Showing papers on "Streamlines, streaklines, and pathlines published in 1993"

The wake instability in viscoelastic flow past confined circular cylinders

Abstract: Laser Doppler velocimetry (LDV) and video flow visualization are used to investigate the creeping motion of a highly elastic, constant-viscosity fluid flowing past a cylinder mounted centrally in a rectangular channel. A sequence of viscoelastic flow transitions are documented as the volumetric flow rate past the cylinder is increased and elastic effects in the fluid become increasingly important. Velocity profiles clearly show that elasticity has almost no effect on the kinematics upstream of the cylinder, but that the streamlines in the wake of the cylinder are gradually shifted further downstream . Finite element calculations with a nonlinear constitutive model closely reproduce the evolution of the steady two-dimensional velocity field. However, at a well defined set of flow conditions the steady planar stagnation ow in the downstream wake is experimentally observed to become unstable to a steady, three-dimensional cellular structure. The Reynolds number at the onset of the flow instability is less than 0.05 and inertia plays little role in the flow transition, LDV measurements in the wake close to the cylinder reveal large spatially periodic fluctuations of the streamwise velocity that extend along the length of the cylinder and more than five cylinder radii downstream of the cylinder. Fourier analysis shows that the characteristic spatial wavelength of these flow perturbations scales closely with the cylinder radius R . Flow visualization combined with LDV measurements also indicates that the perturbations in the velocity field are confined to the narrow region of strongly extensional flow near the downstream stagnation point. A second flow transition is observed at higher flow rates that leads to steady translation of the cellular structure along the length of the cylinder and time-dependent velocity oscillations in the wake. Measurements of the flow instability are presented for a range of cylinder sizes, and a stability diagram is constructed which shows that the onset point of the wake instability depends on both the extensional deformation of the fluid in the stagnation flow and the shearing flow between the cylinder and the channel.

The instability of precessing flow

Abstract: An explanation is put forward for the instability observed within a precessing, rotating spheroidal container. The constant vorticity solution for the flow suggested by Poincare is found to be inertially unstable through the parametric coupling of two inertial waves by the underlying constant strain field. Such resonant couplings are due either to the elliptical or shearing strains present which elliptically distort the circular streamlines and shear their centres respectively. For the precessing Earth's outer core, the shearing of the streamlines and the ensuing shearing instability are the dominant features. The instability of some exact, linear solutions for finite precessional rates is established and used to corroborate the asymptotic analysis. A complementary unbounded analysis of a precessing, rotating fluid is also presented and used to deduce a likely upperbound on the growth rate of a small disturbance. Connection is made with past experimental studies.

Anisotropic convection with implications for the upper mantle

Abstract: On the basis of polycrystalline theory describing the plasticity in olivine and enstatite, the flow in a convection cell has been simulated using a finite element formulation. The spatial variations in anisotropic properties are computed from the textures that evolve with the flow. A kinematically constrained equilibrium-based assumption is used to partition the macroscopic deformation among crystals within an aggregate. We model the convection for one specific cell geometry and two sets of boundary conditions. A complete map of textures throughout the cell is obtained. The textured convection cell is structurally very heterogeneous and textures along streamlines do not correlate with the finite strain. The results of the simulations indicate that during up welling a strong texture develops rapidly. It convects during spreading and is attenuated during subduction. Results are compared with features of the upper mantle. In our predictions the pattern of preferred orientation during spreading is inclined to the flow coordinates due to deformation by simple shear. This is contrary to Hess' [1964] intuition that (001) slip planes of olivine orient themselves parallel to the flow planes, yet the pattern is consistent with natural fabric data. Significant differences are observed as a function of depth within the cell. The variations in the p wave velocities in this textured model mantle are analyzed and correspond well with observed seismic data.

Implicit stream surfaces

Abstract: Streamlines and stream surfaces are well known techniques for the visualization of fluid flow. For steady velocity fields, a streamline is the trace of a particle, and a stream surface is the trace of a curve. Here a new method is presented for the construction of stream surfaces. The central concept is the representation of a stream surface as an implicit surface f (x) = C. After the initial calculation of f a family of stream surfaces can be generated efficiently by varying C. The shapes of the originating curves are defined by the value of f at the boundary. Two techniques are presented for the calculation of f: one based on solving the convection equation, the other on backward tracing of the trajectories of grid points. The flow around objects is discussed separately. With this method irregular topologies of the originating curves and of the stream surfaces can be handled easily. Further, it can also be used for other visualization techniques, such as time surfaces and stream volumes. Finally, an effective method for the automatic placement of originating curves is presented. >

A generalization of Bernoulli's theorem.

