Cyclone–anticyclone vortex asymmetry mechanism and linear Ekman friction

Allowance for the linear Ekman friction has been found to ensure a threshold (in rotation frequency) realization of the linear dissipative–centrifugal instability and the related chiral symmetry breaking in the dynamics of Lagrangian particles, which leads to the cyclone–anticyclone vortex asymmetry. An excess of the fluid rotation rate ω₀ over some threshold value determined by the fluid eigenfrequency ω (i.e., ω₀ > ω) is shown to be a condition for the realization of such an instability. A new generalization of the solution of the Karman problem to determine the steady-state velocity field in a viscous incompressible fluid above a rotating solid disk of large radius, in which the linear Ekman friction was additionally taken into account, has been obtained. A correspondence of this solution and the conditions for the realization of the dissipative–centrifugal instability of a chiral-symmetric vortex state and the corresponding cyclone–anticyclone vortex asymmetry has been shown. A generalization of the well-known spiral velocity distribution in an “Ekman layer” near a solid surface has been established for the case where the fluid rotation frequency far from the disk ω differs from the disk rotation frequency ω₀.     

Electro-hydrodynamic propulsion of counter-rotating Pickering drops

Insulating particles or drops suspended in carrier liquids may start to rotate with a constant frequency when subjected to a uniform DC electric field. This is known as the Quincke rotation electro-hydrodynamic instability. A single isolated rotating particle exhibit no translational motion at low Reynolds number, however interacting rotating particles may move relative to one another. Here we present a simple system consisting of two interacting and deformable Quincke rotating particle covered drops, i.e. deformable Pickering drops. The drops attract one another and spontaneously form a counter-rotating pair that exhibits electro-hydrodynamic driven propulsion at low Reynolds number flow.     

Hall effect on unsteady hydromagnetic flow in a rotating channel permeated by an inclined magnetic field in the presence of an oscillator

In continuation with Ghosh (Czech. J. Phys47 (1997) 787) author has extended the problem of an unsteady hydromagnetic flow in a rotating environment in the presence of an inclined magnetic field with the positive direction of the axis of rotation permeated by a fluid-pulse oscillator along the axis of rotation when the Hall current is taken into account. Author has studied that the laminar flow breaks down and it becomes turbulent when the frequency is very high, i.e., ωT=π/2; thermonuclear reaction becomes significant subject to a maximum dissipation of energy into smallest eddies when the kinetic energy is transformed into heat. It is investigated that the Hall current plays a significant role in determining the unsteady MHD flow behaviour subject to an intrinsic stability of the flow pattern in relation with a modified Ghosh inertial frequency ω=(1/2){[4K ² + 2mM ² cosϑ/(1 +m ²)]² − [M ² sin² ϑ/(1 +m ²)]²∼^1/2 in a rotating system which seems to have disappeared in the literature since 1942.     

Hydromagnetic flow in a rotating channel permeated by an inclined magnetic field in the presence of an oscillator

A steady hydromagnetic flow of a viscous incompressible electrically conducting fluid confined between a perfectly conducting rotating parallel plate channel due to a constant pressure gradient permeated by an inclined magnetic field with the positive direction of the axis of rotation in the presence of an oscillator along the axis of rotation is investigated. The influence of these parameters, viz.M ² (the Harmann number) andK ² (the rotation parameter), describes a new relationG _MK ² =16K ⁴–M ⁴sin⁴ which defines the fundamental relation between the hydromagnetic force and the coriolis force. It is noticed that the laminar flow breaks down when the velocity is very large, i.e.,u+iv= and it becomes turbulent when the frequency is very high, i.e.,T=1/2. The rate of heat transfer is analysed when the frequency is very high, i.e.,T=1/2.     

Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium

We report the observation of dynamo action in the von Kármán sodium experiment, i.e., the generation of a magnetic field by a strongly turbulent swirling flow of liquid sodium. Both mean and fluctuating parts of the field are studied. The dynamo threshold corresponds to a magnetic Reynolds number R(m) approximately 30. A mean magnetic field of the order of 40 G is observed 30% above threshold at the flow lateral boundary. The rms fluctuations are larger than the corresponding mean value for two of the components. The scaling of the mean square magnetic field is compared to a prediction previously made for high Reynolds number flows.     

