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Journal of Wind Engineering
and Industrial Aerodynamics 88 (2000) 213230
Experimental measurements and computations ofthe wind-induced
ventilation of a cubic structure
M.P. Strawa, C.J. Bakerb,*, A.P. Robertsonc
aSchool of Civil Engineering, University of Nottingham,
UKbSchool of Civil Engineering, University of Birmingham Edgbaston,
Birmingham B15 2TT, UK
cSilsoe Research Institute, Bedfordshire, UK
Abstract
This paper presents the results of an experimental, theoretical
and computational
investigation of the wind-driven ventilation through a 6m cube
with openings on oppositefaces. Measurements were made of the
surface pressures coecients and mean and totalventilation rates
through the cube for the faces with the openings both normal and
parallel to
the wind. These measurements were then compared with a number of
methods for theprediction of mean and fluctuating ventilation
rates. For the normal configuration the meancomponent of
ventilation was considerably greater than the fluctuating
component, whilst forthe parallel configuration the mean component
was close to zero, and the ventilation was
dominated by the fluctuating component. For the normal
configuration the standarddischarge coecient method was shown to
significantly underpredict the mean ventilationrate. A CFD
calculation was however reasonably accurate in this regard. By
contrast, for
the parallel configuration the use of the standard discharge
coecient resulted in asmall overprediction of the measured values
of ventilation rate. The relative magnitudesof the ventilation
produced by the various fluctuating flow mechanisms (broad
banded,
resonant and shear layer) were established, and methods of
calculating the total ventilationrate from the mean and fluctuating
components discussed. Finally, a simple method ispresented for the
estimation of shear layer ventilation. # 2000 Elsevier Science
Ltd.All rights reserved.
Keywords: Wind-induced ventilation; Discharge coecient;
Full-scale experiments; CFD
*Corresponding author. Tel.: +44-121-414-5067; fax:
+44-121-414-3675.
E-mail address: [email protected] (C.J. Baker).
0167-6105/00/$ - see front matter # 2000 Elsevier Science Ltd.
All rights reserved.PII: S 0 1 6 7 - 6 1 0 5 ( 0 0 ) 0 0 0 5 0 -
7
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1. Introduction
The natural ventilation through a building consists of two
components theventilation caused by thermal effects, and that
caused by wind effects. It is with thefundamental nature of the
second of these effects that this paper is concerned, andthus
attention is restricted to relatively high wind speed conditions.
The wind-drivenventilation itself is commonly considered to consist
of two components a meancomponent driven by the mean pressure field
at the ventilation openings, and afluctuating component driven by
the fluctuating pressures and unsteady flowsaround the openings.
The former is likely to be dominant when there are a numberof
openings around the buildings, in regions of different wind-induced
pressures.The second component is likely to be dominant when there
is only one majoropening on the building, or where all openings are
in regions of similar pressure.This fluctuating component of
ventilation can be further considered to consistof a number of
distinct phenomena [1]. The first mechanism is referred to
ratherloosely in [1] as continuous airflow, and seems to represent
fluctuations in theventilation flow caused by surface pressure
fluctuations at the openings across awide range of frequencies. In
what follows we will refer to this mode of unsteadyventilation as
broad banded ventilation. The second mechanism is pulsationflow,
caused by a body of fluid being driven perpendicular to the opening
by thedifference between the external and internal pressures. Such
ventilation flows aresignificantly affected by the geometry of the
enclosure, and by air compressibility.The ventilation rate spectrum
will have a peak at the Helmholz resonant frequencyof the
enclosure, and for this reason this mode will be referred to in
what followsas resonant ventilation. The third is known as eddy
penetration, and is caused byfluid transfer due to eddies in
unstable shear layers that exist when the externalflow is across
the orifice. This will be referred to as shear layer ventilation in
whatfollows.In the past a number of experimental investigations
have been carried out to
investigate wind driven ventilation for example, at wind tunnel
scale the work ofRefs. [25] and at full scale the work of Refs.
[58]. A number of methods also existfor calculating the ventilation
due to the components listed above. Mean ventilationrates can be
calculated using simple zonal methods based on orifice flows [9].
