Investigation of solids segregation of binary mixtures in a rotating drum at various Froude numbers

To investigate the effect of the Froude number(Fr)on solid segregation in a rotating drum,a two dimensional mathematical modelling on solids behaviour in horizontally oriented rotating drums operated in rolling,cascading and cataracting modes has been carried out by using Euler-Euler multi-fluid model in Fluent6.2 environment.Small particles and big particles are used in the work as binary mixtures to investigate segregation characteristics.The effect of Froude number(rotating velocity)on the flow field is investigated.It is found that the model captures the main features of solids motion and segregation in the drum and numerical results agree well with limited experimental data for solid velocity.

Effects of Froude number and geometry on water entry of a 2-D ellipse

By using the finite volume method with volume of fluid model and global dynamic mesh technique, the effects of Froude number and geometry on the water entry process of a 2-D ellipse are investigated numerically. For the time history of the vertical force, the computational fluid dynamics（CFD） results match the experimental data much better than the classical potential-flow theories due to the consideration of the viscosity, turbulence, surface tension, gravity, and compressibility. The results show that the position of peak pressure on ellipse shifts from the spray root to the bottom of ellipse at a critical time. The critical time changes with the geometry and Froude number. By studying the vertical force, the ellipse water entry process can be divided into the initial and late stages based on the critical dimensionless time of about 0.1. The geometry of the ellipse plays a dominant role in the initial stage, while the Froude number is more important in the late stage of entry. The classical Wagner theory is extended to the ellipse water entry, and the predicted maximum value of vertical force coefficient in the initial stage is 4？a/b that matches the CFD results very well, where a and b are the horizontal axis and vertical axis of the ellipse parallel and perpendicular to the initial calm water surface, respectively.

Experimental investigation of the optimization of stilling basin with shallowwater cushion used for low Froude number energy dissipation

Energy dissipations induced by the hydraulic jump and the trajectory jet are the most widely known as the two dissipation modes at the downstream of flood discharging structures, which are often considered quite different even contradictory. However, such two energy dissipators can be used jointly and harmonically. In this paper, a new type of stilling basin with a shallow-water cushion and a triangular bottom deflector is proposed based on two different scale physical model tests of the flood discharging tunnel No.2 of Luding hydropower project. The experimental results show that the flow regime of the hydraulic jump in the presented stilling basin with bottom deflector enjoys a good and stable performance within a large range of flow rates and the energy dissipation rate is considerably high as compared to the conventional stilling basin even at a low Froude number. The results also indicate that the stilling basin with triangular bottom deflector has a better performance in improving the potential cavitation erosion according to the analysis of the pressure and the cavitation number compared to the trapezoidal one. The proposed new type of shallow-cushion stilling basin with a shallow-water cushion can be applied in similar energy dissipation projects with low Froude number and large range of flow rates.

Hydraulics of crest spillway with large unit discharge and low Froude number

With respect to the crest spillway with large unit discharge and low Froude number, the hydraulics of the slit-type energy dissipater at the outlet should be noticed due to the complicated flow regimes. In the present paper, some issues about hydraulic characteristics were experimentally investigated by means of five slit-type outlets and four tetrahedrons, including the flow choking, impact to river banks and jet trajectory. The main findings are as follows. The critical Froude number for the flow choking decreases with increasing outlet width of the slit-type energy dissipater. If the flow Froude number is expressed by the parameters just before this energy dissipater, the tetrahedron placed inside the side wall of the outlet could efficiently avoid the flow impact to the river bank of same side, and compared with the jet trajectory of the slit-type energy dissipater, the outlet with tetrahedron has different trajectory trend, i.e., the distance of the jet trajectory decreases with the increase of the water head due to special form of the outlet tetrahedron.

Effect of an Artificial Caudal Fin on the Performance of a Biomimetic Fish Robot Propelled by Piezoelectric Actuators

This paper addresses the design of a biomimetic fish robot actuated by piezoeeramic actuators and the effect of artificial caudal fins on the fish robot＇s performance. The limited bending displacement produced by a lightweight piezocomposite actuator was amplified and transformed into a large tail beat motion by means of a linkage system. Caudal fins that mimic the shape of a mackerel fin were fabricated for the purpose of examining the effect of caudal fm characteristics on thrust production at an operating frequency range. The thickness distribution of a real mackerel＇s fin was measured and used to design artificial caudal fins. The thrust performance of the biomimetic fish robot propelled by fins of various thicknesses was examined in terms of the Strouhal number, the Froude number, the Reynolds number, and the power consumption. For the same fm area and aspect ratio, an artificial caudal fin with a distributed thickness shows the best forward speed and the least power consumption.