Experimental manifestation of vortices and Rossby wave blocking at the MHD excitation of quasi-two-dimensional flows in a rotating cylindrical vessel

Experiments on the excitation of counterpropagating zonal flows by the magnetohydrodynamic (MHD) method in a rotating cylindrical vessel with a conic bottom have been performed. Flows appear in a conducting fluid layer in the field of ring magnets under the action of a radial electric field. The velocity fields have been reconstructed by the particle image velocimetry (PIV) method. In the fast rotation regimes with a thin fluid layer, where the Rossby-Obukhov scale does not exceed the characteristic sizes of the vessel, the system of perturbations appears with almost immobile blocked anticyclones in the outer part of the flow and rapidly moving cyclones in the main stream. The diagram of regimes is plotted in the variables of the relative angular velocities of the averaged zonal flow and transfer of vortices about the system rotation axis. Attention is focused on the results for the regions of the diagram with slow motion of vortices with respect to the rotating coordinate system near the parameters for stationary Rossby waves (blocking of circulation). The results are compared to the results previously obtained in similar experiments using the source-sink method.     

Motion of fluid and a solid core in a spherical cavity rotating in an external force field

The motion of a fluid in a rotating spherical cavity with a free light spherical body under the perturbing effect of an external force field perpendicular to the rotation axis is investigated experimentally. It is shown that the external field excites the lagging differential rotation of the core occupying the central position in the cavity under the action of a centrifugal force. The regularities of the averaged rotation of the body and the motion of fluid shaped as the Taylor-Proudman column are investigated. The sequential threshold manifestation of various instability types of the Taylor-Proudman column with an increase in the velocity of the differential body rotation is found. Initially a new type of instability manifests itself, and a two-dimensional system of vortexes elongated along the rotation axis is formed inside the column. Then the development of azimuthal two-dimensional waves at the column boundary is observed. It is shown that the Reynolds number calculated through the velocity of the differential body rotation determines the threshold transitions. A map of motion modes of a fluid in a spherical layer on a plane of dimensionless parameters is plotted.     

f-Mode instability in relativistic neutron stars

We present the first calculation of the basic properties of the f-mode instability in rapidly rotating relativistic neutron stars, adopting the Cowling approximation. By accounting for dissipation in neutron star matter, i.e., shear or bulk viscosity and superfluid mutual friction, we calculate the associated instability window. For our specific stellar model, a relativistic polytrope, we obtain a minimum gravitational growth time scale (for the dominant ?=m=4 mode) of the order of 10(3)-10(4) s near the Kepler frequency Ω(K) while the instability is active above ～0.92 Ω(K) and for temperatures ～(10(9)-2×10(10)) K, characteristic of newborn neutron stars.     

A note on unsteady hydromagnetic flow in a rotating channel permeated by an inclined magnetic field in the presence of an oscillator

Ghosh [Czech. J. Phys.46 (1996) 85] has extended the problem of an unsteady hydromagnetic flow (MHD) in a rotating environment permeated by an inclination of a uniform magnetic field with the positive direction of the axis of rotation; a fluid-pulse oscillator is applied along the axis of rotation in order to explain the validity of a physical situation of a steady flow under the conditions and configurations as stated by Ghosh in the paper cited above. It is investigated that the unsteady MHD flow has an intrinsic stability subject to Ghosh inertial frequency in relation withG _MK ² =(16K ⁴ −M ⁴ sin⁴ θ)^1/2, where MHD flow stability parameter of the Earth’s liquid core is taken into account, which seems to have disappeared in the literature since 1942. It is important to say that the thermonuclear reaction indicates a maximum dissipation of energy into smallest eddies when the kinetic energy is transformed into heat.     

Capillary hysteresis in a confined swirling two-fluid flow

This experimental study describes a hysteresis—a vivid manifestation of strongly nonlinear flow physics. A sealed vertical cylindrical container of radius 45 mm and height 90 mm is filled with water and sunflower oil. The rotating lid drives swirl and themeridional circulation of both fluids. As the rotation strength Re increases, the oil–water interface rises near the axis, touches the lid at Re = Re₁, and moves toward the container sidewall. Then as Re decreases, the interface returns to the axis and separates fromthe lid at Re = Re₂ < Re₁. At each Re from the range, Re₂ < Re < Re₁, two different stable steady flow states are observed, which is typical of hysteresis. The hysteresis only occurs if a volume fraction of oil is small. The hysteresis disappears as the oil fraction exceeds a threshold, which is around 0.4.     

