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In the course of the search for a flow pattern optimal for culture growth in vortex bioreactors, our experiments discovered striking flow patterns that existing theoretical models cannot explain. Three immiscible liquids fill a vertical open cylindrical container whose sidewall is still, while the bottom disk rotates driving a fluid motion. The centrifugal force pushes the lower liquid (L, aqueous glycerol) from the axis to the periphery near the bottom, creating its toroid circulation that in turn drives middle liquid (M, sunflower oil) and upper liquid (U, alcoholic glycerin) circulations. With increasing rotation, counterflows develop near both interfaces LM and MU in upper fluids: the liquids move toward (away from) the axis below (above) the interface that seems paradoxical. Then, unusual topological transformations occur again in the middle liquid flow caused by competition between effects of radial friction and centrifugal forces. Near cylinder boundary at interface MU, new reverse circulation zone developed where the radial velocity became zero and then change sign. These counterintuitive results wait for their theoretical explanation and formulation of new contact conditions at the LM and MU interfaces. [ABSTRACT FROM AUTHOR]

This experimental study reveals a striking nonlinear-physics phenomenon of fundamental and practical interest—changing conditions at the interface of two swirling immiscible fluids filling a vertical cylindrical container. To this end, we use a new measurement technique significantly advanced compared with prior studies. The rotating bottom disk drives a steady axisymmetric flow of both fluids. The lower fluid makes the centrifugal circulation (CC): It spirals on toroid surfaces going to the periphery near the bottom and going back to the axis near the interface. At a slow rotation (Re = 100), the upper fluid makes the anti-centrifugal circulation. As the rotation intensifies (Re = 175), the upper-fluid flow reverses into CC near the interface-axis intersection. For strong swirl (Re = 500), the CC occurs at the entire interface. In prior studies, the spatial resolution (1 mm) was insufficient to resolve the near-interface velocity field. Here, we use the advanced (light field) measurement technique, which has significantly better resolution (0.14 mm) and clearly shows that the radial velocity at the interface is negative for small Re and becomes zero for large Re. During these metamorphoses, the topology of the lower-fluid flow remains invariant, the interface has no visible deformation, and the flow is steady and axisymmetric. [ABSTRACT FROM AUTHOR]

The paper reports the results of experimental and numerical studies of vortex motion in an industrial-scale glass bioreactor (volume, 8.5 L; reactor vessel diameter D, 190 mm) filled 50–80%. The model culture medium was a 65% aqueous glycerol solution with the density ρg = 1150 kg/m3 and kinematic viscosity νg = 15 mm2/s. The methods of particle image velocimetry and adaptive track visualization allow one to observe and measure the vortex motion of the culture medium. In this work, the vortex flow investigation was performed in a practical bioreactor at the operation regimes. Our research determines not only the optimal flow structure, but also the optimal activator rotation speed, which is especially important in the opaque biological culture. The main result is that, similar to the case of two rotating immiscible liquids, a strongly swirling jet is formed near the axis, and the entire flow acquires the pattern of a miniature gas–liquid tornado. The aerating gas interacts with the liquid only through the free surface, without any mixing. This intensifies the interphase mass transfer due to the high-speed motion of the aerating gas. [ABSTRACT FROM AUTHOR]

This experimental study reveals a curious phenomenon—hysteresis in a lab-scale two-liquid flow. The rotating bottom disk drives a toroidal circulation of water–glycerin solution (lower fluid) and sunflower oil (upper fluid) in a vertical cylindrical container. As the rotation speeds up, the solution–oil interface and the oil–air (free) surface deform rising near the sidewall and depressing near the axis as typical of whirlpools. We choose that the oil–solution volume ratio be small (having in mined oil-pollution applications) but not too small (for convenient observation). As the rotation speeds up, the oil separates from the sidewall and collects in the solution funnel. Next, the interface touches the bottom, and this is the point of no return. The centrifugal force pushes the near-bottom oil to the periphery and the buoyancy pushes oil upward. The Rayleigh–Taylor instability breaks the interface, and oil droplets disperse in the solution. If before this breakdown, the rotation starts to decrease, the oil separates from the bottom at the angular velocity ω being remarkably smaller than that for which the oil touches the bottom. Therefore, the hysteresis is a capillary-induced phenomenon. [ABSTRACT FROM AUTHOR]

