Showing papers on "Hele-Shaw flow published in 1970"
246 citations
TL;DR: In this article, the results of a numerical evaluation of the Navier-Stokes equations of motion for the case of a viscous fluid streaming past a sphere are presented in terms of the length of the standing eddy behind the sphere and the angle of flow separation at the sphere.
Abstract: The results of a numerical evaluation of the Navier-Stokes equations of motion for the case of a viscous fluid streaming past a sphere are presented in terms of the length of the standing eddy behind the sphere and in terms of the angle of flow separation at the sphere. Emphasis was placed on calculating these quantities at Reynolds numbers between 20 and 40 where no reliable theoretical or experimental values are available. In support of these calculations, it is shown that the values for the drag on a sphere previously calculated by us from the Navier-Stokes equations of motion by the same numerical technique as that used for calculating the eddy length and angle of flow separation agree well with our recent, extensive drag measurements for a wide Reynolds number interval. Our results are used to make a comparison between drag and flow field as predicted by analytical solutions and numerical solutions to the Navier-Stokes equations of motion. Some limitations of the analytical solutions to predict correct values for the drag, and to describe the correct nature of the flow field, are pointed out. It is shown further that a plot of [(D/Ds) – 1] versus log NRe, where D is the actual drag on a sphere, Ds is the Stokes drag, and NRe is the Reynolds number, reveals that the variation of the drag on a sphere with Reynolds number follows well defined regimes, which correlate well with the regimes of the flow field around a sphere. A similar relationship between ‘drag-regime’ and flow field pattern is discussed for the case of viscous flow past a cylinder.
120 citations
TL;DR: In this article, numerical techniques and solutions for compressible and incompressible laminar separated flows using time dependent finite difference equations using time-dependent finite difference equation are presented.
Abstract: Numerical techniques and solutions for compressible and incompressible laminar separated flows using time dependent finite difference equations
68 citations
TL;DR: In this article, the mean velocities, turbulence intensities, scales and energy spectra measured in this flow indicate two regions of appreciably different characteristics: a wall region near the plane surfaces is found to occur with flow characteristics close to those found near walls of other turbulent shear flows when these are expressed in terms of the wall similarity parameters.
Abstract: Turbulent flow between two plane surfaces in relative shearing motion has been studied with air in a belt-type apparatus with one fixed surface. Mean velocities, turbulence intensities, scales and energy spectra measured in this flow indicate two regions of appreciably different characteristics. A wall region near the plane surfaces is found to occur with flow characteristics close to those found near walls of other turbulent shear flows when these are expressed in terms of the wall similarity parameters. A core region, of width at least three-eights the distance between the planes, appears away from these evidencing the characteristics of the homogeneous turbulence predicted by von Karman. The mean velocity has a linear gradient in this region and the turbulence intensity and scales are essentially constant; in fact, homogeneity is strongly suggested. For a more than two-fold range in flow Reynolds numbers (center line velocity 15 fps to 35 fps) the microscale is found to be constant, the macroscale increases linearly and the relative intensity is constant.
67 citations
TL;DR: The steady axisymmetric flow in the inlet region of a circular cylindrical tube is studied, with emphasis on the entry flow at lower (but finite) Reynolds numbers, and on flow in which arbitrary axial and radial velocity distributions are prescribed at the entry section.
67 citations
TL;DR: In this article, the authors considered viscous flow in a circular cylindrical tube containing an infinite line of rigid spheroidal particles equally spaced along the axis of the tube.
Abstract: Viscous flow in a circular cylindrical tube containing an infinite line of rigid spheroidal particles equally spaced along the axis of the tube is considered for (a) uniform axial translation of the spheroids (b) flow past a line of stationary spheriods and (c) flow of the suspending fluid and spheroids under an imposed pressure gradient. The fluid is assumed to be incompressible and Newtonian. The Reynolds number is assumed to be small and the equations of creeping flow are used. Two types of solutions are developed: (i) an exact solution in the form of an infinite series which is valid for ratios of the spheroid diameter to the tube diameter up to 0.80, (ii) an approximate solution using lubrication theory which is valid for spheroids which nearly fill the tube. The drag on each spheroid and the pressure drop are computed for all cases. Both prolate and oblate spheroids are considered. The results show that the drag and pressure drop depend on the spheroidal diameter perpendicular to the axis of tube primarily and the effects of the spheroidal thickness and spacing are secondary. The results are of interest in connection with mechanics of capillary blood flow, sedimentation, fluidized beds, and fluid-solid transport.
