An Adaptive Cartesian Mesh Based Method to Simulate Turbulent Flows of Multiple Rotating Surfaces

An efficient Cartesian cut-cell/level-set method based on a multiple grid approach to simulate turbulent turbomachinery flows is presented. The finite-volume approach in an unstructured hierarchical Cartesian setup with a sharp representation of the complex moving boundaries embedded into the computational domain, which are described by multiple level-sets, ensures a strict conservation of mass, momentum, and energy. Furthermore, an efficient kinematic motion level-set interface method for the rotation of embedded boundaries described by multiple level-set fields on a computational domain distributed over several processors is introduced. This method allows the simulation of multiple boundaries rotating relatively to each other in a fixed frame of reference. To demonstrate the efficiency of the numerical method and the quality of the computed findings the generic test problem of a rotating cylinder surrounded by a stationary hull and the flow over a ducted rotating axial fan with a stationary turbulence generating grid at the inflow are simulated. The computational results of the axial fan show a good agreement with the experimental data.     

Numerical simulation of free surface flows with the level set method using an extremely high-order accuracy WENO advection scheme

Three-dimensional dynamic gas–liquid flow simulations that accurately track the phase interface are numerically challenging. This article presents a numerical study of the performance of the level-set phase–interface tracking method when combined with extremely high order (7th to 11th) weighted essentially non-oscillatory (WENO) advection schemes for gas–liquid free surface flows. Comparisons between simulation results and prior benchmark results suggest that such a combination of methods can be satisfactorily applied to the level-set and Navier-Stokes equations for free surface flow simulations when volume conservation is enforced at every time step, and minor numerical oscillations are suppressed through use of an artificial viscosity term. In particular, simulations of solid body rotation, the unsteady flow following an ideal dam break, tank sloshing, and the rise of a single bubble all agree with analytical or experimental results to within ± 3.12% when the level-set method is combined with an 11th order WENO scheme. Furthermore, use of an 11th order WENO advection scheme actually has a computational cost advantage because, for the same accuracy, it can be used on a coarser grid when compared with a more-common second-order advection scheme; computational savings of up to 87% are possible.     

凹形多面体离散单元的水平集函数接触算法

多面体模型理论上可构造任意颗粒形态,然而受单元接触算法的限制,仅用于凸形颗粒材料的离散元模拟。对于具有凹形特征的多面体单元,单个接触点的搜索算法难以精确计算单元间的作用力。考虑多面体单元间存在单个或多个接触点的计算特性,本文发展了适用于凸形和凹形多面体颗粒材料的水平集函数接触算法。该方法通过点-三角形单元距离计算方法和奇-偶数判定方法建立多面体单元的零水平集函数和空间水平集函数,并对水平集函数进行三线性插值,可得到多面体单元间的单个或多个接触点。为检验水平集函数接触算法的可靠性,对球形和凹形多面体颗粒材料的堆积和倒塌过程进行离散元模拟,并分析颗粒形状对堆积密度和休止角的影响规律。     

Simulations of single bubbles rising through viscous liquids using Smoothed Particle Hydrodynamics

The shapes and dynamics of single bubbles rising through viscous fluids are studied using the SPH (Smoothed Particle Hydrodynamics) approach. This fully Lagrangian, particle-based method is applied to compute the complete two-phase flow, both inside the bubbles as well as around them. For that purpose, a multi-phase formulation of the SPH method that can address large density differences is retained, while surface tension effects are explicitly accounted for through a CSF (Continuum Surface Force) model. Numerical simulations have been performed for different regimes (corresponding to different relative importance of surface tension, viscosity and buoyancy effects) and the predicted topological changes as well as the terminal velocity and drag coefficients of bubbles are validated. The numerical outcomes are assessed not only with respect to reference experimental data but also with respect to other numerical methods, namely the Front-Tracking and the Lattice Boltzmann Methods. It is believed that this study corresponds to a new application of SPH approaches for two-phase flow simulations and results reveal the interest of this method to capture fine details of gas–liquid systems with deformable and rapidly changing interfaces.     

Flame Surface Density in Turbulent Premixed V-Flame with Buoyancy

A fractional step numerical model is established for turbulent premixed combustion with buoyancy. The flame front propagation is described by the level-set method. Simulated results without buoyancy have been previously validated with available experimental data on a premixed V-flame. A new formula is presented to fit the flame surface density with respect to the reaction progress variable in a turbulent premixed V-flame. By numerical simulations, dynamical behaviour of the flame under the interaction of turbulence, exothermicity and buoyancy are investigated.     

