Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

  title={Linear stability analysis of detonations via numerical computation and dynamic mode decomposition},
  author={Dmitry Kabanov and Aslan R. Kasimov},
  journal={arXiv: Fluid Dynamics},
We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The… 

Detonation modeling with the particles on demand method

A kinetic model based on the particles on demand method is introduced for gas phase detonation hydrodynamics in conjunction with the Lee–Tarver reaction model. The proposed model is realized on two-

Effect of equivalence ratio fluctuations on planar detonation discontinuities

Abstract We propose a linear asymptotic theory to describe the propagation of planar detonation fronts through heterogeneous mixtures of reactive gases consisting of random fluctuations in the fuel

Detonation model using Burgers equation and a pulsed reaction

This study uses a simplified detonation model to investigate the behaviour of detonations with galloping-like pulsations. The reactive Burgers equation is used for the hydrodynamic equation, coupled

Modeling thermodynamic trends of rotating detonation engines

The formation of a number of co- and counter-rotating coherent combustion wave fronts is the hallmark feature of the Rotating Detonation Engine (RDE). The engineering implications of wave topology

Multiplicity of detonation regimes in systems with a multi-peaked thermicity

The study investigates detonations with multiple quasi-steady velocities that have been observed in the past in systems with multi-peaked thermicity, using Fickett's detonation analogue. A

Resonance and mode locking in gaseous detonation propagation in a periodically nonuniform medium

In this work, we analyze numerically the dynamics of one-dimensional gaseous detonations propagating in a mixture with periodically varying properties such as density, temperature, or mixture

Data-driven surrogates of rotating detonation engine physics with neural ordinary differential equations and high-speed camera footage

  • J. Koch
  • Physics
    Physics of Fluids
  • 2021
Interacting multi-scale physics present in the Rotating Detonation Engine lead to diverse nonlinear dynamical behavior, including combustion wave mode-locking, modulation, and bifurcations. In this

Two separate decay timescales of a detonation wave modeled by the Burgers equation and their relation to its chaotic dynamics.

A simplified detonation model is used to investigate the behavior of detonations with galloping-like pulsations, revealing a sawtooth evolution of the front velocity with a period-averaged detonation speed equal to the Chapman-Jouguet velocity.

A minimal hyperbolic system for unstable shock waves

Shock wave structures in an isentropically unstable heat-releasing gas

In this work, we analytically and numerically investigate the types of stationary gasdynamic waves formed in a heat-releasing medium with isentropic (acoustic) instability. As the mathematical model,



Mode selection in weakly unstable two-dimensional detonations

A formulation of the reactive Euler equations in the shock-attached frame is used to study the two-dimensional instability of weakly unstable detonation through direct numerical simulation. The

Linear stability of idealized detonations

  • G. Sharpe
  • Mathematics
    Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 1997
In this paper we describe a new normal‐modes approach to the linear stability problem of an idealized detonation having an Arrhenius form of the reaction rate, with emphasis on Chapman–Jouguet

Recent Results on Stability of Planar Detonations

We describe recent analytical and numerical results on stability and behavior of viscous and inviscid detonation waves obtained by dynamical systems/Evans function techniques like those used to study

Cellular detonation stability. Part 1. A normal-mode linear analysis

A detailed investigation of the hydrodynamic stability to transverse linear disturbances of a steady, one-dimensional detonation in an ideal gas undergoing an irreversible, unimolecular reaction with

Efficient numerical stability analysis of detonation waves in ZND

As described in the classic works of Lee--Stewart and Short--Stewart, the numerical evaluation of linear stability of planar detonation waves is a computationally intensive problem of considerable

Calculation of linear detonation instability: one-dimensional instability of plane detonation

The detonation stability problem is studied by a normal mode approach which greatly simplifies the calculation of linear instability of detonation in contrast to the Laplace transform procedure used

Initial-value problem for small disturbances in an idealized one-dimensional detonation

The solution of the initial-value problem for linearized reactive Euler equations is presented as an expansion into modes of discrete and continuous spectra in the case of one-dimensional

Stability of Step Shocks

The hydrodynamic stability of a steady, plane, step shock through a fluid medium with arbitrary equation of state is investigated through consideration of the initial‐value problem for the