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

PASSIVE SCALAR MIXING ENHANCEMENT AND MULTI-STRUCTURE
TURBULENCE DOWNSTREAM OF A GRID AND A POROUS
OBSTRUCTION

Dana Duong
Department of Mechanical Engineering
University of Ottawa
Ottawa, ON K1N 6N5, Canada
dduon101@uottawa.ca

Stavros Tavoularis
Department of Mechanical Engineering
University of Ottawa
Ottawa, ON K1N 6N5, Canada
stavros.tavoularis@uottawa.ca

ABSTRACTof L, the turbulent kinetic energy per unit mass k and its dissipation rate ε, as Cε = εL/(2k/3)3/2 . Considering that, in gridturbulence, there is a flow region near the grid, where Cε grows
monotonically and beyond which Cε ≈ const. (Tavoularis &Nedić, 2017), Eq. 2 implies that, if the far-field condition(σ ≫ L) is satisfied at the start of the Cε ≈ const. region, it
will continue being satisfied further downstream, so that theplume will grow at the same rate as the turbulence scale does.
The analysis also indicates that, if the far-field condition is notsatisfied at the start of the Cε ≈ const. region, it will neverbe satisfied and the plume will keep growing at a slower rate
than L does. The previous observations lead to the following
strategy for enhancing the spreading of the plume, thus improving scalar mixing in decaying grid turbulence: introduce a
disturbance close to the source, so that the plume will be wide
enough as to satisfy the far-field condition early in its evolution and then keep growing at its highest possible rate, whichis the rate of growth of L. The crucial step is to implement
this strategy as efficiently as possible. Introducing a relatively
large solid obstruction in the plume would spread the plume,
but would also create a large wake, where the turbulence structure would be very different from grid turbulence and the analysis would not hold, even approximately. Moreover, the scalarreleased by the source may take considerable distance to be entrained in the wake. After considering different possibilities,
we decided to use an array of small cylinders, which would act
like a porous obstruction, thus allowing the scalar to penetrate
the array as well as reducing the disturbance to the grid turbulence. Of course, the turbulence structure behind the array
would have contributions from the upstream grid turbulence,as well as contributions of the wakes of the cylinders and thehigh-speed flows between them. Consequently, this region will
have a structure that is the result of more than one distinct
turbulence generation mechanisms and may be described as
multi-structure turbulence (Nedić & Tavoularis, 2018).

Turbulent diffusion and mixing of heat, introduced passively by a thin ribbon in grid-generated turbulence, was enhanced drastically by a small array of thin cylinders, positioned closely downstream of the ribbon. A multi-structure
flow region with an increasing dissipation parameter wasformed behind the array and relaxed towards grid turbulence,
albeit maintaining a turbulence intensity and an integral lengthscale that were twice as large as those in the absence of thearray.

INTRODUCTION
Turbulent mixing and diffusion of scalar properties, suchas heat and the concentration of an admixture, have been studied extensively, due to their importance in combustion, chemical reactions, spreading of pollutants and transmission of airborne pathogens. Much of our understanding of these phenomena has been based on studies under idealised conditions, butsuch findings are also relevant to many practical conditions.
Early studies of scalar dispersion from concentrated sources inhomogeneous turbulence (Taylor, 1922; Batchelor, 1949) havebeen adapted to estimate the far-field half-width of a scalar
plume, generated by a line source in a uniform stream, asσ ≈ (2u′2 L2 x1 /U 1 )1/2 for σ ≫ L2

(1)

where x1 is the distance from the source, U 1 is the mean velocity, u′2 is the standard deviation of the transverse turbulent
velocity and L22,2 is the transverse integral length scale. Morerecently, scalar diffusion theory was extended to account for
turbulence decay, as would be the case for grid-generated turbulence (Tavoularis & Nedić, 2017). In this case, the far-field
plume half-width was estimated as−1/2

σ ∝ CεL1(2)

