The Description and Scaling Behavior for the Inner Region of the Boundary Layer for 2-D Wall-bounded Flows

TL;DR

This paper introduces a new moment-based method for describing the viscous-dominated inner region of turbulent boundary layers, addressing limitations of traditional models and providing a more consistent scaling approach.

Contribution

A novel second derivative-based moment method is proposed that defines experimentally accessible boundary layer parameters without differentiation, improving upon traditional fixed-location models.

Findings

The new length scale parameter acts as a similarity parameter for velocity profiles.

It removes theoretical inconsistencies present in Prandtl Plus scaling.

The new parameters perform similarly to Prandtl Plus when the Rotta similarity constraint holds.

Abstract

A second derivative-based moment method is proposed for describing the thickness and shape of the region where viscous forces are dominant in turbulent boundary layer flows. Rather than the fixed location sublayer model presently employed, the new method defines thickness and shape parameters that are experimentally accessible without differentiation. It is shown theoretically that one of the new length parameters used as a scaling parameter is also a similarity parameter for the velocity profile. In fact, we show that this new length scale parameter removes one of the theoretical inconsistencies present in the traditional Prandtl Plus scaling's. Furthermore, the new length parameter and the Prandtl Plus scaling parameters perform identically when operating on experimental datasets if the Rotta similarity constraint (u_tau/u_e = constant) holds. This means that many of the past successes ascribed to the Prandtl Plus scaling also apply to the new parameter set but without one of the theoretical inconsistencies. Examples are offered to show how the new description method is useful in exploring the actual physics of the boundary layer.