竖直上升气液泡状流数学模型封闭的研究

竖直上升管气液两相流广泛应用于相变传热、核反应堆等工业过程。本文以竖直上升气液两相流为研究对象,运用欧拉双流体模型,针对表观液速为0.45m/s、表观气速分别为0.015m/s和0.1m/s的泡状流数值模拟过程中的升力、壁面润滑力、湍流扩散力、气泡诱导湍流（BIT）等封闭模型,开展数值模拟比较研究。模拟发现：①低气速泡状流中,升力和壁面润滑力的同时加入能够改善壁面附近的气含率,气泡在这两个力作用下在径向上达到一个相对平衡,得到与实验气含率类似的壁面峰,模拟的液相速度较合理;低气速时,BIT的影响可以忽略。②高气速泡状流中,BIT对气-液两相流的模拟结果影响比较明显,湍动耗散源项的加入能使液速分布的模拟结果得到改善,Troshko模型相对Sato模型更能反映气泡诱导湍流对液相湍流的作用。③高气速时升力的引入使气含率产生壁面峰,加入湍流扩散力能使峰值略微降低,但仍没有解决高气速时引入升力出现的气含率壁面峰问题,说明在径向上湍流扩散力还不足以抵抗升力。     

Comparison of Eulerian QBMM and classical Eulerian–Eulerian method for the simulation of polydisperse bubbly flows

The spatial gas distribution of poly-disperse bubbly flows depends greatly on the bubble size. To reflect the resulting polycelerity, more than two momentum balance equations (typically for the gas and liquid phases) have to be considered, as done in the multifluid approach. The inhomogeneous multiple-size group model follows this approach, also combined with a population balance model. As an alternative, in a previous work, an Eulerian quadrature-based moments method (E-QBMM) was implemented in OpenFOAM; however, only the drag force was included. In this work, different nondrag forces (lift, wall lubrication, and turbulent dispersion) are added to enable more complex test cases to be simulated. Simulation results obtained using E-QBMM are compared with the classical E–E method and validated against experimental data for different test cases. The results show that there is good agreement between E-QBMM and E–E methods for mono-disperse cases, but E-QBMM can better simulate the separation and segregation of small and large bubbles.     

Numerical study of bubbly upflows in a vertical channel using the Euler–Lagrange two-way model

Bubbly flows exist extensively in industrial processes, so it is very meaningful to study hydrodynamic characteristics of them to improve efficiency of bubbly flow equipments. This paper introduces a numerical method of the Euler–Lagrange two-way model for the air–water bubbly flows in detail. The flow field is simulated by using direct numerical simulations (DNS) in Euler frame of reference, while the bubble dynamics are fully analyzed by integration of Newtonian equations of motion taking into account interphase interaction forces including drag force, lift force, wall lift force, pressure gradient force, virtual mass force, gravity force, buoyant force, and inertia force in Lagrange frame of reference. The coupling between phases is considered by regarding the interphase interaction forces as a momentum source term of the continuous phase. Bubbles distribution and turbulent statistics of the liquid phase are comprehensively analyzed. The results show that an overwhelming majority of bubbles cluster near the walls, and turbulent structures of the liquid phase are modified to some certain by addition of bubbles, namely, the mean streamwise velocity become increased at the core of the channel, the wall-normal and spanwise turbulent intensities and Reynolds stress are reduced. Redistribution of turbulent energy from the streamwise velocity components to wall-normal and spanwise velocity components is also suppressed due to the addition of bubbles.     

