Premixed turbulent combustion modeling using tabulated detailed chemistry and PDF

Tabulated chemistry and presumed probability density function (PDF) approaches are combined to perform RANS modeling of premixed turbulent combustion. The chemistry is tabulated from premixed flamelets with three independent parameters: the equivalence ratio of the mixture, the progress of reaction, and the specific enthalpy, to account for heat losses at walls. Mean quantities are estimated from presumed PDFs. This approach is used to numerically predict a turbulent premixed flame diluted by hot burnt products at an equivalence ratio that differs from the main stream of reactants. The investigated flame, subjected to high velocity fluctuations, has a thickened-wrinkled structure. A recently proposed closure for scalar dissipation rate that includes an estimation of the coupling between flame wrinkling and micromixing is retained. Comparisons of simulations with experimental measurements of mean velocity, temperature, and reactants are performed.     

Evaporating droplets in turbulent reacting flows

Three-dimensional direct numerical simulations are carried out to determine the effects of turbulence on the preferential segregation of an evaporating spray and then to study the evolution of the resulting mixture fraction topology and propagating flame. First, the mixing between an initially randomly dispersed phase and the turbulent gaseous carrier phase is studied with non-evaporating particles. According to their inertia and the turbulence properties, the formation of clusters of particles is analyzed (formation delay, cluster characteristic size and density). Once the particles are in dynamical equilibrium with the surrounding turbulent flow, evaporation is considered through the analysis of the mixture fraction evolution. Finally, to mimic ignition, a kernel of burnt gases is generated at the center of the domain and the turbulent flame evolution is described.     

Improvement of the pressure algorithm of the stand-alone PDF method to treat unsteady three-dimensional turbulent reacting flows

This paper deals with the particle-mesh probability density function (PDF) method. It shows how an existing but less precise pressure algorithm for the stand-alone method can be improved. The present algorithm is able to handle the general case of an unsteady three-dimensional turbulent reacting flow. The transport equation of the joint PDF of velocity and composition is solved with a particle method. Open boundary conditions are realized and for statistical reasons a simple but effective particle splitting procedure is applied.

Based on a simple configuration, the properties of the presented improved pressure algorithm are analysed. It is shown which numerical condition must be taken care of so that the algorithm is able to correct the particle positions such that the normalization condition is fulfilled as accurately as specified.

To verify the algorithm the combustion of a methane–air mixture enclosed in an open simulation volume is calculated. It is shown that the simple particle splitting algorithm works very effectively in the studied case. The behaviour of the improved pressure algorithm is examined by different calculations. To analyse the convergence of the algorithm, the particle number per cell and the grid spacing are varied. To demonstrate the accuracy, a statistically stationary inflow/outflow configuration is used and the numerical solution is compared to an analytical one. For a less symmetric test case, the previous unsteady combustion problem is simulated, including an additional mean velocity in one direction.

The presented improved pressure algorithm provides the opportunity to calculate unsteady three-dimensional turbulent reacting flows with a stand-alone method, and offers an alternative to the complex hybrid finite-volume/particle PDF method.     

Modelling of turbulent reacting flows in furnace devices

The spatial combustion of turbulent jets in furnace devices is modelled numerically basing on equations for multi-component turbulent reacting gaseous mixtures. The dependencies are obtained for the influence of the secondary air velocity and composition of gaseous components on torch configuration at a diffusion combustion process. The effect of regime parameters on the increase in torch sizes, which arises at the interaction of secondary air with gaseous components, has been elucidated.     

