高密度和高粘度比率下气液两相流动的数值模拟

本文在VOF方法的基础上,采用粗细两套网格对高密度和高粘度比率下的气液两相流动模拟进行了研究分析.在细网格中求解流体体积函数方程,在粗网格中采用交错网格求解动量方程和压力修正方程,通过粗细网格间的数据传递获得求解动量方程时需要的准确的界面密度和粘度及控制体密度,克服了高密度和高粘度比率下通过插值方法计算界面密度和粘度及控制体密度带来较大误差的困难,保证了质量和动量同时守恒.高密度和高粘度比率下气液两相流动中气液交界面处密度、速度和压力急剧变化,为了保证格式的有界性和稳定性,采用稳定的有界高阶组合格式STOIC.最后模拟了不同工况下气泡在液体中的运动,并通过实验和模拟结果验证了方法的可行性及准确性.     

运动激波和气泡串相互作用的初步数值模拟

通过对激波和流体界面相互作用诱导的大变形界面演化的数值模拟,验证Level set方法精确模拟多个流体界面的有效性.采用2阶迎风TVD求解欧拉方程得到流场解,采用5阶WENO求解Level set方程追踪多流体界面,采用GFM方法处理流体内界面.利用文[1]的计算结果校核本文程序.在此基础上,对运动激波和气泡串相互作用过程进行了初步数值模拟,得到了不同时刻运动激波和圆管内的两个气泡作用后的演化图象,包括压力和密度等值线分布.计算结果表明:针对推广后的多界面Level set方程,该方法仍可高质量地捕捉多个流体界面.     

具有复杂界面的三维弹性液滴动力学模拟

具有复杂界面特性(如界面弹性、界面抗弯特性等)的弹性液滴(如血液细胞)的动力学行为对理解血流等液滴群流动极其重要。本文采用界面追踪法(Front tracking method)捕捉界面演变,界面有限元考虑界面弹性和抗弯特性,有限差分法求解控制方程,发展了研究复杂界面液滴动力学的直接数值模拟方法。通过模拟球形弹性液滴的变形运动验证了该方法的准确性,进而研究了线性剪切流场中弹性液滴的坦克履带式、摇摆式和翻滚式运动。     

完全变光滑长度SPH法及其实现

提出完全变光滑长度SPH法及其算法实现.方程组基于对称形式核函数近似,SPH密度演化方程与变光滑长度方程隐式关联;在Springel提出的全守恒SPH方程组基础上,通过将分散核近似形式改进为对称核近似形式得到SPH动量方程和能量方程.采用迭代求解密度演化方程和变光滑长度方程,显式求解SPH动量方程和能量方程,增加的计算量相对很少.给出三个1D激波管算例和2D Sedov算例验证方法的有效性.数值结果表明,算法保持动量和能量的守恒律,解决了传统SPH法中由于变光滑长度影响带来的计算误差,且在模拟2DSedov问题时能得到比Springel方法更准确的压强峰值位置和中心压强值.特别适合于模拟爆炸与冲击、大变形大扭曲等密度梯度和光滑长度梯度剧烈变化的问题.     

基于元胞自动机的气动光学光线追迹算法

对于含激波等大密度脉动结构气动光学流场,沿着直线路径对折射率积分会带来较大的光程误差.因此,数值求解光线方程进行光线追迹是必要的.与数值求解光线方程不同,元胞自动机(cellular automata,CA)通过给定光线位置和方向变换规则来模拟光线在介质中传输路径.本文基于已有的实验测量、数值仿真所获得的高超声速流场密度场数据,分别采用数值求解光线方程法和CA光线追迹算法进行光线追迹,进而得到光线出射流场后的光程差.结果表明, CA算法对于二维气动光学流场中光线追迹的适用性,且较数值求解光线方程方法具有更高的效率.     

凝固前沿和气泡相互作用的大密度比格子玻尔兹曼方法模拟

建立了二维双组分两相流的大密度比格子玻尔兹曼方法 (lattice Boltzmann method, LBM)模型. 该模型基于改进的Shan-Chen伪势多相流LBM模型, 结合采用不同时间步长的方法, 实现密度比达800以上的气液两相流模拟. 为了对模型进行验证, 模拟了在不同气液相互作用系数和密度比条件下气泡内外压力差与其半径之间的关系, 其结果满足Laplace定律. 将所建立的大密度比LBM与介观尺度的元胞自动机(cellular automaton, CA)和有限差分法(FDM)相耦合, 用LBM模拟气液两相流, 用CA方法模拟固相生长, 用有限差分法模拟温度场, 采用LBM-CA-FDM耦合模型对定向凝固过程中凝固前沿的气泡与液-固界面之间的相互作用进行模拟研究. 结果表明, 绝热气泡的存在影响了温度场分布, 使得凝固前沿接近气泡时, 液-固界面凸起, 在不同的固相生长速度条件下, 出现凝固前沿淹没气泡或气泡脱离凝固前沿的不同情况, 模拟结果与实验结果符合良好. 关键词： 格子玻尔兹曼方法 元胞自动机 凝固 气泡     

反场构型等离子体中Grad-Shafranov方程的数值解

基于反场构型(field-reversed configuration)渐近理论,编写了反场构型等离子体中二维Grad-Shafranov方程的数值模拟代码,研究了不同拉长形状的反场构型剖面.通过模拟,得到了磁面坐标系中反场构型等离子体压强及梯度分布,同时求解了大拉长比、不同分界面(separatrix)类型的磁通量分布.研究结果表明,等离子体压强梯度随着磁通量呈线性增长,在分界面处发生突变;分界面处的等离子体压强越高,分界面内部的压强会更高,即具有更高的等离子体β值,反映了反场构型较好的约束效果.     