Thefundamental equation that is used to obtain the dimensionless
mean discharge,through an orifice, Q, is the simple discharge
coecient relationship
Q CdDCp
p; 1
where DCp is the mean pressure difference across the orifice and
Cd is the orificedischarge coecient. Here, and in all that follows,
the actual discharge is nondimensionalised with the opening area
and the reference velocity. The dischargecoecient is conventionally
taken as 0.61, which is the value for an orifice with flowparallel
to its axis. However it should be noted that it is a weak function
of Reynoldsnumber and is a strong function of orifice shape and
thickness. This equation arisesfrom the use of the energy and
continuity equations, and the discharge coecientallows for real
flow effects. As the flow is steady inertial effects are assumed to
be
M.P. Straw et al. / J. Wind Eng. Ind. Aerodyn. 88 (2000)
213230214
-
negligible. The effect of flow across the orifice (i.e. in its
plane) is not usuallyconsidered (but see Ref. [4]), although for
many ventilation openings on the surfaceof buildings there may be a
significant crossflow. In what follows it will be seen thatwe will
be analysing flow through a structure with two openings of equal
area. In thiscase Eq. (1) can be written as
Q CdDCp=2
q: 2
In this case the pressure coecient difference is that measured
across the twoopenings, and the factor of
2p
is because the two openings are effectively in series.In recent
years, CFD packages have become a more popular tool for the
prediction of mean ventilation flows [10], principally through
the direct integrationof flow across the ventilation openings.
Using such methods it is not necessary toassume a value for
discharge coecient. Further if such calculations are based on
acalculated flow field around the building, they will, in
principle, take into accountany cross flow effects that might
exist.Determination of the fluctuating components of ventilation is
considerably more
complex. Perhaps, the first thing to appreciate is that whilst
flow through anindividual ventilation opening can be either in or
out (positive or negative), bydefinition ventilation is a measure
of the total air exchange and both inflows andoutflows result in
positive ventilation. Having said this let us firstly consider
broadbanded ventilation. Broad banded fluctuations follow the
fluctuations in theoncoming wind across a wide range of
frequencies. Most of the energy in suchfluctuations will be at
relatively low frequencies (50.1Hz) and correspond to large-scale
variations in wind direction, and consequent changes in the flow
patternaround the structure. This ventilation mechanism can
effectively be regarded as amodification of the mean ventilation
mechanism. For a two opening enclosure suchas will be considered
here, the total ventilation due to the mean and broad
bandedfluctuating mechanisms together is given by the area
underneath the ventilation timehistory divided by the length of
record. If the ventilation time history does notchange sign i.e.
the magnitude of the fluctuations is less than the mean, this of
coursecorresponds simply to the mean ventilation rate. If the value
of the fluctuations isgreater than the mean, then there will be
some rectification of the ventilation timeseries around zero and
the total ventilation due to these two mechanisms will be inexcess
of the mean value. If we assume that in such a case we have
sinusoidalvariations in ventilation with a true non-dimensional
mean Q and a true non-dimensional r.m.s. value of sQ then it is
straightforward to show that the total non-dimensional ventilation
rate due to the mean and broad banded ventilationmechanisms is
given by
QB Q 22p
p
!sQ
1 1
2
Q
sQ
2s: 3
The true mean and r.m.s. values mentioned above would be such as
could becalculated from velocity measurements in the ventilation
outlets. Eq. (3) applies only
M.P. Straw et al. / J. Wind Eng. Ind. Aerodyn. 88 (2000) 213230
215
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for Q=sQ52p
. Above this value, the total ventilation is equal to the
meanventilation.When calculating the resonant ventilation, the
usual approach is to derive the
momentum equation for each opening, for a slug of fluid that is
forced in and out ofthe orifice by the difference between the
internal and external pressures see Refs.[2,4,11,12] amongst
others, and thus compressibility and inertia effects are taken
intoaccount. This thus represents a type of ventilation that is not
allowed for in thedischarge coecient approach. These equations are
then combined with thecontinuity equation to give a set of
non-linear equations that are then either solvednumerically or
linearised using one of a number of approaches to produce
equationsthat are analytically tractable. These are second-order
differential equations relatingthe discharge through each opening
(and the internal pressure coecient) to theexternal pressure
coecient at the openings. Frequency-domain approaches are thenused
to calculate the relationship between the external pressure
spectrum, theinternal pressure spectrum and the ventilation rate
spectrum. Ref. [13] shows that theuse of the technique of proper
orthogonal decomposition of the surface pressure fieldleads to an
elegant solution for these parameters. The ventilation rate
spectrum isgiven by
SQR oru2R=2B 2 Q2
1 ST1 Q2
21 ST2 . . . . . . : :
1 o2=o2n 2 2co=on 2 4
where o is an angular frequency, on is the natural frequency of
the system ABN=rL0:5 and c is the damping of the system
K=2rLABN0:5; r is thedensity of air, uR is a reference velocity, K
is a coecient of linearisation, A is theorifice area, L is the
effective orifice length (actual orifice length 0:89 Ap ) and N
isthe number of orifices; B gPR=V where g is the ratio of specific
heat, PR is areference pressure and V is the volume of the
enclosure;
Qi
Pj Pixj=N where
Pixj is the eigenvector of mode i at point j, the position of
the openings on thesurface; STi is the spectrum of mode i.In
deriving the above equation the linearisation method of Ref. [11]
has been used,
although other approaches would be equally valid. It can be seen
from the form ofthe above equations that the ventilation spectrum
will peak at the resonant(Helmholz) frequency of the system. For
most buildings this frequency will be quitehigh (>1Hz). Further
note that the spectrum will tend to zero at low
frequencies.Physically, this corresponds to the filtering out of
long period fluctuations, due to thefinite size of the enclosure.
