Showing papers on "Velocity gradient published in 1981"

Spectral modelling of homogeneous non-isotropic turbulence

Abstract: The paper describes a method to calculate homogeneous anisotropic turbulent fields associated with a constant mean velocity gradient. The equations governing the Fourier transform of the triple velocity correlations are closed by using an extended eddy-damped quasi-normal approximation. An angular parametrization of the second-order spectral tensor is introduced in order to integrate analytically all the directional terms over a spherical shell. Numerical solutions of the model are presented for typical homogeneous anisotropic flows.

Flow birefringence of concentrated polymer solutions in two‐dimensional flows

Abstract: Synopsis The results of flow birefringence measurements are reported for polymer solutions of moderate concentration subjected to a wide range of two-dimensional flows. These flows were generated in a four-roll mill which enables one to systematically vary the ratio of the vorticity to the rate of strain in the flow while holding the velocity gradient constant. It is shown that steady-state birefringence data collected over a wide range of flow types can be correlated against the eigenvalue of the velocity gradient tensor, in agreement with criterion for strong and weak flows from model calculations. Transient birefringence measurements in which purely extensional flows were started from rest are also reported. It was observed that the birefringence went through a pronounced overshoot in time for two different polymer/solvent systems. Flow induced increases in the solution turbidity were also observed and the increased turbidity remained constant over a period of many hours after extensional flows were arrested. The birefringence, on the other hand, decayed to zero almost immediately after the flows were stopped. These changes in the turbidity suggest that crystallization of the polymer was occurring. The qualitative results of experiments are compared to recent network model calculations using the theory of Yamamoto for concentrated polymer systems. It is found that this model can predict qualitatively many of the experimental observations if the function describing the breakage of polymer chain entanglements is allowed to depend on the conformation of the polymer segments bridging the entanglements. In particular, this dependency of the entanglement breakage on the conformation of the network segments leads to a predicted overshoot of birefringence when purely extensional flows are started from rest. It is also demonstrated through this model that birefringence data taken over a wide range of flow types can be used to estimate the degree to which the network deforms affinely with the flow field.

Non-equilibrium molecular dynamics simulation and generalized hydrodynamics of transverse modes in molecular fluids

Abstract: We present a generalized hydrodynamic theory of transverse motion in molecular fluids. The theory considers the coupled motion of the molecular orientation, symmetric and antisymmetric components of the microscopic stress tensor, molecular spin, and transverse momentum density. We have conducted non-equilibrium molecular dynamics simulations, of the Lennard-Jones diatomic fluid, which are designed to test the way in which this theory describes the time dependent responses of orientation, stress and spin to an applied velocity gradient. A primary aim of the work is the evaluation of the dimensionless shear-orientation parameter which appears in this theory and in various theories of depolarized light scattering and flow birefringence. The systems studied correspond to fluorine at 70 K, fluorine at 120 K and carbon dioxide at 273 K, all at approximately atmospheric pressure. We find that may be estimated by measuring the steady state orientation density induced by a uniform applied velocity gradient; we obt...

Skin friction drag measurements by LDV.

Abstract: A laser Doppler velocimeter employing a microscope objective as the receiving lens has been developed for measuring fluid velocity inside the boundary layer flow field with a spatial resolution of 40 microns. The method was applied for direct measurement of aerodynamic skin friction drag from the measured velocity gradient at the wall. Experimental results obtained on skin friction and on velocity components in a turbulent boundary layer on a low speed wind tunnel showed good agreement with previously reported data using conventional instruments such as hot-wire anemometers and Preston tubes. The method thus provides a tool for measurement and control of skin friction on aerodynamic bodies without perturbing the flow field.

The effect of a second-order velocity discontinuity on elastic waves near their turning point

Abstract: Summary. The rather abrupt changes in velocity gradient which have some- times been proposed, notably in the upper mantle and near the base of the mantle, have an effect equivalent to that of one or more second-order discon- tinuities, where partial reflection occurs due to a change in curvature of the wavefront across these discontinuities. The effect is ignored in the classical WKBJ approximation to the wave functions, but it can be explicitly demon- strated by applying the extended WKBJ method (Langer's approximation) to a piecewise smooth layered model. For the purpose of ths study it is convenient to represent the response of such a model by a generalized reflection coefficient. For a model of one or a system of several second-order discontinui- ties (approximating a change in velocity gradient over a finite depth interval), the reflection coefficient can be perhaps surprisingly large for long-period waves near their turning point. It is shown that this effect can significantly alter the amplitude decay of sfj waves diffracted around the core, in models where a change in velocity gradient near the core-mantle boundary consti- tutes a low-velocity zone at the base of the mantle; such models have recently been proposed. With the same velocity gradients, the effect on P diffraction is less important. The results for SH diffraction in these models support the conclusion that a small amplitude decay must be explained by a velocity decrease with depth, i.e. a low-velocity zone at the base of the mantle.