Abstract: The conservation of potential vorticity Q can be expressed as ∂(ρQ/∂t + ∇·J = 0, where J denotes the total flux of potential vorticity. It is shown that J is related under statistically steady conditions to the Bernoulli function B by J = ∇θ × ∇B,where θ is the potential temperature. This relation is valid even in the nonhydrostatic limit and in the presence of arbitrary nonconservative forces (such as internal friction) and heating rates. In essence, it can be interpreted as a generalization of Bernoulli's theorem to the frictional and diabatic regime. The classical Bernoulli theorem—valid for inviscid adiabatic and steady flows—states that the intersections of surfaces of constant potential temperature and constant Bernoulli function yield streamlines. In the presence of frictional and diabatic effects, these intersections yield the flux lines along which potential vorticity is transported.

Particle diffusion in a meandering jet

Abstract: The process of turbulent mixing across an ideal model of a meandering Gulf Stream is studied considering particle motion in two dimensions. The turbulent motion is modeled using a “random flight” model that assumes that the evolution of the turbulent velocity along trajectories is a Markov process, with the velocity at one time step depending linearly on the velocity at the previous step. This turbulent field is superimposed on a meandering jet (similar to the one considered by Bower (1991)) propagating steadily eastward. In Bower's model the particles are constrained to move along streamlines in the translating frame; in our model the turbulent motion allows the particles to cross streamlines, resulting in an exchange between the different regions of the flow. The major exchange occurs between the “jet core” region and the “recirculating” regions moving with the meanders. Particles launched in the jet core tend to be lost from the jet in plumes at the extrema of the meanders and to be entrained in successive recirculation regions. When in the recirculation regions, particles tend to be trapped and homogenized. The exchange between the jet and the “far field” depends only on diffusion mechanisms and is small for the short integration time considered. An application of the kinematic techniques considers the distribution of biological species across the jet. The tendency for “patches” of organisms to develop in the recirculation regions is observed. In a two-species case, where the species have affinities for the environment on opposite sides of the jet, there is a linear change in species composition across the jet. Patches forming on either side of the jet consist of an admixture of the two species, with the population for the crest or trough environment dominating.

Users manual for the nasa lewis three-dimensional ice accretion code (lewice 3d).

Abstract: A description of the methodology, the algorithms, and the input and output data along with an example case for the NASA Lewis 3D ice accretion code (LEWICE3D) has been produced. The manual has been designed to help the user understand the capabilities, the methodologies, and the use of the code. The LEWICE3D code is a conglomeration of several codes for the purpose of calculating ice shapes on three-dimensional external surfaces. A three-dimensional external flow panel code is incorporated which has the capability of calculating flow about arbitrary 3D lifting and nonlifting bodies with external flow. A fourth order Runge-Kutta integration scheme is used to calculate arbitrary streamlines. An Adams type predictor-corrector trajectory integration scheme has been included to calculate arbitrary trajectories. Schemes for calculating tangent trajectories, collection efficiencies, and concentration factors for arbitrary regions of interest for single droplets or droplet distributions have been incorporated. A LEWICE 2D based heat transfer algorithm can be used to calculate ice accretions along surface streamlines. A geometry modification scheme is incorporated which calculates the new geometry based on the ice accretions generated at each section of interest. The three-dimensional ice accretion calculation is based on the LEWICE 2D calculation. Both codes calculate the flow, pressure distribution, and collection efficiency distribution along surface streamlines. For both codes the heat transfer calculation is divided into two regions, one above the stagnation point and one below the stagnation point, and solved for each region assuming a flat plate with pressure distribution. Water is assumed to follow the surface streamlines, hence starting at the stagnation zone any water that is not frozen out at a control volume is assumed to run back into the next control volume. After the amount of frozen water at each control volume has been calculated the geometry is modified by adding the ice at each control volume in the surface normal direction.

