Showing papers on "Hele-Shaw flow published in 1991"

On the dynamics of near-wall turbulence

Abstract: A model of the dynamic physical processes that occur in the near-wall region of a turbulent flow at high Reynolds numbers is described The hairpin vortex is postulated to be the basic flow structure of the turbulent boundary layer It is argued that the central features of the near-wall flow can be explained in terms of how asymmetric hairpin vortices interact with the background shear flow, with each other, and with the surface layer near the wall The physical process that leads to the regeneration of new hairpin vortices near the surface is described, as well as the processes of evolution of such vortices to larger-scale motions farther from the surface The model is supported by recent important developments in the theory of unsteady surface-layer separation and a number of `kernel' experiments which serve to elucidate the basic fluid mechanics phenomena believed to be relevant to the turbulent boundary layer Explanations for the kinematical behaviour observed in direct numerical simulations of low Reynolds number boundary-layer and channel flows are given An important aspect of the model is that it has been formulated to be consistent with accepted rational mechanics concepts that are known to provide a proper mathematical description of high Reynolds number flow

Observations on the elastic instability in cone-and-plate and parallel-plate flows of a polyisobutylene Boger fluid

Abstract: Experimental measurements of the shear stress and normal stresses in the viscometric flow of a well-characterized polyisobutylene/polybutene solution between a cone-and-plate and between parallel plates show the onset of an “anti-thixotropic” flow transition, which results in a time-dependent, apparent shear-thickening of the viscosity and first normal stress difference. Measurements of the critical conditions for the onset of the flow transition, made by systematically varying the plate separation in the parallel-plate geometry, demonstrate that this rotational instability is a function of the angular velocity in the flow and initially grows exponentially in time, in agreement with theoretical predictions for an Oldroyd-B model. However, experiments show that the disturbance which causes this flow transition is nonaxisymmetric, over-stable in time and subcritical in γ. Spectral analysis also shows that the nonlinear flow which ultimately develops is temporally aperiodic. These features of the flow transition do not agree with the existing theoretical analysis. The experimentally constructed flow-stability diagram shows that, for a given fluid, the instability occurs at a critical Deborah number which is insensitive to the specific geometrical parameters, temperature, and shear-rate of the flow. This interpretation of the elastic instability clarifies recent measurements of the flow stability for the Ml viscoelastic test fluid.

Two-layer hydraulics: a functional approach

Abstract: A new approach for investigating two-layer hydraulic exchange flows in channels is introduced. The approach is based on the functional formalism of Gill (1977) and applied to the flow through a contraction in width and to flow over a simple sill. The sill geometry is an extension of that looked at by earlier workers, in particular Farmer & Armi (1986) who used a Froude-number-plane approach. In the present paper a simple relationship between the composite Froude number and the hydraulic functional is derived, though the functional approach may also be applied to channels where a Froude number is not readily defined. The ability to trace roots of this functional from one reservoir to the other is a prerequisite for the flow to be realizable. Two hydraulic transitions are required for the flow to be fully controlled and the exchange flow rate to be maximal. If only one hydraulic transition is present, the flow is governed by the conditions in one of the reservoirs and the exchange flow rate is found to be submaximal. The flow along a channel is found to be very sensitive to small departures from symmetry about a horizontal plane. The response of the interface to the introduction of a net (barotropic) flow is found to be a discontinuous function of the strength of the forcing for some range of sill heights.

Pressure and heat transfer in cross flow over cylinders between two parallel plates

Abstract: Heat transfer and fluid flow over a row of in-line cylinders placed between two parallel plates are studied numerically. Flow is incompressible, two-dimensional, and laminar. The spacing between cylinders causes three different separation patterns. When the spacing is small, the separated flow between cylinders is stable. As the spacing increases, flow in the separated zone becomes temporal and periodic. At higher spacing, the separated flow is local and does not extend to the next cylinder. In general, the pressure drop in the flow and heat transfer to the flow are spatially periodic, indicating fully developed characteristics

Direct Finite-Difference Simulations Of Turbulent Flow

Abstract: Report discusses use of upwind-biased finite-difference numerical-integration scheme to simulate evolution of small disturbances and fully developed turbulence in three-dimensional flow of viscous, incompressible fluid in channel. Involves use of computational grid sufficiently fine to resolve motion of fluid at all relevant length scales.

