Showing papers on "Hele-Shaw flow published in 1985"

Compressible fluid flow

Abstract: 1. Fundamental Concepts and Definitions. 2. Equation of Flow. 3. Isentropic Flow. 4. Normal Shock Waves. 5. Adiabatic Frictional Flow in a Constant-Area Duct. 6. Flow with Heat Interaction and Generalized Flow. 7. Two-Dimensional Waves. 8. Linearized Flow. 9. Method of Characteristics. 10. Computational Fluid Dynamics. 11. Methods of Experimental Measurements. Appendix: Tables and Figures. General References. Index.

Stokes flow in arbitrary two-dimensional domains: shear flow over ridges and cavities

Abstract: A method is described for solving the integral equations governing Stokes flow in arbitrary two-dimensional domains. It is demonstrated that the boundary-integral method provides an accurate, efficient and easy-to-implement strategy for the solution of Stokes-flow problems. Calculations are presented for simple shear flow in a variety of geometries including cylindrical and rectangular, ridges and cavities. A full description of the flow field is presented including streamline patterns, velocity profiles and shear-stress distributions along the solid surfaces. The results are discussed with special relevance to convective transport processes in low-Reynolds-number flows.

Development of viscous fingering patterns.

Abstract: The development of viscous fingering patterns has been observed from very early times to deep in the nonlinear regime for the flow of immiscible liquids in a Hele-Shaw cell. If the dimensionless viscosity contrast, $A$, is large, the number of fingers decreases rapidly with time after the initial pattern is established. If $A\ensuremath{\simeq}0$, all fingers grow through the entire time range of this experiment. For all values of $A$ there is a power-law relation between the length of the longest finger and the time.

Finger-interaction mechanisms in stratified Hele-Shaw flow

Abstract: Interactions between a few fingers in sharply stratified Hele-Shaw flow are investigated by numerical integration of the initial-value problem. It is shown that fingers evolving from an initial perturbation of an unstable interface consisting of a single wave are rather insensitive to variations of the control parameters governing the flow. Initial perturbations with at least two waves, on the other hand, lead to important finger-interaction and selection mechanisms at finite amplitude. On the basis of the results reported here many features of an earlier numerical study of the ‘statistical-fingering’ regime can be rationalized.

Numerical investigation of the steady viscous flow past a stationary deformable bubble

Abstract: A method for solving the Navier–Stokes equations in domains with moving boundaries is proposed. By means of a coordinate transformation, the region under consideration is converted to a region with known boundaries which are coordinate surfaces. An appropriate difference scheme with an algorithm for its implementation is constructed. The method is applied to the case of steady incompressible viscous flow past a resting deformable bubble. Results are obtained for wide ranges for Reynolds and Weber numbers and compared with other theoretical or experimental works in the common regions for the governing parameters. A separation of the flow and the occurrence of a toroidal vortex in the rear of the bubble is observed and verified through a number of computations. Typical flow patterns as well as a variety of practically important relations between the parameters of the flow are shown graphically.

The flow of a viscous incompressible fluid past a normal flat plate at low and intermediate Reynolds numbers: the wake

Abstract: The Navier-Stokes equations are solved numerically for the steady separated flow past a normal flat plate for Reynolds numbers in the range 0.1 ≤ R ≤ 20. Eddy dimensions together with the position of the vortex centre are presented and compared with the few other estimates and predictions available. Streamlines and equivorticity lines are also given. The main result of interest is the extremely good comparison with experimental results over this range of Reynolds numbers. The method of solution is based on an artificial time-dependent procedure using a distorted time. Results are given only for the steady-state flow.

Experiments on the stability of crossflow vortices in swept-wing flows

Abstract: Experiments are conducted which demonstrate the feasibility of creating crossflow vortices in a flat-plate flow. A swept leading edge and contoured wind-tunnel walls produce a strong pressure gradient and a typical swept-wing flow on the plate. Detailed three-dimensional measurements, made within the boundary layer using hot-wire anemometry, are supplemented with different flow-visualization techniques. Data are presented on the mean flow characteristics as well as on the behavior of the crossflow vortices. Comparisons are made with theoretical flow-field and stability calculations.

