Direct Numerical Simulation Analysis Research Articles

Statistical behavior of fuel mass fraction variance transport in turbulent flame–droplet interaction: A direct numerical simulation analysis

ABSTRACTThree-dimensional direct numerical simulations (DNS) data of statistically planar turbulent spray flames propagating into monodisperse droplets for different values of droplet diameter ad and droplet equivalence ratio ϕd have been used to analyze the statistical behavior of the fuel mass fraction variance and its transport in the context of Reynolds-averaged Navier–Stokes (RANS) simulations. The algebraic closure, which was previously derived for high Damköhler number turbulent stratified mixture combustion, has been shown not to capture statistical behavior of for turbulent spray flames, because the underlying assumptions behind the original modeling are invalid for the cases considered in this analysis. The modeling of the unclosed terms of the variance transport equation (i.e., the turbulent transport term T1, the reaction rate contribution T3, the evaporation contribution T4, and the dissipation rate term –D2) has been analyzed in the context of RANS simulations. The models previously proposed in the context of turbulent gaseous stratified flames have been considered here to assess their suitability for turbulent spray flames. Model expressions have been identified for and −D2 which have been shown to perform satisfactorily in all cases considered in the current study. However, the model previously proposed for T3 in the context of turbulent gaseous stratified flames has been found to be inadequate for turbulent spray flames and further consideration of the modeling of this unclosed term is therefore necessary.

Modeling of Lewis number dependence of scalar dissipation rate transport for Large Eddy Simulations of turbulent premixed combustion

ABSTRACTThe influences of differential diffusion of heat and mass on the Favre-filtered scalar dissipation rate (SDR) transport have been analyzed and modeled using a priori analysis of Direct Numerical Simulations (DNS) data of freely propagating statistically planar turbulent premixed flames with different values of global Lewis number, Le. The DNS data has been explicitly filtered using a Gaussian filter to obtain the unclosed terms of the Favre-filtered SDR transport equation, arising from turbulent transport (T1), density variation due to heat release (T2), strain rate contribution due to the alignment of scalar and velocity gradients (T3), correlation between the gradients of reaction rate and reaction progress variable (T4), molecular dissipation of SDR (−D2), and diffusivity gradients f(D). The statistical behaviors of these terms and their scaling estimates reported in a recent analysis have been utilized here to propose models for these unclosed terms in the context of Large Eddy Simulations (LES) and the performances of these models have been assessed using the values obtained from explicitly filtered DNS data. These newly proposed models are found to satisfactorily predict both the qualitative and quantitative behaviors of these unclosed terms for a range of filter widths Δ for all Le cases considered here.

Flow topology and alignments of scalar gradients and vorticity in turbulent spray flames: A Direct Numerical Simulation analysis

Flame structure, flow topology and the relative alignments of principal strain rates with scalar gradients and the vorticity vector in turbulent spray flames arising from mono-disperse droplets have been analysed using three-dimensional Direct Numerical Simulations (DNS) data. An extensive parametric analysis has been performed for a range of values of droplet equivalence ratio (ϕd), droplet diameter (ad) and turbulence intensity (u′). The results have been analysed to analyse the statistical behaviours of the alignments of the gradients of mixture fraction and reaction progress variable and of the vorticity vector (ω→) with the local principal strain rates. The resulting alignments of reactive scalar gradient and vorticity with local principal strain rates in droplet-laden flames have been compared to those observed for a gaseous stoichiometric premixed flame under the same turbulent flow conditions. The differences in behaviour have been identified in terms of the statistical behaviours of scalar gradient and vorticity alignments with local principal strain rates in terms of the eight local flow topologies, classified as either focal (four topologies) or nodal (four topologies), in four zones across the flame: leading edge, preheat zone, burning reactants and trailing edge. This information has in turn been utilised to offer detailed physical explanations for the observed differences in alignment statistics of reactive scalar gradient and vorticity between turbulent premixed and spray flames. The implications of scalar gradient and vorticity alignment on the statistical behaviours of scalar–turbulence interaction and vortex stretching terms have been discussed in detail along with explanations for their dependences on droplet size, droplet equivalence ratio and turbulence intensity.

