Showing papers on "Streamlines, streaklines, and pathlines published in 1971"
01 Jan 1971
TL;DR: In this article, the authors considered the structure of straight line vortices in a uniform two-dimensional straining field and showed that the shape of a vortex line depends on its shape and the detailed vorticity distrivation.
Abstract: The velocity of a vortex line depends on its structure, i.e. the shape of the cross-section and the detailed vorticity distribution. As a first step towards an understanding of how the structure depends on the motion and the construction of a valid approximation for the motion of vortex lines in general flow fields, we consider the structure of straight line vortices in a uniform two-dimensional straining field. Two cases are considered in detail, irrotational strain and simple shear. In the first case, it is shown that steady exact solutions of the inviscid equations exist, in which the boundary of the vortex is an ellipse with principal axes at 45° to the principal axes of strain. There are two possible axis ratios provided e/ωo 0.15, and it is believed from some numerical work that in this case the strain field will cause the vortex to break up. For simple shear, there is one steady shape of elliptical form if the shear rotation and vorticity are in the same sense and e′<ωo, where e′ is the rate of shear. The major axis is parallel to the streamlines and the shape is stable to two-dimensional deformations. For shear rotation and vorticity in opposite senses, there are two steady elliptical shapes if e′/ωo<0.21, with major axes perpendicular to the streamlines. The more elongated form is unstable, and the less elongated one is stable. Disturbances of three-dimensional form are also considered in the limit of extremely large axial wavelength.
219 citations
TL;DR: In this paper, the authors used the time concentration profile from discharging well of a labeled recharging-discharging well pair to evaluate an aquifer's porosity and dispersion constant.
Abstract: A method described in this report uses the time concentration profile from the discharging well of a labeled recharging-discharging well pair to evaluate an aquifer's porosity and dispersion constant. The technique is applicable for pulse tracer injection and recirculation. Derived equations allow prediction of streamline arc lengths and travel times between wells along streamlines. Adjacent streamlines joining the two wells define crescents that approximate dispersion columns of known length. The summation of breakthrough curve concentration profiles for flow through these individual columns provides a composite breakthrough curve for the entire flow field. Analysis of a tracer test using tritium in a fractured carbonate aquifer near Carlsbad, New Mexico, provided a dispersion constant of 125 feet and a porosity of 12.0%, values consistent with known properties of the aquifer.
88 citations
TL;DR: In this paper, an Oseen-type linearisation is employed to obtain equations for slow viscoelastic flow past submerged objects, where the velocity of propagation of shear waves emerges as a primary ordering parameter.
69 citations
TL;DR: In this paper, the authors measured the turbulent heat transfer rate on the conical surface of a 9° half-angle cone in a MO, = 10.6 nitrogen flow at various angles of attack, where the boundary layer was tripped in order to attain turbulent flow over the model.
Abstract: Turbulent heat-transfer rates measured on the conical surface of a blunt 9° half-angle cone in a MO, = 10.6 nitrogen flow at various angles of attack are presented. The measurements were made at a nominal Rem/ft of 12(10)6 at angles of attack of a = 0°, 2.5°, 5°, 10°, 15°, and 20°. The boundary layer was tripped in order to attain turbulent flow over the model. Detailed distributions of the heat-transfer rate and surface pressure were obtained in the circumferential (A<£ = 22.5°) as well as the axial directions (S/RN < 10). Turbulent heat-transfer rates computed along inviscid surface streamlines, wherein the streamline pattern was determined utilizing the experimental pressure distributions, are compared to the data. Good agreement is obtained in the regions where the assumption of neglecting the effect of entropy swallowing utilized in the analysis is valid. The turbulent heat-transfer formulation proposed by Vaglio-Laurin as being applicable in three-dimensional flows is shown to be a good approximation for these test conditions. The influence of streamline spreading is demonstrated as well as the relative accuracy of equivalent cone techniques. The results of numerical calculations of the surface pressure are compared to the data and good agreement is achieved, except in regions where viscous-inviscid interactions become important.
60 citations
TL;DR: In this article, the authors studied the flow in a scraped-surface heat exchanger (SSHE) and established that the flow was either in the Couette flow regime or in the Taylor vortices regime.
58 citations
TL;DR: In this article, a study of the motion of dye streamers on the surface of a sphere in a close packed cubic array of spheres is presented, where the singular points of the limiting streamlines are identified as saddle points.
