Showing papers on "Velocity gradient published in 2013"

Normal stresses in concentrated non-Brownian suspensions

Abstract: We present an experimental approach used to measure both normal stress differences and the particle phase contribution to the normal stresses in suspensions of non-Brownian hard spheres. The methodology consists of measuring the radial profile of the normal stress along the velocity gradient direction in a torsional flow between two parallel discs. The values of the first and the second normal stress differences, is obtained. Most of our results compare well with the different experimental and numerical data present in the literature. In particular, our results show that the magnitude of the particle stress tensor component and their dependence on the particle volume fraction used in the suspension model balance proposed by Morris & Boulay (J. Rheol., vol. 43, 1999, p. 1213) are suitable.

Massive molecular gas flows in the Abell 1664 brightest cluster galaxy

Abstract: We report ALMA Early Science CO(1-0) and CO(3-2) observations of the brightest cluster galaxy (BCG) in Abell 1664. The BCG contains 1.1x10^{10} solar masses of molecular gas divided roughly equally between two distinct velocity systems: one from -250 to +250 km/s centred on the BCG's systemic velocity and a high velocity system blueshifted by 570 km/s with respect to the systemic velocity. The BCG's systemic component shows a smooth velocity gradient across the BCG center with velocity proportional to radius suggestive of solid body rotation about the nucleus. However, the mass and velocity structure are highly asymmetric and there is little star formation coincident with a putative disk. It may be an inflow of gas that will settle into a disk over several 10^8 yr. The high velocity system consists of two gas clumps, each ~2 kpc across, located to the north and southeast of the nucleus. Each has a line of sight velocity spread of 250-300 km/s. The velocity of the gas in the high velocity system tends to increase towards the BCG center and could signify a massive high velocity flow onto the nucleus. However, the velocity gradient is not smooth and these structures are also coincident with low optical-UV surface brightness regions, which could indicate dust extinction associated with each clump. If so, the high velocity gas would be projected in front of the BCG and moving toward us along the line of sight in a massive outflow most likely driven by the AGN. A merger origin is unlikely but cannot be ruled out.

Granular shear flows of flat disks and elongated rods without and with friction

Abstract: Granular shear flows of flat disks and elongated rods are simulated using the Discrete Element Method. The effects of particle shape, interparticle friction, coefficient of restitution, and Young's modulus on the flow behavior and solid phase stresses have been investigated. Without friction, the stresses decrease as the particles become flatter or more elongated due to the effect of particle shape on the motion and interaction of particles. In dense flows, the particles tend to have their largest dimension aligned in the flow direction and their smallest dimension aligned in the velocity gradient direction, such that the contacts between the particles are reduced. The particle alignment is more significant for flatter disks and more elongated rods. The interparticle friction has a crucial impact on the flow pattern, particle alignment, and stress. Unlike in the smooth layer flows with frictionless particles, frictional particles are entangled into large masses which rotate like solid bodies under shear. In dense flows with friction, a sharp stress increase is observed with a small increase in the solid volume fraction, and a space-spanning network of force chains is rapidly formed with the increase in stress. The stress surge can occur at a lower solid volume fraction for the flatter and more elongated particles. The particle Young's modulus has a negligible effect on dilute and moderately dense flows. However, in dense flows where the space-spanning network of force chains is formed, the stress depends strongly on the particle Young's modulus. In shear flows of non-spherical particles, the stress tensor is found to be symmetric, but anisotropic with the normal component in the flow direction greater than the other two normal components. The granular temperature for the non-spherical particle systems consists of translational and rotational temperatures. The translational temperature is not equally partitioned in the three directions with the component in the flow direction greater than the other two. The rotational temperature is less than the translational temperature at low solid volume fractions, but may become greater than the translational temperature at high solid volume fractions.

Analysis of HDG Methods for Oseen Equations

Abstract: We propose a hybridizable discontinuous Galerkin (HDG) method to numerically solve the Oseen equations which can be seen as the linearized version of the incompressible Navier-Stokes equations. We use same polynomial degree to approximate the velocity, its gradient and the pressure. With a special projection and postprocessing, we obtain optimal convergence for the velocity gradient and pressure and superconvergence for the velocity. Numerical results supporting our theoretical results are provided.

