations with the most appropriate inlet data were accompanied with profiles of turbulent quantities obtained with a proposed method. This method was contrasted to other approaches popular in the literature: the pre-inlet pipe and the separate cold flow simulations of a burner. The methodology was validated on two laboratory-scale jet flames: Delft Jet-in-Hot-Coflow and Sandia CHN B. The simulations were carried out with open source code OpenFOAM.FindingsThe proposed relations for turbulence kinetic energy and its dissipation rate at the inlet are found to provide results comparable to those obtained with the use of experimental data as inlet boundary conditions. Moreover, from a certain location downstream the jet, weakly dependent on the Reynolds number, the influence of inlet conditions on flow statistics was found to be negligible.Originality/valueThis work reveals the consequences of the use of rather crude assumptions made for inlet boundary conditions. Proposed formulas for the profiles for k and epsilon are attractive alternatives to other approaches aiming to determine the inlet boundary conditions for turbulent jet flows.

CFD modeling of a industrial-scale steam methane reforming furnace

Hydrogen is a required key material for petroleum refineries that convert crude oil into products with higher economic value and is often produced by the steam methane reforming (SMR) process, which synthesizes hydrogen and carbon oxides from methane and superheated steam in the presence of a nickel-based catalyst network in a steam methane reformer. To investigate methods for improving profits for a reformer while avoiding costly on-site parametric studies, a high-fidelity model of a steam methane reformer can be investigated. Motivated by this, the present work focuses on developing a computational fluid dynamics (CFD) model of an industrial-scale steam methane reformer that consists of 336 reforming reactors, 96 burners and 8 flue gas tunnels. The motivation for choosing the modeling strategies used in the industrial-scale steam methane reformer CFD model is discussed and is based on expected transport phenomena and chemical reactions within the reformer. Specifically, the finite rate/eddy dissipation turbulence-chemistry interaction model, global kinetic models of hydrogen/methane combustion, global kinetic model of the SMR process and standard k-∊ turbulence model with the ANSYS Fluent enhanced wall treatment function are used to simulate the formation and consumption rates of all chemical components of the system. In addition, an empirical correlation for estimating the radiative properties of a homogeneous gas mixture, Kirchhoff’s law, Lambert Beer’s law and the discrete ordinate method are employed to simulate radiative heat transfer in the furnace side of an industrial-scale steam methane reformer. Moreover, the modeling strategies of the reforming tubes developed in our previous work are adopted to model 336 reforming tubes in the reformer. Subsequently, the boundary conditions (i.e., the reforming tube feed, burner feed and the energy leakage through the combustion chamber refractory wall) of the industrial-scale reformer CFD model are derived based on typical plant data. The simulation results produced by the industrial-scale reformer CFD model are shown to be in agreement with typical plant data reported in the SMR literature, with the simulation data generated by an industrial-scale reforming tube CFD model and with the simulation data generated by a reforming Gibbs reactor model, which validates the chosen modeling strategies and allows the CFD data to be considered to represent actual plant data with sufficient accuracy for use in industrial operating parameter studies.

Assessment of turbulence-chemistry interaction models in the computation of turbulent non-premixed flames

The present work reports on the assessment of different turbulence-chemistry interaction closures for the modelling of turbulent non-premixed combustion. Two-dimensional axisymmetric simulations have been carried out based on three different laboratory flames. The methane fueled, piloted jet flame Sandia D, the simple jet syngas flame and the so-called Delft Jet-in-Hot Coflow flame are studied. All the flames can be characterised as non-premixed but differ by some features which are taken into account through appropriate modelling approach.