48 citations
Abstract: The problem of heat transfer at high Peclet number Pe from a sphere freely rotating in a simple shear field is considered theoretically for the case of small shear Reynolds numbers. It is shown that the present problem is in many respects similar to that of heat transfer past a freely rotating cylinder which was recently solved by Frankel & Acrivos (1968). By taking advantage of the close analogy between these two problems, an approximate method of solution is developed according to which the asymptotic Nusselt number for Pe → ∞ is 9, i.e. 4½ times its value for pure conduction. As in the corresponding case of the cylinder, the fact that the asymptotic Nusselt number is independent of Pe results from the presence of a region of closed streamlines which completely surrounds the rotating sphere.
48 citations
TL;DR: In this article, a study of the combined free and forced convective heat transfer and fluid flow in a rotating curved circular tube for the fully developed flow with the thermal boundary condition of constant heat flux per unit length of tube was made.
48 citations
TL;DR: In this article, the stability of the laminar mixing region between two uniform streams is investigated by numerically solving the linear sixth-order equation for the disturbance amplitude function, which is, therefore, regular at the critical point, where the mean flow velocity and disturbance phase speed are equal.
Abstract: The stability of the laminar mixing region between two uniform streams is investigated by numerically solving the linear sixth‐order equation for the disturbance amplitude function. This equation includes the effects of both viscosity and heat‐conduction and is, therefore, regular at the critical point, where the mean flow velocity and disturbance phase speed are equal. Both the neutral stability curve and curves of constant amplification rate are computed for various Richardson numbers. The results show that the damping effects of diffusion are quite small and, therefore, that the Richardson number is the dominant parameter governing the stability of the flow. Streamlines are computed for neutral disturbances and it is found that, in the inviscid limit for long waves, the flow pattern approaches the configuration obtained previously by Taylor in his study of a discontinuous three‐layer model.
47 citations
TL;DR: In this article, a simple theoretical model for coastal upwelling is presented, which is driven by surface wind stress acting on homogeneous water of constant depth adjacent to a long straight coastline.
Abstract: As a step in understanding the complicated dynamics of coastal upwelling areas, a simple theoretical model is examined. The motion is driven by surface wind stress acting on homogeneous water of constant depth adjacent to a long straight coastline. Order-of-magnitude analysis is used to argue that the upwelling is induced by the horizontal divergence of a lateral, frictional boundary layer. A vertical integration of the equations of motion shows the necessity of retaining the pressure gradient term in the longshore direction even though the velocity field is two-dimensional. The motion in the lower return layer and upper Ekman layer is analyzed. It is found that the surface layer motion may he deduced independently of the return flow layer. The mass flux pumped into it should not be affected by bathymetry or stratification, provided that the depth is much greater than the Ekman layer depth. Streamlines are shown for different surface wind stress orientations. The results show that some upwelling ...
45 citations
TL;DR: In this article, an analytical solution is developed to describe the steady, closed streamline velocity field within a cylindrical cavity with a uniformly translating wall at low Reynolds numbers, where regions of fluid are segmented by a moving train of bubbles or plugs.
Abstract: An analytical solution is developed to describe the steady, closed streamline velocity field within a cylindrical cavity with a uniformly translating wall at low Reynolds numbers. The solution has application for the case of two-phase flow in a tube where regions of fluid are segmented by a moving train of bubbles or plugs, such as in the pulmonary and peripheral capillaries of the body where segments of plasma are trapped between red blood cells. The mathematical approach presented in this study can in principle be useful in the analysis of a wide class of closed-streamline creeping-flow problems.
01 Aug 1971
TL;DR: In this article, the effects of curvature on the turbulence and hence the transport properties of axial and decaying tangential velocity fields using isothermal air as the working fluid in an annulus with a single diameter ratio.
Abstract: : An important feature of many flows encountered in practice (such as inturbomachinery) is the fact that the streamlines may be curved, thereby introducing a pressure gradient in the direction perpendicular to the main flow direction The purpose of the present research is to isolate the effects of curvature (swirl) on the turbulence and hence the transport properties The experimental effort is concerned with mapping out the details of the developing axial and decaying tangential velocity fields using isothermal air as the working fluid in an annulus with a single diameter ratio (di/do) = 04) and at a single bulk Reynolds number of 130,000 Interest is centered on a critical discussion of the data reduction techniques for obtaining the radial variations of the axial and tangential momentum diffusivities
TL;DR: The streamlines outside and inside liquid drops in an immiscible liquid undergoing plane shear flow were studied theoretically as discussed by the authors, and the equations for the inner (closed) streamlines and for the equatorial periods of circulation of particles moving on inner and outer streamlines, already partially known, have been systematically derived and also shown to depend on the drop/medium viscosity ratio λ.
