Analysis of the Characteristics, Physical Concepts and Entropy Generation in a Turbulent Channel Flow Using Vortex Blob Method

In this paper, using vortex blob method (VBM), turbulent flow in a channel is studied and physical concepts of turbulence are obtained and discussed. At first, time-averaged velocities,  and , and then their fluctuations are calculated. To clarify turbulence structures, velocity fluctuations and  are plotted. It is observed that turbulence structures occupy different positions and move with convection velocity. To verify the second law of thermodynamics, averaged vorticity and its fluctuations as well as averaged entropy and its fluctuations are calculated. Contours of these fluctuations  show that their positions coincide with the positions of turbulence structures and both positions move with the same velocity. Correlation coefficient of velocity fluctuations between two points, and temporal correlation coefficient at a point, which have significant role in understanding physics of turbulence, are calculated and plotted. Having obtained these coefficients, time  and space micro-scales and then  turbulence energy dissipation rate () are obtained. Also, spatial-temporal correlation coefficients is calculated and then for turbulence structures microscale of time (memory), microscale of space (size) and convection velocity of structures are found. These scales estimate their life and size. Having obtained dual correlation coefficients, spectral studies of the velocity fluctuations, and , are performed, which include both frequency amplitude (related to temporal correlation coefficient) and wave number (related to special correlation coefficient). In fact, spectral study of fluctuations is Fourier transform (Cosine) of these fluctuations. Finally, dropping rate of this transform is compared with available data in turbulence literature.