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.

The Flow Simulation and Experimental Study of Low-Specific-Speed High-Speed Complex Centrifugal Impellers＊

Based on the Navier-Stokes equations and the Spalart-Allmaras turbulence model, three-dimensional turbulent flow in four low-specific-speed centrifugal impellers are simulated numerically and analyzed. The relative velocity distribution, pressure distribution and static pressure rise at the design point are obtained for the regular impeller with only long blades and three complex impellers with long, mid or short blades. It is found that the back flow region between long-blade pressure side and mid-blade suction side is diminished and is pushed to pressure side of short blades near the outlet of impeller at suction side by the introduction of mid, short blades, and the size of back flow becomes smaller in a multi-blade complex impeller. And the pressure rises uniformly from inlet to outlet in all the impellers. The simulated results show that the complex impeller with long, mid and short blades can improve the velocity distribution and reduce the back flow in the impeller channel. The experimental results show that the back flow in the impeller has an important influence on the performance of pump and a more-blade complex impeller with long, mid and short blades can effectively solve low flow rate instability of the low-specific-speed centrifugal pump.

Numerical Simulation of Gas-Liquid Flow in a Stirred Tank with a Rushton Impeller

The gas-liquid flow field in a stirred tank with a Rushton diskturbine, including the impeller region, was numerically simulatedusing the improved inner-outer iterative procedure. Thecharacteristic features of the stirred tank, such as gas cavity andaccumulation of gas at the two sides of wall baffles, can be capturedby the simulation. The simulated results agree well with availableexperimental data. Since the improved inner-outer iterative algorithmdemands on empirical formula and experimental data for the impellerregion, and the approach seems generally applicable for simulatinggas-liquid stirred tanks.

An improved large eddy simulation of two-phase flows in a pump impeller

An improved large eddy simulation using a dynamic second-order sub-grid-scale （SGS） stress model has been developed to model the governing equations of dense turbulent particle-liquid two-phase flows in a rotating coordinate system, and continuity is conserved by a mass-weighted method to solve the filtered governing equations. In the cur- rent second-order SGS model, the SGS stress is a function of both the resolved strain-rate and rotation-rate tensors, and the model parameters are obtained from the dimensional consistency and the invariants of the strain-rate and the rotation-rate tensors. In the numerical calculation, the finite volume method is used to discretize the governing equations with a staggered grid system. The SIMPLEC algorithm is applied for the solution of the discretized governing equations. Body- fitted coordinates are used to simulate the two-phase flows in complex geometries. Finally the second-order dynamic SGS model is successfully applied to simulate the dense turbu-lent particle-liquid two-phase flows in a centrifugal impeller. The predicted pressure and velocity distributions are in good agreement with experimental results.

3D Particle Image Velocimetry Test of Inner Flow in a Double Blade Pump Impeller

The double blade pump is widely used in sewage treatment industry,however,the research on the internal flow characteristics of the double blade pump with particle image velocimetry（PIV） technology is very little at present.To reveal inner flow characteristics in double blade pump impeller under off-design and design conditions,inner flows in a double blade pump impeller,whose specific speed is 111,are measured under the five off-design conditions and design condition by using 3D PIV test technology.In order to ensure the accuracy of the 3D PIV test,the external trigger synchronization system which makes use of fiber optic and equivalent calibration method are applied.The 3D PIV relative velocity synthesis procedure is compiled by using Visual C＋＋ 2005.Then absolute velocity distribution and relative velocity distribution in the double blade pump impeller are obtained.Test results show that vortex exists in each condition,but the location,size and velocity of vortex core are different.Average absolute velocity value of impeller outlet increases at first,then decreases,and then increases again with increase of flow rate.Again average relative velocity values under 0.4,0.8,and 1.2 design condition are higher than that under 1.0 design condition,while under 0.6 and 1.4 design condition it is lower.Under low flow rate conditions,radial vectors of absolute velocities at impeller outlet and blade inlet near the pump shaft decrease with increase of flow rate,while that of relative velocities at the suction side near the pump shaft decreases.Radial vectors of absolute velocities and relative velocities change slightly under the two large flow rate conditions.The research results can be applied to instruct the hydraulic optimization design of double blade pumps.

