Subgrid Variance Research Articles

Theoretical derivation and a priori validation of a new scalar variance-based sub-grid drag force model for simulation of gas–solid fluidized beds

A novel sub-grid drag force model is proposed for coarse-grid Euler–Euler simulation of gas–solid fluidized beds. Starting from a transport equation for the drift velocity, an equilibrium condition is used as a basis to derive a new algebraic drift velocity model. The sub-grid correlations that show up are closed by a large-eddy PDF approach inspired from LES of turbulent reacting flows. The new analytical model only depends on the resolved slip velocity and on a few sub-grid moments of the solid volume fraction. Then, a conditional averaging procedure shows that the new model can be properly captured by a simple functional expression that only requires a closure for the sub-grid variance of the solid volume fraction. A priori validation studies show that the drift velocity is predicted with high accuracy (R2>0.90) for a large range of filter widths and for both Geldart A and Geldart B particles.

Effect of orographic gravity wave drag on Northern Hemisphere climate in transient simulations of the last deglaciation

Long transient simulations of the last deglaciation are increasingly being performed to identify the drivers of multiple rapid Earth system changes that occurred in this period. Such simulations frequently prescribe temporal variations in ice sheet properties, which can play an important role in controlling atmospheric and surface climate. To preserve a model’s standard performance in simulating climate, it is common to apply time dependent orographic variations, including parameterised sub-grid scale orographic variances, as anomalies from the pre-industrial state. This study investigates the causes of two abrupt climate change events in the Northern Hemisphere extratropics occurring between 16 and 14 thousand years ago in transient simulations of the last deglaciation from the Hadley Centre coupled general circulation model (HadCM3). One event is characterized by regional Northern Hemisphere changes comprising a centennial scale cooling of ~ 10 °C across Fennoscandia followed by rapid warming in less than 50 years as well as synchronous shifts in the Northern Annular Mode. The second event has comparable but temporally reversed characteristics. Sensitivity experiments reveal the climate anomalies are exclusively caused by artificially large values of orographic gravity wave drag, resulting from the combined use of the orographic anomaly method along with a unique inclusion of transient orography that linearly interpolates between timesteps in the ice sheet reconstruction. Palaeoclimate modelling groups should therefore carefully check the effects of their sub-grid scale orographic terms in transient palaeoclimate simulations with prescribed topographic evolution.

A Parameterization of Turbulent Dissipation and Pressure Damping Time Scales in Stably Stratified Inversions, and its Effects on Low Clouds in Global Simulations

AbstractIt is difficult for coarse‐resolution global models of the atmosphere to accurately simulate the observed distribution of low clouds. In particular, it is difficult for moist turbulence closure models to simulate sufficiently bright near‐coastal stratocumulus (Sc) without simulating overly bright marine shallow cumuli (Cu). To parameterize bright Sc, a turbulence parameterization must damp the turbulent fluxes of heat and moisture above cloud top in order to prevent excessive entrainment of dry air into cloud top. To parameterize dim shallow Cu, the subgrid variances of temperature and moisture must remain large, in order to permit partial cloudiness. However, damping the fluxes but not the variances just above cloud top is difficult if a parameterization uses a single “master” time scale to damp both. In nature, the above‐cloud fluxes are damped by pressure fluctuations, whereas scalar variances are damped by a different process, namely, turbulent dissipation. In a stably stratified inversion above cloud, pressure damping is large but turbulent dissipation is small. To avoid this problem, a multitime scale parameterization for damping has been developed. The damping parameterization has been implemented in a global model and evaluated. The parameterization is capable of dimming shallow Cu while producing adequately bright Sc.