An analytical study of transport in Stokes flows exhibiting large-scale chaos in the eccentric journal bearing

Abstract: In the present work, we apply new tools from the field of adiabatic dynamical systems theory to make quantitative predictions of various important mixing quantities in quasi-steady Stokes flows which possess slowly varying saddle stagnation points. Many of these quantities can be obtained before experiments or numerical simulations are performed using only knowledge of the streamlines in steady-state flows and the externally determined flow parameters. The location and size of the main region in which mixing occurs is determined to leading order by the slowly sweeping instantaneous stagnation streamlines. Tracer patches get stretched by an amount O(l/e) during each period, and the average striation thickness of the patch decreases by a factor of e in the same time. Also, the rate of stretching of material interfaces is bounded from below with an analytically obtained exponentially growing lower bound. Finally, the highly regular appearance of islands in quasi-steady Stokes’ flows is explained using an extension of the KAM theory. As an example to illustrate these results, we study the transport of passive scalars in a low Reynolds number flow in the two-dimensional eccentric journal bearing when the angular velocities of the cylinders are slowly modulated, continuously and periodically in time, with frequency e. In contrast to the flows usually studied with dynamical systems, these slowly varying systems are singular perturbation (apparently far from integrable) problems exhibiting large-scale chaos, in which the non-integrability is due to the slow, continuous O( 1) modulation of the position of the saddle stagnation point and the two streamlines stagnating on it.

Construction of three-dimensional images of flow structure via particle tracking techniques

Abstract: Construction of three-dimensional images of flow structure, based on the quantitative velocity field, is assessed for cases where experimental data are obtained using particle tracking technique. The experimental data are in the form of contiguous planes of particle images. These contiguous data planes are assumed to correspond to successive spatial realizations in steady flow, or to phase-referenced realizations in an unsteady flow. Given the particle images on contiguous planes, the in-plane velocity fields are determined. Then, the out-of-plane velocity field is obtained using a spectral interpolation method. Application of this method allows, in principle, construction of the three-dimensional vorticity field and the streamline patterns. A critical assessment is made of the uncertainties arising from the in-plane interpolation of the velocity field obtained from particle tracking and the evaluation of the out-of-plane velocity component. The consequences of such uncertainties on the reconstructed vorticity distributions and streamline patterns are addressed for two basic types of vortex flows: a columnar vortex, for which the streamlines are not closed and are spatially periodic in the streamwise direction; and for a spherical (Hill's) vortex exhibiting closed streamline patterns, and no spatial periodicity.

Convective heat transfer in turbulized flow past a hemispherical cavity

Abstract: The flow structure and the local heat transfer coefficients on the surface of a hemispherical cavity are investigated. It is found that the position of streamlines along the cavity surface resembles that of the electric dipole containing a «source» and a «sink». The «sink» is an eddy which entrains air from the cavity into the free stream flow. As the level of the free stream turbulence grows, the mean value of the heat transfer coefficient on the cavity surface increases. However, in this case the effective use of the cavity for enhancing heat transfer is reduced

Laminar Natural Convection in Internally Finned Horizontal Annuli

Abstract: An analysis is made of the laminar natural convection in two internally finned horizontal annuli. The governing equations were solved numerically by a control-volume-based finite difference method. Information about the flow patterns and temperature distributions is presented through velocity vectors, streamlines, and isotherm plots. The effects of Rayl1eigh number and fin height on the Nusselt numbers are presented for two selected fin orientations. Variations of the local Nusselt numbers along the inner cylinder are also presented. In the cases studied, orientations of the internal fins are found to have insignificant effects on the average Nusselt number.

Bluff-body drag reduction by passive ventilation

Abstract: The drag of a sphere at highRe can be reduced to more than half its value by passive ventilation from the stagnation region to the base. Simultaneously, the flow field around the base is stabilized and made symmetric, leading to reduction of unsteady aerodynamic forces. At highRe, the vent flow breaks through the dead water region associated with the near wake and aerodynamically streamlines the base. The streamlining is done by virtue of a base-vortex-ring beyond the point of turbulent boundary layer separation. A mean flow model for the flow around the vented sphere is proposed.

