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Wind tunnel investigation of natural ventilation through multiple stacks. Part 1: Mean values
Building and Environment 46 (2011) 1380e1392
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Wind tunnel investigation of natural ventilation through multiple stacks. Part 1: Mean values B. Wang a, D.W. Etheridge a, *, M. Ohba b a b
School of the Built Environment, University of Nottingham, NG7 2RB, UK School of Architecture and Wind Engineering, Tokyo Polytechnic University, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 July 2010 Received in revised form 19 December 2010 Accepted 6 January 2011
Wind tunnel experiments have been performed on a scale model to study unsteady natural ventilation through multiple stacks. A previously developed hot-wire technique was used to obtain both mean and instantaneous flow characteristics. The work is described in two Parts. Part 1 concentrates on the mean flows, since it is these that are usually used for design purposes. Stacks are a potential means of ensuring that the required flow pattern is obtained over a range of conditions, so that flow direction (rather than just magnitude) is an important issue. Two distinct ways in which a wind tunnel can be used for design are considered. The first is to measure surface wind pressures, from which flow directions can be inferred or calculated. The second way is to carry out direct measurements of the stack flows (magnitude and direction). Both of these ways are examined using the measured data and their advantages and disadvantages are discussed. The accuracy of the hot-wire technique was examined on the basis of the mass balance when only stacks are present. The effects of Reynolds number and wind direction on flows and pressures are presented. An investigation of the effect of opening configuration on wind pressure coefficients surprisingly revealed that in some cases the coefficients were affected. The effect of external flow on the discharge coefficients of the stacks was found to be consistent with earlier results on single stacks. There is evidence that the effect on the orifice coefficients is more important for envelope flow modeling. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Natural ventilation Wind tunnel modeling Hot-wire technique Stacks Reynolds number Discharge coefficient
1. Introduction 1.1. Background Ventilation stacks are becoming increasingly common in the design of naturally ventilated buildings. They offer a method for achieving a fixed flow pattern irrespective of internal and external conditions e.g. upward stack flow should be maintained under all wind conditions and opening configurations, at least with positive buoyancy, by positioning the stack outlet at high level in a region of relatively low wind pressure. The paper describes an experimental investigation of unsteady natural ventilation in an environmental wind tunnel. The model was equipped with four identical stacks and four sharp-edged orifices and various combinations of these were tested. The investigation is a continuation of the work reported in Refs. [1e3]. In those investigations a single stack and orifice were tested. The technique was subsequently used to investigate flow reversal in a single ventilation stack of a real building [4]. Apart from * Corresponding author. Tel.: þ44 0 115 951 3171; fax: þ44 0 115 951 3159. E-mail address: [email protected] (D.W. Etheridge). 0360-1323/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2011.01.007
this work and that described in Ref. [5], there seem to have been few studies of wind effects on ventilation stacks using environmental wind tunnels. An important and probably unique feature of this investigation is that simultaneous measurements were made of instantaneous flows and pressure differences in up to four stacks. Such measurements are rare, yet they provide a greater insight into the flows than can be obtained from measurements of time-averages alone. In particular, the phenomenon of intermittent flow reversal can be investigated. This is important, because the change from purely upward flow to purely downward flow is not abrupt. Furthermore, the effects of correlations between the wind pressures and the stack flows can be determined. These phenomena become more complex as the number of stacks is increased. However, time-averaged (mean) values are used for design purposes. Part 1 of this paper therefore concentrates on mean values and the relevance of the results to design. In accordance with this, a conventional steady envelope flow model is used to calculate mean flow rates for comparison with the measured values. Part 2 of the paper deals with instantaneous flow rates and pressures and comparisons with an unsteady envelope flow model.
B. Wang et al. / Building and Environment 46 (2011) 1380e1392
Nomenclature A C D d Cp Cz H L p q Re r rv S t u
area of openings [m2] coefficient defined by Equation (12) coefficient defined by Equation (12) diameter of the opening [m] pressure coefficient discharge coefficient defined by Equation (2) reference height [m] depth of the opening [m] pressure due to wind [Pa] volume flow rate through the opening [m3/s] Reynolds number, defined by Equations (8) and (9) time reversal percentage [%] volume reversal percentage [%] separation distance [mm] time [s] air velocity through the opening [m/s]
The tests formed part of a collaboration between Tokyo Polytechnic University (TPU) and the University of Nottingham (UNott). TPU have focused their attention on measurement and theoretical modeling of relatively large openings (e.g. [6]), whereas UNott have concentrated on stacks and small orifices. Tests at TPU were carried out by one of the authors (B. Wang) in February and March 2008 [7], and some preliminary results were presented at AWAS’08 in May 2008. The present paper is a more detailed presentation and analysis of the results, including some tests carried out in the UNott wind tunnel. Further details of the work are given in Ref. [8]. 1.2. Use of wind tunnels for design purposes Fig. 1 shows the model used for the present investigations. Although it does not represent a particular building, one can imagine it as a scale model of a building equipped with four stacks and four air vents. It is assumed here that the design objective is to maintain upward flow in the stacks under different conditions (wind direction, opening configuration). For design the aim of the wind tunnel tests would be to investigate this, by determining the
Uref V Vc D Cp Dp
f r
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reference wind speed [m/s] volume of space [m3], crossflow velocity [m/s] pressure coefficient difference defined by Equation (1) pressure difference [Pa] wind direction density of air [kg/m3]
Subscripts b building I internal o orifice, opening st stack i, 1,2,3,4 opening number Superscripts overbar time average prime’ fluctuating value
direction and magnitude of the stack flows. There are two basic ways in which this can be done i.e. by measurement of pressures, from which the stack flows can be inferred or calculated, or by direct measurement of the stack flows. 1.2.1. Measurement of pressures The pressure coefficient is defined as
Cp ¼
pw pref 0:5rU 2
(1)
where pw and pref are the pressures due to air motion. The following four methods for determining stack flow direction (and in some cases, the magnitude) from pressure measurements are considered. Methods 1, 2 and 3 are the simplest, since they require only measurements of time-averaged pressures. The performance of these methods is described in Sections 7 and 8. Methods 4 and 5 require time records of pressures. Their performance is described in Part 2. Method 1 Measurement of mean wind pressure coefficients Cp , at the positions of the openings (no openings present). With this
Fig. 1. Sketch of model showing positions of orifices and view of model in wind tunnel.
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information and with an estimated value for the internal pressure coefficient CpI , the mean pressure difference across each opening is obtained e.g.