A Bimodal Diagnostic Cloud Fraction Parameterization. Part II: Evaluation and Resolution Sensitivity

AbstractA wide range of approaches exists to account for subgrid cloud variability in regional simulations of the atmosphere. This paper addresses the following questions: 1) Is there still benefit in representing subgrid variability of cloud in convection-permitting simulations? 2) What is the sensitivity to the cloud fraction parameterization complexity? 3) Are current cloud fraction parameterizations scale-aware across convection-permitting resolutions? These questions are addressed for regional simulations of a 6-week observation campaign in the U.S. southern Great Plains. Particular attention is given to a new diagnostic cloud fraction scheme with a bimodal subgrid saturation-departure PDF, described in Part I. The model evaluation is performed using ground-based remote sensing synergies, satellite-based retrievals, and surface observations. It is shown that not using a cloud fraction parameterization results in underestimated cloud frequency and water content, even for stratocumulus. The use of a cloud fraction parameterization does not guarantee improved cloud property simulations, however. Diagnostic and prognostic cloud schemes with a symmetric subgrid saturation-departure PDF underestimate cloud fraction and cloud optical thickness, and hence overestimate surface shortwave radiation. These schemes require empirical bias-correction techniques to improve the cloud cover. The new cloud fraction parameterization, introduced in Part I, improves cloud cover, liquid water content, cloud-base height, optical thickness, and surface radiation compared to schemes reliant on a symmetric PDF. Furthermore, cloud parameterizations using turbulence-based, rather than prescribed constant subgrid variances, are shown to be more scale-aware across convection-permitting resolutions.

Analysis of the Closures of Sub-grid Scale Variance of Reaction Progress Variable for Turbulent Bunsen Burner Flames at Different Pressure Levels

The statistical behaviour and modelling of the sub-grid variance of reaction progress variable have been analysed based on a priori analysis of direct numerical simulation (DNS) data of turbulent premixed Bunsen burner flames at different pressure levels. An algebraic expression for sub-grid variance, which can be derived based on a presumed bi-modal sub-grid distribution of reaction progress variable with impulses at unburned reactants and fully burned products, has been found to be inadequate for the purpose of prediction of sub-grid variance even for the flames in the wrinkled flamelets/corrugated flamelets regime. Moreover, an algebraic model, which is often used for modelling sub-grid variance of passive scalars, has been found to significantly overpredict the sub-grid variance of reaction progress variable for all the cases considered here. The modelling of the unclosed terms of the sub-grid variance transport equation has been analysed in detail. Suitable model expressions have been identified for the sub-grid flux of variance, reaction rate contribution and scalar dissipation rate based on a priori analysis of DNS data. It has been found that the alternation of pressure does not have any significant impact on the closures of sub-grid flux of variance but a model parameter for the Favre-filtered scalar dissipation rate needs to be modified to account for the variation of pressure.

Meso‐scale contribution to air–sea turbulent fluxes at GCM scale

AbstractParametrizations of sea surface turbulent fluxes used in general circulation models (GCMs) assume horizontal homogeneity of atmospheric properties at the grid‐cell scale. The present study assesses the contribution of the meso‐scale (i.e., subgrid) to the grid‐scale surface fluxes, for GCM resolution ranging from 20 to 200 km, and thus quantifies the associated GCM surface flux error. A coarse‐graining method allows for an a priori analysis of the subgrid information. It is based on an atmospheric reference dataset produced by the convection‐permitting operational model AROME. The meso‐scale relative contribution to GCM‐scale fluxes exceeding 10% is shown to have large regional patterns, with large values (up to 90%) and high frequency of occurrence (up to 76% of the time). These meso‐scale motions are not necessarily due to convective activity but also occur frequently under dynamical perturbation conditions. Contributions to surface fluxes, at both the GCM scale and the meso‐scale, are disentangled through a Reynolds decomposition. It is found that temperature and humidity meso‐scale heterogeneities do not contribute much to the GCM‐scale fluxes. The subgrid dynamical processes are the main meso‐scale contribution and consist of two parts. The first one represents the wind magnitude and wind direction heterogeneities and corresponds to the so‐called gustiness approach. It is clarified that the contribution of the gustiness wind in the transfer coefficients cannot be neglected. The second part is the contribution of the wind speed subgrid variance, which contributes up to 10% of the GCM‐scale momentum flux.

