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

THREE-DIMENSIONAL MEASUREMENTS OF FLOW AND SCALAR DISPERSIONTHROUGH A STADIUM USING MRI

Megan Colpo, Ty Homan, Zachary Zalar, Michael J. Benson, Andrew J. Banko
Civil & Mechanical Engineering
United States Military Academy
752 Thayer Rd, West Point, NY 10996
ty.homan@westpoint.edu
Christopher J. Elkins, John K. Eaton
Mechanical Engineering
Stanford University
488 Escondido Mall, Stanford, CA 94305
celkins@stanford.edu

ABSTRACT
A contaminant release within a stadium is studied
experimentally using MRI techniques. The stadium geometry
includes several realistic features, such as tunnels and a large
roof opening, that enable ventilation and affect internal flow.
MRI techniques are well suited for resolving flows inchallenging internal geometries, and the three-dimensional
measurements provide detailed insight into the complex flow
and scalar dispersion occurring in, through, and around thestadium. Three-component velocity measurements wereobtained for 0 and 45 degree wind angles measured relative tothe minor axis of the roof opening. In both orientations,
openings on the sides of the stadium provide most of the
inflow, while the large roof opening provides most of theoutflow. The data also demonstrate differences between theflow fields in the two orientations. Pressure gradients in the 0
degree orientation cause flow to enter the stadium via
openings on its leeward side, while flow exits the stadium
through openings on that side in the 45 degree case. The
velocity results suggest that the 45 degree orientation yields ahigher level of ventilation overall. Concentration
measurements were obtained for the 0 degree wind angle, anddemonstrate that recirculation causes contaminant to collect inthe windward side of the stadium. Contaminant primarily exits
the stadium through the roof, forming an elevated downstream
plume. High concentrations within the stadium relative to thewake suggest that contaminant residence times within thestadium are significant. Along with providing detailed insight
into ventilation dynamics, the MRI datasets are expected to beadvantageous for robust model evaluation efforts.

with well-posed boundary conditions to evaluate accuracy andinform model improvement.
While many experimental and computational studies havefocused on external urban canopy flows (Britter and Hanna,
2003; Lateb et al., 2016), there have been fewer investigations
involving flow through buildings or structures with porous
features. Additional complexity is introduced in such
scenarios, as openings and porous features enable interactions
between internal and external flow. Van Hooff et al.
conducted several computational studies related to flow anddispersion through a stadium, with the intent of providing
insights related to ventilation (2010), pollutant exposure(2013), and more. The computational results were detailed;however, validation was performed using sparse experimental
data and could be improved by comparing to full-fieldmeasurements.
Obtaining detailed experimental data is challenging for
scenarios involving naturally ventilated buildings. Restrictive
internal geometries can prevent the usage of techniques thatare either intrusive or require optical access. Moreover, thelarge spatial variability inherent to internal-external flowinteraction poses a challenge for the resolution of conventional
measurement techniques. Most experimental studies related tobuilding ventilation have been performed in wind tunnels withthe aid of discrete probes (Ohba et al., 2001; Jiang et al., 2003).
In-situ measurements have also been obtained at full scale,commonly employing pressure transducers or anemometers(Caciolo et al., 2011; Lo and Novoselac, 2012). Because thesetechniques are challenged by the small pressure differences
associated with natural ventilation, other studies use tracer-gas
methods as an indirect form of measurement (Remion et al.,2019). In general, the aforementioned studies are limited by
the use of discrete measurement devices, which are typicallyintrusive and challenged to resolve complex flow.
A suite of experimental methods uses Magnetic
Resonance Imaging (MRI) to non-optically and nonintrusively measure flow quantities for internal or external
flow in arbitrarily complex geometries. Measurements aretaken inside a water channel, allowing for the precise control
of inlet and boundary conditions. Additionally, inlet
conditions are directly measured as part of the resulting
dataset. MRI methods yield full-field, three-component mean

INTRODUCTION
Prediction of flow and scalar dispersion within the built
environment is relevant for structural design, air quality
management, and threat response. However, computational
fluid dynamics (CFD) models are challenged by the broad
range of length scales inherent to urban areas, as the dynamic
atmospheric boundary layer interacts with buildings and otherobjects to yield a complex flow field (Blocken, 2015). CFD
simulations therefore require robust experimental datasets

