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@By
Abdul Majid Ismail
1.0
Abstract
Naturally ventilated buildings in hot-humid countries require “large openings” for effective cross-flow of air. Prediction of ventilation rates based on the pressure coefficients data established for wind loading calculation requires further correction. Experiments were conducted to investigate and established the required correction factors. The suggested correction factors are based on porosity that is suitable for tropical conditions.
Keywords: Porosity, large opening, pressure coefficient, wind tunnel test.
2.0 Introduction
Prediction of
ventilation rates either manually or with the aid of “CFD” is normally based
on pressure data acquired from wind tunnel experiments using reduced
scale-models [1]. The reduced scale-models used in establishing the pressure
coefficients are normally made of solid blocks and are “bluff body” models
similar to those used in the structural wind loading calculation. According to Awbi (1994) [2], the pressure values obtained
from this type of experimental method may be slightly overestimated. The reduced
scale-models within the range of 1:100 to 1:500 scale factors are too small to
cater for any design of openings. Furthermore,
small openings of a large-scale factor cannot possibly be modeled in the
boundary layer wind tunnel accurately with a satisfactory similarity in the
Reynolds number [3].
In reality, naturally ventilated buildings in hot-humid countries require “large openings” for effective cross-flow of air. Therefore, if “large openings” are to be considered for the walls of actual buildings, further corrections to the wind pressure data obtained from bluff body models are essential. Theoretically, large openings may distort the wind data established from solid body models, and this requires further investigation. The investigation into the effect of the “porosity” of large openings requires very specific experiments using a smaller scaling factor or bigger models.
2.0
Review
of the related theory on porosity
Most research that has been carried out deals mainly with the relative porosity of a typical wall for the purpose of structural wind loading calculation [4]. There is no specific research on the effect of porosity in relation to naturally ventilated buildings with large openings that are suitable for the tropics [5]. If there are inlet and outlet openings on the facades of a building, a pressure difference will be developed between them, and theoretically air will flow from the higher-pressure end to the low-pressure end. The pressure distribution around the building will now be different from that of a solid building, and a new steady state condition will be set.
Pr = Aw / At ----------------(i)
At = wall area including window (m2)
Q a A (pe - pi)1/2 ---------------------(ii)
Where: pe = external pressure (Pa)
For orifice flow, equation (ii) can be expressed as:
Q = Cd Ad {2(pe-pi)/r}1/2------------------(iii)
Where: Cd = 0.61 (the discharge coefficient)
Ad = the area of equivalent sharp-edged orifice
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Figure
1.1: Cross-section of a room.
Consider that the air is flowing continuously from the windward opening into the interior and out through the leeward opening. Applying the flow continuity, the inflow and outflow balance, then:
A1 (p1 - pi)1/2 = A2 (pi - p2)1/2 -------------(iv)
(pi - p2) / (p1 - pi) = (A1 / A2)2 ------------(v)
Substituting the window area (Aw = Pr At) from Equation (i) into Equation (v):
(pi - p2) / (p1 - pi) = (Pr1 At1 / Pr2 At2)2
(pi - p2) / (p1 - pi) = (Pr1 / Pr2)2 ----------------------(vi)
Dp2 / Dp1 = (Pr1 / Pr2)2 ------------------(vii)
For a building with similar openings all over its envelope, the value of the porosity does not affect the internal pressure directly; it affects the mean pressure, which indirectly affects the internal pressure. However, if the area of inlet or outlet is much larger than the opposite wall porosity, the internal pressure will be directly affected by the porosity. Cook (1990) [4] highlighted that, if the area of a large opening is three times larger than the sum of the distributed porosity of the opposite wall, the internal pressure will rise so that only about 10% of the pressure drop is taken by the wall with the opening, and the remaining 90% will be taken by the opposite wall. If the large opening is equal in area to the sum of the distributed porosity of the opposite wall, the pressure is shared equally.
