scholarly journals The virtual origin as a first-order correction for the far-field description of laminar jets

2002 ◽  
Vol 14 (6) ◽  
pp. 1821-1824 ◽  
Author(s):  
Antonio Revuelta ◽  
Antonio L. Sánchez ◽  
Amable Liñán
Keyword(s):  
Order Correction ◽  
Far Field ◽  
First Order ◽  
Virtual Origin ◽  
Laminar Jets ◽  
First Order Correction

Steady detonation propagation in a circular arc: a Detonation Shock Dynamics model

2016 ◽  
Vol 807 ◽  
pp. 87-134 ◽  
Author(s):  
Mark Short ◽  
James J. Quirk ◽  
Chad D. Meyer ◽  
Carlos Chiquete
Keyword(s):  
Surface Wave ◽  
Angular Speed ◽  
Order Correction ◽  
Two Dimensional ◽  
Normal Surface ◽  
Circular Arc ◽  
First Order ◽  
Shock Dynamics ◽  
First Order Correction ◽  
Steady Detonation

We study the physics of steady detonation wave propagation in a two-dimensional circular arc via a Detonation Shock Dynamics (DSD) surface evolution model. The dependence of the surface angular speed and surface spatial structure on the inner arc radius ($R_{i}$), the arc thickness ($R_{e}-R_{i}$, where $R_{e}$ is the outer arc radius) and the degree of confinement on the inner and outer arc is examined. We first analyse the results for a linear $D_{n}$–$\unicode[STIX]{x1D705}$ model, in which the normal surface velocity $D_{n}=D_{CJ}(1-B\unicode[STIX]{x1D705})$, where $D_{CJ}$ is the planar Chapman–Jouguet velocity, $\unicode[STIX]{x1D705}$ is the total surface curvature and $B$ is a length scale representative of a reaction zone thickness. An asymptotic analysis assuming the ratio $B/R_{i}\ll 1$ is conducted for this model and reveals a complex surface structure as a function of the radial variation from the inner to the outer arc. For sufficiently thin arcs, where $(R_{e}-R_{i})/R_{i}=O(B/R_{i})$, the angular speed of the surface depends on the inner arc radius, the arc thickness and the inner and outer arc confinement. For thicker arcs, where $(R_{e}-R_{i})/R_{i}=O(1)$, the angular speed does not depend on the outer arc radius or the outer arc confinement to the order calculated. It is found that the leading-order angular speed depends only on $D_{CJ}$ and $R_{i}$, and corresponds to a Huygens limit (zero curvature) propagation model where $D_{n}=D_{CJ}$, assuming a constant angular speed and perfect confinement on the inner arc surface. Having the normal surface speed depend on curvature requires the insertion of a boundary layer structure near the inner arc surface. This is driven by an increase in the magnitude of the surface wave curvature as the inner arc surface is approached that is needed to meet the confinement condition on the inner arc surface. For weak inner arc confinement, the surface wave spatial variation with the radial coordinate is described by a triple-deck structure. The first-order correction to the angular speed brings in a dependence on the surface curvature through the parameter $B$, while the influence of the inner arc confinement on the angular velocity only appears in the second-order correction. For stronger inner arc confinement, the surface wave structure is described by a two-layer solution, where the effect of the confinement on the angular speed is promoted to the first-order correction. We also compare the steady-state arc solution for a PBX 9502 DSD model to an experimental two-dimensional arc geometry validation test.

Nearly free-molecular slit flow at finite pressure and temperature ratios

1971 ◽  
Vol 50 (3) ◽  
pp. 565-577 ◽  
Author(s):  
P. Y. Wang ◽  
E. Y. Yu
Keyword(s):  
Mass Flow ◽  
Total Mass ◽  
Noble Gas ◽  
Order Correction ◽  
Linear Boltzmann Equation ◽  
Molecular Flow ◽  
First Order ◽  
Slit Flow ◽  
Isothermal Case ◽  
First Order Correction

An analytical study is made of nearly free-molecular flow of a noble gas from one reservoir to another through a two-dimensional slit, with finite pressure and temperature ratios across the slit. The fundamental solution of the linear Boltzmann equation is employed in the study. The total mass flow is calculated to the first-order correction terms, of the order of α ln α and α, where α is the inverse Knudsen number. The coefficients of these terms are in general multiple integrals, but they become explicit functions of the pressure and temperature ratios after the multiple integrations are carried out by using Krook collision model. When the general result is simplified to the isothermal case the first-order correction has a negative value, indicating the reduction of the total mass flow due to intermolecular collisions in the counter flows.

First-Order Correction Field of Circularly Polarized Ultra-Short Pulse and Its Acceleration Effect

2009 ◽  
Vol 29 (6) ◽  
pp. 1586-1590
Author(s):  
张绍银 Zhang Shaoyin ◽  
许长谭 Xu Changtan ◽  
艾树涛 Ai Shutao
Keyword(s):  
Short Pulse ◽  
Order Correction ◽  
Circularly Polarized ◽  
First Order ◽  
First Order Correction ◽  
Ultra Short Pulse

ANALYTIC FIRST-ORDER EIKONAL MODEL FOR HEAVY-ION ELASTIC SCATTERINGS

2010 ◽  
Vol 19 (10) ◽  
pp. 1947-1960
Author(s):  
YONG JOO KIM ◽  
JONG-KWAN WOO ◽  
MOON HOE CHA
Keyword(s):  
Phase Shift ◽  
Cross Sections ◽  
Theoretical Method ◽  
Heavy Ion ◽  
Reaction Cross ◽  
Order Correction ◽  
Model Calculations ◽  
First Order ◽  
Eikonal Model ◽  
First Order Correction

We present analytic expressions for the zero-order eikonal phase shift and its first-order correction by approximating a distance between two colliding nuclei. This formalism has been applied to elastic scatterings of the 12 C + 40 Ca and the 12 C + 90 Zr systems at E lab = 420 MeV , and the 16 O + 40 Ca and the 16 O + 90 Zr ones at E lab = 1503 MeV . The calculated angular distributions, taking into account up to the analytic first-order eikonal phase shift, are found to be in fairly good agreement with the observed data. The reaction cross-sections obtained from the present model produce very excellent agreements with ones of exact first-order eikonal model calculations. We have found that analytic eikonal phase shift including the first-order correction is one theoretical method to the analysis of heavy-ion elastic scattering.

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