Reynolds number dependence of azimuthal and streamwise pipe flow structures

Abstract

This paper revisits the study by Baileyet al.(J. Fluid Mech., vol. 615, 2008, pp. 121–138), adopting a higher-fidelity calibration approach to reveal subtle flow variations with Reynolds numbers that were not discernible previously. The paper aims therefore to provide insights into the characteristics of azimuthal and streamwise pipe flow structures adopting two-point joint statistics and spectral analysis for shear Reynolds numbers in the range$2\times {10^3}\le {Re_\tau }\le {16\times {10^3}}$, where${Re_\tau }$is based on the wall friction velocity$u_{\tau }$, the pipe radius$R$, and the fluid kinematic viscosity$\nu$. The streamwise velocity fluctuations were measured at four wall-normal locations,$0.1\le {x_{{2}}/R}\le {0.7}$, covering the logarithmic and core regions of fully developed turbulent pipe flow based on 35–41 azimuthal probe separations using, simultaneously, two single hot-wire probes. A uniquein situcalibration approach for both probes was adopted where a potential flow was insured, resulting in consistent and precise pipe flow data. The azimuthal velocity correlation, the cross-power spectral density and the coherence function of the streamwise velocity fluctuations are discussed, revealing a clear dependence of the azimuthal scales of the large and very large flow motions on the wall-normal location, the azimuthal separation, the streamwise wavenumber and the Reynolds number. Along the logarithmic region, a linear growth of the azimuthal scales of the large- and very-large-scale structures was observed; however, they do scale nonlinearly and reach their maximum sizes in the core region, i.e. near the centreline of the pipe. Additionally, the streamwise very-large- and large-scale motions were evaluated using the premultiplied energy spectra, showing wavelengths${\approx }{18R}$and${\approx }{3R}$for${Re_{\tau }}\approx {16\times {10^3}}$at half of the pipe radius, respectively.