Compressible Direct Numerical Simulation Research Articles

Effects of pressure gradient on the evolution of velocity-gradient tensor invariant dynamics on a controlled-diffusion aerofoil at

A weakly compressible flow direct numerical simulation of a controlled-diffusion aerofoil at $8^{\circ }$ geometrical angle of attack, a chord-based Reynolds number of $Re_{c}=150\,000$ and a Mach number of $M=0.25$ based on the free-stream velocity relevant to many industrial applications was conducted to improve the understanding of the impact of the pressure gradient on the development of turbulent structures. The evolution equations for the two invariants $Q$ and $R$ of the velocity-gradient tensor have been studied at various locations along the aerofoil chord on its suction side. The shape of the mean evolution of the velocity-gradient tensor invariants were found to vary strongly when the flow encounters favourable, zero and adverse pressure gradients and as well for different wall-normal locations. The coupling between the pressure-Hessian tensor and the velocity-gradient tensor was found to be the major factor that causes these changes and is greatly influenced by the mean pressure-gradient condition and the wall-normal distance. Striking differences exist from the mean trajectories of this coupling at least in the log layer and outer layer subject to different mean pressure gradients. The nonlinearity and viscous diffusion effects keep their respective invariant characters regardless of the pressure-gradient effects and wall-normal locations. The wall and the mean adverse pressure gradient were both found to suppress the vortical stretching features of the flow. These features are of great importance for the development of future turbulence models on wall-bounded flows, especially on surfaces with significant curvature such as cambered aerofoils and blades for which significant mean pressure gradients exist.

Effects of Turbulence Intensity and Biogas Composition on the Localized Forced Ignition of Turbulent Mixing Layers

ABSTRACTThree-dimensional compressible Direct Numerical Simulations (DNS) have been used to investigate the localized forced ignition of statistically planar mixing layers of biogas/air mixtures for different levels of turbulence intensity and biogas composition. The biogas is represented by a CH/CO mixture and a two-step mechanism involving incomplete oxidation of CH to CO and HO, and an equilibrium between the CO oxidation and the CO dissociation has been used. This two-step mechanism captures the variation of the unstrained laminar flame speed with equivalence ratio and CO dilution with sufficient accuracy when compared with detailed chemistry results. A successful ignition of CH/CO/air mixing layer initially gives rise to a tribrachial flame structure involving fuel-rich and lean premixed branches on either side of the diffusion flame stabilized on the stoichiometric mixture fraction iso-surface. Long after the energy deposition has ended, the lean branch may merge with the diffusion flame, but edge flame propagation along the stoichiometric mixture fraction iso-surface is observed at all stages. The highest heat release rate (HRR) is obtained on the rich premixed branch irrespective of the turbulence intensity and biogas composition, but its magnitude decreases with increasing CO dilution. The most probable edge flame displacement speed decreases in time and converges to its theoretical value for laminar cases. As the turbulence level increases, the edge flame displacement speed assumes a larger range of values, although its mean is consistently lower than the corresponding laminar one. Furthermore, in the turbulent cases, the probability of finding negative values of the edge flame displacement speed has been found to be non-zero. This probability is larger than the one of finding positive values for the cases failing to reach a self-sustained flame propagation without the energy deposition assistance. This becomes more probable as the turbulence intensity and CO dilution increase. This is reflected in the diminished burning extent, quantified in terms of burned gas volume, with increasing turbulence intensity and CO dilution.

Direct Numerical Simulation of Head-On Quenching of Statistically Planar Turbulent Premixed Methane-Air Flames Using a Detailed Chemical Mechanism