CFD simulation of single-phase flow in flotation cells:Effect of impeller blade shape,clearance,and Reynolds number

A series of numerical simulations of turbulent single-phase flows are performed to understand the flow and mixing characteristics in a laboratory scale flotation tank.Four impeller blade shapes covering a wide range of surface areas and lip lengths are considered to highlight and contrast the flow behavior predicted in the impeller stream.The mean flow close to the impeller is fully characterized by considering velocity components along the axial direction at different radial locations.Normalized results suggest the development of a comparatively stronger axial velocity component for a blade design with the smallest lip length,called big-tip impeller here.Normalized turbulent kinetic energy profiles close to the impeller reveal the existence of an asymmetric trailing vortex pair.The highest turbulence kinetic energy dissipation rates are observed close to the impeller blades and stator walls where the radial jet strikes the stator walls periodically.Furthermore,liquid phase mixing in the flotation cell is studied using transient scalar tracing simulations providing mixing time data.Finally,pumping capacity and efficiency of different impeller designs are calculated based on which the impeller blade design with a rectangular blade design is found to perform most efficiently.

Numerical Study of Solid-Liquid Two-Phase Flow in Stirred Tanks with Rushton Impeller (Ⅰ) Formulation and Simulation of Flow Field

The critical impeller speed, N_(JS), for complete suspension of solidparticles in the agitated solid-liquid two-phase system in baffled stirred tanks with a standardRushton impeller is predicted using the computational procedure proposed in Part Ⅰ. Three differentnumerical criteria are tested for determining the critical solid suspension. The predicted N_(JS)is compared with those obtained from several empirical correlations. It is suggested the mostreasonable criterion for determining the complete suspension of solid particles is the positive signof simulated axial velocity of solid phase at the location where the solid particles are mostdifficult to be suspended.

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.

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.

Three-Dimensional Simulation of Hydrodynamic Mechanism of Fluidized Bed Methanation

Organic solid waste(OSW)contains many renewable materials.The pyrolysis and gasification of OSW can realize resource utilization,and its products can be used for methanation reaction to produce synthetic natural gas in the specific reactor.In order to understand the dynamic characteristics of the reactor,a three-dimensional numerical model has been established by the method of Computational Fluid Dynamics(CFD).Along the height of the reactor,the particle distribution in the bed becomes thinner and the mean solid volume fraction decreases from 4.18%to 0.37%.Meanwhile,the pressure fluctuation range decreased from 398.76 Pa at the entrance to a much lower value of 74.47 Pa at the exit.In this simulation,three parameters of gas inlet velocity,operating temperature and solid particle diameter are changed to explore their influences on gas-solid multiphase flow.The results show that gas velocity has a great influence on particle distribution.When the gas inlet velocity decreases from 6.51 to 1.98 m/s,the minimum height that particles can reach decreases from 169 to 100 mm.Additionally,as the operating temperature increases,the particle holdup inside the reactor changes from 0.843%to 0.700%.This indicates that the particle residence time reduces,which is not conducive to the follow-up reaction.Moreover,with the increase of particle size,the fluctuation range of the pressure at the bottom of the reactor increases,and its standard deviation increases from 55.34 to 1266.37 Pa.

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.

Effect of pitched short blades on the flow characteristics in a stirred tank with long-short blades impeller

This work focuses on the design improvement of the long-short blades(LSB)impeller by using pitched short blades(SBs)to regulate the flow field in the stirred vessel.After mesh size evaluation and velocity field validation by the particle image velocimetry,large eddy simulation method coupled with sliding mesh approach was used to study the effect of the pitched SBs on the flow characteristics.We changed the inclined angles of the SBs from 30°to 60°and compared the flow characteristics when the impeller was operated in the down-pumping and up-pumping modes.In the case of down-pumping mode,the power number is relatively smaller and vortexes below the SBs are suppressed,leading to turbulence intensification in the bottom of the vessel.Whereas in the case of up-pumping mode,the axial flow rate in the center increased significantly with bigger power number,resulting in more efficient mass exchange between the axial and radial flows in the whole vessel.The LSB with 45°inclined angle of the SBs in the up-pumping mode has the most uniform distributions of flow field and turbulent kinetic energy compared with other impeller configurations.