三维非结构聚合多重网格法数值模拟研究

在三维非结构网格上应用聚合式多重网格技术来加速Euler方程的收敛过程．自行设计了一种高效率的网格聚合方法．采用四重三维非结构网格，在每一层网格上采用有限体积法进行计算．通过对M6翼型的数值求解验证了多重网格加速收敛的高效性．     

数值模拟过冷水滴撞击翼型表面的收集特性

为了研究过冷水滴撞击翼型表面的收集特性,本文采用欧拉两相流法建立了气流控制方程和水滴运动控制方程,并采用有限体积法对方程进行了求解。为了使水滴体积分数在数值迭代过程中保持为正值,本文在水滴控制方程中引入了一个变量A,使得迭代过程更加平稳。求解水滴控制方程,并得到了翼型表面的水滴收集特性。对过冷水滴撞击翼型表面的收集特性进行了研究,在平均水滴直径不同的情况下,将单尺寸分布与多尺寸分布情况下的局部收集系数进行了对比;发现:局部收集系数在驻点附近比较一致,随着离驻点的距离越来越大,局部收集系数产生偏差;多尺寸分布的水滴撞击极限远大于单尺寸下的计算值。同时本文还讨论了过冷水滴的大小对局部水收集系数和撞击极限的影响,发现平均水滴直径越大,局部水滴收集系数和撞击区域越大。     

非稳态沙波纹流场的数值模拟

风成沙波纹是沙质地表在风力作用下形成的最基本的地貌类型.本文研究了沙波纹在形成过程中,风场对波纹的形态变化的响应.采用目前比较流行的有限体积法,通过求解非稳态情况下的Navier-Stokes方程来计算风场;地表形态采用阶梯网格进行逼近,为了对地表形态变化进行有效的控制,根据相关参数采用正弦函数作为沙波纹的基本形状;最后根据计算结果详细讨论了沙波纹从形成到稳定的发展过程中地表流场的行为变化特征.     

连续分层海洋中内波传播的一种数值模式

基于Euler方程,使用有限体积法建立了一种密度为连续分层情况下、适应水深变化的水域中内波传播的数值模式.为了使计算格式能够达到二阶精度,对流项的处理使用了TVD (total variation diminishing)格式.将SIMPLE算法引入连续分层海洋中内波的数值计算,为了简化计算并方便地适应多种TVD格式,在计算预估速度场时采用了显式格式,而没有采用传统的隐式格式;鉴于在原始的SIMPLE算法中没有涉及到由于密度扰动而引起的静水压力场的改变问题,给出了该问题的计算方法.因此改进了SIMPLE算法.出流边界的处理采用阻尼消波和Sommerfeld辐射条件相结合的方式,以使内波得到有效的衰减和释放.将等水深水域的数值解和理论解进行了比较,两者吻合较好;并对存在潜堤时数值计算的不同时刻密度变化的空间分布进行了详细的定性分析.计算结果表明,所建立的数值模式能有效地模拟内波的传播和变形.      

关于椭圆接触弹流润滑Hamrock-Dowson膜厚公式的再思考

使用常用的Hamrock-Dowson公式计算椭圆点接触中心油膜厚度时发现:当维持接触区中心赫兹压力为常数,增加椭圆比k_e超过一定值时,得到的中心膜厚不升反降,这与其物理本质相悖. 应用有限单元法重新对等温椭圆接触弹流润滑问题进行了数值计算,提出新的表征椭圆接触的综合几何参数. 在较大的速度和载荷范围内下,依据数值计算结果,拟合出修正端泄因子和修正中心膜厚公式. 修正公式与数值计算结果相吻合,且正确地表达了膜厚与椭圆比的关系.      

基于SIMPLER算法的多重网格方法研究

以二维方腔顶盖驱动流为模型,将多重网格方法和SIMPLER算法进行耦合,对不同雷诺数下多重网格加速SIMPLER算法和SIMPLER算法的计算效率进行了对比,数值计算表明:多重网格加速SIMPLER算法不仅能够解决SIMPLER算法不能准确模拟较高雷诺数流场的问题,而且其计算效率远远高于SIMPLER算法.本文也对松弛因子的选取、多重网格实现形式以及网格层数对多重网格加速SIMPLER算法的影响进行了研究,从而为多重网格加速SIMPLER算法的实施提供了计算技术.     

