Cylindrical tank of fluid oscillating about a state of steady rotation

1970 ◽  
Vol 41 (3) ◽  
pp. 581-592 ◽  
Author(s):  
Chang-Yi Wang
Keyword(s):  
Boundary Layer ◽  
Angular Velocity ◽  
Flow Field ◽  
Boundary Layers ◽  
Experimental Measurements ◽  
Centrifugal Forces ◽  
Cylindrical Tank ◽  
Side Walls ◽  
Steady Rotation ◽  
Axis Of Symmetry

A cylindrical tank, full of fluid, is oscillating with frequency ω and rotating with angular velocity Ω about its axis of symmetry. It is assumed that the amplitude of oscillation, δ, is small and the viscosity is low such that boundary layers exist. Analysis shows that the unsteady boundary layer is of thickness [ε/(1 − 2Ω/ω)]½ on the top and bottom plates and of thickness ε½ on the side walls, where ε = ν/2ω. The interior unsteady flow shows source-like behaviour at the corners. The steady flow field is caused by the steady component of the non-linear centrifugal forces coupled with an induced steady rotation of the interior. This rotation, of order δ2ω, is prograde when Ω/ω < 0·118 and retrograde otherwise. Maximum retrograde rotation occurs at Ω/ω = 0·5. A steady boundary layer of thickness [ε/(1 − 2Ω/ω)]½ exists on the top and bottom plates, and of thicknesses \[ \epsilon^{\frac{1}{2}},\quad (\nu/L^2\Omega)^{\frac{1}{3}},\quad (\nu/L^2\Omega)^{\frac{1}{4}} \] on the side walls. Experimental measurements of the interior induced steady rotation compare well with theory.

Slow steady rotation of axially symmetric bodies in a viscous fluid

1961 ◽  
Vol 10 (1) ◽  
pp. 17-24 ◽  
Author(s):  
R. P. Kanwal
Keyword(s):  
Angular Velocity ◽  
Flow Field ◽  
Viscous Fluid ◽  
Stokes Flow ◽  
Flow Problem ◽  
Analytic Solutions ◽  
The Body ◽  
Axially Symmetric ◽  
Steady Rotation ◽  
Axis Of Symmetry

The Stokes flow problem is considered here for the case in which an axially symmetric body is uniformly rotating about its axis of symmetry. Analytic solutions are presented for the heretofore unsolved cases of a spindle, a torus, a lens, and various special configurations of a lens. Formulas are derived for the angular velocity of the flow field and for the couple experienced by the body in each case.

Decreasing the Side Wall Contamination in Wind Tunnels

1983 ◽  
Vol 105 (4) ◽  
pp. 435-438 ◽  
Author(s):  
T. Motohashi ◽  
R. F. Blackwelder
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Laminar Boundary Layer ◽  
Three Dimensional ◽  
Side Wall ◽  
Wind Tunnels ◽  
Turbulent Fluid ◽  
Side Walls ◽  
Suction Slot

To study boundary layers in the transitional Reynolds number regime, the useful spanwise and streamwise extent of wind tunnels is often limited by turbulent fluid emanating from the side walls. Some or all of the turbulent fluid can be removed by sucking fluid out at the corners, as suggested by Amini [1]. It is shown that by optimizing the suction slot width, the side wall contamination can be dramatically decreased without a concomitant three-dimensional distortion of the laminar boundary layer.

On the definition of the secondary flow in three-dimensional cascades

2009 ◽  
Vol 223 (6) ◽  
pp. 667-676 ◽  
Author(s):  
G Persico ◽  
P Gaetani ◽  
V Dossena ◽  
G D'Ippolito ◽  
C Osnaghi
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Secondary Flow ◽  
Boundary Layers ◽  
Complex Geometry ◽  
Flow Direction ◽  
Flow Analysis ◽  
Secondary Flows ◽  
Streamwise Vorticity ◽  
Reference Flow

The present article proposes a novel methodology to evaluate secondary flows generated by the annulus boundary layers in complex cascades. Unlike two-dimensional (2D) linear cascades, where the reference flow is commonly defined as that measured at midspan, the problem of the reference flow definition for annular or complex 3D linear cascades does not have a general solution up to the present time. The proposed approach supports secondary flow analysis whenever exit streamwise vorticity produced by inlet endwall boundary layers is of interest. The idea is to compute the reference flow by applying slip boundary conditions at the endwalls in a viscous 3D numerical simulation, in which uniform total pressure is prescribed at the inlet. Thus the reference flow keeps the 3D nature of the actual flow except for the contribution of the endwall boundary layer vorticity. The resulting secondary field is then derived by projecting the 3D flow field (obtained from both an experiment and a fully viscous simulation) along the local reference flow direction; this approach can be proficiently applied to any complex geometry. This method allows the representation of secondary velocity vectors with a better estimation of the vortex extension, since it offers the opportunity to visualize also the region of the vortices, which can be approximated as a potential type. Furthermore, a proficient evaluation of the secondary vorticity and deviation angle effectively induced by the annulus boundary layer is possible. The approach was preliminarily verified against experimental data in linear cascades characterized by cylindrical blades, not reported for the sake of brevity, showing a very good agreement with the standard methodology based only on the experimental midspan flow field. This article presents secondary flows obtained by the application of the proposed methodology on two annular cascades with cylindrical and 3D-designed blades, stressing the differences with other definitions. Both numerical and experimental results are considered.