Sub-grid Reaction Progress Variable Variance Closure in Turbulent Premixed Flames

The statistical behaviour and modelling of the sub-grid variance of reaction progress variable have been analysed based on a priori analysis of Direct Numerical Simulation (DNS) data of freely propagating statistically planar turbulent premixed flames with different turbulence intensities. It has been found that an algebraic expression, which can be derived based on a presumed bi-modal sub-grid distribution of reaction progress variable with impulses at unburned reactants and fully burned products, is inadequate for the purpose of prediction of sub-grid variance. An algebraic model, which is often used for modelling sub-grid variance of passive scalars, has been found to significantly overpredict the sub-grid variance of reaction progress variable for the cases considered here. The statistical behaviours of the terms of the sub-grid variance have been analysed in detail and explained based on scaling arguments. It has been found that reaction rate and molecular dissipation contributions play leading order roles in the transport of sub-grid reaction progress variable variance and they remain in approximate equilibrium for large filter widths. Suitable model expressions have been identified for the sub-grid flux of variance, reaction rate contribution and scalar dissipation rate based on a priori analysis of DNS data.

A priori analysis of sub-grid variance of a reactive scalar using DNS data of high Ka flames

Direct numerical simulations (DNS) of low and high Karlovitz number (Ka) flames are analysed to investigate the behaviour of the reactive scalar sub-grid scale (SGS) variance in premixed combustion under a wide range of combustion conditions (regimes). An order of magnitude analysis is performed to assess the importance of various terms in the variance evolution equation and the analysis is validated using the DNS results. This analysis sheds light on the relative behaviour among turbulent transport and production, scalar dissipation and chemical processes involved in the evolution of the SGS variance at different Ka. The common expectation is that the variance equation shifts from a reaction-dissipation balance at low Ka to a production–dissipation balance at high Ka with diminishing reaction contribution. However, in large eddy simulation (LES), a high Ka alone does not make the reaction term negligible, as the relative importance of the reaction term has a concurrent increase with filter size. The filter size can be relatively large compared with the Kolmogorov length scale in practical LES of high Ka flames, and as a consequence a reaction–production–dissipation balance may prevail in the variance equation even in a high Ka configuration, and this possibility is quantified using the DNS analysis in this work. This has implications from modelling perspectives, and therefore two commonly used closures in LES for the SGS scalar dissipation rate are investigated a priori to estimate the importance of the above balance in LES modelling. The results are explained to highlight the interplay among turbulence, chemistry and dissipation processes as a function of Ka.

Evaluation of autoconversion and accretion enhancement factors in general circulation model warm-rain parameterizations using ground-based measurements over the Azores

Abstract. A great challenge in climate modeling is how to parameterize subgrid cloud processes, such as autoconversion and accretion in warm-rain formation. In this study, we use ground-based observations and retrievals over the Azores to investigate the so-called enhancement factors, Eauto and Eaccr, which are often used in climate models to account for the influence of subgrid variance of cloud and precipitation water on the autoconversion and accretion processes. Eauto and Eaccr are computed for different equivalent model grid sizes. The calculated Eauto values increase from 1.96 (30 km) to 3.2 (180 km), and the calculated Eaccr values increase from 1.53 (30 km) to 1.76 (180 km). Comparing the prescribed enhancement factors in Morrison and Gettleman (2008, MG08) to the observed ones, we found that a higher Eauto (3.2) at small grids and lower Eaccr (1.07) are used in MG08, which might explain why most of the general circulation models (GCMs) produce too-frequent precipitation events but with too-light precipitation intensity. The ratios of the rain to cloud water mixing ratio (qr/qc) at Eaccr=1.07 and Eaccr=2.0 are 0.063 and 0.142, respectively, from observations, further suggesting that the prescribed value of Eaccr=1.07 used in MG08 is too small to simulate precipitation intensity correctly. Both Eauto and Eaccr increase when the boundary layer becomes less stable, and the values are larger in precipitating clouds (CLWP>75 gm−2) than those in non-precipitating clouds (CLWP<75 gm−2). Therefore, the selection of Eauto and Eaccr values in GCMs should be regime- and resolution-dependent.

