Choke-free flow in trapezoidal channels with change in bed elevation

Solutions for choke-free flow in a trapezoidal channel, with rise in bed elevation that may occur with partial filling up of the channel bottom, are discussed. In this analysis, the side slopes of the channel are assumed to be the same before and after the transition. Considering smooth and gradual transition zones, equations of energy and continuity are solved for subcritical and supercritical upstream flow conditions to determine the maximum limiting rise in bed elevation. The ranges of the upstream flow depths are also obtained for the choke-free condition, using the continuity equation of the upstream flow. A list of symbols is given at the end of the paper     

Three-Dimensional CFD Modeling for Optimization of Invert Trap Configuration to Be Used in Sewer Solids Management

Flow field prediction and optimization of invert trap configuration have been carried out by using three-dimensional computational fluid dynamics (CFD) modeling with the help of FLUENT software using renormalization group (RNG) k-ε along with the discrete phase model (DPM). A hexagonal/tetrahedral shape and map-type nonuniform grid were chosen to discretize the entire computational domain, and a control volume finite difference method was used to solve the governing equations. In the present study, five different invert trap configurations (rectangular with and without lid on both sides, trapezoidal, trapezoidal with rectangular base, and rectangular with trapezoidal base with lid on both sides) have been simulated for the flow of three different inert sediment types (sand, styrocell, and plastic beads) at six flow rates (0.35, 0.70, 1.05, 1.35, 4.55, and 9.95 Lps) for each trap. The discharges selected in the present study cover the entire range of discharge expected in channels during dry weather flow and monsoon. The simulation results are capable of showing particle trajectories and the effect of flow rate and trap geometry on the flow patterns developed within the trap. Based on 3-D CFD modeling and experimental measurements, it has been concluded that the invert trap having a rectangular shape with trapezoidal base with lids on both sides is the most efficient trap configuration with highest sediment retention ratio.     

Glow discharge in external magnetic field in hypersonic flow of rarefied gas

A two-dimensional computational model is used to investigate the gasdynamic structure of a rarefied (pressure of several torr) hypersonic flow of molecular nitrogen in a plane channel, with a glow discharge maintained between two surfaces of this channel. An asymmetric configuration of electrodes is considered, namely, the cathode is a narrow strip located on the lower surface of the channel, and the upper surface of the channel is a continuous anode. The fundamental possibility is studied of using an external magnetic field transverse to the flow for modifying the shock-wave structure of flow in the channel.A two-dimensional conjugate electrogasdynamic model is given, which includes equations of continuity, Navier-Stokes equations, equations of conservation of energy, and equations of continuity of charged particles in ambipolar approximation. The real thermophysical and transport properties of molecular nitrogen are included.It is demonstrated that the use of a surface glow discharge in a rarefied hypersonic flow enables one to effectively modify the shock-wave structure of flow and, thereby, consider discharges of this type as additional means of control over rarefied gas flows.     

A finite boundary method for fluid flow field computations

A powerful new finite boundary concept of seeking field solution, at few selected regions in the solution domain, is introduced. Also a highly economical finite boundary method (FBM) which would greatly reduce the size of the coefficient matrix of the resulting system of simultaneous algebraic equations, requiring lesser computer memory and lesser computing time, is developed. Fluid flow fields governed by the basic elliptic partial differential equations—the Laplace's and the Poisson's equations—in two independent variables are mainly considered. The computational merits of the FBM are shown by solving, as an example, a simple representative flow problem, and the relevant computational finite boundary formulae are given in tabular form. The formulae are numerically derived based on a generalized method presented here. The added feature of the FBM is that it proves to be equally economical even when the solution is sought in the entire flow domain. The problem of steady-state viscous flows governed by the Navier-Stokes equations, the system of two simultaneous partial differential equations—the Poisson's equation and the vorticity transport equation—makes the FBM doubly economical. The possibility of developing an efficient hybrid computational algorithm, for curved problem boundaries, in conjunction with the finite element method, is discussed. The extension of FBM to transient, non-elliptic problems and to three-dimensional problem fields is also indicated. The FBM has been discussed in a more detailed manner so as to clearly bring out the advantages of the new finite boundary concept.     