Use of models for lift, wall and turbulent dispersion forces acting on bubbles for poly-disperse flows

Closure laws are needed for the qualification of CFD codes for two-phase flows. In case of bubbly and slug flow, forces acting on the bubbles usually model the momentum transfer between the phases. Several models for such forces can be found in Literature. They show, that these forces depend on the liquid flow field as well as on the size and the shape of the bubbles. A validation of consistent sets of bubble force models for poly-disperse flows is given, basing on a detailed experimental database for vertical pipe flows, which contains data on the radial distribution of bubbles of different size as well as local bubble size distributions. A one-dimensional (1D) solver provides velocity profiles and bubble distributions in radial direction. It considers a large number of bubble size classes and is used for the comparison with the experiments. The simplified model was checked against the results of full 3D simulations done by the commercial code CFX-5.7 for simplified monodisperse cases. The effects of the number of bubbles classes as well as the effect of the lateral extension of the bubbles were analyzed. For the validation of bubble force models measured bubble size distributions were taken as an input for the calculation. On basis of the assumption of an equilibrium of the lateral bubble forces, radial volume fraction profiles were calculated separately for each bubble class. In the result of the validation of different models for the bubble forces, a set of Tomiyama lift and wall force, deformation force and Favre averaged turbulent dispersion force was found to provide the best agreement with the experimental data. Some discrepancies remain at high liquid superficial velocities.     

Effect of interfacial forces and turbulence models on predicting flow pattern inside the bubble column

The numerical approaches have been used in many studies to predict the flow pattern inside the bubble column reactors because of the difficulties that are still found in designing and scaling-up the bubble columns. This review makes an effort to show suitable interfacial forces i.e., drag force, lift force, turbulent dispersion models and virtual mass and turbulence models such as standard k–ɛ model, Reynolds Stress Model, Large Eddy Simulation to predict flow pattern inside the bubble column using Eulerian–Eulerian. The effect of various interfacial forces and turbulence models on gas–liquid velocity and gas hold-up in bubble column is critically reviewed.     

Relative importance of the lift force on heavy particles due to turbulence driven secondary flows

Saffman lift forces on dense particles due to gradients in both streamwise and cross-stream velocities in a downward, fully developed turbulent square duct flow at Re_τ = 360 are studied using large eddy simulations. Volume fraction of the dispersed phase is low enough (≤ 10^− 5) that the one-way coupling approach is reasonable, i.e., two-way coupling and particle-particle collisions are not considered. Eulerian and Lagrangian approaches are used to treat the continuous and dispersed phases, respectively. Subgrid stresses are modeled with the dynamic subgrid kinetic energy model of Kim and Menon [W.W. Kim and S. Menon. Application of the localized dynamic subgrid-scale model to turbulent wall-bounded flows, AIAA 97-0210, 1997.]. The particle equation of motion includes drag, lift forces due to both the streamwise and cross-stream velocity gradients, gravity, and is integrated using the fourth-order accurate Runge-Kutta scheme. Dependence of particle drag and lift forces on duct cross-sectional location and particle response time is demonstrated using the mean value contours and probability density functions (PDFs) of particle forces. It is shown that the streamwise component of the mean drag force experienced by particles of all response times is a deceleration force, i.e. on average, fluid streamwise velocity lags the particle streamwise velocity. Secondly, the two wall-normal (or lateral) components of the mean drag force are oriented such that the particles experience a net mean force toward the duct corners. PDFs of particle drag force components show that smaller response time particles experience a wider range of drag force about the mean value, as compared to the more inertial particles. Contours of mean wall-normal lift forces due to streamwise velocity gradients show that this force predominantly acts toward the duct walls and that the maximum lift force occurs close to the walls. PDFs of lift force due to streamwise velocity gradients show that the range of fluctuations increases with particle response time, but the dependence on particle response time is weaker compared to drag force. Lift forces due to cross-stream velocity gradients are at least an order of magnitude smaller than lift forces due to streamwise velocity gradients and are found to decrease in their range of fluctuations with particle response time. It is demonstrated that lift forces due to secondary flow velocity gradients are not as important as those due to streamwise velocity gradients in a square duct flow.     

