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Showing papers on "Hele-Shaw flow published in 1997"


Journal ArticleDOI
TL;DR: In this article, a self-sustaining process for wall-bounded shear flows is investigated, which consists of streamwise rolls that redistribute the mean shear to create streaks that wiggle to maintain the rolls.
Abstract: A self-sustaining process conjectured to be generic for wall-bounded shear flows is investigated. The self-sustaining process consists of streamwise rolls that redistribute the mean shear to create streaks that wiggle to maintain the rolls. The process is analyzed and shown to be remarkably insensitive to whether there is no-slip or free-slip at the walls. A low-order model of the process is derived from the Navier–Stokes equations for a sinusoidal shear flow. The model has two unstable steady solutions above a critical Reynolds number, in addition to the stable laminar flow. For some parameter values, there is a second critical Reynolds number at which a homoclinic bifurcation gives rise to a stable periodic solution. This suggests a direct link between unstable steady solutions and almost periodic solutions that have been computed in plane Couette flow. It is argued that this self-sustaining process is responsible for the bifurcation of shear flows at low Reynolds numbers and perhaps also for controlling the near-wall region of turbulent shear flows at higher Reynolds numbers.

914 citations


Journal ArticleDOI
TL;DR: This method combines the advantage of the two approaches and gives a second-order Eulerian discretization for interface problems and is applied to Hele?Shaw flow, an unstable flow involving two fluids with very different viscosity.

279 citations


Journal ArticleDOI
TL;DR: In this paper, an existing design of conductivity probe for the measurement of void fraction has been developed and tested, and the probe's response to different void distributions supported the calibration results.

239 citations


Journal ArticleDOI
TL;DR: In this paper, a numerical study of laminar incompressible flows in symmetric plane sudden expansions was carried out, and the results revealed that the flow remains symmetric up to a certain Reynolds number depending on the expansion ratio, while asymmetries appear at higher Reynolds numbers.
Abstract: A numerical study of laminar incompressible flows in symmetric plane sudden expansions was carried out. Computations were performed for various Reynolds number and expansion ratios. The results revealed that the flow remains symmetric up to a certain Reynolds number depending on the expansion ratio, while asymmetries appear at higher Reynolds numbers. The computations indicated that the critical Reynolds number of the symmetry‐breaking bifurcation reduces when increasing the expansion ratio while the flow regains symmetry downstream of an initial channel length. The flow asymmetries were verified by comparing several discretization schemes up to fourth order of accuracy as well as various iterative solvers.

218 citations


Journal ArticleDOI
TL;DR: In this paper, the simulation of 3D gas-particle flow through a fibrous filter has been studied for different Stokes numbers to study the influence of hydrodynamics on particle deposition.

209 citations


Journal ArticleDOI
TL;DR: In this paper, the flow induced by a long bubble steadily displacing a liquid confined by two closely located parallel plates or by a cylindrical tube of small diameter is numerically analyzed.
Abstract: The flow induced by a long bubble steadily displacing a liquid confined by two closely located parallel plates or by a cylindrical tube of small diameter is numerically analyzed. The technique employed solves the complete set of governing equations simultaneously. The present analysis encompasses, and also extends, the whole range of Capillary values previously studied with various numerical techniques. The results shown uncover a type of recirculating flow pattern that appears to have been overlooked before. The effects of the inertial forces on the liquid flow rate are also assessed.

