Adverse-Pressure-Gradient Effects on Turbulent Boundary Layers: Statistics and Flow-Field Organization
Adverse-Pressure-Gradient Effects on Turbulent Boundary Layers: Statistics and Flow-Field Organization
Carlos Sanmiguel Vila 0 1
Ramis O¨ rlu¨ 0 1
Ricardo Vinuesa 0 1
Philipp Schlatter 0 1
Andrea Ianiro 0 1
Stefano Discetti 0 1
0 Linne ́ FLOW Centre, KTH Mechanics , SE-100 44 Stockholm , Sweden
1 Aerospace Engineering Group, Universidad Carlos III de Madrid , Legane ́s , Spain
This manuscripts presents a study on adverse-pressure-gradient turbulent boundary layers under different Reynolds-number and pressure-gradient conditions. In this work we performed Particle Image Velocimetry (PIV) measurements supplemented with LargeEddy Simulations in order to have a dataset covering a range of displacement-thicknessbased Reynolds-number 2300 < Reδ∗ < 34000 and values of the Clauser pressure-gradient parameter β up to 2.4. The spatial resolution limits of PIV for the estimation of turbulence statistics have been overcome via ensemble-based approaches. A comparison between ensemble-correlation and ensemble Particle Tracking Velocimetry was carried out to assess the uncertainty of the two methods. The effects of β, Re and of the pressure-gradient history on turbulence statistics were assessed. A modal analysis via Proper Orthogonal Decomposition was carried out on the flow fields and showed that about 20% of the energy contribution corresponds to the first mode, while 40% of the turbulent kinetic energy corresponds to the first four modes with no appreciable dependence on β and Re within the investigated range. The topology of the spatial modes shows a dependence on the Reynolds number and on the pressure-gradient strength, in line with the results obtained from the analysis of the turbulence statistics. The contribution of the modes to the Reynolds stresses and the turbulence production was assessed using a truncated low-order reconstruction with progressively larger number of modes. It is shown that the outer peaks in the Reynolds-stress profiles are mostly due to large-scale structures in the outer part of the boundary layer.
Wall turbulence; PTV; PIV; POD
1 Introduction
The quest for a better understanding of turbulent boundary layers (TBLs) is one of the main
research goals of the turbulence community since many decades, as stated for instance in
Ref. [
1
]. Wall-bounded turbulence is present in many relevant fluid-flow problems such as
the flow around wings, land and sea vehicles, or in turbines, compressors, etc. Simplified
scenarios, such as the zero-pressure-gradient (ZPG) TBL developing over a flat plate, have
been investigated to understand the fundamental aspects of wall-bounded turbulence.
Unfortunately, ZPG conditions are nearly never encountered in real-life applications; instead, the
majority of flow problems are under the effect of complex pressure gradients. In particular,
adverse pressure gradients might produce flow separation with the consequent losses in
performances. Under these conditions, the applicability of the knowledge from ZPG TBLs to
decelerating boundary layers is still rather limited [
2, 3
]. Despite the existence of a number
of simulations and experiments on adverse-pressure-gradient (APG) TBLs (among many
others, see e.g. Refs. [
2–9
]), there is still no clear understanding of the isolated effects of
the imposed pressure-gradient, of its upstream history and of the Reynolds number. The
wider parametric space with respect to ZPG TBLs and the importance of history effects in
the development of the flow are some of the reasons which make the study of these flows
challenging. In an attempt to reduce the number of parameters which characterize the
history effects, most of the APG studies are performed in a state of near-equilibrium. This
implies that the mean velocity deficit in the outer part is self-similar at sufficiently high
Reynolds numbers as discussed, among others, in Ref. [
1
]. The streamwise evolution of the
free-stream velocity U∞(x) in an APG TBL under near-equilibrium conditions follows a
power-law relation such that U∞ = C(x − x0)m. Here C is a constant, x0 is a virtual origin
and the exponent m ranges between −1/3 < m < 0 [
10
].
Some important features of APG flows have already been clarified in the past decades.
The most recognizable feature of an APG TBL is the more prominent wake of streamwise
mean velocity profile [
11
]. The strengthened wake reflects the local state of the boundary
layer as a consequence of the impact of history effects experienced by the flow. The wake
strength is connected to the Clauser pressure-gradient parameter β [
12
], which is defined
as β = (δ∗/τw)(dP /dx), where δ∗ is the displacement thickness, τw is the mean wall-shear
stress, and dP /dx is the derivative of the static pressure along the streamwise coordinate.
As β increases, the mean velocity profile develops a larger wake region and the
streamwise variance profile exhibits an outer peak, which is related to the development of more
energetic large-scale motions [
(...truncated)