Linearized predictions of secondary flows in turbulent channels with strip-type roughness heterogeneity

Turbulent wall-bounded flows subjected to a lateral roughness heterogeneity develop secondary currents, with strength depending on the surface properties. In this work, secondary flows in pressure-driven channels with strip-type roughness are investigated using Reynolds-Averaged Navier-Stokes (RANS) equations, with the Spalart-Allmaras turbulence model to close the equations. A nonlinear Reynolds stress model is also used to capture the anisotropic Reynolds stresses, required to generate secondary flows. Assuming a small roughness height, linear RANS equations governing secondary flows are obtained.

The flow organization predicted by the linear model agrees with available experimental and numerical data. For increasing strip width, the secondary flows tend to occupy the entire half-height of the channel. Their strength peaks when the spacing between the strips is ~1.4 times the half channel height. This is due to the properties of the Navier-Stokes operator linearised around the turbulent mean profile. Tertiary flows are predicted for wide strips, modifying the flow organization. Similarities and differences between strip- and ridge-type roughness are finally observed. Since the governing equations are linear, a combination of these two effects is possible and will be discussed in the talk.