54 citations
TL;DR: In this paper, it was shown that manufacturing tolerances of several thousandths of an in. in passage dimension have a significant influence on the overall heat transfer and flow friction behavior.
Abstract: Several current designs for high effectiveness gas turbine regenerators involve low Reynolds number fully developed, laminar flow type surfaces. Such surfaces consist of cylindrical flow passages, of small hydraulic radius, in parallel. The cylinder geometry may, as examples, be triangular, as in some glass-ceramic surfaces, or rectangular, as in deepfold metal foil surfaces. This presentation demonstrates that manufacturing tolerances of several thousandths of an in. in passage dimension have a significant influence on the overall heat transfer and flow friction behavior. The analysis is also useful in rationalizing the difference between theory and test results for the basic heat transfer (j factor) and friction (f factor) characteristics as a function of Reynolds number for various surfaces of the laminar flow type.
30 citations
TL;DR: Polymeric materials flow at tube entrance, discussing pressure drop and flow birefringent patterns at tapered and sharp entrances as discussed by the authors, and discussing flow patterns at tube entrances.
Abstract: Polymeric materials flow at tube entrance, discussing pressure drop and flow birefringent patterns at tapered and sharp entrances
26 citations
TL;DR: Two dimensional unsteady fluid flow in square cavity numerically analyzed from continuity and Navier-Stokes equations and recorded as computer-generated motion picture as mentioned in this paper was shown in the movie.
Abstract: Two dimensional unsteady fluid flow in square cavity numerically analyzed from continuity and Navier-Stokes equations and recorded as computer-generated motion picture
24 citations
TL;DR: In this paper, the free-surface equations for subcritical unsteady one-dimensional flow are solved by four different formulations, each based on the method of characteristics, and the advantages and disadvantages of each procedure are given.
Abstract: The solutions of the free-surface equations for subcritical unsteady one-dimensional flow are solved by four different formulations, each based on the method of characteristics. Advantages and disadvantages of each procedure are given. Examples emphasize the important features and corroborate a stability criteria that is presented. The implicit characteristics grid approach is the most accurate for overland flow situations or analysis of single channels; however, it is not useful for complex systems. The explicit rectangular grid is the simplest to program but may lead to instabilities if very large time increments are used. The latter method is also comparatively expensive for long duration transients.
22 citations
TL;DR: In this article, the principles of variational calculus are applied to solve the nonlinear partial differential equation for steady and unsteady unconfined non-Darcy flow through porous media.
Abstract: The principles of variational calculus are applied to solve the nonlinear partial differential equation for steady and unsteady unconfined non-Darcy flow through porous media. A functional is proposed which will yield solutions for the laminar, transitional and turbulent flow regimes. The solution represents the minimization of the rate of energy dissipation with enforced flow continuity. A finite element scheme is used to obtain the minimizing field. Examples of the method applied to steady and unsteady free surface flow is described in a rectangular rockfill section. The finite element and experimental flow fields are in good agreement.
TL;DR: The radial flow of a gas in which transition from viscous to slip to free molecule flow occurs is studied theoretically and experimentally as discussed by the authors, and the results indicate the effective separation to be slightly less than the sum of the measured flatness deviations of each disk.
01 Feb 1970
TL;DR: In this article, the flow field generated by two coaxial jets was investigated experimentally with hot-wire anemometers and the area ratio between the external and internal nozzle was varied as well as the velocity issuing from each of the nozzles.
