Showing papers on "Hele-Shaw flow published in 1984"

Characteristics of the Flow around Two Circular Cylinders Arranged in Tandem : 2nd Report, Unique Phenomenon at Small Spacing

Abstract: In the previous paper, three flow patterns were found at small spacing between two cylinders arranged in tandem as follows: the first is a flow without reattachment of the shear layer separated from the upstream cylinder, the second is an unstable flow and the third is an unique flow like that the frequency of the vortex shedding is nearly constant regardless of the free stream velocity. The purpose of this paper is to investigate the conditions of the occurrence of the above flow patterns and their flow characteristics in more detailed. It becomes clear that the unstable flow is caused by the intermittent reattachment of the shear layer onto the downstream cylinder, the unique phenomenon on the Strouhal numner occurs in the range of 2.5×104≤Re≤6.5×104 and is a transition phenomenon due to interference between the two cylinders. Beyond Re=6.5×104, the Strouhal number becomes again constant.

The stability of two-dimensional linear flows

Abstract: A theoretical investigation is made of the linear stability of a viscous incompressible fluid undergoing a steady, unbounded two‐dimensional flow in which the velocity field is a linear function of position. Such flows are approximately generated by a four‐roll mill device which has many experimental applications, and can be characterized completely by a single parameter λ which ranges from λ=0 for simple shear flow to λ=1 for pure extensional flow. The linearized velocity disturbance equations are analyzed for an arbitrary spatially periodic initial disturbance to give the asymptotic behavior of the disturbance at large time for 0≤λ≤1. In addition, a complete analytical solution of the vorticity disturbance equation is obtained for the case λ=1. It is found that unbounded flows with 0<λ≤1 are unconditionally unstable. An instability criterion relating the initial disturbance wave vector α to the steady flow strain rate E, kinematic viscosity ν, and the parameter λ is obtained. This criterion shows that for all admissible values of E and ν, a wave vector α may be found which corresponds to disturbances that grow exponentially in time. The growth of these disturbances is accompanied by a growth of vorticity oriented along the principal axis of extensional strain in the case λ=1. The results of this investigation also confirm the established fact that simple shear flow (λ=0) is stable to all infinitesimal spatially periodic disturbances.

Characteristics of the Flow around a Square Prism

Abstract: Experimental investigations on the characteristics of the flow around a square prism at angles of attack (0°≤α≤45°) were carried out in the range of subcritical Reynolds numbers. For α<15°, the perfect separated regime may be further subdivided into synunetric and unsymuetric flows at α=5°. For 15°

Three-dimensional viscous flows with large secondary velocity

Abstract: A new system of approximation equations is derived for three-dimensional steady viscous compressible flows in which a primary-flow direction is present, but in which both transverse velocity components can be large. Previous approaches which address simplification of the steady Navier-Stokes equations are discussed, and a new approach is proposed. The transverse velocity vector which corrects a given potential flow has been decomposed into potential and rotational components. It is found that the potential-velocity vector may be assumed small, whereas the rotational-velocity vector may be assumed small, whereas the rotational velocity vector and hence the composite secondary flow can be of order unity. This assumption leads to a system of governing equations whose characteristic polynomial has a non-elliptic form for arbitrary Mach numbers. The resulting non-elliptic approximation equations can be solved as an initial/boundary-value problem. Computed results confirm the small scalar-potential approximation.

Secondary flows in a plane channel: their relationship and comparison with turbulent flows

Abstract: Two- and three-dimensional non-stationary viscous-fluid flows in a plane channel are considered. By means of efficient computational algorithms for direct integration of the incompressible Navier-Stokes equations the evolution of these flows over large time intervals is simulated. Classes of two- and three-dimensional non-stationary flows with stationary integral characteristics (the flow rate, mean pressure gradient, total energy of pulsations etc.) were found. Such flows are called secondary flows. Two-dimensional secondary flows have only qualitative similarity to turbulent flows observed in experiments. Three-dimensional secondary flows agree very well, even quantitatively, with turbulent flows. The principal characteristics of turbulent flows such as drag coefficient, mean-velocity profile, the distributions of the pulsation velocity components and some others are reproduced in three-dimensional secondary flows with good accuracy.

Turbulence in pulsatile flows.