Design of a single-phase PTS numerical experiment for a reference Direct Numerical Simulation

The integrity assessment of the Reactor Pressure Vessel (RPV) is considered to be an important issue for lifetime extension of nuclear reactors. A severe transient that can threaten the integrity of the RPV is the existence of a Pressurized Thermal Shock (PTS) during a Loss-of-Coolant Accident (LOCA). A PTS consists of a rapid cooling of the RPV wall under pressurized conditions that may induce the criticality of existing or postulated defects inside the vessel wall. The most severe PTS event has been identified by Emergency Core Cooling (ECC) injection during a LOCA. The traditional one-dimensional system codes fail to reliably predict the complex three-dimensional thermal mixing phenomena in the downcomer occurring during the ECC injection. Hence, CFD can bring real benefits in terms of more realistic and more predictive capabilities. However, to gain trust in the application of CFD modelling for PTS, a comprehensive validation programme is necessary. In the absence of detailed experimental data for the RPV cooling during ECC injection, high fidelity Direct Numerical Simulation (DNS) databases constitute a valid alternative and can serve as a reference.The aim of this work is to design a numerical experiment aimed to generate a high quality reference DNS database for a simplified PTS scenario. This takes into account the turbulent mixing in the downcomer and the evolution of the temperature distribution for both structures and fluid during a single-phase flow PTS scenario. In spite of simplifications, such a DNS analysis represents a very demanding application. A priori, it should be demonstrated that all the relevant turbulent scales will be fully resolved, which requires a huge computational power. A wide range of Reynolds Averaged Navier–Stokes (RANS) calculations are performed in order to determine a realistic PTS computational domain. Furthermore, the resulting numerical experiment is optimized in terms of geometry, boundary conditions, and physical properties.

Statistical Behavior of Scalar Dissipation Rate in Head-On Quenching of Turbulent Premixed Flames: A Direct Numerical Simulation Analysis

ABSTRACTThe statistical behavior of the scalar dissipation rate (SDR) and its transport in the context of Reynolds averaged Navier Stokes (RANS) simulations has been analyzed for head-on quenching of turbulent premixed flames using a three-dimensional simplified chemistry based direct numerical simulations (DNS) database. The flame quenching statistics have been analyzed in terms of wall Peclet number (i.e., non-dimensional distance of the flame in the wall normal direction) and non-dimensional wall heat flux magnitude . It has been found that flame wrinkling induces fluctuations of wall heat flux in turbulent cases and the magnitude of the maximum wall heat flux increases with increasing root-mean-square turbulent velocity .The closure of mean reaction rate using the SDR of reaction progress variable in the near wall region has been assessed based on a priori analysis of DNS data. It has been demonstrated that the existing SDR-based reaction rate closure does not work satisfactorily near the wall. A modification to this existing closure has been proposed, which is found to satisfactorily predict the mean reaction rate of reaction progress variable in the near wall region and approaches the existing closure away from the wall. The wall effects on the unclosed terms of the SDR transport equation have been analyzed and the order of magnitude estimates of the leading order contributors to the SDR transport have been utilized to modify an existing algebraic SDR closure to account for the near wall effects. A priori DNS analysis suggests that the proposed modification to the aforementioned SDR closure provides satisfactory prediction both away from and near to the wall.

Breaking axi-symmetry in stenotic flow lowers the critical transition Reynolds number

Flow through a sinuous stenosis with varying degrees of non-axisymmetric shape variations and at Reynolds number ranging from 250 to 750 is investigated using direct numerical simulation (DNS) and global linear stability analysis. At low Reynolds numbers (Re < 390), the flow is always steady and symmetric for an axisymmetric geometry. Two steady state solutions are obtained when the Reynolds number is increased: a symmetric steady state and an eccentric, non-axisymmetric steady state. Either one can be obtained in the DNS depending on the initial condition. A linear global stability analysis around the symmetric and non-axisymmetric steady state reveals that both flows are linearly stable for the same Reynolds number, showing that the first bifurcation from symmetry to antisymmetry is subcritical. When the Reynolds number is increased further, the symmetric state becomes linearly unstable to an eigenmode, which drives the flow towards the non-axisymmetric state. The symmetric state remains steady up to Re = 713, while the non-axisymmetric state displays regimes of periodic oscillations for Re ≥ 417 and intermittency for Re ≳ 525. Further, an offset of the stenosis throat is introduced through the eccentricity parameter E. When eccentricity is increased from zero to only 0.3% of the pipe diameter, the bifurcation Reynolds number decreases by more than 50%, showing that it is highly sensitive to non-axisymmetric shape variations. Based on the resulting bifurcation map and its dependency on E, we resolve the discrepancies between previous experimental and computational studies. We also present excellent agreement between our numerical results and previous experimental results.

