Extension of the Wall-Driven Enclosure Flow Problem to Toroidally Shaped Geometries of Square Cross-Section

1996 ◽  
Vol 118 (4) ◽  
pp. 779-786 ◽  
Author(s):  
L. M. Phinney ◽  
J. A. C. Humphrey
Keyword(s):  
Cross Section ◽  
Fluid Motion ◽  
Radius Of Curvature ◽  
Two Dimensional ◽  
Coordinate Direction ◽  
Concave Wall ◽  
Center Vortex ◽  
Convex Wall ◽  
Two Dimensional Flow ◽  
Moving Fluid

The two-dimensional wall-driven flow in an enclosure has been a numerical paradigm of long-standing interest and value to the fluid mechanics community. In this paradigm the enclosure is infinitely long in the x-coordinate direction and of square cross-section (d × d) in the y-z plane. Fluid motion is induced in all y-z planes by a wall (here the top wall) sliding normal to the x-coordinate direction. This classical numerical paradigm can be extended by taking a length L of the geometry in the x-coordinate direction and joining the resulting end faces at x = 0 and x = L to form a toroid of square cross-section (d × d) and radius of curvature Rc. In the curved geometry, axisymmetric fluid motion (now in the r-z planes) is induced by sliding the top flat wall of the toroid with an imposed radial velocity, ulid, generally directed from the convex wall towards the concave wall of the toroid. Numerical calculations of this flow configuration are performed for values of the Reynolds number (Re = ulidd/ν) equal to 2400, 3200, and 4000 and for values of the curvature ratio (δ = d/Rc) ranging from 5.0 · 10−6 to 1.0. For δ ≤ 0.05 the steady two-dimensional flow pattern typical of the classical (straight) enclosure is faithfully reproduced. This consists of a large primary vortex occupying most of the enclosure and three much smaller secondary eddies located in the two lower corners and the upper upstream (convex wall) corner of the enclosure. As δ increases for a fixed value of Re, a critical value, δcr, is found above which the primary center vortex spontaneously migrates to and concentrates in the upper downstream (concave wall) corner. While the sense of rotation originally present in this vortex is preserved, that of the slower moving fluid below it and now occupying the bulk of the enclosure cross-section is reversed. The relation marking the transition between these two stable steady flow patterns is predicted to be δcr1/4 = 3.58 Re-1/5 (δ ± 0.005).

Flow Visualization by Means of Contactless Inductive Flow Tomography in the Presence of a Magnetic Brake

2015 ◽  
Vol 15 (1) ◽  
pp. 41-48 ◽  
Author(s):  
Matthias Ratajczak ◽  
Thomas Wondrak ◽  
Klaus Timmel ◽  
Frank Stefani ◽  
Sven Eckert
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Magnetic Fields ◽  
Flow Field ◽  
Continuous Casting ◽  
Flow Structure ◽  
Cross Section ◽  
Two Dimensional ◽  
Slab Casting ◽  
Two Dimensional Flow

AbstractIn continuous casting DC magnetic fields perpendicular to the wide faces of the mold are used to control the flow in the mold. Especially in this case, even a rough knowledge of the flow structure in the mold would be highly desirable. The contactless inductive flow tomography (CIFT) allows to reconstruct the dominating two-dimensional flow structure in a slab casting mold by applying one external magnetic field and by measuring the flow-induced magnetic fields outside the mold. For a physical model of a mold with a cross section of 140 mm×35 mm we present preliminary measurements of the flow field in the mold in the presence of a magnetic brake. In addition, we show first reconstructions of the flow field in a mold with the cross section of 400 mm×100 mm demonstrating the upward scalability of CIFT.

Towed Underwater SPIV Measurement of Flow Fields Around a Surface-Piercing Cylinder With Free Surface Effects

2015 ◽  
Author(s):  
Jeonghwa Seo ◽  
Bumwoo Han ◽  
Shin Hyung Rhee
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Surface Wave ◽  
Flow Field ◽  
Cross Section ◽  
Surface Effects ◽  
Flow Fields ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
Wave Induced

Effects of free surface on development of turbulent boundary layer and wake fields were investigated. By measuring flow field around a surface piercing cylinder in various advance speed conditions in a towing tank, free surface effects were identified. A towed underwater Stereoscopic Particle Image Velocimetry (SPIV) system was used to measure the flow field under free surface. The cross section of the test model was water plane shape of the Wigley hull, of which longitudinal length and width were 1.0 m and 100 mm, respectively. With sharp bow shape and slender cross section, flow separation was not expected in two-dimensional flow. Flow fields near the free-surface and in deep location that two-dimensional flow field was expected were measured and compared to identify free-surface effects. Some planes perpendicular to longitudinal direction near the model surface and behind the model were selected to track development of turbulent boundary layer. Froude numbers of the test conditions were from 0.126 to 0.40 and corresponding Reynolds numbers were from 395,000 to 1,250,000. In the lowest Froude number condition, free-surface wave was hardly observed and only free surface effects without surface wave could be identified while violent free-surface behavior due to wave-induced separation dominated the flow fields in the highest Froude number condition. From the instantaneous velocity fields, Time-mean velocity, turbulence kinetic energy, and flow structure derived by proper orthogonal decomposition (POD) were analyzed. As the free-surface effect, development of retarded wake, free-surface waves, and wave-induced separation were mainly observed.

