Second Type Of Flow Research Articles

Dispersion relations for periodic water waves with surface tension and discontinuous vorticity

We derive the dispersion relation for water waves with surface tension and having a piecewise constant vorticity distribution. More precisely, we consider here two scenarios; the first one is that of a flow with constant non-zero vorticity adjacent to the flat bed while above this layer of vorticity we assume the flow to be irrotational. The second type of flow has a layer of non-vanishing vorticity adjacent to the free surface and is irrotational below.

The dynamics of intrusions into a density-stratified crossflow

Buoyant fluid from a steady source (such as a volcanic eruption) in a stratified environment (such as the atmosphere) rises to an equilibrium level where it spreads as a homogenous intrusion. Here the dynamics of such an intrusion in the presence of a mean ambient flow are examined with semi-analytical models. The intrusive flow is irrotational, and is governed by mass conservation and a form of the Bernoulli equation that relates the intrusion velocity and its thickness. Two types of source are considered—one in which the initial flow from the source is radially symmetric, which is appropriate for weak crosswinds, and another in which it is unidirectional, which also applies to strong crosswinds. In the absence of wind, the outward flow from the radial source is radially uniform and supercritical in the hydraulic sense, with decreasing thickness and increasing speed with distance from the source. In the presence of a crosswind, however, unless the crosswind is very strong a stagnation point exists on the upstream side of the radial source, where the intrusion thickness reaches a maximum. There are two types of flow solution: those where the flow is wholly subcritical, and others where the flow is “transcritical,” being subcritical on the upstream side of the source, and supercritical on the downstream side. It is these transcritical solutions with a supercritical spreading tail that are relevant to flows from isolated sources. For these flows, the upstream stagnation point is quite close to the source, and its position is remarkably insensitive to the strength of the crossflow, relative to that of the source. As a consequence, the position of this stagnation point gives a direct measure of the strength of the source. The external flow is mostly directed horizontally around the intrusion, much as if the latter were a rigid obstacle. The behaviour of the flow in the far-field tail of the intrusion is analysed for both the inviscid case, and for the more realistic one in which the intrusive flow is affected by the drag of its motion relative to that of the environment. The second type of flow, from the unidirectional source, has the same asymptotic behaviour, but the near-field flow changes with increasing distance, from one with maximum thickness on the centerline to one with minimum thickness there. Apart from the fluid dynamical aspects, the results have potential significance for interpretation of geological sediments.

Searching for the fastest dynamo: Laminar ABC flows

The growth rate of the dynamo instability as a function of the magnetic Reynolds number R(M) is investigated by means of numerical simulations for the family of the Arnold-Beltrami-Childress (ABC) flows and for two different forcing scales. For the ABC flows that are driven at the largest available length scale, it is found that, as the magnetic Reynolds number is increased: (a) The flow that results first in a dynamo is the 2 1/2-dimensional flow for which A=B and C=0 (and all permutations). (b) The second type of flow that results in a dynamo is the one for which A=B≃2C/5 (and permutations). (c) The most symmetric flow, A=B=C, is the third type of flow that results in a dynamo. (d) As R(M) is increased, the A=B=C flow stops being a dynamo and transitions from a local maximum to a third-order saddle point. (e) At larger R(M), the A=B=C flow reestablishes itself as a dynamo but remains a saddle point. (f) At the largest examined R(M), the growth rate of the 2 1/2-dimensional flows starts to decay, the A=B=C flow comes close to a local maximum again, and the flow A=B≃2C/5 (and permutations) results in the fastest dynamo with growth rate γ≃0.12 at the largest examined R(M). For the ABC flows that are driven at the second largest available length scale, it is found that (a) the 2 1/2-dimensional flows A=B,C=0 (and permutations) are again the first flows that result in a dynamo with a decreased onset. (b) The most symmetric flow, A=B=C, is the second type of flow that results in a dynamo. It is, and it remains, a local maximum. (c) At larger R(M), the flow A=B≃2C/5 (and permutations) appears as the third type of flow that results in a dynamo. As R(M) is increased, it becomes the flow with the largest growth rate. The growth rates appear to have some correlation with the Lyapunov exponents, but constructive refolding of the field lines appears equally important in determining the fastest dynamo flow.

