Showing papers on "Streamlines, streaklines, and pathlines published in 1984"

Turbulent flow over large-amplitude wavy surfaces

Abstract: The laser-Doppler velocimeter is used to measure the mean and the fluctuating velocity for turbulent flow over a solid sinusoidal wave surface having a wavelength λ of 50.8 mm and a wave amplitude of 5.08 mm. For this flow, a large separated region exists, extending from x/λ = 0.14 to 0.69. From the mean velocity measurements, the time-averaged streamlines and therefore the extent of the separated region are calculated. Three flow elements are identified: the separated region, an attached boundary layer, and a free shear layer formed by the detachment of the boundary layer from the wave surface. The characteristics of these flow elements are discussed in terms of the properties of the mean and fluctuating velocity fields.

The boundary layer induced by a convected two-dimensional vortex

Abstract: The response of a wall boundary layer to the motion of a convected vortex is investigated. The principal cases considered are for a rectilinear filament of strength –κ located a distance a above a plane wall and convected to the right in a uniform flow of speed U∞*. The inviscid solution predicts that such a vortex will remain at constant height a above the wall and be convected with constant speed αU∞*. Here α is termed the fractional convection rate of the vortex, and cases in the parameter range 0 [les ] α < 1 are considered. The motion is initiated at time t* = 0 and numerical calculations of the developing boundary-layer flow are carried out for α = 0, 0.2, 0.4, 0.55, 0.7, 0.75 and 0.8. For α < 0.75, a rapid lift-up of the boundary-layer streamlines and strong boundary-layer growth occurs in the region behind the vortex; in addition an unusual separation phenomenon is observed for α [les ] 0.55. For α [ges ] 0.75, the boundary-layer development is more gradual, but ultimately substantial localized boundary-layer growth also occurs. In all cases, it is argued that a strong inviscid–viscous interaction will take place in the form of an eruption of the boundary-layer flow. The generalization of these results to two-dimensional vortices with cores of finite dimension is discussed.

Three-Dimensional Streamlines in Dupuit-Forchheimer Models

Abstract: An approximate method is presented for determining streamlines in three dimensions using two-dimensional Dupuit-Forchheimer models. The latter models of horizontal flow, which may comprise several aquifers, are based on the assumption that the resistance to flow in the vertical direction is neglected. This assumption does not preclude the occurrence of flow in the vertical direction; vertical components of flow are determined in an approximate fashion by requiring continuity of flow. The problem of leakage from a shallow pond above an unconfined aquifer is discussed as an example of determining streamlines in three dimensions. The errors induced by the approximation are determined for a few idealized flow problems that can be solved exactly.

A numerical investigation of magnetic field generation in a flow with chaotic streamlines

Abstract: High resolution numerical simulations extending those of Arnold and Korkina (1983) reveal the existence of at least two windows for kinematic dynamo action in a spatially periodic flow with chaotic streamlines. These occur at moderate magnetic Reynolds number R (8–18) and at high R (27 to 200 or more).

A Lagrangian Porous Media Mass Transport Model

Abstract: The mathematical simulation of advective dispersive contaminant transport in groundwater involving large Peclet numbers is subject to numerical difficulties. For most numerical models the computational cost and computer core requirements escalate as the Peclet number increases. A two-dimensional Galerkin finite element model for flow and Lagrangian mass transport in porous media has been developed to alleviate numerical and computational difficulties. The solution methodology involves a linear triangular mesh which tracks along streamlines calculated from a flow equation having the stream function as the dependent variable. A comparison of this model to Eulerian or fixed coordinate type models showed this model to be accurate and stable at a reduced computational effort. For an actual field contamination problem which contains large vertical concentration gradients, the simulated results compared with observed data.