The instability of rotating fluid columns subjected to a weak external Coriolis force

Abstract: Instabilities in rotating fluid columns subjected to a weak external Coriolis force are studied. External Coriolis force alters the base flow distorting circular streamlines of the unperturbed columns. The inviscid part of the modified flow (0,r,−2er sin φ) is an exact solution of Euler equations. Here e is the strength (nondimensional) of imposed Coriolis force. It is shown that this distortion leads to three‐dimensional instabilities. The instability mechanism is generic. It occurs in many flows having circular streamlines distorted by a spectrum of modes cos mφ, sin mφ (m=2 corresponds to elliptical instability). The instabilities occur for wavelengths and frequencies at the intersection points of dispersion curves for the unperturbed columns. Moreover, the instabilities occur at the points of intersection for which modes are coupled with the external Coriolis mode. Here a case is studied where axisymmetric and helical modes are involved in interactions leading to fully three‐dimensional flows. It is shown that rotating fluid columns are unstable to disturbances whose axial wavelengths lie in a band, whose width is proportional to the strength e of imposed Coriolis force. Parametric resonance between a pair of inertial waves (natural modes of oscillation) and the external Coriolis mode is the physical explanation for the instabilities. Numerical results are presented on growth rates of mixed modes and on widths of unstable regions. The growth rates depend linearly on the strength of external Coriolis force. It is shown that viscosity shifts the instability tongues to positive values of ‖e‖. The results of small‐amplitude perturbation analysis are compared with full numerical simulations of the Navier–Stokes equations. Comments are made on competition between centrifugal and parametric instabilities in Taylor–Couette systems subjected to an external Coriolis force studied in Wiener et al. [J. Stat. Phys. 64, 913 (1991)] and Ning et al. [J. Stat. Phys. 64, 927 (1991)].

Elliptical instabilities of stratified, hydromagnetic waves

Abstract: The stability of a uniformly-rotating, electrically-conducting, stratified fluid is discussed under conditions of slight tidal straining. The ensuing steady flow consisting of elliptical streamlines and magnetic field lines is linearly unstable through the resonant coupling of two free waves of the system. New families of linear waves consisting of modified Poincare, “slow” hydromagnetic and, in the case of axial stratification, internal evanescent waves are isolated upon a rotating fluid bearing an axial current. All possible resonant couplings between these waves are examined. Stable radial stratification is found to be a destabilizing influence on some elliptical couplings and always so for slow hydromagnetic waves. Internal evanescent waves can be stimulated elliptically in the case of axial stratification and typically possess boundary-layer structure. In all cases studied, including in the presence of a central core, the preferred mode of disturbance is a tipping over, or spinover, of the b...

Perturbation Boundary Element Method for Heterogeneous Reservoirs: Part 1-Steady-State Flow Problems

Abstract: A perturbation boundary element method (BEM) for steady-state flow problems in heterogeneous media is developed, and various aspects of the model are tested. The perturbation series obtained by the BEM gives the complete solution for the original governing equation. For highly heterogeneous problems, Pade approximants are effective to accelerate the rate of convergence and to convert a divergent series into a convergent solution. Because the model does not suffer from numerical dispersion and grid orientation effects, it is possible to track streamlines accurately.

Fast dynamos with finite resistivity in steady flows with stagnation points

Abstract: Results of the kinematic fast dynamo problem for two classes of steady incompressible flows are presented. These flows are the ABC flow and the spatially aperiodic flow of Lau and Finn [Physica D 57, 238 (1992)]. In a range of parameters, these three‐dimensional flows have stagnation points (A and B type) and there are chaotic streamlines. The chaos is associated with the intermingled stable and unstable manifolds of the stagnation points. In the aperiodic flow the chaos takes the form of chaotic scattering. The growth rate of the dynamos for the aperiodic flow is found to obey a certain scaling law with resistivity η (as η→0), from which the results are extrapolated to the limit η→0 (infinite magnetic Reynolds number). Numerical results are presented indicating that fast kinematic dynamos can exist in these flows and that chaotic flow is a necessary condition. The structure of the dynamo magnetic fields is also shown, in particular, the relationship between the regions of maximal field strength and the invariant dynamical structures of the aperiodic flow. For the aperiodic flow, the unstable mode has a real frequency and these regions consist of two fingers of oppositely directed field. These regions rotate about a streamline (the one‐dimensional unstable manifold) coming out of the type A stagnation point. For the ABC flow with A=B=C, it is found that there are two dynamo modes: an oscillating mode and a purely growing mode. The mode crossing occurs at magnetic Reynolds number between 300 and 350, with the purely growing mode dominating for larger magnetic Reynolds numbers. For the oscillating mode, the region of large ‖B‖ is similar to that for the aperiodic flow. For the purely growing mode, the region of large ‖B‖ is localized in single fingers about the one‐dimensional unstable manifolds. The distribution function of ln‖B‖ is observed to be approximately Gaussian for both modes of the ABC flow. The distribution function for the mode found for the aperiodic flow has a much more complex structure, apparently associated with the escape of streamlines in chaotic scattering.

