Influence of Tailwater Depth and Pile Position on Scour Downstream of Block Ramps

Scour control downstream of hydraulic structures is an important topic in hydraulic engineering. Block ramps or rock chutes are often used to control scour downstream of hydraulic structures and have the peculiarity to be ecofriendly. Although these structures assure great energy dissipation, the rapid passage from supercritical to subcritical flow at the toe results in a scour hole with geometric parameters that have to be evaluated in order to avoid foundation problems. For this reason, the analysis of the scour process and the comprehension of the hydrodynamic mechanisms on which it is based are extremely important. In this paper, the results of systematic experimental tests are shown that analyze both the influence of the stilling basin tailwater depth and the ramp toe stabilizing structures, for both uniform and nonuniform channel bed materials. In fact, block ramps are generally stabilized by inserting piles or micropiles at the toe. The upper edge level of piles or micropiles was found a relevant parameter for the scour hole geometry. Simple novel relationships that account for tailwater depth, pile position, and bed material gradation are developed to evaluate the main lengths of the scour hole, in the case in which a free hydraulic jump in a mobile bed occurs. These simple relationships give engineers helpful instruments in block ramp design.     

Hydraulics of 3D Plunge Pool Scour

The main flow features of three-dimensional plunge pool scour are explored in this experimental research for steady flow conditions. These include the maximum depth of the scour hole, its streamwise geometry, and the maximum width, the maximum height of the ridge, its shape in plan view, and its profile. Expressions for all these parameters are presented in terms of the basic scour variables, including the approach flow densimetric Froude number, the jet impact angle, the jet diameter, and the tailwater elevation above the originally horizontal sediment bed. This research is based on a previous work relating to two-dimensional plunge pool scour. Differences between the two phenomena are outlined, and the results are discussed in terms of engineering applications. The results of the two works allow for the prediction of the most salient features of plunge pool scour for both the dynamic and the static scour holes.     

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.     

The role of melt pool behavior in free-jet melt spinning

The influence of melt pool behavior on the competition between the nucleation of crystalline solidification products and glass formation is examined for an Fe-Si-B alloy. High-speed imaging of the melt pool, analysis of ribbon microstructure, and measurement of ribbon geometry and surface character all indicate upper and lower limits for melt spinning (MS) rates for which fully amorphous ribbons can be achieved. Comparison of the relevant time scales reveals that surface-controlled melt pool oscillation may be the dominant factor governing the onset of unsteady thermal conditions accompanied by varying amounts of crystalline nucleation observed near the lower limit. At high rates, the influence of these oscillations is minimal due to very short melt pool residence times. However, microstructural evidence suggests that the entrapment of gas pockets at the wheel-metal interface may play a critical role in establishing the upper rate limit. An observed transition in wheel-side surface character with an increasing MS rate supports this contention.     

Deflector Ski Jump Hydraulics

Ski jumps are a standard element of dam spillways for an efficient energy dissipation if takeoff velocities are large, and stilling basins cannot be applied. This laboratory study investigates the hydraulic performance of a triangular-shaped, rather than the conventional circular-shaped, bucket placed at the takeoff of ski jumps. The following items were addressed: (1) pressure head maximum and pressure distribution along the triangular-shaped bucket; (2) takeoff characteristics as a function of the bucket deflector angle and the relative bucket height including the lower and the upper jet trajectories; (3) jet impact characteristics in a prismatic tailwater channel including the shock wave formation and the height of recirculation depth below the jet cavity; (4) energy dissipation across the ski jump, from the approach flow channel to downstream of jet impact; and (5) choking flow conditions of the flip bucket. A significant effect of the approach flow Froude number, the relative bucket height, and the deflector angle is found. A comparison with previous results for the circular-shaped bucket geometry indicates a favorable behavior of the novel bucket design.     

Composition control in the direct laser-deposition process

Laser-engineered net shaping (LENS) is a solid freeform fabrication process that has the capability of producing functionally graded material (FGM) components by selectively depositing different powder materials in the melt pool at specific locations in the structure during part buildup. The composition in each layer of an FGM is dependent upon the degree of dilution between the substrate (or previous layer) and powder material. A study on the effects of LENS processing parameters (laser power, travel speed, and powder mass flow rate) on dilution was conducted for deposits of H-13 tool steel and copper powder on H-13 tool steel substrates. When varying a single processing parameter while holding all others constant, the dilution was found to increase with increasing laser input power and travel speed and decrease with increasing powder mass additions into the melt pool. A method for estimating dilution in LENS deposits was developed from knowledge of LENS process efficiencies and material thermophysical properties. A reasonable correlation was shown to exist between the experimentally measured dilution and the dilution calculated from the model.     

