Application of 2D Numerical Model to Unsteady Performance Evaluation of Vertical-Axis Tidal Current Turbine

Abstract Tidal current energy is renewable and sustainable, which is a promising altemative energy resource for the future elec- tricity supply. The straight-bladed vertical-axis turbine is regarded as a useful tool to capture the tidal current energy especially under low-speed conditions. A 2D unsteady numerical model based on Ansys-Fluent 12.0 is established to conduct the numerical simulation, which is validated by the corresponding experimental data. For the unsteady calculations, the SST model, 2x 105 and 0.01 s are se- lected as the proper turbulence model, mesh number, and time step, respectively. Detailed contours of the velocity distributions around the rotor blade foils have been provided for a flow field analysis. The tip speed ratio （TSR） determines the azimuth angle of the appearance of the torque peak, which occurs once for a blade in a single revolution. It is also found that simply increasing the incident flow velocity could not improve the turbine performance accordingly. The peaks of the averaged power and torque coeffi- cients appear at TSRs of 2.1 and 1.8, respectively. Furthermore, several shapes of the duct augmentation are proposed to improve the turbine performance by contracting the flow path gradually from the open mouth of the duct to the rotor. The duct augmentation can significantly enhance the power and torque output. Furthermore, the elliptic shape enables the best performance of the turbine. The numerical results prove the capability of the present 2D model for the unsteady hydrodynamics and an operating performance analy- sis of the vertical tidal stream turbine.

A Finite Volume Method with Unstructured Triangular Grids for Numerical Modeling of Tidal Current

The finite volume method （FVM） has many advantages in 2-D shallow water numerical simulation. In this study, the finite volume method is used with unstructured triangular grids to simulate the tidal currents. The Roe scheme is applied in the calculation of the intercell numerical flux, and the MUSCL method is introduced to improve its accuracy. The time integral is a two-step scheme of forecast and revision. For the verification of the present method, the Stoker＇s problem is calculated and the result is compared with the mathematically analytic solutions. The comparison indicates that the method is feasible. A sea area of a port is used as an example to test the method established here. The result shows that the present computational method is satisfactory, and it could be applied to the engineering fields.

Numerical Tidal Current Modeling Using Fine Boundary-Fitted Grids for Tidal Flats

Fine grids with small spacing in boundary-fitted coordinates are normally used to treat the computation of fluid dynamics for estuarine areas and tidal flats. However, the adoption of Cartesian components of velocity vectors in this kind of non-orthogonal coordinates will definitely result in a difficulty in solving implicitly the transformed momentum equations, and also complicate the wet-dry point judgement used for flood areas. To solve this problem, equations in terms of generalized contravariant velocity vectors in curvilinear coordinates are derived in the present study, by virtue of which, an Alternative-Direction-Implicit numerical scheme in non-orthogonal grids would then be easily obtained, and wet-dry point judgement would as well be largely simplified. A comparison is made between the explicit scheme and implicit scheme, showing that the present model is accurate and numerically stable for computations of fluid dynamics for estuarine areas and tidal flats.

Numerical modeling of tidal current of LNG terminal in Caofeidian,Bohai Sea

In order to reasonably simulate tidal currents around small structures such as piles in a large-scale model domain, a 2-D hydrodynamic integrated model for Bohai Sea is established with the finite element method. The grid can be discretionarily refined as a non-structure triangle or quadrilateral so that piers can be treated as one or several impermeable elements with an area of 20 to 30 km^2 in a model domain over 85 700 km^2. The computational results of tidal levels and horizontal velocities are in good agreement with the field data. Based on the computed results by the model, the layout of an open 105 DWT liquefied natural gas （LNG）terminal in Caofeidian, Bohal Sea is effectively and reasonably optimized. It can be concluded that the model is suitable and reasonable for direct simulation of tidal currents around small structures in projects.

Analysis of Tidal Current Energy Potential in the Major Channels of the Bohai Strait Based on Delft3D

The utilization and development of tidal current energy can help alleviate the current energy shortage,improve the global ecological environment,and maintain sustainable development.In this study,numerical simulation is carried out on a rectangular grid using Delft3D.The tidal current energy potential of the major channels in the Bohai Strait is further simulated and estimated by comparing the simulated and measured data.Results show that the flow module in Delft3D has good modeling ability for the assessment of tidal current energy potential.The average flow velocity,maximum flow velocity,and energy flow density are consistent.The Laotieshan Channel,located in the northern part of the Bohai Strait,shows a large tidal current energy potential.The maximum flow velocity of this channel can reach 2 m s-1,and the maximum energy flow density can exceed 500 W m-2.The tidal current energy in the Laotieshan Channel is more than 10 times that in other channels.Therefore,this study advocates for the continued exploration and exploitation of the tidal current energy resources in the Laotieshan Channel.

