格子Boltzmann亚格子模型的研究

为了将格子Boltzmann法应用于大雷诺数流动的模拟,本文将Smagorinsky亚格子模型和LBGK模型相结合,并对该亚格子LBM模型进行了研究。利用该亚格子LBM模型,对二维顶盖驱动流进行了模拟,得到了若干大雷诺数下流线图和方腔中心线上无量纲速度分布。计算结果与基准解进行比较,两者相互吻合。     

流函数Navier-Stokes方程的交替方向部分隐式和完全隐式解法

本文给出了数值求解以流函数表示的Navier-Stokes方程的交替方向部分隐式和交替方向完全隐式方法;作为算例,计算了低雷诺数的二维方腔流动问题,并与已知结果进行了比较。     

气体动力学直接模拟Monte Carlo的高效GPU并行计算

实现了基于计算统一设备架构(CUDA)的直接模拟Monte Carlo(DSMC)并行算法,改进了原有多图形处理器(GPU)数据之间传输并行算法,数值模拟计算二维Couette流和二维顶盖驱动方腔流,定量比较了CPU、单GPU和多GPU并行计算的结果和计算时间.结果表明单GPU并行计算相对CPU计算的加速效果可以达到10~30倍,双GPU并行计算加速效果可以达到40~60倍,多GPU并行计算的加速效率接近100%,且计算精度能够得到良好保证.     

具有径向进出流的转—静盘腔流动与换热的数值研究

本文对具有径向进出流的转－静盘腔结构的流动和传热过程进行了数值计算研究,文中研究了旋转雷诺数和无量纲流动速率对盘腔内流动换热过程的影响。在盘腔的核心区采用标准的κ－ε模型,近壁区采用Ｌａｕｎｄｅｒ－Ｓｈａｒｍａ低雷诺数ｋ－ε模型。与实验结果的对比表明本文的计算方法是合理的,计算结果揭示了该型盘腔结构的流动传热基本特征和规律。     

三维曲面腔顶盖驱动流的MRT-LBM研究

采用多松弛时间格子玻尔兹曼方法(MRT-LBM)的D3Q15模型分别对长方体腔、圆柱腔、半圆柱腔、旋转双曲面腔、旋转椭球面腔、半球腔以及两种组合腔体的三维顶盖驱动腔流进行数值模拟, 比较分析各腔体内流线分布、流速等值线分布和涡心的发展, 对于典型腔体模拟不同雷诺数下的流动情况。结果表明: 在同一雷诺数下, 曲面边界不仅能消除从边界产生的次涡, 还会导致腔内主涡的分离, 增大中心纵剖面纵向回流速度; “上长方体+下半圆柱”腔内流函数分布与边界贴合度最高。当雷诺数不断增大时, 半圆柱腔内主涡逐渐分离成两个同向涡, “上圆柱+下半球”腔内始终保持着圆柱腔与半球腔内的基本流动特征; 而长方体腔内主涡涡心保持在同一高度, 次涡逐渐增强, “上长方体+下半圆柱”腔内流动愈加规则, 主涡逐渐下沉, 流速等值线分布逐渐趋于中心小、四周大。     

ADI方法求解Navier-Stokes方程的一个改进格式

ADI方法常被用来计算不可压缩Navier-Stokes方程^[1]。在处理涡度方程的非线性项和涡度在壁面上的条件时,通常采用滞后的方法对涡度方程和流函数方程分别求解。然而,非线性项的滞后破坏了ADI方法的完全二阶精度;涡度方程和流函数方程分别求解减弱了两个方程的耦合性;涡度壁面条件的滞后则破坏了方法的完全隐式。本文在应用ADI方法求解涡度方程和流函数方程时应用了一种交替线性化的技术,对涡度方程和流函数方程耦合求解,内点和边界点上的涡度和流函数值同时求出。因此,ADI方法保持了完全的二阶精度,避免了上面所提到的问题。作者应用这一方法计算了雷诺数R_θ等于1,10,100,500,1000时的二维方腔流动(空间步长h=1/20)。计算结果表明:这一方法保持了通常ADI方法的优点,可以应用大的时间步长。最后补充计算了雷诺数R_θ=2000的二维方腔流动。     

Navier-Stokes方程的最小二乘等几何方法

基于Hermite多项式的C¹型单元构造复杂,限制了最小二乘有限元法的应用.引入高阶光滑的非均匀有理B样条作为基函数简化C¹型单元构造,提出求解黏性不可压流动Navier-Stokes方程的最小二乘等几何方法.用Newton法或Picard法对Navier-Stokes方程线性化,用线性化偏微分方程的余量定义最小二乘泛函,导出最小二乘变分方程,用NURBS构造高阶光滑的有限维空间来近似速度场和压力场.计算表明:本文方法计算的二维顶盖驱动流数值解能准确描述流动状况,计算的二维通道内圆柱绕流全局质量损失由最小二乘有限元法的6%降为0.018%,该方法可用于Navier-Stokes方程的求解,并且具有较好的质量守恒性.     

