Computational fluid dynamics simulation of gas-liquid two phases flow in 320 m~3 air-blowing mechanical flotation cell using different turbulence models

According to the recently developed single-trough floating machine with the world's largest volume(inflatable mechanical agitation flotation machine with volume of 320 m3) in China, the gas-fluid two-phase flow in flotation cell was simulated using computational fluid dynamics method. It is shown that hexahedral mesh scheme is more suitable for the complex structure of the flotation cell than tetrahedral mesh scheme, and a mesh quality ranging from 0.7 to 1.0 is obtained. Comparative studies of the standard k-ε, k-ω and realizable k-ε turbulence models were carried out. It is indicated that the standard k-ε turbulence model could give a result relatively close to the practice and the liquid phase flow field is well characterized. In addition, two obvious recirculation zones are formed in the mixing zones, and the pressure on the rotor and stator is well characterized. Furthermore, the simulation results using improved standard k-ε turbulence model show that surface tension coefficient of 0.072, drag model of Grace and coefficient of 4, and lift coefficient of 0.001 can be achieved. The research results suggest that gas-fluid two-phase flow in large flotation cell can be well simulated using computational fluid dynamics method.     

Numerical simulation of air entrainment and suppression in pump sump

The dynamics of air entrainment and suppression schemes in a pump sump are investigated. Four different turbulence models(standard k-ε model, realizable k-ε model, renormalization group(RNG) k-ε model and shear-stress transport(SST) k-ω model) and the volume of fluid(VOF) multiphase model are employed to simulate the three-dimensional unsteady turbulent flow in a pump sump. The dynamic processes of air entrainment are simulated under conditions of relatively high discharge and low submergence; the mechanism of air entrainment is discussed in detail. Then suppression means for air entrainment is adopted by placing a circular plate on the intake pipe at three different heights. The results show: the position and structure of the free-surface vortices, sidewall-attached vortices, back wall-attached vortices, and floor-attached vortices calculated by SST k-ω turbulence model agree well with the experimental data. The two main contributors for air entrainment are pressure difference and vortex strength. By placing a circular plate in the middle of the intake pipe under water, air entrainment is suppressed because vortex strength is reduced.     

Heat Transfer and Flow Characteristics Predictions with a Refined k-ε-fu Turbulent Model in Impinging Jet

Local heat transfer and flow characteristics in a round turbulent impinging jet for Re≈23 000 is predicted numerically with the RANS approach and a k-ε-f_u turbulence model. The heat transfer predictions and turbulence parameters are verified against the axis-symmetric free jet impingement measurements and compared with previous other turbulence models, and results show the k-ε-f_u model has a good performance in predictions of the local wall heat transfer coefficient, and in agreement with measurements in mean velocity profiles at different radial positions as well. The numerical model is further used to examine the effect of the fully confined impingement jet on the local Nusselt number. Local Nusselt profiles in x and y-centerlines for the target plate over three separation distances are predicted. Compared with the experimental data, the numerical results are accurate in the central domain around the stagnation region and present a consistent structure distribution.     

Numerical simulation and analysis of water flow over stepped spillways

Numerical simulation of water flow over the stepped spillway is conducted using Mixture multiphase flow model. Different turbulence models are chosen to enclose the controlling equations. The turbulence models investigated are realizable k-ε model, SST k-ω model, v2-f model and LES model. The computational results by the four turbulence models are compared with experimental ones in the following aspects: mean velocity, the spanwise vorticity and the growth of the turbulent boundary layer thickness in the st...     

A hybrid RANS/LES model for simulating time-dependent cloud cavitating flow around a NACA66 hydrofoil

Cloud cavitating flow is highly turbulent and dominated by coherent large-scale anisotropic vortical structures. For the numerical investigation of such a class of flow, large eddy simulation(LES) is a reliable method but it is computationally extremely costly in engineering applications. An efficient approach to reduce the computational cost is to combine Reynolds-averaged Navier–Stokes(RANS) equations with LES used only in the parts of interest, such as massively separated flow regions. A new hybrid RANS/LES model, the modified filter-based method(FBM), is proposed in the present study which can perform RANS or LES depending on the numerical resolution. Compared to the original FBM, the new method has three modifications: the state-of-the-art shear stress transport(SST) model replaces the k-? model as a baseline RANS model. A shielding function is introduced to obviate the switch from RANS to LES occurring inside the boundary layer. An appropriate threshold controlling the switch from RANS to LES is added to achieve an optimal predictive accuracy. The new model is assessed for its predictive capability of highly unsteady cavitating flows in a typical case of cloud cavitation around a NACA66 hydrofoil. The new model results are compared with data obtained from the Smagorinsky LES and SST model based on the same homogeneous Zwart cavitation model. It is found that the modified FBM method has significant advantages over SST model in all aspects of predicted instantaneous and mean flow field, and its predictive accuracy is comparable to the Smagorinsky LES model even using a much coarser grid in the simulations.     

