黄社华, 魏庆鼎. 激光测速粒子对复杂流动的响应研究——Ⅰ颗粒非恒定运动数学模型及其数值方法[J]. 水科学进展, 2003, 14(1): 20-27.
引用本文: 黄社华, 魏庆鼎. 激光测速粒子对复杂流动的响应研究——Ⅰ颗粒非恒定运动数学模型及其数值方法[J]. 水科学进展, 2003, 14(1): 20-27.
HUANG She-hua, WEI Qing-ding. On velocity response of tracing particles in laser-based velocimetry to complex flows, 1, mathematical model for small particle motion and verification of numerical methods[J]. Advances in Water Science, 2003, 14(1): 20-27.
Citation: HUANG She-hua, WEI Qing-ding. On velocity response of tracing particles in laser-based velocimetry to complex flows, 1, mathematical model for small particle motion and verification of numerical methods[J]. Advances in Water Science, 2003, 14(1): 20-27.

激光测速粒子对复杂流动的响应研究——Ⅰ颗粒非恒定运动数学模型及其数值方法

On velocity response of tracing particles in laser-based velocimetry to complex flows, 1, mathematical model for small particle motion and verification of numerical methods

  • 摘要: 流体激光测速的精度与示踪粒子的跟随特性即流体中异质粒子的非恒定运动特性密切相关。首先对粒子非恒定运动方程进行了探讨,着重考虑了在高颗粒雷诺数时该方程的修正问题,简要分析了该方程的数学属性,并构造了这类方程的数值计算方法。分析表明,高颗粒雷诺数下的粒子非恒定运动方程为非线性奇异积分方程,而当颗粒雷诺数小于1时,则线性化为第二类渥尔特拉(Volterra)积分方程。以几种均匀流中球形小颗粒的非恒定运动为算例,计算结果与其解析解及有关实验数据的比较表明,数值方法具有良好的计算精度。

     

    Abstract: The application of laser-based velocimetry in experimental researches of flows is closely involved in tracking ability of particles whose density or initial velocity is different from that of fluid.The transient mot ion equation of small particles is analyzed for numerical investigation of particles velocity in response to complicated flow, with particular emphasis on modification of the motion equation at high particle Reynolds number.The mathematical features of part icle transient motion equation are simply clarified and a numerical method to solve it is developed.It is analytically demonstrated that at high particle Reynolds number the particle transient motion equation is a nonlinear integral equation with singularity, while it is simplified to the second Volterra integral equation when particle Reynolds number is smaller than unit.By comparison of the calculat ing results of particle transient motion in uniform flows with corresponding analytical and experimental results, the numerical method is verified to be well valid.

     

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