Showing papers on "Velocity gradient published in 1999"

Reversing the perturbation in nonequilibrium molecular dynamics: an easy way to calculate the shear viscosity of fluids.

Abstract: A nonequilibrium method for calculating the shear viscosity is presented. It reverses the cause-and-effect picture customarily used in nonequilibrium molecular dynamics: the effect, the momentum flux or stress, is imposed, whereas the cause, the velocity gradient or shear rate, is obtained from the simulation. It differs from other Norton-ensemble methods by the way in which the steady-state momentum flux is maintained. This method involves a simple exchange of particle momenta, which is easy to implement. Moreover, it can be made to conserve the total energy as well as the total linear momentum, so no coupling to an external temperature bath is needed. The resulting raw data, the velocity profile, is a robust and rapidly converging property. The method is tested on the Lennard-Jones fluid near its triple point. It yields a viscosity of 3.2-3.3, in Lennard-Jones reduced units, in agreement with literature results.

Lagrangian tetrad dynamics and the phenomenology of turbulence

Abstract: A new phenomenological model of turbulent fluctuations is constructed by considering the Lagrangian dynamics of four points (the tetrad). The closure of the equations of motion is achieved by postulating an anisotropic, i.e., tetrad shape dependent, relation of the local pressure and the velocity gradient defined on the tetrad. The nonlocal contribution to the pressure and the incoherent small scale fluctuations are modeled as Gaussian white “noise.” The resulting stochastic model for the coarse-grained velocity gradient is analyzed approximately, yielding predictions for the probability distribution functions of different second- and third-order invariants. The results are compared with the direct numerical simulation of the Navier–Stokes. The model provides a reasonable representation of the nonlinear dynamics involved in energy transfer and vortex stretching and allows the study of interesting aspects of the statistical geometry of turbulence, e.g., vorticity/strain alignment. In a state with a constan...

Momentum transfer for practical flow computation in compound channels

Abstract: A new theoretical 1D model of compound channels flows-the exchange discharge model-is presented. The interactions between main channel and floodplains are taken into account as a momentum transfer proportional to the product of the velocity gradient at the interface by the mass discharge exchanged through this interface due to turbulence. Geometrical changes in cross sections are also modeled; they generate a similar momentum transfer, proportional to the actual mass transfer. Both effects are incorporated into the flow equations as an additional head loss. This make the formulation suitable for stage-discharge computation but also enables practical water-profile simulations. The model is tested successfully against available experimental data for (1) stage-discharge relations; and (2) water-profile computation applied to a field case.

Near-Bottom Turbulence Measurements in a Partially Mixed Estuary: Turbulent Energy Balance, Velocity Structure, and Along-Channel Momentum Balance

Abstract: A set of moored, bottom-mounted and shipboard measurements, obtained in a straight section of the lower Hudson estuary during late summer and early fall of 1995, determine velocity, density, and along-channel pressure gradient throughout the 15-m water column, as well as providing direct eddy-correlation estimates of Reynolds stress and indirect inertial-range estimates of dissipation within 3 m of the bottom. The analysis focuses on testing 1) a simplified turbulent kinetic energy equation, in which production balances dissipation; 2) the Prandtl–Karman law of the wall, which is a relationship between bottom stress and near-bottom velocity gradient; and 3) a simplified depth-integrated along-channel momentum balance involving local acceleration, pressure gradient, and bottom stress. Estimates of production and dissipation agree well throughout the entire record. The relationship between bottom stress and velocity gradient is consistent with the law of the wall within approximately 1 m of the sea...

Ring Diagram Analysis of Near-Surface Flows in the Sun

Abstract: Ring diagram analysis of solar oscillation power spectra obtained from Michelson Doppler Imager data is carried out to study the velocity fields in the outer part of the solar convection zone. The three-dimensional power spectra are fitted to a model that has a Lorentzian profile in frequency and includes the advection of the wave front by horizontal flows in order to obtain the two components of the subsurface flows as a function of the horizontal wave number and radial order of the oscillation modes. This information is then inverted using the optimally localized averages method and regularized least squares method to infer the variation in horizontal flow velocity with depth. The average rotation velocity at different latitudes obtained by this technique agrees reasonably with helioseismic estimates made using frequency-splitting data. The shear layer just below the solar surface appears to consist of two parts, with the outer part measuring up to a depth of 4 Mm where the velocity gradient does not show any reversal up to a latitude of 60°. In the deeper part the velocity gradient shows reversal in sign around a latitude of 55°. The zonal flow velocities inferred in the outermost layers appear to be similar to those obtained by other measurements. A meridional flow from equator poleward is found. It has a maximum amplitude of about 30 m s-1 near the surface, and the amplitude is nearly constant in the outer shear layer.

