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Showing papers on "Reynolds number published in 1977"


Journal ArticleDOI
TL;DR: In this article, the phase interface in a capillary and the spreading of viscous fluid drops on solid surfaces are solved, and the dependence of this angle on the velocity with allowance for capillary forces is determined.
Abstract: Fluid motion along a smooth, solid surface is examined when the free surface forms a final visible angle with the solid boundary. The dependence of this angle on the velocity with allowance for capillary forces is determined. The Reynolds number is small. The problem of the motion of the phase interface in a capillary and the spreading of viscous fluid drops on solid surfaces are solved. Experimental results are explained. Up to now, not only were analytical results lacking in this field, but also there was not even a precise formulation of the problem (see the review in [1]).

1,074 citations



Journal ArticleDOI
TL;DR: A series of experiments designed to reveal the properties of high Reynolds number vortex rings, using flow-visualization and laser-Doppler techniques, has uncovered several interesting and unexpected results as mentioned in this paper.
Abstract: A series of experiments designed to reveal the properties of high Reynolds number vortex rings, using flow-visualization and laser-Doppler techniques, has uncovered several interesting and unexpected results. Starting at the beginning of the motion, at a nozzle, and proceeding downstream, these include the following. A formation process that is strongly Reynolds number dependent.The amount of vorticity that appears downstream is very close to that predicted by a simple ‘slug’ model. However flow-visualization studies show that such a model is an oversimplification and that an excess of ring vorticity is probably cancelled by the ingestion of vorticity of opposite sign at the nozzle lip.(iii) A new, bimodal form of vortex-core instability has been observed at moderate but not high Reynolds numbers.Azimuthal inhomogeneities in the breaking of these, and the normal instability waves, create an ‘axial’ flow along the vortex core in the turbulent ring. This axial flow takes the form of a propagating wave that has many characteristics of a solitary wave. It is hypothesized that this axial flow prevents further ring instability.The long-term behaviour of the turbulent ring is marked by dramatic changes in its growth rate, which are probably related to changes in the ‘organization’ of the vortex core. The descriptive turbulent-ring model developed in Maxworthy (1974) is substantially confirmed by these experiments and by observation of ring propagation through a stratified ambient fluid.

373 citations


Journal ArticleDOI
TL;DR: In this article, the axisymmetric and spiral vortex breakdowns to imposed flow transients reported previously are confirmed, and are traced to the shedding of starting and stopping vortices from swirl vanes.
Abstract: Flow visualization studies and laser Doppler anemometer measurements on swirling water flows reveal six distinct types of very large amplitude disturbance modes of the vortex core. Three, ’’axisymmetric’’ and spiral vortex breakdowns, and the ’’double helix,’’ have been described by others. A definite order of evolution in parameter space (Reynolds number and circulations) occurs, and is described. Puzzling responses of the axisymmetric and spiral vortex breakdowns to imposed flow transients reported previously are confirmed here, and are traced to the shedding of starting and stopping vortices from swirl vanes. Conclusions bearing upon the validity of some theories of vortex breakdown are possible from the data.

368 citations


Journal ArticleDOI
TL;DR: In this article, the average characteristics of two important scales of motion in the outer region of turbulent boundary layers: large scale motions (average length 1.6δ) and typical eddy motion (average streamwise length approximately 200 ν/u τ).
Abstract: The technique of simultaneous hot‐wire anemometry and flow visualization has been used to determine the average characteristics of two important scales of motion in the outer region of turbulent boundary layers: large scale motions (average length 1.6δ), and ’’typical eddy’’ motions (average streamwise length approximately 200 ν/u τ). Results showed that the Reynolds number dependent ’’typical eddies’’ produced most of the Reynolds stress in the outer half of the layer at R ϑ≈1200, and that they are formed on the upstream side of large scale motions at all Reynolds numbers investigated. This phase relationship explains the scaling of the frequency of occurrence of outer layer bursts (which are identified with ’’typical eddies’’) on the free stream velocity and overall boundary layer thickness, although it is found that the lengths of the ’’typical eddies’’ scale on inner layer variables. In the log region, roughly one‐half of the large scale motions sampled had zone‐averaged streamwise velocity defects. Ensemble averaged results showed that they were associated with significant Reynolds stress contributions. A structural model showing the phase relationship of ’’typical eddies’’ and large scale motions is presented.

