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This article reports an analysis of the first detailed chemistry direct numerical simulation (DNS) of a high Karlovitz number laboratory premixed flame. The DNS results are first compared with those from laser-based diagnostics with good agreement. The subsequent analysis focuses on a detailed investigation of the flame area, its local thickness and their rates of change in isosurface following reference frames, quantities that are intimately connected. The net flame stretch is demonstrated to be a small residual of large competing terms: the positive tangential strain term and the negative curvature stretch term. The latter is found to be driven by flame speed–curvature correlations and dominated in net by low probability highly curved regions. Flame thickening is demonstrated to be substantial on average, while local regions of flame thinning are also observed. The rate of change of the flame thickness (as measured by the scalar gradient magnitude) is demonstrated, analogously to flame stretch, to be a competition between straining tending to increase gradients and flame speed variations in the normal direction tending to decrease them. The flame stretch and flame thickness analyses are connected by the observation that high positive tangential strain rate regions generally correspond with low curvature regions; these regions tend to be positively stretched in net and are relatively thinner compared with other regions. High curvature magnitude regions (both positive and negative) generally correspond with lower tangential strain; these regions are in net negatively stretched and thickened substantially.

In this paper we study the essential role of Darrieus–Landau (DL), hydrodynamic, cellular flame-front instability in the propagation of expanding turbulent flames. First, we analyse and compare the characteristic time scales of flame wrinkling under the simultaneous actions of DL instability and turbulent eddies, based on which three turbulent flame propagation regimes are identified, namely, instability dominated, instability–turbulence interaction and turbulence dominated regimes. We then perform experiments over an extensive range of conditions, including high pressures, to promote and manipulate the DL instability. The results clearly demonstrate the increase in the acceleration exponent of the turbulent flame propagation as these three regimes are traversed from the weakest to the strongest, which are respectively similar to those of the laminar cellularly unstable flame and the turbulent flame without flame-front instability, and thus validating the scaling analysis. Finally, based on the scaling analysis and the experimental results, we propose a modification of the conventional turbulent flame regime diagram to account for the effects of DL instability.

The dissipation element analysis is applied to the mixture fraction fields of a series of datasets from direct numerical simulations of non-premixed temporally evolving jet flames with jet Reynolds numbers ranging from 4500 to 10 000 and varying stoichiometric mixture fractions. Dissipation elements are space-filling regions where a scalar field behaves monotonically and allow for the analysis of scalar fields in homogeneous isotopic turbulence as well as in complex, highly inhomogeneous and anisotropic flows such as turbulent flames. Statistics of the dissipation element parameters of non-premixed flames are compared to those obtained from non-reacting jets. It is found that the universality of the normalized length distribution of the dissipation elements observed in non-reacting cases also holds true for the reacting flows. The characteristic scaling with the Kolmogorov micro-scale $\\eta$ is obtained as well. The effects of combustion on the scalar difference in the dissipation elements are shown and are found to diminish as the Reynolds number and the fuel dilution is increased. The dissipation elements provide the means for a local comparison of the turbulent and characteristic flame scales. A new regime diagram for non-premixed combustion is introduced using coherent structures in the scalar fields, the dissipation element parameters for a local classification of the turbulent flame surface into flamelet-like zones and fine-scale mixing zones in addition to the burning and non-burning zones. The soundness of the regime diagram and the potential consequences for combustion modelling in the individual regimes is demonstrated by the investigation of the correlation between the chemical field and the dissipation element parameters in the individual regimes.

