12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19–22, 2022

NEAR-FIELD TURBULENCE IN A MULTI-FAN WIND TUNNEL

Jovan Nedić and Austin L’Ecuyer
Department of Mechanical Engineering
McGill University
817 Sherbrooke Street West, Montréal, Québec H3A 0C3, Canada
jovan.nedic@mcgill.ca

ABSTRACTaway. What is still unknown, however, is how the turbulence
evolves in the region closer to the fans.
One of the major attractions for using MFWT for generating turbulence is that it affords the user with increased control over the flow patterns they can create. For example, byalternating the speed between adjacent fans in a checkerboard
pattern, one can, in theory, replicate the conditions of a passive
grid. Moreover, it is possible to examine the effects of initialshear on the turbulence statistics, by changing the ratio of two
velocities given by the fans. Therefore, a shear parameter

We examine turbulence generated by a multi-fan windtunnel, comprised of a 9x9 grid of small fans which can be
individually controlled. A checkerboard pattern is considered,
where the fans are alternatively set to one of two different velocities. It is shown that the turbulence intensity and integral
length scale can be increased by increasing the shear ratio,
defined as the ratio between the higher and lower velocities
given to the fans. Moreover, the turbulence generated by themulti-fan wind tunnel has strong similarities to decaying gridturbulence, exhibiting a region of faster decaying turbulencecloser to the fans. This region was also found to exhibit nonequilibrium properties, namely one where the dissipation parameter was not constant.

Sr = U2 /U1(1)

can be defined, where U2 is the higher of the two velocities i.e.,
U2 ≥ U1 . This implies that 1 ≤ Sr ≤ ∞, where the upper limit
corresponds to the case of U1 = 0 m/s. The objective of thisstudy is to investigate the near-field of MFWT-generated turbulence for such a flow pattern, and determine to what extent
the turbulence is similar, or dissimilar, to turbulence generated
by passive grids. A hypothesis that we would also like to examine is whether increasing the shear ratio of the fans will leadto increased turbulence levels and integral scales.

INTRODUCTION
A variety of different methods have been employed in thepast to generate decaying homogeneous and isotropic turbulence. The most classical approach has been the use of passive
grids, which are comprised of an array of regularly spaced perpendicular bars with a thickness d, to create a mesh with aspacing of M. A vast body of work has utilised these grids toexamine the fundamental theories of turbulence. The Taylorbased Reynolds number they create, however, has typically
been confined to Reλ < 150, which decreases with increasing downstream distance from the grid. In order to increase
the range of possible Reλ , Makita (1991) developed an “active grid” comprised of rectangular bars or rods with an arrayof triangular agitator wings on bars attached to motors; thebars and agitator wings spin, which is the active part of thegrid. The bars randomly change direction and rotation speed
which creates the highest turbulent kinetic energy and integral
length scale. Over the years, through various design tweaks
and modifications to the algorithms used to actuate the motors(Mydlarski, 2017), have resulted in large Reλ , in some cases
as high as Reλ = 1100 (Larssen & Devenport, 2011).
A recent advancement in wind tunnel turbulence generation has been the use of multi-fan wind tunnels (MFWT),
whereby the turbulence is generated by an array of small fansarranged in a planar grid, ideally with each fan being controlled separately. Originally designed to generate atmosphericboundary layers (Nishi et al., 1999), recent efforts have examined ways in which the turbulence can be controlled via dynamic modulation of all of the fans (Ozono et al., 2006; Ozono& Ikeda, 2018; Takamure & Ozono, 2019), again with the objective of recreating atmospheric conditions. The region wheresuch properties of the flow were considered are notably far
from the fans themselves, often more than 30 fans dimensions

EXPERIMENTAL FACILITY
A new multi-fan wind tunnel (MFWT) was constructed
for the purpose of this study. A total of N = 81 fans were used
to create a 9-by-9 2D planar grid, as shown in fig. 1; the gridof fans is referred to as the fan wall. Each fan unit was F = 80mm in width and height, and pushed fluid through an opening
with an outer diameter of Do = 78 mm and an inner diameter of
Di = 36 mm. The motors, located within the centre of the fanunit, was driven by a pulse-width modulated (PWM) signal,
provided by a National Instruments NI PCIe-6341 multifunction I/O (input/output) device connected to a BNC-2110 connector block. Currently, only four unique PWMs can be sent
to the fans. The grid of fans are secured by a structure made of
3 mm thick medium density fiberboard (MDF); this resulted in
the square test section having a height and width of 750 mmby-750 mm i.e. W = 750 mm, as shown in fig. 1. The subsequent fan spacing, from centre-to-centre, is hence M = 83
mm. Given the open area through which fluid is pushed byeach fan, and the total cross-sectional area of the facility, one
can calculate an open area ratio as

