Experimental Measurements and Computations Of

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

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

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


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


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


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

-


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.


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).


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.


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


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


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


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.


(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 }


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.


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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