Showing papers on "Shear flow published in 1970"

The mechanics of an organized wave in turbulent shear flow

Abstract: Some preliminary results on the behaviour of controlled wave disturbances introduced artificially into turbulent channel flow are reported. Weak plane-wave disturbances are introduced by vibrating ribbons near each wall. The amplitude and relative phase of the streamwise component of the induced wave is educed from a hot wire signal, allowing the wave speed and attenuation characteristics and the wave shape to be traced downstream. The normal component and wave Reynolds stress have been inferred from these data. It appears that Orr–Sommerfeld theories attempted to date are inadequate for description of these waves.

Experiments on nearly homogeneous turbulent shear flow

Abstract: With a transverse array of channels of equal widths but differing resistances, we have generated an improved approximation to spatially homogeneous turbulent shear flow. The scales continue to grow with downstream distance, even in a region where the mean velocity gradient and one-point turbulence moments (component energies and shear stress) have attained essentially constant values. This implies asymptotic non-stationarity in the basic Eulerian frame convected with the mean flow, behaviour which seems to be inherent to homogeneous turbulent shear flow.Two-point velocity correlations with space separation and with space-time separation yield characteristic departures from isotropy, including clear ‘upstream–downstream’ unsymmetries which cannot be classified simply as axis tilting of ellipse-like iso-correlation contours.The high wave-number structure is roughly locally isotropic although the turbulence Reynolds number based on Taylor ‘microscale’ and r.m.s. turbulent velocity is only 130. Departures from isotropy in the turbulent velocity gradient moments are measurable.The approximation to homogeneity permits direct estimation of all components of the turbulent pressure/velocity-gradient tensor, which accounts for inter-component energy transfer and helps to regulate the turbulent shear stress. It is found that its principal axes are aligned with those of the Reynolds stress tensor. Finally, the Rotta (1951, 1962) linear hypothesis for intercomponent energy transfer rate is roughly confirmed.

The temperature and strain-rate dependence of the shear strength of mild steel

Abstract: An account is given of experiments in which the shear flow stress of mild steel was measured at temperatures from 195 to 713°K and strain rates from 10−3 to 4 × 104 sec−1 The experimental results obtained at room temperatures are compared with those of earlier tension tests The rate sensitivity of the flow stress, (∂τ/∂ In γ) T , is found to be a decreasing function of temperature, except at the highest strain rates; at these rates a large increase in the rate sensitivity is observed, the flow stress at constant temperature varying approximately linearly with strain rate The data are interpreted in terms of thermal activation rate theory and the theory of the damping of dislocation motion by phonon viscosity

Role of Landau damping in crossed-field electron beams and inviscid shear flow

Abstract: Under certain circumstances the problem of the stability of low‐density crossed‐field electron beams is precisely analogous to the problem of the stability of incompressible inviscid shear flows The electron density, the drift velocity, and the potential correspond to the fluid vorticity, velocity, and the stream function, respectively Neutrally stable normal modes of oscillation that are found when certain suitable step‐function unperturbed electron density (vorticity) profiles are assumed seem to disappear when small gradients are present In the context of a Laplace transform solution of the initial value problem, the vanishing normal modes can be found by analytic continuation of the solution onto another sheet of the cut complex ω plane The “recovered” modes are found to be damped by a fluid‐wave resonant interaction which closely resembles the Landau damping of plasma oscillations in warm plasmas by particle‐wave resonance An interesting feature of the neutral waves is that they have a negative energy and so are destabilized by the removal of energy from the system (for example, by slightly dissipative walls) The sign and magnitude of the Landau damping term is evaluated for a simple case and compared (for the electronic case) with the growth provoked by slightly lossy walls

Bounds for turbulent shear flow

Abstract: Bounds on the transport of momentum in turbulent shear flow are derived by variational methods. In particular, variational problems for the turbulent regimes of plane Couette flow, channel flow, and pipe flow are considered. The Euler equations resemble the basic Navier–Stokes equations of motion in many respects and may serve as model equations for turbulence. Moreover, the comparison of the upper bound with the experimental values of turbulent momentum transport shows a rather close similarity. The same fact holds with respect to other properties when the observed turbulent flow is compared with the structure of the extremalizing solution of the variational problem. It is suggested that the instability of the sublayer adjacent to the walls is responsible for the tendency of the physically realized turbulent flow to approach the properties of the extremalizing vector field.

