纳米颗粒多相流体动力学研究及应用

纳米颗粒多相流研究是目前多相流研究中新的研究方向及重点发展领域.为探索纳米尺度多相流相间作用机理及内部存在机制,采用理论分析及数值计算手段,对一般动力学方程的封闭处理、颗粒碰撞率宏观模型的有效构建、颗粒凝并系统动力学演变特性的机理分析、非稀相问题碰撞率的求取、双变量问题求解方法的建立以及一些实际应用进行了系统研究,提出了新的针对纳米尺度颗粒动力学演变的一般动力学方程求解方法,并将其应用于实际工业过程问题的研究.该文对上述研究工作进行了综述.     

发育生物学中模式形成的力学模型

对所有多细胞生物体而言,其个体发育均涉及由初始的单个细胞开始,经过在时间和空间上细胞有序地增殖、凋亡、分化、迁移等诸多过程,并最终生成物种特异的生物模式.对模式形成的机制的探讨一直是发育生物学的中心课题.目前已就这个问题积累了大量的分子生物学、生物化学、数学、力学等多学科的研究数据并提出了一些模式形成的理论,然而,迄今为止,模式形成的真正机制仍然很不清楚而需进一步的深入探索.本文简要介绍了生物发育过程中模式形成的一些典型的力学模型,重点在于力学模型的建立及其模型本身的介绍,而对其数值模拟和具体应用很少涉及.      

雾层两相耦合流场及气溶胶颗粒物的动力学性质

雾层气溶胶系统涉及复杂的动力学演变过程:碰撞、凝并、破碎、冷凝/蒸发、成核、沉积、表面化学反应等.因此,发展雾层与气相流场耦合的Eulerian-Lagrangian两相流模型、颗粒动力学及随机轨道模型,考虑重力、曳力、布朗力、Basset力等对颗粒相的作用.基于SIMPLE和多重Monte Carlo算法求解颗粒群平衡方程,自行开发了FAD程序首先对室内燃烧源细微颗粒物的扩散实验展开数值模拟,计算结果与实验数据吻合较好.将建立的模型和方法数值研究气溶胶污染物在雾环境中的输运过程,分析雾消散阶段颗粒相浓度、平均尺度的时空分布.结果显示:当时间演化至60 min,雾滴的平均尺度减小到初始的65.67％,而气溶胶颗粒最大数目对应的尺度为0.006 μm.     

高速双锥绕流中热化学与输运模型影响研究

激波与边界层之间相互作用是高超声速飞行中的常见现象,对飞行器气动性能与飞行安全至关重要.对于高焓来流,流场中通常存在复杂的物理化学现象,此时准确模拟流场中激波边界层相互作用的难度大,相关物理化学建模仍有待进一步考察和研究.本文针对最近文献中纯净空气高超声速双锥绕流实验开展数值研究,分别研究了不同热化学模型与输运模型对壁面压力与热流的影响.热力学模型包括完全气体、热力学平衡和非平衡模型,化学模型包括冻结和非平衡化学模型,输运模型包括经典的Wilke/Blottner/Eucken模型与更加复杂的Gupta/SCEBD模型,以及考虑壁面催化/非催化影响的模型.计算了6个不同算例,涵盖了低焓至高焓来流等不同工况.壁面压力与热流的数值计算结果与实验结果符合较好;对于低焓来流,计算结果主要受到分子内能分布的影响,输运模型对计算结果的影响不大;对于高焓来流,一方面计算结果受到化学反应与壁面催化的影响较大,另一方面不同输运模型对计算结果的影响也更加明显.      

化学输运动力学过程的数学模型

本文从化学流体力学观点出发,对应用相当广泛的一类化学输运动力学过程进行了理论分析,建立了数学模型,求得了数学解.在此基础上,提出了化学输运动力学过程的等价单元系及生产作业序列的记忆效应等有实际意义的概念.     

