Showing papers on "Velocity gradient published in 1991"

Inertial migration of a small sphere in linear shear flows

Abstract: The motion of a small, rigid sphere in a linear shear flow is considered. Saffman's analysis is extended to other asymptotic cases in which the particle Reynolds number based on its slip velocity is comparable with or larger than the square root of the particle Reynolds number based on the velocity gradient. In all cases, both particle Reynolds numbers are assumed to be small compared to unity. It is shown that, as the Reynolds number based on particle slip velocity becomes larger than the square root of the Reynolds number based on particle shear rate, the magnitude of the inertial migration velocity rapidly decreases to very small values. The latter behaviour suggests that contributions that are higher order in the particle radius may become important in some situations of interest.

An experimental and theoretical investigation of the dilution, pressure and flow-field effects on the extinction condition of methane-air-nitrogen diffusion flames

Abstract: Velocity fields, and extinction conditions for methane-air diffusion flames are measured for an opposed-flow nozzle-type burner system and calculated by a numerical-integration, routine for pressures from 0.25 to 2.5 atm and for dilutions having fixed stoichiometric mixture fractions with oxidizer-stream oxygen mass fractions from 0.233 to 0.190. Imposition of boundary conditions ranging from potential flow to plug flow reveals that changes on the order of a factor of two in the oxidizer-side strain rate at extinction can be produced by changes in opposed-flow burner design. It is shown that the maximum velocity gradient, however which occurs on the fuel side of the main reaction zone, achieves a value at extinction that is relatively insensitive to the boundary conditions of the flow. The results explain differences found by different investigators on influences of dilution on extinction strain rates and show that most counterflow burners are closer to the plug-flow limit than to the potential-flow limit. Strain rates at extinction without dilution are shown to increase with increasing pressure over the above-stated range, countrary to previously observed behaviors with dilution or at very high pressures. This behavior is explained as a consequence of decreasing peak radical concentration with increasing pressure.

The stability of a sheared density interface

Abstract: This study investigates the stability of stratified shear flows when the density interface is much thinner than, and displaced with respect to, the velocity interface. Theoretical results obtained from the Taylor–Goldstein equation are compared with experiments performed in mixing layer channels. In these experiments a row of spanwise vortex tubes forms at the level of maximum velocity gradient which, because of the profile asymmetry, is displaced from the mean interface level. As the bulk Richardson number is lowered from a high positive value the effects of these vortex tubes become more pronounced. Initially the interface cusps under their influence, then thin wisps of fluid are drawn from the cusps into asymmetric Kelvin–Helmholtz billows. At lower Richardson numbers increasingly more fluid is drawn into these billows. The inherent asymmetry of flows generated in mixing layer channels is shown to preclude an effective study of the Holmboe instability. Statically unstable flows (negative Richardson numbers) are subject to the Rayleigh–Taylor instability. However, if the absolute value of the Richardson number is sufficiently small the Kelvin–Helmholtz instability dominates initially.

Zone broadening and dilution in rectangular and trapezoidal asymmetrical flow field-flow fractionation channels

Abstract: A new trapezoidal geometry of the asymmetrical flow field-flow fractionation (FFF) channel introduces an additional means to regulate the longitudinal flow velocity. The trapezoidal geometry, where the breadth decreases on going toward the channel outlet, makes it possible to level out the steep linear velocity gradients that can appear in the rectangular channels. Equations for the channel flow velocity gradient and the void time are derived

Kinetic theory and rheology of dilute, nonhomogeneous polymer solutions

Abstract: A phase‐space kinetic theory of dilute polymer solutions is developed to account for the effects of nonhomogeneous velocity and stress fields. The theory allows the configuration distribution function to depend on spatial location and explicitly treats the polymer molecule as an extended object in space. Constitutive equations for the mass flux vector and stress tensor are derived that predict polymer migration induced by stress gradients and nonuniform velocity gradients. In addition, the constitutive equation for stress contains a diffusive term in stress, and hence the model does not fall within the class of simple fluids. Simple shear flow between parallel plates is solved to illustrate the features of the constitutive equations. Asymptotic analysis and numerical calculations show the formation of boundary layers in stress, velocity gradient, and polymer concentration that arise near solid walls as a result of preferential orientation of the polymer molecules there. The thickness of these layers scale...