DCpst1 ¼ Cpst1 CpI DCpo1 ¼ Cpo1 CpI
(2)
By assuming that the sign of the flow rate is the same as the sign of DCp (which is a valid assumption, except possibly when intermittent flow reversal occurs), the flow pattern is immediately obtained. If the only concern is to maintain a fixed flow direction in the stacks, this information may be all that is required. This is the simplest technique, but it requires an estimate of CpI and the results are sensitive to the chosen value. Method 2 Measurement of mean wind pressure coefficients and the internal pressure coefficient (openings present). This is the same as method 1, except the openings are present and CpI is measured, so in that sense the values of DCp are accurately known. However, CpI is likely to be dependent on Reynolds number due to the stack lengths. Method 3 Measurement of mean wind pressure coefficients for use in a steady flow envelope model. The values of Cp are used in a conventional envelope flow model, to determine both the magnitude and direction of the individual flow rates, using fullscale flow characteristics for the openings. This can perhaps be described as the conventional approach. It should be more accurate than method 1, in that it takes account of the steady (still-air) flow characteristics of the openings to determine CpI . On the other hand, methods 2 and 3 should give similar results, because method 3 is basically a simulation of method 2. It is unlikely that one would go to the expense of wind tunnel testing just for the purpose of applying methods 1 and 2, because method 3 requires little further effort and it is of interest to see how they compare with method 3. A conventional envelope flow model relies on the pseudosteady flow assumption and takes no account of the unsteady nature of the flow through the openings due to wind turbulence. Furthermore, it ignores any changes in discharge coefficient Cz due to external flow effects. These effects can be quite large, particularly for sharp-edged orifices [1]. This will lead to errors in the calculated value of CpI . In terms of determining flow direction therefore, this approach may be no better than method 2. The advantage of method 3 is that the flow rates are calculated as well as the directions, although the results will of course be subject to uncertainties. Methods 1, 2 and 3 require only the measurement of timeaveraged pressures. Furthermore, the measurements do not have to be made simultaneously at all points. The fourth method requires more demanding measurements of pressures. Method 4 Simultaneous measurement of instantaneous pressures at the openings, which allows calculations with an unsteady envelope flow model. This method is considered in Part 2, Section 5. There is a fifth method, which is less demanding in that it does not require simultaneous measurements i.e. measurement of instantaneous pressures to allow standard deviations to be determined. In principle, these can be used with the mean values to assess the level of flow reversal [9]. This method is briefly discussed in Part 2, Section 4. 1.2.2. Direct flow measurement The distinct advantage of flow measurement over pressure measurement is that both turbulence effects and external flow effects are present in the results. The distinct disadvantage is that the openings can introduce significant Re effects. The effects are dependent on the shape and size of the openings. For sharp-edged orifices, Re effects should be small. For long openings, such as the stacks that are tested here, Re effects can be expected to be
significant. Model-scale results will be obtained at opening Reynolds number Re0 that are typically one or two orders of magnitude less than full-scale. As a result, Cz is much less for the model than for full-scale. To some extent this problem can be reduced by distorting the model opening, A [10]. It is the product CzA that is important, so if it is anticipated that Cz at model scale will be 30% less than the full-scale value, the model-scale value of A can be increased by 30%. This is only an approximate remedy, but the consequential errors could well be less than those arising from neglect of the effects of turbulence and external flow. The dependence of Cz on Re for stacks at model scale can be clearly seen in the earlier investigations with a single stack, referred to above. They can also be seen in the present results (Section 6). These results are of practical interest in relation to external flow effects on Cz. One would not expect the results to be changed by the use of eight openings rather than two and this expectation is confirmed, with one proviso, the effect of internal air motion when Dp is very low, which is discussed in Part 2. 1.3. Objectives of present paper In Part 1 the objectives are: 1) to describe briefly the experimental technique - Section 2 2) to present the observed effects of Reynolds number, wind direction and opening configuration on mean flow properties Sections 3e6 3) to present the results of Methods 1, 2 and 3 for determining stack flow direction from wind tunnel measurements of pressures. The results of the first two methods are presented in Section 7. The third method is presented in Section 8. 2. Experimental techniques 2.1. Wind tunnel and model Fig. 1 shows the model installed in one of the environmental wind tunnels at TPU. Descriptions of the TPU and UNott tunnels can be found respectively in Refs. [11] and [12]. For the TPU tunnel, the mean velocity profile(streamwise component) followed a power law with an index of 0.32. The turbulence intensity had a maximum of 0.27, decreasing to 0.09 at the top of the boundary layer. The corresponding values for the UNott tunnel were 0.23. 0.24 and 0.1 (these values are for the resultant velocity component, since they were obtained with a single hot-wire). The model and measuring equipment were developed at UNott. The model was equipped with four identical stacks on the roof, and four sharp-edged orifices (one on each of the four walls), as shown in the sketch in Fig. 1. A dual hot-wire probe in each of the stacks, allowed simultaneous measurement of the instantaneous flow rate of the stacks. At the same time, the external pressures at the stacks and the orifices and the internal pressure could be measured. The dimensions of the rectangular box are 500 250 200 mm. There are four identical circular stacks fixed on each corner of the roof. Fig. 2 shows details of the stack. The total length of the stack is 188 mm, the diameter is 16.8 mm and the venturi diameter is 10 mm. The dual hot-wire is fixed in the center of the venturi area. The diameter of the sharp-edged orifice is the same as the stack. A plan view of stack and orifice positions relative to the wind directionf, is shown in Fig. 3. In some of the following Figures, a shorthand notation is used to identify the opening configuration e.g. “S34 O12” denotes that stacks 3 and 4 and orifices 1 and 2 were open.
B. Wang et al. / Building and Environment 46 (2011) 1380e1392
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Pressure measurement has the distinct advantage that external surface pressures due to wind should be nominally independent of building Reynolds number, Reb, unless the building has a streamline form and even then the high turbulence levels associated with flows around buildings should reduce the dependency. It is generally accepted that surface pressure coefficients determined from scale models of sharp-edged buildings are applicable to fullscale Reb. In contrast, the internal pressure coefficient CpI , depends on the flow through the openings and may therefore be dependent on Reb, partly due to the dependency of q on Re0 for certain types of opening. It is also to be expected that the external pressure distribution is unchanged by the presence of small openings, and the openings used here are small in relation to the surface in which they lie. This expectation is discussed in Section 5, where it will be seen that the expectation was not always fulfilled. 2.3. Direct flow rate measurement
Fig. 2. Stack geometry and hot-wire probe.
2.2. Pressure measurement Nine pressure tappings were used on the model i.e. one for each of the stacks and the orifices and one internal tapping. Each tapping could be connected to its own pressure transducer (Furness FC044), with the other side of the transducer connected to a reference pressure. The reference pressure was taken within an empty box in the still air of the wind-tunnel laboratory. Fig. 4 shows the connections for one stack and the internal pressure. A pitot-static tube was mounted in the freestream of the wind tunnel to measure the dynamic pressure, from which the reference wind speed Uref was obtained.