绝热层流泡状流运动的双流体模型

绝热层流泡状流是泡状流研究中的一个基础范例 .目前描述绝热层流泡状流常采用的双流体模型由于相间作用考虑欠缺而适用性差 .本文结合理论和实验研究结果导出了描述壁面“排斥”作用的表达式 ,并建立了一个封闭的双流体模型 .模型预测值和实验值的比较表明 ,由于相间作用的合理考虑 ,扩大了该模型的适用范围     

Application of a modified Eulerian model to study the particle deposition on a vertical surface in turbulent flow

In this study the v2-f model was used with the two-phase Eulerian approach to predict the particle deposition rate on a vertical surface in a turbulent flow. The standard Eulerian particle model was adopted from the literature and modified, considering the majority of particle transport mechanisms in the particle deposition rate. The performance of the modified model was examined by comparing the rate of particle deposition on a vertical surface with the experimental and numerical data in a turbulent channel flow available in the literature. The model took into account the effects of drag force, lift force, turbophoretic force, electrostatic force, inertia force and Brownian/turbulent diffusion on the particle deposition rate. Electrostatic forces due to mirror charging and charged particles under the influence of an electric field were considered. The predictions of the modified particle model were in good agreement with the experimental data. It was observed that when both electrostatic forces are present they are the dominant factor in the deposition rate in a wider range of particle sizes.     

CHARACTERIZATION OF HYDRODYNAMIC LIFT FORCES BY FIELD-FLOW FRACTIONATION. INERTIAL AND NEAR-WALL LIFT FORCES

Sedimentation/steric FFF has been used to measure hydrodynamic lift forces exerted on 2-30 μm latex microspheresdnven by flow through a 95 cm long ribbonlike FFF channel of ∼ 127 um thickness. Following a previous study, lift forces are examined as a function of shear rate, distance from the wall, and sphere size. Here, in contrast to the earlier study, measured lift forces are extended downward into a range corresponding to theoretical values of the inertial lift force. After corrections are made for secondary relaxation, it is found, as before, that a near-wall lift force proportional to l/δ (where δ is the particle-wall distance) dominates lift effects at small δ's. As δ increases and this force decays, the measured lift force assumes a value in good agreement with the inertial lift force predicted by the theory of Cox and Brenner as extended by subsequent workers. Over a broad range of conditions explored in almost 300 measurements, the results are consistent with a total lift force that equals the sum of near-wall and inertial contributions. Possible sources of error in the analysis are examined and various explanations for the near-wall lift force are discussed.     

Numerical simulation of the dynamic flow behavior in a bubble column: A study of closures for turbulence and interface forces

Numerical simulations of the bubbly flow in two square cross-sectioned bubble columns were conducted with the commercial CFD package CFX-4.4. The effect of the model constant used in the sub-grid scale (SGS) model, C_S, as well as the interfacial closures for the drag, lift and virtual mass forces were investigated. Furthermore, the performance of three models [Pfleger, D., Becker, S., 2001. Modeling and simulation of the dynamic flow behavior in a bubble column. Chemical Engineering Science, 56, 1737-1747; Sato, Y., Sekoguchi, K.,1975. Liquid velocity distribution in two-phase bubble flow. International Journal of Multiphase Flow 2, 79-95; Troshko, A.A., Hassan, Y.A., 2001. A two-equation turbulence model of turbulent bubbly flows. International Journal of Multiphase Flow 27, 1965-2000] to account for the bubble-induced turbulence in the k-ε model was assessed. All simulation results were compared with experimental data for the mean and fluctuating liquid and gas velocities. It is shown that the simulation results with C_S=0.08 and 0.10 agree well with the measurements. When C_S is increased, the effective viscosity increases and subsequently the bubble plume becomes less dynamic. All three bubble-induced turbulence models could produce good solutions for the time-averaged velocity. The models of Troshko and Hassan and Pfleger and Becker reproduce the dynamics of the bubbly flow in a more accurate way than the model of Sato and Sekoguchi. Based on the comparison of the results obtained for two columns with different aspect ratio (H/D=3 and H/D=6), it was found that the model of Pfleger and Becker performs better than the model of Troshko and Hassan, while the model of Sato and Sekoguchi performs the worst. It was observed that the interfacial closure model proposed by Tomiyama [2004. Drag, lift and virtual mass forces acting on a single bubble. Third International Symposium on Two-Phase Flow Modeling and Experimentation, Pisa, Italy, 22-24 September] performs better for the taller column. With the drag coefficient proposed by Tomiyama, the predicted slip velocity agrees well with the experimental data in both columns. The virtual mass force has a small influence on the investigated bubbly flow characteristics. However, the lift force strongly influences the bubble plume dynamics and consequently determines the shape of the vertical velocity profile. In a taller column, the lift coefficient following from the model of Tomiyama produces the best results.     

