A K-εTWO-EQUATION TURBULENCE MODEL FOR THE SOLID-LIQUID TWO-PHASE FLOWS

A two-equation turbulence model has been dereloped for predicting two-phase flow the two equations describe the conserration of turbulence kinetic energy and dissipation rate of that energy for the incompressible carrier fluid in a two-phase flow The continuity, the momentum, K and εequations are modeled. In this model,the solid-liquid slip veloeites, the particle-particte interactions and the interactions between two phases are considered,The sandy water pipe turbulent flows are sueeessfuly predicted by this turbulince model.

CFD simulation of impeller shape effect on quality of mixing in two-phase gas–liquid agitated vessel

Mixing efficiency in two-phase gas–liquid agitated vessel is one of the important challenges in the industrial processes.Computational fluid dynamics technique(CFD)was used to investigate the effect of four different pitched blade impellers,including 15°,30°,45°and 60°,on the mixing quality of gas–liquid agitated vessel.The multiphase flow behavior was modeled by Eulerian–Eulerian multiphase approach,and RNG k-εwas used to model the turbulence.The CFD results showed that a strong global vortex plays the main role on the mixing quality of the gas phase in the vessel.Based on the standard deviation criterion,it was observed that the axial distribution of the gas phase in the 30°impeller is about 55%better than the others.In addition,the results showed that the 30°impeller has a uniform radial distribution over the other impellers and the maximum gas phase holdup in the vessel.Investigation of the power consumption of the impellers showed that the 30°impeller has the highest power consumption among the other pitched blade impellers.Also,examine the effect of same power condition for pitched blade impellers showed that the 30°impeller has the best mixing quality in this condition.

Analysis of the Flow Field Characteristics Associated with the Dynamic Rock Breaking Process Induced by a Multi-Hole Combined External Rotary Bit

The characteristics of the flow field associated with a multi-hole combined external rotary bit have been studied by means of numerical simulation in the framework of an RNG k-εturbulence model,and compared with the results of dedicated rock breaking drilling experiments.The numerical results show that the nozzle velocity and dynamic pressure of the nozzle decrease with an increase in the jet distance,and the axial velocity of the nozzle decays regularly with an increase in the dimensionless jet distance.Moreover,the axial velocity related to the nozzle with inclination angle 20°and 30°can produce a higher hole depth,while the radial velocity of the nozzle with 60°inclination can enlarge the hole diameter.The outcomes of the CFD simulations are consistent with the actual dynamic rock breaking and pore forming process,which lends credence to the present results and indicates that they could be used as a reference for the future optimization of systems based on the multi-hole combined external rotary bit technology.

INFLUENCES OF CASTING SPEED AND SEN DEPTH ON FLUID FLOW IN THE FUNNEL TYPE MOLD OF A THIN SLAB CASTER

In recent years, thin slab continuous casting technology has been widely used to improve the quality of the product and to reduce the cost. One of the challenges faced by this technology is to design reasonable flow patterns, which strongly affect the surface and inner properties of the final slab in the mold. With the fixed scales and complex geometrical structures of nozzle and funnel type mold, a series of numerical simulations are made to analyze the flow patterns in melt steel using finite volume method based on structured body fitted coordinate grids. The CFD （computational fluid dynamics） package is validated first using one typical case described in previously published studies, and then it is developed to study the effect of operational parameters on fluid flow in thin slab caster. Two operational parameters, casting speed and SEN （submerged entry nozzle） depth, are mainly considered for numerical analysis. On the basis of present simulations, the reasonable SEN submergence depths corresponding to different casting speeds are suggested according to fluid flow characteristics like, flow jet impingement on the narrow side of the mold, flow speed of the melt steel beneath the meniscus and the recirculation region. This is the first stage of study on the numerical analysis of the whole thin slab casting process with electromagnetic brake.

Theoretical and numerical study of hydraulic characteristics of orifice energy dissipator

