Erosion of Sand by Circular Impinging Water Jets with Small Tailwater

This technical note presents the results of an experimental study of the erosion of loose cohesionless sand beds by impinging circular water jets with a minimum depth of tailwater. Measurements were made of both the maximum dynamic and static scour depths and the radius of the scour hole. It was found that the dynamic scour depth is about three times that of static scour at the asymptotic state. Dimensional arguments and experimental results are used to show that the main dimensions of the scour hole at the asymptotic state are a function of the densimetric Froude number F0′ = U0′/, where U0′ = velocity of the jet at the original level of the sand bed; g = acceleration due to gravity; D = mean diameter of the sand particles; ρ = density of the eroding fluid; and Δρ = difference between particle and fluid densities. Useful correlations have been developed to estimate the size of the scour holes. Also included is a comparison between the erosion caused by submerged and unsubmerged impinging circular jets.     

Erosion Function Apparatus for Scour Rate Predictions

Scour is the number one cause of bridge failures. Scour in coarse grained soils (sand, gravel) is relatively well known, but scour in fine grained soils (silt, clay) and weak rock is not. In coarse grained soils, scour takes place very rapidly and the scour rate is rarely an issue because one flood is likely to create the maximum scour depth. In fine grained soils, the scour process is much slower; as a result, even after a hundred years, a bridge may not experience the maximum depth of scour. Therefore, in fine grained soils it becomes necessary to predict the rate at which scour takes place. A new apparatus called the EFA (Erosion Function Apparatus; 〈http:∕/tti.tamu.edu∕geotech∕scour〉) has been built and tested to measure the erosion rate of fine grained soils; the EFA can also be used to measure the erosion rate of coarse grained soils if necessary. The end of a Shelby tube sample from the bridge site is fitted through a tight opening at the bottom of a pipe with a rectangular cross section. Water flows through the pipe and erodes the soil sample, which protrudes 1 mm above the bottom of the pipe. The rate at which the sample erodes is measured, and the shear stress imposed by the water on the soil is calculated. The plot of erosion rate versus shear stress is the result of an EFA test. It indicates the critical shear stress at which erosion starts and the rate of erosion beyond that shear stress. This function can be used to predict the rate of scour at a bridge.     

Effect of Jet Air Content on Plunge Pool Scour

The effect of air discharge on plunge pool scour was investigated by using a simplified experimental configuration. Instead of considering the complete arrangement involving chute and deflector resulting in an air-water jet impinging on a sediment surface, the mixture flow was produced with a circular pipe for which the air concentration and the jet diameter close to impact on the free water surface are known. The results of this study were primarily directed to the definition of a three-phase Froude number that accounts for the combined effects of an air-water mixture jet on scour. The analysis of data allows simple estimates of the scour geometry including a generalized scour profile, the width of scour, and the temporal advance of the extreme scour depths. It was pointed out that for a certain water velocity and selected grain characteristics, the addition of air to the jet results in an increase of scour depth. However, if the reference would be the air-water mixture velocity, scour depth decreases significantly by the addition of air to the jet.     

Influence of Cohesion on Scour under Submerged Circular Vertical Jets

The results of an experimental study on scour under submerged circular vertical jets of water in cohesionless and cohesive sediments are presented. The difference between scour patterns in cohesionless and cohesive sediments is identified. In cohesive sediments, the variations of maximum depth and volume of scour have been studied with respect to the percentage of clay content, dry density, antecedent moisture content, etc. Empirical relationships have been proposed for the maximum depth and volume of scour for both nonplastic and plastic cohesive sediments. The range of data for the applicability of the proposed relationships is specified.     

Non‐Circular Hydraulic Jump on a Moving Surface due to an Impinging Circular Free Surface Jet of Water

Liquid jet impingement has many industrial cooling applications such as metal manufacturing and steel cooling on run‐out tables (ROT). The development of the wetting front around the impingement point of a jet is central in jet impingement cooling. In this paper, the effects of moving target surface and jet Reynolds number on wetted zone and on the formation and location of hydraulic jump (HJ) are explored through a series of industrial‐scale experiments of an impinging circular free surface long water jet with high Reynolds number of 11 000–50 000 and industrial jet parameters. The moving test surface impacts the radial evolution of circular wetted zone in all directions and alter the circular HJ at the wetting front into a non‐circular contour that depends on the jet Re number. The limited relations in the literature do not represent these measured shapes and do not appropriately predict radii of HJ in industrial scale. A new correlation for radius of non‐circular HJ has been derived in this study that compared more accurately to the experimental data. Numerical simulations of radial impingement flow on moving surface were performed using a variant of k–ε turbulent model and results are compared to the experimental data. The computational results for the wetting front were found to be close to the experimental data indicating the appropriate performance of the turbulent model.     

