Modeling Three-Dimensional Multiphase Flow Using a Level Contour Reconstruction Method for Front Tracking without Connectivity

Three-dimensional multiphase flow and flow with phase change are simulated using a simplified method of tracking and reconstructing the phase interface. The new level contour reconstruction technique presented here enables front tracking methods to naturally, automatically, and robustly model the merging and breakup of interfaces in three-dimensional flows. The method is designed so that the phase surface is treated as a collection of physically linked but not logically connected surface elements. Eliminating the need to bookkeep logical connections between neighboring surface elements greatly simplifies the Lagrangian tracking of interfaces, particularly for 3D flows exhibiting topology change. The motivation for this new method is the modeling of complex three-dimensional boiling flows where repeated merging and breakup are inherent features of the interface dynamics. Results of 3D film boiling simulations with multiple interacting bubbles are presented. The capabilities of the new interface reconstruction method are also tested in a variety of two-phase flows without phase change. Three-dimensional simulations of bubble merging and droplet collision, coalescence, and breakup demonstrate the new method's ability to easily handle topology change by film rupture or filamentary breakup. Validation tests are conducted for drop oscillation and bubble rise. The susceptibility of the numerical method to parasitic currents is also thoroughly assessed.     

The Lattice Solid Model to Simulate the Physics of Rocks and Earthquakes: Incorporation of Friction

The particle-based lattice solid model developed to study the physics of rocks and the nonlinear dynamics of earthquakes is refined by incorporating intrinsic friction between particles. The model provides a means for studying the causes of seismic wave attenuation, as well as frictional heat generation, fault zone evolution, and localisation phenomena. A modified velocity–Verlat scheme that allows friction to be precisely modelled is developed. This is a difficult computational problem given that a discontinuity must be accurately simulated by the numerical approach (i.e., the transition from static to dynamical frictional behaviour). This is achieved using a half time step integration scheme. At each half time step, a nonlinear system is solved to compute the static frictional forces and states of touching particle-pairs. Improved efficiency is achieved by adaptively adjusting the time step increment, depending on the particle velocities in the system. The total energy is calculated and verified to remain constant to a high precision during simulations. Numerical experiments show that the model can be applied to the study of earthquake dynamics, the stick–slip instability, heat generation, and fault zone evolution. Such experiments may lead to a conclusive resolution of the heat flow paradox and improved understanding of earthquake precursory phenomena and dynamics.     

垂直排液过程不稳定性的数值模拟

为分析线框排液实验中液膜表面出现的不稳定现象及其成因,针对含有不溶性活性剂的线框液膜排液过程,模拟液膜底部的不稳定现象,分析Marangoni效应、膨胀黏性和扰动波数因素的影响。结果表明：底部扰动在排液开始比较剧烈,而后快速减弱,到排液后期又逐渐增强。排液开始的扰动是由初始扰动引起,而排液后期的扰动与活性剂分布有关。较弱的Marangoni效应可增强表面扰动,而较强的Marangoni效应则减弱底部扰动,使液膜呈刚性,发生表面逆流现象;较高的膨胀黏性减慢液膜排液进程,降低表面速度,且能抑制Marangoni效应引起的逆流现象;波数较大的扰动使液膜在排液初期的扰动变强,但对排液后期的稳定性不产生影响。     

新型分离结晶法的三维数值模拟研究

本文借助三维数值模拟的方法,对微重力条件下新型分离结晶Bridgman生长过程中熔体内部的热毛细对流进行模拟计算。结果表明:(1)Ma数较小时,流动为稳态流动;当Ma数超过一定数值后,流动发展为非稳态热毛细对流。(2)狭缝宽度越大,流动越容易失稳。(3)随着高径比的增大,狭缝处流胞的流动范围增大。     

A Volume of Fluid Based Method for Fluid Flows with Phase Change

This paper presents a numerical method directed towards the simulation of flows with mass transfer due to changes of phase. We use a volume of fluid (VOF) based interface tracking method in conjunction with a mass transfer model and a model for surface tension. The bulk fluids are viscous, conducting, and incompressible. A one-dimensional test problem is developed with the feature that a thin thermal layer propagates with the moving phase interface. This test problem isolates the ability of a method to accurately calculate the thermal layers responsible for driving the mass transfer in boiling flows. The numerical method is tested on this problem and then is used in simulations of horizontal film boiling.     