Pressure drop in cross flow across tube bundles

Abstract: The commonest methods of calculating the pressure drop in cross flow across tube bundles are discussed, and a new method, which is valid over a wide range of Reynolds numbers, is described. A comparison of the calculated coefficients of the pressure drop with experimental values from the literature shows that these new equations have the smallest deviations.

Isothermal flow past a blowing sphere

Abstract: Steady, axisymmetric, isothermal, incompressible flow past a sphere with uniform blowing out of the surface is investigated for Reynolds numbers in the range 1 to 100 and surface velocities up to 10 times the free stream value. A stream-function-velocity formulation of the flow equations in spherical polar co-ordinates is used and the equations are solved by a Galerkin finite-element method. Reductions in the drag coefficients arising from blowing are computed and the effects on the viscous and pressure contributions to the drag considered. Changes in the surface pressure, surface vorticity and flow patterns for two values of the Reynolds number (1 and 40) are examined in greater detail. Particular attention is paid to the perturbation to the flow field far from the sphere.

Self-sustained radial oscillating flows between parallel disks

Abstract: The flow-visualization methods of dye injection, hydrogen-bubble generation and paraffin mist are employed to investigate radial flow between parallel circular disks with a steady influx. Three distinct flow patterns are observed in the range of Re between 1.5 and 50. (1) Steady flow without boundary-layer separation and re-attachment, for Re < Rec. (2) A self-controlled flow oscillation which decays further downstream, in the range of Rec [les ] Re < Ret. (3) A self-sustained flow fluctuation which develops into a laminar-turbulent transition with a reverse transition further downstream, when Re [ges ] Ret. Rec and Ret are the critical and transition Reynolds number, respectively.The oscillating flows are caused by a vortex street consisting of vortices (i.e. separating annular bubbles) that separate periodically and alternately from both disks. Finite-difference solutions of the unsteady vorticity transport equation broadly agree with certain experimental observations. The study concludes that the separation and reattachment of shear layers in the radial flow through parallel disks are unsteady phenomena and the sequence of nucleation, growth, migration and decay of the vortices is self-sustained.

A comparison of Euler and Navier-Stokes solutions for supersonic flow over a conical delta wing

Abstract: The flow around a thin elliptic cone at Mach number 2 and angle of attack 10 deg is simulated numerically, comparing the results obtained using a fine grid and the Navier-Stokes (NS) equations with those obtained using both coarse and fine grids and the Euler (E) equations. On the coarse grid, the E results are found to reproduce roughly the NS predictions of leading-edge separation and primary and secondary vortices on the leeward surface, but the E solution on the fine NS grid (showing no separation and a crossflow-shock-induced vorticity) reveals this agreement to be spurious. The fine-grid E prediction is shown to be a valid solution of the E equations, indicating their unsuitability as approximators of viscous flow. The imposition of a Kutta condition on the E computation is found to be ineffective in correcting this discrepancy.

The vortical structure of bounded turbulent shear flow

Abstract: Further evidence from the literature of the last several years for a “hairpin-vortex” model of transitional and fully developed bounded turbulent shear flows is cited and discussed. Added to the body of previous evidence [Wallace (1982)], it provides new information about the vortical organization of these flows and their kinematic and dynamic processes.