An improved high-order scheme for DNS of low Mach number turbulent reacting flows based on stiff chemistry solver

We present an improved numerical scheme for numerical simulations of low Mach number turbulent reacting flows with detailed chemistry and transport. The method is based on a semi-implicit operator-splitting scheme with a stiff solver for integration of the chemical kinetic rates, developed by Knio et al. [O.M. Knio, H.N. Najm, P.S. Wyckoff, A semi-implicit numerical scheme for reacting flow II. Stiff, operator-split formulation, Journal of Computational Physics 154 (2) (1999) 428–467]. Using the material derivative form of continuity equation, we enhance the scheme to allow for large density ratio in the flow field. The scheme is developed for direct numerical simulation of turbulent reacting flow by employing high-order discretization for the spatial terms. The accuracy of the scheme in space and time is verified by examining the grid/time-step dependency on one-dimensional benchmark cases: a freely propagating premixed flame in an open environment and in an enclosure related to spark-ignition engines. The scheme is then examined in simulations of a two-dimensional laminar flame/vortex-pair interaction. Furthermore, we apply the scheme to direct numerical simulation of a homogeneous charge compression ignition (HCCI) process in an enclosure studied previously in the literature. Satisfactory agreement is found in terms of the overall ignition behavior, local reaction zone structures and statistical quantities. Finally, the scheme is used to study the development of intrinsic flame instabilities in a lean H₂/air premixed flame, where it is shown that the spatial and temporary accuracies of numerical schemes can have great impact on the prediction of the sensitive nonlinear evolution process of flame instability.     

Evaporation rates of droplet arrays in turbulent reacting flows

Studies of regularly ordered droplet arrays facilitate the analysis of local effects on evaporation rates. This work investigates, using Direct Numerical Simulations (DNS), the effects of droplet density and flow conditions on evaporation of kerosene droplets in inert and reactive convective environments. A novel model, coupling a mass conservative Level Set approach with the Ghost Fluid method, is used. The rates obtained from the DNS are compared to two evaporation models based on heat and mass transfer numbers commonly used for RANS methods and Large Eddy Simulations (LES). The results show that predictions of evaporation rates of dense sprays using these models has a limited success. The use of the 1/3-rule to calculate mixture properties results in underpredictions of the evaporation rates by around 20% to 50% in most of the cases studied. The models can only predict the DNS results accurately with errors lower than 2%, if the properties in the evaporation rate models are based on properties in the near field around the droplet. Further studies on the effects of turbulence on the evaporation process showed no evident correlation between the evaporation rates and the subgrid kinetic energy relating the effects of turbulence to vapour dispersion away from the droplet surface.     

Finite-rate chemistry effects in turbulent opposed flows: comparison of Raman/Rayleigh measurements and Monte Carlo PDF simulations

This study reports results from experimental and numerical investigations of a partially premixed turbulent opposed methane/air jet flame. Experimentally determined properties of the scalar and the flow field are compared to the results from a Monte Carlo simulation. One-dimensional spatially resolved Raman/Rayleigh scattering serves to quantify the mean species concentrations and temperature, whereas laser Doppler velocimetry is used to measure axial and radial velocity components. The simulation is simplified by using a one-dimensional formulation. It includes a Reynolds-stress turbulence model and a Monte Carlo simulation of the joint scalar probability density function (PDF). A non-uniform Monte Carlo particle distribution is used to minimize stochastic errors. The flame is operated close to extinction with strong interactions between turbulence and chemistry. Comparisons between experimental and numerical results reveal a good agreement of mixture fraction profiles along the centreline. However, species scatter plots and mixture fraction PDFs show discrepancies between experiment and simulation. Numerical simulations over-predict the extinction limits and therefore under-predict the intermittent nature of turbulence and mixing of the scalars.     

Structure analysis of turbulent mixing patterns in inert and reactive turbulent liquid flows

The paper contains an extended summary of an invited plenary talk given at the Workshop on Active Chaos at the Los Alamos National Laboratory on 29-31 May 2001 by one of us (F.S.R.). (c) 2002 American Institute of Physics.     

A consistent-splitting approach to computing stiff steady-state reacting flows with adaptive chemistry

Splitting techniques have been used extensively for computing reacting flows with detailed chemistry. Nevertheless, there are still some open questions with respect to efficiency and the error introduced by splitting. In this paper, the accuracy and effectiveness of split-operator methods for computing steady-state reacting flows are determined. A fully coupled scheme is described together with two splitting schemes: a standard Strang-splitting scheme and a consistent-splitting scheme, all with implicit transport computations. The effect of splitting errors on the convergence and solution accuracy is investigated analytically using a one-dimensional scalar equation. The accuracy with respect to the original discretized equations is tested for an H₂/O₂ burner flame. Finally, consistent splitting is combined with an adaptive chemistry approach to compute three partially premixed laminar methane flames using detailed chemistry (217 reactions). The calculations confirm that HCO radical concentration is an excellent surrogate for heat release rate.     