神经网络对于翼型绕流流场的重构

本文试图通过神经网络重构二维低雷诺数翼型绕流非定常流场。首先通过局部径向基函数(LRBF)求解器求解不可压缩流动控制方程得到计算域内流场信息,然后随机选取一些时空域内的数据点(包含位置信息和速度信息)作为训练数据代入神经网络进行训练。先学习训练得到流动的雷诺数后进行流场的重构,并与LRBF求解器得到的数值结果进行对比。流动计算中雷诺数设置为200,攻角为20°,计算域离散采用局部节点加密技术以减少计算量。     

基于树网格的格子Boltzmann方法以及曲线边界的处理

将格子玻尔兹曼方法(LBM)和BFECC技术相结合,在四叉树网格上实现,并用于二维不可压缩流动的求解.二维四叉树(三维八叉树)网格是一种非均匀网格,利用树结构进行数据存储,具有非常高的检索效率.BFECC是一种数值技巧,可以把求解输运方程的奇数阶格式通过误差修正提高一阶精度.基于四叉树网格的LBM,引入BFECC后,能有效减小输运过程中非均匀网格插值产生的误差,在总体上实现二阶精度,和经典的LBM方法相当.最后给出二维顶盖驱动方腔流动算例和二维圆柱绕流算例,从中可以看出格式的有效性.     

二维空腔黏性流的格子Boltzmann方法模拟

用13速六方格子BhatnagarGrossKrook(缩写为BGK)模型模拟二维空腔黏性流.给出了上边界流体作匀速运动时,具有不同雷诺数的空腔黏性流的流场速度分布情况,模拟了在雷诺数Re=3000时,流场中的涡旋形成过程及流场稳定后,腔内密度、压力和温度的分布情况 关键词：     

Experimental Investigation of Mixed Convection in a Channel With an Open Cavity

Mixed convection in an open cavity with a heated wall bounded by a horizontally unheated plate is investigated experimentally. The cavity has the heated wall on the inflow side. Mixed convection fluid flow and heat transfer within the cavity is governed by the buoyancy parameter, Richardson number (Ri), and Reynolds number (Re). The results are reported in terms of wall temperature profiles of the heated wall and flow visualization for Re = 100 and 1000, Ri in the range 30–110 (for Re = 1000) and 2800–8700 (for Re = 100), the ratio of the length to the height of cavity (L/D) is in the range 0.5–1.5, and the ratio of the channel height to cavity height (H/D) is in the range of 0.5 and 1.0. The present results show that the maximum dimensional temperature rise values decrease as the Reynolds and the Richardson numbers decrease. The flow visualization points out that for Re = 1000 there are two nearly distinct fluid motions: a parallel forced flow in the channel and a recirculation flow inside the cavity. For Re = 100 the effect of a stronger buoyancy determines a penetration of thermal plume from the heated plate wall into the upper channel. Nusselt numbers increase when L/D increase in the considered range of Richardson numbers.     

Experimental Investigation of Opposing Mixed Convection in a Channel with an open Cavity Below

Abstract

In this article, mixed convection in an open cavity with a heated wall bounded by a horizontal unheated plate is investigated experimentally. The heated wall is on the opposite side of the forced inflow. The results are reported in terms of wall temperature profiles of the heated wall and flow visualization. The range of pertinent parameters used in this experiment are Reynolds numbers (Re) from 100 to 2,000 and Richardson numbers (Ri) from 4.3 to 6,400. Also, the ratio between the length and the height of cavity (L/D) ranges from 0.5–2.0, and the ratio between the channel and cavity height (H/D) is equal to 1.0. The lack of experimental results on mixed convection in a channel with an open cavity below was an impetus for investigating this configuration when one cavity vertical wall is heated at uniform heat flux. The present results show that at the lowest investigated Reynolds number, the surface temperatures are lower than the corresponding surface temperatures for Re = 2,000 at the same ohmic heat flux. The flow visualization shows that for Re = 1,000, there are two nearly distinct fluid motions: a parallel forced flow in the channel and a recirculation flow inside the cavity. For Re = 100, the effect of a stronger buoyancy determines a penetration of thermal plumes from the heated plate wall into the upper channel. Moreover, the flow visualization shows that for lower Reynolds numbers, the forced motion penetrates inside the cavity, and a vortex structure is adjacent to the unheated vertical plate. At higher Reynolds numbers, the vortex structure has a larger extension while L/D is held constant.     

Power fluctuations in a closed turbulent shear flow

We study experimentally the power consumption P of a confined turbulent flow at constant Reynolds number Re. We analyze in details its temporal dynamics and statistical properties, in a setup that covers two decades in Reynolds numbers. We show that nontrivial power fluctuations occur over a wide range of amplitudes and that they involve coherent fluid motions over the entire system size. As a result, the power fluctuations do not result from averaging of independent subsystems and its probability density function Pi(P) is strongly non-Gaussian. The shape of Pi(P) is Reynolds number independant and we show that the relative intensity of fluctuations decreases very slowly as Re increases. These results are discussed in terms of an analogy with critical phenomena.     