高速双锥绕流中热化学与输运模型影响研究

激波与边界层之间相互作用是高超声速飞行中的常见现象,对飞行器气动性能与飞行安全至关重要.对于高焓来流,流场中通常存在复杂的物理化学现象,此时准确模拟流场中激波边界层相互作用的难度大,相关物理化学建模仍有待进一步考察和研究.本文针对最近文献中纯净空气高超声速双锥绕流实验开展数值研究,分别研究了不同热化学模型与输运模型对壁面压力与热流的影响.热力学模型包括完全气体、热力学平衡和非平衡模型,化学模型包括冻结和非平衡化学模型,输运模型包括经典的Wilke/Blottner/Eucken模型与更加复杂的Gupta/SCEBD模型,以及考虑壁面催化/非催化影响的模型.计算了6个不同算例,涵盖了低焓至高焓来流等不同工况.壁面压力与热流的数值计算结果与实验结果符合较好;对于低焓来流,计算结果主要受到分子内能分布的影响,输运模型对计算结果的影响不大;对于高焓来流,一方面计算结果受到化学反应与壁面催化的影响较大,另一方面不同输运模型对计算结果的影响也更加明显.     

颗粒介质固-流态转变的理论分析及实验研究

颗粒介质由大量离散的颗粒聚集而成,因而与传统固体和流体不同,运动过程中的颗粒介质中可能同时存在多种流态及其相互间复杂的转换过程. 颗粒介质弹性失稳机理、不可恢复应变量化是研究颗粒介质固态和流态及固-流态转变的关键. 在前期建立的双颗粒温度热力学(two-granular-temperature, TGT) 理论基础上,确定了颗粒介质的弹性稳定性条件,建立了不可恢复应变流动法则,搭建了描述颗粒固态-液态及其相互转化的简单模型. 颗粒堆积体坍塌过程是典型的颗粒介质固态和流态及其转变过程,因此本文首先开展了25 167 个陶颗粒堆积体坍塌过程的实验研究,并使用基于TGT 理论的物质点方法和离散元方法对物理实验进行了模拟. 结果表明,模型数值结果与物理实验在颗粒堆坍塌过程中的形态、速度分布等细节上吻合很好,同时也发现了现阶段所使用的物质点方法和TGT 理论的不足. 初步说明TGT 理论可以实现颗粒介质固态和流态,以及状态转变的描述.      

柔性微粒介电泳分离过程的多尺度模拟

介电泳分离是一种高效的微细颗粒分离技术,利用非均匀电场极化并操纵分离微流道中的颗粒. 柔性微粒在介电泳分离过程中同时受多种物理场、多相流和微粒变形等复杂因素的影响,仅用单一的计算方法对其进行模拟存在一定的难度,本文采用有限单元——格子玻尔兹曼耦合计算的方法处理这一难题.介观尺度的格子玻尔兹曼方法将流体看成由大量微小粒子组成,在离散格子上求解玻尔兹曼输运方程,易于处理多相流及大变形问题,特别适合模拟柔性颗粒在介电泳分离过程中的变形情况.另一方面,介电泳分离过程的模拟需求解流体、电场和微粒运动方程,计算量相当庞大,通过有限单元法求解介电泳力,提高计算效率.利用这种多尺度耦合计算方法,对一款现有的介电泳芯片分离过程进行了模拟.分析了微粒在电场作用下产生的介电泳力,揭示了介电泳力与电场变化率等因素之间的关系.对微粒运动轨迹及其变形的情况进行了研究,发现微粒的变形主要与流体剪切作用有关.这种多尺度耦合计算方法,为复杂微流体的计算提供了一种有效的解决方案.      