4.0 Latest research findings
4.1 Proposed correction factor by Awbi (1994) from
Chand et.al (1992)
Vref / V10 = 1.7 (href / 400)0.28 -------------(vii) {See Appendix}
where: href = reference height
Vref = reference velocity
400 = gradient height at 0.28 power law
V10 = meteorological wind speed at height of 10 m above ground in open country.
Vi / Vref = F (1 - 0.82 a) -------------(viii)
where: Vi = the corrected wind speed at the inlet opening
For rectangular openings, the correction factor (F) is given by:
F = 1.1 {1 + (Ai / Ao)2}-0.5 -----------------(ix)
Chand et al. (1992) [5] carried
out an investigation to develop the empirical relationship between the rates of
airflow through buildings and the power law exponent for different types of
terrain. He used wind tunnel
measurements for wind profiles representing open country, suburban and urban
terrain. The investigations were
carried out using a model of a room 4.2 x 3.6 x 3 m high at a 1:30 scale factor.
Identical openings of 15% of the floor areas on the longer walls were
used in the experiments. The sill heights were kept at 0.9
m and the window height at 1.1 m, which were established to be the optimum
dimensions from his earlier findings.
The actual window area Aw = 15% of (4.2 x 3.6) = 2.268 m2
The longer wall area At = 4.2 x 3.0 = 12.6 m2
Therefore:
The porosity Pr = Aw / At = (2.268 / 12.6) x 100 = 18%.
4.0
Further investigation and wind tunnel test
4.1 The scale models and experimental
setup
A scale model
at 1:40 scale factor of a room of a typical floor measuring 10 m x 10 m x 4 m
high was constructed from 3/4 cm clear “perspex”.
The typical floor unit was placed over a solid block measuring 10 m x 10
m x 6 m high. This was intended to
disassociate the anemometer readings from any interference of the turbulence
effect of the ground roughness. The
windward front and the rear leeward facades of the model were made to be
detachable to cater for the variation in window sizes.
Five sets of window openings ranging from the smallest 9% to 45% porosity
were made from 10 detachable piece of “perspex”.
Figure 1.2
shows the model of the typical floor and the sizes of openings. The window sill was fixed at 1.5 m from the base of the unit
or 1.0 m clear above the floor level. The
variation to the window height was made to include the 2 m (50 mm actual
dimension) maximum height of opening and the 0.4 m (10 mm actual dimension)
minimum height. The widths of the
openings were maintained at 9 m with an equal distance of 0.5 m from the corner
wall.
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Figure 1.2: Model of the
typical office floor and the variations in porosity values
The Laser
Doppler Anemometer (LDA) is a non-contact optical instrument for investigating
flow fields in gases and liquids [7]. The
anemometer, which was used in the velocity measurements, is an integrated
laser-optics system type. The advantage of the LDA system is that it uses no
probe at the measuring point, and therefore no disturbance to the flow occurs.
Furthermore, the device can be used in an area that is inaccessible by a
normal anemometer. The system is
made up of three main components [8]:
1.
The
integrated laser-optics unit, which comprises a laser and a probe connected by a
fibre optic cable to the unit. The
optic unit is then linked to a velocity analyser (FVA) and “FLOware”
software on a computer.
2.
The
Flow Velocity Analyser (FVA) which has special detection and validation
techniques that can measure signals and detects velocity direction quite
accurately.
3.
The
“FLOware” that is an application programme for (LDA) measurements performed
with a “Dantec” Flow Velocity analyser (FVA).
The software will be used to analyse signals obtained by the laser probe.
The experiment
was carried out using basic scale-model as shown in Figure 1.2 to investigate
only the effect of simultaneous variation of identical size inlet and outlet
openings (identical porosity rate).
The
model was placed at the centre of the turntable with the opening normal to the
wind direction. The measuring point
of the inward velocity (Vi) was at the centre point of the windward
window (Figure 1.3). The model,
which was made from clear “perspex”, was transparent enough for the laser
beams to pass through. Smoke was
passed through the tunnel to generate seedling.