Improvement and application of wall function boundary condition for high-speed compressible flows

In order to develop a wall function boundary condition for high-speed flows so as to reduce the grid-dependence of the simulation for the skin friction and heat flux,a research was performed to improve the compressible wall function boundary condition proposed by Nichols.Values of parameters in the velocity law-of-the-wall were revised according to numerical experiments and the expression of temperature law-of-the-wall was modified based on theoretical analysis and numerical simulation.Besides,the formula of the heat conduction term in near-wall region was derived so that the coupling between the wall function boundary condition and CFD code was realized more accurately.Whereafter,the application study of the modified wall function was carried out.The numerical case of supersonic turbulent boundary layer on a flat plate illustrated that the modified wall function produces reasonable results of skin friction and heat flux,and profiles of velocity,temperature and turbulent eddy viscosity for coarse grids with the initial wall spacing of y+<400,and that the modifications to the original wall function can obviously improve the simulation precision.As for the application of separation flows,it was found from the numerical cases of supersonic cavity flow and hypersonic axisymmetric compression corner that the compressible velocity law-of-the-wall originally established based on the fully-developed attached turbulent boundary layer approximately holds in the near-wall region inside the separation flows,which ensures that reliable skin friction and heat flux can be given by the wall function inside the separation flows,while for the region near separation and reattachment points,the wall function gives results with a relatively large error,because the velocity law-of-the-wall used in the wall function takes on obvious deviation from the real velocity profiles near the separation and reattachment points.     

Computer simulation on the controlled cooling of 82B high-speed rod

A modified temperature-phase transformation field coupled nonlinear mathematical model was made and used in com- puter simulation on the controlled cooling of 82B high-speed rods.The surface temperature history and volume fraction of pearlite as well as the phase transformation history were simulated by using the finite element software Marc/Mentat.The simulated results were compared with the actual measurement and the agreement is good which can validate the presented computational models.     

Simplified mathematical model of inter-turn short circuit of field windings in hydro-generators and its application

Inter-turn short circuit of field windings is a common electrical fault of generators.Simulation is an important method of investigating the fault and providing data support for fault monitoring.However,huge numbers of pole pairs and damper loops in large hydro-generators would lead to lengthy calculation time,hindering scientific research and engineering application.To deal with this problem,we analyze a theoretical basis for a damper winding simplified model and then propose an equivalent treatment method.Through the analysis of steady-state current harmonic characteristics of generators with different stator winding configurations during the fault,the simplified models suitable for steady-state calculation are derived from two aspects,namely,additional rotor harmonic current frequency characteristics and the relationship of the amplitude as well as the phase of each branch current of the stator.The calculation and experimental results of the two simplified models are then compared to verify the models’ correctness.A calculation example of the Three Gorges left bank VGS generator shows few deviations between the calculation results of the simplified model and the original model.Moreover,the calculation time using the simplified model is 1/1500 that using the original model,which provides a more effective tool for on-line fault monitoring.Finally,the sensitivity-verification application of the fault-monitoring scheme based on the stator steady-state unbalanced current RMS is depicted.The result shows that the scheme can monitor two-turn short circuits of field windings in the Three Gorges generator and provide high sensitivity.     

Reasonable Ball Size of Ball Mill for Preparing Coal Water Fuel and Forecasting Productive Capacity

By using the matrix theory, a 5-parameter grinding mathematical model is established. Based on the properties of feed coal and requirements for size distribution of final product, the model gives the required grinding probability for various particles and corresponding ball size distribution. By using this model, 3 different sizes of ball mill are designed and put into commercial use for coal water fuel. The forecasted ball mill capacity, the particle sizes and particle size distribution as well as the coal water fuel quality parameters are all in line with industrial operation results, which have provced the suitability of the model.     

Numerical Simulation of Gas-Solid Flow in Square Cyclone Separators with Downward Exit

Cyclone separators are widely used in industrial applications. The separation efficiency and pressure drop are the most important parameters to evaluate the performance of processing system. In the simulations, the flow behavior of gas and particles within a square cyclone separator is simulated by means of computational fluid dynamics. The RNG k - ε model and the Reynolds stress model （RSM） are used to model gas turbulence. The flow behavior is examined in the term of tangential velocity components, static pressure and pressure drop contour plots for flow field and solid volume fraction. The effects of the turbulence model and solid volume fraction on the square cyclone are discussed. The results indicate that the pressure drop increases with the increase of solid volume fraction, and increase with the increase of inlet velocities for two turbulence models, moreover, the simulations resuhs are compared with pressure field. For all runs, the RSM model gives a higher pressure drop compared to the RNG k - ε model. The RSM model provides well the forced vortex and free vortex, and captures better the phenomena occurring during intense vortex flow in the presence of walls within cyclone separators.     

