鼓泡床中超声驻波的模拟及其对气泡的调制机理

采用计算流体动力学（CFD）的方法，数值生成了鼓泡床中一对声换能器以16kHz高频振动引发的超声场。数值计算是基于包括粘性影响的可压缩流体基本守恒方程，并耦合了水的状态方程。模拟结果表明，在本研究所用的几何布置和换能器与时间相关的速度入口边界条件下，反应器中形成了一个稳定的驻波声场；由于波的非线性以及水的粘性，压力波节点呈现出轻微的时间漂移性。模拟结果与前人的实验结果定性吻合。在模拟的声压分布的基础上，分析了驻波声场调制气泡的机理。如比较熟知，气泡在驻波声场作用下或者向压力波节点运动或者向压力波腹点运动，取决于气泡尺寸与共振尺寸的关系。     

An efficient S-DDM iterative approach for compressible contamination fluid flows in porous media

In this paper, we develop an efficient splitting domain decomposition method (S-DDM) for compressible contamination fluid flows in porous media over multiple block-divided sub-domains by combining the non-overlapping domain decomposition, splitting, linearization and extrapolation techniques. The proposed S-DDM iterative approach divides the large domain into multiple block sub-domains. In each time interval, the S-DDM scheme is applied to solve the water head equation, in which an efficient local multilevel scheme is used for computing the values of water head on the interfaces of sub-domains, and the splitting implicit scheme is used for computing the interior values of water head in sub-domains; and the S-DDM scheme is then proposed to solve the concentration equation by combining the upstream volume technique. Numerical experiments are performed and analyzed to illustrate the efficiency of the S-DDM iterative approach for simulating compressible contamination fluid flows in porous media. The developed method takes the excellent attractive advantages of both the non-overlapping domain decomposition and the splitting technique, and reduces computational complexities, large memory requirements and long computational durations.     

An interaction potential based lattice Boltzmann method with adaptive mesh refinement (AMR) for two-phase flow simulation

The lattice Boltzmann method (LBM) for two-phase flow simulation is often hindered by insufficient resolution at the interface. As a result, the LBM simulation of bubbles in bubbling flows is commonly limited to spherical or slightly deformed bubble shapes. In this study, the adaptive mesh refinement method for the LBM is developed to overcome such a problem. The approach for this new method is based on the improved interaction potential model, which is able to maintain grid-independent fluid properties in the two-fluid phases and at the interface. The LBM–AMR algorithm is described, especially concerning the LBM operation on a non-uniform mesh and the improved interaction potential model. Numerical simulations have been performed to validate the method in both single phase and multiphase flows. The 2D and 3D simulations of the buoyant rise of bubbles are conducted under various conditions. The agreement between the simulated bubble shape and velocity with experiments illustrates the capability of the LBM–AMR approach in predicting bubble dynamics even under the large bubble deformation conditions. Further, the LBM–AMR technique is capable of simulating a complex topology change of the interface. Integration of LBM with AMR can significantly improve the accuracy and reduce computation cost. The method developed in this study may appreciably enhance the capability of LBM in the simulation of complex multiphase flows under realistic conditions.     

Influence of different interfaces on laser propulsion in water environment

The dynamics of laser-induced semispherical cavitation bubbles are investigated by means of an optical beam deflection method. The bubbles were generated in water in the vicinity of three different interfaces: including water–air, water–colloid and water–solid, and also in the bulk. Numerical simulation shows that the propelled surface obtains more energy and longer propulsion from the semispherical bubble than from the spherical bubble during the first expansion of the bubble. The collapse time of the quasi-semispherical bubble is significantly less than the Rayleigh collapse time of the spherical bubble for all the cases considered in this work. The influence of water–air or water–solid interfaces on the collapse time of a semispherical bubble is similar to that of a spherical bubble. As the bubble energy grows, the effect of the water–colloid interface changes gradually from that of the water–solid to that of the water–air interface. In other words, the energy of the bubble dictates whether the water–colloid interface behaves as a water–solid or a water–air interface.     

