• Partially filled pipe flow is investigated using a Reynolds stress turbulence model. • RANS-RSM provide similar results to DNS with a much lower computational cost. • Position of maximum streamwise velocity found below the free surface-velocity dip. • Effect of inner secondary cell is considerable on various turbulent flow properties. • Vorticity is generated and convected at the pipe corners touching free surface. Turbulent secondary currents or the in-plane motions significantly affect the velocity, temperature and turbulence fields in a partially filled pipe flow. In this study, turbulent partially filled pipe flow is studied using the Reynolds stress baseline (BSL) turbulence model to investigate secondary currents and their effect on streamwise velocity, vorticity, wall shear stress and Reynolds stresses. Five flow depth ratios ( d / D = 44 - 80 % ) at a constant bulk Reynolds number ( Re b = 30 , 000 ) are examined. Simulated results of streamwise, secondary velocity and wall shear stress show strong agreement with published experimental studies. A key finding is the presence of an additional pair of secondary cells at the mixed corners of the pipe cross-section which diminish in size with increasing flow depth. These inner corner cells are important because they are shown to contribute to the localised peaks of wall shear stress at the pipe corners and reduction of vorticity magnitude (on one half plane). Irrespective of the size of these inner cells, vorticity generation and convection are found to be dominant near the pipe corners. Friction factor for partially filled pipe flows is found to slightly increase with flow depth while matching values predicted by Prandtl’s relation for smooth pipes. Finally, the Reynolds stress distribution on the pipe cross-section is also investigated which shows that the present approach broadly captures the stress profiles and that secondary currents significantly distort the stress contours through changing velocity gradients. The present results enhance the understanding of partially filled pipe flows established by previous experimental studies.
Bose et al. (Wed,) studied this question.