3D Direct Numerical Simulations Research Articles

A DNS study of the physical mechanisms associated with density ratio influence on turbulent burning velocity in premixed flames

Data obtained in 3D direct numerical simulations of statistically planar, 1D weakly turbulent flames characterised by different density ratios σ are analysed to study the influence of thermal expansion on flame surface area and burning rate. Results show that, on the one hand, the pressure gradient induced within a flame brush owing to heat release in flamelets significantly accelerates the unburned gas that deeply intrudes into the combustion products in the form of an unburned mixture finger, thus causing large-scale oscillations of the burning rate and flame brush thickness. Under the conditions of the present simulations, the contribution of this mechanism to the creation of the flame surface area is substantial and is increased by σ, thus implying an increase in the burning rate by σ. On the other hand, the total flame surface areas simulated at σ = 7.53 and 2.5 are approximately equal. The apparent inconsistency between these results implies the existence of another thermal expansion effect that reduces the influence of σ on the flame surface area and burning rate. Investigation of the issue shows that the flow acceleration by the combustion-induced pressure gradient not only creates the flame surface area by pushing the finger tip into the products, but also mitigates wrinkling of the flame surface (the side surface of the finger) by turbulent eddies. The latter effect is attributed to the high-speed (at σ = 7.53) axial flow of the unburned gas, which is induced by the axial pressure gradient within the flame brush (and the finger). This axial flow acceleration reduces the residence time of a turbulent eddy in an unburned zone of the flame brush (e.g. within the finger). Therefore, the capability of the eddy for wrinkling the flamelet surface (e.g. the side finger surface) is weakened owing to a shorter residence time.

Strouhal–Reynolds number relationship for flow past a circular cylinder

The Strouhal–Reynolds number ($St{-}Re$) relationship for flow past a circular cylinder in the low $Re$ range of $Re\leqslant 1000$ is investigated through two- (2D) and three-dimensional (3D) direct numerical simulations (DNS). An improved method is proposed for the determination of the separating velocity and the wake width to allow for a better estimation of the wake Strouhal number $St^{\ast }$. For $Re$ in the extended laminar regime calculated by 2D DNS, the $St^{\ast }$ values are found to be more uniform than the original $St$ for the 2D flow. It is also found that the $St^{\ast }$ values for the 2D and 3D flows agree well in the laminar regime of $Re$ up to approximately 270. In addition, uniform $St^{\ast }$ values are also obtained for different mode A and mode B flow structures triggered artificially by using different cylinder span lengths in DNS. It is demonstrated that the drop in $St$ (with respect to its 2D counterpart) with the development of different 3D wake structures is due to the decrease in the separating velocity and the increase in the wake width for a 3D flow, rather than the existence of a particular wake structure such as pure mode A or vortex dislocation. However, as the wake flow becomes increasingly turbulent with further increase in $Re$, the $St^{\ast }$ value for the 3D flow increases gradually and deviates from its 2D counterpart, since for turbulent 3D flows the vortex shedding frequency scales on a length smaller than the wake width.

Characterization of transition from Darcy to non-Darcy flow with 3D pore-level simulations

We characterize seepage flow in porous media via a series of three-dimensional (3D) direct numerical simulations (DNSs) of Navier-Stokes flows in representative volume elements (RVEs) at the pore level. The immersed boundary method with a fixed staggered grid is employed for calculations based on the finite difference method in the pore domain formed with spatially arranged rigid particles in RVEs. The numerical results of the DNSs with different particle sizes and different seepage flow velocities are volume-averaged over the RVEs to evaluate the permeability coefficients of the seepage flows and are ordered according to the Reynolds numbers for porous media. After the numerical scheme is validated with a simple RVE model, the transition from Darcy to non-Darcy flow, for which experimental results have reported in the literature, is demonstrated in terms of the calculated permeability coefficients and examined based on the pore-level flow characteristics to clarify the mechanism of the permeability change, i.e. the macroscopic behaviour of RVEs related to the Reynolds number.