Conditional statistics of inert droplet effects on turbulent combustion in reacting mixing layers

Direct numerical simulation (DNS) of turbulent reacting mixing layers laden with evaporating inert droplets is used to assess the droplet effects in the context of the conditional moment closure (CMC) for multiphase turbulent combustion. The temporally developing mixing layer has an initial Reynolds number of 1000 based on the vorticity thickness with more than 16 million Lagrangian droplets traced. An equivalent mixture fraction incorporating the inert vapour mass fractions clearly demonstrates the effects of vapour dilution on the mixture. Instantaneous fields and conditional statistics, such as the singly conditioned scalar dissipation rate, the gas temperature 〈 T _g|η 〉, conditional variance of the gas temperature 〈 T _g ^”2|η 〉 and conditional covariance between the fuel mass fraction and gas temperature 〈 Y _f ^” T _g ^”|η 〉 show considerable droplet effects. Comparison between the droplet-free and droplet-laden reacting mixing layer cases suggests significant extinction in the latter case. The resulting large conditional fluctuations around the conditional means contradict the basic assumption behind the first-order singly conditioned CMC. More sophisticated CMC approaches, such as doubly conditioned or second-order CMCs are, in principle, better able to incorporate the effects of evaporating droplets, but significant modelling challenges exist. The scalar dissipation rate doubly conditioned on the mixture fraction and a normalized gas temperature 〈 χ | η, ζ 〉 exemplifies the modelling complexity in the CMC of multiphase combustion.     

Conditional statistics of nonreacting and reacting sprays in turbulent flows by direct numerical simulation

Conditional statistics concerning evaporation and combustion of a spray are investigated in homogeneous, isotropic, and decaying two-dimensional (2D) turbulence. Randomly distributed, polydisperse droplets of n-heptane go through single-step combustion chemistry. Attention is focused on parametric effects of initial Sauter mean radius (SMR), turbulence level and droplet velocity in both reacting and nonreacting cases. A simple linear model for the conditional evaporation rate is proposed and validated against DNS data. A conventional β-probability density function (pdf) is shown to be valid with no peak occurring on the fuel side. The amplitude mapping closure (AMC) model works well for the conditional scalar dissipation rate with evaporating and reacting sprays. Parametric study shows that initial SMR and droplet velocity are major factors affecting conditional flame structures, whereas the effect of reaction is not significant except during autoignition.     

In-Situ Adaptive Manifolds: Enabling computationally efficient simulations of complex turbulent reacting flows

Reduced-order manifold approaches to turbulent combustion modeling traditionally involve precomputation of manifold solutions and pretabulation of the thermochemical database versus a small number of manifold variables. However, additional manifold variables are required as the complexity of turbulent combustion processes increases through consideration of, for example, multi-modal, non-adiabatic, or non-isobaric combustion, or combustion featuring multiple and/or inhomogeneous inlets. This increase in the number of manifold variables comes with an increase in the computational cost of precomputing a greater number of manifold solutions, most of which are never actually utilized in a CFD calculation. The memory required to store the pretabulated high-dimensional thermochemical database also increases, practically limiting the complexity of manifold-based combustion models. In this work, a new In-Situ Adaptive Manifolds (ISAM) approach is developed that overcomes this limitation by combining ‘on-the-fly’ calculation of manifold solutions with In-Situ Adaptive Tabulation (ISAT), enabling the use of more complex manifold-based turbulent combustion models. The performance of ISAM is evaluated via LES of turbulent nonpremixed jet flames with both hydrogen and hydrocarbon fuels. A performance assessment indicates that the computational overhead associated with ISAM compared to pretabulation ranges from negligible up to a factor of two, with most of this overhead associated with convolution of the thermochemical state against a presumed subfilter PDF. In addition, the memory requirements of ISAM are more than two orders of magnitude less than conventional tabulation. These results demonstrate the potential for ISAM to accommodate significantly more complex manifold-based combustion models.     