190 citations


Journal ArticleDOI
TL;DR: In this paper, a three-dimensional simulation of the step geometry for 100 ⩽ Re⩽ 800 and correctly predicts the primary reattachment lengths, thus confirming the influence of three dimensionality.
Abstract: A numerical investigation of laminar flow over a three-dimensional backward-facing step is presented with comparisons with detailed experimental data, available in the literature, serving to validate the numerical results. The continuity constraint method, implemented via a finite element weak statement, was employed to solve the unsteady three-dimensional Navier–Stokes equations for incompressible laminar isothermal flow. Two-dimensional numerical simulations of this step geometry underestimate the experimentally determined extent of the primary separation region for Reynolds numbers Re greater than 400. It has been postulated that this disagreement between physical and computational experiments is due to the onset of three-dimensional flow near Re ≈ 400. This paper presents a full three-dimensional simulation of the step geometry for 100⩽ Re⩽ 800 and correctly predicts the primary reattachment lengths, thus confirming the influence of three-dimensionality. Previous numerical studies have discussed possible instability modes which could induce a sudden onset of three-dimensional flow at certain critical Reynolds numbers. The current study explores the influence of the sidewall on the development of three-dimensional flow for Re greater than 400. Of particular interest is the characterization of three-dimensional vortices in the primary separation region immediately downstream of the step. The complex interaction of a wall jet, located at the step plane near the sidewall, with the mainstream flow reveals a mechanism for the increasing penetration (with increasing Reynolds number) of three-dimensional flow structures into a region of essentially two-dimensional flow near the midplane of the channel. The character and extent of the sidewall-induced flow are investigated for 100⩽Re⩽ 800. © 1997 John Wiley & Sons, Ltd.

156 citations


Journal ArticleDOI
TL;DR: In this article, the steady flow in rectangular cavities is investigated both numerically and experimentally, and it is found that the basic two-dimensional flow is not always unique.
Abstract: The steady flow in rectangular cavities is investigated both numerically and experimentally. The flow is driven by moving two facing walls tangentially in opposite directions. It is found that the basic two-dimensional flow is not always unique. For low Reynolds numbers it consists of two separate co-rotating vortices adjacent to the moving walls. If the difference in the sidewall Reynolds numbers is large this flow becomes unstable to a stationary three-dimensional mode with a long wavelength. When the aspect ratio is larger than two and both Reynolds numbers are large, but comparable in magnitude, a second two-dimensional flow exists. It takes the form of a single vortex occupying the whole cavity. This flow is the preferred state in the present experiment. It becomes unstable to a three-dimensional mode that subdivides the basic streched vortex flow into rectangular convective cells. The instability is supercritical when both sidewall Reynolds numbers are the same. When they differ the instability is subcritical. From an energy analysis and from the salient features of the three-dimensional flow it is concluded that the mechanism of destabilization is identical to the destabilization mechanism operative in the elliptical instability of highly strained vortices.

146 citations


Journal ArticleDOI
TL;DR: In this article, the main flow features of subcritical junction flows are explored, based on an extended hydraulic model study, and the flow conditions chosen resulted in flows that are governed by the Froude similarity law.
Abstract: The main flow features of subcritical junction flows are explored, based on an extended hydraulic model study. The flow conditions chosen resulted in flows that are governed by the Froude similarity law. So-called simple junctions with junction angles of 30°, 60°, and 90° were tested. The main emphasis was made in determining the characteristics of the lateral flow and the flow contraction in the tailwater branch. Further, expressions for the momentum correction coefficients, the lateral wall pressure force, and the ratio of flow depths in the lateral and upstream branches were provided. A rational approach for the momentum contribution of the lateral branch is presented and applied for the prediction of the backwater effect across a simple junction. The complex flow pattern is further documented with selected photographs such that a rather complete description of junction flow is now available.

135 citations


Book
01 Jan 1997
TL;DR: The equations of steady one-dimensional compressible flow have been studied in this paper, where the authors introduce the concept of two-dimensional flow hypersonic flow and high temperature flows low density flows.
Abstract: The equations of steady one-dimensional compressible flow some fundamental aspects of compressible flow one-dimensional isentropic flow normal shock waves oblique shock waves expansion waves - Prandtl-Meyer flow variable area flow adiabatic flow with friction flow with heat addition generalized quasi one-dimensional flow numerical analysis of one-dimensional flows aerodynamic heating an introduction to two-dimensional compressible flow hypersonic flow high temperature flows low density flows.

