On the Hydrodynamic Thickness of Cellular Detonations

Lee, J. H. S.; Radulescu, Matei I.

doi:10.1007/s10573-005-0084-1

Cited by 46 publications

(19 citation statements)

References 30 publications

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“…First, the results of select cases are analyzed via a densityweighted (Favre), spatio-temporal averaging method. Using this analysis, which was introduced to the field of detonation by Lee and Radulescu [3], Radulescu et al [4], and Sow et al [19]. Mi et al interpreted the super-CJ propagation, resulting from a system with highly concentrated sources that instantaneously deposit energy after a fixed delay time, as weak detonations owing to the non-equilibrium condition at the average sonic surface.…”

Section: Discussionmentioning

confidence: 99%

Propagation of gaseous detonation waves in a spatially inhomogeneous reactive medium

Higgins

et al. 2017

Phys. Rev. Fluids

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Detonation propagation in a compressible medium wherein the energy release has been made spatially inhomogeneous is examined via numerical simulation. The inhomogeneity is introduced via step functions in the reaction progress variable, with the local value of energy release correspondingly increased so as to maintain the same average energy density in the medium, and thus a constant Chapman Jouguet (CJ) detonation velocity. A one-step Arrhenius rate governs the rate of energy release in the reactive zones. The resulting dynamics of a detonation propagating in such systems with one-dimensional layers and two-dimensional squares are simulated using a Godunov-type finite-volume scheme. The resulting wave dynamics are analyzed by computing the average wave velocity and one-dimensional averaged wave structure. In the case of sufficiently inhomogeneous media wherein the spacing between reactive zones is greater than the inherent reaction zone length, average wave speeds significantly greater than the corresponding CJ speed of the homogenized medium are obtained. If the shock transit time between reactive zones is less than the reaction time scale, then the classical CJ detonation velocity is recovered. The spatio-temporal averaged structure of the waves in these systems is analyzed via a Favre averaging technique, with terms associated with the thermal and mechanical fluctuations being explicitly computed. The analysis of the averaged wave structure identifies the super-CJ detonations as weak detonations owing to the existence of mechanical non-equilibrium at the effective sonic point embedded within the wave structure. The correspondence of the super-CJ behavior identified in this study with real detonation phenomena that may be observed in experiments is discussed. * Corresponding author: andrew.higgins@mcgill.ca 2

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Section: Discussionmentioning

confidence: 99%

Propagation of gaseous detonation waves in a spatially inhomogeneous reactive medium

Higgins

et al. 2017

Phys. Rev. Fluids

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“…In order to provide an explanation of this finding, the results of select simulations reported in the prior section were analyzed using the conventional pressure/specific volume (p-v) representation of thermodynamic states. Following the approach developed by Lee & Radulescu [32], Radulescu et al [46], and Sow et al [55], the flow field of the wave propagating in a discrete source detonation will be analyzed in a moving reference frame and the flow at each point in the domain will be averaged over time. This will enable the average structure of the wave to be compared to the classical structure of the ZND model of a detonation, as visualized in the p-v diagram.…”

Section: Discussionmentioning

confidence: 99%

“…The sonic point in the one-dimensional averaged wave structure is located at the position at where u * + c * = 0. The importance of using a mean steady detonation profile to determine the location of the effective sonic plane was highlighted by Lee & Radulescu [32]. Figure 8 shows the simulation results for the case of continuous (i.e., Γ = 1) lab-fixed energy sources, Q = 50, τ = 0.1, and γ = 5/3 analyzed using the Favre averaging approach and p-v representation of thermodynamic states.…”

Section: Discussionmentioning

confidence: 99%

Effect of spatial discretization of energy on detonation wave propagation

Timofeev

Higgins

2017

J. Fluid Mech.

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Detonation propagation in the limit of highly spatially discretized energy sources is investigated. The model of this problem begins with a medium consisting of a calorically perfect gas with a prescribed energy release per unit mass. The energy release is collected into sheet-like sources that are now embedded in an inert gas that fills the spaces between them. The release of energy in the first sheet results in a planar blast wave that propagates to the next source, which is triggered after a prescribed delay, generating a new blast, and so forth. The resulting wave dynamics as the front passes through hundreds of such sources is computationally simulated by numerically solving the governing one-dimensional Euler equations in the lab-fixed reference frame. Two different solvers are used: one with a fixed uniform grid and the other using an unstructured, adaptively refined grid enabling the limit of highly concentrated, spatially discrete sources to be examined. The two different solvers generate consistent results, agreeing within the accuracy of the measured wave speeds. The average wave speed for each simulation is measured once the wave propagation has reached a quasi-periodic solution. The effect of source delay time, source energy density, specific heat ratio, and the spatial discreteness of the sources on the wave speed is studied. Sources fixed in the lab reference frame versus sources that convect with the flow are compared as well. The average wave speed is compared to the ideal Chapman-Jouguet (CJ) speed of the equivalent homogenized media. Velocities in excess of the CJ speed are found as the sources are made increasingly discrete, with the deviation above CJ being as great as 15%. The deviation above the CJ value increases with decreasing values of specific heat ratio γ. The total energy release, delay time, and whether the sources remain lab-fixed or are convected with the flow do not have a significant influence on the deviation of the average wave speed away from CJ. A simple, ad hoc analytic model is proposed to treat the case of zero delay time (i.e., source energy released at the shock front) that exhibits qualitative agreement with the computational solutions and may explain why the deviation from CJ increases with decreasing γ. When the sources are sufficiently spread out so as to make the energy release of the media nearly continuous, the classic CJ solution is obtained for the average wave speed. Such continuous waves can also be shown to have a time-averaged structure consistent with the classical ZND structure of a detonation. In the limit of highly discrete sources, temporal averaging of the wave structure shows that the effective sonic surface does not correspond to an equilibrium state. The average state of the flow leaving the wave in this case does eventually reach the equilibrium Hugoniot, but only after the effective sonic surface has been crossed. Thus, the super-CJ waves observed in the limit of highly discretized sources can be understood as weak detonations due to the...

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“…The details of this boundary condition can be found elsewhere [16,42]. The existence of an average Chapman and Jouguet state, at the end of reaction zone, makes this concept attractive for simulating detonation waves [43]. Considering this concept, the NRBC is used to truncate the computational domain.…”

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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On the Hydrodynamic Thickness of Cellular Detonations

Cited by 46 publications

References 30 publications

Propagation of gaseous detonation waves in a spatially inhomogeneous reactive medium

Propagation of gaseous detonation waves in a spatially inhomogeneous reactive medium

Effect of spatial discretization of energy on detonation wave propagation

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

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