Comparison of Three Inner‐Variable Approaches to Establish an Accurate Method for Turbulent Boundary Layers

An inner‐variable integral theory was derived for solving incompressible two‐dimensional turbulent boundary layers. This new derivation incorporated major improvements to the earlier inner‐variable approach of White (1974) and Das and White (1986) by including a better wake function and a superior pressure gradient‐wake correlation. Initially, the derivation from the first principle led to three nonlinear ordinary differential equations that must be solved simultaneously to yield important boundary layer parameters. Subsequently, to simplify the theory, it was systematically reduced in two steps: first to a two‐equation method, and next to a one‐equation method. Then comparisons were carried out among the three methods using well‐established experimental data from a wide range of flows. The two‐equation method gave the best overall performance and was selected as the standard method. Finally, it was tested against additional experiments, giving reliable predictions against eleven different experimental flows under diverse flow conditions.