A 3D hydrodynamic numerical model of the Río de la Plata and Montevideo’s coastal zone

The 3D hydrodynamic numerical model MOHID was applied in the Río de la Plata and Montevideo coastal zone in order to represent the main dynamics and to study its complex circulation pattern. The hydrodynamic model was calibrated and validated considering the following main forces: fresh water flow, astronomical and meteorological tides in the oceanic boundary, and wind acting on the water surface. A series of water levels measured at six coastal stations and vertical profiles of current velocity measured at four different locations in the estuarine zone of the Río de la Plata were used for calibrating and validating the hydrodynamic model. The calibration process was carried out in two steps. First the astronomical waves propagation was calibrated comparing harmonic constants of observed and computed sea surface elevation data. Next, both the astronomical and meteorological wave propagation was calibrated. Direct comparison of scatter plot and root-mean square errors of model results and field data were used when evaluating the calibration quality. The calibrated model shows good agreement with the measured water surface level in the entire domain with mean error values being minor than 20% of the measured data and correlation factors higher than 0.74. Also, the intensity and velocity direction observed in the currents data are well represented by the model in both bottom and surface levels with errors similar to 30% of the currents data components. Using the 3D calibrated model the bottom and surface residual circulation for a four month period of time was analyzed.     

Three-dimensional numerical modeling of thermohaline and wind-driven circulations in the Persian Gulf

The Persian Gulf circulation is investigated with respect to the relevant forcing mechanism including wind stress and thermohaline surface fluxes by using a three-dimensional numerical hydrodynamic model. The model results show a correlation between the strength of the bottom layer outflow of the Persian Gulf and that of the Indian Ocean Surface Water (IOSW) inflow into the Gulf. The inflow of IOSW into the Gulf attain maximum values in May–June in conjunction with peak bottom outflow through the Hormuz Strait. The results of sensitivity experiment indicate that circulation is dominated by thermohaline flows at almost all parts of the Gulf. The heat fluxes play an essential role on the general circulation of the Persian Gulf. In spring and summer, the wind stress generates southeast-flowing surface currents of magnitude about 5 cm/s along the Saudi Arabia and Iranian coasts on the northern Gulf. In winter and autumn, due to weak static stability, the wind produces mesoscale eddies in most parts of the Gulf. In winter and spring the wind stress acts to reinforce the thermohaline circulation of deep outflow. Conversely, in summer and autumn the wind forcing acts in opposition to the thermohaline forcing and causes a bottom inflow from Oman Sea into the Gulf.     

Numerical modelling of residual flow and salinity in the Río de la Plata

The Río de la Plata discharges into the Atlantic Ocean. The particular characteristics of the study area, the variable width and shallowness of the river, the high fluvial discharges and the dynamic processes involving interactions between river discharges, tidal currents and wind, generate complex velocity and salinity fields. We applied the hydrodynamic model RMA-10 to examine the effects of various forcing (tides, flow discharge and winds) on residual currents and salinity fields in the Río de la Plata, focusing on the outer zone of the river. The RMA-10 code, developed by Ian King, is a multiparameter finite element model representing estuarine flow in three dimensions. In this study the model has been applied in a depth-averaged-baroclinic mode and a series of observed data is used for model calibration and verification. The model result shows that it is able to simulate velocity and the salinity fields with a reasonable accuracy. The analysis of residual currents in the river, when forced by freshwater discharge and astronomical tide, shows that the flow discharge takes place mainly over the shallower areas of the river and that the saline water is advected up-river through the deeper channels. The numerical simulations show that the winds from the South-West and North-East quadrants have a great influence over the salinity and velocity fields.     

A stratified model of flow in a coastal trench

A stratified model of the circulation in a deep, narrow trench adjacent to a coast is described. The flow in the trench is driven by surface wind stress, coastal runoff and inflow at one end. The model is being developed to investigate the Norwegian coastal current flowing through the Norwegian Trench.     