波浪作用下直立结构物附近强湍动掺气流体运动的数值模拟

波浪破碎卷入气体易对建筑物受力产生压力振荡, 了解波浪作用下建筑物附近掺气水流的运动特性是精确计算建筑物受力的前提. 基于OpenFOAM开源程序包和修正速度入口造波方法建立三维数值波浪水槽, 模型采用S-A IDDES湍流模型进行湍流封闭, 并采用修正的VOF 方法捕捉自由液面, 数值模拟了规则波在1:10的光滑斜坡上与直立结构物的相互作用过程, 重点分析了结构物附近的水动力和掺气水流运动特性. 结果表明, 建立的数值模型能精确地捕捉波浪作用下直立结构物附近的自由液面的变化以及气泡输运过程, 较好地描述气体卷入所形成的气腔形态以及多气腔之间的融合、分裂等过程; 波浪与直立结构物相互作用产生强湍动掺气水流, 其运动过程十分复杂; 掺气流体输运过程中水气界面周围一直伴随着涡的存在, 其中, 气泡的分裂与周围正负涡量剪切作用密切相关, 且其输运轨迹主要受周围流场的影响; 研究揭示了结构物附近湍动能与掺气特性的关系, 发现波浪作用下直立结构物附近湍动能的分布与掺气水流特征参数(气泡数量、空隙率)整体呈现一定的线性关系.      

Accurate and Efficient Implementation of Pore-Morphology-based Drainage Modeling in Two-dimensional Porous Media

We have developed an efficient and accurate numerical implementation for pore-morphological modeling of drainage in two-dimensional, totally wetting porous media. The new numerical method uses level sets to describe the fluid distribution and polygons that can be defined with subgrid scale accuracy for the pore boundaries, while a previously developed approach represents the phases by pixels arranged on a square lattice. We analyze and compare the previous and new method. For both approaches, the simulated fluid saturations are first-order accurate. For the level-set approach, the simulated interfacial lengths converge to the real values, while the pixel approach yields biased results. The level-set method is orders of magnitudes faster than the pixel method.     

THE CONSTITUTIVE RELATION OF CRACK-WEAKENED ROCK MASSES UNDER AXIAL-DIMENSIONAL UNLOADING

An accurate and efficient numerical method for solving the crack-crack interaction problem is presented. The method is mainly by means of the dislocation model, stress superposition principle and Chebyshev polynomial expansion of the pseudo-traction. This method can be applied to compute the stress intensity factors of multiple kinked cracks and multiple rows of periodic cracks as well as the overall strains of rock masses containing multiple kinked cracks under complex loads. Many complex computational examples are given. The dependence of the crack-crack interaction on the crack configuration, the geometrical and physical parameters, and loads pattern, is investigated. By comparison with numerical results under confining pressure unloading, it is shown that the crack-crack interaction under axial-dimensional unloading is weaker than those under confining pressure unloading. Numerical results for single faults and crossed faults show that the single faults are more unstable than the crossed faults. It is found from numerical results for different crack lengths and different crack spacing that the interaction among kinked cracks decreases with an increase in length of the kinked cracks and the crack spacing under axial-dimensional unloading.     

Interactions of multiple spark-generated bubbles with phase differences

This paper aims to study the complex interaction between multiple bubbles, and to provide a summary and physical explanation of the phenomena observed during the interaction of two bubbles. High-speed photography is utilized to observe the experiments involving multiple spark-generated bubbles. Numerical simulations corresponding to the experiments are performed using the Boundary Element Method (BEM). The bubbles are typically between 3 and 5 mm in radius and are generated either in-phase (at the same time) or with phase differences. Complex phenomena are observed such as bubble splitting, and high-speed jetting inside a bubble caused by another collapsing bubble nearby (termed the ‘catapult’ effect). The two-bubble interactions are broadly classified in a graph according to two parameters: the relative inter-bubble distance and the phase difference (a new parameter introduced). The BEM simulations provide insight into the physics, such as bubble shape changes in detail, and jet velocities. Also presented in this paper are the experimental results of three bubble interactions. The interesting and complex observations of multiple bubble interaction are important for a better understanding of real life applications in medical ultrasonic treatment and ultrasonic cleaning. Many of the three bubble interactions can be explained by isolating bubble pairs and classifying their interaction according to the graph for the two bubble case. This graph can be a useful tool to predict the behavior of multiple bubble interactions.     

Comparison of several models for multi-size bubbly flows on an adiabatic experiment

This paper deals with the modelling and numerical simulation of isothermal bubbly flows with multi-size bubbles. The study of isothermal bubbly flows without phase change is a first step towards the more general study of boiling bubbly flows. Here, we are interested in taking into account the features of such isothermal flow associated to the multiple sizes of the different bubbles simultaneously present inside the flow. With this aim, several approaches have been developed. In this paper, two of these approaches are described and their results are compared to experimental data, as well as to those of an older approach assuming a single average size of bubbles. These two approaches are (i) the moment density approach for which two different expressions for the bubble diameter distribution function are proposed and (ii) the multi-field approach. All the models are implemented into the NEPTUNE_CFD code and are compared to a test performed on the MTLOOP facility. These comparisons show their respective merits and shortcomings in their available state of development.     