On the circulating boiling bed energy

Energy losses through gas filtration in a circulating boiling bed have been analyzed. The expression of the power needed for sustaining the internal circulation of particles has been obtained. On this basis the theoretical dependence for determining the carrying capacity of the flow and the lower boundary of existence of a circulating boiling bed (minimum transport velocity) has been established. Simple engineering formulas for calculating the bed drag and the maximum transport velocity have been obtained.     

Numerical investigation of laminar separated flow through a channel with symmetric double expansion

Summary Two-dimensional Navier-Stokes equations have been solved numerically by a finite difference technique on a staggered grid for investigating the laminar flow of an incompressible viscous fluid through a channel with symmetric double expansion. A coordinate transformation has been employed to map the infinite irregular domain into a finite regular computational domain. At higher Reynolds numbers the flow becomes time-dependent and asymmetric. Such unsteadiness and asymmetry remains in the flow even up to turbulent flow conditions. The Pressure-Poisson equation has been solved and a pressure-velocity correction scheme has been invoked. Depending on the geometry and Reynolds number, secondary separation has been observed.     

Modeling electrowinning process in an expanded bed electrode

A theoretical model has been developed to describe the flow behavior of conducting particles in a fluidized bed electrode for electro winning of metal ions present in the dilute solution. Model equations have been developed for potential and current distributions and mass transfer rates. The influence of operating parameters on particle growth has been critically examined. It has been observed from the present investigation that the particle size increased with electrolysis time. The present model simulations have been compared with the experimental data reported in the literature and observed that the model predictions satisfactorily match with the reported experimental findings.     

An analytical model for bedload layer thickness

A theoretical study has been carried out to determine the thickness of the bedload layer in an open channel turbulent flow with non-cohesive sediment, which is very crucial in sediment transport problems as this is treated as saltation height of a sediment particle and the reference level in suspension studies. A new expression of viscous shear stress is proposed, which is a function of effective viscosity of sediment–fluid mixture, velocity gradient and volumetric concentration of sediment particles. During particle collisions, impact shear stress is generated, which is another important parameter near the sediment bed. By including both the shear stresses, an expression for the thickness of the bedload layer is developed. The predicted bedload layer thickness is a function of viscous coefficient, impact coefficient, particle diameter, relative mass density of sediment particle, maximum bed concentration and non-dimensional shear stress. It agrees reasonably well when compared with a wide class of experimental data under different hydraulic conditions.     

Adsorption of zinc on bed sediment of River Hindon: adsorption models and kinetics

The paper presents a study of zinc adsorption using the experimental data on bed sediments of River Hindon in western Uttar Pradesh (India). The effect of various operating variables, viz., initial concentration, solution pH, sediment dose, contact time, and particle size, have been studied. The optimum contact time needed to reach equilibrium was of the order of 60 min and was independent of initial concentration of zinc ions. The extent of adsorption increased with an increase of pH. Furthermore the adsorption of zinc increases with increasing adsorbent doses and decreases with the adsorbent particle size. The content of iron, manganese and organic matter in various fraction of sediment decreases with increasing particle size indicating the possibility of the two geochemical phases to act as the active support material for the adsorption of zinc ions. The adsorption data follows both Langmuir and Freundlich adsorption models. Isotherms were used to determine thermodynamic parameters, viz., free energy change, enthalpy change and entropy change. The negative values of free energy change indicate spontaneous nature of the adsorption while positive values of enthalpy change suggest the endothermic nature of the adsorption of zinc on bed sediment of the River Hindon. The positive values of entropy change indicate randomness at the solid/solution interface.     

Effects of bed-load movement on flow resistance over bed forms

The effect of bed-load transport on flow resistance of alluvial channels with undulated bed was experimentally investigated. The experiments were carried out in a tilting flume 250mm wide and 12.5m long with glass-sides of rectangular cross-section and artificial dune shaped floor that was made from Plexi-glass. Steady flow of clear as against sediment-laden water with different flow depths and velocities were studied in the experiments with a fine sand (d ₅₀ = 0.5mm). The results indicate that the transport of fine particles (d ₅₀ = 0.5mm) can decrease the friction factor by 22% and 24% respectively for smooth and rough beds. Increasing the bed-load size (d ₅₀ = 2.84 mm) can decrease the friction factor by 32% and 39% respectively for smooth and rough beds. The decrease in flow resistance is due to filling up of the troughs of dunes. This separation zone is responsible for increasing the flow resistance. On the upstream side of dunes condition is similar to plane bed. Presence of bed-load causes to increase the shear velocity and hence increasing flow resistance. But decreasing in flow resistance is more and it causes to decrease the total flow resistance. Grains saturated the troughs in the bed topography, effectively helping in smoothening of bed irregularities.     

