Showing papers on "Hele-Shaw flow published in 1976"

Experiments on transition to turbulence in an oscillatory pipe flow

Abstract: Experiments on transition to turbulence in a purely oscillatory pipe flow were performed for values of the Reynolds number Rδ, defined using the Stokes-layer thickness δ = (2ν/ω)½ and the cross-sectional mean velocity amplitude U, from 19 to 1530 (or for values of the Reynolds number Re, defined using the pipe diameter d and U, from 105 to 5830) and for values of the Stokes parameter λ = ½d(ω/2ν)½ (ν = kinematic viscosity and ω = angular frequency) from 1·35 to 6·19. Three types of turbulent flow regime have been detected: weakly turbulent flow, conditionally turbulent flow and fully turbulent flow. Demarcation of the flow regimes is possible on Rλ, λ or Re, λ diagrams. The critical Reynolds number of the first transition decreases as the Stokes parameter increases. In the conditionally turbulent flow, turbulence is generated suddenly in the decelerating phase and the profile of the velocity distribution changes drastically. In the accelerating phase, the flow recovers to laminar. This type of partially turbulent flow persists even at Reynolds numbers as high as Re = 5830 if the value of the Stokes parameter is high.

Foundations of aerodynamics: bases of aerodynamic design

Abstract: The Fluid Medium. Kinematics of a Flow Field. Dynamics of Flow Fields. Irrotational Incompressible Flow About Two-Dimensional Bodies. Aerodynamic Characteristics of Airfoils. The Finite Wing. Introduction to Compressible Fluids. Energy Relations. Some Applications of One-Dimensional Compressible Flow. Waves. Linearized Compressible Flow. Airfoils in Compressible Flows. Wings and Wing-Body Combinations in Compressible Flow. The Dynamics of Viscous Fluids. Incompressible Laminar Flow in Tubes and Boundary Layers. Laminar Boundary Layers in Compressible Flow. Flow Instabilities and Transition from Laminar to Turbulent Flow. Turbulent Flows. Airfoil Design, Multiple Surfaces, Vortex Lift, Secondary Flows, Viscous Effects. Appendices. Tables. Oblique Shock Chart. References. Index.

A complete second-order theory for the unsteady flow about an airfoil due to a periodic gust

Abstract: A uniformly valid second-order theory is developed for calculating the unsteady incompressible flow that occurs when an airfoil is subjected to a convected sinusoidal gust. Explicit formulas for the airfoil response functions (i.e., fluctuating lift) are given. The theory accounts for the effect of the distortion of the gust by the steady-state potential flow around the airfoil, and this effect is found to have an important influence on the response functions. A number of results relevant to the general theory of the scattering of vorticity waves by solid objects are also presented.

STAN5: A program for numerical computation of two-dimensional internal and external boundary layer flows

Abstract: A large variety of two dimensional flows can be accommodated by the program, including boundary layers on a flat plate, flow inside nozzles and diffusers (for a prescribed potential flow distribution), flow over axisymmetric bodies, and developing and fully developed flow inside circular pipes and flat ducts. The flows may be laminar or turbulent, and provision is made to handle transition.

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

Abstract: The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

Drag on an axially symmetric body in the Stokes’ flow of micropolar fluid

Abstract: The Stokes’ flow problem is considered for micropolar fluids in which the obstacle has an axis of symmetry, and the flow at distant points is uniform and parallel to this axis. A general expression for the drag is derived by using the arguments involving an axisymmetric point force and application is illustrated for the flow past a sphere.

A moving-wall boundary layer with reverse flow

Abstract: The problem of uniform flow past a flat plate whose surface has a constant velocity λU opposite in direction to that of the mainstream is considered for large values of the Reynolds number R. In a previous communication (Klemp & Acrivos 1972) it was shown that, if the region of reverse flow which is established next to the plate as a consequence of its motion is O(R−1/2) in thickness, the appropriate laminar boundary-layer equations have a solution provided λ ≤ 0·3541. Here the analysis is extended to the range λ > 0·3541, which cannot be treated using a conventional boundary-layer approach. Specifically, it is found that for λ > 0·3541 the flow consists of three overlapping domains: (a) the external uniform flow; (b) a conventional boundary layer with reverse flow for xs 1.Also, detailed streamline patterns were obtained numerically for various λ's in the range of 0 ≤ λ ≤ 2 using a novel computational scheme which was found to be more efficient than that previously reported. Interestingly enough, the drag first decreased with λ, reached a minimum at λ = 0.3541, and then increased monotonically until, at λ = 2, it was found to have attained essentially the value predicted from the asymptotic λ → ∞ similarity solution available in the literature. Thus it is felt that the present numerical results plus the two similarity solutions for λ = 0 and for λ → ∞ fully describe the high-R steady flow for all non-negative values of λ.