Localized measurement of longitudinal and transverse flow velocities in colloidal suspensions using optical coherence tomography.

Abstract: We report on localized measurement of the longitudinal and transverse flow velocities in a colloidal suspension using optical coherence tomography. We present a model for the path-length resolved autocorrelation function including diffusion and flow, which we experimentally verify. For flow that is not perpendicular to the incident beam, the longitudinal velocity gradient over the coherence gate causes additional decorrelation, which is described by our model. We demonstrate simultaneous imaging of sample morphology and longitudinal and transverse flow at micrometer scale in a single measurement.

Three-dimensional flow visualization in the wake of a miniature axial-flow hydrokinetic turbine

Abstract: Three-dimensional 3-component velocity measurements were made in the near wake region of a miniature 3-blade axial-flow turbine within a turbulent boundary layer. The model turbine was placed in an open channel flow and operated under subcritical conditions (Fr = 0.13). The spatial distribution of the basic flow statistics was obtained at various locations to render insights into the spatial features of the wake. Instantaneous and phase-averaged vortical structures were analyzed to get insights about their dynamics. The results showed a wake expansion proportional to the one-third power of the streamwise distance, within the first rotor diameter. Wake rotation was clearly identified up to a distance of roughly three rotor diameters. In particular, relatively high tangential velocity was observed near the wake core, but it was found to be nearly negligible at the turbine tip radius. In contrast, the radial velocity showed the opposite distribution, with higher radial velocity near the turbine tip and, due to symmetry, negligible at the rotor axis. Larger turbulence intensity was found above the hub height and near the turbine tip. Strong coherent tip vortices, visualized in terms of the instantaneous vorticity and the λ2 criterion, were observed within the first rotor diameter downstream of the turbine. These structures, influenced by the velocity gradient in the boundary layer, appeared to loose their stability at distances greater than two rotor diameters. Hub vortices were also identified. Measurements did not exhibit significant tip–hub vortex interaction within the first rotor diameter.

Benchmark problems for mixtures of rarefied gases. I. Couette flow

Abstract: The planar Couette flow for gaseous mixture He–Ar is calculated by the direct simulation Monte Carlo method based on ab initio potential over the whole range of the gas rarefaction for several values of the mole fraction and for two values of the wall speed. The smaller value of the speed corresponds to the limit when the nonlinear terms are negligible, while the larger value describes a nonlinear flow. The shear stress, velocity gradient, temperature, and mole fraction profiles are presented. The reported results can be used as benchmark data to test model kinetic equations for gaseous mixtures. To study the influence of the intermolecular potential, the same simulations are carried out for the hard sphere molecular model. A relative deviation of the results based on this model from those based on the ab initio potential are analyzed. It is pointed out that the difference between the shear stresses of the two potentials for the linearized solution is within 1%, while it reaches 6% for the nonlinear cases.

Turbulent friction drag reduction using electroactive polymer and electromagnetically driven surfaces

Abstract: This work reports aerodynamic testing of two spanwise-oscillating surfaces fabricated out of electroactive polymers (EAPs) in the dielectric form of actuation, and of an electromagnetic-driven linear motor. Hot-wire and PIV measurements of velocity and direct measurement of friction drag using a drag balance are presented. A maximum of 16 % surface friction reduction, as calculated by the diminution of the wall-normal streamwise velocity gradient, was obtained. Among other quantities, the spatial dependence of the drag reduction was investigated. When this spatial transient and portions which are static are accounted for, the direct drag measurements complement the hot-wire data. PIV measurements, where the laser beam was parallel to the oscillating surface at y + ≈ 15, support the hot-wire data. The two actuators are original in design, and significant contributions have been made to the development of EAPs. This experiment is the first to aerodynamically test EAP actuators at such a large scale and at a relatively moderate Re.

