Numerical solution of laminar flow generated in an annulus by rotating screens

Summary The governing equation and the appropriate boundary condition describing stationary laminar flow in a curved channel and in an annulus with one (upper) and two (upper and lower) rotating screens, were solved numerically by finite-difference method. In the curved channel multiple solutions were obtained in accordance with the predictions of previous theoretical and experimental investigations. In contrast to that, no multiple solutions were found for the flow in an annulus, neither with two nor with one rotating screen. The numerically computed axial velocity distributions in annulus were compared to the corresponding experimental profiles measured in a turbulent flow of a homogeneous fluid created in annulus by one or two rotating screens. The qualitative agreement between the results was unexpectedly good.     

Laminar flow in an annulus between two concentric rotating porous spheres

Summary An analysis is presented for the steady laminar flow of an incompressible Newtonian fluid in an annulus between two concentric porous spheres with injection/suction at their boundaries. The inner sphere rotates with constant angular velocity about its own fixed axis, while the outer sphere is stationary. A solution of the Navier-Stokes equations is obtained by employing a regular perturbation technique. The solution obtained is in the form of a power series expansion in terms of the rotational Reynolds number Re, and an injection/suction Reynolds number Re _w , and is valid for small values of these parameters. Results for the velocity distributions, streamlines, and viscous torques for various values of the flow parameters Re, Re _w , and radius ratios are presented. Viscous torques at the inner and outer spheres are compared with those obtained from the numerical solution of the Navier-Stokes equations, in order to find the range of Re and Re _w for which this solution is accurate.     

Turbulent flow and heat transfer in a rotating slit-shaped channel

A two-parameter turbulence model is used to numerically study flow and heat transfer in a channel rotating about its transverse axis.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, No. 5, pp. 720–726, May, 1985.     

Turbulent flow in an intake-manifold

Three-dimensional, turbulent fluid flow analysis with computational methods has emerged as a viable tool in the design process of engine components for passenger cars. If applied in the early stages of the component development such analysis can help reduce the product development time drastically, and may support the design engineer to evaluate several competing design aspects before product completion. However the grid generation for complex geometries still poses a difficult and time consuming taks which strongly influences the accuracy of the numerical solution. The present paper studies the numerical solution of the flow in an inlet-manifold of a five-cylinder engine with two intake-ports for each cylinder. A fast and reliable grid generation technique is discussed in detail. The finite volume based Navier-Stokes solver with schemes of first and second order accuracy for the convective terms is used. Numerical results at several mass flow rates and different boundary conditions at the intake ports are compared with measurements. Finally, the computational results are discussed with respect to their applicability to support the design process of an inlet-manifold.     

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.     

Turbulent flow in a boundary layer on the inlet and outlet sides of a rotating channel

Expressions are obtained for approximately determining the shear stresses on the outlet and inlet sides of a rotating channel on the basis of a turbulence energy balance equation, A. N. Kolmogorov's hypothesis, and the Monin-Obukhov similitude theory.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 6, pp. 977–986, December, 1981.     

Onset of vorticity in a rotating annulus of helium II

We present measurements of the critical angular velocity for the onset of vorticity in a rotating annulus. The measurements of the critical velocity were made over a temperature range from 1.5 to 2.165 K, and are consistently lower than theoretical predictions by about 20%. Nor do our results agree within experimental uncertainty with previous measurements of the critical velocity in an annulus. It appears that the discrepancies can be explained by the presence and growth of high concentrations of residual vorticity which prevent the system from achieving the lowest free energy state. We find that vorticity perpendicular to the axis of rotation grows as the angular velocity is increased and that the axial mutual friction coefficientB″ is 0.     

Turbulent flow in a cylindrical channel

The distribution function for turbulent frictional stress is proposed for flow in a cylindrical channel. Formulas are obtained for the calculation of the velocity distribution according to the well-known law of hydraulic drag of the channel.     

Vortex breakdown generated by off-axis bifurcation in a cylinder with rotating covers

Summary Vortex breakdown of bubble type is studied for the flow in a cylinder with rotating top and bottom covers. For large ratios of the angular velocities of the covers, we observe numerically that the vortex breakdown bubble in the steady regime may occur through the creation of an off-axis vortex ring. This scenario does not occur in existing bifurcation theory based on a simple degeneracy in the flow field. We extend the theory to cover a non-simple degeneracy, and derive the associated bifurcation diagrams. We show that the vortex breakdown scenario involving a vortex ring can be explained from this theory, and that the numerically generated bifurcation diagrams are consistent with the theory.     