Separation from the surface of two equal spheres in Stokes flow

Abstract: In this paper, it is shown that if two spheres of equal radii are placed axisymmetrically in a steady Stokes stream, separation of the flow from the spheres occurs if the distance between their centres is less than approximately 3-67 times the sphere radius. For spheres whose spacing is less than this value, wakes form on both spheres and the fluid within the wakes moves in closed eddy type motion. When the distance between the centres of the spheres is less than approximately 3.22 times the sphere radius, a cylinder of fluid links both spheres, and within this cylinder the fluid rotates in one or more ring vortices, the number of vortices increasing as the distance between the spheres is decreased. When the spheres are in contact, the fluid rotates in an infinite set of nested ring vortices.

Unsteady evolution of a horizontal jet in a stratified fluid

Abstract: The unsteady laminar flow due to the penetration of a horizontal jet of constant density into a stratified fluid is considered. A numerical solution of the Navier–Stokes equations under the Boussinesq approximation is obtained by means of an implicit finite-difference method. Results for different values of the Reynolds and internal Froude numbers are given and discussed.

Numerical Methods for Separated Flow Solutions around a Circular Cylinder

Abstract: Numerical solutions of the Navier-Stokes equations were obtained for separated flows around a circular cylinder at Reynolds numbers 40, 80, and 200. The flowfields were obtained by using three finite-difference techniques. The implicit scheme solved by matrix factorizations gave the best accuracy and used the least computer time. The flow pattern in the recirculating region of a circular cylinder begins to oscillate as the Reynolds number exceeds 40. The calculated drag coefficients, separation angles, and Strouhal numbers were compared with available experimental data. Computational inaccuracy resulting from numerical approximations needs to be identified before a complicated flow phenomenon can be realistically analyzed.

The behavior of a sphere in non-homogeneous flows of a viscoelastic fluid

Abstract: The motion of a sphere, freely suspended in a second-order fluid under the condition of a non-homogeneous flow field is investigated. Neglecting fluid inertia and, to be consistent, also particle inertia a general result is derived. For Couette flow between rotating cylinders as well as for two-dimensional and circular Poiseuille flow, respectively, excellent agreement with experimental observations results. While for the two-dimensional converging flow essentially no deviation from the corresponding results for a Newtonian fluid is found drastic differences show up for the converging flow in a conical duct. Preferably in the narrow cones rather large spheres come to a halt (Uebler-effect). For small spheres no such effect is predicted but a now phenomenon arises: For cones whose half angle lies close to 80° or exceeds that value some of the spheres end up in the region of secondary flow. The resulting separation effect could be diminished by decreasing the cone angle.

The stability of the decaying flow in a suddenly blocked channel

Abstract: The stability of the decaying laminar flow in a suddenly blocked channel is investigated. The partial differential system governing the stability of the flow is solved using a WKB type of approach. It is shown that the first term of the WKB expansion of the disturbance velocity field is just that obtained by a quasi-steady approach. The flow is found to be unstable at quite small Reynolds numbers. This instability is associated with the inflexional nature of the velocity profiles of the decaying flow.

Computation of the flow between a rotating and a stationary disk

Abstract: A numerical exploration of multiple-cell solutions for the flow between a rotating and a stationary disk is carried out systematically by the continuation method. The paper confirms and extends the work of Mellor, Chapple & Stokes. The results include the discovery of one-, two-, three- and five-cell solution regions which have not been reported before.

Pressure and Velocity Distributions in Pulsating Turbulent Pipe Flow Part 1 Theoretical Treatments

Abstract: Fundamental equations for pulsating turbulent flow in a circular tube containing a slightly compressible fluid are derived by describing Reynolds stress in terms of eddy viscosity, for whose distribution five models are introduced. Analytical solutions based on each model are developed for steady flow velocity, oscillating velocity and wave propagation constant. Comparison of these solutions for each model shows that the four-region model proposed by Karman is rather reasonable enough to illustrate the flow behaviours. The distributions of oscillating velocities, wave propagation constant, and oscillating pressures based on the four-region model at low frequencies and small Reynolds numbers are similar to those at high frequencies and small Reynolds numbers are similar to those at high frequencies and large Reynolds numbers. Because of the assumption of time-invariant eddy viscosity profile, the low frequency values of wave propagation constant should not be reliable. The analogy of these turbulent flow solutions with the laminar ones is shown schematically.

