The hydrodynamic structure of unstable cellular detonations

2007 ◽  
Vol 580 ◽  
pp. 31-81 ◽  
Author(s):  
MATEI I. RADULESCU ◽  
GARY J. SHARPE ◽  
CHUNG K. LAW ◽  
JOHN H. S. LEE
Keyword(s):  
Numerical Simulations ◽  
Reaction Zone ◽  
Detonation Waves ◽  
Zone Structure ◽  
Mean Values ◽  
One Dimensional ◽  
Hydrodynamic Fluctuations ◽  
Cellular Detonations ◽  
Global Reaction ◽  
Sonic Surface

The study analyses the cellular reaction zone structure of unstable methane–oxygen detonations, which are characterized by large hydrodynamic fluctuations and unreacted pockets with a fine structure. Complementary series of experiments and numerical simulations are presented, which illustrate the important role of hydrodynamic instabilities and diffusive phenomena in dictating the global reaction rate in detonations. The quantitative comparison between experiment and numerics also permits identification of the current limitations of numerical simulations in capturing these effects. Simulations are also performed for parameters corresponding to weakly unstable cellular detonations, which are used for comparison and validation. The numerical and experimental results are used to guide the formulation of a stochastic steady one-dimensional representation for such detonation waves. The numerically obtained flow fields were Favre-averaged in time and space. The resulting one-dimensional profiles for the mean values and fluctuations reveal the two important length scales, the first being associated with the chemical exothermicity and the second (the ‘hydrodynamic thickness’) with the slower dissipation of the hydrodynamic fluctuations, which govern the location of the average sonic surface. This second length scale is found to be much longer than that predicted by one-dimensional reaction zone calculations.

scholarly journals The role of unsteadiness in direct initiation of gaseous detonations

2000 ◽  
Vol 421 ◽  
pp. 147-183 ◽  
Author(s):  
CHRIS A. ECKETT ◽  
JAMES J. QUIRK ◽  
JOSEPH E. SHEPHERD
Keyword(s):  
Numerical Simulations ◽  
Decay Rate ◽  
Wave Front ◽  
Reaction Zone ◽  
Critical Energy ◽  
Local Analysis ◽  
Zone Structure ◽  
Gaseous Detonations ◽  
Release Wave ◽  
Direct Initiation

An analytical model is presented for the direct initiation of gaseous detonations by a blast wave. For stable or weakly unstable mixtures, numerical simulations of the spherical direct initiation event and local analysis of the one-dimensional unsteady reaction zone structure identify a competition between heat release, wave front curvature and unsteadiness. The primary failure mechanism is found to be unsteadiness in the induction zone arising from the deceleration of the wave front. The quasi-steady assumption is thus shown to be incorrect for direct initiation. The numerical simulations also suggest a non-uniqueness of critical energy in some cases, and the model developed here is an attempt to explain the lower critical energy only. A critical shock decay rate is determined in terms of the other fundamental dynamic parameters of the detonation wave, and hence this model is referred to as the critical decay rate (CDR) model. The local analysis is validated by integration of reaction-zone structure equations with real gas kinetics and prescribed unsteadiness. The CDR model is then applied to the global initiation problem to produce an analytical equation for the critical energy. Unlike previous phenomenological models of the critical energy, this equation is not dependent on other experimentally determined parameters and for evaluation requires only an appropriate reaction mechanism for the given gas mixture. For different fuel–oxidizer mixtures, it is found to give agreement with experimental data to within an order of magnitude.

scholarly journals Plane thermonuclear detonation waves initiated by proton beams and quasi-one-dimensional model of fast ignition

2014 ◽  
Vol 33 (1) ◽  
pp. 65-80 ◽  
Author(s):  
Alexander A. Charakhch'yan ◽  
Konstantin V. Khishchenko
Keyword(s):  
Detonation Wave ◽  
Fusion Reaction ◽  
Plasma Heating ◽  
Symmetry Plane ◽  
Detonation Waves ◽  
Proton Beams ◽  
One Dimensional ◽  
Wide Range ◽  
The One ◽  
Α Particles

AbstractThe one-dimensional problem on bilatiral irradiation by proton beams of the plane layer of condensed DT mixture with length 2H and density ρ0 ≤ 100ρs, where ρs is the fuel solid-state density at atmospheric pressure and temperature of 4 K, is considered. The proton kinetic energy is 1 MeV, the beam intensity is 1019 W/cm2 and duration is 50 ps. A mathematical model is based on the one-fluid two-temperature hydrodynamics with a wide-range equation of state of the fuel, electron and ion heat conduction, DT fusion reaction kinetics, self-radiation of plasma and plasma heating by α-particles. If the ignition occurs, a plane detonation wave, which is adjacent to the front of the rarefaction wave, appears. Upon reflection of this detonation wave from the symmetry plane, the flow with the linear velocity profile along the spatial variable x and with a weak dependence of the thermodynamic functions of x occurs. An appropriate solution of the equations of hydrodynamics is found analytically up to an arbitrary constant, which can be chosen so that the analytical solution describes with good accuracy the numerical one. The gain with respect to the energy of neutrons G ≈ 200 at Hρ0 ≈ 1 g/cm2, and G > 2000 at Hρ0 ≈ 5 g/cm2. To evaluate the ignition energy Eig of cylindrical targets, the quasi-1D model, limiting trajectories of α-particles by a cylinder of a given radius, is suggested. The model reproduces the known theoretical dependence Eig ~ ρ0−2 and gives Eig = 160 kJ for ρ0 = 100ρs ≈ 22 g/cm3.

scholarly journals Parabolic bursting, spike-adding, dips and slices in a minimal model

2019 ◽  
Vol 14 (4) ◽  
pp. 406
Author(s):  
Mathieu Desroches ◽  
Jean-Pierre Francoise ◽  
Martin Krupa
Keyword(s):  
Qualitative Analysis ◽  
Numerical Simulations ◽  
Phase Portrait ◽  
Minimal Model ◽  
Bifurcation Theory ◽  
Minimal System ◽  
Dimensional System ◽  
Slow Flow ◽  
Van Der Pol ◽  
One Dimensional

A minimal system for parabolic bursting, whose associated slow flow is integrable, is presented and studied both from the viewpoint of bifurcation theory of slow-fast systems, of the qualitative analysis of its phase portrait and of numerical simulations. We focus the analysis on the spike-adding phenomenon. After a reduction to a periodically forced one-dimensional system, we uncover the link with the dips and slices first discussed by J.E. Littlewood in his famous articles on the periodically forced van der Pol system.

Revisiting V-3 Canon for the Application of Single Stage Gas Gun

2017 ◽  
Author(s):  
Arun Tom Mathew ◽  
Tirumala Rao Koka ◽  
Murali Krishnan Payangapadan
Keyword(s):  
Design Of Experiments ◽  
Numerical Simulations ◽  
Response Surface ◽  
Three Dimensional ◽  
Optimal Location ◽  
Single Stage ◽  
One Dimensional ◽  
Alternative Design ◽  
Gas Gun ◽  
Gas Guns

Single stage gas guns are typically used for accelerating the projectiles in bird and hail impact tests of aerospace components and engines. In this paper an alternative design for single stage gas gun is studied, which is derived from V3 canon. Three dimensional numerical simulations is carried out for the optimal secondary connection angle with the main barrel. A one dimensional code is developed for the V3 canon based design. Design of experiments conducted to find the response surface for the optimal location of the secondary connection, volume and pressure of the secondary tank.

Sign in / Sign up

Export Citation Format

Share Document