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022
velocity and concentration data at O(106) points over a threedimensional domain (Benson et al., 2019). As such, MRI
measurements provide new opportunities for model validationin challenging internal geometries. MRI techniques have been
applied to scaled experiments involving both mock urban
arrays (Shim et al., 2019; Owkes et al., 2020) and geometry
related to the JU2003 tests (Benson et al., 2019; Homan et al.,2021), with demonstrated utility for CFD validation (Brown
et al., 2020).
In the present study, MRI methods have been applied tothe measurement of flow and dispersion in, through, andaround a generalized stadium structure. The stadium geometry
was inspired by Van Hooff et al. (2010) and has a roof
structure with a rectangular open section, as well as fourtunnels similar in design to what may be used for ingress andegress to seating areas. Velocity component measurements
were obtained for two wind directions and concentration data
were measured for one of the orientations. The measurements
provide insight into ventilation and dispersion characteristics
and should be useful for future validation efforts.

25mm

92mm

Figure 1. Side view of Stadium geometry showing
generalized stadium features such as stadium entrances(green), open roof, roof slits (red), and roof supports(blue).

EXPERIMENTAL METHODS
An idealized stadium model (see Fig. 1-4) was designed
as a 1:2060 representation of basic features of the Amsterdam
Arena used by Van Hooff et al. (2010). The model also
represents generic features from other stadiums (e.g, roof
opening, multi-level seating, etc.). To minimize blockage inthe channel, the height of the model was scaled to a height of
25 mm and an outside diameter of 92 mm. These dimensions
were selected to ensure that a blockage ratio of 0.12 within thechannel was met, while providing the capacity to create porous
features that were realistic and could be captured by the
resolution of the MRI measurements. The geometry featuresa partially open roof design with four entrances at ground level
accessible via ramps. The 6 mm x 6 mm cross-section of eachentrance accommodated nine voxels of data with a 1.2 mm
scan resolution. Other key features allowed for at least one
voxel in each plane. The stadium interior has two levels ofseating around a circular event arena and four external sets ofsupports for a roof with a rectangular opening. Four openings,
hereafter referred to as ventilation gaps, were added just below
the roof to simulate retractable roof designs. These design
decisions were chosen to mimic common stadium features andallow flow both through and around the stadium via multiple
openings. At the base of the stadium is a flange connecting itto the bottom of the water channel section and which could be
rotated to vary the wind angle by 22.5 degree increments. A
passive scalar was released from an injector in the base of thestadium via of an array of 2.0 mm holes at the stadium floor
fed by a plenum. The hole array was designed to injectcontaminant at low velocity across the entire stadium so theeffects of ventilation features could be directly observed.
The stadium was housed within a 2.2 m long water
channel (see Fig. 5) that consists of three gridded diffuser
sections and a contraction to increase flow uniformity. To
develop a fully turbulent boundary layer, representative ofneutrally stable conditions within an urban canopy, flow
travels through an upstream section with a four-row cuboid
building array with 14 mm x 14 mm bases. The cuboid sizing
is similar to buildings surrounding a stadium, and the array isplaced far enough upstream so that mean flow effects areminimized near the stadium. This distance was approximatedusing the results in Lien and Yee (2004). The array ends 160

Figure 2. Side view section cut of stadium geometry
showing two floor seating (blue and green) and roof slits(red).
90°
67.5°
45°

22.5°

FLOW

0°

Figure 3. Top view of stadium geometry showing
rotation and wind angles

Figure 4. Side view of injector geometry showing inlet,
plenum, and hole arrays.

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

Diffuser and Grids

Contraction

Roughness

160 mmFigure 5. Section cut of water channel.