Stability of a sand bed subjected to a shear flow of low Froude number

Abstract: The problem of sand bed stability is formulated and solved for a model in which the local slope of the free surface is small relative to the slope of the perturbed lower boundary The solution shows the bed to be unstable to perturbations of wavelength greater than the wavelengths for which the inertia of the sediment grains is important Wave speeds and growth rates from numerical calculations are presented and compared with long- and short-wave asymptotic expressions Although the fluctuating velocity field in the nonuniform flow is approximated by a constant eddy viscosity, a general picture of the relationship between the flow over a perturbed boundary and the observed geometrical and dynamical parameters of the resulting boundary waves can be developed It is shown that the sand bed instability is due to local accelerations of a shear flow caused by the nonuniform boundary If either the shear or the acceleration is eliminated from the analysis, the instability cannot be found On the other hand, no wavelength is defined by such an analysis, and it is shown that the wavelength is determined by spatial adjustments in the turbulent velocity field

Diffusive destabilisation of the baroclinic circular vortex

Abstract: It is shown that, even for vanishingly small diffusivities of momentum and heat, a rotating stratified zonal shear flow is more unstable to zonally symmetric disturbances than would be indicated by the classical inviscid adiabatic criterion, unless σ, the Prandtl number, = 1. Both monotonic instability, and growing oscillations ("overstability") are involved, the former determining the stability criterion and having the higher growth rates. The more σ differs from 1, the larger the region in parameter space for which the flow is stable by the classical criterion, but actually unstable. If the baroclinity is sufficiently great for the classical criterion also to indicate instability, the corresponding inviscid adiabatic modes usually have the numerically highest growth rates. An exception is the case of small isotherm slope and small σ. A single normal mode of the linearized theory is also, formally, a finite amplitude solution; however, no theoretical attempt is made to assess the effect of finit...

Simple shear flow round a rigid sphere: inertial effects and suspension rheology

Abstract: An analysis is presented of the flow field near a neutrally-buoyant rigid spherical particle immersed in an in compressible Newtonian fluid which, at large distances from the particle, is undergoing simple shear flow. Subject to conditions of continuity of stress at the particle surface and to conditions of zero net torque and zero net force on the sphere, the effect of fluid inertia on the velocity and pressure fields in the vicinity of the particle has been computed to for a dilute (non-interacting) suspension of spheres. In addition it is found that inertial effects give rise to a non-isotropic normal stress.

Stability of a Plane Parallel Flow with Variable Vertical Shear and Unstable Stratification

Abstract: A study is made of stability properties of perturbations superimposed on an unstably stratified plane parallel flow with variable vertical shear. Two different types of instability which may take place in the flow are found: one is a thermal instability modified by a shear flow, and the other is an inertial instability modified by a thermal stratification. Unstable perturbations of the thermal type are distinguished from those of the inertial type in terms of the Richardson number. The thermal instability is most favorable for development of a three-dimensional longitudinal perturbation whose wavelength in the direction parallel to the basic flow is much longer than that in the direction perpendicular to the basic flow. A preferred perturbation of the inertial instability, however, is of a two-dimensional transverse mode. Amplification of transverse perturbations of thermal origin is reduced by the influence of a shear flow regardless of the presence of variable shear in the basic flow. We conclude that a shear flow in general is responsible for the formation of longitudinal convection roll, and a variable shear slightly affects characteristics of thermal instability of a constant shear flow.

