The motion of an ellipsoid in tube flow at low Reynolds numbers

1996 ◽  
Vol 324 ◽  
pp. 287-308 ◽  
Author(s):  
Masako Sugihara-Seki
Keyword(s):  
Initial Conditions ◽  
Flow Direction ◽  
Major Axis ◽  
Oblate Spheroid ◽  
Reynolds Numbers ◽  
Prolate Spheroid ◽  
Stable Configuration ◽  
Axis Ratio ◽  
Low Reynolds Numbers ◽  
Freely Suspended

The motion of a rigid ellipsoidal particle freely suspended in a Poiseuille flow of an incompressible Newtonian fluid through a narrow tube is studied numerically in the zero-Reynolds-number limit. It is assumed that the effect of inertia forces on the motion of the particle and the fluid can be neglected and that no forces or torques act on the particle. The Stokes equation is solved by a finite element method for various positions and orientations of the particle to yield the instantaneous velocity of the particle as well as the flow field around it, and the particle trajectories are determined for different initial configurations. A prolate spheroid is found to either tumble or oscillate in rotation, depending on the particle–tube size ratio, the axis ratio of the particle, and the initial conditions. A large oblate spheroid may approach asymptotically a steady, stable configuration, at which it is located close to the tube centreline, with its major axis slightly tilted from the undisturbed flow direction. The motion of non-axisymmetric ellipsoids is also illustrated and discussed with emphasis on the effect of the particle shape and size.

OSCILLATING VISCOUS FLOW OVER PROLATE SPHEROIDS

1999 ◽  
Vol 23 (1A) ◽  
pp. 83-93 ◽  
Author(s):  
R.S. Alassar ◽  
H.M. Badr
Keyword(s):  
Free Stream ◽  
Layer Structure ◽  
Major Axis ◽  
Periodic Variation ◽  
Reynolds Numbers ◽  
Prolate Spheroid ◽  
Oscillating Flow ◽  
Axis Ratio ◽  
Pressure Surface ◽  
Prolate Spheroids

The axisymmetric viscous oscillating flow over a prolate spheroid is considered. The oscillations are harmonic and the free stream is always parallel to the spheroid major axis. The flow is governed by the Strouhal and the Reynolds numbers as well as the spheroid axis ratio. In the present paper, we only investigate the effect of Reynolds number while keeping the Strouhal number and the axis ratio unchanged. The results are presented in terms of the periodic variation of the drag coefficient, pressure, surface vorticity, separation angle, the wake length, and the streamline and vorticity patterns for Reynolds numbers ranging from 5 to 100. Upon averaging the stream function and vorticity over one complete oscillation, the double boundary-layer structure observed in the case of a sphere is confirmed for the range of parameters considered.

Hydromechanics of low-Reynolds-number flow. Part 3. Motion of a spheroidal particle in quadratic flows

1975 ◽  
Vol 72 (1) ◽  
pp. 17-34 ◽  
Author(s):  
Allen T. Chwang
Keyword(s):  
Flow Direction ◽  
Major Axis ◽  
Prolate Spheroid ◽  
Spheroidal Particle ◽  
Axis Ratio ◽  
Reynolds Number Flow ◽  
Singularity Method ◽  
Principal Axes ◽  
Angular Velocities ◽  
Low Reynolds

Exact solutions in closed form have been found using the singularity method for various quadratic flows of an unbounded incompressible viscous fluid at low Reynolds numbers past a prolate spheroid with an arbitrary orientation with respect to the fluid. The quadratic flows considered here include unidirectional paraboloidal flows, with either an elliptic or a hyperbolic velocity distribution, and stagnation-like quadratic flows as typical representations. The motion of a force-free spheroidal particle in a paraboloidal flow has been determined. It is shown that the spheroid rotates about three principal axes with angular velocities governed by a set of Jeffery orbital equations with the rate of shear evaluated at the centre of the spheroid. These angular velocities depend on the minor-to-major axis ratio of the spheroid and its instantaneous orientation, but are independent of its actual size. The spheroid also translates at a variable speed, depending on its orientation relative to the surrounding fluid, along a straight path parallel to the main flow direction without any side drift or migration. This ‘jerk’ motion obeys a trajectory equation which is size dependent.