The Interaction of Thermal Radiation in Optically Thick Boundary Layers

1967 ◽  
Vol 89 (4) ◽  
pp. 309-312 ◽  
Author(s):  
J. L. Novotny ◽  
Kwang-Tzu Yang
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Boundary Layers ◽  
Optical Thickness ◽  
Asymptotic Expansions ◽  
Energy Equation ◽  
Two Dimensional ◽  
Small Temperature ◽  
Dimensional Boundary

An analysis is presented to examine the role of the Rosseland or optically thick approximation in convection-radiation interaction situations. The analysis is formulated for the flow of a gray gas in a laminar two-dimensional boundary layer under the restriction of small temperature differences within the flow field. The boundary-layer energy equation is treated using the method of matched asymptotic expansions based on a parameter which characterizes the optical thickness of the gas. Two illustrative examples of the resulting equations are presented.

scholarly journals Оscillations of closed conical shells with complex rotation

2020 ◽  
pp. 127-132
Author(s):  
Petro Lizunov ◽  
Eduard Kriksunov ◽  
Oleksandr Fesan
Keyword(s):  
Angular Velocity ◽  
Center Of Mass ◽  
Shell Element ◽  
Inertial Forces ◽  
Centrifugal Forces ◽  
Construction Engineering ◽  
Conical Shells ◽  
Gyroscopic Moment ◽  
Axis Of Symmetry ◽  
The Right

The paper consider a system of two closed conical shells connected by a central rigid insert rotating in opposite directions in a central force field with a constant angular velocity around the axis of symmetry of the system. The shell element is subjected to a load consisting of gravitational and inertial forces, but at large values of the angular velocity of the system, the gravitational loads can be neglected. The gyroscopic interaction between the rotational portable motion of the system and the relative elastic oscillations of the elements is a source of excitation of precession oscillations, which may be resonant or unstable. Occurring when changing the axis of orientation of the system gyroscopic moment causes the appearance of alternating stresses, which significantly affect the strength and reliability of the shells. Such problems arise in construction engineering, mechanical engineering, aircraft construction, space engineering and other sectors of the economy. The main load acting on the elements of such systems are significant centrifugal forces of inertia, which significantly affect the strength characteristics of structures. Taking into account the periodicity of the right-hand side and the coefficients of the system of resolving equations, with the help of the projection method it is possible to reduce the resolving equations to the system of ordinary differential equations, which approximately replaces the original one. The solution of the obtained system of equations makes it possible to determine the forms of oscillations and forces in a composite conical shell at various parameters of the shell and the ratios of the velocities of the shell's own rotation and the rotation of its center of mass.

scholarly journals Конвективный теплообмен во вращающемся полом цилиндре с торцевой стенкой

2020 ◽  
Vol 46 (14) ◽  
pp. 29
Author(s):  
В.А. Архипов ◽  
О.В. Матвиенко ◽  
А.С. Жуков ◽  
Н.Н. Золоторёв
Keyword(s):  
Heat Transfer ◽  
Angular Velocity ◽  
Flow Field ◽  
Convective Heat Transfer ◽  
Hollow Cylinder ◽  
Convective Heat ◽  
Axis Of Symmetry ◽  
End Wall

The method and results of calculating the flow field and convective heat transfer in a hollow cylinder with end wall rotating around the axis of symmetry with varying angular velocity and height of the cylinder are presented

The axisymmetric convective regime for a rigidly bounded rotating annulus

1968 ◽  
Vol 32 (4) ◽  
pp. 625-655 ◽  
Author(s):  
Michael E. Mcintyre
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Axisymmetric Flow ◽  
Side Wall ◽  
Boundary Layer Equations ◽  
Wall Boundary Layer ◽  
Ekman Layers ◽  
Interior Flow ◽  
Side Walls ◽  
Annular Container

The axisymmetric flow of liquid in a rigidly bounded annular container of heightH, rotating with angular velocity Ω and subjected to a temperature difference ΔTbetween its vertical cylindrical perfectly conducting side walls, whose distance apart isL, is analysed in the boundary-layer approximation for small Ekman numberv/2ΩL2, withgαΔTHv/4Ω2L2K∼ 1. The heat transfer across the annulus is then convection-dominated, as is characteristic of the experimentally observed ‘upper symmetric regime’. The Prandtl numberv/kis assumed large, andHis restricted to be less than about 2L. The side wall boundary-layer equations are the same as in (non-rotating) convection in a rectangular cavity. The horizontal boundary layers are Ekman layers and the four boundary layers, together with certain spatialaveragesin the interior, are determined independently of the interior flow details. The determination of the latter comprises a ‘secondary’ problem in which viscosity and heat conduction are important throughout the interior; the meridional streamlines are not necessarily parallel to the isotherms. The secondary problem is discussed qualitatively but not solved. The theory agrees fairly well with an available numerical experiment in the upper symmetric regime, forv/k[bumpe ] 7, after finite-Ekmannumber effects such as finite boundary-layer thickness are allowed for heuris-tically.