124 citations


Journal ArticleDOI
TL;DR: In this paper, the authors study the parallel flow in a Hele-Shaw cell of two immiscible fluids, a gas and a viscous liquid, driven by a given pressure gradient.
Abstract: We study experimentally the parallel flow in a Hele–Shaw cell of two immiscible fluids, a gas and a viscous liquid, driven by a given pressure gradient. We observe that the interface is destabilized above a critical value of the gas flow and that waves grow and propagate along the cell. The experimental threshold corresponds to a velocity difference of the two fluids in good agreement with the inviscid Kelvin–Helmholtz instability, while the wave velocity corresponds to a pure viscous theory deriving from Darcy’s law. We report our experimental results and analyze this instability by the study of a new equation where the viscous effects are added to the Euler equation through a unique drag term. The predictions made from the linear stability analysis of this equation agree with the experimental measurements.

Journal ArticleDOI
TL;DR: In this article, the displacement of miscible fluids between two parallel plates, for different values of the Peclet number Pe and of the viscosity ratio M, was studied.
Abstract: We study the displacement of miscible fluids between two parallel plates, for different values of the Peclet number Pe and of the viscosity ratio M. The full Navier–Stokes problem is addressed. As an alternative to the conventional finite difference methods, we use the BGK lattice gas method, which is well suited to miscible fluids and allows us to incorporate molecular diffusion at the microscopic scale of the lattice. This numerical experiment leads to a symmetric concentration profile about the middle of the gap between the plates; its shape is determined as a function of the Peclet number and the viscosity ratio. At Pe of the order of 1, mixing involves diffusion and advection in the flow direction. At large Pe, the fluids do not mix and an interface between them can be defined. Moreover, above M∼10, the interface becomes a well-defined finger, the reduced width of which tends to λ∞=0.56 at large values of M. Assuming that miscible fluids at high Pe are similar to immiscible fluids at high capillary numbers, we find the analytical shape of that finger, using an extrapolation of the Reinelt–Saffman calculations for a Stokes immiscible flow. Surprisingly, the result is that our finger can be deduced from the famous Saffman–Taylor one, obtained in a potential flow, by a stretching in the flow direction by a factor of 2.12.

Journal ArticleDOI
TL;DR: In this paper, the authors consider flow in a Hele- Shaw cell for which the upper plate is being lifted uniformly at a specified rate, which puts the fluid under a lateral straining flow, sucking in the interface and causing it to buckle.
Abstract: We consider flow in a Hele - Shaw cell for which the upper plate is being lifted uniformly at a specified rate. This lifting puts the fluid under a lateral straining flow, sucking in the interface and causing it to buckle. The resulting short-lived patterns can resemble a network of connections with triple junctions. The basic instability - a variant of the Saffman - Taylor instability - is found in a version of the two-dimensional Darcy's law, where the divergence condition is modified to account for the lifting of the plate. For analytic data, we establish the existence, uniqueness and regularity of solutions when the surface tension is zero. We also construct some exact analytic solutions, both with and without surface tension. These solutions illustrate some of the possible behaviours of the system, such as cusp formation and bubble fission. Further, we present the results of numerical simulations of the bubble motion, examining in particular the distinctive pattern formation resulting from the Saffman - Taylor instability, and the effect of surface tension on a bubble evolution that in the absence of surface tension would fission into two bubbles. AMS classification scheme numbers: 76E30, 76D45

Journal ArticleDOI
TL;DR: In this paper, the authors used a sliding mesh method for various Reynolds numbers, mostly in the laminar regime, to calculate the flow pattern created by a pitched blade turbine, and concluded that this method is suitable for the prediction of flow patterns in stirred tanks.
Abstract: The flow pattern created by a pitched blade turbine was calculated using a sliding mesh method for various Reynolds numbers, mostly in the laminar regime. This method allows flow pattern calculations without the use of any experimental boundary conditions. The results compared favourably with experimental data obtained by laser-Doppler velocimetry. At low Reynolds number, the impeller creates a radial flow pattern rather than axial and the pumping number decreases with decreasing Reynolds number. It is concluded that the sliding mesh method is suitable for the prediction of flow patterns in stirred tanks.

