搅拌槽内液-固两相体系的数值研究(Ⅰ)流场的数值模拟

Three-dimensional solid-liquid flow is mathematically formulated by means of the “two-fluid” approach and the two-phase k-ε-Ap turbulence model. The turbulent fluctuation correlations appearing in the Reynolds time averaged governing equations are fully incorporated. The solid-liquid flow field and solid concentration distribution in baffled stirred tanks with a standard Rushton impeller are numerically simulated using an improved “inner-outer” iterative procedure. The flow pattern is identified via the velocity vector plots and a recirculation loop with higher solid concentration is observed in the central vicinity beneath the impeller. Comparison of the simulation with experimental data on the mean velocities and the turbulence quantities of the solid phase is made and quite reasonable agreement is obtained except for the impeller swept volume. The counterpart of liquid phase is presented as well. The predicted solid concentration distribution for three experimental cases with the average solid concentration up to 20% is also found to agree reasonably with the experimental results published in the literature.     

涡流桨搅拌槽内流动非稳定性的大涡模拟

The aim of this work is to investigate the flow instabilities in a baffled, stirred tank generated by a single Rushton turbine by means of large eddy simulation （LES）. The sliding mesh method was used for the coupling between the rotating and the stationary frame of references. The calculations were carried out on the ＂Shengcao-21C＂ supercomputer using a computational fluid dynamics （CFD） code CFX5. The flow fields predicted by the LES simulation and the simulation using standard κ-ε model were compared to the results from particle image velocimetry （PIV） measurements. It is shown that the CFD simulations using the LES approach and the standard κ-ε model agree well with the PIV measurements. Fluctuations of the radial and axial velocity are predicted at different frequencies by the LES simulation. Velocity fluctuations of high frequencies are seen in the impeller region, while low frequencies velocity fluctuations are observed in the bulk flow. A low frequency velocity fluctuation with a nondimensional frequency of 0.027Hz is predicted by the LES simulation, which agrees with experimental investigations in the literature. Flow circulation patterns predicted by the LES simulation are asymmetric, stochastic and complex, spanning a large portion of the tanks and varying with time, while circulation patterns calculated by the simulation using the standard κ-ε model are symmetric. The results of the present work give better understanding to the flow instabilities in the mechanically agitated tank. However, further analysis of the LES calculated velocity series by means of fast Fourier transform （FFT） and/or spectra analysis are recommended in future work in order to gain more knowledge of the complicated flow phenomena.     

规整填料内单相流的LDV实验研究

To date, many models have been developed to calculate the flow field in the structured packing by the computational fluid dynamics （CFD） technique, but little experimental work has been carried out to serve the vali-dation of flow simulation. In this work, the velocity profiles of single-phase flow in structured packing are measured at the Reynolds numbers of 20.0, 55.7 and 520.1, using the laser Doppler velocimetry （LDV）. The time-averaged and instantaneous velocities of three components are obtained simultaneously. The CFD simulation is also carried out to numerically predict the velocity distribution within the structured packing. Comparison shows that the flow pattern, velocity distribution and turbulent kinetic energy （for turbulent flow） on the horizontal plane predicted by CFD simulation are in good agreement with the LDV measured data. The values of the x-and z-velocity components are quantitatively well predicted over the plane in the center of the packing, but the predicted y-component is sig-nificantly smaller than the experimental data. It can be concluded that experimental measurement is important for further improvement of CFD model.     

Unsteady RANS and detached eddy simulation of the multiphase flow in a co-current spray drying☆

A detached eddy simulation (DES) and a k-ε-based Reynolds-averaged Navier–Stokes (RANS) calculation on the co-current spray drying chamber is presented. The DES used here is based on the Spalart–Al maras (SA) turbu-lence model, whereas the standard k-ε(SKE) was considered here for comparison purposes. Predictions of the mean axial velocity, temperature and humidity profile have been evaluated and compared with experimental measurements. The effects of the turbulence model on the predictions of the mean axial velocity, temperature and the humidity profile are most noticeable in the (highly anisotropic) spraying region. The findings suggest that DES provide a more accurate prediction (with error less than 5%) of the flow field in a spray drying chamber compared with RANS-based k-εmodels. The DES simulation also confirmed the presence of anisotropic turbulent flow in the spray dryer from the analysis of the velocity component fluctuations and turbulent structure as il us-trated by the Q-criterion.     