Tetrahedron deformation and alignment of perceived vorticity and strain in a turbulent flow

Abstract: We describe the structure and dynamics of turbulence by the scale-dependent perceived velocity gradient tensor as supported by following four tracers, i.e., fluid particles, that initially form a regular tetrahedron. We report results from experiments in a von Karman swirling water flow and from numerical simulations of the incompressible Navier-Stokes equation. We analyze the statistics and the dynamics of the perceived rate of strain tensor and vorticity for initially regular tetrahedron of size r0 from the dissipative to the integral scale. Just as for the true velocity gradient, at any instant, the perceived vorticity is also preferentially aligned with the intermediate eigenvector of the perceived rate of strain. However, in the perceived rate of strain eigenframe fixed at a given time t = 0, the perceived vorticity evolves in time such as to align with the strongest eigendirection at t = 0. This also applies to the true velocity gradient. The experimental data at the higher Reynolds number suggests ...

The B1 shock in the L1157 outflow as seen at high spatial resolution

Abstract: We present high spatial resolution (750 AU at 250 pc) maps of the B1 shock in the blue lobe of the L1157 outflow in four lines: CS (3-2), CH3OH (3_K-2_K), HC3N (16-15) and p-H2CO (2_02-3_01). The combined analysis of the morphology and spectral profiles has shown that the highest velocity gas is confined in a few compact (~ 5 arcsec) bullets while the lowest velocity gas traces the wall of the gas cavity excavated by the shock expansion. A large velocity gradient model applied to the CS (3-2) and (2-1) lines provides an upper limit of 10^6 cm^-3 to the averaged gas density in B1 and a range of 5x10^3< n(H2)< 5x10^5 cm^-3 for the density of the high velocity bullets. The origin of the bullets is still uncertain: they could be the result of local instabilities produced by the interaction of the jet with the ambient medium or could be clump already present in the ambient medium that are excited and accelerated by the expanding outflow. The column densities of the observed species can be reproduced qualitatively by the presence in B1 of a C-type shock and only models where the gas reaches temperatures of at least 4000 K can reproduce the observed HC3N column density.

Unveiling the detailed density and velocity structures of the protostellar core b335

Abstract: We present an observational study of the protostellar core B335 harboring a low-mass Class 0 source. The observations of the H13CO+(J = 1-0) line emission were carried out using the Nobeyama 45 m telescope and Nobeyama Millimeter Array. Our combined image of the interferometer and single-dish data depicts detailed structures of the dense envelope within the core. We found that the core has a radial density profile of n(r)r –p and a reliable difference in the power-law indices between the outer and inner regions of the core: p 2 for r 4000 AU and p 1.5 for r 4000 AU. The dense core shows a slight overall velocity gradient of ~1.0 km s–1 over the scale of 20, 000 AU across the outflow axis. We believe that this velocity gradient represents a solid-body-like rotation of the core. The dense envelope has a quite symmetrical velocity structure with a remarkable line broadening toward the core center, which is especially prominent in the position-velocity diagram across the outflow axis. The model calculations of position-velocity diagrams do a good job of reproducing observational results using the collapse model of an isothermal sphere in which the core has an inner free-fall region and an outer region conserving the conditions at the formation stage of a central stellar object. We derived a central stellar mass of ~0.1 M ☉, and suggest a small inward velocity, in the outer core at 4000 AU. We concluded that our data can be well explained by gravitational collapse with a quasi-static initial condition, such as Shu's model, or by the isothermal collapse of a marginally critical Bonnor-Ebert sphere.

Two-layer model for open channel flow with submerged flexible vegetation

Abstract: A two-layer model for predicting the vertical distribution of stream-wise velocity in open channel flow with submerged flexible vegetation is proposed Using the predicted deflection height of the flexible vegetation determined via the large-deflection cantilever beam theory, the flow is vertically separated into a bottom vegetation layer and an upper free water layer, and corresponding momentum equations for each layer are formulated In the bottom vegetation layer, the resistance caused by the deflected plants is calculated accounting for plant bending rather than adopting the existing resistance formula for erect rigid vegetation For the upper free water layer, a new type of polynomial velocity distribution is suggested instead of the traditional logarithmic velocity distribution to obtain a zero velocity gradient at the water surface To validate the proposed model, the published experimental data are employed

A constraint for the subgrid-scale stresses in the logarithmic region of high Reynolds number turbulent boundary layers: A solution to the log-layer mismatch problem

Abstract: This paper addresses one of the most persisting problems in wall-modeled large eddy simulation (LES): the overshoot of the mean velocity gradient near the wall, often referred to as the “log-layer mismatch” problem. An analysis of the relationship between turbulent kinetic energy budgets and mean velocity gradient is elaborated for both direct numerical simulations and LES of fully developed channel flow at high Reynolds number. Based on the analysis, a self-adaptive Smagorinsky model for LES of high-Reynolds-number boundary layer flows is proposed, in which the Smagorinsky coefficient is dynamically adjusted so that a logarithmic mean velocity distribution is captured. The model is then implemented in a second-order finite-volume code, and applied to a high-Reynolds-number channel flow with rough walls. We find that the desired logarithmic mean velocity distribution is well predicted for different resolutions and grid aspect ratios.