Plane Turbulent Wall Jets on Rough Boundaries with Limited Tailwater

Combining the results of a laboratory study of plane turbulent wall jets on rough boundaries with shallow tailwater, with the results of an earlier work of Rajaratnam on wall jets on rough boundaries with deep tailwater, this paper attempts to describe the effects of boundary roughness and tailwater depth on the characteristics of plane turbulent wall jets on rough beds, which are important in the field of hydraulic engineering. The time-averaged axial velocity profiles at different sections in the wall jet were found to be similar, with some difference from the profile of the classical plane wall jet. The normalized boundary layer thickness δ/b, where b is the length scale of the velocity profile, was equal to 0.35 for wall jets on rough boundaries compared to 0.16 for the classic wall jet. Two stages were seen to exist in the decay of the maximum velocity um as well as in the growth of the length scale, with the first stage corresponding to that of deep tailwater and the second stage to shallow tailwater. In the first stage, the decay of the maximum velocity um at any section in terms of the velocity u0 at the slot, with the longitudinal distance x in terms of L which is the distance where um = 0.5U0, was described by one general function, for smooth as well as rough boundaries. The length scale L in terms of slot width decreases as the relative roughness of the boundary increases. The onset of the second stage was not affected significantly by the bed roughness. The growth rate of the length scale b of the wall jet increased from 0.076 for a smooth boundary to about 0.125 for a relative roughness ks/b0 in the range of 0.25 to 0.50, where ks is the equivalent sand roughness and b0 is the thickness of the jet at the slot.     

Screen-Type Energy Dissipator for Hydraulic Structures

Laboratory experiments have shown that screens or porous baffles with a porosity of about 40% could be used as effective energy dissipators below small hydraulic structures, either in a single wall or a double wall mode. The experiments were carried out for a range of supercritical Froude numbers F1 from about 4 to 13, and the relative energy dissipation was appreciably larger than that produced by the corresponding classical hydraulic jumps. These screens or porous baffles produced free hydraulic jumps, forced hydraulic jumps, and in some cases submerged jumps. The flow leaving these screens was found to be supercritical with a Froude number approximately equal to 1.65 and a tailwater depth equal to 0.28 times the subcritical sequent depth y2* of the classical hydraulic jump with the same F1. To produce a secondary jump downstream of the screens, the tailwater depth needed was found to be about one half of y2*.     

Effect of Stilling Basin Geometry on Clear Water Scour Morphology Downstream of a Block Ramp

The scour mechanism downstream of a block ramp in clear water conditions is quite a complex phenomenon that depends on several parameters. Majors role are played by ramp configuration, hydraulic conditions (downstream tailwater level and discharge), material granulometry, and stilling basin geometry. Previous studies analyzed both the scour phenomenon and the effects of all the parameters involved except the last one (i.e., the case in which the ramp has the same width as the downstream stilling basin) and the case of symmetrically expanding stilling basins. This last basin configuration represents an optimal equilibrium between the necessity to dissipate energy and to create a natural pool for the biological species, thus it has a prominent ecological value. The present paper aims to assess the effect of both the width and length of the downstream stilling basin on scour features and flow pattern in clear water conditions. Different scour morphology types are distinguished and classified according to hydraulic and geometric conditions. Simple novel relationships are proposed to evaluate the scour depth and length and the maximum water level in the stilling basin. The results are valid for unsubmerged block ramps.     

Effect of Welding Speed on Gas Metal Arc Weld Pool in Commercially Pure Aluminum: Theoretically and Experimentally

Temperature and velocity fields, and weld pool geometry during gas metal arc welding (GMAW) of commercially pure aluminum were predicted by solving equations of conservation of mass, energy and momentum in a three-dimensional transient model. Influence of welding speed was studied. In order to validate the model, welding experiments were conducted under the similar conditions. The calculated geometry of the weld pool were in good agreement with the corresponding experimental results. It was found that an increase in the welding speed results in a decrease peak temperature and maximum velocity in the weld pool, weld pool dimensions and width of the heat-affected zone (HAZ). Dimensionless analyses were employed to understand the importance of heat transfer by convection and the roles of various driving forces in the weld pool. According to dimensionless analyses droplet driving force strongly affected fluid flow in the weld pool.     