Stadium

Channel Exit

110 mm2.2 mdominates in the 0 degree orientation, causing flow torecirculate from the leeward side of the stadium cavity, acrossthe floor, and finally vertically upwards at the windward side.
Recirculation is also dominant in the 45 degree orientation,
especially under the large roof overhangs.
The streamwise velocity fields for both the 0 and 45
degree stadium orientations are represented in Figure 7 with
contour planes located at two heights. As demonstrated by thecontours, the stadium creates an obstruction within the flow
field that causes mainstream flow to accelerate. Freestream
velocity increases from 0.415 m/s to a maximum of
approximately 0.45 m/s above the stadium (an 8% increase).
A significant increase also occurs around the sides of thestadium. A large, separated flow region exists in the wake ofthe stadium, where flow generally tends to move upwards
from ground level and against the direction of bulk flow near
the leeward side of the stadium. This region is especiallyprominent in the 45 degree orientation, due to the roof support
columns which widen the stadium’s exterior profile withrespect to incoming flow and cause the wake to beasymmetric.

mm upstream of the stadium followed by a regular grid ofshort cylinders representing uniform roughness so that thebuilding wakes recover prior to interacting with the stadium
Within the 110 mm by 196 mm main channel, the bulk
velocity was 0.3 m/s, giving a Reynolds number of 10,500
based on the stadium height of 25 mm. For the stadium
entrances, the Reynolds number is 290 based on the tunnel
height and the measured velocity as described in Figure 8.
Based on the cuboid the height and the bulk velocity, thecuboid Reynolds number was 4700. The velocity through thehole array in the stadium floor was 0.0485 m/s. As shown in
Figure 4, the hole array covers the entire floor of the stadiumto provide an evenly distributed contaminant injection thatminimizes interference with the natural velocity profiles
inside the stadium.
Magnetic resonance velocimetry (MRV) and magnetic
resonance concentration (MRC) were used to measure the 3D
mean velocity and concentration fields in and around thestadium. Both techniques utilized a GE Discovery MR750
3.0T Magnetic Resonance Imaging (MRI) system at theRichard M. Lucas Center at Stanford University. MRV used
an aqueous solution of 0.06 M CuSO4 and a phase-contrast
sequence as described in Elkins and Alley (2007) to acquirethe 3D, 3-component mean velocity field on an isotropic
Cartesian grid with 1.2 mm resolution. MRC was conductedat the same scan resolution and used a fast-spoiled gradientecho sequence (Banko et al., 2020). Three scan types are used
to construct the concentration field: background scans using
plain water for the main and injection flow, reference scans
using 0.02 M CuSO4 solution for the main and injection flows,
and standard scans using water for the main flow and 0.02 M
CuSO4 solution for the injection flow. A second, higher
concentration standard scan using 0.1 M CuSO4 solution was
also incorporated to improve signal-to-noise ratio in low
concentration regions of the plume. The concentration field iscomputed by background-subtracting the standard scans andthen normalizing by the difference between reference andbackground scans, and therefore varies from unity in theinjector to zero in the freestream (Banko et al., 2020). The
resulting uncertainties were approximately 6% of thefreestream velocity for MRV and 4% of the injectedconcentration for MRC.

Figure 6. Side profile of the stadium with arrows to illustrate
key flow mechanisms and directions at centerplane.
The interior of the stadium is largely shielded from bulk
flow in both orientations; however, several porous features
enable an interaction between internal and external flow. Nearground level, windward facing tunnels provide the primarymeans of inflow as impinging bulk flow creates a highpressure region at the front of the stadium. In the 0 degreeorientation, support columns obstruct flow near the windward
tunnel entrances, although flow into the stadium persists. In
the 45 degree orientation, fast-moving flow enters the stadium
via a tunnel aligned closely with the bulk flow direction.
Towards the top of the stadium, roof level ventilation gaps
provide another primary means of inflow. Flow accelerates
through a ventilation gap oriented directly upstream in the 0
degree case, and in the 45 degree case, two ventilation gaps
provide exposure to fast moving flow from the windward
direction.

RESULTS
Flow Field Analysis
Figure 6 provides an illustration of the key flowmechanisms and directions within the stadium at thecenterplane. Flow within the stadium is complex and threedimensional, generally following characteristics of driven
cavity flow (Shankar and Deshpande, 2000). A large vortex

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

Figure 7. Contour planesof streamwise velocity
normalized by bulk
velocity located at thehorizontal midplane of
the tunnels (left) and the
midplane of the roof level
ventilation gaps (right)
for the two stadiumorientations: 0 degrees(a) and 45 degrees (b).
Red lines on thegeometry thumbnails
indicate plane locations.