Measurement of (Vi) was carried out by focusing the laser
beams on to the measuring point and observing the frequency shift of the light
scattered by moving particles [1]. Figure
1.3 shows the set-up of the measuring point and the relative positioning of the
laser beams. Two data loggers for
measurement of (Vi) and (Vref) were set-up close to the
tunnel window.
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Figure
1.3: The set-up of the measuring
point and the relative positioning of the coherent laser beams.
The optics
units were set at the differential or fringe mode where two coherent laser beams
intersect and interfere in the volume of intersection, thus forming interference
fringes [9]. The photo-detector
measures the difference between the two Doppler-shifted scattered beams.
The Doppler frequency, fD, is given by [8]:
fD = (2ux / l ) Sin
( q /2)
Where:
ux
= the particle velocity component in the x directions (normal to laser beam)
(m/s)
l =
wavelength of the laser beam (m)
q =
angle between the incident beams (deg).
The LDA system
work is based on the shift in the light frequency produced by moving particles
passing through the fringe, and these require the flow to be seeded with
particles. Smoke particles were
used in the tracking of the flow by the laser detector. The electrical signals of the frequency change detected by
the optic units were sent to the FVA and to the computer output as histogram,
means and rms. values and turbulence intensity.
The
corresponding reference velocity (Vref) for each set of (Vi)
readings was taken from the static pitot probe located at 0.8 m above the tunnel
floor. This reference static
pressure probe was connected to the electrical manometer which converted the
mechanical into an electrical signal and into the data logger. The readings of both (Vi) and (Vref)
were taken simultaneously for every set of experimental input.
The wind tunnel speeds were retained high with the fan varying from about
8 - 11 m/s. This was to avoid any
laminar flow developed through the window openings.
4.2 Experimental results and analysis
Wind flow
through the windward and leeward openings of four different porosity values (9%,
18%, 27%, 36% & 45%) were subjected to five different fan speeds (of 75, 80,
85, 90 & 95). Six mean readings
of (Vi) and (Vref) for every set of porosity values were
recorded. The pressure value of the
reference pressure in (cm of water) was converted into Pascal (Pa) by
multiplying each value by 98.067 (1 cm. of water = 98.0665 Pa).
The pressure value was then converted into the relative velocity values
using the relationship:
V = (2 p / r)0.5
Vref = {2 x (pref x 98.067) / 1.225}0.5.
The reference
velocity at the height of the building was obtained from the power law formula:
Vref250 = Vref (250 / 800)0.28
Where 250 mm
was the height of the model and 800 mm was the tunnel reference height.
The results of the experiment were analysed and summerised graphically in the following figures:
Figure
1.4(a): Variation of (Vi ) with fan speed for different porosity
values.
Figure
1.4(b): Variation of the velocity
ratio (Vi / Vref ) with fan speed for different porosity
values.
Figure
1.4(c): Effect of porosity on the
velocity ratio (Vi / Vref ) for different porosity values.
From the analysis carried out on the data collected from experiment, the findings may be summarised as follows:
1.
For
simple rectangular cross-openings (inlet and outlet of identical size), the
inflow velocity at the inlet opening (Vi) increases linearly with the increase
in the external wind speed {Figure 1.4(a)}.
2.
Except
for the £
9% porosity opening, the larger the inlet opening or the higher the porosity
value of the inlet, the greater will be the inflow velocity (Vi) at
the inlet opening {Figure 1.4(a)}.
3. Except for the £ 9% porosity opening, the velocity ratio (Vi / Vref) is almost constant and independent of external wind speed, provided the Reynolds number is maintained within the turbulence flow limit {Figure 1.4 (b)}.
4.
The
velocity ratio (Vi / Vref) is not constant but varies with
different sizes of cross openings or porosity values {Figure 1.4 (c)}.
