Measurements and prediction of fully developed turbulent flow in an equilateral triangular duct

Abstract

Fully developed air-flows through an equilateral triangular duct of 12·7 cm sides were investigated over a Reynolds number range of 53 000 to 107 000. Based on equivalent hydraulic diameter, friction factors were found to be about 6% lower than for pipe flow. Mean axial velocity distributions near the wall were describable by the inner law of the wall (when based on local wall shear stress) but the constants differ slightly from those for pipe flow. As expected, the secondary flow pattern was found to consist of six counter-rotating cells bounded by the corner bisectors. Maximum secondary velocities of about 1 ½% of the bulk velocity were observed. The effects of secondary currents were evident in the cross-sectional distributions of mean axial velocity, wall shear stress and Reynolds stresses, and very prominent in the turbulent kinetic energy distribution. For the flow prediction, the vorticity production terms were expressed by modelling the Reynolds stresses in the plane of the cross-section in terms of gradients in the mean axial velocity and a geometrically calculated turbulence length scale. The experimental and predicted characteristics of the flow are shown to be in good agreement.

Calculation of turbulence-driven secondary motion in ducts with arbitrary cross-section

“…A comprehensive review of experimental data for ducts with regular cross-section can be found in Demuren and Rodi [3]. Additional data for irregularly-shaped channels are reported by Rodet [4], Aly et a1 [5], and Seale [6], for trapezoidal, triangular and simlated rod-bundle-type cross-sections, respectively.…”

“…In each case, the channel cross-section is constant in the streamwise direction, and the flow is nominally fully-developed. 1) studied experimentally by Aly et a1 [5] at Reynolds number of 53,000, based on the bulk velocity and the hydraulic diameter. Measurements were made in one-sixth of the duct cross-section a t a plane 133 diameters from the inlet.…”

Calculation of turbulence-driven secondary motion in ducts with arbitrary cross section

“…There are 5 corners, all different from each other. We have combinations of intersections of straight walls, curved walls and symmetry planes.…”

Mechanism for initiating secondary currents in channel flows

“…Keulegan (1938) also touched upon the need to separate the flow cross-sectional area into different regions; he suggested that the bisectors of base angles of the channel could be used to divide the flow region because the flow characteristics in regions separated by it are different from each other. The bisectors have been widely used to separate two conjoining secondary currents (Aly et al 1978). Chien and Wan (1999) concisely explained the physical meaning of Einstein's idea in terms of how the turbulent energy should be transferred and eventually dissipated as heat at the boundary .…”