Instantaneous topology of the unsteady leading-edge vortex at high angle of attack

Abstract: A new topological structure is defined for flow over a delta wing undergoing transient pitching maneuvers at high angle of attack. This instantaneous structure differs substantially from the traditional topology observed for stationary wings at low angle of attack. The leading edge vortex is found to exhibit an outward-spiraling motion corresponding to an unstable focus. In addition, the streamlines separating from the leading edge are not entrained into the vortex core in the instantaneous sense. The instantaneous topology is determined from highresolution measurements over the crossflow plane by locating and categorizing the critical points of the instantaneous sectional streamlines. The three-dimensional, instantaneous streamline pattern corresponding to this topological structure is constructed by phase referencing the velocity fields at various chordwise locations. This approach allows three-dimensional characterization of the unstable focus of the leading-edge vortex and its relation to the feeding sheet.

Numerical simulation of extrudate swell for Oldroyd-B fluids using the stream-tube analysis and a streamline approximation

Abstract: In this paper, the stream-tube method is applied to the numerical simulation of axisymmetric extrudate swell of Oldroyd-B fluids. The analysis permits computation of the flow by considering stream tubes separately, from the wall to the inside, in a mapped computational domain where the streamlines are parallel and straight. The present study follows a previous paper on the swelling problem for a fluid obeying a memory-integral equation. A simpler numerical model is proposed here, in which the singularity in the vicinity of the junction point between the wall and the free surface, considered in the previous work, is not examined explicitly. Several values of the parameter β of the Oldroyd-B model, from β = 0.01 to β = 1 (Maxwell model) are considered. The algorithm converges for a broad range of Weissenberg numbers. Results are consistent with the numerical data in the literature. CPU time and storage area are reduced.

Secondary flow of a Casson fluid in a slightly curved tube

Abstract: The fully developed, steady flow of a Casson fluid through a slightly curved tube of circular cross-section has been analysed. The solution is developed by successive approximation from the perturbation of flow of a Casson fluid in a straight tube. The resulting differential equations have been solved by a finite difference method followed by an iterative procedure. Velocity distribution, pressure and nature of the streamlines have been obtained for different values of yield number and Reynolds number. For specific values of the yield number, the results have been compared with those for a Bingham fluid. Comparing the results with a Newtonian fluid, the effect of yield number has been determined.

Azimuthal instability of divergent flows

Abstract: We investigate a new mechanism for instability (named divergent instability ), characterized by the formation of azimuthal cells, and find it to be a generic feature of three-dimensional steady axisymmetric flows of viscous incompressible fluid with radially diverging streamlines near a planar or conical surface. Four such flows are considered here: (i) Squire–Wang flow in a half-space driven by surface stresses; (ii) recirculation of fluid inside a conical meniscus; (iii) two-cell regime of free convection above a rigid cone; and (iv) Marangoni convection in a half-space induced by a point source of heat (or surfactant) placed at the liquid surface. For all these cases, bifurcation of the secondary steady solutions occurs: for each azimuthal wavenumber m = 2, 3,…, a critical Reynolds number ( Re * ) exists. The intent to compare with experiments led us to investigate case (iv) in more detail. The results show a non-trivial influence of the Prandtl number ( Pr ): instability does not occur in the range 0.05 Pr Re * ( m ) exists and has bounded limits as Pr tends to either zero or infinity. A nonlinear analysis shows that the primary bifurcations are supercritical and produce new stable regimes. We find that the neutral curves intersect and subcritical secondary bifurcation takes place; these suggest the presence of complex unsteady dynamics in some ranges of Re and Pr . These features agree with the experimental data of Pshenichnikov & Yatsenko ( Pr = 10 3 ).