Dynamic behavior of an unsteady turbulent boundary layer

Abstract: This paper reports experiments on an unsteady turbulent boundary layer. The upstream portion of the flow is steady (in the mean). In the downstream region, the boundary layer sees a linearly decreasing free-stream velocity. This velocity gradient oscillates in time, at frequencies ranging from zero to approximately the bursting frequency. Considerable detail is reported for a low-amplitude case, and preliminary results are given for a higher amplitude sufficient to produce some reverse flow. For the small amplitude, the mean velocity and mean turbulence intensity profiles are unaffected by the oscillations. The amplitude of the periodic velocity component, although as much as 70% greater than that in the free stream for very low frequencies, becomes equal to that in the free stream at higher frequencies. At high frequencies, both the boundary layer thickness and the Reynolds stress distribution across the boundary layer become frozen. The behavior at larger amplitude is quite similar. Most importantly, at sufficiently high frequencies the boundary layer thickness remains frozen at its mean value over the oscillation cycle, even though flow reverses near the wall during a part of the cycle.

A Study on the Laminar-Flow Heat Transfer Between a Two-Dimensional Water Jet and a Flat Surface with Constant Heat Flux

Abstract: The authors obtained more accurate solutions of the boundary layer momentum and energy equations for a wedge-type flow by the electronic computer using the Runge-Kutta method and deduced an approximate equation of the temperature gradient at the wall with a high accuracy. When a two-dimensional water jet with finite nozzle width strikes normally on a flat surface, it forms a flow field which can be divided into two flow regions ; the first one is an impingement zone and the other is a uniform parallel flow zone. It is the purpose of this paper to estimate local heat transfer coefficients in such a flow field, where the velocity gradient just outside the boundary layer changes along a flat surface and to study theoretically the effect of the nozzle height above the flat plate on the local heat transfer coefficient Furthermore the calculated results were compared with experimental ones of local heat transfer coefficients along a flat surface with constant heat flux.

Ultrasonic distance measurement appts. - has velocity correction system which uses extra transducer to monitor fixed reference path length

Abstract: The height of loose material (6) on a conveyor belt (5) is measured by ultrasonic transducers (1,2,3) which radiate short pulses in a narrow beam (11,21,31) and receive the reflected pulses from the material. The measurement is subject to error because velocity of propagation varies with temp. and pressure and there may be a velocity gradient due to moisture in the material. Velocity error is corrected by an extra transducer (4 or 4') which measures the delay time over a reference path (41 or 41') to a fixed reflector (40 or 40'). The position of the reference path is chosen to have as nearly as possible the same propagation conditions as the measurement paths (11,21,31) without being disturbed by loose material flying about.

Improved method for calculating transonic velocities on blade-to-blade stream surfaces of a turbomachine

Abstract: A method was developed to improve the accuracy of an existing computer program used to calculate transonic velocities on a blade-to-blade surface of a turbomachine. The method eliminates problems encountered in obtaining solutions with the velocity gradient equation when large gradients in velocity occur through the blade row. With the improved method, results indicate that the transonic solution can be obtained by scaling the velocities obtained at the reduced mass flow rate where all velocities are subsonic thereby eliminating the need for a solution of the velocity gradient equation. Solutions obtained with the scaling method on a two dimensional compressor cascade and an axial turbine stator show good agreement with experimental data. The results obtained for the stationary blade rows and comparison of analytical results obtained with and without the present method suggest that the method will yield an improved solution for centrifugal compressor impellers.

Lateral P-Velocity Gradients near Major Strike-Slip Faults in California.

Abstract: The P-wave velocity in shallow crystalline rock decreases systematically from a normal value of about 5.5 kilometers per second 20 kilometers or more from the Garlock and San Andreas faults to less than 3 kilometers per second at distances of less than 2 kilometers from these faults. This lateral velocity gradient closely resembles the shear stress profile. It is proposed that the velocity gradient results from increased fracturing nearer these major strike-slip faults and that this fracturing dominates the response of the shallow crust to tectonic stress.

Infinitesimal perturbations of extensional motions

Abstract: Constitutive equations for the stresses generated in a compressible non-Newtonian fluid undergoing motions consisting of a steady, isochoric extentional flow plus a superimposed infinitesimal perturbation were obtained using simple fluid theory. No restriction is placed on the form of the basic motion except that each component of its velocity gradient is linearly related to a flow parameter having dimentions of inverse time called the strain-rate. The analysis shows that at most three strain-rate dependent relaxation moduli are needed to describe the stresses caused by perturbing the flow. Furthemore, an imcompressible fluid undergoing a motion with two eqaul extensional rate, is completely described by only one such function. Consistency relations between the moduli and the materials functions governing the stresses in the basic motion are given. Also, applications of the theory are demonstrated for the cases of: (1) in-line linear oscillations, (2) shear-wave propagation and (3) acoustic wave propagation.

