Velocity distribution function and correlations in a granular Poiseuille flow

2010 ◽  
Vol 653 ◽  
pp. 175-219 ◽  
Author(s):  
MEHEBOOB ALAM ◽  
V. K. CHIKKADI
Keyword(s):  
Shear Rate ◽  
Poiseuille Flow ◽  
High Velocity ◽  
Elastic Limit ◽  
Distribution Functions ◽  
Transitional Flow ◽  
Wall Region ◽  
Surprising Result ◽  
Granular Gas ◽  
Wide Range

Probability distribution functions of fluctuation velocities (P(ux) and P(uy), where ux and uy are the fluctuation velocities in the x- and y-directions, respectively; the gravity is acting along the periodic x-direction and the flow is bounded by two walls parallel to the y-direction) and the density and the spatial velocity correlations are studied using event-driven simulations for an inelastic smooth hard disk system undergoing gravity-driven granular Poiseuille flow (GPF). It is shown that for GPF with smooth and/or perfectly rough walls the Maxwellian/Gaussian is the leading-order distribution over a wide range of densities in the quasi-elastic limit, which is a surprising result, especially for a dilute granular gas for which the Knudsen number belongs to the transitional flow regime. The signature of wall-roughness-induced dissipation mainly shows up in the P(ux) distribution in the form of a sharp peak for negative velocities in the near-wall region. Both P(ux) and P(uy) distributions become asymmetric with increasing dissipation at any density, and the emergence of density waves, which appear in the form of sinuous wave/slug at low-to-moderate values of mean density, makes these asymmetries stronger, especially in the presence of a slug. At high densities, the flow degenerates into a dense plug (where the density approaches its maximum limit and the shear rate is negligibly small) around the channel centreline and two shear layers (where the shear rate is high and the density is low) near the walls. The distribution functions within the shear layer follow the characteristics of those at moderate mean densities. Within the dense plug, the high-velocity tails of both P(ux) and P(uy) appear to undergo a transition from Gaussian in the quasi-elastic limit to power-law distributions at large inelasticity of particle collisions. For dense flows, it is shown that although the density correlations play a significant role in enhancing the velocity correlations when the collisions are sufficiently inelastic, they do not induce velocity correlations when the collisions are quasi-elastic for which the distribution functions are close to Gaussian. The combined effect of enhanced density and velocity correlations around the channel centreline with increasing inelastic dissipation seems to be responsible for the emergence of non-Gaussian high-velocity tails of distribution functions.

On the nominal transverse shear strain to characterize the severity of creasing

TAPPI Journal ◽  
2018 ◽  
Vol 17 (04) ◽  
pp. 231-240
Author(s):  
Douglas Coffin ◽  
Joel Panek
Keyword(s):  
Shear Strain ◽  
Transverse Shear ◽  
Elastic Limit ◽  
Experimental Results ◽  
Transverse Shear Strain ◽  
Maximum Strain ◽  
Machine Direction ◽  
Engineering Approach ◽  
Wide Range ◽  
Analytic Expression

A transverse shear strain was utilized to characterize the severity of creasing for a wide range of tooling configurations. An analytic expression of transverse shear strain, which accounts for tooling geometry, correlated well with relative crease strength and springback as determined from 90° fold tests. The experimental results show a minimum strain (elastic limit) that needs to be exceeded for the relative crease strength to be reduced. The theory predicts a maximum achievable transverse shear strain, which is further limited if the tooling clearance is negative. The elastic limit and maximum strain thus describe the range of interest for effective creasing. In this range, cross direction (CD)-creased samples were more sensitive to creasing than machine direction (MD)-creased samples, but the differences were reduced as the shear strain approached the maximum. The presented development provides the foundation for a quantitative engineering approach to creasing and folding operations.

scholarly journals Planetary Nebulae in M31: Abundances, and comparison with bright Planetary Nebulae in the LMC

1997 ◽  
Vol 180 ◽  
pp. 475-476
Author(s):  
M. G. Richer ◽  
G. Stasińska ◽  
M. L. McCall
Keyword(s):  
Planetary Nebula ◽  
Luminosity Function ◽  
Large Population ◽  
Wavelength Region ◽  
Planetary Nebulae ◽  
Surprising Result ◽  
Population Synthesis ◽  
Abundance Distribution ◽  
Wide Range ◽  
The Mean