This experimental study reveals a counterflow slip at the interface of two immiscible fluids filling a sealed vertical cylindrical container whose bottom disk rotates while other walls are stationary. An advanced particle image velocimetry helps us analyze and quantify streamline patterns and velocity profiles of the steady axisymmetric flows of both fluids. As the angular velocity of a disk increases, starting from zero, three changes occur in topology of the upper-fluid flow while topology of the lower-fluid flow remains invariant. These changes result in the counterflow slip at the entire interface, whose nature is speculatively discussed and requires further research. [ABSTRACT FROM AUTHOR]

This experimental and numerical study discusses the formation of double vortex breakdown in a swirling flow of two immiscible fluids where new circulation cells evolve in both fluids. The rotating lid drives the steady axisymmetric motion in a sealed vertical cylindrical container whose other walls are stationary. As the rotation intensifies, multiple topological changes occur in the flow. This study explains how two new circulation cells (vortex breakdown bubbles) almost simultaneously develop near the centers of both upper and lower fluids while the flow remains steady and axisymmetric. Such multi-cell flows can help provide fine, gentle, and nonintrusive mixing in chemical and biological reactors. [ABSTRACT FROM AUTHOR]

This experimental study reveals a spectacular and important phenomenon—double vortex breakdown—in a swirling flow of two immiscible fluids where vortex breakdown bubbles evolve simultaneously in both fluids. The rotating lid drives the steady axisymmetric motion in a sealed vertical cylindrical container whose other walls are stationary. As the rotation intensifies, topological metamorphoses occur, resulting in a multicellular flow. Two new circulation cells (vortex breakdown bubbles) simultaneously develop near the centers of both fluids while the flow remains steady and axisymmetric. Such a pattern can help provide fine, gentle, and nonintrusive mixing in chemical and biological reactors. [ABSTRACT FROM AUTHOR]

This paper describes the first experimental evidence of the vortex breakdown development in the lower fluid in a sealed vertical cylindrical container in which two immiscible fluids circulate, driven by a rotating lid. The lower fluid is water, and the upper fluid is sunflower oil. In both fluids, the rotation generates centrifugal meridional circulations separated by a thin anticentrifugal circulation layer attached to the interface from below. An advanced technique of particle image velocimetry and proper laser illumination allows for the measurement of velocity and recognition of the patterns of flow in oil and water. As the rotation speeds up, a tornadolike swirling ascending jet forms near the axis-bottom intersection. A circulation cell (vortex-breakdown bubble, VBB) then emerges near the center of the water domain, approaches the bottom, and disappears. This scenario of the appearance and disappearance of the VBB is similar to that occurring in a single-fluid flow and in the upper fluid of a two-fluid flow. [ABSTRACT FROM AUTHOR]

This experimental and numerical study of a two-fluid swirling flow reveals a discontinuity of the radial velocity at the interface. The motion is driven by the rotating lid in a sealed vertical cylindrical container. The upper fluid radially diverges near the lid, goes downward near the sidewall, converges to the axis near the interface, and rises near the axis. This centrifugal circulation drives a bulk counter-circulation of the lower fluid at a slow rotation. As the rotation intensifies, a new circulation cell emerges in the lower fluid. The numerical simulations, performed under the continuity condition for all velocity and stress components, predict that the new cell emerges near the bottom and expands upward. In contrast, the new cell emerges near the interface and expands downward in the experiment. A slip condition is proposed for the radial velocity at the interface. The slip occurs due to the centrifugal force and difference in the fluid densities. The numerical simulations, performed with the slip condition, agree with the experiment. [ABSTRACT FROM AUTHOR]

