Showing papers on "Streamlines, streaklines, and pathlines published in 1970"

Model study of plasmapause motion

Abstract: The ambient plasma in the equatorial plane is predominantly subject to the E×B drift. By approximating the earth's magnetic field by a dipole, characteristic steady state streamlines in the equatorial plane are determined, assuming the interaction between the solar wind and the magnetosphere is characterized by a constant electric field directed from dawn to dusk in the equatorial plane. The steady state plasmapause corresponds to the stagnation streamline in this flow. If the magnitude of the dawn-dusk field is suddenly increased, the plasmasphere bulge moves toward the sun. By suddenly decreasing the magnitude of this field, the bulge can be made to corotate with the earth. The model computations indicate that the spatial configuration of the plasmapause can be very complex, especially near the bulge, because its position depends upon the past history of the magnetosphere.

Natural convection in enclosed porous media with rectangular boundaries

Abstract: Numerical methods are used to solve the field equations for heat transfer in a porous medium filled with gas and bounded by plane rectangular surfaces at different temperatures. The results are presented in terms of theoretical streamlines and isotherms. From these the relative increases in heat transfer rate, corresponding to natural convection, are obtained as functions of 3- dimensionless parameters: the Darcy number Da, the Rayleigh number Ra, and a geometric aspect ratio L/D. A possible correlation using the lumped parameter Da Ra is proposed for Da Ra greater than about 40. (33 refs.)

The flow of a tubular film. Part 1. Formal mathematical representation

Abstract: An expansion scheme is developed to describe the steady axisymmetric flow of a thin tubular liquid film of varying radius; the necessary small parameter is provided by the ratio between the characteristic film thickness and the characteristic tube radius. The co-ordinate system used is an orthogonal one based on the fluid interface and the fluid streamlines. The differential equations that arise thus treat the metric as an unknown set of variables. The method is restricted to situations dominated by viscous forces. Reference is made to numerical solutions that have been obtained in connexion with an industrial polymer-film-blowing process.

Numerical study of steady flow past spheroids

Abstract: Numerical methods have been used to investigate the steady incompressible flow past oblate and prolate spheroids for Reynolds numbers up to 100. The ratio of minor to major axis of the spheroids investigated were 0·9, 0·5 and 0·2, together with 1·0, which represents the limiting case of a sphere. The pressure distribution and the skin and form drag coefficients were numerically evaluated for the various Reynolds numbers. Streamlines, equi-vorticity lines and equivelocity lines are presented and show in detail the flow characteristics.

A wake source model for bluff body potential flow

Abstract: A theory is presented for two-dimensional incompressible potential flow external to a symmetrical bluff body and its wake. The desired flow-separation points are made the critical points of a conformal transformation to a complex plane in which surface sources in the wake create stagnation conditions at the critical points. The stagnation streamlines then transform to tangential separation streamlines in the physical plane, with separation at the desired pressure. The position and strength of the sources are determined by the requirements of separation position and pressure coefficient. The flow inside the separation streamlines is ignored and base pressure is assumed constant at the separation value. Features of the theoretical model include a finite wake width, a pressure distribution on the separation streamlines decreasing asymptotically towards the free stream value at infinity and a simple analytic expression for the pressure distribution on the body. Comparisons of the theory with experimental data and with other theories are presented for the normal plate, the circular cylinder, the 90° wedge, and the elliptical cylinder. Although simpler to apply than the other theories, the present theory produces at least as good agreement with the experimental data.

