用双流体模型模拟超声速气固两相流动

采用了双流体模型对JPL(Jet Propulsion Laboratory)喷管中气固两相流动以及超声速射流两相流动进行了数值模拟,并研究了可压缩两相流动中气相与颗粒的相互作用规律.自主开发的一般曲线坐标系下二维轴对称可压缩双流体程序Solve2D,对气相求解Navier-Stokes(N-S)方程组,采用k-ε湍流模型,颗粒相求解Euler方程组.对JPL喷管内的两相流场和湍流两相射流流场进行了数值模拟,研究了不同颗粒质量百分数以及不同颗粒直径时的气固两相流场的流动规律.

气泡/液滴运动的Level Set方法模拟研究

利用Level Set方法，结合投影法求解了描述气泡/液滴运动的Navier-Stokes方程。对地面常重力场中不同大小的空气泡在高黏度糖浆溶液中的自由上升运动现象，数值模拟结果与实验观测结果符合甚好，表明该方法能够计算大密度比和黏度比$(>1000:1)$情况下的气液两相流动。而对等密度液滴的热毛细迁移现象的数值模拟结果同样能够与实验结果相一致，表明该方法同样适于研究具有Marangoni效应的两相流动现象，特别是在空间微重力环境中的气液两相传热现象中的局部流动与传热问题。

三维波流数值水槽的构建方法

为了模拟波浪与水流的联合作用,基于Reynolds平均的Navier-Stokes方法,构建了一个三维波流数值水槽. 使用该模型对不同出流边界条件进行了对比分析. 结果表明:引入合理的入流和出流边界条件,可以保证在计算稳定后,水槽平均水面基本保持不变. 垂向时均流速分布的计算结果与实验数据吻合良好. 这表明:该波流数值水槽具有较好的波流特性,可用于计算波浪与水流、以及与三维固定结构之间相互作用.

可压缩湍流直接数值模拟

本书是以作者及其研究小组多年来的研究工作为基础撰写的，主要是可压缩湍流的直接数值模拟。全书共分两部分。第一部分为数值模拟方法：针对可压缩湍流的多尺度非定常非稳定流动特征，所构造的高精度差分格式（高于三阶精度），分析了各种高精度差分格式的数值行为特征和模拟小尺度物理结构、分辨非定常间断面的能力，重点分析了正确模拟多尺度物理结构及其非线性干扰对数值方法的要求。第二部分是物理问题的直接数值模拟：根据可压缩湍流的流动物理特征，所建立的求解可压缩Navier-Stokes方程的高精度数值模拟方法，详细描述了不稳定流和可压缩湍流的直接数值模拟，以及在此基础上所发现的一些新的物理现象。直接数值模拟主要针对典型可压缩湍流，包括均匀各向同性湍流、槽道湍流、平面混合流、射流、平板边界层湍流和钝楔、钝锥边界层湍流等，重点是可压缩湍流从层流转捩到湍流的直接数值模拟及其流动机理的研究。书中还介绍了我课组所研制的高精度、高效并行算法的软件。

Enhancements of the simulation method on the edge effect in resin transfer molding processes

In resin transfer molding processes, small clearances exist between the fiber preform and the mold edges, which result in a preferential resin flow in the edge channel and then disrupt the flow patterns during the mold filling stage. A mathematical model including the effect of cavity thickness on resin flow was developed for flow behavior involving the interface between an edge channel and a porous medium. According to the mathematical analysis of momentum equations in a fully developed rectangular duct and formulations of the equivalent edge permeability, comparing with three-dimensional Navier-Stokes equations, the governing equations were modified in the edge channel. The volume of fluid (VOF) method was applied to track the flow front. A simple case is numerically simulated using the modified governing equations. The effects of edge channel width and cavity thickness on flow front and inlet pressure are analyzed, and the evolution characteristics of simulated results are in agreement with the experimental results. (c) 2007 Elsevier B.V. All rights reserved

Reactive Mold Filling in Resin Transfer Molding Processes with Edge Effects

Reactive mold filling is one of the important stages in resin transfer molding processes, in which resin curing and edge effects are important characteristics. On the basis of previous work, volume-averaging momentum equations involving viscous and inertia terms were adopted to describe the resin flow in fiber preform, and modified governing equations derived from the Navier-Stokes equations are introduced to describe the resin flow in the edge channel. A dual-Arrhenius viscosity model is newly introduced to describe the chemorheological behavior of a modified bismaleimide resin. The influence of the curing reaction and processing parameters on the resin flow patterns was investigated.

Numerical wave flume study on wave motion around submerged plates

Nonlinear interaction between surface waves and a submerged horizontal plate is investigated in the absorbed numerical wave flume developed based on the volume of fluid (VOF) method. The governing equations of the numerical model are the continuity equation and the Reynolds-Averaged Navier-Stokes (RANS) equations with the k-epsilon turbulence equations. Incident waves are generated by an absorbing wave-maker that eliminates the waves reflected from structures. Results are obtained for a range of parameters, with consideration of the condition under which the reflection coefficient becomes maximal and the transmission coefficient minimal. Wave breaking over the plate, vortex shedding downwave, and pulsating flow below the plate are observed. Time-averaged hydrodynamic force reveals a negative drift force. All these characteristics provide a reference for construction of submerged plate breakwaters.

Effects of buoyancy on Langmuir circulation

Based on the Navier-Stokes equation, an equation describing the Langmuir circulation is derived by a perturbation method when the influences of Coriolis force and buoyancy force are both considered. The approach used in the analysis is similar to the works carried out by Craik and Leibovich [J. Fluid Mech. 73 (1976) 401], Leibovich [J. Fluid Mech. 79 (1977) 715] and Huang [J. Fluid Mech. 91 (1979) 191]. Potential applications of the equation proposed are discussed in the area of Antarctic circumpolar current.