It is thus likely that the broad banded and resonantventilation
spectra will be separated in the frequency domain. From such
spectra ther.m.s. values of non-dimensional ventilation rate sQR
can thus be found. Then,assuming to a first approximation that the
variation is sinusoidal, the ventilation dueto this mechanism can
be shown to be given as
QR sQR2p
p: 5
M.P. Straw et al. / J. Wind Eng. Ind. Aerodyn. 88 (2000)
213230216
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The particular utility of this method is that, when applied to
the case with more thanone opening, it obviates the need for the
calculation of the cross spectra of pressuresbetween orifices that
would otherwise be required. This becomes particularlysignificant
where the number of openings becomes large. This being said, in
whatfollows we will consider only the two opening case, for which
the main use of Eqs. (4)and (5) lies in their relative
simplicity.With regard to the other unsteady ventilation mechanism
due to shear layer
unsteadiness across orifices, to the authors knowledge, no
methods exist for theprediction of non-dimensional ventilation due
to this mechanism QS. Note howeverthat as this type of ventilation
is driven by the momentum of the fluid parallel to theopening, any
ventilation caused by this mechanism will be in addition to
thatproduced by the other mechanisms.Thus it is possible to
calculate both steady and unsteady ventilation through a
number of different approaches. The question then arises as to
how the totalventilation can be predicted. Full scale ventilation
measurements are usually madeusing tracer gas experiments (see
below) which effectively give the total ventilation ofthe enclosure
and it is this quantity that needs to be predicted. If the
meanventilation rate is much greater than the fluctuating
ventilation, then the total nondimensional ventilation Q should be
given by QQR QS . If the meanventilation is close to zero then the
total ventilation will be given byQB QR QS .This paper presents the
results of a large scale experiment of wind driven
ventilation and uses the experimental data to calculate
ventilation rates by a varietyof methods. A simple geometric
arrangement has been chosen that, it is hoped, willallow a
fundamental understanding of the ventilation flow mechanisms to be
gained.The experiments will also provide a simple test case for the
different methods ofcalculating mean and unsteady ventilation
rates. The nature of the experiments isdescribed in Section 2.
Section 3 then presents the experimental results, together withthe
results of calculations of the mean ventilation rates (using direct
velocitymeasurements, a calculation based on Eq. (2) and CFD
calculations), the broadbanded ventilation rate (based both on the
use of a time varying form of Eq. (2) andon Eq. (3)), the resonant
ventilation rate (based on Eqs. (4) and (5)), and the
totalventilation, using various combinations of the above methods.
Section 4 goes on topresent a simple method for the calculation of
shear layer ventilation, and itsadequacy is discussed. Finally,
conclusions are drawn in Section 5.
2. The experiments
The experiments were carried out on a 6m cube constructed on an
exposed site atSilsoe Research Institute. The cube was built on a
turntable such that it could berotated to any angle relative to the
approaching wind direction. Two 1m squareopenings were cut with
their axes on the vertical centreline 0.5m above the centre
onopposite sides of the cube (i.e. the bottom of the openings were
at a height of 3.0m
M.P. Straw et al. / J. Wind Eng. Ind. Aerodyn. 88 (2000) 213230
217
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above the ground). Further details of the cube are given in Ref.
[14]. Two sets ofexperimental results are presented as follows.
(a) The normal case with the faces containing the openings
positioned normal to thewind i.e. with the openings on the windward
and the leeward sides.
(b) The parallel case with the faces containing the openings
positioned parallel tothe wind i.e. with the openings on the side
faces.
