THE STUDY ON THREE-DIMENSIONAL MATHEMATICAL MODEL OF RIVER BED EROSION FOR WATER-SEDIMENT TWO-PHASE FLOW

Based on the tensor analysis of water-sediment two-phase how, the basic model equations for clear water flow and sediment-laden flow are deduced in the general curve coordinates for natural water variable-density turbulent how. Furthermore, corresponding boundary conditions are also presented in connection with the composition and movement of non-uniform bed material. The theoretical results are applied to the calculation of the float open caisson in the construction period and good results are obtained.

Analytical solution to one-dimensional mathematical model of flow and morphological evolution in open channels

The evolution of open-channel flow and morphology can be simulated by one-dimensional(1D) mathematical models. These models are typically solved by numerical or analytical methods. Because the behavior of variables can be explained by explicit mathematical determinations,compared to numerical solutions,analytical solutions provide fundamental and physical insights into flow and sediment transport mechanisms. The singular perturbation technique derives a hierarchical equation of waves and describes the evolutionary nature of disturbances in hyperbolic systems. The wave hierarchy consists of dynamic,diffusion,and kinetic waves. These three types of waves interact with each other in the process of propagation. Moreover,the Laplace transform is implemented to transform partial differential equations into ordinary differential equations. Analytical expressions in the wave front are subtracted by the approximation of kinetic and diffusion models. Moreover,an analytical solution consists of a linear combination of the kinetic wave front and the diffusion wave front expressions,pursuing to describe the physical mechanism of motion in open channels as completely as possible. Analytical solutions are presented as a combination of exponential functions,hyperbolic functions,and infinite series. The obtained analytical solution was further applied to the simulation of flood path and morphological evolution in the Lower Yellow River. The phenomenon of increased peak discharge in the downstream reach was successfully simulated. It was encouraging that the results were in good agreement with the observed data.

A Thermal-Hydraulic Coolant Channel Module (CCM) for Single- and Two-Phase Flow

A theoretical “drift-flux based thermal-hydraulic mixture-fluid coolant channel model” is presented. It is the basis to a corresponding digital “Coolant Channel Module (CCM)”. This purpose derived “Separate-Region Mixture Fluid Approach” should yield an alternative platform to the currently dominant “Separate-Phase Models” where each phase is treated separately. Contrary to it, a direct procedure could be established with the objective to simulate in an as general as possible way the steady state and transient behaviour of characteristic parameters of single- and/or (now non-separated) two-phase fluids flowing within any type of heated or non-heated coolant channels. Their validity could be confirmed by a wide range of verification and validation runs, showing very satisfactory results. The resulting universally applicable code package CCM should provide a fundamental element for the simulation of thermal-hydraulic situations over a wide range of complex systems (such as different types of heat exchangers and steam generators as being applied in both conventional but also nuclear power stations, 1D and 3D nuclear reactor cores etc). Thereby the derived set of equations for different coolant channels (distinguished by their key numbers) as appearing in these systems can be combined with other ODE-s and non-linear algebraic relations from additional parts of such an overall model. And these can then to be solved by applying an appropriate integration routine. Within the solution procedure, however, mathematical discontinuities can arise. This due to the fact that along such a coolant channel transitions from single- to two-phase flow regimes and vice versa could take place. To circumvent these difficulties it will in the presented approach be proposed that the basic coolant channel (BC) is subdivided into a number of sub-channels (SC-s), each of them being occupied exclusively by only a single or a two-phase flow regime. After an appropriate nodalization of the BC (and thus its SC-s) and after applying a “modified finite volume method” together with other special activities the fundamental set of non-linear thermal-hydraulic partial differential equations together with corresponding constitutive relations can be solved for each SC separately. As a result of such a spatial discretization for each SC type (and thus the entire BC) the wanted set of non-linear ordinary differential equations of 1st order could be established. Obviously, special attention had to be given to the varying SC entrance or outlet positions, describing the movement of boiling boundaries or mixture levels along the channel. Including even the possibility of SC-s to disappear or be created anew during a transient.

