Fluid Rotation Research Articles

Effects of slip on steady Bödewadt flow and heat transfer of an electrically conducting non-Newtonian fluid

The steady flow and heat transfer arising due to the rotation of a non-Newtonian fluid at a larger distance from a stationary disk is extended to the case where the disk surface admits partial slip. The constitutive equation of the non-Newtonian fluid is modeled by that for a Reiner–Rivlin fluid. The fluid is subjected to an external uniform magnetic field perpendicular to the plane of the disk. The momentum equation gives rise to a highly nonlinear boundary value problem. Numerical solution of the governing nonlinear equations are obtained over the entire range of the physical parameters. The effects of slip, non-Newtonian fluid characteristics and the magnetic interaction parameter on the momentum boundary layer and thermal boundary layer are discussed in detail and shown graphically. It is observed that slip has prominent effects on the velocity and temperature fields.

Marker transport in a composite vortex

Using a coloring method, the pattern of the transport of a compact spot of markers in a composite vortex created by a uniformly rotating disk, which is located on the bottom of a cylindrical tank, is investigated. The markers were formed by droplets of an aqueous solution of uranyl or ink, which fell down on the free surface of the fluid. In a quiescent fluid, the spot of the markers was transformed into a slowly sinking cascade of vortices. The markers introduced at the center of the cavity on the composite-vortex surface formed a spiral branch. For a non-central introduction of the markers, two spiral branches were formed, one growing in the direction of the fluid rotation and the other growing in the direction, opposite to the rotation. The markers penetrate into the interior of the composite vortex along isolated cylindrical surfaces. The geometrical parameters of the flow are presented.

Discussion: “Rotordynamic Force Prediction of Centrifugal Compressor Impellers Using Computational Fluid Mechanics” by J. J. Moore, D. L. Ransom, and F. Viana

The authors are to be commended for an interesting demonstraion of computational fluid dynamics CFD methods in the analyis of rotordynamic forces for impellers in centrifugal compresors. CFD approaches clearly represent the future for this mportant calculation. As they state, data are vitally needed to nchor predictions for impeller coefficients for compressors. In act, better data would also be helpful for pump impellers. The ata of Bolleter et al. 4 yield whirl frequency ratios that range pward from 0.75 to 2.2. To the extent that the destabilizing orces arise from fluid rotation, WFR cannot exceed the average ircumferential velocity ratio, and more reasonable values would e on the order of 0.5 as predicted by the authors . The authors provide an illuminating discussion of the Wachel odel and its current variations with comparisons to their CFD pproach. They mentioned Gupta’s MS thesis 6 , but apparently verlooked the more accessible 2006 work by Gupta and Childs 1 who use a bulk-flow model to predict the forces for the front nd back compressor shroud faces and compared their predictions o Wachel’s formula. Gupta and Childs showed reasonable agreeent with measured results for pump impellers from Bolleter et l. and presented calculated results for the forces developed by the hroud faces of an industrial compressor. In reviewing CFD literature related to calculation of rotordyamic coefficients for impellers, the authors overlooked the first uch calculation by Baskharone et al. 2 . In 1994, he used a nite-element CFD model and produced reasonable comparisons o measured results by Bolleter et al. In Ref. 8 , Moore showed omparable comparisons for Bolleter’s measured pump data using i Moore’s CFD developments, ii Childs’ bulk-flow predictions 5 , and iii predictions of Baskharone et al.. In their Summary and Conclusions section, the authors state, Based on this result, it can be concluded that the majority of the estabilizing force of a centrifugal impeller arises from the shroud assage, not the impeller-to-diffuser interaction, since the instabilty can be predicted by the shroud force alone.” Are the authors uggesting that this is a new and unexpected outcome? In regard

