Flow in a Whirling Rotor Bearing

1979 ◽  
Vol 46 (4) ◽  
pp. 767-771 ◽  
Author(s):  
J. Brindley ◽  
L. Elliott ◽  
J. T. McKay
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Outer Cylinder ◽  
Constant Angular Velocity ◽  
Annular Region ◽  
Circular Cylinders ◽  
Clearance Ratio ◽  
Inertia Effects ◽  
Bearing Clearance ◽  
Resultant Forces

We examine the flow in the annular region between two infinitely long parallel circular cylinders when the axis of the inner cylinder travels in a circular whirl orbit about the axis of the outer cylinder. One or both of the cylinders rotate with constant angular velocity. The analysis is restricted to small values of both clearance ratio and modified Reynolds number. Corrections for curvature and inertia effects are included using an expansion in terms of the above parameters. The resultant forces exerted by the fluid on the cylinders are calculated for the cases when the bearing clearance is completely filled with lubricant and also when cavitation occurs.

Mathematical modeling of Couette flow in anomalous thermoviscous liquid

2011 ◽  
Vol 8 (1) ◽  
pp. 143-152
Author(s):  
S.F. Khizbullina
Keyword(s):  
Mathematical Modeling ◽  
Angular Velocity ◽  
Numerical Experiment ◽  
Temperature Dependence ◽  
Steady Flow ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Flow Regimes ◽  
Constant Angular Velocity ◽  
Coaxial Cylinders

The steady flow of anomalous thermoviscous liquid between the coaxial cylinders is considered. The inner cylinder rotates at a constant angular velocity while the outer cylinder is at rest. On the basis of numerical experiment various flow regimes depending on the parameter of viscosity temperature dependence are found.

Closed-streamline flows past rotating single cylinders and spheres: inertia effects

1975 ◽  
Vol 72 (4) ◽  
pp. 605-623 ◽  
Author(s):  
G. G. Poe ◽  
Andreas Acrivos
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Simple Shear ◽  
Reynolds Numbers ◽  
Rotating Cylinder ◽  
Asymptotic Solutions ◽  
Flow Around A Cylinder ◽  
Inertia Effects ◽  
Freely Suspended ◽  
Cylinders And Spheres

The flow around a cylinder and a sphere rotating freely in a simple shear was studied experimentally for moderate values of the shear Reynolds number Re. For a freely rotating cylinder, the data were found to be consistent with the results obtained numerically by Kossack & Acrivos (1974), at least for Reynolds numbers up to about 10. Rates of rotation of a freely suspended sphere were also obtained over the same range of Reynolds numbers and showed that, with increasing Re, the dimensionless angular velocity does not decrease as fast for a sphere as it does for a cylinder. In both cases, photographs of the streamline patterns around the objects were consistent with this behaviour. Furthermore, it was found in each case that the asymptotic solutions for Re [Lt ] 1 derived by Robertson & Acrivos (1970) for a cylinder and by Lin, Peery & Schowalter (1970) for a sphere are not valid for Reynolds numbers greater than about 0.1, and that the flow remains steady only up to values of Re of about 6.

The slow motion of a sphere in a rotating, viscous fluid

1964 ◽  
Vol 20 (2) ◽  
pp. 305-314 ◽  
Author(s):  
Stephen Childress
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Viscous Fluid ◽  
Classical Problem ◽  
Slow Motion ◽  
Reynolds Numbers ◽  
Constant Angular Velocity ◽  
Axis Of Rotation ◽  
Small Reynolds Numbers ◽  
Analytical Result

The uniform, slow motion of a sphere in a viscous fluid is examined in the case where the undisturbed fluid rotates with constant angular velocity Ω and the axis of rotation is taken to coincide with the line of motion. The various modifications of the classical problem for small Reynolds numbers are discussed. The main analytical result is a correction to Stokes's drag formula, valid for small values of the Reynolds number and Taylor number and tending to the classical Oseen correction as the last parameter tends to zero. The rotation of a free sphere relative to the fluid at infinity is also deduced.

