scholarly journals Asymptotic solution and numerical simulation of homogeneous condensation in expansion cloud chambers

1996 ◽  
Vol 105 (19) ◽  
pp. 8804-8821 ◽  
Author(s):  
C. F. Delale ◽  
M. J. E. H. Muitjens ◽  
M. E. H. van Dongen
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Solution ◽  
Homogeneous Condensation

scholarly journals Asymptotic theory of resonant flow in a spheroidal cavity driven by latitudinal libration

2012 ◽  
Vol 692 ◽  
pp. 420-445 ◽  
Author(s):  
Keke Zhang ◽  
Kit H. Chan ◽  
Xinhao Liao
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Asymptotic Solution ◽  
Slip Boundary Condition ◽  
Viscous Boundary Layer ◽  
Slip Boundary ◽  
Oblate Spheroidal ◽  
Spheroidal Cavity ◽  
Viscous Boundary

AbstractWe consider a homogeneous fluid of viscosity $\nu $ confined within an oblate spheroidal cavity, ${x}^{2} / {a}^{2} + {y}^{2} / {a}^{2} + {z}^{2} / ({a}^{2} (1\ensuremath{-} {\mathscr{E}}^{2} ))= 1$, with eccentricity $0\lt \mathscr{E}\lt 1$. The spheroidal container rotates rapidly with an angular velocity ${\mbit{\Omega} }_{0} $, which is fixed in an inertial frame and defines a small Ekman number $E= \nu / ({a}^{2} \vert {\mbit{\Omega} }_{0} \vert )$, and undergoes weak latitudinal libration with frequency $\hat {\omega } \vert {\mbit{\Omega} }_{0} \vert $ and amplitude $\mathit{Po}\vert {\mbit{\Omega} }_{0} \vert $, where $\mathit{Po}$ is the Poincaré number quantifying the strength of Poincaré force resulting from latitudinal libration. We investigate, via both asymptotic and numerical analysis, fluid motion in the spheroidal cavity driven by latitudinal libration. When $\vert \hat {\omega } \ensuremath{-} 2/ (2\ensuremath{-} {\mathscr{E}}^{2} )\vert \gg O({E}^{1/ 2} )$, an asymptotic solution for $E\ll 1$ and $\mathit{Po}\ll 1$ in oblate spheroidal coordinates satisfying the no-slip boundary condition is derived for a spheroidal cavity of arbitrary eccentricity without making any prior assumptions about the spatial–temporal structure of the librating flow. In this case, the librationally driven flow is non-axisymmetric with amplitude $O(\mathit{Po})$, and the role of the viscous boundary layer is primarily passive such that the flow satisfies the no-slip boundary condition. When $\vert \hat {\omega } \ensuremath{-} 2/ (2\ensuremath{-} {\mathscr{E}}^{2} )\vert \ll O({E}^{1/ 2} )$, the librationally driven flow is also non-axisymmetric but latitudinal libration resonates with a spheroidal inertial mode that is in the form of an azimuthally travelling wave in the retrograde direction. The amplitude of the flow becomes $O(\mathit{Po}/ {E}^{1/ 2} )$ at $E\ll 1$ and the role of the viscous boundary layer becomes active in determining the key property of the flow. An asymptotic solution for $E\ll 1$ describing the librationally resonant flow is also derived for an oblate spheroidal cavity of arbitrary eccentricity. Three-dimensional direct numerical simulation in an oblate spheroidal cavity is performed to demonstrate that, in both the non-resonant and resonant cases, a satisfactory agreement is achieved between the asymptotic solution and numerical simulation at $E\ll 1$.

