Showing papers on "Streamlines, streaklines, and pathlines published in 1969"

An Experimental Investigation of the Influence of Speed and Scale on the Strain-Rate in a Zone of Intense Plastic Deformation

Abstract: Experiments are described in which an explosive quick-stop device and printed grids (0.002 in square) were used to measure the deformation (streamlines of flow) in the zone of intense shear in which the removed chip is formed in orthogonal machining. A method is given for calculating the strain-rate from the experimental streamlines and it is shown that both the maximum and mean values of the maximum shear strain-rate in this zone are directly proportional to speed (shear velocity) and inversely proportional to scale (depth of cut).

Spherical cap bubbles with laminar wakes

Abstract: The steady rise of a given amount of gas in an infinite liquid under the action of buoyancy forces is examined. The shape of the bubble is that of a spherical cap. Behind the bubble there is a region of closed streamlines where the flow is assumed to be steady and rotational. The predicted velocity and geometry of the cap agree well with observation for a limited range of values of the Reynolds number.

A class of three-dimensional, optimum hypersonic wings.

Abstract: A limiting case of hypersonic flow is considered in which Mm —> °o • the flow deflections are small so that hypersonic small-disturbance theory applies. Within this framework there are various, known, exact solutions for flow past axisymmetric bodies. These flows are those for which the shock shape follows a power law rs '~ x*. The idea used in this paper is to construct the compression side of a lifting wing from the known streamlines in the flow behind the power-law shock wave. By considering families of such wings an optimum problem is considered, namely, to find the wing with given lift which produces a minimum wave resistance. The optimum problem is solved by variatioiial methods. Numerical results are are obtained for a range of n from ^ to 10, with y = 1.4.

On steady recirculating flows

Abstract: Integral constraints are derived for steady recirculating flows of nearly incompressible fluids, arising from the action of a small amount of viscosity and heat conduction. These constraints are then combined with the inviscid nondiffusive incompressible flow equations to show that two-dimensional flows containing closed nested streamlines, or three-dimensional flows with closed nested stream surfaces, are isothermal. In the former case it is shown that the vorticity is constant, and in the latter case there is an analogous result when the flow is axially symmetric and confined to axial planes. For a circular cell free convection problem, the interior temperature and vorticity are determined from the boundary conditions by an approximate integration of the boundary layer equations.

Programs for Computation of Velocities and Streamlines on a Blade-to-Blade Surface of a Turbomachine

Abstract: This paper describes Fortran programs that give the solution to the two-dimensional, subsonic, nonviscous flow problem on a blade-to-blade surface of revolution of a turbomachine. Flow may be axial, radial, or mixed. There may be a change in stream channel thickness in the through-flow direction. Either single, tandem, or slotted blades may be handled as well as blade rows with splitter vanes. Also, small regions may be magnified to give more detail where desired, such as around a leading or trailing edge or through a slot. The method is based on a finite difference solution of the stream function equations. Numerical examples are shown to illustrate the type of blades which can be analyzed, and to show results which can be obtained. Results are compared with experimental data.Copyright © 1969 by ASME

Study on Flow Characteristics in Right-Angled Pipe Fittings : 1st Report, On Case of Water Flow

Abstract: The flow characteristics of water through right-angled pipe fittings were studied by theoretical and experimental method. By means of the theory of two-dimensional potential flow, streamlines and pressure distributions along the walls of right-angled branching canals, in which the flow separated at the branch corner, were evaluated and compared with the experimental results. Both results coincided very well. From the calculated and experimental results, the mechanisms of the pressure loss of right-angled pipe fittings were analyzed. The pressure loss in the main flow was equivalent to the pressure loss of a sudden enlargement and that in the branch flow to the sum of the pressure loss of a sudden contraction and a sudden enlargement.

Stream channel concept applied to water flood performance calculations for multi-well, multi-zone three component cases

Abstract: The Higgins-Leighton technique for estimating waterflood performance was expanded to include the calculation of fluid production and injection for a multi-well, multi-zone system with asymmetrical drainage areas. This 2-dimensional, analytical method is based on the computer solution of streamlines, shape factors, waterflood performance by channels, and well-zone-field production combinations. The flow regime for each injector-producer pair in the system is represented by a series of channels whose sides are bounded by streamlines. Each channel may have a unique value for porosity, water saturation, and permeability. The channels are divided into equal volume cells to permit approximation of Buckley-Leverett linear displacement, with radial flow occurring through the cells adjacent to the producer and injector, and linear flow through the remaining cells. Initial conditions may include gas saturation for partial depletion. Streamline positions are generated from the solution of the flow potential in the Laplace equation for steady-state flow of 2 fluids of unit mobility in a uniform bed of constant porosity, water saturation, and absolute permeability.

Gas-treating apparatus

Abstract: A gas-treating apparatus for causing a nonhomogeneous stream of gases to flow through a casing and to become homogeneously mixed in a relatively short span of time and space A baffle extends laterally from the inner surface of the casing partially across the casing so that the outside streamlines of the forward flow do not attach readily to the inner surface of the casing The inner edge of the baffle defines an opening which has an area and shape that correspond with the cross-sectional area and shape of the casing

Gradually Varied Flow

Abstract: 2.1.1 General. Gradually varied flow is non-uniform flow in which the change of depth in the channel occurs but gradually, in the direction of flow. As a result the streamlines in any restricted locality can be considered straight and parallel and the resulting pressure distribution will therefore be hydrostatic. This restriction on the flow conditions also enables the Bernoulli equation to be used to evaluate the fluid energy. It is known that the Bernoulli equation, as well as the hydrostatic pressure distribution, breaks down when the streamlines become significantly curved. The criterion of streamline curvature will be used to distinguish between gradually varied flow and rapidly varied flow although in practice the exact point of distinction is indeterminate.

