CFD modeling of hydrodynamic characteristics of a gas–liquid two-phase stirred tank

A three-dimensional CFD model was developed in this work to simulate hydrodynamic characteristics of a gas–liquid two-phase stirred tank with two six-bladed turbines and four baffles, coupling of the Multiple Size Group model to determine bubble size distribution. Important hydrodynamic parameters of the multi-phase system such as volume-averaged overall and time-averaged local gas holdups and axial liquid velocities along time and transversal courses were simulated and analyzed in detail, under varied operating conditions (inlet air flow rate and impeller rotation speed). Model predictions of local transient gas holdup and liquid velocity distributions on vertical and horizontal sections of the tank were also carried out. The overall flow patterns were discussed in detail to assess the mixing. Bubble size distributions were further predicted to reveal the unique properties of gas phase. Experimental measurements of overall gas holdups and local axial liquid velocities were used to validate the developed model.     

Computational fluid dynamics and experimental study of the hydrodynamics of a gas–solid tapered fluidized bed

In the present work, experimental and numerical studies for the hydrodynamics in a gas–solid tapered fluidized bed have been carried out. The experimental results obtained by carrying out experiments in a tapered fluidized bed for glass bead (spherical) of 2.0 mm and dolomite (non-spherical particles) of 2.215 mm in diameter, were compared with the computational fluid dynamics (CFD) simulation results, using a commercial CFD software package, Fluent. The gas–solid flow was simulated using the Eulerian–Eulerian model and applying the kinetic theory of granular flow for solid particles. The Gidaspow drag model was used to calculate the gas–solid momentum exchange coefficients. Pressure drops predicted by the CFD simulations agreed reasonably well with experimental measurements for both types (spherical and non-spherical) of particles. Good agreement was also obtained between experimental and CFD predicted bed expansion ratios for both types of particles. Present study provides a useful basis for further works on the CFD of tapered fluidized bed.     

Computational modelling of bubbles,droplets and particles in metals reduction and refining

A multi-phase framework is typically required for the CFD modelling of metals reduction processes. Such processes typically involve the interaction of liquid metals, a gas (often air) top space, liquid droplets in the top space and injection of both solid particles and gaseous bubbles into the bath. The exchange of mass, momentum and energy between the phases is fundamental to these processes. Multi-phase algorithms are complex and can be unreliable in terms of either or both convergence behaviour or in the extent to which the physics is captured. In this contribution, we discuss these multi-phase flow issues and describe an example of each of the main “single phase” approaches to modelling this class of problems (i.e., Eulerian–Lagrangian and Eulerian–Eulerian). Their utility is illustrated in the context of two problems – one involving the injection of sparging gases into a steel continuous slab caster and the other based on the development of a novel process for aluminium electrolysis. In the steel caster, the coupling of the Lagrangian tracking of the gas phase with the continuum enables the simulation of the transient motion of the metal–flux interface. The model of the electrolysis process employs a novel method for the calculation of slip velocities of oxygen bubbles, resulting from the dissolution of alumina, which allows the efficiency of the process to be predicted.     

超声波测速仪的计算流体力学数值模拟研究

超声波测速仪是一种利用超声波发射接收装置,通过发射接收时间来计算来流速度的一种仪器装置.目前国内许多研究都关注在如何消除测速仪的测量误差上,对于模型结构对测量风场的影响研究较少.为了考察测速仪的测量精度,本研究以模型结构对测量区域风速的影响作为关注的重点,采用计算流体力学方法模拟了从低速到高速的不同来流风速下的绕流流场,计算出位于测速仪中心区域的速度分布和不同截面上的平均速度,以判断测速仪模型结构对中心测量区域风速的影响程度.该研究结果表明在测速探头平面内测量到的速度值,无论在低速和高速时均最为准确.采用计算流体力学数值模拟方法可为今后的测速仪模型设计和改造提供准确的依据.     

Modelling dispersion in laminar and turbulent flows in an open channel based on centre manifolds using 1D-IRBFN method

Centre manifold method is an accurate approach for analytically constructing an advection–diffusion equation (and even more accurate equations involving higher-order derivatives) for the depth-averaged concentration of substances in channels. This paper presents a direct numerical verification of this method with examples of the dispersion in laminar and turbulent flows in an open channel with a smooth bottom. The one-dimensional integrated radial basis function network (1D-IRBFN) method is used as a numerical approach to obtain a numerical solution for the original two-dimensional (2-D) advection–diffusion equation. The 2-D solution is depth-averaged and compared with the solution of the 1-D equation derived using the centre manifolds. The numerical results show that the 2-D and 1-D solutions are in good agreement both for the laminar flow and turbulent flow. The maximum depth-averaged concentrations for the 1-D and 2-D models gradually converge to each other, with their velocities becoming practically equal. The obtained numerical results also demonstrate that the longitudinal diffusion can be neglected compared to the advection.     