Multiphase flow models for hydraulic fracturing technology

The technology of hydraulic fracturing of a hydrocarbon-bearing formation is based on pumping a fluid with particles into a well to create fractures in porous medium. After the end of pumping, the fractures filled with closely packed proppant particles create highly conductive channels for hydrocarbon flow from far-field reservoir to the well to surface. The design of the hydraulic fracturing treatment is carried out with a simulator. Those simulators are based on mathematical models, which need to be accurate and close to physical reality. The entire process of fracture placement and flowback/cleanup can be conventionally split into the following four stages: (i) quasi-steady state effectively single-phase suspension flow down the wellbore, (ii) particle transport in an open vertical fracture, (iii) displacement of fracturing fluid by hydrocarbons from the closed fracture filled with a random close pack of proppant particles, and, finally, (iv) highly transient gas-liquid flow in a well during cleanup. The stage (i) is relatively well described by the existing hydralics models, while the models for the other three stages of the process need revisiting and considerable improvement, which was the focus of the author’s research presented in this review paper. For stage (ii), we consider the derivation of a multi-fluid model for suspension flow in a narrow vertical hydraulic fracture at moderate Re on the scale of fracture height and length and also the migration of particles across the flow on the scale of fracture width. At the stage of fracture cleanaup (iii), a novel multi-continua model for suspension filtration is developed. To provide closure relationships for permeability of proppant packings to be used in this model, a 3D direct numerical simulation of single phase flow is carried out using the lattice-Boltzmann method. For wellbore cleanup (iv), we present a combined 1D model for highly-transient gas-liquid flow based on the combination of multi-fluid and drift-flux approaches. The derivation of the drift-flux model from conservation olaws is criticall revisited in order to define the list of underlying assumptions and to mark the applicability margins of the model. All these fundamental problems share the same technological application (hydraulic fracturing) and the same method of research, namely, the multi-fluid approach to multiphase flow modeling and the consistent use of asymptotic methods. Multi-fluid models are then discussed in comparison with semi-empirical (often postulated) models widely used in the industry.

Accuracy consideration by DRP schemes for DNS and LES of compressible flow computations

Several dispersion relation-preserving (DRP) spatially central discretizations are considered as the base scheme in the framework of the Yee & Sjögreen low dissipative nonlinear filter approach. In addition, the nonlinear filter of Yee & Sjögreen with shock-capturing and long time integration capabilities is used to replace the standard DRP linear filter for both smooth flows and flows containing discontinuities. DRP schemes for computational aeroacoustics (CAA) focus on dispersion error consideration for long time linear wave propagation rather than the formal order of accuracy of the scheme. The resulting DRP schemes usually have wider grid stencils and increased CPU operations count compared with standard central schemes of the same formal order of accuracy. For discontinuous initial data and long time wave propagation of smooth acoustic waves, various space and time DRP linear filter are needed. For acoustic waves interacting with shocks and turbulence induced noise, DRP schemes with linear filters alone usually are not capable of simulating such flows. The investigation presented in this paper is focused on the possible gain in efficiency and accuracy by spatial DRP schemes over standard central schemes having the same grid stencil width for general direct numerical simulations (DNS) and large eddy simulations (LES) of compressible flows. Representative test cases for both smooth flows and problems containing discontinuities for 3D DNS of compressible gas dynamics are included.

Direct numerical simulation of ignition of syngas (H2/CO) mixtures with temperature and composition stratifications relevant to HCCI conditions

In this paper, ignition characteristics of syngas (H2/CO) under homogeneous charge compression ignition environment have been studied using direct numerical simulation (DNS) and detailed reaction mechanism with temperature stratification. 2D DNS are performed by varying several parameters such as fuel composition, temperature fluctuation (T′) and with different temperature and composition correlations. Results show that high H2 content syngas mixture exhibits increase in peak mean heat release rate (HRR) and decrease in spreading of mean HRR. Also, for large T′, deflagration mode of ignition becomes dominant source of HRR and reduces the effects of fuel composition on peak mean HRR. On the contrary, spontaneous mode of ignition becomes dominant source of HRR and occurs more homogenously for small T′, and this phenomenon becomes significant for low H2 content syngas mixture. The effect of different correlations between temperature and composition on ignition in syngas illustrate that HRR occurs from mixed mode of deflagration and spontaneous ignition for uncorrelated cases, whereas spontaneous mode of ignition occurring homogeneously is the major source of HRR for negatively correlated cases.