Sharp interface immersed-boundary/level-set method for wave–body interactions

A sharp interface Cartesian grid method for the large-eddy simulation of two-phase turbulent flows interacting with moving bodies is presented. The overall approach uses a sharp interface immersed boundary formulation and a level-set/ghost–fluid method for solid–fluid and fluid–fluid interface treatments, respectively. A four-step fractional-step method is used for velocity–pressure coupling, and a Lagrangian dynamic Smagorinsky subgrid-scale model is adopted for large-eddy simulations. A simple contact angle boundary condition treatment that conforms to the immersed boundary formulation is developed. A variety of test cases of different scales ranging from bubble dynamics, water entry and exit, landslide-generated waves, to ship hydrodynamics are performed for validation. Extensions for high Reynolds number ship flows using wall-layer models are also considered.     

Numerical simulation of drop impact on a liquid–liquid interface with a multiple marker front-capturing method

The gravity-driven motion of a droplet impacting on a liquid–liquid interface is studied. The full Navier–Stokes equations are solved on a fixed, uniform grid using a finite difference/front-capturing method. For the representation of fluid–fluid interfaces, a coupled Level-Set/Volume-Of-Fluid method [M. Sussman, E.G. Puckett, A coupled Level-Set and Volume-of-Fluid method for computing 3D and axisymmetric incompressible two-phase flows, J. Comp. Phys. 162 (2000) 301–337] is used, in which we introduce the novel approach of describing separate interfaces with different marker functions. As a consequence, we prevent numerical coalescence of the droplet and the liquid–liquid interface without excessive (local) grid refinement. To validate our method, numerical simulations of the drop impact event are compared with experiments [Z. Mohamed-Kassim, E.K. Longmire, Drop impact on a liquid–liquid interface, Phys. Fluids 15 (2003) 3263–3273]. Furthermore, a comparison is made with the numerical results of [A. Esmaeeli, G. Tryggvason, Direct numerical simulations of bubbly flows. Part 2. Moderate Reynolds number arrays, J. Fluid Mech. 385 (1999) 325–358] for an array of rising bubbles. The investigation shows that the multiple marker approach successfully prevents numerical coalescence of interfaces and adequately captures the effect of surface tension.     

Efficient numerical methods for multiple surfactant-coated bubbles in a two-dimensional stokes flow

We present efficient and highly accurate numerical methods to compute the deformation of surfactant-coated, two-dimensional bubbles in a slow viscous flow. Surfactant acts to locally alter the surface tension and thereby change the nature of the interface motion. In this paper, we restrict our attention to the case of a dilute insoluble surfactant. The convection–diffusion equation for the surfactant concentration on the interface is coupled with the Stokes equations in the fluid domain through a boundary condition based on the Laplace-Young condition. The Stokes equations are first recast as an integral equation and then solved using a fast-multipole accelerated iterative procedure. The computational cost per time-step is only O(N log N) operations, with N being the number of discretization points on the interface. The bubble interfaces are described by a spectral mesh and is advected according to the fluid velocity in such a manner so as to preserve equal arc length spacing of marker points. This equal arc length framework has the dual advantage of dynamically maintaining the spatial mesh and allowing efficient, implicit treatment of the stiffest terms in the dynamics. Several phenomenologically different examples are presented.     

On the HLLC Riemann solver for interface interaction in compressible multi-fluid flow

In this work, the HLLC Riemann solver, which is much more robust, simpler and faster than iterative Riemann solvers, is extended to obtain interface conditions in sharp-interface methods for compressible multi-fluid flows. For interactions with general equations of state and material interfaces, a new generalized Roe average is proposed. For single-phase interactions, this new Roe average does not introduce artificial states and satisfies the U-property exactly. For interactions at material interfaces, the U-property is satisfied by introducing ghost states for the internal energy. A number of numerical tests suggest that the proposed Riemann solver is suitable for general equations of state and has an accuracy comparable to iterative Riemann solvers, while being significantly more robust and efficient.     