The hydrodynamics of secondary flow phenomena in a disc‐shaped gas vortex unit (GVU) is investigated using experimentally validated numerical simulations. The simulation using ANSYS FLUENT® v.14a reveals the development of a backflow region along the core of the central gas exhaust, and of a counterflow multivortex region in the bulk of the disc part of the unit. Under the tested conditions, the GVU flow is found to be highly spiraling in nature. Secondary flow phenomena develop as swirl becomes stronger. The backflow region develops first via the swirl‐decay mechanism in the exhaust line. Near‐wall jet formation in the boundary layers near the GVU end‐walls eventually results in flow reversal in the bulk of the unit. When the jets grow stronger the counterflow becomes multivortex. The simulation results are validated with experimental data obtained from Stereoscopic Particle Image Velocimetry and surface oil visualization measurements. © 2018 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 64: 1859–1873, 2018 [ABSTRACT FROM AUTHOR]

To clarify the three-dimensional (3D) structure of near-wall jets observed in disc-like gas vortex units (GVUs), experimental and numerical studies are performed. The experimental results are obtained using stereoscopic particle image velocimetry (PIV), laser doppler anemometry, pressure probes and surface oil flow visualization techniques. The first three techniques have been used to investigate the bulk flow hydrodynamics of the vortex unit. Surface oil flow visualization is adopted to visualize streamlines near the end-walls of the vortex unit. The surface streamlines help to determine the azimuthal and radial velocity components of the radial near-wall jets. Simulations of the vortex unit using FLUENT® v.14a are simultaneously performed, computationally resolving the near-wall jet regions in the axial direction. The simulation results together with the surface oil flow visualization establish the 3D structure of the near-wall jets in GVUs for the first time in literature. It is also conjectured that the near-wall jets develop due to the combined effect of bulk flow acceleration and swirl. The centrifugal force diminishes in the vicinity of the end-walls. The radially inward pressure gradient in these regions, no longer balanced by the centrifugal force, pushes gas radially inward thus developing the near-wall jets. © 2016 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 63: 1740-1756, 2017 [ABSTRACT FROM AUTHOR]

This paper reveals the flow topology hidden in the experimental study by Fujimoto and Takeda ["Topology changes of the interface between two immiscible liquid layers by a rotating lid," Phys. Rev. E 80, 015304(R) (2009)]. Water and silicone oil fill a sealed vertical cylindrical container. The rotating top disk induces the meridional circulation and swirl of both fluids. As the rotation strength Reo increases, the interface takes shapes named, by the authors, hump, cusp, Mt. Fuji, and bell. Our numerical study reproduces the interface geometry and discloses complicated flow patterns. For example at Reo = 752, where the interface has the "Mt. Fuji" shape, the water motion has three bulk cells and the oil motion has two bulk cells. This topology helps explain the interface geometry. In addition, our study finds that the steady axisymmetric flow suffers from the shear-layer instability for Reo > 324, i.e., before the interface becomes remarkably deformed. The disturbance energy is concentrated in the water depth. This explains why the instability does not significantly affect the interface shape in the experiment. [ABSTRACT FROM AUTHOR]

A unique normalized radial pressure profile characterizes the bed of a gas-solid vortex reactor over a range of particle densities and sizes, solid capacities, and gas flow rates: 950-1240 kg/m3, 1-2 mm, 2 kg to maximum solids capacity, and 0.4-0.8 Nm3/s (corresponding to gas injection velocities of 55-110 m/s), respectively. The combined momentum conservation equations of both gas and solid phases predict this pressure profile when accounting for the corresponding measured particle velocities. The pressure profiles for a given type of particles and a given solids loading but for different gas injection velocities merge into a single curve when normalizing the pressures with the pressure value downstream of the bed. The normalized-with respect to the overall pressure drop-pressure profiles for different gas injection velocities in particle-free flow merge in a unique profile. © 2015 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 61: 4114-4125, 2015 [ABSTRACT FROM AUTHOR]