Numerical analysis of the flow through a corrugated tube with application to arterial prostheses

Abstract: Steady and oscillating axisymmetric laminar flows are determined by a finite-difference solution of the vorticity and continuity equations for an incompressible fluid contained in a straight concertina-shaped tube far from its ends. In steady flow the size of the wall corrugations is varied as well as the Reynolds number of the flow. In unsteady flow one tube geometry is studied, and the parameters varied are the Reynolds number, the ratio of the mean volume flow rate to its amplitude, and the frequency of oscillation. The analysis produces streamlines, particle paths and the pressure difference across a length of the tube. The resistance to the flow is determined in terms of an equivalent cylindrical tube diameter.In steady flow the onset of flow separation and the growth of the separated region of flow is determined. The equivalent diameter is found to be principally a function of the product of Reynolds number and the non-dimensional pressure difference. This product depends on the height of the wall corrugations and less strongly on Reynolds number and the length of the corrugations. Resistance increases with increasing height of the corrugations. Comparison is made with other computational and experimental values of the pressure difference.In unsteady flow the mean velocity to amplitude ratio has little effect except on the particle paths. The flow pattern is found to be governed by the Stokes number (radius × (2π/(kinematic viscosity × period))½) and the Reynolds number. There is a region of quasi-steady flow at the time of zero acceleration at maximum flow, but unsteady flow in between. The mixing produced by radial convection is restricted to the outer parts of the tube where the wall is corrugated. In oscillating flow the resistance relative to a cylindrical tube decreases as frequency and Reynolds number increase.In the medical application of the work the concern is whether sustained stagnant regions occur in the corrugations and whether there is a large change in resistance relative to a cylindrical tube. This part of the investigation was made with an arterial waveform which contained six harmonics. It is found that there are no regions of stagnant fluid in the range of parameters considered. The difference between the variation with the flow parameters of the resistance of the corrugated tube and of a cylindrical tube was found not to be large.

Terraced channels for reducing afterbody drag

Abstract: A fluid flow control for reducing the drag associated with an upswept afterbody includes a pair of ridges forming substantially symmetric flow channels arranged in an approximately helical fashion on either side of the afterbody so as to intersect at approximately the centerline of the undersurface. Each ridge has a generally rearward pitch so that the flow channels form a substantially V-shaped configuration rearwardly. The flow channels cross the local fluid flow streamlines at an optimum angle for producing a strong vortex core along the channel length with the vortex rotating in a direction counter to that normally found in the wake of conventional upswept afterbodies.

Vortex-generating coolant-flow-passage design for increased film-cooling effectiveness and surface coverage

Abstract: The thermal film-cooling footprints observed by infrared imagery for three coolant-passage configurations embedded in adiabatic-test plates are discussed. The configurations included a standard round-hole cross section and two orientations of a vortex-generating flow passage. Both orientations showed up to factors of four increases in both film-cooling effectiveness and surface coverage over that obtained with the round coolant passage. The crossflow data covered a range of tunnel velocities from 15.5 to 45 m/sec with blowing rates from 0.20 to 2.05. A photographic streakline flow visualization technique supported the concept of the counterrotating apability of the flow passage design and gave visual credence to its role in inhibiting flow separation.

Solution of the three-dimensional Navier-Stokes equations for a steady laminar horseshoe vortex flow

Abstract: : A low Mach number formulation of the three-dimensional Navier-Stokes equations is solved for a steady laminar horseshoe vortex flow, using a time-iterative approach. A split linearized block implicit algorithm is used, with central spatial differences in a transformed coordinate system. The stability of this algorithm in three dimensions is examined for a scalar convection model problem, and results are obtained which suggest that the algorithm is both conditionally stable and rapidly convergent when nonperiodic inflow/outflow boundary conditions are used. A new form of artificial dissipation which acts along physical streamlines instead of coordinate grid lines is also tested and found to introduce less error when the local flow direction is not aligned with the computational grid. An accurate solution for a laminar horseshoe vortex flow is computed using an improved solution algorithm with small artificial dissipation. This solution does not change significantly when the mesh spacing is halved using (15 x 15 x 15) and (29 x 29 x 29) grids. Very good convergence rates were obtained, such that residuals were reduced by a factor of 1/100 in 30 and 60 iterations respectively, for 3,375 and 24,389 grid points. (Author).

Effect of curvature on three-dimensional boundary layer stability

Abstract: The problem of the stability of a three-dimensional laminar boundary layer formed on a curved surface is considered. A calculation scheme, which takes account of the curvature of the flow streamlines and of the surface is proposed for the prediction of the development of small amplitude temporal disturbances. Computations have been performed for the flow over the windward face of an infinitely long yawed cylinder and comparisons have been made with experimental data. These indicate that the theory correctly predicts many of the features of the unstable laminar flow. The theory also suggests that transition, in this particular situation, is dominated by traveling disturbance waves and that, at the experimentally observed transition location, the wave which has undergone greatest total amplification has an amplitude ratio of approximately e to the 11th. When the effects of curvature are omitted the maximum amplitude ratio at transition is about e to the 17th.