An Efficient Algorithm for Truncating Spatial Domain in Modeling Light Scattering by Finite-Difference Technique

The finite-difference time domain technique is one of the most robust and accurate numerical methods for the solution of light scattering by small particles with arbitrary composition and geometry. In practice, this method requires that the spatial domain for the computation of near-field be truncated. An absorbing boundary condition must be imposed in conjunction with this truncation. The performance of this boundary condition is essential to the stability of numerical computations and the reliability of results. In the present study, a new boundary condition, referred to as the mixed T algorithm, has been developed, which is a generalization of the transmitting boundary condition originally developed by Liao and co-workers. The present algorithm does not require spatial interpolation for wave values at interior grid points. In addition, it produces two minima of spurious reflections at small and large incident angles, allowing efficient absorption of the scattered waves at the boundary for large incident angles. When the third-order mixed T algorithm is used, the reflection coefficient of the boundary is less than 1% for incident angles from 0° to about 70°. We find that the numerical instability associated with the transmitting boundary condition is caused by the location-dependent amplitude of outgoing waves in the vicinity of the boundary. For this reason, the mixed T algorithm is stabilized by consistently introducing diffusive coefficients into the boundary equation. When the stabilized algorithm is applied, the near-field within the truncated domain can be computed by using single-precision arithmetic without overflows for more than 10⁵steps in the time-marching iteration. Finally, the new absorbing boundary condition is validated by carrying out numerical experiments involving the propagation of a TM wave excited by a sinusoidal point source, simultaneous simulation of the wave propagation in small and large domains, and the scattering of a TM wave by an infinite circular cylinder.     

中等半径比反向旋转圆Couette系统流动稳定性的实验和数值研究

圆Couette系统已成为研究从层流转捩为湍流以及有限几何尺寸对图案选择影响的范例.本文以实验和计算机模拟方法研究中等半径比圆Couette系统的稳定性.考察同轴独立旋转圆筒之间的粘性不可压缩流体运动，推广了经典的Rayleigh离心不稳定性理论，导出稳定性判据，用来定量地确定稳定界限.实验采用了流动显示和激光散射技术.仪器有半径比η=0.699，形状比Γ=18.流动状态相图中的显著特征是新的首次失稳态：当外筒静止或反向旋转时，首次失稳出现具有非零方位角波数的螺旋涡流，在轴向和方位角方向为行进波，而并非与时间无关的Taylor涡.初步实验所得的转捩Reynolds数与数值计算结果一致.实验室和数值实验显示出半径比对图案形成和转捩序列的影响. 关键词：     

Simultaneous selective detection of multiple quantum spectra

A three-dimensional multiple-quantum NMR experiment that produces individual spectra of all quantum orders is described. The separation of different quantum orders is accomplished via Fourier transformation with respect to the phase of the first two pulses of a generic three-pulse multiple-quantum sequence. This dramatically reduces the time required to obtain several selectively detected spectra and enhances the sensitivity and digital resolution from that obtained using the original two-dimensional technique. The experiment is demonstrated on the protons of para-chlorotoluene dissolved in the nematic liquid crystal Merck ZLI-1132.     

Preliminary study of two immiscible liquid layers subjected to a horizontal temperature gradient

Marangoni convection, driven by interfacial instability due to a surface tension gradient, presents a significant problem in the crystal growth process. To achieve better materials processing, it is necessary to suppress and control this convection, especially in crystal growth using Liquid Encapsulated Czochralski techniques in which the melt is encapsulated in an immiscible medium. Marangoni convection can occur at the liquid-liquid interface and at the gas-liquid free surface. Buoyancy driven convection can also affect and complicate the flow. The present report studied Marangoni convection in a two-liquid layer system in an open and enclosed cavity. Flow in the cavity was subjected to a horizontal temperature gradient. Interactive flow near the liquid-liquid interface was measured by the Particle Image Velocimetry (PIV) technique. The measured flow field is in good agreement with numerical predictions.     

A High-Order Discontinuous Galerkin Method for 2D Incompressible Flows

In this paper we introduce a high-order discontinuous Galerkin method for two-dimensional incompressible flow in the vorticity stream-function formulation. The momentum equation is treated explicitly, utilizing the efficiency of the discontinuous Galerkin method. The stream function is obtained by a standard Poisson solver using continuous finite elements. There is a natural matching between these two finite element spaces, since the normal component of the velocity field is continuous across element boundaries. This allows for a correct upwinding gluing in the discontinuous Galerkin framework, while still maintaining total energy conservation with no numerical dissipation and total enstrophy stability. The method is efficient for inviscid or high Reynolds number flows. Optimal error estimates are proved and verified by numerical experiments.     