Since the interest here is with stacks, it is necessary to determine the direction as well as the magnitude of the flow through each stack. The concept of a time-averaged flow direction is valid e.g. it is defined as upward flow when this occurs for more than 50% of the time and vice versa. But it is not very meaningful in the sense that a stack that has reversed flow for 49% of the time clearly is not performing satisfactorily. It is therefore necessary to consider the reversal percentage, r %. To determine r it is necessary to record instantaneous flow rates and the hot-wire technique was developed for this purpose. The basic equipment is inexpensive and compact, so that simultaneous measurements in multiple stacks can easily be made. A description of the measurement technique and the calibration technique can be found in Ref. [12]. As shown in Fig. 2, a hot-wire probe (Dantec 55P71s) is mounted in the middle of each stack. The standard 55P71 probe consists of two parallel hot-wires, but the probes were specially modified so that the two wires were 5 out of parallel in one plane [2]. Each hotwire was connected to a Dantec MiniCTA anemometer. The instantaneous direction of the flow in a stack is determined by comparing the instantaneous voltage outputs of the two hot-wires. The upstream wire is the one with the higher voltage output. The magnitude of the volume flow rate is then obtained from the calibration of the upstream wire. Unsteady calibration of each wire is carried out in situ using an oscillating piston. A steady calibration at the higher flow rates is carried out using a positive displacement meter (as shown in Fig. 4). The final calibration curve is obtained from a combination of these results. It is recognized that errors will arise due to the changing relationship between volume flow rate and the velocity recorded by the wire (due to changes in the shape of the velocity profile associated with unsteady flow). Prior to each measurement, the zero flow voltage is measured and this is used to account for any changes in tunnel air temperature. 2.4. Determination of still-air Cz The still-air discharge coefficient Cz of an opening is defined in terms of the time-averaged values of the volume flow rate and the pressure difference across the opening:
Cz h
Fig. 3. Plan view of stack and orifice positions, with wind direction.
sffiffiffiffiffiffiffiffiffiffi r q A 2:Dp
(3)
where q is the time-averaged value of flow rate, Dp is the timeaveraged pressure difference across the opening and (for a stack).
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Fig. 4. Arrangement for steady calibration and determination of Cz.
Dp ¼ pst pI
(4)
drI V ¼ r1 q1 þ r2 q2 þ r3 q3 þ r4 q4 dt
(5)
The measurement of still-air Cz is carried out at the same time as the steady calibration, by measuring the pressure difference across the opening. Fig. 4 shows the arrangement, which employs a domestic gas meter (U6 type) and a fan. The gas meter was used to measure the time-averaged volume flow rate q, and the fan and valve were used to provide a nominally constant flow. Since the ends of the stacks are not identical, Cz will depend on flow direction. The time-averaged value of pressure difference across the stack, Dp (Dp ¼ pst pI ), was measured simultaneously using the pressure transducers. By adjusting the valve, a range of volume flow rates can be generated, thereby values of Cz with different volume flow rates can be obtained.
Since the flow is steady in the mean, each variable can be expressed as the sum of a mean and fluctuating part i.e.
2.5. Mean flow balance
Since the pressure fluctuations are small compared to atmospheric pressure, the errors associated with the r0 q0 terms on the right-hand side should be much less than 1%. Similarly, the mean pressure differences are less than 100 Pa, so any differences between the densities in the terms on the left-hand side should be less than 0.1%. Hence, if V is constant (V0 ¼ 0), equation (7) indicates that the mean
(6)
Substituting Equation (5) into Equation (4) and taking the timeaverage leads to the following equation (the time-average of the product of a mean value and a fluctuating value is zero).
dr0 dV 0 þ V 0 I r01 q01 r02 q02 dt dt r03 q03 r04 q04
r1 q1 þ r2 q2 þ r3 q3 þ r4 q4 ¼ r0I
0.0003
(7)
Stack 1 Stack 2
0.0002 0.0002
Stack 3 Stack 4
0.0001
Sum
0.0001
q (m3/s)
Simultaneous hot-wire measurements on multiple stacks with no other openings, provides a stringent and unique check on the overall accuracy of the technique, in the sense that the measured volume flow rates should satisfy the continuity equation (conservation of mass). Fig. 5 shows results for a symmetrical configuration, where the flows through stacks 1 and 4 were inward at all times (and virtually equal in magnitude). Similarly for stacks 2 and 3, except the flows were outward. The sum of the flow rates is also shown. Relative to the total outflow, the sum ranges from 5% to 8% of the total ventilation rate. In a truly steady flow the sum should be equal to zero and this is clearly not so. However, an error less than 10% in the measurement of ventilation rate is not bad. It compares favorably with other techniques, such as tracer gas techniques. The most likely cause of the error lies in the calibration of the hotwires. The systematic nature of the error (increasing with Uref ) is consistent with this. On this basis, an uncertainty of 10% in the mean flow rates is probably a reasonable estimate of the accuracy of the technique. It is also possible that the difference between the inflow and outflow rates is associated with the unsteady nature of the flow. To examine this it is necessary to consider the unsteady form of the mass conservation equation:
r ¼ r þ r0 ; q ¼ q þ q 0 ; V ¼ V þ V 0
0.0000 -0.0001 -0.0001 -0.0002 -0.0002 -0.0003 -0.0003 0
1
2
3
4
5
6
Uref (m/s)
Fig. 5. Mean flow rate balance (four stacks, no orifice), f ¼ 0.
7
B. Wang et al. / Building and Environment 46 (2011) 1380e1392
0.20 0.15 Stack Stack Stack Stack
0.10 us t/Uref
volume flow rates should sum to zero. The possible effect of the terms containing V0 has been estimated by assuming that V0 and r0I vary sinusoidally with a phase difference that maximizes the terms. With amplitudes for V0 and r0I of 5% and 1% of their mean values, and a frequency of 5 Hz, the effective volume flow rates from the two terms are both approximately 2 107 m3/s. This is less than 1% of the smallest observed sum, so it would seem that the calibrations are the main reasons for the non-zero sums. In passing it should be noted that for instantaneous flow rates, unsteady effects can be larger, because there is no time averaging (see Part 2).
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0.05
1 2 3 4
0.00 -0.05 -0.10
3. Effect of Reynolds number on Cp, q and r
-0.15
Ideally the nondimensional results should be independent of Reynolds number. The two relevant Reynolds numbers, namely building Reynolds number and opening Reynolds number, are defined as follows:
rUref H Reb h m Re0 h
-0.20 0
1
2
3 4 Uref (m/s)
5
6
7
Fig. 7. Variation of ust/Uref with Uref (four stacks, no orifice).
