Conditional Scalar Dissipation Rate Research Articles

Flame structure and broadening in turbulent premixed jet flames

High-resolution and high signal-to-noise (SNR) planar Rayleigh scattering thermometry measurements are performed to investigate preheat and reaction zone broadening, turbulent transport of high-temperature gases, and the internal flame structure in a series of highly turbulent, lean (ϕ = 0.75), premixed methane-air turbulent jet flames. These flames are characterized by turbulence intensities ranging from u′/SL of 35 to 150 and turbulent Reynolds numbers approaching 104, as determined from separate particle image velocimetry (PIV) measurements. Average flame profiles obtained using a gradient-based flame reconstruction method and probability density functions (PDFs) of the preheat, reaction, and thermal layer thicknesses show substantial broadening of the preheat and thermal layers. Instantaneous preheat zones are broadened by as much as a factor of 30 compared to laminar flames, with an average broadening approaching a factor of 14 for the most turbulent case. Moderate broadening of the reaction layer is observed with up to a factor of eight times that of a laminar premixed flame for instantaneous realizations and an average broadening of four times that of a laminar flame for the most turbulent case. Conditional statistics of temperature obtained at isodistance contours within and upstream of the preheat zone show large shifts towards significantly higher temperatures compared to laminar flame values. In addition, broad temperature distributions and reduced thermal gradients at each position provide strong evidence of persistent turbulent transport of high-temperature gases ahead of the preheat zone. Finally, a detailed analysis of scalar dissipation rate statistics and dissipation layer topology was conducted. The conditional mean scalar dissipation rates for the turbulent flames show significant reductions compared to calculated laminar flame values and a shift towards higher values of the reaction progress variable (CT) for increasing turbulence levels. PDFs show a transition from near-Gaussian to highly negatively skewed with increasing turbulence levels, where the most probable values of the scalar dissipation rate shift towards higher values of CT, indicating that the primary reaction zone and flame front are subjected to increased strain. In terms of structure, no significant broadening of the small-scale dissipation layers was observed with increasing turbulence intensity. However, as turbulence intensity increases, there is a transition from a sparse number of continuous layers to a large number of shorter, ”broken”, nearly straight segments. The reduction of individual layer lengths (i.e., ”breaking”) is favored over increases in dissipation layer wrinkling, where the sharp decreases in the local dissipation rate values are highly correlated with regions of high curvature. A final notable outcome of this work is that there were negligible differences in all statistical and topological results when moving between the two highest turbulent cases, even though the turbulence intensity, turbulent Reynolds number, and the turbulence Karlovitz number increased substantially (70 - 120%). This implies that there may be an asymptotic limit in which turbulence affects flame behavior for the current configuration.

Local Equilibrium and Discretization Effects on the Prediction of Scalar Dissipation Rates in Large Eddy Simulation of Turbulent Non-Premixed Combustion

ABSTRACT The effects of discretization and local equilibrium on the prediction of scalar dissipation rates are investigated by performing large-eddy simulation (LES) of a turbulent-piloted jet diffusion flame, Sandia Flame D. As a way to reduce the discretization errors on the prediction of scalar dissipation, an approach to use a higher-order finite difference scheme only for the evaluation of scalar gradients in a scalar dissipation model, while keeping the overall accuracy of the numerical method at second order, is investigated. Results indicate that the fourth-order scheme improves the accuracy with negligible addition to computational cost. With the improved evaluation of scalar gradients, the local equilibrium assumption, which is used in the algebraic model, is investigated by solving the subgrid-scale variance transport equation, where a model coefficient in a scaling-based relaxation model for subgrid-scale scalar dissipation is varied. It is found that the conditional mean scalar dissipation rates are insensitive to the model coefficient. This insensitivity is attributed to the prevalence of local equilibrium. A rapid decay of imbalance between production and dissipation of subgrid-scale scalar fluctuations is seen in both the predicted scalar dissipation and the transport budget in the variance equation. It is argued that since, at high Reynolds numbers, the transport of the scalar fluctuations occurs over a timescale larger than the subgrid-scale mixing timescale, its contribution to the evolution of subgrid-scale variance is statistically insignificant except near the nozzle exit where different streams begin to mix and scalar layers evolve rapidly. Consequently, the conditional (and unconditional) mean scalar dissipation rates in LES tend to depend solely on the production of subgrid-scale scalar fluctuations in most regions of turbulent jet flames, when the modeling is based on the Kolmogorov scaling.