A method to calculate design tide levels on the basis of numerical model of tidal current and its application

In order to determine the design tide levels in the areas without measured tide level data, especially in the areas where it is difficult to measure tidal levels, a calculation method based on a numerical model of tidal current is proposed. The essentials of the method are described, and its application is illustrated with an example. The results of the application show that the design tide levels calculated by the method are close to those determined by long-time measured tide level data, and its calculation precision is high, so it is feasible to use the method to determine the design tide levels in the areas.

Three-dimensional tidal current numerical model of the Oujiang Estuary

The characteristics of three-dimensional （3-D） tidal current in the Oujiang Estuary are investigated according to in situ observations. The Oujiang Estuary has features of irregular coastline, complex topography, many islands, moveable boundary, and submerged dyke, therefore, σ 3-D numerical model oil an unstructured triangular grid has been degeloped. The σ coordinate transforination, the moveable boundary and submerged dyke treatment techniques were employed in the model so it is suitable for the tidal simulations in the Oujing Estuary with submerged dyke and moveable boundary problems. The model is evaluated with the in situ data, and the results show that the calculated water elevations at 19 stations and currents at 19 profiler stations are in good agreement with measured data both in magnitude and phase. This numerical model is applied to the 3-D tidal circulation simulations of experiments in stopping flow transport through the South Branch of the Oujiang Estuary, and the feasibility to cutoff the flow in the South Branch of the Oujiang Estuary is demonstrated by numerical simulation experiments. The developed numerical model simulated the 3-D tidal current circulations in complicated coastal and estuarine waters very well.

An Application of Finite Volume WENO Schemeto Numerical Modeling of Tidal Current

A depth-averaged 2-D numerical model for unsteady tidal flow in estuaries is established by use of the finite volume WENO scheme which maintains both uniform high order accuracy and an essentially non-oscillatory shock transition on unstructured triangular grid. The third order TVD Range-Kutta method is used for time discretization. The model has been firstly tested against four cases： 1） tidal forcing, 2） seiche oscillation, 3） wind setup in a closed bay, and 4） onedimensional dam-break water flow. The results obtained in the present study compare well with those obtained from the corresponding analytic solutions idealized for the above four cases. The model is then applied to the simulation of tidal circulation in the Yangpu Bay, and detailed model calibration and verification have been conducted with measured tidal current in the spring tide, middle tide, and neap tide. The overall performance of the model is in qualitative agreement with the data observed in 2005, and it can be used to calculate the flow in estuaries and coastal waters.

2D Coupled 3D:A New Numerical Model for Dual - Structured - Aquifer System

This paper points out that a successful numerical simulation is to construct a correct conceptional model which is very dose to the natural condition. A new model, two dimensional coupled three dimensional model (2D -3D ) is presented in the Present paper,which is the most suitable one for the dual - structured - aquifer system. An example of Wenyinghu area is shown.By using the 2D-3D model, a satisfied result of the simulated area is achieved.

Modeling assessment of tidal current energy in the Qiongzhou Strait, China

In the present study, an existing three-dimensional finite volume computational ocean model （FVCOM） was refined and configured including an algorithm for computing the power density and mean power density at Qiongzhou Strait of China. The refined model was validated with the measured tidal levels and tidal currents at different gauging stations. The model results are in reasonable agreement with the measured data. Based on the modeling results, we assess the resource of the tidal stream energy in the Qiongzhou Strait and discuss the temporal and the spatial distribution of the tidal current energy there. The conclusion is extracted： the higher power density occurs in the middle area of the strait, and lower at both sides. Characteristics of power density such as the maximum possibility speed, maximum power density during the spring tide period and the neap tide period, have the similar distribution. The southeast part and central area of the strait are of rich tidal current energy, where the maximum possibility speed can reach to 4.6 m/s, and the maximum power density of the spring tide period and the neap tide period can reach 5 996 and 467 W/mz separately in the surface layer The annual mean power density can reach 819 W/m2. Statistical length of accumulative time of the velocity exceeding 0.7 m/s is about 4 717 h at local point during a year. The total theoretical tidal current energy resource is approximately 189.55 MW and the available exploited energy on present technology condition is 249, 20.2 and 263 GW/a separately by using the methods FLUX, FARM and GC in the Qiongzhou Strait.