Direct 2D simulation of small gas bubble clusters: from the expansion step to the equilibrium state

A numerical strategy, based on an adaptive finite element method, is proposed for the direct two‐dimensional simulation of the expansion of small clusters of gas bubbles within a Newtonian liquid matrix. The velocity and pressure fields in the liquid are first defined through the Stokes equations and are subsequently extended to the gas bubbles. The liquid–gas coupling is imposed through the stress exerted on the liquid by gas pressure (ruled by an ideal gas law) and by surface tension. A level set method, combined with a mesh adaptation technique, is used to track liquid–gas interfaces. Many numerical simulations are presented. The single bubble case allows to compare the simulations to an analytical model. Simulations of the expansion of small clusters are then presented showing the interaction and evolution of the gas bubbles to an equilibrium state, involving topological rearrangements induced by Plateau's rule. Copyright © 2006 John Wiley & Sons, Ltd.     

Characterization of plunging liquid jets: A combined experimental and numerical investigation

This paper presents a combined experimental and numerical study of the flow characteristics of round vertical liquid jets plunging into a cylindrical liquid bath. The main objective of the experimental work consists in determining the plunging jet flow patterns, entrained air bubble sizes and the influence of the jet velocity and variations of jet falling lengths on the jet penetration depth. The instability of the jet influenced by the jet velocity and falling length is also probed. On the numerical side, two different approaches were used, namely the mixture model approach and interface-tracking approach using the level-set technique with the standard two-equation turbulence model. The numerical results are contrasted with the experimental data. Good agreements were found between experiments and the two modelling approaches on the jet penetration depth and entraining flow characteristics, with interface tracking rendering better predictions. However, visible differences are observed as to the jet instability, free surface deformation and subsequent air bubble entrainment, where interface tracking is seen to be more accurate. The CFD results support the notion that the jet with the higher flow rate thus more susceptible to surface instabilities, entrains more bubbles, reflecting in turn a smaller penetration depth as a result of momentum diffusion due to bubble concentration and generated fluctuations. The liquid average velocity field and air concentration under tank water surface were compared to existing semi-analytical correlations. Noticeable differences were revealed as to the maximum velocity at the jet centreline and associated bubble concentration. The mixture model predicts a higher velocity than the level-set and the theory at the early stage of jet penetration, due to a higher concentration of air that cannot rise to the surface and remain trapped around the jet head. The location of the maximum air content and the peak value of air holdup are also predicted differently.     

INVESTIGATION OF BUBBLE-BUBBLE INTERACTION EFFECT DURING THE COLLAPSE OF MULTI-BUBBLE SYSTEM

通过直接数值模拟方法对多泡在压力驱动下的溃灭过程进行了研究。气相满足理想气体正压模型,液相为不可压 流体,采用基于压力的方法求解多泡的两相流场。数值研究表明,在多泡流场中,中心气泡的溃灭过程明显不同于单泡,存在总体溃灭延迟现象和后期加速现象。随着周围气泡数的增多或气泡间距的减小,中心气泡的溃灭时间增长,溃灭时的压力峰值增大。结合理论定性分析发现,气泡运动不仅受远场压力的驱动,还受周围气泡诱导压力场的影响。周围气泡的诱导压力经历先减小后增大的过程,从而使受其影响的中心气泡产生先延迟后加速的特征。     

Mass conservation and reduction of parasitic interfacial waves in level-set methods for the numerical simulation of two-phase flows: A comparative study

A commonly used class of methods for the numerical simulation of two-phase flows is level set. It is often reported though that this method does not accurately conserve mass of each fluid, unlike other interface capturing techniques such as volume-of-fluid. A further concern besides mass conservation is the formation of any parasitic currents. Since the initial formulation of level-set methods, however, numerous modifications have been proposed, and it does not seem clear whether mass conservation errors and parasitic currents are problematic for all of these and, if not, what key steps could be taken to avoid them. Furthermore, results reported in the literature are often for benchmark tests in two dimensions, and it is not clear whether a good performance there holds up in three dimensions. We undertake here a comparative study, reporting test results in two and three dimensions for various level-set methods on a variety of problems. Kinematical tests are first performed for prescribed velocity fields, followed by benchmark tests including the solution of the Navier–Stokes equations. It is shown that higher-order schemes for spatial and temporal discretization may improve mass conservation and avoid interface distortion. In particular, two reinitialization methods that are straightforward to implement perform very well at all these tests. It is demonstrated that some schemes introduce parasitic oscillations in the simulation of Rayleigh–Taylor instability.     

