Direct Numerical Simulation Database Research Articles

Statistical properties of pressure-Hessian tensor in a turbulent channel flow

A direct numerical simulation database of a weakly compressible turbulent channel flow with bulk Mach number 1.56 is studied in detail, including the geometrical relationships between the pressure-Hessian tensor and the vorticity/strain-rate tensor, as well as the mechanism of the pressure-Hessian tensor contributing to the evolution of invariants of the velocity gradient tensor. The results show that the geometrical relationships between the pressure-Hessian tensor and the vorticity/strain-rate tensor in the central region of the channel are consistent with that of isotropic turbulence. However, in the buffer layer with relatively stronger inhomogeneity and anisotropy, the vorticity tends to be aligned with the first or second eigenvector of the pressure-Hessian tensor in the unstable focus/compressing topological region, and tends to be aligned with the first eigenvector of the pressure-Hessian tensor in the stable focus/stretching topological region. In the unstable node/saddle/saddle and stable node/saddle/saddle topological regions, the vorticity prefers to lie in the plane of the first and second eigenvectors of the pressure-Hessian tensor. The strain-rate and the pressure-Hessian tensors tend to share their second principal direction. Moreover, for the coupling between the pressure-Hessian tensor and the principal strain rates, we clarify the influence on dissipation, the nonlinear generation of dissipation and the enstrophy generation. The decomposition of the pressure-Hessian tensor further shows that the slow pressure-related term dominates the pressure-Hessian tensor's contribution, and the influence of inhomogeneity and anisotropy mainly originates from the inhomogeneity and anisotropy of the fluctuating velocity. These statistical properties would be instructive in formulating dynamical models of the velocity gradient tensor for wall turbulence.

A comparison between head-on quenching of stoichiometric methane-air and hydrogen-air premixed flames using Direct Numerical Simulations

Head-on quenching of statistically planar stoichiometric methane-air and hydrogen-air flames has been compared based on a Direct Numerical Simulation (DNS) database. Due the absence of OH at the wall CO cannot be oxidised anymore which leads to the accumulation of carbon monoxide in the near-wall region during flame quenching of stoichiometric methane-air flames. Furthermore, for both fuels, low-temperature reactions at the wall have been found to give rise to accumulation of HO2 and H2O2 during flame quenching. As a result of this, a non-zero heat release rate can be observed at the wall during flame-wall interaction and this effect is particularly strong for the head-on quenching of the stoichiometric hydrogen-air premixed flame. The minimum Peclet number (i.e. normalised flame quenching distance) and the normalised wall heat flux magnitude are found to be smaller in the stoichiometric hydrogen-air flame than in the stoichiometric methane-air premixed flame. Moreover, it has been found that the flame quenching distance tends to decrease under turbulent conditions for the head-on quenching of the stoichiometric hydrogen-air premixed flame but the quenching distances for laminar and turbulent conditions remain comparable for the stoichiometric methane-air premixed flame. The mean reaction rate of reaction progress variable is not properly predicted in the near-wall region by well-known closures for the Flame Surface Density (FSD) or scalar dissipation rate (SDR). For FSD based mean reaction rate closure, it has been observed that recently proposed, simple chemistry DNS based, near-wall corrections perform satisfactorily for both fuels for the detailed chemistry case without adjustment of the model parameters. However, the previously proposed near-wall modification to an algebraic SDR closure based on simple chemistry data performs satisfactorily for the head-on quenching of stoichiometric methane-air premixed flame but it is found to be less effective in the case of the head-on quenching of stoichiometric hydrogen-air premixed flame. Moreover, the prediction of the mean heat release rate for head-on quenching of the stoichiometric hydrogen-air premixed flame cannot be achieved by the mean reaction rate closure of the reaction progress variable based on the mass fraction of a major species because of the important role played by intermediate species in the heat release rate at the wall.