Lift and drag forces on a sphere attached to a wall in a Blasius boundary layer

Lift and drag forces on a sphere attached to a planar wall, over which a laminar flat plat boundary layer flows, are examined numerically in this study. Particle Reynolds number ranged from 0.1–250, which represents steady, laminar flow about the sphere, and the plate Reynolds number was held constant at 32 400. A finite-volume computational fluid dynamics program was utilised. Simulation results were validated against analytical results for drag and lift in creeping flow and against experimental results available in the literature for lift at higher particle Reynolds number. The model results were curve-fitted and interpolating drag and lift coefficient functions are reported. The lift and drag results are shown to be weakly dependent upon plate Reynolds number. The resulting correlations are expected to be useful in the development of particle impending motion and aerosol entrainment predictions of particles adhering to planar walls.     

Aerosol Particle Removal and Re-entrainment in Turbulent Channel Flows - A Direct Numerical Simulation Approach

Aerosol particle removal and re-entrainment in turbulent channel flows are studied. The instantaneous fluid velocity field is generated by the direct numerical simulation (DNS) of the Navier - Stokes equation via a pseudospectral method. Particle removal mechanisms in turbulent channel flows are examined and the effects of hydrodynamic forces, torques and the near-wall coherent vorticity are discussed. The particle resuspension rates are evaluated, and the results are compared with the model of Reeks. The particle equation of motion used includes the hydrodynamic, the Brownian, the shearinduced lift and the gravitational forces. An ensemble of 8192 particles is used for particle resuspension and the subsequent trajectory analyses. It is found that large-size particles move away roughly perpendicular to the wall due to the action of the lift force. Small particles, however, follow the upward flows formed by the near-wall eddies in the low-speed streak regions. Thus, turbulent near-wall vortical structures play an important role in small particle resuspension, while the lift is an important factor for reentrainment of large particles. The simulation results suggests that small particles (with τ_p⁺ ≤ 0.023) primarily move away from the wall in the low-speed streaks, while larger particles (with τ_p⁺ ≥ 780) are mostly removed in the high-speed streaks.     

Multi-fluid simulation of turbulent bubbly pipe flows

Radial distributions of void fraction α_G, bubble aspect ratio E, phasic velocities V_G and V_L and turbulent kinetic energy k in bubbly pipe flows are measured using an image processing method and a laser Doppler velocimetry. Multi-fluid simulations are conducted to examine applicability of state-of-the-art closure relations to the turbulent bubbly pipe flows. The experimental results indicate that aspect ratio of bubbles in the near wall region takes a higher value than that of free rising bubbles due to the presence of wall, and that the change in the aspect ratio induces decrease in relative velocity between bubbles and liquid in the near wall region. Drag coefficient C_D of a bubble in a bubbly pipe flow tends to increase with magnitude of shear flow, and the effect of shear flow on C_D is estimated by the correlation proposed by Legendre and Magnaudet (1998). Comparison between the simulated and the measured results indicate that the effects of bubble shape and shear flow on drag force acting on bubbles should be taken into account for accurate predictions of bubbly pipe flows. The turbulence models proposed by Lopez de Bertodano et al. (1994) and by Hosokawa and Tomiyama (2004a) give good predictions for turbulence modification caused by bubbles.     