A new approach to flow problems past a porous plate

Abstract: A new method to simulate flows past a two-dimensional porous plate is proposed. The method is a simple ap- plication of a discrete vortex method that has been well established for flows past an inclined flat plate. In this method, a flow past a porous plate is described as superposition of the velocity potential of a uniform flow on that of a flow past a flat plate. The effect of porosity is replaced by that of a mass flow rate of the approaching freestream passing through the plate. Calculated flow features are compared with experiments. It is shown that the present method is effective in the simulation of the flow past a porous plate. an example, Koo and James3 devised a mathematical model for steady two- dimensional flow through a screen. In the model, the screen is replaced by a source distribution and the stream function is adjusted to give the correct mass and momentum flow across the screen. The results predict drag with reasonable accuracy so far as the solidity of the screen is small. As demonstrated by the photographs taken by Inoue et al.,5'6 however, one of the important features of flow past a porous plate is the vortex shedding from the edges of the plate. The vortices shed con- tinuously from the edges tend to dominate the flowfield with the increasing solidity of the plate. Thus, in order to correctly analyze the flowfield past a porous plate, the effect of the vor- tices shed from the edges should be taken into consideration. In this paper, a new method to analyze the flowfield past a porous plate is proposed. It is well known that a discrete vortex method is quite effective in simulating a high Reynolds number flow past an inclined flat plate.7"9 In this method, the effect of vortices shed from the edges of the plate is properly treated. Thus, if we can add the effect of porosity to the flow past a flat plate, then the flow past a porous plate may be ade- quately analyzed. Our idea is that the effect of porosity can be expressed by superposition of the velocity potential of a uniform flow on the velocity potential of a flow past a flat plate. In the next section, the problem is formulated mathematically and the method of solution is described. Mathematical Formulation and Numerical Procedure First, we consider a flow past a flat plate. The fluid is assumed to be set in motion impulsively from rest. This situa- tion can be realized experimentally by moving the plate im- pulsively in an otherwise stationary fluid. At the initial in- stance, the flow is assumed to be irrotational and, therefore, the velocities of the flow are infinite at both edges of the plate. In order to remove this divergence, vortices are generated so that they suppress the divergence at the edges (Kutta condi- tion). The viscosity plays its role only at this moment of vortex generation and, except for this moment, the flow is assumed to be inviscid. As in the previous studies,7"9 the motion of the

A Schwarz-Christoffel Method for Generating Two-Dimensional Flow Grids

Abstract: A new coordinate generation technique, developed by Davis for external flows, is extended to allow for accurate grid generation for a variety of complex internal flow configurations. The approach is based on numerical integration of the Schwarz-Christoffel transformation for polygonal surfaces. It is shown to be second-order accurate with mesh size due to analytic treatment of boundary singularities. The method is flexible enough to allow for treatment of severe internal geometries, for a high degree of control of mesh spacing, and for generation of either orthogonal or nonorthogonal grids. In addition, this technique directly provides the two-dimensional incompressible potential flow solution for internal flows, as well as a simple expression for calculating the grid metric coefficients. Sample cases include symmetric and asymmetric channel, diffuser, and cascade flows.

High-speed compressible flow and other advection-dominated problems of fluid dynamics

Abstract: Finite element methods are described for modeling high speed compressible flows with strong advection, problems important to aerodynamics. The situations are characterized by high pressure and temperature gradients, transients and the appearance of discontinuities, factors which require mesh refinement during computations. Techniques are developed for temporal and spatial discretization of a model problem. Several observations are made regarding the explicit and implicit features of the calculations, the use of the Lax-Wendroff scheme to produce a mass-matrix for obtaining accurate results for transients, methods of performing stability analyses, and simplification techniques. Examples are provided of solving the nonlinear shallow-water equations and describing compressible flows, particularly transonic flows. Domain splitting is defined for improving the calculations at each time step and in different parts of the flow regime while simultaneously advancing the calculations towards a solution.

Effect of Vortex Generators on the Flow around a Circular Cylinder Normal to an Airstream

Abstract: Experimental investigations were carried out to examine the effect of vortex generators on the characteristics of the flow around a circular cylinder in a cross flow in the range of subcritical Reynolds numbers. The Strouhal number, the static pressure distribtion, the R.M.S. values of the fluctuating pressure, the position of the separation of flow and the structure of the boundary layer have been measured. The flow patterns can be classified according to the position and the height of the generator rows, and the roughness Reynolds number. Characteristics of these flow patterns and the relationship among them were clarified.

