Showing papers on "Streamlines, streaklines, and pathlines published in 1978"

An experimental map of the internal structure of a vortex breakdown

Abstract: The flow field of an 'axisymmetric' vortex breakdown has been mapped using a laser-Doppler anemometer. The interior of the recirculation zone is dominated by energetic, non-axisymmetric, low frequency periodic fluctuations. Spectra for a number of points inside this zone, as well as time-averaged swirl and axial velocity profiles both inside and outside the recirculation zone, have been obtained. The time-averaged streamlines in the interior show an unexpected two-celled structure attributed to the action of the fluctuations. Although the present experiment deals with one particular breakdown, flow-visualization studies indicate that the case examined is typical of the 'axisymmetric' form of breakdown over a range of flow conditions.

The plane turbulent impinging jet

Abstract: This paper presents an experimental study of the turbulent structure on the centre-line of a two-dimensional impinging jet. The mean velocity, turbulent stresses, triple velocity products and temporal derivatives were measured and the energy balances for the three fluctuating components were calculated. The results indicate a selective stretching of vortices in the direction in which the streamlines spread near the wall, causing anisotropy in this region. The distribution of energy among various frequencies was found from spectral measurements. These measurements revealed the existence of a neutral frequency above which the energy was attenuated by viscous dissipation and below which it was augmented by a vortex-stretching mechanism.

Dynamic stall of an oscillating airfoil

Abstract: Unsteady separated boundary layers and wakes were studied by investigating flow past an oscillating airfoil which in part models the retreating blade stall on the helicopters. The Navier-Stokes equations in terms of the vorticity and stream function for laminar flow were solved to determine the flow field around a modified NACA 0012 airfoil. After a fully developed flow was determined at zero incidence, the airfoil was oscillated in pitch through an angle of attack range from 0 deg to 20 deg. The computed streamlines during this pitch-up motion are in qualitative agreement with the trajectories of air bubbles observed in water tunnel experiments conducted with a NACA 0012 airfoil under the same conditions. During the pitch-down motion of the airfoil, the computed flow patterns cannot be compared with the experiments because the trajectories of air bubbles intersect.

Particle Trajectories in Swirling Flows

Abstract: The ability to utilize fuels which form participate matter upon combustion (e.g., coal) in a gas turbine depends in part upon an understanding of the nature of particle trajectories in swirling flows. Although a number of investigators have studied specific flows or developed specific computational methods for particle trajectories in swirling flows, none have obtained solutions which are general in nature. In this paper a series of exact general solutions for trajectories of spherical particles in free-vortex swirling flow have been obtained in the absence of aerodynamic lift phenomena. As would be expected from related works, it has been found that for low particle Reynolds numbers (Stokes flow) the degree to which a particle either follows the flow streamlines or is centrifuged out across them is essentially described by a single dimensionless parameter, the Stokes number. For higher particle Reynolds numbers the results can be presented in terms of two relevant parameters, one of which may be the Stokes number. Furthermore, even in this latter case the results indicate that the Stokes number is the dominant parameter. Based on these results a number of conclusions have been drawn on the nature of particle trajectories in turbine airfoil passages, and in centrifugal separators.

A theoretical study of the effects of wall conductivity, non-uniform magnetic fields and variable-area ducts on liquid-metal flows at high Hartmann number

Abstract: Flows of incompressible, electrically conducting liquids along ducts with electrically insulating or weakly conducting walls situated in a strong magnetic field are analysed. Except over a short length along the duct where the magnetic field strength and/or the duct cross-sectional area vary, the duct is assumed to be straight and the field to be uniform and aligned at right angles to the duct. Magnitudes of the field strength B0 and the mean velocity V are taken to be such that the Hartmann number M [Gt ] 1, the interaction parameter N (= M2/Re) [Gt ] 1 (Re being the Reynolds number of the flow) and the magnetic Reynolds number Rm [Lt ] 1.For an O(1) change in the product VB0 along the duct across the non-uniform region, it is shown that:(i) In the non-uniform region the streamlines and current flow lines follow surfaces containing the field lines satisfying , the integration being carried out along the field line within the duct; these surfaces are equipotentials and isobarics. This leads to(ii) a tube of stagnant, but not current-free fluid at the centre of the duct parallel to the field lines around which the flow divides to bypass it. To accommodate this flow,(iii) the usual uniform field/straight duct flow is disturbed over very large distances upstream and downstream of this region, the maximum length O(duct radius × M½) occurring in a non-conducting duct;(iv) a large pressure drop is introduced into the pressure distribution regardless of the direction of the flow, the effect being most severe in a non-conducting duct, where the drop is O(duct radius × (uniform field/straight duct pressure gradient) × M½);(v) in the part of the duct with the lower value of VB0 a region of reverse flow occurs near the centre of the duct and the stagnant fluid.