翼型冰增长和结冰影响的数值模拟研究

翼面结冰是威胁飞行安全的重要因素之一.本文对于霜状结冰,在给定的结冰气候条件下,采用数值方法,预测整个结冰过程,建立冰增长模型,求解水滴轨迹运动方程,分析结冰过程中翼型绕流流场的变化,以及冰层的发展和形成过程.针对给定的三种不同冰型,即钝头型、尖头型和双角型,进一步采用结构化网格生成技术,结合中心有限体积法和LU-SGS隐式算法,利用B-L代数湍流模型,完成了绕流流场的N-S方程数值模拟,分析不同形状的冰型对翼型绕流及气动特性的影响.计算结果与试验数据进行了对比,表明采用的方法是正确、可行的.     

非结构混合网格高超声速绕流与磁场干扰数值模拟

对均匀磁场干扰下的二维钝头体无粘高超声速流场进行了基于非结构混合网格的数值模拟.受磁流体力学方程组高度非线性的影响及考虑到数值模拟格式的精度,目前在此类流场的数值模拟中大多使用结构网格及有限差分方法,因而在三维复杂外形及复杂流场方面的研究受到限制.本文主要探索使用非结构网格(含混合网格)技术时的数值模拟方法.控制方程为耦合了Maxwell方程及无粘流体力学方程的磁流体力学方程组,数值离散格式采用Jameson有限体积格心格式,5步Runge-Kutta显式时间推进.计算模型为二维钝头体,初始磁场均匀分布.对不同磁感应强度影响下的高超声速流场进行了数值模拟,并与有限的资料进行了对比,得到了较符合的结果.     

供油温度对润滑状态影响的试验观察与数值模拟

采用球-盘点接触光干涉润滑油膜测量装置,观察了不同供油温度下的接触区润滑状态.结果表明,随着供油温度的升高,润滑油黏度降低,润滑油成膜能力整体下降,接触区润滑状态在较大速度范围内处于边界润滑和混合润滑区间;温度升高还将导致膜厚曲线斜率增大,壁面温差是其诱因,通过数值模拟证实了壁面温差的影响;速度增加使接触区润滑状态向等黏度-刚性区间转化;温度和载荷使接触区润滑状态趋向于压黏-弹性区间.系统散热也会对油膜厚度产生影响.     

床面上直立圆柱的三维湍流数值模拟

从数值预报桥墩等结构物床面局部冲刷的角度发展绕直立圆柱的三维湍流的数值模拟技术. 基于Wilcox的k-ω两方程湍流模式，采用基于有限体积法的压力修正SIMPLE算法, 计算了绕床面直立圆柱的三维湍流流场，分析了光滑和粗糙床面两种情况下的流动情况. 通过系列的验证计算，表明该计算模型能够比较准确地反映不同外来流条件下绕直立圆柱的流场. 计算结果揭示了床面粗糙度对绕圆柱的湍流流动的影响.     

Numerical studies of the fingering phenomena for the thin film equation

We present a new interpretation of the fingering phenomena of the thin liquid film layer through numerical investigations. The governing partial differential equation is h_t + (h²?h³)_x = ??·(h³?Δh), which arises in the context of thin liquid films driven by a thermal gradient with a counteracting gravitational force, where h = h(x, y, t) is the liquid film height. A robust and accurate finite difference method is developed for the thin liquid film equation. For the advection part (h²?h³)_x, we use an implicit essentially non‐oscillatory (ENO)‐type scheme and get a good stability property. For the diffusion part ??·(h³?Δh), we use an implicit Euler's method. The resulting nonlinear discrete system is solved by an efficient nonlinear multigrid method. Numerical experiments indicate that higher the film thickness, the faster the film front evolves. The concave front has higher film thickness than the convex front. Therefore, the concave front has higher speed than the convex front and this leads to the fingering phenomena. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical simulation of flow in Hartmann resonance tube and flow in ultrasonic gas atomizer

