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Vortex shedding effects in grid-generated turbulence

G.Melina∗1, P. J. K. Bruce1, and J. C. Vassilicos1

1Department of Aeronautics, Imperial College London, London SW7 2AZ, UK

May 17, 2016

Abstract

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

Tu than FSG17, despite SSG having a smaller blockage ratio. However the higher Tu 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 xpeak moves downstream and Tu considerably decreases in the production

region. For FSG17 the vortex shedding is less intense and it disappears more quickly, in terms of x/xpeak,

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.

1 Introduction

During the last decade multiscale/fractal-generated turbulence has been widely investigated, both experimen-

tally (e.g. Hurst and Vassilicos, 2007; Valente and Vassilicos, 2011; Nagata et al., 2013; Weitemeyer et al., 2013;

Goh et al., 2014; Gomes-Fernandes et al., 2015; Nedić et al., 2015; Cafiero et al., 2015; Baj et al., 2015) and with

Direct Numerical Simulations (DNS) (e.g. Nagata et al., 2008; Laizet and Vassilicos, 2012; Suzuki et al., 2013;

Zhou et al., 2014; Laizet and Vassilicos, 2015; Dairay et al., 2015). At a large distance from a perturbing grid in

its turbulence decay region on the centreline, where the turbulence intensity Tu decreases along the streamwise

direction x, fractal square grids with blockage ratio σ = 25% produce higher values of Tu if compared to a

regular grid with σ = 34% and with a similar effective mesh size Meff for the same inlet velocity U∞ and for

the same dimensional distance x from the grid (Mazellier and Vassilicos, 2010). Laizet and Vassilicos (2015)

performed DNS simulations of the flow downstream of fractal grids and of regular grids with comparable σ and

similar Meff and for a similar Reynolds number based on Meff . The latter study shows that when averaging

the turbulence intensity over a plane parallel to the grid, for the same x this is higher for fractal grids than for

regular grids downstream of the location of its peak value. However the same study shows that upstream of the

location of this maximum, the plane-averaged turbulence intensity is higher for regular grids than for fractal

grids. The distance xpeak from the grid, where Tu is maximum on the centerline, is the streamwise extent of the

turbulence production region, where Tu increases with x, and is representative of the location where the wakes,

originating from the largest bars of the grid, meet on the centreline. The distance xpeak can be approximately

predicted in terms of the wake-interaction length scale x∗ = L20/t0 (Mazellier and Vassilicos, 2010), where L0 is

∗Email address for correspondence: g.melina13@imperial.ac.uk

1

the length of the bars of the largest iteration of the square pattern, and t0 is their thickness in a plane normal

to the direction of the flow.

Gomes-Fernandes et al. (2012) theoretically motivated and experimentally demonstrated that (i) xpeak/x ∗

is inversely proportional to the drag coefficient cd of the largest bars of the grid and that (ii) the value of Tu

at xpeak, Tupeak, is proportional to cdt0/L0. The latter result suggests that we can use a grid made of a single

square (Laizet et al., 2015) designed with a large ratio t0/L0, so that Tu is high while σ, and presumably also

the static pressure drop, is small.

Fractal geometries have proved to be an effective solution for suppressing vortex shedding downstream of

particular objects. In axisymmetric turbulent wakes produced by fractal plates, the vortex shedding energy is

reduced by up to 60% compared to the case of circular and square plates with the same frontal area (Nedić

et al., 2015). Nedić and Vassilicos (2015) showed that by increasing the number of fractal iterations in an

airfoil’s (NACA 0012) trailing edge with multiscale modifications, the energy of vortex shedding decreases too.

It is believed that the fractal modification of the perimeter affects the vortex shedding formation mechanism

and re-distributes the turbulent kinetic energy among a broader range of scales (frequencies).

Mazellier and Vassilicos (2010) discovered that, downstream of fractal square grids, strong rare decelerating

flow events occur in the turbulence production region. As a result, the probability density functions (PDFs)

of the velocity fluctuations u appear highly left-skewed and characterised by large values of flatness. On the

contrary, advancing further downstream in the turbulence decay region, the skewness and the flatness of u

gradually get close to values typical of a Gaussian distribution. These observations lead to some new research

questions. (1) Are these features typical of fractal grids or are they also observable with regular and single-scale

grids? (2) Which phenomena can affect the magnitude of these events, given in particular that in the turbulence

production region the wakes shed from the largest bars of the grid have not fully met yet. (3) Does vortex

shedding play a significant role in the production region, especially when the value of t0 is considerably high?

(4) If yes, how are the statistics of the velocity fluctuations affected by the vortex shedding energy content? (5)

Is vortex shedding attenuated in the production region of fractal grids, as a result of the presence of the smaller

geometrical iterations?

The aim of this paper is to provide some answers to these research questions. We first characterise the flow

downstream of three types of turbulence-generating grids placed in a wind tunnel. We consider a regular grid

(RG60), a fractal square grid (FSG17) and a single square grid (SSG) with the highest value of t0/L0. We

perform single-component hot-wire measurements downstream of the grids, mainly on the centerline. We also

quantify the static pressure drop along the centerline by traversing a Pitot-static tube. We focus on some of the

effects induced by the vortex shedding originating from the largest bars of the grids. For this purpose we also

consider a novel 3D turbulence generator (SSG+SP) which is formed by SSG and a set of four splitter plates

detached from it.

It is well known that, among passive techniques, vortex shedding suppression by using splitter plates is

one of the simplest and most effective solutions (Akilli et al., 2005). Roshko (1954) showed that, when a long

splitter plate is attached downstream of a circular cylinder with diameter D, cd is reduced as a result of the

vortex shedding suppression. Apelt and West (1975) performed experiments on splitter plates past bluff bodies

and investigated the effect of Lsp, where Lsp is the length of the splitter plate. They found that regular vortex

shedding is completely suppressed when the reattachment of the flow occurs on the splitter plate. This happens

for Lsp/D ≥ 3 for a plate normal to the flow and for Lsp/D ≥ 5 for a circular cylinder. This last result also holds for a splitter plate attached to a rectangular prism, as shown by Ali et al. (2011). However, when

long splitter plates are used, a well-developed vortex street arises from the combined bluff body/splitter plate.

Vortex shedding can also be reduced using a shorter detached splitter plate placed at a distance xsp from the

bluff body, where xsp is measured until the splitter plate’s leading edge. Roshko (1954) found that by using a

splitter plate with Lsp/D = 1.14 detached from a circular cylinder at ReD = 14500, an optimal position exists

for which vortex shedding attenuation is maximum and cd is minimum; ReD is the Reynolds number based on

D. This optimum occurs for xsp/D = 2.7. Similar results were obtained by performing DNS at lower ReD. Lin

and Wu (1994) found an optimal distance xsp/D = 2.5 for Lsp/D = 2 and ReD = 100, Hwang et al. (2003)

2

x

y

z

Figure 1: Sketch of the wind tunnel’s test section.

report an optimal value xsp/D = 2.7 for Lsp/D = 1 and ReD = 160.

In this work we identify an optimal distance xsp/t0 between the splitter plates and SSG from a limited

number of such distances that we have been able to ex