Three-dimensional numerical simulation of the flow past a circular cylinder based on LES method

The hydrodynamic characteristics of a rigid, single, circular cylinder in a three dimensional, incompressible, uniform cross flow were calculated using the large-eddy simulation method of CFX5. Solutions to the three dimensional N-S equations were obtained by the finite volume method. The focus of this numerical simulation was to research the characteristics of pressure distribution （drag and litt forces） and vortex tubes at high Reynolds numbers. The results of the calculations showed that the forces at every section in the spanwise direction of the cylinder were symmetrical about the middle section and smaller than the forces calculated in two dimensional cases. Moreover, the flow around the cylinder obviously presents three dimensional characteristics.

Three-dimensional Computational Fluid Dynamics Modeling of Two-phase Flow in a Structured Packing Column

Characterizing the complex two-phase hydrodynamics in structured packed columns requires a power- ful modeling tool. The traditional two-dimensional model exhibits limitations when one attempts to model the de- tailed two-phase flow inside the columns. The present paper presents a three-dimensional computational fluid dy- namics （CFD） model to simulate the two-phase flow in a representative unit of the column. The unit consists of an CFD calculations on column packed with Flexipak 1Y were implemented within the volume of fluid （VOF） mathe- matical framework. The CFD model was validated by comparing the calculated thickness of liquid film with the available experimental data. Special attention was given to quantitative analysis of the effects of gravity on the hy- drodynamics. Fluctuations in the liquid mass flow rate and the calculated pressure drop loss were found to be quali- tatively in agreement with the experimental observations.

Analytic homotopy solution of generalized three-dimensional channel flow due to uniform stretching of the plate

In this communication a generalized three- dimensional steady flow of a viscous fluid between two infinite parallel plates is considered. The flow is generated due to uniform stretching of the lower plate in x- and y-directions. It is assumed that the upper plate is uniformly porous and is subjected to constant injection. The governing system is fully coupled and nonlinear in nature. A complete analytic solution which is uniformly valid for all values of the dimensionless parameters β Re and λ is obtained by using a purely analytic technique, namely the homotopy analysis method. Also the effects of the parameters β Re and λ on the velocity field are discussed through graphs.

Real-time Three-Dimensional Color Doppler Flow Imaging： An Improved Technique for Quantitative Analysis of Aortic Regurgitation

The recently introduced real-time three-dimensional color Doppler flow imaging （RT-3D CDFI） technique provides a quick and accurate calculation of regurgitant jet volume （RJV） and fraction. In order to evaluate RT-3D CDFI in the noninvasive assessment of aortic RJV and regurgitant jet fraction （RJF） in patients with isolated aortic regurgitation, real-time three-dimensional echocardiographic studies were performed on 23 patients with isolated aortic regurgitation to obtain LV end-diastolic volumes （LVEDV）, end-systolic volumes （LVESV） and RJV, and then RJF could be calculated. The regurgitant volume （RV） and regurgitant fraction （RF） calculated by two-dimensional pulsed Doppler （2D-PD） method served as reference values. The results showed that aortic RJV measured by the RT-3D CDFI method showed a good correlation with the 2D-PD measurements （r= 0.93, Y=0.89X＋ 3.9, SEE= 8.6 mL, P〈0.001 ）; the mean （SD） difference between the two methods was - 1.5 （9.8） mL. % RJF estimated by the RT-3D CDFI method was also correlated well with the values obtained by the 2D-PD method （r=0.88, Y=0.71X＋ 14.8, SEE= 6.4 %, P〈0. 001）; the mean （SD） difference between the two methods was -1.2 （7.9） %. It was suggested that the newly developed RT-3D CDFI technique was feasible in the majority of patients. In patients with eccentric aortic regurgitation, this new modality provides additional information to that obtained from the two-dimensional examination, which overcomes the inherent limitations of two-dimensional echocardiography by depicting the full extent of the jet trajectory. In addition, the RT-3D CDFI method is quick and accurate in calculating RJV and RJF.

