Showing papers on "Streamlines, streaklines, and pathlines published in 1977"

Flow behaviour of blood cells and rigid spheres in an annular vortex.

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.

A porous prolate-spheroidal model for ciliated micro-organisms

Abstract: A fluid-mechanical model is developed for representing the mechanism of propulsion of a finite ciliated micro-organism having a prolate-spheroidal shape. The basic concept is the representation of the micro-organism by a prolate-spheroidal control surface upon which certain boundary conditions on the tangential and normal fluid velocities are prescribed. Expressions are obtained for the velocity of propulsion, the rate of energy dissipation in the fluid exterior to the cilia layer, and the stream function of the motion. The effect of the shape of the organism upon its locomotion is explored. Experimental streak photographs of the flow around both freely swimming and inert sedimenting Paramecia are presented and good agreement with the theoretical prediction of the streamlines is found.

Numerical Computation of Space Shuttle Laminar Heating and Surface Streamlines

Abstract: Exact inviscid flowfield codes are used, together with a quasi-three-dimensional boundary-layer analysis, to provide estimates of the windward surface heating and streamline patterns of the shuttle orbiter vehicle under laminar flow conditions. The accuracy and limitations of the methods are established by comparison with available wind-tunnel experiments and with more exact numerical solutions for simple flows. Flight predictions are presented showing the effects of finite-rate (nonequilibrium) chemical reactions, and the effects of varying boundary-layer edge conditions due to the growth of the boundary layer into the inviscid flow (entropy-layer swallowing). Differences between flowfield predictions at wind-tunnel and nominal flight conditions are discussed.

Revised FORTRAN program for calculating velocities and streamlines on the hub-shroud midchannel stream surface of an axial-, radial-, or mixed-flow turbomachine or annular duct. 2: Programmer's manual

Abstract: A FORTRAN IV computer program has been developed that obtains a detailed subsonic or shock free transonic flow solution on the hub-shroud midchannel stream surface of a turbomachine. The blade row may be fixed or rotating, and the blades may be twisted and leaned. Flow may be axial, mixed, or radial. Upstream and downstream flow variables may vary from hub to shroud, and provisions are made to correct for loss of stagnation pressure. The results include velocities, streamlines, and flow angles on the stream surface and approximate blade surface velocities.

Electrohydrodynamic mixing and instability induced by co‐linear fields and conductivity gradients

Abstract: Scaling laws for field induced mixing of a semi‐insulating liquid of uniform viscosity η and permittivity e, but of inhomogeneous conductivity, are deduced for motions with characteristic times long compared with viscous‐diffusion and charge relaxation times. In an electric field, E, time is shown to scale with electric‐viscous time τev=η/eE2. An experiment involving mixing of a highly conducting thin layer into a lesser conducting bulk region uses temporal current evolution to confirm scaling. A simple mixing model is shown to correlate with experimental results. Linear instability mechanisms underlying the mixing process are described by a bulk‐coupled model, with viscous diffusion effects included. Eigenfrequencies are determined as they depend on conductivity variation and ratio of viscous diffusion to electric‐viscous time. Static instabilities and overstabilities are predicted. Corresponding eigenfunctions and streamlines lend insights into the onset of instability leading to a turbulent mixing state.

An Investigation of Separated Flow about a Hemisphere-Cylinder at 0- to 19-Deg Incidence in the Mach Number Range from 0.6 to 1.5

Abstract: : A wind tunnel investigation was conducted of the separated flow about a hemisphere-cylinder at incidence from 0 to 19 deg in the Mach number range from 0.6 to 1.5. At zero incidence, a nose separation bubble is revealed from analysis of shadowgraphs and surface pressure distributions between Mach numbers 0.7 and 0.9. The basic differences between the present nose separation bubble and the leading-edge separation bubble of airfoils are discussed. A multiple shock system, consisting of a lambda shape shock and two normal shocks, prevails in the flow field as a result of the viscous/inviscid interaction which is strongest at M at infinity = 0.85. Velocity field measurements utilizing a laser velocimeters were obtained for M at infinity = 0.85. The concept of an effective body and the particle dynamics are used to analyze the velocity. For incidences from 5 to 19 deg, shadowgraphs, surface pressures, and oil flow pictures showing the separation patterns and limiting streamlines were obtained through the Mach number range. Two separation regions, the nose separation bubble and the crossflow separation zone, were found to exist simultaneously. Concentrated vortices standing at the leeside forebody were found, and the mechanism and conditions for their appearance and discussed.

