Three-dimensional numerical simulation of crown spike due to coupling effect between bubbles and free surface

The motion of gas bubbles beneath a free surface will lead to a spike of fluid on the free surface. The distance of the bubbles to the free surface is the key factor to different phenomena. When the inception distance varies in some range, crown phenomenon would happen after the impact of weak buoyancy bubbles, so this kind of spike is defined as crown spike in the present paper. Based on potential flow theory, a three-dimensional numerical model is established to simulate the motion of the free-surface spike generated by one bubble or a horizontal line of two in-phase bubbles. After the downward jet formed near the end of the collapse phase, the simulation of the free surface is performed to study the crown spike without regard to the toroidal bubble＇s effect. Calculations about the interaction between one bubble and free surface agree well with the experimental results conducted with a high-speed camera, and relative error is within 15%. Crown spike in both single- and two-bubble cases are simulated numerically. Different features and laws of the motion of crown spike, depending on the bubble-boundary distances and the inter-bubble distances, have been investigated.

The study on three-dimensional numerical model and fronts of the Jiulong Estuary and the Xiamen Bay

Applying the methods of on-site observation and dynamic model, the research on the fronts at the Jiulong Estuary has been carried out, during which spatial and temporal distribution, dynamic characteristics and formation mechanism of salinity fronts are analyzed and discussed. The research shows that the estuarine fronts mainly lie in the area from the Jiyu Islet to the Haimen Island, outside of Yuweizai to Hulishan cross-section, the near coast of Yuweizai and the south of the Songyu-Gulangyu Channel. The fronts in the former two regions are formed directly by plume, while the one near the coast of Yuweizai is a tidal intrusion front caused by flood current and the one at the south of the Songyu-Gulangyu Channel is the result of current shear transformation. Under normal circumstances, fresh water of the Jiulong River mainly influences the inside of the Xiamen Bay, and when it is in typhoon seasons, plume front can affect the Taiwan Strait and has an effect on the biogeochemical Drocesses in the strait.

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.

Numerical Simulation of Saline Intrusion and Purging in Long SeaOutfalls with Three-Dimensional Model

Saline intrusion into marine sewage ouffalls will greatly decrease the efficiency of sewage disposal. In order to investigate the mechanisms of this flow, in this paper, a three-dimensional numerical model based on FVM （Finite Volume Method） is established, The RNG κ-ε model is selected for turbulence modeling. The time-averaged vohtme fraction equations are introduced to simulate the stratification and inteffaeial exchange of sewage and seawater in outfalls. Validity of the established three-dimensional numerical model is evaluated by comparisons of numerical results with experimental data. With this three-dimensional numerical model, the internal flow characteristics in ouffalls for different sewage discharges are simulated. The results indicate that for a low sewage discharge, saline circulates in the outfall due to intrusion and both the inflowing momentum and the inteffaeial turbulent mixing are important mechanisms to extrude the saline. For a high sewage discharge, saline intrusion could be avoided. The inflow momentum is the main mechanism to extrude the saline and the inteffacial turbulent mixing is nut important relatively. Even at a high sewage discharge, the saline wedge would be retained in the main ouffall pipe after the risers are purged. It takes a long time for this saline wedge to be extruded by interracial turbulent mixing.

A three-dimensional numerical calculation of the wind-driven thermohaline and tide-induced Lagrangian residual current in the Bohai Sea

On the basis of a three-dimensional weakly nonliear theory of Lagrangian residual current in the Baroclinic shallow seas, a diagnostic numerical calculation of wind-driven, thermohaline and tide-induced Lagrangian residual current in the Bohai Sea is made. The model involves the Richardson number in the eddy viscosity coefficient, wind, thcrmolialine and tidal effects in the focing terms. The runoff of the Huanghe River and a part of the Huanghai Warm Water coming from the Huanghai Sea through the Bohai Sea Strait is also considered. The velocity-splitting method is adopted. The wind-driven circu lation, thermohaline circulation and the tide-induced Lagrangian residual circulation are also obtained individually and analysed. The dynamics of the three main eddies in the Lagrangian mean circulation is discussed. Finally, the numerical result is partly verified with the observed data.

