Reynolds number rotational

It is essential for the rotating-disc that the flow remain laminar and, hence, the upper rotational speed of the disc will depend on the Reynolds number and experimental design, which typically is 1000 s or 10,000 rpm. On the lower lunit, 10 s or 100 rpm must be applied in order for the thickness of tlie boundary layer to be comparable to that of the radius of the disc. 

As the Reynolds number rises above about 40, the wake begins to display periodic instabiUties, and the standing eddies themselves begin to oscillate laterally and to shed some rotating fluid every half cycle. These still laminar vortices are convected downstream as a vortex street. The frequency at which they are shed is normally expressed as a dimensionless Strouhal number which, for Reynolds numbers in excess of 300, is roughly constant ... 

A turbine flowmeter consists of a straight flow tube containing a turbine which is free to rotate on a shaft supported by one or more bearings and located on the centerline of the tube. Means are provided for magnetic detection of the rotational speed, which is proportional to the volumetric flow rate. Its use is generally restric ted to clean, noncorrosive fluids. Additional information on construction, operation, range, and accuracy can be obtained from Holzbock (Instruments for Measurement and Control, 2d ed., Reinhold, New York, 1962, pp. 155-162). For performance characteristics of these meters with liquids, see Shafer,y. Basic Eng., 84,471-485 (December 1962) or May, Chem. Eng., 78(5), 105-108 (1971) and for the effect of density and Reynolds number when used in gas flowmetering, see Lee and Evans, y. Basic Eng., 82, 1043-1057 (December 1965). 

Power Consumption of Impellers Power consumption is related to fluid density, fluid viscosity, rotational speed, and impeller diameter by plots of power number (g P/pN Df) versus Reynolds number (DfNp/ l). Typical correlation lines for frequently used impellers operating in newtonian hquids contained in baffled cylindri-calvessels are presented in Fig. 18-17. These cui ves may be used also for operation of the respective impellers in unbaffled tanks when the Reynolds number is 300 or less. When Nr L greater than 300, however, the power consumption is lower in an unbaffled vessel than indicated in Fig. 18-17. For example, for a six-blade disk turbine with Df/D = 3 and D IWj = 5, = 1.2 when Nr = 10. This is only about... 

Impeller Reynolds Number a dimensionless number used to characterize the flow regime of a mixing system and which is given by the relation Re = pNDV/r where p = fluid density, N = impeller rotational speed, D = impeller diameter, and /r = fluid viscosity. The flow is normally laminar for Re <10, and turbulent for Re >3000. 

Hicks et al. [8] developed a correlation involving the Pumping number and impeller Reynolds number for several ratios of impeller diameter to tank diameter (D /D ) for pitched-blade turbines. From this coiTclation, Qp can be determined, and thus the bulk fluid velocity from the cross-sectional area of the tank. The procedure for determining the parameters is iterative because the impeller diameter and rotational speed N appear in both dimensionless parameters (i.e., Npe and Nq). 

For rotating cylinders the exponent x for Reynolds number is very often unity for turbulent flow, and therefore L may be included in the constant term for a particular geometry of cynlinder. 

BTU/hr. sq.ft. over a wide range of viscosities and rotational speeds. This is equivalent to the thermal resistance of a fluid film equal to about 1/2 the clearance between the helical agitator and the vessel wall. This represents Reynolds numbers in the range of 10 to 10. This is the region of creeping flow where, with no inertial effects, there is little displacement of the fluid adjacent to the wall. 

The high velocities in the Ekman layers and the thinness of the layers strongly enhance the heat transfer between the gas and the sidewalls. There exist a variety of well-esfablished analytical and experimental correlations for fhe heaf fransfer between gas and a rotating disc (or the wall of fhe vessel). Cobb and Saunders [15] correlated their experimental investigations of fhe average laminar heaf fransfer with the Reynolds number Re = < 2.4 x lO ... 

