Showing papers on "Velocity gradient published in 1969"

Velocity gradients at the wall for flow around a cylinder at Reynolds numbers from 5 × 10 3 to 10 5

Abstract: Electrochemical techniques have been used to measure the velocity gradients at the surface of a cylinder for Reynolds numbers from 5 × 103 to 105. This is a companion study to that already reported by Dimopoulos & Hanratty (1968) for a Reynolds number range of 60–360. The use of a specially designed sandwich electrode enabled the direction of the velocity gradient as well as its magnitude to be measured. Of particular interest is the region of definite length after separation where the velocity gradient is negative, followed by an ill-defined region where the flow moves in the positive direction. Still farther downstream the direction of flow changes with time in an irregular fashion. The measured velocity gradients prior to separation are described satisfactorily by boundary-layer theory. The presence of a splitter plate in the rear of the cylinder eliminates periodic fluctuations in the wake and has a significant effect on the boundary layer prior to separation.

A travel time and amplitude interpretation of a marine refraction profile: Primary waves

Abstract: Oceanic refraction surveys are interpreted almost exclusively on a time basis yielding layered crustal models. This study utilizes more of the observed information by requiring the model to produce similar waveforms as well as travel times. Theoretical seismograms based on possible travel time models are compared with the first few seconds of observed recording. Closely spaced comparisons are made along a 120-km profile located north of the Hawaiian Islands. The final model indicates: (1) a high positive velocity gradient in the upper layers above the main oceanic layer. (2) a relatively homogeneous oceanic layer with a sharp velocity discontinuity at the crust-mantle interface. (3) a small positive velocity gradient in the upper mantle.

The effect of a velocity gradient at the base of the mantle on diffracted P waves in the shadow

Abstract: Asymptotic expressions for the P-wave solution near a turning point may be combined with the boundary conditions prevailing at the mantle-core boundary to obtain an asymptotic expression for the reflection coefficient at this boundary that preserves the diffraction effects of curvature and velocity gradient. Increasing the velocity gradient is shown to increase the decay coefficient for the diffracted wave in the shadow. Consideration of recent published data and some new short-period data suggests that regional differences in the decay of this signal may be due to difference in the gradient at the base of the mantle.

Theory of the Steady Slow Motion of Non-Newtonian Fluids through a Tapered Tube

Abstract: A theory of the steady slow motion of non-Newtonian fluids through a tapered tube is presented. It is assumed that the fluid is characterized by a time-independent flow curve and that the tapering angle is very small. It is further assumed that the coefficient of viscosity η which appears in the relationship between the stress and the strain rate of a non-Newtonian fluid is not a constant, but a function of the velocity gradient. General formulae for the shear stress, velocity and flow are obtained. These formulae are similar to those for a straight tube of uniform cross section.

Inviscid reacting flow near a stagnation point

Abstract: A reacting flow free of molecular transport exhibits noteworthy behaviour in the neighbourhood of a blunt, symmetrical stagnation point. A local analytical study using the Lighthill-Freeman gas model reveals the basic structure of such a flow. Chemical activity is found to affect some, but not all, of the local characteristics of the flow. Unaffected are the pressure and velocity fields near the stagnation point, where the pressure varies quadratically and the velocity varies linearly as in an inert flow. In addition, the stagnation point is found to be in chemical equilibrium for all non-zero reaction rates. On the other hand the density, temperature, and concentration fields are affected by the non-equilibrium reactions. The extent of this effect can be predicted on the basis of a reaction parameter that measures the rate of reaction in terms of the velocity gradient at the stagnation point. A rapidly reacting flow (with reaction parameter greater than unity) approaches the stagnation point with vanishing gradients of density and temperature, whereas a slowly reacting flow approaches with infinite gradients. The flow field is represented mathematically by functions that are regular along the body but non-analytic in the normal direction. Numerical computations support the validity of the local closed-form solution, and provide information on the local effects of the chemical history of the flow.

