Anisotropy Invariants of Reynolds Stress Tensor in a Duct Flow and Turbulent Boundary Layer

Abstract

The present study shows that the Reynolds stress anisotropy tensor for turbulent flow depends both on the nature of the surface and the boundary conditions of the flow. Contrary to the case of turbulent boundary layers with k-type surface roughness, the measured anisotropy invariants of the Reynolds stress tensor over a series of spanwise square bars separated by rectangular cavities (k-type) in duct flows show that roughness increases the anisotropy. There is a similarity between the effect of roughness on channel flow turbulence and that on pipe flow turbulence. The present data show that the effect of introducing a surface roughness significantly perturbs the entire thickness of the turbulent flow.

Structure of turbulent channel flow with square bars on one wall

“…For large values of w=k, a region of constant F extends over about 3k. A comparison of F at the same y for y > 3k could lead to the conclusion of Mazouz et al (1998) (and in disagreement with what is generally found in the literature) that roughness increases the anisotropy. In fact, at the geometrical centreline of w=k ¼ 7, the differences between hu 2 i and hv 2 i or hw 2 i are larger than for a smooth channel.…”

Influence of PIV interrogation area on turbulent statistics up to 4th order moments in smooth and rough wall turbulent flows

“…It is important to note that experimental support for the similarity hypothesis is, however, not unanimous. For example, measurements reported by Mazouz et al [23] over k-type two-dimensional bars in a fully developed channel demonstrated that u + is independent of surface roughness but v + and w + are lower on the rough wall than the corresponding smooth wall. In their zero pressure gradient turbulent boundary layer measurements over smooth wall, wire mesh and transverse rods, Korgstad and Antonia [12] observed that surface roughness enhanced the levels of the turbulent intensities (u + , v + ) and Reynolds shear stress (Àu + v + ) in the outer region.…”

Particle image velocimetry study of turbulent flow over transverse square ribs in an asymmetric diffuser

“…A comprehensive review of prior rough wall studies can be found in many articles, for example, Bakken et al 4 and Jiménez. 5 Most of these studies were experimental, and were performed in zero pressure gradient ͑ZPG͒ turbulent boundary layers ͑Krogstad et al 6 and Connelly et al 7 ͒ and fully developed pipe and channel flows ͑Mazouz et al 8 ͒. The roughness elements used in previous studies include sand grains, wire mesh and twodimensional transverse ribs.…”