Homogeneous Turbulence in Bubbly Flows

Abstract: The present study is devoted to the interaction between a swarm of bubbles and a turbulent field in a linear shear flow. The transversal and longitudinal evolutions of the void fraction and of the Reynolds stress tensor have been measured. When the air bubbles are blown uniformly into the shear, the void fraction profiles exhibit a strong gradient which can be explained by kinematical effects. No void migration has been observed. The behavior of the Reynolds tensor indicates that the nonisotropy induced by the mean velocity gradient decreases when the void fraction increases. A simple mechanism is proposed to interpret this fact, and a turbulence model based on one-point closures is compared to the experimental data.

Velocities and concentrations in oscillatory flow over beds of sediment

Abstract: Measurements are reported of the velocity and concentration distributions both within and above two beds of sediment in oscillatory flow. The experiments were carried out in an oscillatory flow water tunnel, the velocities were measured with a laser-Doppler anemometer and the concentrations of sediment with resistance probes operating through the sidewall of the tunnel. The sediments studied consisted of nylon granules of median diameter 4.0 mm and Perspex of median diameter 0.7 mm. Most of the beds were plane for the tests with the 0.7 mm sediment and rippled for those with the 4 mm sediment.The measured velocity profile could be divided into three regions: a central region in which the amplitude and phase of the velocity increased almost linearly with height and two outer regions in which the variation in velocity with height was much less rapid. It is suggested that at very high sediment transport rates the central region covers almost the entire depth of the moving bed but that at lower transport rates the outer regions are more significant.The effect of sediment movement on the velocity distribution above the bed is very marked. Bed roughness length is increased and the velocity amplitude falls off more slowly with height than for fixed beds under similar conditions.Within the bed the shear stress increases almost linearly with depth. Apparent viscosity also increases steadily with depth below the surface of the bed.The measurements of concentrations are in good agreement with the results of other investigators in the region above the moving bed. Within the bed the time-mean concentration rises steadily, with distance below the initial bed surface, towards the limiting value for a stationary bed. The concentration record also shows a fluctuation during the course of the cycle at twice the frequency of the fundamental oscillation. The amplitude of this fluctuation in concentration decreases with depth below the initial bed level. The phase variation with height is close to that of zero velocity gradient, within the moving bed.

Local isotropy of the smallest scales of turbulent scalar and velocity fields

Abstract: The validity of Kolmogorov's hypothesis of statistical independence of large and small scales and consequent local isotropy of the smallest scales of turbulence in a homogeneous fluid is supported by recent experimental measurements of spectra of spatial gradients of scalar and velocity fields. Deviations from spectral local isotropy at the low-wavenumber end of the gradient spectra produce an apparent local anisotropy in terms of moments of the gradients, suggesting that the local anisotropy inferred from measured scalar and velocity gradient moments by earlier workers is not inconsistent with true local isotropy of the smallest scales. For turbulence in a stably stratified fluid, local isotropy is rapidly destroyed when buoyancy forces are dynamically important. Are the statistical properties of the smallest scales of turbulent scalar and velocity fields locally isotropic ? The idea that statistical properties of turbulence dominated by the spatial structure of the smallest scales of scalar and velocity fields might be locally isotropic stems from the work of Kolmogorov (1941 a, b). Central to this idea is the notion of a sufficiently broad cascade of turbulent kinetic energy from large to small scales, through which the influence of large-scale anisotropy is not transmitted to the smallest scales. After a sufficient number of cascade steps the statistical properties of quantities dominated by the smallest scales may exhibit no preferred spatial direction. The larger the Reynolds number, the larger the effective number of steps in the cascade, improving the possibility of local isotropy as the Reynolds number increases.