356 citations


DissertationDOI
01 Jan 1977
TL;DR: In this paper, the extent of mixing in two-dimensional free turbulent shear flows was measured using a concentration probe with a frequency response of 100 kHz and a spatial resolution of 0.1 mm.
Abstract: The extent of molecular mixing in several two-dimensional free turbulent shear flows was measured using a concentration probe with a frequency response of 100 kHz and a spatial resolution of 0.1 mm. The flows investigated were (i) a shear layer in which the gases on either side of the layer are of unequal density, (ii) a shear layer in which the gases on either side of the layer are of equal density, and (iii) a wake in which the gases on either side of the wake are of unequal densities. The extent of mixing was measured as a function of Reynolds number for the first case. It was found that at a critical Reynolds number the extent of molecular mixing sharply increased (25%). Power spectral density curves of the concentration time histories also indicated a marked increase in the high frequency fluctuations above this Reynolds number. A shadowgraph investigation of this phenomenon revealed that three-dimensional Taylor-type vortices whose axes of rotation are basically in the flow direction exist in the flow in addition to the two-dimensional large structures previously observed. These Taylor vortices were found to be unstable above the critical Reynolds number and were producing the increase in molecular mixing. The growth and development of the two-dimensional large structures were found to be basically unaffected by this instability. It is proposed that the fully developed turbulence of shear flows is maintained by a combination of the development of the large structures and of the coupling between the large structures and these unstable Taylor vortices. These data were also used to predict results for shear flows in which diffusion-limited chemical reactions have been incorporated.

318 citations


Journal ArticleDOI
TL;DR: In this article, the authors measured the dimensionless threshold stress and its dependence on grain protrusion and found that the threshold stress for grains resting on the top of an otherwise flat bed in a turbulent stream was measured and found to be 0.01 -considerably less than previously reported values of 0.03-0.06 for beds where all grains were at the same level.
Abstract: Shields (1936) found that the dimensionless shear stress necessary to move a cohesionless grain on a stream bed depended only on the grain Reynolds number. He ignored the degree of exposure of individual grains as a separate parameter. This report describes experiments to measure the dimensionless threshold stress and its dependence on grain protrusion, which was found to be very marked. The threshold stress for grains resting on the top of an otherwise flat bed in a turbulent stream was measured and found to be 0.01 –considerably less than previously-reported values of 0.03–0.06 for beds where all grains were at the same level. It is suggested that the new lower value be used in all turbulent flow situations where the bed is of natural sediments or unlevelled material. An hypothesis is proposed that the conventional Shields diagram implicitly contains variation with protrusion between the two extremes of (i) large grains and large Reynolds numbers, with small relative protrusion, and (ii) small grains, low Reynolds numbers, and protrusion of almost a complete grain diameter. In view of this, the extent of the dip in the Shields plot is explicable in that it represents a transition between two different standards of levelling as well as the transition between laminar and turbulent flow past the grains, the range of which it overlaps considerably.

286 citations


01 Jan 1977
TL;DR: The effects of dynamic stall on airfoils oscillating in pitch were investigated by experimentally determining the viscous and inviscid characteristics of the airflow on the NACA 0012 airfoil and on several leading-edge modifications as mentioned in this paper.
Abstract: The effects of dynamic stall on airfoils oscillating in pitch were investigated by experimentally determining the viscous and inviscid characteristics of the airflow on the NACA 0012 airfoil and on several leading-edge modifications. The test parameters included a wide range of frequencies, Reynolds numbers, and amplitudes-of-oscillation. Three distinct types of separation development were observed within the boundary layer, each leading to classical dynamic stall. The NACA 0012 airfoil is shown to stall by the mechanism of abrupt turbulent leading-edge separation. A detailed step-by-step analysis of the events leading to dynamic stall, and of the results of the stall process, is presented for each of these three types of stall. Techniques for flow analysis in the dynamic stall environment are discussed. A method is presented that reduces most of the oscillating airfoil normal force and pitching-moment data to a single curve, independent of frequency or Reynolds number.