The stagnation flow behind a sphere

Abstract: The flow of a viscoelastic liquid past a rigid sphere held on the centreline of a circular cylinder is examined both experimentally (laser Doppler velocimetry) and theoretically (finite elements). The study focuses on the stagnation flow along the centreline behind the sphere. In this region elastic properties provide an enhanced decelerating force on the fluid far from the sphere, leading to the well documented downstream shift in the streamlines relative to the flow of a Newtonian fluid. It has been less widely reported, however, that a corresponding acceleration effect close to the sphere may be sufficient to cause a localized upstream shift in the streamlines. Here the acceleration of the fluid exceeds that of the Newtonian fluid. This effect is quite separate from any similar behaviour produced by the presence of shear-thinning properties. Such a phenomenon has already been predicted for the case of unbounded flow past a cylinder or a sphere. In the current study we observe this effect experimentally and then use finite element simulations to show that it depends strongly on the fluid properties and the flow geometry. The conditions prevailing in most previous studies of this problem do not favour the observation of this enhanced acceleration.

Natural convection in a cavity with fins attached to both vertical walls

Abstract: Numerical calculations are presented for two-dimensional natural convection flow inside an air-filled cavity with fins/baffles—of length 0.1, 0.3, and 0.5 of the cavity width—attached along both the heated and the cooled side of the cavity. The governing equations in the stream function-vorticity formulation are solved using finite differences. The Arakawa differencing scheme is used to represent the convection terms. Flow characteristics are investigated for three baffle lengths and Grashof numbers in the range of 9.0 x 103 to 1.0 x 105. A multicellular flow structure is found to exist for a baffle length of 0.1. However, when the baffle length is equal to 0.3 or greater, the fluid flow breaks down into secondary circulations—in addition to the primary circulation— and that, in turn, results in higher heat transfer rates across the two sides of the cavity. Nomenclature Gr = Grashof number, g/3ATw3/v2 h = baffle length N = number of baffles Pr = Prandtl number, via T = temperature u' = nondimensional velocity in £ direction v' = nondimensional velocity in £ direction w = cavity width z = cavity length a = thermal diffusivity j8 = coefficient of thermal expansion d = baffle thickness £ = nondimensional spatial coordinate 0 = nondimensional temperature A = cavity aspect ratio, z/w v = kinematic viscosity £ = nondimensional spatial coordinate r = nondimensional time ^ = nondimensional stream function i// = stream function H = nondimensional vorticity co = vorticity

Mixer ejector flow distributor

Abstract: An apparatus for attaining improved flow uniformity through and at the exit of an air duct by mixing and distributing the air flow. The apparatus has a wall containing a plurality of convoluted corrugations or lobes arranged in conjunction with an airfoil shaped faired body to form an ejector passage between the wall and the faired body. There is a primary flow passage on the side of the wall opposite the ejector passage. The corrugations extend into both the primary flow and ejector flow passages so that a lobe in one passage is a trough in the other passage. Air flow in the primary flow passage acts to cause a flow through the ejector passage and thus a suction in the inlet to the ejector passage. The suction acts upon streamlines around the apparatus to obtain improved downstream air flow performance. One embodiment of the flow distributor increases the spreading half angle at the exit of an air flow duct. Another embodiment improves the velocity distribution profile across the duct downstream of a bluff body in the duct.

Radiation‐driven thermocapillary flows in optically thick liquid films

Abstract: A thin liquid film on a horizontal solid surface undergoing radiative heat transfer with an external heat source and the surrounding environment is considered. Thermal gradients along the free surface give rise to a thermocapillary flow in the liquid that is opposed by a hydrostatic pressure gradient within the film. Transient and steady‐state solutions are obtained for the interfacial shape and temperature and the velocity field. These results are compared with those from another model, in which a temperature distribution is imposed on the free surface of the film. At a critical value of the dynamic Bond number, a cusp in the form of a free‐surface slope discontinuity appears in this fixed free‐surface temperature model, but not in the radiation model. When the Bond number is less than this critical value, the time required to thin the film by a significant fraction of its original thickness is much larger with the radiation model. It is shown how the thermal boundary conditions used in the models directly cause these differences.

Flow Separation over the Inclined Step

Abstract: Flow field investigations were carried out in a backward-facing single-sided step flow with variation of the wall inclination angle. The aim of this investigation was to determine the differences in turbulent flow field quantities when compared to the 90° step geometry. The inclination angle was varied between 10° and 90°. Reynolds numbers (based on step height H) were realized up to 64000. Additionally, the influence of the expansion ratio on the flow field was to investigate with three different ratios 1.48, 2.0, 3.27. Velocity data were measured by laser Doppler anemometry allowing to determine integral flow quantities as e.g. separation streamlines or reattachment lengths. The experiments should both, contribute to the understanding of the phenomenology of separated flows and establish a comprehensive data base for the validation of numerical codes.