Summary of in-flight flow visualization obtained from the NASA high alpha research vehicle

Abstract: A summary of the surface and off-surface flow visualization results obtained in flight on the F-18 high alpha research vehicle (HARV) is presented, highlighting the extensive 3-D vortical flow on the aircraft at angles of attack up to 50 degs The emitted fluid technique, as well as tufts and flow cones, were used to document the surface flow A smoke generator system injected smoke into the vortex cores generated by the forebody and leading edge extensions (LEXs) Documentation was provided by onboard still and video, by air-to-air, and by postflight photography The surface flow visualization techniques revealed laminar separation bubbles near the forebody apex, lines of separation on the forebody and LEX, and regions of attached and separated flow on the wings and fins The off-surface flow visualization techniques showed the path of the vortex cores on the forebody and LEX as well as the LEX vortex core breakdown location An interaction between the forebody and LEX vortices was noted The flow over the surfaces of the vertical tail was categorized into regions of attached, unsteady, or separated flow using flow tufts

Automated pattern eduction from turbulent flow diagnostics

Abstract: The development of an automated technique for the eduction of 3-D spatial patterns in vector or scalar diagnostics was completed. The method is based on an iterative convolution between a trial pattern and the data field. It was applied to the analysis of low Reynolds number turbulent channel flow and homogeneous shear flow. The results yielded new information on the dominant flow structures in these flows, particularly with respect to the spatial relationships between various forms of organized motion. A particular application of the pattern eduction method, which is tentatively referred to as an 'adaptive wavelet transformation', is proposed with the objective of investigating the way turbulence structure changes with scale. Preliminary results using data from homogeneous turbulent shear flow simulations are presented. At the low Reynolds numbers of the simulations, there is no evidence of scale similarity. The small scales appear to be associated with the edges of the larger scale vortical structures.

Modeling three‐dimensional flow about ellipsoidal inhomogeneities with application to flow to a gravel‐packed well and flow through lens‐shaped inhomogeneities

Abstract: Analytic functions are superimposed to model three-dimensional steady groundwater flow in regions containing one or more Inhomogeneities shaped like prolate or oblate ellipsoids of revolution. Each function and the sum of such functions are solutions of Laplace's equation, the governing differential equation for steady groundwater flow. The functions are implemented in a manner that provides exact continuity of flow across the entire boundary of each inhomogeneity. In general, continuity of head is provided at specified control points on the boundary and is approximated between control points. For the case of one inhomogeneity in a uniform flow field, it turns out that there is exact continuity of head across the entire surface of the inhomogeneity. The method is implemented in a computer program written by the author. Two applications are demonstrated: (1) flow to a gravel-packed well and (2) flow through a series of lens-shaped inhomogeneities. The examples demonstrate that the approximation of continuity of head can be made acceptable for many problems. A possible application of the technique would be testing various theories regarding contaminant migration and dispersion by simulating flow and chemical diffusion through large numbers of lens-shaped inhomogeneities.

Growth of natural dams by deposition from steady supersaturated shallow flow

Abstract: The frequent occurrence in nature of dams or terraces deposited from supersaturated flows prompted the hypothesis that wavelike but quasi-steady solid profile shapes may develop after sufficient time has elapsed. Dressler's (1978) approximate equations are used to describe steady fluid flow over a curved accreting surface, including a Chezy term to represent flow resistance. The case of a transition from subcritical to supercritical flow is treated, which leads to solutions for dams but excludes terraces. It is assumed that deposition is controlled principally by the diffusive resistance of the laminar sublayer, the thickness of which is almost inversely proportional to the flow velocity, lag effects being neglected on the assumption of large length scale/depth ratios. From the equations, the length scale of both the fluid flow and the solid profile is fixed by flow depth, and is relatively unaffected by slow temporal variations of the degree of supersaturation. The depth is defined by an upstream boundary condition on flow rate. This is taken constant as the surface grows, so that for selfsimilarity the profile moves in uniform translation. The direction of growth (“growth angle”) of the profile is expected to be nonhorizontal and is not known a priori. Here it is determined by the requirements of the geometrical boundary condition needed to satisfy the quasisteady growth assumption. The profile shape can be calculated from predetermined conditions, e.g., known values of the Froude number and drag coefficient. In applications involving the inverse problem, theoretical profiles have been fitted to photographs of natural dams with apparent success, and values of the Froude number and drag coefficient have been deduced. The study of these systems may be relevant to problems of mineral deposition.

Separated flow in a driven trapezoidal cavity

Abstract: Numerical solutions of the Navier–Stokes equations governing shear flow in a trapezoidal enclosure have been obtained at fine grid resolutions using an efficient multigrid calculation procedure. The effects of flow Reynolds number and wall boundary conditions are studied in detail. Interesting flow patterns are observed to develop, especially at high Reynolds numbers. To the author’s knowledge, such a flow development has not been reported previously.