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

Large eddy simulations with three-dimensional finite-volume Conditional Moment Closure (CMC) model are performed for a hydrogen/nitrogen lifted flame with detailed chemical mechanism. The emphasis is laid on the influences of mesh resolution and convection scheme of finite-volume CMC equations on predictions of reactive scalars and unsteady flame dynamics. The results show that the lift-off height is underestimated and the reactive scalars are over-predicted with coarser CMC mesh. It is also found that further refinement of the CMC mesh would not considerably improve the results. The time sequences of the most reactive and stoichiometric hydroxyl radical mass fractions indicate that finer CMC mesh can capture more unsteady details than the coarser CMC mesh. Moreover, the coarse CMC mesh has lower conditional scalar dissipation rate, which would promote the earlier auto-ignition of the flame base. Besides, the effects of the convection scheme for the CMC equations (i.e., upwind, central differencing and their blends) on the lifted flame characteristics are also investigated. It is shown that different convection schemes lead to limited differences on the time-averaged temperature, mixture fraction and species mass fractions. Moreover, the root-mean square values of hydrogen and hydroxyl mass fractions show larger deviation from the measurements with hybrid upwind and central differencing scheme, especially around the flame base. Furthermore, the distributions of the numerical fluxes on the CMC faces also show obvious distinctions between the upwind and blending schemes. The budget analysis of the individual CMC terms shows that a sequence of CMC faces has comparable contributions with upwind scheme. However, with the hybrid schemes, the instantaneous flux is dominantly from limited CMC faces. The reactivity of a CMC cell is more easily to be affected by its neighbors when the upwind scheme is used.

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

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

Modelling of Conditional Scalar Dissipation Rate in Turbulent Premixed Combustion

In turbulent premixed flames, for the mixing at a molecular level of reactants and products on the flame surface, it is crucial to sustain the combustion. This mixing phenomenon is featured by the scalar dissipation rate, which may be broadly defined as the rate of micro-mixing at small scales. This term, which appears in many turbulent combustion methods, includes the Conditional Moment Closure (CMC) and the Probability Density Function (PDF), requires an accurate model. In this study, a mathematical closure for the conditional mean scalar dissipation rate, <Nc|ζ>, in Reynolds, Averaged Navier–Stokes (RANS) context is proposed and tested against two different Direct Numerical Simulation (DNS) databases having different thermochemical and turbulence conditions. These databases consist of lean turbulent premixed V-flames of the CH4-air mixture and stoichiometric turbulent premixed flames of H2-air. The mathematical model has successfully predicted the peak and the typical profile of <Nc|ζ> with the sample space ζ and its prediction was consistent with an earlier study.

Modeling of sub-grid conditional mixing statistics in turbulent sprays using machine learning methods

Deep artificial neural networks (ANNs) are used for modeling sub-grid scale mixing quantities such as the filtered density function (FDF) of the mixture fraction and the conditional scalar dissipation rate. A deep ANN with four hidden layers is trained with carrier-phase direct numerical simulations (CP-DNS) of turbulent spray combustion. A priori validation corroborates that ANN predictions of the mixture fraction FDF and the conditional scalar dissipation rate are in very good agreement with CP-DNS data. ANN modeled solutions show much better performance with a mean error of around 1%, which is one order of magnitude smaller than that of standard modeling approaches such as the β-FDF and its modified version. The predicted conditional scalar dissipation rate agrees very well with CP-DNS data over the entire mixture fraction space, whereas conventional models derived for pure gas phase combustion fail to describe ⟨N|ξ = η⟩ in regions with higher mixture fraction and low probability. In the second part of this paper, uncertainties associated with ANN predictions are analyzed. It is shown that a suitable selection of training sets can reduce the size of the necessary test database by ∼50% without compromising the accuracy. Feature importance analysis is used to analyze the importance of different combustion model parameters. While the droplet evaporating rate, the droplet number density, and the mixture fraction remain the dominant features, the influence of turbulence related parameters only becomes important if turbulence levels are sufficiently high.