Multigrid Solution of the Incompressible Navier–Stokes Equations for Density-Stratified Flow past Three-Dimensional Obstacles

The steady incompressible Navier–Stokes equations in three dimensions are solved for neutral and stably stratified flow past three-dimensional obstacles of increasing spanwise width. The continuous equations are approximated using a finite volume discretisation on staggered grids with a flux-limited monotonic scheme for the advective terms. The discrete equations which arise are solved using a nonlinear multigrid algorithm with up to four grid levels using the SIMPLE pressure correction method as smoother. When at its most effective the multigrid algorithm is demonstrated to yield convergence rates which are independent of the grid density. However, it is found that the asymptotic convergence rate depends on the choice of the limiter used for the advective terms of the density equation, and some commonly used schemes are investigated. The variation with obstacle width of the influence of the stratification on the flow field is described and the results of the three-dimensional computations are compared with those of the corresponding computation of flow over a two-dimensional obstacle (of effectively infinite width). Also given are the results of time-dependent computations for three-dimensional flows under conditions of strong static stability when lee-wave propagation is present and the multigrid algorithm is used to compute the flow at each time step.     

A Residual-Based Compact Scheme for the Compressible Navier–Stokes Equations

A simple and efficient time-dependent method is presented for solving the steady compressible Euler and Navier–Stokes equations with third-order accuracy. Owing to its residual-based structure, the numerical scheme is compact without requiring any linear algebra, and it uses a simple numerical dissipation built on the residual. The method contains no tuning parameter. Accuracy and efficiency are demonstrated for 2-D inviscid and viscous model problems. Navier–Stokes calculations are presented for a shock/boundary layer interaction, a separated laminar flow, and a transonic turbulent flow over an airfoil.     

Unstructured Adaptive Grid Flow Simulations of Inert and Reactive Gas Mixtures

Unstructured adaptive grid flow simulation is applied to the calculation of high-speed compressible flows of inert and reactive gas mixtures. In the present case, the flowfield is simulated using the 2-D Euler equations, which are discretized in a cell-centered finite volume procedure on unstructured triangular meshes. Interface fluxes are calculated by a Liou flux vector splitting scheme which has been adapted to an unstructured grid context by the authors. Physicochemical properties are functions of the local mixture composition, temperature, and pressure, which are computed using the CHEMKIN-II subroutines. Computational results are presented for the case of premixed hydrogen–air supersonic flow over a 2-D wedge. In such a configuration, combustion may be triggered behind the oblique shock wave and transition to an oblique detonation wave is eventually obtained. It is shown that the solution adaptive procedure implemented is able to correctly define the important wave fronts. A parametric analysis of the influence of the adaptation parameters on the computed solution is performed.     

Numerical investigation of hydrodynamics behaviour of melt layer during laser cutting of steel

Understanding of the melt layer hydrodynamic behaviour during laser-cutting process under gas jet assistance is of high importance for cut quality control. In the present work, a numerical model is developed to calculate the three-dimensional behaviour of the melt flow on the kerf front, while an inert gas jet interacts with the melt film. Fluent CFD code is used to solve the governing hydrodynamic equations by finite volume method. The results show that the melt flow on the kerf front reveals a strong instability, which depends on the cutting speed and on the gas jet velocity. Global flow behaviour (gas and molten metal flows) computed using a laminar model, reveals oscillations of the gas–metal liquid interface, which is assimilated to Kelvin–Helmholtz instability. The origin of this instability is discussed in terms of instabilities in thermal dynamics and hydrodynamics. Instability in thermal dynamics is related to the localized melting, while the instability in hydrodynamics is governed by forces balance between gas and resistant surface tension.     

An Incompressible Three-Dimensional Multiphase Particle-in-Cell Model for Dense Particle Flows

A three-dimensional, incompressible, multiphase particle-in-cell method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to an Eulerian grid and then mapping back computed stress tensors to particle positions. A subgrid particle, normal stress model for discrete particles which is robust and eliminates the need for an implicit calculation of the particle normal stress on the grid is presented. Interpolation operators and their properties are defined which provide compact support, are conservative, and provide fast solution for a large particle population. The solution scheme allows for distributions of types, sizes, and density of particles, with no numerical diffusion from the Lagrangian particle calculations. Particles are implicitly coupled to the fluid phase, and the fluid momentum and pressure equations are implicitly solved, which gives a robust solution.     

Monotonicity Preserving Weighted Essentially Non-oscillatory Schemes with Increasingly High Order of Accuracy