射流通道内方柱发热器件的几何设计北大核心CSCD

基于构形理论,建立了二维射流通道内导热基座上方柱离散热源的散热优化模型.给定离散热源的总纵截面面积和热源高度为约束条件,以系统最高温度和熵产率为优化目标,以各热源的长度比为优化变量进行了几何设计,并分析了射流速度和热源间距对热源最优构形的影响.当射流速度和热源间距给定时,均存在最优长度比使系统最高温度和熵产率最低,但对应不同射流速度和热源间距的最优长度比不同.研究结果可为方柱发热器件的热设计提供理论指导.     

含高浓度悬浮固粒运动射流稳定性研究

首先用连续介质耦合模型推导出含高浓度悬浮固粒运动射流的空间稳定性方程,然后借助渐进分析法和欧拉守恒差分格式,用有限差分数值解法得到不同流向位置、流场雷诺数、固粒属性和喷射装置运动速度时流场的稳定性特征曲线,说明喷射装置的反向运动使不稳定扰动频率范围扩大,正向运动则相反。固粒抑制流场的不稳定性,随着固粒等效斯托克斯数的减小,这种效应增强。这些结论,对于两相运动射流发展的认识有重要意义。     

Numerical study of flow asymmetry and self-sustained jet oscillations in geometrically symmetric cavities

In this paper we present the results of numerical investigation of self-sustained oscillations of a jet confined in a symmetric cavity. This work represents an attempt to reproduce empirical observations of asymmetric flows in geometrically symmetric systems and to extend the jet flow investigations to more complex possible scenarios. A well-known example of such two-dimensional flow has been reported experimentally and reproduced numerically for simple flow [E. Schreck, M. Schaefer, Numerical study or bifurcation in three-dimensional sudden channel expansions, Comput. Fluids 29 (2000) 583–593]. It has been found that for some particular control parameter, above its critical value (bifurcation point), the jet can be deflected to either of the two sides of the cavity. In this paper we report a similar behaviour which is, however, characterized by a more complicated flow pattern. While simple flow appears only within small cavity lengths the complex flows develops with increased cavity lengths. Unlike stationary asymmetric solutions accompanied by cavity jet oscillations, as experimentally reported in e.g., [A. Maurel, P. Ern, B.J.A. Zielinska, J.E. Wesfreid, Experimental study of self-sustained oscillations in a confined jet, Phys Rev. E 54 (1996) 3643–3651], in our investigations of both simple and complex asymmetric flow we observed the slow periodical drift of the jet from one to another side of the cavity. The essential control parameters were Reynolds number Re and the ratio length to inlet width L/d. According to experiments of Maurel et al. (1996), the jet is stable and symmetric, when both L/d and Re are below certain critical values, otherwise jet oscillations appear in both experiment and our simulation (cavity oscillations regime). However, further increase of either (or both) L/d and Re leads of so called free jet type oscillations regime. This paper describes complex jet behaviour within the later oscillations regime. We believe that both simple “classical” and “our” complex stationary asymmetric solutions (as well as superimposed cavity-type and free-jet oscillations) can be explained based on physical arguments as already done in previous works. However, the origin of slow drift motion remains still to be resolved. This might be of high importance for clear distinguishing between relevant physical and numerical features in future codes developments.     

Dual synchronization based on two different chaotic systems: Lorenz systems and Rössler systems

In this paper, we improve and extend the works of Liu and Davids [Dual synchronization of chaos, Phys. Rev. E 61 (2000) 2176–2179] which only introduce the dual synchronization of 1-D discrete chaotic systems. The dual synchronization of two different 3-D continuous chaotic systems, Lorenz systems and Rössler systems, is discussed. And a sufficient condition of dual synchronization about the two different chaotic systems is obtained. Theories and numerical simulations show the possibility of dual synchronization and the effectiveness of the method.     

