The Structure of Zero, Favorable and Adverse Pressure Gradient Turbulent Boundary Layers

The effects of pressure gradient on an initially zeropressure-gradient turbulent boundary layer are investigated. We consider both adverse and favourable pressure gradients at matched Reynolds number as compared with the zero pressure gradient case. The data are also acquired using matched sensor parameters so that an unambiguous comparison can be made. The results show that energy increases throughout the turbulent boundary layer as the pressure gradient increases. It is also found that the large-scale motions are much more energetic for adverse pressure gradients compared with the other cases. The outer region of the flow appears most affected by the pressure gradient in this regard. The streak spacing in the near-wall viscous region is found to be unaffected by the pressure gradients, which is in contrast to other studies in the literature. INTRODUCTION Of the turbulent boundary layer flows, the canonical zero-pressure-gradient (ZPG) case, on a flat plate with constant free-stream velocity, has received the most attention. Recent reviews on these flows (Smits et al. 2011, Marusic et al. 2010, Klewicki 2010) discuss the recent findings with respect to scaling, Reynolds numbers effects, and the role of coherent structures and very-large-scale motions in these flows. It is of interest to see how these features change once the boundary layers encounter a streamwise favorable pressure gradient (FPG) or adverse pressure gradient (APG), as this is a common occurrence in many engineering systems. Pressure gradient flows have also received considerable attention (Clauser 1954, Cal et al. 2008, Krogstad & Skare 1995, Marusic & Perry 1995, Aubertine & Eaton 2000, and many others) but in recent times there has been renewed interest in the light of independent wall-shear stress measurements that have brought into question the universal scaling behaviour of the near-wall and logarithmic regions (Nagib et al. 2009, Bourassa & Thomas 2009, Monty et al. 2011). A recent DNS study of an adverse pressure gradient boundary layer by Lee & Sung (2009) has also raised questions as to how the coherent structures are affected from the largest structures in the flow (Hutchins & Marusic 2007) to the near-wall sublayer streaks (Kline et al. 1967). Lee & Sung report that under strong adverse pressure gradients the near-wall streaks are weakened, with the spanwise spacing between the streaks becoming irregular and increasing in size to 400 viscous wall units, which is approximately four times larger than that of the ZPG flow. For FPG flows, these streak spacings have also been reported to be above the nominal ZPG value of 100 viscous wall units (Bourassa and Thomas 2009). A survey from various studies of streak spacing for different pressure gradient flows is shown in table 1. From these results, it is noted that significant effects are seen in the near-wall region (by the change in streak spacing). However, all the studies in table 1 were performed at different Reynolds numbers. Here, Reθ = θU1/ν is the Reynolds number based on momentum thickness θ , where U1 is the local free stream velocity and ν is kinematic viscosity. Recent studies in ZPG flows have demonstrated that Reynolds number effects vary even beyond Reynolds numbers traditionally considered high: The contribution from the log region to the overall turbulence production increases with Reynolds number (Marusic et al. 2010) and large-scale structures which inhabit the log region amplitude-modulate the near-wall region (Mathis et al. 2009). In an attempt to isolate any Reynolds number effects, we have designed experiments where we maintain the Reynolds number at Re = δUτ/ν ≈ 1900, where δ is the boundary layer thickness, and Uτ is friction velocity. Throughout this paper, x, y and z are the streamwise, spanwise and wall-normal directions respectively, and nor-