A three-dimensional compressible Direct Numerical Simulation (DNS) analysis has been carried out for head-on quenching of a statistically planar stoichiometric methane-air flame by an isothermal inert wall. A multi-step chemical mechanism for methane-air combustion is used for the purpose of detailed chemistry DNS. For head-on quenching of stoichiometric methane-air flames, the mass fractions of major reactant species such as methane and oxygen tend to vanish at the wall during flame quenching. The absence of text {OH} at the wall gives rise to accumulation of carbon monoxide during flame quenching because text {CO} cannot be oxidised anymore. Furthermore, it has been found that low-temperature reactions give rise to accumulation of text {HO}_{2} and mathrm {H}_{2}mathrm {O}_{2} at the wall during flame quenching. Moreover, these low temperature reactions are responsible for non-zero heat release rate at the wall during flame-wall interaction. In order to perform an in-depth comparison between simple and detailed chemistry DNS results, a corresponding simulation has been carried out for the same turbulence parameters for a representative single-step Arrhenius type irreversible chemical mechanism. In the corresponding simple chemistry simulation, heat release rate vanishes once the flame reaches a threshold distance from the wall. The distributions of reaction progress variable c and non-dimensional temperature T are found to be identical to each other away from the wall for the simple chemistry simulation but this equality does not hold during head-on quenching. The inequality between c (defined based on text {CH}_{4} mass fraction) and T holds both away from and close to the wall for the detailed chemistry simulation but it becomes particularly prominent in the near-wall region. The temporal evolutions of wall heat flux and wall Peclet number (i.e. normalised wall-normal distance of T = 0.9 isosurface) for both simple and detailed chemistry laminar and turbulent cases have been found to be qualitatively similar. However, small differences have been observed in the numerical values of the maximum normalised wall heat flux magnitude left ({Phi }_{max } right )_{mathrm {L}} and the minimum Peclet number (Pe_{min })_{mathrm {L}} obtained from simple and detailed chemistry based laminar head-on quenching calculations. Detailed explanations have been provided for the observed differences in behaviours of left ({Phi }_{max }right )_{mathrm {L}} and (Pe_{min })_{mathrm {L}}. The usual Flame Surface Density (FSD) and scalar dissipation rate (SDR) based reaction rate closures do not adequately predict the mean reaction rate of reaction progress variable in the near-wall region for both simple and detailed chemistry simulations. It has been found that recently proposed FSD and SDR based reaction rate closures based on a-priori DNS analysis of simple chemistry data perform satisfactorily also for the detailed chemistry case both away from and close to the wall without any adjustment to the model parameters.

Computation of the bluff-body sound generation by a self-consistent mean flow formulation

The sound generated by the flow around a circular cylinder is numerically investigated by using a finite-element method. In particular, we study the acoustic emissions generated by the flow past the bluff body at low Mach and Reynolds numbers. We perform a global stability analysis by using the compressible linearized Navier-Stokes equations. The resulting direct global mode provides detailed information related to the underlying hydrodynamic instability and data on the acoustic field generated. In order to recover the intensity of the produced sound, we apply the self-consistent model for non-linear saturation proposed by Mantič-Lugo, Arratia, and Gallaire [“Self-consistent mean flow description of the nonlinear saturation of the vortex shedding in the cylinder wake,” Phys. Rev. Lett. 113, 084501 (2014)]. The application of this model allows us to compute the amplitude of the resulting linear mode and the effects of saturation on the mode structure and acoustic field. Our results show excellent agreement with those obtained by a full compressible simulation direct numerical simulation and those derived by the application of classical acoustic analogy formulations.

Shock-induced energy transfers in dense gases

Dense gases are characterised by molecules featuring large numbers of active degrees of freedom (quantified by the cv/R ratio). The isentropes in such gases have the distinct property of following rather closely the isotherms (the two become identical in the limit of cv/R going to infinity). Near the liquid-vapour critical point, this makes the isentropes very shallow and possibly concave (in the pressure-specific volume diagram). Whilst shallow isentropes are desirable when designing expanders (i.e. a large specific-volume increase may be achieved for virtually no pressure drop), could such extreme compressibility effects modify turbulence in a profound manner? This paper discusses two particularly interesting aspects: (i) shock-refraction properties (i.e. the way a shock can redistribute the energy of incoming perturbations), (ii) enstrophy production in homogeneous turbulence. A linear interaction analysis (LIA) is conducted on the shock configuration for which the incoming perturbation is decomposed into linear modes of the compressible Euler equations. The transmission coefficients relative to each eigen modes are solved analytically and results are compared against fully non-linear compressible direct numerical simulation reproducing the weak perturbation of an isolated two-dimensional compression shock wave. The linear analysis is found to be capable of predicting the shock-induced redistribution of the energy of the incoming perturbation between the different eigen modes. Non-ideal gas effects are observed both analytically and numerically with especially an unusual selective response for some particular choice of incoming Mach number. A two-dimensional isotropic turbulence configuration is then numerically investigated for the case of an inviscid compressible dense-gas flow close to the liquid-vapour critical point. Strong non-ideal-gas effects on enstrophy production are observed with the formation of eddy shocklets. In both cases non-convex isentropes close to the liquid-vapour critical point are extremely influential in letting both the shock and the turbulence redistribute any supply of turbulence kinetic energy in ways which are simply not observable in ideal gases. This will hopefully spark enthusiasm amongst turbulence modellers (and their end users?).