Hydraulic model with roughness coefficient updating method based on Kalman filter for channel flood forecast

A real-time channel flood forecast model was developed to simulate channel flow in plain rivers based on the dynamic wave theory. Taking into consideration channel shape differences along the channel, a roughness updating technique was developed using the Kalman filter method to update Manning＇s roughness coefficient at each time step of the calculation processes. Channel shapes were simplified as rectangles, triangles, and parabolas, and the relationships between hydraulic radius and water depth were developed for plain rivers. Based on the relationship between the Froude number and the inertia terms of the momentum equation in the Saint-Venant equations, the relationship between Manning＇s roughness coefficient and water depth was obtained. Using the channel of the Huaihe River from Wangjiaba to Lutaizi stations as a case, to test the performance and rationality of the present flood routing model, the original hydraulic model was compared with the developed model. Results show that the stage hydrographs calculated by the developed flood routing model with the updated Manning＇s roughness coefficient have a good agreement with the observed stage hydrographs. This model performs better than the original hydraulic model.

Numerical Study on Plume Interaction Above An AlternatingDiffuser in Stagnant Water

The plume interaction above an alternating diffuser in stagnant water is studied with 3D Reynolds-averaged NavierStokes equations （RANS） combined with a buoyancy-extended κ-ε model. The steady three-dimensional turbulent flow and temperature fields are computed by use of the finite volume method on a non-uniform high resolution orthogonal grid. The numerical predictions demonstrate a generic flow pattern for different turbulent heated jet discharges： the buoyant jets on each side of the diffuser first merge to form an essentially two-dimensional plume which bends back toward the diffuser centerline due to a low pressure cavity. In general, an under-pressure exists in the cavity until the plumes merge; the pressure increases to slightly positive afterwards. Two-dimensionality of the scalar and flow field is attained much later than the point of zero pressure. The position of merging point is governed by mainly four parameters - the discharge densimetfic Froude number, the port diameter and space, and the horizontal distance between alternating jet nozzles. A formula from numerical simulations is obtained through regression analysis and it is used to predict the position of plume merging point. The predicted temperature fields are comparable to previous experiments.

Uniform Flow of Molten Metals in Rectangular Open Channels

The flow of liquids in open channels has been studied since ancient Rome. However, the vast majority of published reports on flow in open channels are focused on the transport of drinking water and sewage disposal. The literature on the transport of molten metals in open channels is quite scarce. In this work, the uniform flow of pig iron and molten aluminum in rectangular open channels is studied. Specific energy curves are constructed and critical heights are analytically determined. The transition from subcritical to supercritical flow is analyzed as a function of the angle of inclination of the channel and the roughness of its walls. Manning’s equation is applied to the pig iron flow using data reported in the literature for molten aluminum. The need to correct the roughness coefficient for pig iron is observed in order to obtain results consistent with those previously reported.

Drag increment of internal waves generated by horizontally moving spheroid in supercritical regime

A theory on the drag increment of internal waves with a spheroid moving horizontally at a high velocity （or for large internal Froude number） in uniformly vertically stratified fluid （or ocean） is presented in the present paper. A surface source distribution is employed to model a hydrodynamic interaction between the spheroid and the stratified fluid. From theoretical results, it is shown that there exists an asymptote of zero-drag increment in supercritical regimes, where internal Froude numbers are larger than the critical internal Froude numbers. When the spheroid reduces to a sphere, the results in this paper is in good agreement with the previous theoretical and experimental results of the sphere.

Estimation of hydraulic jump on corrugated bed using artificial neural networks and genetic programming

Artificial neural networks （ANNs） and genetic programming （GP） have recently been used for the estimation of hydraulic data. In this study, they were used as alternative tools to estimate the characteristics of hydraulic jumps, such as the free surface location and energy dissipation. The dimensionless hydraulic parameters, including jump depth, jump length, and energy dissipation, were determined as functions of the Froude number and the height and length of corrugations. The estimations of the ANN and GP models were found to be in good agreement with the measured data. The results of the ANN model were compared with those of the GP model, showing that the proposed ANN models are much more accurate than the GP models.