Triple-deck and direct numerical simulation analyses of high-speed subsonic flows past a roughness element

This paper is concerned with the boundary-layer separation in subsonic and transonic flows caused by a two-dimensional isolated wall roughness. The process of the separation is analysed by means of two approaches: the direct numerical simulation (DNS) of the flow using the Navier–Stokes equations, and the numerical solution of the triple-deck equations. Since the triple-deck theory relies on the assumption that the Reynolds number ($\mathit{Re}$) is large, we performed the Navier–Stokes calculations at $\mathit{Re}=4\times 10^{5}$ based on the distance of the roughness element from the leading edge of the flat plate. This $\mathit{Re}$ is also relevant for aeronautical applications. Two sets of calculation were conducted with the free-stream Mach number $\mathit{Ma}_{\infty }=0.5$ and $\mathit{Ma}_{\infty }=0.87$. We used different roughness element heights, some of which were large enough to cause a well-developed separation region behind the roughness. We found that the two approaches generally compare well with one another in terms of wall shear stress, longitudinal pressure gradient and detachment/reattachment points of the separation bubbles (when present). The main differences were found in proximity to the centre of the roughness element, where the wall shear stress and longitudinal pressure gradient predicted by the triple-deck theory are noticeably different from those predicted by DNS. In addition, DNS predicts slightly longer separation regions.

Assessment of Reynolds Averaged Navier–Stokes Modeling of Scalar Dissipation Rate Transport in Turbulent Oblique Premixed Flames

The statistical behavior of scalar dissipation rate (SDR) transport of reaction progress variable and its modeling in the context of Reynolds averaged Navier–Stokes (RANS) simulations has been analyzed based on a-priori analysis of direct numerical simulation (DNS) data for a turbulent premixed V-flame configuration. It has been found that the terms in the scalar dissipation rate transport equation originating from density variation due to heat release, chemical reaction rate gradient, molecular dissipation, and diffusivity gradient are the major contributors to the scalar dissipation rate transport for different downstream axial locations from the flame holder. By contrast, the contribution of turbulent transport of scalar dissipation rate assumes negligible values in comparison to the unclosed terms due to density variation, chemical reaction rate gradient, molecular dissipation, and diffusivity gradient. The statistical behaviors of the unclosed terms arising from density variation, chemical reaction rate gradient, and molecular dissipation for V-flame have been found to be qualitatively consistent with previous results for statistically planar flames. The models for the unclosed turbulent transport, density variation, chemical reaction rate gradient, and molecular dissipation terms of the scalar dissipation rate transport equation, which were proposed based on previous a-priori analysis of statistically planar flames, have been found to predict the corresponding terms satisfactorily at different downstream axial locations in the V-flame configuration considered here. The present analysis shows that the unclosed term in the scalar dissipation rate transport equation originating from diffusivity gradient can assume magnitudes comparable to the density variation contribution to the SDR transport equation, and a model has been proposed for the combined contribution of the chemical reaction rate gradient, molecular dissipation, and diffusivity gradient terms, which has been found to satisfactorily predict the corresponding quantity extracted from DNS data at different axial locations.

Numerical investigation of localised forced ignition of pulverised coal particle-laden mixtures: A Direct Numerical Simulation (DNS) analysis

Localised forced ignition of mono-disperse pulverised coal particle-laden mixtures has been analysed based on three-dimensional Direct Numerical Simulations for the carrier phase with simplified chemistry for the combustion of volatile gases. The coal particles are treated as point sources and tracked in a Lagrangian manner. The coupling between Eulerian gaseous and Lagrangian particulate phases has been achieved by appropriate source terms in the mass, momentum, energy and species conservation equations. A detailed parametric analysis has been carried out to analyse the effects of particle equivalence ratio Φp (which is defined based on the total available primary volatile fuel in the particulate phase), root-mean-square of turbulent velocity u′ and particle diameter dp on the early stages of combustion. Both non-premixed and premixed modes of combustion have been observed in the reaction zone for the flames resulting from localised ignition. An increase in Φp is found to be detrimental for sustaining combustion, whereas a reduction in particle size may adversely affect the extent of burning. It has been found that an increase in u′ increases the rate of mixing of devolatilised fuel with the surrounding air, which, though beneficial for sustaining combustion, increases the heat transfer rate from the hot gas kernel, thus leading to flame extinction for high values of u′. Detailed physical explanations have been provided to explain the observed effects of Φp, root-mean-square turbulent velocity fluctuation u′ and particle diameter dp on combustion of coal particle-laden mixtures following successful localised forced ignition.