Papaloizou-Pringle instability of magnetized accretion tori

Hot accretion tori around a compact object are known to be susceptible to a global hydrodynamical instability, the so-called Papaloizou-Pringle (PP) instability, arising from the interaction of non-axisymmetric waves across the corotation radius, where the wave pattern speed matches the fluid rotation rate. However, accretion tori produced in various astrophysical situations (e.g., collapsars and neutron star binary mergers) are likely to be highly magnetized. We study the effect of magnetic fields on the PP instability in incompressible tori with various magnetic strengths and structures. In general, toroidal magnetic fields have significant effects on the PP instability: For thin tori (with the fractional width relative to the outer torus radius much less than unity), the instability is suppressed at large field strengths with the corresponding toroidal Alfven speed $v_{A\phi}\go 0.2r\Omega$ (where $\Omega$ is the flow rotation rate). For thicker tori (with the fractional width of order 0.4 or larger), which are hydrodynamically stable, the instability sets in for sufficiently strong magnetic fields (with $v_{A\phi}\go 0.2 r\Omega$). Our results suggest that highly magnetized accretion tori may be subjected to global instability even when it is stable against the usual magneto-rotational instability.

Spatial coherence, mean wave tilt, and mean local wave-propagation vector of a Laguerre-Gaussian beam passing through a random phase screen

The spatial evolution of the energy distribution and local wave-propagation vector of a fluctuating laser vortex beam is studied. The beam’s fluctuations are induced by its propagation through a thin (in comparison with the total propagation path) layer of a turbulent medium (phase screen). It is shown that the vortex energy flow typical for a coherent beam is also manifested in the mean parameters of a partially coherent beam. In particular, the mean wave tilt is representable as a sum of the vortex and potential components. The rotor of the vector field of mean wave tilts plays the determining part in the circular energy motion. The vortex component for a screen with a quadratic structure function of phase fluctuations corresponds to one of the models of rotational fluid motion called the Scully vortex. The potential component of the mean energy direction field can result in beam focusing with an increase in the distance from the screen. The direction of the mean energy flow lines (mean diffraction rays) allows for an analogy between the evolution of an optical vortex carried by a Laguerre-Gaussian beam and the breakdown of the rotational fluid flow.

Lagrangian formulation of noncommutative fluid models

In this work we study Lagrangian formulations for the noncommutative versions of the irrotational and rotational fluid models. These formulations will be obtained by using the Faddeev–Jackiw symplectic formalism. In this context, interesting results will be revealed, for example, a chiral behavior into both fluid models comes up. In fact, distinct and non-dynamically equivalent Lagrangian descriptions of the noncommutative versions of the fluid models can be proposed.

Some investigations on the enhancement of boiling heat transfer from planer surface embedded with continuous open tunnels

Boiling heat transfer from a flat surface can be enhanced if continuous open tunnel type structures are embedded in it. Further, improvement of boiling heat transfer from such surfaces has been tried by two separate avenues. At first, inclined tunnels are embedded over the solid surface and an effort is made to optimize the tunnel inclination for boiling heat transfer. Surfaces are manufactured in house with four different inclinations of the tunnels with or without a reentrant circular pocket at the end of the tunnel. Experiments conducted in the nucleate boiling regime showed that 45° inclination of the tunnels for both with and without base geometry provides the highest heat transfer coefficient. Next, active fluid rotation was imposed to enhance the heat transfer from tunnel type surfaces with and without the base geometry. Rotational speed imparted by mechanical stirrer was varied over a wide range. It was observed that fluid rotation enhances the heat transfer coefficient only up to a certain value of stirrer speed. Rotational speed values, beyond this limit, reduce the boiling heat transfer severely. A comparison shows that embedding continuous tunnel turns out to be a better option for the increase of heat transfer coefficient compared to the imposition of fluid rotation. But the behavior of inclined tunnels under the action of fluid rotation is yet to be established and can be treated as a future scope of the work.

Clustering of Charged Inertial Particles in Turbulence

Holographic measurements of the clustering of electrically charged, inertial particles in homogenous and isotropic turbulent flow reveal novel particle dynamics. When particles are identically charged, Coulomb repulsion introduces a length scale below which inertial clustering is suppressed such that the radial distribution function (RDF) mimics that of a nonideal gas. The result is described with a Fokker-Planck framework modeling inertial clustering as a diffusion-drift process modified to include Coulomb interaction. The peak in the RDF is well predicted by the balance between the particle terminal velocity under Coulomb repulsion and a time-averaged "drift" velocity obtained from the nonuniform sampling of fluid strain and rotation due to finite particle inertia. The resulting functional form of the RDF matches the measurements closely, providing support for the drift-diffusion description of particle clustering.

