Showing papers on "Streamlines, streaklines, and pathlines published in 1981"

Relationship between blood flow direction and endothelial cell orientation at arterial branch sites in rabbits and mice.

Abstract: The orientation of endothelial cells near arterial branch sites has been compared with flow streamlines near the arterial wall. We detected cell orientation by examining cell impressions in vascular casts of rabbit and mouse arterial branch sites. Flow streamlines were assessed in glass models with flow parameters approximating mean in vivo values. At high Reynolds numbers (large arteries), secondary flow develop near branch sites, and this was reflected in the pattern of streamlines near the vessel wall. At symmetrical Y bifurcations, streamlines originating near the inner wall of the branches are directed toward the lateral wall; thus they appear to wind around the daughter vessels and merge on the lateral wall. A similar phenomenon was observed on a 90 degree side branch. When flow conditions in the Y bifurcation and side branch models approximated those at the iliac bifurcation and renal artery origin, respectively, the streamlines near the walls were almost identical to the patterns of endothelial cell orientation. At very low Reynolds numbers, no secondary flow phenomena occurred and streamlines followed branch geometry. This mimicked endothelial cell orientation in very small vessels. Hence the influence of mean blood flow on endothelial cell was well predicted by the model studies.

Streamlines in and around porous particles

Abstract: Streamlines around spherical porous particles are calculated when the undisrupted velocity of the surrounding fluid is either constant or a linear function of position. Settling particles are always drained by open streamlines. The particles in a simple shear flow are drained by open streamlines when the dimensionless radius is lower than a critical value. Results are discussed in terms of aggregation and disaggregation.

Visualization of Transition in the Flow over an Airfoil Using the Smoke-Wire Technique

Abstract: The smoke-wire technique was used for visualization of the transition of the free shear layer associated with the laminar separation bubble of a NACA 663-018 airfoil section at low Reynolds number (Rec = 50,000120,000). The smoke-wire technique allows for the introduction of fine smoke streaklines into the flowfield through the electrical resistive heating of a very fine wire which has been coated with oil and which is located upstream from the leading edge of the airfoil section. Streakline data were collected using both high speed still and motion picture photography.

Low-Prandtl-number convection in a layer heated from below

Abstract: Steady solutions in the form of two-dimensional rolls are obtained numerically for convection in a horizontal layer of a low-Prandtl-number fluid heated from below. Prandtl numbers in the range 0·001 [les ] P [les ] 0·71 are investigated for Rayleigh numbers between the critical value, R = 1708, and R = 20,000 in the case of rigid boundaries. The calculations reveal that the convective heat transport is relatively independent of the Prandtl number at Rayleigh numbers greater than a finite critical value R2 of the order of 5 × 103. At R = 10,000 the convective heat transport varies by only about 30% for Prandtl numbers in the range investigated. As the Rayleigh number is increased above the critical value R2, the streamlines of the convection flow become circular, independent of the horizontal wavelength as long as the latter is larger than or about equal to twice the height of the layer.

Turbulent convective velocities /broadband and wavenumber dependent/ in a plane jet

Abstract: An investigation into the magnitude and direction of the convective velocity in a plane air jet was performed. Convective velocities were obtained from cross-correlation measurements. They are defined as the ratio of the spacing between two hot-wire probes and the time delay between their signals to reach maximum correlation. These velocities were larger in magnitude than the local mean velocities for lateral distances greater than the half-width of the jet. Frequency analysis of the convective velocity indicates that the large-scale eddies move slower than the mean flow while the small scales move faster. Based on the convective velocity vector, broadband ‘convection lines’ were defined and found to point outward with respect to the streamlines for all values of y/b [Gt ] 0·5. Likewise, frequency investigation indicates that ‘convection lines’ point outward for all y/b [Lt ] 1·3 and then inward for larger values of y/b.

Analysis of longitudinal dispersion in unsaturated flow: 1. The analytical method

Abstract: An analytical technique is developed for the analysis of solute displacement in unsaturated soils involving one-, two-, or three-dimensional flow with fixed streamlines. The transport processes are separated into two parts: convection with the mean flow and dispersive mixing. The convective process is solved exactly using the method of characteristics; the effects of dispersion are incorporated in the analysis by using singular perturbation techniques. The analytical technique is illustrated by application to solute transport during steady and transient infiltration. It is observed that nonuniform moisture content in space results in stretching or contracting of a solute pulse as it travels through the soil, with or without the presence of dispersive mixing. For transient infiltration into initially moist unsaturated systems the rate of solute displacement is usually much smaller than the rate of movement of moisture change.