Asymptotic solution of shock tube flows with homogeneous condensation

1995 ◽  
Vol 287 ◽  
pp. 93-118 ◽  
Author(s):  
Can F. Delale ◽  
Günter H. Schnerr ◽  
Jürgen Zierep
Keyword(s):  
Shock Wave ◽  
Asymptotic Solution ◽  
Shock Tube ◽  
Complete Solution ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Droplet Growth ◽  
Homogeneous Condensation ◽  
Shock Fitting ◽  
Supercritical Flows

The asymptotic solution of shock tube flows with homogeneous condensation is presented for both smooth, or subcritical, flows and flows with an embedded shock wave, or supercritical flows. For subcritical flows an analytical expression, independent of the particular theory of homogeneous condensation to be employed, that determines the condensation wave front in the rarefaction wave is obtained by the asymptotic analysis of the rate equation along pathlines. The complete solution is computed by an algorithm which utilizes the classical nucleation theory and the Hertz–Knudsen droplet growth law. For supercritical flows four distinct flow regimes are distinguished along pathlines intersecting the embedded shock wave analogous to supercritical nozzle flows. The complete global solution for supercritical flows is discussed only qualitatively owing to the lack of a shock fitting technique for embedded shock waves. The results of the computations obtained by the subcritical algorithm show that most of the experimental data available exhibit supercritical flow behaviour and thereby the predicted onset conditions in general show deviations from the measured values. The causes of these deviations are reasoned by utilizing the qualitative global asymptotic solution of supercritical flows.

scholarly journals On precessing flow in an oblate spheroid of arbitrary eccentricity

2014 ◽  
Vol 743 ◽  
pp. 358-384 ◽  
Author(s):  
Keke Zhang ◽  
Kit H. Chan ◽  
Xinhao Liao
Keyword(s):  
Numerical Simulation ◽  
Angular Velocity ◽  
Direct Numerical Simulation ◽  
Asymptotic Solution ◽  
Temporal Structure ◽  
Oblate Spheroid ◽  
Frame Of Reference ◽  
Viscous Effects ◽  
Homogeneous Fluid ◽  
Spheroidal Cavity

AbstractWe consider a homogeneous fluid of viscosity $\nu $ confined within an oblate spheroidal cavity of arbitrary eccentricity $\mathcal{E}$ marked by the equatorial radius $d$ and the polar radius $d \sqrt{1-\mathcal{E}^2}$ with $0<\mathcal{E}<1$. The spheroidal container rotates rapidly with an angular velocity ${\boldsymbol{\Omega}}_0 $ about its symmetry axis and precesses slowly with an angular velocity ${\boldsymbol{\Omega}}_p$ about an axis that is fixed in space. It is through both topographical and viscous effects that the spheroidal container and the viscous fluid are coupled together, driving precessing flow against viscous dissipation. The precessionally driven flow is characterized by three dimensionless parameters: the shape parameter $\mathcal{E}$, the Ekman number ${\mathit{Ek}}=\nu /(d^2 \delimiter "026A30C {\boldsymbol{\Omega}}_0\delimiter "026A30C )$ and the Poincaré number ${\mathit{Po}}=\pm \delimiter "026A30C {\boldsymbol{\Omega}}_p\delimiter "026A30C / \delimiter "026A30C \boldsymbol{\Omega}_0\delimiter "026A30C $. We derive a time-dependent asymptotic solution for the weakly precessing flow in the mantle frame of reference satisfying the no-slip boundary condition and valid for a spheroidal cavity of arbitrary eccentricity at ${\mathit{Ek}}\ll 1$. No prior assumptions about the spatial–temporal structure of the precessing flow are made in the asymptotic analysis. We also carry out direct numerical simulation for both the weakly and the strongly precessing flow in the same frame of reference using a finite-element method that is particularly suitable for non-spherical geometry. A satisfactory agreement between the asymptotic solution and direct numerical simulation is achieved for sufficiently small Ekman and Poincaré numbers. When the nonlinear effect is weak with $\delimiter "026A30C {\mathit{Po}}\delimiter "026A30C \ll 1$, the precessing flow in an oblate spheroid is characterized by an azimuthally travelling wave without having a mean azimuthal flow. Stronger nonlinear effects with increasing $\delimiter "026A30C {\mathit{Po}}\delimiter "026A30C $ produce a large-amplitude, time-independent mean azimuthal flow that is always westward in the mantle frame of reference. Implications of the precessionally driven flow for the westward motion observed in the Earth’s fluid core are also discussed.