In a recent article, Nedić & Tavoularis (2016) showed thatdecaying grid turbulence has three distinct regions, namely, adeveloping region, a partially developed region, and a fully

where L1 is the streamwise integral length scale and the turbulent kinetic energy dissipation parameter is defined, in terms

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

Figure 1: Sketches of a) the general experimental arrangement, b) a front views of the perforated plate (thick black lines),

the obstruction frontal area (Grey rectangle) and the heating ribbon (black horizontal line), c) the different cylinder arraysand d) the different flow regions.

developed region, and that the streamwise extent of each region depends on the shape and the mesh size of the grid. An
important finding for the present purposes is that, in the developing region, Cε grows monotonically, before approaching an
asymptote in the fully developed region. These authors also
found that, for sufficiently small mesh sizes, the developing
region is essentially non-existent. This implies that the choiceof grid is crucial in satisfying the far-field condition. Amongthe many available grids in our laboratory, the one that had thesmallest mesh, but also a developing region, was found to be asquare-mesh perforated plate with a mesh size M = 50.8 mm.
The general goal of this research is to devise a practicalmethod for enhancing scalar mixing in a turbulent flow. In
particular, we wished to widen the plume generated by a scalarline source in grid turbulence by inserting a porous obstruction
closely behind it. We also wished to explore the relationshipbetween the plume spread and the turbulence properties in themulti-structure region behind the obstruction.

downstream of the source, namely, about 1.25M downstreamof the grid. Tests were performed for nine array configurations,shown in Fig. 1c. The test section side walls past the cylinderarray were adjusted to be slightly diverging, to compensate thepressure field for boundary layer growth.
Measurements of the streamwise and transverse (i.e., vertical) velocity components and the fluctuating temperature
were made with a home-made, three-wire probe. The velocity sensors, arranged in a cross-wire configuration, were madeof tungsten and had a diameter of 2.5 µm, a sensing length of
0.85 mm and a separation distance of 0.5 mm. The length-todiameter ratio was 340, which is sufficiently large for end conduction effects to be negligible. The temperature sensor (coldwire) was made of platinum and had a diameter of 0.6 µm
and a length-to-diameter ratio of 800; this sensor was etchedfrom Wollaston wire and spot-welded onto the prongs. The
cold wire was supplied with a current of 0.3 mA by a lownoise, high-gain homemade circuit. The mean temperature
close to the three-wire probe was measured with a miniaturethermistor. The hot-wire signals were corrected for temperature effects, using an instantaneous temperature value that was
the sum of the time-averaged temperature, measured with thethermistor, and the mean-free temperature fluctuation, measured with the cold wire. The reported temperature rise in
the heated flow was the difference between the locally measured temperature and the temperature upstream of the heatedsource, measured with a pre-calibrated resistance temperaturedetector (RTD). The hot-wire and cold-wire signals were lowpass filtered with analog filters, having cutoff frequencies of,respectively, 14 kHz, and 4 kHz, digitised at a rate of 30 kHz
and recorded over 30 s for each test. The cross-wire probe
was calibrated in situ using a velocity-pitch-map calibration
method.
The streamwise integral time scale T1 was determinedby integrating the temporal autocorrelation coefficient of thestreamwise velocity fluctuations to its first zero-crossing. The
streamwise integral length scale was then estimated as L1 =APPARATUS AND MEASUREMENT PROCEDURES
The experiments were performed in an open-circuit windtunnel, shown schematically in Fig. 1a. The test section has
a height h = 305 mm, a width of 1.5h and a length of 16.6h.
A square-mesh perforated plate (“grid”, shown in Fig. 1b),
machined from a 16 gauge steel sheet with a thickness of 1.59mm and having a mesh size M = 50.8 mm (= 0.167h) and asolid bar width w = 6.8 mm (namely, a solidity of 0.25), wasinserted across the flow. An electrically heated ribbon, madeof Nichrome alloy and having a thickness of 0.13 mm and awidth of 1.59 mm, was inserted at a location that was 25.4 mm(= 0.50M) downstream of the grid, to serve as the source ofa passive scalar (i.e., temperature rise); the heating power was
the same for all reported tests. Arrays of ceramic rods, 3.2
mm in diameter and spaced by 5.5 mm, centre-to-centre, in
equilateral arrangements, were positioned 38 mm (= 0.75M)