Electrohydrodynamic Oscillating Piston Problem

Abstract: The linearization method of Prandtl-Glauert type is applied to the electrohydrodynamic supersonic flow over a wavy wall. But it is found that it has no solutions satisfying the appropriate boundary conditions. Thus, a simplified model of an oscillating piston problem for this flow is considered. Numerical solutions of this problem are obtained as the initial value problem. The density distributions and the streamlines are calculated. It is found that sufficiently far from the piston, shocks are fully developed.

Surface conditions in the leeward region of a blunt cone at angle of attack in hypersonic flow.

Abstract: : The results of a wind tunnel investigation of separated flow over a blunt cone at angle of attack are presented. Surface pressure and oil flow data were obtained at a free stream Mach number of 14.2 and a free stream Reynolds number per foot of 650,000. A three-dimensional separation model for hypersonic flow over a blunt cone at angle of attack is proposed. The leeward side of the cone contains an initial region of attached, converging flow followed by a divergence into the separated region. The separated region does not originate from a singular point on the leeward meridian. In place of the expected singular point was a 'neck' through which fluid passed from the upstream attached flow region into the separated region. Symmetrical separation lines developed downstream of the neck as the surface streamlines diverged. There was no evidence of reverse flow or subsonic communication with the base region. The separated region was considered to have the characteristics of symmetrical supersonic helical vortices. (Author)

Magnetohydrodynamic flow past axisymmetric bodies with aligned magnetic field

Abstract: The steady axially symmetric flow of an inviscid incompressible fluid of small conductivity, embedded in a strong magnetic field, past fixed bodies is studied as a problem of finite perturbation. The magnetic Reynolds number is assumed small so that the magnetic field is unperturbed. The flow depends on the parameter β which is proportional to the product of conductivity and the square of the magnetic field strength. The flow past a semi‐infinite body and a sphere is numerically calculated and the solution indicates that the effect of the body is felt upstream. This upstream influence is convected by the flow and appears as a nondiffusive boundary layer and a wake for the semi‐infinite body and the sphere, respectively. The drag and the various boundary layer and wake characteristics decrease with β. The classical Bernoulli function H ( =p + 12 u2) decreases along streamlines and the pressure distribution on the surface of the bodies changes appreciably from the corresponding nonmagnetic value.

New features of the method of integral relations for the blunt body problem.

Abstract: The opposite trends were observed when the normal velocity component at the wall was taken negative. The skin friction is increased in the suction region, and since the tangential velocity components are again changed in different proportions, the slope of the limiting streamlines exhibits variations similar to those shown in Fig. 3. However, for the suction problem, the streamlines are deflected to the right of the unperturbed streamlines in Fig. 4. In other words, the effect of the suction on the streamline curvature may be compared with a reduction of the pressure gradient. This result suggested that suction can be used to reduce if not avoid the drift of the flow inside the boundary layer due to the pressure gradients. Such a flowfield has been analysed in Ref. 5: It was found that the magnitude of the normal velocity component at the wall had to be of the order of 50 so that the flow direction in the neighborhood of the wall would be .the same as that for the inviscid flow. It is clear that boundary-layer theory is inadequate to predict accurately the change of the flow characteristics inside the boundary layer for such extreme boundary conditions. It is, however, remarkable that the integration scheme did not break down as could have been expected. This shows the great flexibility of finite-difference solutions, which definitely will become a powerful tool for analysing three-dimensional boundary layers.

Numerical experiments on the formation of a tornado funnel under an intensifying vortex

Abstract: A tornado-like vortex, which intensifies with time, is imposed on the upper boundary of the boundary layer. The downward development of this axisymmetric vortex is studied by numerical integration of the flow equations. The contour of the visible tornado funnel has been computed for various times. The streamlines, the field of pressure deviation, and of the tangential velocity are presented for a time close to the steady state. The influence of a varying eddy diffusion coefficient is investigated.

Supersonic wake flow visualization

Abstract: Supersonic wake flow visualization, obtaining direct photographs of various smoke streamlines

Free Streamline Analysis of Two Dimensional Jet

Abstract: A technique of integration across free streamlines is developed to derive parametric equations describing characteristics of a jet discharging from a two-dimensional slot. The technique is illustrated by applying it to a case study which is an investigation of flow characteristics past a wedge shaped obstacle placed symmetrically near the end of channel. Equations are developed which relate the deflection angle of the free jet, width of the jet, and the boundary geometry. The equations are expressed in terms of the integration functions, which are presented graphically. The accuracy of the functions is verified for some cases using solutions obtained by direct integration.

FORTRAN 4 program calculates velocities and streamlines in a tandem blade turbomachine

Abstract: Computer program gives blade-to-blade solution of the two-dimensional, subsonic, compressible, nonviscous flow problem for a circular or straight infinite cascade of tandem or slotted turbomachine blades. The method of solution is based on the stream function using iterative solution of nonlinear finite-difference equations.