TL;DR: In this paper, the authors studied thermal convection flow of water between two vertical parallel plates held at different temperatures and found that the flow pattern between the plates and the type of distributions of the velocity and temperature depend almost only on the Rayleigh number A.
Abstract: Experimental studies on thermal convection flow of water between two vertical parallel plates held at different temperatures were carried out. The flow pattern between the plates and the type of distributions of the velocity and the temperature depend almost only on the Rayleigh number A . ( A =γ Δ T g d 3 /(κν), Δ T being the temperature difference, d the distance between the plates, γ the thermal expansion coefficient, κ the thermal diffusivity, ν the kinematic viscosity, and g the acceleration of gravity.) As the Rayleigh number becomes larger, the flow tends to the type of boundary layer flow. There has been found a critical value of the Rayleigh number, such that, below it the flow is always laminar and above it the flow becomes unstable. Beyond the critical value (\(A_{\text{crit.}}{\fallingdotseq}12{\times}10^{6}\)) wavy motions of streamlines appear, then they develop to rows of periodic vortices and eventually burst into turbulent flow.
TL;DR: In this article, the authors argue that the steady adiabatic flow of a fluid is isenthalpic along streamlines, and that the Joule-Kelvin coefficient of the fluid can therefore be used to predict the temperature change during decompression.
Abstract: WALDBAUM1 has suggested that, when mantle material convects according to the model of Turcotte and Oxburgh2, the temperature of an isolated rising mass will increase, “even in the idealized case where friction, viscosity and turbulence are ignored”. He argues from the premise that the steady adiabatic flow of a fluid is isenthalpic along streamlines: the Joule–Kelvin coefficient of the fluid can therefore be used to predict the temperature change during decompression.
01 Aug 1971
TL;DR: In this article, the main program and each subprogram are described by defining the pertinent symbols involved and presenting a detailed flow diagram and complete computer program listing, including input and output parameters.
Abstract: A description of the computer program used for heating rate calculation for blunt bodies in hypersonic flow is given. The main program and each subprogram are described by defining the pertinent symbols involved and presenting a detailed flow diagram and complete computer program listing. Input and output parameters are discussed in detail. Listings are given for the computation of heating rates on (1) a blunted 15 deg half-angle cone at 20 deg incidence and Mach 10.6, (2) a blunted 70 deg slab delta wing at 10 deg incidence and Mach 8, and (3) the HL-10 lifting body at 20 deg incidence and Mach 10. In addition, the computer program output for two streamlines on the blunted 15 deg half-angle cone is listed. For Part 1, see N71-36186.
TL;DR: The effects of nonuniform properties of an equilibrium plasma in a segmented magnetohydrodynamic generator are investigated in this article, where the shape of the current streamlines depends strongly on wall temperature, free stream Mach number, and boundary layer thickness.
Abstract: The effects of nonuniform properties of an equilibrium plasma in a segmented magnetohydrodynamic generator are investigated. The current distribution is distorted more for laminar flow than for turbulent flow. The shape of the current streamlines depends strongly on wall temperature, free stream Mach number, and boundary layer thickness. For fine segmentation ratio (s/h≈0.1), the current densities are uniform at distances 10% of the channel height away from the walls. Since the two‐dimensional effects are confined to this narrow region, the changes of the current distribution outside this region are due to changes in flow properties. The current distribution on the electrode is most sensitive to the electrode temperature. For hot walls, current shorting between adjacent electrodes is important and is significantly affected by the boundary layer type and free stream Mach number. Boundary layer thickness is of minor importance. Shorting decreases as the wall temperature decreases and eventually disappears w...
01 Mar 1971
TL;DR: In this paper, the analysis of the Navier-Stokes equations in streamwise coordinates is extended to cover viscous flow for both plane twodimensional and axisymmetric flow.