黄河调水调沙试验对泥沙粒径变化影响分析

2002～2004年,黄河水利委员会相继开展了3次基于不同调度方式和不同空间尺度的调水调沙试验。本文中通过对试验期间小浪底水库及黄河下游河道悬移质、床沙质泥沙颗粒级配在时间和空间上的变化分析,说明小浪底水库淤粗排细有利于调整库区泥沙淤积形态和出库细颗粒泥沙向大海输移;下游河道中悬移质泥沙平均中数粒径沿程变粗,试验达到了全面冲刷河槽的目的。     

Formation of natural pH gradients in a microfluidic device under flow conditions: model and experimental validation

A new isoelectric focusing technique has been developed that incorporates natural pH gradient formation in microfluidic channels under flowing conditions. In conjunction, a one-dimensional finite difference model has been developed that solves a system of algebraic-ordinary differential equations that describe the phenomena occurring in the system, including hydrolysis at the electrodes, buffering effects of weak acids and bases, and mass transport due to both diffusion and electrophoresis. A quantitative, noninvasive, optically based method of monitoring pH gradient formation is presented, and the experimental data generated by this method are found to be in good agreement with model predictions. In addition, the model provides a theoretical explanation for initially unexpected experimental results. Model predictions are also shown to match well with experimental results of microfluidic isoelectric focusing of a single protein species. Accounting for the nonuniform velocity profile, characteristic of pressure-driven flow in microfluidic channels, is found to improve predictions of dynamic pH changes close to the electrodes and overall time required to reach steady state, but to reduce the accuracy of dynamic pH change predictions in other regions of the channel.     

Sediment transport over a flat bed in a unidirectional flow: simulations and validation

A discrete particle model is described which simulates bedload transport over a flat bed of a unimodal mixed-sized distribution of particles. Simple physical rules are applied to large numbers of discrete sediment grains moving within a unidirectional flow. The modelling assumptions and main algorithms of the bedload transport model are presented and discussed. Sediment particles are represented by smooth spheres, which move under the drag forces of a simulated fluid flow. Bedload mass-transport rates calculated by the model exhibit a low sensitivity to chosen model parameters. Comparisons of the calculated mass-transport rates with well-established empirical relationships are good, strongly suggesting that the discrete particle model has captured the essential elements of the system physics. This performance provides strong justification for future interrogation of the model to investigate details of the small-scale constituent processes which have hitherto been outside the reach of previous experimental and modelling investigations.     

Numerical simulation of thermogravitational energy transport of a hybrid nanoliquid within a porous triangular chamber using the two-phase mixture approach

This study is a computational investigation of transient thermogravitational energy transport in H₂O/Al₂O₃ nanoliquid and water-based copper/aluminum oxide hybrid nanofluid (water/Al₂O₃-Cu) inside a horizontal isosceles triangular enclosure with porous medium. The governing equations for two-phase mixture flow have been derived by the use of Darcy-Brinkman model for porous media without the Forchheimer term (inertia loss). The control equations have been discretized using the finite volume technique. The effects of porosity factor, Rayleigh number, and Darcy number on the liquid motion and transient energy transport have been studied. The results have shown that convective thermal transmission in the nanofluid inside the triangular cavity generally consists of three phases: initial, transient, and quasi-steady, all of which are described in detail. It has been found that a rise of the porosity factor, Rayleigh number, or Darcy number always leads to an increment of the average Nusselt number and energy transport intensity. It has been also observed that with a rise of the Darcy number and strengthening of flow motion (convection), the instability in both flow and temperature fields increases and the distribution of isotherms and streamlines becomes completely asymmetric.     

Sediment transport in an active erodible channel bend of Brahmaputra river

Spatial variation of sediment transport in an alluvial sand-bed river bend needs to be understood with its influencing factors such as bank erosion, secondary current formation, land spur and bed-material characteristics. In this study, detailed hydrographic surveys with Acoustic Doppler Current Profiler (ADCP) were conducted at an active erodible river bend to measure suspended load, velocity, bathymetric profile and characteristics of the bed material. Study indicates the presence of multi-thread flow in the channel bend. Local variation of sediment transport is primarily controlled by active bank erosion, land spur and sand bar formation. Vertical distribution of suspended sediment concentration follows a power function with normalized depth. Average bed-material concentration at the reach level is computed from observed sediment profiles, and is compared against various sediment transport functions. Results show that the sediment transport function suggested by Yang gives better predictions for this reach. Transverse bed slopes at critical survey transects were computed from the bathymetric data and evaluated with analytical approaches. Out of three analytical approaches used, Odgaard’s approach estimates the bed slopes fairly close to the observed one. These two functions are suitable in the Brahmaputra river for further morphological studies.     

