Cavity Formation during Asymmetric Water Entry of Rigid Bodies

This work numerically evaluates the role of advancing velocity on the water entry of rigid wedges, highlighting its influence on the development of underpressure at the fluid–structure interface, which can eventually lead to fluid detachment or cavity formation, depending on the geometry. A coupled FEM–SPH numerical model is implemented within LS-DYNA, and three types of asymmetric impacts are treated: (I) symmetric wedges with horizontal velocity component, (II) asymmetric wedges with a pure vertical velocity component, and (III) asymmetric wedges with a horizontal velocity component. Particular attention is given to the evolution of the pressure at the fluid–structure interface and the onset of fluid detachment at the wedge tip and their effect on the rigid body dynamics. Results concerning the tilting moment generated during the water entry are presented, varying entry depth, asymmetry, and entry velocity. The presented results are important for the evaluation of the stability of the body during asymmetric slamming events.

Magnetohydrodynamic convective flow of nanofluid in double lid-driven cavities under slip conditions

In this paper, we introduced a numerical analysis for the effect of a magnetic field on the mixed convection and heat transfer inside a two-sided lid-driven cavity with convective boundary conditions on its adjacent walls under the effects of the presence of thermal dispersion and partial slip. A single-phase model in which the water is the base fluid and a copper is nanoparticles is assumed to represent the nanofluid. The bottom and top walls of the cavity move in the horizontal direction with constant speed, while the vertical walls of the cavity are stationary. The right wall is mentioned at relatively low temperature and the top wall is thermally insulated. Convective boundary conditions are imposed to the left and bottom walls of the cavity and the thermal dispersion effects are considered. The finite volume method is used to solve the governing equations and comparisons with previously published results are performed. It is observed that the increase in the Hartmann number causes that the shear friction near the moving walls is enhanced and consequently the horizontal velocity component decreases.

The problem of the flow of fluid to an imperfect drill hole

This article studies seepage flows arising from the selection of hydrocarbons from imperfect drill-holes. The authors observe the problem of pressure field in a homogeneous isolated isotropic homogeneous reservoir perforated in the range, completely contained in the layer of a common width.<br> To construct an analytical asymptotic solution, the single-layer initial problem is replaced by an equivalent three-layer symmetric, including the piezoconductivity equations for the perforated, covering, and underlying non-perforated layers, the initial and boundary conditions; on the conditional boundary of the perforated and non-perforated layers, the conditions of pressure and flow equality are specified (conjugation conditions). The solution of the problem is assumed to be regular&nbsp;— the value of the desired function, and, if necessary, its derivative at infinity is zero.<br> The problem is formulated in dimensionless quantities for the functions of the pressure deviation from its unperturbed distribution, normalized to the amplitude value of the depression. To solve the problem, the authors have developed an asymptotic method of a formal parameter. The solution of the problems for the zero and first coefficients of the asymptotic expansion is found in the space of the Laplace&nbsp;— Carson images in the variable <i>t</i>.<br> Based on the formulas obtained and the Darcy law, the authors construct graphical depen­dencies for the vertical and horizontal components of the fluid velocity filtered from the periphery to the well.<br> The computational experiment illustrates that there are no vertical flows at the exit to the well in the perforated part of the reservoir, and when removed from the well, these flows are different from zero, which indicates the presence of interlayer flows even in homogeneous imperfect drill holes. In the center of the perforated layer, such flows are absent, since the transverse velocity component vanishes. At the same time, the inflow in an imperfect drill hole is uneven, and the maximum modulus of the horizontal velocity component on all curves is reached at the boundary of the perforation interval.

Comparison of Driving Rain Index Calculated According to EN 15927-3 to the CFD Simulation and Experimental Measurement

Wind-driven rain or driving rain is a rain which has given a horizontal velocity component by the wind. It can be the important moisture source for building façades and has been of the great concern in building science. In this article, the normative method described in STN EN ISO 15927-3:2009, was used for calculation of driving rain impact on vertical surfaces. This amount of rain was compared to the CFD simulation for selected location and to the experimental measurement carried out by wind-driven rain gauge.

Viscous Flows Driven by Uniform Shear over a Porous Stretching Sheet in the Presence of Suction/Blowing

An analysis is carried out to study the steady two-dimensional flow of an incompressible viscous fluid past a porous deformable sheet, which is stretched in its own plane with a velocity proportional to the distance from the fixed point subject to uniform suction or blowing. A uniform shear flow of strain rate β is considered over the stretching sheet. The analysis of the result obtained shows that the magnitude of the wall shear stress increases with the increase of suction velocity and decreases with the increase of blowing velocity and this effect is more pronounced for suction than blowing. It is seen that the horizontal velocity component (at a fixed streamwise position along the plate) increases with the increase in the ratio of shear rate β and stretching rate (c) (i.e., β/c) and there is an indication of flow reversal. It is also observed that this flow reversal region increases with the increase in β/c.