近自由面的多个水下爆炸气泡相互作用研究

将气泡运动阶段周围的流场假设为无黏、无旋、不可压缩的理想流体,运用边界积分法模拟流场中气泡的运动,并开发了三维计算程序,计算值与实验值吻合较好.用该方法模拟了近自由面多气泡之间的相互作用,包括同相气泡和异相气泡. 通过计算发现,气泡的周期随两气泡中心的距离减小而增大,这是由于多气泡之间存在抑制作用,特别是对异相气泡,这种抑制作用更加明显,称之为多气泡之间的抑制效应. 无论有、无自由面存在,多气泡之间均存在抑制效应,由于抑制效应导致同相与异相气泡相互耦合作用的动态特性存在巨大的差异,这些现象可为将来研究多个同时或延时产生的水下爆炸气泡的威力提供参考.      

Overpressure generation and repetition of collapsing microbubbles induced by shock wave reflection in a narrow gap

This paper reports the summary of experiments performed to successive generate small-scale underwater shock waves by means of shock-induced collapse of microbubbles confined in a narrow gap. The project is motivated to develop a method for efficient inactivation of marine bacteria contained in ship ballast water by high impulsive pressure loading. The shock wave–air bubbles interaction was visualized by shadowgraph; the images were recorded by ImaCon200, and simultaneous pressure measurements were performed by using an optical fiber pressure transducer with higher temporal resolution. Attaching small air bubbles on a single nylon fiber and placing it in a confined space, we demonstrated sequential generation of impulsive high pressures at the successive collapses of small bubbles at incident and reflected shock loadings. The values of the very short impulsive pressures that occurred repeatedly for a relatively long term are found high enough to inactivate marine bacteria.     

Numerical simulation of dielectric bubbles coalescence under the effects of uniform magnetic field

In this research, the co-axial coalescence of a pair of gas bubbles rising in a viscous liquid column under the effects of an external uniform magnetic field is simulated numerically. Considered fluids are dielectric, and applied magnetic field is uniform. Effects of different strengths of magnetic field on the interaction of in-line rising bubbles and coalescence between them were investigated. For numerical modeling of the problem, a computer code was developed to solve the governing equations which are continuity, Navier–Stokes equation, magnetic field equation and level set and reinitialization of level set equations. The finite volume method is used for the discretization of the continuity and momentum equations using SIMPLE scheme where the finite difference method is used to discretization of the magnetic field equations. Also a level set method is used to capture the interface of two phases. The results are compared with available numerical and experimental results in the case of no-magnetic field effect which show a good agreement. It is found that uniform magnetic field accelerates the coalescence of the bubbles in dielectric fluids and enhances the rise velocity of the coalesced bubble.     

Structural weight minimization under stress constraints and multiple loading

In this paper we present an approach for structural weight minimization under von Mises stress constraints and multiple load-cases. The minimization problem is solved by using the topological derivative concept, which allows the development of efficient and robust topology optimization algorithms. Since we are dealing with multiple loading, the resulting sensitivity is obtained as a sum of the topological derivatives associated with each load-case. The derived result is used together with a level-set domain representation method to devise a topology design algorithm. Several numerical examples are presented showing the effectiveness of the proposed approach.     

近水面水下爆炸二维Level-set数值模拟

水下爆炸是一个多介质、动边界、瞬态非线性过程,捕捉介质之间交界面的变化是数值模拟的一个难点.本文采用Level-set方法来描述水下爆炸气体产物和流体交界面以及自由表面变化,应用TVD (Total Variation Diminishing) 计算技术求解Level-set流场,首先建立了近水面水下爆炸的二维数值方法,然后,将该方法推广到流场内有刚性结构的情况,考虑了冲击波和刚性结构物的相互作用.为了模拟无限边界流场问题,引进了Thompson建立的无反射边界条件.     

Numerical simulations of the primary Bjerknes force experienced by bubbles in a standing ultrasonic field: Nonlinear vs. linear

The primary Bjerknes force experienced by a population of multiple bubbles in a liquid set in a nonlinear ultrasonic standing field and their translation are calculated and analyzed by numerical simulations. The force field is evaluated by considering the nonlinear bubble oscillations as well as the nonlinear character of the ultrasonic pressure field (both variables are unknown in the coupled nonlinear differential system). The results at small amplitudes agree with the classical theory on bubble translation, depending on the driving frequency in relation to the bubble resonance. It is shown that, when amplitudes are raised, the force field exhibits important modifications that strongly affect the motion of the bubbles and the way they form agglomerates. An analysis is performed on the importance of the terms in the differential system that provoke (a) the nonlinearity of the bubble oscillations and (b) the nonlinearity of the acoustic wave. This study reveals that both features should be considered to better approximate the primary Bjerknes force field. Simulations of the nonlinear ultrasonic field after the bubbles form agglomerates under the influence of this force are also performed.