Weakly non-Boussinesq convection in a gaseous spherical shell.

We examine the dynamics associated with weakly compressible convection in a spherical shell by running 3D direct numerical simulations using the Boussinesq formalism [Spiegel and Veronis, Astrophys. J. 131, 442 (1960)AJLEEY0004-637X10.1086/146849]. Motivated by problems in astrophysics, we assume the existence of a finite adiabatic temperature gradient ∇T_{ad} and use mixed boundary conditions for the temperature with fixed flux at the inner boundary and fixed temperature at the outer boundary. This setup is intrinsically more asymmetric than the more standard case of Rayleigh-Bénard convection in liquids between parallel plates with fixed temperature boundary conditions. Conditions where there is substantial asymmetry can cause a dramatic change in the nature of convection and we demonstrate that this is the case here. The flows can become pressure- rather than buoyancy-dominated, leading to anomalous heat transport by upflows. Counterintuitively, the background temperature gradient ∇T[over ¯] can develop a subadiabatic layer (where g·∇T[over ¯]<g·∇T_{ad}, where g is gravity) although convection remains vigorous at every point across the shell. This indicates a high degree of nonlocality.

Floquet stability analysis in the wake of a NACA0015 airfoil at post-stall angles of attack

We perform a Floquet stability analysis in the wake of a NACA0015 airfoil, with four angles of attack, α=20°, 17.5°, 15°, and 12.5°, considered. The central aim is to predict the secondary instabilities at the fixed moderate angles of attack, which are sufficiently large for massive separation from the airfoil, while at the same time allowing the formation and travelling of surface vortex on the airfoil, differentiating from the cases with very large angles of attack. We divide the angles of attack into two groups. We report that mode C is the first unstable mode for both groups, and which is also the only unstable mode for the small angles of attack, i.e., α=15° and α=12.5°, while for the high angles of attack, i.e., α=20° and α=17.5°, four unstable modes are observed. They are mode A, mode quasi-periodic, mode SL, and mode SS. The modes SL and SS are both subharmonic but with different wave numbers. We conjecture that these two subharmonic modes are resulted from the splitting of mode C. A comparison in the base flow topologies between the two groups shows that the different instability behaviors are probably due to their different flow patterns of the base flows. Three-dimensional direct numerical simulations (DNSs) have also been employed to study the physical realizability of the dominant unstable modes. A good consistency between the Floquet analysis and the 3D DNS results is achieved, indicating that the dominance of the linear instability is responsible for such a three-dimensional flow as the Reynolds number is not far from the critical value. Moreover, we find that the critical Reynolds numbers for the onset of three-dimensional instability fall into the range of 159.7–234.2 by defining this new Reynolds number according to the width of the flow wake. These values are very close to that of a bluff body. Furthermore, we note that the corresponding Strouhal numbers are around 0.17 for all the angles of attack, implying the relevance of three-dimensional instabilities to the wake dynamics or more specifically the fluctuation in the wake.

Subcritical Thermal Convection of Liquid Metals in a Rapidly Rotating Sphere.

Planetary cores consist of liquid metals (low Prandtl number Pr) that convect as the core cools. Here, we study nonlinear convection in a rotating (low Ekman number Ek) planetary core using a fully 3D direct numerical simulation. Near the critical thermal forcing (Rayleigh number Ra), convection onsets as thermal Rossby waves, but as Ra increases, this state is superseded by one dominated by advection. At moderate rotation, these states (here called the weak branch and strong branch, respectively) are smoothly connected. As the planetary core rotates faster, the smooth transition is replaced by hysteresis cycles and subcriticality until the weak branch disappears entirely and the strong branch onsets in a turbulent state at Ek<10^{-6}. Here, the strong branch persists even as the thermal forcing drops well below the linear onset of convection (Ra=0.7Ra_{crit} in this study). We highlight the importance of the Reynolds stress, which is required for convection to subsist below the linear onset. In addition, the Péclet number is consistently above 10 in the strong branch. We further note the presence of a strong zonal flow that is nonetheless unimportant to the convective state. Our study suggests that, in the asymptotic regime of rapid rotation relevant for planetary interiors, thermal convection of liquid metals in a sphere onsets through a subcritical bifurcation.