Numerical simulation of three-dimensional tidal current in the Bobal Sea

The model equations with tbree-dimensional, time-dependent, nonlinear Navier-Stokes equations are transformed by sigma-transformation.On the basis of the process splitting technique, the fluid flow problems are divided into two parts:the vertically-intopated equations (external mode) and the vertical structure equations(internal mace). The first set of equations being the propagation of the tidal weves and the ADI numerical scheme has ben chosen to solve them. Conerning the vertical structure equations, they are solved by means of leapfrog stepping procedure.The main features of the tide and associated tidal current in the Bohai Sea are examined with this 3-D model.To have a good reproduction of vertical structure, the column is divided into 10 layers and the M2 tidal current is computed in detail. The simulation reveal the spetial structure and some important characteristics of the tidal current of the Bohai Sea. The application of the 3-D madel to forecasting of the tidal current in the Bobal Sea has been Performed as an illustration.

Numerical Simulation of the Three-Dimensional Wave-Induced Currents on Unstructured Grid

By coupling the three-dimensional hydrodynamic model with the wave model, numerical simulations of the three- dimensional wave-induced current are carried out in this study. The wave model is based on the numerical solution of the modified wave action equation and eikonal equation, which can describe the wave refraction and diffraction. The hydrodynamic model is driven by the wave-induced radiation stresses and affected by the wave turbulence. The numerical implementation of the module has used the finite-volume schemes on unstructured grid, which provides great flexibility for modeling the waves and currents in the complex actual nearshore, and ensures the conservation of energy propagation. The applicability of the proposed model is evaluated in calculating the cases of wave set-up, longshore currents, undertow on a sloping beach, rip currents and meandering longshore currents on a tri-cuspate beach. The results indicate that it is necessary to introduce the depth-dependent radiation stresses into the numerical simulation of wave-induced currents, and comparisons show that the present model makes better prediction on the wave procedure as well as both horizontal and vertical structures in the wave-induced current field.

THEORETICAL STUDY OF THREE-DIMENSIONAL NUMERICAL MANIFOLD METHOD

The three-dimensional numerical manifold method（NMM） is studied on the basis of two-dimensional numerical manifold method. The three-dimensional cover displacement function is studied. The mechanical analysis and Hammer integral method of three-dimensional numerical manifold method are put forward. The stiffness matrix of three-dimensional manifold element is derived and the dissection rules are given. The theoretical system and the numerical realizing method of three-dimensional numerical manifold method are systematically studied. As an example, the cantilever with load on the end is calculated, and the results show that the precision and efficiency are agreeable.

A three-dimensional Eulerian method for the numerical simulation of high-velocity impact problems

In the present paper, a three-dimensional （3D） Eulerian technique for the 3D numerical simulation of high-velocity impact problems is proposed. In the Eulerian framework, a complete 3D conservation element and solution element scheme for conservative hyperbolic governing equations with source terms is given. A modified ghost fluid method is proposed for the treatment of the boundary conditions. Numerical simulations of the Taylor bar problem and the ricochet phenomenon of a sphere impacting a plate target at an angle of 60~ are carried out. The numerical results are in good agreement with the corresponding experimental observations. It is proved that our computational technique is feasible for analyzing 3D high-velocity impact problems.

Three-dimensional discrete element numerical simulation of Paleogene salt structures in the western Kuqa foreland thrust belt

Taking the Paleogene salt strata in the west of Kuqa foreland thrust belt as study object, the deformation features of salt structure in the compression direction and perpendicular to the compression direction were examined to find out the control factors and formation mechanisms of the salt structures. By using the three-dimensional discrete element numerical simulation method, the formation mechanisms of typical salt structures of western Kuqa foreland thrust belt in Keshen and Dabei work areas were comprehensively analyzed. The simulation results show that the salt deformation in Keshen and Dabei work areas is of forward spread type, with deformation concentrated in the piedmont zone;the salt deformation is affected by the early uplift near the compression end, pre-existing basement faults, synsedimentary process and the initial salt depocenter;in the direction perpendicular to the compression direction, salt rocks near the compression end have strong lateral mobility with the velocity component moving towards the middle part, and the closer to the middle, the larger the velocity will be, so that salt rocks will aggregate towards the middle and deform intensely, forming complex folds and separation of salt structures from salt source, and local outcrop with thrust faults. Compared with 2 D simulation, 3 D simulation can analyze salt structures in the principal stress direction and direction perpendicular to the principal stress, give us a full view of the formation mechanisms of salt structures, and guide the exploration of oil and gas reservoirs related to salt structures.