Journal ArticleDOI
TL;DR: In this article, a detailed experimental investigation of the flow was conducted using Laser Doppler Anemometry (LDA) in the close vicinity of the permeable boundary of a porous medium.
Abstract: Fluid flow at the interface of a porous medium and an open channel is the governing phenomenon in a number of processes of industrial importance. Traditionally, this has been modeled by applying the Brinkman’s modification of Darcy’s law to obtain the velocity profile in terms of an additional parameter known as the “apparent viscosity” or the “slip coefficient”. To test this ad hoc approach, a detailed experimental investigation of the flow was conducted using Laser Doppler Anemometry (LDA) in the close vicinity of the permeable boundary of a porous medium. The porous medium used in the experiments consisted of a network of continuous glass strands woven together in a random fashion.

01 Feb 1997
TL;DR: In this paper, a numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries, which greatly reduced the cost and complexity of the computations.
Abstract: A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.

Journal ArticleDOI
TL;DR: In this paper, the effect of fluid elasticity on stability of viscoelastic Boger fluids has been investigated using pressure drop measurements along the flow direction as a function of flow rate as well as flow visualization.
Abstract: Low Reynolds number flow of Newtonian and viscoelastic Boger fluids past periodic square arrays of cylinders with a porosity of 0.45 and 0.86 has been studied. Pressure drop measurements along the flow direction as a function of flow rate as well as flow visualization has been performed to investigate the effect of fluid elasticity on stability of this class of flows. It has been shown that below a critical Weissenberg number (Wec), the flow in both porosity cells is a two-dimensional steady flow, however, pressure fluctuations appear above Wec which is 2.95±0.25 for the 0.45 porosity cell and 0.95±0.08 for the higher porosity cell. Specifically, in the low porosity cell as the Weissenberg number is increased above Wec a transition between a steady two-dimensional to a transient three-dimensional flow occurs. However, in the high porosity cell a transition between a steady two-dimensional to a steady three-dimensional flow consisting of periodic cellular structures along the length of the cylinder in the space between the first and the second cylinder occurs while past the second cylinder another transition to a transient three-dimensional flow occurs giving rise to time- dependent cellular structures of various wavelengths along the length of the cylinder. Overall, the experiments indicate that viscoelastic flow past periodic arrays of cylinders of various porosities is susceptible to purely elastic instabilities. Moreover, the instability observed in lower porosity cells where a vortex is present between the cylinders in the base flow is amplifieds spatially, that is energy from the mean flow is continuously transferred to the disturbance flow along the flow direction. This instability gives rise to a rapid increase in flow resistance. In higher porosity cells where a vortex between the cylinders is not present in the base flow, the energy associated with the disturbance flow is not greatly changed along the flow direction past the second cylinder. In addition, it has been shown that in both flow cells the instability is a sensitive function of the relaxation time of the fluid. Hence, the instability in this class of flows is a strong function of the base flow kinematics (i.e., curvature of streamlines near solid surfaces), We and the relaxation time of the fluid.

Journal ArticleDOI
TL;DR: In this paper, the velocity profiles obtained by a 3-D lattice BGK simulation are successfully compared to the analytical results in the one-and two-fluid cases, and the velocity profile at the interface is strictly a parabola.
Abstract: The parallel flow of one or two fluids of contrasted viscosities through a rectangular channel of large aspect ratio is studied. The usual result for an infinite aspect ratio is that the velocity profile is parabolic throughout the gap and flat in the other direction. For a finite aspect ratio a deviation from this usual profile is found in boundary layers along the edges of the channel or close to the interface. The extension of these boundary layers is of the order of the small dimension of the channel. In the two-fluid case we find, however, that the velocity profile at the interface is strictly a parabola. The velocity profiles obtained by a 3-D lattice BGK simulation are successfully compared to the analytical results in the one- and two-fluid cases.

