Similitude of Large-Scale Turbulence in Experiments on Local Scour at Cylinders

The writers’ experiments on local scour at vertical cylinders placed in a sand bed show that similitude of large-scale turbulence is an important consideration influencing equilibrium depth of local scour. For the range of cylinder diameters used in their experiments, the writers identify a direct trend between equilibrium scour depth (normalized with cylinder diameter) and the intensity and frequency of large-scale turbulence shed from each cylinder; values of normalized scour depth increased when cylinder diameter decreased. The writers offer a scour-depth adjustment factor to account for this trend, which essentially is a scale effect incurred with experiments involving three independent length scales: cylinder diameter, bed-particle diameter, and flow depth. The consequent similitude consideration, or scale effect, has general significance for laboratory studies of local scour associated with hydraulic structures in sediment beds.     

Turbulent Flow through Idealized Emergent Vegetation

This paper presents results of several large-eddy simulations (LES) of turbulent flow in an open channel through staggered arrays of rigid, emergent cylinders, which can be regarded as idealized vegetation. In this study, two cylinder Reynolds numbers, RD = 1,340 and RD = 500, and three vegetation densities are considered. The LES of the lowest density and at RD = 1,340 corresponds to a recently completed laboratory experiment, the data of which is used to validate the simulations. Fairly good agreement between calculated and measured first- and second-order statistics along measurement profiles is found, confirming the accuracy of the simulations. The high resolution of the simulations enables an explicit calculation of drag forces, decomposed into pressure and friction drag, that are exerted on the cylinders. The effect of the cylinder Reynolds number and the cylinder density on the drag and hence on the flow resistance is quantified and in agreement with previous experimental studies. Turbulence structures are visualized through instantaneous pressure fluctuations, isosurfaces of the Q-criterion and contours of vertical vorticity in horizontal planes. Analysis of velocity time signals and distributions of drag and lift forces over time reveals that flow and turbulence are more influenced by the vegetation density than by the cylinder Reynolds number.     

Effects of Time and Channel Geometry on Scour at Bridge Abutments

Experiments are described to investigate local scour at bridge abutments. The experiments were performed in a two-stage channel using abutments that extended different distances onto the floodplain including right up to the edge of the main channel (Melville, Type III). To ensure the largest scour depths the conditions on the floodplain upstream of the abutment were close to critical conditions for the bed material. The time evolution of the scour and the ultimate scour depth were measured. The time development of the local scour corresponded well with the theories of Ettema and Franzetti and the theory of Whitehouse for scour at horizontal cylinders in the marine environment. Melville has suggested that scour at abutments on floodplains can be approximated by scour in rectangular channels if an imaginary boundary is assumed, separating the flow in the main channel from that on the floodplain. The experimental results confirm the validity of Melville's suggestion for the configurations tested in the experiments.     

Scour at Submerged Cylindrical Obstacles under Steady Flow

Results of an experimental study on clear-water scour at submerged cylindrical obstacles (circular cylinders) in uniform bed sediments under steady flow are presented. The scour depths at submerged circular cylinders are compared with the scour depths at corresponding unsubmerged cylinders (extended above the free surface of flow) of the same diameters under similar flow and bed sediment conditions. The scour depth decreases with an increase in submergence ratio. A submergence factor is introduced to determine the scour depth at a submerged cylinder from the information of the scour depth at an unsubmerged cylinder of the same diameter. In addition, the flow fields along the upstream vertical plane of symmetry of unsubmerged and submerged cylinders are presented through vector plots, which reveal that the dimension and strength of the horseshoe vortex decreases with an increase in submergence ratio. The horseshoe vortex circulations, which decrease with an increase in submergence ratio, are computed from the vorticity contours by using the Stokes theorem.     

Terminal Velocity of Cylinders Rolling in Uniform Flows

Ordnance remediation projects suggest that understanding the motion of cylinders (the approximate shape of ordnance) in flows would help to predict regions of ordnance mobility, to prioritize remediation efforts, and to improve the design of engineering works to trap ordnance. In simplified experiments, the characteristics of motion of smooth, unrestrained cylinders in contact with a smooth horizontal bed were investigated in flume experiments with steady, uniform flows. Eight cylinders were tested with varying specific gravities and diameters. At low flows, the cylinders follow trends similar to those noted in sediment particle studies. Incipient motion velocities were highest for the heavier cylinders. At high flows, the terminal velocity of the cylinders was limited to 60–80% of the free-stream flow. Potential flow derivations imply a maximum velocity ratio of 71%. Use of potential flow theory was considered valid (as an estimator) based on previous studies of boundary-layer control that suggest the moving surface of the cylinder minimizes the wake downstream of the cylinder, and therefore only a thin boundary layer is present around the cylinder.     