Monotone switches in implicit algorithms for potential equations applied to transonic flows

Abstract: Numerical calculations of transonic flows by potential equations typically use algorithms that change the method of calculation for regions of subsonic and supersonic flow. In this paper, implicit approximatefactorization algorithms are modified to use the monotonic switch in the type of finite differencing that was developed by Godunov for the Euler equations. Calculations of flows over airfoils by these algorithms are compared with calculations by other commonly used methods. For the small-disturbance potential equation, comparisons are made with the Murman-Cole method for both steady and unsteady flows. For the full potential equation, comparisons are made with the method of Hoist and Ballhaus for steady flows. The comparisons show that the monotone methods are more stable. For steady flows, converged solutions are obtained for cases where the older methods fail. For unsteady flows, solutions are obtained for cases where the Murman-Cole switch requires a time step more than ten times smaller in order for the calculations to remain stable. These improvements are achieved with no increase in computer storage and only minor modifications in current codes.

Low Reynolds number circular Couette flow past a wavy wall

Abstract: Theoretical and experimental results show that it is possible to obtain flow separation or reverse flow for low Reynolds number shear flow past a wavy wall The region of reverse flow depends on the amplitude of the wall waves as well as the gap width A comparison between the fourth‐order perturbation results and experiment is given

Viscid/inviscid interaction analysis of separated trailing-edge flows

Abstract: An analytical procedure based on finite Reynolds number, viscid/inviscid interaction theory is presented for predicting high Reynolds number flow past an airfoil trailing edge. This effort stems from the need to provide efficient prediction methods for local strong interaction regions and, in particular, local flow separations. Attention is focused on subsonic laminar flow past a thin-airfoil trailing edge where local separation is induced by airfoil thickness or loading. Solutions are determined using interacting boundary-layer theory in which the outer in-, viscid and inner viscous flows are determined simultaneously and matched through a global semi-inverse iteration procedure until a converged result for the complete flowfield is obtained. Detailed results for attached and separated laminar trailing-edge flows are presented including streamline patterns for thick and loaded trailing edges.

Computational technique for compressible vortex flows past wings at large incidence

Abstract: A computational technique based on the integral solution of the full potential equation has been developed for the solution of three-dimensional subcritical flows past wings at high angles of attack. The problem includes two sources of nonlinearities: a boundary-oriented nonlinearity (separated flow roll-up) and a region-oriented nonlinearity (flow compressibility). The former is represented by a nonlinear vortex lattice, while the latter is represented by a source distribution within a finite computational volume. The solution is obtained by using double iteration cycles, a separated flow (wake) iteration cycle, and a compressibility iteration cycle. The computational technique is applied to a delta wing and the results show that the technique is accurate, promising, and efficient.

Euler and Navier-Stokes solutions for supersonic shear flow past a circular cylinder

Abstract: Euler and Navier-Stokes solutions of the supersonic shear flow past a circular cylinder are obtained. These solutions are used to study the basic flow structure around the cylinder. Both the inviscid and viscous calculations show the formation of a large recirculating flow region around the front stagnation point. The calculations further show that the overall size of the recirculating region is approximately the same for the Euler and Navier-Stokes solutions but the inside structure is quite different. The inviscid flow shows only one vortex whereas the viscous flow shows two vortices inside the recirculating flow region. The inner vortex in the Navier-Stokes solution is formed primarily due to the viscous effects near the body surface and its size depends upon the Reynolds number. It is found that with increasing Reynolds number, the inner vortex diminishes in size and the Navier-Stokes solution asymptotically approaches the Euler solution. These results indicate that the Euler equations may correctly predict certain high Reynolds number separation phenomenon in flows with natural inviscid vorticity source.

Flow regime transitions in vertical upward three-phase gas-liquid- solid flow

Abstract: Models are developed to predict the effect of solids on flow regime transitions in vertical upward gas-liquid-solid flow. Available experimental data collected in two inch and six inch diameter experimental columns are compared with theoretical model predictions.