Showing papers on "Streamlines, streaklines, and pathlines published in 1976"

Two-dimensional turbulence above topography

Abstract: In a turbulent two-dimensional flow enstrophy systematically cascades to very small scales, at which it is dissipated. The kinetic energy, on the other hand, remains at large scales and the total kinetic energy is constant. Above random topography an initially turbulent flow tends to a steady state with streamlines parallel to contours of constant depth, anticyclonic around a bump. A numerical experiment verifies this prediction. In a closed basin on a beta-plane the solution with minimum enstrophy implies a westward flow in the interior, returning in narrow boundary layers to the north and south. This result is interpreted using a parameterization of the effects of the eddies on the large-scale flow. The numerical solution is in qualitative agreement, but corresponds to a minimum of a more complex measure of the total enstrophy than the usual quadratic integral.

Internal electrohydrodynamic instability and mixing of fluids with orthogonal field and conductivity gradients

Abstract: The interface between two miscible fluids which have identical mechanical properties but disparate electrical conductivities and are stressed by an equilibrium tangential electric field is studied experimentally and theoretically. A bulk-coupled electrohydrodynamic instability associated with the diffusive distribution of fluid conductivity at the interface is experimentally observed.The configuration is modelled using a layer of exponentially varying conductivity spliced on each surface to a constant-conductivity fluid half-space. Over-stable (propagating) modes are discovered and characterized in terms of the complex growth rate and fastest growing wavenumber, with the conductivity ratio and an inertia-viscosity time-constant ratio as parameters. In the low inertia limit, growth rates are governed by the electric-viscous time τ = η/eE2. Instability is found also with the layer of varying conductivity bounded by rigid equipotential walls. A physical mechanism leading to theoretically determined fluid streamlines in the form of propagating cells is described.At relatively high electric fields, large-scale mixing of the fluid components is observed. Photocell measurements of distributions of average fluid properties demonstrate evolution in time on a scale determined by τ.

Quantum mechanical streamlines. III. Idealized reactive atom–diatomic molecule collision

Abstract: An atom–diatomic molecule collision is simulated by considering an idealized potential energy surface which is a two‐dimensional duct with an adjustable potential in the corner region. This potential is symmetric with respect to an interchange of the x and y Cartesian coordinates. Explicit expressions for the wavefunctions are obtained which make use of this symmetry. Also analytical relations are obtained between the transmission and reflection coefficients and their phases. Quantum mechanical streamlines are computer graphed for a large number of energies and positive, negative, and zero values of the potential energy in the corner region. Special attention is given to the quantized vortices (surrounding wavefunction nodes) which appear in the streamlines. When only one energy channel is open, the streamlines are symmetric and the flux is antisymmetric. This occurs because the wavefunction is a linear combination (with complex coefficients) of two real solutions, one symmetric, the other antisymmetric. ...

Numerical simulation of waste movement in steady groundwater flow systems

Abstract: The finite element method based on a Galerkin technique is used to formulate the problem of simulating the two-dimensional transient movement of conservative or nonconservative wastes in a steady state saturated groundwater flow system. The convection-dispersion equation is solved in two ways: in the conventional Cartesian coordinate system and in a transformed coordinate system equivalent to the orthogonal curvilinear coordinate system of streamlines and normals to those lines. The two formulations produce identical results. A sensitivity analysis on the dispersion parameter ‘dispersivity’ is performed, establishing its importance in convection-dispersion problems. Examples involving the movement of nonconservative contaminants described by distribution coefficients and examples with variable input concentration are also given. The model can be applied to environmental problems related to groundwater contamination from waste disposal sites.

Quantum mechanical streamlines. IV. Collision of two spheres with square potential wells or barriers

Abstract: Quantum mechanical streamlines and probability density contours help in the understanding of collision dynamics by showing what happens during the collision. This is illustrated by considering the elastic scattering of two particles which interact with a spherically symmetric square potential, V (r) =0 when r≳a and V (r) =C when r

Magnetohydrodynamic flow due to the discharge of an electric current in a hemispherical container

Abstract: In this paper we consider the flow field induced in an incompressible viscous conducting fluid in a hemispherical bowl by a symmetric discharge of electric current from a point source at the centre of the plane end of the hemisphere. This plane end is a free surface. We construct an analytic solution for the slow viscous flow and a numeriacl solution for the nonlinear problem. The streamlines in an axial cross-section form two sets of closed loops, one on either side of the axis. Our computations indicate that, for a given fluid, when the discharged current reaches a certain magnitude the velocity field breaks down. This breakdown probably originates at the vertex of the hemispherical container.