On entry-flow effects in bifurcating, blocked or constricted tubes

Abstract: For practically uniform entry conditions, the features of the steady laminar flow produced by a particular small distortion of the walls of a channel or pipe are shown to alter first from those of the corresponding external situation when the distortion is in an ‘adjustment zone’, sited a large distance O(R⅗l) from the inlet; R ([Gt ] 1) and l signify respectively a typical Reynolds number and length scale of the incompressible fluid motion. The planar channel flow there develops an extended triple-deck structure, with an unknown inviscid core motion bounded by two-tiered boundary layers near the walls. In three-dimensional pipe flow, where a similar structure occurs, the induced secondary motion has a jet-like nature close to the wall. The size and position of the indentation govern the flow properties within this adjustment regime and both can lead to large-scale effects being propagated. The most substantial effects occur if an indentation, interior blockage or bifurcation is sited just downstream of the adjustment stage in a channel. In a pipe, however, such a siting induces much less upstream influence, and instead the most significant long-scale disturbances are generated when the pipe is constricted asymmetrically over a small length. Vortex motion can then be provoked far beyond the constriction, the sense of rotation changing as the fluid moves further downstream, while upstream source-like secondary flow is found.

The Rayleigh problem for a wavy wall

Abstract: The problem of the flow generated in a viscous fluid by the impulsive motion of a wavy wall is treated as a perturbation about the known solution for a straight wall. It is shown that, while a unified treatment for high and low Reynolds numbers is possible in principle, the two limiting cases have to be treated separately in order to get results in closed form. It is also shown that a straightforward perturbation expansion in Reynolds number is not possible because the known solution is of exponential order in that parameter. At low Reynolds numbers the waviness of the wall quickly ceases to be of importance as the liquid is dragged along by the wall. At high Reynolds numbers on the other hand, the effects of viscosity are shown to be confined to a narrow layer close to the wall and the known potential sohtion emerges in time. The latter solution is a good illustration of the interaction between a viscous fluid field and its related inviscid field.

Parallel Flow Between Corrugated Plates

Abstract: The present paper investigates the parallel flow between two fixed corrugated plates. The question is given a constant pressure gradient, is the flow rate affected by the phase difference?

Poiseuille flow and thermal creep flow in long, rectangular channels in the molecular and transition flow regimes

Abstract: The theoretical Poiseuille flow and the thermal creep flow for rarefied gases in a long, rectangular channel are computed using the BGK model of the Boltzmann equation and diffuse scattering from the walls. These results are compared with available experimental data for Poiseulle flow. The present work provides a way to compute flow in a rectangular channel that is estimated to be accurate to ±5% for common gases.

Model for calculation of capture radii of a high gradient magnetic separator at moderate Reynolds numbers

Abstract: HGMS involves the impingement and attachment of particles of varying magnetic susceptibility on fine ferromagnetic fibers placed in a homogeneous background field. A model was developed to allow numerical calculation of capture radii of the fibers for Various particles under the influence of magnetic, gravitational, hydrodynamic and inertial forces. Both the magnetic and flow fields are calculated for an elliptical fiber to simulate approximately real shapes. For almost all practical cases of HGMS, the Reynolds numbers will be in the region intermediate between purely viscous and potential flow (Re 0.1-40). Therefore, a boundary layer is superimposed upon the solution for potential flow. The effect of loading on the capture radius may be evaluated by adjusting the flow pattern to allow for particle build-up.

Poiseuille flow in a pipe with axially symmetric wavy walls

Abstract: The effect of small amplitude wall waviness on the steady flow in a pipe is studied. Friction factors, Reynolds stresses, and mean velocity profiles are obtained for various Reynolds numbers, wall wave amplitudes, and wavenumbers. The results agree qualitatively with the experiments of Batra, Fulford, and Dullien and contradict the classical ’’Moody’’ diagram which represents the laminar friction factor as independent of wall roughness. The mean velocity profiles obtained suggest that wall roughness may cause pipe flow to be unstable to infinitesimal disturbances at a finite Reynolds number.

Simulation of Hydraulic Processes in Open Channels

Abstract: Techniques combining the deterministic and stochastic methods have been developed to compute and simulate various hydraulic processes in open channels, such as the three-dimensional distribution of flow velocity, steady and unsteady flows, flow resistance, secondary currents, and unsteady dispersion. The deterministic approach, using a curvilinear coordinate system based on the velocity distribution of flow, is used to deal with the basic hydrodynamic part of analysis. The stochastic approach is used to treat the irregular channel geometry that tends to cause uncertainties in simulated hydraulic processes in open channels. The techniques can be used to simulate the three-dimensional velocity distribution of (primary) flow, unsteady dispersion, and sediment transport, secondary currents, steady and unsteady flows, and flow resistance (Manning’s n.) In computing an unsteady flow it was found that the use of mean cross sections, without the geometrical irregularity of channel, causes errors in the peak and recession part of computed hydrographs, although it has the advantages of being simple and insensitive to uncertain Manning’s n.