Effects of Mixture Distribution on Localized Forced Ignition of Stratified Mixtures: A Direct Numerical Simulation Study

ABSTRACTThe influences of initial mixture distribution on localized forced ignition of globally stoichiometric stratified mixtures have been analyzed using three-dimensional compressible direct numerical simulations. The globally stoichiometric mixtures (i.e., ) for different root-mean-square (rms) values of equivalence ratio (i.e., = 0.2, 0.4, and 0.6) and the Taylor micro-scale of equivalence ratio variation (i.e., 2.1, 5.5, and 8.3 with being the Zel’dovich flame thickness of stoichiometric mixture) have been analyzed for different initial rms values of turbulent velocity . The equivalence ratio variation is initialized following both Gaussian and bi-modal distributions for a given set of values of and in order to analyze the effects of mixture distribution. The localized forced ignition is accounted for by considering a source term in the energy conservation equation that deposits energy for a stipulated time interval. It has been demonstrated that the initial equivalence ratio distribution has significant effects on the extent of burning of stratified mixtures following successful localized forced ignition. It has been found that an increase in ) has adverse effects on the burned gas mass, whereas the effects of on the extent of burning are non-monotonic and dependent on for initial bi-modal mixture distribution. The initial Gaussian mixture distribution exhibits an increase in burned gas mass with decreasing , but these cases are more prone to flame extinction for high values of than the corresponding bi-modal distribution cases. Detailed physical explanations have been provided for the observed mixture distribution, , , and dependences on the extent of burning following localized forced ignition of stratified mixtures.

Effects of fuel Lewis number on localised forced ignition of turbulent homogeneous mixtures: A numerical investigation

The influences of fuel Lewis number LeF (ranging from 0.8 to 1.2) on localised forced ignition and early stages of combustion of stoichiometric and fuel-lean homogeneous mixtures have been analysed using simple chemistry three-dimensional compressible direct numerical simulations for different values of root-mean-square velocity fluctuation and the energy deposition characteristics (i.e. characteristic width and the duration of energy deposition by the ignitor). The localised forced ignition is modelled using a source term in the energy transport equation, which deposits energy in a Gaussian manner from the centre of the ignitor over a stipulated period of time. The fuel Lewis number LeF has been found to have significant influences on the extent of burning of stoichiometric and fuel-lean homogeneous mixtures. It has been shown that the width of ignition energy deposition and the duration over which the ignition energy is deposited have significant influences on the success of ignition and subsequent flame propagation. An increase in the width of ignition energy deposition and the duration of energy deposition for a given amount of ignition energy have been found to have detrimental effects on the ignition event, which may ultimately lead to misfire. For a given value of [Formula: see text] ( LeF), the rate of heat transfer from the hot gas kernel increases with increasing LeF[Formula: see text], which in turn leads to a reduction in the extent of overall burning for both stoichiometric and fuel-lean homogeneous mixtures but the detrimental effects of high values of [Formula: see text] on localised forced ignition are particularly prevalent for fuel-lean mixtures. Detailed physical explanations have been provided for the observed [Formula: see text] and energy deposition characteristics effects.

Numerical investigation of two-phase flame structures in a simplified coal jet flame

The coal flame structures are investigated based on a three-dimensional compressible point-source direct numerical simulation (DNS) of a turbulent simplified coal jet flame. The coal particles are treated as point sources and tracked in the Lagrangian frame considering the interphase transfers. A comprehensive coal combustion model, including the evaporation, devolatilization and char combustion, is applied. The reaction mechanism of CH4 is adopted for gas combustion. In this paper, the general flame features and particle distributions are investigated and three typical flame structures of coal jet flames, namely interspersed flame, stripe flame and stable continuous flame, are identified. By analyzing the temporal evolution of the flame structures, the stable flame formation process is obtained intuitively. It is also found that these three typical flame zones have similar gaseous reaction and the non-premixed flame dominates. The strong reaction is more likely to appear at the locations with small vorticity and high scalar dissipation rate. Compared with purely gaseous flames, the scalar dissipation rate is not only related to turbulent micro-mixing between the fuel and oxidizer flows but also the devolatilization process. By testing the heat release rate proportion of the three zones, it is found that the contribution of interspersed flame is less. The stripe flame contributes about 26% and is important to the whole stable flame formation.