These two cases represent distinctly different ventilation
conditions. One wouldexpect the former to be dominated by mean flow
effects, and the second byfluctuating flow effects. Reference wind
conditions were measured using a sonicanemometer mounted at cube
height (6m), 2m to the side of the cube and 18mupstream. The
atmospheric boundary layer at the site has been measured in the
pastand shown to be a typical rural boundary layer with a surface
roughness length ofapproximately 0.01m.The following measurements
were carried out.
(a) Pressure measurements on the external surfaces of the cube
(with the openingsclosed the sealed case) and within the cube (with
the openings exposed theopen case), using pressure tappings and
probes connected to pressuretransducers sampled at 5Hz.
(b) Three-dimensional velocity measurements within the cube
using a sonicanemometer, sampled at 20Hz. Measurements were made
within the cubealong the cube centreline, around the openings and
also across a number ofplanes perpendicular to the plane of the
opening.
(c) Tracer gas measurements using carbon monoxide (CO) sampled
with a GFCAmbient CO analyser at a frequency of 0.1Hz. A constant
injection method wasutilised with the tracer gas being released at
nine equally spaced points withinthe structure. The sampling point
was varied in order to ensure that adequatemixing was taking place.
The tracer gas measurements provided the totaleffective wind driven
ventilation. Leakage tests were performed for the sealedcase.
For the purposes of the present investigation the results were
analysed to determinethe mean and unsteady pressure and velocity
characteristics at the orifice positionsand within the cube. Table
1 shows the values of the mean and r.m.s. referencevelocities for
both geometric configurations and for the sealed and open
cases,together with the values of the mean and standard deviations
of external and internalpressure coecients and the mean and
standard deviations of the dimensionless flowrates at the openings,
as calculated from the velocity measurements. The actualmeasured
values of the flow rates were non-dimensionalised with the
referencevelocity and the orifice area. The total dimensionless
flow rate out of the cube, asmeasured by the tracer gas
experiments, is also shown. Leakage from the cube hasbeen allowed
for in arriving at this figure. Note that, for the normal
configuration,the flow rate values are given as measured (which was
at a point 0.2m into the cube
M.P. Straw et al. / J. Wind Eng. Ind. Aerodyn. 88 (2000)
213230218
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Table1
Flowcharacteristics
Norm
alcase
Parallelcase
Mean
Standard
deviation
Mean
Standard
deviation
Reference
velocity
sealedcase
(m/s)
11.78
2.47
11.37
2.50
Reference
velocity
open
case
(m/s)
6.70
1.44
7.20
1.40
Externalpressure
coe
cientopening1
0.87
0.439
0.649
0.380
Externalpressure
coe
cientopening2
0.390
0.186
0.698
0.347
Internalpressure
coe
cientopen
case
0.081
0.203
Notmeasured
Notmeasured
Opening1non-dimensionaldischarge
Qands Q
0.884(m
easured)
0.67(corrected)
0.136(m
easured)
0.103(corrected)
0.113(m
easured)
0.101(m
easured)
Opening2non-dimensionaldischarge
Qands Q
0.681(m
easured)
0.71(corrected)
0.103(m
easured)
0.107(corrected)
0.115(m
easured)
0.105(m
easured)
Totalnon-dimensionaloutflowtracergasQ
0.787
}0.380
-
M.P. Straw et al. / J. Wind Eng. Ind. Aerodyn. 88 (2000) 213230
219
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from the centre of the plane of the orifice) and also corrected
to the mean value at theplane of the orifice. This correction was
carried out using the results of the CFDcalculations (see below) by
multiplying by the ratio of the calculated mean velocity atthe
orifice plane to the calculated velocity at the measurement point.
When thisprocess has been carried out it can be seen that the
discharges at the two orifices aresimilar to each other as would be
expected.Firstly, consider the normal case. The pressure coecient
on the front face is
positive, and that on the rear face is negative as expected. The
different ventilationresults obtained from the velocity
measurements can be seen to be reasonablyconsistent, with a value
of Q of 0.69 ( 0.02) and a value of sQ of 0.105 ( 0.002).The
overall measured ventilation rate Q is 0.787, suggesting that
around 10% of theventilation is accounted for by resonant
ventilation and shear layer ventilation. Forthe parallel case the
situation is rather different. The pressure coecients at each ofthe
two openings are very similar (but not identical, suggesting that
the sides of thecube were not completely parallel to the mean flow
direction). Q is around 0.1 whilstthe measured Q is around 0.4,
suggesting a relatively greater fluctuating componentthan in the
normal configuration.The reference velocity spectra and external
pressure coecient spectra are shown
in Fig. 1 for the two configurations. The velocity spectra for
all three velocitycomponents are broadly as expected with a slope
close to the value of 53 at highfrequencies. The spectrum of the
vertical component is flatter than the othersas would be expected
in such near ground conditions. The pressure spectra are
Fig. 1. Velocity and pressure coecient spectra.