Calculation of main flows of a memory-integral fluid in an axisymmetric contraction at high Weissenberg numbers

Abstract: A memory-integral equation is considered for numerical flow simulation in a four-to-one circular contraction. The stream-tube analysis, which has been used previously for viscoelastic flow in the swelling problem, is now considered for a duct flow where recirculations are encountered. The method enables computation of the main flow field in a mapped domain of the physical domain where the transformed streamlines are parallel and straight. The primary unknowns of the problem are the transformation and the pressure, and a simple scheme may be developed for evaluating the kinematic quantities involved by a memory-integral equation. The Goddard-Miller constitutive model, already investigated for simulation of the swelling flow of a polystyrene material, is employed. Time evolution and related kinematic quantities are easily taken into account for the computation of stresses. A mixed formulation is adopted and the relevant non-linear equations are solved numerically by the Levenberg-Marquardt algorithm. A satisfactory convergence is obtained up to a Weissenberg number of 30. The results, though related to the main flow in the circular abrupt contraction, clearly show the growing effects of the singularity at the section of contraction and the importance of the recirculating zone near the salient corner.

Natural convection in partitioned enclosures with localized heating

Abstract: The aim of the present investigation was to study numerically the natural convection in partitioned enclosures with localized heating from below. Two‐dimensional equations of conservation of mass, momentum and energy, with the Boussinesq approximation are solved using finite difference method. Various geometrical parameters were: aspect ratio A = 0.4−0.6, isothermal surface length B = 0.5, its position C = 0.3, partition position D = 0.5−1.0, its length E = 0.2−0.6, heat source length X = 0.05−1.00, and its position e = variable. The Rayleigh number was varied from 103 to 106. The results are reduced in terms of the normalized Nusselt number as a function of the Rayleigh number, and other non‐dimensional geometrical parameters. The isotherms and streamlines are produced for various Rayleigh numbers and geometrical conditions.

Trapping, percolation, and anomalous diffusion of particles in a two-dimensional random field

Abstract: We analyze from first principles the advection of particles in a velocity field with HamiltonianH(x, y)=¯ V 1 y−¯ V 2 x+W 1 (y)-W 2 (x), whereW i , i=1, 2, are random functions with stationary, independent increments. In the absence of molecular diffusion, the particle dynamics are very sensitive to the streamline topology, which depends on the mean-to-fluctuations ratioρ=max(|¯V1¦/Ū; ¦¯V2|/Ū), withŪ =〈|W 1 ′|2〉1/2=rms fluctuations. Remarkably, the model is exactly solvable forρ ⩾1 and well suited for Monte Carlo simulations for all ρ, providing a nice setting for studying seminumerically the influence of streamline topology on large-scale transport. First, we consider the statistics of streamlines forρ=0, deriving power laws for pnc(L) and 〈λ(L)〉, which are, respectively, the escape probability and the length of escaping trajectories for a box of sizeL, L » 1. We also obtain a characterization of the “statistical topography” of the HamiltonianH. Second, we study the large-scale transport of advected particles withρ > 0. For 0 <ρ < 1, a fraction of particles is trapped in closed field lines and another fraction undergoes unbounded motions; while for ρ⩾ 1 all particles evolve in open streamlines. The fluctuations of the free particle positions about their mean is studied in terms of the normalized variablest − v/2[x(t)−〈x(t)〉] andt −v/2 [y(t)-〈(t)〉]. The large-scale motions are shown to be either Fickian (ν=1), or superdiffusive (ν=3/2) with a non-Gaussian coarse-grained probability, according to the direction of the mean velocity relative to the underlying lattice. These results are obtained analytically for ρ ⩾ 1 and extended to the regime 0<ρ<1 by Monte Carlo simulations. Moreover, we show that the effective diffusivity blows up for resonant values of $$(\bar V_1 ,\bar V_2 )$$ ) for which stagnation regions in the flow exist. We compare the results with existing predictions on the topology of streamlines based on percolation theory, as well as with mean-field calculations of effective diffusivities. The simulations are carried out with a CM 200 massively parallel computer with 8192 SIMD processors.