NUMERICAL SIMULATION OF 3-D TURBULENT FLOWS OVER DREDGED TRENCHES

A 3- D free surface flow in open channels based on the Reynolds equations with the k-ε turbulence closure model is presented in this paper. Insted of the 'rigid lid' approximation, the solution of the free surface equation is implemented in the velocity-pressure iterative procedure on the basis of the conventional SIMPLE method. This model was used to compute the flow in rectangular channels with trenches dredged across the bottom. The velocity, eddy viscosity coefficient, turbulent shear stress, turbulent kinetic energy and elevation of the free surface can be obtained. The computed results are in good agreement with previous experimental data.

NUMERICAL COMPUTATION OF 3-D TURBULENT FLOW IN TURBINE CASCADE

Ⅰ. INTRODUCTIONThe flow phenomena that exist in the advanced turbomachinery are extremely complex and propose a challenge to the engineers and scientists to improve the design procedure. The rapid progress of high speed and large capacity computers has encouraged the development of computational fluid dynamics that has had an increasingly important influence on turbomachinery blade design and analysis. Compared with the inviscid solver, the N.S.

Numerical simulation of a combined oxidation ditch flow using 3D k-ε turbulence model

The standard three dimensional（3D） k-ε turbulence model was applied to simulate the flow field of a small scale combined oxidation ditch. The moving mesh approach was used to model the rotor of the ditch. Comparison of the computed and the measured data is acceptable. A vertical reverse flow zone in the ditch was found, and it played a very important role in the ditch flow behavior. The flow pattern in the ditch is discussed in detail, and approaches are suggested to improve the hydrodynamic performance in the ditch.

A CFD Based Investigation of the Unsteady Hydrodynamic Coefficients of 3-D Fins in Viscous Flow

The motion of the fins and control surfaces of underwater vehicles in a fluid is an interesting and challenging research subject.Typically the effect of fin oscillations on the fluid flow around such a body is highly unsteady, generating vortices and requiring detailed analysis of fluid-structure interactions.An understanding of the complexities of such flows is of interest to engineers developing vehicles capable of high dynamic performance in their propulsion and maneuvering.In the present study, a CFD based RANS simulation of a 3-D fin body moving in a viscous fluid was developed.It investigated hydrodynamic performance by evaluating the hydrodynamic coefficients (lift, drag and moment) at two different oscillating frequencies.A parametric analysis of the factors that affect the hydrodynamic performance of the fin body was done, along with a comparison of results from experiments.The results of the simulation were found in close agreement with experimental results and this validated the simulation as an effective tool for evaluation of the unsteady hydrodynamic coefficients of 3-D fins.This work can be further be used for analysis of the stability and maneuverability of fin actuated underwater vehicles.

Conical Sonic-Supersonic Solutions for the 3-D Steady Full Euler Equations

This paper concerns the sonic-supersonic structures of the transonic crossflow generated by the steady supersonic flow past an infinite cone of arbitrary cross section.Under the conical assumption,the three-dimensional(3-D)steady Euler equations can be projected onto the unit sphere and the state of fluid can be characterized by the polar and azimuthal angles.Given a segment smooth curve as a conical-sonic line in the polar-azimuthal angle plane,we construct a classical conical-supersonic solution near the curve under some reasonable assumptions.To overcome the difficulty caused by the parabolic degeneracy,we apply the characteristic decomposition technique to transform the Euler equations into a new degenerate hyperbolic system in a partial hodograph plane.The singular terms are isolated from the highly nonlinear complicated system and then can be handled successfully.We establish a smooth local solution to the new system in a suitable weighted metric space and then express the solution in terms of the original variables.

