Abstract
This Rapid Communication investigates boundary layer flows with a pressure gradient using a similarity/integral analysis of the continuity equation and momentum equation in the streamwise direction. The analysis yields useful analytical relations for , the mean wall-normal velocity at the edge of the boundary layer, and for the skin friction coefficient in terms of the boundary layer parameters and in particular , the Rotta-Clauser pressure gradient parameter. The analytical results are compared with experimental and numerical data and are found to be valid. One of the main findings is that for large positive (an important effect of an adverse pressure gradient), the friction coefficient is closely related to as , because , and become approximately constant. Here, is the boundary layer thickness, is the displacement thickness, is the momentum thickness, and is the shape factor. Another finding is that the mean wall-normal velocity at the edge of the boundary layer is related to other flow variables as , where is the streamwise velocity at the edge of the boundary layer. At zero pressure gradient, this relation reduces to , as recently derived by Wei and Klewicki [Phys. Rev. Fluids 1, 082401 (2016)].
- Received 28 April 2017
DOI:https://doi.org/10.1103/PhysRevFluids.2.092601
©2017 American Physical Society