The gas flow in the Hartmann resonance tube is numerically investigated by the finite volume method based on the Roe solver.The oscillation of the flow is studied with the presence of a needle actuator set along the nozzle axis.Numerical results agree well with the theoretical and experimental results available.Numerical results indicate that the resonance mode of the resonance tube will switch by means of removing or adding the actuator.The gas flow in the ultrasonic gas atomization (USGA) nozzle is also studied by the same numerical methods.Oscillation caused by the Hartmann resonance tube structure,coupled with a secondary resonator,in the USGA nozzle is investigated.Effects of the variation of parameters on the oscillation are studied.The mechanism of the transition of subsonic flow to supersonic flow in the USGA nozzle is also discussed based on numerical results.     

Robust design and numerical simulation on drag reduction by a mixture film for liquid turbulence in a channel

An important way of increasing the speed and lowering the fuel consumption of ships is by decreasing the frictional drag. One of the most promising techniques for reducing drag is the use of air bubbles. The goal of this investigation is to establish a set of optimum robust parametric levels for drag reduction by a mixture (air–water) film in turbulent channel flow. Based on the conditions laid out by the Taguchi orthogonal array method, turbulent flows, with air bubbles injected into a channel, are simulated using commercial computational fluid dynamics software. The local shear stress on the upper wall is computed to evaluate the efficiency of drag reduction. Many factors can affect drag reduction. The factors investigated in this study are the rate of air injection, bubble size, area of air injection, flow speed, and measured position of the shear stress. These factors have been investigated through the analysis of variance, which has revealed that the rate of air injection and water flow speed dominate the efficiency of drag reduction by a mixture film. According to the results, the drag can be reduced by an average of 83.4%; and when the configuration of the parametric levels is optimum the maximum drag reduction of 88.5% is achieved. Copyright © 2008 John Wiley & Sons, Ltd.     

Efficient simulation of multidimensional continuum and non-continuum flows by a parallelised unified gas kinetic scheme solver

We develop an efficient, parallel, gas-kinetic solver for computing both continuum and non-continuum flows over non-Cartesian geometries by utilising the unified gas kinetic scheme (UGKS). UGKS, however, requires the computationally expensive update of a six-dimensional phase space at each time step restricting its application to canonical, laminar problems and simple geometries. In this paper, we demonstrate that the applications of UGKS can be increased by parallelising it and combining it with a recently developed, Cartesian grid method (UGKS-CGM). We demonstrate that our Cartesian grid methodology as well as UGKS parallelization perform and scale well on a range of numerical test cases even for a very large number of cores. Finally, we demonstrate that the solver accurately computes canonical turbulence at low Knudsen numbers. These results demonstrate that the parallelised UGKS code can be utilised to effectively study the non-equilibrium effects of rarefaction on laminar and turbulent non-continuum flows.     

Numerical simulation of free‐surface flow using the level‐set method with global mass correction

A new numerical method that couples the incompressible Navier–Stokes equations with the global mass correction level‐set method for simulating fluid problems with free surfaces and interfaces is presented in this paper. The finite volume method is used to discretize Navier–Stokes equations with the two‐step projection method on a staggered Cartesian grid. The free‐surface flow problem is solved on a fixed grid in which the free surface is captured by the zero level set. Mass conservation is improved significantly by applying a global mass correction scheme, in a novel combination with third‐order essentially non‐oscillatory schemes and a five stage Runge–Kutta method, to accomplish advection and re‐distancing of the level‐set function. The coupled solver is applied to simulate interface change and flow field in four benchmark test cases: (1) shear flow; (2) dam break; (3) travelling and reflection of solitary wave and (4) solitary wave over a submerged object. The computational results are in excellent agreement with theoretical predictions, experimental data and previous numerical simulations using a RANS‐VOF method. The simulations reveal some interesting free‐surface phenomena such as the free‐surface vortices, air entrapment and wave deformation over a submerged object. Copyright © 2009 John Wiley & Sons, Ltd.     