Pattern formation in Taylor-Couette flow of dilute polymer solutions: dynamical simulations and mechanism

We report spatiotemporal pattern formation in Taylor-Couette flow (i.e., flow between rotating cylinders) of viscoelastic dilute polymer solutions obtained for the first time from first-principles dynamical simulations. Solution structures with varying spatial and temporal symmetries, such as rotating standing waves, flames, disordered oscillations, and solitary vortex solutions which include diwhirls (stationary and axisymmetric) and oscillatory strips (axisymmetric or nonaxisymmetric), are observed, depending on the ratio of fluid relaxation time to the time period of inner cylinder rotation. The flow-microstructure coupling mechanisms underlying the pattern formation process are also discussed.     

Effects of hall current on MHD Couette flow in a rotating system with arbitrary magnetic field

Author has studied the MHD Couette flow in a rotating environment with non- conducting walls in the presence of an arbitrary magnetic field. The solution in dimensionless form contains four pertinent flow parameters, viz. the Hartmann number, the rotation parameter which is the reciprocal of the Ekman number, the Hall current parameter, and the angle of inclination of the magnetic field to the positive direction of the axis of rotation. An interplay of hydromagnetic force and Coriolis force with an inclusion of Hall current plays a significant role in determining the MHD flow behaviour. The velocity and induced magnetic field distributions are depicted graphically. Also, the numerical results of shear stresses and the rate of mass flows are presented graphically.     

Polarization reversal in multiferroic TbMnO3 with a rotating magnetic field direction

For the memory application of magnetoelectric multiferroics, not only bistability (i.e., ferroelectricity) but also the switching of the polarization direction with some noneverlasting stimulus is necessary. Here, we report a novel method for the electric polarization reversal in TbMnO3 without the application of an electric field or heat. The direction of the magnetic-field-induced polarization along the a axis (Pa) is memorized even in the zero field where Pa is absent. The polarization direction can be reversed by rotating the magnetic-field direction in the ab plane.     

Impact of co- and counter-swirl on flow recirculation and liftoff of non-premixed oxy-flames above coaxial injectors

Controlling the flame shape and its liftoff height is one of the main issues for oxy-flames to limit heat transfer to the solid components of the injector. An extensive experimental study is carried out to analyze the effects of co- and counter-swirl on the flow and flame patterns of non-premixed oxy-flames stabilized above a coaxial injector when both the inner fuel and the annular oxidizer streams are swirled. A swirl level greater than 0.6 in the annular oxidizer stream is shown to yield compact oxy-flames with a strong central recirculation zone that are attached to the rim of central fuel tube in absence of inner swirl. It is shown that counter-swirl in the fuel tube weakens this recirculation zone leading to more elongated flames, while co-swirl enhances it with more compact flames. These results obtained for high annular swirl levels contrast with previous observations made on gas turbine injectors operated at lower annular swirl levels in which central recirculation of the flow is mainly achieved with counter-rotating swirlers. Imparting a high inner swirl to the central fuel stream leads to lifted flames due to the partial blockage of the flow at the injector outlet by the central recirculation zone that causes high strain rates in the wake of the injector rim. This partial flow blockage is more influenced by the level of the inner swirl than its rotation direction. A global swirl number is then introduced to analyze the structure of the flow far from the burner outlet where swirl dissipation takes place when the jets mix. A model is derived for the global swirl number which well reproduces the evolution of the mass flow rate of recirculating gases measured in non-reacting conditions and the flame liftoff height when the inner and outer swirl levels and the momentum flux ratio between the two streams are varied.     

An empirical correlation between spray dispersion and spray tip penetration from an edge detection of visualized images under the flow condition of a solid body rotating swirl

In this study, spray tip penetration and dispersion in high-pressure environment were simulated experimentally with an emphasis on the swirl effect. A rotating constant volume chamber was designed in order to generate a swirl that could be varied continuously with a flow field that closely resembled the solid-body rotation. An emulsified fuel was injected into the chamber and the developing process of fuel spray was observed. The effect of swirl on the spray dispersion was analyzed by measuring the dispersion area as a function of the spray tip penetration and the time after the start of the injection. The effect of swirl on the spray dispersion was quantified through getting a relationship between the swirl and the dispersion. The experimental results of the spray dispersion with time after the fuel injection process began showed similar characteristics to those of the spray tip penetration with time after the start of the fuel injection. The spray dispersion characteristics while varying the spray tip penetration were also investigated. The results showed that the spray dispersion depends linearly on the spray tip penetration, when it is small. As the spray tip penetrates into longer distance, the dispersion depends on the spray tip penetration to the power of 1.6.     