Journal ArticleDOI
TL;DR: In this article, the steady flow of an incompressible material of the Bingham viscoplastic type along a rectangular duct is calculated using finite differencing of the partial differential equation governing the fluid motion.
Abstract: The steady flow of an incompressible material of the Bingham viscoplastic type along a rectangular duct is calculated. This flow has importance in a number of geophysical problems. A numerical solution to the problem is found using finite differencing of the partial differential equation governing the fluid motion. The flow is seen to consist of a plug in the center of the duct with dead regions of “no-flow’’ at the corners, due to the rectangular cross section. The variation of this flow pattern as a function of two nondimensional parameters, the yield stress and the aspect ratio, is investigated.

Journal ArticleDOI
TL;DR: In this article, the effects of buoyancy on the stability and morphology of Taylor-Couette flow have been analyzed using a hybrid Chebyshev collocation/Fourier spectral method.
Abstract: Numerical simulations of the effects of buoyancy on the stability and morphology of Taylor–Couette flow have been conducted. The three-dimensional equations of motion are discretized using a hybrid Chebyshev collocation/Fourier spectral method. The problem geometry consists of an air-filled vertical annulus with radius ratio, η=ri/ro=0.5 (where ri and ro are the inner and outer radii, respectively), and aspect ratio, Γ=L/(ro−ri)=10 (where L is the height of the annulus). The flow is generated by combined heating and rotation of the inner cylinder. Results for various values of the Reynolds number, Re, and Grashof number, Gr, show several bifurcations of the system. The most notable change in flow structure with increasing rotational effects is the onset of spiral flow in certain parameter ranges. Compared to existing analytical and experimental results, the current numerical results show good agreement.

Journal ArticleDOI
TL;DR: In this article, the formulation of the governing equations that describe flow of fluids in porous media was discussed and various types of fluid flow, ranging from single-phase flow to compositional flow, were considered.
Abstract: In this paper we discuss the formulation of the governing equations that describe flow of fluids in porous media Various types of fluid flow, ranging from single-phase flow to compositional flow, are considered It is shown that all the differential equations governing these types of flow can be effectively rewritten in a fractional flow formulation; ie, in terms of a global pressure and saturation (or saturations), and that mixed finite element methods can be accurately exploited to solve the pressure equation Numerical results are presented to see the performance of the mixed methods for the flow equations in three space dimensions

Journal ArticleDOI
TL;DR: In this paper, a large eddy simulation (LES) with the Smagorinsky subgrid-scale model was used to solve the filtered three-dimensional incompressible Navier-Stokes equations.
Abstract: A steady approach flow around a circular cylinder is investigated by using a large eddy simulation (LES) with the Smagorinsky subgrid-scale model A second-order accurate in time fractional-step method and a combined finite-difference/spectral approximation are employed to solve the filtered three-dimensional incompressible Navier-Stokes equations To demonstrate the viability and accuracy of the method, we present results at Reynolds numbers of 100, 3 × 103 , 2 × 104 , and 442 × 104 At Re = 100, the physical flow is two-dimensional and the calculation is done without use of the LES method For the higher values of Re, the flow in the wake is three-dimensional and turbulent and the LES method is necessary to describe the flow accurately Calculated values of lift and drag coefficients and Strouhal number are in good agreement with the experimentally determined values at all of the Reynolds numbers for which calculation was done