New P3D Hydraulic Fracturing Model Based on the Radial Flow

Pseudo three-dimension (P3D) hydraulic fracturing models often overpredict the fracture height for a poorly contained fracture. To solve this problem, a new method is presented in shaping the P3D fracture geometry on the basis of the fundamental theory and the original 1D fluid flow is replaced with a more representatively radial flow. The distribution of the fluid in the modified fluid field is analyzed and a sound explanation to the problem is given. Due to the consideration of the fluid flow in the vertical direction, the modified model can predict the fracture height much better. To validate the rationality of the radial fluid flow assumption, the distribution of the fluid in the modified fluid field is simulated with the plane potential flow by using finite element method. And the results agree effectively with those from the assumption. Through comparing with the full 3D model, the results show that this new P3D model can be used to aid the fracturing design and predict the fracture height under poorly contained situation.     

Modeling unbalanced rotor system with continuous viscoelastic shaft by frequency-dependent shape function

A reduced-order dynamic model for an unbalanced rotor system is developed, taking the coupling between torsional and lateral vibrations into account. It is assumed that a shaft is regarded as a continuous viscoelastic shaft with unbalanced and small deformation properties. The equations of motion for the torsional and lateral vibrations are derived using Lagrange＇s approach with the frequency-dependent shape function. The rotor torsional vibration is coupled with the lateral vibrations by unbalance elements in a way of excitations. Simulation and experiment results show clearly that the torsional vibration has strong impact on the rotor lateral vibrations, and it causes subharmonic and superharmonic excitations through unbalance elements, which leads to the superharmonic resonances in the lateral vibrations. This model with low-order and high accuracy is suitable for rotor dynamic analysis in real time simulation as well as for active vibration control syntheses.     

Establishmen and vertification of an improved similitude law for dynamic ice force model test

To study the similitude laws for dynamic ice force model test which is a hot problem in ice mechanics.In this paper,a new modified similitude law for dynamic ice force model test is proposed based on ice-induced virbration theory and two reasonable assumptions.And the new law is vertified with an ice-induced pier virbration example.The numerical calculation results show that,firstly,the error of frequency factor between test value and theory value is small as well as that of displacement and velocity;Secondly,the time scale completely meet the similitude relation,the waveforms anastomotic well,and the phenomenon of offset and omit do not occur;Thirdly,as the damping ratio between prototype and model is nearly equal,the improved similitude law will still be applied.Therefore,the new modified similitude law is feasible to study dynamic ice force model test and can provide reference for the ice mechanics.     

Thermodynamic Study on Process in Copper Converters(The slag-making stage)

The so-called Goto's model was modified by introducing a parameter of the oxygen efficiency from industrial trials, as well as the selected and newly re-assessed thermodynamic data. The application of the model to copper converters in Guixi Smelter has been carried out by the combination of thermodynamic calculations with the mass and heat balance using the plant data obtained in industrial trials for many heats. For the slag-making stage, good agreements have been reached betWeen the calculated and measured temperature, blowing time as well as the contents for main elements in the matte and the slag. Relativel}' large deviations for contents of Zn and Pb in the slag may be caused by the complex chemical composition of the real molten slag, which ma}; result in a large difference of γzn. and γPb,adopted with their real values. It is noted that the model can simulate the slag-making stage of copper converting process in industrial Pierce-Smith converters well.     

Removal of anionic ions from single material solution by bauxite tailings modified with FeCl3·6H2O

The adsorbabilities of the unmodified and modified bauxite tailings for Cr（Ⅵ）, As（Ⅴ） and F（Ⅰ） ions were investigated. Batch experiments were carried out to determine the removal rate as a function of adsorbent dosage, solution pH value and shaking time. The results show that the maximum removal rates of Cr（Ⅵ）, As（Ⅴ） and F（Ⅰ ） are respectively 99%, 99% and 90% by using the modified bauxite tailings. The isoelectric point of the unmodified bauxite tailings is 3.6, and that of the modified bauxite tailings is 5.0, which shifts to lower pH values in Cr（Ⅵ） solution. This indicates a specific adsorption of the anionic species on the modified bauxite railings. A new band of Cr2O72 appears in the FTIR, showing that Cr（Ⅵ） is adsorbed on the modified bauxite railings in the form of chemistry adsorption. The adsorption data of Cr（Ⅵ） on the modified bauxite tailings are well described by Freundlich model. The investigations of kinetic models show that pseudo-second-order kinetic model provides the best correlation for the experimental data.     