A Stokes model with cavitation for the numerical simulation of hydrodynamic lubrication

We present a cavitation model based on the Stokes equation and formulate adaptive finite element methods for its numerical solution. A posteriori error estimates and adaptive algorithms are derived, and numerical examples illustrating the theory are supplied, in particular with comparison to the simplified Reynolds model of lubrication. Copyright © 2010 John Wiley & Sons, Ltd.     

气体速度对液膜在预膜板表面流动形态影响的LBM模拟

为了探究气流剪切作用对航空燃油在气动雾化喷嘴预膜板上流动形态的影响,首先对基于相场理论的两相流格子Boltzmann模型进行修正,并通过经典算例验证了修正后模型的准确性和可靠性.随后利用该模型模拟了同向气流驱动下液膜在水平预膜板表面上的流动,分析了气流速度对液膜流动形态的影响规律.研究表明,该模型可准确追踪具有大密度比...     

Development of an efficient numerical model for hail impact simulation based on experimental data obtained from pressure sensitive film

Aircraft are subjects to a number of unpredictable loadings that can seriously affect their performance. In the spirit of ever increasing the safety of passengers, hail impact has been studied. This paper shows the progress that has been made using pressure sensitive film to measure the hail impact event. Moreover, the smooth particle hydrodynamics (SPH) method in LS-DYNA is used to create a numerical model in order to validate the numerical hail model so that it can be used in future advanced simulations of hail impact on components of aircraft. Results show that the SPH method can be effectively used to create a numerical hail model and that pressure sensitive film is a simple and inexpensive tool to capture the experimental data.     

A parallel monolithic algorithm for the numerical simulation of large‐scale fluid structure interaction problems

A novel parallel monolithic algorithm has been developed for the numerical simulation of large‐scale fluid structure interaction problems. The governing incompressible Navier–Stokes equations for the fluid domain are discretized using the arbitrary Lagrangian–Eulerian formulation‐based side‐centered unstructured finite volume method. The deformation of the solid domain is governed by the constitutive laws for the nonlinear Saint Venant–Kirchhoff material, and the classical Galerkin finite element method is used to discretize the governing equations in a Lagrangian frame. A special attention is given to construct an algorithm with exact total fluid volume conservation while obeying both the global and the local discrete geometric conservation law. The resulting large‐scale algebraic nonlinear equations are multiplied with an upper triangular right preconditioner that results in a scaled discrete Laplacian instead of a zero block in the original system. Then, a one‐level restricted additive Schwarz preconditioner with a block‐incomplete factorization within each partitioned sub‐domains is utilized for the modified system. The accuracy and performance of the proposed algorithm are verified for the several benchmark problems including a pressure pulse in a flexible circular tube, a flag interacting with an incompressible viscous flow, and so on. John Wiley & Sons, Ltd.     

A non‐iterative implicit algorithm for the solution of advection–diffusion equation on a sphere

A numerical algorithm for the solution of advection–diffusion equation on the surface of a sphere is suggested. The velocity field on a sphere is assumed to be known and non‐divergent. The discretization of advection–diffusion equation in space is carried out with the help of the finite volume method, and the Gauss theorem is applied to each grid cell. For the discretization in time, the symmetrized double‐cycle componentwise splitting method and the Crank–Nicolson scheme are used. The numerical scheme is of second order approximation in space and time, correctly describes the balance of mass of substance in the forced and dissipative discrete system and is unconditionally stable. In the absence of external forcing and dissipation, the total mass and L₂‐norm of solution of discrete system is conserved in time. The one‐dimensional periodic problems arising at splitting in the longitudinal direction are solved with Sherman–Morrison's formula and Thomas's algorithm. The one‐dimensional problems arising at splitting in the latitudinal direction are solved by the bordering method that requires a prior determination of the solution at the poles. The resulting linear systems have tridiagonal matrices and are solved by Thomas's algorithm. The suggested method is direct (without iterations) and rapid in realization. It can also be applied to linear and nonlinear diffusion problems, some elliptic problems and adjoint advection–diffusion problems on a sphere. Copyright © 2015 John Wiley & Sons, Ltd.