Climate disturbance in the eastern Democratic Republic of Congo

The coal flame structures are investigated based on a three-dimensional compressible point-source direct numerical simulation (DNS) of a turbulent simplified coal jet flame. The coal particles are treated as point sources and tracked in the Lagrangian frame considering the interphase transfers. A comprehensive coal combustion model, including the evaporation, devolatilization and char combustion, is applied. The reaction mechanism of CH4 is adopted for gas combustion. In this paper, the general flame features and particle distributions are investigated and three typical flame structures of coal jet flames, namely interspersed flame, stripe flame and stable continuous flame, are identified. By analyzing the temporal evolution of the flame structures, the stable flame formation process is obtained intuitively. It is also found that these three typical flame zones have similar gaseous reaction and the non-premixed flame dominates. The strong reaction is more likely to appear at the locations with small vorticity and high scalar dissipation rate. Compared with purely gaseous flames, the scalar dissipation rate is not only related to turbulent micro-mixing between the fuel and oxidizer flows but also the devolatilization process. By testing the heat release rate proportion of the three zones, it is found that the contribution of interspersed flame is less. The stripe flame contributes about 26% and is important to the whole stable flame formation.

Effects of Fuel Lewis Number on Localised Forced Ignition of Globally Stoichiometric Stratified Mixtures: a Numerical Investigation

The influences of fuel Lewis number L e F on localised forced ignition of globally stoichiometric stratified mixtures have been analysed using three-dimensional compressible Direct Numerical Simulations (DNS) for cases with L e F ranging from 0.8 to 1.2. The globally stoichiometric stratified mixtures with different values of root-mean-square (rms) equivalence ratio fluctuation (i.e. ϕ ′= 0.2, 0.4 and 0.6) and the Taylor micro-scale l ϕ of equivalence ratio ϕ variation (i.e. l ϕ /l f = 2.1, 5.5 and 8.3 with l f being the Zel’dovich flame thickness of the stoichiometric laminar premixed flame) have been considered for different initial rms values of turbulent velocity u ′. A pseudo-spectral method is used to initialise the equivalence ratio variation following a presumed bi-modal distribution for prescribed values of ϕ ′ and l ϕ /l f for global mean equivalence ratio 〈ϕ〉=1.0. The localised ignition is accounted for by a source term in the energy transport equation that deposits energy for a stipulated time interval. It has been observed that the maximum values of temperature and the fuel reaction rate magnitude increase with decreasing L e F during the period of external energy deposition. The initial values of L e F , u ′/S b(ϕ=1), ϕ ′ and l ϕ /l f have been found to have significant effects on the extent of burning of the stratified mixtures following localised ignition. For a given value of u ′/S b(ϕ=1), the extent of burning decreases with increasing L e F . An increase in u ′ leads to a monotonic reduction in the burned gas mass for all values of L e F in all stratified mixture cases but an opposite trend is observed for the L e F =0.8 homogeneous mixture. It has been found that an increase in ϕ ′ has adverse effects on the burned gas mass, whereas the effects of l ϕ /l f on the extent of burning are non-monotonic and dependent on ϕ ′ and L e F . Detailed physical explanations have been provided for the observed L e F , u ′/S b(ϕ=1), ϕ ′ and l ϕ /l f dependences.