Simulation of subcritical flow pattern in 180° uniform and convergent open-channel bends using SSIIM 3-D model

In meandering rivers, the flow pattern is highly complex, with specific characteristics at bends that are not observed along straight paths. A numerical model can be effectively used to predict such flow fields. Since river bends are not uniform-some are divergent and others convergent-in this study, after the SSIIM 3-D model was calibrated using the result of measurements along a uniform 180° bend with a width of 0.6 m, a similar but convergent 180v bend, 0.6 m to 0.45 m wide, was simulated using the SSI1M 3-D numerical model. Flow characteristics of the convergent 180° bend, including lengthwise and vertical velocity profiles, primary and secondary flows, lengthwise and widtbwise slopes of the water surface, and the helical flow strength, were compared with those of the uniform 180° bend. The verification results of the model show that the numerical model can effectively simulate the flow field in the uniform bend. In addition, this research indicates that, in a convergent channel, the maximum velocity path at a plane near the water surface crosses the channel＇s centerline at about a 30° to 40° cross-section, while in the uniform bend, this occurs at about the 50° cross-section. The varying range of the water surface elevation is wider in the convergent channel than in the uniform one, and the strength of the helical flow is generally greater in the uniform channel than in the convergent one. Also, unlike the uniform bend, the convergent bend exhibits no rotational cell against the main direction of secondary flow rotation at the 135° cross-section.

EFFECT OF SUBMERGED ENTRY NOZZLE (SEN) PARAMETERS AND SHAPE ON 3-D FLUID FLOW IN MOULD FOR BEAM BLANK CONTINUOUS CASTING

According to turbulent theory and characteristics of beam blank continuous casting, 3-D model to represent the flow of beam blank mould is established. The predicted results indicate that the exit obliquity of up 15°(+15°) should be adopted, which will benefit the floatation of non-metallic inclusion and purification of the molten steel. When the nozzle angle is 120°, the flow pattern is reasonable. Proper nozzle depth can be 200mm. Turbulent kinetic of meniscus can be reduced by adopting the square nozzle and suitable area of side outlet when casting speed increases. The results are consistent with those of water model experiment, so the model is exact and reasonable. The model can provide important information for design of SEN and defining of immersion depth.

SECOND-MOMENT CLOSURE FOR MODELLING THE NEAR-WALL TURBULENCE IN 3D MEAN FLOWS

A second-moment closure for the near-wall turbulence is proposed. The limiting behaviour of this closure near a wall is consistent with that of the exact Reynolds-stress transport equations, and it converts asymptotically into a high- Reynolds-number closure remote from the wall. The closure is applied to a pressure- driven 3D transient channel flow. The predicted results are in fair agreement with the DNS data.

Predication of 3-D Viscous Flowfield of a Centrifugal Impeller

A three-dimensional viscous code has been developed to solve Reynolds-averaged Navier-Stokes equations. The governing equations in finite volume form are solved by two-step Runge-Kutta scheme with implicit residual smoothing. The eddy viscous is obtained using the Baldwin-Lomax model. A prediction of the 3-D turbulent flow and the performance in the “all-over controlled vortex distribution” centrifugal impeller with a vaneless diffuser has been made for the compressor at design and off-design condition. The predicted effi-ciency is a little higher than the experiment data. These results suggest that the present calculation code is able to determine the flow development in the impeller and also the turbulence model in the centrifugal im-peller should be improved.

A Higher-Efficient Non-Hydrostatic Finite Volume Model for Strong Three-Dimensional Free Surface Flows and Sediment Transport

In order to accurately simulate strong three-dimensional （3-D） free surface flows and sediment transport, the fully 3- D non-hydrostatic pressure models are developed based on the incompressible Navier-Stokes equations and convection-diffusion equation of sediment concentration with the mixing triangle and quadrilateral grids. The governing equations are discretized with the unstructured finite volume method in order to provide conservation properties of mass and momentum, and flexibility with practical application. It is shown that it is first-order accurate on nonuniform plane two-dimensional （2-D） grids and second-order accurate on uniform plane grids. A third-order approximation of the vertical velocity at the top-layer is applied. In such a way, free surface zero stress boundary condition is satisfied maturely, and very few vertical layers are needed to give an accurate solution even for complex discontinuous flow and short wave simulation. The model is applied to four examples to simulate strong 3-D free surface flows and sediment transport where non-hydrostatic pressures have a considerable effect on the velocity field. The newly developed model is verified against analytical solutions with an excellent agreement.