A three-dimensional ice-sheet flow solution

An accurate three-dimensional reduced model (shallow-ice approximation) flow with velocity depending on all three spatial coordinates is constructed for the commonly adopted isotropic viscous law with temperature-dependent rate factor. The solution is for steady flow with a prescribed temperature distribution, but can be extended to flow with a coupled energy balance, and to unsteady flow. The accuracy hinges on the reduction to a two-point ordinary differential equation problem for the surface profile, on an unknown span, for which established accurate numerical methods are available. This is achieved by setting one horizontal velocity component in elliptic cylindrical coordinates to zero, but the other two components depend on all three spatial variables. While not of direct physical interest, such an ‘exact’ solution is valuable as a test solution for the large-scale numerical codes commonly used in ice-sheet modelling, which have not yet been subjected to such a comparison.

Turbulent boundary layer under a solitary wave

The boundary layer generated by the propagation of a solitary wave is investigated by means of direct numerical simulations of continuity and Navier–Stokes equations. The obtained results show that, for small wave amplitudes, the flow regime is laminar. Turbulence appears when the wave amplitude becomes larger than a critical value which depends on the ratio between the boundary-layer thickness and the water depth. Moreover, turbulence is generated only during the decelerating phase, or conversely, turbulence is present only behind the wave crest. Even though the horizontal velocity component far from the bed always moves in the direction of wave propagation, the fluid particle velocity near the bottom reverses direction as the irrotational velocity decelerates. The strength and length of time of flow reversal are affected by turbulence appearance. Also the bed shear stress feels the effects of turbulence presence.

Camassa–Holm, Korteweg–de Vries and related models for water waves

In this paper we first describe the current method for obtaining the Camassa–Holm equation in the context of water waves; this requires a detour via the Green–Naghdi model equations, although the important connection with classical (Korteweg–de Vries) results is included. The assumptions underlying this derivation are described and their roles analysed. (The critical assumptions are, (i) the simplified structure through the depth of the water leading to the Green–Naghdi equations, and, (ii) the choice of submanifold in the Hamiltonian representation of the Green–Naghdi equations. The first of these turns out to be unimportant because the Green–Naghdi equations can be obtained directly from the full equations, if quantities averaged over the depth are considered. However, starting from the Green–Naghdi equations precludes, from the outset, any role for the variation of the flow properties with depth; we shall show that this variation is significant. The second assumption is inconsistent with the governing equations.)Returning to the full equations for the water-wave problem, we retain both parameters (amplitude, ε, and shallowness, δ) and then seek a solution as an asymptotic expansion valid for, ε → 0, δ → 0, independently. Retaining terms O(ε), O(δ2) and O(εδ2), the resulting equation for the horizontal velocity component, evaluated at a specific depth, is a Camassa–Holm equation. Some properties of this equation, and how these relate to the surface wave, are described; the role of this special depth is discussed. The validity of the equation is also addressed; it is shown that the Camassa–Holm equation may not be uniformly valid: on suitably short length scales (measured by δ) other terms become important (resulting in a higher-order Korteweg–de Vries equation, for example). Finally, we indicate how our derivation can be extended to other scenarios; in particular, as an example, we produce a two-dimensional Camassa–Holm equation for water waves.

Spray deposition within plant canopies

Spray deposition was measured within canopies of bracken fern (Pteridium aquilinum) and greenleaf manzanita (Arctostaphylos patula) following ground application of a spray mixture containing water a fluorescent tracer and surfactant A high proportion of spray (3538) reached the ground through manzanita canopies whereas only 113 reached the ground through a bracken canopy Spray deposition was closely linked to the quantity of foliage projected on a plane normal to the trajectory of droplets passing through the canopy Droplets that had trajectories with a significant horizontal velocity component were more effectively captured because of an increase in the quantity of foliage in their path

Wave-induced boundary layer flows above and in a permeable bed

In this paper, the oscillatory and steady streaming velocities over a permeable bed are studied both theoretically and experimentally. Three different sizes of glass beads are used to construct permeable beds in laboratory experiments: the diameters of the glass beads are 0.5 mm, 1.5 mm, and 3.0 mm, respectively. Several experiments are performed using different wave parameters. A one-component laser-doppler velocimeter (LDV) is used to measure the horizontal velocity component inside the Stokes boundary layer above the solid and permeable surfaces. It is observed that neither oscillatory nor steady velocity components vanish on the permeable surface. The ‘slip velocities’ increase with increasing permeability. Based on the laminar flow assumption and the order of magnitude of the parameters used in the experiments, a perturbation theory is developed for the oscillatory velocity and the steady wave-induced streaming in the boundary layers above and inside the permeable bed. The theory confirms many experimental observations. The theory also provides the damping rate and the phase changes caused by the permeable bed.