Asymptotic behaviour at the wall in compressible turbulent channels

The asymptotic behaviour of Reynolds stresses close to walls is well established in incompressible flows owing to the constraint imposed by the solenoidal nature of the velocity field. For compressible flows, thus, one may expect a different asymptotic behaviour, which has indeed been noted in the literature. However, the transition from incompressible to compressible scaling, as well as the limiting behaviour for the latter, is largely unknown. Thus, we investigate the effects of compressibility on the near-wall, asymptotic behaviour of turbulent fluxes using a large direct numerical simulation (DNS) database of turbulent channel flow at higher than usual wall-normal resolutions. We vary the Mach number at a constant friction Reynolds number to directly assess compressibility effects. We observe that the near-wall asymptotic behaviour for compressible turbulent flow is different from the corresponding incompressible flow even if the mean density variations are taken into account and semi-local scalings are used. For Mach numbers near the incompressible regimes, the near-wall asymptotic behaviour follows the well-known theoretical behaviour. When the Mach number is increased, turbulent fluxes containing wall-normal components show a decrease in the slope owing to increased dilatation effects. We observe that $R_{vv}$ approaches its high-Mach-number asymptote at a lower Mach number than that required for the other fluxes. We also introduce a transition distance from the wall at which turbulent fluxes exhibit a change in scaling exponents. Implications for wall models are briefly presented.

Ascending–descending and direct–inverse cascades of Reynolds stresses in turbulent Couette flow

The interaction between small- and large-scale structures and the coexisting bottom-up and top-down processes are studied in a turbulent plane Couette flow, where space-filling longitudinal rolls appear at relatively low values of the Reynolds number $Re$ . A direct numerical simulation database at $Re_\tau =101$ is built to replicate the highest $Re$ considered in recent experimental work by Kawata & Alfredsson (Phys. Rev. Lett., vol. 120, 2018, 244501). Our study is based on the exact budget equations for the second-order structure function tensor $\left \langle {\delta u_i \delta u_j} \right \rangle$ , i.e. the anisotropic generalized Kolmogorov equations (AGKE). The AGKE study production, redistribution, transport and dissipation of every Reynolds stress tensor component, considering simultaneously the physical space and the space of scales, and properly define the concept of scale in the inhomogeneous wall-normal direction. We show how the large-scale energy-containing motions are involved in the production and redistribution of the turbulent fluctuations. Both bottom-up and top-down interactions occur, and the same is true for direct and inverse cascading. The wall-parallel components $\left \langle {\delta u \delta u} \right \rangle$ and $\left \langle {\delta w \delta w} \right \rangle$ show that both small and large near-wall scales feed the large scales away from the wall. The wall-normal component $\left \langle {\delta v \delta v} \right \rangle$ is different, and shows a dominant top-down dynamics, being produced via pressure-strain redistribution away from the wall and transferred towards near-wall larger scales via an inverse cascade. The off-diagonal component shows a top-down interaction, with both direct and inverse cascades, albeit the latter takes place within a limited range of scales.

Flame Surface Density based mean reaction rate closure for Reynolds averaged Navier Stokes methodology in turbulent premixed Bunsen flames with non-unity Lewis number

The Flame Surface Density (FSD) based mean reaction rate closure proposed by Prof. K.N.C. Bray and co-workers in the context of Reynolds Averaged Navier-Stokes simulations has been a-priori analysed using a Direct Numerical Simulation (DNS) database of turbulent premixed Bunsen flames with different characteristic Lewis numbers representing the strict flamelet regime (i.e. high Damköhler number and low Karlovitz number combustion). The statistical behaviours of stretch factor, orientation factor and wrinkling length scale have been assessed for non-unity Lewis number conditions to identify their Lewis number dependencies. The assumption of presumed bimodal distribution has been found to be rendered invalid close to the nozzle exit where the unresolved wrinkling remains relatively small even when the flow parameters at the nozzle exit represent high Damköhler number and low Karlovitz number conditions. Although the PDF of reaction progress variable shows some resemblance to a bimodal distribution away from the nozzle exit, the Bray-Moss-Libby expressions which can be derived for infinitely large values of Damköhler number have been found to show considerable deviations from the Reynolds averaged reaction progress variable and reaction progress variable variance extracted from DNS data even though these cases represent the wrinkled/corrugated flamelets regime combustion based on nozzle exit conditions. This suggests that it might be necessary to solve a modelled scalar variance transport equation even in the strict flamelet regime instead of using the algebraic relation for the scalar variance. It has been found that the characteristic Lewis number has a major influence on the orientation factor, wrinkling length scale, and the stretch factor. Furthermore, these parameters are found to be (sometimes strong) functions of the axial distance from the nozzle exit. Known parameterisations for the wrinkling length scale and the stretch factor have been shown to be unable to capture the correct variation across the flame brush based on a-priori analysis of DNS data. The variability of the orientation factor and the inadequacy of existing relations to approximate other quantities such as the stretch factor, wrinkling factor and the Reynolds averaged reaction progress variable have the potential to severely limit the performance of algebraic FSD based mean reaction rate closures in turbulent premixed flames within the flamelet regime.