It is shown that the viscous fluid motion in the depth of a narrow cavity is a counterflow moving and periodically varying along the cavity length. The obtained exact solutions of the Stokes equations describe unsteady three-dimensional flows, developing as the distance from the cavity surface increases. The found asymptotic motion is common for a variety of boundary conditions and cavity shapes. Creeping flows between parallel and inclined planes, coaxial cylinders, and concentric cones are particularly addressed. For these flows, the analytical asymptotes and numerical results merge as the gap width decreases. [ABSTRACT FROM AUTHOR]

The off-axis emergence of vortex breakdown (VB) is revealed. The steady axisymmetric flow in a vertical sealed cylinder, which is partially filled with water and the rest is filled with air, is driven by the rotating bottom disk. The numerical simulations show that VB can emerge away from the rotation axis, interface, and walls. As the rotation intensifies, VB first develops in the water region. If the water height is less (larger) than nearly one half of the cylinder radius, VB emerges off (on) the axis. As the rotation further increases, the off-axis VB ring touches the interface and then a thin countercirculation layer develops in the air flow above the water VB domain. This two-fluid VB ring shrinks (it even disappears in a very shallow whirlpool) as the interface approaches the bottom disk. [ABSTRACT FROM AUTHOR]

This numerical study of the axisymmetric motion of a viscous incompressible fluid in an elongated cylindrical container explains how colliding counterflows develop. Two swirling flows enter the container through peripheral inlets and leave it through central exhausts symmetrically from both ends. Different flow rates, characterized by the Reynolds number Re, are studied for a fixed swirl number. For small Re, the throughflow (TF) is limited to the inlet-exhaust vicinities and a few circulation cells occupy the rest of the interior. As Re grows, (i) the circulation cells disappear while the TF reaches the container's midsection and becomes U shaped, moving near the sidewall inward and going back near the container axis; elongated circulation regions develop separating the TF branches; (ii) the flow convergence to the axis focuses near the container's midsection, resulting in the vortex breakdown development; (iii) the swirl-induced low pressure causes suction of the ambient fluid through the central parts of the exhausts; (iv) the suction flow reaches the container's midsection, turns around, mixes with the driving TF, forms an annular outflow, and leaves through the exhaust periphery. The two factors, (a) swirl decay due to friction at the sidewall and (b) the focused flow convergence to the axis, constitute the physical mechanism of the colliding counterflows. Such flow pattern is favorable for a vortex solid-fuel combustor. [ABSTRACT FROM AUTHOR]

This numerical study of an axisymmetric motion of a viscous incompressible fluid in an elongated cylindrical container explains how a swirling inflow develops the global meridional circulation and two U-shaped throughflows (TFs). For moderate values of the Reynolds (Re) number, there is a single U-shaped TF: The fluid moves from the peripheral annular inlet near the sidewall to the dead end, turns around, goes back near the axis, and leaves the container through the central exhaust. A Re increases, vortex breakdown occurs near the dead end. If the exhaust orifice is wide, the ambient fluid is sucked into the container near its axis, reaches the dead-end vicinity, merges with the U-shaped TF, and goes back inside an annular region. Thus, a double counter-flow develops, where the fluid moves to the dead end near both the sidewall and the axis and goes back in between. The physical mechanism of the double counterfiow is a swirl decay combined with the focused flow convergence near the dead end. This double counterfiow is beneficial for combustion applications. [ABSTRACT FROM AUTHOR]

A liquid issuing from a capillary needle adopts a cone-jet structure if the liquid is further driven by a coflowing gas jet. In the present work, flow patterns appearing in this cone-jet structure are studied by the volume-of-fluid numerical method. Axisymmetric motions of the liquid and gas, both treated as viscous incompressible fluids, are simulated. As the gas/liquid mass ratio increases, the meridional circulation develops in the meniscus region of the liquid flow. As the ratio exceeds a threshold, the flow becomes time periodic and droplet generating. Swirl, added in the gas jet, affects the liquid flow in two ways. First, the threshold value increases with swirl. Second, the circulation region transforms from the bubble-like into ring-like pattern and then becomes two-cellular. As swirl further increases, the cells separate, one cell disappears, and a new cell emerges being attached to the needle wall. The predicted metamorphoses of the flow topology might be important for atomization of a liquid fuel. [ABSTRACT FROM AUTHOR]