Removal of anionic ions from single material solution by bauxite tailings modified with FeCl3·6H2O

The adsorbabilities of the unmodified and modified bauxite tailings for Cr(Ⅵ), As(Ⅴ) and F(Ⅰ) ions were investigated. Batch experiments were carried out to determine the removal rate as a function of adsorbent dosage, solution pH value and shaking time. The results show that the maximum removal rates of Cr(Ⅵ), As(Ⅴ) and F(Ⅰ) are respectively 99%, 99% and 90% by using the modified bauxite tailings. The isoelectric point of the unmodified bauxite railings is 3.6, and that of the modified bauxite tailings is 5.0, which shifts to lower pH values in Cr(Ⅵ) solution. This indicates a specific adsorption of the anionic species on the modified bauxite tailings. A new band of Cr2O72- appears in the FTIR, showing that Cr(Ⅵ) is adsorbed on the modified bauxite tailings in the form of chemistry adsorption. The adsorption data of Cr(Ⅵ) on the modified bauxite tailings are well described by Freundlich model. The investigations of kinetic models show that pseudo-second-order kinetic model provides the best correlation for the experimental data.     

Coupling model for calculating prestress loss caused by relaxation loss,shrinkage,and creep of concrete

The calculation model for the relaxation loss of concrete mentioned in the Code for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts(JTG D62—2004) was modified according to experimental data. Time-varying relaxation loss was considered in the new model. Moreover, prestressed reinforcement with varying lengths(caused by the shrinkage and creep of concrete) might influence the final values and the time-varying function of the forecast relaxation loss. Hence, the effects of concrete shrinkage and creep were considered when calculating prestress loss, which reflected the coupling relation between these effects and relaxation loss in concrete. Hence, the forecast relaxation loss of prestressed reinforcement under the effects of different initial stress levels at any time point can be calculated using the modified model. To simplify the calculation, the integral expression of the model can be changed into an algebraic equation. The accuracy of the result is related to the division of the periods within the ending time of deriving the final value of the relaxation loss of prestressed reinforcement. When the time division is reasonable, result accuracy is high. The modified model works excellently according to the comparison of the test results. The calculation result of the modified model mainly reflects the prestress loss values of prestressed reinforcement at each time point, which confirms that adopting the finding in practical applications is reasonable.     

Influence of preload discreteness on air-operated separation process of low-shock separation device

To investigate the influence of design parameters on the performance of separation device,the structure and air-operated test of a low-shock separation device are introduced and analyzed in this paper.According to the law of energy conservation and aerodynamics,a mathematical model is built.Because the preload used to ensure the connection reliability has the discreteness,which will influence the separation process,the influence of preload discreteness on the air-operated separation process is simulated and tested.Simulation results are consistent with the experimental results.It is shown that the change of preload has an obvious influence on the separation process.The study is useful for the design and optimization of separation device.     

Numerical Simulation of Methane Distribution and Sensor Placement in 2-Dimension Roadway

In order to provide a theoretical basis for methane sensor placement in the vertical direction of a tunnel, the software Fluent was used to simulate methane distribution. A geometric roadway model was established and divided by grids. Methane distribution in both level and vertical sections was simulated using a realizable k-ε model with the Fluent software according to a conservation equation in a turbulent state, a turbulent kinetic energy equation and a turbulent dissipation rate equation. The realizable k-ε model and the Fluent software were used to simulate methane distribution according to the principle of the conservation equation in a state of turbulent flow. The results show that after overflowing, a methane level with a certain thickness is formed. Methane density curves at three specific levels were internally consistent and methane density at higher levels is denser than that at lower levels. Methane distribution becomes thinner in the direction of wind and methane in the vertical direction becomes uniform if wind speed is high. The distance be- tween sensors and roof should be less than 300 mm which is in agreement with mine safety regulations.     

Active suspension with optimal control based on a full vehicle model

The 7-DOF model of a full vehicle with an active suspension is developed in this paper. The model is written into the state equation style. Actuator forces are treated as inputs in the state equations. Based on the basic optimal control theory, the optimal gains for the control system are figured out. So an optimal controller is developed and implemented using Matlab/Simulink, where the Riccati equation with coupling terms is deduced using the Hamilton equation. The all state feedback is chosen for the controller. The gains for all vehicle variables are traded off so that majority of indexes were up to optimal. The active suspension with optimal control is simulated in frequency domain and time domain separately, and compared with a passive suspension. Throughout all the simulation results, the optimal controller developed in this paper works well in the majority of instances. In all, the comfort and ride performance of the vehicle are improved under the active suspension with optimal control.