Lateral Shear Layer and Its Velocity Distribution of Flow in Rectangular Open Channels

The lateral velocity distribution of flow in the shear layer of open channel is required to many problems in river and eco-environment engineering, e.g. distribution of pollutant dispersion, sediment transport and bank erosion, and aquatic habitat. It is not well understood about how the velocity varies laterally in the wall boundary layer. This paper gives an analytical solution of lateral velocity distribution in a rectangular open channel based on the depth-averaged momentum equation proposed by Shiono & Knight. The obtained lateral velocity distributions in the wall shear layer are related to the two hydraulic parameters of lateral eddy viscosity (λ) and depth-averaged secondary flow (Γ) for given roughened channels. Preliminary relationships between the above two parameters and the aspect ratio of channel, B/H, are obtained from two sets of experimental data. The lateral width (δ) of the shear layer was investigated and found to relate to the λ and the bed friction factor (f), as described by Equation (26). This study indicates that the lateral shear layer near the wall can be very wide (δ/H = 14.6) for the extreme case (λ = 0.6 and f = 0.01).

A numerical model for air concentration distribution in self-aerated open channel flows

The self-aeration in open channel flows, called white waters, is a phenomenon seen in spillways and steep chutes. The air distribution in the flow is always an important and fundamental issue. The present study develops a numerical model to predict the air concentration distribution in self-aerated open channel flows, by taking the air-water flow as consisting of a low flow region and an upper flow region. On the interface between the two regions, the air concentration is 0.5. In the low flow region where air concentration is lower than 0.5, air bubbles diffuse in the water flow by turbulent transport fluctuations, and in the upper region where air concentration is higher than 0.5, water droplets and free surface roughness diffuse in the air. The air concentration distributions obtained from the diffusion model are in good agreement with measured data both in the uniform equilibrium region and in the self-aerated developing region. It is demonstrated that the numerical model provides a reasonable description of the self-aeration region in open channel flows.

3-D hybrid LES-RANS model for simulation of open-channel T-diversion flows

The study of flow diversions in open channels plays an important practical role in the design and management of open-channel networks for irrigation or drainage. To accurately predict the mean flow and turbulence characteristics of open-channel dividing flows, a hybrid LES-RANS model, which combines the large eddy simulation （LES） model with the Reynolds-averaged Navier-Stokes （RANS） model, is proposed in the present study. The unsteady RANS model was used to simulate the upstream and downstream regions of a main channel, as well as the downstream region of a branch channel. The LES model was used to simulate the channel diversion region, where turbulent flow characteristics are complicated. Isotropic velocity fluctuations were added at the inflow interface of the LES region to trigger the generation of resolved turbulence. A method based on the virtual body force is proposed to impose Reynolds-averaged velocity fields near the outlet of the LES region in order to take downstream flow effects computed by the RANS model into account and dissipate the excessive turbulent fluctuations. This hybrid approach saves computational effort and makes it easier to properly specify inlet and outlet boundary conditions. Comparison between computational results and experimental data indicates that this relatively new modeling approach can accurately predict open-channel T-diversion flows.

LARGE EDDY SIMULATION OF PULSATING TURBULENT OPEN CHANNEL FLOW

Pulsating turbulent open channel flow has been investigated by the use ofLarge Eddy Simulation (LES) tech-nique coupled with dynamic Sub-Grid-Scale (SGS) model for turbulentSGS stress to closure the governing equations. Three-dimensional filtered Navier-Stokes equationsare numerically solved by a fractional — step method. The objective of this study is to deal withthe behavior of the pulsating turbulent open channel flow and to examine the reliability of the LESapproach for predicting the pulsating turbulent flow. In this study, the Reynolds number (Re_τ) ischosen as 180 based on the friction velocity and the channel depth. The frequency of the drivingpressure gradient for the pulsating turbulent flow ranges low, medium and high value. Statisticalturbulence quantities as well as the flow structures are analyzed.

Numerical Modelling of Performance of R22 and R290 in Adiabatic Capillary Tubes Considering Metastable Two-Phase Region ——Theoretical Model Description and Validation

A homogeneous theoretical model is developed to predict the performance of R22 and R290 in adiabatic capillary tubes. The model is based on conservation equations of mass, momentum and energy. Metastable both liquid and two-phase flow regions are considered in the model. In metastable two-phase region, superheated liquid is introduced into the metastable mixture viscosity and two methods are presented to evaluate it. The model is validated by comparing the predicted pressure and temperature profile and mass flow rate with several investigators′ experimental data of R22 and one of its alternatives R290 reported in literature. All of the predicted mass flow rates are within ±800 of measured values. Comparisons are also made between the present model and other investigators′ models or sizing correlation. The model can be used for design or simulation calculation of adiabatic capillary tubes.