A DNS Study of Closure Relations for Convection Flux Term in Transport Equation for Mean Reaction Rate in Turbulent Flow

The present work aims at modeling the entire convection flux overline {rho mathbf {u}W} in the transport equation for a mean reaction rate overline {rho W} in a turbulent flow, which (equation) was recently put forward by the present authors. In order to model the flux, several simple closure relations are developed by introducing flow velocity conditioned to reaction zone and interpolating this velocity between two limit expressions suggested for the leading and trailing edges of the mean flame brush. Subsequently, the proposed simple closure relations for overline {rho mathbf {u}W} are assessed by processing two sets of data obtained in earlier 3D Direct Numerical Simulation (DNS) studies of adiabatic, statistically planar, turbulent, premixed, single-step-chemistry flames characterized by unity Lewis number. One dataset consists of three cases characterized by different density ratios and is associated with the flamelet regime of premixed turbulent combustion. Another dataset consists of four cases characterized by different low Damköhler and large Karlovitz numbers. Accordingly, this dataset is associated with the thin reaction zone regime of premixed turbulent combustion. Under conditions of the former DNS, difference in the entire, overline {rho {u}W}, and mean, tilde {u}overline {rho W}, convection fluxes is well pronounced, with the turbulent flux, overline {rho u^{prime prime }W^{prime prime }}, showing countergradient behavior in a large part of the mean flame brush. Accordingly, the gradient diffusion closure of the turbulent flux is not valid under such conditions, but some proposed simple closure relations allow us to predict the entire flux overline {rho mathbf {u}W} reasonably well. Under conditions of the latter DNS, the difference in the entire and mean convection fluxes is less pronounced, with the aforementioned simple closure relations still resulting in sufficiently good agreement with the DNS data.

A Conditional Moment Closure Study of Chemical Reaction Source Terms in SCCI Combustion

The objective of this study is to evaluate conditional moment closure (CMC) approaches to model chemical reaction rates in compositionally stratified, autoigniting mixtures, in thermochemical conditions relevant to stratified charge compression ignition (SCCI) engines. First-order closure, second-order closure and double conditioning are evaluated and contrasted as options in comparison to a series of direct numerical simulations (DNSs). The two-dimensional (2D) DNS cases simulate ignitions in SCCI-like thermochemical conditions with compositionally stratified n-heptane/air mixtures in a constant volume. The cases feature two different levels of stratification with three mean temperatures in the negative-temperature coefficient (NTC) regime of ignition delay times. The first-order closure approach for reaction rates is first assessed using hybrid DNS-CMC a posteriori tests when implemented in an open source computational fluid dynamics (CFD) package known as OpenFOAM $^{{\circledR }}$ . The hybrid DNS-CMC a posteriori tests are not a full CMC but a DNS-CMC hybrid in that they compute the scalar and velocity fields at the DNS resolution, thus isolating the first-order reaction rate closure model as the main source of modelling error (as opposed to turbulence model, scalar probability density function model, and scalar dissipation rate model). The hybrid DNS-CMC a posteriori test reveals an excellent agreement between the model and DNS for the cases with low levels of stratification, whereas deviations from the DNS are observed in cases which exhibit high level of stratifications. The a priori analysis reveals that the reason for disagreement is failure of the first-order closure hypothesis in the model due to the high level of conditional fluctuations. Second-order and double conditioning approaches are then evaluated in a priori tests to determine the most promising path forwards in addressing higher levels of stratification. The a priori tests use the DNS data to compute the model terms, thus directly evaluating the model assumptions. It is shown that in the cases with a high level of stratification, even the second-order estimation of the reaction rate source term cannot provide a reasonably accurate closure. Double conditioning using mixture-fraction and sensible enthalpy, however, provides an accurate first-order closure to the reaction rate source term.