M.P. Straw et al. / J. Wind Eng. Ind. Aerodyn. 88 (2000)
213230220
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broadly similar in form to the velocity spectra. Fig. 2 shows
the spectra of theinternal pressure coecient plotted in the form of
spectral density frequency/variance. There is an indication of a
small high-frequency peak in the internalpressure spectrum at
around 2Hz. This will be seen to be of some significance inwhat
follows.The measured longitudinal velocity distribution through the
cube for the normal
configuration, on the centre-line directly between openings, is
shown in Fig. 3together with CFD predictions. In this figure the
actual velocity is normalised with areference velocity. The CFD
calculations will be discussed further below. At thispoint it is
sucient to state that the curves are similar in form, although
theexperimental values vary rather more across the cube than the
predicted values. Itcan be seen that the velocity at the windward
opening reduces rapidly with arecovery towards the leeward opening.
It would be expected that the velocity at theopenings should be
equal for mass conservation. However, as mentioned above itwas not
possible to measure velocities in the plane of the openings, with
the nearestpoint being 0.2m from the plane (hence the use of
corrected values as outlinedabove). The results of Table 1 suggest
that the average values at the openings should
Fig. 2. Internal pressure spectrum plot of spectral density
frequency/variance against frequency.
Fig. 3. Velocity distribution through the cube (normal
configuration).
M.P. Straw et al. / J. Wind Eng. Ind. Aerodyn. 88 (2000) 213230
221
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be 0.69. This implies that the measurements near the windward
opening were madein a strongly accelerated vena contracta region.To
enable the method of Ref. [13], to be used to calculate the
unsteady ventilation
rate, a proper orthogonal decomposition was carried out on the
surface pressurecoecients around the centre line of the cube for
both configurations. Fig. 4 showsthe distribution of the first
three eigenvectors that are obtained in the analysis andthe
proportion of fluctuating energy associated with each mode for the
normal and
Fig. 4. Results of POD analysis for cube.
M.P. Straw et al. / J. Wind Eng. Ind. Aerodyn. 88 (2000)
213230222
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parallel configurations. The modal spectra for the first three
modes for eachconfiguration are also shown. Note that in the plots
for the normal case tappings,15 are on the windward face of the
cube, tappings 611 on the cube roof andtappings 1216 on the leeside
of the cube. For the parallel case tappings 15 and 1216 are on the
side faces of the cube, and tappings 611 are on the roof. The
centre ofthe orifices corresponds to the positions of tappings 3
and 14. For the normal casethe mode shapes are broadly as expected,
with the shape of the first mode mirroringthat of the external
pressure distribution, suggesting that this mode is due
tolongitudinal turbulence fluctuations (see Ref. [13]). The
physical cause of the secondmode is not obvious, but in Ref. [13]
it is suggested that it might be related to theunsteadiness induced
by the distortion of longitudinal turbulence as it passes aroundthe
cube. Ref. [13] further relates the third mode to vertical
turbulence fluctuations.For the parallel case, the first mode is
flat, and similar in form to the mean pressuredistribution, again
suggesting that this is caused by longitudinal
turbulencefluctuations. The second mode is highly asymmetric, and
may well be caused bylarge-scale vortex shedding from the cube. The
third mode is symmetric, and mayagain be related to vertical
turbulence fluctuations. As is usual in such analysis,nearly all of
the energy is contained within the first few modes, suggesting that
theseries in Eqs. (2) and (3) can be truncated after a few terms
with little loss ofprecision. The spectra are similar in form to
the reference velocity spectra, with themode 3 spectra showing
relatively more energy at high frequencies, which would beexpected
if this mode were related to vertical turbulence fluctuations.
3. Calculation of ventilation rates
3.1. Mean ventilation rates normal case
The non-dimensional mean ventilation rates Q were calculated for
the normal caseusing two methods as follows:
(a) Using the discharge coecient formula (Eq. (2)) for the
measured mean pressurecoecients, and a standard value of the
discharge coecient of 0.61. Thepressure coecient increment (DCp)
was taken as that measured betweentappings 3 and 14 for the sealed
cube measurements.
