On Universal Velocity Profile of Turbulent Flow in Round Pipe

Abstract

The paper proposes a new algebraic model for describing turbulence in a round pipe. The model relies on the assumption that two hypotheses are sufficient for description of the mean velocity of turbulent motion: the Prandtl mixing length hypothesis and the hypothesis of fractal intermittency near pipe walls. The model was constructed with application of the “maximum simplicity” principle, which made it possible to significantly reduce the empirical constants to two constants that have a clear physical meaning and are universal. It is shown that the mean velocity profile calculated by this model coincides with high accuracy with experimental data in the entire flow region, including both the near-wall region and the region of developed turbulence at the pipe axis. The deviation from the results of known experiments does not exceed the measurement uncertainty for the entire range of Reynolds numbers greater than 20000. The results obtained indicate the possibility of constructing a turbulence model for flow in pipes and ducts without empirical constants.