Singularities in three-dimensional turbulent boundary-layer calculations and separation phenomena

Abstract: The possibility of the occurrence of singularities in three-dimensional turbulent boundary-layer calculations in the direct mode is studied here. For this, the system of the entrainment and global momentum equations is used and it is shown that the system is totally hyperbolic. It is demonstrated that singularities can be formed by focusing of the wall streamlines which are also characteristic lines of the system of equations. It should be emphasized that such a wall streamline configuration should not be confused with the separation phenomenon. An analogy is established with the unsteady two-dimensional case for which singularities are also formed by focusing of the characteristic lines. The singularities are avoided in the inverse mode. The formulation and implementation of the method are presented and an application to an experimental case with separation is discussed.

Nongradient Theory for Oblique Turbulent Flames with Premixed Reactants

Abstract: An earlier analysis based on second-order closure and the Bray-Moss-Libby model of premixed combustion is applied to infinite, planar turbulent flames which are oblique to the oncoming reactants and which have undeflected mean streamlines. In such flames all three mechanisms, dilatation, Reynolds shear stresses, and mean pressure gradient, contribute to the balance of turbulent kinetic energy. Examination of the appropriate conservation equations in primitive form indicates that the intensity of the fluctuations of the velocity component normal to the flame and the mean flux of product in that direction are independent of obliquity. Thus earlier findings regarding countergradient diffusion and production of turbulence due to the mean pressure gradient prevail in oblique flames. The mean flux of product in the tangential direction and the intensity of the fluctuations of the velocity component in that direction are calculated. It is found that the mean streamlines of parcels of reactants and products are significantly different from one another and from the mean streamline. The intensities downstream of highly oblique turbulent flames are predicted to lead to two-dimension al turbulence in the plane containing the normal and tangential coordinates.

Axisymmetric Stokes flows due to a rotlet or stokeslet near a hole in a plane wall: filtration flows

Abstract: The axially symmetric Stokes-flow problems occurring when a point source, rotlet or stokeslet is situated along the axis through the centre of a circular hole in a solid plane wall are examined. Exact solutions of the governing equations are obtained in terms of toroidal coordinates and their use in modelling the flows caused by a small particle translating and rotating near to a filter pore is considered. First-order expressions are derived for the effects of the wall and hole upon the hydrodynamic force and torque on the particle for situations in which the particle dimensions are small in comparison with its distance from the solid portion of the plane wall. The resulting expressions apply to any centrally symmetric particle, not necessarily axisymmetric. Finally, expressions are derived for the motion of a neutrally buoyant sphere suspended in a flow through a hole. It is demonstrated that such a particle will generally migrate across the streamlines of the undisturbed flow - away from or towards the symmetry axis of the flow, according as the particle is approaching or receding from the hole. Such migratory motion may be of importance in the flow of suspensions through orifices and stenoses.

An exact solution for the slow flow of a general linear viscoelastic fluid through a slit

Abstract: An exact solution for the low Reynolds Number flow of an upper convected general linear viscoelastic fluid through a slit is presented. The solution, which is believed to be isolated, involves radial streamlines. Two of the more obvious possible further solutions for converging flow are shown to fail. A comparison with experimental results of stress-birefringence measurements shows a good qualitative agreement with a special case of the exact solution. The theoretical work of Strauss is examined. A particular case of his result is retrieved in a manner which gives new information about its general validity.