Integrated hydrodynamic model for simulation of river-lake-sluice interactions

In this paper, an integrated model for simulating the hydrodynamic process of river-lake-sluice (RLS) systems is presented. It includes a novel one-dimensional (1D) and two-dimensional (2D) coupling method called the coupling-zone iteration-correction (CZIC) method, and an improved numerical algorithm for the sluice problem. The 1D river-network model and the 2D lake model are coupled by establishing a coupling region, and iterative correction is carried out to ensure the accurate transfer of hydraulic parameters. The convergence conditions of the CZIC method are discussed theoretically, and the proper spatial step of the coupling zone is adopted according to different inflow conditions to ensure stable computation. In order to deal with the transition of flow regimes during the gate operation, a method for calculating the discharge capacity is presented. In addition, a general difference coefficient of the river reach is deduced for hydrodynamic calculation with sluices included. Simulations on open channels demonstrate that (1) simulated values of the CZIC method are consistent with the results of the full 2D model; (2) the sluice solving algorithm can stably handle the flow transition between the orifice flow and weir flow. Furthermore, the developed integrated model is applied to the middle and lower reaches of the Huaihe River, including the Hongze Lake and fifteen sluices. Numerical simulation results reproduced the hydrodynamic process during the flood season of 2007 accurately and efficiently. The errors of the present model are also compared with that of the MIKE model, and the results show that the proposed methods perform better than MIKE, especially in rising and flood periods. Therefore, it seems likely that the developed integrated model will work well in hydrodynamic modelling of large-scale complex RLS systems.     

Numerical modelling of salinity variations due to wind and thermohaline forcing in the Persian Gulf

Salinity is an important component of the marine system. Due to shallow nature of the Persian Gulf, the salinity has been influenced by both wind driven and surface thermohaline fluxes (heat and moisture fluxes). In this study, the seasonal distribution of salinity and its variations due to wind stress and thermohaline forcing are investigated by using a three-dimensional hydrodynamic model, Coupled Hydrodynamical–Ecological Model for Regional and Shelf Seas (COHERENS). The simulation results show that the salinity in the Persian Gulf experiences dramatic spatial and temporal variations. The influence of the thermohaline forcing is considerably more than the wind stress on the salinity. The effect of the surface thermohaline fluxes over the salinity field is generally to increase the salinity for almost all the water column during the year. This effect is high during September–November where the evaporative surface salinity flux dominates over inflow of low-salinity values of Indian Ocean Surface Water. The wind forcing at the most regions of the Persian Gulf, in particular at the United Arab Emirate (UAE) coast and Bahrain–Qatar shelf, freshens the water all the year round. The wind and thermohaline forcing in March–June have strong potential to generate stratification in salinity structure. The model predictions, which are successful in simulating many features of observed pattern, indicate that the surface water of the Gulf is saltier in winter than that in spring and early summer. Both heat fluxes and wind stress play an important role for this seasonal cycle of the surface salinity.     

Environmental flows for the Yangtze Estuary based on salinity objectives

Environmental flows based on the salinity objectives for China’s Yangtze Estuary were quantified to assess the impacts of changing freshwater inflow on the estuarine ecosystem. The salinity objectives for three benthos habitats in the Yangtze Estuary were studied to determine their requirements during the most critical period of the year. The temporal variation in the natural monthly river discharge represented the temporal variation of the ecological objectives used to maintain natural flow regimes. A numerical model, coupled a hydrodynamic processes model with a salinity model and validated using field data of tidal height, current velocity, and salinity at different stations, was developed to simulate the spatial distribution of salinity as a function of the variation in freshwater inflows. The prediction results of the proposed model agreed well with the field data. Considering the salinity objectives for the different habitats, the environmental flow requirements for the Yangtze Estuary were determined. Annual environmental flows should be 9.63 × 10¹¹, 6.32 × 10¹¹, and 4.70 × 10¹¹ m³ for the high, medium, and minimum objectives, which are equivalent to 104%, 68%, and 50% of the annual river discharge, respectively. The periods from September to November should be considered as the critical seasons to maintain the minimum environmental flows in the Yangtze Estuary.     

Study of storm surge due to Typhoon Linda (1997) in the Gulf of Thailand using a three dimensional ocean model