Compressible direct numerical simulation with a hybrid boundary condition of transitional phenomena in natural convection

We investigate the phenomena involved in the transition from laminar to turbulent flow in natural convection through a channel using compressible direct numerical simulation (DNS). The Roe numerical scheme with preconditioning and dual time stepping is employed to handle slow natural convection flows with large temperature differences and variable densities. A hybrid boundary condition that combines absorbing and non-reflecting boundary conditions is applied at the inlet and outlet, which does not require a priori knowledge of the flow rate. No empirically derived turbulence parameters are required in the DNS code. The numerical predictions are qualitatively consistent with published experimental data and the transition point can be accurately captured. Our results show that the transitional phenomena can be naturally induced by the interactions between the buoyancy force and shear stress without prescribing any fluctuations at the inlet. We submit that the numerical scheme and model configuration developed in this study has the potential to be a benchmark case for evaluating the accuracy of other turbulence models.

Effects of Energy Deposition Characteristics on Localised Forced Ignition of Homogeneous Mixtures

The effects of the characteristic width of the energy deposition profile and the duration of energy deposition by the ignitor on localised forced ignition of stoichiometric and fuel-lean homogeneous mixtures have been analysed using simplified chemistry three-dimensional compressible Direct Numerical Simulation (DNS) for different values of root-mean-square turbulent velocity fluctuation. The localised forced ignition is modelled using a source term in the energy transport equation, which deposits energy in a Gaussian manner from the centre of the ignitor over a stipulated period of time. It has been shown that the width of ignition energy deposition and the duration over which ignition energy is deposited have significant influences on the success of ignition and subsequent flame propagation. An increase in the width of ignition energy deposition (duration of energy deposition) for a given amount of ignition energy has been found to have a detrimental effect on the ignition event, which may ultimately lead to misfire. Moreover, an increase in u′ gives rise to augmented heat transfer rate from the hot gas kernel, which in turn leads to a reduction in the extent of overall burning for both stoichiometric and fuel-lean homogeneous mixtures but the detrimental effects of high values of u′ on localised ignition are particularly prevalent for fuel-lean mixtures.

Wavepackets in Boundary Layers Close to Transonic Speeds

In practical situations, natural transition determines the transition to turbulence process. Experimental evidence suggest that the wave packet evolution is related closely to natural transition. The major part of numerical works on wave packets are focused on incompressible, supersonic and hypersonoc flows, subsonic ones are probably the less researched. A compressible DNS code was developed, several code validation tests were performed, including a simulation of an experiment of wave packets 1. The evolution of wave packets on compressible boundary layer in a flat plate is studied by Direct Numerical Simulations (DNS), to investigate the effect of Mach number in the initial nonlinear stages. For Mach 0.9 were considered three cases: linear, nonlinear and interaction between two packets. Results suggest that subharmonic mechanism is the most probable scenario at the initial nonlinear stages.

Compressible Direct Numerical Simulation of Low-Pressure Turbines—Part I: Methodology

Modern low pressure turbines (LPT) feature high pressure ratios and moderate Mach and Reynolds numbers, increasing the possibility of laminar boundary-layer separation on the blades. Upstream disturbances including background turbulence and incoming wakes have a profound effect on the behavior of separation bubbles and the type/location of laminar-turbulent transition and therefore need to be considered in LPT design. Unsteady Reynolds-averaged Navier–Stokes (URANS) are often found inadequate to resolve the complex wake dynamics and impact of these environmental parameters on the boundary layers and may not drive the design to the best aerodynamic efficiency. LES can partly improve the accuracy, but has difficulties in predicting boundary layer transition and capturing the delay of laminar separation with varying inlet turbulence levels. Direct numerical simulation (DNS) is able to overcome these limitations but has to date been considered too computationally expensive. Here, a novel compressible DNS code is presented and validated, promising to make DNS practical for LPT studies. Also, the sensitivity of wake loss coefficient with respect to freestream turbulence levels below 1% is discussed.