Global POD-Galerkin ROMs for Fluid Flows with Moving Solid Structures

Traditional proper orthogonal decomposition (POD)-Galerkin projection for reduced-order models (ROMs) of fluid flows is based on a fixed domain. The current method removes this limitation by considering a single combined domain of fluid and solid, whereas the original solid boundary conditions are reinforced by additional ROM terms. The combined domain requires a new inner product defined in the same combined domain to compute POD modes and the projection of equations. Solid motion is considered first as a continuous motion, then a decomposed motion, represented by a few solid modes to further reduce the computational cost. This new global approach was applied first on a two-dimensional direct numerical simulation (DNS) database of the flow past an oscillatory cylinder, and then on a three-dimensional DNS database of the flow past an oscillatory sphere. Last, the approach was applied on a high-resolution particle image velocimetry database from an experiment at higher Reynolds number of the flow past a pitching-up NACA0012 airfoil. The ROMs derived by the global POD-Galerkin projection approach, for all three moving-boundary cases, have shown adequate accuracy in the reconstruction of flow fields and the prediction of key aerodynamic features while keeping very low computational costs.

Error propagation and conditioning analysis of DNS data of turbulent viscoelastic channel flows

In the context of drag reduction phenomenon, direct numerical simulation (DNS) of turbulent viscoelastic flows is a very useful tool able to provide information that is not possible with experiments and that can be used for modeling purposes. A rare and challenging task is to provide measures for statistical errors that are present in DNS data. In the present communication, we employ a method to quantify the statistical convergence of the DNS turbulent viscoelastic channel flows from the unbalance on the mean momentum equation. In addition, we conduct a conditioning analysis of the resultant numerical linear system of this problem. We compare results from different research groups. We found that DNS databases of viscoelastic flows can induce high error propagation in the mean velocity. As a consequence, larger sampling times are needed to achieve a statistically converged Reynolds stress tensor. The conditioning analysis has shown that elasticity enhances conditioning. • We discuss the DNS importance for turbulence modeling. • Uncertainty and statistical error are analyzed in the DNS context. • Equations for mean viscoelastic turbulence (VT) are ill-conditioned. • Error propagation in the mean velocity field related to VT is high. • Statistical quantities, like Reynolds stress, in VT need to be more converged.

Resolvent-based estimation of turbulent channel flow using wall measurements

We employ a resolvent-based methodology to estimate velocity and pressure fluctuations within turbulent channel flows at friction Reynolds numbers of approximately 180, 550 and 1000 using measurements of shear stress and pressure at the walls, taken from direct numerical simulation (DNS) databases. Martiniet al.(J. Fluid Mech., vol. 900, 2021, p. A2) showed that the resolvent-based estimator is optimal when the true space–time forcing statistics are utilised, thus providing an upper bound for the accuracy of any linear estimator. We use this framework to determine the flow structures that can be linearly estimated from wall measurements, and we characterise these structures and the estimation errors in both physical and wavenumber space. We also compare these results to those obtained using approximate forcing models – an eddy-viscosity model and white-noise forcing – and demonstrate the significant benefit of using true forcing statistics. All models lead to accurate results up to the buffer layer, but only using the true forcing statistics allows accurate estimation of large-scale logarithmic-layer structures, with significant correlation between the estimates and DNS results throughout the channel. The eddy-viscosity model displays an intermediate behaviour, which may be related to its ability to partially capture the forcing colour. Our results show that structures that leave a footprint on the channel walls can be accurately estimated using the linear resolvent-based methodology, and the presence of large-scale wall-attached structures enables accurate estimations through the logarithmic layer.

