On the tulip flame formation: the effect of pressure waves

The effects of pressure waves on the tulip flame formation in closed and semi-open tubes were studied using numerical simulations of the fully compressible Navier-Stokes equations coupled to a detailed chemical model for stoichiometric hydrogen air mixture. Rarefaction waves generated by the decelerating flame are shown to be the primary physical process leading to the flame front inversion and the tulip flame formation for spark and for planar ignited flames in closed tubes. In the case of a spark ignited flame, the first rarefaction wave is generated by the flame, which is decelerating due to the reduction in flame surface area as the flame skirt touches the tube walls. Flame collisions with pressure waves in a closed tube result in additional deceleration stages and rarefaction waves that shorten the time of the tulip flame formation.Comment: 13 pages, 12 figure

On the mechanism of "tulip flame" formation: the effect of ignition sources

The early stages of hydrogen-air flame dynamics and the physical mechanism of tulip flame formation were studied using high-resolution numerical simulations to solve the two-dimensional fully compressible Navier-Stokes equations coupled with a one-step chemical model, which was calibrated to obtain the correct the laminar flame velocity-pressure dependence. The formation of tulip flames was investigated for a flame ignited by a spark or by a planar ignition and propagating to the opposite closed or open end. For a flame ignited by a spark on-axis at the closed end of the tube and propagating to the opposite closed or open end, a tulip flame is created by a tulip-shaped axial velocity profile in the unburned gas flow near the flame front caused by the rarefaction wave(s) created by the flame during the deceleration stage(s). It is shown that, in a tube with both closed ends, this mechanism of tulip flame formation also holds for flames initiated by planar ignition. The deceleration stages in the case of planar ignition are caused by collisions of the flame front with pressure waves reflected from the opposite end of the tube. In the case of a flame initiated by planar ignition and propagating toward the open end, the mechanism of tulip flame formation is related to the stretching of the flame skirt edges backward along the side wall of the tube due to wall friction, which leads to the formation of bulges in the flame front near the tube walls. The bulges grow and finally meet at the axis of the tube, forming a tulip-shaped flame. Regardless of the method of flame initiation at the closed end, no distorted tulip flame is formed when the flame propagates to the open end of the tube.Comment: 37 pages, 12 figures. arXiv admin note: text overlap with arXiv:2209.0070

On the formation of a tulip flame in closed and semi-open tubes

The paper examines the mechanism of the tulip flame formation for the flames propagating in closed tubes of various aspect ratios and in a half-open tube. The formation of tulip flames in 2D channels is studied using high resolution direct numerical simulations of the reactive Navier Stokes equations coupled with a detailed chemical model for a stoichiometric hydrogen/air flame. It is shown that rarefaction waves generated by the flame during the deceleration stage play a key role in the tulip-shaped flame formation. The interaction of the reverse flow created behind the rarefaction wave with previously produced be accelerating flame flow in the unburned gas, results in the decrease of the flow velocity in the near field zone ahead of the flame and in the increase of the boundary layer thickness. The profile of the axial velocity close ahead of the flame takes the form of an inverted tulip. Therefore, the flame front acquires a tulip shape repeating to a large extent the shape of the of the axial velocity profile in the upstream flow.Comment: 44 pages, 23 figure

Bifurcation of pulsation instability in one-dimensional H2−O2 detonation with detailed reaction mechanism

Classical modes of one-dimensional (1D) detonation characterized by a simplified reaction model are reproduced by using a real chemical kinetics for the H2−O2 system with argon dilution. As Ar dilution is varied, the bifurcation points of pulsating instability are identified and a formed bifurcation diagram is compared with that obtained by the one-step reaction model. Eventually, the numerical results demonstrate that, for real detonations with detailed chemistry, the criterion of Ng et al. works well on prediction of the 1D detonation instability. Furthermore, the detonability limits are found respectively at low and high Ar dilutions. Above the high Ar dilution limit, detonations decays to the minimum level where long autoignition time and small heat release rate make reestablishment impossible for both 1D and 2D simulations. However, below the low Ar dilution limit, a 1D detonation cannot be sustained due to high instability, while the corresponding cellular detonation can propagate sustainably due to the role of transverse instability

Superconvergence of the local discontinuous Galerkin method for nonlinear convection-diffusion problems

Abstract In this paper, we discuss the superconvergence of the local discontinuous Galerkin methods for nonlinear convection-diffusion equations. We prove that the numerical solution is ( k + 3 / 2 ) $(k+3/2)$ th-order superconvergent to a particular projection of the exact solution, when the upwind flux and the alternating fluxes are used. The proof is valid for arbitrary nonuniform regular meshes and for piecewise polynomials of degree k ( k ≥ 1 $k\geq1$ ). The numerical experiments reveal that the property of superconvergence actually holds true for general fluxes

High-order bound-preserving discontinuous Galerkin methods for stiff multispecies detonation

© 2019 Society for Industrial and Applied Mathematics In this paper, we develop high-order bound-preserving discontinuous Galerkin (DG) methods for multispecies and multireaction chemical reactive flows. In this problem, density and pressure are nonnegative, and the mass fraction for the ith species, denoted as zi, 1 ≤ i ≤ M, should be between 0 and 1, where M is the total number of species. In [C. Wang, X. Zhang, C.-W. Shu, and J. Ning, J. Comput. Phys., 231 (2012), pp. 653-665], the authors have introduced the positivity-preserving technique that guarantees the positivity of the numerical density, pressure, and the mass fraction of the first M − 1 species. However, the extension to preserve the upper bound 1 of the mass fraction is not straightforward. There are three main difficulties. First of all, the time discretization in [C. Wang, X. Zhang, C.-W. Shu, and J. Ning, J. Comput. Phys., 231 (2012), pp. 653-665] was based on Euler forward. Therefore, for problems with stiff source, the time step will be significantly limited. Secondly, the mass fraction does not satisfy a maximum principle, and most of the previous techniques cannot be applied. Thirdly, in most of the previous works for gaseous denotation, the algorithm relies on the second-order Strang splitting methods where the flux and stiff source terms can be solved separately, and the extension to high-order time discretization seems to be complicated. In this paper, we will solve all the three problems given above. The high-order time integration does not depend on the Strang splitting; i.e., we do not split the flux and the stiff source terms. Moreover, the time discretization is explicit and can handle the stiff source with large time step. Most importantly, in addition to the positivity-preserving property introduced in [C. Wang, X. Zhang, C.-W. Shu, and J. Ning, J. Comput. Phys., 231 (2012), pp. 653-665], the algorithm can preserve the upper bound 1 for each species. Numerical experiments will be given to demonstrate the good performance of the bound-preserving technique and the stability of the scheme for problems with stiff source terms

Convergence properties of detonation simulations

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