Velocity and Concentration Distributions in Sheet Flow above Plane Beds

Abstract: This paper reports the results of experiments on particle-water flow over plane-topped stationary beds. The particles used were silica sands having d50 of 0.30 and 0.56 mm and Bakelite particles having d50 of 1.05 mm. The facility was a recirculating loop with pipe of 105-mm internal diameter. Data comprised measurements of hydraulic gradient, volumetric discharge, temperature, concentration profiles, velocity profiles, and delivered concentrations. The thickness of the sheet-flow layer is found to vary in proportion to the shear stress. The velocity at the top of the layer is found to be ∼9.4 times the shear velocity, and a simple relation expresses the velocity gradient at this height. The Richardson number at the top of the sheet flow averages ∼0.035, decreasing with increasing ratio of particle fall velocity to shear velocity.

Effect of microbubbles on the structure of turbulence in a turbulent boundary layer

Abstract: The time-averaged velocity and turbulence intensity distributions were measured by a laser Doppler velocimeter in a turbulent boundary layer filled with microbubbles. The void fraction distribution was also measured using a fiber-optic probe. The velocity decreased in the region below 100 wall units with an increase in bubble density. This led to a decrease in the velocity gradient at the wall, which was consistent with a decrease in shearing stress on the wall. The turbulence intensity in the buffer layer increased at a low microbubble density, and then began to decrease with an increasing microbubble density. Based on the present measurements, the mechanism of turbulence reduction by microbubbles is discussed and a model is proposed.

Seismic waves converted from velocity gradient anomalies in the Earth’s upper mantle

Abstract: Summary Modelling of elastic wave propagation in 1-D structures is frequently performed using reflectivity techniques in which the Earth’s velocity profile is approximated by stacks of homogeneous layers. The complete reflection/transmission (R/T) response of a zone with arbitrary 1-D depth variation (including both gradients and discontinuities in material properties) can, however, be calculated using invariant embedding techniques. Results from earlier studies are here extended to derive exact expressions for R/T matrices in arbitrary, 1-D anisotropic media using a form of Born approxi-mation valid for thin scatterers and which does not assume small perturbations in material properties. The R/T matrices are solutions to a system of non-linear, ordinary differential equations of Ricatti type and may be manipulated using standard R/T matrix algebra. In an equivalent description, the wavefield within the heterogeneous zone is considered in terms of depth-dependent contributions from up- and downgoing waves propagating within the embedding reference medium. This leads to efficient calculation of the internal wavefield using R/T matrices of the heterogeneous stratification and portions thereof at minor additional expense. Mode conversion of teleseismic P and S phases from velocity gradients is examined by way of examples and comparison with three-component data from broad-band stations of the Yellowknife seismic array. The frequency dependence of such wave interactions depends on the differences in vertical slowness between incident and scattered modes. It is shown that significant energy is converted from transition zones with extent L<λP/2, a broader interval than will generally produce intramode reflections. A layer structure identified from Ps conversions near 75 km depth below the Slave craton is shown to be compatible with a ~ 10 km thick gradient zone in which anisotropy increases from ambient levels to δVp= ± 5 per cent, δVs= ± 2.5 per cent at a discontinuous upper boundary. This characterization supports a previous interpretation as the upper strata of a former oceanic plate juxtaposed against overriding lithosphere during an ancient episode of shallow subduction.

