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

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.