A New Method of Fractal Analysis Using Wavelet Transform and its Application in Tumbling Flow Analysis

Abstract

In this study, we proposed a new method to calculate the fractal dimension in order to evaluate the change of the eddy structure of tumbling flow. The procedure of our method is 1) Carrying out wavelet transform of the turbulence and obtaining the information of the turbulence about both time and frequency. 2) Calculating the fractal dimension at each time from the wavelet transform of the turbulence. 3) Evaluating change of the eddy structure in the turbulence by using the fractal dimension obtained. As a result, the fractal dimension first decreases a little at the time of the tumbling flow broken down and then the fractal dimension increases near TDC. that is, the eddies that are generated by the tumbling flow which has broken down have larger scale and transmit the energy to the small eddies in the compression stroke.