2

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

Figure 2: Normalised mean temperature and temperature fluctuation profiles without and with the obstructions at threedownstream locations; the reference temperature rise was ∆Tre f = 0.44 K.
T1U 1 . The derivative (∂ u1 /∂t)2 was calculated by extrapolating corresponding finite differences to a zero time lag.
Using Taylor’s frozen flow approximation, the Taylor mih
i1/2
2
, the
croscale was calculated as λ = U 1 u′2
1 /(∂ u1 /∂t)structions, velocity fluctuations in the streamwise and transverse directions were found to be about 0.1%. The Reynolds
number, based on the grid mesh size, was ReM = U∞ M/ν ≈34, 000.

turbulence Reynolds number was calculated as Reλ = u′1 λ /ν,where ν is the kinematic viscosity of air, and the turbulent kinetic energy dissipation rate was estimated as ε =215νu′2
1 /λ . The Kolmogorov microscale was then calculated
1/4
as η = ν 3 /εand the dissipation parameter was calculated as Cε = (L1 ε)/u′3
1 . Lastly, the Taylorian diffusivity wascalculated as D = u′2
2 L1 /2.

Preliminary measurements downstream of each of thenine cylinder arrays showed that, in general, the mean temperature profiles had a nearly Gaussian shape, with a peak thatwas substantially lower than that in unobstructed grid turbulence, while the plume was substantially wider. The additional
spread of heat in the presence of the obstruction is attributed
to two interacting, but distinct, effects. First, the warm wakeof the source is either split by the first cylinder or diverted towards one side of it, in both cases tending to displace heatedfluid away from the source plane. This process is repeated, as
the displaced warm fluid reaches the second and subsequentcylinders. One is also reminded that the near field of a squaremesh grid consists of square jets, surrounded by short horizontal and vertical wakes, so that the flow reaching the ob-

RESULTS AND DISCUSSION
All measurements were taken at a fixed inlet velocity of
U∞ = 10.0 m/s, calculated from the mean pressure difference
across the wind tunnel contraction. In the absence of flow ob-

312th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19–22, 2022
struction is strongly three-dimensional. Second, the cylinders
produce additional turbulent fluctuations, which are superimposed on the grid turbulence, as well increasing the size of theenergy containing motions; both effects enhance turbulent diffusion. The effect of the obstructions on the plume spread isquite strong, despite the fact that the frontal projection of a full
cylinder array is merely 0.076h in height.

