In this study, a large eddy simulation (LES) for fully-developed turbulent flows through the missing pipes, which is a part of circular cross-section cut by a straight line, using the immersed boundary (IB) method is performed with six central half angles. In the case of the central half angle is π/4 or less, even if the shape of the cross section changes, the flow resistance barely increases and the required driving force does not change. When the central half angle is between π/3 and 2π/3, the secondary flow of Prandtl's second kind occurs at the same level as that in the square duct and exerts a great influence on the distributions of the turbulence energy and Reynolds stress.
OKAMOTO et al. (Wed,) studied this question.