(b) Using a CFD solution of the flow through the cube (using
CFX-F3D).Simulations utilised the RNG k2e turbulence model with
CCCT differencing. Afully independent grid utilising 2 105 cells
produced a fully converged solutionof the external flow field and
the consequent internal airflow pattern. Bothexternal and internal
flow fields were simulated simultaneously. This required adomain of
sucient size that would not affect the external flow field around
thecube. The domain size utilised was 5 cube heights upstream,
above and to theside of the cube, and 10 cube heights downstream.
Data from the site of the cubewas used to develop a mean boundary
layer profile in terms of both velocity andturbulent kinetic energy
profiles with a roughness height of 0.01m. This
M.P. Straw et al. / J. Wind Eng. Ind. Aerodyn. 88 (2000) 213230
223
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calculation was only carried out for the normal configuration,
as the symmetryof the cube suggests a zero value should be
predicted if the cube sides wereperfectly aligned with the
flow.
The results of these calculations are shown in Table 2. It can
be seen that thedischarge coecient method significantly
underpredicts the mean discharge throughthe cube. This could be for
a number of reasons inaccuracies in the methods ofmeasuring the
experimental discharges (but this is unlikely given the consistency
ofthe various results); the assumed (ideal) value of the discharge
coecient being toolow or the pressure coecients measured in the
sealed cube case being significantlydifferent when the openings
were present. Detailed pressure measurements aroundthe orifice
would be required to determine whether this was the case. The
CFDprediction provides a result which is far closer to the measured
mean ventilation rate.
3.2. Combined mean and broad banded unsteady ventilation
calculations the parallelcase
For the parallel case the combined mean and broad banded
ventilation rate QBwas calculated in three ways as follows:
(a) Using Eq. (3) with the true mean and standard deviation Q
and sQ as given bythe velocity measurements in the plane of the
openings i.e. assuming theadequacy of Eq. (3) that was derived for
a sinusoidal fluctuation.
(b) As in (a) but with Q and sQ calculated from the time series
of obtained by usingEq. (2) with the time series of the pressure
coecient difference, with the flowdirection taken into account i.e.
allowing for positive and negative values of theflow through any
one opening.
(c) Directly from the integration of the time series produced in
(b), but with theabsolute (rectified) values of the ventilation
rectified about zero.
The results shown in Table 3 are reasonably consistent. The two
values obtainedusing the discharge coecient assumption ((b) and
(c)) are close to each other, whichgives some confidence in the use
of Eq. (3). These are both above the value obtainedusing the
velocity measurements, suggesting that in this case the standard
value ofthe discharge coecient is somewhat too high. The absolute
differences are howeversmall. It is of interest to note at this
point that the value of ventilation rate calculatedusing the mean
values of the pressure coecients in Table 1 to form the
pressurecoecient difference, results in a value of non-dimensional
ventilation of 0.095 which
Table 2
Mean ventilation rates Q normal case
Values from velocity measurements 0.67/0.71
Discharge coecient method 0.483
CFD calculations 0.648
M.P. Straw et al. / J. Wind Eng. Ind. Aerodyn. 88 (2000)
213230224
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is close to the mean value from the velocity measurements, but
significantly less thanthe calculated values of QB.
3.3. Resonant ventilation calculations
The resonant ventilation rates were also calculated using the
frequency domainmethod [13] and the technique of proper orthogonal
decomposition (Eqs. 4 and 5).The following values were assumed for
the parameters in Eqs. (4) and (5) uR 6:7 m=s, A 1 m2, L 1:09 m
(based on an actual orifice length of 0.2m),V 216 m3, g 1:4, PR 100
000 Pa These give values of on and c of 30.8 r/s and0.142,
respectively.The results of the calculation give a natural
frequency for the ventilated cube
system of 4.9Hz. It can be seen from Fig. 2 that the internal
pressure spectrum showsa peak at about 2Hz which may correspond to
this natural frequency. Thisdifference is likely to be caused by
leakage from the cube and the flexibility of the sideof the cube,
causing a change in the effective bulk modulus of the flow. It can
beshown that this is equal to the product PRg in Eqs. (4) and (5).
Ref. [4] points outthat the effect of building flexibility can
reduce the effective value of this parameter toas low as 20% of the
normal value. This is consistent with the observed shift in
thenatural frequency from its predicted value. To allow for this
effect the measurednatural frequency will be used in what follows.