Abstract: : The flow field generated by two coaxial jets was investigated experimentally with hot-wire anemometers. The area ratio between the external and internal nozzle was varied as well as the velocity issuing from each of the nozzles. The distribution of the mean velocities, turbulence intensities, and shear stresses were determined for the various cases. The development of the flow field and its approach to a self-preserving state is discussed. The Reynolds numbers based on the nozzle diameters varied from 0 to 100,000 and the velocities were low enough that the flow can be considered incompressible. (Author)
TL;DR: In this paper, the effect of skin friction drag by suspending solid particles in air is investigated and a theory is presented to try and explain some of the complex flow phenomena encountered in a two-phase flow system.
Abstract: The purpose of this study was to obtain extensive experimental data on the effect of skin-friction drag by suspending solid particles in air. The investigation was divided into two parts: The first study consisted of obtaining extensive experimental data on the pressure gradients (which are proportional to skin friction) encountered in circular pipes when a mixture of air with solid particles suspended in it flows through the pipe. The second part deals with the skin friction as measured on a flat plate placed flush with the floor of a wind tunnel having a dusty sub-layer. These studies involved a large range of Reynolds numbers, particle sizes, and weight-flow ratios. A theory is also presented to try and explain some of the complex flow phenomena encountered in a two-phase flow system.
TL;DR: In this paper, the accelerated flow of a viscous fluid due to a suddenly established discharge in a two-dimensional conduit expansion has been determined by numerical integration of the governing differential equation.
Abstract: The accelerated flow of a viscous fluid due to a suddenly established discharge in a two-dimensional conduit expansion has been determined by numerical integration of the governing differential equation. The complete form of the equation for diffusion and convection of vorticity was employed. The Reynolds number of the flow, based on the prescribed disharge, was 200. The growth of the separation zone, assuming symmetric flow, was determined. Flow and vorticity pattern were calculated at short interval of time; a selection of those pattern is presented, as well a curves showing the variation with time of the principal kinematic characteristics of the unsteady flow through the expansion.
TL;DR: In this article, a nomograph has been developed to facilitate the calculation of pressure loss in a laminar flow system, which can be used to predict the flow pattern and also serve as important factors in determining the pressure loss.
TL;DR: In this paper, it was shown that the non-Newtonian characteristics of polar fluids are more pronounced in pipe flow than in any of the other flow configurations considered here, and that the principal non-newtonian characteristic of polar fluid in these flow configurations is an increased effective viscosity which is dependent upon the relative size and configuration of the flow situation.
Abstract: The effective viscosity of a polar fluid is a measure of the amount of traditional shear viscosity the polar fluid will appear to possess in a particular flow situation. Four classical flow configurations are considered here; Couette flow, plane Poiseuille flow, pipe flow, and flow between concentric rotating cylinders. The principal non‐Newtonian characteristic of polar fluids in these flow configurations is an increased effective viscosity which is dependent upon the relative size and configuration of the flow situation. It is shown that the non‐Newtonian characteristics of polar fluids are more pronounced, and thus probably more easily measured, in pipe flow than in any of the other flow configurations considered here.
TL;DR: In this article, the formation of a shock in a viscous flow is studied and a discussion of the accuracy and practicality of a numerical analysis of the problem is given; it is concluded that, although very accurate results may be obtained, in principle, regardless of the Reynolds number of the flow, the assumption of a sharp discontinuity is the only practical way to handle flows whose Reynolds number per unit length is higher than 100.
TL;DR: In this article, the surface pressure, forces and moments are obtained for bodies oscillating with small amplitude about their steady equilibrium position and on bodies in small amplitude gust fields, respectively.
Abstract: This paper describes a very general method for determining the unsteady, two-dimensional, incompressible flow about one or more bodies of arbitrary shape. Specifically the surface pressure, forces and moments are obtained for bodies oscillating with small amplitude about their steady equilibrium position and on bodies in small amplitude gust fields. The equilibrium configuration of the bodies may also be arbitrary. Calculated results for single bodies in and out of gust fields are compared to results obtained by existing methods. Calculations and comparisons are also presented for two interacting bodies.
01 Aug 1970
TL;DR: In this article, the authors showed that the jet-plume-induced flow separation on asymmetric bodies at 3.00, 4.50, and 6.00 Mach numbers can be achieved.