A finite element computer model of the hole pressure problem

Abstract: This paper extends some earlier work in which consideration was given to the flow of a second-order visco-elastic liquid through a channel composed of two parallel plates, one plate having a rectangular slot cut into it perpendicular to the flow direction. In the present work the problem is re-solved for the case of an implicit Oldroyd-type model and solutions obtained using a numerical finite element technique. Severe numerical convergence difficulties are encountered when the elasticitiy of the liquid is increased. The relationship between the ratio of the hole pressure to first normal-stress difference and the Reynolds number is investigated for both Newtonian and elastic liquids and the results compared with a simple analytical analysis of Tanner and Pipkin and with the second-order fluid results of the previous paper. It is found that the value of this ratio falls as the Reynolds number is increased from zero up to 10 but that the rate of decay is less than for the second-order liquid. However in the present work elasticity is found to have a significant effect even at small Reynolds numbers, so that the ratio can deviate quite considerably from the Tanner-Pipkin theoretical value of 0.25. Streamline patterns plotted for various flow conditions indicate that both inertia and elasticity bring about an asymmetry in the streamlines which dip into the hole, and in the vortex contained within the hole, but that the two factors work against one another so that it is possible for an elastic liquid to see a symmetric pattern for Reynolds numbers considerably beyond the range of the Tanner-Pipkin theory.

Fluid flow of ablated plasma from planar targets

Abstract: Using a novel diagnostic technique, the streamlines of the flow of plasma from a laser‐irradiated target are observed for the first time. Implications for far‐field ion measurements and similarity to a simple fluid flow are noted.

Approximate and exact numerical computation of supersonic flow over an airfoil

Abstract: An approximate solution is developed for two-dimensional, steady, inviscid supersonic flow over an airfoil. This approximation produces accurate results for a wide range of Mach numbers and airfoil thicknesses. It is used as the starting point for a rapidly convergent iterative numerical solution of the exact equations. A co-ordinate system consisting of the principal characteristics and streamlines is employed. Examples computed for a symmetric airfoil reveal several interesting features in the tail shock and the flow behind the airfoil.

Numerical Method For the Two-dimensional Freezing Problem Around a Horizontal Cylinder Encompassing a Density Inversion Point

Abstract: A numerical method for the two-dimensional freezing problem around a horizontal cylinder involving a maximum density point was presented. This problem offers a complex one involving the natural convection flow around the freezing front and the heat conduction inside it, and no exact analysis of it has been performed so far. The present numerical method utilizes the so-called boundary fixing method in which both the boundaries of body and freezing front are immobilized and it is applicable to general multi-dimensional moving boundary problems. Example calculations are made for steady freezing front shape, temperature distribution in solid phase, and also isotherms, streamlines, and Nusselt number distribution around the cylinder

Streamlines and path lines in peristaltic flow at high reynolds numbers

Abstract: An investigation is made on streamlines and path lines in a two-dimensional channel subjected to periodic changes in cross-sectional area. High Reynolds number flows are dealt with to bring out the possibilities of engineering application of fluid mixing by peristalsis. A potential flow analysis is developed on the basis of periodic source distributions located far away from the channel. A simplified approximate solution is derived and compared in good agreement with visual observations carried out at Reynolds numbers as high as 103. A condition which makes the approximate solution irrotational is presented. Under zero time-mean flow conditions, a fluid particle near the oscillating wall undergoes a net forward displacement, while the one away from the wall retrogrades, contrary to results at low Reynolds numbers. A distinction is found between the period of wall oscillation and the time required for a particle to complete its one cycle of trajectory.

Two-Dimensional Slow Viscous Flow Due to the Motion of Flat Plate over a Plane Wall

Abstract: Two-dimensional slow viscous flow due to sliding of a semiinfinite flat plate over a perpendicular plane wall at a distance is investigated on the basis of Stokes' approximation. Streamlines and pressure distributions are determined from exact formal expressions of the stream function and the pressure field obtained by use of the Wiener-Hopf technique. It is also found that the force on the plate increases logarithmically as the clearance diminishes. The case in which the flow is caused by a pressure difference between up- and down-stream infinity with the planes at rest is also considered.

Applications of the concept of generalized vorticity to space plasmas

Abstract: A reformulation of the momentum equation for electrons or ions in a collisionless plasma leads to an equation which describes the behavior of the plasma in terms of a generalized vorticity. This vorticity is both divergence-free and conserved along plasma flow streamlines. When the plasma has zero vorticity, a special relation is established which appears to have application to small scale magnetic features within both conventional space plasmas and superconductors.