Numerical simulation of sediment lifted by waves and transported by tidal currents

The analysis of the scabed processes of a muddy coast has been described in this paper. On the basisof the basic differential equation of tidal current and sediment movement influenced by waves, a numerical simulation system for sediment lifted by waves and transported by tidal currents and scabed processes has been established by using MADI method, and applied to the sea area of Tianjin Port with good results.

Approach of moving boundary and its application in 3D tidal current simulation of Changjiang (Yangtze) River Estuary based on ECOMSED model

Considering three-dimensional model ECOMSED can not simulate wetting-drying of shoal with its fixed boundary, an approach to represent moving boundary in the model is introduced here. This approach smoothly joints the internal and external mode by making use of wetting and drying technique and is verified by a numerical test which presents a good agreement with the previous test results obtained by other researchers. A three dimensional numerical model is established to simulate the hydrodynamics in spring tide in the Changjiang （Yangtze） River estuary by this modified ECOMSED model which is also validated through the observed field data, the simulation presents a good periodic tidal change. It also successfully simulates the tidal current of computational areas and reproduces the tidal flat intermittent appearance.

Debris flow simulation 2D(DFS 2D):Numerical modelling of debris flows and calibration of friction parameters

Debris flows are rapid mass movements with a mixture of rock,soil and water.High-intensity rainfall events have triggered multiple debris flows around the globe,making it an important concern from the disaster management perspective.This study presents a numerical model called debris flow simulation 2D(DFS 2D)and applicability of the proposed model is investigated through the values of the model parameters used for the reproduction of an occurred debris flow at Yindongzi gully in China on 13 August 2010.The model can be used to simulate debris flows using three different rheologies and has a userfriendly interface for providing the inputs.Using DFS 2D,flow parameters can be estimated with respect to space and time.The values of the flow resistance parameters of model,dry-Coulomb and turbulent friction,were calibrated through the back analysis and the values obtained are 0.1 and 1000 m/s^(2),respectively.Two new methods of calibration are proposed in this study,considering the crosssectional area of flow and topographical changes induced by the debris flow.The proposed methods of calibration provide an effective solution to the cumulative errors induced by coarse-resolution digital elevation models(DEMs)in numerical modelling of debris flows.The statistical indices such as Willmott's index of agreement,mean-absolute-error,and normalized-root-mean-square-error of the calibrated model are 0.5,1.02 and 1.44,respectively.The comparison between simulated and observed values of topographic changes indicates that DFS 2D provides satisfactory results and can be used for dynamic modelling of debris flows.

Numerical and Experimental Study of the 3D Effect on Connecting Arm of Vertical Axis Tidal Current Turbine

Vertical axis tidal current turbine is a promising device to extract energy from ocean current. One of the important components of the turbine is the connecting arm, which can bring about a significant effect on the pressure distribution along the span of the turbine blade, herein we call it 3D effect. However, so far the effect is rarely reported in the research, moreover, in numerical simulation. In the present study, a 3D numerical model of the turbine with the connecting arm was developed by using FLUENT software compiling the UDF（User Defined Function） command. The simulation results show that the pressure distribution along the span of blade with the connecting arm model is significantly different from those without the connecting arm. To facilitate the validation of numerical model, the laboratory experiment has been carried out by using three different types of NACA aerofoil connecting arm and circle section connecting arm. And results show that the turbine with NACA0012 connecting arm has the best start-up performance which is 0.346 m/s and the peak point of power conversion coefficient is around 0.33. A further study has been performed and a conclusion is drawn that the aerofoil and thickness of connecting arm are the most important factors on the power conversion coefficient of the vertical axis tidal current turbine.

Numerical Analysis of Steady Smoldering of Biomass Rods

Understanding the steady mechanism of biomass smoldering plays a great role in the utilization of smoldering technology.In this study numerical analysis of steady smoldering of biomass rods was performed.A two-dimensional(2D)steady model taking into account both char oxidation and pyrolysis was developed on the basis of a calculated propagation velocity according to empirical correlation.The model was validated against the smoldering experiment of biomass rods under natural conditions,and the maximum error was smaller than 31%.Parameter sensitivity analysis found that propagation velocity decreases significantly while oxidation area and pyrolysis zone increase significantly with the increasing diameter of rod fuel.