Assessment of sub-grid scalar flux modelling in premixed flames for Large Eddy Simulations: A-priori Direct Numerical Simulation analysis

The performances of different models for sub-grid scalar flux for premixed turbulent combustion in the context of Large Eddy Simulations (LES) have been assessed based on a Direct Numerical Simulation (DNS) database of freely propagating turbulent premixed flames with a range of different values of Ret where Damköhler and Karlovitz numbers are altered independently of each other to bring about the variation of Ret, whereas the heat release parameter τ is kept unaltered. It has been found that the sub-grid scalar flux exhibits local counter-gradient transport for all cases considered here. However, the extent of counter-gradient transport decreases with decreasing values of filter width Δ and for increasing values of the ratio of the root-mean-square turbulent velocity fluctuation to the unstrained laminar burning velocity u′/SL. The performance of several algebraic models has been assessed with respect to explicitly filtered DNS data. The standard gradient hypothesis based model does not adequately capture both the qualitative and quantitative behaviours of sub-grid scalar flux for all cases for all filter widths. The models which account for local flame normal acceleration perform better than the standard gradient hypothesis model. In general the performance of the models, which account for the alignment of local resolved velocity and scalar gradients, remains relatively better than the performance of the other existing models. Detailed physical explanations have been provided for the observed model performances.

Assessment of the performances of sub-grid scalar flux models for premixed flames with different global Lewis numbers: A Direct Numerical Simulation analysis

The statistical behaviours of sub-grid flux of reaction progress variable has been assessed for premixed turbulent flames with global Lewis number Le (=thermal diffusivity/mass diffusivity) ranging from 0.34 to 1.2 using a Direct Numerical Simulation (DNS) database of freely propagating statistically planar flames. It is known that the sub-grid scalar flux shows counter-gradient transport when the velocity jump across the flame due to heat release overcomes the effects of turbulent velocity fluctuation. The results show that the sub-grid scalar flux components exhibit counter-gradient transport for all cases considered here. The extent of counter-gradient transport increases with increasing filter width Δ and decreasing value of Le. This is due to the fact that flames with Le≪1 (e.g. Le=0.34) exhibit thermo-diffusive instabilities, which in turn increases the extent of counter-gradient transport. The effects of heat release and flame normal acceleration weaken with increasing Le. Several established algebraic models have been assessed in comparison to the sub-grid scalar flux components extracted from explicitly filtered DNS data in terms of their correlation coefficients at the vector level and their mean variation conditional on the Favre-filtered progress variable. The gradient transport closure does neither capture the quantitative nor the qualitative behaviour of the different sub-grid scalar flux components for all filter widths in all cases considered here. Models which account for local flame normal acceleration perform better, especially when the flame remains completely unresolved. In particular those models that account for the alignment of local resolved velocity and scalar gradients by using a tensor diffusivity, perform relatively better than the other alternative models irrespective of Le.

Modeling of Entropy Generation in Turbulent Premixed Flames for Reynolds Averaged Navier–Stokes Simulations: A Direct Numerical Simulation Analysis

The modeling of the mean entropy generation rate S·"' gen¯ due to combined actions of viscous dissipation, irreversible chemical reaction, thermal conduction and mass diffusion (i.e., T¯1,T¯2,T¯3, and T¯4) in the context of Reynolds averaged Navier–Stokes (RANS) simulations has been analyzed in detail based on a direct numerical simulation (DNS) database with a range of different values of heat release parameter τ, global Lewis number Le, and turbulent Reynolds number Ret spanning both the corrugated flamelets (CF) and thin reaction zones (TRZ) regimes of premixed turbulent combustion. It has been found that the entropy generation due to viscous dissipation T¯1 remains negligible in comparison to the other mechanisms of entropy generation (i.e., T¯2,T¯3, and T¯4) within the flame for all cases considered here. A detailed scaling analysis has been used to explain the relative contributions of , and T¯4 on the overall volumetric entropy generation rate S·"' gen¯ in turbulent premixed flames. This scaling analysis is further utilized to propose models for T¯1,T¯2,T¯3, and T¯4 in the context of RANS simulations. It has been demonstrated that the new proposed models satisfactorily predict T¯1,T¯2,T¯3, and T¯4 for all cases considered here. The accuracies of the models for T¯1,T¯2,T¯3, and T¯4 have been demonstrated to be closely linked to the modeling of dissipation rate of turbulent kinetic energy and scalar dissipation rates (SDRs) in turbulent premixed flames.