We have obtained spectra of 28 planetary nebulae in the bulge of M31 using the MOS spectrograph at the Canada-France-Hawaii Telescope. Typically, we observed the [O II] λ3727 to He I λ5876 wavelength region at a resolution of approximately 1.6 å/pixel. For 19 of the 21 planetary nebulae whose [OIII]λ5007 luminosities are within 1 mag of the peak of the planetary nebula luminosity function, our oxygen abundances are based upon a measured [OIII]λ4363 intensity, so they are based upon a measured electron temperature. The oxygen abundances cover a wide range, 7.85 dex < 12 + log(O/H) < 9.09 dex, but the mean abundance is surprisingly low, 12 + log(O/H)–8.64 ± 0.32 dex, i.e., roughly half the solar value (Anders & Grevesse 1989). The distribution of oxygen abundances is shown in Figure 1, where the ordinate indicates the number of planetary nebulae with abundances within ±0.1 dex of any point on the x-axis. The dashed line indicates the mean abundance, and the dotted lines indicate the ±1 σ points. The shape of this abundance distribution seems to indicate that the bulge of M31 does not contain a large population of bright, oxygen-rich planetary nebulae. This is a surprising result, for various population synthesis studies (e.g., Bica et al. 1990) have found a mean stellar metallicity approximately 0.2 dex above solar. This 0.5 dex discrepancy leads one to question whether the mean stellar metallicity is as high as the population synthesis results indicate or if such metal-rich stars produce bright planetary nebulae at all. This could be a clue concerning the mechanism responsible for the variation in the number of bright planetary nebulae observed per unit luminosity in different galaxies (e.g., Hui et al. 1993).

scholarly journals Kinematics of Nuclei of Sc Galaxies

1980 ◽  
Vol 5 ◽  
pp. 191-191
Author(s):  
V. C. Rubin
Keyword(s):  
High Velocity ◽  
Stellar Population ◽  
Hii Regions ◽  
Emission Lines ◽  
High Luminosity ◽  
Rotation Curves ◽  
Velocity Gradients ◽  
Wide Range ◽  
Central Regions ◽  
Velocity Dispersions

For a sample of 21 Sc galaxies with a wide range of luminosities, of radii, and of masses, W. K. Ford and I have obtained spectra and determined rotation curves. By their kinematical behavior in their central regions, the Sc’s can be separated into two groups. Some galaxies, generally small and of low luminosity, have shallow central velocity gradients, reflecting their low central masses and densities. Other galaxies, most often large ones of high luminosity, have steep central velocity gradients. One reason this separation by central velocity gradients is of interest is because these galaxies exhibit other significant spectral differences which go hand-in-hand with the kinematical differences.The small, low luminosity galaxies show emission lines of Hα and [NII], with nuclear Ha sharp and stronger than [NII], and little or no stellar nuclear continuum, just as conventional HII regions. In contrast, the high luminosity galaxies show broad nuclear emission, with [NII] stronger than Ha. These galaxies have a strong red stellar continuum, arising from a red stellar population. The cause of the Hα[NII] intensity reversal in the nuclei of some galaxies remains unknown. However, the strong [NII] emission in generally high luminosity galaxies with massive nuclei, nuclei which show strong red continua, suggests that [Nil] intensity correlates with nuclear luminosity, and in turn with the density and velocity properties of the nuclear populations. We would expect high velocity dispersions and high bulge luminosities for galaxies with strong nuclear [NII] and steep central velocity gradients.

A statistical approach to micro-plastic strain in metals

1966 ◽  
Vol 1 (5) ◽  
pp. 415-421 ◽  
Author(s):  
A Esin ◽  
W J D Jones
Keyword(s):  
Plastic Strain ◽  
Elastic Limit ◽  
Statistical Approach ◽  
Physical Reality ◽  
General Concept ◽  
Distribution Functions ◽  
Point Of View ◽  
Plastic Strains ◽  
Statistical Point ◽  
Suggested Approach

The paper presents an outline of a theory of micro-inhomogeneity of stresses and strains resulting from the micro-structural properties of engineering materials. The problem is approached from a statistical point of view and it is experimentally shown that the degree of micro-inhomogeneity can be defined by normal distribution functions. Using the experimental results a general concept is postulated which takes into account the physical reality as completely as is practicable. It is shown that the suggested approach can be used to take into account the micro-plastic strains which exist while the material is nominally within the elastic limit.

scholarly journals Monte Carlo Calculations of the Radial Distribution Functions for a Proton?Electron Plasma

1965 ◽  
Vol 18 (2) ◽  
pp. 119 ◽  
Author(s):  
AA Barker
Keyword(s):  
Monte Carlo ◽  
Crystal Lattice ◽  
Radial Distribution ◽  
Lattice Theory ◽  
Electron Plasma ◽  
Distribution Functions ◽  
Radial Distribution Functions ◽  
Monte Carlo Calculations ◽  
Wide Range ◽  
General Method

A general method is presented for computation of radial distribution functions for plasmas over a wide range of temperatures and densities. The method uses the Monte Carlo technique applied by Wood and Parker, and extends this to long-range forces using results borrowed from crystal lattice theory. The approach is then used to calculate the radial distribution functions for a proton-electron plasma of density 1018 electrons/cm3 at a temperature of 104 OK. The results show the usefulness of the method if sufficient computing facilities are available.