scholarly journals Transition in circular Couette flow

1965 ◽  
Vol 21 (3) ◽  
pp. 385-425 ◽  
Author(s):  
Donald Coles
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Discrete Spectrum ◽  
Couette Flow ◽  
Travelling Waves ◽  
Outer Cylinder ◽  
Spectral Lines ◽  
Wave Number ◽  
Cascade Process ◽  
Spectral Evolution

Two distinct kinds of transition have been identified in Couette flow between concentric rotating cylinders. The first, which will be called transition by spectral evolution, is characteristic of the motion when the inner cylinder has a larger angular velocity than the outer one. As the speed increases, a succession of secondary modes is excited; the first is the Taylor motion (periodic in the axial direction), and the second is a pattern of travelling waves (periodic in the circumferential direction). Higher modes correspond to harmonics of the two fundamental frequencies of the doubly-periodic flow. This kind of transition may be viewed as a cascade process in which energy is transferred by non-linear interactions through a discrete spectrum to progressively higher frequencies in a two-dimensional wave-number space. At sufficiently large Reynolds numbers the discrete spectrum changes gradually and reversibly to a continuous one by broadening of the initially sharp spectral lines.These periodic flows are not uniquely determined by the Reynolds number. For the case of the inner cylinder rotating and the outer cylinder at rest, as many as 20 or 25 different states (each state being defined by the number of Taylor cells and the number of tangential waves) have been observed at a given speed. As the speed changes, theso states replace each other in a repeatable but irreversible pattern of transitions; vortices appear or disappear in pairs, and waves are added or subtracted. More than 70 such transitions have been found in the speed range up to about 10 times the first critical speed. Regardless of the state, however, the angular velocity of the tangential waves is nearly constant at 0.34 times the angular velocity of the inner cylinder.The second kind of transition, which will be called catastrophic transition, is characteristic of the motion when the outer cylinder has a larger angular velocity than the inner one. At a fixed Reynolds number, the fluid is divided into distinct regions of laminar and turbulent flow, and these regions are separated by interfacial surfaces which may be propagating in either direction. Under some conditions the turbulent regions may appear and disappear in a random way; under other conditions they may form quite regular patterns. One common pattern of particular interest is a spiral band of turbulence which rotates at very nearly the mean angular velocity of the two walls without any change in shape except possibly an occasional shift from a right-hand to a left-hand pattern. One example of this spiral turbulence is being studied in some detail in an attempt to clarify the role played in transition by interfaces and intermittency.

Periodic Fluid Flow and Heat Transfer in a Square Cavity Due to an Insulated or Isothermal Rotating Rectangular Object

2009 ◽  
Author(s):  
Y.-C. Shih ◽  
J. M. Khodadadi ◽  
H.-W. Dai ◽  
Liwu Fan
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Angular Velocity ◽  
Aspect Ratio ◽  
Reynolds Numbers ◽  
Constant Angular Velocity ◽  
Square Cavity ◽  
Nusselt Numbers ◽  
Flow And Heat Transfer ◽  
Aspect Ratios