The Analysis of Direct Numerical Simulation and Experiment in Critical Point of Transitional Flow

In order to study the lower critical point in transitional area of pipe, we used the method of direct numerical simulation to simulate fluid flow and contrasted it with experiment. The result showed that the flow state is close to laminar. Along the pipe axis, the change of pressure is not obviously. The changing rate of axial velocity U near wall region was significantly greater than in the mainstream area, it proved the important role of viscous force.

Turbulence structure behind the shock in canonical shock–vortical turbulence interaction

AbstractThe interaction between vortical isotropic turbulence (IT) and a normal shock wave is studied using direct numerical simulation (DNS) and linear interaction analysis (LIA). In previous studies, agreement between the simulation results and the LIA predictions has been limited and, thus, the significance of LIA has been underestimated. In this paper, we present high-resolution simulations which accurately solve all flow scales (including the shock-wave structure) and extensively cover the parameter space (the shock Mach number, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}M_s$, ranges from 1.1 to 2.2 and the Taylor Reynolds number, ${\mathit{Re}}_{\lambda }$, ranges from 10 to 45). The results show, for the first time, that the turbulence quantities from DNS converge to the LIA solutions as the turbulent Mach number, $M_t$, becomes small, even at low upstream Reynolds numbers. The classical LIA formulae are extended to compute the complete post-shock flow fields using an IT database. The solutions, consistent with the DNS results, show that the shock wave significantly changes the topology of the turbulent structures, with a symmetrization of the third invariant of the velocity gradient tensor and ($M_s$-mediated) of the probability density function (PDF) of the longitudinal velocity derivatives, and an $M_s$-dependent increase in the correlation between strain and rotation.

Effects of Equivalence Ratio and Turbulent Velocity Fluctuation on Early Stages of Pulverized Coal Combustion Following Localized Ignition: A Direct Numerical Simulation Analysis

This study utilized three-dimensional direct numerical simulations (DNS) in order to analyze the effects of turbulent velocity fluctuation, equivalence ratio based on volatile primary fuel in the p...

Validation and implementation of algebraic LES modelling of scalar dissipation rate for reaction rate closure in turbulent premixed combustion

The closure of the filtered reaction rate of the reaction progress variable using an algebraic model for Favre-filtered Scalar Dissipation Rate (SDR) N∼c in turbulent premixed combustion has been assessed in the context of Large Eddy Simulations (LES). This assessment consists of a priori Direct Numerical Simulation (DNS) analysis based on freely propagating statistically planar turbulent premixed flames and a posteriori analysis, involving the LES simulations of a well-documented rectangular dump combustor configuration with sudden expansion (i.e. ORACLES burner) and a premixed flame stabilised on a triangular bluff body flame holder (i.e. Volvo Rig). It has been found that the newly developed SDR model satisfactorily captures N∼c obtained from explicitly filtered DNS data. The predictions of this SDR based LES closure in the ORACLES burner and Volvo Rig configurations exhibit good agreement with experimental results without requiring any major modification to the model parameters. The predictions of the SDR model for the LES of the ORACLES burner and Volvo Rig have been compared to those of two algebraic Flame Surface Density (FSD) models, which yielded satisfactory agreement with experimental data in a previous analysis. The performance of the SDR based closure remains either comparable to or better than the FSD based closures for the two test configurations considered in this analysis.

Double-Diffusive Recipes. Part II: Layer-Merging Events

Abstract This study explores the dynamics of thermohaline staircases: well-defined stepped structures in temperature and salinity profiles, commonly observed in regions of active double diffusion. The evolution of staircases in time is frequently characterized by spontaneous layer-merging events. These phenomena, the authors argue, are essential in regulating the equilibrium layer thickness in fully developed staircases. The pattern and mechanics of merging events are explained using a combination of analytical considerations, direct numerical simulations, and data analysis. The theoretical merger model is based on the stability analysis for a series of identical steps and pertains to both forms of double diffusion: diffusive convection and salt fingering. The conceptual significance of the proposed model lies in its ability to describe merging events without assuming from the outset specific power laws for the vertical transport of heat and salt—the approach adopted by earlier merging models. The analysis of direct numerical simulations indicates that merging models based on the four-thirds flux laws offer adequate qualitative description of the evolutionary patterns but are less accurate than models that do not rely on such laws. Specific examples considered in this paper include the evolution of layers in the diffusive staircase in the Beaufort Gyre of the Arctic Ocean.