(b)

(a)

Figure 8 provides quantitative insight into the amount offlow moving in or out of the stadium through the tunnels androof level ventilation gaps. The flow could not be directly
integrated due to partial volume effects. Instead, velocities
were obtained along the length of the tunnel centerlines andnear the center of the ventilation gaps. The plots indicate thatfor the 0 degree orientation, flow enters the stadium throughleeward openings in addition to the windward openings. In
fact, flow into the stadium through the leeward tunnels(tunnels 1 and 4) is approximately one quarter of flow throughthe windward tunnels (tunnels 2 and 3). Flow through tunnels
2 and 3 is likely impeded by the small separation regions
created by the nearby roof support columns (c.f. Fig. 7). Flowalso enters the stadium through the leeward ventilation gap(gap 1). The velocity of this flow is over one third of thevelocity of flow through the windward gap, which issignificant given that the windward gap is directly exposed to
freestream flow. Inflows on the leeward side in this orientation
occur due to a pressure differential that is created by partialpressure recovery in the stadium wake and low pressure above
the stadium roof.
Flow through the leeward tunnels (tunnels 1 and 2) in the
45 degree orientation is more complex. Recirculation withintunnel 1 (the most leeward tunnel) causes flow on the bottom
half of the tunnel to move towards the stadium exterior, while
flow on the top half of the tunnel moves towards the interior.
The large jet created by tunnel 3, which faces directly
upstream, likely reduces the interior-exterior pressure
difference across tunnel 1, preventing flow in tunnel 1 frompreferring a global direction. Inflow through tunnel 4, on theother hand, is not much larger than inflow through the leeward
tunnels in the 0 degree case. The windward ventilation gaps
(gaps 3 and 4) in the 45 degree case each provide a comparable
inflow to the windward gap in the 0 degree case, while gaps 1
and 2 enable more outflow than any gap in the 0 degree case.
These results demonstrate that ventilation through stadium
openings is strongly influenced by changes in wind angle.
Flow through some openings experiences not only a change inmagnitude, but also a reversal of direction, as is the case forthe leeward tunnels and roof level gap in the 0 degree case.
The final and most substantial means of ventilation is the
opening in the stadium roof. For both orientations, the roof
opening is the primary means by which flow exits the stadium.
The 45-degree opening is angled with respect to the

1

0.8

0.6

0.4

0.2

0

-0.2
1

2

3

4

3

4

Tunnel

1.2

1

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6
1

2

Ventilation Gap

Figure 8. Bar graphs depicting characteristic velocity
magnitudes at the centerlines of the tunnels and roof level
ventilation gaps for both stadium orientations: 0 degrees (blue)and 45 degrees (red). Flow into the stadium is given by positive
values, while flow out is given by negative values. Labels on
the geometry thumbnails indicate the locations that correspondwith the numbers on the x-axes of the charts. The arrows
indicate the freestream flow direction for each stadiumorientation.

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022
flow moves into the stadium through these tunnels as well.
These findings agree with the data shown in Fig. 8.
Figure 11 depicts contours of streamwise velocity andconcentration on the vertically orientated stadium centerplane.
In general, much of the flow within the lower portion of thestadium moves against the direction of external flow, whilecloser to the roof, flow moves in the direction of external flow(see also Fig. 6). The effects of this internal recirculation cause
the windward side of the stadium cavity to experience thehighest levels of contamination. Flow entering the stadium
through the ventilation gap on the windward face does little toprevent contamination of the stands, and instead attaches tothe bottom surface of the roof overhang. This is consistent
with general behavior of wall jets and could also be due to thedirection of recirculating flow within the stadium. Flow also
enters the stadium through the ventilation gap on the leeward
face of the stadium. In this case, the incoming flow does not
attach to the bottom surface of the roof, possibly due to thesmaller inflow velocity compared to the strength ofrecirculation within the stadium, and instead, it dilutes somecontamination over the second level stands. The velocity andconcentration results indicate that recirculation within thestadium is strong enough to influence both the internal
concentration field and ventilating flows.