Experimental determination of temperature profiles in a sheared granular bed containing two and three sizes of particles

An experiment to measure granular temperature in a sheared low density granular bed containing a range of sizes of particles has been performed. Using positron emission particle tracking, a single particle was tracked from different size phases. From the coordinate data, the second moment of the velocity fluctuations about the mean flow in each direction was determined. It was found that the larger particles are “hotter” and that most of the energy is contained in the θ (shearing) direction fluctuations. Evidence was found for Knudsen layer and higher order Burnett effects, suggesting extensions of the Navier-Stokes approaches are necessary to describe heat transport in polydisperse systems.     

明满交替流动计算方法研究及其实验验证

大型水电工程的尾水隧洞中可能会发生明满交替流动,给电站过渡过程带来很大影响,需要建立合理可行的明满交替流动数值计算模型。针对常用的明满交替流动数值差分格式在明满流分界面通过计算节点时计算不稳定的问题,提出了一种新的计算方法——特征隐式格式法,其主要思路是将动量和连续方程转化为双曲型方程组的标准形式进行差分。通过某电站尾水隧洞水工水力学模型实验专门对该方法进行验证,表明该计算方法是正确的。     

Effects of initial stage of dam-break flows on sediment transport

Experimental and numerical studies of dam-break flows over sediment bed under dry and wet downstream conditions are investigated and their effects on sediment transport and bed change on flow are illustrated. Dam-break waves are generated by suddenly lifting a gate inside the flume for three different upstream reservoir heads. The flow characteristics are detected by employing simple and economical measuring technique. The numerical model solves the two-dimensional Reynolds-Averaged Navier–Stokes (RANS) equations with k-ε turbulence closure using the explicit finite volume method on adaptive, non-staggered grid. The model is validated with laboratory data and is extended for simulating non-equilibrium sediment transport and bed evolution process. The volume of fluid technique is used to track the evolution of the free surface, satisfying the advection equation. The comparison study reveals that the current model is capable of defining the dam-break flow and improves the accuracy of determining morphological changes at the initial stages of the dam-break flow. A good agreement between the model solutions and the experimental data is observed.     

Calculation of an electromagnetic field in a three-phase inductionpump with a compensating winding

A three-phase inductor which generates a magnetic traveling field is often used in induction liquid metal pumps. Due to the finite length of the inductor an alternating magnetic field component occurs, which should be compensated. An analysis of the electromagnetic field of an induction pump with a rectangularly shaped transport channel and a flat three-phase inductor possessing a compensating winding is presented. It is based on a computational model which takes into account the finite length and width of an inductor winding and nonuniform velocity distribution along the liquid metal depth. The calculations of magnetic flux density distributions in liquid zinc were carried out for an induction pump with and without compensating winding     

Upscaled DEM-CFD model for vibrated fluidized bed based on particle-scale similarities

Simulation based on discrete element method (DEM) coupled with computational fluid dynamics (CFD), coupled DEM-CFD, is a powerful tool for investigating the details of dense particle–fluid interaction problems such as in fluidized beds and pneumatic conveyers. The addition of a mechanical vibration to a system can drastically alter the particle and fluid flows; however, their detailed mechanisms are not well understood. In this study, a DEM-CFD model based on a non-inertial frame of reference is developed to achieve a better understanding of the influence of vibration in a vibrated fluidized bed. Because the high computational cost of DEM-CFD calculations is still a major problem, an upscaled coarse-graining model is also employed. To realize similar behaviors with enlarged model particles, non-dimensional parameters at the particle scale were deduced from the governing equations. The suitability and limitations of the proposed model were examined for a density segregation problem of a binary system. To reduce the computational costs, we show that the ratio between the bed width and model particle size can be reduced to a minimum value of 100; to obtain similar segregation behaviors, the ratio between the bed height and model particle size is considered unchanged.