A study of impact of the reclamation and artificial island projects on tidal currents and sediment concentration in radial sand ridge field of the South Yellow Sea

The two-dimensional hydrodynamic model, MIKE21, is applied to simulate the tidal currents and sediment concentration in the radial sand ridges of the South Yellow Sea. Results are in accordance with in situ observations. Then the variations of tidal currents and suspended sediment concentration caused by reclamation and artificial islands projects are simulated. The results show that the impacts are limited around the project areas. After the projects, the fan-shaped, Jianggang centered tidal current pattern would be replaced by a pattern which is formed by two tidal paths. One locates at the Xiyang channel in north-south direction, and the other locates at the Huangshayang channel in east-west direction. The reclamation of Tiaozini separates the waters into south portion and north portion. The changes of sediment concentrations coincide with those of currents. Both the sediment concentrations and tidal currents increase at the northwest of Dongsha and the south of Gaoni, while both decrease at the north and south of Tiaozini, and the east and southwest of Dongsha.

Quasi-3D Numerical Simulation of Tidal Hydrodynamic Field

Based on the 2D horizontal plane numerical model, a quasi-3D numerical model is established for coastal regions of shallow water. The characteristics of this model are that the velocity profiles;can be obtained at the same time when the equations of the value of difference between the horizontal current velocity and its depth-averaged velocity in the vertical direction are solved and the results obtained are consistent with the results of the 2D, model. The circulating flow in the rectangular area induced by wind is simulated and applied to the tidal flow field of the radial sandbanks in the South Yellow Sea. The computational results from this quasi-3D model are in good agreement with analytical results and observed data. The solution of the finite difference equations has been found to be stable, and the model is simple, effective and practical.

A 2-D Non-local Closure Model for Atmospheric Boundary Layer Simulations

In this paper a new approach for PBL simulation, the non-local closure scheme based on the transient turbulence theory has been used. It was set up as an alternative to local closure schemes which physical concept is reasonable and distinct. A 2-D non-local closure model was developed in order to study the PBL structure and simulatesome interesting atmospheric processes over non-ulliform underlying surface, especially under the convective and unique weather conditions, such as sea-land circulation and the TIBL structure. The modelled results show good agreement with field measurement.

Numerical Modeling of Sediment Transport and Its Effect on Algal Biomass Distribution in Lake Pontchartrain Due to Flood Release from Bonnet CarréSpillway

In order to protect the city of New Orleans from the Mississippi River flooding, the Bonnet Carré Spillway (BCS) was constructed from 1929 to 1936 to divert flood water from the river into Lake Pontchartrain and then into the Gulf of Mexico. During the BCS opening for flood release, large amounts of freshwater, nutrients, sediment, etc. were discharged into Lake Pontchartrain, and caused a lot of environmental problems. To evaluate the environmental impacts of the flood water on lake ecosystems, a two-dimensional numerical model was developed based on CCHE2D and applied to simulate the flow circulation, sediment transport and algal biomass distribution in Lake Pontchartrain. The effect of sediment concentration on the growth of algae was considered in the model. The numerical model was calibrated using field measured data provided by USGS, and then it was validated by the BCS Opening Event in 1997. The simulated results were generally in good agreement with filed data and satellite imagery. The field observation and numerical model show that during the spillway opening for flood release, the sediment concentration is very high, which greatly restricts the growth of algae, so there is no algal bloom observed in the lake. After the closure of BCS, the sediment concentration in the lake reduces gradually, and the nutrient concentration of the lake is still high. Under these conditions, numerical results and satellite imagery showed that the chlorophyll concentration was high and algal bloom might occur.

万宁港北渔港避风锚地扩建工程潮流分析研究

渔港避风锚地潮流流速、流态对船舶安全停泊具有重要影响。针对万宁港北渔港避风锚地扩建工程的实施,结合工程水域历史大小潮水文观测资料,采用二维潮流模型对工程实施前后的潮流流态进行模拟研究,分析工程实施以后流场特征及其可能对周边水动力环境带来的影响。研究结果表明:工程实施后,航道疏浚水深增加,过水断面面积相应增加,航道处在二维平面上表现为流速略有减小。与此同时,由于航道浚深,水流向航道处集中,航道两侧的分流作用减弱,流速也略有减小;与小海南汊道整治工程实施叠加后,南汊道的分流作用明显;小海北汊道分流作用减弱,流速下降。