This paper focuses on the physical mechanism of elongated counterflows occurring in vortex tubes and hydrocyclones. To this end, a new solution to the Navier–Stokes equations is obtained which describes a flow pattern consisting of two through-flows and the global meridional circulation. One of the through-flows has U-shape geometry. It is shown that swirl decay due to fluid-wall friction induces both the U-shape through-flow and the circulation. The circulation does not deteriorate particle separation. The solution illustrates how the swirl-induced pressure distribution drives the counterflow and results in the paradoxical centrifugal stratification where the high-density fluid located at the periphery is hot while the low-density fluid located near the axis is cold. [ABSTRACT FROM AUTHOR]

The global meridional circulation of a viscous fluid, caused by swirl decay in a cylindrical container, is studied. To this end, a new solution to the Navier–Stokes equations is obtained, and simple experiments are performed to verify the predictions of the theory. The swirl decay mechanism explains elongated counterflows in hydrocyclones and vortex tubes sometimes extending over a hundred diameters. [ABSTRACT FROM AUTHOR]

The numerical study of the steady axisymmetric air-water flow in a vertical sealed cylinder, driven by the rotating top disk, describes topological transformations as the rotation intensifies. The air meridional flow (AMF) and swirl induce meridional motions of opposite directions in water. For slow (fast) rotation, the effect of AMF (swirl) dominates. For very fast rotation, large-scale regions of clockwise meridional circulation in air and water are separated by a thin layer of anticlockwise circulation adjacent to the interface in water. This pattern develops for other fluids as well. Physical reasoning behind the flow evolution is provided. [ABSTRACT FROM AUTHOR]

This numerical study of the steady axisymmetric motion of a viscous incompressible fluid in a sealed cylindrical container with one end wall rotating reveals that swirl decay, induced by friction at the sidewall, plays an important role in the development of vortex breakdown (VB). When the flow is slow, it is multi-cellular. As the flow strength increases (i) meridional circulation becomes global, (ii) flow convergence toward the axis focuses near the still end wall, (iii) a few local minima of pressure appear, (iv) a few flow reversals occur near the axis, and (v) circulation regions merge and an elongated double counterflow develops. Stages (i)-(v) are common for a number of vortex devices. If the swirl decay is diminished by additional rotation of the sidewall, VB disappears. [ABSTRACT FROM AUTHOR]

• Experimental study of swirling two-fluid flow in a vertical cylinder. • The rotating lid drives a steady axisymmetric circulation. • A jump of a swirl velocity at the interface is observed. • The Moffatt eddy occurs near the interface-sidewall intersection. • The results can be important for bioreactors. Recent theoretical and numerical studies predict the Moffatt eddies near the interface-wall intersection in a two-fluid flow. The current work provides the first experimental evidence of this phenomenon of fundamental interest. It also reveals a jump of the azimuthal velocity at the interface which can be important for vortex bioreactors. The rotating lid drives a two-fluid flow in a vertical cylindrical container whose other walls are stationary. Near the lid, the centrifugal force pushes the upper fluid to the sidewall thus developing its centrifugal meridional circulation. This motion drives the bulk counter-circulation and the Moffatt eddies in the lower fluid at a slow rotation. Using sunflower oil for the upper fluid, water-glycerin or alcohol-glycerin solutions for the lower fluid, and assemble averaging of PIV images allow for velocity measurement and flow visualization even in a creeping motion. This advanced experimental technique helps detect velocity jumps, occurring at the interface and the Moffatt outermost eddy. [ABSTRACT FROM AUTHOR]