Length-Scale Similarity of Turbulent Organized Structures over Surfaces with Different Roughness Types

Abstract: We examine the similarity of turbulent organized structures over smooth and very rough wall flows. Turbulent flow fields in horizontal cross-sections were measured using particle image velocimetry, and the characteristics of turbulent organized structures over four types of surfaces were investigated. Measurements were conducted at several measurement heights across the internal boundary layer. The length and width of turbulence structures were quantified using a two-point correlation method. We selected two thresholds of two-point correlation coefficients to consider both large-scale and small-scale structures; the validity of these choices was examined through the analyses using proper orthogonal decomposition. For large-scale structures, the length and aspect ratios (streamwise length/spanwise width) of structures were highly correlated with the velocity gradient for each measurement height and boundary-layer thickness. This relationship was also examined in the results of previous studies, and the scaling of the aspect ratio with the non-dimensional velocity gradient again showed the importance of the velocity gradient, with slight differences found between smooth and rough surfaces. In contrast, the small-scale structures exhibited weak dependency on the velocity gradient and boundary-layer thickness. Instantaneous snapshots of turbulent organized structures at the same shear level also displayed differences in small-scale structures, but the structures of the organized motions resembled each other, as in the results of the two-point correlation method.

Shear flows of a new class of power-law fluids

Abstract: We consider the flow of a class of incompressible fluids which are constitutively defined by the symmetric part of the velocity gradient being a function, which can be non-monotone, of the deviator of the stress tensor. These models are generalizations of the stress power-law models introduced and studied by J. Malek, V. Průsa, K.R. Rajagopal: Generalizations of the Navier-Stokes fluid from a new perspective. Int. J. Eng. Sci. 48 (2010), 1907–1924. We discuss a potential application of the new models and then consider some simple boundary-value problems, namely steady planar Couette and Poiseuille flows with no-slip and slip boundary conditions. We show that these problems can have more than one solution and that the multiplicity of the solutions depends on the values of the model parameters as well as the choice of boundary conditions.

Structures and dynamics of small scales in decaying magnetohydrodynamic turbulence

Abstract: The topological and dynamical features of small scales are studied in the context of decaying magnetohydrodynamic turbulent flows using direct numerical simulations. Joint probability density functions (PDFs) of the invariants of gradient quantities related to the velocity and the magnetic fields demonstrate that structures and dynamics at the time of maximum dissipation depend on the large scale initial conditions at the examined Reynolds numbers. This is evident in particular from the fact that each flow has a different shape for the joint PDF of the invariants of the velocity gradient in contrast to the universal teardrop shape of hydrodynamic turbulence. The general picture that emerges from the analysis of the invariants is that regions of high vorticity are correlated with regions of high strain rate S also in contrast to hydrodynamic turbulent flows. Magnetic strain dominated regions are also well correlated with region of high current density j. Viscous dissipation (∝S2) as well as Ohmic dissipati...

Shear-induced diffusion of red blood cells in a semi-dilute suspension

Abstract: The diffusion of red blood cells (RBCs) in blood is important to the physiology and pathology of the cardiovascular system. In this study, we investigate flow-induced diffusion of RBCs in a semi-dilute system by calculating the pairwise interactions between RBCs in simple shear flow. A capsule with a hyperelastic membrane was used to model an RBC. Its deformation was resolved using the finite element method, whereas fluid motion inside and outside the RBC was solved using the boundary element method. The results show that shear-induced RBC diffusion is significantly anisotropic, i.e. the velocity gradient direction component is larger than the vorticity direction. We also found that the motion of RBCs during the interaction is strongly dependent on the viscosity ratio of the internal to external fluid, and the diffusivity decreases monotonically as the viscosity ratio increases. The scaling argument also suggests that the diffusivity is proportional to the shear rate and haematocrit, if the suspension is in a semi-dilute environment and the capillary number is invariant. These fundamental findings are useful to understand transport phenomena in blood flow.