Large eddy simulation of turbulent stratified combustion using dynamic thickened flame coupled with tabulated detailed chemistry

• A SGS model of DTF coupled with FGM is developed for investigating stratified flame. • LES transport equation for covariance in the DTF-FGM model is deduced. • An in-depth analysis for the flame structures of Cambridge stratified flames is achieved. A sub-grid scale (SGS) combustion model of the dynamic thickened flame (DTF) coupled with flamelet generated manifolds (FGM) approach (i.e. DTF-FGM) is developed to investigate Cambridge stratified flames. Two issues in developing the DTF-FGM model are addressed. Firstly, the copula method is extended to construct a multivariate joint probability density function (PDF) of the tabulated scalars. A modified laminar flamelet PDF is incorporated to describe the probable asymmetric multimodal distribution for the reaction progress variable. Secondly, large eddy simulation (LES) transport equations for the tabulated scalars, relevant sub-grid variances and covariance in the DTF-FGM model are deduced. LES of Cambridge stratified flames is performed with the DTF-FGM model and the widely used SGS combustion model which combines a presumed PDF with FGM (i.e. PPDF-FGM). Detailed comparisons between simulations and experiments are carried out to evaluate the SGS combustion models and mesh resolution effects. Meanwhile, an in-depth analysis for the flame structures of Cambridge stratified flames is also achieved. The results indicate that the developed SGS combustion model considering the effect of correlations between the mixture fraction and reaction progress variable has the ability to solve the stratified flame structures under LES mesh resolution exactly at a reasonable computational cost.

Characterization of Subgrid-Scale Variability in Particulate Matter with Respect to Satellite Aerosol Observations

Recent use of satellite observations of aerosol optical depth (AOD) to characterize surface concentrations of particulate matter (PM) air pollution has proven extremely valuable in estimating exposures for health effects studies. While the spatial resolutions of satellite data provide far better coverage than existing fixed site surface monitoring stations, they are not able to capture atmospheric processes such as dilution of primary pollutants that vary at small spatial scales. As a result, small-scale variability due to highly localized sources such as traffic may be poorly represented, which in turn may lead to exposure measurement error in epidemiological analyses. Using a fixed spatial grid representing 4.4 km Multiangle Imaging SpectroRadiometer (MISR) aerosol observations, we examined the spatial variability in fine and coarse mode PM (PM2.5 and PM2.5–10 respectively) measured at ground monitors from a unique spatially-dense sampling campaign in Southern California. We found that while the variance in measured PM2.5 differed seasonally (warm 6.82 μg2/m6 and cool 24.5 μg2/m6) across the study region, the average subgrid (<4.4 km) variance did not (warm 2.03 μg2/m6 and cool 2.43 μg2/m6) and was significantly smaller. On the other hand, ground monitor PM2.5–10 concentrations showed large variance in warm (18.6 μg2/m6) and cool (20.6 μg2/m6) seasons, as well as seasonal differences in subgrid variance (warm 8.90 μg2/m6 and cool 3.28 μg2/m6). Geostatistical analysis of the semivariance as a function of distance indicated that variability in measured PM2.5 and PM2.5–10 concentrations was relatively constant for spatial scales of one to five kilometers, but there was evidence of small-scale (~500 m) variability in PM2.5–10 concentrations in the cool season. The lack of small-scale spatial variability in the warm season was likely due to large photochemical contributions to regional PM2.5, and greater regional contributions to PM2.5–10 from windblown dust. In contrast, in the cool season there tends to be greater localized concentrations from primary traffic sources due to stronger nocturnal inversions and delayed morning winds reducing dilution that contribute to greater spatial heterogeneity. Overall, these results suggest that regional contributions tend to dominate PM2.5, and spatial resolutions of satellite observations including the 4.4 km MISR and 3 km MODIS aerosol products aptly capture relevant spatial variability. Coarse PM2.5–10 can have seasonally dependent localized contributions, leading to small-scale variability below current satellite aerosol product resolutions.