Low Reynolds numbers flow past an ellipsoid of revolution of large aspect ratio

1965 ◽  
Vol 23 (4) ◽  
pp. 657-671 ◽  
Author(s):  
Yun-Yuan Shi
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Three Dimensional ◽  
Major Axis ◽  
Reynolds Numbers ◽  
The Body ◽  
Large Aspect Ratio ◽  
Low Reynolds Numbers ◽  
Ellipsoid Of Revolution ◽  
Limiting Case

The results of Proudman & Pearson (1957) and Kaplun & Lagerstrom (1957) for a sphere and a cylinder are generalized to study an ellipsoid of revolution of large aspect ratio with its axis of revolution perpendicular to the uniform flow at infinity. The limiting case, where the Reynolds number based on the minor axis of the ellipsoid is small while the other Reynolds number based on the major axis is fixed, is studied. The following points are deduced: (1) although the body is three-dimensional the expansion is in inverse power of the logarithm of the Reynolds number as the case of a two-dimensional circular cylinder; (2) the existence of the ends and the variation of the diameter along the axis of revolution have no effect on the drag to the first order; (3) a formula for drag is obtained to higher order.

Heat and Mass Transfer in Fixed Beds at Low Reynolds Numbers

1980 ◽  
Vol 102 (4) ◽  
pp. 736-741 ◽  
Author(s):  
L. R. Glicksman ◽  
F. M. Joos
Keyword(s):  
Nusselt Number ◽  
Flow Direction ◽  
Packed Bed ◽  
Reynolds Numbers ◽  
Experimental Measurements ◽  
Local Concentration ◽  
Low Reynolds Numbers ◽  
Nusselt Numbers ◽  
Predicted Values ◽  
Fixed Beds

In a fixed or fluidized bed at low particle Reynolds numbers, the overall or effective Sherwood and Nusselt number has been found by many investigators to be much less than unity. The limiting value of the particle Sherwood or Nusselt number based on local concentration or temperature differences is shown to be equal to or greater than unity. An analytical model was established using realistic packed bed geometries to allow for diffusion in the flow direction, channeling due to nonuniformities in bed voidage and different particle sizes, and inaccuracies in the experimental measurements. The predicted values of the effective Sherwood and Nusselt numbers are found to agree closely with experimental measurements for gases and liquids. Diffusion is shown to be the primary mechanism for the fall-off in the effective bed characteristics.

Pressure Gradient and Leading Edge Effects on the Corner Boundary Layer

1979 ◽  
Vol 30 (3) ◽  
pp. 471-484 ◽  
Author(s):  
M. Zamir ◽  
A.D. Young
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Flow Direction ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Flat Plates ◽  
Low Reynolds Numbers ◽  
Small Incidence ◽  
Made In

SummaryResults are presented of velocity and pressure measurements made in the initially laminar boundary layer in a streamwise corner formed by two flat plates at 90° to each other set at various incidences. The leading edges of the plates were sharp in contrast to earlier tests with an aerofoil type leading edge. It was found impossible to obtain a steady enough flow for useful measurements to be made at zero incidence and pressure gradient, a small incidence associated with a favourable pressure gradient was necessary. This is believed to be because of the development of separation bubbles at the sharp leading edge at very small incidences due to small variations of flow direction to be expected in a wind tunnel. The profiled nose used in earlier tests afforded flow conditions much closer to the ideal theoretical model involving zero pressure gradient, but it is argued that any nose however shaped may introduce disturbances in the form of characteristic secondary flows that may well determine the downstream response of the boundary layer. In any case the corner flow is highly unstable at all but very low Reynolds numbers, and in the absence of a region of favourable pressure gradient a Reynolds number in terms of distance downstream of the leading edge greater than about 105is unlikely to be attained in practice with the flow remaining smooth and laminar.

Mechanism of determination of the shedding frequency of vortices behind a cylinder at low Reynolds numbers

1978 ◽  
Vol 89 (1) ◽  
pp. 49-60 ◽  
Author(s):  
Michio Nishioka ◽  
Hiroshi Sato
Keyword(s):  
Stability Theory ◽  
Linear Growth ◽  
Flow Direction ◽  
Reynolds Numbers ◽  
Linear Growth Rate ◽  
Low Reynolds Numbers ◽  
Direct Measurements ◽  
Vortex Streets ◽  
Low Reynolds ◽  
The Stability

Two kinds of experiment were made in the wake of a cylinder at Reynolds numbers ranging between 20 and 150. One was a close look at the structure of the vortex street with a stationary cylinder at Reynolds numbers greater than 48. The other experiment was made at lower Reynolds numbers with a cylinder vibrating normal to the flow direction. In this case an artificially induced small-amplitude fluctuation grows exponentially with the rate predicted by the stability theory. Because of the similarity between the two kinds of wake, we postulate that the shedding of the vortex at low Reynolds numbers is initiated by the linear growth, namely, the fluctuation with the frequency of maximum linear growth rate develops into vortex streets. By using the measured width of the wake at the stagnation point in the wake and the result of the stability theory, we could calculate the Strouhal number for Reynolds numbers ranging from 48 to 120. The predicted Strouhal numbers agree well with the values from direct measurements.