Numerical Solution of the Navier-Stokes Equations for a Three-Dimensional Corner

Abstract: A three-dimensional, time dependent Navier-Stokes code employing MacCormack's finite-difference scheme has been developed. Successful comparisons were performed for analytic solutions first to validate the numerical procedure. The strong inviscid-viscous interacting flow field for a three-dimensional compression corner at a Mach number of 12.5 and a Reynolds number of 1.21 x 10 was then computed and compared with experiment. The computed result nearly duplicated the experimental observations, including wall pressure, heat transfer, oil flow streamline pattern, and impact pressure flowfield survey. The numerical result not only verified the experimental finding of an extensive penetrating inviscid stream (inviscid finger) in the corner region as the source of the extremely high local rate of heat transfer, but also revealed an embedded crossflow supersonic region in the viscous vortex. The present result tends to substantiate the separation criterion established by the limiting line theory, in which the separation line is defined as an envelope of limiting streamlines. This investigation demonstrated that numerical methods may be used to determine the general features of complex threedimensional flows.

Nonlinear steady incompressible lifting-surface analysis with wake roll-up

Abstract: The problem of lifting surfaces in steady incompressible flow is considered in terms of an integral equation relating the potential discontinuity on wing and wake to the normal derivative of the potential (normal wash) on the lifting surface. The integral equation is approximated by a system of linear algebraic equations obtained by dividing the surfaces into small quadrilateral elements and by assuming the potential discontinuity and the normal wash to be constant within each element. The wake geometry is obtained through iteration by satisfying the condition that the velocity be tangent to the surface of the wake and that the potential discontinuity be constant along the streamlines. Numerical results are in good agreement with existing ones

The Six Roll Mill: Unfolding an Unstable Persistently Extensional Flow

Abstract: The six roll mill produces steady two-dimensional flows with three incoming and three outgoing streams of fluid. Each flow is generated by a particular set of roller speeds represented by a point in 'control space', and is characterized by its 'critical points', at which the fluid velocity vanishes. A surface $\Sigma $ separates control space into regions whose flows have different numbers of critical points; on $\Sigma $ the critical points are degenerate. For the system studied, $\Sigma $ is the 'elliptic umbilic catastrophe' in the classification of Thom. By using glycerol in the mill, a sequence of flows was explored, corresponding in control space to a loop intersecting $\Sigma $. The observed streamline patterns agree well with computer simulations. When the mill contained a 2% solution of polyethylene oxide in water the sequence of observed flow patterns was very different. This can be explained by the long chain molecules becoming persistently extended along the outgoing streamlines issuing from critical points, and the resulting sheets of high extension inhibiting the development of large strain rates in the outgoing fluid streams; the breaking of symmetry between inflows and outflows is shown to explain the observed flow patterns. The high extension of the polymer molecules was observed as intense localized flow birefringence. The diminution in this intensity near degenerate critical points can be used to give rapid estimates of macromolecular relaxation time.

An investigation of non-newtonian flow past a sphere

Abstract: Any experimental work on the flow of a polymer solution or any theoretical analysis on the basis of a visoelastic constitutive equation does not always bring out viscoelastic effects but may be showing a non-Newtonian viscosity effect. Therefore, in order to obtain a clear understanding about viscoelastic effects, it is desirable to have a sufficient knowledge of the non-Newtonian viscosity effect. To facilitate this, finite-difference numerical solutions of non-Newtonian flow were carried out using a non-Newtonian viscous model for the Reynolds numbers of 0.1, 1.0, 20 and 60. Drag force measurements and flow visualization experiments were also performed over a wide range of experimental conditions using polymer solutions. The present work appears to support the following idea: When compared with the Newtonian case on the basis of DV∞P/η0, where η0 is the zero shear viscosity, it is on account of the non-Newtonian viscosity that the friction and pressure drags decrease, that the separating vortices behind the sphere become larger, and that no shift occurs in the streamlines. On the other hand, it is due to viscoelasticity that the normal force drag increases, that the separating vortices behind the sphere become smaller, and that an upstream shift occurs in the streamlines.

Rotating elliptic cylinders in a viscous fluid at rest or in a parallel stream

Abstract: Numerical solutions are presented for laminar incompressible fluid flow past a rotating thin elliptic cylinder either in a medium at rest at infinity or in a parallel stream. The transient period from the abrupt start of the body to some later time (at which the flow may be steady or periodic) is studied by means of streamlines and equi-vorticity lines and by means of drag, lift and moment coefficients. For purely rotating cylinders oscillatory behaviour from a certain Reynolds number on is observed and explained. Rotating bodies in a parallel stream are studied for two cases: (i) when the vortex developing at the retreating edge of the thin ellipse is in front of the edge and (ii) when it is behind the edge.

