Study On Drag-reducing Characteristics Of Turbulent Channel Flow Based On Chaos Theory

Additive drag reduction is closely related with flow characteristics of turbulence .There are studies show that flow characteristics of turbulence is chaotic. In this paper chaos theory is applied to drag reduction of channel turbulence for the first time. The conclusions have some reference value for further research in mechanism of drag reduction in channel turbulent flow.Chaotic time series analysis is an important means to study the complex nonlinear dynamic systems. The calculation of strange attractor's correlation dimension and the characteristic quantities of Kolmogrov entropy and the largest Lyapunov index and Hurst index consists of the chaotic time series analysis. Achieving the algorithm of characteristic quantities of chaos by programming with Matlab software is an integral way to analyze chaos. Near wall region of channel turbulent flow includes three different flow regions,which are viscous sublayer, transition layer and logarithm law layer The streamwise velocity of five different locations in three layers can be obtained by using direct numerical simulation. Each set of data consists of 200000 numbers which are numerical simulation quantities of velocity related with time. Ten teams of numbers constitute the ten time series.Based on the algorithm of characteristic quantities achieving by Matlab software, we can get the chaotic characteristic quantities of each time series after processing the time series. According to the meaning of characteristic quantities the results show that both water and additive drag reduction solution in channel are chaotic. Furthermore, the chaotic characteristic quantities of water and additive drag reduction solution are obviously different. In the direction of wall-normal, the correlation dimension of water's time series ranges from 2.88 to 4.58 while that of additive drag reduction solution is from 1.56 to 2.76. Fractional correlation dimensions indicate that both water and additive drag reduction solution have chaotic characteristics and that water is more chaotic than additive drag reduction solution. The largest Lyapunov index of water is from 0.0104 to 0.0420 while that of additive drag reduction solution varies from 0.0024 to 0.0102. The largest Lyapunov indexes of water and additive drag reduction solution are above zero. Obviously, both water and additive drag reduction solution are chaotic and additive drag reduction solution is less chaotic than water. The Kolmogrov entropy of water changes from 0.15 to 0.33 while from 0.02 to 0.07 for additive drag reduction solution. The higher the Kolmogrov entropy value, the greater the information loss rate and the more chaotic. The Hurst index of water is between 0.6647 and 0.7460 while that of additive drag reduction solution is from 0.9234 to 0.9877. Both the Hurst index of water and additive drag reduction solution is between 0.5 and 1. The fact indicates that water and additive drag reduction solution are chaotic and has the character of long-term memory. Overall, adding surfactant active agent to the channel turbulence changes and regulates the flow of channel turbulence, which reaches the effect of drag reduction macroscopically.