RANS

Based on the Reynolds averaging method (the long-time average of a quantity or ensemble average, proposed by Osborne Reynolds, 1842-1912), Reynolds-averaged Navier-Stokes (RANS) approaches have been the most prevalent until now. The effect of turbulent fluctuations appears in a Reynolds-stress term that must be modeled if the system is to be closed. Reynolds-stress models are successful (whereas turbulent viscosity models are not) in calculations that concern flows with significant mean streamline curvature, flows with strong swirls or mean-rotating phases, secondary flows in ducts, and flows with rapid variations in the mean flow.