Turbulent secondary flows in channels with no-slip and shear-free boundariesстатья
Статья опубликована в высокорейтинговом журнале
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Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 7 июля 2021 г.
Аннотация:A simple principle is formulated, which makes it possible to explain and, in some cases,to predict the shape of secondary flows of Prandtl’s second kind that arise in turbulentflows in straight pipes of non-circular cross-section. The motion along the no-slip wall isdirected in the direction of reduction of pressure. Therefore, the direction of the secondarymotion along the perimeter of the pipe cross-section can be determined by the location ofthe mean wall pressure local extrema. Velocity fluctuations along a curved wall cause themean wall pressure change, the greater the change, the greater the curvature of the wall.Thus, the location of local wall pressure extrema is consistent with the wall curvature.In a number of cases, an approximate picture of secondary flows can be predicted apriori using only symmetry considerations and a wall curvature analysis. The conditionsfor the formation of a secondary flow change on a free surface where, in addition topressure, Reynolds stresses act on the fluid particles, and the result of their interactionis unknown in advance. A turbulent flow in a rectangular channel is considered, in whichone of the walls (upper) is shear-free. Application of the formulated principle dictates thepresence of secondary flows in the upper corners, with a downward motion along the solidsidewalls. This contradicts the popular point of view about the shape of secondary flowsin open channels, according to which the motion along the sidewalls is directed upwardtowards the corner and then towards the centre of the channel along the free surface. Thepaper presents the direct numerical simulation (DNS) results showing that along with thelarge-scale secondary flow, which generally agrees with the traditional picture, there isa smaller-scale single-vortex secondary flow with the opposite direction of rotation in thevicinity of each upper corner. The presence of a no-slip wall is an important element of thedescribed mechanism of secondary flow formation. In this regard, the question logicallyarises about the possibility of the occurrence of secondary flows in the corners betweentwo free boundaries. A series of DNS of turbulent flows in a square duct with two solidand two free adjacent walls have been carried out. It was found that the Reynolds stress forces in the vicinity of the corner between free boundaries are potential, are neutralizedby the pressure gradient, and therefore do not create a secondary flow.