(8)
rud m
(9)
where r denotes the density of air (kg/m3), H the height of the building (m), d the diameter of the opening (m), u the mean velocity in the stack (uhq=A) and m the viscosity (Ns/m2). A dependence of envelope flow rates on Reb can be considered in two parts i.e. dependence of the external pressure coefficient, Cp (and the external velocity field) on wind tunnel speed (Reb) and dependence of the discharge coefficient on flow rate (Re0). The latter is discussed in Section 7. Fig. 6 illustrates the dependence of Cp on reference wind speed for the case of four stacks and no orifices. Independence of Cp on Reb can be seen for Uref higher than about 4 m/s. Figs. 7 and 8 illustrate the observed dependence of dimensionless flow rate u/Uref on wind speed for two cases i.e. four stacks alone and four stacks with two orifices. Flow into the box (downward stack flow) is defined as positive. When the Cp is independent of wind speed, one would still expect to see a dependence of u/Uref , due the dependence of Cz on Re0. Rather surprisingly this is more evident in Fig. 8 than in Fig. 7. Fig. 7 corresponds to the case where there are no sharp-edged orifices, so one would expect Re effects to be greater. However there is another factor at work, namely that Cz is also a function of Vc/u, particularly with sharp-edged orifices [2].
This can lead to misleading indications of the effect of building Reynolds number Reb. The quantity Vc is the crossflow velocity in the external flow close to the opening. The results in Figs. 7 and 8 were obtained with a fixed wind direction, so Vc/Uref should be nominally constant. However, Vc/Uref could vary with Reb, and the effect on u/Uref could be different to the effect of Cp variations. Unfortunately it was not possible to measure Vc. Previous investigations with a single stack and orifice have shown that the degree of flow reversal r is closely related to the properties (mean and standard deviation) of the instantaneous pressure difference across the two openings. The fact that there were only two openings for those investigations makes interpretation and analysis of results easier. The present investigation is concerned with flow reversal with multiple stacks. Fig. 9 shows the dependence of r on Reb of two opening configurations, i.e. two stacks with two orifices and four stacks with two orifices. One can see a dependence of r on Reb, which indicates that higher r is expected at full scale. Calculations of this effect using the unsteady QT model are given in Part 2. 4. Effect of wind direction Fig. 10 shows Cp variation with wind direction for two stacks and four orifices. Fig. 11 shows the corresponding variation of r with
0.00
0.4 Internal
-0.05
stack 1
0.2
stack 2 stack 3
0
-0.10
stack 4
u/Uref
Stack 1
Cp
Orifice 1 Orifice 2
-0.2
Stack 2 -0.15
Stack 3 Stack 4
-0.4
-0.20
-0.6
-0.25
-0.8
-0.30
0
1
2
3
4
5
6
Uref (m/s) Fig. 6. Variation of Cp with Uref (four stacks, orifice 1 and 2).
7
0
1
2
3 Uref (m/s)
4
5
6
Fig. 8. Variation of ust/Uref with Uref (four stacks, orifice 1 and 2).
7
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100
100
S34_O12 Stack 3 90
S34_O12 Stack 4
90
S1234_O12 Stack 1 80
80
S1234_O12 Stack 4
Stack 1
70
70
60
60
r (%)
r (%)
Stack 3
50
50
40
40
30
30
20
20
10
10 0
0 0
20000
40000
60000
80000
0
100000
45
90
180
Fig. 11. Variation of r with wind direction (stack 1 and 3, four orifices).
Fig. 9. Variation of r with Reb.
wind direction for the two stacks. Whether or not flow reversal occurs depends primarily on the relative values of Cp at the openings and on the relative sizes of the openings. For the wind-alone case, it is a relatively simple matter to calculate the flows with an envelope flow model. When buoyancy is involved, the problem is more difficult, since account needs to be taken of the dependence of stack temperature on flow direction. However, the effects of buoyancy are not considered here. Simply using the values Cp of can be misleading, as shown by the fact that flow reversal was observed for f ¼ 0, 90 and 180, but no flow reversal was observed for f ¼ 45 and 135. The stack Cp values are close to the orifice values for the first three wind directions, whereas the most negative stack Cp values were observed for the second two directions. Flow reversal always occurred at some wind directions for all opening configurations tested. 5. Effect of opening configuration on Cp In principle one would expect the opening configuration to have little effect on the mean wind pressures, because the openings are flush and their areas are small in relation to the areas of the surfaces in which they lie. This expectation is a basic assumption in
0.4
0.2
0.0
Cp
135
Wind direction
Reb
conventional envelope flow models. Most of the results satisfy this expectation, but not all Table 1 shows values of stack Cp obtained with different opening configurations at two wind directions. For f ¼ 0, it can be seen that Cp1 and Cp4 change considerably when two orifices are added, but not when a further two orifices are added. At this wind direction, stacks 1 and 4 are located at the leeward side. For f ¼ 180, stacks 2 and 3 become the leeward ones. When the number of orifices increases from two to four, the decrease of stack outlet pressure is less obvious than that when it increases from zero to two, indicating that the stack outlet pressure located in the leeward zone is more sensitive to the change of number of orifices. Results for f ¼ 90 are given in Fig. 12, for two stacks alone and two stacks with four orifices. It can be seen that none of the orifice Cp are affected, and only one of the two stacks (only two stacks were open). Results for f ¼ 0 are given in Fig. 13, for the same opening configurations. It can be seen that none of the Cp are affected. There is a clear indication in the above results (and in others that are not presented) that the orifice Cp are not affected by the opening configuration, but the stack Cp can be affected. The results for the orifices display very good repeatability, and any changes that occur are so small that they can be ignored in the design process (at least for the configurations tested here). The changes that have been observed for the stacks are significant, in the sense that they are not due to poor repeatability. Two possible explanations are as follows. In terms of the flow around the exterior of the model, the presence of an opening corresponds to a source (outward flow) or a sink (inward flow). If the opening lies in an attached boundary layer, the flow through the opening will lead to a change in the local displacement thickness of the layer. The disturbance to the pressure
-0.2
-0.4
Table 1 External pressure coefficients of stacks with different numbers of open orifices. NB “4S” denotes 4 stacks, no orifices, “4S 2O” denotes 4 stacks, 2 orifices.
Stack 1 Stack 3 Orifice 1 Orifice 2 Orifice 3 Orifice 4
-0.6
-0.8 0
45
90 wind direction
135
Fig. 10. Cp variation with wind direction (stacks 1 and 3, four orifices).