Journal ArticleDOI
TL;DR: In this article, an experimental investigation is described for a concentric annular flow over an axisymmetric sudden expansion by using both flow visualization and laser-Doppler anemometry (LDA) techniques.
Abstract: In this paper, an experimental investigation is described for a concentric annular flow over an axisymmetric sudden expansion by using both flow visualization and laser-Doppler anemometry (LDA) techniques. Depending upon the value of the Reynolds number and whether the Reynolds number was increased or decreased, four typical flow patterns were classified according to the characteristics of the central and corner recirculation zones. The flow patterns are open annular flow, closed annular flow, vortex shedding, and stable central flow. Bifurcation for this flow occurred when 230 < Re < 440, which was verified by observing the variation of the reattachment length. The spatial growth of velocity fluctuations from the measurements demonstrated a tendency that shedding vortices behind the centrebody more strongly affect the reattachment length than flows without a centrebody.

Journal ArticleDOI
TL;DR: In this article, a simple theoretical model that permits one to investigate surface-tension-driven flows with complex interface geometry is proposed, which consists of a Hele-Shaw cell filled with two different fluids and subjected to a unidirectional temperature gradient.
Abstract: We formulate a simple theoretical model that permits one to investigate surface-tension-driven flows with complex interface geometry The model consists of a Hele-Shaw cell filled with two different fluids and subjected to a unidirectional temperature gradient The shape of the interface that separates the fluids can be arbitrarily complex If the contact line is pinned, ie unable to move, the problem of calculating the flow in both fluids is governed by a linear set of equations containing the characteristic aspect ratio and the viscosity ratio as the only input parameters Analytical solutions, derived for a linear interface and for a circular drop, demonstrate that for large aspect ratio the flow field splits into a potential core flow and a thermocapillary boundary layer which acts as a source for the core An asymptotic theory is developed for this limit which reduces the mathematical problem to a Laplace equation with Dirichlet boundary conditions This problem can be efficiently solved utilizing a boundary element method It is found that the thermocapillary flow in non-circular drops has a highly non-trivial streamline topology After releasing the assumption of a pinned interface, a linear stability analysis is carried out for the interface under both transverse and longitudinal temperature gradients For a semi-infinite fluid bounded by a freely movable surface long-wavelength instability due to the temperature gradient across the surface is predicted The mechanism of this instability is closely related to the long-wave instability in surface-tension-driven Benard convection A linear interface heated from the side is found to be linearly stable The possibility of experimental verification of the predictions is briefly discussed

Journal ArticleDOI
TL;DR: In this article, the surface roughness of isotropic rough surfaces has been studied numerically and the flow factors given in the so-called average flow model have been calculated.
Abstract: The lubrication of isotropic rough surfaces has been studied numerically, and the flow factors given in the so-called Average Flow Model have been calculated. Both pressure flow and shear flow are considered. The flow factors are calculated from a small bearing part, and it is shown that the flow in the interior of this subarea is nearly unaffected by the bearing part's boundary conditions. The surface roughness is generated numerically, and the Reynolds equation is solved by the finite element method. The method used for calculating the flow factors can be used for different roughness patterns.

Journal ArticleDOI
TL;DR: A parallel finite volume method for unstructured grids is used for a direct numerical simulation of the flow around a sphere at Re = 5000, which provides a data base for future model evaluations.
Abstract: A parallel finite volume method for unstructured grids is used for a direct numerical simulation of the flow around a sphere at Re = 5000 (based on the sphere diameter and undisturbed velocity). The observed flow structures are confirmed by visualization experiments. A quantitative analysis of the Reynolds averaged flow provides a data base for future model evaluations.

