Showing papers on "Hele-Shaw flow published in 1968"

Peristaltic pumping with long wave lengths at low reynolds number.

Abstract: : Pumping by means of an infinite train of peristaltic waves is investigated under conditions for which (1) the relevant Reynolds number is small enough for inertial effects to be negligible and (2) the wavelength-diameter ratio is large enough for the pressure to be considered uniform over the cross-section. Theoretical results are presented for both plane and axi-symmetric geometries, and for amplitude ratios ranging from zero to full occlusion. For a given amplitude ratio, the theoretical pressure rise per wavelength decreases linearly with increasing time-mean flow. An experiment with a quasi-two-dimensional apparatus confirmed the theoretical values. Calculations of the detailed fluid motions reveal that under many conditions of operation the net time-mean flow is the algebraic difference between a forward time-mean flow in the core of the tube and a backward ('reflux') time-mean flow near the periphery. The percentage of reflux flow can be very high. This reflux phenomenon is probably of physiologic significance in the functioning of the ureter and the gastro-intestinal system. A second fluid mechanical peculiarity with physiological implications is that of 'trapping': under certain conditions an internally-circulating bolus of fluid, lying about the axis, is transported with the wave speed as though it were trapped by the wave. (Author)

Maximum dissipation resulting from lift in a slow viscous shear flow.

Abstract: Lift tensor for three dimensional body in linear shear flow at low Reynolds numbers, discussing orientation stability

Laminar flow in a pipe at low and moderate reynolds numbers

Abstract: The laminar flow of a homogeneous viscous liquid in the inlet of a pipe is investigated numerically for a range of small and moderate Reynolds numbers where the boundary layer approximation is inapplicable. Velocity profiles and other characteristics of the flow are calculated and the results compared with approximate results obtained by other methods. The limiting case of vanishingly small Reynolds number is also treated analytically.

Stability of Parallel Flow between Concentric Cylinders

Abstract: Linear stability of parallel flow in concentric annulus for infinitesimal axisymmetric disturbances

Velocity gradients at the wall for flow around a cylinder for Reynolds numbers between 60 and 360

Abstract: This paper shows how electrochemical techniques can be used in studies of flow around solid objects to measure the velocity gradient at the solid boundary. The method holds the advantages that it is not necessary to calibrate and that the test element is easy to fabricate. A study of the distribution of the wall velocity gradient around a cylinder of 1 in. diameter indicates that boundary-layer theory correctly predicts the measurements between the front stagnation point and the separation for Reynolds number, R , greater than 150. The wall velocity gradients in the wake are much smaller than in the front part of the cylinder and they reveal a minimum which is quite close to the separation point.

Nonlinear Flow Through Granular Media

Abstract: Relative roles of steady and unsteady fluid motion in causing deviation from the linear Darcy resistance law are described. Air velocities and turbulence intensities were measured within the pores of a gravel bed by hot-wire anemometers. Results indicate that although the linear resistance relation ceases to be valid at a Reynolds number of about 2, velocity fluctuations do not begin until the Reynolds number is about 100, and turbulence is not fully established until it is at least 800. Studies of water flow through a coarse sand bed showed that convergence of the macro-streamlines significantly reduced the resistance at Reynolds numbers over about 10, the proportionate reduction increasing with flow. The observations are interpreted in terms of flow through coiled pipes or round immersed objects, and four regimes of flow through granular media are proposed.

Secondary flow in a Hele-Shaw cell

Abstract: Riegels (1938) investigated the breakdown of Hele-Shaw flow in a Hele-Shaw cell with unusually large separation distance 2h* between the walls. A theoretical outer expansion for the velocity was constructed in the case where the obstacle is a circular cylinder, using an intuitive inner boundary condition that seems to be correct in the limit h* → 0, but without explicit matching with the inner expansion.An inner expansion has now been found, and it shows that the solution in the inner layer forces terms into the outer expansion that are larger than those found by Riegels whenever h* is finite and not zero.

