Maximum Tip Velocity Research Articles

Multi-scale modeling of equiaxed dendritic solidification of Al-Cu at constant cooling rate

To provide quantitative predictions, multiscale models of dendritic solidification (e.g., GEM, DNN, CAFE) need to be validated and require model parameters, which can be calculated by phase-field simulations. We report on a multiscale modeling of dendritic solidification in samples that are cooled homogeneously at a constant rate. We consider three Al-Cu alloys and samples from thin to bulk thickness. We investigate how the alloy composition, the distance between the equiaxed dendrites and the sample thickness influence the transient growth velocity of the primary tips. Using 3D phase-field simulations, we calculate the tip selection parameter based on the microsolvability theory. We show that the selection parameter depends principally on the ratio between the sample thickness and the smallest tip diffusion length during the transient growth (D/vm , where vm is the maximum tip velocity). The extracted tip selection parameters are then used as inputs for three-dimensional grain envelope model (GEM) simulations. The comparison between TIPF and GEM shows that the GEM can reproduce transient growth of interacting equiaxed dendrites during cooling and can account for sample confinement effects.

Revisiting the Taylor-Culick approximation: Retraction of an axisymmetric filament

We numerically study the retraction of an axisymmetric viscous filament in a passive surrounding fluid. The analysis focuses on the evolution of the tip velocity, from the early stage of the filament retraction until it reaches its final equilibrium spherical shape. The problem is governed by two control parameters: the Ohnesorge number, Oh, which measures the relative importance of viscous and surface tension effects, and the initial aspect ratio of the filament, A. We investigate the influence of Oh over a wide range of aspect ratios. The small-Oh regime is characterized by the occurrence of a spherical blob at the extremity of the filament. This feature has a key impact on the tip dynamics, which moves with an oscillating velocity whose mean value is close to the Taylor-Culick prediction. The oscillatory behavior of the tip velocity is explained through a simple mass-spring model. This regime is also characterized by the presence of capillary waves, with a phase velocity slightly larger than the Taylor-Culick velocity. Surface oscillations are also observed when the filament reaches its final spherical shape; the corresponding period agrees well with predictions of the linear theory. At intermediate Oh and large A, the tip velocity reaches a value close to the Taylor-Culick prediction. However, for smaller aspect ratios, the maximum tip velocity is much smaller than this prediction, and does not exhibit any oscillation. The recoil dynamics is qualitatively and quantitatively different at high Oh. In this case, the radius of the filament grows uniformly over time and no blob forms, making the tip velocity decrease after a short transient. A self-similar solution is found to closely match the numerical results in this regime.

Bendway Weir Riprap Sizing Criteria

AbstractBendway weirs are submerged, in-stream rock structures that redirect impinging flow away from outer-banks toward the center of a channel. Riprap weirs are composed of stone and sized using the average channel velocity in conjunction with existing design guidance. A physical model study and field study were conducted to determine the magnitude of the convective velocity that accelerates around the tip or toe of the weir. The ratio of the maximum tip velocity to the average channel velocity (prior to weir installation) was determined to be approximately 1.70. Stone sizing criteria that significantly increase the riprap median size over traditional approaches were presented for consideration.

Turbulent drag reduction through oscillating discs

AbstractThe changes in a turbulent channel flow subjected to sinusoidal oscillations of wall flush-mounted rigid discs are studied by means of direct numerical simulations (DNS). The Reynolds number is ${Re}_{\tau }=180$, based on the friction velocity of the stationary-wall case and the half-channel height. The primary effect of the wall forcing is the sustained reduction of wall-shear stress, which reaches a maximum of 20 %. A parametric study on the disc diameter, maximum tip velocity, and oscillation period is presented, with the aim of identifying the optimal parameters which guarantee maximum drag reduction and maximum net energy saving, the latter computed by taking into account the power spent to actuate the discs. This may be positive and reaches 6 %. The Rosenblat viscous pump flow, namely the laminar flow induced by sinusoidal in-plane oscillations of an infinite disc beneath a quiescent fluid, is used to predict accurately the power spent for disc motion in the fully developed turbulent channel flow case and to estimate localized and transient regions over the disc surface subjected to the turbulent regenerative braking effect, for which the wall turbulence exerts work on the discs. The Fukagata–Iwamoto–Kasagi identity is employed effectively to show that the wall-friction reduction is due to two distinguished effects. One effect is linked to the direct shearing action of the near-wall oscillating-disc boundary layer on the wall turbulence, which causes the attenuation of the turbulent Reynolds stresses. The other effect is due to the additional disc-flow Reynolds stresses produced by the streamwise-elongated structures which form between discs and modulate slowly in time. The contribution to drag reduction due to turbulent Reynolds stress attenuation depends on the penetration thickness of the disc-flow boundary layer, while the contribution due to the elongated structures scales linearly with a simple function of the maximum tip velocity and oscillation period for the largest disc diameter tested, a result suggested by the Rosenblat flow solution. A brief discussion on the future applicability of the oscillating-disc technique is also presented.

A study of the influence of initial liquid volume on the capillary flow in an interior corner under microgravity

In this work the influence of initial liquid volume on the capillary flow in an interior corner is studied systematically by microgravity experiments using the drop tower, under three different conditions: the Concus–Finn condition is satisfied, close to and dissatisfied. The capillary flow is studied by discussing the movement of tip of the meniscus in the corner. Experimental results show that with the increase of initial liquid volume the tip location increases for a given microgravity time, the achievable maximum tip velocity increases and the flow reaches its maximum tip velocity earlier. However, the results for the three different conditions show some difference.