Flow around Cylinders in Open Channels

This paper presents the results of an experimental study of flow around cylindrical objects in an open channel. Cylindrical objects of equal diameter and four heights were tested under similar flow conditions producing four different levels of submergence, including a surface piercing bridge-pier-like cylinder. Different flow elements and their locations were identified using a set of flow visualization tests. Observations made from the flow visualization tests were then verified by measurements of bed-shear stress and deflected flow velocity around the cylinders. Horse-shoe vortex systems were found to appear closer to the submerged cylinders compared to a surface piercing cylinder. The increase in dimensionless bed-shear stress is found to be inversely related to the level of submergence of the cylinders. Bed-shear stress results presented in this paper will be valuable for a qualitative understanding of the scour potential of flow around submerged cylinders. Mean velocity profiles in the deflected flow region were analyzed in terms of the theories of three-dimensional turbulent boundary layer. Submergence of a cylinder has been found to suppress alternate vortex shedding and produce stronger three-dimensional flows in the downstream wake. Perry and Joubert’s model was found to be sufficiently accurate to predict the deflected velocity magnitudes around submerged cylinders. Overall, the present study will provide valuable knowledge of hydraulics of flow around submerged structures (e.g., simple fish habitat structures).     

Theoretical Solution of Dam-Break Shock Wave

A mathematical model of dam-break shock waves, or flood waves, in channels of trapezoidal cross section is presented. When the model is applied to channels of rectangular cross section, a new theoretical solution expressed using one independent multinominal algebraic equation is derived. In the past, the solution had to be described using three interrelated equations. The new equation indicates that the hydraulic parameters of a shock wave—such as depth and velocity of flow, and velocity of discontinuity—are determined only by the ratio of initial downstream depth to initial upstream depth. The model shows that results from the new equation are completely equivalent to those of the set of old equations. In addition, the flood hydrograph produced by a dam break at any time or any site can be described by a single curve in terms of dimensionless variables.     

Use of Brink Depth in Discharge Measurement

The behavior of free surface flow at a rectangular free overfall is studied experimentally to obtain a relation between the brink depth and the flow rate. A series of experiments were conducted in a tilting flume with wide range of flow rates covering subcritical, critical, supercritical regimes, and two different roughnesses in order to develop a relationship between the discharge and the brink depth. An equation is proposed to determine the flow rate using the brink depth for a channel of known roughness and bed slope.     

Modeling Study of Free Overfall in a Rectangular Channel with Strip Roughness

Results from combined laboratory experimental and turbulent numerical modeling studies are presented to investigate the effects of bed roughness (discrete square strips) and slope on the flow over a free overfall in a rectangular channel. A broad range of model parameters such as the bed roughness, channel slope, and incoming upstream Froude number is investigated. The water surface profiles upstream of the brink of the channel, the velocity fields in cavity between two strips, and end depth (water depth at the brink of the channel) are simulated, measured, and discussed for various input conditions. The results show that for a given dimension of bed roughness the relative spacing of roughness (defined as the ratio of the center to center distance to the height of the strip) has a significant effect on the flow. The computational results are in good agreement with the experimental measurements.     

Turbulent Bed Shear Stress under Symmetric and Asymmetric Waves: Experimental and Numerical Results

A new instrument built to directly measure the bottom shear stress under different conditions of periodic waves is presented. Similar to classical Taylor’s cylindrical viscosimeter, the instrument is formed by two concentric cylinders, and the space between them is filled with water. The internal cylinder is fixed whereas the external cylinder, with a specific roughness, rotates following a given unsteady velocity time history. The shear stress at the outer cylinder wall is measured by using a torque meter. Both monochromatic and sawtooth-shaped waves have been tested, and the experimental shear stress time histories were compared with the results obtained from a numerical model.     

Scour around Pile in Combined Waves and Current

This paper presents the results of an experimental study on scour around a pile subject to combined waves and current. Irregular waves were used in the experiments, which were carried out both for codirectional waves and for waves propagating perpendicular to the current. The measured scour depth is plotted as a function of Ucw = Uc/(Uc + Um) for various values of the Keulegan-Carpenter number KC in which Uc is the undisturbed current velocity and Um is the maximum value of the undisturbed orbital velocity at the sea bottom. In the experiments, KC ranges from 5 to about 30 and Ucw from 0 to 1. The results show that the scour depth increases with increasing current component of the flow. The scour depth attains its steady-current value for Ucw > 0.7.     