A hybrid numerical simulation of isotropic compressible turbulence

A novel hybrid numerical scheme with built-in hyperviscosity has been developed to address the accuracy and numerical instability in numerical simulation of isotropic compressible turbulence in a periodic domain at high turbulent Mach number. The hybrid scheme utilizes a 7th-order WENO (Weighted Essentially Non-Oscillatory) scheme for highly compressive regions (i.e., shocklet regions) and an 8th-order compact central finite difference scheme for smooth regions outside shocklets. A flux-based conservative and formally consistent formulation is developed to optimize the connection between the two schemes at the interface and to achieve a higher computational efficiency. In addition, a novel numerical hyperviscosity formulation is proposed within the context of compact finite difference scheme for the smooth regions to improve numerical stability of the hybrid method. A thorough and insightful analysis of the hyperviscosity formulation in both Fourier space and physical space is presented to show the effectiveness of the formulation in improving numerical stability, without compromising the accuracy of the hybrid method. A conservative implementation of the hyperviscosity formulation is also developed. Combining the analysis and test simulations, we have also developed a criterion to guide the specification of a numerical hyperviscosity coefficient (the only adjustable coefficient in the formulation). A series of test simulations are used to demonstrate the accuracy and numerical stability of the scheme for both decaying and forced compressible turbulence. Preliminary results for a high-resolution simulation at turbulent Mach number of 1.08 are shown. The sensitivity of the simulated flow to the detail of thermal forcing method is also briefly discussed.     

On the thermodynamic behaviors and interactions between bubble pairs: A numerical approach

Thermodynamic behaviors and interactions between bubble pairs are important to better understand the cavitation phenomena. In this study, a compressible two-phase model, accounting for thermal effects to investigate the thermodynamic behaviors and interactions between bubble pairs, is developed in OpenFOAM. The volume of fluid (VOF) method is adopted to capture the interface. Validations are performed by comparing the simulation results of a single bubble and bubble pairs with corresponding experimental data. The dynamical behaviors of bubble pairs and their thermodynamic effect at different relative distances γ are investigated and discussed, which help reveal the bubble cloud dynamics. The quantitative analysis of γ effects on the maximum temperature during bubble collapse is performed with three distinct stages identified. For a single bubble collapsing near the rigid surface, the thermodynamic characteristics at different relative distances are similar to that of the bubble pairs, but the maximum temperature is higher since the single bubble can collapse to a smaller volume.     

一种基于MOF界面重构的二维中心型MMALE方法

发展了一种基于MOF（Moment of Fluid）界面重构的二维中心型MMALE（Multi-Material Arbitrary Lagrangian-Eulerian）方法.其中,流体力学方程组采用中心型拉氏方法进行离散求解.混合网格的热力学封闭采用Tipton压力松弛模型.混合网格内的界面重构采用MOF方法,并对MOF方法作了简化和改进.重映步采用一种基于多边形剪裁算法的精确积分守恒重映方法.计算了若干数值例子,包括二维漩涡发展问题、Sedov问题、激波与氦气泡相互作用问题、水中强激波与空气泡相互作用问题、二维RT不稳定性问题等.数值算例表明,该方法具有二阶精度,能够计算界面两侧密度比和压力比很大的问题,并且其健壮性优于交错型MMALE方法,适合计算多介质复杂流体动力学问题.     

激波作用不同椭圆氦气柱过程中流动混合研究

在激波与气柱相互作用问题中,压力与密度间断不平行产生的斜压涡量会引起流动的不稳定性,从而促进物质间的混合.本文基于双通量模型,结合五阶加权基本无振荡(WENO)格式,求解多组分二维Navier-Stokes方程,分析激波作用面积相同结构不同的椭圆气柱所致的流动和混合.数值结果清晰地显示了激波诱导Richtmyer-Meshkov不稳定性引起的气柱界面变形和波系演化.同时定量地从界面运动、界面结构参数变化(长度和高度)、气柱体积压缩率、环量及混合率等角度分析激波诱导的流动混合机制,研究椭圆几何构型对氦气混合过程的影响.结果表明,界面及相关参数的演化与气柱初始形状密切相关.当激波沿椭圆长轴作用于气柱时,气柱前端出现空气射流结构,且射流不断增长并渗透到下游界面,致使气柱分离成两个独立涡团,离心率越大,射流发展越快;同时激波作用气柱后在界面处产生不规则反射现象.圆形气柱界面演化与这种作用情形类似.当激波沿椭圆短轴作用于气柱时,界面上游出现类平面结构,随后平面上下缘处产生涡旋,主导流动发展,激波在界面作用产生规则反射,离心率越大,这些现象越明显.界面高度、长度、体积压缩率也因此有所差异.对界面演化、环量和混合率的综合分析表明,激波沿长轴作用于气柱且离心率较大时,流动发展较快,不稳定性导致的流动越复杂,越有利于氦气与环境介质的混合.     