Evaluation and Improvement of Turbulence Parameterization inside Deep Convective Clouds at Kilometer-Scale Resolution

A challenge for cloud-resolving models is to make subgrid schemes suitable for deep convective clouds. A benchmark large-eddy simulation (LES) was conducted on a deep convective cloud with 50-m grid spacing. The reference turbulence fields for horizontal grid spacings of 500 m, 1 km, and 2 km were deduced by coarse graining the 50-m LES outputs, allowing subgrid fields to be characterized. The highest values of reference subgrid turbulent kinetic energy (TKE) were localized in the updraft core, and the production of subgrid TKE was dominated by thermal effects at coarser resolution (2 and 1 km) and by dynamical effects at finer resolution than 500 m. Countergradient areas due to nonlocal mixing appeared on the subgrid vertical thermodynamical fluxes in the updraft core and near the cloud top. The subgrid dynamical variances were anisotropic but the difference between vertical and horizontal variances diminished with increasing resolution. Then offline and online evaluations were conducted for this deep convective case with two different parameterization approaches at kilometer-scale resolution and gave the same results. A commonly used eddy-diffusivity turbulence scheme underestimated the thermal production of subgrid TKE and did not enable the countergradient structures to be reproduced. In contrast, the approach proposed by Moeng, parameterizing the subgrid vertical thermodynamical fluxes in terms of horizontal gradients of resolved variables, reproduced these characteristics and limited the overestimation of vertical velocity.

Large eddy simulation of turbulent lifted flame in a hot vitiated coflow using tabulated detailed chemistry

Large eddy simulation (LES) of Cabra flame is carried out by a sub-grid scale (SGS) model of tabulated detailed chemistry combined with presumed probability density function (PDF). The chemistry table is constructed by utilizing the coupling of auto-ignition model and premixed flame propagation model. The copula method is applied to build multivariate joint PDF of mixture fraction and reaction progress variable. LES transport equations for characteristic scalars, relevant sub-grid variances and covariance are deduced. The LES results show that the developed SGS model can give an accurate prediction for lift-off height and flame structures. The stabilization mechanism and combustion regime of Cabra flame are discussed.

A global data set of soil hydraulic properties and sub-grid variability of soil water retention and hydraulic conductivity curves

Abstract. Agroecosystem models, regional and global climate models, and numerical weather prediction models require adequate parameterization of soil hydraulic properties. These properties are fundamental for describing and predicting water and energy exchange processes at the transition zone between solid earth and atmosphere, and regulate evapotranspiration, infiltration and runoff generation. Hydraulic parameters describing the soil water retention (WRC) and hydraulic conductivity (HCC) curves are typically derived from soil texture via pedotransfer functions (PTFs). Resampling of those parameters for specific model grids is typically performed by different aggregation approaches such a spatial averaging and the use of dominant textural properties or soil classes. These aggregation approaches introduce uncertainty, bias and parameter inconsistencies throughout spatial scales due to nonlinear relationships between hydraulic parameters and soil texture. Therefore, we present a method to scale hydraulic parameters to individual model grids and provide a global data set that overcomes the mentioned problems. The approach is based on Miller–Miller scaling in the relaxed form by Warrick, that fits the parameters of the WRC through all sub-grid WRCs to provide an effective parameterization for the grid cell at model resolution; at the same time it preserves the information of sub-grid variability of the water retention curve by deriving local scaling parameters. Based on the Mualem–van Genuchten approach we also derive the unsaturated hydraulic conductivity from the water retention functions, thereby assuming that the local parameters are also valid for this function. In addition, via the Warrick scaling parameter λ, information on global sub-grid scaling variance is given that enables modellers to improve dynamical downscaling of (regional) climate models or to perturb hydraulic parameters for model ensemble output generation. The present analysis is based on the ROSETTA PTF of Schaap et al. (2001) applied to the SoilGrids1km data set of Hengl et al. (2014). The example data set is provided at a global resolution of 0.25° at https://doi.org/10.1594/PANGAEA.870605.

