Distribution of liquid over a random packing. V. Dependence of the coefficient of radial spreading of liquid D on the size and form of the packing element and on the mean density of wetting

1968 ◽  
Vol 33 (8) ◽  
pp. 2636-2645 ◽  
Author(s):  
V. Staněk ◽  
V. Kolář
Keyword(s):  
Random Packing ◽  
Packing Element ◽  
Radial Spreading ◽  
The Mean

Experimental Analysis and Flow Visualization of a Thin Liquid Film on a Stationary and Rotating Disk

1991 ◽  
Vol 113 (1) ◽  
pp. 73-80 ◽  
Author(s):  
S. Thomas ◽  
A. Faghri ◽  
W. Hankey
Keyword(s):  
Free Surface ◽  
Film Thickness ◽  
Liquid Film ◽  
Flow Visualization ◽  
Thin Liquid Film ◽  
Rotating Disk ◽  
Radial Spreading ◽  
Frictional Forces ◽  
The Mean ◽  
The Waves

The mean thickness of a thin liquid film of deionized water with a free surface on a stationary and rotating horizontal disk has been measured with a nonobtrusive capacitance technique. The measurements were taken when the rotational speed ranged from 0–300 rpm and the flow rate varied from 7.0–15.0 lpm. A flow visualization study of the thin film was also performed to determine the characteristics of the waves on the free surface. When the disk was stationary, a circular hydraulic jump was present on the disk. Upstream from the jump, the film thickness was determined by the inertial and frictional forces on the fluid, and the radial spreading of the film. The surface tension at the edge of the disk affected the film thickness downstream from the jump. For the rotating disk, the film thickness was dependent upon the inertial and frictional forces near the center of the disk and the centrifugal forces near the edge of the disk.

Random sequential packing simulations in three dimensions for aligned cubes

1989 ◽  
Vol 26 (3) ◽  
pp. 664-670 ◽  
Author(s):  
Douglas W. Cooper
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Random Packing ◽  
Limit Problem ◽  
Three Dimensions ◽  
Standard Errors ◽  
Cube Root ◽  
Random Errors ◽  
Infinite Region ◽  
The Mean

This particular three-dimensional random packing limit problem is to determine the mean fraction of a cubic space that would be occupied by aligned, fixed, equalsize cubes, placed at random locations sequentially until no more can be added. No analytical solution has yet been found for this problem. Simulation results for a finite region and finite number of attempts were extrapolated to an infinite number of attempts (N →∞) in an infinite region by multiple linear regression, using volume fraction occupied (F) as a linear combination of the ratio of the length of the small cube sides (S) to the length of the cubic region side (L) and the cube root of the ratio of the region volume to the total volume of cubes tried, (L3/NS3)⅓. These results for random packing in a volume with penetrable walls can be adjusted with a multiplicative correction factor to give the results for impenetrable walls. A total of N = 107 attempts at placement were made for L/S = 20/1 and N = 14 × 106 attempts were made for L/S = 10/1. The results for volume fraction packed are correlated by F = 0.430(±0.008) + 0.966(±0.072)(S/L) – 0.236(±0.029)(L3/NS)⅓. The numbers in parentheses are twice the standard errors of estimate of the coefficients, indicating the 95% confidence intervals due to random errors. This value for the packing density limit, 0.430 ± 0.008, is slightly larger than that given by a conjecture by Palásti [10], 0.4178. Our value is consistent with that obtained by rather different simulation methods by Jodrey and Tory [8], 0.4227 ± 0.0006, and by Blaisdell and Solomon [2], 0.4262.

Mean Concentration Field of a Jet in a Uniform Counter-Flow

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
Luis A. Torres ◽  
Mohammad Mahmoudi ◽  
Brian A. Fleck ◽  
David J. Wilson ◽  
David Nobes
Keyword(s):  
Linear Growth ◽  
Concentration Field ◽  
Flow Region ◽  
Counter Flow ◽  
Scaling Factors ◽  
Scalar Concentration ◽  
Planar Laser ◽  
Radial Spreading ◽  
The Mean ◽  
Mean Concentration

An experimental investigation of the scaling factors of mean scalar concentration field of jets issuing into a uniform counter-flow stream is presented. The centerline decay and radial spreading of the mean concentration field were measured by using planar laser induced fluorescence. Jet to counter-flow velocity ratios ranging between 4 to19 were investigated for two different jet diameters. The 5% contour of the mean concentration field of the jet was used to define new scaling factors that generate universal forms for the centerline concentration decay. The jet growth rate in the radial direction was found to be divided into two regions where a linear growth was observed and a region characterized by a power law. Empirical expressions are introduced which predict concentration decay in the established flow region in both the axial and radial directions.