Measurement of turbulent wall velocity gradients using cylindrical waves of laser light

Abstract: A new optical instrument has been developed for direct measurement of instantaneous velocity gradients at the bounding wall. Light emerging from two tiny optical slits in the surface is used to form a “fan of fringes” in the region very near the wall. Doppler frequency of the light scattered by the seed particles is directly proportional to the velocity gradient. The system has been used to measure the statistics of the streamwise and spanwise velocity gradients in a turbulent boundary layer. The streamwise and spanwise rms fluctuations were found to be 38% and 11% of the mean streamwise value respectively. The latter result is subject to a large uncertainty.

Generalized Taylor dispersion phenomena in unbounded homogeneous shear flows

Abstract: Generalized Taylor dispersion theory is extended so as to enable the analysis of the transport in unbounded homogeneous shear flows of Brownian particles possessing internal degrees of freedom (e.g. rigid non-spherical particles possessing orientational degrees of freedom, flexible particles possessing conformational degrees of freedom, etc.). Taylor dispersion phenomena originate from the coupling between the dependence of the translational velocity of such particles in physical space upon the internal variables and the stochastic sampling of the internal space resulting from the internal diffusion process. Employing a codeformational reference frame (i.e. one deforming with the sheared fluid) and assuming that the eigenvalues of the (constant) velocity gradient are purely imaginary, we establish the existence of a coarse-grained, purely physical-space description of the more detailed physical-internal space ( microscale ) transport process. This macroscale description takes the form of a convective–diffusive ‘model’ problem occurring exclusively in physical space, one whose formulation and solution are independent of the internal (‘local’-space) degrees of freedom. An Einstein-type diffusion relation is obtained for the long-time limit of the temporal rate of change of the mean-square particle displacement in physical space. Despite the nonlinear (in time) asymptotic behaviour of this displacement, its Oldroyd time derivative (which is the appropriate one in the codeformational view adopted) tends to a constant, time-independent limit which is independent of the initial internal coordinates of the Brownian particle at zero time. The dyadic dispersion-like coefficient representing this asymptotic limit is, in general, not a positive-definite quantity. This apparently paradoxical behaviour arises due to the failure of the growth in particle spread to be monotonic with time as a consequence of the coupling between the Taylor dispersion mechanism and the shear field. As such, a redefinition of the solute's dispersivity dyadic (appearing as a phenomenological coefficient in the coarse-grained model constitutive equation) is proposed. This definition provides additional insight into its physical (Lagrangian) significance as well as rendering this dyadic coefficient positive-definite, thus ensuring that solutions of the convective–diffusive model problem are well behaved. No restrictions are imposed upon the magnitude of the rotary Peclet number, which represents the relative intensities of the respective shear and diffusive effects upon which the solute dispersivity and mean particle sedimentation velocity both depend. The results of the general theory are illustrated by the (relatively) elementary problem of the sedimentation in a homogeneous unbounded shear field of a size-fluctuating porous Brownian sphere (which body serves to model the behaviour of a macromolecular coil). It is demonstrated that the well-known case of the translational diffusion in a homogeneous shear flow of a rigid, non- fluctuating sphere (for which the Taylor mechanism is absent) is a particular case thereof.

Estimates of solar wind velocity gradients between 0.3 and 1 AU based on velocity probability distributions from Helios 1 at perihelion and aphelion

Abstract: We have estimated the average velocity gradients for the solar wind protons by comparing the velocity probability distributions at 0.3 and at 1 AU Assuming a power law radial dependence, we find, for a full 6-year data set, that the gradients for the lowest velocity ranges are about R0.1 to R0.14 and that the power index decreases steadily with increasing velocity until the slope is near zero for the high-speed solar wind. However, upon examining the solar cycle dependence we find that this trend for the velocity gradient to decrease with increasing velocity is a characteristic primarily of the increasing solar activity and solar maximum period and is almost absent in the solar minimum data. The solar wind above 500 km/s during solar minimum shows an average acceleration similar to the slow wind, about 55 to 85 km/s/AU. On the other hand, winds above 350 km/s from the period of increasing solar activity and solar maximum show essentially no average acceleration beyond 0.3 AU.

