Beverley McKeon

Wall-bounded turbulent flows at high Reynolds numbers: Recent advances and key issues

Wall-bounded turbulent flows at high Reynolds numbers have become an increasingly active area of research in recent years. Many challenges remain in theory, scaling, physical understanding, experimental techniques, and numerical simulations. In this paper we distill the salient advances of recent origin, particularly those that challenge textbook orthodoxy. Some of the outstanding questions, such as the extent of the logarithmic overlap layer, the universality or otherwise of the principal model parameters such as the von Karman “constant,” the parametrization of roughness effects, and the scaling of mean flow and Reynolds stresses, are highlighted. Research avenues that may provide answers to these questions, notably the improvement of measuring techniques and the construction of new facilities, are identified. We also highlight aspects where differences of opinion persist, with the expectation that this discussion might mark the beginning of their resolution.

Further observations on the mean velocity distribution in fully developed pipe flow

The measurements by Zagarola & Smits (1998) of mean velocity profiles in fully developed turbulent pipe flow are repeated using a smaller Pitot probe to reduce the uncertainties due to velocity gradient corrections. A new static pressure correction (McKeon & Smits 2002) is used in analysing all data and leads to significant differences from the Zagarola & Smits conclusions. The results confirm the presence of a power-law region near the wall and, for Reynolds numbers greater than 230×10^3 (R+ >5×10^3), a logarithmic region further out, but the limits of these regions and some of the constants differ from those reported by Zagarola & Smits. In particular, the log law is found for 600<y+ <0.12R+ (instead of 600<y+ <0.07R+), and the von Karman constant κ, the additive constant B for the log law using inner flow scaling, and the additive constant B∗ for the log law using outer scaling are found to be 0.421 ± 0.002, 5.60 ± 0.08 and 1.20 ± 0.10, respectively, with 95% confidence level (compared with 0.436±0.002, 6.15±0.08, and 1.51±0.03 found by Zagarola & Smits). The data also confirm that the pipe flow data for ReD ≤ 13.6×10^6 (as a minimum) are not affected by surface roughness.

Static pressure correction in high Reynolds number fully developed turbulent pipe flow

Measurements are reported of the error in wall static pressure reading due to the finite size of the pressure tapping. The experiments were performed in incompressible turbulent pipe flow over a wide range of Reynolds numbers, and the results indicate that the correction term (as a fraction of the wall stress) continues to increase as the hole Reynolds number

Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels

d^+=u_\tau d/\nu

Modal Analysis of Fluid Flows: An Overview

increases, contrary to previous studies. For small holes relative to the pipe diameter the results follow a single curve, but for larger holes the data diverge from this universal behaviour at a point that depends on the ratio of the hole diameter to the pipe diameter.

Step Excrescence Effects for Manufacturing Tolerances on Laminar Flow Wings

We study the Reynolds number scaling and the geometric self-similarity of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (2010), in order to obtain a description of the streamwise turbulence intensity from direct consideration of the Navier-Stokes equations. Under this formulation, the velocity field is decomposed into propagating waves (with single streamwise and spanwise wavelengths and wave speed) whose wall-normal shapes are determined from the principal singular function of the corresponding resolvent operator. Using the accepted scalings of the mean velocity in wall-bounded turbulent flows, we establish that the resolvent operator admits three classes of wave parameters that induce universal behavior with Reynolds number on the low-rank model, and which are consistent with scalings proposed throughout the wall turbulence literature. In addition, it was shown that a necessary condition for geometrically self-similar resolvent modes is the presence of a logarithmic turbulent mean velocity. We identify the scalings that constitute hierarchies of self-similar modes that are parameterized by the critical wall-normal location where the speed of the mode equals the local turbulent mean velocity. For the rank-1 model subject to broadband forcing, the integrated streamwise energy density takes a universal form which is consistent with the dominant near-wall turbulent motions. When the shape of the forcing is optimized to enforce matching with results from direct numerical simulations at low turbulent Reynolds numbers, further similarity appears. Representation of these weight functions using similarity laws enables prediction of the Reynolds number and wall-normal variations of the streamwise energy intensity at high Reynolds numbers (

Relaminarisation of Reτ = 100 channel flow with globally stabilising linear feedback control

{Re}_\tau \approx 10^3 - 10^{10}

A reduced-order model of three-dimensional unsteady flow in a cavity based on the resolvent operator

).

An Approach to Measuring Step Excrescence Effects in the Presence of a Pressure Gradient

Simple aerodynamic configurations under even modest conditions can exhibit complex flows with a wide range of temporal and spatial features. It has become common practice in the analysis of these flows to look for and extract physically important features, or modes, as a first step in the analysis. This step typically starts with a modal decomposition of an experimental or numerical dataset of the flow field, or of an operator relevant to the system. We describe herein some of the dominant techniques for accomplishing these modal decompositions and analyses that have seen a surge of activity in recent decades. For a non-expert, keeping track of recent developments can be daunting, and the intent of this document is to provide an introduction to modal analysis that is accessible to the larger fluid dynamics community. In particular, we present a brief overview of several of the well-established techniques and clearly lay the framework of these methods using familiar linear algebra. The modal analysis techniques covered in this paper include the proper orthogonal decomposition (POD), balanced proper orthogonal decomposition (Balanced POD), dynamic mode decomposition (DMD), Koopman analysis, global linear stability analysis, and resolvent analysis.

Correspondence between Koopman mode decomposition, resolvent mode decomposition, and invariant solutions of the Navier-Stokes equations

Manufacturing tolerances for laminar flow wings can be significantly tighter than those of conventional aircraft. The tighter tolerances can significantly affect the assessment of the practicality of designing for laminar flow. However, existing data on the effects of excrescences typical of manufacturing process are limited. Further, information on the effects—often beneficial—of pressure gradient present on the laminar flow wings is not generally available. To address these concerns, a series of experiments has been undertaken to examine the effects of surface steps in the presence of pressure gradients. The step geometries were selected to represent those that result from actual aircraft manufacturing processes. The range of pressure gradients correspond to those typical of laminar flow wings. Initial experiments were conducted in a low-speed wind tunnel. Later experiments used a novel propelled-model test facility. The results of these studies show that the allowable sizes of surface excrescences for laminar flow wings may be significantly greater than has conventionally been assumed. This could significantly influence the more widespread use of laminar flow for drag reduction, resulting in more efficient aircraft.