Simulating magnetic nanoparticle behavior in low-field MRI under transverse rotating fields and imposed fluid flow

In the presence of alternating-sinusoidal or rotating magnetic fields, magnetic nanoparticles will act to realign their magnetic moment with the applied magnetic field. The realignment is characterized by the nanoparticle's time constant, τ. As the magnetic field frequency is increased, the nanoparticle's magnetic moment lags the applied magnetic field at a constant angle for a given frequency, Ω, in rad s⁻¹. Associated with this misalignment is a power dissipation that increases the bulk magnetic fluid's temperature which has been utilized as a method of magnetic nanoparticle hyperthermia, particularly suited for cancer in low-perfusion tissue (e.g., breast) where temperature increases of between 4 and 7 °C above the ambient in vivo temperature cause tumor hyperthermia. This work examines the rise in the magnetic fluid's temperature in the MRI environment which is characterized by a large DC field, B₀. Theoretical analysis and simulation is used to predict the effect of both alternating-sinusoidal and rotating magnetic fields transverse to B₀. Results are presented for the expected temperature increase in small tumors ( radius) over an appropriate range of magnetic fluid concentrations (0.002-0.01 solid volume fraction) and nanoparticle radii (1-10 nm). The results indicate that significant heating can take place, even in low-field MRI systems where magnetic fluid saturation is not significant, with careful the goal of this work is to examine, by means of analysis and simulation, the concept of interactive fluid magnetization using the dynamic behavior of superparamagnetic iron oxide nanoparticle suspensions in the MRI environment. In addition to the usual magnetic fields associated with MRI, a rotating magnetic field is applied transverse to the main B₀ field of the MRI. Additional or modified magnetic fields have been previously proposed for hyperthermia and targeted drug delivery within MRI. Analytical predictions and numerical simulations of the transverse rotating magnetic field in the presence of B₀ are investigated to demonstrate the effect of Ω, the rotating field frequency, and the magnetic field amplitude on the fluid suspension magnetization. The transverse magnetization due to the rotating transverse field shows strong dependence on the characteristic time constant of the fluid suspension, τ. The analysis shows that as the rotating field frequency increases so that Ωτ approaches unity, the transverse fluid magnetization vector is significantly non-aligned with the applied rotating field and the magnetization's magnitude is a strong function of the field frequency. In this frequency range, the fluid's transverse magnetization is controlled by the applied field which is determined by the operator. The phenomenon, which is due to the physical rotation of the magnetic nanoparticles in the suspension, is demonstrated analytically when the nanoparticles are present in high concentrations (1-3% solid volume fractions) more typical of hyperthermia rather than in clinical imaging applications, and in low MRI field strengths (such as open MRI systems), where the magnetic nanoparticles are not magnetically saturated. The effect of imposed Poiseuille flow in a planar channel geometry and changing nanoparticle concentration is examined. The work represents the first known attempt to analyze the dynamic behavior of magnetic nanoparticles in the MRI environment including the effects of the magnetic nanoparticle spin-velocity. It is shown that the magnitude of the transverse magnetization is a strong function of the rotating transverse field frequency. Interactive fluid magnetization effects are predicted due to non-uniform fluid magnetization in planar Poiseuille flow with high nanoparticle concentrations.     