Simple rotational flows

Abstract: The paper develops and discusses some new additions to the available stock of analytical solutions of the nonlinear equations of fluid motion. The motions are steady, two-dimensional and devoid of viscous or other rotational forces (although such forces must have been significant during any starting process). The fluid density is constant.The solutions are in two groups, referred respectively to Cartesian and polar co-ordinates. In both the stream function is of separable form, i.e. expressible as a product of two functions, each dependent on one co-ordinate. A remarkable variety of motions is revealed. Those that are most significant physically are described as bends (rapid transitions from one rectilinear flow to another) or as loops (closed, non-circular, vortex-type flows). The effects of boundary layers at walls or instability are not explored.The paper closes with a mention of some preliminary experiments on loop flows in which all streamlines are ellipses and some discussion of the applicability of bend flows. Generalizations to axisymmetric flows and compressible flows are also mentioned briefly.

Low supersonic flow over hemisphere-cylinder at incidence

Abstract: A wind-tunnel investigation was conducted of the flow about a hemisphere-cylinder at incidence up to 19 deg in the low supersonic Mach number range from 1.1 to 1.5. Shadowgraphs, surface pressures, and oil flow pictures showing the separation patterns and limiting streamlines were obtained through the Mach number range. Surface pressure data were compared to inviscid calculations for the nonseparated regions for M^ > 1.2. Two separation regions, the nose separation bubble and the crossflow separation zone, were found to exist simultaneously. A concentrated vortex pair was found standing on the leeside of the forebody, and the mechanism for its appearance is discussed. The distribution of normal-force, total normal-force, and axial-force coefficients and center of pressure are presented and compared with available data and a simple theoretical prediction.

Dilute polymer solutions in elongational flow

Abstract: A series of experiments is described using solutions of various concentrations of Polyox coagulant flowing through porous beds of spherical particles. Results are reported, similar to those obtained by James and McLaren, which show a substantial increase in drag. The onset of this drag increase from solvent flow seems to occur at a constant Deborah number multiplied by the square root of the concentration. The flow in a bundle of symmetrical convergent‐divergent channels which may serve as a model for a porous medium is analyzed. The presence of elongated particles in the fluid will alter the flow pattern in such a channel from that given by the Stokes’ solution. Assuming the particles to be aligned parallel to the mean flow direction, this flow re‐arrangement will attenuate the effect of the particles on the dissipation of mechanical energy. Extended molecules may be misaligned with the streamlines in the diverging section of the channel, which could explain the large increase in drag observed with dilute polymer solutions in porous beds.

The round laminar jet: the development of the flow field

Abstract: The development of the flow field of a jet emanating from a point source of momentum in an infinite incompressible fluid of density σ is considered. The flow field is assumed to be due to the application of a constant force F0 at the origin. The problem is formulated in terms of the dimensionless variable λ = (vt)½/r, where v is the kinematic viscosity of the fluid, t the time from the application of the force and r the distance from the origin. At a station r the flow field is dipolar, with the dipole axis in the direction of F0, for all t satisfying the inequalities vt Lt; r2 and F0t2 [Lt ] 4πρr4. Also, at a given time t the streamlines of the developing flow field in a section through the axis of symmetry of the problem form closed loops about a stagnation point. If this occurs at λ = λm, the stagnation point propagates to infinity, along a straight line emanating from the origin, with speed v½/2λmt½, where λm = λm(F0) decreases as F0 increases. The larger F0 is the faster the steady state is established.

Unsteady supersonic aerodynamic theory for interfering surfaces by the method of potential gradient

Abstract: A generalized solution of the hyperbolic wave equation was further developed to relate the velocity components at a field point to the potential gradient distribution in the dependence domain. Singular integrals were evaluated in closed form, with numerical integration methods for more complex but analytic functions. Idealization of the lifting surfaces by trapezoidal elements with two sides parallel to the streamlines is computationally efficient. Streamwise integrals were performed analytically, and spanwise integrals were neccessary only on element leading and trailing sides. All integrands vanish on the Mach cone. Pressure distribution on a double delta wing and generalized aerodynamic coefficients for three AGARD planforms were calculated and compared with available results.

Unsteady supersonic aerodynamic theory by the method of potential gradient

Abstract: A generalized solution of the hyperbolic wave equation has been derived by one of the authors. The method used has been further developed to relate the velocity components at a field point to the potential gradient distribution in the dependence domain. Singular integrals have been evaluated in closed form, whereas numerical integration methods are suggested for treating more complex but analytic functions. Idealization of the lifting surfaces by trapezoidal elements with two sides parallel to the streamlines is computationally efficient because line integrations along the other two sides need only be considered. Furthermore, all the integrands vanish on the Mach cone and the need for determining the hyperbolic curves of intersection of the cone with the lifting surface is avoided. Generalized aerodynamic coefficients for three AGARD planforms have been calculated and compared with the available results.

