Calculations of a Curved-Pipe Flow Using Reynolds Stress Closure

Abstract

It has been observed that as a fully developed turbulent flow enters a curved bend the anisotropy of the normal stresses near the outer bend (furthest from the centre of the bend curvature) increases. According to the arguments of vorticity generation, a sudden increase in the anisotropy of the normal stresses may lead to the formation of a secondary flow of the second kind. If this secondary motion is to be calculated, then a near-wall Reynolds stress closure that can mimic the anisotropic turbulence behaviour near a wall has to be used. This study presents the results of just such an attempt. In addition, two high Reynolds number closures assuming wall functions in the near-wall region are tested for their ability to replicate the behaviour of the normal stresses in a curved-pipe flow. These two closures differ in their modelling of the pressure-strain terms. Consequently, the effects of near-wall and pressure-strain modelling on curved-pipe flow calculations can be examined. Comparisons are also made with recent curved-pipe flow measurements. The results show that pressure-strain modelling alone is not sufficient to predict the rapid rise of the anisotropy of the normal stresses near the outer bend, and hence the formation of the secondary flow of the second kind. Overall, the near-wall Reynolds stress closure gives a more accurate prediction of the measured mean flow and turbulence statistics, and a realistic calculation of the secondary flow of the second kind near the outer bend.