Computational analysis of transient phenomenon followed by the periodic state of laminar flow and heat transfer due to a rectangular rotating object in a square cavity is investigated. A finite-volume-based fixed-grid/sliding mesh computational methodology utilizing primitive variables is used. Rectangular rotating objects with different aspect ratios (AR = 1, 2, 3, 4) are placed in the middle of a square cavity. The motionless object is set in rotation at time t = 0 with a constant angular velocity. For the insulated and isothermal objects, the cavity is maintained as differentially-heated and isothermal enclosures, respectively. Natural convection heat transfer is neglected. For a given shape of the object and a constant angular velocity, a range of rotating Reynolds numbers are covered for a Pr = 5 fluid. The Reynolds numbers were selected so that the flow field is not affected by the Taylor instabilities (Ta < 1750). The periodic flow field, the interaction of the rotating objects with the recirculating vortices at the four corners and the periodic channelling effect of the traversing vertices are clearly elucidated. The corresponding thermal fields in relation to the evolving flow patterns and the skewness of the temperature contours in comparison to conduction-only case were discussed. The skewness is observed to become more marked as the Reynolds number is lowered. Transient variations of the average Nusselt numbers of the respective systems show that for high Re numbers, a quasi-periodic behavior due to the onset of the Taylor instabilities is dominant, whereas for low Re numbers, periodicity of the system is clearly observed. Time-integrated average Nusselt numbers of the insulated and isothermal object systems were correlated to the rotational Reynolds number and the aspect ratio of the rectangle. For high Re numbers, the performance of the system is independent of the aspect ratio. On the other hand, with lowering of the hydraulic diameter (i.e. bigger objects), objects with the highest and lowest aspect ratios exhibit the highest and lowest heat transfer, respectively. High intensity of the periodic channelling and not its frequency are identified as the cause of the observed enhancement.

Finite difference code for velocity and surface traction of a Fluid between Two Eccentric Spheres

2015 ◽  
Vol 11 (1) ◽  
pp. 2960-2971
Author(s):  
M.Abdel Wahab
Keyword(s):  
Velocity Field ◽  
Angular Velocity ◽  
Finite Difference ◽  
Numerical Study ◽  
Outer Sphere ◽  
Equation Of Motion ◽  
Annular Region ◽  
Surface Traction ◽  
Angular Velocities ◽  
Axis Passing

The Numerical study of the flow of a fluid in the annular region between two eccentric sphere susing PHP Code isinvestigated. This flow is created by considering the inner sphere to rotate with angular velocity 1  and the outer sphererotate with angular velocity 2  about the axis passing through their centers, the z-axis, using the three dimensionalBispherical coordinates (, ,) .The velocity field of fluid is determined by solving equation of motion using PHP Codeat different cases of angular velocities of inner and outer sphere. Also Finite difference code is used to calculate surfacetractions at outer sphere.

scholarly journals Aerodynamics of smooth and rough square-section prisms at incidence in very high Reynolds-number cross-flows

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Nils Paul van Hinsberg
Keyword(s):  
Reynolds Number ◽  
Cross Sections ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Surface Boundary ◽  
Experimental Proof ◽  
Surface Boundary Layer ◽  
Pitch Moment ◽  
The Mean ◽  
High Reynolds

Abstract The aerodynamics of smooth and slightly rough prisms with square cross-sections and sharp edges is investigated through wind tunnel experiments. Mean and fluctuating forces, the mean pitch moment, Strouhal numbers, the mean surface pressures and the mean wake profiles in the mid-span cross-section of the prism are recorded simultaneously for Reynolds numbers between 1$$\times$$ × 10$$^{5}$$ 5 $$\le$$ ≤ Re$$_{D}$$ D $$\le$$ ≤ 1$$\times$$ × 10$$^{7}$$ 7 . For the smooth prism with $$k_s$$ k s /D = 4$$\times$$ × 10$$^{-5}$$ - 5 , tests were performed at three angles of incidence, i.e. $$\alpha$$ α = 0$$^{\circ }$$ ∘ , −22.5$$^{\circ }$$ ∘ and −45$$^{\circ }$$ ∘ , whereas only both “symmetric” angles were studied for its slightly rough counterpart with $$k_s$$ k s /D = 1$$\times$$ × 10$$^{-3}$$ - 3 . First-time experimental proof is given that, within the accuracy of the data, no significant variation with Reynolds number occurs for all mean and fluctuating aerodynamic coefficients of smooth square prisms up to Reynolds numbers as high as $$\mathcal {O}$$ O (10$$^{7}$$ 7 ). This Reynolds-number independent behaviour applies to the Strouhal number and the wake profile as well. In contrast to what is known from square prisms with rounded edges and circular cylinders, an increase in surface roughness height by a factor 25 on the current sharp-edged square prism does not lead to any notable effects on the surface boundary layer and thus on the prism’s aerodynamics. For both prisms, distinct changes in the aerostatics between the various angles of incidence are seen to take place though. Graphic abstract

scholarly journals Angular velocity of a sphere in a simple shear at small Reynolds number