In fluid dynamics the behavior in this system is described by the full set of hydrodynamic equations. This behavior can be characterized by the Reynolds number. Re, which is the ratio of characteristic flow scales to viscosity scales. We recall that the Reynolds number is a measure of the dominating terms in the Navier-Stokes equation and, if the Reynolds number is small, linear terms will dominate if it is large, nonlinear terms will dominate. In this system, the nonlinear term, (u V)u, serves to convert linear momentum into angular momentum. This phenomena is evidenced by the appearance of two counter-rotating vortices or eddies immediately behind the obstacle. Experiments and numerical integration of the Navier-Stokes equations predict the formation of these vortices at the length scale of the obstacle. Further, they predict that the distance between the vortex center and the obstacle is proportional to the Reynolds number. All these have been observed in our 2-dimensional flow system obstructed by a thermal plate at microscopic scales. ... 

Figure 2. Radial-axial velocity field and temperature contours for a rotating-disk reactor at an operating condition where a buoyancy-driven recirculation vortex has developed. The disk temperature is HOOK, the Reynolds number is 1000, Gr/Re / = 6.2, fo/f = 1.28, and L/f = 2.16. The disk radius is 4.9 cm, the spin rate is 495 rpm. The maximum axial velocity is 55.3 cm/sec. The gas is helium.

For Reynolds numbers higher than 5,000 (usually the case in practice), the blend number (t99.A0 is only slightly dependent on the Reynolds number. In this region the blend time becomes inversely proportional to the speed of rotation. It is also dependent on the geometric characteristics of both the tank and the stirrer as shown below ... 

This is most easily achieved by rotating the inner cylinder and keeping the outer fixed in the laboratory frame. Note, however, that this geometry leads to the formation of Taylor vortex motion if inertial effects become important (Reynolds number Re 1). Most rheo-NMR experiments are actually performed at low Re. In the cylindrical Couette, the natural coordinates are cylindrical polar (q, <(>, z) so the shear stress is denoted and is radially dependent as q 2. The strain rate across the gap is given by [2]... 

The flow domain of TCP can be described by two dimensionless hydrodynamic parameters, corresponding to the rotational speed of the inner cylinder and the imposed axial flow rate the Taylor number, To, and the axial Reynolds number, Re, respectively ... 

The rotation rate should ensure forced convection on the one hand, but laminar flow on the other, so that it remains well below the conditions of the critical Reynolds number, above which turbulent flow sets in ... 

Figure 6. Flow around a sphere. The system size is 50 x 25 x 25 with y = 8 particles per cell. The gravitational field strength was g = 0.005 and the rotation angle for MPC dynamics was a — ti/2. Panel (a) is for a Reynolds number of Re — 24 corresponding to X = 1.8 while panel (b) is the flow for Re = 76 and X = 0.35. (From Ref. 30.)...

In convective diffusion to a rotating disk, the characteristic velocity V0 is given by the product of the disk radius r, as a characteristic dimension of the system, and the radial velocity co, so that the Reynolds number is given by the equation... 

The behavior of a rotating sphere or hemisphere in an otherwise undisturbed fluid is like a centrifugal fan. It causes an inflow of the fluid along the axis of rotation toward the spherical surface as shown in Fig. 1(a). Near the surface, the fluid flows in a spirallike motion towards the equator as shown in Fig. 1(b) and (c). On a rotating sphere, two identical flow streams develop on the opposite hemispheres. The two streams interact with each other at the equator, where they form a thin swirling jet toward the bulk fluid. The Reynolds number for the rotating sphere or hemisphere is defined as ... 

To describe the velocity profile in laminar flow, let us consider a hemisphere of radius a, which is mounted on a cylindrical support as shown in Fig. 2 and is rotating in an otherwise undisturbed fluid about its symmetric axis. The fluid domain around the hemisphere may be specified by a set of spherical polar coordinates, r, 8, , where r is the radial distance from the center of the hemisphere, 0 is the meridional angle measured from the axis of rotation, and (j> is the azimuthal angle. The velocity components along the r, 8, and (j> directions, are designated by Vr, V9, and V. It is assumed that the fluid is incompressible with constant properties and the Reynolds number is sufficiently high to permit the application of boundary layer approximation [54], Under these conditions, the laminar boundary layer equations describing the steady-state axisymmetric fluid motion near the spherical surface may be written as ... 

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