Analysis of Combined Radiation and Forced Convection Heat Transfer in 3D Laminar Flow over an Inclined Forward Facing Step

In the current study, a numerical investigation of three-dimensional combined convection-radiation heat transfer over an inclined forward facing step (FFS) in a horizontal rectangular duct is presented. The fluid is treated as a gray, absorbing, emitting and scattering medium. To simulate the incline surface of FFS, the blocked-off method is employed in this study. The set of governing equations for gas flow are solved numerically using the CFD technique to obtain the temperature and velocity fields. Since the gas is considered as a radiating medium, all of the convection, conduction and radiation heat transfer mechanisms are presented in the energy equation. For computation of radiative term in energy equation, the radiative transfer equation (RTE) is solved numerically by the discrete ordinates method (DOM) to find the divergence of radiative heat flux distribution inside the radiating medium. The effects of optical thickness, radiation-conduction parameter and albedo coefficient on heat transfer behavior of the system are carried out.

EXPERIMENTAL STUDY OF 3-D TURBULENT BEND FLOWS IN OPEN CHANNEL

A generalized hend flow model, treating a 90° single bend and 60° continuous hends, was designed to quantitatively describe 3-D turhulenee mechanism of circulating notfully-developed flow in open channels with hends. The 3-D fluctuating veloeities of turbulent flow were measured and analyzed with a 3 D acoustic-Doppler velocimeter. Formula for 3 D turbulent intensity was derived using the dimension analysis approaeh. Expressions of vertical turbulent intensity distributions were obtained with the multivariant-rcgression theo ry, whieh agree with experiment data. Distrihutions of turbulent intensity and turbulent stress were characterized, and their relationships were concluded. In the bend-turbulent flow core region, longitudinal and lateral turbulent-intensity distri hutions are coincident with linear distribution, hut in nearwall region are coincident with the Gamma distribution. Verotical turbulent intensity distributions are coincident with the Rayleigh distribution. Herein, it is concluded that the bend turbulence is anisotropic.

3-D NUMERICAL STUDY OF LAMINAR AND TURBULENT FLOW INSIDE A 90-DEG-BEND SQUARE AND FLAT DUCT

With the application of body-fitted coordinate method and the standard k-epsilon equations,the rtumericat sotution to the averaged N-S equations is obtained.Laminar and turbu- tent flows inside a 90-Deg-Bent duct are studied,yielding good results.

THE NUMERICAL PREDICTION OF DEVELOPING TURBULENT FLOW IN 3-D RECTANGULAR DUCTS

Comparisons are made between experimental data and numerical predictions based on the k-e turbulent model of low Reynolds number applicable to developing turbulent flow in rectangular ducts of arbitrary aspect ratio.The numerical procedure utilizes the separated-layers finite-analytical method.The merits of the k-e turbulent model of low Reynolds number and the computation procedure are assessed by means of comparison with results,referred to that of the length-scale model and the full-Reynolds-stress model used in recent years.

Formation of the Tibetan Plateau during the India-Eurasia Convergence:Insight from 3-D Multi-Terrane Thermomechanical Modeling

Various models exist to explain the formation of the Tibetan Plateau,including“tectonic escape”,“pure shear thickening”,“convective removal of the lithospheric mantle”,and“lower crustal flow”model.The first two models are primarily constructed on pure mechanical models but are unable to reasonably explain the tension and shear phenomena inside the plateau.The latter two are rheological dynamic models based on deep geophysical observations.However,the spatial range of the lower crustal flow and its role in the plateau formation/uplift remain controversial.Five multi-terrane viscoplastic thermomechanical models were constructed to simulate the uplift and lithospheric structure change of the Tibetan Plateau during the post-collision stage(since 35 Ma)under the convergence of the Indian Plate.Results show that the plateau's formation begins with crustal thickening,blocked by strong terranes at the northern plateau,and expanded laterally to the east.The lithosphere thickens gradually and experiences delamination at its base,elevating temperature within the crust and forming partial melting layers in the central plateau.As convergence persists on the southern side,the northern plateau's lithosphere bends downward and undergoes delamination,further heating the crust and promoting the northward and eastward flow of partial melting layers,leading to secondary uplift around the plateau.