Structures and dynamics of small scales in decaying magnetohydrodynamic turbulence

Abstract: The topological and dynamical features of small scales are studied in the context of decaying magnetohydrodynamic turbulent flows using direct numerical simulations. Joint probability density functions (PDFs) of the invariants of gradient quantities related to the velocity and the magnetic fields demonstrate that structures and dynamics at the time of maximum dissipation depend on the large scale initial conditions. This is evident in particular from the fact that each flow has a different shape for the joint PDF of the invariants of the velocity gradient in contrast to the universal teardrop shape of hydrodynamic turbulence. The general picture that emerges from the analysis of the invariants is that regions of high vorticity are correlated with regions of high strain rate $\bm S$ also in contrast to hydrodynamic turbulent flows. Magnetic strain dominated regions are also well correlated with region of high current density $\bm j$. Viscous dissipation ($\propto \bm S^2$) as well as Ohmic dissipation ($\propto \bm j^2$) reside in regions where strain and rotation are locally almost in balance. The structures related to the velocity gradient possess different characteristics than those associated with the magnetic field gradient with the latter being locally more quasi-two dimensional.

On the role of reflections, refractions and diving waves in full-waveform inversion

Abstract: Full-waveform inversion suffers from local minima, due to a lack of low frequencies in data. A reflector below the zone of interest may, however, help in recovering the long-wavelength components of a velocity perturbation, as demonstrated in a paper by Mora. With the Born approximation for a perturbation in a reference model consisting in two homogeneous isotropic acoustic half-spaces and the assumption of infinitely large apertures available in the data, analytic expressions can be found that describe the spatial spectrum of the recorded seismic signal as a function of the spatial spectrum of the inhomogeneity. Diving waves can be included if the deeper part of the homogeneous model is replaced by one that has a vertical velocity gradient. We study this spectrum in more detail by separately considering scattering of direct, reflected and head waves, as well as singly and multiply reflected diving waves for a gradient model. Taking the reflection coefficient of the deeper reflector into account, we obtain sensitivity estimates for each wavetype. Although the head waves have a relatively small contribution to the reconstruction of the velocity perturbation, compared to the other waves, they contain reliable long-wavelength information that can be beneficial for full-waveform inversion. If the deeper part has a constant positive velocity gradient with depth, all the energy eventually returns to the source-receiver line, given a sufficiently large acquisition aperture. This will improve the sensitivity of the scattered reflected and refracted wavefields to perturbations in the background model. The same happens for a zero velocity gradient but with a very high impedance contrast between the two half-spaces, which results in a large reflection coefficient.

Comparison of different models of substrate inhibition in aerobic batch biodegradation of malathion

Abstract: Drag reduction in fully developed turbulent pipe flow with 4 concentrations (200 to 500 wppm or mg/kg) of low molecular weight sodium carboxymethylcellulose (CMC) in aqueous solutions was investigated experimentally. Drag reduction was determined by pressure drop measurements. Maximum drag reduction achieved was 22% using 500 wppm CMC solution. To observe the impact of the presence of CMC on the flow, ultrasound Doppler velocimetry (UDV) was employed to monitor the instantaneous velocity distributions. Experimental measurements were used to calculate Fanning friction factor and radial distributions of the axial time-averaged velocity, velocity fluctuation (turbulent intensity), and eddy viscosity. Two impacts of increasing CMC concentration on the flow field were observed. The first effect was the decrease in the mean velocity gradient, especially near the wall, with increasing polymer amount, which in turn gave rise to a lower friction factor or pressure drop. Furthermore, smaller eddy viscosities were obtained in the flow. The second impact of polymer addition was on the velocity fluctuation or turbulent intensity variation along the radial distribution. Presence of the polymer suppressed the velocity fluctuations near the wall while the intensity in the turbulent core region became stronger than in the case of lower or no polymer addition.

Effect of elongational flow on ferrofuids under a magnetic field.

