| The asymptotic invariance principle (AIP) and the Near-Asymptotic method have been successfully explored for the non-equilibrium turbulent boundary layer, the turbulent boundary layer with separation, and the forced convection turbulent boundary layer subject to the external pressure gradient.; Using the AIP, it is found that even the non-equilibrium flows, defined as the pressure parameter Λ ≠ constant, are in equilibrium but only locally. Each local region of these flows is characterized by a constant pressure parameter. The adverse pressure gradient (APG) region of a non-equilibrium flow is characterized by a single value of Λ ≅ 0.22, which is the same as the case of equilibrium flows. In addition, it has been found that the outer part of separating boundary layers also remains in equilibrium and is characterized by a constant pressure parameter. The pressure parameter, Λ&thetas;, is nearly the same for all the APG flows with eventual separation; in particular, Λ&thetas; = 0.21 ± 0.01. Subsequently, a single velocity profile should exist for all APG flows, which has been confirmed by the Zagarola/Smits scaling, U∞δ∗/δ.; Using the pressure parameter Λ&thetas; along with the integral momentum equation, a shape factor of Hsep = 2.76 ± 0.23 is predicted for the turbulent boundary layer at separation. This value is in close agreement with the intermittent transitional detach (ITD) position for the experimental data studied here. With the correlation from Sandborn & Kline (1961), a “separation zone” has been proposed, which proves to be very meaningful in predicting separation in boundary layer flows. Moreover, this separation zone emphasizes the fact that separation in the turbulent boundary layer is a process instead of a single event as indicated by Simpson et al. (1981) and others.; Furthermore, the similarity analysis is developed for a 2-D steady incompressible forced convection turbulent boundary layer subject to the external pressure gradient. Two new scalings have been obtained for the inner and outer region, respectively. When normalized by the new scalings, all the temperature profiles collapse into a single curve regardless of the effects from the pressure gradient, upstream conditions and the Péclet number dependence. Using the new temperature scalings, a power law function has been derived for the temperature profile in the overlap region by means of the Near-Asymptotic method. Meanwhile, the inner composite temperature profile and the wake function have been proposed empirically. Thus, the entire composite temperature profile is constructed and presented, which can describe the experimental data with ZPG and APG very well over the entire boundary layer even at the finite Péclet number. The prediction error has been calculated with an uncertainty less than 3% for the ZPG flow and 5% for the APG flow. Furthermore, a power form of the heat transfer law has been predicted, and a theoretical prediction of the thermal displacement thickness is also proposed.; The results are compared with the classical studies, and some other recent investigations. These new scalings and new composite temperature profiles perform much better than others, especially in removing the effects from upstream conditions and different strengths of the pressure gradient. |