Assessment of turbulence modeling for massively-cooled turbulent boundary layer flows with transpiration cooling

We assess Reynolds-averaged Navier–Stokes (RANS) turbulent closures for the prediction of a turbulent boundary layer with transpiration cooling via comparison with a high-fidelity direct numerical simulation database. This study considers the canonical zero-pressure gradient, flat-plate, turbulent boundary layer over a massively cooled wall, with transpiration cooling. The simulations are conducted at a low-subsonic Mach number and we study two transpiration cooling configurations with uniform and slit injection at various blowing ratios. The DNS and RANS simulation setups are nearly identical. The RANS-based turbulence models perform well in the qualitative estimation of the velocity and thermal boundary layer evolution at low-blowing ratios (F = 0.2 and 0.6%); more significant differences are noted at higher blowing ratios (F=2.0%). The RANS models, especially the Spalart–Allmaras model, over-predict turbulence production near the wall which results in faster growth in the boundary thickness; this error becomes more pronounced at higher blowing ratios. Despite the greater mixing of momentum, the thermal mixing is under-predicted compared to the DNS in the uniform blowing case but over-predicted for the slit case. These results suggest that modeling errors in the temperature distribution due to turbulent thermal flux modeling can be significant even if the velocity is correctly modeled.

Analysis of the development of the flame brush in turbulent premixed spherical flames

The thickness of the turbulent flame brush is central to the modeling of premixed turbulent combustion and the theory of turbulent diffusion is often applied to explain the growth of the brush with varying success. However, numerous studies have shown that the brush evolves differently from the dispersion of material points on the account of flame propagation, density changes across the front, and hydrodynamic instabilities. Modifications to turbulent diffusion theory to incorporate these effects are challenging since the theory is Lagrangian. In this article, we present an alternate Eulerian framework based on the surface density formalism. We employ the proposed framework to analyze a database of direct numerical simulations of spherical turbulent premixed flames in decaying isotropic turbulence and recover mechanisms for which scaling laws are proposed and assessed against data. We characterize quantitatively two mechanisms: one related to the mean velocity gradient induced by thermal expansion and the other due to flame propagation in the presence of curvature. We demonstrate that the net effect of these two processes is to hinder the growth of the turbulent flame brush in the present configuration. Our analysis supports the notion that the turbulent flame brush does not grow indefinitely, rather it attains a maximum thickness.

Assessment of Extrapolation Relations of Displacement Speed for Detailed Chemistry Direct Numerical Simulation Database of Statistically Planar Turbulent Premixed Flames

A three-dimensional Direct Numerical Simulation (DNS) database of statistically planar H_{2} - air turbulent premixed flames with an equivalence ratio of 0.7 spanning a large range of Karlovitz number has been utilised to assess the performances of the extrapolation relations, which approximate the stretch rate and curvature dependences of density-weighted displacement speed S_{d}^{*}. It has been found that the correlation between S_{d}^{*} and curvature remains negative and a significantly non-linear interrelation between S_{d}^{*} and stretch rate has been observed for all cases considered here. Thus, an extrapolation relation, which assumes a linear stretch rate dependence of density-weighted displacement speed has been found to be inadequate. However, an alternative extrapolation relation, which assumes a linear curvature dependence of S_{d}^{*} but allows for a non-linear stretch rate dependence of S_{d}^{*}, has been found to be more successful in capturing local behaviour of the density-weighted displacement speed. The extrapolation relations, which express S_{d}^{*} as non-linear functions of either curvature or stretch rate, have been found to capture qualitatively the non-linear curvature and stretch rate dependences of S_{d}^{*} more satisfactorily than the linear extrapolation relations. However, the improvement comes at the cost of additional tuning parameter. The Markstein lengths LM for all the extrapolation relations show dependence on the choice of reaction progress variable definition and for some extrapolation relations LM also varies with the value of reaction progress variable. The predictions of an extrapolation relation which involve solving a non-linear equation in terms of stretch rate have been found to be sensitive to the initial guess value, whereas a high order polynomial-based extrapolation relation may lead to overshoots and undershoots. Thus, a recently proposed extrapolation relation based on the analysis of simple chemistry DNS data, which explicitly accounts for the non-linear curvature dependence of the combined reaction and normal diffusion components of S_{d}^{*}, has been shown to exhibit promising predictions of S_{d}^{*} for all cases considered here.