Tuning a multi-fluid model for gas lift simulations in wells

A multi-fluid formulation based on the k–? turbulence closure is used for modeling bubbly flow in vertical pipes. Each bubble-size group is considered as a separate dispersed phase. The current k–? based multi-fluid models suffer from the problem of large overprediction of void fraction peak and lead to satisfactory results in limited ranges. In this study, first, we establish a model for gas lift simulations in wells. For this purpose, we propose new modified lift and wall force coefficients by tuning the model with many experimental databases. As shown here, the tuned multi-fluid model is able to predict flows in all the three bubbly flow subregimes, namely the wall-peak, core-peak, and transition subregimes, with reasonable accuracy. The predictions by the tuned model are compared with other numerical simulations, as well. Finally, the tuned model is used to simulate gas-lift problems in oil wells and the performance of eight empirical and semi-empirical correlations for predicting pressure drop is investigated, carefully. It is observed that, there is a correlation (i.e. Guet, S., Ooms, G., Oliemans, R.V.A., Mudde, R.F., 2004. Bubble size effect on low liquid input drift-flux parameters. Chem. Eng. Sci. 59, 3315–3329) which predicts gravitational pressure drop in very good agreement with the tuned multi-fluid model in all ranges of bubble diameters, including the wall-peak and core-peak regimes.     

Numerical and experimental investigation of the lift force on single bubbles

In recent years CFD has proven itself as a valuable tool for gaining insight in flow phenomena in general and complex multiphase flows arising in process equipment in particular. However for (dispersed) multiphase flows, the reliability of the outcome of these computations depends in a sensitive way on the correctness of the representation of the phase interactions (for instance due to drag and lift forces) which leads to the well-known and difficult closure problem. In this paper we report results of direct numerical simulations supplemented with dedicated experiments to obtain quantitative data for the representation of the lift force. This force is known to be responsible for the segregation of small and large (deformed) bubbles in bubbly flows through pipes and bubble columns.Both numerical simulations using an improved front tracking (FT) model and experiments under well-defined conditions have been performed for air bubbles rising through water/glycerine mixtures, where the bubble diameter, liquid viscosity and linear shear rate were varied. The numerical simulations show a good agreement with the correlation presented by Legendre and Magnaudet (1998) for spherical bubbles at sufficiently high Reynolds numbers. For large deformed bubbles a good agreement with the correlation by Tomiyama et al. (2002) was found over a wide range of liquid viscosities, although the computed lift force was always slightly lower. Therefore a new correlation has been proposed, which combines a fit of the numerical data for deformed bubbles with the correlation by Legendre and Magnaudet (1998) for small bubbles. Finally, it was shown that the shear rate has no significant influence on the drag and lift coefficient.An experimental set-up (similar to the one used by Tomiyama) was constructed using a running belt submerged in a liquid, consisting of a glycerine–water mixture of varying viscosity. PIV measurements have been used to calibrate the linear shear field and to obtain the flow profile around the bubbles. Contrary to the numerical simulations, the experimental data show a very strong influence of the shear rate on the lift force coefficient. This may be attributed to the rigid behaviour of the contaminated bubble surface, which changes the shear stress at the bubble interface.     

Modeling of core flow in a gas-solids riser

The heterogeneous flow structure in gas-solids riser reactors is typically represented by an upward solids flow in the core region and a back-mixing downward solids flow in the wall region. The hydrodynamic and reaction characteristics in these two regions are highly different, as most reactions with fresh catalyst solids occur in the core region and mostly spent catalyst solids are found in the wall region. Gross understanding on gas-solids riser flow can be conveniently obtained from a cross-section averaged one-dimensional modeling approach, which is probably only valid for the core region. The success of such an approach, however, has to rely on the appropriate modeling of controlling mechanisms of riser flows. Our recent studies show that commonly-employed Richardson-Zaki equation overestimates the hydrodynamic forces in the dense phase and acceleration regimes; there is also a non-negligible effect of solids collision on solids acceleration, and the wall effect should be taken into account in terms of wall boundary and back flow mixing. In this paper we propose a new mechanistic modeling to describe the hydrodynamics of upward flow of solids in a gas-solids riser, with new formula of hydrodynamic phase interactions. The modeling results are validated against published measurements of pressure and solids volume fraction in a wide range of particle property, gas velocity and solid mass flux. Parametric effects of operation conditions such as transport gas velocity and solid mass flux on hydrodynamic characteristics of riser flows are predicted.     