A dual-scale turbulence model for gas-liquid bubbly flows☆

A dual-scale turbulence model is applied to simulate cocurrent upward gas–liquid bubbly flows and validated with available experimental data. In the model, liquid phase turbulence is split into shear-induced and bubble-induced turbulence. Single-phase standard k-εmodel is used to compute shear-induced turbulence and another transport equation is added to model bubble-induced turbulence. In the latter transport equation, energy loss due to interface drag is the production term, and the characteristic length of bubble-induced turbulence, simply the bubble diameter in this work, is introduced to model the dissipation term. The simulated results agree well with experimental data of the test cases and it is demonstrated that the proposed dual-scale turbulence model outperforms other models. Analysis of the predicted turbulence shows that the main part of turbulent kinetic en-ergy is the bubble-induced one while the shear-induced turbulent viscosity predominates within turbulent vis-cosity, especially at the pipe center. The underlying reason is the apparently different scales for the two kinds of turbulence production mechanisms:the shear-induced turbulence is on the scale of the whole pipe while the bubble-induced turbulence is on the scale of bubble diameter. Therefore, the model reflects the multi-scale phe-nomenon involved in gas–liquid bubbly flows.     

搅拌萃取塔内单相流动不同雷诺平均湍流模型结果的比较

The flow field of liquid phase (water) of agitated extraction columns is simulated with the help of computational fluid dynamics (CFD). Four kinds of Reynolds-averaged turbulence models, i.e. the standard k-ε model, the RNG (renormaiization group) k-ε model, the realizable k-ε model and the Reynolds stress model, are compared in detail in order to judge which is the best model in terms of the accuracy, less CPU time and memory required. The performance of the realizable k-ε model is obviously improved by reducing the model constant from c2 = 1.90 to c2 = 1.61. It is concluded that the improved realizable k-ε model is the optimal model.     

齿边浮阀塔内气相流场的数值模拟和分析

A three-dimensional computational fluid dynamics （CFD） model for gas flow through a serrated valve tray was presented. The flow field, as well as the dry-pressure drop of the valve under the full-opening condition was simulated based on the proposed model by using FLUENT 6.0 software. Compared with the values of dry-pressure dro.p in different turbulent models, the.simulated.results using RNG κ-ε model are in reasonable agreement with experimental data, indicating that RNG κ-ε model is suitable in simulating gas flow through the serrated valve tray. Then the CFD model combining RNG κ-ε model was used to study the three-dimensional gas flow through the considered serrated valve tray. The simulated results showed that various eddies existed on the serrated valve tray, and both the eddy and the non-eddy areas were nearly equal. The existence of addendum can decrease the eddy area caused by gas passing through the lateral outlet slots. The size of eddies can be reduced by optimizing the distance between valves.     

甲烷/空气射流燃烧中氮氧化物生成模型的研究

With the development of reaction kinetics and transfer science, the modeling of NOx formation plays more and more important roles in the protection of environment and the design of combustion reactors; in this case, turbu-lence-chemistry model and NOx formation model are the two most important aspects. For thermal NOx mechanism, this article studied the CH4/air system and applied a set of latest NO formation rate constants published at the Leed University which replaced the original model code in FLUENT to increase its precision on prediction of NO concentration. The realizable k-ε model, Reynold Stress model and standard k-ε model were also investigated to predict the turbulent combustion reaction, which indicated that the simulation results of velocities, temperatures and concentrations of combustion productions by the standard k-ε model were in good accordance with the experimental data. With the application of the simulation results to the experimental data to fit some important kinetic parameters in the equation of O atom model and revision of the equation later, this article obtained a new NO formation rate model. It has been proved that the prediction of the developed model coincides well with the measurements.     

