Shinnosuke Nishiki

Modelling of turbulent scalar flux in turbulent premixed flames based on DNS databases

A transport equation for scalar flux in turbulent premixed flames was modelled on the basis of DNS databases. Fully developed turbulent premixed flames were obtained for three different density ratios of flames with a single-step irreversible reaction, while the turbulent intensity was comparable to the laminar burning velocity. These DNS databases showed that the countergradient diffusion was dominant in the flame region. Analyses of the Favre-averaged transport equation for turbulent scalar flux proved that the pressure related terms and the velocity–reaction rate correlation term played important roles on the countergradient diffusion, while the mean velocity gradient term, the mean progress variable gradient term and dissipation terms suppressed it. Based on these analyses, modelling of the combustion-related terms was discussed. The mean pressure gradient term and the fluctuating pressure term were modelled by scaling, and these models were in good agreement with DNS databases. The dissipation terms and the velocity–reaction rate correlation term were also modelled, and these models mimicked DNS well.

Modeling of flame-generated turbulence based on direct numerical simulation databases

Turbulent premixed flames propagating in homogeneous isotropic turbulent flows were simulated directly with a single-step irreversible reaction. Two cases were calculated, case H, with a high-density ratio of flame p u / p b =7.53, and case L, low-density ratio of flame p u / p b =2.50, while u′/u L was nearly equal to unity. We obtained databases of fully developed stationary turbulent flames. These databases were investigated by analyzing the transport equation for turbulent kinetic energy to study flame-generated turbulence and its models. We found that turbulent fluctuations of all components, especially the streamwise component, were amplified in the flame brush and that flame-generated turbulence increased for a larger density ratio of the flame. Analysis based on the Favre-averaged transport equation for turbulent kinetic energy showed that pressure-related terms produced kinetic energy in the flame brush, the mean pressure gradient term was most important in case H and the pressure work term was most important in case L. On the other hand, the diffusion and dissipation term and velocity gradient term decreased kinetic energy. Next, modeling of the important terms in the balance equations were discussed. The mean pressure gradient term, pressure dilatation term, and additional dissipation components were modeled and compared with the direct numerical simulation (DNS) results. The mean pressure gradient term was modeled with assumption on the density, and the model was in good agreement with DNS. The other two terms were also modeled by scaling and these models mimicked DNS well.

A direct numerical simulation study of vorticity transformation in weakly turbulent premixed flames

Database obtained earlier in 3D Direct Numerical Simulations (DNS) of statistically stationary, 1D, planar turbulent flames characterized by three different density ratios σ is processed in order to investigate vorticity transformation in premixed combustion under conditions of moderately weak turbulence (rms turbulent velocity and laminar flame speed are roughly equal to one another). In cases H and M characterized by σ = 7.53 and 5.0, respectively, anisotropic generation of vorticity within the flame brush is reported. In order to study physical mechanisms that control this phenomenon, various terms in vorticity and enstrophy balance equations are analyzed, with both mean terms and terms conditioned on a particular value c of the combustion progress variable being addressed. Results indicate an important role played by baroclinic torque and dilatation in transformation of average vorticity and enstrophy within both flamelets and flame brush. Besides these widely recognized physical mechanisms, two other effects are documented. First, viscous stresses redistribute enstrophy within flamelets, but play a minor role in the balance of the mean enstrophy Ω ¯ ¯ ¯ within turbulent flame brush. Second, negative correlation u ′ ⋅∇Ω ′ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ between fluctuations in velocity u and enstrophy gradient contributes substantially to an increase in the mean Ω ¯ ¯ ¯ within turbulent flame brush. This negative correlation is mainly controlled by the positive correlation between fluctuations in the enstrophy and dilatation and, therefore, dilatation fluctuations substantially reduce the damping effect of the mean dilatation on the vorticity and enstrophy fields. In case L characterized by σ = 2.5, these effects are weakly pronounced and Ω ¯ ¯ ¯ is reduced mainly due to viscosity. Under conditions of the present DNS, vortex stretching plays a minor role in the balance of vorticity and enstrophy within turbulent flame brush in all three cases.

DNS assessment of relation between mean reaction and scalar dissipation rates in the flamelet regime of premixed turbulent combustion

The linear relation between the mean rate of product creation and the mean scalar dissipation rate, derived in the seminal paper by K.N.C. Bray [‘The interaction between turbulence and combustion’, Proceedings of the Combustion Institute, Vol. 17 (1979), pp. 223–233], is the cornerstone for models of premixed turbulent combustion that deal with the dissipation rate in order to close the reaction rate. In the present work, this linear relation is straightforwardly validated by analysing data computed earlier in the 3D Direct Numerical Simulation (DNS) of three statistically stationary, 1D, planar turbulent flames associated with the flamelet regime of premixed combustion. Although the linear relation does not hold at the leading and trailing edges of the mean flame brush, such a result is expected within the framework of Brays theory. However, the present DNS yields substantially larger (smaller) values of an input parameter cm (or K2 = 1/(2cm − 1)), involved by the studied linear relation, when compared to the commonly used value of cm = 0.7 (or K2 = 2.5). To gain further insight into the issue and into the eventual dependence of cm on mixture composition, the DNS data are combined with the results of numerical simulations of stationary, 1D, planar laminar methane–air flames with complex chemistry, with the results being reported in terms of differently defined combustion progress variables c, i.e. the normalised temperature, density, or mole fraction of CH4, O2, CO2 or H2O. Such a study indicates the dependence of cm both on the definition of c and on the equivalence ratio. Nevertheless, K2 and cm can be estimated by processing the results of simulations of counterpart laminar premixed flames. Similar conclusions were also drawn by skipping the DNS data, but invoking a presumed beta probability density function in order to evaluate cm for the differently defined cs and various equivalence ratios.