Modeling and experimental validation of subgrid scale scalar variance at high Schmidt numbers

This paper is focused on the subgrid closure model for fluctuations of the passive scalar concentration in liquids at different Schmidt numbers. The simulations and experiments were carried out in two impinging jet reactors of a different scale. Distributions of concentration variance, predicted with the use of the literature subgrid scale models, were compared with experimental data obtained by a planar laser induced fluorescence technique. The results of large eddy simulation supplemented with the two subgrid-scale variance models are in very good agreement with experiments. Since the scale similarity LES model described in the literature requires a priori defined value of a model coefficient, further results of the dynamic model are presented in this work.

Large Eddy Simulation of Turbulent Premixed Swirling Flames Using Dynamic Thickened Flame with Tabulated Detailed Chemistry

A sub-grid scale (SGS) combustion model by combining dynamic thickened flame (DTF) with flamelet generated manifolds (FGM) tabulation approach (i.e. DTF-FGM) is developed for investigating turbulent premixed combustion. In contrast to the thickened flame model, the dynamic thickening factor of the DTF model is determined from the flame sensor, which is obtained from the normalized gradient of the reaction progress variable from the one-dimensional freely propagating premixed flame simulations. Therewith the DTF model can ensure that the thickening of the flame is limited to the regions where it is numerically necessary. To describe the thermo-chemistry states, large eddy simulation (LES) transport equations for two characteristic scalars (the mixture fraction and the reaction progress variable) and relevant sub-grid variances in the DTF-FGM model are presented. As to the evaluation of different SGS combustion models, another model by utilizing the combination of presumed probability density function (PPDF) and FGM (i.e. PPDF-FGM) is also described. LES of two cases with or without swirl in premixed regime of the Cambridge swirl burner flames are performed to evaluate the developed SGS combustion model. The predicted results are compared with the experimental data in terms of the influence of different LES grids, model sensitivities to the thickening factor, the wrinkling factor, and the PPDF of characteristic scalars, the evaluation of different modelling approaches for the sub-grid variances of characteristic scalars, and the predictive capability of different SGS combustion models. It is shown that the LES results with the DTF-FGM model are in reasonable agreement with the experimental data, and better than the results with the PPDF-FGM approach due to its ability to predict better in regions where flame is not resolved.

Detailed chemistry LES/CMC simulation of a swirling ethanol spray flame approaching blow-off

A swirling ethanol spray flame in conditions close to blow-off has been simulated using Large Eddy Simulation (LES) and the Conditional Moment Closure (CMC) combustion model aiming to further validate the capability of the LES/CMC approach to capture local extinctions in turbulent spray flames. A detailed chemical mechanism was used and a transport equation of the mixture fraction sub-grid variance, with spray interaction terms included, was solved. Numerical results are in good agreement with the experiment in terms of both instantaneous and mean flame shape and droplet velocity and size. Local extinctions were detected in the region around the bluff-body, resulting in a fluctuating lift-off of the flame there, and the probability density function of the lift-off height was in very good agreement with the experiment, suggesting that the degree of local extinction is captured quantitatively. Analysis of the CMC equation suggested that local extinction was influenced by both transport in physical space and high scalar dissipation rate. The modelling of the latter needs development in areas where the spray evaporation is strong enough to increase significantly the sub-grid mixture fraction fluctuations and their small-scale gradients, possibly leading to deviations from the present usual approach of relating the sub-grid scalar dissipation to the sub-grid mixture fraction variance.