180
Wind direction
0
0
0
180
Openings
4S
4S 2O
4S 4O
4S 2O
180 4S 4O
Cp1 Cp2 Cp3 Cp4
0.32 0.54 0.55 0.30
0.17 0.53 0.55 0.17
0.16 0.54 0.56 0.16
0.55 0.18 0.18 0.52
0.52 0.16 0.15 0.50
B. Wang et al. / Building and Environment 46 (2011) 1380e1392
0.7
0.4 0.3
0.6
Cps1 Cps3 Cpo1 Cpo2 Cpo3 Cpo4
0.1 0
0.5
Cz
0.2
Cps
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-0.1
0.4 0.3 Stack 1
-0.2
Stack 2
0.2
-0.3 -0.4
Stack 3 Stack 4
0.1
-0.5
0.0 0
-0.6 S13
500
1000
1500
Rest
S13_O1234
Fig. 14. Variation of Cz with Rest with external flow (four stacks, no orifices).
opening configuration Fig. 12. Stack and orifice Cp with two open stacks and increasing number of orifices for f ¼ 90.
distribution will be localized. However, if the opening lies in a separated flow region, with reattachment, the presence of the opening flows could change the shape of the separated region (and the nature of reattachment). A change in shape of a separation region is effectively a change in shape of the model, so the effects could be more far-reaching. Another possibility lies in the position of the tapping used for the stack Cp. This is discussed in Part 2.
present results for multiple stacks are examined in the light of the earlier findings and it will be seen that they are in agreement. 6.1. Still-air values The still-air discharge coefficient is a major parameter in design calculations. The values obtained from the still-air calibration are included in Fig. 16, in the form of Cz against Rest. The results are very close to the earlier results. In particular, Cz with inward flow is greater than that with outward flow, due to the fact that DCp is obtained with one pressure tapping inside the stack. 6.2. Effect of external flow
6. Discharge coefficient of stacks Envelope flow models (steady and unsteady) make use of the still-air discharge coefficients of openings. In previous work Ref. [1] and [3], it was found that the discharge coefficient in the presence of flow can differ from the still-air value, depending on the external flow conditions. For a stack it was found that the external flow has little effect on stack Cz for upward flow, and a significant effect for reversed flow. The basic reason for this is that with upward flow, the external flow only affects the outlet boundary condition. The
Figs. 14 and 15 show the observed variation of stack Cz with Rest for two opening configurations in the presence of wind; the first configuration has four stacks alone and the second has four stacks and two orifices. In Fig. 14 stacks 2 and 3 have outward flow and there is close agreement between them and with the still-air case (Fig. 16). (NB In Fig. 15 of [1], the stacks were incorrectly identified). This reflects the fact that the outlet conditions have little effect on the upstream flow in the stack (except that the outlet pressure determines the flow rate). Stacks 1 and 4 have inward flow and their curves lie above the corresponding still-air curve. The high Cz
0.4
0.7 0.2
Cps1 Cps3 Cpo1 Cpo2 Cpo3 Cpo4
Cps
0
0.6 0.5 0.4
Czst
-0.2
0.3
Stack 1
-0.4
Stack 2 0.2
Stack 3
-0.6
Stack 4
0.1 -0.8 S13
S13_O1234 opening configuration
0.0 0
500
1000
1500
2000
Rest Fig. 13. Stack and orifice Cp with two open stacks and increasing number of orifices for f ¼ 0.
Fig. 15. Variation of Cz with Rest, outward flow (four stacks, orifice 1 and 2).
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0.7
Stack 3 0.2 estimated Cpint
0.6 0.1
u/Uref
0.5
measured Cpint
DelCp and u/U
Cz
0
0.4 Inward steady cal 0.3
Outward steady cal Outward Unsteady
0.2
-0.1
-0.2
Inward Unsteady Stack1 Inward Unsteady Stack4
0.1
-0.3 0
45
90
135
180
0 0
500
1000
1500 Rest
2000
2500
-0.4
3000
Fig. 16. Cz variation with Rest compared with still-air results (four stacks, no orifice).
Fig. 18. Calculated DCp and measured u/Uref of Stack 3 (four stacks, four orifices).
values suggest that there is a downward momentum component in the external flow that contributes to the total driving force of the flow in the stacks. For these two points a different definition of Cz would probably be appropriate i.e. one based on a total pressure containing 0:5rVc2 so that Equation (4) is replaced by:
Dp ¼ pst þ 0:5rVc2 pI
wind direction
calculated 0.2
(10) 0.1
0
q/AUref
In practice, it is not possible to use this definition, because Vc is not known. The results for stacks 1 and 3 are not identical. This can probably be explained by differences between the external flow conditions at the stacks, although calibration errors may play a role. In Fig. 15, all the stacks have outward flow, with reversal percentages less than 50%. There is some scatter, probably reflecting the fact that r is non-zero in some cases. Fig. 16 compares the results in Fig. 14 with the still-air results. An underlying for calculation methods can be seen i.e. the good agreement between the unsteady and steady (still-air) results for outward flow, and the poor agreement that occurs when the flow is inward. The significant differences between the Cz values of stacks 1 and 4 are not due to differences in the stack Reynolds numbers. They are probably caused by asymmetry of the external flow field,
-0.1 q st 1/A Uref q st 2/A Uref
-0.2
q st 3/A Uref q st 4/A Uref
-0.3 0
45 wind direction
90
Measured 0.2
Stack 1 0.2 0.1 estimated Cpint
0.1
q/AUref
DelCp and u/U
u/Uref
0
measured Cpint
0
-0.1 -0.1
-0.2
q st 1/A Uref q st 2/A Uref
-0.2
-0.3
q st 3/A Uref q st 4/A Uref
-0.4 0
45
90
135
180
-0.3 0
wind direction
Fig. 17. Calculated DCp and measured u/Uref of Stack 1 (four stacks, four orifices).
45 wind direction
Fig. 19. Variation of q/AUref (four stacks, no orifice).
90
B. Wang et al. / Building and Environment 46 (2011) 1380e1392
but slight differences in the stack box shapes and in the positions of pressure tappings may be contributory factors. 7. Determination of flow directions from pressures Figs. 17 and 18 show the measured values of u/Uref for stacks 1 and 3 respectively from a test with constant Uref and varying wind direction. They also show the calculated DCp using methods 1 and 2. If these methods were reliable, the calculated DCp and measured u/Uref should have the same sign, and one could use the methods to determine flow reversal. Stacks 2 and 4 were sealed, but the four orifices were open. It can be seen that flow reversal (downward flow) was observed at f ¼ 0 for stack 1 and at f ¼ 90 and 180 for stack 3. In each figure, the solid line shows the calculated DCp obtained with method 1, where the value of CpI is taken as the weighted arithmetic mean of the Cpi. The weighting uses the product CzA, where Cz for the stacks has been taken as one-half that for the orifices.
CPI ¼
n X i¼1
C A Cpi Pn zi i i¼0 Czi Ai
(11)
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The argument for this weighting is that the internal pressure is determined by the balance of the individual flow rates and that each flow rate is proportional to CzA, rather than Cz or A alone. It can be seen that the reversal for stack 1 is not apparent and neither are the reversals for stack 3 (although the 90 result is close to reversal). Using a weighting based on A (i.e. CpI is the simple arithmetic mean of the Cpi) gives the same result. The calculated DCp for method 2, using the measure internal pressure coefficient, are shown by the dashed line and it can be seen that two of the three reversals are apparent. 8. Comparisons with steady envelope flow model A conventional steady envelope flow model (method 3) has been used to calculate stack flow rates and the results are compared with the measured values. This has been done for the following conditions:(i) a fixed wind speed and varying flow direction; four stacks alone and four stacks with two orifices
calculated
calculated
0.2
0.2 q stack 1 q stack 3
0.1
q/AUref
q/AUref
0.1
0
0
-0.1
-0.1 q st 1/A Uref -0.2
-0.2
q st 2/A Uref q st 3/A Uref q st 4/A Uref
-0.3
-0.3 0
45 wind dirction
0
90
45
135
180
measured
measured 0.2
0.2
0.1
0.1
0
0
q/AUref
q/AUref
90 wind direction
-0.1
-0.1 q st 1/A Uref q st 2/A Uref
-0.2
q stack 1
-0.2
q st 3/A Uref q stack 3
q st 4/A Uref -0.3
-0.3 0
45 wind direction Fig. 20. Variation of q/AUref (four stacks, orifice 1 and 2).