Fluid mixing apparatus

Abstract: A fluid mixing apparatus having means for producing vortex-like motions of the fluids introduced therein, one embodiment of such an apparatus, for example, using two concentrically mounted inner and outer members, preferably cylindrical, moveable relative to each other at rotational speeds such as to produce the desired vortex-like motions of the fluids introduced into the region therebetween. In one embodiment thereof, the vortex-like motions may be obtained at relatively low rotational speeds by the use of V-shaped grooves on the inner member. In addition, suitable means can further be used to generate a de-stabilizing force for the fluids in a direction substantially perpendicular to the velocity streamlines thereof to further enhance the mixing effectiveness and to improve the quality of the mix, such de-stabilizing force in one embodiment, for example, being generated by the application of an electric field across the region between the inner and outer members.

Experimental evaluation of streamline patterns and separated flows in a series of branching vessels with implications for atherosclerosis and thrombosis.

Abstract: Flow conditions in four models representing the aortic bifurcation, iliac bifuraction, and a renal artery branch were investigated at volumetric flow rates corresponding to Reynolds numbers from 1000 to 4000 over the complete range of flow division between daughter vessels. Qualitative flow streamline patterns and quantitative definition of those flow conditions leading to disturbed flow (flow separation ) were determined primarily at steady flow with a limited set of pulsatie experiments. Under conditions of no flow separation, common characteristic streamline patterns not parallel to the center lines of parent or daughter tubes were found for all models. These effects were accentuated with increasing Reynolds number. Flow separation was inducible through alteration of flow division between daughter vessels or by an increase in flow rate. Each of the four models had distinct combinations of flow division ratio and flow rate which gave: (1) no flow separation, (2) flow separation at the outside of the right daughter tube, and (3) flow separation at the outside of the left daughter tube. Models representing the renal artery also had regions of simultaneous left- and righthand separation on the outside of their daughter tubes. The separated flows observed here displayed streamlines forming an open vortex with flows entering and leaving. These regions, which occur only at distinct combinations of flow rate and flow division, may be key centers where platelet aggregates may form, release constituents, and cause vessel injury.

Advection — Diffusion in the Presence of Surface Convergence

Abstract: Frontal zones are regions of convergence associated with relatively strong vertical motions. They also contain singularities in the horizontal velocity field such as lines of convergence, to which an infinite number of streamlines converge. A complicated velocity structure thus exists in the frontal zone.

Recycling flow over bottom topography in a rotating annulus

Abstract: Steady flow of an incompressible homogeneous fluid over shallow topography in a rotating annulus is considered. The flow is driven by a differentially rotating lid. The recycling nature of the system means that prescribed upstream conditions are not available to close the problem. Consideration of the balance of transport across streamlines for the geostrophic flow leads to a general circulation condition; namely $\Gamma(\psi) = \frac{1}{2}\Gamma_T(\psi)$ , where ϕ is the stream function for the geostrophic flow, Λ is the circulation around a streamline and Λ T is the circulation around the same path calculated using the prescribed upper surface velocity. Using this condition, stream functions for the linear viscous and nonlinear quasi-inviscid flow can be found. Solutions for these two limits, and linearized perturbation solutions for the transition regime between them, are presented for flow over ridges in the annulus.