Statistical Theory for the Stochastic Burgers Equation in the Inviscid Limit

Abstract: A statistical theory is developed for the stochastic Burgers equation in the inviscid limit. Master equations for the probability density functions of velocity, velocity difference and velocity gradient are derived. No closure assumptions are made. Instead closure is achieved through a dimension reduction process, namely the unclosed terms are expressed in terms of statistical quantities for the singular structures of the velocity field, here the shocks. Master equations for the environment of the shocks are further expressed in terms of the statistics of singular structures on the shocks, namely the points of shock generation and collisions. The scaling laws of the structure functions are derived through the analysis of the master equations. Rigorous bounds on the decay of the tail probabilities for the velocity gradient are obtained using realizability constraints. We also establish that the probability density function of the velocity gradient has a left power tail with exponent -7/2.

On the relationship between the mean flow and subgrid stresses in large eddy simulation of turbulent shear flows

Abstract: The present study sheds light on the subgrid modeling problem encountered in the large eddy simulation (LES) of practical flows, where the turbulence is both inhomogeneous and anisotropic due to mean flow gradients. The subgrid scale stress (SGS) tensor, the quantity that is key to the success of LES, is studied here in such flows using both analysis and direct numerical simulation (DNS). It is shown that the SGS tensor, for the case of inhomogeneous flow, where the filtering operation is necessarily performed in physical space, contains two components: a rapid part that depends explicitly on the mean velocity gradient and a slow part that does not. The characterization, rapid and slow, is adopted by analogy to that used in the modeling of the pressure–strain in the Reynolds-averaged Navier–Stokes equations. In the absence of mean flow gradients, the slow part is the only nonzero component and has been the subject of much theoretical study. However, the rapid part can be important in the inhomogeneous flo...

Entry mass transfer in axial flows through randomly packed fiber bundles

Abstract: An analysis of the effects of nonuniform fiber packing on external mass-transfer coefficients for axial flows through bundles of parallel, axially oriented fibers is presented in the entry mass-transfer limit. In this limit, one can obtain an analytic solution to the mass-transfer boundary-layer equations in terms of the velocity gradient on the fiber surface for either a constant wall flux or constant wall concentration. To explicitly calculate mass-transfer coefficients, a numerical approximation for the velocity gradient is obtained from the conservation of momentum equations using the boundary-element method. Results indicate that the effective mass-transfer coefficient depends strongly on fiber packing. Regions of higher fiber packing have lower flows and lower mass-transfer coefficients than regions of lower packing. The net effect is a dramatic decrease in overall mass-transfer coefficient relative to mass-transfer coefficients in regularly packed fiber bundles.

Flow of a Johnson–Segalman fluid between rotating co-axial cylinders with and without suction

Abstract: The Johnson–Segalman fluid has a non-monotone relationship between the shear stress and velocity gradient in simple shear flows for a certain range of material parameters resulting in solutions with discontinuous velocity gradients for planar and cylindrical Poiseuille flow. This has been used to explain the phenomenon of “Spurt”. Rao and Rajagopal [ Acta Mechania , to be published] have shown that the addition of suction necessarily smoothens the solutions for planar Poiseuille and cylindrical Poiseuille flows. Here we study the effect of a different geometry on the flow of a Johnson–Segalman fluid. The problems of cylindrical Couette flow, cylindrical Couette flow with suction (or injection) and Hamel flow are studied and it is found that the boundary condition can have an interesting effect on the regularity of the solution. The presence of suction increases the regularity of the solution, i.e. solutions with discontinuous velocity gradients are not possible.

Shear-induced anisotropy in liquid thermal conduction

Abstract: Operators for elastic strain and for inelastic strain rate are introduced to describe a small volume V in a liquid undergoing steady Couette flow at high shear rate. An information-theoretic distribution is constructed depending on the operators and on and , the ensemble averages which, along with the heat flow components, constitute the measured information. Two components, and , stemming from self-diffusion and phonons, are identified in the heat flux. The distribution is used to calculate which, unlike , depends on and in such a way as to imply that the thermal conductivity tensor exhibits anisotropies and when the velocity gradient . Such anisotropies can be inferred from computer simulations of self-diffusion under shear.

