Showing papers on "Streamlines, streaklines, and pathlines published in 1988"

Eddies, streams, and convergence zones in turbulent flows

Abstract: Recent studies of turbulent shear flows have shown that many of their important kinematical and dynamical properties can be more clearly understood by describing the flows in terms of individual events or streamline patterns These events or flow regions are studied because they are associated with relatively large contributions to certain average properties of the flow, for example kinetic energy, Reynolds stress, or to particular processes in the flow, such as mixing and chemical reactions, which may be concentrated at locations where streamlines converge for fast chemical reactions (referred to as convergence or C regions), or in recirculating eddying regions for slow chemical reactions The aim of this project was to use the numerical simulations to develop suitable criteria for defining these eddying or vortical zones The C and streaming (S) zones were defined in order to define the whole flow field It is concluded that homogeneous and sheared turbulent flow fields are made up of characteristic flow zones: eddy, C, and S zones A set of objective criteria were found which describe regions in which the streamlines circulate, converge or diverge, and form high streams of high velocity flow

A descriptive theory of fingering during infiltration into layered soils

Abstract: An etiological hypothesis is offered to explain the occasional occurrence of fingering during infiltration and redistribution. The basic hypothesis is that a spatially distributed flow field, such as a planar wetting front, tends to constrict where the flow accelerates. This constriction may cause the flow field, if it is wide, to break into discrete, concentrated (partial volume) currents. Thus, initially parallel streamlines tend to converge and thereby form spatially separated currents when the velocity increases along the direction of flow. This can occur particularly during infiltration, at the transition from a less permeable toplayer to a more permeable sublayer, if the conductivity of the sublayer at the suction of water entry exceeds the flux through the toplayer. This simple hypothesis fits the criterion of Occam's razor and should lend itself to experimental testing.

Three‐dimensional centrifugal‐type instabilities in inviscid two‐dimensional flows

Abstract: In this paper the classical Rayleigh centrifugal instability theory is extended to general inviscid two‐dimensional flows. Sufficient conditions for centrifugal instability are that the streamlines be convex closed curves in some region of the flow, with the magnitude of the circulation decreasing outward. If these conditions are satisfied, a class of three‐dimensional short‐wave instabilities can be constructed, which are localized near the streamline on which the exponent of a certain matrix Floquet problem is maximized.

Natural convection in vertical enclosures containing simultaneously fluid and porous layers

Abstract: A numerical and experimental study is reported of natural convection in a vertical rectangular fluid enclosure that is partially filled with a fluid-saturated porous medium. Velocities, stresses, temperatures, and heat fluxes are assumed to be continuous across the fluid/porous-medium interface, and the conservation equations for the fluid and the porous regions are combined into a single set of equations for numerical solution. Thermocouples as well as a Mach-Zehnder interferometer are used to measure temperature distributions and infer fluid flow patterns within the fluid and the porous medium. For various test cells, porous-layer configurations and fluid-solid combinations, the model predictions show excellent agreement with the experimental measurements. It is found that the intensity of natural convection is always much stronger in the fluid regions, while the amount of fluid penetrating into the porous medium increases with increasing Darcy and Rayleigh numbers. The degree of penetration of fluid into the porous medium depends strongly on the porous-layer geometry and is less for a horizontal porous layer occupying the lower half of the test cell. If penetration takes place, the flow patterns in the fluid regions are significantly altered and the streamlines show cusps at the fluid/porous-medium interfaces. For a high effective-thermal-conductivity porous medium, natural convection in the medium is suppressed, while the isotherms bend sharply at the fluid/porous-medium interface.

Deformation around a rising diapir modeled by creeping flow past a sphere

Abstract: A new experimental method for determining the pattern of flow and three-dimensional progressive finite deformation of fluid elements in low Reynolds number (Re) viscous flow has been applied to creeping flow past a rigid sphere falling in a cylinder. This is intended as a model analogue of natural rock deformation associated with magmatic and solid-state diapirs rising through ductile crust. The kinematics of finite strain in such analogue experiments may give useful information on the development of natural structures. The experiment and a new method for quantifying the progressive finite deformation of fluid volumes in the transparent Newtonian test fluid used (SGM36) are discussed in detail. The progressive finite deformation of fluid flowing along specific streamlines passing the sphere appears to be complex and largely a function of the initial distance of fluid volumes and the particular streamlines which they follow from the flow axis. The progressive deformation history in the material surrounding a rising spherical diapir is characterized by progressive flattening and rotation of material above and progressive stretching below the sphere. The results compare favorably with the external strain pattern associated with post tectonic, mesozonal diapiric intrusions.