Influence of Wood Debris Accumulation on Bridge Pier Scour

This note deals with the influence of debris accumulation on scour around bridge piers. Clear-water experiments in different hydraulic conditions have been carried out with three wood debris shapes: rectangular, triangular, and cylindrical. A wide range of debris thickness and width were studied in order to determine their influence on the maximum scour hole depth temporal evolution. The ratio of the pier diameter to the channel width was varied between 0.05 and 0.12 with total bridge contractions up to 20%. A proposed relation presents a simple design procedure to predict the increase in scour depth, which mainly depends on the flow contraction due to the debris accumulation.     

Effect of Shape on Incipient Motion of Large Solitary Particles

The aim of this study is to investigate the effect of shape and size of solid particles on their initiation of motion in open channel flows. Initial motions of 22 solitary particles having different shapes and sizes were observed in a tilting flume of rectangular cross section. A smooth fixed bed and an obstructing element of smaller height with respect to the particle size was used throughout the experiments. The ratio of the height of the obstructing element to the height of the particle was kept constant at 1/5. By either changing the slope of the tilting flume or the discharge, or both, a range of shear stress values was obtained. Various equations and graphical representations in terms of dimensionless bed shear stress, grain Reynolds number, and the ratio of flow depth to grain diameter were presented to determine the flow conditions corresponding to the initiation of motion of solitary particles of given shapes. The experiments have revealed that critical flow conditions are dependent not only on the particle size and shape but also on the ratio of flow depth to grain diameter.     

Ice Boom Simulations and Experiments

A three-dimensional discrete element model (DEM) was developed to simulate ice boom operation in a rectangular channel. The model simulates the motion of each individual ice floe, the interaction between adjacent floes, the interaction of the floes with the walls and boom, and the water drag applied to the floes on the underside of the ice accumulation. The DEM simulations were compared with a parallel set of physical model tests using natural ice. The DEM successfully reproduced the observed magnitude and distribution of the forces on the boom and the channel sides as the boom retained a surge of drifting ice. Variations in channel side roughness produced similar changes in the division of forces between the boom and sidewalls in the simulations and model tests. Finally, the load distribution between the boom and the channel sides and the effect of channel side roughness in the context of granular ice-jam theory were analyzed.     

Hydraulic Jumps in an Inclined Rectangular Chute Contraction

Hydraulic jumps in an inclined rectangular chute contraction were studied in this paper. Theoretical equations for the sequent-area and sequent-depth ratios for hydraulic jumps in the contraction were developed considering the effects of contracting width and sloping bottom. The equation of the sequent-area ratio (instead of the sequent-depth ratio) has the same form as the traditional Belanger equation for the sequent-depth ratio for hydraulic jumps in a horizontal rectangular constant-width channel (HRCW channel). A modified approach Froude number M, including the effects of contracting width and sloping bottom, was introduced to replace the approach Froude number F1 in analyzing hydraulic jumps in the contraction. Laboratory experiments of hydraulic jumps in inclined contractions were also conducted to verify the theoretical sequent-area ratio and also to develop the empirical equations of the location of the start of the jump, flow depth of the start of the jump, length of the jump, and energy loss of the jump. The calculation procedure for the application of the presented equations is also provided in this paper.     

Modeling freckle formation in three dimensions during solidification of multicomponent alloys

The formation of macrosegregation defects known as “freckles” was simulated using a three-dimensional finite element model that calculates the thermosolutal convection and macrosegregation during the dendritic solidification of multicomponent alloys. A recently introduced algorithm was used to calculate the complicated solidification path of alloys of many components, which can accommodate liquidus temperatures that are general functions of liquid concentrations. The calculations are started from an all-liquid state, and the growth of the mushy zone is followed in time. Simulations of a Ni-Al-Ta-W alloy were performed on a rectangular cylinder until complete solidification. The results reveal details of the formation of freckles not previously observed in two-dimensional simulations. Liquid plumes in the form of chimney convection emanate from channels within the mushy zone, with similar qualitative features previously observed in transparent systems. Associated with the formation of channels, there is a complex three-dimensional flow produced by the interaction of the different solutal buoyancies of the alloy solutes. Regions of enhanced solid growth develop around the channel mouths, which are visualized as volcanoes on top of the mushy zone. The prediction of volcanoes differs from our previous calculations with multicomponent alloys in two dimensions, in which the volcanoes were not nearly as apparent. These and other features of freckle formation phenomena are illustrated.     

