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_b²) (dP/dx) - k turbulent kinetic energy per unit mass, - k⁺ dimensionless turbulent kinetic energy, k/(^*)² - P static pressure - Re Reynolds number, U_bD_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; u²/^*, v²/^*, w²/^* - 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, (¯V²+¯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