Numerical solution of under-resolved detonations

Tosatto, Luca; Vigevano, Luigi

doi:10.1016/j.jcp.2007.10.011

Cited by 33 publications

(31 citation statements)

References 24 publications

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“…Numerical simulations of the reacting flows deal with the time-dependent Navier-Stokes equations which include strongly nonlinear terms in the right hand part and become stiff if the characteristic time scales of the corresponding processes (chemical kinetics, relaxation etc.) are much less than characteristic gasdynamical time scales [51][52][53][54][55][56]. The stiff terms in the equations demand using specific methods to achieve reliable solution.…”

Section: Appendix A: the Numerical Methodsmentioning

confidence: 99%

Ignition of deflagration and detonation ahead of the flame due to radiative preheating of suspended micro particles

Иванов

Киверин

Liberman

2015

Combustion and Flame

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We study a flame propagating in the gaseous combustible mixture with suspended inert solid micro particles. The gaseous mixture is assumed to be transparent for the radiation emitted by the combustion products, while particles absorb and re-emit the radiation. Thermal radiation heats the particles, which in turn transfer the heat to the surrounding unburned gaseous mixture by means of heat conduction, so that the gas phase temperature lags that of the particles. We consider different scenarios depending on the spatial distribution of the particles, their size and the number density. In the case of uniform spatial distribution of the particles the radiation causes a modest increase of the temperature ahead of the flame and corresponding modest increase of the combustion velocity. The effects of radiation preheating as stronger as smaller the normal flame velocity. On the contrary, in the case of non-uniform distribution of the particles, such that the particles number density is relatively small in the region just ahead of the flame front and increases in the distant region ahead of the flame, the preheating caused by the thermal radiation absorption may trigger additional independent source of ignition. This scenario requires the formation of a temperature gradient with the maximum temperature sufficient for ignition in the region of denser particles cloud ahead of the advancing flame. Depending on the steepness of the temperature gradient formed in the unburned mixture, either deflagration or detonation can be initiated via the Zeldovich's gradient mechanism. The ignition and the resulting combustion regimes depend on the number density profile and, correspondingly, on the temperature profile which is formed in effect of radiation absorption and gas-dynamic expansion. In the case of coal dust flames propagating through a layered dust cloud the effect of radiation heat transfer can result in the propagation of combustion wave with velocity up to 1000m/s and can be a plausible explanation of the origin of dust explosion in coal mines.

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Section: Appendix A: the Numerical Methodsmentioning

confidence: 99%

Ignition of deflagration and detonation ahead of the flame due to radiative preheating of suspended micro particles

Иванов

Киверин

Liberman

2015

Combustion and Flame

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“…The test case is the Arrhenius case considered in several papers (see Refs. 2,7,[30][31][32] ). The initial values consist of totally burned gas on the left-hand side and totally unburned gas on the right-hand side.…”

Section: Spurious Behavior Of Numerical Schemesmentioning

confidence: 99%

“…WENO5/SR and WENO5fi+split can capture the correct structure using fewer grid points than those in Helzel et al 31 and Tosatto & Vigevano. 32 It is remarked that with such a coarse grid it is not possible to resolve the detonation front within one to several grid cells. Here we only concern with the correct speed of discontinuities propagation using a very coarse grid.…”

Section: Spurious Behavior Of Numerical Schemesmentioning

confidence: 99%

1D and 2D Simulaations Related to the NASA Electric Arc Shock Tube Experiments

Kotov

Yee

Panesi

et al. 2013

21st AIAA Computational Fluid Dynamics Conference

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The goal of this study is to gain an understanding of the computational challenges for the numerical simulations related to the experiments on the NASA Electric Arc Shock Tube (EAST). The paper focuses on the spurious numerics which take place in numerical simulations of the problems containing stiff source terms and discontinuities. Some results of the previous study on the spurious behavior of numerical methods are given first. Then the results of the 1D and 2D EAST simulations using a simplified physical model are presented. The obtained results illustrate the phenomena that the discontinuity locations depend on grid spacing and numerical method for this problem.

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“…Helzel [21] proposed a modified fractional step method for under-resolved detonation waves, in which the exact Riemann solution is required to determine where burning should occur. Tosatto & Vigevano [43] proposed a MinMax method, based on a two-value variable reconstruction within each cell, where the appropriate maximum and minimum values of the unknown are considered within the local neighbouring cells. In [45] Wang et al proposed a new high-order finite-difference method utilizing the idea of Harten ENO subcell resolution method for stiff source terms with a single reaction and in [47] well-balanced high-order nonlinear filter schemes were added to the subcell resolution method for reacting flows, effectively delaying the onset of wrong speed of propagation in coarse grids and moderate stiff source terms.…”

Section: Introductionmentioning

confidence: 99%

A split random time-stepping method for stiff and nonstiff detonation capturing

Wang

Pan

et al. 2019

Combustion and Flame

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In this paper, a new fractional step method is proposed for simulating stiff and nonstiff chemically reacting flows. In stiff cases, a well-known spurious numerical phenomenon, i.e. the incorrect propagation speed of discontinuities, may be produced by general fractional step methods due to the under-resolved discretization in both space and time. The previous random projection method has been successfully applied for stiff detonation capturing in under-resolved conditions. Not to randomly project the intermediate state into two presumed equilibrium states (completely burnt or unburnt) as in the random projection method, the present study is to randomly choose the time-dependent advance or stop of a reaction process. Each one-way reaction has been decoupled from the multi-reaction kinetics using operator splitting and the local smeared temperature due to numerical dissipation of shock-capturing schemes is compared with a random one within two limited temperatures corresponding to the advance and its inverse states, respectively, to control the random reaction. The random activation or deactivation in the reaction step is thus promising to correct the deterministic accumulative error of the propagation of discontinuities. Extensive numerical experiments, including model problems and realistic reacting flows in one and two dimensions, demonstrate this expectation as well as the effectiveness and robustness of the method. Meanwhile, for nonstiff problems when spatial and temporal resolutions are fine, the proposed random method recovers the results as general fractional step methods, owing to the increasing possibility of activation with diminishing randomness by adding a shift term.

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Numerical solution of under-resolved detonations

Cited by 33 publications

References 24 publications

Ignition of deflagration and detonation ahead of the flame due to radiative preheating of suspended micro particles

Ignition of deflagration and detonation ahead of the flame due to radiative preheating of suspended micro particles

1D and 2D Simulaations Related to the NASA Electric Arc Shock Tube Experiments

A split random time-stepping method for stiff and nonstiff detonation capturing

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