Exterior and interior metrics with quadrupole moment

We present the Ernst potential and the line element of an exact solution of Einstein's vacuum field equations that contains as arbitrary parameters the total mass, the angular momentum, and the quadrupole moment of a rotating mass distribution. We show that in the limiting case of slowly rotating and slightly deformed configuration, there exists a coordinate transformation that relates the exact solution with the approximate Hartle solution. It is shown that this approximate solution can be smoothly matched with an interior perfect fluid solution with physically reasonable properties. This opens the possibility of considering the quadrupole moment as an additional physical degree of freedom that could be used to search for a realistic exact solution, representing both the interior and exterior gravitational field generated by a self-gravitating axisymmetric distribution of mass of perfect fluid in stationary rotation.

Equilibrium magnetohydrodynamic flows of liquid metals in magnetorotational instability experiments

A theoretical analysis of equilibrium magnetohydrodynamic flows in annular channels is performed from the perspective of establishing required conditions for liquid metal magnetorotational instability (MRI) experiments. Two different types of fluid rotation are considered: electrically driven flow in an annular channel and Taylor–Couette flow between rotating cylinders. The structure of these flows is studied within a unified approach as a function of the Hartmann and Reynolds numbers. The parameters appropriate for realization of MRI experiments are determined.

Novel heat dissipation design for light emitting diode applications

The authors offer a new design in support of efficient heat dissipation for light emitting diodes (LEDs). In the first part of this paper we discuss improvements in LED packaging materials and layer assembly, and then describe the addition of a thin layer of electroplated copper to the LED base assembly to reduce thermal resistance and increase thermal diffusion efficiency. Also described is a three-dimensional finite element simulation that we performed to verify the proposed design (0.75, 1, and 3 W LED chip temperatures) and a LED heat transfer behavior analysis. The results indicate that the addition of a 9 mm2 electroplated copper layer to the LED base assembly improved LED thermal dissipation by reducing chip temperature by 5°C compared to LEDs without the copper layer packaging. In the second part of this paper we describe (a) our heat pipe system/heat sink design for LED illumination, and (b) experiments in which we changed both working fluid mass and rotation angle to determine their effects on heat pipe cooling. Our results indicate that the most efficient heat dissipation occurred when an added heat pipe was arranged horizontally. Good heat dissipation was observed for heat pipes containing 2.52 g of water (temperature reduced by 50°C). Larger water volumes failed to dissipate additional heat due to the presence of steam inside the pipe.

A second order turbulence model based on a Reynolds stress approach for two-phase boiling flow. Part 1: Application to the ASU-annular channel case

High-thermal performance PWR (pressurized water reactor) spacer grids require both low pressure loss and high critical heat flux (CHF) properties. Numerical investigations on the effect of angles and position of mixing vanes and to understand in more details the main physical phenomena (wall boiling, entrainment of bubbles in the wakes, recondensation) are required. In the field of fuel assembly analysis or design by means of CFD codes, the overwhelming majority of the studies are carried out using two-equation eddy viscosity models (EVM), especially the standard K– ɛ model, while the use of Reynolds Stress Transport Models (RSTM) remains exceptional. But extensive testing and application over the past three decades have revealed a number of shortcomings and deficiencies in eddy viscosity models. In fact, the K– ɛ model is totally blind to rotation effects and the swirling flows can be regarded as a special case of fluid rotation. This aspect is crucial for the simulation of a hot channel in a fuel assembly. In fact, the mixing vanes of the spacer grids generate a swirl in the coolant water, to enhance the heat transfer from the rods to the coolant in the hot channels and to limit boiling. First, we started to evaluate computational fluid dynamics results against the AGATE-mixing experiment: single-phase liquid water tests, with Laser-Doppler liquid velocity measurements upstream and downstream of mixing blades. The comparison of computed and experimental azimuthal (circular component in a horizontal plane) liquid velocity downstream of a mixing vane for the AGATE-mixing test shows that the rotating flow is qualitatively well reproduced by CFD calculations but azimuthal liquid velocity is underestimated with the K– ɛ model. Before comparing performance of EVM and RSTM models on fuel assembly geometry, we performed calculations with a simpler geometry, the ASU-annular channel case. A wall function model dedicated to boiling flows is also proposed.