Effects of turbulent length scale on the bending effect of turbulent burning velocity in premixed turbulent combustion

The effects of turbulent integral length scale to flame thickness ratio on the bending effect of turbulent burning velocity variation have been analysed based on a three-dimensional Direct Numerical Simulation database of statistically planar turbulent premixed flames with a characteristic Lewis number of unity propagating into forced unburned gas turbulence. It has been demonstrated that Damköhler's first hypothesis remains valid for the cases considered here and this has been utilised to explain the bending effect by analysing the terms in the generalised Flame Surface Density (FSD) transport equation. Under steady-state, the flame surface area generation by the FSD tangential strain rate term remains in equilibrium with the flame surface destruction by the FSD curvature term. It has been found that the length scale ratio influences the relative contributions of the dilatation and normal strain rate to the flame surface area generation due to tangential strain rate. Similarly, relative contributions of the flame surface area destruction due to the curvature terms arising from the combined reaction and normal diffusion component of displacement speed, and the tangential diffusion component of displacement speed are affected by the length scale ratio. The propensity of the flame area generation due to the normal strain rate term and the dominance of the flame area destruction arising from the tangential diffusion component of displacement speed are strengthened with decreasing length scale ratio. The flame surface area destruction due to the FSD curvature term arising from tangential diffusion component of displacement speed strengthens with increasing turbulence intensity and it becomes the major contributor to the destruction of flame surface area for large turbulence intensities. However, the inner cut-off scale, which also limits maximum possible flame area generation by the FSD strain rate term under statistically stationary state, determines the maximum possible destruction of flame surface area for a given length scale ratio and this is manifested in the bending effects of turbulent burning velocity and flame surface area. At high turbulence intensities, the turbulent burning velocity levels off at a smaller value for the smaller length scale ratio, which is consistent with Damköhler's second hypothesis and has been explained based on scaling arguments utilising the leading order balance between the strain rate and curvature contributions to the flame surface area evolution for large turbulence intensities characterised by large Karlovitz number and small Damköhler number values.

Compressibility effects on hypersonic turbulent channel flow with cold walls

Compressibility effects on velocity and temperature fluctuations in hypersonic turbulence over cold walls are investigated by exploiting a direct numerical simulation database. We found that the compressibility effects are enhanced by the decrease in wall temperature, which is directly reflected by the rapid increase in velocity divergence and turbulent Mach number. Helmholtz decomposition is adopted to evaluate the genuine compressibility effects by splitting the velocity fluctuation into a solenoidal component and a dilatational component. As the wall temperature decreases, the vertical motion is gradually dominated by the dilatational component, while the wall-parallel motions still by the solenoidal component. The dilatational components tend to decrease the skin friction by around 4%–6%. The instantaneous and conditionally averaged field around strong compressive motions further suggests that the dilatational structures behave as traveling-wave packets surrounded by vortex clusters. To improve the strong analogy between temperature and velocity fluctuations, their correlation in spectral space is studied. The results show that they are strongly correlated at the scales of energy-containing motions, but they are mutually independent at small scales.