Numerical integrations using the three dimensional ocean model based on the princeton ocean model (POM) were applied for the study of both sea level elevation and ocean circulation patterns forced by the wind fields during typhoons that moved over the Gulf of Thailand (GoT). The simulation concerned a case of Typhoon Linda which occurred during November 1-4, 1997. Typhoon Linda was one of the worst storms that passed the Gulf of Thailand and hit the southern coastal provinces of Thailand on November 3, 1997. It caused flooding and a strong wind covering large areas of agriculture and fisheries, which destroyed households, utilities and even human lives. The model is the time-dependent, primitive equation, Cartesian coordinates in a horizontal and sigma coordinate in the vertical. The model grid has 37 × 97 orthogonal curvilinear grid points in the horizontal, with variable spacing from 2 km near the head of the GoT to 55 km at the eastern boundary, with 10 sigma levels in the vertical conforming to a realistic bottom topography. Open boundary conditions are determined by using radiation conditions, and the sea surface elevation is prescribed from the archiving, validation and interpretation of satellite oceanographic data (AVISO). The initial condition is determined from the spin up phase of the first model run, which was executed by using wind stress calculated from climatological monthly mean wind, restoring-type surface heat and salt and climatological monthly mean freshwater flux. The model was run in spin up phase until an ocean model reached an equilibrium state under the applied force. A spatially variable wind field taken from the European Centre for Medium-Range Weather Forecasts (ECMWF) is used to compute the wind stress directly from the velocity fluctuations. Comparison of tendency between the sea surface elevations from model and the observed significant wave heights of moored buoys in the Gulf of Thailand under Seawatch project is investigated. The model predicts the sea level elevation up to 68.5 cm at the Cha-Am area located in the north of where the typhoon strands to the shore. Results of sea level elevation show that there is an area of peak set-up in the upper gulf, particularly in the western coast, and the effects of the storm surge are small at the lower gulf. During the entire period of this study, the surge in the gulf was induced by the northeasterly wind blowing over it.     

Subsonic solutions of hydrodynamic model for semiconductors

This paper is concerned with the existence and uniqueness of the steady-state solution of hydrodynamic model for semiconductor devices. Boundary conditions are prescribed by vorticity on inflow boundary as well as by electron density, temperature, and normal component of electron velocity on whole boundary. If the ambient temperature is large, and if both vorticity on inflow boundary and the variation of density on boundary are small, a unique subsonic solution exists. © 1997 by B.G. Teubner Stuttgart–John Wiley & Sons Ltd.     

Finite element modelling of surface waves in a channel

A variational formulation of the vertically-integrated differential equations for free surface wave motion is presented. A finite element model is derived for solving this nonlinear system of hydrodynamic equations. The time integration scheme employed is discussed and the results obtained demonstrate its good stability and accuracy.Several applications of the model are considered: the first problem is an open channel of uniform depth and the second an open channel of linearly varying depth. The ‘inflow’ boundary condition is prescribed in terms of the velocity which represents a wavemaker and/or a flow source, while the ‘outflow’ boundary condition is specified in terms of the water elevation. The outflow condition is adjusted for two cases, a reflecting boundary (finite channel) and a non-reflecting boundary (open-ended channel). The latter boundary condition is examined in some detail and the results obtained show that the numerical model can produce the non-reflecting boundary that is similar to the analytical radiation condition for waves. Computational results for a third problem, involving wave reflection from a submerged cylinder, are also presented and compared with both experimental data and analytical predictions.The simplicity and the performance of the computational model suggest that free surface waves can be simulated without excessively complicated numerical schemes. The ability of the model to simulate outflow boundary conditions properly is of special importance since these conditions present serious problems for many numerical algorithms.     

Evaluation of reduction behavior of blast furnace dust particles during in-flight process with experiment aided mathematical modeling

In-flight reduction technology is a flexible process that allows recycling of the fine iron bearing metallurgical dusts efficiently. In this work, a mathematical model, incorporating introduced experimental kinetic parameters, was developed to accurately evaluate the reduction behavior of blast furnace (BF) dust particles during flight. A detailed evaluation of particle residence time, thermal history and reduction degree conversion were used to eliminate the deviations related to the assumptions of constant particle velocity and temperature in the experiment. The results show that the particle velocity decreases along the longitudinal direction of the reactor for a long distance and reaches a constant low velocity at the middle part of the reaction zone. The calculated particle residence time is 0.15–0.44 s less than the experimentally estimated value. The particle temperature reaches the isothermal temperature at the 0.15 m position from the reaction zone bottom. An obvious transition of reduction degree of dust particle is found when particle temperature reaches over 1640 K. The prediction accuracy of the model was improved by using the optimized kinetic parameters, namely pre-exponential factor and activation energy.     