Abstract: To set up a mathematical model for the flow of complex magnetic fluids, noninteracting magnetic particles with a small volume or an even point size are typically assumed. Real ferrofluids, however, consist of a suspension of particles with a finite size in an almost ellipsoid shape as well as with particle-particle interactions that tend to form chains of various lengths. To come close to the realistic situation for ferrofluids, we investigate the effect of elongational flow incorporated by the symmetric part of the velocity gradient field tensor, which could be scaled by a so-called transport coefficient ${\ensuremath{\lambda}}_{2}$. Based on the hybrid finite-difference and Galerkin scheme, we study the flow of a ferrofluid in the gap between two concentric rotating cylinders subjected to either a transverse or an axial magnetic field with the transport coefficient. Under the influence of a transverse magnetic field with ${\ensuremath{\lambda}}_{2}=0$, we show that basic state and centrifugal unstable flows are modified and are inherently three-dimensional helical flows that are either left-winding or right-winding in the sense of the azimuthal mode-2, which is in contrast to the generic cases. That is, classical modulated rotating waves rotate, but these flows do not. We find that under elongational flow (${\ensuremath{\lambda}}_{2}\ensuremath{ e}0$), the flow structure from basic state and centrifugal instability flows is modified and their azimuthal vorticity is linearly changed. In addition, we also show that the bifurcation threshold of the supercritical centrifugal unstable flows under a magnetic field depends linearly on the transport coefficient, but it does not affect the general stabilization effect of any magnetic field.

Measurement of fluid velocity development in laminar pipe flow using laser Doppler velocimetry

Abstract: In this paper we present a non-intrusive experimental approach for obtaining velocity gradient profiles in a transparent smooth pipe under laminar flow conditions (Re = 925) using a laser Doppler velocimeter (LDV). Measurements were taken within the entrance region of the pipe at l = 300 mm and l = 600 mm from the pipe inlet, in addition to measurements of the fully developed flow at l = 1800 mm. The obtained results show how the velocity profile from upstream of the pipe develops into a classical laminar profile downstream, which matches the theoretical profile well. Additionally, a brief summary of historical information about the development of flow measurement techniques, in particular LDV, is provided.

Understanding the dynamical structure of pulsating stars: The center-of-mass velocity and the Baade-Wesselink projection factor of the β Cephei star α Lupi

Abstract: Context. High-resolution spectroscopy of pulsating stars is a powerful tool to study the dynamical structure of their atmosphere. Lines asymmetry is used to derive the center-of-mass velocity of the star, while a direct measurement of the atmospheric velocity gradient helps to determine the projection factor used in the Baade-Wesselink methods of distance determination. Aims. We aim at deriving the center-of-mass velocity and the projection factor of the β Cephei star α Lup. Methods. We present HARPS (High Accuracy Radial velocity Planetary Search) high spectral resolution observations of α Lup. We calculate the first-moment radial velocities and fit the spectral line profiles by a bi-Gaussian to derive line asymmetries. Correlations between the γ-velocity and the γ-asymmetry (defined as the average values of the radial velocity and line asymmetry curves respectively) are used to derive the center-of-mass velocity of the star. By combining our spectroscopic determination of the atmospheric velocity gradient with a hydrodynamical model of the photosphere of the star, we derive a semi-theoretical projection factor for α Lup. Results. We find a center-of-mass velocity of Vγ = 7.9 ± 0.6 kms −1 and that the velocity gradient in the atmosphere of α Lup is null. We apply to α Lup the usual decomposition of the projection factor into three parts, p = p0fgradfog (originally developed for Cepheids), and derive a projection factor of p = 1.43 ± 0.01. By comparing our results with previous HARPS observations of classical Cepheids, we also point out a linear relation between the atmospheric velocity gradient and the amplitude of the radial velocity curve. Moreover, we observe a phase shift (Van Hoof effect), whereas α Lup has no velocity gradient. New HARPS data of a short-period β Cephei star, τ 1 Lup, are also presented in this paper. Conclusions. By comparing Cepheids and β Cephei stars, these results bring insight into the dynamical structure of pulsating star atmospheres, which helps to better understand the k-term problem and the Baade-Wesselink p-factor for Cepheids.