scholarly journals Exact solution and high frequency asymptotic methods in the wedge diffraction problem

2016 ◽  
Vol 14 (38) ◽  
pp. 9-28
Author(s):  
Hernan G. Triana ◽  
Andrés Navarro Cadavid
Keyword(s):  
Numerical Simulation ◽  
Exact Solution ◽  
Asymptotic Solution ◽  
High Frequency ◽  
Asymptotic Methods ◽  
Diffraction Problem ◽  
Approximate Solutions ◽  
Point Of View ◽  
Simulation Tool ◽  
Computational Point

AbstractThe Sommerfeld exact solution for canonical 2D wedge diffraction problem with perfectly conducting surfaces is presented. From the integral formulation of the problem, the Malyuzhinets solution is obtained and this result is extended to obtain the general impedance solution of canonical 2D wedge problem. Keller’s asymptotic solution is developed and the general formulation of exact solution it’s used to obtain general asymptotic methods for approximate solutions useful from the computational point of view. A simulation tool is used to compare numerical calculations of exact and asymptotic solutions. The numerical simulation of exact solution is compared to numerical simulation of an asymptoticmethod, and a satisfactory agreement found.  Accuracy dependence with frequency is verified.

scholarly journals Asymptotic solution of transonic nozzle flows with homogeneous condensation. I. Subcritical flows

1993 ◽  
Vol 5 (11) ◽  
pp. 2969-2981 ◽  
Author(s):  
Can F. Delale ◽  
Günter H. Schnerr ◽  
Jürgen Zierep
Keyword(s):  
Asymptotic Solution ◽  
Homogeneous Condensation ◽  
Nozzle Flows

Solar Internal Rotation and Dynamo Waves: A Two-Dimensional Asymptotic Solution in the Convection Zone

2000 ◽  
Vol 179 ◽  
pp. 379-380
Author(s):  
Gaetano Belvedere ◽  
Kirill Kuzanyan ◽  
Dmitry Sokoloff
Keyword(s):  
Magnetic Field ◽  
Asymptotic Solution ◽  
Internal Rotation ◽  
Convection Zone ◽  
General Idea ◽  
Dynamo Model ◽  
Axially Symmetric ◽  
Dynamo Action ◽  
Regeneration Rate ◽  
Dynamo Waves

Extended abstractHere we outline how asymptotic models may contribute to the investigation of mean field dynamos applied to the solar convective zone. We calculate here a spatial 2-D structure of the mean magnetic field, adopting real profiles of the solar internal rotation (the Ω-effect) and an extended prescription of the turbulent α-effect. In our model assumptions we do not prescribe any meridional flow that might seriously affect the resulting generated magnetic fields. We do not assume apriori any region or layer as a preferred site for the dynamo action (such as the overshoot zone), but the location of the α- and Ω-effects results in the propagation of dynamo waves deep in the convection zone. We consider an axially symmetric magnetic field dynamo model in a differentially rotating spherical shell. The main assumption, when using asymptotic WKB methods, is that the absolute value of the dynamo number (regeneration rate) |D| is large, i.e., the spatial scale of the solution is small. Following the general idea of an asymptotic solution for dynamo waves (e.g., Kuzanyan &amp; Sokoloff 1995), we search for a solution in the form of a power series with respect to the small parameter |D|–1/3(short wavelength scale). This solution is of the order of magnitude of exp(i|D|1/3S), where S is a scalar function of position.

Water uptake by substituted amylose tablets: experimentation and numerical simulation

2009 ◽  
Vol 00 (00) ◽  
pp. 090904073309027-8
Author(s):  
H.W. Wang ◽  
S. Kyriacos ◽  
L. Cartilier
Keyword(s):  
Numerical Simulation ◽  
Water Uptake
Sign in / Sign up

Export Citation Format

Share Document