The mean value of the velocity ratio for different porosity values is
summarised in Table 1.1 and shown in Figure 1.4(d) below.
Table 1.1: Mean
velocity ratio for various porosity values
|
% POROSITY |
MEAN Vi / Vref |
|
9% |
0.69 |
|
18% |
0.64 |
|
27% |
0.66 |
|
36% |
0.72 |
|
45% |
0.81 |
Figure
1.4(d): Mean velocity ratio (Vi
/ Vref ) for different porosity values.
Chand et.al.
(1992) [5] developed a relationship for cross-ventilation through two identical
inlet and outlet openings for different types of terrain, and arrived at the
Equation (viii). The correction
factor (F) is given by the relationship in Equation (ix).
Solving for F in the case of identical openings:
F =
1.1 {1 + Ai / Ao)2}-0.5
= 1.1 {1 + (1)2}-0.5
= 0.78
Substituting
(F = 0.78) into Equation (vii):
Vi
/ Vref = F (1 - 0.82 a
)
=
0.78 (1 - 0.82 a )
The
power law exponent a
simulated in the wind tunnel is 0.28:
Therefore:
Vi
/ Vref = 0.78 {1 - (0.82 x 0.28)}
= 0.78 {1 - 0.23} = 0.78
{0.77} = 0.60
The porosity
of the model used by Chand et.al. (1992) is 18%.
The value of the velocity ratio (Vi
/ Vref) for the 18% porosity deduced from the wind tunnel test
(Experiment 1) as shown in Table 1.1 is 0.64. The value is relatively close to the calculated value derived
using Chands’ Formula that is 0.6. However,
the experiment reveals that the relationship of the velocity ratio derived using
the above formula does not hold for porosity values other than 18%.
Table 1.1 and Figure 1.5(d) show the actual values of velocity ratios
acquired from the wind tunnel experiment.
The pressure values used in normal calculation were derived from the wind tunnel pressure coefficient (Cp) by multiplying each value with a constant multiplier, 0.24. This constant value of 0.24 is obtained by considering the mean Malaysian meteorological wind speed of 1.5 m/s. The present findings (Table 1.1) and the proposal by Awbi (1994) [2] cause corrections to be made in order to anticipate different sizes of openings or porosity values. It must be appreciated the actual size of window openings in the tropics varies within the optimum range of 18% to 45% porosity. The new corrected pressure values for the above range of porosity values can be calculated as follows.
(i) New corrected pressure values (pwm’)
for 18% porosity:
The
relationship between the wind induced pressures and pressure coefficients with
the porosity effect excluded is given by:
pwm
= 0.5 Cp x 1.225 x Vref2 = Cp x 0.613 x 1.982
{Appendix}
pwm = 2.4 Cp
Where:
pwm
= wind induced pressures for the Malaysian condition (porosity effect
excluded)
Vref
= relative velocity at
reference height (= 1.98 m/s)
The new
corrected reference velocity relative to the mean meteorological wind speed of
1.5 m/s can be calculated from the relationship:
Vi
/ Vref = 0.64 (from
Table 1.1)
Therefore:
Vref = Vi / 0.64 --------------(x)
From Equation
(vii) and the power law relationship
Vref / V10 = 1.7 (href / 400)0.28
For the scale
factor of 1:200 & href is 160 m.
Therefore:
Vref
= 1.32 V10 -------------(xi)
Substituting Vref
in Eqn.(x) into Eqn. (xi)
Vi
/ 0.64 = 1.32 V10
Vi = 0.64 x 1.32 x 1.5 = 1.26 m/s
The new
corrected inflow velocity relative to the meteorological mean wind speed of 1.5
m/s is 1.26 m/s
Using Vi =
1.26 m/s as the new corrected reference velocity, the new corrected pressure
value for 18% porosity is given by:
pwm’
= Cp x 0.613 x 1.262 = 0.97 Cp
where pwm’
is the new corrected wind induced pressure for 18% porosity.
