EFFECT OF CURVATURE ON THE VELOCITY PROFILE AND BOUNDARY-LAYER IN FLOW-THROUGH A CURVED CHANNEL

We assess the base flow through a curved channel within the framework of a study of Gortler instability in the boundary layers in how over a concave wall. The base flow is defined as the flow without the three- dimensional effects of the instability. We present experimental, analy tical, and numerical results of flows over curved walls. We address th e variation of the boundary layer thickness as well as the flow outsid e the boundary layer. We show that in a curved channel? the two-dimens ional flow accelerates over the convex wall while it decelerates over the concave wall. The 2D numerical simulation demonstrates the importa nce of a longitudinal pressure gradient that always appears in such a geometry. In addition, we qualitatively discuss some modifications to the two-dimensional flow under the influence of three-dimensional Ekma n cells (also called Dean cells) or centrifugal instabilities of the G ortler or Dean type. We explain the origin of what is commonly known i n the literature as ''the transition from two to four rolls'' for flow through a curved channel of square or circular cross section.