Experimental investigation of the supersonic flow past a slender cone at high incidence

Abstract: The supersonic flow field past a circular cone of semi-apex angle 7·5° at incidences up to 26° has been investigated experimentally at a free-stream Mach number of 2·94 The experiments were made using a five-hole conical-head directional probe Since the flow past the cone was found to be conical, the flow phenomena may be described in a plane perpendicular to the cone axis This paper gives the direction of the conical streamlines, the conical sonic line and the conical Mach number in such a plane, all of which may be deduced from the measurements At incidences exceeding twice the cone semi-apex angle a separated flow regime was observed which consisted of two main vortices on either side of the leeward plane of symmetry, and probably also two secondary vortices close to the cone surface From incidences of 17° onwards, an embedded region of conical supersonic flow terminated by a shock wave was revealed At 22°, approximately, a second embedded shock wave was measured close to the cone surface and extended slightly across the leeward plane of symmetry This shock wave may have been generated by the vortex system, which induced supersonic cross-flow components towards the cone

Transfert de chaleur par convection naturelle dans une couche poreuse limitée par deux cylindres coaxiaux horizontaux

Abstract: Natural convection in a porous medium is studied for the geometrical configuration defined by two concentric horizontal cylinders with isothermal and impermeable surfaces, representing a cylinder or a pipe insulated by a layer of porous material. Two methods of investigation are used to approach the phenomenon: experiments on a cell of large aspect ratio (cylinder length to outside diameter), and a numerical model on a two-dimensional plane area. The experimental results reveal three different regimes according to the value of the Rayleigh number. For a finite radial gradient, thermoconvective phenomena develop in the annular layer, but as long as these are not amplified too much, the isotherms remain practically concentric with the cylinders, and heat transfer occurs essentially through conduction. At higher Rayleigh numbers natural convection develops in the form of two-dimensional counter-rotational vortices which are symmetrical with respect to a vertical plane containing the axis common to both cylinders. The third regime, observed at higher Rayleigh numbers, corresponds to a fluctuating evolution of the temperature field which becomes three-dimensional. As the inside cylinder is warmer, instabilities occur in the upper part of the model causing some periodicity of the temperature distribution along a generatrix, with a period of about the radius difference. A relative increase in the heat transfer between the cylinders due to the instabilities is observed. A two-dimensional numerical model, using the method of finite differences, enables us to describe the first two regimes observed experimentally, and to define the temperature field and the streamlines for a given Rayleigh number. The total heat transfer calculated is represented by a correlation between the Nusselt and the rayleigh numbers for many values of the ratio of the radii. The different results are then compared and analysed from a physical point of view.

The viscous drag on cylinders falling symmetrically between parallel walls

Abstract: An analogue technique for the approximate solution of the biharmonic equation is used to determine the viscous drag at Reynolds number approaching zero for cylinders falling symmetrically in a liquid between parallel walls. Results obtained show good agreement with numerical solutions, with results by direct experiment and with the work of other authors. Streamlines are obtained with a maximum error of 2% and vorticities and viscous drag forces with a maximum error of approximately 10%.

Flow Patterns Upstream of Isokinetic Dust Sampling Probes

Abstract: In isokinetic sampling from a gas stream it is usually assumed that the flow pattern upstream of the sampling probe is not affected by the presence of the probe. That some probes do seriously affect the gas streamlines is shown by velocity traverses taken with a hot wire anemometer under controlled flow conditions in a wind tunnel. The degree to v/hich the streamlines are affected depends on the wall thickness and taper of the nozzle, the stem diameter, as well as on the size and proximity of sampling accessories in the vicinity of the nozzle. For a probe to cause negligible disturbance under isokinetic conditions it should have a sharp-edged nozzle with little or no outside bevel, and the stem of the probe should be at least 11 stem diameters downstream from the nozzle inlet.

Boundary‐value problems in stratified shear flows with a nonlinear critical layer

Abstract: Approximate solutions of nonlinear boundary‐value problems arising in inviscid stratified shear fluid flows over relatively small obstacles are considered. The presence of a critical layer in the flow field leads to a failure of the linear theory, necessitating the derivation of a nonlinear critical layer equation. The solution of this second‐order differential equation for the horizontal velocity is found to be discontinuous along the streamline which passes through the upstream critical point. In the analysis, three constants of motion along a streamline are used to study flows involving slip and split streamlines emanating from this point. The matching of the critical layer (inner) and the linearized outer solutions is discussed and some examples of steady flows over an obstacle and waves propagating with constant speed are given.

