Abstract

The inertial sublayer of adverse pressure-gradient (APG) turbulent boundary layers is investigated using new experimental measurements ( $7000 \lesssim \delta ^+ \lesssim 7800$ ), existing lower Reynolds number experimental ( $\delta ^+ \approx 1000$ ) and computational ( $\delta ^+<800$ ) data sets, where $\delta ^+$ is the friction Reynolds number. In the present experimental set-up the boundary layer is under modest APG conditions, where the Clauser PG parameter $\beta$ is ${\leq }1.8$ . Well-resolved hot-wire measurements are obtained at the Flow Physics Facility at the University of New Hampshire in the region of an APG ramp. Comparisons are made with zero pressure-gradient turbulent boundary layer (ZPG TBL) experimental data at similar Reynolds number and numerical simulation data at lower Reynolds number. The main aims of the present study centre on the inertial sublayer of the APG TBL and the degree to which its characteristics are similar to those of the ZPG TBL. This investigation utilizes equation-based analyses and empirical approaches. Among other results, the data suggest that even though the APG TBL streamwise variance does not exhibit a logarithmic profile (unlike the ZPG TBL) both ZPG and APG TBLs exhibit distance-from-the-wall scaling on the inertial sublayer. Theoretical arguments suggest that wall-distance scaling resulting from a self-similar dynamics is consistent with both a single velocity scale leading to a log-law in mean velocity profile as well as multiple velocity scales leading to a power-law mean velocity profile.

Highlights

  • Owing to their technological significance, turbulent boundary layers have, and continue to be, the subject of intense study

  • This study focuses on four traits of the inertial sublayer: (1) logarithmic behaviour in the mean velocity profile; (2) position of the inertial sublayer in relation to the RS, uv profile; (3) properties of the turbulent stresses, including the decay of the streamwise velocity fluctuation variances, u2; and (4) the distance-from-the-wall scaling of various turbulence properties

  • Similar to the analysis carried out for channel and zero pressure-gradient turbulent boundary layer (ZPG TBL) flows, we introduce the small parameter whose values are each associated with a ‘scaling patch’. (See, the Appendix (A.1) for the definition of a scaling patch.) For adverse pressure-gradient (APG) TBLs the modified RS takes the following form: y+

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Summary

Introduction

Owing to their technological significance, turbulent boundary layers have, and continue to be, the subject of intense study For the purposes of modelling and conceptual understanding, it is useful to know those aspects of PG boundary layers that are describable as an extension of those found in the canonical flow Toward this aim, the present study broadly seeks to clarify the connections between the inertial sublayer of TBLs subjected to moderately adverse pressure-gradients (APG) and the inertial sublayer (logarithmic layer) of the ZPG TBL. In the case of an APG TBL, at subsonic speeds the free stream flow decelerates, and there is a new time scale associated with the PG, tPG = −(dU∞/dx)−1. This introduces a new non-dimensional number (the Clauser PG parameter):. For all of the flows studied history effects are expected to have only a relatively small influence on the dynamical structure

Inertial sublayer
Present study
Indicator function
Stress balance
Higher-order statistics
Spectra
Quantifying the PG
Facility and ramp
Pressure distribution
Hot-wire anemometry
Measurement parameters
Probe performance
Data sources
Flow statistics
Stresses
Skewness and kurtosis
Conclusions
Logarithmic behaviour in the mean velocity profile
Properties of the turbulent stresses including decay of u2
Distance-from-the-wall scaling of variance turbulence properties
Closing comments
Basic notion of scaling patches
Application of scaling patch to wall-flow mean momentum equation
Properties that guarantee the existence of scaling patches
Applying to APG TBLs
Findings
Summary
Full Text
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