Stochastic Flow Analysis for Predicting River Scour of Cohesive Soils

Damage to bridge crossings during flood events endangers the lives of the traveling public and causes costly disruptions to traffic flow. The most common causes of bridge collapse are scouring of the streambed and banks and erosion of highway embankments. This study couples a synthetic river flow simulation technique with a scour model for cohesive soils and determines the expected scour depth for a given lifetime of the bridge. A fractionally differenced autoregressive integrated moving average model generates synthetic streamflow sequences of the same length as the expected lifetime of the bridge. The scour model predicts the progression of scour depth through time in a multilayered soil. The model is used to determine the scour depth associated with different replicates of the synthetic flow sequences of the same length as the lifetime of the bridge. The probability distribution of scour depth is estimated by repeating this simulation procedure over a number of independent realizations of streamflow series for a given life of the bridge. This approach provides a framework for the probabilistic design and risk analysis of bridge foundations subjected to scour.     

Hydraulics of Submerged Jet Subject to Change in Cohesive Bed Geometry

The results of an experimental investigation of the time variation of scour hole and the flow characteristics of the quasi-equilibrium state of scour of a cohesive bed downstream of an apron due to a submerged horizontal jet issuing from a sluice opening are presented. Experiments were carried out with natural cohesive sediment for various sluice openings, jet velocities, and lengths of apron. Attempts are made to explain the similarity existing either in the process of scour or in the scour profiles that the scour holes follow downstream of an apron. The scour profiles at different times follow a particular geometrical similarity and can be expressed by a polynomial using relevant parameters. The characteristic parameters affecting the time variation of scour depth are identified based on the physical reasoning and dimensional analysis. An equation for time variation of maximum scour depth is obtained empirically. The diffusion characteristics of the submerged jet, growth of boundary layer thickness, velocity distribution within the boundary layer, and shear stress at the quasi-equilibrium state of scour are also investigated. The expression of shear stress is obtained from the solution of the von Kármán momentum integral equation.     

Two-Dimensional Scour Hole Problem: Role of Fluid Structures

An experimental program was carried out to understand scour caused by a plane wall jet. A two-dimensional laser Doppler anemometer was used to characterize the velocity field at various locations in the scour hole region. Observations indicate that different types of flow structures influence scour at different time periods. Based on the present tests, the entire test duration is divided into five time zones. Following vigorous scour caused principally by jet shear forces and impingement at the start of the test and during early time periods, the flow was characterized by the presence of longitudinal axial vortices, turbulent bursts, and movement of the jet impingement point during the later stages. Attempts were made to distinguish the fluid structures at asymptotic conditions. The scour hole region was characterized by the presence of randomly forming and disappearing streaks, laterally located concave shaped depressions, rolling and ejection of the bed material. Through analysis of higher order moments and quadrant decomposition, sweep and ejection type events were observed, which can potentially contribute to scour.     

Bridge Pier Scour in Clay-Sand Mixed Sediments at Near-Threshold Velocity for Sand

Local scour at circular bridge piers embedded in a clay-sand-mixed bed was investigated in laboratory flume experiments. The effects of clay content, water content, and sand size on maximum equilibrium scour depth, equilibrium scour hole geometry, scouring process, and time variation of scour were studied at velocities close to the threshold velocities for the sand in the clay-sand mixture. It was observed that clay content and water content were the key parameters that effect the scouring process, scour hole geometry, and maximum equilibrium scour depth. The bridge pier scouring process in clay-sand mixtures involved different dominating modes for removal of sediment from scour hole: chunks-of-aggregates, aggregate-by-aggregate, and particle-by-particle. Regression-based equations for estimation of nondimensional maximum scour depth and scour hole diameter for piers embedded in clay-sand mixtures having clay content of <40% and water content of <40% were proposed as functions of pier Froude number, clay content, water content, and bed shear strength.     

Experimental Parametric Study of Suffusion and Backward Erosion

Within hydraulic earth structures (dikes, levees, or dams), internal seepage flows can generate the entrainment of the soil grains. Grain transportation affects both particle size distributions and porosity, and changes the mechanical and hydraulic characteristics of the earth’s structure. The occurrence of failures in new earth structures due to internal erosion demonstrates the urgency of improving our knowledge of these phenomena of erosion. With this intention, a new experimental device has been developed that can apply hydraulic stresses to reconstituted consolidated cohesive soils without cracks in order to characterize the erosion evolution processes that might be present. A parametric study was conducted to examine the influence of three critical parameters on clay and sand erosion mechanisms. When the hydraulic gradient was low, it was concluded that the erosion of the structure’s clay fraction was due to suffusion. When the hydraulic gradient increased, it was concluded that the sand fraction erosion initiation was due to backward erosion. The extent of the erosion was dependent on the clay content. The study underlines the complexity of confinement stress effects on both erosion phenomena.     

