Compressibility effects on secondary motions in turbulent square duct flows

• Implicit large-eddy simulations are performed to investigate compressibility effects of turbulent flows in square ducts. • Secondary motions redistribute the wall shear stress and heat flux, generating a local peak near the duct corner at the highest Mach numbers. • Generalized Reynolds analogy for the mean velocity and temperature fields remains valid, the resemblance between their fluctuations is weakened. This study employs implicit large-eddy simulation to investigate the compressibility effects of turbulent flows in square ducts across a range of bulk Mach numbers and bulk temperatures. We focus on the impact on secondary flows and the associated momentum and heat transport. The results show that secondary motions redistribute the wall shear stress and heat flux, generating a local peak near the duct corner at the highest Mach numbers. This is attributed to changes in the attenuation of the mean streamwise vorticity near the wall. While the generalized Reynolds analogy for the mean velocity and temperature fields remains valid, the resemblance between their fluctuations is weakened. This occurs because the large-scale secondary circulations become significant compared to turbulent fluctuations in the outer region, leading to a deviation of the turbulent Prandtl number from unity.