may be summarised as follows.
(a) Closely downstream of it, the obstruction increased themean velocity deficit along the centreline to a level thatwas well above the already significant level in the absence of the obstruction, which is attributed to the gridbars and the ribbon wake. This deficit diminished withdownstream distance, so that the mean flow in the core
became nearly uniform at x1 /M = 60. At that location,
the boundary layers on the top and bottom walls may beseen to occupy roughly a quarter of the cross-section each,with very weak velocity peaks persisting at the boundary
layer edges; these peaks are interpreted to be remnants of
upstream flow maxima between bar-generated wakes.
(b) The streamwise turbulent velocity fluctuation level behindthe obstruction was nearly twice the unobstructed value inthe entire test section, which means that the obstruction
generated a permanent increase in turbulence level.
(c) The transverse turbulent velocity fluctuations behind theobstruction followed the same overall patterns as thestreamwise fluctuations. It is interesting to note that, at
x1 /M = 6, u′2 was somewhat larger than u′1 , as the obstruction diverted flow away from the centreline. Further
downstream, the ratio u′1 /u′2 , both without and with obstructions, settled at a level in the range 1.1 − 1.2, which
is somewhat larger than typical values in turbulence generated by grids with solidities that are higher than thepresent one (Comte-Bellot & Corrsin, 1966).
(d) The shear stress correlation coefficient was only mildly
affected by the obstruction. It is interesting to note that,without and with the obstruction, this coefficient hadpeaks of about ±0.25, which points to a persisting mild
anisotropy throughout the measuring section. This is attributed to the relatively small solidity of the grid and thelimited streamwise distance available in the present test
section for the flow anisotropy to diminish further.
(e) The obstruction nearly doubled the integral length scale,and such increase was maintained downstream.
(f) The obstruction increased drastically the turbulent diffusivity D ≈ u′2
2 L1 /2 in its wake. Close to the obstruction,
the increase was by an order of magnitude and peakedon the centreline, but, further downstream, the turbulent
diffusivity maintained a fairly uniform value in the flow
core, which was roughly four times the corresponding unobstructed value. This increase in D is consistent with thedrastic enhancement of scalar mixing.
(g) The Taylor microscale was essentially unaffected by theobstruction; this indicates that the obstruction increased
both the velocity fluctuations and their temporal derivative by the same amount. Nevertheless, there was a verysmall correlation (≲ 0.1 for x1 /M ≥ 24) between the velocity and its derivative. A physical justification for thelack of influence of the obstruction on the Taylor microscale remains to be found.
(h) The turbulence Reynolds number was roughly doubled by
the obstruction, as a result of the increase of the turbulence level.
(i) The dissipation rate was nearly tripled close to the obstruction and maintained a comparable increase in the entire test section, while its level diminished rapidly.
(j) The dissipation parameter was significantly reduced by
the obstruction, with the reduction diminishing with distance from the obstruction and vanishing far downstream.

Figure 3: Plume spread without and with the obstruc-tions.

Most effective in reducing the peak temperature rise was
Array 1, so all measurements reported here were taken for thisconfiguration. Profiles of the mean temperature rise ∆T atthree streamwise stations are shown in Fig. 2. These values
have been normalised by a constant reference temperature rise∆Tre f = 0.44 K, which is equal to the peak mean temperaturerise in the unobstructed flow at x1 /M = 6. Although the unobstructed plume extended entirely within the flow core region(namely, it did not reach the boundary layers along the top andbottom walls), the obstructed plume grew wider than the core,encroaching into the boundary layers at the furthest station,
where x1 /h = 10. Fig. 2 also presents the transverse profiles of
the normalised standard deviation θ ′ of the temperature fluctuations, at the same three streamwise locations. Dual peaks canbe seen in both the unobstructed and obstructed flows, but, inthe obstructed flow, the fluctuations spread further in the transverse direction and had a smaller non- uniformity. As shownin Fig. 3, the obstructed plume was roughly twice as wide as
the unobstructed one. The same figure indicates that the obstruction intensified scalar mixing to the point that, roughly
speaking, the mean temperature rise in the entire test section
far away from the source exceeded half of its peak value. In
contrast, throughout the unobstructed flow, there were significant parts of the test section, where there was no temperaturerise at all. All things considered, we may confidently assertthat the obstruction was quite effective in spreading and mixing the scalar.
To understand the effect of the obstructions, we compared
the turbulence properties in their presence with those in theirabsence. Representative results are shown in Fig. 4. It should
be noted that the various profiles near the grid are not expected
to be two-dimensional, but to have significant spanwise nonuniformity, generated by the vertical bars of the grid. It isalso noted that the heating ribbon, which was given a small
twist, had a measurable momentum wake, although we foundno signs of buoyancy effects due to the heating. The results

These results support the expectation that the wake of theoverall obstruction was a multi-structure region, which tended

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

Figure 4: Transverse profiles of the main turbulence properties at three representative streamwise locations; the axis scales

for L1 , D and ε at the three streamwise locations have been adjusted to make the values in the plots readable.