Resin Impregnation During the Manufacturing of Composite Materials Subject to Prescribed Injection Rate

Abstract: A numerical investigation into the area of resin impregnation during the manufacturing of composite materials is undertaken using a macroscopic flow through porous media ap proach. This study is specifically directed at modeling the resin transfer molding and resin film stacking advanced composite manufacturing processes. Quasi-steady state isothermal flow is assumed and a two-dimensional Darcy Law based stream function formulation is utilized. The resultant single governing equation for each quasi-steady timestep is solved along with proper boundary conditions using the method of boundary-fitted coordinate systems encompassing numerical grid generation. The resultant code is validated by a comparison with previously published results for flow into a rectangular mold with a point source and a line sink. Streamlines, pressure distributions, velocity profiles, and temporal liquid free surface positions are then presented for the flow into a mold of general irregular geometry encasing both isotropic and anis...

The Vortex Growth of a K.b.k.z. Fluid in An Abrupt Contraction

Abstract: A constitutive equation of the K.B.K.Z. type is used to describe the flow behavior of LDPE melts in abrupt contractions. The numerical algorithm is the finite element method based on a fixed mesh while the strain history is calculated along streamlines. It is shown that the calculations based on the K.B.K.Z. model do predict the occurrence of vortices at relatively low values of the Weissenberg number, which in general is not the case with other less realistic models.

Nonlinear streaming due to the oscillatory stretching of a sheet in a viscous fluid

Abstract: An elastic sheet is stretched back and forth in a viscous fluid. The problem is governed by a nondimensional parameterS which represents the relative magnitude of frequency to stretching rate. The Navier-Stokes equations are solved by matched asymptotic expansions for largeS. Due to nonlinearity there exists boundary layers ofO(S −1/2). The unsteady oscillatory flow contains both basic and higher harmonic oscillations. The induced steady streamlines show a saddle like flow which is different from that of acoustic streaming.

Hydromagnetic screw dynamo

Abstract: We solve the problem of magnetic field generation by a laminar flow of conducting fluid with helical (screw-like) streamlines for large magnetic Reynolds numbers, Rm. Asymptotic solutions are obtained with help of the singular perturbation theory. The generated field concentrates within cylindrical layers whose position, the magnetic field configuration and the growth rate are determined by the distribution of the angular, Ω, and longitudinal, Vz, velocities along the radius. The growth rate is proportional to Rm−½. When Ω and Vz are identically distributed along the radius, the asymptotic forms are of the WKB type; for different distributions, singular-layer asymptotics of the Prandtl type arise. The solutions are qualitatively different from those obtained for solid-body screw motion. The generation threshold strongly depends on the velocity profiles.

Wave transport of deep mantle material

Abstract: Fluid with a certain density and viscosity can rise by buoyant Poiseuille flow through a conduit1 within a second fluid of greater density and viscosity. Such conduits exhibit a rich behaviour characteristic of nonlinear systems, an aspect of which is the formation of solitary waves2,3. Here we present theoretical and experimental studies of these systems. Both approaches reveal that solitary waves trap material in a cell with closed streamlines and that the central streamline velocity is faster than the wave speed. Hence, parcels of deep material are transported directly upward over large distances. This is in contrast to the usual situation in which wave propagation through a medium causes only small displacement of fluid particles. Material in these parcels will be far less contaminated by diffusion from the surroundings than would be material in ordinary pipe flow. In addition, solitary waves are more efficient than buoyant spheres at conveying material upward. We suggest that such waves might exist in the Earth's mantle, conveying uncontaminated deep mantle material to the surface of the Earth.