281 citations


Journal ArticleDOI
TL;DR: In this paper, the authors used laser-Doppler anemometry to quantify the velocity field of water in a 90° bend of 40 x 40mm cross-section; the bend had a mean radius of 92mm and was located downstream of a 1[sdot ]8m and upstream of a 2m straight section.
Abstract: Calculated values of the three velocity components and measured values of the longitudinal component are reported for the flow of water in a 90° bend of 40 x 40mm cross-section; the bend had a mean radius of 92mm and was located downstream of a 1[sdot ]8m and upstream of a 1[sdot ]2m straight section. The experiments were carried out at a Reynolds number, based on the hydraulic diameter and bulk velocity, of 790 (corresponding to a Dean number of 368). Flow visualization was used to identify qualitatively the characteristics of the flow and laser-Doppler anemometry to quantify the velocity field. The results confirm and quantify that the location of maximum velocity moves from the centre of the duct towards the outer wall and, in the 90° plane, is located around 85% of the duct width from the inner wall. Secondary velocities up to 65% of the bulk longitudinal velocity were calculated and small regions of recirculation, close to the outer corners of the duct and in the upstream region, were also observed.The calculated results were obtained by solving the Navier–Stokes equations in cylindrical co-ordinates. They are shown to exhibit the same trends as the experiments and to be in reasonable quantitative agreement even though the number of node points used to discretize the flow for the finite-difference solution of the differential equations was limited by available computer time and storage. The region of recirculation observed experimentally is confirmed by the calculations. The magnitude of the various terms in the equations is examined to determine the extent to which the details of the flow can be represented by reduced forms of the Navier–Stokes equations. The implications of the use of so-called ‘partially parabolic’ equations and of potential- and rotational-flow analysis of an ideal fluid are quantified.

220 citations


Journal ArticleDOI
TL;DR: In this article, an exact solution of the Navier-Stokes equation for unsteady flow is a semi-infinite contracting or expanding circular pipe is calculated and reveals the following characteristics of this type of flow.
Abstract: Physiological pumps produce flows by alternate contraction and expansion of the vessel. When muscles start to squeeze its wall the valve at the upstream end is closed and that at the downstream end is opened, and the fluid is pumped out in the downstream direction. These systems can be modelled by a semi-infinite pipe with one end closed by a compliant membrane which prevents only axial motion of the fluid, leaving radial motion completely unrestricted. In the present paper an exact similar solution of the Navier–Stokes equation for unsteady flow is a semi-infinite contracting or expanding circular pipe is calculated and reveals the following characteristics of this type of flow. In a contracting pipe the effects of viscosity are limited to a thin boundary layer attached to the wall, which becomes thinner for higher Reynolds numbers. In an expanding pipe the flow adjacent to the wall is highly retarded and eventually reverses at Reynolds numbers above a critical value. The pressure gradient along the axis of pipe is favourable for a contracting wall, while it is adverse for an expanding wall in most cases. These solutions are valid down to the state of a completely collapsed pipe, since the nonlinearity is retained in full. The results of the present theory may be applied to the unsteady flow produced by a certain class of forced contractions and expansions of a valved vein or a thin bronchial tube.

204 citations


Journal ArticleDOI
P. Vasseur1, R. G. Cox1
TL;DR: In this article, singular perturbation techniques are used to calculate the migration velocity of a spherical particle sedimenting, at low Reynolds numbers, in a stagnant viscous fluid bounded by one or two infinite vertical plane walls.
Abstract: Singular perturbation techniques are used to calculate the migration velocity of a spherical particle sedimenting, at low Reynolds numbers, in a stagnant viscous fluid bounded by one or two infinite vertical plane walls. The method is then used to study the migration of a pair of spherical particles sedimenting either in unbounded fluid or in fluid bounded by a plane vertical wall. The migration phenomenon is studied experimentally by recording the trajectory of a spherical particle settling through a viscous fluid bounded by parallel vertical plane walls. Duct- to particle-diameter ratios in the range of 27 to 48 were used with the Reynolds number based on the particle radius being between 0·03 and 0·136.In all cases the particle is observed to migrate away from the walls until it reaches an equilibrium position at the axis of the duct. The experimentally determined migration velocities agree well with those predicted by the present theory.