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

Three-dimensional solid-liquid flow is mathematically formulated by means of the "two-fluid" approach and the two-phase k-ε-Ap turbulence model. The turbulent fluctuation correlations appearing in the Reynolds time averaged governing equations are fully incorporated. The solid-liquid flow field and solid concentration distribution in baffled stirred tanks with a standard Rushton impeller are numerically simulated using an improved "inner-outer" iterative procedure. The flow pattern is identified via the velocity vector plots and a recirculation loop with higher solid concentration is observed in the central vicinity beneath the impeller. Comparison of     

用扩散流动模型分析悬浮床内的气固两相向上流动

A mathematical model of two-dimensional turbulent gas-particle two-phase flow based on the modified diffusion flux model (DFM) and a numerical simulation method to analyze the gas-particle flow structures are developed. The modified diffusion flux model, in which the acceleration due to various forces is taken into account for the calculation of the diffusion velocity of particles, is applicable to the analysis of multi-dimensional gas-particle two-phase turbulent flow. In order to verify its accuracy and efficiency, the numerical simulation by DFM is compared with experimental studies and the prediction by κ-ε-κp two-fluid model, which shows a reasonable agreement. It is confirmed that the modified diffusion flux model is suitable for simulating the multi-dimensional gas-particle two-phase flow.     

各向异性k-ε湍流模型在Rushton桨搅拌槽三维流场整体数值模拟中的应用

根据搅拌槽内的流动呈各向异性的特点 ,引入适用于强旋转流场的各向异性k -ε湍流模型 ,用改进的内外迭代法对有挡板的Rushton桨搅拌槽进行了整体数值模拟 .利用文献中对搅拌槽内流场测定结果 ,给出了适用于Rushton桨搅拌槽的各向异性湍流黏度系数值 .模拟计算得到了搅拌槽内的流场分布和脉动速度分布 ,并同标准k -ε湍流模型计算结果及文献数据进行比较 .结果表明 ,各向异性k -ε湍流模型能成功反映Reynolds应力、湍流动能等湍流特征量 ,明显优于标准k -ε湍流模型 .     

Numerical simulation of turbulent flow in a baffled stirred tank with an explicit algebraic stress model

An explicit algebraic stress model (EASM) was used to simulate anisotropic turbulent flows in baffled stirred tanks equipped with a standard Rushton turbine. The quantitative predictions of velocity components, turbulence kinetic energy, Reynolds stresses and turbulence energy dissipation rate in the context of anisotropic turbulence were conducted to assess the comprehensive performance of the EASM. A lot of efforts have been made to ensure numerical stability during the calculations such as using a good initial flow field, manipulating source terms and adjusting under-relaxation factors. The predicted results were also compared with experimental data and other simulation results obtained using the standard k–ε model, algebraic stress model (ASM), Reynolds stress model (RSM) and large eddy simulation (LES). All the simulations were run with in-house codes. The simulation results show that agreement between the EASM predictions and experimental values is satisfactory. The EASM is consistently superior to the standard k–ε model when predicting both peak values and trend of variation in velocities and turbulence quantities. In comparison to the RSM, the EASM has almost the same predictive accuracy. The EASM is inferior to the LES on the prediction of turbulence kinetic energy. Nevertheless, the computational cost of the EASM is significantly lower than that of the LES, which is an obvious advantage in practical applications.     

应用SSTk-ω湍流模型计算Rushton搅拌釜流场

应用SSTkω-湍流模型对Rushton搅拌釜流场进行了计算,并与文献报道实验数据以及标准k-ε模型、RNGkω-模型预测结果进行了比较。结果表明SSTkω-模型所计算的排除流量准数与实验值相差较小,桨叶区速度场与实验数据吻合较好,略优于标准k-ε模型,同时也给出了近壁区的计算结果。在湍动动能的预报上,SSTk-ω模型值与标准k-ε模型比较接近,优于RNGkε-模型,但与实验值都还不同程度地存在着一些差异。     