On the classification of some model equations for viscoelasticity

Abstract: We classify and derive a canonical form for a linearization of the upper convected Maxwell model for steady viscoelastic fluid flow. We show that there are always two families of characteristic curves which follow the streamlines and across which the solution may be discontinuous. If the product of the Weissenberg number and the Reynolds number is greater than one, then two additional families of characteristic curves exist.

A note on the instantaneous streamlines, pathlines and pressure contours for a cavitation bubble near a boundary

Abstract: Instantaneous streamlines, particle pathlines and pressure contours for a cavitation bubble in the vicinity of a free surface and near a rigid boundary are obtained. During the collapse phase of a bubble near a free surface, the streamlines show the existence of a stagnation point between the bubble and the free surface which occurs at a different location from the point of maximum pressure. This phenomenon exists when the initial distance of the bubble is sufficiently close to the free surface for the bubble and free surface to move in opposite directions during collapse of the bubble. Pressure calculations during the collapse of a cavitation bubble near a rigid boundary show that the maximum pressure is substantially larger than the equivalent Rayleigh bubble of the same volume.

On the numerical simulation of two-dimensional time-dependent flows of oldroyd fluids part 1: basic method and preliminary results

Abstract: An investigation is carried out into numerical techniques to be used to solve time-dependent flow of Oldroyd liquids. A finite-difference method is derived which is stable for low elasticity but which must be modified by stress and vorticity smoothing in order to obtain solutions at higher values of elasticity. The Two-dimensional flow past a circular cylinder is used as a test problem. It is found that, at low elasticity, although the early development of the flow is quite different from the equivalent Newtonian situation, these differences diminish as time goes on and one is left with streamlines which differ only very slightly from the Newtonian flow field. As elasticity is increased, however, the initial departure from Newtonian streamlines persists and one sees develop areas of recirculating fluid near to the cylinder surface. The effective radius of the cylinder is thus increased and a much larger area of fluid is disturbed by the presence of the cylinder. These predictions are compared with available experimental evidence.

Boundary effects on a submerged jet group

Abstract: A vortex model is employed to calculate the flow induced by a line group of submerged high velocity shallow water jets discharging in proximity to a shoreline boundary. Based on an inviscid flow model, a kinematic and dynamic boundary condition are formulated along the unknown lines of velocity discontinuity downstream of the multiple jets. This results in two governing nonlinear integral equations in terms of the unknown circulation strength along the unknown slip streamlines. The numerically computed two dimensional momentum-induced flow shows that, as the jet group is placed closer to the boundary, the contraction of the slipstream becomes stronger, resulting in a decrease of the induced flow. All of the features predicted by the theory are in good agreement with experimental results of this and previous investigations.

Numerical studies of stratified air flow over a mountain ridge on the rotating earth

Abstract: The non-linear equations describing adiabatic, quasi-static flow of stably stratified air over a mountain ridge on the rotating f- plane are integrated numerically in time, using potential temperature as vertical coordinate. The initial state is a horizontal, parallel flow over level ground, and the cosine-shaped, 400 km wide ridge, oriented normal to the initial flow, is allowed to grow to full height in 20 h. The potential vorticity remains constant in each isentropic surface, and this condition is used in the calculations instead of the mass continuity equation. Results of calculations starting with 4 different initial wind profiles are shown. After about 5 model days of integration, the motion within the integration area of length 4 Mm settled down to a nearly steady flow. This flow exhibits a system of gravity-inertia lee waves with dominating wavelengths comparable to the mountain width. The prominent wavelengths seem in all calculations to be limited to waves shorter than the inertia wavelength at the lower boundary (for which the particle frequency equals the Coriolis parameter). The waves are discussed in the light of linear theory and ray tracing. In a case where the initial wind velocity decreases with height, there is a clear tendency towards formation of pure horizontal, undamped inertia waves in the layer of wind shear, with cycloid-shaped horizontal trajectories. Besides the wave pattern, the stationary flow also shows a large-scale turning of the streamlines, to the left on the upstream side and to the right on the lee side, with a distinct anticyclonic bend over the mountain ridge. The formation of this turning is explained as a consequence of the loss of mass through the open boundaries connected with the growth of the mountain; thus the turning depends on the formulation of the inflow and outflow boundary conditions. Unless the large-scale turning is strictly symmetric with respect to the mountain ridge, the flow will possess a component along the ridge, with a corresponding geostrophic pressure gradient which together with the wave drag will contribute to the total horizontal force acting on the mountain. DOI: 10.1111/j.1600-0870.1984.tb00237.x