Influence of nozzle geometry on polystyrene degradation in convergent flow

Abstract: Polymer degradation is readily observed in flows where the extensional component surpasses the rotational component of the velocity gradient. This type of flow is conveniently obtained by pushing a liquid into a convergent channel across an orifice. Kinetics of chain scission is sensitive to subtle modification of the coil conformation, which in turn depends on the details of the pervading flow field. By changing the orifice diameter and the conical angle of the inlet, it is possible to modify the spatial distribution of the velocity gradient, and hence, the residence time of a fluid element in the high strain-rate region. Degradation yields, measured under π-conditions in decalin by Gel Permeation Chromatography, showed a strong dependence on the fluid velocity at the orifice, but not on the magnitude of the strain-rate. This result is contrary to the common belief that assumes viscous friction, proportional to the strain-rate, is the determining factor for the scission rate of a bond under stress. Rather, experimental findings tend to indicate that the driving force for chain scission was provided by the energy accumulated in the coil during the flow-induced deformation process. The sharp propensity for mid-chain scission was maintained regardless of the nozzle geometry.

Application of an inverse mass transfer method to the measurement of turbulent fluctuations in the velocity gradient at the wall

Abstract: The frequency response of the concentration boundarylayer is often a concern when flush mounted mass transfer probes are used to measure turbulent fluctuations in the velocity gradient at a wall. Present practice involves the use of a solution of the mass balance equation which is linear in the fluctuating quantities. An inverse mass transfer method is explored in this paper, which avoids the linearization assumption. Improved measurements of the amplitude probability distribution and of the frequency spectrum of the streamwise component of the fluctuating velocity gradient are presented. In particular, values of rms level, skewness and flatness of 0.37, 0.96, 4.2 are obtained, in good agreement with a recent study by Alfredson, Johansson, Haritonidis and Eckelmann.

Continuum opacity produced by spectral lines in supernovae and similar expansions

Abstract: Within rapidly expanding objects such as supernovae, the large velocity gradient Doppler spreads the spectral lines to such an extent that even relatively weak transitions affect the propagation of radiation. It is shown that under appropriate conditions (involving the separation between lines and the velocity gradient), the effects of many lines within a small frequency interval produce a contribution to the transfer equation which acts like an ordinary continuum opacity. This expansion opacity is a surprisingly simple function of the Sobolev optical depth of the lines. The dependence of this opacity on frequency, temperature, density, velocity gradient (1/time), and heavy element abundance is evaluated.

Shear Wave Velocity Structure from Interface Waves at Two Deep Water Sites in the Pacific Ocean

Abstract: The shear wave velocity structure of two deep ocean sites has been studied by detonating explosives on the ocean floor and examining the slowly moving Stoneley waves that were generated at the ocean floor interface. At the southern California site, the structure was found to be uniform insofar as the relatively sparse sampling can resolve. At the central California site, the velocities and velocity gradients were found to be variable over the space of 1 or 2 km. At both sites, the shear wave velocity at the seafloor is very low, between 27 and 32 m s-1. The shear wave velocity gradient at the southern California site in the top 1 m of the sediments is 5.2 ni s-1m-1and 3.1 m s-1 m1in the next 100 m. At the northern site, the velocity gradient for the top 1 ni varies between 5.0 m s_1m1and 8.0 m s-1to1and for the next 20 m it varies between 4.5nis-1m-1and 7.0nis1m1.

Experimental and numerical investigation of soot deposition in laminar stagnation point boundary layers

Abstract: Soot deposition from a hot gas flow to a cooled solid wall is investigated numerically and experimentally for laminar stagnation point flows. Numerical predictions of soot deposition are made by solving the coupled momentum, energy, and soot transport equations, which include the effects of variable transport properties and thermophoretic transport (i.e. mass transport down a temperature gradient) of soot particles. The results of the numerical computations indicate that the deposition rate, expressed in terms of the deposition velocity, increase with an increasing potential flow velocity gradient and decrease as the wall temperature approaches the freestream temperature. In addition, an insitu laser diagnostic technique is developed which provides simultaneous measurement of the soot deposit thickness and freestream soot concentration. The technique uses two laser beams (488 and 632 nm wavelength) coincident at a point adjacent to the deposition surface to measure the thickness of the deposit and the light extinction by airborne soot particles. Comparison of the experimental results to the numerical model indicates a critical velocity gradient beyond which the “sticking” fraction for the soot significantly decreases. This velocity gradient, which corresponds to maximum deposition, has been found to be approximately 2000 sec −1 for soot produced from fuel rich air/ethylene mixtures.

