Velocity gradient

About: Velocity gradient is a research topic. Over the lifetime, 3013 publications have been published within this topic receiving 77120 citations.

Optimization of Particle Image Velocimeters

Abstract: The spatial resolution, detection rate, accuracy and reliability of a particle image velocimeter depend critically upon careful selection of a number of parameters of the PIV system and the fluid. An analytical model has been developed to analyze the effects of variation of experimental parameters which optimize the system. A set of six nondimensional parameters which are most significant in optimizing the PIV autocorrelation algorithm are derived. They are the data validation criterion, the particle image density, the relative in-plane image displacement, the relative out-of-plane displacement, a velocity gradient parameter and the ratio of the mean image diameter to the interrogation spot diameter. A comparison is made with the method of analysis by Young’s fringes to show this set of parameters is most significant there and the analysis is valid for both methods of PIV system interrogation.A study of a range of specific velocity fields has been undertaken to determine the influence of these parameters in each case and recommendations are made for interrogation of these velocity fields. The presence of velocity gradients in the velocity field has been examined for the cases of pure shear and solid body rotation. Corrections for the statistical bias are developed, with recommendations for minimizing bias effects and loss of signal strength.The spatial resolution, detection rate, accuracy and reliability of a particle image velocimeter depend critically upon careful selection of a number of parameters of the PIV system and the fluid. An analytical model has been developed to analyze the effects of variation of experimental parameters which optimize the system. A set of six nondimensional parameters which are most significant in optimizing the PIV autocorrelation algorithm are derived. They are the data validation criterion, the particle image density, the relative in-plane image displacement, the relative out-of-plane displacement, a velocity gradient parameter and the ratio of the mean image diameter to the interrogation spot diameter. A comparison is made with the method of analysis by Young’s fringes to show this set of parameters is most significant there and the analysis is valid for both methods of PIV system interrogation.A study of a range of specific velocity fields has been undertaken to determine the influence of these parameters ...

On the equations of fully fluidized granular materials

Abstract: Equations for fully fluidized granular materials are proposed and are solved in a simple case. In fully fluidized granular materials, the granular particles slip or collide with each other and energy is dissipated. In describing the energy dissipation process characteristic to granular materials, a measure of random motion of granular particles is introduced as a new internal variable. We derive the constitutive equations by using a simple kinematical model of the collision of particles. The set of equations for fully fluidized granular materials obtained has properties similar to the equations that describe turbulence. For reasonable assumptions, these equations predict the results of Bagnold, namely that the shear and normal stress depend upon the square of the velocity gradient. In case of steady one-dimensional gravity flow the calculated flow profiles resemble experimental ones.

A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow

Abstract: Fully developed incompressible turbulent pipe flow at bulk-velocity- and pipe-diameter-based Reynolds number ReD=44000 was simulated with second-order finite-difference methods on 630 million grid points. The corresponding Karman number R+, based on pipe radius R, is 1142, and the computational domain length is 15R. The computed mean flow statistics agree well with Princeton Superpipe data at ReD=41727 and at ReD=74000. Second-order turbulence statistics show good agreement with experimental data at ReD=38000. Near the wall the gradient of with respect to ln(1−r)+ varies with radius except for a narrow region, 70 0.4. For 5300 0.4. A rationale based on the curvature of mean velocity gradient profile is proposed to understand the perplexing existence of logarithmic mean velocity profile in very-low-Reynolds-number pipe flows. Beyond ReD=44000, axial turbulence intensity varies linearly with radius within the range of 0.15 < 1−r < 0.7. Flow visualizations and two-point correlations reveal large-scale structures with comparable near-wall azimuthal dimensions at ReD=44000 and 5300 when measured in wall units. When normalized in outer units, streamwise coherence and azimuthal dimension of the large-scale structures in the pipe core away from the wall are also comparable at these two Reynolds numbers.

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.