Effect of the conditional scalar dissipation rate in the conditional moment closure

In the context of modeling turbulent scalar mixing using probability density function (PDF) methods, the treatment of molecular mixing is of paramount importance. The conditional moment closure (CMC) offers a high-fidelity description for molecular mixing in nonpremixed flows. Recent work has demonstrated that first-order CMC can be implemented numerically using the moments of the conditioning variable and first-order joint moments of the scalar of interest. When solving the CMC using, for example, quadrature-based moment methods (QBMM), a functional form must be chosen for the conditional scalar dissipation rate (CSDR) of the conditioning variable. In prior work, the CSDR was chosen to produce a β-PDF for the conditioning variable (mixture fraction) at steady state. This choice has the advantage that the system of moment equations used in QBMM-CMC can be written in closed form. In this work, an alternative choice for the CSDR is investigated, namely, the amplitude mapping closure (AMC). With the AMC, the moment equations can be closed using the quadrature method of moments incorporated into a realizable ordinary differential equation solver. Results are compared with the β-CSDR closure for binary, passive scalar mixing in homogeneous single- and disperse-phase turbulent flows. It is also demonstrated that the moment formulation of CMC provides a straightforward method for modeling the effect of differential diffusion in the context of CMC.

Systematic study of the impact of chemistry and radiation on extinction and carbon monoxide formation at low scalar dissipation rates

In fire flames scalar dissipation rates in the reaction zone are low and radiation becomes important for extinction. The chemistry mechanism also strongly affects extinction and CO formation. The present study applies the unsteady laminar flamelet approach (or, equivalently, the conditional moment closure (CMC) method in mixture fraction domain, without transport in physical space). Six chemistry mechanisms are analyzed. In addition to adiabatic conditions, three radiation models are considered: RADCAL-based gray gas; weighted sum of gray gases (WSGG); and prescribed radiative fraction model. The oxygen mass fraction values for extinction are discussed, diluting the oxidizer by adding nitrogen. Carbon monoxide profiles are reported as well. The radiative fraction model is not capable of predicting the strong radiative effects at low scalar dissipation rates, while the RADCAL-based and the WSGG model are able to do so. The analysis of extinction and CO reveals strong sensitivity to the mesh in mixture fraction space, as well as to the shape of the conditional scalar dissipation rate profile. Results with the ARM2 mechanism and GRI3 are in very close agreement, so that significant time savings are possible, using ARM2.

Conditional scalar dissipation rate modeling for turbulent spray flames using artificial neural networks

Machine learning techniques have been used for the closure of the conditional scalar dissipation rate in turbulent spray flames. Statistical data are extracted from carrier-phase direct numerical simulation (CP-DNS) results for the generation of artificial neural networks that are trained to predict the conditional scalar dissipation rate such that they could serve as a sub-grid model for large eddy simulations of spray combustion. A quantitative error assessment suggests that predictions of the conditionally averaged dissipation rate are in excellent agreement with CP-DNS data. Further comparison with commonly used models for the unconditionally filtered dissipation rate promises significant improvements if ANNs are used for closure. The artificial neural networks also help to identify the important features that affect the local dissipation rates. The results suggest that few - mostly droplet related - parameters suffice as input features for accurate ANNs. This is in contradiction to standard modeling techniques that are solely based on gas phase properties and highlights the need to revisit scalar dissipation rate modeling for spray flames if analytical expressions are to be used.