Local hydraulic jump effects on sediment deposition in open-channel flume experiments

When a river channel is narrow,bifurcated,or intersected,or when extreme weather or geological disasters cause shed rock masses to occupy a river flood channel,local hydraulic jumps may develop in the channel.Natural disasters such as landslides,floods,and debris flows occur upstream,will result in large transport rate of large-sized gravel particles.Those particles may be blocked in hydraulic jump areas,causing river channel water depth to rise.In this study,the effect of local hydraulic jumps on the sediment deposition rate was investigated in flume experiments.The ratio of upstream and downstream Froude numbers,particle size,Sediment supply intensity,and flow discharge all affected the sediment deposition rate.With increases in the ratio of upstream and downstream Froude numbers,particle size,and sediment supply intensity,the sediment deposition rate increased.The sediment deposition rate decreased with an increase in flow discharge.Approach hydraulic conditions and particle properties jointly determined the sediment deposition rate in a hydraulic jump section,and an empirical formula was developed using those parameters to calculate the sediment deposition rate.Thus,to identify risks and prevent disasters in mountain rivers,local changes in hydraulic conditions and particle properties need to be jointly evaluated.

INCIPIENT MOTION OF NON-COHESIVE SEDIMENT UNDER ICE COVER-AN EXPERIMENTAL STUDY

Based on a series of experiments under both ice-covered and free surface conditions, the present article discusses the role of flow velocity and critical shear Reynolds number for incipient motion of bed material. The influence of the resistance coefficients of both the underside of the ice cover and the channel bed on the location of the maximum velocity has been discussed. In addition, the impacts of ice and composite resistance coefficients on flow velocity for incipient motion of bed material have been assessed. The diagram describing the critical shear Reynolds number and the dimensionless shear stress for the incipient motion of sediment under ice covered conditions with different under cover resistance coefficient has been established. The effects of grain size on densimetric Froude number for incipient motion of bed material have been investigated. A relationship between the densimetric Froude number for incipient motion of bed material and the median grain size of bed material as well as the roughness coefficient of channel bed and roughness coefficient of ice cover has been established.

FACTORS INFLUENCING BENDING RIGIDITY OF SUBMERGED VEGETATION

The bending rigidity of submerged vegetation is closely related with vegetative drag force. This work aims at determining the effects of flow conditions and characteristics of vegetation on the bending rigidity of submerged vegetation. Based on the dimensional analysis method, the factors influencing the bending rigidity of individual submerged vegetation were analyzed. The relationship between the relative bending rigidity and its influencing factors was investigated by experimental observation, and a relative bending rigidity expression for submerged vegetation was obtained by means of multiple linear regression method. The results show that the submerged vegetation has three states under different inflow conditions, and the each critical relative bending rigidity of individual submerged vegetation was determined for the different states of submerged vegetation.

THREE-DIMENSIONAL NUMERICAL SIMULATION OF INTAKE MODEL WITH CROSS FLOW

The hydrodynamics of a pump sump consisting of a main channel, pump sump, and intake pipe is examined using Truchas a three-dimensional Navier-Stokes solver, with a Large Eddy Simulation （LES） turbulence model. The numerical results of streamwise velocity profiles and flow patterns are discussed and compared with experimental data of Ansar and Nakato. Fairly good agreement is obtained. Furthermore, unlike Ansar et al.＇s inviscid solution, the proposed numerical model includes the effect of fluid viscosity and considers more realistic simulation conditions. Simulation results show that viscosity affects the prediction of flow patterns and that the streamwise velocity can be better captured by including cross flow. The effects of the submergence Froude number on the free surface and streamwise velocity are also examined. The free surface significantly fluctuates at high submergence Froude number flows and the corresponding distribution of streamwise velocity profiles exhibits a trend different from that obtained for low submergence Froude number flows.

Flow choking characteristics of slit-type energy dissipaters

In this paper, the behavior of the flow choking, including the critical and developing states, was experimentally investiga- ted by means of five slit-type outlets, characterized by the outlet width, the contraction angle and the opening of the working gate. The results showed that the approach flow Froude number of the critical choking decreases if the outlet width increases, or the con- traction angle decreases, or the opening increases. There is the hysteresis when the flow choking develops, i.e., the Froude numbers of the appearance and disappearance of the flow choking at the increasing discharge regime are all larger than those at the decreasing discharge regime. For various widths of the outlets, the differences between the critical Froude numbers at small opening are much larger than thoset at large opening. The change range from appearance to disappearance of the flow choking at small opening is smaller than that at large opening.