scholarly journals Hydromechanics of low-Reynolds-number flow. Part 4. Translation of spheroids

1976 ◽  
Vol 75 (4) ◽  
pp. 677-689 ◽  
Author(s):  
Allen T. Chwang ◽  
Theodore Y. Wu
Keyword(s):  
Major Axis ◽  
Reynolds Numbers ◽  
Prolate Spheroid ◽  
Stream Velocity ◽  
Semi Major Axis ◽  
Reynolds Number Flow ◽  
Flow Past ◽  
Flow Part ◽  
Number Flow ◽  
Low Reynolds

The problem of a uniform transverse flow past a prolate spheroid of arbitrary aspect ratio at low Reynolds numbers has been analysed by the method of matched asymptotic expansions. The solution is found to depend on two Reynolds numbers, one based on the semi-minor axis b, Rb = Ub/v, and the other on the semi-major axis a, Ra = Ua/v (U being the free-stream velocity at infinity, which is perpendicular to the major axis of the spheroid, and v the kinematic viscosity of the fluid). A drag formula is obtained for small values of Rb and arbitrary values of Ra. When Ra is also small, the present drag formula reduces to the Oberbeck (1876) result for Stokes flow past a spheroid, and it gives the Oseen (1910) drag for an infinitely long cylinder when Ra tends to infinity. This result thus provides a clear physical picture and explanation of the ‘Stokes paradox’ known in viscous flow theory.

scholarly journals Free-fall experiments of volcanic ash particles using a 2-D video disdrometer

2019 ◽  
Vol 12 (10) ◽  
pp. 5363-5379 ◽  
Author(s):  
Sung-Ho Suh ◽  
Masayuki Maki ◽  
Masato Iguchi ◽  
Dong-In Lee ◽  
Akihiko Yamaji ◽  
...  
Keyword(s):  
Volcanic Ash ◽  
Free Fall ◽  
Oblate Spheroid ◽  
Vertical Axis ◽  
Prolate Spheroid ◽  
Terminal Velocity ◽  
Atmospheric Conditions ◽  
Axis Ratio ◽  
Mean Values ◽  
Ash Fall

Abstract. Information of aerodynamic parameters of volcanic ash particles, such as terminal velocity, axis ratio, and canting angle, are necessary for quantitative ash-fall estimations with weather radar. In this study, free-fall experiments of volcanic ash particles were accomplished using a two-dimensional video disdrometer under controlled conditions. Samples containing a rotating symmetric axis were selected and divided into five types according to shape and orientation: oblate spheroid with horizontal rotating axis (OH), oblate spheroid with vertical axis (OV), prolate spheroid with horizontal rotating axis (PH), prolate spheroid with vertical rotating axis (PV), and sphere (Sp). The horizontally (OH and PH) and vertically (OV and PV) oriented particles were present in proportions of 76 % and 22 %, and oblate and prolate spheroids were in proportions of 76 % and 24 %, respectively. The most common shape type was OH (57 %). The terminal velocities of OH, OV, PH, PV, and Sp were obtained analyzing 2-D video disdrometer data. The terminal velocities of PV were highest compared to those of other particle types. The lowest terminal velocities were found in OH particles. It is interesting that the terminal velocities for OH decreased rapidly in the range 0.5<D<1 mm, corresponding to the decrease in axis ratio (i.e., smaller the particle, the flatter the shape). The axis ratios of all particle types except Sp were found to be converged to 0.94 at D>2 mm. The histogram of canting angles followed unimodal and bimodal distributions with respect to horizontally and vertically oriented particles, respectively. The mean values and the standard deviation of entire particle shape types were close to 0 and 10∘, respectively, under calm atmospheric conditions.

Velocity Profiles of Flow at Low Reynolds Numbers

1970 ◽  
Vol 37 (1) ◽  
pp. 2-4 ◽  
Author(s):  
S. Abarbanel ◽  
S. Bennett ◽  
A. Brandt ◽  
J. Gillis
Keyword(s):  
Viscous Flow ◽  
Stokes Flow ◽  
Initial Conditions ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Straight Channel ◽  
Numerical Work ◽  
Low Reynolds Numbers ◽  
Quarter Plane ◽  
Numerical Effect

Earlier numerical work on viscous flow in the inlet region of a straight channel indicated some curious features in the velocity profiles. These are now investigated further to establish that they are not merely a numerical effect and that, moreover, they persist, even if the initial conditions are modified so as to remove the singularity at the inlet. The method used is to consider a physically similar problem of Stokes flow in a quarter-plane which can be solved analytically.

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