A new method to calculate unsteady particle kinematics and drag coefficient in a subsonic post-shock flow

Abstract

We introduce a new method (piecewise integrated dynamics equation fit, PIDEF) that uses the particle dynamics equation to determine unsteady kinematics and drag coefficient (C D ) for a particle in subsonic post-shock flow. The uncertainty of this method is assessed based on simulated trajectories for both quasi-steady and unsteady flow conditions. Traditional piecewise polynomial fitting (PPF) shows high sensitivity to measurement error and the function used to describe C D , creating high levels of relative error ( 1) when applied to unsteady shock-accelerated flows. The PIDEF method provides reduced uncertainty in calculations of unsteady acceleration and drag coefficient for both quasi-steady and unsteady flows. This makes PIDEF a preferable method over PPF for complex flows where the temporal response of C D is unknown. We apply PIDEF to experimental measurements of particle trajectories from 8-pulse particle tracking and determine the effect of incident Mach number on relaxation kinematics and drag coefficient of micron-sized particles.

Drag of Shock-Accelerated Microparticles

“…If C D (t) is known, this equation can be integrated numerically or analytically to determine an expression for the particle position versus time. The full description of the piecewise fitting method to determine drag coefficient from the particle position, including uncertainty analysis, can be found in Bordoloi et al [18].…”

“…2 shows measured particle positions for many different experiments, with four different particle tracks highlighted in colour. The particle drag, velocities and accelerations are calculated using a piecewise fitting method that is described in [18].…”

12th International Symposium on Particle Image Velocimetry (PIV 2017)

“…Stereoscopic measurement offers three-component data for turbulent kinetic energy spectra. The resulting spectra reveal two regions exhibiting power-law dependence describing the turbulent decay.The paper by Bordoloi et al [2] presents a new method (piecewise integrated dynamics equation fit, (PIDEF)) that uses the particle dynamics equation to determine unsteady kinematics and drag coefficient (C D ) for a particle in subsonic post-shock flow. The uncertainty of this method is assessed based on simulated trajectories for both quasisteady and unsteady flow conditions.…”

“…The paper by Bordoloi et al [2] presents a new method (piecewise integrated dynamics equation fit, (PIDEF)) that uses the particle dynamics equation to determine unsteady kinematics and drag coefficient (C D ) for a particle in subsonic post-shock flow. The uncertainty of this method is assessed based on simulated trajectories for both quasisteady and unsteady flow conditions.…”