Numerical simulation of turbulent flow through Schiller's wavy pipe

The development of incompressible turbulent flow through a pipe of wavy cross-section was studied numerically by direct integration of the Navier-Stokes equations. Simulations were performed at Reynolds numbers of 4.5 x 10(3) and 10(4) based on the hydraulic diameter and the bulk velocity. Results for the pressure resistance coefficient lambda were found to be in excellent agreement with experimental data of Schiller (Z. Angew. Math. Mech., vol. 3, 1922, pp. 2-13). Of particular interest is the decrease in lambda below the level predicted from the Blasius correlation, which fits almost all experimental results for pipes and ducts of complex cross-sectional geometries. Simulation databases were used to evaluate turbulence anisotropy and provide insights into structural changes of turbulence leading to flow relaminarization. Anisotropy-invariant mapping of turbulence confirmed that suppression of turbulence is due to statistical axisymmetry in the turbulent stresses.