A numerical method for stratified shear flows over a long obstacle

Abstract: The nonlinear problem of steady flow of an incompressible stratified fluid of finite depth over an obstacle is investigated by using a numerical algorithm which solves both obstacle height and flow fields simultaneously instead of solving the flow fields, given the obstacle height. We also find, for a given upstream condition, a maximum obstacle height over which steady flows are possible, not allowing discontinuities or closed streamlines. This maximum height is a functional of the upstream density stratification and the velocity shear. We calculate this functional dependence for a number of specific upstream conditions. It is also shown that the number of layers required in the model to represent a flow field increases as the Froude number decreases or as the vertical wave number increases. The hydrostatic and finite depth assumptions are essential in our method.

Supersonic, nonequilibrium corner expansion flow of ionized argon

Abstract: The nonequilibrium corner‐expansion flow field of partially ionized argon was solved numerically using the method of characteristics. The solution assumed a steady, two‐dimensional, and inviscid field. The main feature of the present solution, as compared with previous numerical solutions for the corner‐expansion flows, is in the relaxation of the requirement that thermal equilibrium be maintained throughout the expansion. As a result, the electron temperature was found to be higher than that of the heavy particles. This is expected, since most of the energy released during the recombination process is absorbed by the free electrons. The specific solution reported here, solved the expansion field for two different corners (−5° and −15°) expansion angle), when both had the same pre‐corner flow conditions. Fair agreement was found between the present numerical solution and the experimental results regarding the density and degree of ionization changes along streamlines. Consequently, the present technique can be used with confidence for the flow of various plasmas.

Nonlinear wave propagation in a two-dimensional steady transonic flow

Abstract: When we look at photographs of real transonic flows which are predicted to be shockless, we find a very large number of weak shocks almost perpendicular to the streamlines. These are no more than almost-trapped upstream-propagating nonlinear waves. In this paper we try to obtain a simple approximate equation which gives their complete history and takes into account both their turning effect, owing to a non-zero gradient of the fluid velocity in a direction normal to the streamlines, and also the finite radius of curvature of the wave front. We first give a brief discussion of a few results which can be easily obtained from the solution of the approximate equation and then compute the history of two nonlinear pulses by numerically integrating the equation.

On the origin of the hole pressure

Abstract: One wall of a slit die apparatus contains a slot filled with the test liquid. Photographs of marked streamlines near the slot mouth show a pronounced curvature. A 0.5% aqueous solution of Separan AP 30 and molten polystyrene and polyethylene were investigated at low values of Reynolds number (Re < 1.0). In each case, streamlines are convex towards the slot mouth. This supports the hypothesis ofTanner andPipkin which attributes hole pressures in flowing viscoelastic liquids to the combined effect of holegenerated streamline curvature and shear-generated normal stress differences.

An inviscid bluff-body wake model which includes the far-wake displacement effect

Abstract: This paper presents an inviscid bluff-body wake model which correctly takes into account the displacement effect of the far wake by means of an appropriate source–sink system located behind the body The separating streamlines, which in previous inviscid wake models have been regarded as the time-averaged shear layers emanating from the separation points within a small distance downstream of the body, can be interpreted as the displacement surface of the wake throughout the whole region of flow behind the body The solutions for a normal flat plate, a circular cylinder and a 90° wedge are worked out and compared with experiments, where possible The theoretical pressure distributions agree fairly well with the experimental ones The shape of the separating streamlines obtained from the present theory is physically reasonable and compares well with experimental results for a normal plate and a 90° wedge

Investigation of Three-Dimensional Flow Separation on Fuselage Configurations.

Abstract: : A method is described for calculating the complete pressure distribution on a body with separated flow. The boundary layer characteristics are calculated along several streamlines up to the point where separation is predicted. The separated flow is modeled by streamwise panels of uniform vorticity attached to the body near the predicted separation line. Comparisons are presented of calculated and experimental pressure distributions for a cylinder, a sphere and the BO105 fuselage. The results are in fair agreement, but there are certain features of the results and restrictions of the source/vortex inviscid model which need improvement. (Author)

Effect of viscosity on internal waves from a source in a wall

Abstract: The solution for a line source of oscillatory strength kept at the origin in a wall bounding a semi-infinite viscous imcompressible stratified fluid is presented in an integral form. The behaviour of the flow at far field and near field is studied by an asymptotic expansion procedure. The streamlines for different parameters are drawn and discussed. The real characteristic straight lines present in the inviscid problem are modified by the viscosity and the solutions obtained are valid even at the resonance frequency.

Method for fiber alignment using fluid-dynamic forces

Abstract: A method and apparatus are provided for aligning individual fibers parallel to the main fluid stream that is conveying them, using fluid-dynamic forces. This method and apparatus are based on the use of converging streamlines in a nearly irrotational flow to provide the necessary moments to rotate the fibers so that they become parallel to the streamlines. Counterflow jets are provided to create the desired streamline behavior in a main fluid stream. The irrotationality of the flow and the nearly parallel streamlines thus prevent further fiber rotation downstream.