Different factors affecting the efficiency of the orifice energy dissipator were investigated based on a series of theoretical analyses and numerical simulations. The main factors investigated by dimension analysis were identified, including the Reynolds number （Re）, the ratio of the orifice diameter to the inner diameter of the pipe （ did ）, and the ratio of distances between orifices to the inner diameter of the pipe （ LID ）. Then, numerical simulations were conducted with a k-ε two-equation turbulence model. The calculation results show the following： Hydraulic characteristics change dramatically as flow passes through the orifice, with abruptly increasing velocity and turbulent energy, and decreasing pressure. The turbulent energy appears to be low in the middle and high near the pipe wall. For the energy dissipation setup with only one orifice, when Re is smaller than 105, the orifice energy dissipation coefficient K increases rapidly with the increase of Re. When Re is larger than l05, K gradually stabilizes. As diD increases, K and the length of the recirculation region L1 show similar variation patterns, which inversely vary with diD. The function curves can be approximated as straight lines. For the energy dissipation model with two orifices, because of different incoming flows at different orifices, the energy dissipation coefficient of the second orifice （K2） is smaller than that of the first. If LID is less than 5, the K value of the LID model, depending on the variation of/（2, increases with the spacing between two orifices L, and an orifice cannot fulfill its energy dissipation function. If LID is greater than 5, K2 tends to be steady; thus, the K value of the LID model gradually stabilizes. Then, the flow fully develops, and L has almost no impact on the value of K.

Numerical simulation of air-water two-phase flow over stepped spillways

Stepped spillways for significant energy dissipation along the chute have gained interest; popularity among researchers; dam engineers. Due to the complexity of air-water two-phase flow over stepped spillways, the finite volume computational fluid dynamics module of the FLUENT software was used to simulate the main characteristics of the flow. Adopting the RNG k- turbulence model, the mixture flow model for air-water two-phase flow was used to simulate the flow field over stepped spillway with the PISO arithmetic technique. The numerical result successfully reproduced the complex flow over a stepped spillway of an experiment case, including the interaction between entrained air bubbles; cavity recirculation in the skimming flow regime, velocity distribution; the pressure profiles on the step surface as well. The result is helpful for understanding the detailed information about energy dissipation over stepped spillways.

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.

Numerical simulation of pressure fluctuation in Kaplan turbine

As it is almost impossible to carry out the prototype hydro-turbine experiment be- fore the power plant is built up, rational prediction of pressure fluctuations in the prototype turbine is very important at the design stage. From this viewpoint, we at first treated the unsteady turbulent flow computation based on the modified RNG k-ε turbulence model through the whole flow passage to simulate the pressure fluctuation in a model turbine. Since fair agreement was recognized between the numerical results and the experimental data, this numerical method was applied to simulate the pressure fluctuations in the prototype turbine. From the comparison of them with the model turbine results, it is seen that their qualitative trend of pres- sure fluctuations are similar, but an appreciable difference is observed between the amplitudes of pressure fluctuation of the prototype turbine and that of the model turbine. Though the present findings may be explained by the effect of Reynolds number, further studies are expected for quantitative interpretation. We paid atten- tion to the interaction between the fluid and turbine structure. Adopting a weak fluid-solid coupling method, we studied the pressure fluctuation in the prototype turbine to clarify how the elastic behavior of runner blades influenced the charac- teristics of pressure fluctuation.

NUMERICAL SIMULATION OF 3-D TURBULENT FLOWS IN A CUT-OFF VALVE AND ANALYSIS OF FLOW CHARACTERISTICS IN PIPE

The 3-D turbulent flows in a valve pipe were described by the incompressibleReynolds-averaged Navier-Stokes equations with an RNG k-ε turbulence model. With the finite volumemethod and a body-fitted coordinate system, the discretised equations were solved by the SIMPLESTalgorithm. The numerical result of a cut-off valve with curved inlet shows the flow characteristicsand the main cause of energy loss when fluid flows through a valve. And then, the boundaries ofvalve were modified in order to reduce the energy loss. The computational results of modified valveshow that the numerical value of turbulent kinetic energy is lower, and that the modified design ofthe 3-D valve boundaries is much better. The analysis of the result also shows that RNG k-εturbulence model can successfully be used to predict the 3-D turbulent separated flows and thesecondary flow inside valve pipes.

Numerical study of the flow in the Yellow River with non-monotonous banks

A 2-D depth averaged RNG k- ε model is developed to simulate the flow in a typical reach of the Upper Yellow River with non-monotonic banks. In order to take account of the effect of the secondary flow in a bend, the momentum equations are modified by adding an additional source term. A comparison between the numerical simulation and the field measurements indicates that the improved 2-D depth averaged RNG k- ε model can improve the accuracy of the numerical simulation. An arc spline interpolation method is developed to interpolate the non-monotonic river banks. The method can also be reasonably applied for the 2-D interpolation of the river bed level. Through a comparison of the water surface gradients simulated in the seven bends of the studied reach, some analytical formulae are improved to reasonably calculate the longitudinal and transverse gradients in meandering river reaches. Furthermore, the positions of the maximum water depth and the maximum velocity in a typical bend are discussed.