An oblique detonation wave in two-phase kerosene–air mixtures over a wedge is numerically studied for the first time. The features of initiation and stabilisation of the two-phase oblique detonation are emphasised, and they are different from those in previous studies on single-phase gaseous detonation. The gas–droplet reacting flow system is solved by means of a hybrid Eulerian–Lagrangian method. The two-way coupling for the interphase interactions is carefully considered using a particle-in-cell model. For discretisation of the governing equations of the gas phase, a WENO-CU6 scheme (Hu et al., J. Comput. Phys., vol. 229 (23), 2010, pp. 8952–8965) and a sixth-order compact scheme are employed for the convective terms and the diffusive terms, respectively. The inflow parameters are chosen properly from real flight conditions. The fuel vapour, droplets and their mixture are taken as the fuel in homogeneous streams with a stoichiometric ratio, respectively. The effects of evaporating droplets and initial droplet size on the initiation, transition from oblique shock to detonation and stabilisation are elucidated. The two-phase oblique detonation wave is stabilised from the oblique shock wave induced by the wedge. As the mass flow rate of droplets increases, a shift from a smooth transition with a curved shock to an abrupt one with a multi-wave point is found, and the initiation length of the oblique detonation increases, which is associated with the increase of the transition pressure. By increasing the initial droplet size, a smooth transition pattern is observed, even if the equivalence ratio remains constant, and the transition pressure decreases. The factor responsible is incomplete evaporation before the detonation fronts, which results in a complicated flame structure, including regimes of formation of oblique detonation, evaporative cooling of droplets and post-detonation reaction.

The present work focuses on the flame–wall interaction (FWI) based on direct numerical simulations (DNS) of a head-on premixed flame quenching configuration at the statistically stationary state. The effects of FWI on the turbulent flame temperature, wall heat flux, flame dynamics and flow structures were investigated. In turbulent head-on quenching, particularly for high turbulence intensity, the distorted flames generally consist of the head-on flame part and the entrained flame part. The flame properties are jointly influenced by turbulence, heat generation from chemical reactions and heat loss to the cold wall boundary. For the present FWI configuration, as the wall is approached, the ‘influence zone’ can be identified as the region within which the flame temperature, scalar gradient and flame dilatation start to decrease, whereas the wall heat flux tends to increase. As the distance to the wall drops below the flame-quenching distance, approximately where the wall heat flux reaches its maximum value, chemical reactions become negligibly weak inside the ‘quenching zone’. A simplified counter-flow model is also proposed. With the reasonably proposed relation between the flame speed and the flame temperature, the model solutions match well with the DNS results, both qualitatively and quantitatively. Moreover, near-wall statistics of some important flame properties, including the flame dilatation, reaction progress variable gradient, tangential strain rate and curvature were analysed in detail under different wall boundary conditions.

In this study, we assess the veracity of models for density-weighted local flame displacement speed of turbulent premixed flames. It will be shown that a combination of two models, one for the weakly stretched laminar flame state and another derived for a configuration where a curved laminar flame interacts with itself to annihilate, can describe most local realizations of a turbulent premixed flame. To that end, we have performed direct numerical simulations of a reactive mixture of hydrogen–air at atmospheric pressure using a detailed chemical reaction mechanism and analysed the dataset with recently developed flame particle tracking techniques. Forward tracking a large number of flame particles from the generating locations of the corresponding flame surfaces (given by backward tracking) to the corresponding annihilating locations, creates a manifold of local states that can represent nearly all possible states realizable for the turbulent premixed flame under consideration. With all the states of the flame accessible over time, we first assess the applicability of the two-parameter Markstein length based flame speed model. It is found that the model prediction is reasonably accurate for a significant part of the flame particles’ lifetime, for turbulent premixed flames with Karlovitz number $O(10)$ . However, during the final stage of annihilation of the flame particles in the negatively curved trailing regions, the local structure of the flame no longer resembles a standard premixed flame, even qualitatively. A new interaction model for the flame displacement speed, during these final stages of annihilation of the flame elements, has been derived.