Assessment of Algebraic Flame Surface Density Closures in the Context of Large Eddy Simulations of Head-On Quenching of Turbulent Premixed Flames

ABSTRACTThe applicability of algebraic large eddy simulation (LES) closures of flame surface density (FSD) for head-on quenching of premixed turbulent flames by an isothermal inert wall has been assessed using 3D direct numerical simulations (DNS) data for different values of root-mean-square turbulent velocity fluctuation, Damköhler and Karlovitz numbers. An algebraic FSD closure, which has been reported to perform relatively satisfactorily among several available models, has been considered for this analysis alongside a model, which has recently been used for LES of flame-wall interaction. The applicability of previously proposed near-wall damping factors for flame surface wrinkling and consumption rate in the context of Reynolds Averaged Navier Stokes (RANS) simulations has also been assessed for LES based on the current a-priori DNS analysis. It has been found that existing models considered for this analysis do not predict the near-wall behavior of the FSD accurately for all cases considered here. Furthermore, the widely used expression (where and are the unburned gas density and the laminar burning velocity, respectively) has been found to overpredict the combined reaction rate and molecular diffusion term in the near-wall region but the agreement between these terms gets better away from the wall. However, does not sufficiently capture the local behavior of the density-weighted surface filtered displacement speed so the correlation coefficient between and the combined reaction rate and molecular diffusion term remains much smaller than unity. It has been found that the damping factors proposed for RANS are not suitable for LES, and they severely damp the near-wall magnitudes of FSD and the combined reaction rate and molecular diffusion term and lead to significant under-predictions. Based on this a-priori analyses new near-wall modifications to the generalized FSD and the combined reaction and molecular diffusion term have been proposed in the context of LES, which have been found to capture both qualitative and quantitative trends obtained from DNS data.

Laminar forced convective heat transfer in helical pipe flow

Laminar forced convective heat transfer in a helical pipe with circular cross section subjected to wall heating was investigated numerically by three-dimensional (3D) direct numerical simulations (DNS) comparing with the experimental data obtained by Shatat (2010). The study was performed for three Prandtl numbers, Pr = 8.5, 7.5 and 4.02, over the wide range of torsion. In 3D steady calculations, we found the appearance of fully-developed axially invariant flow regions, where the averaged Nusselt number (averaged over the peripheral of the pipe cross section) were calculated, being in good agreement with the experimental data. Because of the effect of torsion on the heat transfer characteristics, the averaged Nusselt number exhibits repetition of decrease and increases as torsion increases from zero for all Reynolds numbers. It was found that there exists two maximums and two minimums of the averaged Nusselt number. It is interesting that the global minimum of the Nusselt number occurs at β≅0.1 and the global maximum at β≅0.55.

DNS study of dependence of bulk consumption velocity in a constant-density reacting flow on turbulence and mixture characteristics

3D Direct Numerical Simulation (DNS) study of propagation of a single-reaction wave in forced, statistically stationary, homogeneous, isotropic, and constant-density turbulence was performed in order to evaluate both developing UTt and fully developed UTs bulk turbulent consumption velocities by independently varying a ratio of 0.5 ≤u′∕SL≤ 90 of the r.m.s. turbulent velocity to the laminar wave speed and a ratio of 0.39 ≤L11∕δF≤ 12.5 of the longitudinal integral length scale of the turbulence to the laminar wave thickness. Accordingly, the Damköhler Da=(L11SL)∕(u′δF) and Karlovitz Ka=δF∕(SLτη) numbers were varied from 0.01 to 24.7 and from 0.36 to 587, respectively. Here, τη is the Kolmogorov time scale. The obtained DNS data show that, at sufficiently low Da, the fully developed ratio of UTs∕u′ is mainly controlled by Da and scales as Da. However, such a scaling should not be extrapolated to high Da. The higher Da (or the lower Ka), the less pronounced dependence of UTs∕u′ on a ratio of L11∕δF. Moreover, scaling laws UT∝u′αSL1−α(L11∕δF)β are substantially different for developing UTt and fully developed UTs, i.e., the scaling exponents α and, especially, β depend on the wave-development time. Furthermore, α and, especially, β depend on a method used to evaluate the developing UTt. Such effects can contribute to significant scatter of expressions for UT or ST as a function of {u′, SL, L11, δF}, obtained by parameterizing various experimental databases.