NUMERICAL INVESTIGATION OF THREE-DIMENSIONAL VISCOUS INCOMPRESSIBLE FLOWS IN DIVERGENT CURVED CHANNELS AND TURBULENT MODEL STUDY

In order to make the numerical calculation of viscous flows more convenient for the flows in channel with complicated profile governing equations expressed in the arbitrary curvilinear coordinates were derived by means of Favre density-weighted averaged method, and a turbulent model with effect of curvature modification was also derived. The numerical calculation of laminar and turbulent flown in divergent curved channels was carried out by means of parabolizeil computation method. The calculating results were used to analyze and investigate the aerodynamic performance of talor cascades in compressors preliminarily.

Three-dimensional mixed convection stagnation-point fow past a vertical surface with second-order slip velocity

This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is the first study presenting this very interesting analysis.Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations(ODEs)by using appropriate similarity transformation.These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language.The effects of the governing parameters on the non-dimensional velocity profiles,temperature profiles,skin friction coefficients,and the local Nusselt number are presented in detail through a series of graphs and tables.Interestingly,it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation.The numerical computations of the present work are compared with those from other research available in specific situations,and an excellent consensus is observed.Another exciting feature for this work is the existence of dual solutions.An important remark is that the dual solutions exist for both assisting and opposing flows.A linear stability analysis is performed showing that one solution is stable and the other solution is not stable.We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics.These effects are depicted in graphs and discussed in this paper.The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow,as well as on the heat transfer characteristics.

Microchannel heat sink;Nanofluids;Entropy generation;Numerical analysis;Laminar flow

Based on the Second Law of Thermodynamics, the entropy generation is studied for laminar forced convection flow of different nanoparticles(Al_2 O_3, CuO and SiO_2) mixed with water through a hexagon microchannel heat sink(HMCHS). The effects of different heat fluxes and Reynolds numbers on the entropy generation for different nanofluids, volume fractions and nanoparticles diameter are investigated. The heat flux is in the range of 125 to 500 kW·m^(-2) and the Reynolds numbers vary between 200 and 1500. The thermal, frictional and total entropy generations are calculated by integrating the volumetric rate components over the entire HMCHS. The results clearly show that the rise in the heat flux leads to an increase in the thermal entropy generation for nanofluids and pure water but they don't have any influence on the frictional entropy generation. Moreover, when the Reynolds number increases, the frictional entropy generation increases while the thermal entropy generation decreases. The results revealed that at low heat fluxes and high Reynolds numbers, pure water gives the lowest entropy generation, while at high heat flux the nanofluid has to be used in order to lower the overall irreversibility.

Application of Numerical Simulation for Analysis of Sinking Characteristics of Purse Seine

This study applies the mass-spring system to model the dynamic behavior of a submerged net panel similar to the shooting process in actual purse seine fishing operation. Modeling indicates that there is insufficient stretching with the net panel under the floatline in the prophase of the shooting process. Sinkers at different locations along the leadline descend successively after submergence, and the sinking speed decreases gradually with elapsed time until attainment of a stable state. Designs with different current speeds and sinker weights are executed to determine the dimensional shape and sinking characteristics of the net. The net rigged with greater sinker weight gains significantly greater sinking depth without water flow. Compared with the vertical spread of the net wall in static water, the middle part of the netting presents a larger displacement along the direction of current under flow condition. It follows that considerable deformation of the netting occurs with higher current speed as the sinkers affected by hydrodynamic force drift in the direction of current. The numerical model is verified by a comparison between simulated results and sea measurements. The calculated values generally coincide with the observed ones, with the former being slightly higher than the latter. This study provides an implicit algorithm which saves computational loads for enormous systems such as purse seines, and ensures the accuracy and stability of numerical solutions in a repetitious iteration process.

A stable one-point quadrature rule for three-dimensional numerical manifold method

We present a numerically stable one-point quadrature rule for the stiffness matrix and mass matrix of the three-dimensional numerical manifold method(3D NMM).The rule simplifies the integration over irregularly shaped manifold elements and overcomes locking issues,and it does not cause spurious modes in modal analysis.The essential idea is to transfer the integral over a manifold element to a few moments to the element center,thereby deriving a one-point integration rule by the moments and making modifications to avoid locking issues.For the stiffness matrix,after the virtual work is decomposed into moments,higher-order moments are modified to overcome locking issues in nearly incompressible and bending-dominated conditions.For the mass matrix,the consistent and lumped types are derived by moments.In particular,the lumped type has the clear advantage of simplicity.The proposed method is naturally suitable for 3D NMM meshes automatically generated from a regular grid.Numerical tests justify the accuracy improvements and the stability of the proposed procedure.