Direct numerical simulation (DNS) of the near field of a three-dimensional spatially developing turbulent lifted hydrogen jet flame in heated coflow is performed with a detailed mechanism to determine the stabilization mechanism and the flame structure. The DNS was performed at a jet Reynolds number of 11,000 with over 940 million grid points. The results show that auto-ignition in a fuel-lean mixture at the flame base is the main source of stabilization of the lifted jet flame. A chemical flux analysis shows the occurrence of near-isothermal chemical chain branching preceding thermal runaway upstream of the stabilization point, indicative of hydrogen auto-ignition in the second limit. The Damköhler number and key intermediate-species behaviour near the leading edge of the lifted flame also verify that auto-ignition occurs at the flame base. At the lifted-flame base, it is found that heat release occurs predominantly through ignition in which the gradients of reactants are opposed. Downstream of the flame base, both rich-premixed and non-premixed flames develop and coexist with auto-ignition. In addition to auto-ignition, Lagrangian tracking of the flame base reveals the passage of large-scale flow structures and their correlation with the fluctuations of the flame base. In particular, the relative position of the flame base and the coherent flow structure induces a cyclic motion of the flame base in the transverse and axial directions about a mean lift-off height. This is confirmed by Lagrangian tracking of key scalars, heat release rate and velocity at the stabilization point.

This paper develops an oscillation-free discontinuous Galerkin (OFDG) method for solving the multi-component chemically reacting flows. Two common governing equations are considered: reactive Euler equations and Navier–Stokes equations. Based on our recently developed high-order bound-preserving discontinuous Galerkin method in Du and Yang (J Comput Phys 469:111548, 2022), we add an extra damping term into this scheme to control the spurious oscillations. With the careful construction of the damping term, the proposed method not only achieves non-oscillatory property without sacrificing any order of accuracy but also preserves the conservative property which is the key ingredient of the bound-preserving technique developed in Du and Yang (2022). Therefore, the proposed OFDG method is well-compatible with the bound-preserving limiter in Du and Yang (2022). Similar to Liu et al. (SIAM J Sci Comput 44:A230–A259, 2022), the conservative modified exponential Runge–Kutta method is used to relax the restriction of time step sizes and preserve the conservative property of the fully discrete schemes. Numerical experiments, including one- and two-dimensional space, demonstrate the proposed method has desired properties.

Tubular flames represent a canonical combustion configuration that can simplify reacting flow analysis and also be employed in practical power generation systems. In this paper, a theoretical model for non-premixed tubular flames, with delivery of liquid fuel through porous walls into a swirling flow field, is presented. Perturbation theory is used to analyse this new tubular flame configuration, which is the non-premixed equivalent to a premixed swirl-type tubular burner – following the original classification of premixed tubular systems into swirl and counterflow types. The incompressible viscous flow field is modelled with an axisymmetric similarity solution. Axial decay of the initial swirl velocity and surface mass transfer from the porous walls are considered through the superposition of laminar swirling flow on a Berman flow with uniform mass injection in a straight pipe. The flame structure is obtained assuming infinitely fast conversion of reactants into products and unity Lewis numbers, allowing the application of the Shvab–Zel’dovich coupling function approach.

In this study, we developed a new reacting flow solver based on OpenFOAM (OF) and Cantera, with the capabilities of (i) dealing with detailed species transport and chemistry, (ii) integration using a well-balanced splitting scheme, and (iii) two advanced computational diagnostic methods. First of all, a flaw of the original OF chemistry model to deal with pressure-dependent reactions is fixed. This solver then couples Cantera with OF so that the robust chemistry reader, chemical reaction rate calculations, ordinary differential equations (ODEs) solver, and species transport properties handled by Cantera can be accessed by OF. In this way, two transport models (mixture-averaged and constant Lewis number models) are implemented in the coupled solver. Finally, both the Strang splitting scheme and a well-balanced splitting scheme are implemented in this solver. The newly added features are then assessed and validated via a series of auto-ignition tests, a perfectly stirred reactor, a 1D unstretched laminar premixed flame, a 2D counter-flow laminar diffusion flame, and a 3D turbulent partially premixed flame (Sandia Flame D). It is shown that the well-balanced property is crucial for splitting schemes to accurately capture the ignition and extinction events. To facilitate the understanding on combustion modes and complex chemistry in large scale simulations, two computational diagnostic methods (conservative chemical explosive mode analysis, CCEMA, and global pathway analysis, GPA) are subsequently implemented in the current framework and used to study Sandia Flame D for the first time. It is shown that these two diagnostic methods can extract the flame structure, combustion modes, and controlling global reaction pathways from the simulation data.