On the stability of two-dimensional stagnation flow

Abstract: The paper examines the stability of the uniform flow which approaches a two-dimensional stagnation region formed when a cylinder or a two-dimensional blunt body of finite curvature is immersed in a crossflow. It is shown that such a flow is unstable with respect to three-dimensional disturbances. This conclusion is reached on the basis of a mathematical analysis of a simplified form of the disturbance equation for the stream-wise component of the vorticity vector. The ultimate, or stable, flow pattern is governed by a singular Sturm–Liouville problem whose solution possesses a single eigenvalue. The resulting flow is one in which a regularly distributed system of counter-rotating vortices is super-imposed on the basic, Hiemenz-like pattern of streamlines. The spacing of the vortices is a unique function of the characteristics of the flow, and a theoretical estimate for it agrees well with experimental results. The analysis is extended heuristically to include the effect of free-stream turbulence on the spacing.The problem is similar to the classical Gortler–Hammerlin study of the stability of stagnation flow against an infinite flat plate, which revealed the existence of a spectrum of eigenvalues for the disturbance equation. The present analysis yields the same result when an infinite radius of curvature is assumed for the blunt body.

Low Reynolds number shear flow past a rotating circular cylinder. Part 2. Heat transfer

Abstract: Heat transfer from a cylinder placed symmetrically in a constant shear field is considered experimentally for low values of the shear Reynolds number, but for Peclet numbers Pe as large as 2000. With the cylinder held stationary, the experimentally obtained Nusselt number Nu is found to be in excellent agreement with the theoretically derived asymptotic expression, , for Peclet numbers in excess of 100. In contrast, with the cylinder rotating at a speed corresponding to zero torque, the Nusselt number becomes effectively independent of the Peclet number for Pe > 70. This surprising behaviour, predicted theoretically by Frankel & Acrivos (1968), results from the presence of a region consisting entirely of closed streamlines which surrounds the freely rotating cylinder.

A Theoretical Study of the Flow of Blood in a Capillary with Permeable Wall

Abstract: A hydrodynamical theory of the steady slow motion of blood through a capillary with a permeable wall is presented. It is assumed that the exchange of fluid across the capillary wall obeys Starling's hypothesis, that is, the rate of flow per unit area of the wall surface is proportional to the difference between the pressure of the fluid within and outside of the capillary. It is further assumed that the rate of flow across the capillary wall is very small. Blood is regarded as a homogeneous Newtonian fluid. The expressions for the velocity and pressure distributions within the tube and the volume of the fluid flowing per unit time across a cross section of the tube are obtained. In order to see the motion of the fluid particles, the streamlines are also obtained. Discussions are made from physiological point of view.

Fluid Travel Time between a Recharging and Discharging Well Pair in an Aquifer Having a Uniform Regional Flow Field

Abstract: Equations describing steady state flow between a recharging-discharging pair of wells in a confined aquifer having a uniform regional flow field have been used to obtain a computer solution for the travel time of fluid along streamlines connecting the two wells. The time required for a contaminant or a tracer material to travel from the recharging well to the discharging well, and the timewise variation in concentration of the contaminant can be read directly from generalized plots of the computer solution.

numerical investigation of free convection between two vertical coaxial cylinders

Abstract: Free convection between two vertical coaxial cylinders was studied by solving the governing transport equations as an initial-value problem. The coupled, nonlinear, partial differential equations were converted into a set of difference equations by use of an alternating-direction implicit finite-difference numerical scheme. Twenty-four different combinations of Prandtl and Grashof numbers, and height to annular spacing ratios were used to characterize the problem. The results are presented primarily in the form of contour maps for the steady-state isotherms and streamlines. For Rayleigh numbers greater than 5 × 103, a fully developed boundary-layer flow was found to exist in the cavity. The interior region of the annulus was found to be thermally stratified and to possess a nearly uniform vertical temperature gradient, with a unicellular flow pattern being generated. With Rayleigh numbers of 5 × 104 and greater, it was found that the flow patterns could not be properly described with a grid spacing of 1/10. The variation of the steady-state mean Nusselt number with Prandtl and Rayleigh numbers and with geometric ratios was also investigated.

