Numerical simulation of mechanical breakup of river ice-cover

Ice jams and ice dams in rivers will cause significant rises of water levels. Under extreme conditions, the ice flooding during winter or early spring may occur. In this paper, by considering the fluid-solid coupling effect caused by the water and the ice cover, the mechanisms of the mechanical breakup of the river ice cover are studied. A formula is obtained for determining whether or not the mechanical breakup process would happen under the hydraulic pressure of the flow. Combined with the hydraulic model under the ice covered flow, a numerical model is built and the interaction between the discharge, the hydraulic pressure under the ice cover and the date for the mechanical breakup of the river ice cover is simulated. The simulated results of the dates for the mechanical breakup of the river ice cover agree very well with the field observations of the breakups of the river ice cover in the Hequ Reach of the Yellow River. Therefore, the numerical model might serve as a good preliminary step in studying the breakup of the river ice-cover, evidencing many important parameters that affect the ice-cover process.     

THREE-DIMENSIONAL NUMERICAL SIMULATION OF AERATED FLOWS DOWNSTREAM SUDDEN FALL AERATOR EXPANSION-IN A TUNNEL

Air entrainment is known to be one of efficient and inexpensive methods to prevent cavitation damages in hydropower projects.The shape of sudden expansion-fall is used as a common device for mitigating cavitation erosions.The complex flow patterns with cavitation are numerically simulated by using the realizable k-εturbulence model and the air-water mixture model.The calculated results are compared well with the experimental results as well as those obtained with the k-εturbulence model with the Volume Of Fluid(VOF)Model.The calculated results agree well with the experimental data for the aeration cavity and wall pressure.Moreover,the air concentration near sidewall is simulated by a mixture model.It is found that the mixture turbulence model is superior to the VOF turbulence model.     

Simulation and analysis of ice processes in an artificial open channel

The Middle Route Project for South-to-North Water Transfer, which consists of a long artificial open channel and various hydraulic constructions, is a big water conveyance system. A numerical modeling of water conveyance in the ice period for such large-scale and long distance water transfer project is developed based on the integration of a river ice model and an unsteady flow model with complex inner boundaries. A simplified method to obtain the same flow discharge in the upstream and downstream of the structure by neglecting the storage effect is proposed for dealing with the inner boundaries. According to the measured and design data in winter-spring period, the whole ice process, which includes the formation of the ice cover, its development, the melting and the breaking up as well as the ice-water dynamic response during the gate operation for the middle route, is simulated. The ice characteristics and the water conveyance capacity are both analyzed and thus the hydraulic control conditions for a safety regulation are obtained. At last, the uncertainties of some parameters related to the ice model are discussed.     

Simulations of ice jam thickness distribution in the transverse direction

River ice often forms in the cold regions of northern hemisphere which can lead to ice jams(or ice dams). Water level can be significantly raised due to ice jams. As a consequence, disastrous ice flooding may be resulted, such as the ice jam flooding in the Nechako River in Prince George in winter 2007-2008. In the present study, the equations describing the ice jam thickness in the transverse direction are derived. The impact of the secondary vortex is considered while the cohesive force within ice cubes is neglected in the model. The relationship between the parameter β and the total water depth is established based on the assumption that all other variables except the velocities are kept constant on the same cross section. By using the parameter β and the developed equations, the ice jam thickness in the transverse direction can be predicted. The developed model is used to simulate the ice jam thickness in the transverse direction at the Hequ Reach of the Yellow River in China. The simulated ice jam thicknesses agree well with the field measurements on different cross sections.     

Estimation of discharge and its distribution in compound channels简

Results of research into a compound channel having width ratio(?)in excess of 11 are presented in the form of boundary shear distributions across the compound cross section.New relationship is derived between the percentage of shear carried by the flood plains(%)fp S and the percentage of area occupied by the flood plains(%)fp A.The equation so derived is taken as the basis to develop a new methodology to predict the stage discharge relationship specifically for wide compound channels using Darcy’s friction factor(f)for the main channel and flood plain regions.The methodology also is used for compound channels with smaller width ratios by applying the appropriate relation for%fp S derived earlier by different researchers and seems to work well.Next,as a corollary to the methodology,separate formulae are proposed to estimate flow distribution in main channel and flood plain regions.The proposed method and its corollary are tested for their validity against well-published small-scale data series of previous researchers along with some large-scale data series from EPSRC-FCF(A-Series)compound channel experiments and very good agreement is observed between the measured values and predicted values for total flow as well as zonal distribution of flow.The methodology is also applied to some compound river section data published in literature and is found to serve well the purpose of predicting flow in real world application.This new method gives the least RMS value of error for discharge prediction compared with some other well-known methods used for estimating stage-discharge relation in compound channels by considering all data sets.     