A flow model for gas movement in spouted beds

Abstract: A two-region model of a spouted bed, postulating vertical plug flow of gas in the spout and dispersed plug flow along curved streamlines in the annulus, is proposed. The extent of axial dispersion is accounted for by a coefficient D which is an adjustable parameter of the model. Experimental support for the theory is provided by residence time-distribution data obtained by using helium gas as tracer, covering a wide range of conditions. Values of the coefficient D, determined from a comparison between predicted and observed RTD curves, are generally higher than those reported for packed beds but much smaller than those for fluidized beds.

A nonlinear finite-element analysis of wings in steady incompressible flows with wake roll-up

Abstract: The problem of lifting surfaces and complex aircraft configurations in steady incompressible flow is considered. For lifting surfaces the problem is formulated in terms of an integral equation relating the potential discontinuity on wing and wake to the normal derivative of the potential on the lifting surface. For complex configurations the problem is formulated in terms of an integral equation relating the potential to its normal derivative on the surface of the aircraft. 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 (or the potential discontinuity) and its normal derivative to be constant within each element. The wake geometry is obtained by 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.

A low speed self streamlining wind tunnel

Abstract: A two dimensional test section in a low speed wind tunnel is producing flow conditions free from wall interference. The test section has flexible top and bottom walls, and rigid sidewalls from which the models are mounted spanning the tunnel. All walls are unperforated, and the flexible walls are positioned by screw jacks. To eliminate wall interference, the wind tunnel itself supplies the information required in this streamlining process, when run with the model present. Measurements taken at the flexible walls are used by the tunnel computer to check wall contours. When the static pressure distribution in the test section along a contoured flexible wall matches that computed for an imaginary flow field passing over the outside of the same contour, the wall is a streamline in an infinite flow field and the test section flow is free from wall interference. A series of iterations brings the walls from straight to streamlines. Illustrative aerodynamic data is presented, taken on a bluff body and a lifting wing.

Linear shear flow past a porous particle

Abstract: Linear shear flow past a porous spherical particle is studied using a generalized boundary condition proposed by Jones. The torque on a porous sphere rotating in a quiescent fluid is calculated. Streamlines patterns are illustrated for the case of a particle freely suspended in a simple shear flow. These patterns are shown to differ significantly from those associated with an impermeable rigid sphere. Finally, an expression for the effective viscosity of a dilute suspension of porous spherical particles is obtained.

A computer-aided method for calculating the distributions of strain-rate and strain from an experimental flow field

Abstract: A method of calculating strain-rates and strains from an experimental flow field is developed using simple geometry with polynomials used to represent small segments of the experimental streamlines and the corresponding distance/time along streamline curves. The method is applied to an experimental flow field for plane strain extrusion obtained using printed grids (0.002 inch square), the input to the computer program being the co-ordinates of the grid intersection points and the punch velocity.

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.

Experimental and Theoretical Investigation of Flow Generated by an Array of Porous Tubes

Abstract: A novel scheme of introducing flow into an electric discharge laser (EDL) cavity has been developed and is described here. The flow, which is generated by a grid of parallel porous tubes, has beet studied experimentally and theoretically. Detailed measurements of the flow field structure using hot-wire anemometry have been carried out and some turbulence data obtained near the porous tubes. A theoretical model based on rotational inviscid flow near the porous tubes is developed. The vorticity distribution is chosen to satisfy both the mass flux and no slip conditions on the tube walls. The near field flow exhibits a wake downstream of the tubes. A vorticity diffusion model is introduced to render the flow uniform in the far field. Agreement is shown between experiment and theory.

Thermal Instabilities in Discharging Gas Reservoirs

Abstract: The flow structure in a discharging gas reservoir has been studied using schlieren cinematography. Effects due to discharge orientation, gas species, and vessel wall vibration have been observed. Initially, the internal flow structure has been found to be controlled by the mass sink, with streamlines going in approximate straight lines from the vessel wall to the exit orifice. At later time, free convection dominates and recirculation patterns are established. Discharge orientation can have a dramatic effect on the free convection flow field as well as on the growth and stability of the wall thermal diffusion layer. A jet-like structure (initiated at very early time and believed to be caused by wave effects) was observed to extend from the vessel wall diametrically opposite the exit orifice. When the discharge was parallel to but in the opposite direction of the gravitational vector, this jet-like structure was found to cause an instability in the lower wall diffusion layer. Vessel wall vibration resulted in a standing cellular acoustic wave pattern in the gas which, depending on discharge orientation, caused a violent instability. A model for temperature variation in the thermal diffusion layer is discussed and a numerical solution is given. Results of the predictedmore » thermal diffusion layer histories are compared to data. A discussion of vessel orientation effects on critical Rayleigh number is given.« less