NUMERICAL SIMULATION OF TURBULENT FLOW OF AGITATED LIQUID WITH PITCHED BLADE IMPELLER

The turbulent flow field in an agitated system with baffles was solved numerically using the standard k-e model, an algebraic Reynolds stress model (ASM) and a differential Reynolds stress model (RSM). The commercial software FLOW3D (CFDS, Harwell Laboratories, 1991) was used for this purpose. The aim of the study was to investigate the influence of the impeller boundary conditions and turbulence models to the agreement with experimentally obtained laser-Doppler anemometry data. The boundary conditions for the impeller discharge used in the numerical calculations were obtained as whole-cycle-ensemble averages from experimental LDA-measurements (Fort et al., 1992). Since measurements of the rate of dissipation of turbulent kinetic energy ( ε) was not available the dissipation rate per unit mass in the impeller discharge was estimated from the expression:

where k is the turbulent kinetic energy per unit mass and L the macroscale of turbulence in the pitched blade impeller discharge. The macroscale of turbulence (L) in the impeller boundary condition for e was varied in order to optimize the fit of theoretically obtained profiles of turbulent kinetic energy with experimental data. The constant A was fixed to 0.85 according to Wu and Patterson (1989). The optimal values of L for the different turbulence models were compared with the projected height of the impeller blade (h). All three components of the mean velocity were compared with experimental data for the optimal ratio of L/h for six radial cross-sections in the tank.

The mean velocity field obtained from simulations showed good agreement with experimental data for all models, with somewhat better agreement for the k — e model. An optimal value of the ratio L/h was found to be equal to 2.0 for the k — ε model and 1.3 for the ASM. However, no such optimal value for the RSM could be determined in this study.     

On the second-order moment turbulence model for simulating a bubble column

Two versions of the second-order moment two-phase turbulence model are proposed in this study for simulating bubble-liquid two-phase turbulent velocity fluctuations and their interactions in bubble-liquid flows under the dispersed bubble regime. One of them is a full transport equation model; the other is an algebraic stresses model. The proposed model is used to simulate liquid and gas mean velocities, gas volume fraction, liquid and gas Reynolds stresses and turbulent kinetic energy in a 2-D bubble column. Furthermore, the bubble and liquid velocities, Reynolds stresses and gas volume fraction are measured using the PIV. The simulation results are in good agreement with the PIV results and experimental data in the literature. The studies reveal the liquid recirculation and bubble up-rising flow patterns, and anisotropic liquid and bubble normal Reynolds stresses. Bubble fluctuation is observed to be stronger than liquid fluctuation. Moreover, both the liquid velocity gradient and bubble-liquid interaction are important for the generation of liquid turbulence.     

搅拌釜三维流场的雷诺应力模型数值模拟

引言 近年来,雷诺平均Navier-Stokes方程及其封闭方程组成的湍流模型在应用于搅拌釜复杂湍流现象的模拟上取得了成功,主要是采用标准k-ε[1]、RNG k-ε[2]等模型.     

湍流模型对钝体燃烧器流场模拟的影响

湍流燃烧过程涉及燃烧反应和湍流在微小时间和空间尺度上的耦合,因此湍流模型的有效性对燃烧器流场CFD模拟的准确性有重要影响。采用5种k-ε类和k-ω类两方程模型和雷诺应力模型模拟了钝体燃烧器内冷流流场,并采用PIV测量方法进行了实验验证。比较和分析数值模拟和PIV实验结果发现,不同湍流模型的模拟结果在诸如速度分布和涡结构上存在较大差别,标准k-ε模型和RNGk-ε的模拟流场最接近本文的实验结果。     

用改进的内外迭代法数值模拟Rushton涡轮搅拌槽流场

在有挡板的搅拌槽中，受搅拌桨驱动的液体在挡板的作用下会产生复杂的三维湍流流动.利用“快照”法思路和改进的内外迭代法及k–e湍流模型对Rushton涡轮有挡板的搅拌槽进行了整体数值模拟. 同文献中的实验数据进行了比较，模拟值同实验值基本吻合. 改进后的内外迭代法不依赖经验公式和实验数据，有一定的通用性.