Showing papers on "Velocity gradient published in 1977"

Saltation and suspension trajectories of solid grains in a water stream

Abstract: This paper continues the investigation of the motion of solitary grains in a water stream, reported by Francis (1973)- The trajectories of solid grains are photographed by a multi-exposure technique as they are propelled by water streams along the bed of a laboratory channel. Many thousands of photographs were taken and analysed to determine the positions, velocities and accelerations of the grain. The technique does not take into account the possible effect, in multi-grain transport, of intergranular collisions. The three different modes of transport of grains were all observed — rolling, saltation and suspension, and the proportion of each found for a variety of transport stage w\*/w\*0. The development of suspension is much less rapid than the development of saltation from rolling, but even at the highest stage used, about 3.0, there is still a small amount of rolling. The trajectory dimensions and geometry are shown in relation to the stage which uniquely determines the geometry. Experiments where the grain is suddenly entrained from a stationary position show that several features of the subsequent trajectory are the same as those of a trajectory with a prior history of movement: thus it is inferred that the start of a trajectory is by way of hydrodynamic forces rather than by the conservation of momentum of previous trajectories. Impacts and trajectories were analysed for the coefficient of friction tan cc and for the height of the effective thrust. While tan a is shown to be rather larger than has been suspected in the past, the variation of yn throws light upon predominance of slow fluid near the bed rather than high speed inrushes of fast fluid. Better information is now available for finding the mean forward speed of grains compared to that presented in the earlier paper. There are grounds for believing the existence of a * shear-drift ’ force on grains when they are in a velocity gradient, giving a force opposing gravity: but there is no evidence of a proximity effect of the bed independent of the velocity gradient.

Further experiments in nearly homogeneous turbulent shear flow

Abstract: The experiment of Champagne, Harris & Corrsin in generating and studying a nearly homogeneous turbulent shear flow has been extended to larger values of the dimensionless downstream time or strain by the use of a larger mean velocity gradient in the same wind tunnel. The system appears to reach an asymptotic state in which scales and turbulent energy grow monotonically. Two-point covariances and tensor structure of one-point ‘Reynolds stress’ and ‘pressure/strain-rate covariance’ agree with the earlier case. However, the linear intercomponent energy exchange hypothesis due to Rotta, very roughly confirmed by the earlier experiment, is contradicted by the present data.

Secondary Wind Speed Maxima Inside Plant Canopies

Abstract: It is noted that wind profiles measured in forest and crop canopies normally contain a secondary maximum or a region of very small shear beneath the level of greatest foliage density. One-dimensional models utilizing a turbulent transport coefficient cannot predict a reversed velocity gradient and, as a result, profile analyses normally imply coefficients that are unrealistic or nonsensical. Examination of the equation for the local rate of change of Reynolds stress u′w′ shows that the velocity gradient can reverse in sign if the divergence of the turbulent transport of stress is of opposite sign and exceeds in magnitude the pressure-velocity gradient correlation. Direct measurements of the turbulent transport of u′w′ in corn (Zea mays L.) indicate that its value is considerably larger than in the air layers above and show that stress is transported downward from the upper parts of the vegetation. A one-dimensional model of canopy flow which solves the equations for momentum, Reynolds stress and ...

Deviation of Velocity Gradient Profiles from the “Gap Loading” and “Surface Loading” Limits in Dynamic Simple Shear Experiments

Abstract: The shear‐wave field generated in a linear viscoelastic medium confined between parallel plates (one fixed, the other oscillating sinusoidally in its own plane) has been evaluated and presented in a graphical form convenient for determination of the role of wave propagation effects in dynamic rheological measurements. The transition from closely spaced planes (“gap loading”) to the freely propagating plane wave (“surface loading”) limit is examined; the importance of deviations in magnitude and phase of the gradient profile from the gap loading limit is discussed in terms of high precision dynamic rheological experiments; significant deviations occur for shear wavelength to gap width ratios of 30 or less.

Turbulent fluctuations in the viscous wall region for Newtonian and drag reducing fluids

Abstract: An electrochemical method, which is the mass transfer analog of the hot film anemometer, has been developed to study flow fluctuations in the immediate vicinity of a wall. Electrodes mounted flush with the wall are the cathode of an electrolysis cell. At high enough voltages, the electric current is controlled by the rate of mass transfer to the cathode and the concentration of the reacting species at the surface is zero. These techniques allow the measurement of two components of the fluctuating velocity gradient at the wall. Results have been obtained on the structure of turbulence close to a wall and on the influence of drag reducing polymers on this structure.

