Turbulence structure and turbulence kinetic energy transport in multiscale/fractal-generated turbulence

Abstract

The turbulence structure and turbulence kinetic energy transport in multiscale/fractal-generated turbulence in a wind tunnel are investigated. A low-blockage, space-filling square-type (i.e., fractal elements with square shapes) fractal grid is placed at the inlet of the test section. On the basis of the thickness of the biggest grid bar, t0, and the inflow velocity U∞, the Reynolds numbers (Re0) are set to 5900 and 11 400; these values are the same as those considered in previous experiments [D. Hurst and J. C. Vassilicos, “Scalings and decay of fractal-generated turbulence,” Phys. Fluids 19, 035103 (2007)10.1063/1.2676448; N. Mazellier and J. C. Vassilicos, “Turbulence without Richardson-Kolmogorov cascade,” Phys. Fluids 22, 075101 (2010)10.1063/1.3453708]. The turbulence characteristics are measured using hot-wire anemometry with I- and X-type probes. Generally, good agreements are observed despite the difference in the size of the test sections used: The longitudinal integral length-scale Lu and the Taylor microscale λ, and their ratio Lu/λ, are approximately constant during decay and are independent of the turbulent Reynolds number Reλ. Centerline statistical results support the finding of Mazellier and Vassilicos, namely, that the classical scaling of Lu/λ ∼ Reλ and the Richardson–Kolmogorov cascade are not universal to all boundary-free weakly sheared/strained turbulence. The cross-sectional profiles show that in the entire cross section of the tunnel, Lu/λ hardly changes in the decay region of the rms velocity, which implies that the turbulent field is self-similar. The production and transport of turbulence kinetic energy K in fractal grid turbulence are also investigated from cross-sectional profiles of the advection \documentclass[12pt]{minimal}\begin{document}${\cal A}^*$\end{document}A*, production \documentclass[12pt]{minimal}\begin{document}${\cal P}^*$\end{document}P*, triple-correlation transport \documentclass[12pt]{minimal}\begin{document}${\cal T}^*$\end{document}T*, pressure transport Π*, viscous diffusion \documentclass[12pt]{minimal}\begin{document}${\cal D}^*$\end{document}D*, and dissipation ɛ terms in the K transport equation. In the upstream region, turbulence produced by the biggest grid bar is transported to the central and outward regions by \documentclass[12pt]{minimal}\begin{document}${\cal T}^*$\end{document}T*. In the decay region, there is low turbulence production downstream of the interior of the biggest grid bar; turbulence energy in this region is mainly transported outward rather than toward the central region by \documentclass[12pt]{minimal}\begin{document}${\cal T}(=$\end{document}T(=\documentclass[12pt]{minimal}\begin{document}${\cal T}^*/\varepsilon )$\end{document}T*/ɛ). This characteristic of \documentclass[12pt]{minimal}\begin{document}${\cal T}$\end{document}T may cause a faster decay of K in the central region, as observed by Valente and Vassilicos [“The decay of turbulence generated by a class of multiscale grids,” J. Fluid Mech. 687, 300 (2011)10.1017/jfm.2011.353]. The advection term \documentclass[12pt]{minimal}\begin{document}${\cal A}^*$\end{document}A* is high and positive in the decay region, whereas Π* and \documentclass[12pt]{minimal}\begin{document}${\cal D}^*$\end{document}D* are low.