scholarly journals Analytical studies of the dynamics of gaseous detonations

2012 ◽  
Vol 370 (1960) ◽  
pp. 597-624 ◽  
Author(s):  
Paul Clavin ◽  
Forman A. Williams
Keyword(s):  
Spherical Geometry ◽  
Gaseous Detonation ◽  
Cellular Structures ◽  
Gaseous Detonations ◽  
Stability Threshold ◽  
Analytical Studies ◽  
Direct Initiation ◽  
The Stability ◽  
Dimensional Instability ◽  
Development Stability

The dynamics of gaseous detonation is revisited on the basis of analytical studies. Problems of initiation, quenching, pulsation and cellular structures are addressed. The objective is to improve our physical understanding of the development, stability and structure of gaseous detonations. New insights that have been gained from analytical investigations are emphasized. Specific problems discussed are the direct initiation of detonations in spherical geometry, the spontaneous soft initiation and quenching of detonations in a temperature gradient, the stability threshold and dynamics of galloping detonations, and the multi-dimensional instability threshold and cellular structures of both overdriven and near-Chapman–Jouguet detonations. It will be seen that, although there have been many accomplishments, some outstanding questions remain.

Internal pressure loads due to gaseous detonations

1993 ◽  
Vol 443 (1918) ◽  
pp. 343-366 ◽  
Keyword(s):  
Strong Shock ◽  
Shock Pressure ◽  
Gaseous Detonation ◽  
Flat Surfaces ◽  
Gaseous Detonations ◽  
Reflected Shock ◽  
Several Variables ◽  
Direct Initiation ◽  
Detonation Transition ◽  
Inert Layer

The internal loading of structures and confinements by gaseous detonation is studied using a multidimensional strong-shock physics code. Hydrogen-air-steam mixtures are used in calculations to show phenomena that apply qualitatively to any detonable gaseous fuel-oxidant-diluent mixture. Several variables are considered with respect to loading: ( a ) inert layers of various thicknesses; ( b ) deflagration-to-detonation transition(DDT) location as compared with direct initiation; and ( c ) some variations in geometry or confinement. Relatively thin inert layers are shown to increase the peak reflected shock pressure over that which would occur if the inert layer were not there. Inert layers may also increase impulse under some circumstances. DDT increases peak reflected pressures over those seen for direct initiation because of precompression of unburned gases. DDT may also increase impulses. Peak reflected pressures and impulses are greater in edges and corners than on flat surfaces. Internal obstruction tends to randomize the energy in a detonation wave, decreasing the impulse on structures, and allowing the pressure to equilibrate more rapidly than if there were no obstruction.

Oscillations of a moderately underexpanded choked jet impinging upon a flat plate

1996 ◽  
Vol 315 ◽  
pp. 267-291 ◽  
Author(s):  
Chih-Yu Kuo ◽  
Ann P. Dowling
Keyword(s):  
Experimental Data ◽  
Flat Plate ◽  
Pressure Ratio ◽  
Feedback Mechanism ◽  
Pressure Waves ◽  
Stagnation Flow ◽  
Stability Threshold ◽  
Shock Position ◽  
The Stability ◽  
Plate Distance

The oscillation of a moderately underexpanded choked jet impinging upon a flat plate is investigated both analytically and numerically. The feedback mechanism between oscillations of the standoff-shock and the plate is clarified. Pressure waves produced by the motion of the shock are reflected by the plate. In addition, oscillations in the shock position lead to downstream entropy fluctuations, which generate pressure waves as they are convected through the stagnation flow near the plate. A linear stability analysis is used to investigate the stability threshold and frequencies of oscillation, as a function of jet pressure ratio and nozzle-to-plate distance. The analytical predictions are compared to results from a numerical simulation and to the experimental data of Powell (1988) and Mørch (1963, 1964).

scholarly journals On the stability of a general magnetic field topology in stellar radiative zones

2019 ◽  
Vol 82 ◽  
pp. 365-371
Author(s):  
K. Augustson ◽  
S. Mathis ◽  
A. Strugarek
Keyword(s):  
Magnetic Field ◽  
Global Change ◽  
Magnetic Fields ◽  
Potential Energy ◽  
Massive Stars ◽  
Spherical Geometry ◽  
Stable Region ◽  
Magnetic Field Topology ◽  
The Stability ◽  
The Magnetic Field

This paper provides a brief overview of the formation of stellar fossil magnetic fields and what potential instabilities may occur given certain configurations of the magnetic field. One such instability is the purely magnetic Tayler instability, which can occur for poloidal, toroidal, and mixed poloidal-toroidal axisymmetric magnetic field configurations. However, most of the magnetic field configurations observed at the surface of massive stars are non-axisymmetric. Thus, extending earlier studies in spherical geometry, we introduce a formulation for the global change in the potential energy contained in a convectively-stable region for both axisymmetric and non-axisymmetric magnetic fields.

Determination of the Fluid-Elastic Stability Threshold in the Presence of Turbulence: A Theoretical Study

1989 ◽  
Vol 111 (4) ◽  
pp. 407-419 ◽  
Author(s):  
J. H. Lever ◽  
G. Rzentkowski
Keyword(s):  
Theoretical Study ◽  
Cross Flow ◽  
Elastic Stability ◽  
Mass Ratio ◽  
Response Curves ◽  
Stability Threshold ◽  
Pitch Ratio ◽  
The Stability ◽  
Experimental Findings

A model has been developed to examine the effect of the superposition of turbulent buffeting and fluid-elastic excitation on the response of a single flexible tube in an array exposed to cross-flow. The modeled response curves for a 1.375-pitch ratio parallel triangular array are compared with corresponding experimental data for the same array; reasonably good qualitative agreement is seen. Turbulence is shown to have a significant effect on the determination of the stability threshold for the array, with increasing turbulent buffeting causing a reduction in the apparent critical velocity. The dependence of turbulence response on mass ratio is also found to yield a slight independence between mass and damping parameters on stability threshold estimates, which may account for similar experimental findings. Different stability criteria are compared, and an attempt is made to provide some guidance in the interpretation of response curves from actual tests.

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 Buckling analysis of a non-concentric double-walled carbon nanotube

2020 ◽  
Vol 231 (12) ◽  
pp. 5007-5020 ◽  
Author(s):  
Mohammad Malikan ◽  
Victor A. Eremeyev ◽  
Hamid M. Sedighi
Keyword(s):  
Carbon Nanotubes ◽  
Theoretical Study ◽  
Static Stability ◽  
Governing Equations ◽  
Stability Threshold ◽  
Lennard Jones ◽  
The Stability ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes ◽  
Nonlocal Approach

Abstract On the basis of a theoretical study, this research incorporates an eccentricity into a system of compressed double-walled carbon nanotubes (DWCNTs). In order to formulate the stability equations, a kinematic displacement with reference to the classical beam hypothesis is utilized. Furthermore, the influence of nanoscale size is taken into account with regard to the nonlocal approach of strain gradient, and the van der Waals interaction for both inner and outer tubes is also considered based on the Lennard–Jones model. Galerkin decomposition is employed to numerically deal with the governing equations. It is evidently demonstrated that the geometrical eccentricity remarkably affects the stability threshold and its impact is to increase the static stability of DWCNTs.

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