Journal ArticleDOI
TL;DR: In this paper, a theoretical study indicates that vortex rings at moderate Reynolds numbers are unstable to azimuthal bending waves, and the stability analysis is developed for a certain class of bending waves that are unstable on a line filament in the presence of strain.
Abstract: A theoretical study indicating that vortex rings at moderate Reynolds numbers are unstable to azimuthal bending waves is presented. Only the case of a thin vortex ring with a core of constant vorticity in an inviscid flow is examined. The disturbance flow and the mean flow of the vortex ring are derived as asymptotic solutions near the core; the stability analysis is developed completely for a certain class of bending waves that are unstable on a line filament in the presence of strain. The vortex ring is found to be always unstable for at least two wavenumbers for which waves on a line filament of the same vorticity distribution would not rotate. Published experimental results are cited to support these conclusions.

Journal ArticleDOI
TL;DR: In this paper, the influence of surface roughness on the heat transfer of a circular cylinder to the cross-flow of air has been studied and the transition from a laminar to a turbulent boundary layer as a function of Reynolds number and roughness parameter was investigated.

Journal ArticleDOI
TL;DR: In this paper, high-frequency fluctuations in temperature and velocity were measured at a height of 2 m above a harvested, nearly level field of rye grass, where conditions were both stably and unstably stratified.
Abstract: High-frequency fluctuations in temperature and velocity were measured at a height of 2 m above a harvested, nearly level field of rye grass. Conditions were both stably and unstably stratified. Reynolds numbers ranged from 370000 to 740000. Measurements of velocity were made with a hot-wire anemometer and measurements of temperature with a platinum resistance element which had a diameter of 0[sdot ]5 μm and a length of 1 mm. Thirteen runs ranging in length from 78 to 238 s were analysed.Spectra of velocity fluctuations are consistent with previously reported universal forms. Spectra of temperature, however, exhibit an increase in slope with increasing wavenumber as the maximum in the one-dimensional dissipation spectrum is approached. The peak of the one-dimensional dissipation spectrum for temperature fluctuations occurs at a higher wavenumber than that of simultaneous spectra of the dissipation of velocity fluctuations. It is suggested that the change in slope of the temperature spectra and the dissimilarity between temperature and velocity spectra may be due to spatial dissimilarity in the dissipation of temperature and velocity fluctuations. The temperature spectra are compared with a theoretical prediction for fluids with large Prandtl number, due to Batchelor (1959). Even though air has a Prandtl number of 0[sdot ]7, the observations are in qualitative agreement with predictions of the theory. The non-dimensional wavenumber at which the increase in slope occurs is about 0[sdot ]02, in good agreement with observations in the ocean reported by Grant et al. (1968).For the two runs for which the stratification was stable, the normalized spectra of the temperature derivative fall on average slightly below the mean of the spectra of the remaining runs in the range in which the slope is approximately one-third. Hence the Reynolds number may not have always been sufficiently high to satisfy completely the conditions for an inertial subrange.Universal inertial-subrange constants were directly evaluated from one-dimensional dissipation spectra and found to be 0[sdot ]54 and 1[sdot ]00 for velocity and temperature, respectively. The constant for velocity is consistent with previously reported values, while the value for temperature differs from some of the previous direct estimates but is only 20% greater than the mean of the indirect estimates. This discrepancy may be explained by the neglect in the indirect estimates of the divergence terms in the conservation equation for the variance of temperature fluctuations. There is weak evidence that the one-dimensional constant, and hence the temperature spectra, may depend upon the turbulence Reynolds number, which varied from 1200 to 4300 in the observations reported.

Journal ArticleDOI
TL;DR: In this article, a simulation of 2D turbulence in a square region with periodic boundary conditions has been performed using a highly accurate approximation of the inviscid Navier-Stokes equations to which a modified viscosity has been added.