The slow stationary flow of a micropolar liquid past a sphere

Abstract: The paper is concerned with the slow stationary flow of a micropolar incompressible fluid past a sphere. Adopting the Stokesian approach of neglecting the inertial terms in the momentum equation and the bilinear terms in the balance of first stress moments, the equations are integrated and the flow parameters determined. The drag on the sphere is seen to be more in the present case than that in the case of non-polar fluids. It is found that in spite of the couple stress in the fluid, there is no resultant action by it on the sphere. Numerical work shows that the streamlines in the polar case have greater deflection towards the sphere than in the non-polar (or classical) case.

A numerical solution of unsteady flow in a two-dimensional square cavity

Abstract: Two dimensional unsteady fluid flow in square cavity numerically analyzed from continuity and Navier-Stokes equations and recorded as computer-generated motion picture

Perturbed Two‐Phase Cylindrical Type Flows

Abstract: The flow of an ideal fluid, containing small spherical particles, past a cylinder and a flat plate of finite width standing normal to the stream, is treated by the method of small perturbations. The perturbed equations for arbitrary initial particle density k0 are difficult to solve, even numerically. When the further assumption of small k0 is made, the problem is simplified considerably. For this case the nonlinear equation governing the particle streamlines is given in differential form. The equation governing the particle density distribution is solved by the method of characteristics and the result given in integral form. The Runge–Kutta method is used to obtain numerical solutions and the results are presented graphically. Conformal mapping and analysis are used to find the particle streamlines and density distribution k for the flow past a flat plate of finite width. For both bodies a particle‐free zone exists, whose size depends only on the particle Stokes' number, and in all cases the particle den...

An Actuator-Disc Analysis of Helicopter Wake Geometry and the Corresponding Blade Response

Abstract: : It is assumed that a helicopter rotor in forward flight can be represented by a flat plate. Expressions are developed relating the pressure field to the steady aerodynamic thrust and moment and the time-dependent flapping moment. This pressure field satisfies the zero pressure condition at the center and edge of the disc, the first and second harmonic variation in lift, and Laplace's equation. A computer program was written to calculate the velocity field and streamlines. Two sample cases corresponding to high- and low- speed conditions for the UH-1 rotor were chosen for computation. Both cases showed the tip-vortex phenomenon. In order to examine the sensitivity of blade load calculations to wake geometry, an existing airloads program was modified to accept the computed wake geometry. A comparison of results of this modified program with experimental data indicated that the effect of distorted wake is greater at low advance ratios than at high advance ratios. The reduced sensitivity at high advance ratios may be due to the wake being blown farther behind the rotor and/or the predominance of other aeroelastic parameters.

Convection in a mantle with variable viscosity

Abstract: Studies are made on typical features of convection current in a thin viscous layer on a deep layer of high viscosity. The streamlines in this case are concentrated but not closed in the upper thin layer. The horizontal velocity is one sign in the upper layer and the other sign in the lower. The horizontal mass flux in the upper layer is balanced by the counter-horizontal mass flux in the lower layer. The aspect ratio of the critical perturbation, referred to the whole layer thickness, is not so different from that in the homogeneous layer case. The aspect ratio, referred to the thickness of the thin upper layer in which the current is concentrated, is large, about 30 in a case studied in the present paper. The result will give a theoretical justification for the existence of very flat convection cells supposed to exist in the mantle. The free surface of the fluid is low (high) where the temperature is lower (higher) and the vertical velocity is downward (upward). This may explain the formations of guyots in the Pacific. A quantitative check of this idea and estimations of physical parameters involved in the problem are made.

Current vortices in superconducting films at the surface parallel critical field

Abstract: An idealized superconducting film in a homogeneous magnetic field parallel to the surface is considered in the range of validity of the linearized Ginzburg-Landau equation. The invoking of a simple symmetry principle leads directly to the existence of current vortices (flux tubes) for certain thicknesses and field strengths. Streamlines of the supercurrent for numerical solutions of the equations are shown.

