A universal velocity transformation for boundary layers with pressure gradients
Abstract
The logarithmic law of the wall does not capture the mean flow when a boundary layer is subjected to a strong pressure gradient. In such a boundary layer, the mean flow is affected by the spatio-temporal history of the imposed pressure gradient; and accounting for history effects remains a challenge. This work aims to develop a universal mean flow scaling for boundary layers subjected to arbitrary adverse or/and favourable pressure gradients. We derive from the Navier–Stokes equation a velocity transformation that accounts for the history effects and maps the mean flow to the canonical law of the wall. The transformation is tested against channel flows with a suddenly imposed adverse or favourable pressure gradient, boundary layer flows subjected to an adverse pressure gradient, and Couette–Poiseuille flows with a streamwise pressure gradient. It is found that the transformed velocity profiles follow closely the equilibrium law of the wall.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Aug 25, 2023
- Source ID
- 10.1017/jfm.2023.570
Entities
People
- Kevin P. Griffin
- Peng E. S. Chen
- Wen Wu
- X I A Yang
- Yipeng Shi
Organizations
- National Natural Science Foundation of China
- National Renewable Energy Laboratory
- National Science Foundation
- Office of Naval Research
- Office of Science