Critical reynolds number for sinusoidal flow of water in rigid tubes

Abstract: Experimental friction factor for pulsatile water flow, obtaining empirically pressure drop and flow rate data

Free Surface Shear Flow Over a Wavy Bed

Abstract: An analytical treatment of free surface shear flow over a wavy bed of regular sinusoidal form is developed from the one-dimensional energy equation. The effects of curvilinearity on the velocity and piezometric heads are examined in some detail. The equation is expanded into a series in dimensionless terms to obtain a systematic ordering of the magnitudes of the various terms and associated physical quantities. The third-order equation is linearized and solved to obtain expressions for the phase shift between and amplitude ratio of the bed waves and depth variations. The second-order nonlinear equation is solved numerically for a particular flow, and the profiles are presented graphically. The various flow configurations predicted by the linearized and the nonlinear formulations are discussed in some detail and the occurrence of a bi-stable flow of moderate and high Froude numbers is explained.

Convergent-divergent nozzle flows.

Abstract: Convergent-divergent nozzle flow field solution obtained in form of perturbation about one dimensional flow field

Numerical solutions of compressible and incompressible laminar separated flows.

Abstract: Numerical techniques and solutions for compressible and incompressible laminar separated flows using time dependent finite difference equations

The effect of support position and turbulence intensity on the flow near the surface of a sphere

Abstract: The flow near the surface of a sphere was studied, using a flow visualization technique, for Reynolds numbers from about 4×104 to 2.5×105. It was concluded that the presence of a crossflow support substantially disturbed the flow near the surface of the sphere, especially at supercritical Reynolds numbers. Photographs of the flow patterns around spheres with crossflow supports, and with rear supports, have been presented. Also, measurements were made which show the way in which the turbulence intensity of the free stream influenced the angle of separation at various Reynolds numbers.

Flow problems of swept low-drag suction wings of practical construction at high reynolds numbers*

Abstract: On swept low-drag suction wings, pressure gradients normal to the potential flow direction induce boundary-layer crossflow (FIGURE 1). Since it vanishesat the wall and outer edge of the boundary layer, inflexion points develop in the crossflow boundary layer, which is, therefore, dynamically highly unstable a t higher boundary-layer crossflow Reynolds numbers,t in contrast to the frictional instability of the tangential boundary-layer component. With unstable bounday-layer crossflow, closely-spaced longitudinal disturbance vortices develop, rotating in the same direction. Transition occurs when the boundary-layer crossflow Reynolds number, a t which these vortices are first observed, is exceeded by 50-100 percent. Shortly before transition, according to visual transition observations in a laminar flow tube, with boundary-layer crossflow induced by temperature gradients, the originally straight crossflow-disturbance vortices start oscillating and are distorted three-dimensionally. Lift forces shift displaced vortex elements further away (in the direction normal to the surface toward the outer edge of the boundary layer or wall) from their original location in the boundary layer. As the displaced-vortex elements move into regions of different boundary-layer velocity, the disturbance vorticity increases by longitudinal vortex-stretching and convection. Hairpin vortices develop, become unstable, and “explode” a t the beginning of transition. The generation of hairpin vortices in boundary layers is described by Theodorsen3 and S t ~ a r t . ~ A question arises concerning the stability limit of the boundary-layer crossflow and the amount by which this limit safely can be exceeded on swept laminar suction wings. Since the crossflow-stability limit depends on the shape of the crossflow the tangential and crossflow boundary-layer profiles on swept laminar suction wings were calculated by Raetz’s numerical integration method of the compressible three-dimensional laminar boundary layer.7 For example, FIGURE 2a shows the calculated tangential and cross-

Plane Poiseuille Flow of a Rarefied Gas

Abstract: An analytical solution to the problem of rarefied gas flow in a channel is obtained by the moment method. The expected minimum in volume flow rate is found; the flow rate exhibits an algebraic instead of a logarithmic singularity at low pressures. Present results are compared with the results from other theories and with measurements.

A model for the prediction of velocity and void fraction profiles in two‐phase flow

Abstract: An experimental study of velocity and void-fraction profiles has been carried out for the cocurrent two-phase flow of both air and water, and air and glycerine-water systems. The investigation was restricted to flow in a horizontal, 1 in. diam. tube with primary emphasis on the bubble flow regime. The assumptions which must be made to reduce the general equations of continuity, momentum, and energy to the forms appropriate for two-phase flow are presented and the equations simplified for the case of no local slip. A model is proposed which allows the determination, by trial, of the two-phase velocity and void-fraction profiles. The profiles generated by the use of the model in conjunction with experimental sampling data are presented, the profile shapes are discussed, and their variations with Reynolds and Froude numbers and gas volumetric flow fraction are shown to be self-consistent. The horizontal profiles are found to be in fair agreement with those predicted from Levy's mixing length theory. A correlation scheme is outlined which, supplemented by data over wider ranges of operating conditions, would serve as a method for estimating pressure drops in two-phase flow.