OAR =

1

πN(D2o − D2i )
,
4W 2

(2)

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19–22, 2022

Figure 1. Dimensions, and arrangement, of the fans used to create the turbulent flow field in the multi-fan wind tunnel. Note that theco-ordinate system is centred in the middle of fan 41.
1.1

which for this facility is 0.54. Its function is to act as a corollary to solidity ratio of passive grids. A test section of length
2.4 m was attached to the fan wall, with a traversing mechanism that allowed for measurements in the streamwise x andplanar y, z directions; the co-ordinate system originated at thecentre of the middle fan i.e., fan 41 in fig. 1. The final assembly
allowed for measurements over approximate non-dimensional
distances of 4 ≤ x/M ≤ 22, −1.5 ≤ y/M ≤ 1.5, and −2 ≤z/M ≤ 2. Measurements of the instantaneous streamwise u
and transverse v velocity were obtained using a Dantec Xwire sensor, driven by a Dantec Streamline constant temperature anemometer. Data was sampled at a rate of 75 kHz for
60 seconds, which was sufficient to capture converged statistics, and low-pass filtered (analogue) at 30 kHz. An iterative
method was then used in the post-processing to find the Kolmogorov frequency, with a fourth-order low-pass Butterworth
filter applied digitally to the data at 1.3 times the Kolmorogorv
frequency. Additional post-processing of the cross-wire data
was implemented following the procedure by Burattini (2008)
to account for wire separation effects on velocity derivatives.

1.05

1

0.95

0.9

0.85
5

10

15

20

25

Figure 2. Streamwise development of the centreline mean
velocity for various shear ratios.

RESULTS
Mean flow properties
A calibration was first conducted to relate the PWM signal
sent to the fans to their output flow velocity. Based on thesemeasurements, the operating range of the fans was found tobe 1.5 m/s ≤ U f ≤ 7.9 m/s. In order to investigate the widest
possible range of shear ratios, the bulk freestream velocity was
set to U∞ = 5 m/s, which would allow for shear ratios of 1 ≤Sr ≤ 3.5. Note that Sr = 1 is equivalent to having all the fansoperating at the same velocity, whilst shear ratios of Sr > 1
had the even-numbered fans operating at the same velocity U2 ,which was higher than the velocity U1 from the odd-numberedfans – see fig. 1 for fan numbering system.
The streamwise development of the normalised streamwise velocity, along the centreline of the tunnel (x, 0, 0), isshown in fig. 2 for Sr = 1, 1.5, 2, 2.5, 3, and 3.5. For x > 13M,
the mean flow is approximately constant for all shear ratios;

this is also the downstream location where the planar measurements (not shown here for brevity) indicate that the mean flowis also approximately uniform. For x < 13M, there is a clear
dependence on shear ratio where, somewhat surprisingly, thelarger shear ratios approach u = U∞ faster. Note here that u is
the mean streamwise velocity.
Although such a flow pattern is hypothesised to replicate
the conditions of a passive grid, it is important to stress someof the key differences between the two in the manner in which
turbulence is generated. For a passive grid, an incoming uniform mean flow is pushed through the grid, where wake-likeregions are created behind the bars of the grid, and jet-like regions are created in the space between the bars, with resulting

2

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19–22, 2022
Table 1. Virtual origin x0 /M and the decay exponent m in thenear-field and (x < 13M) and far-field, shown as bold numbersin brackets.

shear produces the turbulence. By changing the solidity ratioof the grid (solid area of bars to cross section of the tunnel),the relative dominance of the wake-like vs. jet-like regions isaltered. For a MFWT, no such regions of wake-like flow exist,
since the flow is pushed out by the fans in the form of a jet,which merge at some distance upstream of the fan. In addition
to this, the rotation of the fans can lead to the creation of amean rotation in the flow, at least in the vicinity of the fans.
Nevertheless, the fundamental principal for turbulence generation remains the same between the two facilities, that being
the creation of a velocity shear.

