A turbulent equilibrium boundary layer near separation

Abstract

The experimental results for an equilibrium boundary layer in a strong adverse pressure gradient flow are reported. The measurements show that similarity in the mean flow and the turbulent stresses has been achieved over a substantial streamwise distance where the skin friction coefficient is kept at a low, constant level. Although the Reynolds stress distribution across the layer is entirely different from the flow at zero pressure gradient, the ratios between the different turbulent stress components were found to be similar, showing that the mechanism for distributing the turbulent energy between the different components remains unaffected by the mean flow pressure gradient. Close to the surface the gradient of the mixing length was found to increase from Kl ≈ 0.41 to Kl ≈ 0.78, almost twice as high as for the zero pressure gradient case. Similarity in the triple correlations was also found to be good. The correlations show that there is a considerable diffusion of turbulent energy from the central part of the boundary layer towards the wall. The diffusion mechanism is caused by a second peak in the turbulence production, located at y/δ ≈ 0.45. This production was for the present case almost as strong as the production found near the wall. The energy budget for the turbulent kinetic energy also shows that strong dissipation is not restricted to the wall region, but is significant for most of the layer.

Vortex Dynamics in Turbulence

“…For a given eddy shape, the mean velocity profile and the u i u j profiles are calculated analytically from the vortex kinematics of the rods, and parameters in the pdfs are fixed by fitting the u 1 u 3 results to those obtained from the mean momentum equation. The model is tested by comparing the profiles of the remaining components of u i u j to the experiments of Skåre & Krogstad (1994) with fair results. The model also produces predictions, which include various one-dimensional spectra of the u i u j , in excess of parameters.…”

Coherent Structures in a Non-equilibrium Large-Velocity-Defect Turbulent Boundary Layer

“…The mean shear rates in the outer region are no longer small in comparison to their near-wall counterparts while near the wall, the importance of viscous forces and of the wall shear stress diminishes. As a result, in contrast to canonical wall-bounded turbulent flows, turbulence activity and production is small near the wall and important in the outer region of the flow [27,18,3]. Marquillie et al [15] have proposed that the outer peaks of Reynolds stresses and production could be related to a streak bursting process, whereas Elsberry et al [3] suggest that it is due to the inflectional instability of the mean velocity profile as in mixing layers.…”

Similarity Scaling for the Inner Region of the Turbulent Boundary Layer

“…It is obvious that the closer the data comes to satisfying the Rotta condition, the more the ß x -scaled Figure 3a: DeGraaff and Eaton [5] velocity profiles taken at 7?^=1430, 2900, and 5200. Figure 5b: Skäre and Krogstad [22] seven velocity profiles.…”

“…14 Figure 6b. The seven full scale velocity profiles from Skäre and Krogstad [22] using Prandtl plus scaling. 14 Figure 7.…”

“…The seven full scale velocity profiles from Skäre and Krogstad [22] using £ t and u e scaling 14 . The seven velocity profiles (black lines) from Skäre and Krogstad [22] using the inferred c f data to calculate ju l 15 Figure 10a. Ten profiles from Schubauer and Klebanoff [32] using the scaled defect profile for the y-axis 19…”