A Mathematical Model of Condensation Heat and Mass Transfer to a Moving Droplet in its Own Vapor

Abstract: A mathematical model appropriate for predicting condensation heat and mass transfer rates along the surface of a droplet moving in pure vapor is developed. A Karman-Pohlhansen type of integral approach was adopted for the solution of vapor-phase boundary layer equations. The diffusion-dominated internal core was solved using a finite difference numerical scheme. The rate-controlling mechanism of pure vapor condensing on a droplet was found in the thermal core region of the liquid phase where the streamlines correspond to the isotherms and diffusion is the primary transport mechanism. The total rate of heat transfer is found to be inversely proportional to the droplet radius. The condensation velocity at the vapor-liquid interface reduces the boundary layer thickness and moves the separation point toward the rear stagnation point. The internal motion also helps increase the transport rates by reducing both the boundary layer thickness and thermal resistance in the liquid phase. The results predicted by this model compare favorably with available experimental values.

Prticle Deposition by Diffusion and Interception from Boundary Layer Flows

Abstract: An expression for the interception efficiency is derived for particles in boundary layer flows over single spheres and cylinders. The analysis is carried out by determining the point of closest approach of a streamline to the collector surface. Particles with radii smaller than this distance on outlying streamlines will not be collected. The interception efficiency is the ratio of the volumetric flow within this streamline to the total flow swept out by the collector. Deposition by interception can be considered a limiting case of the diffusion of particles of finite diameter. Using a well-known transformation, the interception efficiency can be combined with theoretically based correlations for convective diffusion to permit estimation of deposition efficiencies over the whole range in which both diffusion and interception are important.

Three-dimensional laser Doppler anemometer measurements of a jet in a crossflow

Abstract: A three-dimensional laser Doppler anemometer (3D-LDA) was used in a wind tunnel to measure a jet in a crossflow. Measurements were made in the vicinity of a 5-cm-diam jet which issued normally into a 10.65 m/sec wind tunnel crossflow; the velocity ratio Vjet/Vinf was 8. Detailed lateral surveys were made at two elevations (z = cm and 2 cm); both elevations were within the region affected by the boundary layer on the plate. The results are believed to provide reliable velocity field information in the boundary layer of the jet in a crossflow. Turbulence information also is available and believed to be roughly correct, although it may be subject to broadening effects for the lower values of turbulence. A weak vortex pair was observed in the wake at the plate surface. This structure existed in the boundary layer and built confidence because the 3D-LDA was, indeed, able to resolve fine detail in the wake. The capabilities of the 3D-LDA not only allow the making of the velocity surveys, but can be utilized to follow mean streamlines in the flow.

A constant-vorticity riabouchinsky free-streamline flow

Abstract: The well-known Riabouchinsky body-free-streamline-image model is modified by replacing the stagnant fluid cavity by a region of constant-vorticity inviscid flow in which the streamlines form closed curves. Numerical solutions for the model are obtained for a class of flows with prescribed symmetries and given body shape. The possibility of similar extensions of general free-streamline flows is discussed briefly.

On the geometry of magnetohydrodynamic flows

Abstract: In this paper it is shown that the motion of magnetofluid is circulation preserving if the magnetic field is in a direction of no variation. Employing the anholonomic geometric results it is proved that for the circulation preserving and complex lamellar motion of magnetofluids, the Lamb surfaces are developables if and only if the magnitude of the vorticity is constant along the streamlines.