WELL TESTING ANALYSIS FOR HORIZONTAL WELL WITH CONSIDERATION OF THRESHOLD PRESSURE GRADIENT IN TIGHT GAS RESERVOIRS

A fundamental solution for homogeneous reservoir in infinite space is derived by using the point source function with the consideration of the threshold pressure gradient. The fundamental solution of the continuous point source function is then derived based on the Green function. Various boundary conditions of the reservoirs are considered for this case and the corresponding solutions are obtained through the mirror image reflection and the principle of superimposition. The line source solution is obtained by integration. Subsequently, the horizontal-well bottom hole pressure response function for a non-linear gas flow in the homogeneous gas reservoir is obtained, and the response curve of the dimensionless bottom hole pressure and the derivative for a horizontal well in the homogeneous gas reservoir are obtained. In the end, the sensitivities of the relevant parameters are analyzed. The well test model presented in this paper can be used as the basis of the horizontal well test analysis for tight gas reservoirs.     

Modeling of thermodynamics of ice and water in seasonal ice-covered reservoir

A width-averaged 2-D numerical model for simulating vertical distributions of flow and water temperature in reservoirs with an ice cover is developed. In this model, the 2-D flow and water temperature distributions are solved by the finite volume method with the k-? turbulent model. The heat conduction in the ice cover is modeled by the vertical heat transfer and the heat exchanges through the air-ice and ice-water interfaces. The model is applied to a 153 km long reservoir in Songhua River and the simulated results are in a good agreement with the field data of both the vertical water temperature and the ice thickness. The simulated results show that the ice cover thickness in the reservoir is not uniform, the maximum thickness appears in the middle reach, the outflow temperature has an obvious variation as compared with the natural temperature, and a buoyant flow occurs in the reservoir surface at the freeze-up and break-up periods. The model can effectively simulate the water temperature and the ice conditions of large reservoirs in cold regions.     

Comprehensive two-dimensional river ice model based on boundary-fitted coordinate transformation method简

River ice is a natural phenomenon in cold regions, influenced by meteorology, geomorphology, and hydraulic conditions. River ice processes involve complex interactions between hydrodynamic, mechanical, and thermal processes, and they are also influenced by weather and hydrologic conditions. Because natural rivers are serpentine, with bends, narrows, and straight reaches, the commonly-used one-dimensional river ice models and two-dimensional models based on the rectangular Cartesian coordinates are incapable of simulating the physical phenomena accurately. In order to accurately simulate the complicated river geometry and overcome the difficulties of numerical simulation resulting from both complex boundaries and differences between length and width scales, a two-dimensional river ice numerical model based on a boundary-fitted coordinate transformation method was developed. The presented model considers the influence of the frazil ice accumulation under ice cover and the shape of the leading edge of ice cover during the freezing process. The model is capable of determining the velocity field, the distribution of water temperature, the concentration distribution of frazil ice, the transport of floating ice, the progression, stability, and thawing of ice cover, and the transport, accumulation, and erosion of ice under ice cover. A MacCormack scheme was used to solve the equations numerically. The model was validated with field observations from the Hequ Reach of the Yellow River. Comparison of simulation results with field data indicates that the model is capable of simulating the river ice process with high accuracy.     

DuaISPHysics：A numerical tool to simulate real breakwaters

The open-source code DualSPHysics is used in this work to compute the wave run-up in an existing dike in the Chinese coast using realistic dimensions, bathymetry and wave conditions. The GPU computing power of the DualSPHysics allows simulating real-engineering problems that involve complex geometries with a high resolution in a reasonable computational time. The code is first validated by comparing the numerical free-surface elevation, the wave orbital velocities and the time series of the run-up with physical data in a wave flume. Those experiments include a smooth dike and an armored dike with two layers of cubic blocks. After validation,the code is applied to a real case to obtain the wave run-up under different incident wave conditions. In order to simulate the real open sea, the spurious reflections from the wavemaker are removed by using an active wave absorption technique.     