Experiments on entrainment in an annulus with and without velocity gradient across the density interface

Abstract: The entrainment process in a two layer density stratified fluid column was studied experimentally by imposing external shear stress on one or both layers. The experiments have been conducted in an annular tank containing two water layers of different salt concentration and the shear stress was applied by means of rotating screens. The following quantities were measured: the screen velocity (which was kept constant during each experiment), the stress at the upper screen, and vertical profiles of circumferential velocity and density at different radial locations.

Dimensional effects of nozzle-type burner on flow fields and extinction of counterflow twin flames.

Abstract: The flow fields of a counterflow nozzle burner and counterflow twin flames for propane-air mixture stabilized with that burner were measured using LDV. The effects of the burner dimension, i.e., the outlet diameter of two opposed contraction nozzles and the distance between them, on the velocity profiles and extinction limits of the twin flames were examined. Results show that the effects of burner dimension on the extinction limit do not appear when the velocity gradient upstream of the front edge of preheating zone is used as a flow parameter and that the ratio of nozzle distance to nozzle outlet diameter is the main factor determining the dimensional effects on the flow characteristics. It is also shown that the flame stretch rate of the twin flames defined at the stagnation plane is about two times as large as that defined at the cold boundary of the flame.

A method for correcting wall pressure measurements in subsonic compressible flow

Abstract: A theoretical and experimental investigation has been made of the static pressure hole problem in subsonic flow. Thanks to a linearization, the effects of the boundary layer, of the velocity gradient and of the wall curvative could be separated so that a formula of correction containing three influence functions has been obtained. These functions were determined in the case of practical requirements by means of experiments made on appropriate models for two values of the depth-to-diameter ratio and for at least three values of the Mach number.

Experimental study of the induced flow birefringence of a suspension of rigid particles at the transition from Couette flow to Taylor vortex flow

Abstract: The flow birefringence induced in solutions of rigid particles is studied experimentally in the region of the axisymmetrical Taylor vortex flow which arises once the velocity gradient G in the annular gap of a conventional Couette cell reaches a critical value G c . The measurements are performed for several values of G > G c and for 10 radial observation points in the annular gap. Solutions of two types of rigid particles are investigated: the first is a suspension of flattened clay particles like bentonite, while the second contains rod-like particles of tobacco mosaic virus (TMV). The variations of the birefringence intensity Δn and of the extinction angle κ measured in the domain of the axisymmetrical flow show a different behavior according to the shape of the particle in solution. This fact is confirmed theoretically with a good agreement for the measurements performed with solutions of flat particles.

Strong flows of dilute suspensions of microstructure

Abstract: We consider dilute suspensions that have a microstructure that may be characterized by an axial state vector. Examples include axisymmetric particles, line elements of the fluid itself, or, as an approximation, droplets of fluid or polymer molecules. Past studies, in which sufficient conditions for stretch or coherent orientation of the microstructure are obtained for steady flows with homogeneous velocity gradient tensors are shown not to apply to the general situation. Instead, a careful analysis of the microdynamical equations reveals that stretching and orientation of the microstructure by the flow must be analyzed over a time interval. Using techniques from the theory of dynamical systems, a quantitative measure is developed to determine orientations and/or stretched lengths of the microstructure, that are robust and attractive to nearby states. This leads to a strong flow criterion for unsteady flows with inhomogeneous velocity gradient tensors in which the effects of history dependence are apparent. A particular model system is treated in the case of general two-dimensional flow. The sensitivity of the results to changes in the modeling assumptions is investigated.

Aerosol formation in an isothermal stagnation flow

Abstract: An experiment has been performed in a laminar stagnation point flow in which two non-premixed reactants produced an aerosol of sub-micron particles. The reactants were NH3 and HCl. The rate of mixing of the reactants was determined by the velocity gradient or strain rate of the flow; the response of the aerosol dynamics to the flow field was measured with a laser light scattering technique. Laser Doppler Spectroscopy was used to measure the particle size. It was found that the particle size was independent of the strain rate of the flow. On the other hand, the particle number density decreased as the strain rate increased. It is argued that the intensity of light scattered from the aerosol is, therefore, a measure of the amount of product of the relatively slow NH3-HCl reaction.