Thermal diffusion and mixture separation in the acoustic boundary layer

Abstract: Oscillating thermal diffusion in a sound wave in a mixture of two gases is remarkably effective for separating the components of the mixture. We consider this separation process in boundary-layer approximation, with zero temperature gradient and zero concentration gradient along the direction of sound propagation. In the boundary layer, the combination of thermal diffusion with the oscillating temperature gradient and oscillating velocity gradient leads to second-order time-averaged fluxes of the two components of the mixture in opposite directions, parallel to the wave-propagation direction. The oscillating thermal diffusion also adds to the dissipation of acoustic power in the boundary layer, modifying thermal-relaxation dissipation but leaving viscous dissipation unchanged.

Three-Dimensional Flowfield Downstream of an Axial-Flow Turbine Rotor

Abstract: A systematic and comprehensive investigation was performed to provide detailed data on the threedimensional viscous flow phenomena downstream of a modern turbine rotor and to understand the flow physics such as the origin, nature, development of wakes, secondary flow, and leakage flow. The experiment was carried out in the Axial Flow Turbine Research Facility (AFTRF) at The Pennsylvania State University, with velocity measurements taken with a 3-D LDV System. Two radial traverses at 1% and 10% of chord downstream of the rotor were performed. Sufficient spatial resolution was maintained to resolve blade wake, secondary flow, and tip leakage flow. The wake deficit is found to be substantial, especially at 1% of chord downstream of the rotor. At this location, negative axial velocity occurs near the tip, suggesting flow separation in the tip clearance region. Cross-correlations are mainly associated with the velocity gradient of the wake deficit. The radial velocities, both in the wake and in the endwall region, are found to be substantial. Two counter-rotating secondary flows are identified in the blade passage, with one occupying the half span close to the casing and the other occupying the half span close to the hub. The tip leakage flow is restricted to 10% immersion from the blade tip. There are strong vorticity distributions associated with these secondary flows and tip leakage flow. The passage averaged data are in good agreement with design values.

P-wave velocity structure of upper crust in the vicinity of the Yangsan Fault region

Abstract: This study presents the P-wave velocity structure of the upper crust in the vicinity of the Yangsan Fault region based on travel-time inversion of thirty-five digital secmic records obtained by the Korea Institute of Geology, Mining and Materials (KIGAM). The present model consists of 8 horizontal layers with constant velocity in the subsurface depth of 18 km. Two-point ray tracing is applied for travel-time inversion and determination of hypocenteral parameters of the earthquakes to reduce errors resulting from ray path. The computational results of travel-time inversion show that (1) a velocity gradient with depth is nearly constant in the subsurface depth of 8 km, (2) a low-velocity zone exists in the depth between 10 and 15 km, and (3) a relatively large velocity discontinuity appears at about 15 km.

Self-similarity, momentum scaling and Reynolds stress in non-premixed turbulent spray flames

Abstract: An experimental study was conducted in a turbulent spray flame in which droplets were produced ultrasonically at low velocity relative to the host gas. In this fashion, injector-specific effects on the two-phase flow were minimized and a scenario generally characteristic of the far field of practical spray systems could be simulated. Close to the burner exit, the spray flame appeared as a dense column of drops burning with an envelope flame. Further downstream, it opened up slowly in the radial direction and developed a turbulent 'brush' appearance. Measurements of the size, velocity and concentration of the droplets, and of gas-phase velocity and temperature were made by combining a Phase-Doppler interferometric technique with Stokes/anti-Stokes Raman thermometry. The experimental data were used to derive scaling and self-similarity for the Reynolds-averaged continuity and momentum equations using suitable transformations. Results showed three distinct regions, on the basis of the behaviour of the gas axial velocity in the spray flame. In the lower part of the flame, the gas momentum increased because of vaporization. In the intermediate region of the spray flame, the axial velocity decayed along the centreline as an inverse power of the distance from the virtual origin, with exponents smaller than unity. In the upper part of the spray flame, the flow field recovered the axial velocity decay that is typical of incompressible jets, namely as an inverse of the axial distance. Self-similar behaviour held for the axial velocity throughout the intermediate region. The vapour source term in the gas continuity equation scaled approximately as an inverse power of axial distance, and exhibited self-similarity throughout the spray flame. As a result, a simple model of the Reynolds stress term could be formulated, in which two competing contributions appear: one, that is due to turbulent transport, tends to increase the value of the velocity correlation; another, that is due to the vaporization term, tends to reduce the value of the velocity correlation and can be construed as a vaporization-induced tendency towards relaminarization. The first term is modelled by a classic gradient-transport approach yielding an empirical mixing length relating the velocity correlation to the average velocity gradient. Model and experiments are found to be in good agreement, especially sufficiently far from the injector, where one-way coupling between the two phases holds.

