The flow on the centerline of grid-generated turbulence is characterised via hot-wire anemometry for 3 grids with different geometry: a regular grid (RG60), a fractal grid (FSG17) and a single square grid (SSG).Thanks to a higher value of the thickness t0 of its bars, SSG produces greater values of turbulence intensity T u than FSG17, despite SSG having a smaller blockage ratio. However the higher T u for SSG is mainly due to a more pronounced vortex shedding contribution. The effects of vortex shedding suppression along the streamwise direction x are studied by testing a new 3D configuration, formed by SSG and a set of four splitter plates detached from the grid (SSG+SP). When vortex shedding is damped, the centerline location of the peak of turbulence intensity x peak moves downstream and T u considerably decreases in the production region. For FSG17 the vortex shedding is less intense and it disappears more quickly, in terms of x/x peak , when compared to all the other configurations. When vortex shedding is attenuated, the integral length scale Lu grows more slowly in the streamwise direction, this being verified both for FSG17 and for SSG+SP.In the production region, there is a correlation between the vortex shedding energy and the skewness and the flatness of the velocity fluctuations. When vortex shedding is not significant, the skewness is highly negative and the flatness is much larger than 3. On the opposite side, when vortex shedding is prominent, the non-Gaussian behaviour of the velocity fluctuations becomes masked.