Linear stability of non-Newtonian annular liquid sheets

Summary This paper reports a linear stability analysis of a non-Newtonian annular liquid sheet that is surrounded by nonviscous fluids in relative axial motion to it. It is shown that for a stress free basic flow the dispersion relation giving the absolute and convective instability mechanisms can be immediately obtained from the dispersion relation for a Newtonian sheet by introducing a wavenumber dependent viscosity. The stability behavior of the sheet is investigated numerically by a continuation algorithm, by which the solution branches of the dispersion relation, relevant for the stability information, can be traced. The results give a stability picture which covers the whole range of annular sheets from the cylindrical jet to the plane liquid curtain.     

Response of axially excited spherical and conical liquid systems with anchored edges

The response of a spherical annular liquid cone to axial excitation has been determined for a non-viscous liquid. The analytical results are then applied to a semi-spherical system with the apex-angle of .     

Vibrations of an infinitely long flowing liquid jet—Influence of spin and axial flow

For an infinitely long liquid column the influence of axial flow velocity and spin has been investigated. The results are exhibited for axisymmetric mode m=0 and asymmetric modes m=1 and 2. A frictionless liquid shows with the increase of axial flow an increase of the frequency in flow direction and a decrease of the oscillation frequency in the opposite flow direction for axisymmetric motion. It also means that a larger surface tension, larger diameter or larger density of the liquid column exhibit the same behavior. For asymmetric motions the effect of axial velocity w₀ is the opposite. With increasing axial wave length the natural frequencies decrease. At certain axial speed magnitudes both waves move in flow direction with different magnitude. The effect of increasing spin is a decrease of natural frequencies and an instability for smaller axial wave lengths. Viscous effects show usually smaller oscillation frequencies.     

Turbulent helium II flow through different narrow channels

Turbulent helium II flow is investigated in an annular gap of about 10 µm width and in superfilters with a pore size 0.1 µm. Of primary interest is the flow behavior at high mass flow rates. In the cases of both an annular gap and superfilters, deviations from the low-flow-rate behavior are found, which can be attributed to different reasons. Both systems with their separately determined characteristics are then combined in a parallel arrangement in order to study the flow in a channel system with nonuniform dimensions, as is realized, e.g., in a porous plug. The parallel system permits checks of different hypotheses on the flow behavior. The results show that certain simplistic ideas about the internal geometry of a porous plug are inadequate for the hydrodynamic treatment.     

The stability of the narrow-gap Taylor-Couette system with an axial flow

Summary The stability of viscous flow between concentric rotating cylinders with an axial flow due to an axial pressure gradient is considered. The governing equations with respect to three-dimensional disturbances are derived and solved by a direct numerical procedure. Results are given for the case of small-gap approximation. Three typical cases =–1,0 and 0.5 are studied, where represents the ratio of angular velocity of the outer cylinder to that of the inner cylinder. The value of the axial Reynolds numberR is up to 100. It is found that the critical disturbance is a non-axisymmetric mode when the value ofR is sufficiently large, and the transition of the onset mode withR is demonstrated in detail. Results for the critical Taylor number, wave number, vortex incline angle, and relative wave velocity are also determined. The present stability analysis is found to be in agreement with previous experimental studies and particularly reveals the stability characteristics with the variation of .     

Effectiveness of mixing coaxial flows swirled in opposite directions

The mixing of coaxial turbulent flows swirled in opposite directions is experimentally studied. The effectiveness of this mixing is compared with mixing after an agitating grid.Notation z, r, cylindrical coordinate system - r₁, r₂ inside and outside radius of annular channel - H=r₂–r₁ radial gap in annular channel - y=(r–r₁)/H dimensionless radial coordinate - V(v_z, v_r, v) mean velocity vector - v, v_z pulsative components of velocity in the direction of the mean velocity vector and in the axial direction - P_*, P total and static pressure - , loss coefficients Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 407–413, September, 1981.     

