The Effects of Adverse Pressure Gradients on Momentum and Thermal Structures in Transitional Boundary Layers: Part 2—Fluctuation Quantities

Abstract

The effects of adverse pressure gradients on the thermal and momentum characteristics of a heated transitional boundary layer were investigated with free-stream turbulence ranging from 0.3 to 0.6 percent. Boundary layer measurements were conducted for two constant-K cases, K1 = −0.51 × 10−6 and K2 = −1.05 × 10−6. The fluctuation quantities, u′, ν′, t′, the Reynolds shear stress (uν), and the Reynolds heat fluxes (νt and ut) were measured. In general, u′/U∞, ν′/U∞, and νt have higher values across the boundary layer for the adverse pressure-gradient cases than they do for the baseline case (K = 0). The development of ν′ for the adverse pressure gradients was more actively involved than that of the baseline. In the early transition region, the Reynolds shear stress distribution for the K2 case showed a near-wall region of high-turbulent shear generated at Y+ = 7. At stations farther downstream, this near-wall shear reduced in magnitude, while a second region of high-turbulent shear developed at Y+ = 70. For the baseline case, however, the maximum turbulent shear in the transition region was generated at Y+ = 70, and no near-wall high-shear region was seen. Stronger adverse pressure gradients appear to produce more uniform and higher t′ in the near-wall region (Y+ < 20) in both transitional and turbulent boundary layers. The instantaneous velocity signals did not show any clear turbulent/nonturbulent demarcations in the transition region. Increasingly stronger adverse pressure gradients seemed to produce large non turbulent unsteadiness (or instability waves) at a similar magnitude as the turbulent fluctuations such that the production of turbulent spots was obscured. The turbulent spots could not be identified visually or through conventional conditional-sampling schemes. In addition, the streamwise evolution of eddy viscosity, turbulent thermal diffusivity, and Prt, are also presented.

The Effects of Adverse Pressure Gradients on Momentum and Thermal Structures in Transitional Boundary Layers: Part 2 — Fluctuation Quantities

“…In the later stages of transition, the t' distribution at station 8 maintains a nearly constant value of 12% in the region of 10<Y + <50 before receding to the asymptotic values in the turbulent boundary layer at station 13. The t' values in the turbulent flow are larger than they are for both the KI case (not shown, see Mislevy, 1993) and the baseline case in the near-wall region. For the K2 case, the t' distribution reaches the value of a turbulent flow at about station 10 or 11.…”

The Effects of Adverse Pressure Gradients on Momentum and Thermal Structures in Transitional Boundary Layers: Part 1 — Mean Quantities

“…However, the Stanton number, as seen before at high U°,o, develops significant scatter midway throug h transition with a region that indicates a decrease in the heat transfer coefficient. From information indicated by the flow structures in the boundary layer (such as mean velocity profiles, fluctuating velocities, and shape factors), the turbulent region starts at about 1.3 x 10 6 (or the location of Cf,max)• Therefore, if these instabilities are causing the Stanton number scatter, then strangely they are not affecting the mean or fluctuating streamwise velocities (not shown here; see Mislevy, 1993) within the boundary layer. In addition, the C f distribution does not suggest the existence of a separation bubble since no near-zero value for the C f was found.…”

“…The Reynolds stresses and heat fluxes will be presented in Part 2 of this paper. A detailed uncertainty was performed by Mislevy (1993). Representative uncertainty of the mean quantities is listed in Table 1.…”