512th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19–22, 2022

Figure 5: Dissipation parameter vs.

the turbulence

Reynolds number.

to relax to grid turbulence, albeit maintaining a permanentand significant increase in the turbulence intensity and integral
length scale (see flow regions in Fig. 1d). An important finding that deserves further attention is that, as shown in Fig. 5,
the dissipation parameter in the multi-structure region was inversely proportional to the local turbulence Reynolds number.
Such a relationship has also been observed between these twoparameters in multi-structure regions of other flows, includingintermediate regions of decaying grid turbulence (Vassilicos,
2015; Nedić & Tavoularis, 2016), uniformly sheared turbulence disturbed by a grid (Nedić & Tavoularis, 2018), earlystages of turbulent boundary layers (Nedić et al., 2017) anda turbulent boundary layer in a uniformly sheared free stream(Livingston & Tavoularis, 2022).
As a final note, Fig. 6 shows representative profiles ofthe skewness S and flatness F factors of the streamwise velocity derivative, which are indicators of the fine structure. Away
from the grid (x1 /M ≥ 24), S takes values in the vicinity of−0.5 in both the unobstructed and the obstructed flows; suchvalues are typical for fully developed turbulence at moderate
Reynolds numbers. However, closer to the grid (x1 /M = 6),
S takes values that are measurably lower than the value −0.5
without the obstruction and closer to −0.5 with the obstruction; thus, it appears that the effect of the obstruction is to accelerate the development of the fine structure. Moreover, theobstruction increases systematically K throughout the test section, which is consistent with the increase in Reλ and indicatesan enhancement of the internal intermittency of the turbulence.

Figure 6: Transverse profiles of the skewness and flat-ness factor of the streamwise velocity derivative. The
axis scale of F at the last streamwise location has beenadjusted to make the values in the plot readable.

increases in turbulence level, integral length scale and turbulent diffusivity.
Funding for this research was provided by the Natural Sciences and Engineering Research Council of Canada.

REFERENCES
Batchelor, G.K. 1949 Diffusion in a field of homogeneous turbulence. I Eulerian analysis. Austral. J. Chem. 2, 437–450.
Comte-Bellot, G. & Corrsin, S. 1966 The use of a contraction to improve the isotropy of grid-generated turbulence. J.
Fluid Mech. 25, 657–682.
Livingston, C. & Tavoularis, S. 2022 Multi-structure turbulence in a boundary layer with a uniformly sheared freestream. In Proc. TSFP12, Osaka, Japan, July 19–22, 2022,
pp. 1–6.
Nedić, J. & Tavoularis, S. 2016 Measurements of passive
scalar diffusion downstream of regular and fractal grids. J.
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Nedić, J. & Tavoularis, S. 2018 A case study of multi-structure
turbulence: Uniformly sheared flow distorted by a grid. Int.
J. Heat Fluid Flow 72, 233–242.
Nedić, J., Tavoularis, S. & Marusic, I. 2017 Dissipation scaling
in constant-pressure turbulent boundary layers. Phys. Rev.
Fluids 2 (3), 032601.
Tavoularis, S. & Nedić, J. 2017 Taylorian diffusion in mildly
inhomogeneous turbulence. Intern. J. Heat Fluid Flow 67,
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Taylor, G. I. 1922 Diffusion by continuous movements. Proc.
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Vassilicos, J. C. 2015 Dissipation in turbulent flows. Annu.
Rev. Fluid Mech. 47 (1), 95–114.

CONCLUSIONSIn this experimental work, we found that a small arrayof thin cylinders, acting as a localised, porous, flow obstruction, enhanced drastically turbulent diffusion and mixing of apassive scalar injected from a line source in grid turbulence.
The unobstructed scalar plume was confined within the test
section core region, whereas the obstructed plume penetrated
the boundary layers on the test section walls. This is further
confirmed by the fact that the plume spread in the obstructed
flow was twice as large as that in unobstructed grid turbulence.
Transverse profiles of turbulence properties indicated that a
multi-structure flow region was formed behind the array andrelaxed towards grid turbulence, albeit maintaining permanent

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