CHARACTERISTIC ANALYSIS OF THE PLUNGING OF TURBIDITY CURRENTS

Turbidity currents are flows driven by suspended sediment of flood-induced turbid river water with excess density.Such currents are often the governing factor in reservoir sedimentation by transporting fine materials over long distances and delivering the majority of deposition,which thus reduces the storage capacity.Therefore,the design and operation of a reservoir requires an accurate prediction of its occurrence condition and plunging position,which is the objective of the present study.This article presents a verified algebraic slip mixture model including momentum,continuity and algebraic velocity expressions to simulate 2-D turbidity currents.Test experiments in a multiphase flume were carried out.Reynolds number,sediment concentration and densimetric Froude number were used as parameters in the occurrence condition analysis.The plunging of turbidity currents may produce reflux and backflow due to the diving flow at the surface of the clear water.The similar experimental results were also obtained by PIV measurements

Revisit submergence of ice blocks in front of ice cover–an experimental study

The present paper studies the stabilities of ice blocks in front of an ice cover based on experiments carried out in laboratory by using four types of ice blocks with different dimensions. The forces acting on the ice blocks in front of the ice cover are analyzed. The critical criteria for the entrainment of ice blocks in front of the ice cover are established by considering the drag force caused by the flowing water, the collision force, and the hydraulic pressure force. Formula for determining whether or not an ice block will be entrained under the ice cover is derived. All three dimensions of the ice block are considered in the proposed formula. The velocities calculated by using the developed formula are compared with those of calculated by other formulas proposed by other researchers, as well as the measured flow velocities for the entrainment of ice blocks in laboratory. The fitting values obtained by using the derived formula agree well with the experimental results.

Three-dimensional numerical simulation of flow in trapezoidal cutthroat flumes based on FLOW-3D

To solve the common problem of flumes flowmeasurement accuracy without sacrificing water head, a new type of trapezoidal cutthroat flume to measure the discharge in terminal trapezoidal channels is presented.Using the computational fluid dynamic method, threedimensional flow fields in trapezoidal cutthroat flumes were simulated using the RNG k-ε three-dimensional turbulence model along with the Tru VOF technique.Simulations were performed for 12 working conditions,with discharges up to 0.075 m3$s–1 to determine hydraulic performance. Experimental data for the trapezoidal cutthroat flume in terminal trapezoidal channel were also obtained to validate the simulation results. Velocity distribution of the flume obtained from simulation analyses were compared with observed results based on timeaveraged flow field and comparison yielded a solid agreement between results from the two methods, with relative error below 10%. The results indicated that the Froude number and the longitudinal average velocity increased along the convergence section and decreased in the divergent section. In the upper throat, the Froude number was less than 0.5, which meets the water measurement requirement, and the critical flow appeared near the throat section. The maximum water head loss of the trapezoidal cutthroat flume was less than 9% of the total head, compared to the rectangular cutthroat flume,and head loss of trapezoidal cutthroat flume was significantly less. Regression models developed for upstream depth versus discharge under different working conditions were satisfactory, with a relative error of less than 2.06%, which meets the common requirements of flow measurement in irrigation areas. It was concluded that trapezoidal cutthroat flumes can improve flow-measurement accuracy without sacrificing water head.

Aeroelastic scaling laws for gust load alleviation control system

Gust load alleviation （GLA） tests are widely conducted to study the effectiveness of the control laws and methods. The physical parameters of models in these tests are aeroelastic scaled, while the scaling of GLA control system is always unreached. This paper concentrates on studying the scaling laws of GLA control system. Through theoretical demonstration, the scaling criterion of a classical PID control system has been come up and a scaling methodology is provided and veri- fied. By adopting the scaling laws in this paper, gust response of the scaled model could be directly related to the full-scale aircraft theoretically under both open-loop and closed-loop conditions. Also, the influences of different scaling choices of an important non-dimensional parameter, the Froude number, have been studied in this paper. Furthermore for practical application, a compen- sating method is given when the theoretical scaled actuators or sensors cannot be obtained. Also, the scaling laws of some non-linear elements in control system such as the rate and amplitude sat- urations in actuator have been studied and examined by a numerical simulation.

Numerical simulation of scouring funnel in front of bottom orifice

The scouring funnel in front of a bottom orifice under the condition of fixed water levels is simulated by using an Eulerian two-phase model, with onsideration of the flow-particle and particle-particle interactions. The predictions of the scouting funnel shape agree well with laboratory measurements. The flow-field characteristics of the two phases and the influences of the hydraulic and geometric parameters on the shape of the scouring funnel are analyzed on the basis of the computation results. It is revealed that the non-dimensional maximum scour hole parameters, the depthdm / do, the length l,. / do, and the half-width w / do, are linearwith the densimetric Froude number Fro , the main parameter describing the scour hole, the centerline scour depth Dc and the half-scour width Wr vary according to a power law, and the transverse scour profiles exhibit strong similarities, the velocity distribution of the water is confined within the sink-like area near the orifice, and the mutual impact of the flows at the azimuthal sections and the resistances of the walls and the sand layer produce a vortex in the scour hole, that makes the sand particles to be suspended in the water, the exchanging water in the pore water is the main contributor in forcing the sand to move, and transporting the sand in the same direction as the pore water along azimuthal sections.