90
0
45
90
135
wind direction Fig. 21. Variation of q/AUref (stacks 1 and 3, four orifices).
180
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B. Wang et al. / Building and Environment 46 (2011) 1380e1392
(ii) a fixed direction and varying wind speed; four stacks alone and four stacks with two orifices (iii) a fixed wind speed and varying flow direction; two stacks and four orifices. The flow characteristics of the stacks are taken from a quadratic curve-fit to the still-air measurements i.e.
1=Cz2 ¼ C
L þD Rest d
(12)
where L and d are respectively the length and diameter of the stack. C and D are factors obtained from the steady calibration, which relate to stack geometry and flow directions. For upward flow, C ¼ 153.07 and D ¼ 5.739; for downward flow, C ¼ 140.08 and D ¼ 3.692. Except where stated otherwise, the discharge coefficient of the orifices is taken to be 0.68. 8.1. Variation of non-dimensional flow rate with wind direction Figs. 19, 20 and 21 compare the calculated and measured stack flow rates for the three configurations (four stacks alone; four stacks and two orifices; two stacks and four orifices).
For the two configurations shown in Figs. 19 and 20, the sign of the flow is accurately calculated at all wind directions, including 45 where intermittent flow reversal occurs. The overall agreement for the magnitude is reasonably good for the four stacks alone case (Fig. 19), but the agreement deteriorates when two orifices are added (Fig. 20). This deterioration with the number of orifices is more apparent in Fig. 21, where there is poor agreement for the flow direction as well as the magnitude. The observed deterioration of the agreement between calculation and measurement is somewhat surprising, because the simple shape of the orifices and the absence of Reynolds number effects leads one to expect that they should be relatively easy to account for in envelope flow models. However, it is consistent with the finding in [1], namely that the discharge coefficient of an orifice is more affected by installation effects (external crossflow) than a long stack. 8.2. Variation of non-dimensional flow rate with wind speed (building Reynolds number) Figs. 22 and 23 compare the calculated and measured stack flow rates for the two configurations (four stacks alone; four stacks, two orifices).
calculated 0.2
calculated 0.2
0.1 0.1
0
q st 2/A Uref
q/AUref
q/AUref
q st 1/A Uref q st 3/A Uref
0
q st 4/A Uref
q st 1/A Uref q st 2/A Uref
-0.1
q st 3/A Uref q st 4/A Uref
-0.1
-0.2
-0.2
-0.3 0
1
2
3
4
5
6
7
0
1
2
3
Uref (m/s)
4
5
6
7
Uref (m/s)
measured
measured
0.2
0.2
0.1 0.1
q/AUref
q/AUref
q st 1/A Uref q st 2/A Uref q st 3/A Uref
0
q st 4/A Uref
0 q st 1/A Uref q st 2/A Uref q st 3/A Uref
-0.1
q st 4/A Uref
-0.1
-0.2
-0.3
-0.2 0
1
2
3
4
5
6
7
Uref (m/s) Fig. 22. Calculated and measured effects of Reynolds number (four stacks, no orifice).
0
1
2
3
4
5
6
7
Uref (m/s) Fig. 23. Calculated and measured effects of Reynolds number (four stacks, orifice 1 and 2).
B. Wang et al. / Building and Environment 46 (2011) 1380e1392
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Wind
3 2
4 1
3 2
Orifice 2
4 1
Orifice 1
Fig. 24. Flow directions of four stacks, orifices 1 and 2; four stacks alone.
Again it is clear that the agreement is good for the stacks alone case, but relatively poor for the configuration with two orifices. There are two likely reasons for this, one associated with the cross flow effects referred to above and the other with intermittent flow reversal. To appreciate this, Fig. 24 shows the flow directions for the two cases. The evidence from [1] is that Cz can be reduced by 50% or more depending on Vc/u. The flows through orifices 1 and 2 are both inward, so one can expect Cz to be less than the still-air value. The stack Cz is not affected by external flow when the flow is outward, but it can be affected when the flow is inward, and may be increased. Fig. 25 shows the discharge coefficient of the orifice for stillair and wind-on cases. Values of Cz0 for wind-on conditions were calculated from tests with one stack and one orifice, in which the volume flow rates of the orifice and the stack are equal. It can be seen that Cz0 is reduced by the presence of wind. On the basis of Fig. 25, calculations were carried out with (i) Cz of both orifices reduced from 0.68 to 0.5 and (ii) with one Cz0 ¼ 0.61 and the other ¼ 0.5.In both cases, the overall improvement was small. The agreement for stacks 2 and 3 was substantially improved, but it was accompanied by reduced agreement for stacks 1 and 4. There is another possible reason for inaccuracy with stacks 1 and 4. For stacks 1 and 4 the reversal percentage was around 30% and the still-air relationship (equation (12)) may be invalid.
Fig. 25. Discharge coefficients of sharp edged orifice e still-air and wind-on.