A time dependent solution for the blunt body flow of a chemically reacting gas mixture

Abstract: In this paper, a numerical method for determining the inviscid, hypersonic flow of chemically reacting gases about blunt bodies is described. This numerical method solves the direct problem, accurately and efficiently. The steady state solution is found by solving a mixed set of steady state and time dependent equations. In this method, the governing equations are divided into two groups, according to their characteristics, and solved in an iterative cycle. The solution of the transient group, which governs the shock layer flow and pressure distribution, is found using a time dependent technique. The asymptotic solution to the time dependent equations defines the flow pattern and post shock initial conditions to be used in the steady state group. In the steady state group, which governs the state of the shock layer fluid (temperature and composition), the energy and specie conservation equations are integrated along streamlines using an unconditionally stable implicit scheme. The overall process is iterated until the differences between two successive cycles in both groups differ by less than certain prescribed tolerances. The converged solution satisfies the complete set of steady flow equations, and is, therefore, a solution to the problem. The me thod is ideally su i ted for reacting flows because in t e rpo la t ions on functions having large gradients are eliminated, Sample results for three flight conditions are presented and comparisons are made with the results of other investigators. The method is demonstrated to be readily adaptable to a variety of body shapes and chemical models, Complete solutions can be obtained in a few minutes on the computer for complicated chemical models over a complete range of flight conditions.

The Combination Of A Random Walk MethodAnd A Hydrodynamic Model For TheSimulation Of Dispersion Of Dissolved MatterIn Water

Abstract: A three-dimensional particle model with random walk has been applied to simulate the dispersion of dissolved matter in water. The particle model uses flow information obtained with a hydrodynamic model. This flow information is only available at discrete grid points. The grid is curvilinear in the horizontal plane and uses the sigma-coordinate in the vertical. The advective part of the particle model reproduces closed streamlines in recirculation zones. A reflection principle at closed boundaries is given, which does not introduce an artificial diffusion.

Motions of a liquid in a pulsating bulb with application to problems of blood flow.

Abstract: Potential flows of the form ϕ=(ax2+by2+cz2)f(t) may be utilized to represent motions produced in pulsating bulbs. While the initial bulb shape may be arbitrary, sequential shapes are related by affine transformations. Two components appear in the distribution of pressure, one dependent on the instantaneous velocity and the other on the acceleration. For flows with stationary streamlines the inertial impedance is that of a simple mass, and is proportional to the first moment of the actual mass of fluid contained within the bulb. Examples treated are: (1) expanding and collapsing circular cylinders and (2) elliptical cylinders in which the perimeter is held constant.

Axisymmetric flow with heat addition to simulate base-burning

Abstract: A method of calculation is presented for determining the inviscid flow field with heat addition, that surrounds the recirculating bubble, in an axisymmetrie experiment with burning behind a blunt base. As in previous work, the streamlines are chosen and the mode of heat addition determined, although in the present paper it is the streamtube area that is prescribed rather than the streamlines themselves. A discussion is given of the relation to experiment, and of the efficiency of the process.

Computer System For Calculation Of Flow,Resistance And Propulsion Of A Ship At TheDesign Stage

Abstract: The computer system executable on personal computers enables determination of flow parameters of a ship with or without a propeller. The system is based on a potential solution of the threedimensional flow around the hull, taking into account the free water surface. The basis of solution is determination of the distribution of Rankine type singularities on the double hull surface discretized by a number of flat panels. After solving the linear boundary condition the system of ship generated waves is obtained through a transformation of the Bernoulli waves. This transformation is based on an original solution of the Green function for a single pressure pulse and equally original method of superposition of such solutions. The propeller is modelled by lifting surface theory and its interaction with the ship is taken into account by including propeller induced velocity in the boundary condition on the hull. The propeller loading is determined by evaluation of total resistance, thrust deduction and wake fraction using a procedure based on theoretical and empirical relations. The system enables determination of the total and wave resistance, wave profile on waterline, streamlines and pressure distribution on the hull surface, wave system on the free surface for a ship model moving with constant speed on calm water.