Centreline turbulence statistics
Examining the streamwise large-scale isotropy, fig. 3, wenote that urms /vrms ≈ 1 to within 5%, where urms is the root
mean square of the streamwise velocity component. Suchvalues of large-scale isotropy are comparable to the measurements from grid-generated turbulence, particularly thosewhere a secondary contraction was used to specifically improve isotropy (Comte-Bellot & Corrsin, 1966; Hearst &Lavoie, 2016). The nature of the small-scale isotropy is left
for a future study, as the primary objective of this study isa focus on the large-scale turbulence properties generated by
the fans. Homogeneity of the turbulent field was determinedby investigating the spanwise and transverse variation of both
urms and vrms . For x > 13M, the ratio of these values to theircorresponding value on the centreline was found to be constant to within ±5%, which is again inline with previous measurements on grid-generated turbulence. Given this, the remainder of the turbulence statistics are presented along thecentreline only i.e., along (x, 0, 0). It is also worth notingthat the observed large-scale isotropy for this facility is better than what was obtained by Ozono & Ikeda (2018), who hadurms ≈ 1.1vrms , and this at a much further downstream distancefrom the fans, whose facility also included a honeycomb.
By assuming that the spanwise velocity component w(along the z direction) is the same as the transverse velocity
component, we may write the total turbulent kinetic energy
as k = 0.5(u′2 + 2v′2 ), where primes denote fluctuating values (mean subtracted values) of the velocity signal, and theoverline denotes an average. Figure 4a shows the normalised
kinetic energy for a range of shear ratios, where it is evident
that the kinetic energy is decaying with streamwise distance,
as is the case for both passive grids and active grids. Furthermore, we note that increasing the shear ratio increases the tur-

1
0.9
0.8
0.7
20

1.0

-1.44 (6.49)

2.00 (1.06)

1.5-0.98 (3.13)

2.23 (1.58)

2.0

0.27 (2.71)

1.90 (1.54)

2.5

0.49 (3.19)

1.92 (1.45)

3.0-1.48 (2.47)

2.30 (1.52)

3.5-1.58 (5.80)

2.33 (1.17)(3)where m is the decay exponent, x0 is a virtual origin for the
power-law fit, and A is a scaling constant. It is plausible, indeed likely, that all three variables on the right hand side ofeq. (3) are functions of the shear ratio, and is an aspect thatshall be investigated further in a future study. Research overthe last two decades has indicated that decaying grid-generated
turbulence in the vicinity of the grid exhibits two regions with
distinct decay rates of the turbulent kinetic energy (Valente &Vassilicos, 2011; Hearst & Lavoie, 2016; Nedić & Tavoularis,
2016b). To identify if such regions exist in this flow, and extract the corresponding decay rates, the algorithm proposed
by Valente & Vassilicos (2011) is used. Two distinct regions,as indicated by a noticeable change in the decay exponent m,were identified; one in the near-field x < 13M another in the
far-field x ≥ 13M. The decay exponent, and the virtual origin,for each of the shear flows, are presented in table 1. Based onthese results, it does not appear that the virtual origin, or the
decay exponent, are a function of the shear ratio. Nevertheless,there is a clear difference in both the virtual origin and decay
exponent in the two identified regions, most notable of whichis that the decay exponent is higher in the near-field as compared to the far-field. Fits of eq. (3), using the values shown intable 1, are shown in fig. 4a for both regions. If we assume thatthe shear ratio has no discernible influence on the virtual origin
and decay exponents, one can therefore determine the average
decay exponent in the near-field, x < 13M, as mnear = 2.11,
and in the far-field as m f ar = 1.39. These values are similar to
those seen in the near- and far-field of both regular and fractal
grids (e.g., Nedić & Tavoularis, 2016b).
The streamwise variation of the streamwise integral
length scale L11,1 is shown in fig. 4b, which was calculated byintegrating the autocorrelation function to is first zero crossing. Generally, the integral scale increases with streamwise
distance, but remains, for all shear ratios, smaller than the fansize, as well as smaller than the spacing between the fans.
Ozono & Ikeda (2018) similarly observed that the integral
scale was smaller than the fan size, but noted that it tended
towards it far downstream; by x ≈ 60M, L11,1 ≈ 0.93M. By

1.1

15

m



k
x − x0 −m
,
=A
M
U∞2

1.2

10

xo /M

bulent kinetic energy of the flow. For example, at the closest
measurement location of x = 7M, the turbulent kinetic energy
increased by almost 50% when increasing the shear ratio from
Sr = 1 to Sr = 3.5.
As with decaying grid-generated turbulence, we fit the
turbulent kinetic energy with the power law of the form

1.3

5

Sr

25

Figure 3. Large-scale isotropy along the centreline for various shear ratios.

