Free surface vortex

When an open tank with a free surface is stirred with an impeller, a vortex will form around the shaft. It is important to prevent this vortex from reaching the impeller, because entrainment of air in the liquid tends to cause foaming. The shape of the free surface depends upon (among other things) the fluid properties, the speed and size of the impeller, the size of the tank, and the depth of the impeller below the free surface. 

At Re = 130, a weak long-period oscillation appears in the tip of the wake (T2). Its amplitude increases with Re, but the flow behind the attached wake remains laminar to Re above 200. The amplitude of oscillation at the tip reaches 10% of the sphere diameter at Re = 270 (GIO). At about this Re, large vortices, associated with pulsations of the fluid circulating in the wake, periodically form and move downstream (S6). Vortex shedding appears to result from flow instability, originating in the free surface layer and moving downstream to affect the position of the wake tip (Rll, R12, S6). 

Figure 12. Lagrangian path lines at various stages of a Rayleigh-Taylor collapse for the case of two inviscid, incompressible fluids having a density ratio of 2 1. A free surface is present above the dense fluid and the interface between the fluids is indicated for each stage. The simulation shows how later evolution of the fluid flow is dominated by the strength and dynamics of the vortex pair created during the...

The Froude number is associated with the formation of a vortex on the liquid free surface around the impeller shaft. At low impeller speeds... 

The stream-tube method is more closely related to the Protean coordinate approach. It refers to the flow analysis introduced some yeans ago by Clermont [40,53], which may be applied to the study of two- or three-dimensional duct or free surface flows [54-56] and pure circulatory or vortex flows [57]. In this analysis, the unknowns of the problem are, in addition to the pressure p, a one-to-one transformation between the physical flow domain D (or a subdomain D of D)... 

Other types of multiphase fiows are free surface fiows, where there is a well-defined interface between two continuous phases. Examples of such flows can be found in liquid separators, unbaffled mixing vessels where surface deformation occurs when a central vortex forms, mold filling applications, and blow... 

In this coaxial mixer, the primary role of the anchor is to clean up the wall from any accumulated solid lumps and reincorporate them back in the bulk. It also acts as a moving baffle, hampering the creation of a vortex at the liquid free surface. The purpose of the pitched blade turbine is to provide axial pumping so as to promote the resuspension of the solids, and radial dispersion to avoid solids reagglomeration. Finally, the aim of the wetting rods is to ease hydrophobic pigment incorporation by avoiding the creation of surface lumps. ... 

A three dimensional turbulent flow field in unbaffled tank with turbine stirrer or 6-paddle stirrer was numerically simulated by the method of finite volume elements [80], whereas in the case of free surface the vortex profile was also determined using iterative techniques. The prediction of the velocity and turbulence fields in the whole tank and the stirrer power was compared with literature data and their own results. Of the two simulation techniques used, turbulent eddy-viscosity/zc-e turbulence model and the DS model (differential 2. order shear stress), only the latter produced satisfactory results. In particular it proved that fluctuating Coriolis forces have to be taken into account by source terms in the transport equation for the Reynolds shear stress. 

In an ideal fluid with a free surface and potential flow, a vortex ring nearing the surface will tend to dilate. This result can be rationalized by the mathematical construction of an image vortex ring reflected about the interface and approaching from the opposite direction. Fig. 5b depicts the experimental observation of a physical case similar to this type of behaviour. On the other hand, when a no-slip or intermediate-slip interface is... 

See Ref. 1 in Chap. 3. Typical papers from Annual Reviews include A. Leonard, Computing three-dimensional incompressible flows with vortex elements, Annu. Rev. Fluid Mech. 17, 523-59 (1985) M. Y. Hussaini and T. A. Zang, Spectral methods in fluid dynamics, Annu. Rev. Fluid Mech. 19, 339-67 (1987) R. Glowinski and O. Pironneau, Finite element methods forNavier-Stokes equations, Annu. Rev. Fluid Mech. 24, 167-204 (1992) R. Scardovelli and S. Zaleski, Dierect numerical simulation of free-surface and interfacial flow, Annu. Rev. Fluid Mech. 31, 567-603 (1999). 

Estimate which of the dimensionless force ratios in Table 13.1 should be important for the following kinds of flow a) breakup of a jet of liquid into droplets, (b) formation of a vortex in the free surface of the drain of a bathtub,... 

In 1996 using the open litterature a model of the free surface deformation by a vortex has been developed. This model calculates the shape of the free surface, taking into account the local characteristics of the velocity field below the surface. 

Gas can be entrained into the coolant at the free surface by vortexes or falling streams and these should be avoided. It can also be dissolved at hot parts of the surface and then precipitated in the form of small bubbles in the cold pool. To avoid significant acoustic attenuation in the frequency ranges important for ABND, the volume faction of gas in the form of bubbles of diameters of 1 mm or less should be kept below 10". ... 

The kinematics of moving fronts and interfaces has been studied in different physical contexts for over two hundred years. Most notable are the studies of free surfaces in ocean hydrodynamics and vortex sheets in free space (e.g., see Lamb, 1945), and more recently, flame propagation dynamics in combustion analyses. The following derivation, which applies to fluid fronts in porous media, is given in Chin (1993a). Let us consider a moving front or interface located anywhere within a three-dimensional Darcy flow (e.g., any surface marked by red dye), and let (()(x,y,z) denote the porosity. Furthermore, denote by u, v, and w the Eulerian speed components, and describe our interface by the surface locus of points... 