Abstract: The analysis of [1] is extended to cover viscous flow for both plane twodimensional and axisymmetric flow. The equations used are the Navier-Stokes equations in streamwise coordinates, except that for simplicity terms of order μ ▽θ are neglected, where μ is a coefficient of viscosity and θ the flow direction. The supersonic combustion chamber of [1] is used as an example, but the technique of specifying the streamlines in advance has to be modified for a boundary layer with pressure gradient. Thermal conductivity is included but does not have a very important effect. Flow separation is indicated in some circumstances.
01 Jan 1971
TL;DR: Axisymmetric flows with regions of closed streamlines confined by rotational inertia or electromagnetic pinch, for containment for gas core reactors were used for containment of gas core nuclear power stations.
Abstract: Axisymmetric flows with regions of closed streamlines confined by rotational inertia or electromagnetic pinch, for containment for gas core reactors
01 Aug 1971
TL;DR: In this paper, a computer program for calculating inviscid surface streamlines and heat transfer on space shuttle configurations is presented, along with a detailed analysis of the heat transfer process.
Abstract: Computer program for calculating inviscid surface streamlines and heat transfer on space shuttle configurations
01 Jan 1971
TL;DR: The streamline model is a simulation technique which can be used to predict multi-fluid displacements along the streamlines generated from solutions to the diffusivity equation as discussed by the authors, which is used to solve fluid-flow problems in reservoirs which have irregular boundaries, arbitrary well pattern developments, and stratification of microstrata in which cross flow is considered negligible.
Abstract: The streamline model is a simulation technique which can be used to predict multi-fluid displacements along the streamlines generated from solutions to the diffusivity equation. Fluid flow is simulated mathematically by computing streamlines and their generated stream channel volumes numerically using superposition of Laplace flow potential solutions, a corrected Darcy frontal velocity, and first difference movement equations. The effects of differing fluid mobilities and displacement mechanisms are included in the model. Displacement mechanisms which describe 2-phase flow of oil and water and the buildup of an oil bank in injection operations are programmed in the mathematical model. The streamline simulator was designed to solve fluid-flow problems in reservoirs which have irregular boundaries, arbitrary well pattern developments, and stratification of microstrata in which cross flow is considered negligible. Image well techniques are used to mathematically bound arbitrarilyifer or existence, ahead of the hydorfluoric acid front, of a ures which might control the distribution of uraniumacterized by a thermally activated process. he effect of various parameters, temperature, pressure, and steam percent in hydrogen feed. Fifteen experimental runs have been completed using NiMo as the main component of thThe Q/sub 2//sup +/ value obtained for /sup 200/Hg is in agreement with previous work,more » but that for /sup 202/Hg is not. The results obtained are compared with the predictions of various nuclear models, and the mass dependence of Q/sub 2//sup +/ in the region 182 < A < 206 is examined.« less
TL;DR: In this article, the equations governing non-steady isentropic conducting flows are reduced to an associated time-independent system, and solutions are then obtained in which the orthogonal trajectories to the fluid streamlines are ellipses or hyperbolae and the magnetic field lines are rectilinear.
TL;DR: In this article, it was shown that the large scale departures from the mean differential rotation represent nearly horizontal flow, and under certain assumptions deduce a pattern of streamlines for these motions from the doppler line of sight velocities.
Abstract: We show that, if the large scale departures from the mean differential rotation, measured by Howard and Harvey, represent nearly horizontal flow, we may under certain assumptions deduce a pattern of streamlines for these motions from the doppler line of sight velocities. This can be done with data from a single day, without having to construct the total flow from different projections of the (assumed) same velocity vectors seen on different days. Mathematically the method involves integrating a single first order inhomogeneous partial differential equation along a set of characteristic curves which are circles concentric with the center of the solar disk.
TL;DR: In this article, the authors considered the case when the fluid exhausts into a semispace f~om two-dimensional channels located in a wall, the flow in the channels being a developed Poiseuille flow, and the method of linearization with respect to the uniform flow at the entrance sections was used to obtain an analytic solution which is valid quite far downstream.