Journal ArticleDOI
TL;DR: Linear stability analysis is used to predict the onset of instabilities in inertialess viscoelastic planar stagnation flow as discussed by the authors, which is valid in the limit of vanishingly small Reynolds numbers, becomes unstable to localized three-dimensional disturbances.
Abstract: Linear stability analysis is used to predict the onset of instabilities in inertialess viscoelastic planar stagnation flow. Beyond a critical value of the dimensionless flow rate, or Deborah number, the creeping base flow of similarity type, which is valid in the limit of vanishingly small Reynolds numbers, becomes unstable to localized three-dimensional disturbances. Stability calculations of the local similarity type viscoelastic flow in a small region near the stagnation plane are reported for the quasi-linear Oldroyd-B constitutive equation. The stability results for a range of Deborah numbers and viscosity ratio are presented to explore systematically the effects of elasticity and other rheological properties. The onset of instability and the temporal and spatial characteristics of the secondary flow predicted here resemble other purely elastic instabilities measured and predicted for viscoelastic flows in other simple and complex geometries with curved streamlines.

Journal ArticleDOI
TL;DR: In this paper, the flow of a non-Newtonian viscoplastic Bingham fluid over an axisymmetric sudden expansion is studied by numerically solving the governing fullyelliptic continuity and momentum equations.
Abstract: The flow of a non-Newtonian viscoplastic Bingham fluid over an axisymmetric sudden expansion is studied by numerically solving the governing fully-elliptic continuity and momentum equations. Solutions are obtained for a wide range of Reynolds and yield numbers in the laminar flow regime with constant fluid properties. The preset work demonstrates that the finite-difference technique can successfully be employe to obtain solutions to separating/reattaching internal flows of Bingham plastics. The results demonstrate the strong effects of the yield and Reynolds numbers on both th integral and the local structure of the separating and reattaching flow. Higher yield numbers result in larger overall effective viscosities and thus faster flow recover downstream of the sudden expansion. The reattachment length decreases with increas ing yield numbers, eventually reaching an asymptotic nonzero value which, in turn, is dependent on the Reynolds number. The strength of the recirculating flow also decreases with increasing yield numbers.

Journal ArticleDOI
TL;DR: In this article, the convective instability boundary of a Couette flow in the annular region bounded by two co-rotating coaxial cylinders with angular velocities ω1 and ω2, respectively, is studied in the presence of an axial flow due to a constant axial pressure gradient and a radial flow through the permeable walls of the cylinders.
Abstract: The convective instability boundary of a circular Couette flow in the annular region bounded by two co- or counter-rotating coaxial cylinders with angular velocities ω1 and ω2, respectively, is studied in the presence of an axial flow due to a constant axial pressure gradient and a radial flow through the permeable walls of the cylinders. A linear stability analysis is carried out for positive and negative radial Reynolds numbers corresponding to outward and inward radial flows, respectively. Axisymmetric and non-axisymmetric disturbances are considered. In the particular case of no axial flow, the Couette flow is stabilized by an inward, or a strong outward, radial flow, but destabilized by a weak outward radial flow. Non-axisymmetric disturbances lead to instability for some negative values of μ=ω2/ω1. Bifurcation diagrams for combined radial and axial flows are more complicated. For particular values of the parameters of the problem, the Couette flow has regions of stabilization and destabilization in ...

Journal ArticleDOI
TL;DR: In this article, the authors investigate the closed flow between coaxial rotating disks, at moderate to high Reynolds numbers, and show that global (i.e. spatially averaged) quantities can be used to characterize the state of the flow and its degree of turbulence.
Abstract: We investigate the closed flow between coaxial contra rotating disks, at moderate to high Reynolds numbers. We show that global (i.e. spatially averaged) quantities can be used to characterize the state of the flow and its degree of turbulence. We first report measurements on the driving torque and show how it depends on the manner momentum is imparted to the fluid. We then show that pressure measurements at the flow boundary provide a good estimate of the rms velocity fluctuations in the flow and that it reveals the transition to turbulence in the flow volume. Finally, we show that once the transition has occurred, the knowledge of the same global quantities allows the calculation of fundamental turbulence characteristics such as the rms velocity fluctuations, the effective integral length scale L * , Taylor's microscale λ and Kolmogorov's dissipation length η. That these quantities may be obtained from measuring devices removed from the bulk of the flow is of importance for the study of fluid motion in complex geometries and/or using corrosive fluids