Oxygen Transfer at Low Drop Weirs

Oxygen transfer into water at low-drop weirs was studied by using a prototype-scale, recirculating hydraulic flume with a weir width of 0.61 m, and a downstream channel width of 1.22 m. An enhanced-oxygen environment was used to maintain sufficient difference between saturation and upstream dissolved oxygen concentrations to reduce the experimental uncertainty. The variation in the deficit ratio r as a function of tailwater depth H was evaluated by using unit discharges q of 167, 334, and 502 m3∕hr?m and weir heights W of 0.54, 1.04, and 1.36 m. A semitheoretical equation for predicting r as a function of jet Froude number FJ, drop height h, and H was fitted to observed values by nonlinear regression analysis. An assumed value of 0.667 for maximum H∕h (found in the literature) proved acceptable. We concluded that tailwater depths are important to predict oxygen transfer at low-drop weirs, but that designing for optimum tailwater depth to maximize oxygen transfer may not be as important as was previously thought, because large optimum ranges for H∕h were observed in this study.     

Study on Factors Affecting the Structure of High SpeedSteel Ingot Produced by ESR

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Detection of a Pool in Semi-Continuous Castings Made of Heat-Treatable Aluminum Alloys

Various products (sheets, sections, etc.) manufactured by metal forming (rolled products, forged pieces, etc.) from semi-continuous castings are widely used in the aerospace industry. The so-called pool, which is the conical volume of a liquid metal, exists at the top of the liquid metal. Experience demonstrates that the geometry, the depth, and the shape of the pool substantially affect the structure formation in a casting and its quality. The application of a titanium nitride nanopowder, which is introduced in a melt in the volume of a rod, as a modifier allowed us to find the exact geometry of the pool.     

Mathematical modeling of three-dimensional heat and fluid flow in a moving gas metal arc weld pool

Mathematical models capable of accurate prediction of the weld bead and weld pool geometry in gas metal arc (GMA) welding processes would be valuable for rapid development of welding procedures and empirical equations for control algorithms in automated welding applications. This article introduces a three-dimensional (3-D) model for heat and fluid flow in a moving GMA weld pool. The model takes the mass, momentum, and heat transfer of filler metal droplets into consideration and quantitatively analyzes their effects on the weld bead shape and weld pool geometry. The algorithm for calculating the weld reinforcement and weld pool surface deformation has been proved to be effective. Difficulties associated with the irregular shape of the weld bead and weld pool surface have been successfully overcome by adopting a boundary-fitted nonorthogonal coordinate system. It is found that the size and profile of the weld pool are strongly influenced by the volume of molten wire, impact of droplets, and heat content of droplets. Good agreement is demonstrated between predicted weld dimensions and experimently measured ones for bead-on-plate GMA welds on mild steel plate.     

Analysis of the steady state molten pool obtained by heating a substrate with an electron beam

Surface melting and solidification with high powered beams can be used for enhancing surface properties. The dimensions of the molten zone define the extent of the modified properties and are critical parameters which must be predicted during process design. The flow field in the molten pool has been reported to be one of the key factors which controls the dimensions of the surface layer. However, the calculation of this is only possible through complex numerical schemes and there is a need to look for simple analytical expressions which may be adequate. One approach for this search involves the precise determination of the steady state stationary profiles and then developing a method for extending these values to include the effect of beam motion for predicting the pool dimensions during processing. In this paper, a study of the flow field and its effect on the depth and width of the steady state pool is presented, based on numerical and analytical methods. To validate the predictions, an experimental study is carried out using surface melting of Al-4.5 wt%Cu alloy an electron beam. The pool shapes are presented through optical micrographs and the depth and width of the pool is measured from these micrographs. The experiments are then simulated using a numerical model which includes fluid flow. The flow field is analyzed using streamline plots and the predicted pool shapes are compared with the micrographs. Further, the results are compared to an analytical method based on pure conduction and the pool depth and width are predicted when the liquid thermal conductivity is modified. The numerical and analytical predictions of the pool depth and width are found to be in good agreement with the experimental measurements (obtained from steady state stationary pools and from dimensions inferred on extrapolating moving beam measurements to zero velocity). The reasons for the success of the analytical model is discussed with reference to the two-dimensional flow fields and vortices predicted by the numerical model.     