3-D numerical simulation of curved open channel confluence flow with partially non-submerged rigid vegetation

For the study of the effects of partially non-submerged rigid vegetation on the free-surface confluence flow in a curved open channel,a numerical simulation is carried out by using the Volume of Fluid model combined with the porous media model with the software OpenFOAM.The model is first validated by using available experimental measurement data with a good agreement.Then,the characteristics of the separation zone generated by the centrifugal forces and the confluence flow are analyzed.Due to the resistance created by the vegetation,the velocities in the separation zone are more chaotic and the separation zone becomes smaller and more irregular.The reduction of the separation zone area of the vegetated flow in the convex bank is more significant than that in the concave bank.The velocities in the vegetated region become much smaller and remains so in the downstream flow after the vegetation region.Meanwhile,the vegetation compresses and divides the circulations in the flow area,rebuilding a structure with smaller circulations in the main flow and unclear circulations in the vegetation region.In addition,the bed wall shear stresses are significantly smaller in the vegetation region and the separation zone compared to the non-vegetated flow.This implies that the vegetation can have the effect of protecting the river bed from erosion.

Investigation of open channel flow with unsubmerged rigid vegetation by the lattice Boltzmann method

The aquatic vegetation can significantly affect the flow structure,the sediment transport,the bed scour and the water quality in rivers,lakes,reservoirs and open channels.In this study,the lattice Boltzmann method(LBM)is applied in the two-dimensional numerical simulation of the flow structure in a flume with rigid vegetation.A multi-relaxation time model is applied to improve the stability of the numerical scheme for flows with a high Reynolds number.The vegetation induced drag force is added in the lattice Boltzmann equation model in order to improve the simulation accuracy and an algorithm of the multi-relaxation time is developed.Numerical simulations are performed for a wide range of flow and vegetation conditions and are validated by comparing with the laboratory experiments.Analysis of the simulated and experimentally measured flow Helds shows that the numerical simulation can satisfactorily reproduce the laboratory experiments,indicating that the proposed lattice Boltzmann model enjoys a high accuracy for simulating the flow-vegetation interaction in open channels.

Study on the flow structure around discontinued vertically layered vegetation in an open channel

The flow structure and geomorphology of rivers are significantly affected by vegetation patterns. In the present study, the effect of vegetation in the form of discontinuous and vertically double layered patches particularly on the resulting flow turbulence was examined computationally in an open channel. A k-ɛ model was implemented in this research work which was developed using 3-D numerical code FLUENT (ANSYS). After the validation process of numerical model, the impact of discontinuous layered vegetation patches on the flow turbulence was investigated against varying vegetation density and patch length. The mean stream-wise velocities at specified positions showed larger spatial fluctuations directly upstream and downstream of vegetation elements, whereas sharp inflections in the profiles were witnessed at the top of smaller submerged elements i.e. z/hs= 1 (where z is the flow depth and hs is the smaller vegetation height). The reduction in flow velocity due to tall vegetation structure was more as compared with that of short vegetation. The mean velocity in the patch regions was visibly higher than that in the gap regions. The profiles of turbulent flow properties showed more rise and fall within the patches with a high vegetation density i.e. Ss/d= 4;and St/d= 8 (where Ss/d and St/d are the smaller and taller vegetation spacing, while d is the vegetation diameter) as compared with low vegetation density i.e. Ss/d= 8;and St/d= 16. The turbulent flow structure in the large patch and gap regions was found to be more stable than that in the small patches and gaps;whereas, due to the variation in distribution form of the patch, turbulence is relatively unaffected, and the flow structure variation is low. Turbulence was observed to be large, followed by a saw-tooth distribution within the patches;whereas, low turbulence is observed in the non-vegetation regions. The turbulent intensity acquired maximum of 13% turbulence for dense vegetation arrangement as compared to that of sparse arrangement having maximum of 9% turbulent intensity. A noteworthy rise in turbulent kinetic energy and turbulent intensity was witnessed as the flow passed through the vegetated regions. Hence, a non-uniform flow was observed through discontinuous and double layered vegetation patches.