Laser velocimeter measurements in a turbulent flame

Abstract: Measurements of mean velocity, turbulence rate and velocity fluctuations were performed in a constant area combustion chamber, where a premixed air-methane flow is ignited and stabilized by a parallel flow of hot gases acting as a pilot flame. The combustion produces an acceleration of the flow and transverse velocity gradients. Turbulence increases as the combustion develops, velocity fluctuations being maximum in the reaction zone. The influence of the inlet turbulence intensity and the velocity ratio between main stream and hot jet have been investigated; generally speaking, the phenomena are similar. The r.m.s. transverse velocity fluctuation obtained during the tests does not seem to be increased by combustion, and the Reynolds stress u ′ υ ′ ¯ is significant only in the neighborhood of the mixing zone. The numerical prediction of mean velocity and velocity fluctuation leads to a fairly satisfactory agreement with experimental results; the turbulence increase in the combustion zone seems to be closely related to the velocity gradient produced by the flame.

Inversion of Fahraeus effect and effect of mainstream flow on capillary hematocrit

Abstract: The well known Fahraeus effect (1929) states that if whole blood is allowed to flow from a large reservoir into a small circular cylindrical tube, the hematocrit in the tube is smaller than that in the reservoir, and the smaller the tube, the smaller will be the tube hematocrit. This is interpreted as a feature of particulate flow. We find that this relationship is not monotonic in a model experiment in which gelatin particles (circular disks) are suspended in a silicone fluid to simulate blood. When the diameter of the underformed cell is equal to or greater than the tube diameter, the volume fraction of the cells in the tubes increases to a value equal to or greater than that in the reservoir. Thus the Fahraeus effect has a point of inversion. Additional experiments show that the hematocrit in the tube could be greatly influenced by the flow condition outside the entrance of the tube. If the tube is perpendicular to the main direction of flow in the reservoir (as is the case of Barbee and Cokelet's experiment, or in most arteriole-capillary junctions), the velocity gradient and the velocity of flow in the reservoir just outside the entrance to the tube affects the hematocrit in the tube.

Laser velocimeter measurements in a turbulent flame

Abstract: Measurements of mean velocity, turbulence rate and velocity fluctuations were performed in a constant area combustion chamber, where a premixed air-methane flow is ignited and stabilized by a parallel flow of hot gases acting as a pilot flame. The combustion produces an acceleration of the flow and transverse velocity gradients. Turbulence increases as the combustion develops, velocity fluctuations being maximum in the reaction zone. The influence of the inlet turbulence intensity and the velocity ratio between main stream and hot jet have been investigated; generally speaking, the phenomena are similar. The r.m.s. transverse velocity fluctuation obtained during the tests does not seem to be increased by combustion, and the Reynolds stress u ′ υ ′ ¯ is significant only in the neighborhood of the mixing zone. The numerical prediction of mean velocity and velocity fluctuation leads to a fairly satisfactory agreement with experimental results; the turbulence increase in the combustion zone seems to be closely related to the velocity gradient produced by the flame.

Low velocity gradient flow birefringence and viscosity changes in hyaluronate solutions as a function of pH.

Abstract: The flow birefringence and extinction angle over a velocity gradient range of approximately 5–100 sec−1, and the zero shear-viscosity have been obtained from human umbilical cord hyaluronic acid at concentrations of 0.25, 0.125 and 0.0625%, and pHs 6.0, 6.5, 7.0, 7.5, 8.0, and 8.5 and constant ionic strength 0.1. The data indicate a large change in optical anisotropy as a function of pH, with most of the transition in the pH range 7.0–7.5, i.e., across the physiological range. The sign of the anisotropy changes between pH 8.0 and 8.5. These results, together with changes in the extinction angle and intrinsic viscosity as a function of pH, suggest a pH-dependent structural change in the system. Due to the abruptness of the transition, as evidenced by the intrinsic viscosity and flow birefringence, it is probable that the structural transition is cooperative. If the data are interpreted in terms of the Rouse-Zimm Gaussian subchain theory, a modification of the model in terms of the Haller-Cerf concept of internal viscosity is required. Thus, the demonstrated properties of hyaluronate solutions indicate a system with memory of stress. Due to the presence of large concentration effects discernible in the extinction angle measurements, hyaluronic acid probably exists as a network in solution. The results are discussed with respect to the mechanoelectrical transducing properties of hyaluronates and stress-dependent changes in ORD already reported.

Dynamic viscosity of macromolecular liquids for a superposition of static and oscillating velocity gradients

Abstract: Two coupled, inhomogeneous relaxation equations for the friction pressure tensor and the alignment tensor are derived within the framework of irreversible thermodynamics. These equations are solved for a specific geometry, viz. flow between flat plates, and for a velocity gradient of the form Γ0 + Γ1 cos Ωt with small Γ1. From the resulting relation between the (time-dependent) friction pressure tensor and the velocity gradient, the dynamic viscosity and the normal pressure can be inferred. The frequency dependence of the relevant viscosity coefficients is discussed. If Г0, the magnitude of the static part of the velocity gradient is large enough, a type of resonance behavior is found with the resonance frequency Ωres≈(1 + ξ)-1Γ0 where ξ is the ratio between the relation times of the friction pressure tensor and of the alignment tensor.