Abstract: Turbulence during pulsatile flow has been suggested as a possible mechanism to enhance the transport of gases during high-frequency ventilation. Experimental studies on oscillatory flow in straight, circular tubes have identified three types of flow: (a) laminar; (b) conditionally turbulent, in which high-frequency disturbances occur during the decelerating phase of the flow cycle but relaminarize by the beginning of the subsequent accelerating phase; and (c) fully turbulent flow, in which disturbances occur throughout the flow cycle. Fully turbulent flow has been observed only when a mean flow is present, and only laminar or conditionally turbulent flow has been observed for purely oscillatory flow. A critical Reynolds number based on the Stokes layer can be defined, and transition Reynolds numbers between 400 and 550 have been experimentally determined for purely oscillatory flow in a circular tube, although lower values are expected for physiological flows. There are some indications that the structure of oscillating turbulent flow is similar to steady turbulent flow, and preliminary work in our laboratory shows that the spectral content of flows during high-frequency ventilation is similar to that in steady turbulent flow.

Supersonic Separated Flow past a Cylindrical Obstacle on a Flat Plate

Abstract: An experimental investigation of three-dimensional boundary-layer separation on a flat plate ahead of a circular cylinder at Mach 2.36 was made. Emphasis was given to the laminar flow regime and to the flow region upstream of the cylinder. The heights and diameters of the cylinders used in the study were larger than the undisturbed boundary-layer thickness at the cylinder location. Data were obtained by oil flow visualization, Schlieren observations, static pressure measurements, and laser anemometry. Oil flow visualization revealed three separation lines on the flat plate ahead of the cylinder. A postulated flowfield structure, which was suggested by this skin-friction pattern, could not be confirmed by the velocity measurements. Velocity measurements indicated an unsteady flow structure.

Particle motion in Stokes flow near a plane fluid-fluid interface. Part 2. Linear shear and axisymmetric straining flows

Abstract: We consider the motion of a sphere or a slender body in the presence of a plane fluid–fluid interface with an arbitrary viscosity ratio, when the fluids undergo a linear undisturbed flow. First, the hydrodynamic relationships for the force and torque on the particle at rest in the undisturbed flow field are determined, using the method of reflections, from the spatial distribution of Stokeslets, rotlets and higher-order singularities in Stokes flow. These fundamental relationships are then applied, in combination with the corresponding solutions obtained in earlier publications for the translation and rotation through a quiescent fluid, to determine the motion of a neutrally buoyant particle freely suspended in the flow. The theory yields general trajectory equations for an arbitrary viscosity ratio which are in good agreement with both exact-solution results and experimental data for sphere motions near a rigid plane wall. Among the most interesting results for motion of slender bodies is the generalization of the Jeffrey orbit equations for linear simple shear flow.

Variation of Flow Resistance Through Curved Channels

Abstract: An analysis is provided for the spatial variations of flow resistance and other flow characteristics through curved channels reflecting the effects of transverse circulation. Among the assumptions in the analysis, the transverse velocity profile is assumed to remain similar during circulation growth and decay. A mathematical model for computing such variations is developed and it has been verified using limited available data. The results demonstrate that flow resistance or energy expenditure produced by transverse flow can be very significant even for mild curves without flow separation. Because of the important effects of channel curvature, analytical methods developed in this model provide useful techniques for studies of river morphology and sediment transport in meandering streams.

Instability of a Cellular Flow

Abstract: The theory of the instability of parallel periodic flows is extended to the two-dimensional cellular flows. The eigenvalue equation is derived to find the critical Reynolds number to the disturbance with small Floquet exponents. The theory is applied to the cellular flow: U =(-sin y , sin x ) and the critical Reynolds number is found to be \( \sqrt{2}\).

Numerical predictions for laminar source-sink flow in a rotating cylindrical cavity

Abstract: Numerical solutions are presented for steady, axisymmetric, laminar, isothermal, source–sink flow in a rotating cylindrical cavity. These results, which are in good agreement with previously published experimental work, have been used to give a fresh insight into the nature of the flow and to investigate the validity of other theoretical solutions. When the fluid enters the cavity through a central uniform radial source and leaves through an outer sink, it is shown that the flow near the disks can be approximated by two known analytical solutions. If the radial source is replaced by an axial inlet the flow becomes more complex, with a wall jet forming on the downstream disk at sufficiently high flow rates.

Numerical simulation of the viscous flow fields over three-dimensional complicated geometries

Abstract: A 'thin-layer' Navier-Stokes code capable of predicting steady state viscous flows is applied to complicated three-dimensional flow fields. The code is written in a generalized coordinate system, and a recently developed grid generation procedure is used for the flow-field discretization. Application is made to the vortical flow over a delta wing at high angle of attack, and the computed results are compared with experimental results. The results indicate that the present method can capture the physical phenomenon well. It is observed that a leading-edge separation vortex is formed over the wing, as is a secondary separation vortex near the leading edge. The flow field behind the trailing edge is also well described. Application is also made to the transonic flow over the Shuttle configuration. The result appears to be reasonable even though no experimental data are available for comparison. These results indicate that the present approach is capable of computing complicated three-dimensional flow fields.

