Numerical Analyses of Turbulence Structure in Rectangular Ducts with Rough and Smooth Walls: Applicability of Simple Analysis Method using Algebraic Reynolds Stress Model

A numerical analysis has been performed for fully developed turbulent flow in a rectangular duct with smooth and rough walls by using algebraic Reynolds stress model. The wall functions and the universal law of the wall, which are used as the boundary conditions of turbulent energy and dissipation, apply in the present analysis instead of taking shape of roughness element into account. Therefore, the roughness enters through the log law relating the velocity at the first grid point away from the wall with the friction velocity. Two kinds of turbulent flows are examined, i.e., one is the turbulent flow in a rectangular duct with two roughened facing walls and the other is that flow in a rectangular duct with longitudinal ridges located lower and upper walls. These two kinds of calculated results are compared with experimental data each other. As for the comparison of rectangular duct with two roughened facing walls, the present calculated results show less distortion of streamwise velocity than the experimental data. This discrepancy may be attributable to assumption of the uniform roughness wall in calculation and separated flow observed in the experiment. On the other hand, calculated results of rectangular duct with ridges show a reasonable agreement in the streamwise velocity and the distributions of the Reynolds stresses. These examinations suggest the validity of the present method using the wall functions.