United friction resistance in open channel flows

It is now over half a century since Keulegan conducted his open channel flow experiments. Over the past decades, many empirical formulae were proposed based on his results, however, there is still not a combined expression to describe the effects of friction over all hydraulic regions in open channel flows. Therefore, in this letter, based on the analysis of the implicit model and the logarithmic matching method, the results of Keulegan （for authentic experiment data are no longer available, here we adopt the analytical solutions given by Dou） are rescaled into one monotone curve by combining the Reynolds number and the relative roughness of the river bed. A united expression that could cover the entire turbulence regions and be validated with Dou＇s analytical solutions is suggested to estimate the friction factor throughout the turbulent region in open channel flows, with higher accuracy than that of the previous formulas.

An Improved Analytical Model for Vertical Velocity Distribution of Vegetated Channel Flows

The existence of vegetation plays an important role to protect the ecosystem and water environment in natural rivers and wetlands, but it alters the velocity field of flow, consequently influencing the transport of pollutant and biomass. As a pre-requisite for the analysis of environmental capacity in a channel, the vertical velocity distribution of flows has attracted much research attention;however, there is yet lack of a good prediction model available. For the channel with submerged vegetation, the vertical velocity distribution in the lower vegetation layer will be different from that in the upper flow layer of non-vegetation. In this paper, after review on the most recent two-layer model proposed by Baptist et al., the author has proposed an improved two-layer analytical model by introducing a different mixing length scale (λ). The proposed model is based on the momentum equation of flow with the turbulent eddy viscosity assumed as a linear relationship with the local velocity. The proposed model is compared with the Baptist model for different datasets published in the literature, which shows that the proposed analytical model can improve the vertical velocity distribution prediction well compared with the Baptist model for a range of data. This study reveals that the λ is well related with the submergence of vegetation (H/h), as suggested by . When the constant β is taken as 3/100, the proposed model shows good agreement with a wide range of datasets studied: flow depth (H)/vegetation height (h) in 1.25 to 3.33, different vegetation densities of a in 1.1 to 18.5 m−1 (a defined as the frontal area of the vegetation per unit volume), and bed slopes in (1.38 - 4.0) × 10−3.

Optimization model of truck flow at open-pit mines and standards for feasibility test

In order to increase production efficiency at open-pit mines, on the basis oflinear programming, a practical mathematical model for optimizing truck flow was developed, whichimproved the traditional fixed manual schedule method. The model has advantages from linearprogramming and objective programming, makes most handling points working at full capacity and keepsan optimized ratio between trucks and excavators. For ensuring feasibility of the model inpractical production, four standards for feasibility test were proposed. The model satisfied all thestandards. The application in a large scale open-pit iron mine indicated that the model reduced thenumber of required trucks by 10 percent compared with the fixed manual schedule method.

Evaluating Two-Layer Models for Velocity Profiles in Open-Channels with Submerged Vegetation

For submerged vegetated flow, the velocity profile has two distinctive distributions in the vegetation layer in the lower region and the surface layer in the upper non-vegetated region. Based on a mixing-layer analogy, different analytical models have been proposed for the velocity profile in the two layers. This paper evaluates the four analytical models of Klopstra et al., Defina & Bixio, Yang et al. and Nepf against a wide range of independent experimental data available in the literature. To test the applicability and robust of the models, the author used the 19 datasets with various relative depths of submergence, different vegetation densities and bed slopes (1.8 × 10?6 - 4.0 × 10?3). This study shows that none of the models can predict the velocity profiles well for all datasets. The three models except Yang’s model performed reasonably well in certain cases, but Yang’s model failed in most the cases studied. It was also found that the Defina model is almost the same as the Klopstra model, if the same mixing length scale of eddies (λ) is used. Finally, close examination of the mixing length scale of eddies (λ) in the Defina model showed that when λ/h = 1/40(H/h)1/2, this model can predict velocity profiles well for all the datasets used.

A comprehensive review of the modeling of transport phenomenon in the flow channels of polymer electrolyte membrane fuel cells

Reactant gas and liquid water transport phenomena in the flow channels are complex and critical to the performance and durability of polymer electrolyte membrane fuel cells.The polymer membrane needs water at an optimum level for proton conductivity.Water management involves the prevention of dehydration,waterlogging,and the cell’s subsequent performance decline and degradation.This process requires the study and understanding of internal two-phase flows.Different experimental visualization techniques are used to study two-phase flows in polymer electrolyte membrane fuel cells.However,the experiments have limitations in in situ measurements;they are also expensive and time exhaustive.In contrast,numerical modeling is cheaper and faster,providing insights into the complex multiscale processes occurring across the components of the polymer electrolyte membrane fuel cells.This paper introduces the recent design of flow channels.It reviews the numerical modeling techniques adopted for the transport phenomena therein:the two-fluid,multiphase mixture,volume of fluid,lattice Boltzmann,and pressure drop models.Furthermore,this work describes,compares,and analyses the models’approaches and reviews the representative results of some selected aspects.Finally,the paper summarizes the modeling perspectives,emphasizing future directions with some recommendations.