On velocity and reactive scalar spectra in turbulent premixed flames

AbstractKinetic energy and reactive scalar spectra in turbulent premixed flames are studied from compressible three-dimensional direct numerical simulations (DNS) of a temporally evolving rectangular slot-jet premixed flame, a statistically one-dimensional configuration. The flames correspond to a lean premixed hydrogen–air mixture at an equivalence ratio of 0.7, preheated to 700 K and at 1 atm, and three DNS are considered with a fixed jet Reynolds number of 10 000 and a jet Damköhler number varying between 0.13 and 0.54. For the study of spectra, motivated by the need to account for density change, which can be locally strong in premixed flames, a new density-weighted definition for two-point velocity/scalar correlations is proposed. The density-weighted two-point correlation tensor retains the essential properties of its constant-density (incompressible) counterpart and recovers the density-weighted Reynolds stress tensor in the limit of zero separation. The density weighting also allows the derivation of balance equations for velocity and scalar spectrum functions in the wavenumber space that illuminate physics unique to combusting flows. Pressure–dilatation correlation is a source of kinetic energy at high wavenumbers and, analogously, reaction rate–scalar fluctuation correlation is a high-wavenumber source of scalar energy. These results are verified by the spectra constructed from the DNS data. The kinetic energy spectra show a distinct inertial range with a $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}-5/3$ scaling followed by a ‘diffusive–reactive’ range at higher wavenumbers. The exponential drop-off in this range shows a distinct inflection in the vicinity of the wavenumber corresponding to a laminar flame thickness, $\delta _L$, and this is attributed to the contribution from the pressure–dilatation term in the energy balance in wavenumber space. Likewise, a clear spike in spectra of major reactant species (hydrogen) arising from the reaction-rate term is observed at wavenumbers close to $\delta _L$. It appears that in the inertial range classical scaling laws for the spectra involving the Kolmogorov scale are applicable, but in the high-wavenumber range where chemical reactions have a strong signature the laminar flame thickness produces a better collapse. It is suggested that a full scaling should perhaps involve the Kolmogorov scale, laminar flame thickness, Damköhler number and Karlovitz number.

Feasibility investigation of compressible direct numerical simulation with a preconditioning method at extremely low Mach numbers

Compressible direct numerical simulation (DNS) with a preconditioning method is conducted for the turbulent channel flow of at an extremely low Mach number of 0.005. The turbulence statistics are in excellent agreement with incompressible DNS results, which indicates that the preconditioning method is able to accurately simulate the turbulence at an extremely low Mach number under the condition of sufficient resolution without any subgrid scale model or special treatment of numerical dissipation. In addition, the effects of the computational time step are investigated. It is shown that when the time step is shorter than 0.32 wall units, accurate results can be obtained and the total computational time is independent of the length of the time step. This study thus validates the feasibility of the compressible DNS with a preconditioning method for an extremely low Mach number and provides useful guidelines for simulating turbulence.

A Direct Numerical Simulation-Based Analysis of Entropy Generation in Turbulent Premixed Flames

A compressible single step chemistry Direct Numerical Simulation (DNS) database of freely propagating premixed flames has been used to analyze different entropy generation mechanisms. The entropy generation due to viscous dissipation within the flames remains negligible in comparison to the other mechanisms of entropy generation. It has been found that the entropy generation increases significantly due to turbulence and the relative magnitudes of the augmentation of entropy generation and burning rates under turbulent conditions ultimately determine the value of turbulent second law efficiency in comparison to the corresponding laminar values. It has been found that the entropy generation mechanisms due to chemical reaction, thermal conduction and mass diffusion in turbulent flames strengthen with decreasing global Lewis number in comparison to the corresponding values in laminar flames. The ratio of second law efficiency under turbulent conditions to its corresponding laminar value has been found to decrease with increasing global Lewis number. An increase in heat release parameter significantly augments the entropy generation due to thermal conduction, whereas other mechanisms of entropy generation are marginally affected. However, the effects of augmented entropy generation due to thermal conduction at high values of heat release parameter are eclipsed by the increased change in availability due to chemical reaction, which leads to an increase in the second law efficiency with increasing heat release parameter for identical flow conditions. The combustion regime does not have any major influence on the augmentation of entropy generation due to chemical reaction, thermal conduction and mass diffusion in turbulent flames in comparison to corresponding laminar flames, whereas the extent of augmentation of entropy generation due to viscous dissipation in turbulent conditions in comparison to corresponding laminar flames, is more significant in the thin reaction zones regime than in the corrugated flamelets regime. However, the ratio of second law efficiency under turbulent conditions to its corresponding laminar value does not get significantly affected by the regime of combustion, as viscous dissipation plays a marginal role in the overall entropy generation in premixed flames.