Large eddy simulations of the UMD line burner with the conditional moment closure method

The conditional moment closure (CMC) method is applied in combination with large eddy simulations (LES-CMC) to the UMD line burner configuration. This corresponds to a low-strain, buoyant diffusion flame. The low strain rate conditions are representative of fire conditions and the aim of the study is to evaluate LES-CMC results, including radiative effects. Only conditions far from extinction are studied. The weighted sum of grey gases model (WSGGM) for radiation is applied in mixture fraction space. Results are compared to what is obtained when radiation is taken into account as a local loss term in the conditional heat release rate, with prescribed radiative fraction. It is shown that the conditional scalar dissipation rate (CSDR) profile in mixture fraction space and the spatial terms in the transport equations for the conditional quantities have a major impact with the non-local WSGGM approach, while this is not the case in adiabatic simulations, nor in the radiative fraction approach. In the latter, only the value of the CSDR at stoichiometric is important, making this approach less sensitive. However, the latter are not well suited for extinction simulations.

라그랑지안 조건평균방법을 이용한 난류비예혼합 연소의 LES 해석

Lagrangian conditional moment closure(CMC) is applied to large eddy simulation(LES) to analyze turbulent piloted nonpremixed flame(Sandia flame D). It is assumed that the sequentially injected fuel groups share the conditional flame statistics. Coupling between turbulence and chemistry is considered in modeling of the conditional scalar dissipation rate(SDR) which is composed of resolved and subgrid scale modeled terms. Since no additional grid system is required for Lagrangian CMC, LES study is possible without large computation burden. The LES-Lagrangian CMC predicts the major scalar variables(temperature, mixture fraction, and mass fractions of CO, OH, H₂) consistent with measurements both in physical and mixture fraction spaces.

A LES-CMC formulation for premixed flames including differential diffusion

A finite volume large eddy simulation–conditional moment closure (LES-CMC) numerical framework for premixed combustion developed in a previous studyhas been extended to account for differential diffusion. The non-unity Lewis number CMC transport equation has an additional convective term in sample space proportional to the conditional diffusion of the progress variable, that in turn accounts for diffusion normal to the flame front and curvature-induced effects. Planar laminar simulations are first performed using a spatially homogeneous non-unity Lewis number CMC formulation and validated against physical-space fully resolved reference solutions. The same CMC formulation is subsequently used to numerically investigate the effects of curvature for laminar flames having different effective Lewis numbers: a lean methane–air flame with Leeff = 0.99 and a lean hydrogen–air flame with Leeff = 0.33. Results suggest that curvature does not affect the conditional heat release if the effective Lewis number tends to unity, so that curvature-induced transport may be neglected. Finally, the effect of turbulence on the flame structure is qualitatively analysed using LES-CMC simulations with and without differential diffusion for a turbulent premixed bluff body methane–air flame exhibiting local extinction behaviour. Overall, both the unity and the non-unity computations predict the characteristic M-shaped flame observed experimentally, although some minor differences are identified. The findings suggest that for the high Karlovitz number (from 1 to 10) flame considered, turbulent mixing within the flame weakens the differential transport contribution by reducing the conditional scalar dissipation rate and accordingly the conditional diffusion of the progress variable.

Flame thickness and conditional scalar dissipation rate in a premixed temporal turbulent reacting jet

