Shock Relaxation in a Lightly Mass-Loaded Gas

1972 ◽  
Vol 50 (10) ◽  
pp. 1040-1043 ◽  
Author(s):  
K. Dimoff ◽  
P. R. Smy ◽  
J. Lacoste
Keyword(s):  
Light Attenuation ◽  
Relaxation Times ◽  
Suspension System ◽  
Experimental Confirmation ◽  
Mass Loading ◽  
Particulate Phase ◽  
Dust Density ◽  
Simple Analytic Expression ◽  
Low Mass ◽  
Analytic Expression

For very low mass loading, the hydrodynamics of the gas can be regarded as completely uncoupled from effects of the particulate phase. Consequently, a simple analytic expression can be derived for the variation of dust density with time after the passage of a shock through such a gas–dust medium. Experimental confirmation, through the use of an electrostatic suspension system and a simple light attenuation technique, is sensitive enough to detect relaxation times of the order 10−5 s.

A Modeling Study on Particle Dispersion in Wall-Bounded Turbulent Flows

2014 ◽  
Vol 6 (06) ◽  
pp. 764-782 ◽  
Author(s):  
Jian-Hung Lin ◽  
Keh-Chin Chang
Keyword(s):  
Turbulent Flows ◽  
Particle Dispersion ◽  
Hard Sphere Model ◽  
Wall Roughness ◽  
Mass Loading ◽  
Particle Collisions ◽  
Physical Mechanisms ◽  
Parametric Studies ◽  
Low Mass ◽  
Bounded Particle

AbstractThree physical mechanisms which may affect dispersion of particle’s motion in wall-bounded turbulent flows, including the effects of turbulence, wall roughness in particle-wall collisions, and inter-particle collisions, are numerically investigated in this study. Parametric studies with different wall roughness extents and with different mass loading ratios of particles are performed in fully developed channel flows with the Eulerian-Lagrangian approach. A low-Reynolds-numberk–εturbulence model is applied for the solution of the carrier-flow field, while the deterministic Lagrangian method together with binary-collision hard-sphere model is applied for the solution of particle motion. It is shown that the mechanism of inter-particle collisions should be taken into account in the modeling except for the flows laden with sufficiently low mass loading ratios of particles. Influences of wall roughness on particle dispersion due to particle-wall collisions are found to be considerable in the bounded particle–laden flow. Since the investigated particles are associated with large Stokes numbers, i.e., larger thanO(1), in the test problem, the effects of turbulence on particle dispersion are much less considerable, as expected, in comparison with another two physical mechanisms investigated in the study.

scholarly journals Estimating the Risk of Satellite Collisions in Densely Populated Orbit Shells

2021 ◽  
Author(s):  
William Lee ◽  
Paul Martin ◽  
Ann Smith ◽  
Giancarlo Antonucci ◽  
Georgia Brennan ◽  
...  
Keyword(s):  
Time Dependence ◽  
Low Earth Orbit ◽  
Collision Probability ◽  
Earth Orbit ◽  
Limited Information ◽  
Asymptotic Approach ◽  
Optimal Point ◽  
Single Collision ◽  
Simple Analytic Expression ◽  
Analytic Expression

Low Earth Orbit is becoming crowded with satellites. Updating estimates of collision probabilities is important as new deployments are authorised but is difficult because only limited information is given. This report investigates developing analytic estimates of collision probabilities. A survey of approaches reported in the literature is carried out. A collision involving a satellite from the Iridium cluster is reviewed. A simple analytic expression for the collision probability between two satellites is derived using the smallness of several dimensionless ratios appearing in the problem. Single collision probabilities are then extended to orbital planes populated by n satellites with the aim of finding the optimal point at which to traverse such an orbit. This report demonstrates that analytic estimates relevant to the problem can be made. Further work should focus on: making these estimates rigorous by using a formal asymptotic approach, considering multiple orbital planes and introducing time dependence

scholarly journals Polymorphic Phase Control of RDX-Based Explosives

2017 ◽  
Vol 72 (1) ◽  
pp. 28-36 ◽  
Author(s):  
John J. Brady ◽  
Brittney L. Argirakis ◽  
Alexander D. Gordon ◽  
Richard T. Lareau ◽  
Barry T. Smith
Keyword(s):  
Raman Spectra ◽  
Preparation Method ◽  
High Mass ◽  
Initial Mass ◽  
Vibrational Modes ◽  
Mass Loading ◽  
Deposition Technique ◽  
Crystallization Method ◽  
Low Mass ◽  
Initial Deposition

The polymorphic phase of 1,3,5-trinitro-1,3,5-triazine (RDX) was examined as a function of mass loading, solvent, and sample deposition technique. When RDX was deposited at a high mass loading, the vibrational modes in the obtained Raman spectra were indicative of concomitant polymorphism as both the α-RDX and β-RDX phases were present. At low mass loadings, only β-RDX was observed regardless of solvent when using the drop cast crystallization method. However, α-RDX (the thermodynamically stable polymorphic phase observed with visible quantities of the explosive) was observed when RDX deposits were dry transferred. Observation of α-RDX was independent of the initial mass loading or the initial deposition solvent when using the dry transfer methodology. These data indicate that the use of the dry transfer preparation method can be used to successfully prepare RDX-based test articles with the α-RDX phase regardless of the solvent used to initially dissolve the RDX, the initial deposition technique, or the mass loading.

scholarly journals A VALUATION FORMULA FOR MULTI-ASSET, MULTI-PERIOD BINARIES IN A BLACK–SCHOLES ECONOMY

2009 ◽  
Vol 50 (4) ◽  
pp. 475-485
Author(s):  
MAX SKIPPER ◽  
PETER BUCHEN
Keyword(s):  
Closed Form ◽  
Present Value ◽  
Simple Analytic Expression ◽  
Black Scholes ◽  
Analytic Expression

AbstractWe present a new valuation formula for a generic, multi-period binary option in a multi-asset Black–Scholes economy. The payoff of this so-called M-binary is the most general possible, subject to the condition that a simple analytic expression exists for the present value. Portfolios of M-binaries can be used to statically replicate many European exotics for which there exist closed-form Black–Scholes prices.

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