9. Conclusions The UNott hot-wire technique has been used to measure simultaneously the instantaneous magnitude and direction of flow in multiple (up to four) stacks. As far as is known, such measurements have not been made before. The tests were carried out with up to four other openings (sharp-edged orifices), with simultaneous measurements of external and internal pressures. The tests with no other openings allowed an estimate to be made of the overall uncertainty of the stack flow measurements. In terms of the mean ventilation rate, the results indicate an overall uncertainty of about 10%, which compares favorably with other less comprehensive techniques (e.g. tracer gas). Tests over a range of wind tunnel speeds indicate that the external pressure coefficients can be taken as independent of Reynolds number above about 3 or 4 m/s. As expected, there is some dependency of the dimensionless flow rates over the whole range, due to the presence of the stacks. The reversal percentage shows a similar dependency. Examination of the external pressure coefficients for a range of opening configurations revealed that the values for the orifices were independent of the opening configuration. This is what one expects for small openings. However, some effect of opening configuration was observed for the stacks. Tests over a range of wind directions showed that the external pressure coefficients for the stacks were always negative. It obviously does not follow that the stack flows would be always upwards, since this depends on the overall opening configuration. However, even with four orifices present, flow reversal was observed at some wind directions. It should be noted that the value of CzA for an orifice facing the wind is twice that for a stack, whereas CzA for orifices facing other directions could be much lower. The observed effects of external flow on the discharge coefficients are consistent with previous work on single stacks. The measurements have been used to assess three methods for determining stack flow directions from wind tunnel pressure measurements alone. They differ in the way in which the internal pressure is determined. A conventional envelope flow model (in which the internal pressure is calculated) performed the best. However, the main feature of this investigation is that it revealed that the agreement between calculation and measurement deteriorated as the number of orifice openings was increased. This is consistent with earlier work that showed that the discharge coefficients of orifice openings are more susceptible to external flow effects than long stacks. Compared to methods based on pressure measurements, the advantage of the direct hot-wire technique is that the measurements include (i) the effects of wind turbulence, (ii) the effect of crossflow
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on discharge coefficient and (iii) any effect of opening configuration on pressure coefficient and their correlations. However some means of extending the results to full-scale Reynolds numbers is needed. Acknowledgements The work described has been funded by EPSRC (UK), with support from the COE Program at Tokyo Polytechnic University, and this is gratefully acknowledged. References [1] Chui YH, Etheridge DW. External flow effects on the discharge coefficients of two types of ventilation opening. Jnl Wind Eng Ind Aerod 2007;95:225e352. [2] Costola D, Etheridge DW. Unsteady natural ventilation at model scaleeFlow reversal and discharge coefficients of a short stack and an orifice. Building Environ 2007;43:1491e506. [3] Cooper EW, Etheridge DW. Wind tunnel investigation of unsteady flow in a natural ventilation stack. In: Second WERC International Symposium on Architectural wind Engineering. Tokyo: Wind Engineering Research Center; 2007. p. 191e208.
[4] Claesson L, Etheridge DW. Unsteady flow reversal in a natural ventilation stack e model scale tests. Int J Ventilation 2005;4(1):25e35. [5] Alexander DK, Jenkins HG, Jones PJ. A comparison of wind tunnel and CFD methods applied to natural ventilation design. Proc Building Simulation 1997;97(2):321e6. [6] Ohba M, Kurabuchi T, Endo T, Akamine Y, Kamata M, Kurahashi A. “Local dynamic similarity model of cross-ventilation, Part 2-Application of local dynamic similarity model.” Int Jnl Ventilation 2004;2(4):383e94. [7] Etheridge DW, Ohba M, Wang B. Wind tunnel investigation of natural ventilation through multiple stacks. In: The 4th International Conference on Advances in wind and Structures. Korea: AWS’08; 2008. p. 1117e28. [8] Wang B. Unsteady wind effects on natural ventilation, PhD thesis, University of Nottingham, Nottingham, UK, July 2010. [9] Etheridge DW. Unsteady flow effects due to fluctuating wind pressures in natural ventilation design-mean flow rates. Building Environ 2000;35: 111e33. [10] Etheridge DW, Nolan JA. Ventilation measurements at model scale in a turbulent flow. Building Environ 1979;14:53e64. [11] Ohba M, Irie K, Kurabuchi T. Study on airflow characteristics inside and outside a cross-ventilation model, and ventilation flow rates using wind tunnel experiments. Jnl Wind Eng Ind Aerod 2001;89:1513e24. [12] Chiu YH, Etheridge DW. Experimental technique to determine unsteady flow in natural ventilation stacks at model scale. Jnl Wind Eng Ind Aerod 2004;92:291e313.
Contents lists available at ScienceDirect
Building and Environment journal homepage: www.elsevier.com/locate/buildenv
Wind tunnel investigation of natural ventilation through multiple stacks. Part 1: Mean values B. Wang a, D.W. Etheridge a, *, M. Ohba b a b
School of the Built Environment, University of Nottingham, NG7 2RB, UK School of Architecture and Wind Engineering, Tokyo Polytechnic University, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 July 2010 Received in revised form 19 December 2010 Accepted 6 January 2011
Wind tunnel experiments have been performed on a scale model to study unsteady natural ventilation through multiple stacks. A previously developed hot-wire technique was used to obtain both mean and instantaneous flow characteristics. The work is described in two Parts. Part 1 concentrates on the mean flows, since it is these that are usually used for design purposes. Stacks are a potential means of ensuring that the required flow pattern is obtained over a range of conditions, so that flow direction (rather than just magnitude) is an important issue. Two distinct ways in which a wind tunnel can be used for design are considered. The first is to measure surface wind pressures, from which flow directions can be inferred or calculated. The second way is to carry out direct measurements of the stack flows (magnitude and direction). Both of these ways are examined using the measured data and their advantages and disadvantages are discussed. The accuracy of the hot-wire technique was examined on the basis of the mass balance when only stacks are present. The effects of Reynolds number and wind direction on flows and pressures are presented. An investigation of the effect of opening configuration on wind pressure coefficients surprisingly revealed that in some cases the coefficients were affected. The effect of external flow on the discharge coefficients of the stacks was found to be consistent with earlier results on single stacks. There is evidence that the effect on the orifice coefficients is more important for envelope flow modeling. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Natural ventilation Wind tunnel modeling Hot-wire technique Stacks Reynolds number Discharge coefficient
1. Introduction 1.1. Background Ventilation stacks are becoming increasingly common in the design of naturally ventilated buildings. They offer a method for achieving a fixed flow pattern irrespective of internal and external conditions e.g. upward stack flow should be maintained under all wind conditions and opening configurations, at least with positive buoyancy, by positioning the stack outlet at high level in a region of relatively low wind pressure. The paper describes an experimental investigation of unsteady natural ventilation in an environmental wind tunnel. The model was equipped with four identical stacks and four sharp-edged orifices and various combinations of these were tested. The investigation is a continuation of the work reported in Refs. [1e3]. In those investigations a single stack and orifice were tested. The technique was subsequently used to investigate flow reversal in a single ventilation stack of a real building [4]. Apart from * Corresponding author. Tel.: þ44 0 115 951 3171; fax: þ44 0 115 951 3159. E-mail address: [email protected] (D.W. Etheridge). 0360-1323/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2011.01.007
this work and that described in Ref. [5], there seem to have been few studies of wind effects on ventilation stacks using environmental wind tunnels. An important and probably unique feature of this investigation is that simultaneous measurements were made of instantaneous flows and pressure differences in up to four stacks. Such measurements are rare, yet they provide a greater insight into the flows than can be obtained from measurements of time-averages alone. In particular, the phenomenon of intermittent flow reversal can be investigated. This is important, because the change from purely upward flow to purely downward flow is not abrupt. Furthermore, the effects of correlations between the wind pressures and the stack flows can be determined. These phenomena become more complex as the number of stacks is increased. However, time-averaged (mean) values are used for design purposes. Part 1 of this paper therefore concentrates on mean values and the relevance of the results to design. In accordance with this, a conventional steady envelope flow model is used to calculate mean flow rates for comparison with the measured values. Part 2 of the paper deals with instantaneous flow rates and pressures and comparisons with an unsteady envelope flow model.