In this paper we design a class of numerical schemes that are higher-order extensions of the weighted essentially non-oscillatory (WENO) schemes of G.-S. Jiang and C.-W. Shu (1996) and X.-D. Liu, S. Osher, and T. Chan (1994). Used by themselves, the schemes may not always be monotonicity preserving but coupled with the monotonicity preserving bounds of A. Suresh and H. T. Huynh (1997) they perform very well. The resulting monotonicity preserving weighted essentially non-oscillatory (MPWENO) schemes have high phase accuracy and high order of accuracy. The higher-order members of this family are almost spectrally accurate for smooth problems. Nevertheless, they, have robust shock capturing ability. The schemes are stable under normal CFL numbers. They are also efficient and do not have a computational complexity that is substantially greater than that of the lower-order members of this same family of schemes. The higher accuracy that these schemes offer coupled with their relatively low computational complexity makes them viable competitors to lower-order schemes, such as the older total variation diminishing schemes, for problems containing both discontinuities and rich smooth region structure. We describe the MPWENO schemes here as well as show their ability to reach their designed accuracies for smooth flow. We also examine the role of steepening algorithms such as the artificial compression method in the design of very high order schemes. Several test problems in one and two dimensions are presented. For multidimensional problems where the flow is not aligned with any of the grid directions it is shown that the present schemes have a substantial advantage over lower-order schemes. It is argued that the methods designed here have great utility for direct numerical simulations and large eddy simulations of compressible turbulence. The methodology developed here is applicable to other hyperbolic systems, which is demonstrated by showing that the MPWENO schemes also work very well on magnetohydrodynamical test problems.     

Angular Flow in Toroid Cavity Probes

NMR signals from samples that rotate uniformly about the central conductor of a TCD (toroid cavity detector) exhibit frequency shifts that are directly proportional to the sample's angular velocity. This newly observed effect is based on the unique radiofrequency field inside TCDs, which is variable in direction. If a liquid sample is pumped through a capillary tube wound about the central conductor, the frequency shift is proportional to the flow rate. A mathematical relationship between a volumetric flow rate and the frequency shift is established and experimentally verified to high precision. Additionally, two-dimensional flow-resolved NMR spectroscopy for discrimination between components with different flow velocities yet retaining chemical shift information for structural analysis is presented. The application of the two-dimensional method in chromatographic NMR is suggested. Furthermore, utilization of the frequency-shift effect for rheologic studies if combined with toroid-cavity rotating-frame imaging is proposed.     

分离结晶过程中熔体热毛细对流的转变

为了了解微重力条件下新型分离结晶生长过程中熔体热毛细对流的基本特征,利用有限差分法进行了数值模拟,熔体深径比A取1和2,自由界面无因次宽度B分别取0.05、0.075和0.1.当熔体上表面为自由表面时,得到了分离结晶Bridgman生长过程中熔体热毛细对流的流函数和温度分布.计算结果表明:当Ma数较小时,在上下两个自由表面的表面张力的驱动下,熔体内部产生了两个流动方向相反的流胞,流动为稳态流动,随着Ma数的增加,上下自由表面速度增大,温度分布的非线性增加;当Ma数超过某一临界值后,流动将转化为非稳态流动;与熔体上表面为固壁时相比,A=1时的临界Ma数减小,而A=2时的临界Ma数增大;流动失稳的物理机制是流速的变化和阻力的变化之间存在滞后.     

The Adjoint Method for an Inverse Design Problem in the Directional Solidification of Binary Alloys

This paper presents a systematic procedure based on the adjoint method for solving a class of inverse directional alloy solidification design problems in which a desired growth velocityv_fis achieved under stable growth conditions. To the best of our knowledge, this is the first time that a continuum adjoint formulation is proposed for the solution of an inverse problem with simultaneous heat and mass transfer, thermo-solutal convection, and phase change. In this paper, the interfacial stability is considered to imply a sharp solid–liquid freezing interface. This condition is enforced using the constitutional undercooling criterion in the form of an inequality constraint between the thermal and solute concentration gradients,GandG_c, respectively, at the freezing front. The main unknowns of the design problem are the heating and/or cooling boundary conditions on the mold walls. The inverse design problem is formulated as a functional optimization problem. The cost functional is defined by the square of theL₂norm of the deviation of the freezing interface temperature from the temperature corresponding to thermodynamic equilibrium. A continuum adjoint system is derived to calculate the adjoint temperature, concentration, and velocity fields such that the gradient of the cost functional can be expressed analytically. The cost functional minimization process is realized by the conjugate gradient method via the finite element method solutions of the continuum direct, sensitivity, and adjoint problems. The developed formulation is demonstrated with an example of designing the directional solidification of a binary aqueous solution in a rectangular mold such that a stable vertical interface advances from left to right with a desired growth velocity.     

Wave Simulation in Frozen Porous Media

We propose a numerical algorithm for simulation of wave propagation in frozen porous media, where the pore space is filled with ice and water. The model, based on a Biot-type three-phase theory, predicts three compressional waves and two shear waves and models the attenuation level observed in rocks. Attenuation is modeled with exponential relaxation functions which allow a differential formulation based on memory variables. The wavefield is obtained using a grid method based on the Fourier differential operator and a Runge–Kutta time-integration algorithm. Since the presence of slow quasistatic modes makes the differential equations stiff, a time-splitting integration algorithm is used to solve the stiff part analytically. The modeling is second-order accurate in the time discretization and has spectral accuracy in the calculation of the spatial derivatives.