Heat Transfer from a Surface with Spherical Hollows in Boiling of Water and a Steam‐Water Mixture in the Supercritical Region

The authors carried out an experimental investigation of heat transfer in the supercritical zone in flow of water and a steamwater mixture in a vertical annular channel. The interior wall heated by the current was either smooth or with hollows stamped in a straightline order. The application of them increased the heattransfer coefficient by a factor of 1.5–2 and more. The increase in the frictional resistance was much smaller.     

Peristaltic flow of a non-newtonian viscoplastic liquid in a slot channel

The narrow-band asymptotic method [5] has been used to consider the peristaltic flow of a viscoplastic medium in a slot channel. It is found that the mode of flow differs substantially from that in a channel with rigid walls when the axial pressure gradient is small.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 31, No. 3, pp. 499–505, September, 1976.     

The flow and heat transfer between a torsionally oscillating and a stationary disk

Summary The flow between a torsionally oscillating and a stationary disk is considered. The solution in the form of a power series in , the ratio of the amplitude of oscillations to the frequency, is obtained on the assumption that1. The steady streaming motion is shown to be of the order of magnitude . The behaviour of steady radial and axial velocities is clarified. The shearing stress on either disk is also calculated.The problem of heat transfer in this flow field is considered next. The time-averaged Nusselt numbers are calculated up to the third-order approximation in the -expansion. The effect of the steady streaming flow upon the time-averaged heat-transfer rate is discussed.     

Heat Transfer in a Packed Bed at Moderate Values of the Reynolds Number

Results are given of an experimental investigation of the coefficient of wall heat transfer of a round tube filled with a packed medium formed by monodisperse glass spheres of different diameters (d _p = 0.9, 3.2, 8.9 mm) in a stabilized region of heat transfer under conditions of filtering of water and aqueous solution of glycerin. A two-layer model of heat transfer is used to calculate the contribution made by the heat resistance of the flow core and of the wall zone using the measured coefficients of heat transfer and temperature profiles across the packed bed. The form of dependence for the effective coefficient of thermal conductivity is determined. Data are given of the measurement of the coefficient of wall heat transfer of annular channel filled both with a single layer of spheres with packing of two types (cubic and rhombohedral) and with several layers of spheres with random packing in a stabilized region of heat transfer under conditions of filtering of water. It is demonstrated that, in the case of inertial mode of filtering of liquid through the packed bed, the values of the Nusselt number both in the tube and in the annular channel correspond to the relation Nu _e (d _e/D)Pe^1/2 _e . A semi-empirical correlation is suggested, which generalizes well our experimental data (and the data of other authors) on heat transfer in the tube and in the annular channel. A theoretical model is suggested, according to which the variation of heat transfer is defined by the behavior of the effective coefficient of thermal conductivity _ef/ _f Pe^1/2 _d associated with the predominant contribution made to convective heat transfer by the transport processes in vortex cells with closed lines of flow.     

Modeling of vortex structures on the lateral surface of a cylinder in a longitudinal flow

The problem of generation of vortex structures by ejection of a jet through an annular slot on a cylindrical surface in a longitudinal flow is considered. Results of modeling of large-scale vortices and their effect on local characteristics of the wall boundary layer are presented. The modeling is based on numerical integration of the Navier-Stokes equations in an axisymmetric formulation. An unsteady-state flow with separation and entrainment of vortices by the main stream is obtained. The decrease in the friction drag achievable in devices of this kind is estimated.Academic Scientific Complex A. V. Luikov Heat and Mass Transfer Institute, Academy of Sciences of Belarus, Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 5, pp. 527–533, May, 1994.     