A numerical computation of a non-dimensional form of stream water quality model with hydrodynamic advection–dispersion–reaction equations

Mathematical models of water quality assessment problems often arise in environmental science. The modelling often involves numerical methods to solve the equations. In this research, two mathematical models are used to simulate pollution due to sewage effluent in the nonuniform flow of water in a stream with varied current velocity. The first is a hydrodynamic model that provides the velocity field and elevation of the water flow. The second is a dispersion model, where the commonly used governing factor is the one-dimensional advection–dispersion–reaction equation that gives the pollutant concentration fields. In the simulation processes, we used the Crank–Nicolson method system of a hydrodynamic model and the backward time central space scheme for the dispersion model. Finally, we present a numerical simulation that confirms the results of the techniques.     

Correlation of design parameters with performance for electrostatic Precipitator. Part I. 3D model development and validation

As the first part of a two-paper series, this paper develops a three-dimensional model that describes corona discharge, turbulent flow, particle charging and tracking in electrostatic precipitators (ESP). To capture the shielding effects between discharge wires in a multi-wire ESP, the corona-discharge-induced space charge density at an arbitrary point between the discharge wire and grounded plates is specified as the sum of two components: (i) a uniform value on the wire surface which is resolved individually for each wire; and (ii) a space-dependent variation relative to the uniform part. The present model is solved with the finite element method and validated with experimental and numerical results from literature. Good agreement is obtained and illustrated in terms of distributions of electric potential, current density, electrohydrodynamic flow pattern, and particle trajectories, as well as corona current and particle collection efficiency. This validated model will be applied in Part II and integrated with the design-of-experiment approach to analyze both individual and interactive effects of design parameters on ESP performance.     

Axial transport in dry ball mills

Ball mills are used for grinding of rocks, cement clinker and limestone from 10 to 100 mm feed sizes down to sub-millimetre product. They are typically rotating cylinders with diameters from 3 to 6 m and lengths from 6 to 12 m. The flow of particulate solids within these mills can be modelled using the discrete element method (DEM). Typically, such modelling is done for short durations of a few mill revolutions and either in two dimensions or using thin three-dimensional slices through the center of the mill with periodic boundary conditions in the axial direction. This facilitates an understanding of the radial motion of the charge, estimation of power draw and of liner wear, but it cannot provide information about axial transport within the mill. In this paper, we examine the axial transport in dry ball mills. This requires simulation of the entire mill and the full volume of the charge for significant periods of time (thousands of revolutions). We use a simple model for grate discharge that allows prediction of the time varying axial distribution of different particle sizes within a discharging ball mill. The distributions of sub-grate size ‘fines’ is shown to satisfy a one-dimensional diffusion equation with the diffusion coefficient decreasing with grate size. A pulse test, where a single mass of fines in injected at the feed end, is able to quantify the residence time distribution of the fines.     

Analytical modelling for a three-dimensional hydrofoil with winglets operating beneath a free surface

The current study focuses on establishing a theoretical lifting surface model for predicting the hydrodynamic loads acting on the three-dimensional hydrofoil with winglets, which is considerably influenced by the proximity to the free surface through finding the three-dimensional Green’s function for the planar and vertical horseshoe vortices operating below a free surface. The hydrofoil surface is decomposed into a finite number of elements along the span direction and the chord directions, each of which can then be represented by a horseshoe vortex. The linearized free surface boundary condition is applied to analyze the influence of the free surface on the hydrofoil as well as the winglets. The thickness problem is considered using the source distribution among the hydrofoil and winglets surfaces and the analytical Green’s function that satisfies the linearized free surface boundary condition is used. As a sample application, numerical examples were conducted to show the performance of the hydrodynamic characteristics for the hydrofoil with winglets as a function of the Froude number. It was concluded that there are significant efficiency benefits from using winglets inside the free surface proximity effect. These results are substantiated by the comparison with the available published data.     