Velocity and Concentration Fields in Uniform Flow with Coarse Sands

Abstract: The vertical distributions of velocity and concentration for an open-channel flow mixed with coarse sands are investigated by using a mathematical model, taking account of the momentum transfer by the turbulent motion of the sediment mass balance by the diffusion and settling in a two-dimensional steady-state condition. An attempt is made here to obtain the horizontal time-mean velocity component and the sediment concentration quantitatively at a certain depth. An examination of measured velocity profiles plotted on semilogarithmic paper leads to the conclusion that the general characteristic of the flow is greatly affected by the increasing sediment load. The vertical distribution of the time-mean velocity is calculated by following the velocity gradient equation previously proposed. The concentration field is divided into the outer region and the inner region, since in each region the fall velocity varies according to the grain Reynolds number. For computing the concentration of suspended sediment, therefore, the writer proposes two formulas derived from Fick’s diffusion equation. The theoretical results obtained by the velocity and concentration equations are found to be in good agreement with a set of experimental data, for the mean diameters of the sands range from 940 to 1,300 μ\im.

Turbulent Velocity in Flocculation by Means of Grids

Abstract: Eleven types of single circular biplane grids with different diameter (\id) and mesh (\iM) were vertically and constantly oscillated inside a 2 L square jar. The velocity components were measured using a 2D laser doppler anemometer. The average root-mean-square turbulent velocity \iq′ values were found to be relatively constant at both vertical and horizontal points of measurement—a condition that could not be achieved in the case of impeller mixing. Since the mixing intensity was uniform within the jar, the average volume velocity gradient \iG¯ could be applied as the surrogate mixing intensity parameter. It was also found that \iq′ was linearly related to the vertical grid speed and grid physical characteristics, indicating that the mixing was easily controlled. The macro length scale (\iL) was calculated and was found to be constant and proportional to \id or \iM, as it should be in the case of turbulent mixing. This study shows the potential of grids as the mixing devices that can be expected to produce an optimum mixing environment for the flocculation process.

Mean magnetic field generation in sheared rotators

Abstract: A generalized mean magnetic field induction equation for differential rotators is derived, including a compressibility, and the anisotropy induced on the turbulent quantities from the mean magnetic field itself and a mean velocity shear. Derivations of the mean field equations often do not emphasize that there must be anisotropy and inhomogeneity in the turbulence for mean field growth. The anisotropy from shear is the source of a term involving the product of the mean velocity gradient and the cross-helicity correlation of the isotropic parts of the fluctuating velocity and magnetic field, $\lb{\bfv}\cdot{\bfb}\rb^{(0)}$. The full mean field equations are derived to linear order in mean fields, but it is also shown that the cross-helicity term survives to all orders in the velocity shear. This cross-helicity term can obviate the need for a pre-existing seed mean magnetic field for mean field growth: though a fluctuating seed field is necessary for a non-vanishing cross-helicity, the term can produce linear (in time) mean field growth of the toroidal field from zero mean field. After one vertical diffusion time, the cross-helicity term becomes sub-dominant and dynamo exponential amplification/sustenance of the mean field can subsequently ensue. The cross-helicity term should produce odd symmetry in the mean magnetic field, in contrast to the usually favored even modes of the dynamo amplification in sheared discs. This may be important for the observed mean field geometries of spiral galaxies. The strength of the mean seed field provided by the cross- helicity depends linearly on the magnitude of the cross-helicity.

Polymer stretching in an elongational flow

Abstract: Using a constant “velocity gradient” ensemble approach, the average scalar end-to-end separation is calculated as a function of the gradient for an ideal Gaussian polymer chain experiencing longitudinal elongational flow under steady-state conditions. The resulting equation, based on a dumbbell model, exhibits an initial average end-to-end separation equal to the unperturbed random coil value; the separation increases monotonically with increasing velocity gradient, in agreement with recent experimental measurements and with a classical treatment based on a diffusion equation. This approach is contrasted with one based on Hooke’s law where the end separation remains zero with increasing gradient until a critical value of the gradient is reached at which point the chain suddenly expands to an appreciable fraction of its fully extended length.