Simulation of Scour Process in Plunging Pool of Loose Bed-Material

The scouring process in a plunge pool of loose bed with uniform bed-materials due to a two-dimensional plane impinging jet was simulated computationally. The finite-element-based unsteady three-dimensional model, CCHE3D, with k-ε turbulence closure was employed to solve the flow field. It has long been recognized that the unsteady behavior of the turbulent jet fluctuation plays an important role in scouring and transporting sediment in the plunge pool. In order to model this phenomenon realistically, one has to consider the effects of both shear stress and the life force on sediment particles due to pressure fluctuation. The latter has been taken into account by using empirical relationships of flume data. Both of these effects have been incorporated in the nonequilibrium sediment transport model consisting of sediment pickup rate and step length adopted for the jet scour problem. The model constant relating to the fluctuating lift force was calibrated using an empirical equation to predict the quasi-equilibrium scour depth. The results simulated by the model proposed here agree reasonably well with experimental data.     

Threshold Shear Strain for Cyclic Pore-Water Pressure in Cohesive Soils

Threshold shear strain for cyclic pore-water pressure, γt, is a fundamental property of fully saturated soils subjected to undrained cyclic loading. At cyclic shear strain amplitude, γc, larger than γt residual cyclic pore-water pressure changes rapidly with the number of cycles, N, while at γc<γt such changes are negligible even at large N. To augment limited experimental data base of γt in cohesive soils, five values of γt for two elastic silts and a clay were determined in five special cyclic Norwegian Geotechnical Institute (NGI)-type direct simple shear (NGI-DSS), constant volume equivalent undrained tests. Threshold γt was also tested on one sand, with the results comparing favorably to published data. The test results confirm that γt in cohesive soils is larger than in cohesionless soils and that it generally increases with the soil’s plasticity index (PI). For the silts and clay having PI=14–30, γt = 0.024–0.06% was obtained. Limited data suggest that γt in plastic silts and clays practically does not depend on the confining stress. The concept of evaluating pore water pressures from the NGI-DSS constant volume test and related state of stresses are discussed.     

Computing the Trajectory of Free Jets

In recent years, design floods have increased beyond spillway capacity at numerous large dams. When additional spillway capacity is difficult or expensive to develop, designers may consider allowing the overtopping of a dam during extreme events. For concrete arch dams, this often raises issues of potential erosion and scour downstream from the dam, where the free jet initiating at the dam crest impacts the abutments and the downstream river channel. A recent review has shown that a commonly cited equation for predicting the trajectory of free jets is flawed, producing jet trajectories that are much too flat in this application. This could lead analysts to underestimate the amount of scour that could occur near a dam foundation, or conversely to overestimate the extent of scour protection required. This technical note presents the correct and incorrect jet trajectory equations, quantifies the errors associated with the flawed equation, and summarizes practical information needed to model the trajectory of free jets overtopping dam crests.     

The Penetration Behavior of an Annular Gas–Solid Jet Impinging on a Liquid Bath: Comparison with a Conventional Circular Jet

The top-blow injection technique of a gas–solid mixture through a circular lance is used in the Mitsubishi Continuous Smelting Process. One of the inherent problems associated with this injection is the severe erosion of the hearth refractory below the lances. A new configuration of the lance to form an annular gas–solid jet rather than a circular jet was designed in the laboratory scale. With this new configuration, solid particles leave the lance at a much lower velocity than the gas, and the penetration behavior of the jet is significantly different than with the circular lance in which the solid particles leave the lance at the same high velocity as the gas. The results of cold model tests using an air-sand jet issuing from a circular lance and an annular lance into a water bath showed that the penetration of the annular jet is much less sensitive to the variations in particle feed rate as well as gas velocity than that of the circular jet. Correlation equations for the penetration depth for both circular and annular jets show agreement among the experimentally obtained values.     

Flume Tests for Scour in Clay at Circular Piers

Local scour at circular piers founded on clay was studied experimentally in the laboratory to compare the depth of scour in sand and in clay and to investigate the effects of the Reynolds number, Froude number, and approach flow depth on scour depth. The depths of scour in front, at the side, and in the back of the piers were measured as a function of time under steady, gradually varied flow conditions. The measured scour-depth-versus-time curves were fitted with a hyperbola to estimate the equilibrium scour depths. The extrapolated equilibrium scour depths were compared with values predicted by the Federal Highway Administration equation. The results showed that although the rates of scour were much slower in clay than in sand, equilibrium scour in clay was about the same as in sand. It was found that the shape of the scour hole correlates with the pier Reynolds number. At low Reynolds numbers, the depth of scour was about the same all around the piers. At higher Reynolds numbers, the scour holes developed mainly behind the piers with much less scour in front of the piers. It was also found that the extrapolated equilibrium scour depth correlates well with the pier Reynolds number and that the Froude number and relative water depth did not have a significant effect on the scour depth for these experimental conditions.     