On the motion of liquid in a spheroidal cavity of a precessing rigid body

1963 ◽  
Vol 17 (1) ◽  
pp. 1-20 ◽  
Author(s):  
K. Stewartson ◽  
P. H. Roberts
Keyword(s):  
Boundary Layer ◽  
Angular Velocity ◽  
Rigid Body ◽  
Steady Motion ◽  
Viscous Boundary Layer ◽  
Constant Vorticity ◽  
Spheroidal Cavity ◽  
Axis Of Symmetry ◽  
Set Up ◽  
Viscous Boundary

The flow set up in an oblate cavity of a precessing rigid body is examined under the assumptions that the ellipticity of the spheroidal boundary of the fluid is large compared with Ω/ω and that the boundary-layer thickness is small compared with the deviations of the boundary from sphericity (ωis the angular velocity of the rigid body about the axis of symmetry,Ωis the angular velocity with which this axis precesses).The motion of the fluid is found by considering an initial-value problem in which the axis of rotation of the spheroid is impulsively moved at a timet= 0; before that time this axis is supposed to be fixed in space, the fluid and envelope turning about it as a solid body. The solution is divided into a steady motion and transients, and, by evaluating the effects of the viscous boundary layer, the transients are shown to decay with time. The steady motion which remains consists of a primary rigid-body rotation with the envelope, superimposed on which is a circulation with constant vorticity in planes perpendicular toω× (ω×Ω), the streamlines being similarly situated ellipses.The possible effects of the luni-solar precession on the fluid motions in the Earth's core are discussed.

Effects of sandpaper roughness and stream turbulence on the turbulent boundary layer

1999 ◽  
Vol 213 (5) ◽  
pp. 507-515 ◽  
Author(s):  
J. C. Gibbings ◽  
S. M. Al-Shukri
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Skin Friction ◽  
Boundary Layers ◽  
Pipe Flow ◽  
Shape Factor ◽  
Turbulent Boundary Layers ◽  
Experimental Measurements ◽  
Two Dimensional

This paper reports experimental measurements of two-dimensional turbulent boundary layers over sandpaper surfaces under turbulent streams to complement the Nikuradse experiments on pipe flow. The study included the recovery region downstream of the end of transition. Correlations are given for the thickness, the shape factor, the skin friction and the parameters of the velocity profile of the layer. Six further basic differences from the pipe flow are described to add to the five previously reported.

Convection in rectangular cavities with differentially heated end walls

1981 ◽  
Vol 110 ◽  
pp. 433-456 ◽  
Author(s):  
P. G. Simpkins ◽  
T. D. Dudderar
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Boundary Layers ◽  
Numerical Solutions ◽  
Boussinesq Equations ◽  
Basic Structure ◽  
Wall Boundary Layer ◽  
Aspect Ratios ◽  
Different Temperatures ◽  
Secondary Vortices

This paper describes an experimental study of free convection in an enclosed rectangular cavity, the end walls of which are maintained at uniform but different temperatures. The experiments are carried out for a variety of Rayleigh numbers, R = αgΔTh4/κνl, and aspect ratios, L = l/h, for fluids with Prandtl number σ ≥ 10. For R ∼ O(103) it is shown that the basic structure of the flow field is a single two-dimensional cell for 0·25 ≤ L ≤ 9. When R > O(104) the boundary layers on the vertical walls control the flow field, but the basic overall structure remains unicellular. At greater values of R secondary vortices appear for all L ≥ 0·5. As R increases the intensity and then the number of these vortices increases. Measurements of the end-wall boundary-layer profiles at different values of R and L confirm Gill's boundary-layer analysis. The effects of variations of viscosity with temperature are discussed in the context of the observed boundary-layer profiles.Core shear profiles and mass flux measurements are also reported. For L = 1 the observed shear profiles are in good agreement with numerical solutions of the Boussinesq equations. However, when L > 1 the observations suggest that the horizontal boundary layers have a significant effect on the core flow field. The stream function is demonstrated to be L-dependent in the boundary-layer regime, where variations due to R are second order. Similarities between the results of the present work and earlier observations by Elder and by Seki, Fukusaka & Inaba for tall slender cavities (L [Lt ] 1) are discussed.

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