Numerical simulation of three-dimensional unsteady viscous flow past finite cylinders in an unbounded fluid at low intermediate reynolds numbers

Abstract: The flow past finite circular cylinders for Reynolds numbers 40 and 70 were simulated by numerical solutions of the incompressible Navier-Stokes equations. A nonuniform cartesian grid was used for the computation. The numerical scheme used was the QUICK scheme. Comparisons with experimental measurements of Jayaweera and Mason show that the results of the simulation are satisfactory. Features of three-dimensional unsteady viscous flow past finite cylinders, such as the pyramidal wake and the three-dimensional von Karmen vortex street, are successfully simulated.

Viscous Displacement in a Hele-Shaw Cell

Abstract: A Hele-Shaw cell is a pair of parallel plates that are separated by a small gap 6 . The motion of a less viscous fluid displacing a more viscous fluid in this gap under the action of some imposed pressure gradient or gravity or fluid injection has been the study of intensive research over the last decade. (See Saffman1, Bensimon et al2, Homsy3, Pelee4 and Kessler, Koplik & Levine5 for reviews from a range of perspectives). This has been spurred by the newly discovered mathematical analogies between this flow and dendritic crystal growth, directional solidification and diffusion limited aggregation (see references 4,5), though Darcian flow through a porous medium was the original motivation6. In most Hele-Shaw cell studies to date, the geometry consists of a long rectilinear channel where the width of the cell is 2a , with b << a (Figure 1). In this case, the interfacial motion is caused by an imposed pressure gradient which causes the more viscous fluid at infinity to be displaced with velocity V . Alternately, gravity can effect the interfacial displacement.

A finite volume technique to simulate the flow of a viscoelastic fluid

Abstract: Hydrodynamically developing flow of Oldroyd B fluid in the planar die entrance region has been investigated numerically using SIMPLER algorithm in a non-uniform staggered grid system. It has been shown that for constant values of the Reynolds number, the entrance length increases as the Weissenberg number increases. For small Reynolds number flows the center line velocity distribution exhibit overshoot near the inlet, which seems to be related to the occurrence of numerical breakdown at small values of the limiting Weissenberg number than those for large Reynolds number flows. The distributions of the first normal stress difference display clearly the development of the flow characteristics from extensional flow to shear flow.

Secondary cells and separation in developing laminar curved-pipe flows

Abstract: Laminar flows through 180° curved bends of circular cross section are investigated numerically. For small curvature ratio, α, defined as pipe radius over mean bend radius, the governing equations could be parabolized. The equations are solved for an α range of from 0.04 to 0.143, a Dean number (De) range of from 277.5 to 1360, and for a uniform flow, a potential vortex, and a parabolic flow inlet condition. In all these studies a zero cross-stream flow at the inlet is assumed. A detailed study of the effects of α, De, and inlet condition on the secondary flow pattern is carried out. Within the range of parameters investigated, up to three secondary cells are found in the cross-stream half-plane of a curved pipe. They are the Dean-type secondary cell, a secondary separation cell near the inner bend (closest to the center of curvature of the bend), and a third cell near the pipe center. The number of secondary cells in the cross-stream half-plane is greatly influenced by the inlet flow, and to a much lesser extent by α and De. For example, only the Dean cell is found in a curved-pipe flow where α and De are small and the inlet flow is either uniform or a potential vortex. When the inlet condition of the same case is changed to a parabolic flow, a three-cell structure results. Furthermore, as De increases to 1180, incipient axial flow separation begins at around 23° downstream of the curved-pipe entrance. The formation and extent of the separation and third cells are investigated together with their dependence on the parameters studied. This investigation further shows that, within the range of parameters examined, there is no secondary cell occurring near the outer bend, contrary to some earlier findings on fully developed curved-pipe flows.

General Three-Dimensional Viscous Primary/Secondary Flow Analysis

Abstract: Generalized primary/secondary flow equations are derived as an approximation to the Navier-Stokes equations for three-dimensional viscous flows with a dominant flow direction. The primary/secondary flow equations are well posed for solution by spatial marching and can be solved one to two orders of magnitude faster than the Navier-Stokes equations. A key element in the approximations, which is a distinguishing feature of the present approach, is that accuracy is related to curvature terms obtained from a local primary flow direction rather than the coordinate system used to describe geometry of the flowfield. Potential flow streamlines for the flow geometry under consideration are a suitable choice for the primary flow direction. A sequentially decoupled implicit algorithm has been developed that exploits the form of the primary/secondary flow equations to obtain decoupled subsets of equations through choices for dependent variables, the sequence of equations, and the linearization scheme. Each of the equation subsets is solved by efficient and appropriate implicit numerical procedures. Computed solutions for flow in 90-deg bends agree very well with experimental data and NavierStokes solutions. The combined efficiency and accuracy of the approximate equations and solution algorithm make this approach attractive for problems in which a suitable primary flow direction can be identified.