Journal ArticleDOI
TL;DR: In this paper, the stability of fully developed pressure driven plane laminar flow of a Maxwell fluid has been studied using linear hydrodynamic stability theory, and it was shown that the flow is stable to infinitesimal disturbances at low Reynolds numbers.
Abstract: The stability of fully developed pressure driven plane laminar flow of a Maxwell fluid has been studied using linear hydrodynamic stability theory. Elasticity is destabilizing in the inertial regime, but the flow is found to be stable to infinitesimal disturbances at low Reynolds numbers. This result contradicts previous calculations, which predicted a low Reynolds number flow instability at a critical recoverable shear of order unity. The previous calculations were carried out using less accurate numerical methods; the eigenvalue problem which must be solved is a delicate one, requiring sophisticated umerical techniques in order to avoid the calculation of spurious unstable modes. This work has direct bearing on the question of the mechanism of a low Reynolds number extrusion instability known as “melt fracture”. It is observed that the intensity of melt fracture increases with increasing die length for high density polyethylene, and it is therfore believed by some experimentalists that fully-developed die flow is unstable for this polymer above a critical recoverable shear. The analysis appears to be at variance with this interpretation of the experimental results.

Journal ArticleDOI
TL;DR: In this article, a grid turbulence was passed over a wall moving at the stream speed, and the field due to the wall constraint on the normal component of the velocity fluctuations was found to extend further into the flow than the influence of the viscous boundary condition on the tangential component fluctuations.
Abstract: Decaying grid turbulence was passed over a wall moving at the stream speed. For the high Reynolds number of the experiment, the field due to the wall constraint on the normal component of the velocity fluctuations is found to extend further into the flow than the influence of the viscous boundary condition on the tangential-component fluctuations. Measurements of the variances, length scales and spectra of the three velocity components of the turbulence are compared with the results of a previous experiment and with the theoretical predictions for an idealization of the flow. A simple model for some departures from the theory is proposed.

Journal ArticleDOI
TL;DR: An implicit finite difference technique employing orthogonal curvilinear co-ordinates is used to solve the Navier-Stokes equations for peristaltic flows in which both the wall-wave curvature and the Reynolds number are finite as discussed by the authors.
Abstract: An implicit finite-difference technique employing orthogonal curvilinear co-ordinates is used to solve the Navier–Stokes equations for peristaltic flows in which both the wall-wave curvature and the Reynolds number are finite (§2). The numerical solutions agree closely with experimental flow visualizations. The kinematic characteristics of both extensible and inextensible walls (§3) are found to have a distinct influence on the flow processes only near the wall. Without vorticity, peristaltic flow observed from a reference frame moving with the wave will be equivalent to steady potential flow through a stationary wavy channel of similar geometry (§4). Solutions for steady viscous flow (§5) are obtained from simulation of unsteady flow processes beginning from an initial condition of potential peristaltic flow. For nonlinear flows due to a single peristaltic wave of dilatation, the highest stresses and energy exchange rates (§6) occur along the wall and in two instantaneous stagnation regions in the bolus core. A series of computations for periodic wave trains reveals that increasing the Reynolds number from 2[sdot ]3 to 251 yields a modest augmentation in the ratio of flow rate to Reynolds number but induces a much greater increase in the shear stress (§7.1). The transport effectiveness is markedly reduced for pumping against a mild adverse pressure drop (§7.2). Increasing the wave amplitude will lead to the development of travelling vortices within the core region of the peristaltic flow (§7.3).

Journal ArticleDOI
TL;DR: The behaviour of human and frog red cells, platelets and rigid spheres were studied in the annular vortex formed in steady or pulsatile flow at the sudden concentric expansion of a 151 $\mu$ m into 504 $\mu $ m diameter glass tube.
Abstract: The behaviour of human and frog red cells, platelets and rigid spheres were studied in the annular vortex formed in steady or pulsatile flow at the sudden concentric expansion of a 151 $\mu$ m into 504 $\mu$ m diameter glass tube. During a single orbit the measured particle velocities and paths in steady flow were in good agreement with those calculated for the fluid, predicted by theory to circulate in closed orbits. Over longer periods, however, single blood cells and latex spheres $\mu$ m diameter migrated across the streamlines out of the vortex at a rate depending on the Reynolds number whereas spheres and aggregates of red cells > 30 $\mu$ m diameter remained in the vortex at all Reynolds numbers. Similar behaviour was noted in pulsatile flow when the vortex moved in phase with upstream fluid velocity and particles described spiral orbits of continually changing diameter. With red cell suspensions of 15-45% haematocrit in steady flow, migration of the corpuscles was also observed and resulted in the formation of a particle-free vortex. In pulsatile flow, cells were always present in the vortex, but their concentration which varied periodically was lower than that in the mainstream. The formation of aggregates of latex spheres and human platelets through collisions occurring in orbit, and their migration to the vortex centre was also observed.