Hall effects on MHD free-convection flow past an accelerated vertical porous plate

Abstract: The effect of Hall currents on the hydromagnetic free-convection flow of an electrically conducting and incompressible viscous fluid past a uniformly accelerated infinite vertical porous plate is discussed The magnetic Reynolds number is assumed to be small so that the induced magnetic field can be neglected The governing equations of the flow are solved by defining a complex velocity with the help of the Laplace transform method when the Prandtl number is equal to unity The influence of the various parameters on the unsteady flow field is presented for both the cases, cooling and heating of the porous plate by free-convection currents

Short communication on normal flow boundary conditions in finite element codes for two-dimensional shallow water flow

Abstract: Dans la modelisation des eaux de surface la methode de selection de la direction normale appropriee depend en un nœud limite d'element fini de la grille et du type de developpement de la fonction de base (en vitesse ou en flux). On montre que lorsque le developpement est effectue en termes de vitesse, la direction normale appropriee en un nœud varie au cours du temps. Pour la plupart des applications cette variation sera faible

Fluid flow in a rotating channel of square section

Abstract: Laminar flow in a channel rotating about a transverse axis has been studied numerically [1–3] and analytically [4–7] at small Reynolds numbers. The drag coefficient of rotating channels with straight and curvilinear axes has been measured [4, 8, 9]. The present paper gives the results of an experimental investigation into the kinematics of water flow in a channel rotating with different intensities. The flow was visualized by means of hydrogen bubbles and a dye. A study was made of the process of flow separation in a rapidly rotating channel into a core with homogeneous velocity distribution in the direction parallel to the rotation axis and thin shear layers on the walls normal to this axis. The values of the dimensionless numbers were found that correspond to flow rearrangement accompanied by formation of longitudinally oriented vortex structures in the region of higher pressure, and also the values of the rotation parameter needed for the almost complete suppression of turbulence in the region of lower pressure. A general analysis is made of the forms of instability in the different regions of the flow and of the possible flow regimes in a rotating channel.

Steady viscous flow past a circular cylinder

Abstract: Viscous flow past a circular cylinder becomes unstable around Reynolds number Re = 40. With a numerical technique based on Newton's method and made possible by the use of a supercomputer, steady (but unstable) solutions have been calculated up to Re = 400. It is found that the wake continues to grow in length approximately linearly with Re. However, in conflict with available asymptotic predictions, the width starts to increase very rapidly around Re = 300. All numerical calculations have been performed on the CDC CYBER 205 at the CDC Service Center in Arden Hills, Minnesota.

On the steady flow of a Newtonian fluid between two parallel disk

Abstract: We show that the steady flow of a viscous fluid of moderate Reynolds number between two parallel disks has an exact solution which takes the form of a power series Employing this exact solution the two-point boundary value problem for this class of flow is reduced to a nonlinear algebraic system which is then solved by a standard optimization method Results are given for two particular cases, the continuous squeezing flow and the coaxial-disk flow

Nonlinear equation for amplitude of Tollmien-Schlichting waves in a boundary layer

Abstract: The nonlinear evolution of a Tollmien-Schlichting wave is analyzed with allowance for the flow being nonparallel in a boundary layer. In contrast to the early work of Zel'man [19], strict allowance is made for the fact that the extent to which the flow is nonparallel is not independent of the Reynolds number — the departure from parallel flow in a boundary layer is small only at large Reynolds numbers. Therefore, an asymptotic theory of Tollmien-Schlichting waves is constructed under the assumption that the Reynolds number tends to infinity.

An integral equation for immiscible fluid isplacement in a two-dimensional porous medium or Hele-Shaw cell

Abstract: An integral equation for the normal velocity of the interface between two immiscible fluids flowing in a two-dimensional porous medium or Hele-Shaw cell (one fluid displaces the other) is derived in terms of the physical parameters (including interfacial tension), a Green's function and the given interface. When the displacement is unstable, ‘fingering’ of the interface occurs. The Saffman-Taylor interface solutions for the steady advance of a single parallel-sided finger in the absence of interfacial tension are seen to satisfy the integral equation, and the error incurred in that equation by the corresponding Pitts approximating profile, when interfacial tension is included, is shown. In addition, the numerical solution of the integral equation is illustrated for a sinusoidal and a semicircular interface and, in each case, the amplitude behaviour inferred from the velocity distribution is consistent with conclusions based on the stability of an initially flat interface.