Self-excited compressible flow in a pipe-collar nozzle

Abstract: The turbulent flow in a duct with an abrupt increase in its cross-sectional area is very unstable and exhibits strong oscillations. Such a flow is investigated experimentally using a simple device — a pipe–collar nozzle, composed of a convergent nozzle and a pipe lengthened by a collar with an enlarged cross-section. The oscillating flow characteristics are considered over a wide range of flow velocities including both subsonic and transonic flow regimes. Two modes of symmetric and one of asymmetric oscillations are distinguished. For the first mode of symmetric oscillation the jet is separated in each phase of the oscillation cycle, whereas for the second the jet alternately separates and reattaches to the collar wall. Both modes of symmetric oscillations are controlled by shear-layer instability of the collar flow. For low velocities and short collars the oscillation is also affected by the organ-pipe resonance in the preceding pipe. The asymmetric oscillation appears at relatively large flow Mach numbers. This mode exhibits a radial resonance of the jet.

Flow Around Horizontal Circular Cylinder in Shallow Flows

Abstract: This paper describes changes to the flow pattern around a horizontal circular cylinder immersed in shallow open-channel flows, with different gap openings between the cylinder and the bed. Experiments show that the low flow depth causes backup of the upstream flow depth due to choking of the flow. This phenomenon causes the occurrence of a weir-flow condition at the cylinder, where a large drawdown forms. The net result is an increase of the drag force. When a gap is present between the underside of the cylinder and the bed, the oncoming flow divides itself into two components as it approaches the cylinder. The study presents a unique relationship describing the amount of gap flow as a function of the undisturbed flow depth and gap size. Changes to both the drag and lift forces exerted on the cylinder for different flow depth and gap size combinations were measured and reasons for these changes discussed.

Gas‐liquid two‐phase flow in symmetrically dividing horizontal tubes

Abstract: The time-averaged void fraction, pressure drop and flow regime transition behavior of horizontal air-water two-phase flows is studied experimentally and numerically for 2-cm-inner-diameter tubes with various flow dividing junctions at its end The time-average void and pressure drop behavior along the channel is simulated using a two fluid separated flow model The results show that two-phase behavior (flow regime, void fraction, and pressure drop) is affected strongly by the presence of a flow division in the system These effects extend far upstream of the junction for low-momentum flows and far downstream for high-momentum flows Both numerical and experimental results show that there occurs a large increase in void just downstream of the junction owing to the halving of the fluid volume flow rates and the liquid deceleration

Three-dimensional viscous flow computations of high area ratio nozzles for hypersonic propulsion

Abstract: The PARC3D code was selected by the authors to analyze a variety of complex and high-speed flow configurations. Geometries considered for code validation include ramps and corner flows, which are characteristic of inlets and nozzles. Flows with Mach numbers of 3-14 were studied. Both two- and three-dimensional experimental data for shock-boundary-layer interaction were considered to validate the code. A detailed comparison of various flow parameters with available experimental data is presented; agreement between the solutions and the experimental data in terms of pitot pressure profiles, yaw-angle distributions, static pressures, and skin friction is found to be very good. In addition, two- and three-dimensional flow calculations were performed for a hypersonic nozzle. Comparison of the wall pressure results with the published solutions is made for the two-dimensional case.

An Analysis Methodology for Internal Swirling Flow Systems With a Rotating Wall

Abstract: We present an analysis methodology for the calculation of the flow through internal flow components with a rotating wall such as annular seals, impeller cavities, and enclosed rotating disks. These flow systems are standard components in gas turbines and cryogenic engines and are characterized by subsonic viscous flow and elliptic pressure effects. The Reynolds-averaged Navier-Stokes equations for turbulent flow are used to model swirling axisymmetric flow

Modeling of subsonic flow through a compact offset inlet diffuser

Abstract: This paper presents a comparison of computational and experimental results that were obtained during an investigation of compressible flow through a compact, highly offset diffuser. Entrance values for the Mach number and the Reynolds number were 0.341 and 5.75(10)5, respectively. Strong curvature of the diffuser centerline produced extensive separation along one wall, which resulted in an exhaust flow with highly complex crossflow patterns and spatial nonuniformities. Our objective was to evaluate the use of an existing thin-layer Navier-Stokes code (ARC3D) to predict effects of diffuser shape and inlet flow properties on pressure recovery and exit flow quality. Comparisons are shown between computed and measured flow velocity components and wall pressure distributions. Agreement was satisfactory except in regions of separated flow. The Baldwin-Lomax algebraic turbulence model used in the code does not appear to represent adequately this complex separated region. We present preliminary results of computations made with a one-half-equation turbulence model, which accounts for some of the history effects in computing the turbulence length scale. The computed results show that the details of the axial velocity distribution in the separated flow region were quite different for the two turbulence models, but other features of the flow, such as the static pressure distributions, were only slightly affected.