An adaptive implicit–explicit scheme for the DNS and LES of compressible flows on unstructured grids

An adaptive implicit–explicit scheme for Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES) of compressible turbulent flows on unstructured grids is developed. The method uses a node-based finite-volume discretization with Summation-by-Parts (SBP) property, which, in conjunction with Simultaneous Approximation Terms (SAT) for imposing boundary conditions, leads to a linearly stable semi-discrete scheme. The solution is marched in time using an Implicit–Explicit Runge–Kutta (IMEX-RK) time-advancement scheme. A novel adaptive algorithm for splitting the system into implicit and explicit sets is developed. The method is validated using several canonical laminar and turbulent flows. Load balance for the new scheme is achieved by a dual-constraint, domain decomposition algorithm. The scalability and computational efficiency of the method is investigated, and memory savings compared with a fully implicit method is demonstrated. A notable reduction of computational costs compared to both fully implicit and fully explicit schemes is observed.     

Lagrangian coherent structures analysis of gas-liquid flow in a bubble column

The objective of this paper is to apply a new identifying method to investigating the gas-liquid two-phase flow behaviors in a bubble column with air injected into water.In the numerical simulations,the standard k-?turbulence model is employed to describe the turbulence phenomenon occurring in the continuous fluid.The Finite-Time Lyapunov Exponent(FTLE)and Lagrangian Coherent Structures(LCS)are applied to analyze the vortex structures in multiphase flow.Reasonable agreements are obtained between the numerical and experimental data.The numerical results show that the evolution of gas-liquid in the column includes initial and periodical developing stages.During the initial stage,the bubble hose is forming and extending along the vertical direction with the vortex structures formed symmetrically.During the periodical developing stage,the bubble hose starts to oscillate periodically,and the vortexes move along the bubble hose to the bottom of column alternately.Compared to the Euler-system-based identification criterion of a vortex,the FTLE field presents the boundary of a vortex without any threshold defined and the LCS represents the divergence extent of infinite neighboring particles.During the initial stage,the interfaces between the forward and backward flows are highlighted by the LCS.As for the periodical developing stage,the LCS curls near the vortex centers,providing a method of analyzing a flow field from a dynamical system perspective.     

A High-Order Projection Method for Tracking Fluid Interfaces in Variable Density Incompressible Flows

We present a numerical method for computing solutions of the incompressible Euler or Navier–Stokes equations when a principal feature of the flow is the presence of an interface between two fluids with different fluid properties. The method is based on a second-order projection method for variable density flows using an “approximate projection” formulation. The boundary between the fluids is tracked with a second-order, volume-of-fluid interface tracking algorithm. We present results for viscious Rayleigh–Taylor problems at early time with equal and unequal viscosities to demonstrate the convergence of the algorithm. We also present computational results for the Rayleigh–Taylor instability in air-helium and for bubbles and drops in an air–water system without surface tension to demonstrate the behavior of the algorithm on problems with large density and viscosity contrasts.     

