Torque Characteristics for Spherical Annulus Flow

1979 ◽  
Vol 101 (2) ◽  
pp. 284-286 ◽  
Author(s):  
A. M. Waked ◽  
B. R. Munson

The torque needed to rotate concentric spheres when the spherical annulus gap between them is filled with a viscous fluid depends on the Reynolds number and the ratio of the angular velocities of the two spheres. Experimental torque results for low to moderate Reynolds numbers are presented. The secondary flow effect is evident.

1978 ◽  
Vol 100 (1) ◽  
pp. 97-106 ◽  
Author(s):  
K. Nakabayashi

Frictional moment is investigated experimentally for the flow between a rotating inner sphere and a stationary outer one, and for the flow between a rotating outer sphere and a stationary inner one, respectively. The existence of four basic flow regimes for both is verified, and their extent is mapped over a range of Reynolds number-clearance ratio combinations. An empirical formula for the coefficient of frictional moment is obtained for every flow regime. The coefficient of frictional moment obtained for spherical annulus flow is then correlated with that of the flow around a disk rotating in a confined space, and the effect of the surface curvature of rotating bodies is considered.


2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Lalit Kumar Bohra ◽  
Leo M. Mincks ◽  
Srinivas Garimella

Abstract An experimental study on the flow of a highly viscous fluid through small diameter orifices was conducted. Pressure drops were measured for each of nine orifices, including orifices of nominal diameter 0.5, 1, and 3 mm and three different orifice thicknesses, over wide ranges of flow rates and temperatures. The fluid under consideration exhibits steep dependence of the properties (changes of several orders of magnitude) as a function of temperature and pressure and is also non-Newtonian at the lower temperatures. At small values of Reynolds number, an increase in aspect ratio (length/diameter ratio of the orifice) causes an increase in Euler number. It was also found that at extremely low Reynolds numbers, the Euler number was very strongly influenced by the Reynolds number, while the dependence becomes weaker as the Reynolds number increases toward the turbulent regime, and the Euler number tends to assume a constant value determined by the aspect ratio and the diameter ratio. A two-region (based on Reynolds number) model was developed to predict Euler number as a function of diameter ratio, aspect ratio, viscosity ratio, and generalized Reynolds number. It is shown that for such a highly viscous fluid with some non-Newtonian behavior, accounting for the shear rate through the generalized Reynolds number results in a considerable improvement in the predictive capabilities of the model. Over the laminar, transition, and turbulent regions, the model predicts 86% of the data within ±25% for the geometry and operating conditions investigated in this study.


2010 ◽  
Vol 644 ◽  
pp. 107-122 ◽  
Author(s):  
ALFREDO PINELLI ◽  
MARKUS UHLMANN ◽  
ATSUSHI SEKIMOTO ◽  
GENTA KAWAHARA

We have performed direct numerical simulations of turbulent flows in a square duct considering a range of Reynolds numbers spanning from a marginal state up to fully developed turbulent states at low Reynolds numbers. The main motivation stems from the relatively poor knowledge about the basic physical mechanisms that are responsible for one of the most outstanding features of this class of turbulent flows: Prandtl's secondary motion of the second kind. In particular, the focus is upon the role of flow structures in its generation and characterization when increasing the Reynolds number. We present a two-fold scenario. On the one hand, buffer layer structures determine the distribution of mean streamwise vorticity. On the other hand, the shape and the quantitative character of the mean secondary flow, defined through the mean cross-stream function, are influenced by motions taking place at larger scales. It is shown that high velocity streaks are preferentially located in the corner region (e.g. less than 50 wall units apart from a sidewall), flanked by low velocity ones. These locations are determined by the positioning of quasi-streamwise vortices with a preferential sign of rotation in agreement with the above described velocity streaks' positions. This preferential arrangement of the classical buffer layer structures determines the pattern of the mean streamwise vorticity that approaches the corners with increasing Reynolds number. On the other hand, the centre of the mean secondary flow, defined as the position of the extrema of the mean cross-stream function (computed using the mean streamwise vorticity), remains at a constant location departing from the mean streamwise vorticity field for larger Reynolds numbers, i.e. it scales in outer units. This paper also presents a detailed validation of the numerical technique including a comparison of the numerical results with data obtained from a companion experiment.


1966 ◽  
Vol 88 (1) ◽  
pp. 221-228 ◽  
Author(s):  
H. Schlichting ◽  
A. Das

A survey is given of extensive research work on cascade-flow problems carried out in recent years in Germany. A considerable part of this work was done in the Variable Density High Speed Cascade Wind Tunnel of the Deutsche Forschungsanstalt fu¨r Luftfahrt at Braunschweig, in which the Reynolds number and the Mach number of the cascade can be varied independently. For compressor cascades with blades of different thickness ratio extensive measurements of the aerodynamic coefficients have been carried out in a wide range of Mach numbers and Reynolds numbers. For very low Reynolds numbers, as they occur for jet engines in high-altitude flight, the influence of turbulence level on loss coefficients has been investigated. Furthermore, comprehensive investigations on secondary-flow losses are reported. The most important parameters in this connection are the ratio of blade length to blade chord, the tip clearance, the Reynolds number, and the deflection of the flow in the cascade. The influence of all these parameters on the secondary-flow losses has been clarified to a certain extent.


