Simulations of pulsating one-dimensional detonations with true fifth order accuracy

Henrick, Andrew; Aslam, Tariq D.; Powers, Joseph M.

doi:10.1016/j.jcp.2005.08.013

Cited by 110 publications

(135 citation statements)

References 32 publications

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“…To achieve global high accuracy (or convergence rate) of numerical methods, higher-order schemes combined with shock-fitting technique are being developed so as to avoid the corrupting influences of numerical viscosity introduced in common shock-capturing methods (e.g. Henrick, Aslam & Powers 2006;Rawat & Zhong 2010). Nevertheless, the application of shock-fitted methods for highly compressible flows with complex shock topologies remains technically challenging.…”

Section: Methodsmentioning

confidence: 99%

Numerical study on unstable surfaces of oblique detonations

2014

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In this study, the onset of cellular structure on oblique detonation surfaces is investigated numerically using a one-step irreversible Arrhenius reaction kinetic model. Two types of oblique detonations are observed from the simulations. One is weakly unstable characterized by the existence of a planar surface, and the other is strongly unstable characterized by the immediate formation of the cellular structure. It is found that a high degree of overdrive suppresses the formation of cellular structures as confirmed by the results of many previous studies. However, the present investigation demonstrates that cellular structures also appear with degree of overdrive of 2.06 and 2.37, values much higher than ∼1.8 suggested previously in the literature for the critical value defining the instability boundary of oblique detonations. This contradiction could be explained by the use of differently shaped walls, a straight wall used in this study and a custom-designed curved wedge system so as to induce straight oblique detonations in previous studies. Another possible reason could be due to the low and possibly insufficient resolution used in previously published studies. Hence, simulations with different grid sizes are also performed to examine the effect of resolution on the numerical solutions. Using the present results, analysis also shows that although the characteristic lengths of unstable surfaces are different when the incident Mach number changes, these length scales are proportional to tangential velocities. Hence, the interior time determined by the overdrive degree is identified, and its limitation as the instability parameter is discussed.

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Section: Methodsmentioning

confidence: 99%

Numerical study on unstable surfaces of oblique detonations

2014

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“…The perturbation quickly leads to the formation of transverse waves and a 2-D detonation in the channel. It is well demonstrated that to correctly resolve the time-dependent structure of the detonations by numerical simulations very fine meshes should be used ( [12,32,53,60]). In a 2-D simulation, Sharpe [32] observed that a grid resolution less than about 20 cells in HRL gives poor prediction of the detonation structure.…”

Section: Boundary and Initial Conditions And Grid Resolutionmentioning

confidence: 99%

Hydrodynamic Instabilities in Gaseous Detonations: Comparison of Euler, Navier–Stokes, and Large-Eddy Simulation

Mahmoudi

Karimi

Deiterding

et al. 2014

Journal of Propulsion and Power

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A large-eddy simulation is conducted to investigate the transient structure of an unstable detonation wave in two dimensions and the evolution of intrinsic hydrodynamic instabilities. The dependency of the detonation structure on the grid resolution is investigated, and the structures obtained by large-eddy simulation are compared with the predictions from solving the Euler and Navier-Stokes equations directly. The results indicate that to predict irregular detonation structures in agreement with experimental observations the vorticity generation and dissipation in small scale structures should be taken into account. Thus, large-eddy simulation with high grid resolution is required. In a low grid resolution scenario, in which numerical diffusion dominates, the structures obtained by solving the Euler or Navier-Stokes equations and large-eddy simulation are qualitatively similar. When high grid resolution is employed, the detonation structures obtained by solving the Euler or Navier-Stokes equations directly are roughly similar yet equally in disagreement with the experimental results. For high grid resolution, only the large-eddy simulation predicts detonation substructures correctly, a fact that is attributed to the increased dissipation provided by the subgrid scale model. Specific to the investigated configuration, major differences are observed in the occurrence of unreacted gas pockets in the high-resolution Euler and Navier-Stokes computations, which appear to be fully combusted when large-eddy simulation is employed.

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“…Simulations of one-dimensional detonation dynamics have been the subject of a significant number of studies [46,47,72]. Some interesting new work looks at the issue of bifurcation from pulsation and transition to chaos [73], and the issues associated with elimination of shock generated errors by computing in a shockattached frame [74,75]. There are numerous other papers not listed here that have computed the 1-D pulsation.…”

Section: Comparison With Numerics and Computational Requirementsmentioning

confidence: 99%

State of Detonation Stability Theory and Its Application to Propulsion

Stewart

Kasimov

2006

Journal of Propulsion and Power

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We present an overview of the current state of detonation stability theory and discuss its implications for propulsion. The emphasis of the review is on the exact or asymptotic treatments of detonations, including various asymptotic limits that appear in the literature. The role that instability plays in practical detonation-based propulsion is of primary importance and is largely unexplored, hence we point to possible areas of research both theoretical and numerical, that might help improve our understanding of detonation behavior in propulsion devices. We outline the basic formulation of detonation stability theory that starts from linearized Euler equations, describe the algorithm of solution, and present an example that illustrates typical results.shock velocity vector E = activation energy e = internal energy per unit mass including chemical energy f = degree of overdrive H = enthalpy flux across the shock k = transverse wave number k ! = reaction rate constant M = local Mach number relative to the shock M = mass flux across the shock n = shock-attached frame axial coordinate n = unit normal to the shock P = momentum flux across the shock p = pressure Q = heat release per unit mass q = state vector t = unit tangent vector to the shock U = x component of particle velocity in steady shock frame U 1 = x component of particle velocity in unsteady shock frame u = particle velocity vector in laboratory frame u 1 = x component of particle velocity in laboratory frame u 2 = y component of particle velocity v = specific volume x = laboratory frame axial coordinate y = transverse coordinate = perturbation growth rate = ratio of specific heats = reaction progress variable = density = thermicity = shock displacement from the steady position along x axis ! = reaction rate University. He has published extensively in the areas of combustion theory, asymptotic analysis, theory for multidimensional detonation, detonation stability, continuum mechanics of multiphase flows, phase transformations, modeling of energetic materials, solid rocket motor combustion, advanced level set methods, and computational modeling of reactive flow. He is a past associate editor for SIAM Journal of Applied Mathematics, and was a founding (and still serves as a) board member for Combustion Theory and Modelling. In 1987 he was a founder of the SIAM Conferences on Numerical Combustion that are still held worldwide. He was the concept originator and principal investigator for the University of Illinois Center for Advanced Rockets (CSAR).

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Simulations of pulsating one-dimensional detonations with true fifth order accuracy

Cited by 110 publications

References 32 publications

Numerical study on unstable surfaces of oblique detonations

Numerical study on unstable surfaces of oblique detonations

Hydrodynamic Instabilities in Gaseous Detonations: Comparison of Euler, Navier–Stokes, and Large-Eddy Simulation

State of Detonation Stability Theory and Its Application to Propulsion

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