Single Polymers in Elongational Flows: Dynamic, Steady-State, and Population-Averaged Properties

Abstract: The behavior of dilute polymers in an elongational flow has been an outstanding problem in polymer science for several decades [1-3]. In these flows, a velocity gradient along the direction of flow can stretch polymers far from equilibrium. Extended polymers exert a force back on the solvent leading to the important, non-Newtonian properties of dilute polymer solutions such as viscosity enhancement and turbulent drag reduction.

Effects of shear flows on nonlinear waves in excitable media

Abstract: If an excitable medium is moving with relative shear, the waves of excitation may be broken by the motion. We consider such breaks for the case of a constant linear shear flow. The mechanisms and conditions for the breaking of solitary waves and wavetrains are essentially different: the solitary waves require the velocity gradient to exceed a certain threshold, whilst the breaking of repetitive wavetrains happens for arbitrarily small velocity gradients. Since broken waves evolve into new spiral wave sources, this leads to spatio-temporal irregularity.

Probability Density Function of Longitudinal Velocity Increment in Homogeneous Turbulence.

Abstract: Two conditional averages for the longitudinal velocity increment u r are considered: h ( u r ) is the average of the difference of the Laplacian of the velocity field with the u r value fixed, while g ( u r ) is the corresponding one of the square of the difference of the velocity gradient. The fitting formulae for h and g are derived for the 512 3 data of the direct numerical simulation. The computed PDF is characterized as (1) the Gaussian distribution for smaller amplitudes, (2) the exponential distribution for larger ones, and (3) the stretched exponential distribution for intermediate ones due to a factor in front of the exponential function.

Numerical study of three‐dimensional non‐Darcy forced convection in a square porous duct

Abstract: The objective of the present work was to perform a detailed numerical study of laminar forced convection in a three‐dimensional square duct packed with an isotropic granular material and saturated with a Newtonian fluid. Hydrodynamic and heat transfer results are reported for three different thermal boundary conditions. The flow in the porous medium was modeled using the semi‐empirical Brinkman‐Forchheimer‐extended Darcy model which also included the effects of variable porosity and thermal dispersion. Empirical models for variable porosity and thermal dispersion were determined based on existing three‐dimensional experimental measurements. Parametric studies were then conducted to investigate the effects of particle diameter, Reynolds number, Prandtl number and thermal conductivity ratio. The results showed that channeling phenomena and thermal dispersion effects are reduced considerably in a three‐dimensional duct compared with previously reported results for a two‐dimensional channel. It was found that the Reynolds number affects mainly the velocity gradient in the flow channeling region, while the particle diameter affects the width of the flow channeling region. As the Reynolds number increases or as the particle diameter decreases (i.e., when the inertia and thermal dispersion effects are enhanced), the Nusselt number increases. The effects of varing the Prandtl number on the magnitude of the Nusselt number were found to be more significant than those of the thermal conductivity ratio. Finally, the effects of varing the duct aspect ratio on the friction factor can be neglected for small particle diameter (Dp ≤ 0.01) or for high particle Reynolds number (Red ≥ 1000) due to the dominant bulk damping resistance from the porous matrix (Darcy term) or strong inertia effects (Forchheimer term), respectively.

Model for the electrorheological effect in flowing polymeric nematics

Abstract: An analytical model to study the response of a polymeric nematic confined in a rectangular cell, to a dc electric field is presented. The effect of a pressure-driven plane Poiseuille flow and its competition with the electric field is explicitly considered. For the final stationary state where the induced reorientation of the director has already occurred, an aligned structure with a greatly enhanced viscosity (electrorheological effect) is produced. For this same state the first normal stress difference is calculated as a function of position and of the applied field. For this quantity, regions of negative and positive values develop along the direction of the velocity gradient and an increase in the electric field or the flow causes an augmented effect in its profiles. The net force between the plates is also calculated. As the Reynolds number increases, it is found that it also changes sign from positive to negative, and the effect is more pronounced as the strength of the electric field increases. Fin...