Three-dimensional stretched flow of Jeffrey fluid with variable thermal conductivity and thermal radiation

This article addresses the three-dimensional stretched flow of the Jeffrey fluid with thermal radiation. The thermal conductivity of the fluid varies linearly with respect to temperature. Computations are performed for the velocity and temperature fields. Graphs for the velocity and temperature are plotted to examine the behaviors with different parameters. Numerical values of the local Nusselt number are presented and discussed. The present results are compared with the existing limiting solutions, showing good agreement with each other.

MHD three-dimensional flow of Jeffrey fluid with Newtonian heating

The magnetohydrodynamic(MHD) three-dimensional flow of Jeffrey fluid in the presence of Newtonian heating is investigated. Flow is caused by a bidirectional stretching surface. Series solutions are constructed for the velocity and temperature fields. Convergence of series solutions is ensured graphically and numerically. The variations of key parameters on the physical quantities are shown and discussed in detail. Constructed series solutions are compared with the existing solutions in the limiting case and an excellent agreement is noticed. Nusselt numbers are computed with and without magnetic fields. It is observed that the Nusselt number decreases in the presence of magnetic field.

STABILIZATION EFFECT OF FRICTIONS FOR TRANSONIC SHOCKS IN STEADY COMPRESSIBLE EULER FLOWS PASSING THREE-DIMENSIONAL DUCTS

Transonic shocks play a pivotal role in designation of supersonic inlets and ramjets.For the three-dimensional steady non-isentropic compressible Euler system with frictions,we constructe a family of transonic shock solutions in rectilinear ducts with square cross-sections.In this article,we are devoted to proving rigorously that a large class of these transonic shock solutions are stable,under multidimensional small perturbations of the upcoming supersonic flows and back pressures at the exits of ducts in suitable function spaces.This manifests that frictions have a stabilization effect on transonic shocks in ducts,in consideration of previous works which shown that transonic shocks in purely steady Euler flows are not stable in such ducts.Except its implications to applications,because frictions lead to a stronger coupling between the elliptic and hyperbolic parts of the three-dimensional steady subsonic Euler system,we develop the framework established in previous works to study more complex and interesting Venttsel problems of nonlocal elliptic equations.

Three-dimensional cellular automata based particle flow simulations of mechanical properties of talus deposit

Based on three-dimensional cellular automata （CA）, a new stochastic simulation model to simulate the microstructures and particle flow of talus deposit is proposed. Ill addition, an auto-modeling program CARS is developed, with which nunaerical simulations can be conducted conveniently. For the problem of simulating mechanical behaviors of talus deposit, spatial anangement or sphere shapes should be considered. In the new modeling method, four sphere anangement models are developed for the particle flow simulation of talus deposit. Numerical results show that the talus deposit has the mechanical characteristics of typical stress-strain curves, as other rock-like materials. The cohesion of talus deposit decreases with increasing rock content, while the internal friction angle increases with increasing rock contents. Finally, numerical simulation is verified with the results of field test.

Three-dimensional boundary layer flow of Maxwell nanofluid:mathematical model

The present research explores the three-dimensional boundary layer flow of the Maxwell nanofluid. The flow is generated by a bidirectional stretching surface. The mathematical formulation is carried out through a boundary layer approach with the heat source/sink, the Brownian motion, and the thermophoresis effects. The newly developed boundary conditions requiring zero nanoparticle mass flux at the boundary are employed in the flow analysis for the Maxwell fluid. The governing nonlinear boundary layer equations through appropriate transformations are reduced to the coupled nonlin- ear ordinary differential system. The resulting nonlinear system is solved. Graphs are plotted to examine the effects of various interesting parameters on the non-dimensional velocities, temperature, and concentration fields. The values of the local Nusselt number are computed and examined numerically.