With the natural frequency at thisvalue, it is likely that some of
the unsteady ventilation will take place at frequenciesof up to,
say, 10Hz i.e. higher than the sampling frequency. To enable
thecalculations to be made up to this frequency the following
procedure was adopted.
(a) The modal spectra shown in Fig. 2 were fitted with a
power-law curve forfrequencies between 0.25 and 2.5Hz and were
extended to higher frequenciesusing this curve fit.
(b) The measured power spectra were used in the calculations
using Eqs. (1) and (2)at frequencies below 2.5Hz, with the
extrapolated values being used at thehigher frequencies.
Calculations were carried out using the first three POD modes
only i.e. assumingonly three terms in Eqs. (4) and (5) are of
significance. The results of this procedureare shown in Table 4
where the values for the non-dimensional resonant ventilationrates
QR are presented. The immediate thing to notice about these results
is that theventilation rates predicted for the two cases are,
compared to the mean ventilationrates, relatively small. The latter
point will be taken up further below. The
Table 3
Mean and broad banded fluctuating ventilation rates QB parallel
case
Values from velocity measurements of mean and r.m.s. values and
Eq. (3) 0.185
Values from discharge coecient calculations of mean and r.m.s.
values and Eq. (3) 0.207
Values from discharge coecient calculations of ventilation time
histories 0.220
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225
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distribution of the ventilation between modes (i.e. the
different terms in Eqs. (4) and(5)) is, however, very different.
For the normal case the percentage of the dischargethat can be
attributed to modes 1, 2 and 3, respectively, is 51.6%, 47.7% and
1.6%,whilst for the parallel case the corresponding figures are
86.4%, 0% and 13.6%. Theventilation power spectra for each mode
shown in Fig. 5 also illustrate this. For bothcases therefore, the
resonant ventilation seems to be largely due to the modes
thatreflect oncoming longitudinal turbulence fluctuations. Note
also that most of theventilation due to this effect occurs at
frequencies around the resonant frequency(>0.5Hz). At such
frequencies there is little energy in the oncoming wind.
Theventilation due to broad banded ventilation can be expected to
occur mainly atfrequencies significantly lower than this.
3.4. Total ventilation calculations
For the normal case the total ventilation rate measured in the
experiments is thesum of the mean ventilation rate (which
effectively incorporates the broad bandedunsteady ventilation), and
the resonant and shear layer ventilation. For the parallelcase the
total ventilation is approximately given by the sum of the mean and
broadbanded (Eq. (3)), the resonant and shear layer mechanisms (see
Section 1). Table 5compares the measured total discharge with the
sum of the mean values andresonant values calculated in a number of
ways as follows.
(a) From the values of the mean and broad banded mechanisms
calculated from thevelocity measurements in the opening plus the
calculated resonant ventilation
Table 4
Resonant fluctuating ventilation rates QR
Normal configuration Parallel configuration
Resonant ventilation rates 0.008 0.014
Fig. 5. Results of POD resonant ventilation analysis for
cube.
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213230226
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(b) From the values of the mean and broad banded rates
calculated using a standarddischarge coecient, plus the calculated
resonant fluctuating ventilation.
(c) From the value of the mean ventilation calculated using CFD
and the calculatedresonant ventilation (normal configuration
only).
The first point to note is the relative magnitudes of the
fluctuations caused by thedifferent mechanisms with the resonant
ventilation component being relativelysmall for both
configurations. However, for different geometries this will not
alwaysbe the case for example, for single opening enclosures, one
might expect this type ofventilation to play a much greater role.
However the major point that arises is thatthere is still a
significant discrepancy between the measured total ventilation
rates,and the various calculated values of about 0.1 for the normal
case, and 0.2 for theparallel case. It is likely that this
discrepancy is caused by the ventilation mechanismthat has so far
not been considered shear layer ventilation, to which we turn
ourattention next.
4. Shear layer ventilation
It is apparent from what has been said above that the effect of
a cross flow across aventilation opening can be of considerable
importance. In terms of the meanventilation the experimental
results for the normal configuration suggest that ahigher than
expected discharge coecient is required for the ventilation
ratepredicted by Eq. (2) to be consistent with the measured values.
One reason for thisthat was suggested was that the ventilation
might be increased by a cross flow acrossthe orifice. Some
unpublished experimental data obtained recently by staff at
SilsoeResearch Institute suggests that the discharge coecient might
reach values as highas 0.75 with a large cross flow velocity. This
is presumably caused by the directing ofsome external flow directly
into the opening (see Ref. [14]). Whether or not it issensible to
allow for this by an increased discharge coecient is debatable,
althoughit is undoubtedly convenient.