Abstract: The nume~ricaI solution of tire problem of period jet flow was considered in [!] for the case of uniform velocity at the entrance sections~ In the present paper we consider the case when the fluid exhausts into a semispace f~om two-dimensional channels located in a wall, the flow in the channels being a developed Poiseuille flow. The method of linearization with respect to the uniform flow at hnfinity is used to obtain an analytic solution which is valid quite far downstream~ The Navier-Stekes equations are solved numerically in the entrance segment. The effect of different specification of the boundary conditions downstream and the region of their influence was studied numerically. It is shown that the use of the resulting asymptotic soiution to close the Na~ier-Smkes equations downstream permits a reduction of the region of the n m e r i c a l solution of the problem without leading to computational boundary effects which distort the solution. Considered are the influences of the Reynolds number R and the relative channel width a on the flow hydrodynamic characteristics: streamlines, velocity profiles, pressure distribur/on0 and hydrodynami stabilization length. w We consider the two-dimensional steady case of discharge of a viscous incompressible fluid from channels of width 2d, spaced at a distance of 2H in a periodic pattern in a solid wall into the semispace bounded by the wall (Fig. t ) . We select a coordinate system with the y* axis along the wall, and x* along the eentorline of one of the channels. We introduce the dimensionless variables
TL;DR: In this article, a numerical solution of the Navier-Stokes equations for the flow in a duct between parallel plates in the presence of a diaphragm with an orifice at Reynolds number Re=1800 is presented.
Abstract: A numerical solution of the two — dimensional Navier — Stokes equations for the flow in a duct between parallel plates in the presence of a diaphragm with an orifice at Reynolds number Re=1800 is presented. The plots of the resulting streamlines are illustrated and the computed discharge coefficient is compared with the experimental results.
01 Dec 1971
TL;DR: In this article, a general review of different cascade losses is presented with emphasis on the secondary flow, and an analytical analysis utilizing the Squire and Winter secondary flow analysis along with the triangle model for end wall boundary layer proposed by Taylor is detailed in an attempt to show the behavior of streamlines near the end wall.
Abstract: : A general review of different cascade losses is presented with emphasis on the secondary flow. An analytical analysis utilizing the Squire and Winter secondary flow analysis along with the triangle model for end wall boundary layer proposed by Taylor is detailed in an attempt to show the behavior of streamlines near the end wall. (Author)
Journal Article•
TL;DR: A simplified method of calculating turbulent boundary layer development on ship hulls is described in this article, which takes account of convergence or divergence of the external flow streamlines but neglects boundary layer crossflow.
Abstract: A simplified method of calculating turbulent boundary layer development on ship hulls is described. It takes account of convergence or divergence of the external flow streamlines but neglects boundary layer crossflow. Results in fair agreement with experiment are obtained.
01 Jan 1971
TL;DR: In this article, the authors developed and defined methods for obtaining numerical solutions to three-dimensional, free surface, inviscid, incompressible fluid flows and 3-dimensional free surface Darcian flow in porous media.
Abstract: Methods are developed and defined for obtaining numerical solutions to three-dimensional, free surface, inviscid, incompressible fluid flows and three-dimensional free surface Darcian flow in porous media. Since those boundaries consisting of free surface -are unknown a priori, a solution to the space boundary value problem resulting from a formulation in the physical space is very difficult, if not impossible, to obtain. Consequently, the methods described herein are based on a formulation in a space defined by a potential function and two mutually orthogonal stream surfaces whose intersections define the streamlines of the flow. In this space the positions of free surfaces are known. The formulation considers the magnitudes of the cartesian coordinates x, y, and z as the dependent variables. The applicability of the methods are demonstrated by implementing them in a computer program and by obtaining solutions to four problems with slightly different geometries of three-dimensional Darcian seepage flow of water through a dam with a drain over only a portion of the toe. Isometric drawing of the space flownets display the results from these solutions. Also a number of regular flownets are given which were constructed by projecting the points of intersection of the two stream surfaces and/or equipotential surfaces onto horizontal or vertical planes.
TL;DR: In this article, Frankl constructed an example of plane-parallel transonic flow with a normal shock terminating within the flow, and this example was extended by Biibosunov to obtain a curved shock.
Abstract: In [1], for the case in which the exact Chaplygin equation of motion is replaced by the Tricomi equation, Frankl constructed an example of plane-parallel transonic flow with a normal shock terminating within the flow (later this example was extended by Biibosunov to obtain a curved shock [2]). This flow is an analog of the point vortex flow and has concentric circles as streamlines, and a unique dependence of the velocity vector on the Cartesian coordinates is provided everywhere. In the present paper this example is extended to the case of the Chaplygin equation, and the shock is considered to be normal.