Static Josephson effects in circularly symmetric annular junctions

Static Josephson effects in circularly symmetric annular junctions are discussed. When the annular width W of a junction is smaller than _J, analytic solutions can be obtained. For annular width W of a junction larger than _J, the self-field effects must be considered; the solutions can be obtained numerically. For these two cases, called "small junction" and "large junction," respectively, the magnetic field dependence of the critical current I _m of a circularly symmetric annular junction is obtained. Further, for a width W larger than _J, the current density distribution is also given for several magnetic fields. In addition, for a given external magnetic field, when the feeding current I is smaller than the critical current I _m of the circular symmetric annular junction, there are multisolutions under such physical conditions. Finally, the stability of these solutions is also discussed.     

Numerical study of disk driven rotating MHD flow of a liquid metal in a cylindrical enclosure

Summary A numerical study of the steady laminar MHD flow driven by a rotating disk at the top of a cylinder filled with a liquid metal is presented. The governing equations in cylindrical coordinates are solved by a finite volume method. The effect of an axial magnetic field on the flow is investigated for an aspect ratioH/R equal to 1. The magnetic Reynolds number is assumed to be small whereas the interaction parameter,N, is large compared to unity. This allows to derive asymptotic results for the flow solution which are found in good agreement with the numerical calculations. The effect of the top, botton and vertical walls conductivity on the flow is studied. Various combinations of these conductivities are considered. The results obtained showed that one can control the primary flow through a good choice of the electrical conductivity of both the disk and cylinder walls.Notation B Magnetic field - H Height of the cylinder - Ha Hartmann number - jz Axial electric current - N Interaction parameter - P Dimensionless pressure - R Radius of the cylinder - Re Reynolds number - R _m Magnetic Reynolds number - r Dimensionless radius - V _r Dimensionless radial velocity - V _z Dimensionless axial velocity - V Dimensionless azimuthal velocity - Z Dimensionless height Greek symbols Density of the fluid - v Kinematic viscosity - Dynamic viscosity - Electrical conductivity - Angular velocity - Dimensionless electric potential - Thickness of the Ekman layer - Laplacian operator - r Increment of the grid in the radial direction - Z Increment of the grid in the axial direction     

Problem of Heat Transfer with Allowance for Axial Heat Conduction for the Flow of a Liquid in Tubes and Channels

The author presents a computational method for problems of heat transfer in channels with simple and complex twodimensional profiles of the cross sections for the flow of liquid metals where axial heat conduction is taken into account. A comparison with solutions of the heattransfer equation without the term that takes into account the conduction along the flowing liquid is given.     

Study of flow on the surface of fins on cross-finned tubes

The visualization method was used to study the washing of a flow of air over the surface of fins on tubes with external fins in an annular arrangement.Notation S₁ transverse spacing of tubes in bundle - S₂ lengthwise spacing of tubes in bundle - d diameter of tube bearing the fins - h fin height - t fin spacing - fin thickness - finning coefficient - Re Reynolds number calculated from the velocity of the incoming flow U and the diameter d - x_os size of the separation zone A on the OX axis - heat-transfer coefficient Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 28–34, July, 1984.     

Numerical Simulations of Thermocapillary Flow of a Binary Mixture with the Soret Effect in a Shallow Annular Pool

In order to understand the characteristics of thermocapillary flow of a toluene/n-hexane mixture with the Soret effect in a shallow annular pool, a series of three-dimensional numerical simulations were carried out. The shallow annular pool was heated from the outer cylinder and cooled at the inner cylinder. The initial toluene concentration in the toluene/n-hexane mixture varied from 0 to 0.4467. Results indicate that the flow undergoes two transitions from the axisymmetric steady flow to the hydrothermal waves, and then to chaos with the increase of the thermocapillary Reynolds number. The critical thermocapillary Reynolds number for the incipience of the oscillatory flow decreases with the increase of the initial solute concentration. When the thermocapillary flow transits to a three-dimensional oscillatory flow, a concentration fluctuation is observed on the free surface, which is similar to the hydrothermal waves. However, compared with that of the temperature, the dimensionless fluctuation amplitude of the concentration is relatively weak. Furthermore, the fundamental oscillation frequency increases linearly with the initial solute concentration, but the wave number of the hydrothermal waves is almost unchangeable.     

