Author(s): Shu-Qing Yang
Keywords: No Keywords
Abstract: This paper investigates the invalidity of classical log-law and its underlying mechanism in pipe and channel flows. It is widely reported that the log-law is only valid for velocity profile in the near wall region, in outer flow region, the measured velocity is systematically higher (wake-law) or lower than the log-law's prediction, but these deviations have not been well explained. By dividing the wall-normal velocity fluctuation into upward and downward conditions, the conditionally-averaged momentum equations are derived. The theoretical results show that the momentum flux caused by the conditionally upward/downward velocity leads to the invalidity. Based on this discovery, a new equation is proposed to express the velocity, and good agreement is achieved between the measured and predicted velocities.