Simulations numériques d’écoulements diphasiques gaz-liquide par la méthode de volume fini dans des géométries confines

In this paper we present results of volume-of-fluid method based direct numerical simulations of two types of gas-liquid flow in confined geometries. The first flow under consideration is the co-current upward flow of a regular train of gas bubbles within silicon oil in a square vertical mini-channel. Particular attention is given to the influence of the length of the flow unit cell and on the relation between bubble diameter and capillary number. The second type of flow under investigation is that of a swarm of eight bubbles within a narrow plane vertical channel. The numerical data are used to evaluate the budget of the turbulence kinetic energy equation for the liquid phase and to test common closure assumptions for the interfacial term appearing in this equation.

Dust formation and inhomogeneous mass-loss from asymptotic giant branch stars

ABSTRA C T We examine the flow from asymptotic giant branch (AGB) stars when along a small solid angle the optical depth resulting from dust is very large. We consider two types of flows. In the first, small cool spots are formed on the surface of slowly rotating AGB stars. Large quantities of dust are expected to be formed above the surface of these cool spots. We propose that if the dust formation occurs during the last AGB phase when the mass-loss rate is high, the dust shields the region above it from the stellar radiation. This leads to both further dust formation in the shaded region and, owing to lower temperature and pressure, the convergence of the stream toward the shaded region, and the formation of a flow having a higher density than its surroundings. This density contrast can be as high as ,4. A concentration of magnetic cool spots toward the equator will lead to a density contrast of up to a few between the equatorial and polar directions. This process can explain the positive correlation between high mass-loss rate and a larger departure from sphericity in progenitors of elliptical planetary nebulae. In the second type of flow, the high density in the equatorial plane is formed by a binary interaction, where the secondary star is close to, but outside the AGB envelope. The shielding of the radiation by dust results in a very slow and dense flow in the equatorial plane. We suggest this flow as an alternative explanation for the equatorial dense matter found at several hundred astronomical units around several post-AGB binary

Radial inflow within two flat disks

Introduction T HE characteristics of flows confined in narrow gaps formed by two flat circular plates are of interest in industry. Disk-type devices have been widely used in many practical applications.' Two basic nonswirling types of flow can be produced inside the gap: one is developed by supplying the fluid through a centrally located inlet port, and the other is realized by admitting the flow radially through the circumference. For the former case, the streamlines diverge and the gradual decrease of the local Reynolds number based on the gap height gives rise to the interesting phenomenon of relaminarization. In the latter case, the streamlines converge, resulting in a drastic pressure drop similar to that produced in a converging nozzle. The present work focuses on the second type of flow. Previous theoretical studies have concentrated on solutions to the integral equations of motion.~ Lee and Lin attempted a differential solution of the linearized momentum equation to obtain the radial pressure distribution. Their method of treating the equation led them to an expression for pressure that was amenable only to a numerical treatment. Nonetheless, the results obtained have shown a good agreement with the experiment of Ref. 6. In a recent paper, the author, convinced also that only a numerical result for the linearized momentum equation was possible, simplified further the inertial terms. With the additional simplification, he was able to obtain a closed-form solution for the pressure which agreed closely with the numerical results of Ref. 7. In the present Note, closed-form solutions of the linearized momentum equations of Lee and Lin are presented. The inviscid and creeping-flow solutions are shown to be the asymptotes of the general problem. The results have been found to confirm the observation. Analysis and Discussion Consider the nonswirling, steady laminar flow between the disks shown in Fig. 1. Under the assumption that the flow is purely radial, the equations of motion, in nondimensional form, are Continuity:

Observations of rapidly flowing granular-fluid materials

The rapid shearing of a mixture of cohesionless glass spheres and air or water was studied in an annular, parallel-plate shear cell designed after Savage (1978). Two types of flow were observed. In the first type of flow the entire mass of the granular material was mobilized. At high shear rates the shear and normal stresses were found to be quadratically dependent upon the mean shear rate (at constant volume concentration), in general agreement with the observations of Bagnold (1954) and Savage & Sayed (1984), and the ‘kinetic’ theory of Jenkins & Savage (1983). The stresses were found to be weakly dependent on the volume concentration up to approximately 0.5, and strongly dependent above this concentration. For flows in which water was the interstitial fluid, the ratio of the shear stress to the normal stress was slightly higher (than in air), and the stresses at lower shear rates were found to be more nearly linearly related to the shear rate. It is suggested that these effects are contributed to by the viscous dampening of grain motions by the water. The second type of flow was distinguished by the existence of an internal boundary above which the granular material deformed rapidly, but below which the granular material remained rigidly locked in place. The thickness of the shearing layer was measured to be between 5 and 15 grain diameters. The stress ratio at the bottom of the shearing layer was found to be nearly constant, suggesting the internal boundary is a consequence of the immersed weight of the shearing grains, and may be described by a Coulomb yield criterion. A scaled concentration is proposed to compare similar data obtained using different-sized materials or different apparatus. An intercomparison of the two types of flow studied, along with a comparison between the present experiments and those of Bagnold (1954) and Savage & Sayed (1984), suggests that the nature of the boundaries can have a significant effect upon the dynamics of the entire flow.

Flow, mixing and combustion within the quarl of a Swirled, pulverised-coal burner

Measurements are presented of the flow pattern and mixing within the quarl of a 1/9th-scaleair model of a brown coal burner. For flow conditions within the range used in operating burners, two flow types were observed: one, previously reported, where the primary (coal-laden) flow is deflected gradually around a central, swirl-induced, reverse-flow zone; the other, where the primary flow partially penetrates the reverse-flow zone before being deflected rapidly in the radial direction. The combustion behaviour of the coal in each type of flow is predicted by a computationalmodel, and the results compared with limited measurements on an industrial burner. The second type of flow is shown to mix the coal-laden primary flow with the internal reverse flow before mixing with the secondary air flow, resulting in a higher evolution of volatiles and the ignition of a greater proportion of the char mass. The temperature field within the quarl is shown to be dominated by the temperature of the reverse flow.

Internal separated flows at large Reynolds number

Large-Reynolds-number analysis is given for separated flows that have the characteristic feature of being confined in the transverse direction. Two principal limits of the governing equation are obtained depending on whether the streamwise length scale is of order one or of the order of the Reynolds number. The corresponding two types of separated flows are discussed. A method of calculation is given for the second type of flow. It employs an expansion in the eigenfunctions of the Poiseuille flow development and the problem is reduced to solving nonlinear first-order ordinary differential equations that have a tendency to decouple rapidly. The method is tested by a detailed comparison of the results of the present calculation with finite-difference solutions of the Navier-Stokes equations for a channel with sudden expansion. Applicability to other configurations is illustrated by solving the problem of the flow in a channel with a base

Oil Flow, Key Factor in Sleeve-Bearing Performance

Abstract The determination and understanding of the performance characteristics of cylindrical sleeve bearings is based upon three relationships. These are (a) the viscosity-temperature characteristic of the lubricant; (b) the bearing power consumption as a function of oil-film temperature; and (c) the oil flow through the bearing as a function of Sommerfeld number. The first two are well known, and this paper is concerned primarily with the nature and quantitative determination of oil flow, together with the simplified methods for the calculation of bearing performance made possible thereby. The discussion is restricted to those bearings having oil fed under pressure to their oil-distribution grooves. Oil flows from the ends of these bearings because of the pressure in the oil grooves and because of the pressures generated in the load-carrying portion of the oil film. The second type of flow is dependent upon shaft speed. Dimensionless parameters controlling both types of flow have been calculated, and experimental results on several bearing sizes confirm the theory. A detailed study of the circumferential flow of oil in the bearing shows that Petroff’s law is an excellent approximation of power loss up to an eccentricity of 0.7, and that the temperature variation in the oil film may be estimated with simple assumptions. Knowledge of bearing oil-flow characteristics permits the ready calculation of bearing performance by means of the “operating-line method.”