Mechanism of flame evolution along a fine vortex

Flame evolution along an unstretched, fine, straight vortex was numerically simulated when a perpendicular pre-mixed flame interacted with the vortex. The flame developed along the vortex by producing a precursor azimuthal vortex, which accelerated the flame along the straight vortex. Higher density ratios increased the propagation speed and the peak of the azimuthal vorticity attached to the flame tip. At lower density ratios propagation speed was smaller and the peak azimuthal vortices separated from the flame tip. A baroclinic effect produced the azimuthal vortex on the flame during the initial stage of propagation, but convection and stretch effects produced another azimuthal vortex in front of the flame during the later stages. The propagation speed of the flame during later stages was generally proportional to the maximum circumferential velocity of the vortex tube, but the proportionality factor was also a positive function of the density ratio and the Reynolds number of the vortex.

A transport equation for reaction rate in turbulent flows

New transport equations for chemical reaction rate and its mean value in turbulent flows have been derived and analyzed. Local perturbations of the reaction zone by turbulent eddies are shown to play a pivotal role even for weakly turbulent flows. The mean-reaction-rate transport equation is shown to involve two unclosed dominant terms and a joint closure relation for the sum of these two terms is developed. Obtained analytical results and, in particular, the closure relation are supported by processing two widely recognized sets of data obtained from earlier direct numerical simulations of statistically planar 1D premixed flames associated with both weak large-scale and intense small-scale turbulence.

Mechanism of Interaction between a Vortex Pair and a Premixed Flame

Abstract Colliding interaction of a vortex pair with a premixed flame is numerically studied with a two-step reaction model including chain-branching and chain-breaking reactions. The vortex pair has a maximum circumferential velocity ranging from 4.7 to 54.7 times the laminar burning velocity and has a core diameter ranging from 1.1 to 1.55 times the flame thickness. Besides well-known interacting behaviors such as the flame wrinkling by a weak vortex pair and the pocket formation by a moderate vortex pair, an elongation of the concave flame without entraining the burned gas appears in the interaction with a strong vortex pair. The different behaviors of interaction are attributed to the ratio of the moving velocity of the vortex pair to the burning velocity and the criterion is represented by the ratio of the maximum circumferential velocity to the burning velocity. For moderate and strong vortices, vorticity generation due to the baroclinic effect and reduction of distance between vortex cores result i...

Flamelet perturbations and flame surface density transport in weakly turbulent premixed combustion

DNS data obtained under conditions of weak turbulence that are well associated with the flamelet combustion regime are analysed in order (i) to assess the widely-accepted linear relation between the mean mass rate of product creation and the mean Flame Surface Density (FSD) and (ii) to investigate transport of the FSD and the role played by local flamelet perturbations in the FSD transport. While, in line with common expectations, a ratio of is found to be close to the unperturbed laminar flame speed S0L within the largest part of the mean flame brush, this ratio is significantly smaller (larger) than S0L at the leading (trailing) edge of the flame brush. Nevertheless, under the conditions of the present study, this difference in and can be disregarded when computing burning velocity by integrating over the flame brush, provided that is extracted from the DNS data. Even in the case of weak turbulence addressed here, the FSD transport is substantially affected by the difference between local density-weighted displacement speed ρSd/ρu and S0L. This difference is associated with local perturbations of flamelet structure by turbulent eddies, with the local flamelet curvature (strain rate) playing a significantly more (less) important role in the FSD transport under the conditions of the present study. While the difference between ρSd/ρu and S0L in the FSD transport equation can be approximated with a linear function of the local flamelet curvature by processing the DNS data, Markstein lengths associated with such an approximation (i) are scattered, (ii) vary within the mean flame brush, and (iii) differ significantly from the counterpart laminar Markstein length.

Mechanism of Flame Propagation along a Vortex Tube

Vortex tubes are recognized as sinews of turbulence: The length of the vortex tube represents the integral scale of turbulence, the spacing of the nodes of the vortex tube represents the Taylor micro scale, and the diameter of the vortex tube represents the 10 times the Kolmogorov scale (Tanahashi and Miyauchi, 1999). Thus the interaction between a fine vortex tube and a flame seems to be an essential process in turbulent combustion. The aim of this work is to study the mechanism of flame propagation along a fine vortex tube of a premixed gas when the vortex tube interacts perpendicularly with the flame (Chomiak, 1976). It is well known that a premixed flame propagates rapidly with a velocity similar to the maximum circumferential velocity of the vortex core. It is also known that the premixed flame can propagate along the vortex tube when the maximum circumferential velocity is faster than the burning velocity and the core diameter is larger than the flame thickness (Hasegawa et al., 1995). However, the mechanism of the flame propagation is still not clear though several models have been proposed. In this study, the flame propagation along a fine vortex tube is numerically simulated and the mechanism that provokes the flame to propagate along the vortex tube is discussed in terms of the vorticity transport equation.

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 ρuW¯