Fully Developed Plastic Shear Flow of Granular Materials

Abstract: Synopsis A consistent mechanical basis is presented for the mathematical description of plane, plastic shear deformation of frictional, cohesive or cohesionless granular materials The deformation considered is fully developed flow of particles which override each other over long distances It is an idealization of the cataclastic flow by which all faulting processes in loose or slightly consolidated sediments proceed It is shown that granular material in fully developed shear flow exhibits all the essential properties of a perfectly plastic material In particular, it lacks a one-to-one correspondence between strain rates and stresses, as is explained by a discussion of the energy dissipation involved Instead the relation between stress and strain increments reduces to a relation between corresponding principal directions of the two tensors Despite the plastic character of the flow, the flow rules obtained by employing the rheological concept of perfect plasticity to granular materials (perfect soil p

Collision efficiency of equal spherical particles in a shear flow. The influence of London-van der Waals forces

Abstract: A theoretical and experimental approach to the investigation of the influence of London-Van der Waals forces on orthokinetic flocculation is described. The theoretical treatment evaluates the effect of these forces on the interaction of two spherical particles in a laminar shear flow, to give a value of the collision efficiency (stability ratio). The experimental measurements on the flocculation of monodisperse polystyrene beads in a laminar shear flow reported provide a test of the theory. By making use of the theoretical approach described in this paper the London-Hamaker constant for polystyrene in aqueous suspension can be calculated from measurements of orthokinetic flocculation : the values obtained are in good agreement with those derived by other methods. The method additionally provides a means of measuring the “characteristic wavelength” of these forces.

Boundary Shear Distribution in Open Channel Flow

Abstract: BOUNDARY SHEAR DISTRIBUTION IN BOTH ROUGH AND SMOOTH OPEN CHANNELS OF RECTANGULAR AND TRAPEZOIDAL SECTIONS IS OBTAINED BY DIRECT MEASUREMENT OF SHEAR DRAG ON AN ISOLATED LENGTH OF THE TEST CHANNEL UTILIZING THE TECHNIQUE OF THREE POINT SUSPENSION SYSTEM SUGGESTED BY BAGNOLD. EXISTING SHEAR MEASUREMENT TECHNIQUES HAVE BEEN REVIEWED CRITICALLY. COMPARISON OF THE MEASURED DISTRIBUTION HAS BEEN MADE WITH OTHER INDIRECT ESTIMATES, FROM ISOVELS, AND PRESTON TUBE MEASUREMENTS, BASED ON KEULEGAN'S RESISTANCE LAWS. THE DISCREPANCIES BETWEEN THE DIRECT AND INDIRECT ESTIMATES ARE EXPLAINED. OF THE TWO INDIRECT ESTIMATES THE SURFACE PITOT TUBE TECHNIQUE IS FOUND TO BE MORE RELIABLE. THE INFLUENCE OF SECONDARY FLOW ON THE BOUNDARY SHEAR DISTRIBUTION COULD NOT BE ACCURATELY DEFINED IN THE ABSENCE OF A DEPENDABLE THEORY ON SECONDARY FLOW. /ASCE/

Generalized aerodynamic forces on a flexible plate undergoing transient motion in a shear flow with an application to panel flutter

Abstract: Aerodynamic forces for boundary layer profiles of flexible plate under transient motion in shear flow using computer programs

On linearized hydrodynamic modes in statistical physics

Abstract: We formulate the linearized generalized Boltzmann equation as an (asymmetric) eigenvalue problem. This problem has five eigenvalues which tend to zero when the uniformity parameter tends to zero: to second order in this parameter, they correspond to damped sound (two modes), diffusing shear flow (two modes), and diffusing entropy flow (one mode). The microscopic expressions deduced from these results for the transport coefficients agree with the correlation-function formulas. Moreover, the corresponding eigenfunctions are explicitly displayed to lowest order in the uniformity parameter: they are microscopic analogs, in terms ofone-particle distribution functions, of the well-known linearized hydrodynamic modes of macroscopic physics. All results are established to all orders in the interactions.

