SPH管内空气流动的光滑粒子流体动力学模拟研究

摘要日常生活中管道无处不在，对不同管道的研究有助于合理利用其特性，其中对于管道空气流动的流体问题，由于作用原理、结构形式、和用途不相同，在管内流动的时候往往会碰见不同的变形、爆炸等等。随着计算机行业的迅猛发展，一种新兴的拉格朗日型的无网格的光滑粒子法（smoothed particle hydrodynamics，SPH），且被广泛应用于应用工程、天体问题、流体物理等许多领域。80791

本文以空气流动的二维直管和二维弯管为研究对象，基于无网格的光滑粒子法对管内空气流动进行研究分析。分析了 SPH 方法计算所得的粒子位置分布图、速度矢量分布图、速度等值图以及水平中心线和竖直中心线上的速度分布图，并将其与有限元计算方法所得结果进行比较分析，认为：

（1）基于 SPH 下的二维直管的速度等值图与基于传统有限元下的速度等值图近似，且误差保持在一个较小的范围内。

（2）基于 SPH 下的二维弯管的速度等值图与基于传统有限元下的速度等值图差异较大，该 SPH 程序模块无法较好模拟出拐角处的涡能量变化，缺乏相应的涡控制方程，需要对该 SPH 程序模块进行进一步改进。

（3）正确的选择边界处理类型，合理地选择核函数类型、时间步长，合适地放置粒子数目对于提高计算效率、减小误差有明显帮助。

毕业论文关键词：光滑粒子流体动力学；管道；空气流动；数值计算

Abstract Pipeline everywhere in daily life, the study of different pipeline is helpful to rational utilization of its features, including to the problem of pipe air flow of fluid due to the action principle, the structure form, and USES different, often met in pipe flow of the different deformation, explosion, etc。With the rapid development of computer industry, a new smooth particles of Lagrange type meshless method (smoothed particle hydrodynamics, SPH), and is widely used in application engineering, objects, fluid physics, and many other fields。

Based on the air flow two-dimensional straight pipe and the 2 d bend as the research object, based on smooth particles of meshless method to study and analysis on the air flow in pipe。Analyzed the SPH method to calculate the particle position distribution, the velocity vector distribution, velocity contour diagram, and horizontal center line and vertical center line velocity profile, with the finite element method analysis results, think:

(1)based on the two-dimensional straight pipe under the SPH velocity contour and based on the velocity contour under the traditional finite element approximation, and keep in a smaller range of error。

(2)based on the 2 d bend under the SPH speed based on the traditional finite element with equivalent figure contour difference is bigger, the SPH program modules can better simulate the corner vortex of energy change, the lack of corresponding vortex control equation, the need to further improve the SPH program module。

(3)Right choice boundary types, choose the proper function of the nuclear type, time step, properly placed particle number for improving calculation efficiency, reduce the error。

Keywords：Smooth particle method;The pipe;Air flow;Numerical simulation

第一章绪论 1

1。1 研究目的及意义 1

1。2 研究现状 1

1。3 论文主要研究内容 5

1。4 本章小结 5

第二章数学模型 6

2。1 控制方程 6

2。1。1 连续性方程 SPH管内空气流动的光滑粒子流体动力学模拟研究:http://www.youerw.com/wuli/lunwen_94014.html