The Penetration Behavior of an Annular Gas–Solid Jet Impinging on a Liquid Bath: The Effects of the Density and Size of Solid Particles

Top-blow injection of a gas?Csolid jet through a circular lance is used in the Mitsubishi Continuous Smelting Process. One problem associated with this injection is the severe erosion of the hearth refractory below the lances. A new configuration of the lance to form an annular gas?Csolid jet rather than the circular jet was designed in this laboratory. With this new configuration, the solid particles fed through the center tube leave the lance at a much lower velocity than the gas, and the penetration behavior of the jet is significantly different from that with a circular lance where the solid particles leave the lance at the same high velocity as the gas. In previous cold-model investigations in this laboratory, the effects of the gas velocity, particle feed rate, lance height of the annular lance, and the cross-sectional area of the gas jet were studied and compared with the circular lance. This study examined the effect of the density and size of the solid particles on the penetration behavior of the annular gas?Csolid jet, which yielded some unexpected results. The variation in the penetration depth with the density of the solid particles at the same mass feed rate was opposite for the circular lance and the annular lance. In the case of the circular lance, the penetration depth became shallower as the density of the solid particles increased; on the contrary, for the annular lance, the penetration depth became deeper with the increasing density of particles. However, at the same volumetric feed rate of the particles, the density effect was small for the circular lance, but for the annular lance, the jets with higher density particles penetrated more deeply. The variation in the penetration depth with the particle diameter was also different for the circular and the annular lances. With the circular lance, the penetration depth became deeper as the particle size decreased for all the feed rates, but with the annular lance, the effect of the particle size was small. The overall results including the previous work indicated that the penetration behavior of an annular jet is much less sensitive to the variations in operating variables than that of a circular jet. Correlation equations for the penetration depth that show good agreements with the measured values have been developed.     

Erosion of Finite Thickness Sediment Beds by Single and Multiple Circular Jets

Sediment management in reservoirs with the help of water jets has motivated this work. Erosion caused by single and multiple submerged circular turbulent wall jets on a noncohesive sediment bed of finite thickness lying on a fixed boundary was studied with the help of laboratory experiments. Different combinations of jet diameter, jet separation, and sediment thickness to jet diameter ratio were tested. Results show a relation between dimensionless parameters characterizing the steady state bed profile and the densimetric particle Froude number F0 given by the velocity at the nozzle and the effective diameter and submerged specific density of the sediment. Evolution of scour with time confirms previous studies where the erosion was found to initially grow with the logarithm of time up to a certain reference time t*. This time, made dimensionless with a time scale tc involving the volume of sediment scoured and the rate of erosion, was also related to the densimetric Froude number. A comparison with studies regarding erosion of a semiinfinite layer of sediment is also presented.     

多排气雾冲击射流换热过程的试验研究

气雾冷却是带钢连续镀锌后的一种强化冷却方式。气雾冷却装置的设计和运行的关键是掌握气雾换热系数。采用试验方法研究了多排气雾射流冷却高温钢板的换热系数,考察了喷气流量和喷水流量对换热系数的影响。试验结果表明：喷气流量对气雾换热系数影响可以忽略;喷水流量对换热系数影响显著,在喷水流量为0.96～1.59 m^3/h时,换热系数随喷水流量的增加而明显上升,最大可达5 650 W/（m^2.K）;喷雾冷却的换热系数远大于常规喷气冷却,能有效地强化镀后冷却。     

Contact Erosion at the Interface between Granular Coarse Soil and Various Base Soils under Tangential Flow Condition

Under embankment dams and dykes, horizontal groundwater seepage prevails. If the subsoil is layered, and if some coarse layers are not appropriate filters for finer layers, there can be contact erosion at the interface between fine and coarse soils. In order to study contact erosion threshold, some base-soil and coarse-soil combinations were submitted to a flow parallel to the interface between the coarse soil and the base soil. Critical velocities and critical hydraulic gradients were measured for various base soils. Using effective base-soil grain diameter, an empirical expression for critical velocity was proposed that is well adapted for silts or sand/clay mixtures as well as for sands. The mass of eroded soil was measured relative to the flow velocity for each base-soil/coarse-soil setup. The shear stress applied to the interface between base soil and coarse soil was derived from the hydraulic gradient. Using an empirical relationship between applied shear stress and measured eroded mass, erosion rate was estimated for each base-soil/coarse-soil setup.