2016 ◽  
Vol 1 (8) ◽  
Author(s):  
J. Meibohm ◽  
F. Candelier ◽  
T. Rosén ◽  
J. Einarsson ◽  
F. Lundell ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Simple Shear ◽  
Small Reynolds Number

scholarly journals Optimal Taylor–Couette turbulence

2012 ◽  
Vol 706 ◽  
pp. 118-149 ◽  
Author(s):  
Dennis P. M. van Gils ◽  
Sander G. Huisman ◽  
Siegfried Grossmann ◽  
Chao Sun ◽  
Detlef Lohse
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Angular Velocity ◽  
Probability Distribution Function ◽  
Neutral Line ◽  
Velocity Ratio ◽  
Outer Cylinder ◽  
Taylor Number ◽  
Counter Rotation ◽  
Taylor Couette

AbstractStrongly turbulent Taylor–Couette flow with independently rotating inner and outer cylinders with a radius ratio of $\eta = 0. 716$ is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)$ as a function of the Taylor number $\mathit{Ta}$ and the angular velocity ratio $a= \ensuremath{-} {\omega }_{o} / {\omega }_{i} $ in the large-Taylor-number regime $1{0}^{11} \lesssim \mathit{Ta}\lesssim 1{0}^{13} $ and well off the inviscid stability borders (Rayleigh lines) $a= \ensuremath{-} {\eta }^{2} $ for co-rotation and $a= \infty $ for counter-rotation. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)= f(a)\hspace{0.167em} {\mathit{Ta}}^{\gamma } $, with an amplitude $f(a)$ and an exponent $\gamma $. The data are consistent with one effective exponent $\gamma = 0. 39\pm 0. 03$ for all $a$, but we discuss a possible $a$ dependence in the co- and weakly counter-rotating regimes. The amplitude of the angular velocity flux $f(a)\equiv {\mathit{Nu}}_{\omega } (\mathit{Ta}, a)/ {\mathit{Ta}}^{0. 39} $ is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of ${a}_{\mathit{opt}} = 0. 33\pm 0. 04$, i.e. along the line ${\omega }_{o} = \ensuremath{-} 0. 33{\omega }_{i} $. This value is theoretically interpreted as the result of a competition between the destabilizing inner cylinder rotation and the stabilizing but shear-enhancing outer cylinder counter-rotation. With the help of laser Doppler anemometry, we provide angular velocity profiles and in particular identify the radial position ${r}_{n} $ of the neutral line, defined by $ \mathop{ \langle \omega ({r}_{n} )\rangle } \nolimits _{t} = 0$ for fixed height $z$. For these large $\mathit{Ta}$ values, the ratio $a\approx 0. 40$, which is close to ${a}_{\mathit{opt}} = 0. 33$, is distinguished by a zero angular velocity gradient $\partial \omega / \partial r= 0$ in the bulk. While for moderate counter-rotation $\ensuremath{-} 0. 40{\omega }_{i} \lesssim {\omega }_{o} \lt 0$, the neutral line still remains close to the outer cylinder and the probability distribution function of the bulk angular velocity is observed to be monomodal. For stronger counter-rotation the neutral line is pushed inwards towards the inner cylinder; in this regime the probability distribution function of the bulk angular velocity becomes bimodal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating outer cylinder. Finally, a hypothesis is offered allowing a unifying view and consistent interpretation for all these various results.

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