Direct numerical simulation study of statistically stationary propagation of a reaction wave in homogeneous turbulence.

A three-dimensional (3D) direct numerical simulation (DNS) study of the propagation of a reaction wave in forced, constant-density, statistically stationary, homogeneous, isotropic turbulence is performed by solving Navier-Stokes and reaction-diffusion equations at various (from 0.5 to 10) ratios of the rms turbulent velocity U^{'} to the laminar wave speed, various (from 2.1 to 12.5) ratios of an integral length scale of the turbulence to the laminar wave thickness, and two Zeldovich numbers Ze=6.0 and 17.1. Accordingly, the Damköhler and Karlovitz numbers are varied from 0.2 to 25.1 and from 0.4 to 36.2, respectively. Contrary to an earlier DNS study of self-propagation of an infinitely thin front in statistically the same turbulence, the bending of dependencies of the mean wave speed on U^{'} is simulated in the case of a nonzero thickness of the local reaction wave. The bending effect is argued to be controlled by inefficiency of the smallest scale turbulent eddies in wrinkling the reaction-zone surface, because such small-scale wrinkles are rapidly smoothed out by molecular transport within the local reaction wave.

Dual Fuel Combustion of N-heptane/methanol-air-EGR Mixtures

Numerical simulations are performed to study the combustion processes of n-heptane and methanol/air/EGR under high-temperature and high-pressure conditions relevant to a dual-fuel compression-ignition engine. Detailed chemical kinetic mechanism and transport properties are considered in the simulation. The simulations are carried out by performing three-dimensional (3D) direct numerical simulation (DNS) in a cuboid constant volume enclosure and two-dimensional (2D) DNS in a constant volume domain corresponding to the 3D domain. The results reveal three combustion modes involved in dual fuel engines, the ignition of the n-heptane jet, the propagation of thin reaction fronts in the methanol/air/EGR mixture, and finally the onset of ignition of the entire mixture. In dual-fuel combustion under high initial temperature conditions (1000K or higher) the three different combustion modes occur rather quickly with two distinct peaks of heat release corresponding to the two ignition modes. At low temperatures (800K or lower) the ignition delay time of the mixture is longer and more complete mixing is achieved before the onset of a single ignition of the n-heptane/methanol mixture.

Prediction of the secondary wake instability of a circular cylinder with direct numerical simulation

Abstract This paper presents an improved method for the prediction of the critical Reynolds number Recr for the secondary wake instability of flow past a circular cylinder based on three-dimensional (3D) direct numerical simulations (DNS). It is also found that insufficient mesh resolution in the plane perpendicular to the cylinder axis is a major cause for the over-prediction of Recr (∼ 200) reported in the literature using 3D DNS. It is demonstrated that the use of an optimized computational domain and mesh resolution (10 spanwise mesh layers to resolve only a half of a pair of the 3D mode) can reduce the computational cost significantly and yet retain adequate accuracy. The most accurate Recr predicted by the present DNS reduces to 190.74, which is consistent with independent linear stability analysis results of Recr ∼ 190. It is also demonstrated that 3D DNS is capable of accurately predicting the neutral curve for the secondary wake instability with a reasonable computational cost. The general conclusions drawn through a circular cylinder are expected to provide guidance on the prediction of Recr and neutral instability curve for other cylindrical objects.