Calculation of Developing Turbulent Flows in a Rotating Pipe

1991 ◽  
Vol 113 (1) ◽  
pp. 34-41 ◽  
Author(s):  
G. J. Yoo ◽  
R. M. C. So ◽  
B. C. Hwang
Keyword(s):  
Turbulent Flows ◽  
Reynolds Stress ◽  
Circumferential Strain ◽  
Three Dimensional ◽  
Wall Region ◽  
Boundary Layer Flows ◽  
Viscous Effects ◽  
Wide Range ◽  
Turbulence Closures ◽  
Rotating Boundary

Internal rotating boundary-layer flows are strongly influenced by large circumferential strain and the turbulence field is anisotropic. This is especially true in the entry region of a rotating pipe where the flow is three dimensional, the centrifugal force due to fluid rotation is less important, and the circumferential strain created by surface rotation has a significant effect on the turbulence field near the wall. Consequently, viscous effects cannot be neglected in the near-wall region. Several low-Reynolds-number turbulence closures are proposed for the calculation of developing rotating pipe flows. Some are two-equation closures with and without algebraic stress correction, while others are full Reynolds-stress closures. It is found that two-equation closures with and without algebraic stress correction are totally inadequate for this three-dimensional flow, while Reynolds-stress closures give results that are in good agreement with measurements over a wide range of rotation numbers.

The effect of cell tilting on turbulent thermal convection in a rectangular cell

2014 ◽  
Vol 762 ◽  
pp. 273-287 ◽  
Author(s):  
Shuang-Xi Guo ◽  
Sheng-Qi Zhou ◽  
Xian-Rong Cen ◽  
Ling Qu ◽  
Yuan-Zheng Lu ◽  
...  
Keyword(s):  
High Velocity ◽  
Large Scale ◽  
Velocity Measurements ◽  
Cell Width ◽  
Rectangular Cell ◽  
Aspect Ratios ◽  
Wide Range ◽  
Almost All ◽  
Temperature And Velocity Fields ◽  
Pronounced Reduction

AbstractIn this study the influence of cell tilting on flow dynamics and heat transport is explored experimentally within a rectangular cell (aspect ratios ${\it\Gamma}_{x}=1$ and ${\it\Gamma}_{y}=0.25$). The measurements are carried out over a wide range of tilt angles ($0\leqslant {\it\beta}\leqslant {\rm\pi}/2\ \text{rad}$) at a constant Prandtl number ($\mathit{Pr}\simeq 6.3$) and Rayleigh number ($\mathit{Ra}\simeq 4.42\times 10^{9}$). The velocity measurements reveal that the large-scale circulation (LSC) is sensitive to the symmetry of the system. In the level case, the high-velocity band of the LSC concentrates at about a quarter of the cell width from the boundary. As the cell is slightly tilted (${\it\beta}\simeq 0.04\ \text{rad}$), the position of the high-velocity band quickly moves towards the boundary. With increasing ${\it\beta}$, the LSC changes gradually from oblique ellipse-like to square-like, and other more complicated patterns. Oscillations have been found in the temperature and velocity fields for almost all ${\it\beta}$, and are strongest at around ${\it\beta}\simeq 0.48\ \text{rad}$. As ${\it\beta}$ increases, the Reynolds number ($\mathit{Re}$) initially also increases, until it reaches its maximum at the transition angle ${\it\beta}=0.15\ \text{rad}$, after which it gradually decreases. The cell tilting causes a pronounced reduction of the Nusselt number ($\mathit{Nu}$). As ${\it\beta}$ increases from 0 to 0.15, 1.05 and ${\rm\pi}/2\ \text{rad}$, the reduction of $\mathit{Nu}$ is approximately 1.4 %, 5 % and 18 %, respectively. Over the ranges of $0\leqslant {\it\beta}\leqslant 0.15\ \text{rad}$, $0.15\leqslant {\it\beta}\leqslant 1.05\ \text{rad}$ and $1.05\leqslant {\it\beta}\leqslant {\rm\pi}/2\ \text{rad}$, the decay slopes are $8.57\times 10^{-2}$, $3.27\times 10^{-2}$ and $0.24\ \text{rad}^{-1}$, respectively.