The influence of magnetic field on short-wavelength instability of Riemann ellipsoids

We address the question of stability of the so-called S-type Riemann ellipsoids, i.e. a family of Euler flows in gravitational equilibrium with the vorticity and background rotation aligned along the principal axis perpendicular to the flow. The Riemann ellipsoids are the simplest models of self-gravitating, tidally deformed stars in binary systems, with the ellipticity of the flow modelling the tidal deformation. By the use of the WKB theory we show that mathematically the problem of stability of Riemann ellipsoids with respect to short-wavelength perturbations can be reduced to the problem of magneto-elliptic instability in rotating systems, studied previously by Mizerski and Bajer [K.A. Mizerski, K. Bajer, The magneto-elliptic instability of rotating systems, J. Fluid Mech. 632 (2009) 401-430]. In other words the equations describing the evolution of short-wavelength perturbations of the Riemann ellipsoids considered in Lagrangian variables are the same as those for the evolution of the magneto-elliptic-rotational (MER) waves in unbounded domain. This allowed us to use the most unstable MER eigenmodes found in Mizerski et al. [K.A. Mizerski, K. Bajer, H.K. Moffatt, The α-effect associated with elliptical instability, J. Fluid Mech., 2010 (in preparation)] to provide an estimate of the characteristic tidal synchronization time in binary star systems. We use the idea of Tassoul [J.-L. Tassoul, On synchronization in early-type binaries, Astrophys. J. 322 (1987) 856-861] and that the interactions between perturbations significantly increase the effective viscosity and hence the energy dissipation in an Ekman-type boundary layer at the surface of the star. The results obtained suggest that if the magnetic field generated by (say) the secondary component of a binary system is strong enough to affect the flow dynamics in the primary, non-magnetized component, the characteristic tidal synchronization time can be significantly reduced.     

Heat transfer characteristics of decaying swirl flow through a circular tube with co/counter dual twisted-tape swirl generators

The influence of co/counter dual-twisted tapes (CoT/CT) on heat transfer rate in a circular tube has been investigated experimentally. In the experiment, the dual-twisted tapes are placed at the entry of the test tube in two arrangements: (1) each of dual twisted tape was twisted in the same direction that can produce co-swirl flow at the entry and (2) each of dual twisted tape was twisted in the opposite direction that can produce counter-swirl flow. Dual tapes were twisted in three different twist ratios (y/w = 3, 4, and 5) for generating different swirl intensities at the entry of the test section while the single twisted tape (ST) was also the test for comparison. The aim at using the dual twisted tapes is to create co/counter-rotating swirl flows having a significant influence on the flow turbulence intensity at the entry section leading to higher heat transfer enhancement. Average Nusselt numbers of CoT/CT are determined and also compared with those obtained from other similar cases, i.e., ST. The experimental results on the heat transfer rates indicated that the tubes with the dual twisted tapes (CoT/CT) are higher than those with the single tape at the entry section (x/D = 0 to 10). The heat transfer rates at longer distance became lower due to high interaction of each swirl. In addition, the mean Nusselt number and friction factor for the swirl generator created by the CT is nearly similar to CoT results.     

Simulating fire whirls

A numerical investigation of swirling fire plumes is pursued to understand how swirl alters the plume dynamics and combustion. One example is the ‘fire whirl’ which is known to arise naturally during forest fires. This buoyancy-driven fire plume entrains ambient fluid as heated gases rise. Vorticity associated with a mechanism such as wind shear can be concentrated by the fire, creating a vortex core along the axis of the plume. The result is a whirling fire. The current approach considers the relationship between buoyancy and swirl using a configuration based on fixing the heat release rate of the fire and imposing circulation. Large-eddy methodologies are used in the numerical analyses. Results indicate that the structure of the fire plume is significantly altered when angular momentum is imparted to the ambient fluid. The vertical acceleration induced by buoyancy generates strain fields which stretch out the flames as they wrap around the nominal plume centreline. The whirling fire constricts radially and stretches the plume vertically.(Some figures in this article are in colour only in the electronic version; see www.iop.org)     

Visualization of transient three-dimensional flow field with rotating stall in a diagonal flow fan

An Unsteady flow field with rotating stall cells in a high specific-speed diagonal flow fan has been investigated experimentally. Although a general feature of stall cells has already indicated, i.e., the number of stall cells is one and its propagating speed is approximately 80 percent of rotor speed, little has been known about the flow field when a rotating stall occurs because of its unsteadiness. In order to capture the behavior of the rotating stall cell, measurements of the flow field at the rotor inlet were carried out with a single slant hot-wire. Those data were processed by a so-called “double phase-locked averaging” (DPLA) technique, which enabled to capture the flow field of the cell in the reference co-ordinate system fixed to the rotor. As a result, time-dependent ensemble averages of the three-dimensional velocity components at the rotor inlet have been obtained and the behavior of the rotating stall cell has been illustrated with each velocity component.