Random sequential packing simulations in three dimensions for aligned cubes

1989 ◽  
Vol 26 (03) ◽  
pp. 664-670 ◽  
Author(s):  
Douglas W. Cooper
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Random Packing ◽  
Limit Problem ◽  
Three Dimensions ◽  
Standard Errors ◽  
Cube Root ◽  
Random Errors ◽  
Infinite Region ◽  
The Mean

This particular three-dimensional random packing limit problem is to determine the mean fraction of a cubic space that would be occupied by aligned, fixed, equalsize cubes, placed at random locations sequentially until no more can be added. No analytical solution has yet been found for this problem. Simulation results for a finite region and finite number of attempts were extrapolated to an infinite number of attempts (N →∞) in an infinite region by multiple linear regression, using volume fraction occupied (F) as a linear combination of the ratio of the length of the small cube sides (S) to the length of the cubic region side (L) and the cube root of the ratio of the region volume to the total volume of cubes tried, (L 3/NS 3)⅓. These results for random packing in a volume with penetrable walls can be adjusted with a multiplicative correction factor to give the results for impenetrable walls. A total of N = 107 attempts at placement were made for L/S = 20/1 and N = 14 × 106 attempts were made for L/S = 10/1. The results for volume fraction packed are correlated by F = 0.430(±0.008) + 0.966(±0.072)(S/L) – 0.236(±0.029)(L 3/NS)⅓ . The numbers in parentheses are twice the standard errors of estimate of the coefficients, indicating the 95% confidence intervals due to random errors. This value for the packing density limit, 0.430 ± 0.008, is slightly larger than that given by a conjecture by Palásti [10], 0.4178. Our value is consistent with that obtained by rather different simulation methods by Jodrey and Tory [8], 0.4227 ± 0.0006, and by Blaisdell and Solomon [2], 0.4262.

Photo-electric Hβ and uvby photometry

1966 ◽  
Vol 24 ◽  
pp. 170-180
Author(s):  
D. L. Crawford
Keyword(s):  
Narrow Band ◽  
Line Strength ◽  
Interference Filter ◽  
B Stars ◽  
Relative Line ◽  
The Mean ◽  
F Stars ◽  
Two Parameters ◽  
Filter Photometry ◽  
The Continuum

Early in the 1950's Strömgren (1, 2, 3, 4, 5) introduced medium to narrow-band interference filter photometry at the McDonald Observatory. He used six interference filters to obtain two parameters of astrophysical interest. These parameters he calledlandc, for line and continuum hydrogen absorption. The first measured empirically the absorption line strength of Hβby means of a filter of half width 35Å centered on Hβand compared to the mean of two filters situated in the continuum near Hβ. The second index measured empirically the Balmer discontinuity by means of a filter situated below the Balmer discontinuity and two above it. He showed that these two indices could accurately predict the spectral type and luminosity of both B stars and A and F stars. He later derived (6) an indexmfrom the same filters. This index was a measure of the relative line blanketing near 4100Å compared to two filters above 4500Å. These three indices confirmed earlier work by many people, including Lindblad and Becker. References to this earlier work and to the systems discussed today can be found in Strömgren's article inBasic Astronomical Data(7).

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

the effects of resonance with Jupiter in the system of short-period comets

1974 ◽  
Vol 22 ◽  
pp. 193-203
Author(s):  
L̆ubor Kresák
Keyword(s):  
Structural Effects ◽  
Order Resonance ◽  
Mean Motion ◽  
Short Period ◽  
The Mean ◽  
Compound Effect ◽  
Low Order

AbstractStructural effects of the resonance with the mean motion of Jupiter on the system of short-period comets are discussed. The distribution of mean motions, determined from sets of consecutive perihelion passages of all known periodic comets, reveals a number of gaps associated with low-order resonance; most pronounced are those corresponding to the simplest commensurabilities of 5/2, 2/1, 5/3, 3/2, 1/1 and 1/2. The formation of the gaps is explained by a compound effect of five possible types of behaviour of the comets set into an approximate resonance, ranging from quick passages through the gap to temporary librations avoiding closer approaches to Jupiter. In addition to the comets of almost asteroidal appearance, librating with small amplitudes around the lower resonance ratios (Marsden, 1970b), there is an interesting group of faint diffuse comets librating in characteristic periods of about 200 years, with large amplitudes of about±8% in μ and almost±180° in σ, around the 2/1 resonance gap. This transient type of motion appears to be nearly as frequent as a circulating motion with period of revolution of less than one half that of Jupiter. The temporary members of this group are characteristic not only by their appearance but also by rather peculiar discovery conditions.

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