Numerical simulation and analysis of solid-liquid two-phase threedimensional unsteady flow in centrifugal slurry pump

Based on RNG k-ε turbulence model and sliding grid technique, solid-liquid two-phase three-dimensional(3-D) unsteady turbulence of full passage in slurry pump was simulated by means of Fluent software. The effects of unsteady flow characteristics on solid-liquid two-phase flow and pump performance were researched under design condition. The results show that clocking effect has a significant influence on the flow in pump, and the fluctuation of flow velocity and pressure is obvious, particularly near the volute tongue, at the position of small sections of volute and within diffuser. Clocking effect has a more influence on liquid-phase than on solid-phase, and the wake-jet structure of relative velocity of solid-phase is less obvious than liquid-phase near the volute tongue and the impeller passage outlet. The fluctuation of relative velocity of solid-phase flow is 7.6% smaller than liquid-phase flow at the impeller outlet on circular path. Head and radial forces of the impeller are 8.1% and 85.7% of fluctuation, respectively. The results provide a theoretical basis for further research for turbulence, improving efficient, reducing the hydraulic losses and wear. Finally, field tests were carried out to verify the operation and wear of slurry pump.

3D mathematical model for suspended load transport by turbulent flows and its applications

This paper presents a 3D mathematical model for suspended load transport in turbulent flows. Based on Dous stochastic theory of turbulent flow, numerical schemes of Reynolds stresses for anisotropic turbulent flows were obtained. A refined wall function was employed to treat solid wall boundaries. The equations for 2D suspended load motion and sorting of bed material have been expanded into 3D cases. Numerical results are validated by the measured data of the Gezhouba Project, and proved to be in good agreement with the experimental. The present method has been employed to simulate sediment erosion and deposition in the dam area of Three Gorges Project, and for the operation of the project, siltation process and deposition pattern in the near-dam area of the reservoir, size distribution of the deposits and bed material, and flow fields and sediment concentration fields at different time and elevations are predicted. The predicted results are close to the experimental observations in physical model studies. Thus, a new method is established for 3D simulation of sediment motion in dam areas of multi-purpose water projects.

Simulation of Polymer Melt Flow Fields in Intermeshing Co-Rotating Three-Screw Extruders

Three-dimension isothermal flows of polymer melt in the kneading blocks of triangularly-arranged and parallelly-arranged intermeshing co-rotating three-screw extruders are simulated using the finite element package POLYFLOW. Based on the velocity fields calculated, the particle trajectories in both machines are visualized using particle tracking technique. The numerical results indicate that the flow patterns in three-screw extruders are similar to those in twin-screw extruders. The triangularly-arranged three-screw extruder has the largest pumping capacity and also the highest extrusion stability in terms of flowrate fluctuation with screw rotation. The instantaneous mixing and cumulative residence time distribution （RTD） characteristics are also analyzed and compared with traditional intermeshing co-rotating twin-screw extruders. It is shown that the start section of the cumulative RTD curve for the triangularly-arranged machine has a small shoulder, which is attributed to the faster flow in the central region of this type of extruder.

A k-ε Turbulence Model Considering Compressibility in Three-Dimensional Transonic Turbulent Flow Calculation

Based on the standard k-ε turbulence model, a new compressible k-ε model considering the pressure expansion influence due to the compressibility of fluid is developed and applied to the simulation of 3D transonic turbulent flows in a nozzle and a cascade. The Reynolds avenged N-S equations in generalized curvilinear coordinates are solved with implementation of the new model. The high resolution TVD scheme is used to discretize the convective terms. The numerical results show that the compressible k-ε model behaves well in the simulation of transonic internal turbulent flows.

On numerical modeling of low-head direct chill ingot caster for magnesium alloy AZ31

A comprehensive 3D turbulent CFD study has been carried out to simulate a Low-Head(LH)vertical Direct Chill(DC)rolling ingot caster for the common magnesium alloy AZ31.The model used in this study takes into account the coupled laminar/turbulent melt flow and solidification aspects of the process and is based on the control-volume finite-difference approach.Following the aluminum/magnesium DC casting industrial practices,the LH mold is taken as 30 mm with a hot top of 60 mm.The previously verified in-house code has been modified to model the present casting process.Important quantitative results are obtained for four casting speeds,for three inlet melt pouring temperatures(superheats)and for three metal-mold contact heat transfer coefficients for the steady state operational phase of the caster.The variable cooling water temperatures reported by the industry are considered for the primary and secondary cooling zones during the simulations.Specifically,the temperature and velocity fields,sump depth and sump profiles,mushy region thickness,solid shell thickness at the exit of the mold and axial temperature profiles at the center and at three strategic locations at the surface of the slab are presented and discussed.