界面捕捉Level Set方法的(AMR)数值模拟

在流体力学方程的计算中采用高精度WENO格式,用AMR(adaptive mesh refinement)方法提高流场局部分辨率,在采用Level Set函数标定物质界面的计算中用GFM(ghost fluid method)方法进行界面处理,尝试将AMR技术与界面追踪技术相互融合并应用于数值模拟,对不同的模拟结果进行了比较.     

气液两相流的间断有限元模拟

基于非结构网格,给出模拟两相流的统一间断有限元框架.其中,不可压Navier-Stokes方程采用IPDG(Interior penalty discontinuous Galerkin)方法求解;Level Set方程采用RKDG(Runge-Kutta discontinuous Galerkin)方法求解.方腔驱动流在不同Re数时的数值结果验证了该方法在单相流动中的有效性.气泡上升过程的模拟结果表明:该方法避免了重新初始化,且计算量小、实施简单,可有效求解具有运动界面的不可压两相流问题.     

耦合辐射的三维热化学非平衡流数值模拟

发展耦合辐射的三维热化学非平衡流场计算方法,可用于非结构网格.采用Jameson有限体积法求解耦合辐射源项的三维N-S方程.辐射源项通过求解辐射输运方程(Radiative Transport Equation RTE)获得.在空间方向上离散后,采用有限体积法求解辐射输运方程.化学模型包含11个组元,20个化学反应.采用该数值方法计算MUSES-C模型在速度为11.6 km·s^-1时的绕流流场及前驻点处的辐射热流密度.并通过对比,分析热辐射对流场的影响.     

A subgrid computation of the curvature by a particle/level-set method. Application to a front-tracking/ghost-fluid method for incompressible flows

A particle/level-set method is developed to capture the interface between two immiscible phases. No redistance equation is used for the level-set function which is built from an accurate cubic spline interpolation of the markers describing the interface. Mass losses which usually appear with level-set functions are drastically reduced. Interface coupling with the incompressible momentum equation is taken into account thanks to the ghost-fluid method. Indeed, the particles allow an accurate computation of the local interfacial curvatures, and the capillary part of the pressure jump computed across the interface is more accurately evaluated. Results on static drop show a large decrease of spurious currents compared to other methods. Scalar advection validations and convergence studies are carried out as well as tough test-cases involving large density ratios (typically air/water). A better agreement with literature results is shown compared to classical approaches.     

A time-stepping scheme involving constant coefficient matrices for phase-field simulations of two-phase incompressible flows with large density ratios

We present an efficient time-stepping scheme for simulations of the coupled Navier–Stokes Cahn–Hilliard equations for the phase field approach. The scheme has several attractive characteristics: (i) it is suitable for large density ratios, and numerical experiments with density ratios up to 1000 have been presented; (ii) it involves only constant (time-independent) coefficient matrices for all flow variables, which can be pre-computed during pre-processing, so it effectively overcomes the performance bottleneck induced by variable coefficient matrices associated with the variable density and variable viscosity; (iii) it completely de-couples the computations of the velocity, pressure, and the phase field function. Strategy for spectral-element type spatial discretizations to overcome the difficulty associated with the large spatial order of the Cahn–Hilliard equation is also discussed. Ample numerical simulations demonstrate that the current algorithm, together with the Navier–Stokes Cahn–Hilliard phase field approach, is an efficient and effective method for studying two-phase flows involving large density ratios, moving contact lines, and interfacial topology changes.     

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.     

基于局部加密纯无网格法非线性Cahn-Hilliard方程的模拟

为数值求解描述不同物质间相位分离现象的高阶非线性Cahn-Hilliard(C-H)方程,发展了一种基于局部加密纯无网格有限点集法(local refinement finite pointset method,LR-FPM).其构造过程为:1)将C-H方程中四阶导数降阶为两个二阶导数,连续应用基于Taylor展开和加权最小二乘法的FPM离散空间导数;2)对区域进行局部加密和采用五次样条核函数以提高数值精度;3)局部线性方程组求解中准确施加含高阶导数Neumann边值条件.随后,运用LR-FPM求解有解析解的一维/二维C-H方程,分析粒子均匀分布/非均匀分布以及局部粒子加密情况的误差和收敛阶,展示了LR-FPM较网格类算法在非均匀布点情况下的优点.最后,采用LR-FPM对无解析解的一维/二维C-H方程进行了数值预测,并与有限差分结果相比较.数值结果表明,LR-FPM方法具有较高的数值精度和收敛阶,比有限差分法更易数值实现,能够准确展现不同类型材料间相位分离非线性扩散现象随时间的演化过程.     