Toward computationally efficient combustion DNS with complex fuels via principal component transport

We investigate the potential of accelerating chemistry integration during the direct numerical simulation (DNS) of complex fuels based on the transport equations of representative scalars that span the desired composition space using principal component analysis (PCA). The transport of principal components (PCs) can reduce the number of transported scalars and improve the spatial and temporal resolution requirements. The strategy is demonstrated using DNS of a premixed methane–air flame in a 2D vortical flow and is extended to the 3D geometry to demonstrate the resulting enhancement in the computational efficiency of PC transport. The PCs are derived from a priori PCA of the same composition space using DNS. This analysis is used to construct and tabulate the PCs’ chemical source terms in terms of the PCs using artificial neural networks (ANN). Comparison of DNS based on a full thermo-chemical state and DNS based on PC transport with six PCs shows excellent agreement even for terms that are not included in the PCA reduction. The transported PCs reproduce some of the salient features of strongly curved and strongly strained flames. The results also show a significant reduction of two orders of magnitude in the computational cost of the simulations, which enables an extension of the solution approach to 3D DNS under similar computational requirements.

Spanwise effects on instabilities of compressible flow over a long rectangular cavity

The stability properties of two- (2D) and three-dimensional (3D) compressible flows over a rectangular cavity with length-to-depth ratio of $L/D=6$ is analyzed at a free stream Mach number of $M_\infty=0.6$ and depth-based Reynolds number of $Re_D=502$. In this study, we closely examine the influence of three-dimensionality on the wake-mode that has been reported to exhibit high-amplitude fluctuations from the formation and ejection of large-scale spanwise vortices. Direct numerical simulation (DNS) and bi-global stability analysis are utilized to study the instability characteristics of the wake-mode. Using the bi-global stability analysis with the time-average flow as the base state, we capture the global stability properties of the wake-mode at a spanwise wavenumber of $\beta=0$. To uncover spanwise effects on the 2D wake-mode, 3D DNS are performed with cavity width-to-depth ratio of $W/D=1$ and $2$. We find that the 2D wake-mode is not present in the 3D cavity flow for a wider spanwise setting with $W/D=2$, in which spanwise structures are observed near the rear region of the cavity. These 3D instabilities are further investigated via bi-global stability analysis for spanwise wavelengths of $\lambda/D=0.5-2.0$ to reveal the eigenspectra of the 3D eigenmodes. Based on the findings of 2D and 3D global stability analysis, we conclude that the absence of the wake-mode in 3D rectangular cavity flows is due to the release of kinetic energy from the spanwise vortices to the streamwise vortical structures that develops from the spanwise instabilities.

A comparison between direct numerical simulation and experiment of the turbulent burning velocity-related statistics in a turbulent methane-air premixed jet flame at high Karlovitz number

A three-dimensional (3D) direct numerical simulation (DNS) of an experimental turbulent premixed jet flame at high Karlovitz number was studied. The DNS resolution adequately resolves both the flame and turbulence structures. A reduced chemical mechanism for premixed CH4/air flames with NOx based on GRI-Mech3.0 was used, including 268 elementary reactions, and 28 transported species. Consistent post-processing methods were applied to both the DNS and experimental data to evaluate turbulent burning velocity-related statistics, namely the flame surface density (FSD), and the flame curvature. Good agreement was achieved for the 2D comparisons. The DNS data were further analysed and provide 3D statistics unattainable from the experiment. The ratio of the 3D and 2D flame surface densities was estimated. The results are comparable with other values reported for various experimental flames. The 3D and 2D flame curvatures were also compared and their distributions are shown to be quite different owing to the round on-average geometry. Instantaneous images of the heat release surrogate, [CH2O][OH], between the DNS and experiment agreed qualitatively. Various other experimentally obtainable surrogates for heat release rate including [CH2O][H], [CH2O][O], [HCO], and [CH] are also evaluated and compared using the DNS. The inner structure of the flame was compared between the DNS and experiment in terms of the joint PDFs of OH concentration and temperature. Generally good agreement was obtained; discrepancies may be due to the inconsistency of assumed equilibrium levels of OH concentration in the co-flow.