抚河疏山水利枢纽船闸通航水流条件研究

为满足水运需求,解决船闸引航道口门区受河段地形和涉河建筑物影响而导致的通航条件困难等问题,保障船舶安全通行,以抚河疏山水利枢纽船闸工程为例,采用数值模拟方法,对枢纽船闸上游引航道口门区通航条件进行计算分析,针对不良流态问题提出优化方案措施,并对方案前后枢纽通航条件进行对比分析。研究表明,调整船闸平面布置等措施对改善设计阶段的枢纽船闸上引航道口门区通航条件是有效的。研究成果可为抚河疏山水利枢纽船闸工程通航及其他类似河段工程提供技术支持。

基于动网格6DOF模型的框架式流速仪水力特性数值模拟与明渠测流速率常数预测

为分析明渠内框架式流速仪流场特性与运动姿态,同时对流速仪倍常数K和摩阻系数C进行率定,根据不可压缩流体流动的Navier-Stokes方程和SST k-ω湍流模型,结合VOF多相流模型,建立动态网格下的6自由度(6DOF)刚体动力学耦合数值仿真模型,对水冲击流速仪旋桨使之被动旋转过程进行了仿真,分析了流速仪在不同位置对流速仪倍常数K和摩阻系数C的影响规律。结果表明:采用动网格6DOF模型可以较好地模拟框架式流速仪在明渠的流动状态,仿真结果可靠性较高;通过对不同时刻转速与流速拟合曲线分析可知,流速仪位置不同会影响流速仪摩阻系数C,对流速仪倍常数K影响不大。研究结果可为进一步研究框架式流速仪优化和不同含沙水流条件下对流速仪的磨损提供参考。

Analysis on Link Between the Macroscopic and Microscopic Air–Water Properties in Self-Aerated Flows

Self-aeration in high-speed free surface flows occurs commonly and is of interest to ocean engineering, hydraulic engineering, and environmental engineering. For two-phase air–water flows, macroscopic air–water flow properties develop gradually, accompanied by the change of microscopic air–water structures. In this article, representational experimental studies on macroscopic and microscopic characteristics of self-aerated open-channel flows are summarized and compared. The isolated effect of the flow Reynolds number and air quantity on the differences in air count rate and chord size are analyzed and discussed. The results show that the characterized flow depth y, affected by the turbulence transfer, is a specific criterion to distinguish the interior air–water structure development. Two distinct linear trends of self-aeration are found, depending on the y/yvariation with a breaking point at Cmean =0.50. The air count rate and size scale in self-aerated flows are affected by the air quantity of self-aerated flows, even with identical flow Reynolds numbers. Thus, a specific parameter is proposed to assess the air–water structures and a series of self-similarity relationships in self-aeration properties are obtained. The link between macroscopic and microscopic air–water properties results in significant scale effect on air–water structures in self-aerated flows.

基于Flow-3D的多阶明渠工程数学模型研究

[目的]研究灌区多级阶梯明渠水流的水动力特性及泥沙淤积问题,并评价其对多阶明渠工程的影响.[方法]基于VOF方法,在Flow-3D平台上建立了山东省德州市牛角店输水工程的三维数学模型,通过模拟不同工况下的三维多阶明渠水流,对比分析水流流速分布、水面线变化及渠底泥沙淤积情况.[结果]水流流态平稳后,最大流速出现在第二级阶梯上,挟沙水流流速较清水流速大0.50~0.86 m/s;在挑坎及第二级阶梯上,水面线变化幅度较大;随着时间推移,泥沙主要淤积于挑坎前及第三级阶梯底部,200 s时淤积厚度最高达0.143 mm.[结论]在牛角店输水工程施工及后期运行中,适当加固第二级阶梯渠底,提升第二级侧墙高度,并通过调控下游水位以保证灌渠的安全运行.