Initial Velocity Effect on Acceleration Fall of a Spherical Particle through Still Fluid

A spherical particle’s acceleration fall through still fluid was investigated analytically and experimentally using the Basset-Boussinesq-Oseen equation. The relationship between drag coefficient and Reynolds number was studied, and various parameters in the drag coefficient equation were obtained with respect to the small, medium, and large Reynolds number zones. Next, some equations were used to derive the finite fall time and distance equations in terms of certain assumptions. A simple experiment was conducted to measure the fall time and distance for a spherical particle falling through still water. Sets of experimental data were used to validate the relationship between fall velocity, time, and distance. Finally, the initial velocity effect on the total fall time and distance was discussed with different terminal Reynolds numbers, and it was determined that the initial velocity plays a more important role in the falling motion for small terminal Reynolds numbers than for large terminal Reynolds number scenarios

Comparisons of Local Scouring for Submerged Square and Circular Cross-Section Piles in Steady Currents

The local scouring that occurs around submerged vertical piles in steady currents was studied experimentally in this paper. Three experiments were carried out for square cross-section (SC) piles and a circular cross-section (CC) pile with the same width. The key point scour depths, including the center of the upstream boundary point (KC) and the two upstream corners (KM), were observed over time. The two-dimensional profiles and the three-dimensional topography around each pile were measured using a Seatek. The different scouring characteristics of the SC and CC piles were investigated. The experiment results show that the scour depth at KC is much smaller than that of KM. The equilibrium scour depth of the CC pile is far less than that of the SC piles. The scour and deposition distributions were different between the CC and SC piles. The maximum scour depth was found at the lateral rear of the CC pile, and the maximum deposition was observed in sections of the SC piles. The evolutions of the scour depths at KM are predicted using a developed exponential equation

Modeling the formation and migration of sand waves: The role of tidal forcing, sediment size and bed slope effects

Tidal sand waves are rhythmic bedforms existing widely in shallow shelf seas and are formed by the interaction of tidal currents and topography. Using a process-based numerical model, Delft3D, the wave lengths and migration rates of sand waves were simulated and verified with field measurements. The physical mechanism that controls the evolution of sand waves was mainly the balance between bedload transport, suspended load transport and the slope effect. It was found that the bedload transport multiplier, which reflects the bed slope effect, was a key parameter to reproduce the observed sand wave dynamics accurately. If the bedload transport multiplier is tuned with the actual grain size, it fits the observations on wavelength of sand wave much better. Both the migration rates and wavelengths were better predicted by the process-based numerical Delft3D model compared to a linear stability analysis sand wave model, since the former adopted sophisticated process formulations necessary for accurate field predictions. Next, sand wave formation and evolution under different environment settings, including tidal forcing and sediment sizes, were examined systematically. It was found that the preferred wavelength (L FGM, fastest growing mode) of the sand wave increased with increasing tidal current magnitudes and decreasing sand diameters. Sand waves were only formed within a certain range and combination of tidal current magnitude and sand diameters. Downstream- and upstream-migration of sand waves were predicted by considering residual currents or tidal constituent of higher harmonics

Experimental and Numerical Studies on Local Scour around Closely Spaced Circular Piles under the Action of Steady Current

Scour at coastal structures is a serious problem that causes damage to structures. Focusing on scour around typical gravity-type breakwaters, previous studies have revealed that scour is mainly caused by standing waves in the front of structures. For breakwaters, which consist of closely spaced circular piles, scour caused by flow may occupy a dominant position. In the present work, the scour caused by a small velocity intensity flow was studied using both experimental and numerical models. The experiments revealed that the scour depth around closely spaced circular piles was significantly larger than that of a single pile with the same diameter. The numerical model was verified by theoretical values of flow field and experimental values of scour topography. More detailed flow field information is described using a numerical model that can improve the understanding of scour mechanics. Both experimental and numerical models demonstrate that scour first occurs on the side of piles owing to the shrinkage effect of streamlining and then extends forward and backward. In addition, the scour mechanics change with the increase of the pile spacing

Numerical study of wave transmission over double submerged breakwaters using non-hydrostatic wave model

In the present work, a non-hydrostatic wave model SWASH (an acronym of Simulating WAves till SHore) is used to simulate the wave transmission over double trapezoidal submerged breakwaters. The numerical results were compared with the results of the physical model. The comparison indicated the capability of SWASH model to predict the wave transmission over double submerged breakwaters. Influencing factors such as breakwater spacing S/L0, where L0 is the deep-water wavelength, and current were investigated in detail. Moreover, the effects of current on wave transmission were also analyzed. When the relative submerged depth R/H, where R is the submerged depth and H is the wave height, remains at 1.0, the appropriate relative breakwater spacing S/L0 is about 1.11. Current has no obvious effect on the appropriate S/L0, but it will change the shape of wave spectrum. Dissipation of super harmonic wave components is more obvious than that of lower harmonic wave components

Experimental and Numerical Studies on Local Scour around Closely Spaced Circular Piles under the Action of Steady Current

Scour at coastal structures is a serious problem that causes damage to structures. Focusing on scour around typical gravity-type breakwaters, previous studies have revealed that scour is mainly caused by standing waves in the front of structures. For breakwaters, which consist of closely spaced circular piles, scour caused by flow may occupy a dominant position. In the present work, the scour caused by a small velocity intensity flow was studied using both experimental and numerical models. The experiments revealed that the scour depth around closely spaced circular piles was significantly larger than that of a single pile with the same diameter. The numerical model was verified by theoretical values of flow field and experimental values of scour topography. More detailed flow field information is described using a numerical model that can improve the understanding of scour mechanics. Both experimental and numerical models demonstrate that scour first occurs on the side of piles owing to the shrinkage effect of streamlining and then extends forward and backward. In addition, the scour mechanics change with the increase of the pile spacing

Scour at a Submerged Square Pile in Various Flow Depths under Steady Flow

Local scour around submerged piles in currents are common in coastal and offshore engineering. This paper studies the influences of the submergence ratio (flow depth to pile height) on local scour around a square pile in steady flow. Submergence ratio ranging from 1–4, as well as two unsubmerged tests, were tested with a 10 × 10 square pile of 20 cm height. The three-dimensional profiles were measured to study the scour and deposition characteristics. Results show that the maximum scour depth was always at the upstream corner points rather than at the symmetry center point of the pile. The temporal maximum scour depth achieved its equilibrium sate in less than 4 h for each test. The equilibrium scour depths at the upstream corner points were independent of the submergence ratio when the latter was larger than 1.5. These findings give meaningful reference to the numerical simulations and local scour depth protections in the submerged pile cases deeper than which the flow depth does not affect the equilibrium scour depth