Convective heat and mass transfer effects in three-dimensional flow of Maxwell fluid over a stretching surface with heat source

Heat and mass transfer effects in three-dimensional flow of Maxwell fluid over a stretching surface were addressed.Analysis was performed in the presence of internal heat generation/absorption. Concentration and thermal buoyancy effects were accounted. Convective boundary conditions for heat and mass transfer analysis were explored. Series solutions of the resulting problem were developed. Effects of mixed convection, internal heat generation/absorption parameter and Biot numbers on the dimensionless velocity, temperature and concentration distributions were illustrated graphically. Numerical values of local Nusselt and Sherwood numbers were obtained and analyzed for all the physical parameters. It is found that both thermal and concentration boundary layer thicknesses are decreasing functions of stretching ratio. Variations of mixed convection parameter and concentration buoyancy parameter on the velocity profiles and associated boundary layer thicknesses are enhanced. Velocity profiles and temperature increase in the case of internal heat generation while they reduce for heat absorption. Heat transfer Biot number increases the thermal boundary layer thickness and temperature. Also concentration and its associated boundary layer are enhanced with an increase in mass transfer Biot number. The local Nusselt and Sherwood numbers have quite similar behaviors for increasing values of mixed convection parameter, concentration buoyancy parameter and Deborah number.

AN APPLICATION OF TOPOLOGICAL ANALYSIS TO STUDYING THE THREE-DIMENSIONAL FLOW IN CASCADES;PART I—TOPOLOGICAL RULES FOR SKIN-FRICTION LINES AND SECTION STREAMLINES

Based on the working of Lighthill and Hunt et al., in the present paper the author has established the topological rules adapting to analysing the skin-friction lines and the section streamlines in cascades. These rules are (1) for a rotor cascade without shroud band, the total number of nodal points equals that the saddle points on the skin-friction line vector fields in eachpitch range; (2) for an annular or straight cascade with no-clearances at blade ends, the total number of saddle points is two more than that of nodal points on the skin-friction line fields in a pitch; (3) the total number of saddles in the secondary flow fields on cross-sections in cascade is one less than that of nodes; (4) in the section streamline vector fields on a meridian surface penetrating a flow passage, and on leading and trailing edge sections, the total number of nodes is equal to that of saddles; (5) on the streamline vector fields of a blade-to-blade surface, the total number of nodes is one less than that of saddles.

EXPERIMENTAL INVESTIGATION FOR THE EFFECT OF ROTATION ON THREE-DIMENSIONAL FLOW FIELD IN FILM-COOLED TURBINE

An experimental investigation of three-dimensional flow field in a film-cooled turbine model is carried out by using particle image velocimeter （PIV） in a low-speed wind tunnel. The effects of different blowing ratios （M=1.5, 2） on the flow field are studied. The experimental results reveal the classical phenomena of the formation of kidney vortex pair and secondary flow in wake region behind the jet hole. And the changes of the kidney vortex pair and the wake at different locations away from the hole on the suction and pressure sides are also studied. Compared with the flow field in stationary cascade, there are centrifugal force and Coriolis force existing in the flow field of rotating turbine, and these forces bring the radial velocity in the jet flow. The effect of rotatien on the flow field of the pressure side is more distinct than that on the suction side from the measured flow fields in Y-Z plane and radial velocity contours. The increase of blowing ratio makes the kidney vortex pair and the secondary flow in the wake region stronger and makes the range of the wake region enlarged.

The Design of a Three-Dimensional Physical Modeling System for Real-Time Groundwater Flows

In the past decades,physical modeling has been widely used in hydrogeology for teaching,studying and exhibition purposes.Most of these models are used to illustrate hydrogeological profiles,but few can depict three-dimensional groundwater flows,making it impossible to validate groundwater flows simulated by numerical methods with physical modeling.

AN APPLICATION OF TOPOLOGICAL METHOD TO ANALYSING THE THREE-DIMENSIONAL FLOW IN CASCADES(Ⅱ)-TOPOLOGICAL ANALYSIS ON THE VECTOR FIELD PATTERNS OF SKINFRICTIONS AND SECTION STREAMLINES

With an application of topological analysis,in this paper the skin-friction line patterns on compressor and turbine cascade surfaces are depicted and the streamline patterns of the secondary flow fields in the cross-section of a curved pipe and a turbine cascade are drawn under given conditions.In addition the structures of vortices within three-dimensional viscous flow fields in cascades are analysed.