Three-Dimensional Numerical Simulation of Pure Solutocapillary Flow in a Shallow Annular Pool for Mixture Fluid with High Schmidt Number

In order to understand the characteristics of pure solutocapillary flow in a shallow annular pool subjected to a constant radial solutal gradient, a series of three-dimensional numerical simulations were performed. The annular pool was filled with the toluene/n-hexane mixture fluid with the Schmidt number of 142.8. The inner and outer cylinders were respectively maintained at low and high solutal concentrations. Aspect ratio of the annular pool is fixed at ε = 0.15 or 0.05. Results indicate that the solutocapillary flow is steady and axisymmetric at a small solutal capillary Reynolds number. The surface fluid flows radially from the inner cylinder toward the outer cylinder and a return flow exists near the bottom. With the increase of the solutal capillary Reynolds number, an axisymmetric oscillatory flow firstly appears and then becomes a three-dimensional oscillatory flow at ε = 0.15. Whereas at ε = 0.05 a direct transition from the steady and axisymmetric flow to the three-dimensional oscillatory flow is observed. Three types of the flow instabilities are the standing wave, hydrosolutal wave and source/sink type wave instabilities. Furthermore, the physical mechanism of the flow destabilization is analyzed.     

Asymptotic analysis of the flow of shear-thinning foodstuffs in annular scraped heat exchangers

The problem of isothermal flow of a shear-thinning (pseudoplastic) fluid in the gap between two concentric cylinders is considered. A pump provides an axial pressure gradient which causes flow down the device. The outer cylinder is fixed and has scrapers attached to it to cause flow mixing, whilst the inner cylinder rotates about its axis to provide shear and thus thin the fluid. The goal is to determine the optimal distribution of power between rotation and pumping. Although ostensibly the flow is nonlinear and three-dimensional we show that judicious use of fairly straightforward asymptotic methods can yield a great deal of information about the device, including cross-sectional flow predictions and throughput results. Furthermore, these results are derived for a variety of different flow conditions. Some numerical calculations are carried out using a commercial CFD code. These show good agreement with the asymptotic analysis.     

Natural convection in an annulus between two rotating vertical cylinders

Summary A numerical study is conducted to understand the effect of rotation on the axisymmetric flow driven by buoyancy in an annular cavity formed by two concentric vertical cylinders which rotate about their axis with different angular velocities. The inner and outer side walls are maintained isothermally at temperature _c and _h , respectively, while the horizontal top and bottom walls are adiabatic. The vorticity-stream function form of the Navier-Stokes equations and the energy equation have been solved by modified Alternating Direction Implicit method and Successive Line Over Relaxation method. Numerical results are obtained for a wide range of the Grashof number, Gr, nondimensional rotational speeds _i , _o of inner and outer cylinders and for different values of the Prandtl number Pr. The effects of the aspect ratio,A, on the heat transfer and flow patterns are obtained forA=1 and 2. The numerical results show that when the outer cylinder alone is rotating and the Grashof number is moderate, the outward bound flow is confined to a thin region along the bottom surface while the return flow covers a major portion of the cavity. For a given inner or outer cylinder rotation the temperature field is almost independent of the flow in the annulus for fluids with low Prandtl number, while it depends strongly for high Prandtl number fluids. At a high Grashof number, with moderate rotational speeds, the dominant flow in the annulus is driven by thermal convection, and hence an increase in the heat transfer rate occurs. In the case of unit aspect ratio, the flow pattern is unicellular for the rotation of the cylinders in the same direction, and when they rotate in the opposite direction two or more counter rotating cells separated by a stagnation surface are formed. The rate of heat transfer at the hot cylinder is suppressed when its speed of rotation is higher than that of the cooler cylinder. The computed heat transfer and flow patterns are compared with the available results of a nonrotating cylindrical annulus, and good agreement is found.