The First-moment Integral Equations for Boundary Layer Flows and Their Application

The enhancement of skin friction drag and surface heat flux by the transition to turbulence is a crucial physical phenomenon in wall-bounded flows. An interpretable mapping of how various flow phenomena such as turbulence and pressure gradient influence these key surface quantities is desirable for advancing our understanding of fundamental flow physics, as well as informing engineering design analysis and developing efficient flow control techniques. To accomplish such a mapping, in this study, integral forms based on the first-moment of conservation equations are developed. The angular momentum integral (AMI) equation, obtained from the first moment of the momentum equation, yields an identity for the skin friction coefficient (friction drag). Furthermore, the moment of (total) enthalpy integral (MTEI) equation, derived from the first moment of the en- ergy equation, provides a mapping for the Stanton number (surface heat flux). This first-moment approach uniquely isolates the skin friction (or surface heat flux) of a laminar BL in a single term that depends only on the Reynolds number (or Peclet number) most relevant to the flow’s engineer- ing context, hence other terms are interpreted as augmentations or reductions relative to the laminar case having the same Reynolds number (or Peclet number).In the case of zero-pressure-gradient incompressible transitional BLs, the AMI and MTEI equations examine the peak friction drag and surface heat flux during the transition. These tools demonstrate and quantify how the streamwise growth of the BL and the mean wall-normal flux resist the extreme growth of turbulent enhancement via Reynolds shear stress. This rapid growth of turbulence during transition imposes near-wall streamwise acceleration that results in a negative wall-normal velocity very close to the wall. For a fully turbulent regime, the explicit turbulent enhancement is the primary process of near-wall momentum (or heat) flux, not molecular transport. Consequent