Dynamic subgrid scale modeling of turbulent flows using lattice-Boltzmann method

In this paper, we discuss the incorporation of dynamic subgrid scale (SGS) models in the lattice-Boltzmann method (LBM) for large-eddy simulation (LES) of turbulent flows. The use of a dynamic procedure, which involves sampling or test-filtering of super-grid turbulence dynamics and subsequent use of scale-invariance for two levels, circumvents the need for empiricism in determining the magnitude of the model coefficient of the SGS models. We employ the multiple relaxation times (MRT) formulation of LBM with a forcing term, which has improved physical fidelity and numerical stability achieved by proper separation of relaxation time scales of hydrodynamic and non-hydrodynamic modes, for simulation of the grid-filtered dynamics of large-eddies. The dynamic procedure is illustrated for use with the common Smagorinsky eddy-viscosity SGS model, and incorporated in the LBM kinetic approach through effective relaxation time scales. The strain rate tensor in the SGS model is locally computed by means of non-equilibrium moments of the MRT-LBM. We also discuss proper sampling techniques or test-filters that facilitate implementation of dynamic models in the LBM. For accommodating variable resolutions, we employ conservative, locally refined grids in this framework. As examples, we consider the canonical anisotropic and inhomogeneous turbulent flow problem, i.e. fully-developed turbulent channel flow at two different shear Reynolds numbers Re_∗ of 180 and 395. The approach is able to automatically and self-consistently compute the values of the Smagorinsky coefficient, C_S. In particular, the computed value in the outer or bulk flow region, where turbulence is generally more isotropic, is about 0.155 (or the model coefficient ) which is in good agreement with prior data. It is also shown that the model coefficient becomes smaller and approaches towards zero near walls, reflecting the dampening of turbulent length scales near walls. The computed turbulence statistics at these Reynolds numbers are also in good agreement with prior data. The paper also discusses a procedure for incorporation of more general scale-similarity based SGS stress models.     

The impact of reduced chemistry on auto-ignition of H2 in turbulent flows

The auto-ignition behaviour of hydrogen in a turbulent flow field has been studied through a combination of detailed and systematically reduced chemistry with a transported PDF approach closed at the joint-scalar level. Radiation is accounted for through the RADCAL method and the inclusion of enthalpy into the joint-scalar PDF. Molecular mixing is closed using the modified Curl's model with the mixing frequency accounted for via two algebraic closures. The main aim of the work is to compare the impact of alternative chemical mechanisms on auto-ignition and to explore the accuracy that can be expected when reactive scalars are sequentially removed through the application of quasi-steady-state approximations (QSSAs). Two different detailed mechanisms were tested to establish the effects of intrinsic uncertainties in the detailed chemistry and to provide reference points to past work. The mechanisms feature nine solved species and 19 or 20 reversible chemical reactions. The chemical mechanisms were subsequently systematically reduced to five, four and three independent scalars through the successive introduction of QSSAs for H₂O₂, HO₂ and O. Resulting inaccuracies were quantified following each simplification step with reference to experimental data obtained in shock tubes and under turbulent flow conditions in the Cabra burner configuration. A sensitivity analysis was also performed to identify the relative impact of uncertainties in key reactions as compared to systematic simplification process. It was found that alternative recommended rates for the O + H₂ = OH + H reaction have an impact on the point of flame stabilization that is similar to that observed as a consequence of the simplification process. The work also shows that realistic results can be obtained with simplified chemistry. However, it is also concluded that the temporal evolution of the radical pool and the point of stabilization is affected by the introduction of a QSSA for the O radical. Furthermore, it is shown by comparisons with time resolved OH radical data obtained in shock tubes that the progressive elimination of species via QSSA leads to a shortening of ignition delay times and that the same effects are present, but less severe, in turbulent flow fields.     

