Non-linearity of Scaling Law of Instantaneous Pressure Fluctuation Signals in a Circulating Jet Tank
YU Yan-fang WU Jian-hua MENG Hui-bo
College of Mechanical Engineering, Shenyang University of Chemical Technology College of Mechanical Engineering, Shenyang Institute of Chemical Technology College of Mechanical Engineering, Shenyang University of Chemical Technology
Abstract： In order to reveal the nonlinearity of fluid system in the mixing zones of a circulating jet tank, a high-speed acquisition system was employed to measure the instantaneous pressure fluctuation signals at different axial, radial and circumferential positions in turbulent flow region with a range of Re between 3660 and 32940. Both the amplitudes of fluctuation energy and scaling law of extended self-similarity for the structure function of pressure signals were evaluated. The initial parameters on sampling frequency and data length of pressure time series were optimized based on the recurrence rate and amplitudes of fluctuation energy. The experimental results indicated that the relative increasing ratios of amplitude of fluctuation energy were below 0.3% and a linear relationship between logarithm values of amplitude of fluctuation energy and Re existed when the date length was not less than 80000. The logarithm values between the qth- and third-order time structure functions of pressure signals were in accordance with a linear relationship. The scaling exponent x(q) of time structure function was smaller than relative scaling exponent x(q, 3). The profiles of relative scaling exponents x(1, 3) and x(5, 3) [or x(2, 3) and x(4, 3)] were symmetrically distributed about the profile of x(3, 3). The relative scaling exponent x(q, 3) was enlarged with the increase of qm when the order value of q was equal or greater than 4. But the distribution of x(q, 3) was contrary with the increase of polar angle q or r/R when the order value of q was less than 3.