浮力对Langmuir环流的影响

Langmuir环流是发生在上层海洋中纵向的螺旋状涡旋运动，其轴向与风向基本一致。它是一常见的重要海洋现象，与海洋研究的许多重要问题，如海－气交换、海洋混合、海洋环境、海洋遥感、海洋生态和海洋灾害等有着十分密切的关系。 本文在同时考虑科氏力与浮力作用下，从Navier-Stokes方程出发，应用摄动理论，导出一个包含科氏力与浮力影响的Langmuir环流控制方程组。所采用的方法类似于Craik and Leibovich（1976）、Leibovich（1977）及Huang（1979）等人研究Langmuir环流时所采用的研究方法。此外，本文还讨论了所导出的方程组在南极绕极流区域的潜在应用。

Comparison Between Subsonic Flow Simulation and Physical Measurements of Flue Pipes

Direct simulations of wind musical instruments using the compressible Navier Stokes equations have recently become possible through the use of parallel computing and through developments in numerical methods. As a first demonstration, the flow of air and the generation of musical tones inside a soprano recorder are simulated numerically. In addition, physical measurements are made of the acoustic signal generated by the recorder at different blowing speeds. The comparison between simulated and physically measured behavior is encouraging and points towards ways of improving the simulations.

Flow stabilization with active hydrodynamic cloaks

We demonstrate that fluid flow cloaking solutions, based on active hydrodynamic metamaterials, exist for two-dimensional flows past a cylinder in a wide range of Reynolds numbers (Re's), up to approximately 200. Within the framework of the classical Brinkman equation for homogenized porous flow, we demonstrate using two different methods that such cloaked flows can be dynamically stable for Re's in the range of 5-119. The first highly efficient method is based on a linearization of the Brinkman-Navier-Stokes equation and finding the eigenfrequencies of the least stable eigenperturbations; the second method is a direct numerical integration in the time domain. We show that, by suppressing the von Kármán vortex street in the weakly turbulent wake, porous flow cloaks can raise the critical Reynolds number up to about 120 or five times greater than for a bare uncloaked cylinder. © 2012 American Physical Society.

A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs

We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if Hörmander's bracket condition holds at every point of this Hilbert space, then a lower bound on the Malliavin covariance operatorμt can be obtained. Informally, this bound can be read as "Fix any finite-dimensional projection on a subspace of sufficiently regular functions. Then the eigenfunctions of μt with small eigenvalues have only a very small component in the image of Π." We also show how to use a priori bounds on the solutions to the equation to obtain good control on the dependency of the bounds on the Malliavin matrix on the initial condition. These bounds are sufficient in many cases to obtain the asymptotic strong Feller property introduced in [HM06]. One of the main novel technical tools is an almost sure bound from below on the size of "Wiener polynomials," where the coefficients are possibly non-adapted stochastic processes satisfying a Lips chitz condition. By exploiting the polynomial structure of the equations, this result can be used to replace Norris' lemma, which is unavailable in the present context. We conclude by showing that the two-dimensional stochastic Navier-Stokes equations and a large class of reaction-diffusion equations fit the framework of our theory.

On the modelling of the thermal interactions between a spray curtain and an impinging cold gas cloud

A mixed Lagrangian-Eulerian model of a Water Curtain barrier is presented. The heat, mass and momentum processes are modelled in a Lagrangian framework for the dispersed phase and in an Eulerian framework for the carrier phase. The derivation of the coupling source terms is illustrated with reference to a given carrier phase cell. The turbulent character of the flow is treated with a single equation model, modified to directly account for the influence of the particles on the flow. The model is implemented in the form of a 2 D incompressible Navier Stokes solver, coupled to an adaptive Rung Kutta method for the Lagrangian sub-system. Simulations of a free standing full cone water spray show satisfactory agreement with experiment. Predictions of a Water Curtain barrier impacted by a cold gas cloud point to markedly different flow fields for the upward and downward configurations, which could influence the effectiveness of chemical absorption in the liquid phase.

A domain decomposition algorithm for viscous/inviscid coupling

In fluid mechanics, it is well accepted that the Euler equation is one of the reduced forms of the Navier-Stokes equation by truncating the viscous effect. There are other truncation techniques currently being used in order to truncate the Navier-Stokes equation to a reduced form. This paper describes one such technique, suitable for adaptive domain decomposition methods for the solution of viscous flow problems. The physical domain of a viscous flow problem is partitioned into viscous and inviscid subdomains without overlapping regions, and the technique is embedded into a finite volume method. Some numerical results are provided for a flat plate and the NACA0012 aerofoil. Issues related to distributed computing are discussed.

A semi-Lagrangian finite volume method for Newtonian contraction flows

A new finite volume method for solving the incompressible Navier--Stokes equations is presented. The main features of this method are the location of the velocity components and pressure on different staggered grids and a semi-Lagrangian method for the treatment of convection. An interpolation procedure based on area-weighting is used for the convection part of the computation. The method is applied to flow through a constricted channel, and results are obtained for Reynolds numbers, based on half the flow rate, up to 1000. The behavior of the vortex in the salient corner is investigated qualitatively and quantitatively, and excellent agreement is found with the numerical results of Dennis and Smith [Proc. Roy. Soc. London A, 372 (1980), pp. 393-414] and the asymptotic theory of Smith [J. Fluid Mech., 90 (1979), pp. 725-754].