scholarly journals A Study of Glacier Flow for an Open-Pit Mine: An Exercise in Applied Glaciology

1974 ◽  
Vol 13 (69) ◽  
pp. 401-414 ◽  
Author(s):  
S. C. Colbeck
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Greenland Ice Sheet ◽  
Field Work ◽  
Open Pit Mine ◽  
Open Pit ◽  
Two Dimensional ◽  
Ice Flow ◽  
Two Dimensional Flow ◽  
Glacier Flow

As part of the feasibility study for the development of an open-pit mine at the edge of the Greenland ice sheet, a study is made of the ice flow toward the proposed pit. The flow is analyzed by considering the two-dimensional flow along seven cross-sections. The most favorable profile is determined for each cross-section and its flow calculated. The excavation necessary to expose the ore is 106 × 106 m3 of ice. 66 × 106 m3 of ice will have to be removed in order to establish favorable profiles and an additional 7.9 × 106 m3 of ice will have to be removed each year in order to prevent the glacier from thickening and advancing into the mine. Many other glaciological problems must be considered, and field work continues in order to provide more information about the area.

scholarly journals A Study of Glacier Flow for an Open-Pit Mine: An Exercise in Applied Glaciology

1974 ◽  
Vol 13 (69) ◽  
pp. 401-414 ◽  
Author(s):  
S. C. Colbeck
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Greenland Ice Sheet ◽  
Field Work ◽  
Open Pit Mine ◽  
Open Pit ◽  
Two Dimensional ◽  
Ice Flow ◽  
Two Dimensional Flow ◽  
Glacier Flow

As part of the feasibility study for the development of an open-pit mine at the edge of the Greenland ice sheet, a study is made of the ice flow toward the proposed pit. The flow is analyzed by considering the two-dimensional flow along seven cross-sections. The most favorable profile is determined for each cross-section and its flow calculated. The excavation necessary to expose the ore is 106 × 106m3of ice. 66 × 106m3of ice will have to be removed in order to establish favorable profiles and an additional 7.9 × 106m3of ice will have to be removed each year in order to prevent the glacier from thickening and advancing into the mine. Many other glaciological problems must be considered, and field work continues in order to provide more information about the area.

Three-dimensional and multicellular steady and unsteady convection in fluid-saturated porous media at high Rayleigh numbers

1979 ◽  
Vol 94 (1) ◽  
pp. 25-38 ◽  
Author(s):  
Gerald Schubert ◽  
Joe M. Straus
Keyword(s):  
Single Cell ◽  
Cross Section ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Arbitrary Length ◽  
Dimensional Flow ◽  
A Value ◽  
Square Cylinders ◽  
Two Dimensional Flow ◽  
Rayleigh Numbers

In an effort to determine the characteristics of the various types of convection that can occur in a fluid-saturated porous medium heated from below, a Galerkin approach is used to investigate three-dimensional convection in a cube and two-dimensional convection in a square cross-section. Strictly two-dimensional, single-cell flow in a square cross-section is steady for Rayleigh numbers R between 4π2 and a critical value which lies between 300 and 320; it is unsteady at higher values of R. Double-cell, two-dimensional flow in a square cross-section becomes unsteady when R exceeds a value between 650 and 700, and triple-cell motion is unsteady for R larger than a value between 800 and 1000. Considerable caution must be exercised in attributing physical reality to these flows. Strictly two-dimensional, steady, multicellular convection may not be realizable in a three-dimensional geometry because of instability to perturbations in the orthogonal dimension. For example, even though single-cell, two-dimensional convection in a square cross-section is steady at R = 200, it cannot exist in either an infinitely long square cylinder or in a cube. It could exist, however, in a cylinder whose length is smaller than 0.38 times the dimension of its square cross-section. Three-dimensional convection in a cube becomes unsteady when R exceeds a value between 300 and 320, similar to the unicellular two-dimensional flow in a square cross-section. Nusselt numbers Nu, generally accurate to 1%, are given for the strictly two-dimensional flows up to R = 1000 and for three-dimensional convection in cubes up to R = 500. Single-cell, two-dimensional, steady convection in a square cross-section transports the most heat for R < 97; this mode of convection is also stable in square cylinders of arbitrary length including the cube for R < 97. Steady three-dimensional convection in cubes transports more heat for 97 [lsim ] R [lsim ] 300 than do any of the realizable two-dimensional modes. At R [gsim ] 300 the unsteady modes of convection in both square cylinders and cubes involve wide variations in Nu.

