KAUST DepartmentApplied Mathematics and Computational Science Program
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AbstractWe consider a simplified model for the dynamics of one-dimensional detonations with generic losses. It consists of a single partial differential equation that reproduces, at a qualitative level, the essential properties of unsteady detonation waves, including pulsating and chaotic solutions. In particular, we investigate the effects of shock curvature and friction losses on detonation dynamics. To calculate steady-state solutions, a novel approach to solving the detonation eigenvalue problem is introduced that avoids the well-known numerical difficulties associated with the presence of a sonic point. By using unsteady numerical simulations of the simplified model, we also explore the nonlinear stability of steady-state or quasi-steady solutions. © 2014 The Combustion Institute.
SponsorsThe research reported here was supported by King Abdullah University of Science and Technology (KAUST).
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Turbulent deflagrations, autoignitions, and detonationsBradley, Derek; Lawes, Malcolm; Mansour, Morkous S. (Pleiades Publishing Ltd, 2012-09)Measurements of turbulent burning velocities in fan-stirred explosion bombs show an initial linear increase with the fan speed and RMS turbulent velocity. The line then bends over to form a plateau of high values around the maximum attainable burning velocity. A further increase in fan speed leads to the eventual complete quenching of the flame due to increasing localised extinctions because of the flame stretch rate. The greater the Markstein number, the more readily does flame quenching occur. Flame propagation along a duct closed at one end, with and without baffles to increase the turbulence, is subjected to a one-dimensional analysis. The flame, initiated at the closed end of the long duct, accelerates by the turbulent feedback mechanism, creating a shock wave ahead of it, until the maximum turbulent burning velocity for the mixture is attained. With the confining walls, the mixture is compressed between the flame and the shock plane up to the point where it might autoignite. This can be followed by a deflagration to detonation transition. The maximum shock intensity occurs with the maximum attainable turbulent burning velocity, and this defines the limit for autoignition of the mixture. For more reactive mixtures, autoignition can occur at turbulent burning velocities that are less than the maximum attainable one. Autoignition can be followed by quasi-detonation or fully developed detonation. The stability of ensuing detonations is discussed, along with the conditions that may lead to their extinction. © 2012 by Pleiades Publishing, Ltd.
Three-dimensional detonation cellular structures in rectangular ducts using an improved CESE schemeShen, Yang; Shen, Hua; Liu, Kai Xin; Chen, Pu; Zhang, De Liang (IOP Publishing, 2016-11-01)The three-dimensional premixed H2-O2 detonation propagation in rectangular ducts is simulated using an in-house parallel detonation code based on the second-order space–time conservation element and solution element (CE/SE) scheme. The simulation reproduces three typical cellular structures by setting appropriate cross-sectional size and initial perturbation in square tubes. As the cross-sectional size decreases, critical cellular structures transforming the rectangular or diagonal mode into the spinning mode are obtained and discussed in the perspective of phase variation as well as decreasing of triple point lines. Furthermore, multiple cellular structures are observed through examples with typical aspect ratios. Utilizing the visualization of detailed three-dimensional structures, their formation mechanism is further analyzed.
Numerical Computation of Detonation StabilityKabanov, Dmitry (2018-06-03)Detonation is a supersonic mode of combustion that is modeled by a system of conservation laws of compressible fluid mechanics coupled with the equations describing thermodynamic and chemical properties of the fluid. Mathematically, these governing equations admit steady-state travelling-wave solutions consisting of a leading shock wave followed by a reaction zone. However, such solutions are often unstable to perturbations and rarely observed in laboratory experiments. The goal of this work is to study the stability of travelling-wave solutions of detonation models by the following novel approach. We linearize the governing equations about a base travelling-wave solution and solve the resultant linearized problem using high-order numerical methods. The results of these computations are postprocessed using dynamic mode decomposition to extract growth rates and frequencies of the perturbations and predict stability of travelling-wave solutions to infinitesimal perturbations. We apply this approach to two models based on the reactive Euler equations for perfect gases. For the first model with a one-step reaction mechanism, we find agreement of our results with the results of normal-mode analysis. For the second model with a two-step mechanism, we find that both types of admissible travelling-wave solutions exhibit the same stability spectra. Then we investigate the Fickett’s detonation analogue coupled with a particular reaction-rate expression. In addition to the linear stability analysis of this model, we demonstrate that it exhibits rich nonlinear dynamics with multiple bifurcations and chaotic behavior.