Comparison between experimental results and mathematical model

Date: 2015-10-07; view: 556.

In order to predict the motion of particles using the mathematical model, there are four input parameters that should be known. They are the radius of the particle, initial position of the particle from the pressure node, particle compressibility of SiC, and acoustic energy in the fluid. The compressibility of SiC was calculated to be 1.85 using Eq. (2).

Three other variables that were not known were the radius of the particle (r), initial starting position of the particle (x₀) and acoustic energy in the field (E). The equation for the particle trajectory (6) was rewritten and Matlab 5.3 was used for data optimization using a minimization function in the package to obtain the best r, x₀ and E values.

Different combinations of these unknown variables were used as initial guesses for the displacement function and the corresponding optimized values were generated by the fmin search function in the Matlab Optimization software. Any optimization values with radius greater than 6 μm or initial position less than zero or greater than a half wavelength were discarded since the maximum probable size of the SiC particle is less than 12 μm.

The above procedure for optimization was repeated for each experimental data set at different input power values from 0.5 to 5.0 W. Fig. 10 shows the particle trajectories from the experimental results and mathematical model predictions using Eq. Figs. (6) and (43). The experimental data for higher power inputs were comparable to the mathematical model predictions using Eq. (39).

Fig. 10. Particle displacement versus time for 5.0 W power.