Three-dimensional numerical manifold method for heat conduction problems with a simplex integral on the boundary

The three-dimensional numerical manifold method(3D-NMM),which is based on the derivation of Galerkin's variation,is a powerful calculation tool that uses two cover systems.The 3D-NMM can be used to handle continue-discontinue problems and extend to THM coupling.In this study,we extended the 3D-NMM to simulate both steady-state and transient heat conduction problems.The modelling was carried out using the raster methods(RSM).For the system equation,a variational method was employed to drive the discrete equations,and the crucial boundary conditions were solved using the penalty method.To solve the boundary integral problem,the face integral of scalar fields and two-dimensional simplex integration were used to accurately describe the integral on polygonal boundaries.Several numerical examples were used to verify the results of 3D steady-state and transient heat-conduction problems.The numerical results indicated that the 3D-NMM is effective for handling 3D both steadystate and transient heat conduction problems with high solution accuracy.

Design of an Acoustic Levitator for Three-Dimensional Manipulation of Numerous Particles

We present a design of an acoustic levitator consisting of three pairs of opposite transducer arrays.Three orthogonal standing waves create a large number of acoustic traps at which the particles are levitated in mid-air.By changing the phase difference of transducer arrays,three-dimensional manipulation of particles is successfully realized.Moreover,the relationship between the translation of particles and the phase difference is experimentally investigated,and the result is in agreement with the theoretical calculation.This design can expand the application of acoustic levitation in many fields,such as biomedicine,ultrasonic motor and new materials processing.

Three-dimensional simulation method of multipactor in microwave components for high-power space application

Based on the particle-in-cell technology and the secondary electron emission theory, a three-dimensional simulation method for multipactor is presented in this paper. By combining the finite difference time domain method and the panicle tracing method, such an algorithm is self-consistent and accurate since the interaction between electromagnetic fields and particles is properly modeled. In the time domain aspect, the generation of multipactor can be easily visualized, which makes it possible to gain a deeper insight into the physical mechanism of this effect. In addition to the classic secondary electron emission model, the measured practical secondary electron yield is used, which increases the accuracy of the algorithm. In order to validate the method, the impedance transformer and ridge waveguide filter are studied. By analyzing the evolution of the secondaries obtained by our method, multipactor thresholds of these components are estimated, which show good agreement with the experimental results. Furthermore, the most sensitive positions where multipactor occurs are determined from the phase focusing phenomenon, which is very meaningful for multipactor analysis and design.

Pre-reinforcement grout in fractured rock masses and numerical simulation for optimizing shrinkage stoping configuration

Proper room and pillar sizes are both critical factors for safe mining and high ore recovery rate in shrinkage stoping mining of underground metal mines. The rock masses of Tangdan copper mine of China are fractured, which needs much reinforcement and support prior to mining. Cement-sodium silicate grout technology was selected, then its related parameters such as grout pressure, diffusion radius and time were calculated and proposed. In order to test the effect of the pressured grout in the fractured No.4 ore block, field experiments were conducted. To optimize stoping configuration, three-dimensional numerical simulation with ANSYS and FLAC 3 D softwares was proposed. The results show that the drilling porosity and mechanical properties of the rock masses are increased obviously. After grout, ore recovery rate is increased by 10.2 % employing the newly designed stoping configuration compared with the previous. Last, analyzed from the surface movements, roof subsidence and the maximum principal stress of the pillars, the mining safety is probable of being ensured.

Numerical simulation of soft palate movement and airflow in human upper airway by fluid-structure interaction method

In this paper, the authors present airflow field characteristics of human upper airway and soft palate movement attitude during breathing. On the basis of the data taken from the spiral computerized tomography images of a healthy person and a patient with Obstructive Sleep Apnea-Hypopnea Syndrome （OSAHS）, three-dimensional models of upper airway cavity and soft palate are reconstructed by the method of surface rendering. Numerical simulation is performed for airflow in the upper airway and displacement of soft palate by fluid-structure interaction analysis. The reconstructed threedimensional models precisely preserve the original configuration of upper airways and soft palate. The results of the pressure and velocity distributions in the airflow field are quantitatively determined, and the displacement of soft palate is presented. Pressure gradients of airway are lower for the healthy person and the airflow distribution is quite uniform in the case of free breathing. However, the OSAHS patient remarkably escalates both the pressure and velocity in the upper airway, and causes higher displacement of the soft palate. The present study is useful in revealing pathogenesis and quantitative mutual relationship between configuration and function of the upper airway as well as in diagnosingdiseases related to anatomical structure and function of the upper airway.