Table 5
Total ventilation rates
Normal configuration QQR Parallel configuration QB QR Measured
total ventilation Q 0.787 0.380
From velocity measurements
and Eq. (3)+calculated
resonant ventilation
0.69+0.008=0.698 0.185+0.014=0.199
Discharge coecient
calculations+calculated
resonant ventilation
0.483+0.008=0.491 0.207+0.014=0.221, or
0.220+0.014=0.234
CFD calculated mean+
calculated resonant
ventilation
0.648+0.008=0.656 }
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227
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Now let us consider unsteady shear layer ventilation the
so-called eddypenetration mechanism of Ref. [1]. Here the
ventilation is caused by vortices in theshear layer across the
opening transporting flow into and out of the opening.
Simplephysical reasoning suggests that the dimensional ventilation
rate due to thismechanism, qS will be a function of opening length
l, opening width w, velocityparallel to the opening uo, and shear
layer thickness d. A simple dimensional analysisleads to the
functional expression
qSuolw
f n lw;l
d
: 6
Assuming that the opening geometry is fixed and that the
dependence upon the shearlayer thickness is small, this reduces
to
qSuolw
k; 7
where k is a constant.Now writing down the energy equation along
a streamline, and making the (very
approximate) assumption that energy is conserved for a
streamline around a building
0:5ru2R pR 0:5ru2o po; 8where subscript R indicates reference
upstream values, and subscript o indicatesvalues at the opening.
This leads directly to
uouR 1 Cpo 1=2 9
and thus
qS
uRlw1 Cpo1=2 QS1 Cpo1=2
k 10
Using this expression the experimental data allow some estimates
for the parameter kto be obtained. We assume that for each
configuration the ventilation that has so farnot been accounted for
is all due to this mechanism (in dimensionless terms QS isabout 0.1
for the normal case, and 0.2 for the parallel case see Table 5).
Eq. (10) iswritten down for each opening, together with a
continuity equation relating QS tothe sum of the discharges at the
two openings. The values of pressure coecient ateach opening are
given by those in Table 1. One can thus calculate the
ventilationrate for each opening and a value of k for each
configuration. For the normal case itwas thus calculated that the
front opening has a non dimensional ventilation rate of0.023, and
the rear opening of 0.077, with a value of k of 0.065. For the
parallel case,the ventilation is more or less evenly partitioned
between the two openings as wouldbe expected (0.101 and 0.099) with
a value of k of 0.077. Such values of k areconsistent and seem
physically reasonably one would expect an effective
ventilationvelocity to be an order of magnitude smaller than the
velocity outside the shear layeras is implied by these results.
This suggests that the use of Eq. (10) with a value ofk 0:1 should
give a conservative estimate of shear layer ventilation.
M.P. Straw et al. / J. Wind Eng. Ind. Aerodyn. 88 (2000)
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5. Concluding remarks
From the above results and calculations the following
conclusions can be drawn.
(1) For the normal configuration the mean component of
ventilation is significantlygreater than the fluctuating component.
For the parallel configuration the meancomponent is close to zero,
and the ventilation is dominated by fluctuatingeffects.
(2) For the normal configuration the total ventilation is the
sum of the meanventilation, the resonant ventilation and the shear
layer ventilation. For theparallel configuration the total
ventilation is given by the combined mean andbroad banded
ventilation together with the resonant ventilation and the
shearlayer ventilation.
(3) For the normal configuration the mean ventilation rates are
not well predictedby the discharge coecient method using the
standard value of dischargecoecient. The most likely reason for
this is that there is a component of meanventilation due to the
flow across the openings. To allow for this a value ofdischarge
coecient significantly higher than the standard value is required.
Thisventilation was however, well predicted by a routine CFD
calculation of thecombined internal and external flow fields. For
this configuration the resonantventilation component was small, and
the majority of the fluctuating ventilationwas due to the shear
layer ventilation mechanism.
(4) For the parallel configuration the use of the standard
discharge coecientresulted in a small overprediction of the mean
and broad banded ventilationrate. The resonant ventilation was
again small, but represented a largerproportion of the total
fluctuating ventilation. The remainder could beattributed to shear
layer ventilation.
(5) A simple formula has been derived for the prediction of
fluctuating shear layerventilation, but this needs further
verification and calibration before it can bewidely used.
Acknowledgements
During the course of the study the first author was supported by
a Silose ResearchInstitute/University of Nottingham
studentship.
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