A pseudospectral method for solution of the three-dimensional incompressible Navier-Stokes equations

A new Chebyshev pseudospectral technique (based on the projection method that was previously applied by the authors to the solution of two-dimensional incompressible Navier-Stokes equations in primitive variables for nonperiodic boundary conditions) is extended to solve the three-dimensional Navier-Stokes equations. The crucial point of the method is the requirement that the continuity equation be satisfied everywhere in the domain, on the boundaries as well as in the interior. The key feature of the work presented in this paper is that the computer storage requirements of the full matrix inversion resulting from direct solution of the pressure Poisson equation in three dimensions is greatly reduced by considering an eigenfunction decomposition. The method was tested on a two-dimensional driven cavity flow and the results were compared with those of the most accurate finite-difference calculation. The three-dimensional driven cavity flow was then calculated at the same Reynolds numbers as the two-dimensional cases, i.e., Re = 100, 400, and 1000. In the calculated results, three-dimensional boundary effects were observed in all cases and became more apparent with increasing Reynolds number.     

Simulating high Reynolds number flow in two-dimensional lid-driven cavity by multi-relaxation-time lattice Boltzmann method

By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number (Re) flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50,000 in the literature; however, this paper can readily extend the maximum to 1000,000 with the above combination.     

Improving the Stability of the Multiple-Relaxation-Time Lattice Boltzmann Method by a Viscosity Counteracting Approach

Numerical instability may occur when simulating high Reynolds number flows by the lattice Boltzmann method (LBM). The multiple-relaxation-time (MRT) model of the LBM can improve the accuracy and stability, but is still subject to numerical instability when simulating flows with large single-grid Reynolds number (Reynolds number/grid number). The viscosity counteracting approach proposed recently is a method of enhancing the stability of the LBM. However, its effectiveness was only verified in the single-relaxation-time model of the LBM (SRT-LBM). This paper aims to propose the viscosity counteracting approach for the multiple-relaxation-time model (MRT-LBM) and analyze its numerical characteristics. The verification is conducted by simulating some benchmark cases: the two-dimensional (2D) lid-driven cavity flow, Poiseuille flow, Taylor-Green vortex flow and Couette flow, and three-dimensional (3D) rectangular jet. Qualitative and Quantitative comparisons show that the viscosity counteracting approach for the MRT-LBM has better accuracy and stability than that for the SRT-LBM.     

涡轮叶片前缘阵列冲击冷却流动及传热特性数值研究

本文采用SST湍流模型模拟了类前缘通道内蒸汽射流阵列冲击冷却的流动与传热特性,分析了雷诺数(Re=10000~50000)、孔径比(d/H=0.5~0.9)和孔间距比(S/H=2~6)对流动及传热性能的影响规律,得到了相应的传热和摩擦关联式。结果表明:在不同雷诺数下,d/H从0.5到0.9变化时,通道压力损失系数降低了76%~79%,靶面平均努塞尔数降低了45%~49%;S/H从2增至6时,通道压力损失系数增加了1.64~1.92倍,靶面平均努塞尔数增加了54%~64%;增大d/H、减小S/H可有效提高类前缘通道蒸汽冲击冷却的综合热力系数。本文研究结果可为未来先进燃气轮机高温涡轮叶片蒸汽冷却结构的设计提供参考和借鉴。     

出口雷诺数对平面射流自保持性的影响

通过实验研究出口雷诺数对平面湍流射流自保持性的影响. 测量的射流来自相同的喷嘴但不同的雷诺数Re（≡U_jh/ν,其中U_j是出口平均速度、h是窄缝出口的厚度和ν是黏性系数）,其变化范围是Re=4582—57735.所得的数据包括沿轴线的平均速度、湍流强度、积分尺度、高阶矩和能谱. 实验发现,随着Re的增大,平面射流发展减慢,平均速度和湍流强 关键词： 平面射流 雷诺数 自保持性     

Lattice Boltzmann Simulations of Particle-Particle Interaction in Steady Poiseuille Flow

The moving behaviour of two- and three-particles in a pressure-driven flow is studied by the lattice Boltzmann simulation in two dimensions. The time-dependent values, including particles＇ radial positions, translational velocities, angular velocities, and the x-directional distance between the particles are analysed extensively. The effect of flow Reynolds number on particle motion is also investigated numerically. The simulation results show that the leading particle equilibrium position is closer to the channel centre while the trailing particle equilibrium position is closer to the channel wall. If Reynolds number Re is less than 85.30, the larger flow Reynolds number results in the smaller x-directional equilibrium distance, otherwise the x-directional distance increases almost linearly with the increase of time and the particles separate finally. The simulation results are helpful to understand the particle-particle interaction in suspensions with swarms of particles.     

用Lattice Boltzmann方法模拟1/4圆腔内的定常层流运动

分析格子Boltzmann方法中二阶精度的曲线边界处理方法.应用格子Boltzmann方法及其边界处理方法模拟1/4圆腔内的定常层流运动,引入流线图和等涡线图分析流场随Re数的变化.并且发现当Re数在10~100区间内变化时,随着Re数的增大,顺时针旋转流场的涡心位置偏离x轴的角度逐渐减小,而逆时针旋转流场的涡心位置偏离x轴的角度却越来越大.