Application of unstrained flamelet SGS closure for multi-regime premixed combustion

Large eddy simulation of turbulent premixed combustion behind a bluff-body is performed using unstrained flamelet model with a presumed probability density function to calculate filtered reaction rate. The subgrid variance of the progress variable required in this approach is calculated using its transport equation to include contributions from reaction, turbulence and molecular diffusive and dissipative processes at sub-grid scales. The dissipation rate of the variance is obtained using an algebraic closure, which maintains physical consistency among turbulence, reaction and molecular diffusion. Various quantities such as mean velocity, temperature and species mass fractions computed for two bluff-body flames experiencing 2% and 24% turbulence intensities are compared to their respective measurements. These comparisons are very good suggesting that the unstrained flamelet SGS closure works well for multi-regime combustion. The demonstrated success of this modelling framework is explained on a physical basis.

A priori analysis of subgrid scale pressure and heat flux in high pressure mixing and reacting shear layers

Direct Numerical Simulation (DNS) data on high pressure H2/O2 and H2/air flames using the compressible flow formulation, detailed kinetics, a real fluid equation of state, and generalised diffusion are analysed. The DNS is filtered over a range of filter widths to provide exact terms in the Large Eddy Simulation (LES) governing equations, including unclosed terms. The filtered pressure and the filtered heat flux vector are extensively compared with the pressure and the heat flux vector calculated as a function of the filtered primitive variables (i.e. the exact LES term is compared with its form available within an actual LES). The difference between these forms defines the subgrid pressure and the subgrid heat flux vector. The analyses are done both globally across the entire flame, as well as by conditionally averaging over specific regions of the flame; including regions of large subgrid kinetic energy, subgrid scalar dissipation, subgrid temperature variance, flame temperature, etc. In this work, although negligible for purely mixing cases, the gradient of the subgrid pressure is shown to be of the same order as, and larger than, the corresponding divergence of the turbulent subgrid stresses for reacting cases. This is despite the fact that all species behave essentially as ideal gases for this flame and holds true even when the ideal gas law is used to calculate the pressure. The ratio of the subgrid pressure gradient to the subgrid stress tensor divergence is shown to increase with increasing Reynolds number. Both the subgrid heat flux vector and its divergence are found to be substantially larger in reacting flows in comparison with mixing due to the associated larger temperature gradients. However, the divergence of the subgrid heat flux vector tends to be significantly smaller than other unclosed terms in the energy equation with decreasing significance with increasing Reynolds number.

A comparative study of presumed PDFs for premixed turbulent combustion modeling based on progress variable and its variance

Premixed turbulent combustion simulations often use flamelets (1-D laminar flame solutions) and presumed probability density functions (PDF) for modeling turbulence chemistry interaction. The flamelets can also be spatially filtered at multiple length scales to directly tabulate a PDF integrated manifold. Similar to the presumed PDF approach using β-function, the turbulent chemistry is tabulated using two controlling variables: progress variable and its subgrid variance. The performance of manifolds constructed from a premixed flamelet using: β-PDF, spatial filtering at multiple length scales and spatial filtering only at grid scale are compared a priori and a posteriori. Computation of the progress variable subgrid variance is investigated using static as well as dynamic algebraic mixing models. A Direct Numerical Simulation (DNS) database of a turbulent Bunsen flame is used for a priori and a posteriori investigation of the PDFs and the algebraic models. It is observed that algebraic models lead to correct predictions at filter widths smaller than the laminar flame thickness while deviations occur at larger filter widths. A posteriori the manifolds exhibit similar performance on account of the deviation in subgrid variance prediction from the algebraic models. However, the multi filtered flamelet model clearly exhibits a superior a priori performance and needs to be investigated further.