A random walk simulation of scalar mixing in flows through submerged vegetations

The scalar transport phenomena in vertical two-dimensional flows are studied using the random walk method. The established Lagrangian model is first applied to study the idealized longitudinal dispersion in open channels, before being used to investigate the scalar mixing characteristics of the flows through submerged vegetations. The longitudinal dispersion coefficients of the fully-developed boundary layer flows, with and without vegetations, are calculated based on the positions of the particles. A convenient way of incorporating the effects of vegetations is proposed, where all the flow parameters are regarded to be continually distributed over the depth. The simulation results show high accuracy of the developed random walk method, and indicate that the new method of accounting for the vegetation effects is appropriate for all the test cases considered. The predicted longitudinal dispersion coefficients agree well with the measurements. The merit of the new method is highlighted by its simplicity and efficiency in comparison with the conventional method that assumes the discontinuous distribution of the flow parameters over the depth.     

DISPERSION OF CYLINDRICAL PARTICLES IN TURBULENT FLOWS

With consideration of the Stokes drag and virtual mass force, the equations for mean and fluctuating velocities in rotation and translation were given for rigid cylindrical particles moving in a turbulent flow. Then the rotational and translational dispersion coefficients of particle were derived.The relationships between the dispersion coefficients and flow length scale as well as particle characteristic parameters were analyzed. The resulting dispersion coefficients were proved to decrease as the particle length increases. The conclusions are helpful for the further research on the motion of cylindrical particles in turbulent flows.     

NUMERICAL STUDY OF TURBULENT FLOW AROUND TWIN PLATE AT LARGE ATTACK ANGLE

The present work is mainly aimed to study the fluid dynamic force on twin plate in a turbulent flow by solving the governing equations numerically with the well known approach SIMPLE, in which the multiple time scale turbulent k-ε model has been employed to determine the eddy viscosity of turbulent flow field. The turbulence model is used with a restriction for the kinetic energy of smaller turbulent scale to achieve numerical stability. The lengths of recirculation zone for the turbulent flow around twin plate with the definite angle of attack AOA = 50° and constant flow blockage ratio 10% are in good agreement with experimental data, which indicates the wall functions used in the numerical investigation are acceptable as well. It is found that the drag force and distribution of wall pressure are intimately influenced by the arrangement of twin plate at constant flow blockage. The results of multiple time scale k-εmodel are compared with single time scale k-εmodel, indicating that the drag force of     

Impacts of bridge piers on water level during ice jammed period in bend channel——An experimental study

Experiments are carried out in an "S-shaped" flume in the laboratory under both open flow and ice-jammed conditions to study the impacts of bridge piers in a bend channel on the variation of the water level. The variations of the water level under the ice jammed condition with bridge piers are compared to those without bridge piers in an 180° bend channel. Results indicate that the bridge piers in the S-shaped channel have obvious impacts on the ice accumulation and the water level. The increment of the water level with the presence of the bridge piers is less than that without the bridge piers in the channel. Different arrangements of the bridge piers result in different increments of the water level. When one bridge pier is installed in the straight section of the channel(between 2 bends) and another one at the bend apex(for a convex bank), the increment of the water level during the equilibrium ice jammed period is between that with a single bridge pier located in the straight section of the bend channel and that with a single bridge pier located at the bend apex. It is also shown that the increment of the water level during the equilibrium ice jammed period increases with the increase of the average thickness of the ice jams.     

A NOVEL ADAPTIVE σ COORDINATE MODEL AND ITS APPLICA- TIONS TO WAVE AND STRUCTURE INTERACTION

In this paper, a novel adaptive mesh σ coordinate model is proposed for the studies of Wave and Structure Interaction (WSI). The model is validated by using the case of a solitary wave movement in an open channel with constant water depth and the case of nonbreaking solitary wave propagating over a step. Numerical results agree well with the analytical solutions obtained based on the Boussinesq theory, the laboratory data and other numerical model results. The proposed model is then used to study a solitary wave interacting with a suspended fixed structure.     

Impacts of ice cover on local scour around semi-circular bridge abutment简

The presence of ice cover in winter can significantly change the flow field around bridge abutments, which can also cause a different local scour pattern. To investigate the impacts of ice cover, results from a recent flume experiments were presented. Smooth and rough ice covers were created to investigate the impacts of ice cover roughness on the scour geometry around the semi-circular abutment. Three bed materials were used, with 50D s of 0.58 mm, 0.50 mm, 0.47 mm respectively. Scour volume and scour area were calculated. It was found that the maximum scour depth was located 75o inclined to the flume wall. Under rough ice cover, the scour area and scour depth were the largest. An empirical equation on the maximum scour depth was also developed.     

