Topic
Velocity gradient
About: Velocity gradient is a research topic. Over the lifetime, 3013 publications have been published within this topic receiving 77120 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, it was shown that the externally applied velocity field is responsible for the nucleation of the fibrous crystals, subsequent growth is then influenced by both the local streaming of polymer melt around the growing tip of the fibre and the external velocity field.
Abstract: In situ optical observations have been made of the way polyethylene melt can crystallize whilst subject to certain longitudinal velocity gradients. In general crystallization is seen to occur as the generation of fibres 5 to 50 μm in diameter. Hydrodynamic considerations lead to the conclusion that the externally applied velocity field is responsible for the nucleation of the fibrous crystals, subsequent growth is then influenced by both the local streaming of polymer melt around the growing tip of the fibre and the external velocity field. The effect enhanced pressure has on flow induced crystallization is also examined.
62 citations
TL;DR: A model for the path-length resolved autocorrelation function including diffusion and flow is presented and simultaneous imaging of sample morphology and longitudinal and transverse flow at micrometer scale in a single measurement is demonstrated.
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.
62 citations
TL;DR: In this article, a simulation of turbulent flow between a rotating and a stationary disk is performed by integrating the time-dependent Navier-Stokes equations until a statistically steady state is reached and with the aim of providing both long-time statistics and an exposition of coherent structures obtained by conditional sampling.
Abstract: Turbulent flow between a rotating and a stationary disk is studied. Besides its fundamental importance as a three-dimensional prototype flow, such flow fields are frequently encountered in rotor–stator configurations in turbomachinery applications. A direct numerical simulation is therefore performed by integrating the time-dependent Navier–Stokes equations until a statistically steady state is reached and with the aim of providing both long-time statistics and an exposition of coherent structures obtained by conditional sampling. The simulated flow has local Reynolds number r2ω/v = 4 × 105 and local gap ratio s/r = 0.02, where ω is the angular velocity of the rotating disk, r the radial distance from the axis of rotation, v the kinematic viscosity of the fluid, and s the gap width.The three components of the mean velocity vector and the six independent Reynolds stresses are compared with experimental measurements in a rotor–stator flow configuration. In the numerically generated flow field, the structural parameter a1 (i.e. the ratio of the magnitude of the shear stress vector to twice the mean turbulent kinetic energy) is lower near the two disks than in two-dimensional boundary layers. This characteristic feature is typical for three-dimensional boundary layers, and so are the misalignment between the shear stress vector and the mean velocity gradient vector, although the degree of misalignment turns out to be smaller in the present flow than in unsteady three-dimensional boundary layer flow. It is also observed that the wall friction at the rotating disk is substantially higher than at the stationary disk.Coherent structures near the disks are identified by means of the λ2 vortex criterion in order to provide sufficient information to resolve a controversy regarding the roles played by sweeps and ejections in shear stress production. An ensemble average of the detected structures reveals that the coherent structures in the rotor–stator flow are similar to the ones found in two-dimensional flows. It is shown, however, that the three-dimensionality of the mean flow reduces the inter-vortical alignment and the tendency of structures of opposite sense of rotation to overlap. The coherent structures near the disks generate weaker sweeps (i.e. quadrant 4 events) than structures in conventional two-dimensional boundary layers. This reduction in the quadrant 4 contribution from the coherent structures is believed to explain the reduced efficiency of the mean flow in producing Reynolds shear stress.
62 citations
TL;DR: In this article, the deformation ratio S (the ratio of final to original linear velocity), analogous to the draw ratio λ = 1/10 in the cold-drawing process, has no influence on the degree of orientation.
Abstract: The problem of the mechanism of macromolecule orientation occurring in the formation of fibers from polymer melts has been qualitatively analyzed As a result of birefringence, x-ray, and spinning stress investigations carried out on polycapronamide fibers, the main parameters determining orientation have been established They are the parallel velocity gradient along the spinning length, G = dV/dl, and the relaxation factors The deformation ratio S (the ratio of final to original linear velocity), analogous to the draw ratio λ = 1/10 in the cold-drawing process, has no influence on the degree of orientation The orientation by spinning is not accompanied by any such structural transformations as occur through cold-drawing The fibers spun at high velocity gradients consist of well-oriented β-polycapronamide It is thus assumed that the orientation proceeds in the region of the liquid melt-stream as a result of simultaneous action of velocity gradient and thermal relaxation This mechanism, analogous to that causing the familiar streaming orientation of polymer solutions in capillaries or in a Couette apparatus, is different in principle from that of the cold-drawing process
62 citations
TL;DR: In this paper, an optimized, collocated-grid finite-difference scheme was proposed to solve the anisotropic velocity-stress equation in spherical coordinates by using a non-uniform grid to discretize the computational domain.
Abstract: SUMMARY
To simulate seismic wave propagation in the spherical Earth, the Earth’s curvature has to be taken into account. This can be done by solving the seismic wave equation in spherical coordinates by numerical methods. In this paper, we use an optimized, collocated-grid finite-difference scheme to solve the anisotropic velocity–stress equation in spherical coordinates. To increase the efficiency of the finite-difference algorithm, we use a non-uniform grid to discretize the computational domain. The grid varies continuously with smaller spacing in low velocity layers and thin layer regions and with larger spacing otherwise. We use stress-image setting to implement the free surface boundary condition on the stress components. To implement the free surface boundary condition on the velocity components, we use a compact scheme near the surface. If strong velocity gradient exists near the surface, a lower-order scheme is used to calculate velocity difference to stabilize the calculation. The computational domain is surrounded by complex-frequency shifted perfectly matched layers implemented through auxiliary differential equations (ADE CFS-PML) in a local Cartesian coordinate. We compare the simulation results with the results from the normal mode method in the isotropic and anisotropic models and verify the accuracy of the finite-difference method.
62 citations