Correction to flow rate--pressure drop relation in coronary angioplasty: steady streaming effect

The changed flow pattern of pulsatile blood flow in a catheterized stenosed artery has been studied through a mathematical model. The study takes into account the effect of the movement of the flexible catheter influenced by the pulsatile nature of the flow. The contribution of the steady streaming effect brings into focus the existence of a non-zero mean pressure drop in addition to the one predicted by the linear theory -- a fact overlooked by the previous authors. Thus our results are intended to provide a correction to the mean pressure drop usually calculated by neglecting the non-linear inertia terms. The calculations based on the geometry and the flow conditions representing a real physiological situation as closely as possible suggest that depending upon the values of k (where k is the ratio of the catheter size to vessel size) ranging from 0.2 to 0.5 mean pressure drop increases for any frequency parameter. In addition, it is found that depending upon the material properties, a thin catheter experiencing small oscillations due to the flow conditions is likely to influence in the same way as a thicker catheter which remains fairly stationary inside the artery. The results are sensitive to the shape of the wall geometry and will be different for different wall geometries even if the cross-sectional area reduction at the peak of stenosis is kept the same. Interesting streamline patterns depict distinct boundary layer characteristics both at the artery wall and catheter wall. Finally, the effect of catheterization and its movement on various physiologically important flow characteristics-mean pressure drop, impedance, wall stress is studied for different range of catheter size and frequency parameter.     

How the nozzle position affects the geometry of the melt pool in directed energy deposition process

ABSTRACT

This work deals with Directed Energy Deposition (DED) that is a process in which the material is delivered directly into the melt pool. Several kinds of nozzle have been developed and used in this process. However, the position of the nozzle, mainly for the lateral one, plays a crucial role in the geometry and porosity content of the melt pool. Therefore, to investigate the correlation between the lateral nozzle position and the geometry of the melt pool, three different sets of single tracks of Ti–6Al–4V were deposited at different nozzle positions. It was found that helpful information regarding the selection of the optimal position of the lateral nozzle can be obtained from the melt pool features. It can be noticed that by increasing the distance between the nozzle position and substrate, the powder capture decreases and accordingly results in a high depth of fusion zone and also keyhole defect formation.     

Earth Dam with Toe Drain on an Impervious Base

The required height of a toe drain for a homogeneous earth dam on an impervious base has been determined considering reservoir water level, capillary rise for the embankment soil, free board, top width of the earth dam, embankment slopes, and tail-water position, such that the surface of seepage does not develop on the downstream sloping face of the earth dam and capillary saturation above phreatic line is contained well within the downstream sloping face. Using Kozeny’s analytic function, exact solution to the unconfined flow through an earth dam having parabolic equipotential boundaries on either side has been obtained. For straight toe drain face, and for various positions of tailwater, approximate toe drain heights and heights of surface of seepage have been determined using the Kozeny’s function and the method of fragments. It has been found that for an earth dam with 1/2 upstream slope, ?1/3 downstream slope, no tailwater, and 2?m capillary rise, capillary saturation is contained within the earth dam and the phreatic line is prevented from emerging on the downstream sloping face by providing a toe drain of height equal to 1/3 of the height of water level in the reservoir.     

Local Scour Downstream of Positive-Step Stilling Basins

This note focuses on the temporal and spatial evolution of local scour below low-head spillways. Steady-flow experiments were carried out in a 1-m wide and 20-m long rectangular straight channel. The jet was generated by an ogee-crest spillway followed by a positive-step stilling basin. Nearly uniform sandy beds were generally tested, but additional tests were also performed with a special bed of lead spheres. To circumvent the combination of local and general scour phenomena, tailwater depths were set such that tailwater flow intensities were below the threshold of sediment motion. As a consequence, for each run a submerged hydraulic jump formed. Tests were of long durations (of order of days) mainly to achieve conditions of quasi-equilibrium. Based on the data collected, literature approaches are discussed. Then, empirical models are proposed to estimate: (1) the maximum scour depth at the quasi-equilibrium stage and its horizontal distance from edge of stilling basin; (2) the time variation of scour depth; and (3) the axial scour profiles. The proposed equations agree well with experimental data. Findings also highlight that affinity rather than similarity may be the typical property of low-angle eroding jets.