Effect of compressive stress on the dispersion relation of the flexural–gravity waves in a two-layer fluid with a uniform current

The explicitly analytical solution is derived for the dispersion relation of the flexural–gravity waves in a two-layer fluid with a uniform current. The upper fluid is covered by a thin plate with the presence of the elastic, compressive and inertial forces. The density of each of the two immiscible layers is constant. The fluids of finite depth are assumed to be inviscid and incompressible and the motion be irrotational. A linear system is established within the framework of potential theory. A new representation for the dispersion relation of flexural–gravity waves in a two-layer fluid is derived. The critical value for the compressive force is analytically determined. The dispersion relation for the capillary–gravity with an inertial surface in a two-layer fluid can be obtained in parallel. Some known dispersion relations can be recovered from the present solution.     

RESEARCH ON THE CONDITION TO SET A TAILRACE SURGE TANK

When using the draft-tube vacuum to be less than 8. 0m as the rule to set a tailrace surge tank, a mixing function that describes the process of water-hammer vacuum and velocity-head vacuum varied with time is proposed, on the assumption that the guide vane of the hydraulic turbine and the turbine discharge were all changed linearly. An exact maximum of the draft-tube vacuum for the first-phase waterhammer and the last-phase water-hammer is obtained. Finally a much more reasonable formula of critical tailrace length is derived. The results of two cases show that the formula proposed can determine correctly and reasonably whether a tailrace surge tank is needed or not, and are more suitable for project design than the formula suggested by the specification.     

Random atmospheric pressure at the free surface and microseisms in deep ocean

A general stochastic model of the atmospheric pressure at the ocean surface was proposed, in which the pressure variation was represented by a spectral decomposition through a random process of orthogonal increments. From the basic equations of ideal and incompressible fluid a set of perturbation equations up to second order had been derived and solved. The pressure variation in the flow field had been calculated using the explicit solutions obtained, and which demonstrated a clear relation between the atmospheric pressure and the one at the bottom of deep ocean. It can be seen that there is a part of the pressure variation which is not attenuating with the depth. The result had been compared with those of Longuet-Higgins and Kadota et al. and all previous results are contained in the solution given in this artice. The restriction on the previous works with regard to the probability law has been removed, and all conclusions are deduced without specific assumptions. The flexibility of the proposed model allows for further generalization and extension in the physical aspects and statistical treatment.     

REFLECTION OF OBLIQUE INCIDENT WAVES BY PERFORATED CAISSONS WITH TRAVERSE WALL

The interaction of oblique incident waves with infinite number of perforated caissons is investigated. The fluid domain is divided into infinite sub-domains by the caissons, and eigen-function expansion is applied to expand velocity potentials in each domain. A phase relation is introduced for wave oscillation in each caisson, and the structure geometry is considered in constructing the models of reflection waves. The reflected waves with the present analysis include all of the waves traveling in different directions when incident wave period is short. Numerical examinations show that velocities at the inner and outer sides of the front walls of caissons are close to each other, and reflection coefficients satisfy the energy conservation relation very well when porous effect parameter is infinite. Numerical results show that the reflection coefficients of oblique incident waves are smaller for shorter caissons at low frequency, and decrease with the increase of wave incident angle.     

FORMULAE FOR AVERAGE VELOCITY OF GROUNDWATER FLOW AND EXPERIMENTAL EVIDENCE OF NON-DARCY' S FLOW THROUGH A SINGLE FRACTURE

The formulae for average velocity of groundw-ater flow in a single fracture were derived based on the characteristics of fracture properties and hydraulic methods. The results show that the average velocity is proportional to the square root of the hydraulic gradient. In order to verify the results, a laboratory model was established, and the experimental data were analyzed. Experimental results indicate that the relation between the average velocity and hydraulic gradient is nonlinear, and can be fitted with power functions. And for both the unconfined and confined flows, the value of the exponent of power functions are close to 0. 5. Thus the experimental results agree well with those from the theoretical analysis. By comparing the calculated and measured values of the average velocity under the same conditions, the formulae presented herein are more effective than the traditional formula based on Darcy's Law. These results provide the evidences of non-Dar-cy's flow in single fracture.