Effects of working fluid and shaft rotation speed on the performance of HTR plants and the size of CBC turbo-machine

Investigated are the effects of the molecular weight of the working fluid, reactor exit temperature, and shaft rotation speed on the size and number of stages of the turbo-machine as well as the performance of high temperature reactor (HTR) plants with actively cooled reactor pressure vessel and direct or indirect Closed Brayton Cycles (CBCs). The present analyses for working fluids of helium (4 g/mol) and the 15 g/mol He–Xe and He–N 2 binary mixtures are performed for a reactor thermal power of 600 MW, shaft rotation speed of 3000–9000 rpm, and reactor exit temperature from 973 K to 1223 K. For the plants with indirect CBCs, the analyses assume a temperature pinch of 50 K in the IHX. Results show that the CBC compression ratio is relatively low (∼2.6 for He and He–Xe and ∼3.2 for He–N 2), increases very little with increasing the reactor exit temperature and near the maximum thermal efficiency of the plant. For the plants with a direct helium CBC, the thermal efficiency increases from 42% to 51% as the reactor exit temperature increases from 973 K to 1223 K, respectively, versus 37% to 47% for the plants with indirect He-CBC. The HTR plants with indirect He–Xe and He–N 2 CBCs and operating at a turbine inlet temperature of 1123 K have slightly higher thermal efficiencies (45.9% and 45.8%) than the He plant with indirect CBC (45.6%), generating ∼1.6 MWe more electrical power. The molecular weight of the working fluid has a very small effect on the plant thermal efficiency, but significantly reduces the size and number of stages of the CBC turbo-machine. Increasing the shaft rotation speed also decreases the size and number of stages of the CBC turbo-machine.

Motion of a spherical particle inside a liquid film

The motion of a spherical particle inside a liquid film coated on a plane wall is considered under conditions of Stokes flow in the limit of vanishing capillary number where the interfacial deformation is infinitesimal. The problem is formulated in terms of a system of one-dimensional integral equations for the velocity and traction Fourier coefficients along the trace of the interface, wall, and particle contour in a meridional plane, and the solution is found using a boundary-element method. Comprehensive results for the force and torque resistance coefficients are presented in the case of particle rotation and translation in quiescent fluids. The velocity of translation and angular velocity or rotation of a freely suspended particle in simple shear flow are computed and discussed over a broad range of conditions.

Some memories of Juergen

I worked together with Juergen, off and on, for many years. But my most vivid recollections of him are of my Hamburg postdoc in 1960; he was a very valuable mentor. He was always for clarity and rigor. To me the most interesting part of his work was his systematic and highly useful clarification of general relativistic hydrodynamics and kinetic theory. It was a real revelation to see such standard concepts as fluid rotation reappear elegantly and rigorously in a fully relativistic setting. Based on his work in kinetic theory, Juergen, P. Geren and I were able to relate local isotropy observations on particles to spatial isotropy and homogeneity of space-time. Among the many useful lessons I learned from him by example was the importance of being accurate as regards the scope and previous history of a putatively new idea: don’t fool yourself that you own something which really belongs to a colleague or predecessor, and don’t try to sell more than you own. Not even inadvertently, or by implication, or by judicious silence. Nowadays I see lots of disagreements between groups resulting from all concerned failing to observe those straightforward rules— perhaps because the field, the time, the economic climate, and/or the country I now work in are different. To a bystander, the resulting squabbles supply an amusing spectator sport; but, entertainment aside, I like Ehlers’ way better. In this respect, and many others, I was lucky to have him as a role model. Later my respect for him, as a scientist and as a person, only grew. His work on gravitational lensing was very pleasant to study. He will be sorely missed. I hope that our younger replacements can and will emulate his scholarship, breadth, clarity, rigor, and integrity.

Performance of slotted pores in particle manufacture using rotating membrane emulsification

This paper addresses the use of different slotted pores in rotating membrane emulsification technology. Pores of square and rectangular shapes were studied to understand the effect of aspect ratio (1–3.5) and their orientation on oil droplet formation. Increasing the membrane rotation speed decreased the droplet size, and the oil droplets produced were more uniform using slotted pores as compared to circular geometry. At a given rotation speed, the droplet size was mainly determined by the pore size and the fluid velocity of oil through the pore (pore fluid velocity). The ratio of droplet diameter to the equivalent diameter of the slotted pore increased with the pore fluid velocity. At a given pore fluid velocity and rotation speed, pore orientation significantly influences the droplet formation rate: horizontally disposed pores (with their longer side perpendicular to the membrane axis) generate droplets at double the rate of vertically disposed pores. This work indicates practical benefits in the use of slotted membranes over conventional methods.