Solid surfaces, particularly those easily wetted by the dispersed phase, can be major collectors of drops. In the case of a rotating impeller, drops collect and coalesce on blade surfaces to form a condensed film. As this film grows in thickness, it flows under centrifugal forces to the impeller tips and disperses into tiny drops. This process is similar to the breaknp of a cylindrical Uqnid jet. A film of dispersed phase can also collect on free snrfaces, baffles, tank walls, and the impeller shaft, where the surface vortex meets the shaft. In the case of emulsion and suspension polymerization, coalescence also leads to fonUng of heat transfer surfaces. 

In configuration a the solids hopper is simply attached to the solids outlet of the cyclone. This can often lead to the end of the vortex (sometimes referred to as the Vortex tail ) extending downward to the free surface of the solids in the hopper and to the entrainment of some portion of these solids. This is avoided in different ways in the other three configurations. In configuration b a cylindrically-shaped section is attached to the dust exit. As a rule this section is at least half of the height of the cyclone itself. The vortex may terminate in the tube section, or it may extend down into the hopper, especially in... 

Understanding the free surface flow of viscoelastic fluids in micro-channels is important for the design and optimization of micro-injection molding processes. In this paper, flow visualization of a non-Newtonian polyacrylamide (PA) aqueous solution in a transparent polymethylmethacrylate (PMMA) channel with microfeatures was carried out to study the flow dynamics in micro-injection molding. The transient flow near the flow front and vortex formation in microfeatures were observed. Simulations based on the control volume finite element method (CVFEM) and the volume of fluid (VOF) technique were carried out to investigate the velocity field, pressure, and shear stress distributions. The mesoscopic CONNFFESSIT (Calculation of Non-Newtonian How Finite Elements and Stochastic Simulation Technique) method was also used to calculate the normal stress difference, the orientation of the polymer molecules and the vortex formation at steady state. 

When this type of impeller is used, typically four vertical baffle plates, each one-tenth of the tank diameter in width and the total liquid depth in length, are fixed perpendicular to the tank wall so as to prevent any circular flow of liquid and the formation of a concave vortex at the free liquid surface. 

The existence of spiral flow is observed near the short radius of the bend. The water surface is superelevated at the outside wall for the cylindrical free vortex. The element EF is subjected to a centrifugal force mV2/r, which is balanced by an increased hydrostatic force on the left side due to the superelevation of the water surface at C above that at D. The element GH has exactly the same hydrostatic force inward, but the centrifugal force outward is much less because the velocity is decreased by friction near the bottom. This results in a cross flow inward along the bottom of the channel, which is balanced by an outward flow near the water surface, hence the spiral. This spiral flow is largely responsible for the commonly observed erosion of the outside bank of a river bend, with consequent deposition and building of a sand bar near the inside bank. 

It is generally not possible to perceive a convex surface profile, given by the free vortex theory. For most practical purposes the water surface may be supposed to be a straight line from A to B, raised at the outside wall and depressed at the inside, with the slope given by the ordinary superelevation formula used for highway curves, tan 0 = Vz/gr, where r is the radius of the curve to the center of the channel. 

In Cases 6 to 8, rotation and translation velocities of the cylinder are the same, but the cylinder is located at different distances above the boundary layer. The last column of the table shows the ratio of surface speed Ug = Qd/2) to the relative free stream speed, Uoo — c). Except for Case 3 where the cylinder is not rotating, the values given in the last column for all other cases are greater than 2. This parameter value is known to cause limited or no Karman vortex shedding, as noted experimentally in Tokumaru Dimotakis (1993) and Diaz et al. (1983). 

Figure 8.10. Airflow in a hydraulic kiln, (a) On the left, the recirculating air ft om the fans has to take a right-angle bend to enter the plenum space and the airstream breaks free from the surface to form a vortex. This hinders air moving thought the upper layers of the stack, (b) On the right, more uniform airflow with a radiused edge and wide plenum space (Nijdam, 1998).

Fig. 6. Variation of the near-surface radial component of velocity. Panel (a) is for a clean interface panel (b) is for the stearic acid microlayer. All variables are as defined in Fig. 5, u is the radial component of velocity, and U is the vertical free propagation speed of the vortex ring. Velocities are taken along a horizontal section at a depth d/D = 0.03 (0.125 cm). The temporal spacing between curves, At, is 0.15. Taken from McKenna (1997)...

More power is needed to create suspensions of floating than for settling solids. A 45° PBT placed at a depth of T/4 from the surface in combination with a second impeller placed lower down in the vessel usually works well and should avoid gas entrainment. The placement of baffles is critical. If a central vortex is to be used to incorporate solids, the vessel should be baffle-free in the upper half of the tank. Short, wide baffles suspended from the top of the tank extending to a depth of T/3 are an alternative for initiation of engulfment [39]. A large DIT = 0.6, four-blade 45° PBT placed near the bottom of the tank was used in Joosten s work. The minimum speed /V p for just-suspending conditions is given by Equation (9.32) ... 

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