Abstract: Jet-plume-induced flow separation on asymmetric bodies at 3.00, 4.50, and 6.00 Mach numbers
01 Jan 1970
01 Aug 1970
TL;DR: Approximation for distribution of flow properties in angle of attack plane of conical flows is given in this article, where flow properties are assumed to be invariant to the angle of the attack plane.
Abstract: Approximation for distribution of flow properties in angle of attack plane of conical flows
01 Jan 1970
TL;DR: An overview of the problems of flow separation is provided in this paper, where the authors highlight the classical concept of boundary layer flow separation and then the generalized definition of the flow separation.
Abstract: This chapter provides an overview of the problems of flow separation. The problem of flow separation is, perhaps, one of the most important hydrodynamic problems to be investigated intensively to find its solution satisfactorily. Because of the complexity of the problem, a rigorous definition of flow separation and stall should be made. The classical concept of flow separation is because of viscosity; therefore, it is often expressed as boundary layer flow separation or boundary layer separation. The chapter highlights classical concept of flow separation is outlined and then the generalized definition of flow separation. The problem of flow separation is as old as that of boundary layer theory. Ludwig Prandtl, the father of the boundary layer concept, was concerned about flow separation before he started his work on the boundary layer. The chapter highlights multiple instabilities of the overall flow field and of various subfields. As Reynolds number increases, the resulting unsteady, three-dimensional, and interacting vortical patterns become keys to some of the perplexing experimental observations reported by various investigators.
01 Apr 1970
TL;DR: In this paper, a pressure distribution analysis is performed on lifting entry model flat bottom by pressure plume induced, flow separation on liftingentry model flatbottom by pressure distribution analyzer.
Abstract: Jet plume induced, flow separation on lifting entry model flat bottom by pressure distribution analysis
TL;DR: In this paper, the authors considered the problem of simultaneous development of velocity and temperature profiles in the case of a laminar flow in the entrance region between two flat plates, and showed the influence of parameters such as the optical thickness, the ratio of conductive energy to radiative energy and Graetz number on the temperature variation across the duct and the heat transfer rates.
Abstract: Consideration is given to heat transfer for the problem of simultaneous development of velocity and temperature profiles in the case of a laminar flow in the entrance region between two flat plates. The duct consists of two diffuse, black, isothermal parallel surfaces separated by a finite distance. A medium filling the space between plates emits and absorbs thermal radiation. Numerical solutions are obtained for a slug flow (Pr=0), a flow of the inlet region (Pr=1) and a fully developed flow that was shown in the 2nd report, and show the influence of parameters such as the optical thickness, the ratio of conductive energy to radiative energy and Graetz number on the temperature variation across the duct and the heat transfer rates. The radiative heat transfer rate is scarcely affected but the convective one is much affected by flow patterns. An approximate method for the prediction of heat transfer rates in any flow patterns is shown and the results are in good agreement with the exact ones in the region of large optical thickness.
TL;DR: In this paper, the behavior of flow at a high Reynolds number, R, is precisely studied, using the Fourier transformation, and the two characteristic types of flow are shown.
Abstract: The stationary flow of a viscous fluid past a flat plate at a small incidence, θ, is dealt with by Oseen's linearized approximation. The behavior of flow at a high Reynolds number, R , is precisely studied, using the Fourier transformation. The two characteristic types of flow are shown. In the case: 1≪ R ≤ O (1/sin θ), the flow field is the conventional potential flow satisfying the Kutta-Joukowski condition with the thin boundary layer of thickness of \(O(1/\sqrt{R})\) adjacent to the surface of the plate. In the other case: O (1/sin 2 θ)≪ R , the flow field consists of a potential field and a wide viscous wake spreading downstream, where the flow is rotational and the velocity almost vanishes. The latter corresponds to the stalled state of the plate.
TL;DR: In this paper, the effects of small-scale plane or axisymmetrical boundary irregularities on steady parallel flows of incompressible viscous fluid are investigated for the cases of flow between two parallel planes and flow in a cylindrical pipe of circular cross-section.