Journal ArticleDOI
K. Kataoka1, H. Doi1, T. Komai1
TL;DR: In this paper, an experimental investigation was done by the use of electrochemical technique in order to obtain the interrelation between the axial movement of Taylor vortices and the periodically varying rates of heat/mass transfer on the internal surface of the outer cylinder.

Journal ArticleDOI
TL;DR: In this paper, a procedure for numerical solution of the Navier-Stokes equations for flow about arbitrarily shaped two-dimensional bodies is given, based on a technique of automatic numerical generation of a curvilinear coordinate system having a coordinate line coincident with the body contour regardless of its shape.

Journal ArticleDOI
TL;DR: In this article, the equations of motion for turbulent two-dimensional magnetohydrodynamic flows are solved in the presence of finite viscosity and resistivity, for the case in which external forces (mechanical and/or magnetic) act on the fluid.
Abstract: The equations of motion for turbulent two-dimensional magnetohydrodynamic flows are solved in the presence of finite viscosity and resistivity, for the case in which external forces (mechanical and/or magnetic) act on the fluid. The goal is to verify the existence of a magnetohydrodynamic dynamo effect which is represented mathematically by a substantial back-transfer of mean square vector potential to the longest allowed Fourier wavelengths. External forces consisting of a random part plus a fraction of the value at the previous time step are employed, after the manner of Lilly for the Navier-Stokes case. The regime explored is that for which the mechanical and magnetic Reynolds numbers are in the region of 100 to 1000. The conclusions are that mechanical forcing terms alone cannot lead to dynamo action, but that dynamo action can result from either magnetic forcing terms or from both mechanical and magnetic forcing terms simultaneously.

Journal ArticleDOI
TL;DR: In this article, the influence of diffuser geometries and flow inlet conditions on the critical flow angle for reverse flow was examined, and the results were presented in graphs.
Abstract: The authors’ preceding analysis on centrifugal vaneless diffusers is used to examine the influences of diffuser geometries and of flow inlet conditions on the critical flow angle for reverse flow, and the results are presented in graphs. The diffuser width to radius ratio, the inlet Mach number, and the distortion of the inlet velocity distribution have significant influences on the critical flow angle, while the Reynolds number and the boundary layer thickness at the inlet have minor influences.

Journal ArticleDOI
TL;DR: In this article, the effect of high elasticity in flow situations involving elastico-viscous liquids and abrupt changes in geometry is investigated, and the main conclusions from the work are that, in general terms, elasticity works against inertia, reducing the pressure drop caused by the abrupt change in geometry and reducing the area of influence of the bend (for finite Reynolds numbers).
Abstract: This is a theoretical paper which attempts to study for the first time the effect of high elasticity in flow situations involving elastico-viscous liquids and abrupt changes in geometry. It is argued that implicit rheological models are essential in this exercise and, accordingly, the numerical method of solution is forced to recognise the equations of continuity, the stress equations of motion and the rheological equations as separate equations involving velocity, pressure and stress variables with appropriate boundary conditions on these variables. The present paper is concerned with L-shaped and T-shaped geometries, and the effect of elasticity is assessed by comparing the numerical predictions for an elastic liquid with those for an inelastic liquid with the same “viscosity” behaviour. This comparison is facilitated by a simple limiting procedure outlined in Section 2. The main conclusions from the work are that, in general terms, elasticity works against inertia, reducing the pressure drop caused by the abrupt change in geometry and reducing the area of influence of the bend (for finite Reynolds numbers). So far as the stress fields are concerned most interest centres on the corner region, as one would expect, but there is also a region of normal-stress activity, which is generated by “stretching” rather than “shearing”. In an appendix, some consideration is given to the entry-length and exit-length problems. It is concluded that the overall problem is a complex one, since it depends to a large measure on the criterion one uses for “fully-developed” flow. If a fairly crude criterion is used, fluid elasticity is found to decrease the entry-length and increase the exit-length.