Effect of inner structure of centrifugal separator on particle classification performance

This study investigated the effects of the inner structure of a centrifugal separator on particle classification performance. The typical inner structure of centrifugal separators is as follows: a blade, which consists of two orthogonal plates, is inserted into the centrifugal separator to create rigid fluid and particle rotations. The results of the present study demonstrate that centrifugal separator performance was significantly improved by attachment of a cylinder to the center of a conventional blade. Modification of the separator by attachment of the cylinder to the center of the centrifugal separator is expected to prevent the particles in the slurry from passing through the central axis of the centrifugal separator. Hence, the particles are subjected to greater centrifugal force. Both experimental and theoretical results demonstrate that particle classification performance increases as the cylinder radius increases. Thus, it is evident that attachment of a cylindrical blade to the center of the centrifugal separator allows for effective and highly efficient collection of extremely small-classified fine particles.

J0501-4-2 キャビテーションの熱力学的効果における速度と温度の影響(流体機械の研究開発におけるEFD/CFD(4))

The degree of thermodynamic effect depends on rotation speed and fluid temperature. Experiments in liquid nitrogen were conducted, in which the inducer rotational speed and the fluid temperature ware changed to estimate the influence on the thennodynamic effect. In the experiment with lower rotational speed, the cavity length was shorter, and suction perfbnnance was improved than that with higher speed. From the arrange data using the modified non-dimensional thennodynamic parameter Σ^〓_<mod>, the effect of nonlinearity of the vapor pressure curve should be considered to evaluate the thennodynamic effect especially in the case of higher temperature.

A depth-integrated model for weakly dispersive, turbulent, and rotational fluid flows

A set of weakly dispersive Boussinesq-type equations, derived to include viscosity and vorticity terms in a physically consistent manner, is presented in conservative form. The model includes the approximate effects of bottom-induced turbulence, in a depth-integrated sense, as a second-order correction. Associated with this turbulence, vertical and horizontal rotational effects are captured. While the turbulence and horizontal vorticity models are simplified, a model with known physical limitations has been derived that includes the quadratic bottom friction term commonly added in an ad hoc manner to the inviscid equations. An interesting result of this derivation is that one should take care when adding such ad hoc models; it is clear from this exercise that (1) it is not necessary to do so – the terms can be included through a consistent derivation from the viscous primitive equations – and (2) one cannot properly add the quadratic bottom friction term without also adding a number of additional terms in the integrated governing equations. To solve these equations numerically, a highly accurate and stable model is developed. The numerical method uses a fourth-order MUSCL-TVD scheme to solve the leading order (shallow water) terms. For the dispersive terms, a cell averaged finite volume method is implemented. To verify the derived equations and the numerical model, four cases of verifications are given. First, solitary wave propagation is examined as a basic, yet fundamental, test of the models ability to predict dispersive and nonlinear wave propagation with minimal numerical error. Vertical velocity distributions of spatially uniform flows are compared with existing theory to investigate the effects of the newly included horizontal vorticity terms. Other test cases include comparisons with experiments that generate strong vorticity by the change of bottom bathymetry as well as by tidal jets through inlet structures. Very reasonable agreements are observed for the four cases, and the results provide some information as to the importance of dispersion and horizontal vorticity.

On Two Types of Localized Induction Equation

We are looking for motions of the strings and the filaments where they show stretch and/or shrink. For the motion of the extensible string interacting with the external field the string changes its shape by stretch not to valance the elastic force with the external force. We also considered the motion of the stretched thin vortex filament and found exact solutions of the stretched vortex filament. The thin vortex filament is one of the fundamental modes in the fluid and is described by the localized induction equation (LIE). In this short note we would like to discuss two types of LIE for the vortex filament with and without stretch from a standpoint of similarity and difference. For this purpose we review how to derive LIE. The equations of motion for the incompressible and rotational inviscid fluid are given by