Estimating position-time relationships in steady-state, one-dimensional growth zones

Abstract: Two methods are described for estimating position-time relationships (pathlines) in steady, one-dimensional growth zones. Pathlines can be used to provide a time base for spatial data in developmental studies. The methods apply within extension-only zones (zones of growth without cell division) and require data for cell-number densities, or cumulative cell numbers, or mean cell lengths, and for the overall elongation rate of an organ. The first method (“continuous-pathline” method) can be used to estimate spatial velocity fields within extension-only zones and pathlines can then be obtained by integration of the velocity data. This method is based on the continuity equation for cell-number densities. Pathlines can also be estimated using a simple graphical version of this method. The second method (“pathline-coordinate” method) is based on the approximation that a cell of mean length remains of mean length as it moves through the extension-only zone, and can be used to estimate the coordinates of wall pathlines at discrete intervals. The methods are illustrated using published data from studies of apical growth in Zea mays L. roots and of intercalary growth in Triticum aestivum L. leaves.

2-D transonic flow with energy supply by homogeneous condensation: onset condition and 2-D structure of steady Laval nozzle flow

Abstract: A generalized form of the similarity law for the condensation onset Mach number of water vapor in air in the transonic and supersonic range for water vapor flow in moist air is derived from well known basic approaches for supersonic nozzles. These statements are confirmed by extensive experimental investigations in Laval nozzles, as well as by results of other authors and computations on the basis of the Euler equation linked with the classical theory of nucleation and droplet growth. In this experimental research priority is given to the qualitative description of the two-dimensional condensation processes, and their effects in transonic flows in nozzles of different geometrical configuration (e. g. slightly or well curved). A quantitative discussion of 2-D structures in condensation regions requires the introduction of a characteristic angle along streamlines. It is then directly possible to describe the different types of compression disturbances in supersonic flows with heat addition.

The Linear Stability of Nonlinear Mountain Waves: Implications for the Understanding of Severe Downslope Windstorms

Abstract: Two-dimensional vertically propagating steady state internal waves launched by the flow of stratified unboundedfluid over an obstacle of finite height are subjected to a linear stability analysis. Solution of the associatednonseparable boundary value problem reveals an abrupt change in the stability of small amplitude fluctuationswhen the obstacle is sufficiently high to cause streamlines to locally overturn. In addition to the convedvemode which is expected on the basis of even the simplest physical reasoning, a deep resonant mode is alsodiscovered. This resonant mode is, in fact, the dominant form of instability at small supercnticality, and it istrapped in the cavity between the ground and the level of maximum steepening of the streamlines, in which itgrows at the expense of the kinetic energy of the sheared flow which constitutes the finite-amplitude mountainwave. This trapped mode is instrumental in the transition which takes place in breaking mountain waves thatresults in the Occurrence of ...

Numerical simulation studies of the planar entry flow of polymer melts

Abstract: This paper is concerned with the numerical simulation of planar entry flow using a penalty finite element method and the comparison of predictions with flow visualization and birefringence data for two polymer melts. The Phan-Thien Tanner (PTT) model was fit to the steady state shear and extensional viscosity data and the transient extensional viscosity data of both polystyrene and low-density polyethylene (LDPE) melts to obtain the parameters λ, ξ, and ϵ in this model. Agreement was found between the flow visualization and birefringence data and the predictions of streamlines and stress. With some modification of the constitutive equation, the vortex growth and intensity observed for LDPE could be predicted by the use of the PTT model and the material parameters fit to the rheological properties. Likewise, the flow behavior of polystyrene, in which only small vortices with no growth were observed, was also predicted. Furthermore, it was found that the size and intensity of the vortex could be affected by the parameter ϵ in the PTT model which controls the predictions of the extensional viscosity. Based on these results it seems that accurate simulation of entry flow behavior requires the use of a constitutive equation which is capable of giving realistic preciction's of a fluid's extentional flow properties.

Surface flow visualization of separated flows on the forebody of an F-18 aircraft and wind-tunnel model

Abstract: A method of in-flight surface flow visualization similar to wind-tunnel-model oil flows is described for cases where photo-chase planes or onboard photography are not practical This method, used on an F-18 aircraft in flight at high angles of attack, clearly showed surface flow streamlines in the fuselage forebody Vortex separation and reattachment lines were identified with this method and documented using postflight photography Surface flow angles measured at the 90 and 270 degrees meridians show excellent agreement with the wind tunnel data for a pointed tangent ogive with an aspect ratio of 35 The separation and reattachment line locations were qualitatively similar to the F-18 wind-tunnel-model oil flows but neither the laminar separation bubble nor the boundary-layer transition on the wind tunnel model were evident in the flight surface flows The separation and reattachment line locations were in fair agreement with the wind tunnel data for the 35 ogive The elliptical forebody shape of the F-18 caused the primary separation lines to move toward the leeward meridian Little effect of angle of attack on the separation locations was noted for the range reported