Quantum-mechanical streamlines and classical trajectories in elastic scattering

Abstract: The hydrodynamic formulation of quantum mechanics is considered in the semiclassical limit and the relationship between quantum streamlines and classical trajectories is discussed. The flow pattern of the quantum streamlines can be described in terms of the interference of classical trajectories. The flow inside the classically forbidden regions is related to complex-valued classical trajectories. The analytically solvable cases of Coulomb and hard-sphere scattering are investigated in detail.

Experimental studies of viscous effects on cavitation

Abstract: The work reported in this thesis falls into three distinct, though intimately related parts. Part I is concerned with the production of a variable temperature two-phase flow test facility for studying single and two-phase flows around arbitrary two-dimensional bodies. It includes the initial design study required to define an operational envelope for the facility, and the design and constructional features of its main components and ancilliary systems. The design of a two-phase flow vapour ventilation experiment is described, together with the operating procedure for the facility. Part II reports single and two-phase experiments with a two-dimensional circular cylinder, the two-phase flows being generated by inducing natural cavitation. The cavitation inception flow regime was found to be strongly influenced by viscous effects. Three forms of incipient cavitation were observed, two attached or very close to the cylinder surface, and one of a detached nature, occurring well downstream in the wake of the cylindrical test body. These inception modes have been related to the fully wetted viscous flow around the cylinder in the Reynolds number range 10 5 d 6 . The development of cavitation from these three aforementioned incipient states was investigated. Viscous effects were found to influence both the limited and developed cavitation flow regimes. For development of cavitation at Reynolds numbers corresponding broadly to the supercritical range for fully wetted flow, a critical cavitation number was found at which the apparent free stream lines of the flow changed from a concave to a convex disposition. For the experimental configuration used, this critical cavitation number was independent of Reynolds number, for Reynolds numbers above the critical value. With development of cavitation at Reynolds numbers corresponding broadly to the subcritical range for fully wetted flow, no such gross changes in flow pattern were observed, the displacement of the apparent free streamlines of the flow between the limited and fully developed cavitating states being minimal. Part III contains recommendations for modifications to the experimental facility and suggestions for further studies arising from the results reported herein.

Computer Analysis of Flow Visualization Records Obtained by the Smoke-Wire Technique

Abstract: A technique utilizing a “smoke-wire” for introducing controlled sheets of smoke streaklines has been developed over the last two years for flow visualization in wind tunnels. The smoke-wire, which is mounted on a portable probe, has been used to generate vertical or horizontal sheets of smoke streaklines in several regions of interest in various flow fields. Recently, smoke-wire visualization records of the flow downstream of cylinders and turbulence generating grids, and in turbulent boundary layers have been studied with the aid of digital image processing. The photographic records were digitized on an optical drum scanner and stored on digital tape for analysis. Extensive software packages have been developed by our group for studies of turbulence and are available for array processing, statistical computation, and two- and three-dimensional plotting of results on drum and CRT media. Typical processing of the photographs includes multiple image averaging, thresholding, edge and texture detection, streakline following and spectral analysis of the intensity distribution. This paper outlines the first stages of a long range program and reports on preliminary results obtained from computer analysis of records of grid turbulence with mesh Reynolds numbers ranging from 1,500 to 4,000, the far and near wakes of circular cylinders for the Reynolds number ranges 50 to 150 and 5,000 to 10,000 and turbulent boundary layer flow with Reynolds numbers based on momentum thickness from 600 to 3,300.

Geometry of streamlines in fluid flow theory

Abstract: Intrinsic properties of lines of flow has been studied by employing anholonomic co ordinate system consisting of s-lines which are streamlines, n-lines the involutes of s-lines and b- lines the locus of centre of spherical curvature of s-lines This gives rise to only two geometric parameters and interesting have been obtained It was also shown that velocity can be expressed in terms of geometric parameters Constancy of velocity along binormal line implies existence of Lump surface for the motion It is found is not irrotational unless it is plane motion In generalised screw motion it is found that wn/v=constant along the stream line

Influence of Flow-Field Structure on Uranium Isotope Separation in the Separation Nozzle