The scaling of separation bubble in the conical shock wave/turbulent boundary layer interaction

A direct numerical simulation database (Zuo et al., J. Fluid Mech. vol. 877, 2019, 167–195) is analyzed to investigate the size of the separation bubble and the relation with the pressure rise in the conical shock wave/turbulent boundary layer interaction. The characteristics of the separation bubbles in the supersonic turbulent boundary layer induced by conical shock waves are discussed. The inviscid reflected conical shock theory is analyzed, to conclude that regular reflection transition to Mach reflection will occur somewhere along the spanwise direction in the interaction zone. Then, the typical shape of a turbulent separation bubble in the conical shock wave/turbulent boundary layer interaction is described. The scaling between the size of the turbulent separation bubble and moderate conical shock intensities is established, giving a potential alternative method to rapidly predict the size of turbulent separation bubbles, especially in the supersonic viscous corrections under condition of boundary layer separation.

Effect of non-ambient pressure conditions and Lewis number variation on direct numerical simulation of turbulent Bunsen flames at low turbulence intensity

The instantaneous flame front structure of high pressure turbulent premixed Bunsen flames has been analyzed for a wide range of characteristic Lewis numbers using a new Direct Numerical Simulation (DNS) database. High pressure turbulent premixed flames of lean-light fuels are likely to feature both thermo-diffusive and Darrieus–Landau instabilities. As the effects of these instabilities are eclipsed by intense turbulence, the present analysis focuses on flames located at the border of the wrinkled and corrugated flamelets regimes. The flame morphology has been characterized by the skewness and kurtosis of the probability density function (PDF) profiles of the mean and Gaussian curvatures. While skewness alone is not sufficient as a marker to distinguish between thermo-diffusive and Darrieus–Landau instabilities, it has been found that excess kurtosis of Gaussian curvature possibly can be used to distinguish between both instabilities. Further, the inner cut-off length and the fractal dimension have been computed for characterization of flame scales and for parameterization of wrinkling factor models. It has been observed that increasing pressure and decreasing Lewis number give rise to flame instabilities which results in an increased fractal dimension and a decreased inner cut-off scale. For high pressure flames with Lewis numbers around unity, the inner cut-off scale scales very well with the critical wavelength for flame instabilities determined from the theoretical analysis by Matalon and Matkowsky (1982). For small sub-unity Lewis numbers, the flames become unconditionally unstable and the critical wavelength loses its meaning, while the inner cut-off scales continues to decrease with Lewis number and the fractal dimension continues to increase up to a limit of about 7/3. The present findings are in excellent agreement with experimental observations from literature and theoretical analysis of flame instabilities.

Conditioning and accurate solutions of Reynolds average Navier–Stokes equations with data-driven turbulence closures

Abstract

A priori assessment of convolutional neural network and algebraic models for flame surface density of high Karlovitz premixed flames

Accurate modeling of the unresolved flame surface area is critical for the closure of reaction source terms in the flame surface density (FSD) method. Some algebraic models have been proposed for the unresolved flame surface area for premixed flames in the flamelet or thin reaction zones (TRZ) regimes where the Karlovitz number (Ka) is less than 100. However, in many lean combustion applications, Ka is large (Ka > 100) due to the strong interactions of small-scale turbulence and flames. In the present work, a direct numerical simulation (DNS) database was used to evaluate the performance of algebraic FSD models in high Ka premixed flames in the context of large eddy simulations. Three DNS cases, i.e., case L, case M and case H, were performed, where case L is located in the TRZ regime with Ka < 100 and case M and case H are located in the broken reaction zones regime with Ka > 100. A convolutional neural network (CNN) model was also developed to predict the generalized FSD, which was trained with samples of case H and a small filter size, and was tested in various cases with different Ka and filter sizes. It was found that the fraction of resolved FSD increases with increasing filtered progress variable c̃ and decreasing subgrid turbulent velocity fluctuation u′Δ. The performance of CNN and algebraic models was assessed using the DNS database. Overall, the results of algebraic models are promising in case L and case M for a small filter size; the CNN model performs generally better than the algebraic models in high Ka flames and the correlation coefficient between the modeled and actual generalized FSD is greater than 0.91 in all cases. The effects of c̃ and u′Δ on the performance of different models for various cases were explored. The algebraic models perform well with large values of c̃ and small values of u′Δ in high Ka cases, which indicates that they can be applied to high Ka flames in certain conditions. The performance of the CNN model is better than the algebraic models for a large filter size in high Ka cases.