A 2D partially-parabolic procedure for axial-flow turbomachinery cascades

Abstract: A general finite-difference procedure is presented for the calculation of steady, two-dimensional ‘partially-parabolic’ flows, with special reference to turbine cascade problems. It can be used for incompressible, subsonic, supersonic or transonic flows. It can be characterised as an ‘iterative space-marching’ method. The method is more economical in computer storage than time-marching procedures; and computer time is also low. The main distinguishing features of the method are: (a) use of a streamline coordinate system (b) one-dimensional storage for all variables except pressure (c) solution by repeated marching integration from upstream to downstream. The capabilities of the method are demonstrated by application to six different inviscid-flow problems. In each case, computed results are compared with the available analytical or experimental data. Good agreement is shown. The method is capable of including momentum transfer across streamlines by viscous effects; it can easily incorporate a two-equation turbulence model; and heat transfer can be simultaneously calculated.

Streakline flow visualization of discrete hole film cooling with holes inclined 30 deg to surface

Abstract: Film injection from three rows of discrete holes angled 30 deg to the surface in line with mainstream flow and spaced 5 diameters apart in a staggered array was visualized by using helium bubbles as tracer particles. Both the main stream and the film injectant were ambient air. Detailed streaklines showing the turbulent motion of the film mixing with the main stream were obtained by photographing small, neutrally buoyant helium-filled soap bubbles which followed the flow field. The ratio of boundary layer thickness to hole diameter and the Reynolds number were typical of gas turbine film cooling applications. The results showed the behavior of the film and its interaction with the main stream for a range of blowing rates and two initial boundary layer thicknesses.

Streakline flow visualization of discrete-hole film cooling with normal, slanted, and compound angle injection

Abstract: Film injection from discrete holes in a three-row, staggered array with five-diameter spacing was studied for three hole angles: (1) normal, (2) slanted 30 deg to the surface in the direction of the main stream, and (3) slanted 30 deg to the surface and 45 deg laterally to the main stream. The ratio of the boundary layer thickness-to-hole diameter and Reynolds number were typical of gas-turbine film-cooling applications. Detailed streaklines showing the turbulent motion of the injected air were obtained by photographing very small neutrally buoyant, helium-filled soap bubbles which follow the flow field.

Numerical computation of space shuttle heating and surface streamlines

Abstract: Exact inviscid flow-field 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. 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 flow-field predictions at wind-tunnel and nominal flight conditions are discussed.

Steady Plane Flows of Cosserat Fluids

Abstract: Martin’s method of studying steady plane flows of the incompressible viscous fluids is extended to Cosserat fluids. Basic equations to plane steady flows of a Cosserat fluid are recast in a suitable form by employing some results from differential geometry. Two illustrations of the new form of the equations, when the streamlines are straight or involutes of a curve, are also discussed.

Analysis and testing of two-dimensional vented Coanda ejectors with asymmetric variable area mixing sections

Abstract: The analysis of asymmetric, curved (Coanda) ejector flow has been completed using a finite difference technique and a quasi-orthogonal streamline coordinate system. The boundary layer type jet mixing analysis accounts for the effect of streamline curvature in pressure gradients normal to the streamlines and on eddy viscosities. The analysis assured perfect gases, free of pressure discontinuities and flow separation and treated three compound flows of supersonic and subsonic streams. Flow parameters and ejector performance were measured in a vented Coanda flow geometry for the verification of the computer analysis. A primary converging nozzle with a discharge geometry of 0.003175 m x 0.2032 m was supplied with 0.283 cu m/sec of air at about 241.3 KPa absolute stagnation pressure and 82 C stagnation temperature. One mixing section geometry was used with a 0.127 m constant radius Coanda surface. Eight tests were run at spacing between the Coanda surface and primary nozzle 0.01915 m and 0.318 m and at three angles of Coanda turning: 22.5 deg, 45.0 deg, and 75.0 deg. The wall static pressures, the loci of maximum stagnation pressures, and the stagnation pressure profiles agree well between analytical and experimental results.

Asymptotic solution of the equations for a three-dimensional multicomponent laminar boundary layer with large injection

Abstract: The asymptotic method of outer and inner expansions is used to analyze the flow of a multicomponent gas in a three-dimensional boundary layer on a smooth blunt body with large injection. Asymptotic expressions are derived for the friction coefficients, the heat and diffusion fluxes of the components on the surface of the body, and the velocity, temperature, and concentration profiles of the components across the layer of injected gases. It is shown that with large injection the limiting (bottom) streamlines on the surface of the body coincide in the first approximation with the vectorial lines of the pressure gradient.