Journal ArticleDOI
TL;DR: In this paper, the problem of flow of a viscous fluid around a spherical drop at intermediate Reynolds numbers up to Re=200 for arbitrary values of the ratio of dynamic viscosities inside and outside the drop was examined.
Abstract: The problem of flow of a viscous fluid around a spherical drop has been examined for the limiting case of small and large Reynolds numbers in several investigations (see [1–3], for instance; there is a detailed review of various approximate solutions in [4]). For the intermediate range of Reynolds numbers (approximately 1≤Re≤100), where numerical integration of the complete Navier-Stokes equations is necessary, there are solutions of special cases of the problem —flow of air around a solid sphere [5–7], a gas bubble [8, 9], and water drops [10]. The present paper deals with flow around a spherical drop at intermediate Reynolds numbers up to Re=200 for arbitrary values of the ratio of dynamic viscosities Μ=Μ1/Μ2 inside and outside the drop. It is shown that a return flow can arise behind the drop in flow without separation. In such conditions the circulatory flow inside the drop breaks up. An approximate formula for the drag coefficient of the drop is given.

Journal ArticleDOI
TL;DR: In this paper, the flow in a square cavity is studied by solving the full Navier-Stokes and energy equations numerically, employing finite-difference techniques, and solutions are obtained over a wide range of Reynolds numbers from 0 to 50000.
Abstract: The flow in a square cavity is studied by solving the full Navier–Stokes and energy equations numerically, employing finite-difference techniques. Solutions are obtained over a wide range of Reynolds numbers from 0 to 50000. The solutions show that only at very high Reynolds numbers (Re [gt-or-equal, slanted] 30000) does the flow in the cavity completely correspond to that assumed by Batchelor's model for separated flows. The flow and thermal fields at such high Reynolds numbers clearly exhibit a boundary-layer character. For the first time, it is demonstrated that the downstream secondary eddy grows and decays in a manner similar to the upstream one. The upstream and downstream secondary eddies remain completely viscous throughout the range of Reynolds numbers of their existence. It is suggested that the behaviour of the secondary eddies may be characteristic of internal separated flows.

Journal ArticleDOI
TL;DR: In this paper, a numerical study has been made of a two-dimensional model of the motion which takes place in storage tanks used for solar water heating applications and the effect of the entrance Reynolds number and the contribution of buoyancy in promoting stratification have been examined.

Journal ArticleDOI
TL;DR: In this paper, the authors presented numerical solutions for the behavior of particles in the flow through a 90° bend in a pipe of circular cross-section, the radius of the bend being from 4 to 20 times that of the pipe.

Journal ArticleDOI
TL;DR: An axisymmetric numerical model has been developed to simulate Ward's (1972) laboratory experiments as mentioned in this paper, and it is shown that the core radius is independent of the Reynolds number at high Reynolds number.
Abstract: An axisymmetric numerical model has been developed to simulate Ward's (1972) laboratory experiments. It was shown by Davies-Jones (1976) that this experiment is more geophysically relevant than all previous experiments in that Ward's experiment exhibits both dynamical and geometrical similarity to actual tornadoes. Major results are 1) the core size versus inflow angle relationship agrees very nearly with Ward's measurements, 2) the numerical and laboratory surface pressure patterns are in agreement, and 3) it is demonstrated that the core radius is independent of the Reynolds number at high Reynolds number (Ward's data also exhibit this behavior). Based on this axisymmetric model some speculation concerning the nature of the asymmetric multiple vortex phenomenon is made. Furthermore, the numerical model allows the examination of the interior flow field. As a consequence, an explanation is offered in Section 6 for the double-walled structure sometimes observed in natural vortices. The experiments...