streamwise flow direction, and as result, a segment of its
leeward edge is higher than the corresponding segment of its
windward edge. This difference in heights causes somefreestream flow to also be directed into the stadium throughthe 45-degree opening. Flow through the roof in the 0 degreeorientation, on the other hand, is almost exclusively exiting thestadium, balancing flow through the tunnel and slot openings.
Scalar Dispersion Analysis
Concentration data are analyzed for the 0 degreeorientation. Figure 9 displays isosurfaces at three different
concentrations in order to demonstrate general features of thecontaminant plume. After injection, contaminant fills theentirety of the stadium, with the highest concentrations
residing in the windward half of the stadium. The majority ofcontaminant exits the stadium via the large rectangular roof
opening. Concentrations in the stadium wake are relatively
low, being almost entirely below 10%, and the plume
approaches the measurement noise floor by the time it reaches
the downstream end of the test section. This is an indicator that
turbulent mixing is highly effective in the downstream regionsof the test section. High concentrations within the stadium
relative to the wake suggest that contaminant residence times
within the stadium are significant.
While a small amount of contaminant can be seen exiting
the stadium via the side roof ventilation gaps, there is notransport out of the leeward ventilation gap. Interestingly,
there is also little evidence of contaminant exiting via thetunnels. This is consistent with the characteristic velocities
shown in Fig. 8, which demonstrate that all four tunnels in the
0 degree case and the leeward ventilation gap experience
inflow. Contaminant therefore exits the stadium almost
exclusively through the roof opening, which contributes to theelevated nature of the downstream plume. These observations
demonstrate the influence of porous feature ventilation
characteristics on the spatial distribution of the downstream
plume.

Figure 9. Concentration isosurfaces for C=0.05 (a), C=0.1 (b),C=0.3 (c), with flow moving from left to right. Isosurfaces arecolored by height.

Figure 10. Contour planes located at the midplane of thetunnels, colored by concentration (top) and streamwise
velocity (bottom) with velocity vectors displayed.

The velocity field provides insight into many features of
the concentration field. Figure 10 depicts contours of
streamwise velocity and concentration at the horizontal
midplane of the tunnels. Contaminant near the interior ends ofthe windward tunnels is diluted by incoming flow. There isalso little contaminant within the leeward tunnels because

CONCLUSIONSMRI techniques were applied to the measurement of flow
and scalar dispersion within a stadium, yielding threedimensional velocity and concentration fields. Velocity
measurements were obtained for two orientations of the512th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022
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Figure 11. Vertical contour planes located at the centerplaneof the stadium, colored by concentration (top) and streamwise
velocity (bottom).
stadium relative to the freestream flow direction. The data
demonstratesignificant
differencesinventilation
characteristics between the two orientations. In the 45 degreeorientation, more openings are exposed to fast moving flow on
the windward side of the stadium. This enables strong inflows
on that side, while openings on the leeward side enable
outflows. The 0 degree orientation experiences inflows
through the windward side as well, but also demonstrates thatchanges in orientation can cause ventilating flows to reverse
direction: low pressure above the stadium and partial pressure
recovery in the wake foster inflow through leeward tunnels
and roof level gaps. Concentration measurements obtained forthe 0 degree orientation demonstrate that this phenomenon has
an important influence on dispersion, as contaminant exits thestadium almost exclusively through the roof and creates anelevated downstream plume. These results suggest that for
natural ventilation design, it is important to consider theplacement of openings with respect to external flow features
and wind directions.
Ultimately, the three-dimensionality and spatial
variability of both the velocity and concentration fields
suggest the importance and utility of the detailed MRI datasetsfor model validation efforts. Future work will therefore apply
the data to comparisons with CFD simulations that employ
boundary conditions from the experiments. These
comparisons can be enhanced with additional quantitative
analysis of the ventilation characteristics of the stadium (e.g.,using scalar flux calculations). Subsequent MRI experiments
can also be performed to collect velocity and concentration
data for different wind angles, and a transient release can be
explored using phase-locked imaging.
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