The flame structure corresponding to lean hydrogen–air premixed flames in intense sheared turbulence in the thin reaction zone regime is quantified from flame thickness and conditional scalar dissipation rate statistics, obtained from recent direct numerical simulation data of premixed temporally-evolving turbulent slot jet flames [1]. It is found that, on average, these sheared turbulent flames are thinner than their corresponding planar laminar flames. Extensive analysis is performed to identify the reason for this counter-intuitive thinning effect. The factors controlling the flame thickness are analyzed through two different routes i.e., the kinematic route, and the transport and chemical kinetics route. The kinematic route is examined by comparing the statistics of the normal strain rate due to fluid motion with the statistics of the normal strain rate due to varying flame displacement speed or self-propagation. It is found that while the fluid normal straining is positive and tends to separate iso-scalar surfaces, the dominating normal strain rate due to self-propagation is negative and tends to bring the iso-scalar surfaces closer resulting in overall thinning of the flame. The transport and chemical kinetics route is examined by studying the non-unity Lewis number effect on the premixed flames. The effects from the kinematic route are found to couple with the transport and chemical kinetics route. In addition, the intermittency of the conditional scalar dissipation rate is also examined. It is found to exhibit a unique non-monotonicity of the exponent of the stretched exponential function, conventionally used to describe probability density function tails of such variables. The non-monotonicity is attributed to the detailed chemical structure of hydrogen-air flames in which heat release occurs close to the unburnt reactants at near free-stream temperatures.

Application of the Fokker-Planck molecular mixing model to turbulent scalar mixing using moment methods

An extended quadrature method of moments using the β kernel density function (β-EQMOM) is used to approximate solutions to the evolution equation for univariate and bivariate composition probability distribution functions (PDFs) of a passive scalar for binary and ternary mixing. The key element of interest is the molecular mixing term, which is described using the Fokker–Planck (FP) molecular mixing model. The direct numerical simulations (DNSs) of Eswaran and Pope [“Direct numerical simulations of the turbulent mixing of a passive scalar,” Phys. Fluids 31, 506 (1988)] and the amplitude mapping closure (AMC) of Pope [“Mapping closures for turbulent mixing and reaction,” Theor. Comput. Fluid Dyn. 2, 255 (1991)] are taken as reference solutions to establish the accuracy of the FP model in the case of binary mixing. The DNSs of Juneja and Pope [“A DNS study of turbulent mixing of two passive scalars,” Phys. Fluids 8, 2161 (1996)] are used to validate the results obtained for ternary mixing. Simulations are performed with both the conditional scalar dissipation rate (CSDR) proposed by Fox [Computational Methods for Turbulent Reacting Flows (Cambridge University Press, 2003)] and the CSDR from AMC, with the scalar dissipation rate provided as input and obtained from the DNS. Using scalar moments up to fourth order, the ability of the FP model to capture the evolution of the shape of the PDF, important in turbulent mixing problems, is demonstrated. Compared to the widely used assumed β-PDF model [S. S. Girimaji, “Assumed β-pdf model for turbulent mixing: Validation and extension to multiple scalar mixing,” Combust. Sci. Technol. 78, 177 (1991)], the β-EQMOM solution to the FP model more accurately describes the initial mixing process with a relatively small increase in computational cost.

Scalar dissipation rate statistics in turbulent swirling jets

The scalar dissipation rate statistics were measured in an isothermal flow formed by discharging a central jet in an annular stream of swirling air flow. This is a typical geometry used in swirl-stabilised burners, where the central jet is the fuel. The flow Reynolds number was 29 000, based on the area-averaged velocity of 8.46 m/s at the exit and the diameter of 50.8 mm. The scalar dissipation rate and its statistics were computed from two-dimensional imaging of the mixture fraction fields obtained with planar laser induced fluorescence of acetone. Three swirl numbers, S, of 0.3, 0.58, and 1.07 of the annular swirling stream were considered. The influence of the swirl number on scalar mixing, unconditional, and conditional scalar dissipation rate statistics were quantified. A procedure, based on a Wiener filter approach, was used to de-noise the raw mixture fraction images. The filtering errors on the scalar dissipation rate measurements were up to 15%, depending on downstream positions from the burner exit. The maximum of instantaneous scalar dissipation rate was found to be up to 35 s−1, while the mean dissipation rate was 10 times smaller. The probability density functions of the logarithm of the scalar dissipation rate fluctuations were found to be slightly negatively skewed at low swirl numbers and almost symmetrical when the swirl number increased. The assumption of statistical independence between the scalar and its dissipation rate was valid for higher swirl numbers at locations with low scalar fluctuations and less valid for low swirl numbers. The deviations from the assumption of statistical independence were quantified. The conditional mean of the scalar dissipation rate, the standard deviation of the scalar dissipation rate fluctuations, the weighted probability of occurrence of the mean conditional scalar dissipation rate, and the conditional probability are reported.