Device for growing semiconductor at gas phase

Abstract: PURPOSE:To prevent grown layers from becoming nonuniform in the direction of gas flow, by rotating a heating jig, whereon wafers are set, on a plane parallel with the direction of gas flow. CONSTITUTION:A holder 2 is rotated at a speed about a half revolution per second by a magnet 7 centering a rotary shaft 6 on a plane parallel with the flow of gas. The direction of the rotation is reversed in every five seconds. A space with a uniform thickness of about 10cm is defined between the holder 2 and the lid 1 of a reaction furnace to prevent the gas from nonuiformly flowing. According to this constitution, the raw material gas is introduced at a speed ratio of 3:5:3 from three pipes 4 and flows along parallel streamlines and is discharged 5. As a result, wafers do not become different from each other due to the upstream and the downstream effects of the gas flow, while each wafer is not affected by the direction of the gas flow, and the thickness of grown layers and the distribution of impurity concentration are made uniform.

Solutions in Viscous Constantly-Inclined Magnetohydrodynamics

Abstract: Solutions are obtained for spiral flows with circular (constantly-inclined) magnetic lines and for circular flows with spiral magnetic lines. Furthermore, it is established that the only possible constantly-inclined flows with radial magnetic lines or radial streamlines are those in which the streamlines and magnetic lines are orthogonal.

Flow of a liquid with an anisotropic viscosity tensor: a skew initial orientation

Abstract: In this paper some idealized anisotropic fluids— the liquids D and F presented in [1]—are analysed in simple shearing flows and in channel flows The liquids, transversely isotropic initially, are here taken to have a uniform initial orientation in some arbitrary fixed direction in space The discussion therefore generalizes somewhat the analysis in [1] of the same flow situations when special initial orientations were taken (such as parallel to the streamlines) It is generally found that the flow is unsteady, that stresses are time-dependent, and that transverse isotropy does not persist This can be true even if the initial orientation differs only very slightly from a special orientation that would lead to steady, Newtonian behaviour It is found also that, in simple shearing flow, time-dependent lateral shear stresses can be induced; these stresses must be applied through the plates bounding the flow (in addition to the primary driving shear stress and appropriate normal stresses) if rectilinear flow is to be possible Such lateral shear stresses can also arise in pressure-driven channel flow This is showm to imply that, if longitudinal flow is assumed, the associated stress pattern is incompatible with the equations of motion: except with special initial orientations, rectilinear flow of these liquids in a straight-walled channel is not possible In the special cases where retilinear flow is possible, the velocity profile is not necessarily symmetric about the channel axis

The Nonlinear Flow Field Induced by a Point Force in the Presence of a Plane Wall

Abstract: A nonlinear solution is constructed representing the steady flow field generated by the continuous application of a constant point force of magnitude F$\_0$ in an incompressible fluid that is bounded by a fixed plane wall. The force is applied at a fixed distance from the wall, is perpendicular to the wall and directed towards it. The streamlines in a meridian section form closed loops which nest at a stagnation point and it is found that as F$\_0$ increases this stagnation point is displaced towards the wall. It is also found that as F$_0$ increases the total volume flow per unit force decreases.

A quasi-three-dimensional blade surface boundary layer analysis for rotating blade rows

Abstract: A quasi-three-dimensional approximation has been developed for a blade boundary layer which involves the calculation of the effect of nonzero pressure gradients, turbulent flow, and blade twist, but includes only a simple coupling between streamlines. The resulting set of equations is solved using Keller's box scheme. The solution scheme is checked against available incompressible flow solutions and then applied to a NASA low aspect ratio transonic compressor stage for which extensive experimental and computational data are available. It is found that the three-dimensional boundary layer separates significantly sooner and has a much larger influence on rotor performance than would be expected from a two-dimensional analysis.

Subsonic Cascade Flow Analysis by a Finite Element Method

Abstract: A finite element method was developed for analysing steady two-dimensional inviscid subsonic flows through an arbitrary shaped cascade on an arbitrary revolutional surface with a varying channel height. The flows were assumed to be homentropic and homorothalpic. In the method Poisson's equation for stream function is calculated repeatedly by minimization of the functional using linear triangular elements. In order to in crease the accuracy and save the computer time, the treatments of the periodic condition and the kutta condition were improved reasonably and the calculation of velocity was performed by the least square method. As numerical examples, flows through a compressor rotor cascade on a plane were computed and the streamlines, the Mach number contours, pressure contours, and the pressure distributions on the blade surface were obtained. These results agreed well with the results of experiment and the method of streamlines.