Hydromagnetic couette flow of an Oldroyd-B fluid in a rotating system

The motion of electrically conducting, Oldroyd-B and incompressible fluid between two infinitely extended non-conducting parallel plates under a uniform transverse magnetic field, fixed relative to the fluid has been considered. The lower plate is at rest and the upper plate is oscillating in its own plane. The governing partial differential equation of this problem, subject to boundary conditions are solved analytically. The expressions for the steady and unsteady velocity fields for the conducting Oldroyd-B fluid are obtained. The graphs are plotted for different values of dimensionless parameters of the problem and the analysis of the results showed that the flow field is appreciably influenced by the applied magnetic field, the rotation and the material parameters of the fluid.     

Turbulent flow in a cylindrical circular-recess channel

Modeling of a turbulent flow in a cylindrical solid propellant charge channel having a circular recess (compensator) has been performed. Different variants of the compensator position and connection to the channel are discussed. The influence of the geometric and consumption factors on the formation of distributions of the gas-dynamic parameters and characteristics of turbulence in the working region has been investigated. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 6, pp. 116–121, November–December, 2007.     

Source-sink flow in a rotating cylinder

Summary This paper describes the axisymmetric source-sink flow in a rapidly rotating cylinder. Relative fluid motion is induced by the presence of a sink in the bottom corner and a ring source located somewhere in the fluid, at some distance from the solid boundaries. In order to neglect nonlinear effects the volumetric flow rates are assumed to be small, i.e. O(E ^1/2), with E the Ekman number of the flow. The transport from the source to the sink is carried by Ekman layers at the end caps, and a Stewartson layer at the sidewall. At the ring source a free Stewartson layer arises, in which the injected fluid is transported towards the Ekman layers. This Stewartson layer consists of layers of thicknesses E ^1/4 and E ^1/3, which both contribute to the vertical O(E ^1/2) transport. The ring source is enveloped by a ring-shaped region of cross-sectional dimensions O(E ^1/2 × E ^1/2), in which the injected fluid is rearranged before erupting into the E ^1/3 layer. As E ^1/2 E ^1/3, this region appears as an isolated singularity in the E ^1/3 layer; in fact it consists of a combination of an upward and a downward directed source, the strengths of which can be determined by transport arguments. The paper presents an analysis of the E ^1/3-layer structure on the basis of a linear theory; it also describes how the analysis can be extended to the situation in which fluid is injected through an array of sources at different heights.     

Turbulent flow of a fibrous suspension in a pipe

The Henky-Ilyushin equations are used to describe the steady turbulent flow of an incompressible viscoplastic fluid in a pipe. A fibrous suspension is examined as the fluid.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 58, No. 2, pp. 223–229, February, 1990.     

Spectral properties of the nonspherically decaying radiation generated by a rotating superluminal source

The focusing of the radiation generated by a polarization current with a superluminally rotating distribution pattern is of a higher order in the plane of rotation than in other directions. Consequently, our previously published [J. Opt. Soc. Am. A24, 2443 (2007)] asymptotic approximation to the value of this field outside the equatorial plane breaks down as the line of sight approaches a direction normal to the rotation axis, i.e., is nonuniform with respect to the polar angle. Here we employ an alternative asymptotic expansion to show that, though having a rate of decay with frequency (mu) that is by a factor of order mu(2/3) slower, the equatorial radiation field has the same dependence on distance as the nonspherically decaying component of the generated field in other directions: It, too, diminishes as the inverse square root of the distance from its source. We also briefly discuss the relevance of these results to the giant pulses received from pulsars: The focused, nonspherically decaying pulses that arise from a superluminal polarization current in a highly magnetized plasma have a power-law spectrum (i.e., a flux density S infinity mu(alpha)) whose index (alpha) is given by one of the values -2/3, -2, -8/3, or -4.     

Morphology of the nonspherically decaying radiation beam generated by a rotating superluminal source

We consider the nonspherically decaying radiation field that is generated by a polarization current with a superluminally rotating distribution pattern in vacuum, a field that decays with the distance R(P) from its source as R(P)(-1/2), instead of R(P)(-1). It is shown (i) that the nonspherical decay of this emission remains in force at all distances from its source independently of the frequency of the radiation, (ii) that the part of the source that makes the main contribution toward the value of the nonspherically decaying field has a filamentary structure whose radial and azimuthal widths become narrower (as R(P)(-2) and R(P)(-3), respectively) the farther the observer is from the source, (iii) that the loci on which the waves emanating from this filament interfere constructively delineate a radiation subbeam that is nondiffracting in the polar direction, (iv) that the cross-sectional area of each nondiffracting subbeam increases as R(P), instead of R(P)(2), so that the requirements of conservation of energy are met by the nonspherically decaying radiation automatically, and (v) that the overall radiation beam within which the field decays nonspherically consists, in general, of the incoherent superposition of such coherent nondiffracting subbeams. These findings are related to the recent construction and use of superluminal sources in the laboratory and numerical models of the emission from them. We also briefly discuss the relevance of these results to the giant pulses received from pulsars.     