Delayed-feedback control: arbitrary and distributed delay-time and noninvasive control of synchrony in networks with heterogeneous delays

We suggest a delayed feedback control scheme with arbitrary delay for stabilizing a periodic orbit, while maintaining the noninvasiveness of the controller. Since the constraint on the delay to be adjusted to the period of the unstable periodic orbit is not imposed, a richer structure of the dynamics can be observed: Not only weakly unstable, but also strongly unstable periodic orbits are stabilized and even stabilization of orbits with infinite period is achieved. The control mechanism is elucidated for the generic model of a subcritical Hopf bifurcation. A complete bifurcation analysis for the fixed point as well as the periodic orbit is presented and the stability domains are identified. Furthermore, we study the effects of distributed delayed feedback on the stabilization of periodic orbits, and show that larger variance of the delay distribution considerably enlarges the stabilization region in the parameter space. We extend the control scheme to a network of Hopf normal forms coupled with heterogeneous delays. By tuning the coupling parameters, different synchronization patterns, i.e., in-phase, splay, and clustering, can be selected. The characteristic equation for Floquet exponents of the heterogeneous delay network is derived in an analytical form, which reveals the coupling parameters for successful stabilization. The equation takes a unified form for both subcritical and supercritical Hopf bifurcations regardless of the synchronization patterns. Analysis of Floquet exponents and direct numerical simulations show that the heterogeneity in the delays drastically facilitates stabilization and provides an enlarged parameter region for successful control. Finally, we consider the thermodynamic limit in the framework of a mean field approximation and show that heterogeneous delays offer an enhanced performance of control.

Effects of roughness on particle dynamics in turbulent channel flows: a DNS analysis

AbstractDeposition and resuspension mechanisms in particle-laden turbulent flows are dominated by the coherent structures arising in the wall region. These turbulent structures, which control the turbulent regeneration cycles, are affected by the roughness of the wall. The particle-laden turbulent flow in a channel bounded by irregular two-dimensional rough surfaces is analysed. The behaviour of dilute dispersions of heavy particles is analysed using direct numerical simulations (DNS) to calculate the three-dimensional turbulent flow and Lagrangian tracking to describe the turbophoretic effect associated with two-phase turbulent flows in a complex wall-bounded domain. Turbophoresis is investigated in a quantitative way as a function of the particle inertia. The analysis of the particle statistics, in term of mean particle concentration and probability density function (p.d.f.) of wall-normal particle velocity, shows that the wall roughness produces a completely different scenario compared to the classical smooth wall. The effect of the wall roughness on the particle mass flux is shown for six particle populations having different inertia.

Modelling of the Tangential Strain Rate Term in the Flame Surface Density Transport Equation in the Context of Reynolds Averaged Navier Stokes Simulations: A Direct Numerical Simulation Analysis

A direct numerical simulation (DNS) database of freely propagating statistically planar turbulent premixed flames with a range of different values of Karlovitz number Ka, turbulent Reynolds numberRet, heat release parameterτ, and global Lewis number Le has been used to assess the models of the tangential strain rate term in the generalised flame surface density (FSD) transport equation in the context of Reynolds averaged Navier Stokes (RANS) simulations. The tangential strain rate term has been split into contributions arising due to dilatation rateTDand flame normal strain rate (-TN). Subsequently,TDand (-TN) were split into their resolved (i.e.,TD1and (-TN1)) and unresolved (TD2and (-TN2)) components. Detailed physical explanations have been provided for the observed behaviours of the components of the tangential strain rate term. This analysis gave way to the modelling of the unresolved dilatation rate and flame normal strain rate contributions. Models have been identified forTD2and (-TN2) for RANS simulations, which are shown to perform satisfactorily in all cases considered, accounting for the variations in Ka,Ret,τand Le. The performance of the newly proposed models for the FSD strain rate term have been found to be either comparable to or better than the existing models.