An evaluation of gas-phase micro-mixing models with differential mixing timescales in transported PDF simulations of sooting flame DNS

The use of transported probability density function (TPDF) models to predict soot has the strong advantage that the effects of turbulent fluctuations on soot source terms can be rigorously accounted for. However, soot processes are closely coupled to gas-phase composition. Among the open issues for gas-phase micro-mixing is the species-dependence of mixing timescales. The objective is to carry out an evaluation on the effect of incorporating differential mixing timescales among gas-phase species in a TPDF simulation for soot prediction. A DNS having the configuration of a temporally evolving, non-premixed ethylene flame with a four-step, three-moment soot model is considered as the target for evaluation. The DNS dataset is applied to provide key inputs for TPDF simulations to limit the sources of error to micro-mixing. TPDF simulations with the interaction by exchange with the mean (IEM) and modified Curl (MC) models, which impose the same mixing timescale to all species, underpredict soot mass fraction and overpredict extinction levels regardless of the prescribed mixing frequency. By incorporating differential mixing timescales among gas-phase species, IEM-DD and MC-DD models yield notable improvement in predictions of the overall extinction and soot levels, highlighting the benefit of accounting for differential mixing timescales. A TPDF simulation with the Euclidean minimum spanning tree (EMST) model yields even better predictions, illustrating that the localness in composition space remains a critical issue. The indicated species mixing frequencies by the EMST model are shown to follow the DNS results qualitatively, illustrating that the micro-mixing process based on the Euclidean distance in composition space reproduces to a certain extent the differential mixing timescales due to reaction. Finally, it is shown that incorporating differential mixing timescales of soot moments is expected to have limited value as the mixing timescales of soot moments are sufficiently large to safely neglect soot mixing.     

A comparison of different approaches to integrate flamelet tables with presumed-shape PDF in flamelet models for turbulent flames

Flamelet models for turbulent combustion modelling make use of presumed-shape probability density functions (PDFs) for integrating laminar flamelet solutions to obtain an integrated flamelet table that can readily be used for turbulent flame calculations. The existence of non-unique approaches for such an integration has rarely been investigated before. For the first time, this work studies systematically the non-uniqueness of the flamelet table integration approaches. A flamelet model called the flamelet/progress variable model is used in the study, although the issue exists generally in many other flamelet models. Two classes of table integration approaches are investigated, one preserving the laminar flamelet structures during integration and the other not. Three different table integration approaches are examined and compared in detail to provide a thorough understanding of the different approaches. A partially stirred reactor is used as a test case for examining the different approaches. A method based on the transported PDF method is also employed to provide a reference for the assessment of the different flamelet table integration approaches. It is found in general that the flamelet preserving integration approach yields a more reasonable joint PDF of the mixture fraction and the progress variable, and the prediction results are closer to the referenced transported PDF results.     

Computationally-efficient and accurate particle PDF simulations of turbulent combustion using coupled pre-partitioned adaptive chemistry and tabulation

LES/PDF methods are known to provide accurate results for challenging turbulent combustion configurations with strong turbulence-chemistry interactions. These methods are generally applicable as they do not make any assumptions on the topology of the underlying flame structure. However, this added generality comes at an increased computational cost. To mitigate this added cost, the majority of the LES/PDF computations performed to date utilize reduced mechanisms. We recently presented a coupled pre-partitioned adaptive chemistry (PPAC) and tabulation (ISAT) methodology (Newale et al., Comb. Th. Mod., 2019), which retains the fidelity of the detailed mechanism, while keeping the computational cost affordable. This methodology was tested in a partially-stirred reactor configuration. In this work, we describe the developments required for a holistic integration of PPAC-ISAT with a LES/PDF framework. We examine the performance of this coupled methodology in two LES/PDF configurations of Sandia flame D. A smaller simulation domain is initially utilized to characterize the efficiency and accuracy of standalone PPAC and coupled PPAC-ISAT in detail. Then, the performance of PPAC-ISAT is examined in a full-scale LES/PDF simulation. We show that the coupled PPAC-ISAT LES/PDF captures the resolved mean and RMS profiles of temperature and major species mass fractions to within 2% and OH to within 5%, with a reduction in the average simulation wall clock time per time step of 39% over an ISAT implementation using the detailed mechanism.