A simple solution for boundary layer flow of power law fluids past a semi‐infinite flat plate

Abstract: The steady, two-dimensional, incompressible laminar boundary-layer flow of power law fluids past a semi-infinite flat plate is studied analytically by the method of series expansion and the method of steepest descent (Meksyn's method). The shear stress of the fluids considered is proportional to the nth power of the velocity gradient. The solution obtained is a series of gamma function with the coefficient being a function of the material constant, n. The first ten terms of the series solution are then considered for the sum to determine the velocity gradient at the plate, fηη(0). The results obtained for fηη(0) and the coefficient of skin friction are in excellent agreement with the numerical solutions available in the range of 0.1 ≤ n ≤ 2.5.

Mass transfer at the solid-liquid interface for climbing film flow in an annular duct

Abstract: A method utilizing a diffusion controlled electrochemical reaction was used to measure average and instantaneous mass transfer coefficients at the solid-liquid interface in upward gas-liquid climbing film flow in a vertical annular duct. These measurements give some indication of the mechanics of flow of the film, the extent of turbulence at the inner wall, and the effect of film thickness and wave motion on the mass transfer process at the inner wall. Predictions of incipient downflow of the film, shear stress at the inner wall, and interfacial shear stress were obtained from these measurements. Fluctuations in the velocity gradient at the inner wall were also studied. Results of this study are in fair agreement with previous work and with theoretical predictions based on simplified momentum balance concepts.

Drop Shapes in Shear from a Second‐Order Theory

Abstract: The recent second‐order theory of Chaffey and Brenner for the deformation of a drop suspended in an immiscible liquid undergoing slow steady shear flow has a narrow range of validity. The deformation parameter DI (proportional to the product of the velocity gradient, the drop radius, the suspending liquid’s viscosity and the reciprocal of the interfacial tension) must be less than 0.24 if the predicted deformation of drops of low viscosity in Couette flow is to be realistic; for highly viscous drops DI must not exceed 0.1. For all drops in hyperbolic flow and hyperbolic‐radial flow DI must be less than 0.22 and 0.24, respectively. The second‐order approximation, DII, to the observable deformation ratio D (the difference between the drop’s length and width, divided by their sum) exceeds DI for viscous drops in Couette flow but is slightly smaller than DI for drops of low viscosity. Calculated values of DII deviate from experimental data on D. The second‐order theory does predict the lengthening in hyperbolic flow of one drop axis and the shortening of the other two. A new first‐order theory by Cox has a much wider range of validity but does not conflict with the second‐order theory.

A method to define low-altitude rocket exhaust characteristics and impingement effects

Abstract: Semiempirical methods are used to describe the free flowfield from a moderately underexpanded nozzle and to predict the normal impingement effects of pressure and heat-transfer to a flat plate. Results compare favorably with data obtained from the literature and from impingement tests using a highly aluminized solid propellant rocket. In the free flowfield, the supersonic core length and the subsonic, centerline, recovery pressure and temperature distributions are determined from empirical equations. Simplifying assumptions are made in the supersonic region which smooth the complex flow and discontinuities that really exist. Radial distributions are based on the conservation of momentum, the assumption of a Gaussian momentum distribution, and the one-dimensional isentropic flow equations. The Fay-Riddell heating equation describes the laminar stagnation region on the plate. Otherwise, the Van Driest turbulent heating equation is used with the velocity gradient dependent on the plate recovery pressure gradients.

Viscous transonic spiral and radial flow

Abstract: Similarity solutions of the viscous transonic equation describing source and source vortex Ilows have been found. These solutions contain shock-like transitions from the supersonic to the subsonic branch of the corresponding inviscid solutions, while the singularity near the sonic point of the inviscid solutions is shifted to a smaller radius. It is shown that this similarity solu±ion is identical to the transonic viscous compressible source and sink flow solutions of Wu (1955) and Sakurai (1958). Exact solutions of the equations of two-dimensional inviscid compressible flow for source and source vortex or spiral flow contain limiting circles at or near the sonic point where the velocity gradient becomes infinite El, 2, 31. No solutions exist inside these limiting circles. The transonic flow near these lirniting circles, where velocity gradients are large, clearly can no longer be described by an inviscid theory. Application of a viscous transonic theory [4, 5, 6, 71 to the flow in the neighborhood of these limiting circles forms the subject of the present paper. Two- and three-dimensional source and sink flows of a viscous compressible fluid have previously been investigated by Wu [81, Sakurai [91, and Levey El0, 111. Wu and Sakurai found closed form solutions of the one-dimensional Navier-Stokes equations valid in the region of transonic flow. In the present paper the eonnection between the general viscous transonic theory and the special solutions of Wu and Sakurai is shown.