Study of the boundary layer on ship forms

Abstract: This paper presents a theoretical investigation of the development of the boundary layer about a ship. The outer flow conditions, including the streamlines and pressure distributions, are found from linearized, thin-ship theory using the method of Guilloton. Limearized, integral boundary-layer equations appropriate for three-dimensional turbulent flow are integrated numerically along the streamlines to determine the momentum thickness, the shape factor, and the angle of the boundary-layer flow to the outer flow. The results of computations for Series 60, block 0.60 and 0.80 are presented for various Froude numbers and ship lengths.

Some Inviscid “Cat's Eye” Flows

Abstract: Some inviscid flows with the combined shear and periodic disturbance characteristic of the Kelvin “eat's eye” pattern are presented. The solutions have constant vorticity in each region of closed streamlines, with discontinuities in vorticity (but not velocity) allowed across boundaries.

Conjugate Heat Transfer To A Laminar Confined Impinging Planar Jet

Abstract: A numerical analysis for fluid flow and conjugate convection/conduction heat transfer of a single confined air laminar slot jet on a discretely heated finite thickness plate has been performed. A highly non uniform grid has been set up for the resolution of the boundary layer. Streamlines and isotherms patterns at different heat source lengths and jet Reynolds numbers are presented. The local Nusselt number is nearly independent of the impinged plate thickness whereas it is affected by the heater length.

A general-relativistic collisionless plasma

Abstract: A nonrelativistic collisionless plasma model is generalized to the general-relativistic domain By imposing sufficient restrictions and making use of several integrals, the coupled Einstein-Maxwell-Euler equations are reduced to six coupled, ordinary differential equations which may be solved numerically The tangents to the null geodesics are exhibited as functions of the metric-tensor components The normals to the characteristic surfaces for magnetohydrodynamic waves are also exhibited The latter surfaces turn out to coincide with the surfaces generated by the streamlines A spacelike Killing vector, normal to the streamlines is also shown to exist Finally, the Minkowski-space version of the model is considered and some explicit solutions are obtained, including a solution to a Boltzmann equation

Analytical And Numerical Model For A NozzleParticle Collector

Abstract: The objective of this paper is to present an analytical and numerical model for the fluid streamlines and particle trajectories inside a Particle Nozzle Collector. This work is part of a main research project that is being developed by the Technology Center of the Federal University of Alagoas (Brazil). The final objective of this research is the design and the construction of a solid particle Nozzle Collector. To this end, it is necessary to simulate mathematically the pathlines of those particles collected from the atmosphere, so that one can relate the collector's efficiency taking into account the various physical and geometrical parameters, such as diameter, velocity, inertia, concentration, etc. This first part of the research deals with streamlines of the fluid flow, where a methodology was developed using the complex variable analysis and numerical methods to obtain the particle trajectories, for a non-transient and two dimensional flow. Results are obtained taking the inertial parameter as the main cause for the particle collection.

Some exact solutions of stationary gas flows in a perpendicular magnetic field

Abstract: The plane flow of a perfectly conducting gas subject to a perpendicular magnetic field is considered. Ladikov [1] has solved this problem as a special case of the more general solution for a specific condition. It is shown that, following the method of [2], this problem may be reduced to the determination of the unknown function χ which satisfies a partial differential equation. Since the equation for χ is very complex, we have considered only two interesting cases, namely: 1) when the motion is irrotational, and 2) when the pressure is constant along the streamlines.

A Mean Value Theorem in Pore Pressure Evaluation by the Method of Images

Abstract: It is shown that mean pore pressure measured transversally through a rectangular domain in which groundwater flow is taking place from front to rear, the side boundaries being themselves streamlines, varies linearly from one sink (or source) to another provided such sinks or sources are located on the centerline of the domain, midway between the side faces. The computation of the mean pore pressure at any section is easily done. The specific application is to uplift evaluation in concrete dams, but the theorem applies to any problem governed by the Laplace theorem.