Experimental Investigation of the Turbulent Large Scale Temporal Flow in the Wing-Body Junction.

Abstract: : An experimental investigation of the fluid dynamic flow in the wing-body junction was made to reveal the existence of large scale, time-dependent structures. These temporal features are discussed relative to the three major parts of the mean flow: the onset boundary layer, the wing-body junction flow characterized by the horseshoe root vortex, and the wing-body junction wake flow. Distinct flow structures, distinguished by bandwidths, were observed in all parts of the flow. One type of structure was due to the distortion of the existing structure of the onset boundary layer by the wing. A second and a third structure were newly created in the flow by the presence of the wing. These unique structures along the body were boundary layer phenomena, clearly distinguishable from ordinary Strouhal-type shedding at the wing trailing edge. The measurements distinguishing the structures were made using applications of two-point spectral correlation analyses of the flow velocities. The application of this estbalished procedure was made possible by modern high speed data techniques. An orderly framework of definitions and discussion is presented around which additional research can be performed to discover the details of the flow structure. (Author)

Modeling of Three-Dimensional Flow in Turning Channels

Abstract: The structure of developing flows inside curved channels has been investigated numerically using the time-averaged Navier Stokes equations in three dimensions. The equations are solved in primitive variables using finite difference techniques. The solution procedure involves a combination of repeated space-marching integration of the governing equations and correction for elliptic effects between two marching sweeps. Type-dependent differencing is used to permit downstream marching even in the reverse-flow regions. The procedure is shown to allow efficient calculations of turbulent flow inside strongly curved channels as well as laminar flow inside a moderately curved passage. Results obtained in both cases indicate that the flow structure is strongly controlled by local imbalance between centrifugal forces and pressure gradients. Furthermore, distortion of primary flow due to migration of low momentum fluid caused by secondary flow is found to be largely dependent on the Reynolds number and Dean number. Comparison with experimental data is also included.

Resonance in flows with vortex sheets and edges

Abstract: It is shown that the vortex sheet in a slot between two semi-infinite plates does not admit incompressible resonant perturbations. The semi-infinite vortex sheet entering a duct does admit incompressible resonance. These results indicate that the vortex-sheet approximation is less useful for impinging shear flows than for non-impinging flows. They also suggest an important role of downstream vortical disturbances in resonant flows. The general solution for perturbations to flow with a vortex sheet and edges is written in terms of a Cauchy integral. Requirements on the behavior of this solution at edges and at downstream infinity fix the criteria for resonance.

Numerical Simulation of Turbulent Trailing Edge Flows

Abstract: In the past several years, considerable advances have been made in the prediction of transonic trailing-edge flows. For modern supercritical airfoils the trailing edge region is dominated by viscous-inviscid interaction. In the near wake the flow field is complicated by streamline curvature and due to the interaction of the merging of two significantly different shear layers. Integral boundary-layer methods coupled with an inviscid flow-field solution have been successfully applied to both symmetric and asymmetric trailing-edge flows provided there is no boundary layer separation [128, 217, 218]. These methods are not satisfactory for flows with strong adverse pressure gradients leading to significant separated regions [217, 219]. Differential methods employing either a boundary-layer code coupled with an inviscid solution or the mass-averaged Navier—Stokes equations throughout the flow field have also been successful provided separation was not present [210, 218]. Recently an asymmetric trailing-edge flow with a small separated zone was successfully predicted using the Navier—Stokes equations [220]. The ability to calculate trailing-edge flows with large separated zones remains to be tested.

Method and arrangement for influencing the boundary layer of bodies in a fluid flow mainly during stochastic flow fluctuations

Abstract: In order to influence the boundary layer of bodies in a fluid flow with the aim of reducing the resistance or of preventing flow separation, a system of a sensor, a vibration transmitter and a controller is provided which enables stochastic flow fluctuations to be measured at one and the same location, to be analysed, and to be specifically dampened or amplified.

Can the Singularity Be Removed in Time-Dependent Flows?

Abstract: : The evolution of unsteady boundary layers on oscillating airfoils is studied. The computational difficulties associated with the movement of the stagnation point as a function of space and time are solved by using a novel numerical scheme. Calculations are performed for pressure distributions typical of those found near the leading edge of airfoils. Results are presented for two cases. In the first, solutions are obtained for a flow with separation and with prescribed pressure distribution; they infer that a singularity develops and is of the same type as that observed on a circular cylinder started impulsively from rest. In the second, results are obtained for the same flow and the viscous flow solutions are interacted with the external flow by using an inverse boundary-layer method. The interaction seems to remove the singularity, however, these results are preliminary and need to be checked and improved upon. (Author)