Direct Numerical Simulation of Pulverized Coal Combustion in a Hot Vitiated Co-flow

A compressible direct numerical simulation (DNS) solver for pulverized coal combustion has been developed and used to study a pulverized coal jet flame with a Reynolds number of 28 284 based on the nozzle diameter. An eighth-order center differential scheme combined with an explicit tenth-order filter is used for spatial discretization. The classical fourth-order Runge–Kutta method is used for time integration. The characteristic non-reflecting boundary conditions are used to describe the boundary conditions. A comprehensive model for coal combustion is applied, and the reaction mechanism of CH4 with five species and two-step reactions is adopted for gas-phase combustion. The grid system has been carefully designed to make sure that turbulent scales and chemical reaction scales are reasonably resolved and the point-source assumptions of particles are valid. The simulation is partially validated against the experiment, and the particle behavior is investigated. It is found that, in the upstream region, the reaction rate is quite scattered and a single particle is found inside the burning flame to form an individual particle combustion mode. While in the downstream region, the reaction zone is more continuous, with a large number of particles enclosed, which characterizes the group combustion mode. Conditional statistics with respect to the mixture fraction are also obtained to provide insights into coal combustion and the related models.

Determination of three-dimensional quantities related to scalar dissipation rate and its transport from two-dimensional measurements: Direct Numerical Simulation based validation

Three-dimensional compressible Direct Numerical Simulation (DNS) data of freely propagating statistically planar and statistically stationary slot-jet turbulent premixed flames has been used to assess the accuracy of the isotropy-derived correction factors, which relate the two-dimensional projections of the different terms of the Favre-averaged scalar dissipation rate transport equation with their corresponding actual three-dimensional counterparts. The accuracy of these correction factors is assessed using both simplified and detailed chemistry-based DNS data, for a range of values of Karlovitz number Ka, heat release parameter τ, and turbulent Reynolds number Ret. It is shown that the isotropic distribution of the probability density function (pdf) of the angle, ϕ, between the normal vectors of the measurement plane and of the flame surface provides a simple algebraic relation between the scalar dissipation rates evaluated in two and three dimensions (i.e. N∼c and N∼c2D), independent of the considered values of Ka, τ and Ret. The isotropic relations between two-dimensional and three-dimensional counterparts of the curvature and propagation terms in the transport equation of N∼c are also found to work well for all the values of Ka, τ and Ret considered here. However, the relation between the value obtained from two-dimensional projection and the true three-dimensional value for the strain rate term in the N∼c transport equation works well only for large values of Ret and the reasons for this behaviour are explained in detail. It is found that the threshold value of Ret above which the assumption of isotropy yields an accurate relation between two-dimensional projection and three-dimensional values for the strain rate term of the dissipation rate transport equation depends on the regime of the prevailing combustion process.

Determination of 3D flame surface density variables from 2D measurements: Validation using direct numerical simulation

Three-dimensional compressible direct numerical simulation (DNS) data of freely propagating statistically planar turbulent premixed flames have been used to assess the accuracy of the isotropy- derived correction factors, which relate the two-dimensional projections of the different terms of the Reynolds averaged flame-surface density (FSD) transport equation with their corresponding actual three-dimensional counterparts for different values of Karlovitz number Ka, Lewis number Le, heat release parameter τ, and turbulent Reynolds number Ret. It is shown that the isotropic distribution of the surface area weighted probability density function (pdf) of the angle φ between the normal vectors on the measurement plane and on the flame surface provides a simple algebraic relation between the generalised FSDs evaluated in two and three dimensions (i.e., Σ2D and Σ3D), irrespective of the values of Ka,τ,Le, and Ret. Isotropic relations between two-dimensional and three-dimensional counterparts of the surface-averaged curvature and the FSD propagation term are also found to work well for all the values of Ka,τ,Le, and Ret considered in this study. However, the relations between the value obtained from two-dimensional projection and the actual three-dimensional value for the tangential strain rate and curvature terms in the FSD transport equation work well only for the high values of turbulent Reynolds number. The reasons behind the disagreement between the predictions of the relations derived based on isotropy arguments for both the tangential strain rate and curvature terms of the FSD transport equation are explained in detail. It is found that the threshold value of Ret above which the assumption of isotropy yields an accurate relation between two-dimensional projection and three-dimensional values for the tangential strain rate and curvature terms of the FSD transport equation depends on the values of heat release parameter, Lewis number, and the regime of the prevailing combustion process.