On compressible flow in a rotating cylinder

Summary Axisymmetric steady flow of a perfect gas in a rotating cylinder is studied by applying a linearised analysis to a small perturbation about isothermal rigid body rotation. Motivated by present day gas centrifuges, special attention is focussed on the effect of a length-to-radius ratio which increases from unit magnitude to infinity and on the effect of a strong radial density gradient associated with the isothermal rigid body rotation. The Ekman number E _*based on the small radial density scale and the density at the cylinder wall is taken to be small. It appears that the flow outside Ekman boundary layers at the end caps consists of three types. These correspond to 1 L _* E _* ^{% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS% qaaSqaaiaaigdaaeaacaaIYaaaaaaa!386D!\[ - \tfrac{1}{2}\]} E _* ^{% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS% qaaSqaaiaaigdaaeaacaaIYaaaaaaa!386D!\[ - \tfrac{1}{2}\]} L _*, E _* ^–1 andE _* ^–1 L _* where L _*is the ratio of the cylinder-length to the radial density scale. For 1 L _* E _* ^{% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS% qaaSqaaiaaigdaaeaacaaIYaaaaaaa!386D!\[ - \tfrac{1}{2}\]} an inviscid flow in a region of limited thickness near the cylinder wall is found. Due to the strong decrease of the density, radial diffusion is not confined to Stewartson boundary layers at the wall (typical for incompressible flow) but extends in the core. This finds expression in two layers in the centre of the cylinder, parallel to the rotation axis, having a structure similar to both Stewartson layers and adjusting the inviscid flow near the wall to a flow dominated by radial diffusion near the rotation axis. For L _* E _* ^{% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS% qaaSqaaiaaigdaaeaacaaIYaaaaaaa!386D!\[ - \tfrac{1}{2}\]} and L _* E _* ^–1 both Stewartson layers become successively of the same thickness as the density scale. At the same time the corresponding layers in the core go to the wall and join. As a result, for L _* E _* ^–1 radial diffusive processes are significant in the entire cylinder, a situation also known from studies of flows in semi-infinite gas centrifuges.     

Three dimensional flow field due to a vortex and source line spanning an annulus

A theoretical investigation of the three dimensional potential flow field due to a vortex and source line spanning an annulus is carried out in this paper. The three dimensional effects due to finite radius hub and annulus walls are found to be appreciable, especially for a low hub/tip ratio configuration. The discrepancy between the two and three dimensional solutions are found to be large near the hub, moderate at the tip and negligibly small at the mid radius.     

The turbulent nonisothermal flow of an incompressible gas in a circular rotating pipe

The nonisothermal, fully developed turbulent flow of an incompressible gas in a circular rotating cylindrical pipe is discussed. Equations are given for one-point second moments of velocity and temperature pulsations. The results of calculating the thermal characteristics are given.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 18, No. 1, pp. 96–104, January, 1970.     

Fluctuating flow induced by periodic suction through a rotating disk

Summary This paper is concerned with the time-harmonic and time-mean flow induced by a normal periodic suction through a disk rotating in contact with an incompressible viscous fluid. Two separate analytical-numerical solutions are developed for the extreme cases of low and high frequency oscillations, employing the Fettis-Benton method. General formulae for the skin-friction components and the far-field suction velocity are obtained. The deduced quasi-steady results are in agreement with the available numerical results.

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Die durch periodisches Saugen durch eine rotierende Scheibe erzeugte schwankende Strömung

Zusammenfassung Die vorliegende Arbeit behandelt die zeitlich harmonische und die zeitlich gemittelte Strömung, verursacht durch eine periodische Saugwirkung normal durch eine Scheibe, die in einer inkompressiblen zähen Flüssigkeit rotiert. Zwei getrennte analytisch-numerische Lösungen werden mit Hilfe der Fettis-Benton-Methode für die beiden Sonderfälle niedriger bzw. hoher Oszillationsfrequenz hergeleitet. Allgemeine Beziehungen ergeben sich für die Komponenten der Oberflächenreibungskraft und die Sauggeschwindigkeit. Die Ergebnisse für den stationären Fall sind in Übereinstimmung mit numerisch gewonnenen Resultaten.

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On leave from Indian Institute of Technology Kharagpur India