Processing history in extrusion dies and its influence on the state of the polymer extrudate at the die exit

Abstract: A method is proposed to describe the processing history in extrusion dies and its influence on the state of the polymer after processing. The approach differs from conventional processing analysis, which uses the shear viscosity function to calculate pressure drop vs flow rate relations. The approach also differs from heuristic analysis which tries to find empirical correlations between rheological observations and processing behavior. The method is applied to the flow in annular extrusion dies. An integral constitutive equation is chosen to calculate the flow and to describe the flow history at the die exit as memorized. In the analysis, the kinematics are locally approximated by isothermal steady shear flow. The velocity and the velocity gradient are used to determine the Finger strain tensor, the path lines, and the residence times of the deforming material elements. Measures of the state of the polymer at the die exit are chosen to be the stress ratio N1/2τ12 and the free recovery. The free recovery calculations presume that the extrudate is chopped into small volumes of homogeneous flow history. The results of the calculations show the polymer very sensitively reacts to small changes of the die geometry. Important applications of this analysis are film blowing and blow molding, where the extensional behavior during the blowing process outside the die depends greatly on the preceding shaping process inside the die.

Charge liner construction and method

Abstract: A method of reducing the velocity gradient of a shaped charge liner is diosed. A particular construction for the liner is also disclosed which has the same effect. The velocity gradient and jet-tip velocity are both reduced by forming a plurality of relatively small diameter holes in the charge liner before the liner is assembled with the remaining components of an explosive device.

Wave vector and frequency dependent longitudinal viscosity of systems of interacting Brownian particles

Abstract: Using linear response theory the memory function of the concentration-autocorrelation function of interacting Brownian particles is related directly to the change of the longitudinal stress due to fluctuations of the local velocity gradient. This derivation is valid for arbitrary frequencies and wavevectors and defines an intrinsic longitudinal viscosity of the system. It is further shown that the dynamical properties of interacting Brownian particles can be described by generalized hydrodynamic equations and that deviations of the concentration-autocorrelation function from an exponential form can be understood as a visco-elastic effect.

Distortion of Velocity Gradient by Anomalous Viscosity

Abstract: The problem of distortion of velocity gradient by anomalous viscosity of weak electrostatic turbulent plasma is considered. Linear and nonlinear models are employed and several examples are solved. It is shown that the velocity gradient is smoothed out as a result of the momentum transfer by anomalous viscosity. Furthermore, the rate of decay is faster for the linear model when compared with the nonlinear one.

Calculations of Brillouin backscatter in laser-produced plasmas

Abstract: Brillouin backscatter is calculated in an inhomogeneous laser‐produced plasma. Equations for the spatial dependence of the incident reflected and sound waves are numerically integrated through the underdense plasma. Effects investigated are those stabilizing ion heating or nonlinear sound wave dissipation, flow velocity magnitude and gradient, electron heating, and broadband incident laser light. It is found that the effect of velocity gradient and broadband light can be very important in reducing the backscatter.

Calculations of Brillouin backscatter in laser-produced plasmas. Memorandum report

Abstract: Brillouin backscatter is calculated in an inhomogeneous laser produced plasma. Equations for the spatial dependence of the incident reflected and sound wave are numerically integrated through the underdense plasma. Effects investigated are the stabilizing effects of ion heating or nonlinear sound wave dissipation, flow velocity magnitude and gradient, electron heating and broad band incident laser light. We find that the effect of velocity gradient and broad band light can be very important in reducing the backscatter.

A comparison of characteristic features of coherent turbulent structures found using the variable interval time average (VITA) technique and using the pattern recognition technique

Abstract: A quantitative comparison is made of some features of coherent structures called “bursts” found in wall bounded turbulent shear flows. The features have been educted using two entirely different methods: the variable integral time average (VITA) technique of Blackwelder and Kaplan (1976) and the pattern recognition technique of Wallace, Brodkey and Eckelmann (1977). It is found that the instantaneous velocity gradient, aU/ay, normal to the wall is caused, during “bursting”, by a phase shift in the velocity perturbations between two neighboring positions separated in the normal direction. This velocity gradient can be determined from the time derivative of the streamwise velocity and a perturbation convection velocity normal to the wall. Finally a qualitative comparison is made between the time-varying ensemble averaged Reynolds stress educted during “bursting” by the two methods and the method of Lu and Willmarth (1973).