Rheological properties of suspensions of spheres in non-Newtonian media

Abstract: The results of an experimental investigation of the rheologioal properties of dilute suspensions of rigid spheres 100μm in diameter in non-Newtonian pseudoplastic liquids are reported. The shear flow properties of suspensions in a solution of polyisobutylene in tetralin, in aqueous solutions of polyacrylamide and sodium carboxymethylcellulose and in a Newtonian fluid have been investigated at solid concentrations up to 10% by volume. A concentric cylinder viscometer was used, results being corrected for end effects and variations in shear rate across the gap. Results for the Newtonian fluid were not inconsistent with published data. It was found that, within the range of variables investigated, for each of the non-Newtonian fluids the relative fluidity, comparing the suspension and the suspending fluid at the same shear stress, was a function of concentration only whereas the relative fluidity comparing the suspension and the fluid at the same shear rate depended on both concentration and shear rate. The fractional decrease in fluidity produced by a given concentration of spheres in polyisobutylene solution was about double that produced by the same concentration in any of the other fluids. In what are believed to be the first reported measurements of normal stress in suspensions, the first normal stress difference (p 11-p 22 for the fluids was derived from the normal force exerted on the cone of a Rheogoniometer during steady rotation. Over ranges of concentration and shear rate limited by experimental difficulties the ratio of shear rate to normal stress for the suspension divided by the corresponding quantity for the base solution appeared to be a function of concentration only when the liquids were compared at the same normal stress but not when compared at the same shear rate. However, this conclusion was less certain than the corresponding result for relative fluidity.

Low Reynolds number shear flow past a rotating circular cylinder. Part 2. Heat transfer

Abstract: Heat transfer from a cylinder placed symmetrically in a constant shear field is considered experimentally for low values of the shear Reynolds number, but for Peclet numbers Pe as large as 2000. With the cylinder held stationary, the experimentally obtained Nusselt number Nu is found to be in excellent agreement with the theoretically derived asymptotic expression, , for Peclet numbers in excess of 100. In contrast, with the cylinder rotating at a speed corresponding to zero torque, the Nusselt number becomes effectively independent of the Peclet number for Pe > 70. This surprising behaviour, predicted theoretically by Frankel & Acrivos (1968), results from the presence of a region consisting entirely of closed streamlines which surrounds the freely rotating cylinder.

Use of turbulent kinetic energy in free mixing studies

Abstract: The concept that the turbulent kinetic energy equation can be used to determine the shear in a turbulent flowfield through the use of a suitable relation between turbulent shear and turbulent kinetic energy has proved successful in the analysis of turbulent boundary-layer flows. In this paper, the application of a similar approach to the problem of turbulent free mixing of constant-density streams is described. By correlating measurements of turbulent shear and turbulent kinetic energy in a number of constant density free mixing flows, a linear relation between turbulent shear and turbulent kinetic energy is shown to exist. The combination of this relationship and a new rapid technique for the simultaneous solution of an arbitrary number of parabolic partial differential equations allows detailed calculation to be carried out for two-steam mixing systems of interest, one a plane mixing region and the other axisymmetric. Both mixing regions are constant density. Generally satisfactory agreement is achieved for both velocity and turbulent shear distribution. More important than the level of agreement reached, however, is the fact that the method used is more perceptive than previous phenomenological approaches and, thus, offers the promise of eventually leading to greater understanding of turbulent shear flow.

Lagrangian Statistics from Numerically Integrated Turbulent Shear Flow

Abstract: Lagrangian turbulence statistics were obtained from a three‐dimensional numerical model of plane Poiseuille flow at large Reynolds number. Single‐particle Lagrangian correlations were computed and compared with Eulerian space correlations. Although the curves were not self‐similar, a dimensionless scale ratio defined at the e‐folding time was comparable to Eulerian‐Lagrangian scale ratios found in the literature. The numerically obtained mean‐square particle displacements exhibited correct short‐ and long‐time behavior. Mean‐square particle separations were analyzed, and two‐particle Lagrangian velocity correlations taken at the same time were more persistent than Lagrangian autocorrelations. A semiempirical functional form was constructed for the two‐particle velocity correlations which yielded two‐particle distance correlations in good agreement with those of the numerical model. The effect of mean shear on downstream separation was examined. Results indicate a t3 or steeper dependence for downstream me...