The fluid mechanics of fracture and other junctions

Abstract: In connection with solute transfer in fracture networks, Hull and Koslow (1986) proposed proportional routing of streamlines through discontinuous fracture junctions (in which inlet and outlet branches alternate). We apply fluid mechanics to the problem and show that the errors of proportional routing may be unacceptably large when the two inlet discharges and the two outlet discharges both differ greatly in magnitude. In extreme cases one inlet flow is wholly excluded from one of the two outlets, and proportional routing is maximally incorrect. Solutions are established for arbitrary discharge patterns through four-way coplanar junctions: exact solutions for Laplace flows (Hele-Shaw flows and Darcy flows (fractures filled with porous material)) and approximate solutions for Stokes flows. The Laplace solutions apply also to a range of transport processes.

Analysis of incompressible three-dimensional flows using the concept of stream tubes in relation with a transformation of the physical domain

Abstract: This paper presents an analysis of three-dimensional flows based on the concept of stream tubes and streamlines. In the case of incompressible liquids, the physical domain can be transformed, under certain assumptions, into a cylinder where the streamlines are parallel straight lines. In contrast to classical methods, the unknown to be determined is the transformation between the two domains. This analysis generalizes the formulation already proposed for plane and axisymmetric flows.

An Improved Streamline-Generating Technique That Uses the Boundary (Integral) Element Method

Abstract: The boundary element method (BEM) has been used to generate streamlines for homogeneous and sectionally homogeneous reservoirs having irregular boundaries. This technique is superior to earlier methods that use ''image wells'' to simulate the reservoir boundary, especially for cases where the reservoir boundary is irregularly shaped. It has wider applicability to different kinds of reservoirs and eliminates the need for trial-and-error solutions. The errors caused by discretization and numerical approximation arise on and adjacent to the boundaries only, therefore the pressures and pressure gradients on which the streamlines are derived can be calculated with very high accuracy in the interior of the reservoir. Thus, the streamlines generated with this method are expected to be more realistic and representative of the actual physical system.

Fluid flow and solute transport through three-dimensional networks of variably saturated discrete fractures

Abstract: The boundary integral method is used to estimate hydraulic and solute transport properties of unsaturated, fractured rock by solving the boundary value problem within intersecting fracture planes. Flow through both impermeable and permeable rock is determined using two- and three-dimensional formulations, respectively. Synthetic fracture networks are created to perform sensitivity studies, results of which show that: (1) The global hydraulic conductivity is linearly dependent on the product of fracture transmissivity and density for fractures of infinite length: (2) The effect of correlation between fracture length and transmissivity is to increase the global hydraulic conductivity; and (3) Simulated flow through a fractured permeable matrix compare favorably with analytical results. Flow through variably saturated fractures is modeled using a constant capillary head within individual fractures. A simulated free surface compares favorably with an approximate analytic solution and with laboratory results. A simulated free surface compare favorably with an approximate analytic solution and with laboratory results. Simulations indicate zones of water under both positive and negative pressure, as well as regions of air-filled voids. Travel times and breakthrough curves are determined by integrating the inverse velocity over a streamline, and then summing overall streamlines. Faster travel times are noted as fracture saturation decreasesmore » for the fracture network examined. 212 refs., 58 figs., 19 tabs.« less

Flow of dilute polyacrylamide solutions through a sudden planar contraction

Abstract: The flow of partially hydrolyzed polyacrylamide solutions through a 10:12 sudden planar contraction was investigated by means of laser-Doppler anemometry The resultant velocity profiles are compared with those for Newtonian water flow It is shown that velocity profiles of dilute high molecular weight HPAM solutions of concentrations of 25 ppm and 50 ppm exhibit a velocity maximum upstream of the sudden planar contraction They first appear near the wall and move towards the channel axis as the flow approaches the contraction Furthermore, it is found that the centreline velocity profiles of the polymer solution show an earlier response to the downstream flow restriction than water This is associated with enhanced recirculation regions in front of the sudden channel contraction Streamlines calculated from the experimentally obtained velocity data reveal all the characteristics of a diverging flow field upstream of the contraction The experiments reveal that, for the volume flow rate investigated, the flow of dilute polymers remains two-dimensional in the centre throughout the major part of the channel The addition of small amounts of the divalent salt CaCl2 reduces the polymer effects to pure Newtonian flow behaviour