A method for avoiding the acoustic time step restriction in compressible flow

We propose a novel method for alleviating the stringent CFL condition imposed by the sound speed in simulating inviscid compressible flow with shocks, contacts and rarefactions. Our method is based on the pressure evolution equation, so it works for arbitrary equations of state, chemical species etc. and is derived in a straight-forward manner. Similar methods have been proposed in the literature, but the equations they are based on and the details of the methods differ significantly. Notably our method leads to a standard Poisson equation similar to what one would solve for incompressible flow, but has an identity term more similar to a diffusion equation. In the limit as the sound speed goes to infinity, one obtains the Poisson equation for incompressible flow. This makes the method suitable for two-way coupling between compressible and incompressible flows and fully implicit solid–fluid coupling, although both of these applications are left to future work. We present a number of examples to illustrate the quality and behavior of the method in both one and two spatial dimensions, and show that for a low Mach number test case we can use a CFL number of 300 (whereas previous work was only able to use a CFL number of 3 on the same example).     

可压缩与不可压缩流体中Rayleigh Taylor不稳定性的比较

 对比研究了可压缩与不可压缩流体的Rayleigh Taylor不稳定性小扰动阶段的增长速率，其中，压力是密度的任意单值函数，这个函数也即是可压缩流体的状态方程。研究表明：在相同密度分布条件下，可压缩流体的界面扰动增长速率总是比相应的不可压缩流体的界面增长率大，其相对增长率随扰动波长的增加而增大，随两种介质的声速减小而增大，在长波和易压缩流体中，相对增长率可达0.8以上。因此，在某些条件下，流体可压缩性对Rayleigh Taylor不稳定性的影响是不能忽略的。     

An interface capturing method for the simulation of multi-phase compressible flows

A novel finite-volume interface (contact) capturing method is presented for simulation of multi-component compressible flows with high density ratios and strong shocks. In addition, the materials on the two sides of interfaces can have significantly different equations of state. Material boundaries are identified through an interface function, which is solved in concert with the governing equations on the same mesh. For long simulations, the method relies on an interface compression technique that constrains the thickness of the diffused interface to a few grid cells throughout the simulation. This is done in the spirit of shock-capturing schemes, for which numerical dissipation effectively preserves a sharp but mesh-representable shock profile. For contact capturing, the formulation is modified so that interface representations remain sharp like captured shocks, countering their tendency to diffuse via the same numerical diffusion needed for shock-capturing. Special techniques for accurate and robust computation of interface normals and derivatives of the interface function are developed. The interface compression method is coupled to a shock-capturing compressible flow solver in a way that avoids the spurious oscillations that typically develop at material boundaries. Convergence to weak solutions of the governing equations is proved for the new contact capturing approach. Comparisons with exact Riemann problems for model one-dimensional multi-material flows show that the interface compression technique is accurate. The method employs Cartesian product stencils and, therefore, there is no inherent obstacles in multiple dimensions. Examples of two- and three-dimensional flows are also presented, including a demonstration with significantly disparate equations of state: a shock induced collapse of three-dimensional van der Waal’s bubbles (air) in a stiffened equation of state liquid (water) adjacent to a Mie-Grüneisen equation of state wall (copper).     

Numerical simulation of bubble dynamics in a Phan-Thien–Tanner liquid: Non-linear shape and size oscillatory response under periodic pressure

We study non-linear bubble oscillations driven by an acoustic pressure with the bubble being immersed in a viscoelastic, Phan-Thien–Tanner liquid. Solution is provided numerically through a method which is based on a finite element discretization of the Navier–Stokes flow equations. The proposed computational approach does not rely on the solution of the simplified Rayleigh–Plesset equation, is not limited in studying only spherically symmetric bubbles and provides coupled solutions for the velocity, stress fields and bubble interface. We present solutions for non-spherical bubbles, with asphericity being addressed by means of Legendre polynomials or associated Legendre functions. A parametric investigation of the bubble dynamical oscillatory response as a function of the fluid rheological properties shows that the amplitude of bubble oscillations drastically increases as liquid elasticity (quantified by the Deborah number) increases or as liquid viscosity decreases (quantified by the Reynolds number). Extensive numerical calculations demonstrate that increasing elasticity and/or viscosity of the surrounding liquid tend to stabilize the shape anisotropy of an initially non-spherical bubble. Results are shown for pressure amplitudes 0.2–2 MPa and Deborah, Reynolds numbers in the intervals of 1–8 and 0.094–1.256, respectively.