柔性微粒介电泳分离过程的多尺度模拟

介电泳分离是一种高效的微细颗粒分离技术,利用非均匀电场极化并操纵分离微流道中的颗粒.柔性微粒在介电泳分离过程中同时受多种物理场、多相流和微粒变形等复杂因素的影响,仅用单一的计算方法对其进行模拟存在一定的难度,本文采用有限单元-格子玻尔兹曼耦合计算的方法处理这一难题.介观尺度的格子玻尔兹曼方法将流体看成由大量微小粒子组成,在离散格子上求解玻尔兹曼输运方程,易于处理多相流及大变形问题,特别适合模拟柔性颗粒在介电泳分离过程中的变形情况.另一方面,介电泳分离过程的模拟需求解流体、电场和微粒运动方程,计算量相当庞大,通过有限单元法求解介电泳力,可提高计算效率.利用这种多尺度耦合计算方法,对一款现有的介电泳芯片分离过程进行了模拟.分析了微粒在电场作用下产生的介电泳力,揭示了介电泳力与电场变化率等因素之间的关系.对微粒运动轨迹及其变形的情况进行了研究,发现微粒的变形主要与流体剪切作用有关.这种多尺度耦合计算方法,为复杂微流体的计算提供了一种有效的解决方案.     

碳氢燃料超声速燃烧分区实验研究

高保真度空天发动机数值模拟通常基于快速化学反应火焰面假设,即超声速燃烧反应的特征尺度小于湍流Kolmgorov尺度,该模型方法对于氢气燃料仿真计算结果较好,但对于乙烯等碳氢燃料仍需进一步研究.受限于极端环境特种非接触测量技术,目前尚未见超声速燃烧火焰分区判别的实验研究,导致目前超声速燃烧火焰面模型适用性以及分区燃烧物理模型认识不清,进而也制约了数值发动机技术发展.本工作基于自主研发的MHz发动机内窥光纤传感器,针对单边扩张双模态冲压发动机超声速燃烧火焰分区开展实验研究,通过化学自发光信号的最小香农熵定义超声速燃烧的特征时间τsc,根据理论方法和来流工况估算了超声速燃烧的流动特征时间,结合分区燃烧理论分析了双模态超燃冲压发动机内碳氢燃料燃烧的分区情况.通过燃烧分区情况以及与泰勒尺度的比较结果,验证了碳氢燃料超燃冲压发动机典型飞行条件下燃烧室内超声速燃烧处于旋涡小火焰区域(Re?50 000; Da∈1.80～2.60, B区),多尺度湍流涡结构发挥重要作用,并随着相对于泰勒尺度的不同大小,分别对应了不同尺度的涡结构主导该过程.同时给出了当量比、通量比以及来流马赫数对燃烧特征时间的影响规律...     

An operator splitting algorithm for the three-dimensional advection–diffusion equation

Operator splitting algorithms are frequently used for solving the advection–diffusion equation, especially to deal with advection dominated transport problems. In this paper an operator splitting algorithm for the three-dimensional advection–diffusion equation is presented. The algorithm represents a second-order-accurate adaptation of the Holly and Preissmann scheme for three-dimensional problems. The governing equation is split into an advection equation and a diffusion equation, and they are solved by a backward method of characteristics and a finite element method, respectively. The Hermite interpolation function is used for interpolation of concentration in the advection step. The spatial gradients of concentration in the Hermite interpolation are obtained by solving equations for concentration gradients in the advection step. To make the composite algorithm efficient, only three equations for first-order concentration derivatives are solved in the diffusion step of computation. The higher-order spatial concentration gradients, necessary to advance the solution in a computational cycle, are obtained by numerical differentiations based on the available information. The simulation characteristics and accuracy of the proposed algorithm are demonstrated by several advection dominated transport problems. © 1998 John Wiley & Sons, Ltd.     