A CFD model for the prediction of haemolysis in micro axial left ventricular assist devices

This paper describes the development and application of a computational model based upon Computational Fluid Dynamics (CFD) software simulation technology to predict haemolysis in micro Left Ventricular Assist Devices (μ$\mathrm{\mu }$LVAD). A CFD model, capturing the full three dimensional geometry of the device, together with an explicit representation of the rotating machinery based upon a rotating reference frame, is solved transiently. Mixed meshes with the order of a million elements are required to resolve the flow adequately and so to enable solutions in a reasonable time (e.g., 3 h) the model is solved on a high performance parallel cluster. Haemolysis is a measure of damage occurring in the blood and is conceived as accumulating as it passes through parts of the device where it encounters high shear forces. As such, the haemolysis model is based upon tracking the behaviour of particles released at the inlet throughout the flow domain and calculating the damage accumulated by each individual particle as it traverses the device. In order to ensure the model predictions of haemolysis are noise free from a statistically significant perspective then it is demonstrated that the number of particles to be tracked must exceed 20 000 in any simulation experiment. Comparisons with experimental data from a companion paper demonstrate the effectiveness of the CFD simulation embedding the haemolysis model.     

Influence of Mass Loading on Particle-Laden Turbulent Pipe Flow

A CFD code in the framework of OpenFOAM was validated for simulations of particle-laden pipe and channel flows at low to intermediate mass loadings. The code is based on an Eulerian two-fluid approach with Reynolds-averaged conservation equations, including turbulence modeling and four-way coupling. Pipe flow simulations of particles in air against gravity were conducted at Reynolds numbers up to 50000. The particle mass loading was varied and its effect on the mean velocities and turbulent fluctuations of the two phases was studied. Special attention was paid to the influence of mass loading on the centerline velocity and the wall shear velocity of the fluid phase for various flow parameters and particle properties. Empirical correlations were established between these two quantities and the flow Reynolds number, particle Reynolds number, Stokes number and particle to fluid density ratio for a range of particle mass loadings. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Large Eddy Simulation of turbulent confined coaxial swirling jets

Large eddy simulations of swirling flow in a coaxial-jet combustor are reported. Two experimental test cases have been chosen from the literature. In both cases the configuration consists of two coaxial jets which enter into an expansion duct with the annular jet being swirled, the inner jet unswirled. The main features of the flow are well predicted in the simulations. The mean velocities and the turbulent fluctuations are compared with the experimental data and show good agreement. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Performance of turbulence models for flows through rough pipes

The Reynolds-averaged Navier–Stokes (RANS) equations were solved along with turbulence models, namely k–ε, k–ω, Reynolds stress models (RSM), and filtered Navier–Stokes equations along with Large Eddy Simulation (LES) to study the fully-developed turbulent flows in circular pipes roughened by repeated square ribs with various spacings. Solutions of these flows were obtained using the commercial computational fluid dynamics (CFD) software Fluent. The numerical results were validated against experimental measurements and other numerical data published in literature. The performance of the turbulence models was compared and discussed. All the RANS models and LES model were observed to perform equally well in predicting the time-averaged flow statistics. However no instantaneous information can be obtained from the RANS results. Therefore, when a rough overview of the flow process in a pipe roughened by repeated ribs is needed, any one of the RANS models can be of value. On the other hand, the instantaneous as well as time-averaged flows could be studied with more insight using LES, albeit at a cost of CPU effort at least one order higher.     

Numerical verification of stationary solutions for Navier–Stokes problems

We present a numerical method to enclose stationary solutions of the Navier–Stokes equations, especially 2-D driven cavity problem with regularized boundary condition. Our method is based on the infinite dimensional Newton's method by estimating the inverse of the corresponding linearized operator. The method can be applied to the case for high Reynolds numbers and we show some numerical examples which confirm us the actual effectiveness.     

Experimental and numerical study of the cold crucible melting process

The cold crucible, or induction skull melting process as is otherwise known, has the potential to produce high purity melts of a range of difficult to melt materials, including Ti–Al and Ti6Al4V alloys for Aerospace, Ti–Ta and other biocompatible materials for surgical implants, silicon for photovoltaic and electronic applications, etc. A water cooled AC coil surrounds the crucible causing induction currents to melt the alloy and partially suspend it against gravity away from water-cooled surfaces.     

Evaluation of thermal comfort conditions in a classroom equipped with radiant cooling systems and subjected to uniform convective environment

