Velocity gradient

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

Modified log-wake law for zero-pressure-gradient turbulent boundary layers Loi log-trainée modifiée pour couche limite turbulente sans gradient de pression

Abstract: This paper shows that the turbulent velocity profile for zero-pressure-gradient boundary layers is affected by the wall shear stress and convective inertia. The effect of the wall shear stress is dominant in the so-called overlap region and can be described by a logarithmic law in which the von Karman constant is about 0.4 while the additive constant depends on a Reynolds number. The effect of the convective inertia can be described by the Coles wake law with a constant wake strength about 0.76. A cubic correction term is introduced to satisfy the zero velocity gradient requirement at the boundary layer edge. Combining the logarithmic law, the wake law and the cubic correction produces a modified log–wake law, which is in excellent agreement with experimental profiles. The proposed velocity profile law is independent of Reynolds number in terms of its defect form, while it is Reynolds number dependent in terms of the inner variables. The modified log–wake law can also provide an accurate equation for skin friction in terms of the momentum thickness. Finally, by replacing the logarithmic law with van Driest’s mixing-length model in which the damping factor varies with Reynolds number, the modified log–wake law can be extended to the entire boundary layer flow.

Apparent friction coefficient in straight compound channels

Abstract: In compound open channel flow, the strong interaction between the main channel and the shallow floodplains affects considerably the discharge capacity. Since this phenomenon was identified, many authors have estimated experimentally the flow interaction in terms of an apparent shear stress acting at the vertical interface between the main channel and the floodplains. Empirical formulae have been developed to quantify this apparent shear stress, yet without general applicability. Herein, a dimensionally sound expression, depending on the square of the velocity gradient between the main channel and the floodplains, and on the so called “apparent friction coefficient”, is proposed. Its variation with the geometrical and roughness ratios is analysed herein. A generalized formulation to predict the apparent shear stress is presented and validated for a wide range of laboratory data. These include small-scale flumes and the large-scale flood channel facility, with both smooth and rough floodplains.

Extinction of Premixed Flames in a Stagnation Flow Considering General Lewis Number

Abstract: The effects of the velocity gradient on the premixed flame in the stagnation flow field have been studied theoretically considering general Lewis number The steady two-dimensional stagnation flow and the uni-molecular reaction were assumed, and the governing equations were solved numerically The influence of the velocity gradient and the Lewis number on the flame temperature were discussed There are two effects of the velocity gradient on the flame One effect is that the velocity gradient causes the flame temperature to increase or to decrease due to the imbalance between the excess heat flow from the reaction zone to the unburned gas and the excess diffusion flow of the reactant from the unburned gas to the reaction zone, and this effect largely depends on the Lewis number By the velocity gradient, the flame temperature increases when Le>1 and decreases when Le< 1 When Le= 1, the velocity gradient has no effect on the flame temperature Another effect is tha velocity gradient causes the fl

Response of a turbulent boundary layer to random fluctuations in the external stream

Abstract: The growth of the turbulent boundary layer is investigated primarily by means of conditional averages in the outer region (i.e., averages inside and outside the bulges limiting the free edge). The main quantities analyzed are: mean velocities, mean velocity gradients, turbulence intensities, Reynolds stresses, kinetic energy balances, skewness and flatness factors of the velocity and Reynolds stress fluctuations, intermittency factor, and indentations of the free edge. Considerable attention is paid to the cumulative straining process of the turbulence by the mean velocity gradient.

On the hydrodynamics of ‘slip–stick’ spheres

Abstract: The breakdown of the no-slip condition at fluid–solid interfaces generates a host of interesting fluid-dynamical phenomena. In this paper, we consider such a scenario by investigating the low-Reynolds-number hydrodynamics of a novel ‘slip–stick’ spherical particle whose surface is partitioned into slip and no-slip regions. In the limit where the slip length is small compared to the size of the particle, we first compute the translational velocity of such a particle due to the force density on its surface. Subsequently, we compute the rotational velocity and the response to an ambient straining field of a slip–stick particle. These three Faxen-type formulae are rich in detail about the dynamics of the particles: chiefly, we find that the translational velocity of a slip–stick sphere is coupled to all of the moments of the force density on its surface; furthermore, such a particle can migrate parallel to the velocity gradient in a shear flow. Perhaps most important is the coupling we predict between torque and translation (and force and rotation), which is uncharacteristic of spherical particles in unbounded Stokes flow and originates purely from the slip–stick asymmetry.