Non-newtonian viscosity and normal pressure associated with the flow alignment in macromolecular liquids

Abstract: Non-linear constitutive laws previously obtained within the framework of irreversible thermodynamics are applied to the calculation of the flow alignment and the friction pressure tensor of macromolecular liquids. A non-newtonian viscosity is obtained which decreases with increasing magnitude of the velocity gradient. For rigid molecules it reaches a finite asymptotic value, viz. the second newtonian viscosity. The friction pressure tensor contains normal components. The magnitude of this normal pressure is closely related to the change of the viscosity caused by the velocity gradient. Flow alignment and the pressure tensor are also studied for time-dependent (alternating) velocity gradients.

Sector boundary distortion in the interplanetary medium

Abstract: We address the theoretical problem of the effect of a solar wind meridional velocity gradient on the orientation, or tipping, of a line embedded within the interplanetary plasma. We find that rotations of from 30degree to 75degree, between 1.5 solar radii and I AU, are produced when observed values for the solar wind velocity and its meridional gradient are used. This is not a small effect, nor is it difficult to calculate: it is a natural consequence of any meridional velocity gradient in the interplanetary medium. In relating this result to observed sector boundaries we note that the latitude dependence of the width of interplanetary magnetic sectors (dominant polarity or Rosenberg-Coleman effect) implies that sector boundaries at I AU are generally inclined at an angle of from 10degree to 20degree to the solar equatorial plane. Conversely, studies of photospheric magnetic fields have led to the conclusion that sector boundaries near the sun are, on the average, at large angles (approx.90degree) to the solar equatorial plane. If the dominant polarity effect were to be produced by rotation in the interplanetary medium, the sign of the solar wind meridional velocity gradient must not change at the equator, but the gradient does havemore » to change sign for +/- boundary crossings in comparison to -/+ boundary crossings.« less

Inertial motion of a continuum

Abstract: The Burgers equation ut+uux=νuxx represents pure inertial motion except for the effects of viscosity ν. If ν=0, this equation becomes u=0 and describes the inertial motion of a one‐dimensional continuum until the time of formation of discontinuities, or ’’shocks’’. The study of pure inertial motion is extended to an arbitrary number of dimensions. Starting from some initial state of motion each parcel of the continuum may or may not have the intrinsic ability to form a shock, this property being a function of the symmetrical part of the velocity gradient matrix in the vicinity of the parcel. This study determines the conditions for which a parcel will, in fact, form a shock, the time that is required, and the temporal development of the full velocity gradient matrix and of coordinate invariants of the flow such as the divergence and the vorticity.

Spatial interaction in magneto-micropolar continua

Abstract: We consider a micropolar continuum, whose material points are endowed with magnetic moment, in the presence of a magnetic field within the approximation of the quasimagnetostatics. We deduce the balance equations by a suitable averaging technique and then we examine the compatibility of spatial interaction effects with thermodynamics. As a result, we show that such effects are confined to the constitutive equations for the dissipative stressDT, the dissipative couple stressDm and the heat flux q. Moreover, as a consequence of the reduced dissipation inequality, a linear theory would account only for a dependence ofDT,Dm, and q on the velocity gradient, the angular velocity, the gradient of the angular velocity, and on the temperature gradient.

Velocity gradient driven flute instabilities in plasmas

Abstract: The effect of velocity gradient across the magnetic field on the low frequency flute modes is examined in detail, using the normal mode analysis. It is shown that some new type of instabilities driven primarily by the velocitygradient arise and these excited modes eventually attain the convective saturation. The onset of plasma turbulence due to these instabilities may possibly be one of the major contributors for anomalous heating process and enhanced plasma resistivity.

Consolidation by Sand Drains in Initial Gradient Soils

Abstract: Phenomenon of water movement through cohesive soils is important to several fields of engineering. Many investigations on flow through such soils indicate that seepage starts only when the hydraulic gradient exceeds a certain value called the initial or threshold gradient and the velocity gradient. In the absence of the initial gradient, theoretical solutions for radial flow towards sand drains exits. In this note an analytical solution is presented that incorporates the concept of initial gradient to the problem of radial flow to sand drains. The solution is based on the assumptions of equal strain, no smear, constant compressibility and permeability, and time independent external load.

Influence of small polymer additives on the behavior of a linear viscoelastic fluid

Abstract: A system of equations is obtained, describing a dilute polymer solution in an incompressible linear viscoelastic fluid as a nonlinear viscoelastic medium. As an example, motion with a specified velocity gradient is analyzed in the linear approximation. An expression is given for the dynamic modulus of the system in terms of the dynamic modulus of the most viscoelastic fluid containing the macro-molecules and in terms of the polymer concentration.