The ratio of
the corrected pressure value to the actual pressure value is given by:
pwm’
/ pwm = 0.97 / 2.4 = 0.4
pwm’ = 0.4 pwm
Where:
pwm
= the actual wind induced pressure values (porosity effect excluded)
pwm’
= the new corrected pressure values for 18% porosity
Therefore, the new corrected pressure value for 18%
porosity is reduced to about 40% of the actual pressure value obtained from
“bluff body” models.
(ii) Corrected pressure values for 27% porosity:
Vref
= Vi / 0.66 (From Table 1.1)
Vref
= 1.32 V10 {From Equation (xi)}
Vi = 1.32 x 1.5 x 0.66 = 1.3 m/s
Therefore:
pwm’
= Cp x 0.613 x 1.32 = 1.04 Cp
The ratio of
the corrected pressure value to the actual pressure value is given by:
pwm’
/ pwm = 1.04 / 2.4 = 0.43
pwm’
= 0.43 pwm
Therefore, the new corrected pressure value for 27%
porosity is reduced to about 43% of the actual pressure value obtained from
“bluff body” models.
(iii) Corrected pressure values for 36% porosity:
Vref
= Vi / 0.72 (From Table 1.1)
Vref
= 1.32 V10 {From Equation (xi)}
Vi = 1.32 x 1.5 x 0.72 = 1.43 m/s
Therefore;
pwm’
= Cp x 0.613 x 1.432 = 1.25 Cp
The ratio of
the corrected pressure value to the actual pressure value is given by:
pwm’
/ pwm = 1.25 / 2.4 = 0.52
pwm’ =
0.52 pwm
Therefore, the new corrected pressure value for 36%
porosity is reduced to about 52% of the actual pressure value obtained from
“bluff body” models.
(iv) Corrected pressure values for 45% porosity:
Vref
= Vi / 0.81 (From Table 1.1)
Vref
= 1.32 V10 {From Equation (xi)}
Vi = 1.32 x 1.5 x 0.81 = 1.6 m/s
Therefore:
pwm’
= Cp x 0.613 x 1.62 = 1.6 Cp
The ratio of
the corrected pressure value to the actual pressure value is given by:
pwm’
/ pwm = 1.6 / 2.4 = 0.67
pwm’ =
0.67 pwm
Therefore, the new corrected pressure value for 45%
porosity is reduced to about 67% of the actual pressure value obtained from
“bluff body” models.
The correction
factors for the related porosity values are shown in Table 1.2.
These values are essential to convert the pressure coefficients and
pressure values obtained from the “bluff body models.
The factors are applicable only to simple identical rectangular inlet and
outlet cross-flow openings.
Table
1.2: Correction factor for
different porosity values
|
% POROSITY |
Correction
factors of pwm’ derived
from Cp |
Correction
factors of pwm’
derived from pwm |
|
18% |
0.97 Cp |
0.40
pwm |
|
27% |
1.04 Cp |
0.43
pwm |
|
36% |
1.25 Cp |
0.52
pwm |
|
45% |
1.60 Cp |
0.67
pwm |
5.0
Conclusion
From the
experiments on scale-models of a typical office floor in the “large
openings” category it can be concluded that:
The pressure
values obtained from “bluff body” models tests in the wind tunnel are useful
for general wind flow studies.
The “bluff
body” models have to be used in the wind tunnel experiments for high-rise
buildings in order to satisfy the large scale factor.
This is because at this scale factor openings for the whole building
cannot be modelled accurately.
However, substantial corrections have to be made to the pressure values obtained from “bluff body” models if the category of “large openings” is to be considered.
For identical
rectangular cross-openings, the pressure at the opening is effectively reduced
from about 40% to 67% of the bluff body values for an opening area of about 18%
to 45%. The reduction in pressure
also increases for an opening of less than 18%.
This means that
the flow rates are reduced from about 37% for opening area of about 18% to 18%
for opening area of about 45% compared with “bluff body” values.