Solutions for Initial-Boundary-Value Problems Representing Gravity Currents Arising from Variable Inflow

In this article, we report on theoretical and numerical studies of models for suddenly initiated variable inflow gravity currents in rectangular geometry. These gravity currents enter a lighter, deep ambient fluid at rest at a time‐dependent rate from behind a partially opened lock gate and their subsequent dynamics is modeled in the buoyancy‐inertia regime using ½‐layer shallow water theory. The resistance to flow that is exerted by the ambient fluid on the gravity current is accounted for by a front condition which involves a non‐dimensional parameter that can be chosen in accordance with experimental observations. Flow filament theory is used to arrive at expressions for the variable inflow velocity under the assumptions of an inviscid and incompressible fluid moving through an opening of fixed area which is suddenly opened under a lock gate at one end of a large rectangular tank. The fluid in the lock is subjected to a (possibly) time varying pressure applied uniformly over its surface and the finite movement of the free surface is accounted for. Finding this time‐dependent inflow velocity, which will then serve as a boundary condition for the solution of the shallow‐water equations, involves solving forced non‐linear ordinary differential equations and the form of this velocity equation and its attendant solutions will, in general, rule out finding self‐similar solutions for the shallow‐water equations. The existence of self‐similar solutions requires that the gravity currents have volumes proportional to t ^α , where α≥ 0 and t is the time elapsed from initiation of the flow. This condition requires a point source of fluid with very special properties for which both the area of the gap and the inflow velocity must vary in a related and prescribed time‐dependent manner in order to preserve self‐similarity. These specialized self‐similar solutions are employed here as a check on our numerical approach. In the more natural cases that are treated here in which fluids flow through an opening of fixed dimensions in a container an extra dimensional parameter is introduced thereby ruling out self‐similarity of the solutions for the shallow‐water equations so that the previous analytical approaches to the variable inflow problem, involving the use of phase‐plane analysis, will be inapplicable. The models developed and analyzed here are expected to provide a first step in the study of situations in which a storage container is suddenly ruptured allowing a heavy fluid to debouch at a variable rate through a fixed opening over level terrain. They also can be adapted to the study of other situations where variable inflow gravity currents arise such as, for example, flows of fresh water from spring run‐off into lakes and fjords, flows from volcanoes and magma chambers, discharges from locks and flash floods.     

Numerical evaluation of the suppression effect of a free-to-rotate triangular fairing on the vortex-induced vibration of a circular cylinder

The suppression of vortex-induced vibration (VIV) of a circular cylinder with a free-to-rotate triangular fairing in the Reynolds number range of Re = 1100–6100 is numerically investigated using computational fluid dynamics. The unsteady Reynolds-averaged Navier–Stokes equations and the shear stress transport k–ω turbulence model coupled with an improved fourth-order Runge–Kutta method are used to solve the wake flow, the structure's vibration, and the fairing's rotation. The computational model is validated with the available experimental results for a cylinder with an attached short-tail fairing. The numerical results indicate that the triangular fairing has a positive role in suppressing vibration when it achieves a stable position deflected from the flow direction. The suppression effect is sensitive to the incoming flow velocity. The fairing shifts from a stable state to an unstable one when the flow velocity varies. Therefore, maintaining the hydrodynamic stability of the fairing is the key to achieving success in vibration suppression, and the stability is dependent on the characteristic length and the rotational friction. Although the strong flapping of the 70° triangular fairing excites a more vigorous vibration, it may be used as an amplifier of VIV for energy harvesting.     

超声波测速仪的计算流体力学数值模拟研究

超声波测速仪是一种利用超声波发射接收装置,通过发射接收时间来计算来流速度的一种仪器装置.目前国内许多研究都关注在如何消除测速仪的测量误差上,对于模型结构对测量风场的影响研究较少.为了考察测速仪的测量精度,本研究以模型结构对测量区域风速的影响作为关注的重点,采用计算流体力学方法模拟了从低速到高速的不同来流风速下的绕流流场,计算出位于测速仪中心区域的速度分布和不同截面上的平均速度,以判断测速仪模型结构对中心测量区域风速的影响程度.该研究结果表明在测速探头平面内测量到的速度值,无论在低速和高速时均最为准确.采用计算流体力学数值模拟方法可为今后的测速仪模型设计和改造提供准确的依据.     

On determining the profile of steady wind-induced currents

A technique is developed to solve the steady-state hydrodynamic equations which describe wind-induced currents at a point. By using the Galerkin approach, with an expansion of complex coefficients and real functions, a continuous current profile can be computed from sea surface to sea bed for arbitrary vertical variations of viscosity. The method can incorporate slip or no-slip bottom boundary conditions, and gradients of sea surface elevation. The technique is used to investigate the influence of viscosity profile, bed stress and elevation gradient on surface current magnitude and direction. Calculations suggest that viscosity profile, bed stress, and elevation gradient all affect surface current, offering some explanation for the range of surface current magnitudes and directions reported in the literature.