Turbulence topology evolution in weakly turbulent premixed flames

In turbulent premixed flames, not only the isotropy of velocity fluctuations is altered by the thermal expansion effect but also the dissipative structure of the turbulent flow field and the flow topology are also deeply influenced by the flame. Considering the joint probability density function of the second and third invariants of the velocity gradient tensor (VGT)—or its traceless counterpart—is a classical way to deduce the topology of turbulent flows at these smallest scales. These quantities are analyzed by considering direct numerical simulation databases of premixed flame kernel growth in homogeneous isotropic turbulence. Two conditions of turbulence–combustion interaction are considered, which correspond to two distinct values of the Bray number. The analysis of the VGT shows that the propagating premixed flame and its associated density variations significantly modify the turbulence structure and flow topology. To understand this behavior as the flow interacts with the flame front, Lagrangian dynamics of the VGT and its invariants are studied by considering the conditional mean rate of change vectors. Special emphasis is thus placed on the Lagrangian evolution equations of these invariants. To the best of authors' knowledge, this is first time that such budgets are scrutinized under premixed combustion conditions. The pressure Hessian contribution to the VGT invariant transport equations is shown to be one of the leading-order terms in this evolution, making it critically important to the flow dynamics and turbulence structure.

Damköhler number scaling of active cascade effects in turbulent premixed combustion

Effects of combustion heat release on turbulent velocity and scalar statistics are investigated as a function of the Damköhler number using three direct numerical simulation databases of spatially developing turbulent premixed jet flames. At low Karlovitz numbers, where heat-release effects dominate turbulent kinetic energy budgets, their relative significance scales with the integral Damköhler number in a priori Reynolds-Averaged Navier–Stokes (RANS) statistics and the filter Damköhler number in Large Eddy Simulation (LES). The Damköhler-number scaling of counter-gradient transport in this regime follows theoretical arguments underpinning linear-algebraic turbulence models, which explains their efficacy at low Karlovitz numbers. Conversely, at moderate Karlovitz numbers, LES subfilter turbulence is more strongly influenced by heat-release effects than the analogous large-scale RANS turbulence. This is consistent with the notion of an “active cascade,” which postulates that heat-release-induced volumetric expansion competes on intermediate scales with classical forward-cascade energy transfer. LES exposes these dynamics as dominant subfilter-scale physics, unlike in RANS, where they are secondary to the effects of mean-shear production at the large scales. The significance of subfilter-scale interactions is promoted by the LES filter itself, which modifies the RANS spectral basis by incorporating local flame-normal averaging. This is highlighted by comparing LES fields obtained using a 3D filter to those using a modified 2D filter, excluding the flame-normal direction, which significantly reduces the apparent influence of heat-release effects but is not representative of LES in practice. The subfilter modeling challenges posed by these distinctions at moderate Karlovitz numbers and order-unity Damköhler numbers remain to be understood.

Dissipation and dilatation rates in premixed turbulent flames

Velocity dilatation and total, solenoidal, and dilatational dissipation rates of the total flow kinetic energy are extracted from three different direct numerical simulation databases obtained by three independent research groups using different numerical codes and methods (e.g., single-step chemistry and complex chemistry flames) from six different premixed turbulent flames associated with flamelet, thin reaction zone, and broken reaction zone regimes of turbulent burning. The results show that dilatational dissipation can be larger than solenoidal dissipation in the flamelet regime and is substantial in the thin reaction zone regime. Accordingly, the influence of combustion-induced thermal expansion on the dissipation rate is not reduced to an increase in the mixture viscosity by the temperature. A simple criterion for identifying conditions associated with significant dilatational dissipation is discussed, and dilatational dissipation due to the influence of turbulence on mixing in preheat zones is argued to play a role even at high Karlovitz numbers Ka. In particular, the magnitude of dilatation fluctuations and probability of finding negative local dilatation are increased by Ka, thus implying that the impact of molecular transport of species and heat on the dilatation increases with increasing Karlovitz number.