Viscous fluid sealed bush

Abstract: PURPOSE:To secure a flat transfer force characteristic by installing a tubular rubber elastic body interposingly between an inner cylinder and an outer cylinder concentric with the former, sealing a high viscous fluid in an annular liquid chamber installed in an axial intermediate part of this rubber elastic body, and forming a shearing clearance part there. CONSTITUTION:An annular fluid chamber 26 is constituted as circular, fine clearance parts 28, 28 in a gap with an outer cylinder fitting 4 by a trapezoidal projection 18 being projected from the side of respective fittings 2 at a part to be situated at both sides of these inner cylinder fittings 2 in the vibration input direction P. At time of vibration input, pressing force works on a high viscous fluid existing therein works at these fine clearance parts 28, 28, whereby such an action as eliminating the high viscous fluid in the circumferential direction to be shown in an arrow is added from this space. Therefore a flow is produced in the high viscous fluid and thereby shearing force proportionate to a velocity gradient of the flow is generated there, through which effective damping force is also produced and an effective vibro-damping action is securable as the whole bush owing to viscosity resistance force and synergistic effect in shearing clearance parts 22, 22.

Prediction of a three-dimensional turbulent boundary layer on a swept wing.

Abstract: A full second-moment closure which was previously shown to reproduce a weakly three-dimensional boundary layer as well as various two-dimensional flows is employed to calculate the boundary layer on a swept wing. The numerical solutions are extensively compared with the experiments by van den Berg et al. The agreement is generally reasonable. Particular attention is given to the effect of retaining the terms with 'secondary' velocity gradients in the model equations. It is shown that the decrease in the structure parameter (the shear-stress/energy ratio) is attributable, at least partially, to the 'secondary' terms. However, the large lag between the shear stress direction and the velocity gradient direction is not well reproduced. A revision of the redistribution terms is needed to capture this behavior, as suggested by several authors.

Effect of packing arrangement on flow characteristics and mass transfer on the surface of a packing sphere

Abstract: An electrochemical method is applied for estimating and characterizing the velocity gradient and the mass transfer rate in a packed bed. The bed is a simple regular packing arrangement of spheres, surrounded with randomly packed spheres. The objects of study are four types of regular arrangement of spheres. The Reynolds number based on superficial velocity and particle diameter is varied in 30–200. The probe sphere is one of the regularly arranged spheres. It has five small polarized circular electrodes which are flush with the probe sphere surface. Local velocity gradient on the surface of the probe sphere is measured and is represented by a form of contour-line map. Based on this map, the effects of packing arrangement and Reynolds number on the fluid behavior and the mass transfer coefficient are made clear.

空気輸送のシミュレーションのための実験研究 : 第2報, 高レイノルズ数線形せん断流中の球に働く揚抗力

Abstract: Effects of the velocity gradient of linear shear flows at a high Reynolds number (Re, s=4000-35000) on lift and drag applied on a spherical particle are investigated by measuring surface pressure distribution, using a pendant method, and by comparing computed and photographed trajectories of a sphere falling in upward shear flows. It is made clear that lift is applied on a sphere from the higher velocity side to the lower velocity side, that it increases as the velocity gradient becomes greater, and that drag is hardly affected by the velocity gradient.

The effects of coherence and redistribution on radiative transfer in large velocity gradients

Abstract: Radiative transfer in an atmosphere with a velocity gradient is generally treated under the assumption of complete redistribution. Using Monte Carlo techniques we explore the consequences of relaxing this condition within the Sobolev approximation that the velocity gradient is sufficiently large. Two cases of coherent scattering are considered, namely coherence in the atomic frame and coherence in the fluid frame. It is found by computer simulation that coherence in the atomic frame yields escape probabilities almost identical to complete redistribution, whereas coherence in the fluid frame doubles the rate at large optical depths. It is shown that the results are independent of the phase factor for scattering.