Results and Discussion

The simulation was initialized and run for simulation time of 0.01763 s using 1764 time steps. The simulation was recorded and compiled into a video using the feature of Ansys post processing package. The image at each time step was recorded and acted as one frame in the video. The video was recorded at the speed of 30 frames per second. Images at different time-step during one oscillations are shown below.

In order to get the frequency of oscillations, the area of zirconium phase is to be recorded and plotted against corresponding time step. A code is developed using Matlab. First the video is read into the memory and each frame is analyzed. Each frame is then converted to greyscale image. Each pixel of the image is then analyzed using a nested loop and the greyscale value at each cell is stored. Number of cells having the value of more than 29 is added to a counter variable and is stored as area of zirconium phase for that time step. Subsequently, all frames are analyzed and plotted to obtain the oscillation spectrum.

A fast Fourier transform is performed on the data set and a frequency spectrum is generated. A sharp peak is obtained at 170.26 Hz which is the frequency of zirconium sample oscillation in helium atmosphere. The result obtained from numerical simulation are in good agreement with the experiments performed. Further, Eq. 1 can be used to calculate the interfacial or surface tension of Zirconium. Values of density, radius and frequency is put in the equation to obtain the value of surface tension to be 1.473 N/m (Figs. 5, 6 and 7).

Fig. 5 Different stages of oscillation. Two dashed lines were added to show the relative difference in the position of zirconium - helium interface. a Initial condition with 5% ellipticity, b maximum area during oscillation, c minimum area during oscillation and d mean area during the oscillation

Fig. 6 Oscillation spectrum of Zirconium in helium atmosphere

Fig. 7 Frequency spectrum of Zirconium in helium atmosphere

References

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