Measurements of fully developed turbulent flow in a trapezoidal duct

The turbulence characteristics of fully developed isothermal air flows through a symmetric trapezoidal duct were examined experimentally using Pitot tube and hot-wire anemometry over a Reynolds number range of 3.7–11.6×10⁴. The measurements included local wall shear stress and the cross-sectional distributions of mean axial velocity, secondary velocities and Reynolds stresses. Four secondary flow cells were detected in a symmetric half of the duct. Although secondary velocity components were typically less than about 1% of the bulk axial velocity, their effect was especially pronounced on the distributions of turbulent kinetic energy and local wall shear stress.List of symbols a, b, c, d trapezoidal duct dimensions (Fig. 1) - A, B coefficients in log law (Table 1) - D _h equivalent hydraulic diameter - f Darcy friction factor, (2D _h /U _b ² ) (dP/dx) - k turbulent kinetic energy per unit mass, - k ⁺ dimensionless turbulent kinetic energy, k/( ^*)² - P static pressure - Re Reynolds number, U _b D _h / - s distance along inclined wall, measured from top corner (Fig. 1) - u, v, w fluctuating components of the velocities in the x, y, z directions - u ⁺, v ⁺, w ⁺ dimensionless turbulence intensities; u ²/ ^*, v ²/ ^*, w ²/ ^* - u ^* local friction velocity, ( _w /)^1/2 - ^* average friction velocity, (¯gt/)^1/2 - axial mean velocity (time-average) - U _b average mean axial velocity - U _sec resultant of ¯V and ¯W, (¯V ²+¯ ²)^1/2 - U ⁺ dimensionless velocity, /u ^* - ¯V, ¯W mean velocities in the y, z directions (secondary velocities) - x axial direction - y, 2 horizontal and vertical directions (Fig. 1) - z ⁺ dimensionless distance from (and normal to) a wall, zu ^*/v - distance from wall (at y=0) to location of maximum axial velocity - laminar dynamic viscosity - v kinematic viscosity - air density - _w local wall shear stress - ¯ _w average of local wall shear stresses over all walls - ¯ average wall shear stress, (dP/dx) (D _h /4) - corner angle of trapezoidal duct (Fig. 1) A version of this paper was presented at the 10th Symposium on Turbulence, University of Missouri-Rolla, Sept. 22–24, 1986