Investigation of scaling laws in a turbulent boundary layer flow with adverse pressure gradient using PIV

Abstract

We present an experimental investigation and data analysis of a turbulent boundary layer flow at a significant adverse pressure gradient at Reynolds number up to Re θ = 10, 000. We combine large-scale particle image velocimetry (PIV) with microscopic PIV for measuring the near wall region including the viscous sublayer. We investigate scaling laws for the mean velocity and for the total shear stress in the inner part of the boundary layer. In the inner part the mean velocity can be fitted by a log-law. In the outer part of the inner layer the log-law ceases to be valid. Instead, a modified log-law provides a good fit, which is given in terms of the pressure gradient parameter and a parameter for the mean inertial effects. Finally we describe and assess a simple quantitative model for the total shear stress distribution which is local in wall-normal direction without streamwise history effects.

Experimental analysis of the log law at adverse pressure gradient

“…A model for the total shear stress An analytical model for the total shear stress by Coles (1956) and Perry (1966) The local effects on the total shear stress in the inner layer involve p + s and the wall shear stress gradient parameter u + τ,s . Note that an extension of the ansatz (E2a-c) using f = f ( y + (s, y), p + s (s)) accounts for higher-order effects on τ + , involving an additional parameter based on d 2 P/ds 2 , see Knopp et al (2015).…”

Extensive characterisation of a high Reynolds number decelerating boundary layer using advanced optical metrology

“…Adverse pressure gradient boundary layers are particularly problematical. There are indeed some careful experiments available in the literature on APG wall flows (e.g., (Ludwig & Tillman, 1950), (Perry & Shofield, 1973), (Skare & Krogstad, 1994), (Elsbery, et al, 2000), (Perry, et al, 2002), (Nagib, et al, 2004), (Maciel, et al, 2006), (Aubertine, 2006), (Rehgozar et al, 2011), (Joshi et al, 2014 (Knopp, et al, 2015)), but most of them provide only singlepoint turbulence statistics at a few stations, and generally only for one or at best two velocity components. In fact there is virtually no information on the turbulence integral scales which appear in even some of the simplest turbulence models.…”

Adverse-Pressure-Gradient Effects on Turbulent Boundary Layers: Statistics and Flow-Field Organization

“…On the other hand, there is some controversy on whether the logarithmic law of the wall still holds in APG TBL flows [ 15 , 16 ]. There are studies where it is claimed that the law of the wall is still valid, but that the region occupied by the logarithmic law is progressively reduced when the pressure gradient is increased.…”