One-Dimensional Modeling of Turbulent Premixed Jet Flames - Comparison to DNS

The one-dimensional turbulence (ODT) model, formulated in an Eulerian reference frame, is applied to a temporally-evolving premixed turbulent hydrogen plane-jet flame and results are compared with direct numerical simulation (DNS) data. This is the first published study to perform direct comparisons of ODT to DNS for premixed flames. The ODT model solves the full set of conservation equations for mass, momentum, energy, and species on a one-dimensional domain corresponding to the transverse jet direction. The effects of turbulent mixing are modeled via a stochastic process, while the full range of diffusive-reactive length and time scales are resolved directly on the one-dimensional domain. A detailed chemical mechanism for hydrogen combustion consisting of 9 species and 21 reactions and a mixture-averaged transport model are used (consistent with the DNS). Cases with two different Damkohler numbers are considered and comparisons between the ODT and DNS data are shown with respect to flow dynamics and thermochemistry. The ODT compared favorably with the DNS in terms of the overall entrainment as judged by the streamwise velocity profile and in terms of local flamelet structure as judged by progress-variable conditional reaction and scalar dissipation rates. While the ODT agreed qualitatively with the overall flame evolution, the net fuel consumption rate was somewhat over-predicted for a brief early period and under-predicted later on, leading to an overly long flame burnout time. It was demonstrated that adjusting a parameter controlling the selection of large eddies improved the prediction of the peak fuel consumption rate and overall reaction progress but worsened the prediction of jet entrainment. An analysis of the 1D nature of ODT is presented that suggests the FSD in ODT needs to be much higher than the FSD in the DNS in order to achieve the same overall burning rate, suggesting that the FSD is under-predicted by a significant fraction. While the success of the ODT in reproducing many of the salient features of nonpremixed flames has been demonstrated, the current study suggests that improvements are needed when applied to premixed flames. It is also important to note that the DNS required approximately 40×106 CPU hours while the ODT required approximately 103 CPU hours.

Turbulent mixing of passive scalar near turbulent and non-turbulent interface in mixing layers

A direct numerical simulation of a temporally developing mixing layer with a passive scalar transport is performed for various Schmidt numbers (Sc = 0.25, 1, 4, and 8). Turbulent mixing is investigated near the turbulent/non-turbulent interface (TNTI), which is a layer consisting of the turbulent sublayer (TSL) and viscous superlayer (VSL). The irrotational boundary, which is close to the outer edge of the TNTI layer, is detected as the isosurface of small vorticity magnitude. The movement of fluid elements relative to the irrotational boundary movement is analyzed. Once the non-turbulent fluid is entrained into the VSL across the irrotational boundary by the viscous diffusion of vorticity, the fluid moves away from the irrotational boundary in the VSL in the normal direction of the irrotational boundary. After the fluid reaches the TSL, it is transported in the tangential direction of the irrotational boundary and is mixed with the fluid coming from the turbulent core (TC) region. The boundary between the TSL and VSL roughly separates the region (VSL) mostly consisting of the fluid entrained from the non-turbulent flow from the region (TSL) where the fluids from both the TC and non-turbulent regions coexist. Therefore, the scalar value in the VSL is close to the non-turbulent value especially for high Sc cases. Because of a large difference in the scalar between the TSL and VSL, a peak value of the conditional mean scalar dissipation rate appears near the boundary between the TSL and VSL independently of Sc.