A higher-order eulerian scheme for coupled advection-diffusion transport

A new accurate high-order numerical method is presented for the coupled transport of a passive scalar (concentration) by advection and diffusion. Following the method of characteristics, the pure advection problem is first investigated. Interpolation of the concentration and its first derivative at the foot of the characteristic is carried out with a fifth-degree polynomial. The latter is constructed by using as information the concentration and its first and second derivatives at computational points on current time level t in Eulerian co-ordinates. The first derivative involved in the polynomial is transported by advection along the characteristic towards time level t + Δt in the same way as is the concentration itself. Second derivatives are obtained at the new time level t + Δt by solving a system of linear equations defined only by the concentrations and their derivatives at grid nodes, with the assumption that the third-order derivatives are continuous. The approximation of the method is of sixth order. The results are extended to coupled transport by advection and diffusion. Diffusion of the concentration takes place in parallel with advection along the characteristic. The applicability and precision of the method are demonstrated for the case of a Gaussian initial distribution of concentrations as well as for the case of a steep advancing concentration front. The results of the simulations are compared with analytical solutions and some existing methods.     

Heat exchanger design based on chaotic advection

Experiments on hydrodynamic and heat transfer behavior of the flow in a twisted curved channel were conducted in a water tunnel and also in two heat exchanger coils tested in a heat exchanger test facility. The flow regime, designated “chaotic advection,” is a subclass of laminar flow with high mixing properties. Preliminary results show that heat transfer is enhanced due to the chaotic trajectories generated in the flow.     

Gravity Affected Lateral Dispersion and Diffusion in a Stationary Horizontal Porous Medium Shear Flow

Transport of dissolved species by a carrier fluid in a porous medium comprises advection and diffusion/dispersion processes. Hydrodynamic dispersion is commonly characterized by an empirical relationship, in which the dispersion mechanism is described by contributions of molecular diffusion and mechanical dispersion expressed as a function of the molecular Peclét number. Mathematically these two phenomena are modeled by a constant diffusion coefficient and by velocity dependent dispersion coefficients, respectively. Here, the commonly utilized Bear--Scheidegger dispersion model of linear proportionality between mechanical dispersion and velocity, and the more complicated Bear--Bachmat model derived on a streamtube array model porous medium and better describing observed dispersion coefficients in the moderate molecular Peclét number range, will be considered. Analyzing the mixing flow of two parallelly flowing confluent fluids with different concentrations of a dissolved species within the frames of boundary layer theory one has to deal with transverse mixing only. With the Boussinesq approximation being adopted approximate analytical solutions of the corresponding boundary layer system of equations show that there is no effect of density coupling on concentration distributions across the mixing layer in the pure molecular diffusion regime case. With the Peclét number of the oncoming flow growing beyond unity, density coupling has an increasing influence on the mixing zone. When the Peclét number grows further this influence is successively reduced until its disappearance in the pure mechanical dispersion regime.     

Consistent and efficient particle tracking on curvilinear grids for environmental problems

Particle‐tracking models are often used for near field short‐term subgrid transport of substances. The consistency demand at the discrete level does not show up so dominantly for these applications. This demand refers to the use of a numerical advection scheme for particles that is fully compatible with the local mass conserving advection properties of the underlying flow field at the discrete level of that field. A noncompatible scheme will produce both local convergence and local divergence of particles in different parts of the model area and thus erroneous advection results and erroneous concentration patterns. This compatibility in particle tracking is especially important if smooth distributions over larger areas are modelled for longer times. These applications did not occur that often in the past because they require many particles and thus much computation time. These applications occur more frequently nowadays especially for environmental assessment such as for the modelling of transport of fish larvae growing during their journey in the model to juvenile stages. The advection scheme that is developed in this paper is shown to be exactly compatible with hydrodynamic flow fields computed by mass conserving curvilinear grid models. It is not only exact, it is fortunately also very simple to implement and fast, allowing for modelling a huge amount of particles with moderate computation time. Copyright © 2012 John Wiley & Sons, Ltd.     

