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Weakly sheared turbulent flows generated by multiscale inhomogeneous grids

Published online by Cambridge University Press:  13 June 2018

Shaokai Zheng*
Affiliation:
Department of Aeronautics, Imperial College London, London, SW7 2AZ, UK
P. J. K. Bruce
Affiliation:
Department of Aeronautics, Imperial College London, London, SW7 2AZ, UK
J. M. R. Graham
Affiliation:
Department of Aeronautics, Imperial College London, London, SW7 2AZ, UK
J. C. Vassilicos*
Affiliation:
Department of Aeronautics, Imperial College London, London, SW7 2AZ, UK
*
Email addresses for correspondence: s.zheng13@imperial.ac.uk, j.c.vassilicos@imperial.ac.uk
Email addresses for correspondence: s.zheng13@imperial.ac.uk, j.c.vassilicos@imperial.ac.uk

Abstract

A group of three multiscale inhomogeneous grids have been tested to generate different types of turbulent shear flows with different mean shear rate and turbulence intensity profiles. Cross hot-wire measurements were taken in a wind tunnel with Reynolds number $Re_{D}$ of 6000–20 000, based on the width of the vertical bars of the grid and the incoming flow velocity. The effect of local drag coefficient $C_{D}$ on the mean velocity profile is discussed first, and then by modifying the vertical bars to obtain a uniform aspect ratio the mean velocity profile is shown to be predictable using the local blockage ratio profile. It is also shown that, at a streamwise location $x=x_{m}$, the turbulence intensity profile along the vertical direction $u^{\prime }(y)$ scales with the wake interaction length $x_{\ast ,n}^{peak}=0.21g_{n}^{2}/(\unicode[STIX]{x1D6FC}C_{D}w_{n})$ ($\unicode[STIX]{x1D6FC}$ is a constant characterizing the incoming flow condition, and $g_{n}$, $w_{n}$ are the gap and width of the vertical bars, respectively, at layer $n$) such that $(u^{\prime }/U_{n})^{2}\unicode[STIX]{x1D6FD}^{2}(C_{D}w_{n}/x_{\ast ,n}^{peak})^{-1}\sim (x_{m}/x_{\ast ,n}^{peak})^{b}$, where $\unicode[STIX]{x1D6FD}$ is a constant determined by the free-stream turbulence level, $U_{n}$ is the local mean velocity and $b$ is a dimensionless power law constant. A general framework of grid design method based on these scalings is proposed and discussed. From the evolution of the shear stress coefficient $\unicode[STIX]{x1D70C}(x)$, integral length scale $L(x)$ and the dissipation coefficient $C_{\unicode[STIX]{x1D716}}(x)$, a simple turbulent kinetic energy model is proposed that describes the evolution of our grid generated turbulence field using one centreline measurement and one vertical profile of $u^{\prime }(y)$ at the beginning of the evolution. The results calculated from our model agree well with our measurements in the streamwise extent up to $x/H\approx 2.5$, where $H$ is the height of the grid, suggesting that it might be possible to design some shear flows with desired mean velocity and turbulence intensity profiles by designing the geometry of a passive grid.

Type
JFM Papers
Copyright
© 2018 Cambridge University Press 

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