Measurements of the free-stream fluctuations above a turbulent boundary layer

Abstract: In this paper an investigation of the velocity fluctuations in the free stream above an incompressible turbulent boundary layer developing at constant pressure is described. It is assumed that the fluctuations receive contributions from three statistically independent sources: (i) one‐dimensional unsteadiness, (ii) free‐stream turbulence, and (iii) the irrotational motion induced by the turbulent boundary layer. Measurements were made in a wind tunnel with a root‐mean‐square level of the axial velocity fluctuations of about 0.2%. All three velocity components were measured using an X‐wire probe. The unsteadiness was determined from the spanwise covariance of the axial velocity fluctuations, measured using two single‐wire probes. The results show that it is possible to separate the contributions to the rms level of the velocity fluctuations without resorting to the dubious technique of high‐pass filtering. This separation could be extended to the spectral densities of the contributions if measurements of sufficient accuracy were available.

Fully developed multilayer polymer flows in slits and annuli

Abstract: A numerical method has been developed for simulating fully developed multilayer shear flows of non-Newtonian fluids with arbitrary viscosity functions. Poiseuille and combined Poiseuille/Couette flows in both slits arid annuli may be modeled. The method employs a finite difference system where grid points lie on streamlines and move to their correct positions as the solution procedure converges. Interfaces are easily handled as particular stream lines with the equation of motion replaced by a boundary condition. The method is stable for high interface viscosity ratios and readily handles a large number of layers. Many authors have employed power law models to model multi-layer non-Newtonian flows. We find that the power law is sufficient to predict pressure gradients and interface positions in most cases, but gives unrealistically flat velocity profiles, even when truncated at finite viscosity. Results are presented for the Carreau fluid and for the rubber-like liquid with shear thinning via Wagner's strain functional.

Analysis of single‐domain particle flow orientation data

Abstract: Rodlike single‐domain particles tend to orient parallel to the streamlines in an extensional flow, resulting in anisotropy of the bulk magnetic permeability. The suspension is made to flow from a large chamber into a narrow tube which has an oscillator coil wound near its entrance. Particle orientation parallel to the magnetic field of the coil decreases the inductance. (Small changes in orientation can then be accurately measured with a countertimer.) Since both hydrodynamic orientation and Brownian motion depend on the shape characteristics of the particle, the orientation data provide information about the ‘‘effective‐particle’’ shape. The gradients of the inductance with respect to flowrate, in the limits of high and low flowrate, are used to calculate relative changes in the effective‐particle rotary diffusion coefficient. This method is demonstrated with a γ‐Fe2O3 suspension over a wide range of surfactant concentration. Changes in the particle magnetic properties calculated from the flow orientatio...

Magnetohydrodynamic flow in a curved pipe

Abstract: The flow of conductive fluids in highly conductive curved pipes is studied analytically in this paper. The flow is assumed to be steady state, laminar, and fully developed. Coupled continuity, Navier–Stokes, and appropriate Maxwell equations are solved in toroidal coordinates. The dimensionless parameters of the problem are Dean number K and Hartmann number Ha. For low Hartmann numbers [Ha2∼θ(1)], the solution is expanded in a power series of K and Ha2. For intermediate Hartmann numbers [Ha2∼θ(1000)], the solution is expressed as a power series of K. The axial velocity contours are shown to be shifted towards the outer wall. For low Ha, these contours are nearly circular. The effect of a strong transverse magnetic field is to enhance the compression of fluid towards the outer wall. The secondary flow field comprises a symmetric pair of counter‐rotating vortices. A strong magnetic field is found to confine the secondary flow streamlines to a thin layer near the tube wall. The secondary flow rate in the near‐wall boundary layer is increased by the magnetic field. This increase in flow rate raises the possibility of efficient convective cooling of curved first wall tubes in magnetic confinement fusion reactors (MFCR).