A multicomponent multiphase lattice Boltzmann model with large liquid–gas density ratios for simulations of wetting phenomena

A multicomponent multiphase(MCMP) pseudopotential lattice Boltzmann(LB) model with large liquid–gas density ratios is proposed for simulating the wetting phenomena. In the proposed model, two layers of neighboring nodes are adopted to calculate the fluid–fluid cohesion force with higher isotropy order. In addition, the different-time-step method is employed to calculate the processes of particle propagation and collision for the two fluid components with a large pseudoparticle mass contrast. It is found that the spurious current is remarkably reduced by employing the higher isotropy order calculation of the fluid–fluid cohesion force. The maximum spurious current appearing at the phase interfaces is evidently influenced by the magnitudes of fluid–fluid and fluid–solid interaction strengths, but weakly affected by the time step ratio.The density ratio analyses show that the liquid–gas density ratio is dependent on both the fluid–fluid interaction strength and the time step ratio. For the liquid–gas flow simulations without solid phase, the maximum liquid–gas density ratio achieved by the present model is higher than 1000:1. However, the obtainable maximum liquid–gas density ratio in the solid–liquid–gas system is lower. Wetting phenomena of droplets contacting smooth/rough solid surfaces and the dynamic process of liquid movement in a capillary tube are simulated to validate the proposed model in different solid–liquid–gas coexisting systems. It is shown that the simulated intrinsic contact angles of droplets on smooth surfaces are in good agreement with those predicted by the constructed LB formula that is related to Young's equation. The apparent contact angles of droplets on rough surfaces compare reasonably well with the predictions of Cassie's law. For the simulation of liquid movement in a capillary tube, the linear relation between the liquid–gas interface position and simulation time is observed, which is identical to the analytical prediction. The simulation results regarding the wetting phenomena of droplets on smooth/rough surfaces and the dynamic process of liquid movement in the capillary tube demonstrate the quantitative capability of the proposed model.     

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).     

Enhanced interface properties of diamond MOSFETs with Al_2O_3 gate dielectric deposited via ALD at a high temperature

The interface state of hydrogen-terminated(C–H) diamond metal–oxide–semiconductor field-effect transistor(MOSFET) is critical for device performance. In this paper, we investigate the fixed charges and interface trap states in C–H diamond MOSFETs by using different gate dielectric processes. The devices use Al_2O_3 as gate dielectrics that are deposited via atomic layer deposition(ALD) at 80℃ and 300℃, respectively, and their C–V and I–V characteristics are comparatively investigated. Mott–Schottky plots(1/C~2–VG) suggest that positive and negative fixed charges with low density of about 1011 cm~(-2) are located in the 80-℃-and 300-℃ deposition Al_2O_3 films, respectively. The analyses of direct current(DC)/pulsed I–V and frequency-dependent conductance show that the shallow interface traps(0.46 e V–0.52 e V and0.53 e V–0.56 e V above the valence band of diamond for the 80-℃ and 300-℃ deposition conditions, respectively) with distinct density(7.8 × 10~(13) e V~(-1)·cm~(-2)–8.5 × 10~(13) e V-1·cm~(-2) and 2.2 × 1013 e V~(-1)·cm~(-2)–5.1 × 10~(13) e V~(-1)·cm~(-2) for the80-℃-and 300-℃-deposition conditions, respectively) are present at the Al_2O_3/C–H diamond interface. Dynamic pulsed I–V and capacitance dispersion results indicate that the ALD Al_2O_3 technique with 300-℃ deposition temperature has higher stability for C–H diamond MOSFETs.     

信息保存方法在微尺度变温流场中的应用研究

在信息保存法(IP)方法的基础上，提出了一个简单易行的温度模型，该模型可以有效模拟计算有温度变化的流动.此外研究发现，在用IP方法模拟计算的流场局部密度变化很大时，如果采用质量守恒方程的二阶中心差分格式更新信息密度时会使计算发散，因此建议采用一阶迎风格式更新信息密度. 关键词： IP方法 低速流动 微尺度 变温流动     

The importance of self-consistency in determining interface properties of SIN and DIN structures

We develop a method to solve the Bogoliubov–de Gennes equation for superconductors self-consistently, using the recursion method. The method allows the pairing interaction to be either local or nonlocal corresponding to s-and d-wave superconductivity, respectively. Using this method, we examine the properties of various SIN and DIN interfaces. In particular, we self-consistently calculate the spatially varying density of states and the superconducting order parameter. We see that changing the strength of the insulating barrier at the interface, does not, in the case of an s-wave superconductor, dramatically change the low-energy local density of states in the superconducting region near the interface. This is in stark contrast to what we see in the case of a DIN interface where the local particle density of states is changed dramatically. Hence we deduce that in calculating such properties as the conductance of SIN and DIN structures it is far more important to carry out self-consistent calculations in the d-wave case.