Conditional statistics in a planar liquid jet with a second-order chemical reaction

Conditional statistics, conditioned on mixture fraction, are experimentally investigated in a planar liquid jet with a second-order isothermal chemical reaction A+B→R. Reactants A and B are contained in the jet and ambient flows, respectively, and are supplied into the test section under the non-premixed condition. Streamwise velocity, mixture fraction and concentrations of all reactive species are simultaneously measured by using an I-type hot-film probe and an optical fibre probe based on light absorption spectrometry. The cross-streamwise profiles of conditional mean concentrations and conditional mean reaction rate show that the conditional mean concentrations and the conditional mean reaction rate near the jet exit change with the cross-streamwise position, whereas they are independent of the cross-streamwise position in the downstream regions. On the jet centreline, the conditional mean reaction rate has a peak value on the condition that the conditional mean concentration of product R has a peak value. A comparison between the conditional mean reaction rate and the covariance of conditional concentration fluctuations shows that the covariance of conditional concentration fluctuations is so small that a first moment closure model for the conditional mean reaction rate is valid. The conditional mean streamwise velocity is almost linear to the mixture fraction for small mixture fraction fluctuations. The conditional scalar dissipation rate is calculated from the budget of the conditional moment closure equation. The results show that the conditional scalar dissipation rate has a single peak value in the upstream region, whereas in the downstream region, it has two peaks for the large and small mixture fraction values. The conventional mean scalar dissipation rate is calculated from the probability density function of the mixture fraction and the conditional scalar dissipation rate. The conventional mean scalar dissipation rate on the jet centreline decreases in the downstream direction as (x∗)-2.9 (where x∗ is the distance from the virtual origin), which is almost the same as that expected from scaling arguments.

Conditional Moment Closure Modelling of a Lifted H2/N2Turbulent Jet Flame Using the Presumed Mapping Function Approach

A lifted hydrogen/nitrogen turbulent jet flame issuing into a vitiated coflow is investigated using the conditional moment closure (CMC) supplemented by the presumed mapping function (PMF) approach for the modelling of conditional mixing and velocity statistics. Using a prescribed reference field, the PMF approach yields a presumed probability density function (PDF) for the mixture fraction, which is then used in closing the conditional scalar dissipation rate (CSDR) and conditional velocity in a fully consistent manner. These closures are applied to a lifted flame and the findings are compared to previous results obtained usingβ-PDF-based closures over a range of coflow temperatures (Tc). The PMF results are in line with those of theβ-PDF and compare well to measurements. The transport budgets in mixture fraction and physical spaces and the radical history ahead of the stabilisation height indicate that the stabilisation mechanism is susceptible toTc. As in the previousβ-PDF calculations, autoignition around the “most reactive” mixture fraction remains the controlling mechanism for sufficiently highTc. Departure from theβ-PDF predictions is observed whenTcis decreased as PMF predicts stabilisation by means of premixed flame propagation. This conclusion is based on the observation that lean mixtures are heated by downstream burning mixtures in a preheat zone developing ahead of the stabilization height. The spurious sources, which stem from inconsistent CSDR modelling, are further investigated. The findings reveal that their effect is small but nonnegligible, most notably within the flame zone.

Conditional statistics of a laboratory-scale lifted turbulent H2/N2 flame using direct numerical simulation

The direct numerical simulation (DNS) database of a lifted turbulent H2/N2 flame is used to validate models in the framework of conditional moment closure (CMC). The cross-stream dependency of the reactive scalars, the presumed PDF, and the conditional means of the velocity, scalar dissipation rate and turbulent flux are investigated. It is found that in the stabilization region, the conditional mean of YOH varies significantly in the radial direction, indicating CMC grids should be considered in the radial direction. The performances of the β-PDF for both of the mixture fraction and the progress variable are generally satisfactory. However, the PDFs of the DNS results are more complex. The two conditioning variables are proved to be dependent, which makes it more difficult to model the joint PDF. The conditional velocity and scalar dissipation rate are closed with the linear model and AMC model, respectively. The linear model captures the variations of the conditional velocity very well. As for the conditional scalar dissipation rate model, further improvements could be taking into account the skew and bimodal distribution. The gradient diffusion approximation is used for the conditional turbulent flux, the performance of which is found to depend on the estimate of the diffusivity.