312th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19–22, 2022
0.05

increasing the shear ratio one is able to increase the integral
length scale, in some cases by as much as 45%. This is to be
expected, since the turbulent kinetic energy is a function of theshear ratio, whereas the decay exponent, for both regions, isindependent of shear ratio.
Streamwise variation of the Taylor Reynolds number, defined as Reλ = λ urms /ν, along the centreline is presented
in fig. 4c.pNote that the Taylor microscale was estimated as
λ = urms 15ν/ε, using the x-wire estimate for the dissipation rate ε = 3ν[(∂ u/∂ x)2 + 2(∂ v/∂ x)2 ]. Over the entire measurement region, the Taylor Reynolds number for the Sr = 1
case (all fans on at same speed) ranged from Reλ = 140 at
the closest location, reaching a value of Reλ = 85 at x = 22M.
This range of Reynolds numbers is again comparable with passive grids with equivalent mesh spacing; see, for example, theRG80 (mesh spacing = 80 mm) results of Nedić & Tavoularis(2016b). Increasing the shear ratio produced a noticeable increase in Reλ , as much as 40% in some cases. Given theincrease in both the kinetic energy and integral scale, the increase in Taylor Reynolds number is to be expected.
It is worth mentioning that examination of the energy
spectra (not shown here) indicated a clear inertial sub-range,
whose slope was close to -5/3, for all shear ratios and downstream locations. As expected, it was observed that the widthof the inertial sub-range increased with increasing Reλ .
For all turbulence properties presented here, a very clear
increase in all parameters was observed as the shear ratio isincreased from Sr = 1. This therefore suggests that controlof the turbulence parameters is, to some degree, possible bysimply varying the shear ratio. However, the relative changebrought about by increasing the shear ratio does not appear to
be as large as the change in velocity shear; in other words, theincrease from Sr = 1 to Sr = 1.5 is larger than the increase
from Sr = 1.5 to Sr = 2.

0.045
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
5

10

15

20

25

5

10

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25

5

10

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25

0.5
0.45
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0.35
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0.25
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0.15
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0.05

Dissipation scaling

0

The existence of a faster decay rate in the near-field of
decaying grid turbulence is typically associated with nonequilibrium turbulence, namely one where the dissipation parameter Cε ≡ εL11,1 /( 23 k)3/2 ̸= constant. The streamwise
variation of the dissipation parameter, for all shear ratios, isshown in fig. 5, which clearly shows that there is a region in
the vicinity of the fans where Cε ̸= constant. For clarity, we
have indicated the regions where the two different decay exponents of the turbulent kinetic energy were identified, namely
x < 13M and x ≥ 13M. In the near field, Cε is found to be increasing at a constant rate, before reaching a transitional zone
between 13 ≤ x/M ≤ 17, after which it is approximately constant. This transitional region has also been observed in decaying grid turbulence (Valente & Vassilicos, 2011; Hearst &Lavoie, 2016; Nedić & Tavoularis, 2016b). The large scatter in
Cε is primarily attributed to the uncertainty in estimating the
integral length-scale from the measurements, which was determine by considering 1-second blocks of data and estimating
the integral scale from each block. Nevertheless, even with thisscatter, the data clearly exhibits a region where Cε ̸= constant.
It has been observed across a wide range of studies, thatCε ∝ Re−1(Vassilicos, 2015). A notable exception to thisλis uniformly sheared turbulence, where scalings of the formCε ∝ Re−0.6
and Cε ∝ Re0.5
λ were observed only (Nedić &λTavoularis, 2016a). Interestingly, inserting a regular grid into a
uniformly sheared flow produced the oft-found scaling of Cε ∝Re−1
(Nedić & Tavoularis, 2018). The reason for this is still
λunclear. To facilitate a comparison to other non-equilibrium
turbulent shear flows, and in particular to the non-equilibrium

200

180

160

140

120

100

80

Figure 4. a) Decay of turbulent kinetic energy, b) growth of
integral scale , and c) variation of Taylor Reynolds number
with streamwise distance for various shear ratios.