A porosity
correction factor can be applied to “bluff body” measurement to produce more
accurate Cps for openings area of more than 9% of the wall area.
6.0
References
1. Awbi H.B. Ventilation of Buildings, Chapman and Hall, London, 1991.
2. Awbi H.B. “Design consideration for naturally ventilated buildings”, Renewable Energy, Elsevier Science Ltd., Vol. 5, pp. 1081-1090, 1994.
3. Etheridge D.W. “Crack flow equations and scale effect”, Building and Environment, Vol. 12, pp.181-189, 1977.
4. Cook N.J. The Designer’s Guide to Wind Loading of Building Structures, Part 2: Static Structures, Building Research Establishment Report, 1990.
5. Chand, Ishwar et.al. “Studies of effect of mean wind speed profile on the rate of air flow through cross-ventilated enclosures”, Architectural Science Review, Vol. 35, pp.83-88, 1992.
6. Lawson T. A J Handbook: Building Environment, Section 3: Air Movement and Natural Ventilation, The Architects’ Journal Information Library, 27 November 1968.
7. Durst, F. Principles and Practise of Laser-Doppler Anemometry, 2nd. Ed., Academic Press Inc. (London) Ltd., 1981.
8. FLOlite Reference Guide, Dantec Measurement Technology, 1993.
9. FLOware Installation and User Guide, Dantec Measurement Technology, 1993.
The wind speed varies with height according to the power law, and the relationship is given by the following formula and the profiles shown in Figure 5.13:
Vz / Vg = {z / zg}a ----------------(i)
where Vz = speed at height z
Vg = speed at height zg (the gradient height) at the top of the
boundary layer, above which the speed is assumed constant.
a = a number that depends on the roughness terrain.
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Figure 5.13:
Velocity profiles over terrain simulated in the wind tunnel
The Malaysian
condition:
It is assumed that winds are blowing from the open Malaysian meteorological site of terrain roughness a = 0.16 to a town area of roughness a = 0.28.
At the meteorological site, the a = 0.16 power law is appropriate, and the speed at gradient height of 275 m will exceed the 10 m (standard meteorological height) speed by a factor calculated as:
Vg /V10 = {275/10}0.16
Therefore Vg = 1.7 V10 ---------------------(ii)
In the wind tunnel
simulation:
A 0.28 power law profile for a town area was simulated in the wind tunnel. Using a similar power law relationship, the free wind speed at height (H) in the tunnel VH is given by:
VH / Vg = {H / 400}0.28
Therefore VH = Vg {H / 400}0.28 -------------(iii)
The speed at gradient height is equal for both power laws, substituting the value of Vg from equation (ii) into equation (iii):
VH = 1.7 V10 (H / 400) 0.28 --------------(iv)
For the part depth simulation, H is the reference height where the reference dynamic pressure (pref) is associated with the reference velocity (Vref).
Therefore, in this case:
VH = Vref.
The appropriate values for computing the ventilation rates are the mean pressure (time-average) values [8]. The time-average surface pressure is proportional to the wind velocity pressure (pw) in Pa given by Bernoulli’s equation:
pw = Cp x 0.5r Vref2 --------------(v)
Where Cp = pressure coefficient
r= density of air (1.225 kg/m3)
The pressure coefficient (Cp ) is determined by the wind tunnel test as:
Cp = p1 /pref
where p1 = surface pressure on the model over the local outdoor atmospheric
pressure, obtained from the pressure tapping.
pref = reference free wind pressure at height H in the wind tunnel.
Therefore, the actual wind pressure on the building in Malaysia (pwm ) can be calculated from the above and is expressed as:
pwm = Cp x 0.613 Vref2 --------------(vi)
Equation (vi) will be used to determine the equivalent
pressure due to wind at the building surface in Malaysian conditions relative to
the reference velocity derived from the data of the mean wind speed obtained
from the Malaysian meteorological stations.