Laws of motion and aerodynamic drag coefficient for large titanium particles burning in air

The results are reported on the study of burning titanium particles with the diameter of 200–550 µm while free fall in air. Video with the rates of 25 and 500 fps captures the particle trajectories. The mathematical procedure for averaging of particle trajectories was developed. The trajectories can be classified into classes with the particle size variation within each class about 20–30 µm. The evolutions of particle coordinate x(t) and particle velocity v(t) as functions of time t (until the event of particle fragmentation) were presented as generalized functions for each of the size-classes. The comparison of empirical curves x(t) and v(t) with the analytical solutions for this problem about a spherical particle motion under gravity and aerodynamic drag forces gives the effective aerodynamic drag coefficient for a burning-in-air titanium particle in the format Cd = A/Re, where Re is the Reynolds number. For the particles within the tested size range, the parameter A is independent of the particle diameter and equals about 61 ± 2 for the particle motion with the Reynolds number varying from 1 to 10. If we take the aerodynamic drag coefficient Cd = 61/Re and the air viscosity equal to 5.07·10−5 Pa·s, then the motion of burning titanium particles in air can be described by the known analytical solution for a problem of spherical particle motion driven by forces of gravity and drag within the accuracy provided by the empirical equations.