1964 ◽  
Vol 20 (2) ◽  
pp. 305-314 ◽  
Author(s):  
Stephen Childress

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.


2011 ◽  
Vol 133 (7) ◽  
Author(s):  
Omid Mahian ◽  
Asgahr B. Rahimi ◽  
Ali Jabari Moghadam

The effect of suction and blowing in the study of flow and heat transfer of a viscous incompressible fluid between two vertically eccentric rotating spheres is presented when the spheres are maintained at different temperatures and rotating about a common axis while the angular velocities of the spheres are arbitrary functions of time. The resulting flow pattern, temperature distribution, and heat transfer characteristics are presented for the various cases including exponential and sinusoidal angular velocities. These presentations are for various values of the flow parameters including rotational Reynolds number Re, and the blowing/suction Reynolds number Rew. The effects of transpiration and eccentricity on viscous torques at the inner and outer spheres are studied, too. As the eccentricity increases and the gap between the spheres decreases the viscous torque remains nearly unchanged. Results for special case of concentric spheres are obtained by letting eccentricity tend to zero.


1971 ◽  
Vol 49 (2) ◽  
pp. 305-318 ◽  
Author(s):  
B. R. Munson ◽  
D. D. Joseph

The energy theory of hydrodynamic stability is applied to the viscous incompressible flow of a fluid contained between two concentric spheres which rotate about a common axis with prescribed angular velocities. The critical Reynolds number is calculated for various radius and angular velocity ratios such that it is certain the basic laminar motion is stable to any disturbances. The stability problem is solved by means of a toroidal–poloidal representation of the disturbance flow and numerical integration of the resulting eigenvalue problem.


Author(s):  
S. I. Martynov ◽  
T. V. Pronkina ◽  
N. V. Dvoryaninova ◽  
T. V. Karyagina

The model problem of sedimentation of a solid spherical particle in a viscous fluid bordering two solid planar surfaces is considered. To find the solution of the hydrodynamic equations in the approximation of small Reynolds numbers with boundary conditions on a particle and on two planes, a procedure developed for numerical simulation of the dynamics of a large number of particles in a viscous fluid with one plane wall is used. The procedure involves usage of fictive particles located symmetrically to real ones with respect to the plane. To solve the problem of the real particle’s sedimentation in the presence of two planes, a system of fictive particles is introduced. An approximate solution was found using four fictive particles. Basing on this solution, numerical results are obtained on dynamics of particle deposition for the cases of planes oriented parallel and perpendicular to each other. In particular, the values of linear and angular velocities of a particle are found, depending on the distance to each plane and on the direction of gravity. In the limiting case, when one of the planes is infinitely far from the particle, we obtain known results on the dynamics of particle sedimentation along and perpendicular to one plane.


1976 ◽  
Vol 78 (2) ◽  
pp. 317-335 ◽  
Author(s):  
Manfred Wimmer

Some experimental results on incompressible viscous fluid flow in the gap between two concentric rotating spheres are discussed. The flow field in the spherical gap has been studied qualitatively by flow visualization (photographs) and quantitatively by measurements by the hot-wire technique. For a wide range of Reynolds numbers, the friction torque was measured for several gap widths and a relatively simple method of determining the torque theoretically is given. At higher Reynolds numbers instabilities appear. Their different behaviour for relatively small and large gap widths is demonstrated. For the larger gap widths, the different appearance of the Taylor–Görtler vortices, the reason for their generation, their regimes of existence as well as their influence on the friction torque are thoroughly treated. Detailed information is given on the new effect of the dependence of the wavelength of the vortices on the Reynolds number.


2018 ◽  
Vol 140 (12) ◽  
Author(s):  
İlyas Karasu ◽  
Mustafa Özden ◽  
Mustafa Serdar Genç

The performance of the transition models on three-dimensional (3D) flow of wings with aspect ratios (AR) of 1 and 3 at low Reynolds number was assessed in this study. For experimental work; force measurements, surface oil and smoke-wire flow visualizations were performed over the wings with NACA4412 section at Reynolds numbers of 2.5 × 104, 5 × 104, and 7.5 × 104 and the angles of attack of 8 deg, 12 deg, and 20 deg. Results showed that the AR had significant effects on the 3D flow structure over the wing. According to the experimental and numerical results, the flow over the wing having lower ARs can be defined with wingtip vortices, axial flow, and secondary flow including spiral vortex inside the separated flow. When the angle of attack and Reynolds number was increased, wing-tip vortices were enlarged and interacted with the axial flow. At higher AR, flow separation was dominant, whereas wing-tip vortices suppressed the flow separation over the wing with lower AR. In the numerical results, while there were some inconsistencies in the prediction of lift coefficients, the predictions of drag coefficients for two transition models were noticeably better. The performance of the transition models judged from surface patterns was good, but the k–kL–ω was preferable. Secondary flow including spiral vortices near the surface was predicted accurately by the k–kL–ω. Consequently, in comparison with experiments, the predictions of the k–kL–ω were better than those of the shear stress transport (SST) transition.


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