Prediction of hydrodynamic entrance length for single and two-phase flow in helical coils

The hydrodynamic entrance length in helical coils for single and two-phase bubbly flow was studied experimentally and numerically. Development region length and the detailed characteristics of fluid flow have been investigated by varying helical coil parameters such as tube diameter, coil diameter and void fraction. For the CFD simulation of the two-phase fluid flow, the Eulerian–Eulerian model was employed. To calculate the turbulent fluctuations, the SST^k − ω turbulence model has been used. The experimental and numerical simulation of the local parameters demonstrates that the hydrodynamic developing length (L/D) increases when Reynolds number increases in the single and two-phase flows. The obtained results show that the development entrance length increases with the increase of pipe diameter and decreases with the increase of coil diameter. Also, entrance length decreases while curvature ratio of helical coil and void fraction increase. A correlational equation has been suggested to predict the hydrodynamic entrance length as functions of various parameters of the helical coil.     

Aerosol Particle Removal and Re-entrainment in Turbulent Channel Flows – A Direct Numerical Simulation Approach

Aerosol particle removal and re-entrainment in turbulent channel flows are studied. The instantaneous fluid velocity field is generated by the direct numerical simulation (DNS) of the Navier – Stokes equation via a pseudospectral method. Particle removal mechanisms in turbulent channel flows are examined and the effects of hydrodynamic forces, torques and the near-wall coherent vorticity are discussed. The particle resuspension rates are evaluated, and the results are compared with the model of Reeks. The particle equation of motion used includes the hydrodynamic, the Brownian, the shearinduced lift and the gravitational forces. An ensemble of 8192 particles is used for particle resuspension and the subsequent trajectory analyses. It is found that large-size particles move away roughly perpendicular to the wall due to the action of the lift force. Small particles, however, follow the upward flows formed by the near-wall eddies in the low-speed streak regions. Thus, turbulent near-wall vortical structures play an important role in small particle resuspension, while the lift is an important factor for reentrainment of large particles. The simulation results suggests that small particles (with τ _p ⁺ ≤ 0.023) primarily move away from the wall in the low-speed streaks, while larger particles (with τ _p ⁺ ≥ 780) are mostly removed in the high-speed streaks.     

Numerical simulation of three‐dimensional gas‐solid particle flow in a horizontal pipe

A three‐dimensional model of particulate flows using the Reynolds Averaged Navier‐Stokes method is presented. The governing equations of the gas–solids flow are supplemented with appropriate closure equations to take into account all the relevant forces exerted on the solid particles, such as particle‐turbulence interactions, turbulence modulation, particle–particle interactions, particle–wall interactions, as well as gravitational, viscous drag, and lift forces. A finite volume numerical technique was implemented for the numerical solution of the problem. The method has been validated by comparing its results with the limited number of available experimental data for the velocity and turbulence intensity of the gas–particle flow. The results show that the presence of particles in the flow has a significant effect on all the flow variables. Most notably, the distribution of all the parameters becomes asymmetric, because of the gravitational effect on the particles and particle sedimentation. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Transport and Deposition of Angular Fibers in Turbulent Channel Flows

Transport and deposition of angular fibrous particles in turbulent channel flows were studied. The instantaneous fluid velocity field was generated by the direct numerical simulation (DNS) of the Navier-Stokes equation via a pseudo-spectral method. An angular fibers was assumed to consist of two elongated ellipsoids attached at their tips. For a dilute suspension of fibers, a one-way coupling assumption was used in that the flow carries the fibers, but the coupling effect of the fiber on the flow was neglected. The particle equations of motion used included the hydrodynamic forces and torques, the shear-induced lift and the gravitational forces. The hydrodynamic interactions of the high aspect ratio linkage were assumed to be negligibly small. Euler's four parameters (quaternions) were used for describing the time evolution of fiber orientations. Ensembles of fiber trajectories and orientations in turbulent channel flows were generated and statistically analyzed. The results were compared with those for spherical particles and straight fibers and their differences were discussed. Effects of fiber size, aspect ratio, fiber angle, turbulence near wall eddies, and various forces were studied. The DNS predictions were compared with experimental data for straight fibers and a proposed empirical equation model.