The aim of this work is to evaluate numerically the human thermal response that 24 students and 1 teacher feel in a classroom equipped with radiant cooling systems and subjected to uniform convective environments, in lightly warm conditions. The evolution of thermal comfort conditions, using the PMV index, is made by the multi-nodal human thermal comfort model.In this numerical model, that works in transient or steady-state conditions and simulates simultaneously a group of persons, the three-dimensional body is divided in 24 cylindrical and 1 spherical elements. Each element is divided in four parts (core, muscle, fat and skin), sub-divided in several layers, and protected by several clothing layers. This numerical model is divided in six parts: human body thermal system, clothing thermal system, integral equations resolution system, thermoregulatory system, heat exchange between the body and the environment and thermal comfort evaluation.Seven different radiant systems are combined to three convective environments. In the radiant systems (1) no radiant system without warmed curtain, (2) no radiant system with warmed curtain, (3) radiant floors cooling system with warmed curtain, (4) radiant panels cooling system with warmed curtain, (5) radiant ceiling cooling system with warmed curtain, (6) radiant floor and panels cooling system with warmed curtain and (7) radiant ceiling and panels cooling system with warmed curtain are analysed, while in the convective environments (1) without air velocity field and with uniform air velocity field of (2) 0.2 m/s and (3) 0.6 m/s are also analysed. The internal air temperature and internal surfaces temperature are 28 °C, the radiant cooling surfaces temperature are 19 °C and the warmed internal curtains surfaces temperatures, subjected to direct solar radiation, are 40 °C.The numerical model calculates the Mean Radiant Temperature field, the human bodies’ temperatures field and the thermal comfort level, for the 25 occupants, for the 21 analysed situations.Without uniform air velocity field, when only one individual radiant cooling system is used, the Predicted Percentage of Dissatisfied people is lowest when the radiant floor cooling system is applied and is highest when the radiant panel cooling system is applied. When are combined the radiant ceiling or the floor cooling systems with the radiant panel cooling system the Predicted Percentage of Dissatisfied people decreases.When the uniform air velocity increases the thermal comfort level, that the occupants are subjected, increases. When the radiant floor cooling system or the combination of radiant floor and panel cooling systems without uniform air velocity field is applied, the Category C is verified for some occupants. However, with a convective uniform air velocity field of 0.2 m/s the Category B is verified and with a convective uniform air velocity field of 0.6 m/s the Category A is verify for some occupants. In the last situation the Category C is verified, in general, for all occupants.     

Numerical simulation of cavitation dynamics using a cavitation-induced-momentum-defect (CIMD) correction approach

A new unsteady cavitation event tracking model is developed for predicting vapor dynamics occurring in multi-dimensional incompressible flows. The procedure solves incompressible Navier–Stokes equations for the liquid phase supplemented with an additional vapor transport equation for the vapor phase. The novel cavitation-induced-momentum-defect (CIMD) correction methodology developed in this study accounts for cavitation inception and collapse events as relevant momentum-source terms in the liquid phase momentum equations. The model tracks cavitation zones and applies compressibility effects, employing homogeneous equilibrium model (HEM) assumptions, in constructing the source term of the vapor transport model. Effects of vapor phase accumulation and diffusion are incorporated by detailed relaxation models. A modified RNG k–ε model, including the effects of compressibility in the vapor regions, is employed for modeling turbulence effects. Numerical simulations are carried out using a finite volume methodology available within the framework of commercial CFD software code Fluent v.6.2. Simulation results are in good qualitative agreement with experiments for unsteady cloud cavitation behavior in planar nozzle flows. Multitude of mechanisms such as formation of vortex cavities, vapor cluster shedding and coalescence, cavity pinch off are sharply captured by the CIMD approach. Our results indicate the profound influence of re-entrant jet motion and adverse pressure gradients on the cavitation dynamics.     

CFD-modeling of effects of draft tubes on operating condition in spouted beds

Draft tubes are used to increase performance in spouted beds. Performance of these tubes depends on its geometry and location. We can by surveying and CFD modeling of bed provide the best condition. In this work a CFD modeling technique is used to optimize draft tube geometry. First, model accuracy was assessed by comparing the results with experimental results. After it became clear that the model works, it was used to optimize the designing of spouted bed. The Eulerian–Eulerian multifluid modeling approach was applied to predict gas–solid flow behavior. The results present that optimized selection of draft tubes lead to uniform distribution of particle velocity and it can increase also particles circulating.     

Numerical Simulation of Air Flow in Model Room

Efficient, and appropriate indoor air environment is important issue in building design. Air flow patterns which are formed in the room are mainly depended on its geometrical parameters. Investigation of flow patterns are performed on a relatively simple geometry of model room, with a small obstacle (partition) in it. There are several interesting flow phenomena which are present in the model room: flow through sudden geometry expansion, stagnation flow with lateral boundaries, flow over the obstacle, etc. Since the air velocities are low, it is assumed that flow is incompressible. Numerical calculations of these patterns have been done using RANS modeling approach. For all calculations an extended version of open-source CFD software OpenFOAM was used. Several turbulence models have been used for RANS approach, with special attention on their performance in capturing unsteady flow phenomena. Comparison of obtained numerical results and available experimental results for mean velocities shown good agreement. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)