Weakly sheared turbulent flows generated by multiscale inhomogeneous grids

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.