412th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19–22, 2022
1

the kinetic energy, were identified. In a region closer to thefans, namely for x < 13M, the decay rate of the turbulent kinetic energy was found to be mnear = 2.11. For x ≥ 13M, aslower decay rate of m f ar = 1.39 was observed. The decay
rates are similar to those found in decaying grid-generated turbulence, closer to the grid. Examining the dissipation coefficient, it was noted that the region of faster decaying turbulencecoincided with the region where the dissipation coefficient increased with streamwise distance, and was hence not-constant.
In other words, a non-equilibrium turbulence region exists forx ≥ 13M, which eventually transitions to an equilibrium region
where the decay rate is slower and the dissipation coefficientis constant. Overall, the turbulence generated by the multi-fan
wind tunnel was found to exhibit strong similarities, both interms of nature and scaling, to the near-field of decaying gridgenerated turbulence.

0.9

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0.7

0.6

0.5
5

10

15

20

25

Figure 5. Streamwise variation of the dissipation parameterfor different shear ratios.

REFERENCES
1

Burattini, Paolo 2008 The effect of the x-wire probe resolution in measurements of isotropic turbulence. Measurement
Science and Technology 19 (11), 115405.
Comte-Bellot, G & Corrsin, S 1966 The use of a contraction to
improve the isotropy of grid-generated turbulence. Journalof Fluid Mechanics 25 (4), 657–682.
Hearst, R.J & Lavoie, P 2016 Effects of multi-scale and regulargrid geometries on decaying turbulence. Journal of Fluid
Mechanics 803, 528–555.
Larssen, J.V & Devenport, W.J 2011 On the generation oflarge-scale homogeneous turbulence. Experiments in Fluids
50 (5), 1207–1223.
Makita, H 1991 Realization of a large-scale turbulence field ina small wind tunnel. Fluid Dynamics Research 8 (1-4), 53.
Mydlarski, L 2017 A turbulent quarter century of active grids:
from makita (1991) to the present. Fluid Dynamics Research 49 (6), 061401.
Nedić, Jovan & Tavoularis, Stavros 2016a Energy dissipation
scaling in uniformly sheared turbulence. Physical Review E
93 (3), 033115.
Nedić, J & Tavoularis, S 2016b Measurements of passive
scalar diffusion downstream of regular and fractal grids.
Journal of Fluid Mechanics 800, 358–386.
Nedić, J & Tavoularis, Stavros 2018 A case study of multistructure turbulence: Uniformly sheared flow distorted bya grid. International Journal of Heat and Fluid Flow 72,
233–242.
Nishi, A, Kikugawa, H, Matsuda, Y & Tashiro, D 1999 Active control of turbulence for an atmospheric boundary layer
model in a wind tunnel. Journal of Wind Engineering andIndustrial Aerodynamics 83 (1-3), 409–419.
Ozono, S & Ikeda, H 2018 Realization of both high-intensity
and large-scale turbulence using a multi-fan wind tunnel.
Experiments in Fluids 59 (12), 1–12.
Ozono, S, Nishi, A & Miyagi, H 2006 Turbulence generated
by a wind tunnel of multi-fan type in uniformly active andquasi-grid modes. Journal of Wind Engineering and Industrial Aerodynamics 94 (4), 225–240.
Takamure, K & Ozono, S 2019 Relative importance of initialconditions on outflows from multiple fans. Physical Review
E 99 (1), 013112.
Valente, P.C. & Vassilicos, J.C. 2011 The decay of turbulence
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Vassilicos, J.C. 2015 Dissipation in turbulent flows. Annual
Review of Fluid Mechanics 47, 95–114.

0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0.5
50

100

150

200

Figure 6. Scaling between the dissipation parameter and the
Taylor Reynolds number within the non-equilibrium region.

region of decaying grid-generated turbulence, we examine thescaling between Cε and Reλ for this flow. Figure 6 shows thisscaling for the non-equilibrium region as identified in fig. 5
i.e., for x < 13M where mnear = 2.11 and Cε ̸= constant. We
observe a scaling of the form Cε ∝ Re−1
for all shear ratios,
λwhich is the same as what has been observed in decaying gridturbulence (Vassilicos, 2015).

CONCLUSIONSThe turbulent flow field downstream of a multi-fan windtunnel was examined, for a range of shear ratios, at a bulk velocity of U∞ = 5 m/s. By increasing the shear ratio, that being
the ratio between the faster and slower velocities produced by
the fans, it was possible to increase the turbulent kinetic energy, integral length-scale, and Taylor Reynolds number by asmuch as 50%. The mean flow was found to be uniform forx > 13M, where M is the spacing between the fans. The turbulence field was found to be approximately homogeneous andisotropic at approximately the location where the mean flow
became uniform, hence only centreline statistics were considered further. Two distinct regions, based on the decay rate of5