The Nonlinear Critical Layer in a Slightly Stratified Shear Flow

Abstract: An attempt is made in this paper to extend the nonlinear critical layer analysis, as developed for homogeneous shear flows by Benney and Bergeron [1] and Davis [2], to the case of a stratified shear flow. Although the analysis is restricted to small values of the Richardson number evaluated at the edge of the critical layer, it is definitely shown that buoyancy leads to the formation within the critical layer region of thin velocity and thermal boundary layers which tend to reduce the local Richardson number. We suggest that this result has considerable relevance to the phenomenon of clear air turbulence. As in the homogeneous case, no phase change of the disturbance takes place across the nonlinear critical layer.

The mechanics of a perturbation wave in turbulent shear flow.

Abstract: : The behavior of controlled wave disturbances in turbulent channel flow was studied experimentally and theoretically The work is relevant to Landahl's waveguide theory of shear turbulence It is shown that the interaction between the organized waves and the turbulence must be considered in such a theory (Author)

Interaction of grid turbulence with a uniform mean shear

Abstract: Experiments to explore the effect of initial disturbance length-scale on turbulence developed in the presence of a uniform mean shear are the subject of this paper.Flows with nearly the same mean shear (8·6 sec−1) and initially different turbulent scales are generated in a wind tunnel test-section by placing grids just downstream of a honeycomb of uniform cell diameter (¼ in.) and non-uniform cell length. Both round-rod grids of uniform square mesh and parallel-rod construction with roughly equal solidity (0.34) are used. Grid mesh sizes range from in. to 2 in.From the results it is concluded that for a given value of mean shear the imposed length scale fixes the energy level of the resulting turbulence, provided the scale is sufficiently large. When it is reduced below some minimum value the turbulence decays. Also, it is found that two-dimensional flow-generator geometries are more effective than three-dimensional geometries in producing a roughly homogeneous turbulent field with a higher fluctuation level in a shorter distance.

A wave-interaction model for the generation of windrows

Abstract: Interactions of suitable pairs of gravity waves in a shear flow are found to give rise to aperiodic or weakly periodic secondary motions. These secondary flows resemble the ‘Langmuir vortices’ which are associated with the formation of windrows. It seems likely that such wave interactions will play a substantial part in determining the quasi-steady structure of the flow when wind blows over a water surface.

Effect of Internal Viscosity on the Deformation of a Linear Macromolecule in a Sheared Solution

Abstract: The deformation of macromolecules in a solution subjected to time‐dependent shear flow is described by means of a modified Rouse model. Into every segment of this model an internal viscosity force is introduced which is proportional to the rate at which the end‐to‐end distance of the segment is changed, and acts in the direction of the tie line between the end points. No a priori assumptions have been made on the motion of the segments themselves. An analytical solution for the distribution function of the segment lengths can now no longer be derived. At low values of the internal viscosity, an approximate solution can be obtained by means of a perturbation calculus. The effect of internal viscosity on the moments of the distribution function and, hence, on the average dimensions of the macromolecules, can be calculated. It appears that with constant shear flow at high rates of shear, as well as with oscillatory shear at high frequencies, an increase of the internal viscosity results in a decrease of the ...

A phenomenological theory of streaming birefringence

Abstract: Streaming birefringence theory, discussing incompressible fluids, shear and Couette flows, fading memory, deformations

Intrinsic Errors for Pressure Measurements in a Slot along a Flow

Abstract: Any rectilinear flow dynamically possible for a Newtonian fluid is shown to be possible also for a second order fluid. The stress which satisfies the condition of equilibrium is explicitly calculated. The component of stress normal to a wall bounding a shear flow is expressed in terms of the reading of a pressure gauge connected to a narrow slot in the wall, oriented in the direction of flow.

Karman Vortices in the Flow of Drag-reducing Polymer Solutions

Abstract: THE effect on flow properties of adding small quantities of soluble polymers, which are able to change turbulence and form solutions of a different structure, has been reviewed1. Aqueous solutions of polyethylene oxide exhibit viscoelastic properties immediately after the solute has dissolved, but these disappear on ageing. The solution, however, retains its capacity for reducing turbulent resistance of friction in flow near a smooth surface for a long time, although shear flow of the solution accelerates considerably the disappearance of this capacity. Aqueous solutions of the polymer Guar gum do not display continuum viscoelastic properties, but additions of it do reduce turbulent frictional resistance.