Modelization of dispersion of swimming bacteria in Poiseuille flow

2021 ◽  
Author(s):  
Akash Ganesh ◽  
Romain Rescanieres ◽  
Carine Douarche ◽  
Harold Auradou
Keyword(s):  
Shear Rate ◽  
Numerical Simulations ◽  
Poiseuille Flow ◽  
Dispersion Coefficient ◽  
Equations Of Motion ◽  
Critical Shear Rate ◽  
Uniform Shear ◽  
Simple Boundary ◽  
Swimming Bacteria ◽  
Local Shear

&lt;p&gt;We study the shear-induced migration of dilute suspensions of swimming bacteria (modelled as Active elongated Brownian Particles or ABPs) subject to plane Poiseuille flow in a confined channel. By incorporating very simple boundary conditions, we perform numerical simulations of the 3D equations of motion describing the change in position and orientation of the particles. We investigate the effects of confinement, of non-uniform shear and of aspect ratio of the particles on the overall dynamics of the ABPs population.&lt;/p&gt;&lt;p&gt;We particularly study the coupling between the local shear and the change in the orientation of the particles. We thus perform numerical simulations on both the case where the change in the orientation of the ABPs is purely diffusive (decoupled case) and the case where their orientation is coupled to the shear flow (coupled case). We observe that the decoupled case exhibits a Taylor dispersion &lt;em&gt;i.e.&lt;/em&gt;&amp;#160; the effective dispersion coefficient of the ABPs along the direction of the flow is proportional to the square of the imposed shear at all shears.&amp;#160;&lt;/p&gt;&lt;p&gt;However, for all the coupled cases we observe a transition from a Taylor to an active-Taylor regime at a critical shear rate, indicating the effect of shear coupling on the orientation dynamics of the particles. This critical shear rate is directly correlated to the degree of confinement. The change in the dispersion coefficient along the direction of the flow as function of the shear rate is in qualitative agreement with previous studies[1].&amp;#160;&lt;/p&gt;&lt;p&gt;To further understand these results, we also investigate the change in the dispersion coefficient in the other two directions along with the effect of the shape of the particles. We believe that this study should enhance our understanding of dispersion of bacteria through porous media, on surfaces etc. where shear flows are ubiquitous.&amp;#160;&lt;/p&gt;&lt;p&gt;[1] Sandeep Chilukuri, Cynthia H.Collins, and Patrick T. Underhill. Dispersionof flagellated swimming microorganisms in planar poiseuille flow.Physics offluids, 27, (031902):1 &amp;#8211;17, 2015&lt;/p&gt;

scholarly journals The magnetorotational instability prefers three dimensions

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190622
Author(s):  
Jeffrey S. Oishi ◽  
Geoffrey M. Vasil ◽  
Morgan Baxter ◽  
Andrew Swan ◽  
Keaton J. Burns ◽  
...  
Keyword(s):  
Shear Rate ◽  
Angular Velocity ◽  
Laboratory Experiments ◽  
Three Dimensional ◽  
Linear Instability ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Magnetorotational Instability ◽  
Dynamo Action ◽  
Wide Range

The magnetorotational instability (MRI) occurs when a weak magnetic field destabilizes a rotating, electrically conducting fluid with inwardly increasing angular velocity. The MRI is essential to astrophysical disc theory where the shear is typically Keplerian. Internal shear layers in stars may also be MRI-unstable, and they take a wide range of profiles, including near-critical. We show that the fastest growing modes of an ideal magnetofluid are three-dimensional provided the shear rate, S , is near the two-dimensional onset value, S c . For a Keplerian shear, three-dimensional modes are unstable above S  ≈ 0.10 S c , and dominate the two-dimensional modes until S  ≈ 2.05 S c . These three-dimensional modes dominate for shear profiles relevant to stars and at magnetic Prandtl numbers relevant to liquid-metal laboratory experiments. Significant numbers of rapidly growing three-dimensional modes remainy well past 2.05 S c . These finding are significant in three ways. First, weakly nonlinear theory suggests that the MRI saturates by pushing the shear rate to its critical value. This can happen for systems, such as stars and laboratory experiments, that can rearrange their angular velocity profiles. Second, the non-normal character and large transient growth of MRI modes should be important whenever three-dimensionality exists. Finally, three-dimensional growth suggests direct dynamo action driven from the linear instability.

scholarly journals The X-ray view of the Wolf-Rayet stars

1995 ◽  
Vol 163 ◽  
pp. 429-437
Author(s):  
A.M.T. Pollock
Keyword(s):  
High Velocity ◽  
X Ray ◽  
Wide Range ◽  
Colliding Winds

Ever since the earliest work, X-ray observations have been central in the chequered development of the study of interacting high-velocity winds in binaries. This review assesses how confidently the observations of Wolf-Rayet stars may be interpreted as the result of colliding winds, drawing attention to the wide range of X-ray luminosities even among the relatively bright binaries. Although the data do not generally conform to the simplest binary models, some suggestions are made to reconcile theory and observation.

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