On some aspects of fully-developed turbulent flow in rectangular channels

For fully-developed turbulent flow in straight channels of non-circular cross-section, there exists a transverse mean flow superimposed upon the axial mean flow. This transverse flow, commonly known as secondary flow, interacts with the axial mean flow and turbulence structure in a complex manner. In this paper several heretofore unexplored aspects of this type of secondary flow are discussed on the basis of results of an extensive experimental programme which was conducted for steady, incompressible, fully-developed turbulent air flow in both square and rectangular channels. Specifically, the following aspects are examined: (a) the Reynolds-number effect on secondary flow, (b) the directional characteristics of local wall shear stress, (c) the orientation of Reynolds-stress principal planes in a plane normal to the axial flow direction, and (d) the Reynolds equation along a secondary-flow streamline. Within the Reynolds-number range of the investigation, the results indicate that secondary-flow velocities, when non-dimensionalized with either the bulk velocity or the axial mean-flow velocity at the channel centreline, decrease for an increase in Reynolds number. Also, the greatest skewness of local wall shear-stress vectors is shown to occur in the near vicinity of corners where secondary flow is maximum. In addition, it is shown that in planes normal to the axial flow direction, traces of Reynolds stress principal planes are not tangent and normal to lines of constant axial mean-flow velocity. This behaviour is in contrast to that for less complicated turbulent flows, for example, two-dimensional channel flow or circular-pipe flow where such traces are always tangent and normal to lines of constant axial mean-flow velocity in accordance with symmetry considerations. Finally, through experimental evaluation of terms in a momentum balance along a typical secondary-flow streamline, it is shown that secondary flow is the result of small differences in magnitude of opposing forces exerted by the Reynolds stresses and static pressure gradients in planes normal to the axial flow direction.