Flow visualization in long neck Helmholtz resonators with grazing flow

Abstract: Both oscillating and steady flows were applied to a single plexiglass resonator cavity with colored dyes injected in both the orifice and grazing flow field to record the motion of the fluid. For oscillatory flow, the instantaneous dye streamlines were similar for both the short and long-neck orifices. The orifice flow blockage appears to be independent of orifice length for a fixed amplitude of flow oscillation and magnitude of the grazing flow. The steady flow dye studies showed that the acoustic and steady flow resistances do not necessarily correspond for long neck orifices.

Flow visualization in long neck Helmholtz resonators with grazing flow

Abstract: Both oscillating and steady flows were applied to a single plexiglass resonator cavity with colored dyes injected in both the orifice and grazing flow field to record the motion of the fluid. For oscillatory flow, the instantaneous dye streamlines were similar for both the short and long-neck orifices. The orifice flow blockage appears to be independent of orifice length for a fixed amplitude of flow oscillation and magnitude of the grazing flow. The steady flow dye studies showed that the acoustic and steady flow resistances do not necessarily correspond for long neck orifices.

Improved interactive calculation procedure for supersonic flows

Abstract: An interactive numerical procedure has been developed for supersonic viscous flows (either two-dimensional or axisymmetric configurations). The flow field is divided into two regions: (1) an inner region which is highly viscous and mostly subsonic, and (2) an outer region where the flow is supersonic and in which viscous effects are small, but not negligible. This paper presents a detailed description of: I. Outer Region - numerical solution obtained by applying the method of characteristics to a system of equations which includes viscous and conduction transport terms only normal to the streamlines; II. Inner Region - treated by a system of equations of the boundary-layer type that includes higher order effects, such as longitudinal and transverse curvature and normal pressure gradients (equations are coupled and solved simultaneously in physical coordinates, using an implicit finite-difference scheme); III. Interactive Procedure - in the interaction mode, the two regions are coupled iteratively along a matching line, where the Mach number is of the order of 1.2.

Supersonic Flow of Chemically Reacting Gas-Particle Mixtures. Volume II. RAMP - A Computer Code for Analysis of Chemically Reacting Gas-Particle Flows,

Abstract: A computer program written in conjunction with the numerical solution of the flow of chemically reacting gas-particle mixtures was documented. The solution to the set of governing equations was obtained by utilizing the method of characteristics. The equations cast in characteristic form were shown to be formally the same for ideal, frozen, chemical equilibrium and chemical non-equilibrium reacting gas mixtures. The characteristic directions for the gas-particle system are found to be the conventional gas Mach lines, the gas streamlines and the particle streamlines. The basic mesh construction for the flow solution is along streamlines and normals to the streamlines for axisymmetric or two-dimensional flow. The analysis gives detailed information of the supersonic flow and provides for a continuous solution of the nozzle and exhaust plume flow fields. Boundary conditions for the flow solution are either the nozzle wall or the exhaust plume boundary.

Entropy layer in the problem of hypersonic flow over thin blunt bodies which are close to two-dimensional

Abstract: In the problem of the hypersonic flow of a nonviscous thermally nonconducting gas over thin blunt bodies which are close to two-dimensional the solution is constructed in the entropy layer. The construction is achieved by a generalization of the method developed ia [1] in application to bodies close to two-dimensional. The use of an approximate model identifying the effect of the blunting on the gas with the effect of a concentrated force distributed over the edge is important in the construction. The solution is represented in the form of asymptotic expansions. The equations of the hypersonic theory of small perturbations, which is the null approximation in the process of construction of the solution in the form of a series in powers of a small parameter determined as the square of the relative thickness of the body or the relative width of the perturbed region, are obtained in the null approximation in this case. The surface of the blunt body proves to be singular for the null approximation, since the entropy function p/ϱx grows without limit as the surface is approached. The attempt to construct the succeeding approximations leads to strengthening of the singularity. This necessitates the use of the method of deformed coordinates (the PLG method). Basic to the latter is the removal of the singularity, which is not inherent to the exact solution of the problem, through asymptotic expansions with respect to a small parameter not only of the unknown variables, but also of the independent variables, with the subsequent determination of the deformation of the independient variables on the basis of the “quenching” of the singularity. Use of the PLG method allows one to construct a solution which is uniformly applicable in the entire stream, including the entropy layer. In practice, the construction of such a solution leads to the determination of the displacement of the streamlines near the surface of the body, as a result of which the singularity is “absorbed” by the body and the solution outside the body proves to be freed of the singularity. In the null approximation this displacement of the streamlines can be determined in closed form.

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

Abstract: Potential flows 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. The thickness of the pulsatile laminar boundary layer is found to be approximately on millimeter for conditions in the vicinity of the heart. Conditions for separation and turbulence differ from those in steady flow.