A two-dimensional analysis of laser heat addition in converging nozzles

Abstract: The two-dimensional equations of motion describing the interaction between a laser beam and a flowing gas are considered. An implicit numerical scheme is used to solve these equations for unchoked flow through a converging-diverging nozzle. Separate grids are used for the fluid dynamics and the radiation equations. The effects of beam focusing and cross-beam intensity profiles are included. The calculations are based upon real gas properties for all quantities except the gas absorptivity, which is taken as a constant. The solutions contain the expected hot central core region with cool gas near the walls. This results in steep temperature gradients in both the streamwise and cross-stream directions. The absorption zone acts as a blockage in the nozzle causing a nonuniform velocity profile at the inlet and an overall decrease in mass flow. The absorption region also forces the streamlines to move away from the axis of symmetry, although this effect is not strong.

Secondary Flow Induced between Oscillating Circular Cylinders

Abstract: The two-dimensional flow between oscillating circular cylinders is theoretically analyzed. The outer cylinder performs rotatory oscillations and the inner cylinder performs translational oscillations with small amplitude. Particular attention is focused upon a steady secondary streaming owing to the nonlinear hydrodynamic effect. The analytical expression for the secondary streaming is obtained. Streamlines of the secondary streaming are shown for a couple of values of radii of two oscillating circular cylinders. The behavior of the steady secondary streaming induced between two cylinders is clarified.

The characteristics of fluid flow in beds of small glass particles spouted with water

Abstract: The characteristics of beds of small glass particles 0.28, 0.46 and 0.77mm in diameter spouted with water were studied in a half-cylindrical column 51mm in diameter with inlet tube diameter of 3.2mm. The minimum spouting velocity, bed pressure drop at minimum spouting and spout diameter were measured. Assuming Darcy flow, the fluid flow in the annulus is modeled and shown to represent the streamlines quite well. The residence time of the fluid in the annulus is calcuated from the model and compared with experimental data.

A Three-Dimensional Potential Flow Model for the Prediction of the Behavior of Radioactive Plumes

Abstract: A potential flow model was developed to predict wind fields in complex terrain. In this model, wind vectors and airflows are estimated from a velocity potential function. It was found that the velocity potential function is obtained by combining threedimensional doublets at each grid point on a horizontal plane and a uniform stream parallel to the surface of the earth. The strengths of the doublets were expressed as a function of the terrain height at each grid point. Wind components at an arbitrary point were easily calculated from the potential flow model proposed. Consequently, this potential flow model is useful in estimating airflows, the convergence and divergence of the distances between streamlines, and the trajectories of radioactive plumes.

Convection in a horizontal annular porous layer with non-linear density effects

Abstract: This paper presents a theoretical study of heat transfer and flow by natural convection in an annular layer of porous material saturated with cold water and subjected to different thermal boundary conditions. The governing equations are solved, within the Boussinesq and Darcy approximations, using an implicit finite difference method. The results obtained for streamlines and isotherms, velocity and temperature profiles, and local and global Nusselt numbers are analysed in terms of R, the radius of the cavity, [Rcirc]a, a nonlinear Rayleigh number, and γ, an inversion parameter, relating the temperature for maximum density to the wall temperature. It is found that the essential effect of density inversion is to create multicellular flows and to reduce the fluid velocities as well as the convective heat transfer. The problem of a common fluid without density inversion is recovered as a special case of this study

Plane Hydrodynamic flows with steady vorticity: a reduction theorem

Abstract: Besides steady plane flows and unsteady plane flows of constant and steady vorticity, there are only two simple types of plane hydrodynamic flows with steady vorticity. These two types of unsteady flows have steady streamlines that are parallel straight lines or concentric circles.

Effects of concentration and characteristic distributions on electromagnetic separation of polydisperse mixtures

Abstract: The effect of concentration of particulates on electromagnetic and gravitational forces applied to polydisperse mixtures is considered. It is shown that hydrodynamic properties, density, and susceptibility differences, and hence the related forces, are concentration dependent. Examples of particle trajectories flowing across a magnetized wire illustrate the role of concentration as regards flow patterns and capture probabilities. Higher concentration is associated with increased hindrance to deflection of particulates towards the wire, i.e., particles tend to follow streamlines of the fluid. Flow of polydisperse mixtures is dependent not only on concentration but also on particle size, density, and susceptibility distributions. In this context the relevant equations, related to constant and variable force field, are derived and their physical significance discussed.