On the stability of elastico-viscous flows

Abstract: The stability ofCouette flow and planePoiseuille flow of an elastico-viscous liquid is analyzed. It is found that in both cases the flow is less stable than that of Newtonian liquids. The critical wave number is also changed due to the elasticity of the liquid. These changes depend on the type of flow under consideration.

Application of the characteristic method in calculating the time dependent, one-dimensional, compressible flow in a tube wind tunnel

Abstract: Numerical procedures for solving time dependent equations for one dimensional flow through wind tunnels

Slow Ono-Newtonian Flow in a Zone of Separation

Abstract: Slow motions of purely viscous fluids in a two-dimensional conduit expansion are investigated using a finite-difference numerical scheme. The important concepts in the general theory leading to the governing differential equations of the flow are briefly discussed, and the equations are reduced to a convenient form for numerical solution. Contours of stream function, vorticity, and viscosity function in the zone of separation are compared for different values of the flow behavior index, which vary from the shear-thinning, pseudoplastic, range to the shear-thickening, dilatant, range, at four values of the generalized Reynolds number: 0, 16, 32, and 48. The results of the investigation indicate that for the separated flow of power-law fluids, shear-thinning fluids develop shorter, less intense, and more viscous eddies than do shear-thickening fluids at the same Reynolds number. It is also found that the influence of the flow behavior index is different for creeping flows than for flows at higher Reynolds numbers, i.e., at R = 0 the deviation of the eddy characteristics from Newtonian behavior is greater than at higher values of the Reynolds number.

A Study of the Interactions of Turbulent Shear Flow and Displacement Flow between Parallel Walls

Abstract: A mixing length approach is applied to the case of a spiral flow, where pressure flow acts across a Couette flow as in the case of end leakage around a shaft. The mixing length is expressed as a dimensionless function of the modulus of the local velocity vector, drawing upon an empirical relationship based upon wall-law flow data. Results are shown to be in approximate agreement with a set of experimental measurements. This indicates that the computation scheme accounts for the major factors in such flows, where the shear stress chances direction outward from a wall. Contributed to ASLE by the authors.

The flow between two plates of a fluid containing rigid structures.

Abstract: : The flow between two plates of a fluid containing rigid structures is examined analytically Profiles of the velocity and averaged vorticity of the structures for a wide range of cases are given It is found that the velocity profiles can have convex portions near the boundaries and that they may resemble the box shaped profiles characteristic of high Reynolds number Navier-Stokes flow (Author)

Investigation of jet transition phenomena.

Abstract: : The experimental investigation examines jet phenomena, gaseous and liquid, in small submerged and bounded jets. Its general objectives are to acquire experimental data and to develop mathematical expressions for predicting the behavior of fluidic elements and designs. Data are presented for circular nozzles of 0.25 to 4.6 mm and square nozzles of 0.5 to 1.0 mm, observed by Schlieren and Birefringent flow techniques at low Reynolds numbers compatible with miniature fluidic designs. Good correlation between compressible and incompressible flow is obtained. Three principal nondimensional terms are used to evaluate and correlate experimental results. They are Reynolds number, transition number (a relationship of nozzle diameter and length of laminar flow), and momentum number (represented the interaction of two jets). Three sets of tests are described. One measures the transition from laminar flow to turbulence in single submerged jets. The second introduces a secondary jet flow to determine its effect upon transition and deflection of the primary jet. The third involves variations of nozzle geometry commonly used in fluidic elements: sidewall divergence, sidewall setback and reinjection curvature. These geometries provide feedback paths and reflecting surfaces, allowing the jet to produce premature transition. (Author)

Flow density of adiabatic evaporating-liquid flows

Abstract: A description is given of a semiempirical method of determining the flow density of nonequilibrium adiabatic flows of evaporating liquids based on the vortex theory of vapor-phase generation, which establishes a relation between the superheating of the liquid and its flow velocity It is shown that, at subcritical flow rates, evaporation in an adiabatic liquid flow becomes impossible, and a method of determining the critical flow parameters is given