Steady temperature fields in second order fluids

Abstract: It was shown earlier that if a viscometric flow of an incompressible simple fluid takes place between two surfaces held at constant but differing temperatures, and if the temperature gradient exists in the direction of the velocity gradient only, two conductivity coefficients determine the heat flow and the temperature field. In this article, after the zeroth, first and second order asymptotic expansions for the heat flux vector are developed under a fading memory assumption, the temperature fields in a few viscometric flows are determined und the above condition on the temperature gradient. It is found that a reduction in heat transfer can occur under these conditions, which suggests that the present theory may be used to explain the observations in turbulent flows of polymer additives in water.

Application of the method of integral diffusion to investigation of turbulent transfer

Abstract: A number of authors have critically examined semiempirical mixing length theories [1]. A defect of these theories is connected with the fact that the magnitude of the mixing length, which is assumed to be small in constructing the theory, turns out in experiments to be comparable with the characteristic dimensions of the flow region. Thus, the concept of “volume convection” [2–4] or “integral diffusion” [5], which is understood to be a transfer mechanism in which the friction stress is not expressed in terms of the velocity gradient, is introduced along with the concept of “gradient diffusion.” In addition, there are a number of experimental papers [6] in which it is shown that the turbulent friction stress cannot be equal to zero at the place in the flow where the derivative of the velocity is equal to zero. “Mixing length” theory does not describe this effect.

Theoretical Study of the Low-Aspect-Ratio Wing in Uniform Shear Flow : The Case of the Free Stream Velocity Varying in the Spanwise Direction

Abstract: The characteristics of the finite low-aspect-ratio wing in uniform shear flow is analized on the basis of the assumption that the disturbance velocities are small in comparison with the undisturbed flow velocity and that the width of the wing increases gradually in the chordwise direction. This assumption is analogous to that in the Jones' theory for the low-aspect-ratio wing in uniform potential flow. As the result, it is found that the aerodynamic forces acting on the wing are strongly influenced by the velocity gradient of the free shear flow; when the zero-velocity point of the free shear flow comes infinitely closer to the wing tip, the total lift and total drag coefficients become about 20 percent smaller than the values of the wing in uniform potential flow. If the free stream velocity gradient tends to zero (uniform velocity distribution), the present theory agrees perfectly with the Jones' one.

On gravitational instability of the interstellar gas

Abstract: In the galaxy, Jeans' critical length for the interstellar gas is appreciably smaller than the critical length for the stars, a necessary condition for the gravitational instability of the former to have a local character. An accurate discussion of the orders of magnitude involved leads to the establishment of a well defined limiting procedure and to simplified equations in which the effect of stars occurs only through the equilibrium, but disappears from the perturbations. The equations are spatially local, but their coefficients are time-dependent, in that they describe the evolution of a small wave packet dragged along by the supersonic gas motion. They have been solved in several interesting cases by the introduction of an effective, time-dependent wave vector, which describes the deformation of a wave profile due to the velocity gradients. The ordinary Jeans' instability is recovered only when the velocity gradient is a skew tensor; otherwise we find a stabilizing effect in accelerated and sheared flows, a destabilizing effect in a decelerated flow. Possible connections of this model with the observed turbulent structure of the interstellar gas are discussed.

Unsteady Flow in a Reservoir‐Conduit System

Abstract: The one-dimensional method of solution computes successfully the instantaneous average displacement, velocity, and acceleration of fluid in the pipe and the water depth in the reservoir when a valve at the end of the conduit is suddenly opened. Measurements of the instantaneous average fluid displacement in the pipe for different values of B/D (reservoir diameter to pipe diameter) agree very well with the computed values. For a specific inlet geometry and a given value of the ratio of pipe length to pipe diameter, the lumped inertial parameter decreases as B/D increases and reaches a minimum value as B/D becomes infinity. The neglect of the inertia of fluid in the reservoir in computing the unsteady flow characteristics is justifiable if B/D is larger than 90 and L/D much larger than 0.47.