Flow-Establishment Length in Rectangular Channels and Ducts

Laboratory experiments related to open channel hydraulics are generally intended to be carried out in the fully developed flow region of a rectangular flume. The developing region, in channels as well as in ducts, is a complex three-dimensional flow region influenced by secondary circulation and free surface effects, and is therefore not amenable to analytical solution. Laboratory data and a numerical model have been used to study the variation of the length of flow establishment in rectangular channels.     

Flow Interaction of Meandering River with Floodplains

A series of laboratory test results are presented concerning the boundary shear stress, shear force, and discharge characteristics of compound meandering river sections composed of a rectangular main channel and one or two floodplains disposed off to its sides. Five dimensionless parameters are used to form equations representing the total shear force percentage carried by floodplains. A set of smooth and rough sections is studied with an aspect ratio varying from 2 to 5. Apparent shear forces on the assumed vertical, diagonal, and horizontal interface plains are found to be different from zero at low depths of flow and change sign with an increase in depth over the floodplain. A variable-inclined interface is proposed for which apparent shear force is calculated as zero. Equations are presented giving proportion of discharge carried by the main channel and floodplain. The equations agree well with experimental and river discharge data. Using the variable-inclined interface, the error between the measured and calculated discharges for the meandering compound sections is found to be the minimum when compared with that using other interfaces.     

Numerical Simulation and Cold Modeling experiments on Centrifugal Casting

In a centrifugal casting process, the fluid flow eventually determines the quality and characteristics of the final product. It is difficult to study the fluid behavior here because of the opaque nature of melt and mold. In the current investigation, numerical simulations of the flow field and visualization experiments on cold models have been carried out for a centrifugal casting system using horizontal molds and fluids of different viscosities to study the effect of different process variables on the flow pattern. The effects of the thickness of the cylindrical fluid annulus formed inside the mold and the effects of fluid viscosity, diameter, and rotational speed of the mold on the hollow fluid cylinder formation process have been investigated. The numerical simulation results are compared with corresponding data obtained from the cold modeling experiments. The influence of rotational speed in a real-life centrifugal casting system has also been studied using an aluminum-silicon alloy. Cylinders of different thicknesses are cast at different rotational speeds, and the flow patterns observed visually in the actual castings are found to be similar to those recorded in the corresponding cold modeling experiments. Reasonable agreement is observed between the results of numerical simulation and the results of cold modeling experiments with different fluids. The visualization study on the hollow cylinders produced in an actual centrifugal casting process also confirm the conclusions arrived at from the cold modeling experiments and numerical simulation in a qualitative sense.     

Shallow Water Wave Propagation in Convectively Accelerating Open-Channel Flow Induced by the Tailwater Effect

Propagation of shallow water waves in viscous open-channel flows that are convectively accelerating or decelerating under gradually varying water surface profiles is theoretically investigated. Issues related to the hydrodynamics of wave propagation in a rectangular open channel are studied: the effect of viscosity in terms of the Manning coefficient; the effect of gravity in terms of the Froude number; wave translation and attenuation characteristics; nonlinearity and wave shock; the role of tailwater in wave propagation; and free surface instability. A uniformly valid nonlinear solution to describe the unsteady gradually varying flow throughout the complete wave propagation domain at and away from the kinematic wave shock as well as near the downstream boundary that exhibits the tailwater effect is derived by employing the matched asymptotic method. Different scenarios of hydraulically spatially varying surface profiles such as M1, M2, and S1 type profiles are discussed. Results from the nonlinear wave analysis are further interpreted and the influence of the tailwater effect is identified. In addition to the nonlinear wave analysis, a linear stability analysis is introduced to quantify the impact from such water surface profiles on the free surface instability. It is shown that the asymptotic flow structure is composed of three distinct regions: an outer region that is driven by gravity and channel resistance; a near wave shock region dominated by the convective inertia, pressure gradient, gravity and channel resistance; and a downstream boundary impact region where the convective inertia, pressure gradient, gravity and channel resistance terms are of importance. The tailwater effect is demonstrated influential to the flow structure, free surface stability, wave transmission mechanism, and hydrostatic pressure gradient in flow.