THREE-DIMENSIONAL ANALYSIS OF THE FLOW IN THE CYCLONES

This paper gives the detailed mathematical expression of the flow in the spherical coordinates system. Applying the law of conservation of mass, movement theorem of steady flow, and applying the mathematical method of stream function with consideration of the axis symmetry, the three components of velocity quantum of the flow are deduced in detail. Here the overall analysis of the flow is presented in the view of the concept of whole, and the paper gives the necessary corrections of some results of Ref.[1]

Radiation effect on temperature distribution in three-dimensional Couette flow with suction or injection

A theoretical analysis of three-dimensional Couette flow with radiation effect on temperature distribution has been analysed, when the injection of the fluid at the lower stationary plate is a transverse sinusoidat one and its corresponding removal by constant suction through the upper porous plate is in uniform motion. Due to this type of injection velocity, the flow becomes three-dimensional. The effect of Prandtl number, radiation parameter and injection parameter on rate of heat transfer has been examined by the help of graphs. The Prandtl number has a much greater effect on the.temperature distribution than the injection or radiation parameter.

Three-dimensional channel flow of second grade fluid in rotating frame

An analysis is performed for the hydromagnetic second grade fluid flow between two horizontal plates in a rotating system in the presence of a magnetic field. The lower sheet is considered to be a stretching sheet, and the upper sheet is a porous solid plate. By suitable transformations, the equations of conservation of mass and momentum are reduced to a system of coupled non-linear ordinary differential equations. A series of solutions to this coupled non-linear system are obtained by a powerful analytic technique, i.e., the homotopy analysis method （HAM）. The results are presented with graphs. The effects of non-dimensional parameters R, A, M2, a, and K2 on the velocity field are discussed in detail.

A COMPUTER CODE FASTOR-3D FOR TRANSIENT THREE-DIMENSIONAL SIMULATION ON FLOW AND HEAT TRANS-FER WITH POROSITY APPROXIMATION

Upon the conservation of mass, momentum and energy, volume fraction and surface penetrative rate were employed to modify the conservative equations to simulate the effect of blockages on fluid flows and heat transfer. These equations were solved numerically with the finite differential method and the primitive variable approach. This method uses staggered grid and pressure correction schemes. A computer code FASTOR3D integrated the aforementioned algorithm. The preliminary results have been compared with conventional benchmark solutions. With auxiliary software DV, the numerical results were visualized in colorful images to demonstrate the variation of flow patterns and temperature profiles during the transient process. The results of the simulation code for the fluid flows and heat transfer in the sodium pool of a fast breeder reactor are acceptable.

Unsteady three-dimensional boundary layer flow due to a permeable shrinking sheet

The unsteady viscous flow over a continuously permeable shrinking surface is studied. Similarity equations are obtained through the application of similar transformation techniques. Numerical techniques are used to solve the similarity equations for different values of the unsteadiness parameter, the mass suction parameter, the shrinking parameter and the Prandtl number on the velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number. It is found that, different from an unsteady stretching sheet, dual solutions exist in a certain range of mass suction and unsteadiness parameters.

Newtonian heating effects in three-dimensional flow of viscoelastic fluid

A mathematical model is constructed to investigate the three-dimensional flow of a non-Newtonian fluid. An in-compressible viscoelastic fluid is used in mathematical formulation. The conjugate convective process （in which heat the transfer rate from the bounding surface with a finite capacity is proportional to the local surface temperature） in three-dimensional flow of a differential type of non-Newtonian fluid is analyzed for the first time. Series solutions for the nonlinear differential system are computed. Plots are presented for the description of emerging parameters entering into the problem. It is observed that the conjugate heating phenomenon causes an appreciable increase in the temperature at the stretching wall.