An Unsteady Taylor Angle Formula for Liner Collapse

Abstract: : An analytical formula for determining the direction of motion for an explosively driven metal liner under unsteady conditions is presented. This direction is defined by the angle delta between the velocity vector of the liner element and the perpendicular to the initial liner surface. A formula for determining the angle delta was first proposed by G.I. Taylor as sin delta = V/ 2U, where V is the final liner element velocity and U is the velocity by which the detonation wave front sweeps past the liner. This formula is, however, accurate only under steady-state conditions where the detonation wave sweeps past identical cross sections of the explosive-liner geometry. For non-steady cases, the Taylor formula is not applicable since the existence of a velocity gradient or a gradient of the typical acceleration duration along the liner may significantly affect the angle delta. The new formula is tested against both numerical calculations and experimental data and predicts the angle delta more accurately than the steady Taylor formula. The derivation of the formula along with a comparison of its predictions for the angle delta with previous experimental work and two-dimensional code calculations for both a conical- shaped charge and exploding cylinder are presented in this report. (Author)

Turbulence Measurements in Three Dimensional Boundary Layer and Wake around a Ship Model

Abstract: This paper presents results of turbulence measurements in the three dimensional boundary layer and wake around a ship model in a low-speed wind tunnel. Measurements were carried out with a single channel hot-wire anemometer, where two or three types of probes were used to measure the different components of the velocity fluctuations.The conclusions obtained in the present study are summarized as follows. 1) It is possible to measure the three dimensional mean flow, turbulence intensities and Reynolds shearing stresses by using a single channel hot-wire anemometer. 2) The three dimensional direction characteristics of a hot-wire can be approximately expressed by the following equation.Ueff = |U| {sin2α+ a cos2 α + b cos2β} 1/2where Ueff is the effective velocity.α is the angle between the hot-wire and mean flow direction.β is the angle between normal vector to the hot-wire/wire-support plane and mean flow direction.a and b are the experimental constants.3) In three dimensional boundary layer and near wake, the distributions of turbulence intensities are significantly affected by the velocity gradient and the bilge vortices.4) Along a stern stream-line, as the boundary layer thickness grows thicker, the dimensionless eddy viscosity e/Ueδ* is more reduced.

Transfer of line radiation in differentially expanding atmospheres VI the plane parallel atmosphere with expanding and contracting regions

Abstract: The non-LTE radiative transfer problem for a two level atom with complete redistribution over a Doppler profile is solved for a plane parallel slab (overlying a radiating photosphere) that has a velocity field which rises symmetrically from zero at either face to a central maximum. Since the velocity gradient reverses, distant layers of the slab become coupled by radiation that jumps intervening layers. The Feautrier method is used, but an iterative variant is also employed as a check in cases where poorly conditioned matrices are encountered. Approximations are developed to explain some of the principal features. It is found that the source function S tends to have two plateaus with values near 2/3 I sub 0 and 1/3 I sub 0, where I sub 0 is the photospheric continuum incident from below; the larger value lies nearer the photosphere. The upper layers sometimes exhibit a rise in S owing to interconnection by radiation to the base. It is noted that the radiation force is largest at the two faces and the midplane. Some line profiles are found to have unusually steep absorptions at rest frequency because of the low excitation in the uppermost, stationary layers.

The verticle velocity structure in the mantle of beijing-sahalin profile

Abstract: In this paper, the authors study the velocity distribution with depth in the mantle of Beijing-Sahalin Profile, which is based on the records of more than 300 earthquakes in the area from Beijing to Western Aleutian Is., selected from 26 stations consisting of Beijing Network, Dalian, Changchun, Mudan Jiang, Vladivoctok, etc.According to Herglotz-Wiechert's formula, the authors calculate the V-h relation and use it as an initial model to compute the theoretical time-distance curves, and find out the velocity structure which agrees well with the results obtained from the practical time-distance curve. The velocity at the top of the mantle is about 7.8 km/sec. In the covering layer with high velocity, there is a positive velocity gradient, and the low velocity layer appears at the depth about 60-120 km. The velocity increases slowly below 130 Km. There are two transitional layers with greater velocity gradient at the depths of 370-440 km and 600-740 km, the former one having the greater velocity gradient, and its corresponding epicentral distance is 19°. Below 1000 km, the velocity increases a little more rapidly.By the method of Kaila, the results from the calculation of the velocity in the sources of deep earthquakes, whose sources are in the depth about 400 km, agree with the results above.

Method of interpolating data in determining the rheological parameters of a liquid

Abstract: The least-squares method is applied to determine the parameters in the rheological equation of state for the liquid over wide ranges in the velocity gradient and tangential stress

Rheology of blood oscillating in a tube

Abstract: Natural oscillations of liquids in U-tubes exhibit amplitude decay due to friction. The half-cycle logarithmic decrement of amplitude provides information about the friction even when the friction is not linearly proportional to velocity gradient. This paper reports measurements made with human blood at Womersley numbers exceeding unity, and includes laminar and turbulent motions. Results in the laminar range show effects of shear-thinning viscosity even with a hematocrit of 5 per cent.