Abstract: In the separation nozzle process, uranium isotope separation is based on the mass dependence of the centrifugal forces in a fast curved flow consisting of uranium hexafluoride and a light auxiliary gas that is admixed in a high molar excess. The objectives of this investigation are to determine the dependence of the separating characteristics of a centrifugal flow field on its spatial structure. Calculations were carried out for small UF/sub 6/ mole fractions in the light auxiliary gas, so that the complicated ternary diffusion equations are reduced to two simple binary diffusion equations. The calculations show that isotope separation increases with the radial displacement of the UF/sub 6/ streamlines relative to the auxiliary gas. Favorable initial distributions for a large radial shifting of UF/sub 6/ exist when the flux, at the beginning of deflection, is high for small deflection radii, whereas at the end of deflection, the UF/sub 6/ should be concentrated at large radii near the outer deflection wall. Consequently, a radial decrease of flow velocity, a high ratio of nozzle width to deflection radius, and high centrifugal fields at the end of deflection yield high separation effects. Taking into account the interdependence between the gas flow rate, themore » viscous losses, and the diffusion coefficient, the model developed can predict the influence of geometric parameters on the separating characteristics of the nozzle.« less

Transonic nozzle flows of real gases with nonuniform gas properties

Abstract: The transonic flow of a vibrationally relaxing or a chemically reacting gas in a convergent‐divergent nozzle is considered. The procedure used to solve the flow equations is similar to that first used by Hall, and the solution is based on a series expansion in terms of the wall geometry in the transonic region. The nonuniformities of the flow properties across the flow field are taken into consideration. Taulbee and Boraas have already solved such a problem for a frozen flow by a sort of inverse method, in which the governing equations are written with the stream function as an independent variable so as to accomodate the variations in flow properties across the flow field. The problem is solved by a direct method, in which the flow equations are written with generalized coordinates of curvilinear coordinates comprising the streamlines and the system of lines normal to the streamlines, and analytical solutions are obtained for both frozen and equilibrium flows.

Phenomenological aspects of quasi-stationary controlled and uncontrolled three-dimensional flow separations

Abstract: Quasi-steady three dimensional separated flows about bodies of large fineness ratio operating at large angles of incidence or yaw are discussed. The general character of the three dimensional attached boundary layer, the concept of limiting streamlines, and the physics of three dimensional separation and reattachment are among the factors considered. Specific examples are given. The advantages of swept, sharp edges that generate controlled (or fixed) three dimensional flow separations on a vehicle, due to the qualitatively unchanging flow field developed throughout the range of flight conditions, are emphasized.

Hydromagnetic Stokes flow past a rotating sphere

Abstract: In the present investigation we consider hydromagnetic Stokes flow past a rotating sphere. The magnetic field is produced by a magnetic pole placed at the centre of the sphere. The problem is analysed by a combination of perturbation and numerical methods. It is seen that the flow reversal (due to rotation) at the rear portion of the sphere is enhanced as the strength of the magnetic field increases. In addition, we obtain the simultaneous effects of rotation and a magnetic field on the streamlines.

Resonant stellar orbits in spiral galaxies. IV. Hydrodynamic flows in the regions of the lindblad resonances

Abstract: A theory of the steady hydrodynamic flow of the interstellar gas in the regions of the Lindblad resonances of a spiral galaxy is developed. The Lagrangian equation of motion is solved as an orbital problem with the aid of an epicyclic theory of resonant stellar orbits, and the equation of continuity is solved in terms of a stream function. Applications are made to (1) the linear theory of density waves, (2) nonlinearities in the flow which are intrinsic to the resonance phenomenon, (3) the relationship between the streamlines of the flow and the corresponding periodic stellar orbits, and (4) the conditions for the occurrence of shocks in the flow.

The Secondary Flow about a Circular Cylinder Mounted Normal to a Flat Plate

Abstract: Three-dimensional steady incompressible viscous flows about a circular cylinder being mounted with its axis normal to a flat plate were studied numerically. First a finite-difference method using the equations in terms of the pressure p, the velocity u and the vorticity ξ was proposed. In the method the cells in an orthogonal curvilinear coordinate system are used, which consists of the equi-potential lines and the streamlines for a tow-dimensional potential flow past a circular cylinder in a uniform flow. It is convenient to use such coordinates to prescribe the initial and outer boundary conditions and to show the secondary flows. Then the flow patterns for the Reynolds numbers 100 and 500 were calculated. The flow separation and the horseshoe vortex at the front of cylinder, anothervotex generating near the side corner, and the shearing stress at the flat plate and the cylinder walls were discussed.