scholarly journals Resistance to a barrier in the shape of an arc of a circle

1928 ◽  
Vol 117 (777) ◽  
pp. 417-433 ◽  
Keyword(s):  
Free Stream ◽  
Fluid Motion ◽  
Stream Line ◽  
Radius Of Curvature ◽  
Argand Diagram ◽  
Starting Point ◽  
Angular Extent ◽  
Moving Fluid ◽  
Direct Attack ◽  
Streaming Motion

Comparatively little progress in the solution of the problem of discontinuous fluid motion past a curved barrier was made until Levi-Civita formulated a method of transforming that part of the barrier which is in contact with the moving fluid into a semi-circle in an Argand diagram. This, indeed, was the starting point of much work of interest and importance. Useful accounts of the problem of motion past any barrier, together with extensions, are given by Cisotti and Brillouin. Leaving out of account such barriers as are made up of one or more planes, problems which can be solved by the older methods based on Schwartz-Christoffel transformations, the only applications of Levi-Civita’s method to curved barriers seem to be that made by Brillouin in the paper referred to, and those made by S. Brodetsky in 1922. The work of Brillouin. however, and that of other investigators are essentially backward processes, in which a likely expression is written down and the streaming motion implied, as well as the shape of the boundary, are investigated. A more direct attack is obtained by suitably choosing the coefficients in Levi-Civita’s general formula, and arriving at the solution for a given curved barrier by a series of steps in successive approximation. The solution of the problem for a circular barrier placed symmetrically in the streaming fluid has been obtained in this manner by S. Brodetsky. The object of this paper is to solve the problem of the circular barrier placed in any position in the streaming fluid, subject to the condition, however, that neither of the ends of the barrier are in the “dead” fluid— i. e ., the radius of curvature of the free stream line is zero at each end. This immediately restricts the barrier, if convex to the streaming fluid, to be of angular extent less than 110·2°.

scholarly journals Hydrothermal waves in two-dimensional liquid layers with sudden changes in the available cross-section

2017 ◽  
Vol 27 (11) ◽  
pp. 2629-2649 ◽  
Author(s):  
Marcello Lappa
Keyword(s):  
Single Crystals ◽  
Cross Section ◽  
Bottom Wall ◽  
Short Paper ◽  
Two Dimensional ◽  
Content Type ◽  
Thermal Boundary Conditions ◽  
Flow Stabilization ◽  
Wide Range ◽  
Two Dimensional Flow

Purpose Hydrothermal waves represent the preferred mode of instability of the so-called Marangoni flow for a wide range of liquids and conditions. The related features in classical rectangular containers have attracted much attention over recent years owing to the relevance of these oscillatory modes to several techniques used for the production of single crystals of semiconductor or oxide materials. Control or a proper knowledge of convective instabilities in these systems is an essential topic from a material/product properties saving standpoint. The purpose of this study is to improve our understanding of these phenomena in less ordinary circumstances. Design/methodology/approach This short paper reports on a numerical model developed to inquire specifically about the role played by sudden changes in the available cross-section of the shallow cavity hosting the liquid. Although accounting for the spanwise dimension would be necessary to derive quantitative results, the approach is based on the assumption of two-dimensional flow, which, for high-Pr fluids, is believed to retain the essence of the involved physical processes. Findings Results are presented for the case of a fluid with Pr = 15 filling an open container with a single backward-facing or forward-facing step on the bottom wall or with an obstruction located in the centre. It is shown that the presence of steps in the considered geometry can lead to a variety of situations with significant changes in the local spectral content of the flow and even flow stabilization in certain circumstances. The role of thermal boundary conditions is assessed by considering separately adiabatic and conducting conditions for the bottom wall. Originality/value Although a plethora of studies have been appearing over recent years motivated, completely or in part, by a quest to identify new means to mitigate these instabilities and produce accordingly single crystals of higher quality for the industry, unfortunately, most of these research works were focusing on very simple geometries. In the present paper, the causality and interdependence among all the kinematic and thermal effects mentioned above is discussed.

Aerodynamic Throttling of a Two-Dimensional Flow by a Thick Jet

1976 ◽  
Vol 27 (3) ◽  
pp. 229-242 ◽  
Author(s):  
J B Stek ◽  
H Brandt
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Maximum Height ◽  
Pressure Measurements ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Air Jet ◽  
Two Dimensional Flow ◽  
Made In

SummaryThe velocity and pressure distributions in a flow generated by a thick air jet that throttles a confined airstream have been studied analytically and experimentally. Velocity and pressure measurements were made in a duct with a rectangular cross section of 102 mm height and 19 mm depth, through which air flowed at velocities ranging from 65 to 80 m/s. The airstream was throttled by a thick air jet having velocities ranging from 130 to 150 m/s that entered the mainstream at angles ranging from 60° to 135°. The jet-mainstream contour was found to be elliptical and agreement within six per cent was obtained between the theoretically and experimentally determined maximum height of the contour. Jet spreading was found to be linear. The theory permits determination of the velocity profile in the jet and gives velocities that deviate less than ten per cent from values obtained experimentally.

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