Simulation of the Brownian coagulation of nanoparticles with initial bimodal size distribution via moment method

The Brownian coagulation of nanoparticles with initial bimodal size distribution, i.e., mode i and j, is numerically studied using the moment method. Evolutions of particle number concentration, geometric average diameter and geometric standard deviation are given in the free molecular regime, the continuum regime, the free molecular regime and transition regime, the free molecular regime and continuum regime, respectively. The results show that, both in the free molecular regime and the continuum regime, the number concentration of mode i and j decreases with increasing time. The evolutions of particle geometric average diameter with different initial size distribution are quite different. Both intra-modal and inter-modal coagulation finally make the polydispersed size distribution become monodispersed. As time goes by, the size distribution with initial bimodal turns to be unimodal and shifts to a larger particle size range. In the free molecular regime and transition regime, the inter-modal coagulation becomes dominant when the number concentrations of mode i and j are of the same order. The effects of the number concentration of mode i and mode j on the evolution of geometric average diameter of mode j are negligible, while the effects of the number concentration of mode j on the evolution of geometric average diameter of mode j is distinct. In the free molecular regime and continuum regime, the higher the initial number concentration of mode j, the more obvious the variation of the number concentration of mode i.     

Rigorous upscaling of the reactive flow with finite kinetics and under dominant Péclet number

We consider the evolution of a reactive soluble substance introduced into the Poiseuille flow in a slit channel. The reactive transport happens in presence of dominant Péclet and Damköhler numbers. We suppose Péclet numbers corresponding to Taylor’s dispersion regime. The two main results of the paper are the following. First, using the anisotropic perturbation technique, we derive rigorously an effective model for the enhanced diffusion. It contains memory effects and contributions to the effective diffusion and effective advection velocity, due to the flow and chemistry reaction regime. Error estimates for the approximation of the physical solution by the upscaled one are presented in the energy norms. Presence of an initial time boundary layer allows only a global error estimate in L ² with respect to space and time. We use the Laplace’s transform in time to get optimal estimates. Second, we explicit the retardation and memory effects of the adsorption/desorption reactions on the dispersive characteristics and show their importance. The chemistry influences directly the characteristic diffusion width.     

Two-dimensional adaptive Eulerian-Lagrangian method for mass transport with spatial velocity distribution

A Eulerian-Lagrangian scheme is used to solve the two-dimensional advection-dispersion equation. Concentration and its partial differential operator are decomposed into advection and dispersion terms. Thus, advection is formally decoupled from dispersion and solved by continuous forward particle tracking. Dispersion is handled by implicit finite elements on a fixed Eulerian grid. Translation of steep gradients of concentration in advection-dominated flow regimes, is done without numerical distortion. Continuous spatial distribution of velocities are evaluated by using Galerkin's approach in conjunction with Darcy's law based on hydraulic input data from each element. The method was implemented on coarse FE grid with linear shape functions, demonstrating no over/under shooting and practically no numerical dispersion. Simulations, covering a wide range of Peclet numbers, yield high agreement with analytic and practical results.     

A HYDRO-MECHANICAL-CHEMICAL COUPLING MODEL FOR GEOMATERIAL WITH BOTH MECHANICAL AND CHEMICAL DAMAGES CONSIDERED

A general framework of hydro-mechanical-chemical coupling model is proposed for geomaterial subjected to the dual effects of mechanical loading and chemical degradation. Mechanical damage due to microcracks in solid matrix and chemical damage induced by the increase of porosity due to dissolution of matrix minerals as well as their interactions are considered. A special model is proposed for sandstone. The reaction rate is formulated within the framework of mineral reaction kinetics and can thus take into account different dissolution mechanisms of three main mineral compositions under different pH values. The increase of porosity is physically defined by the dissolution of mineral composition and the chemical damage is related to the increase of porosity. The mechanical behavior is characterized by unified plastic damage and viscoplastic damage modeling. The effective stress is used for describing the effect of pore pressure. The elastic parameters and plastic evolution as well as viscoplastic evolution are dependent on chemical damage. The advection, which is coupled with mechanical damage and chemical damage, is considered as the dominant mechanism of mass transfer. The application of model proposed is from decoupled experiments to fully coupled experiment. The model offers a convenient approach to describing the hydro-mechanical-chemical coupled behavior of geomaterial.