B. Wang et al. / Building and Environment 46 (2011) 1380e1392
Nomenclature A C D d Cp Cz H L p q Re r rv S t u
area of openings [m2] coefficient defined by Equation (12) coefficient defined by Equation (12) diameter of the opening [m] pressure coefficient discharge coefficient defined by Equation (2) reference height [m] depth of the opening [m] pressure due to wind [Pa] volume flow rate through the opening [m3/s] Reynolds number, defined by Equations (8) and (9) time reversal percentage [%] volume reversal percentage [%] separation distance [mm] time [s] air velocity through the opening [m/s]
The tests formed part of a collaboration between Tokyo Polytechnic University (TPU) and the University of Nottingham (UNott). TPU have focused their attention on measurement and theoretical modeling of relatively large openings (e.g. [6]), whereas UNott have concentrated on stacks and small orifices. Tests at TPU were carried out by one of the authors (B. Wang) in February and March 2008 [7], and some preliminary results were presented at AWAS’08 in May 2008. The present paper is a more detailed presentation and analysis of the results, including some tests carried out in the UNott wind tunnel. Further details of the work are given in Ref. [8]. 1.2. Use of wind tunnels for design purposes Fig. 1 shows the model used for the present investigations. Although it does not represent a particular building, one can imagine it as a scale model of a building equipped with four stacks and four air vents. It is assumed here that the design objective is to maintain upward flow in the stacks under different conditions (wind direction, opening configuration). For design the aim of the wind tunnel tests would be to investigate this, by determining the
Uref V Vc D Cp Dp
f r
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reference wind speed [m/s] volume of space [m3], crossflow velocity [m/s] pressure coefficient difference defined by Equation (1) pressure difference [Pa] wind direction density of air [kg/m3]
Subscripts b building I internal o orifice, opening st stack i, 1,2,3,4 opening number Superscripts overbar time average prime’ fluctuating value
direction and magnitude of the stack flows. There are two basic ways in which this can be done i.e. by measurement of pressures, from which the stack flows can be inferred or calculated, or by direct measurement of the stack flows. 1.2.1. Measurement of pressures The pressure coefficient is defined as
Cp ¼
pw pref 0:5rU 2
(1)
where pw and pref are the pressures due to air motion. The following four methods for determining stack flow direction (and in some cases, the magnitude) from pressure measurements are considered. Methods 1, 2 and 3 are the simplest, since they require only measurements of time-averaged pressures. The performance of these methods is described in Sections 7 and 8. Methods 4 and 5 require time records of pressures. Their performance is described in Part 2. Method 1 Measurement of mean wind pressure coefficients Cp , at the positions of the openings (no openings present). With this
Fig. 1. Sketch of model showing positions of orifices and view of model in wind tunnel.
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information and with an estimated value for the internal pressure coefficient CpI , the mean pressure difference across each opening is obtained e.g.
DCpst1 ¼ Cpst1 CpI DCpo1 ¼ Cpo1 CpI
(2)
By assuming that the sign of the flow rate is the same as the sign of DCp (which is a valid assumption, except possibly when intermittent flow reversal occurs), the flow pattern is immediately obtained. If the only concern is to maintain a fixed flow direction in the stacks, this information may be all that is required. This is the simplest technique, but it requires an estimate of CpI and the results are sensitive to the chosen value. Method 2 Measurement of mean wind pressure coefficients and the internal pressure coefficient (openings present). This is the same as method 1, except the openings are present and CpI is measured, so in that sense the values of DCp are accurately known. However, CpI is likely to be dependent on Reynolds number due to the stack lengths. Method 3 Measurement of mean wind pressure coefficients for use in a steady flow envelope model. The values of Cp are used in a conventional envelope flow model, to determine both the magnitude and direction of the individual flow rates, using fullscale flow characteristics for the openings. This can perhaps be described as the conventional approach. It should be more accurate than method 1, in that it takes account of the steady (still-air) flow characteristics of the openings to determine CpI . On the other hand, methods 2 and 3 should give similar results, because method 3 is basically a simulation of method 2. It is unlikely that one would go to the expense of wind tunnel testing just for the purpose of applying methods 1 and 2, because method 3 requires little further effort and it is of interest to see how they compare with method 3. A conventional envelope flow model relies on the pseudosteady flow assumption and takes no account of the unsteady nature of the flow through the openings due to wind turbulence. Furthermore, it ignores any changes in discharge coefficient Cz due to external flow effects. These effects can be quite large, particularly for sharp-edged orifices [1]. This will lead to errors in the calculated value of CpI . In terms of determining flow direction therefore, this approach may be no better than method 2. The advantage of method 3 is that the flow rates are calculated as well as the directions, although the results will of course be subject to uncertainties. Methods 1, 2 and 3 require only the measurement of timeaveraged pressures. Furthermore, the measurements do not have to be made simultaneously at all points. The fourth method requires more demanding measurements of pressures. Method 4 Simultaneous measurement of instantaneous pressures at the openings, which allows calculations with an unsteady envelope flow model. This method is considered in Part 2, Section 5. There is a fifth method, which is less demanding in that it does not require simultaneous measurements i.e. measurement of instantaneous pressures to allow standard deviations to be determined. In principle, these can be used with the mean values to assess the level of flow reversal [9]. This method is briefly discussed in Part 2, Section 4. 1.2.2. Direct flow measurement The distinct advantage of flow measurement over pressure measurement is that both turbulence effects and external flow effects are present in the results. The distinct disadvantage is that the openings can introduce significant Re effects. The effects are dependent on the shape and size of the openings. For sharp-edged orifices, Re effects should be small. For long openings, such as the stacks that are tested here, Re effects can be expected to be
significant. Model-scale results will be obtained at opening Reynolds number Re0 that are typically one or two orders of magnitude less than full-scale. As a result, Cz is much less for the model than for full-scale. To some extent this problem can be reduced by distorting the model opening, A [10]. It is the product CzA that is important, so if it is anticipated that Cz at model scale will be 30% less than the full-scale value, the model-scale value of A can be increased by 30%. This is only an approximate remedy, but the consequential errors could well be less than those arising from neglect of the effects of turbulence and external flow. The dependence of Cz on Re for stacks at model scale can be clearly seen in the earlier investigations with a single stack, referred to above. They can also be seen in the present results (Section 6). These results are of practical interest in relation to external flow effects on Cz. One would not expect the results to be changed by the use of eight openings rather than two and this expectation is confirmed, with one proviso, the effect of internal air motion when Dp is very low, which is discussed in Part 2. 1.3. Objectives of present paper In Part 1 the objectives are: 1) to describe briefly the experimental technique - Section 2 2) to present the observed effects of Reynolds number, wind direction and opening configuration on mean flow properties Sections 3e6 3) to present the results of Methods 1, 2 and 3 for determining stack flow direction from wind tunnel measurements of pressures. The results of the first two methods are presented in Section 7. The third method is presented in Section 8. 2. Experimental techniques 2.1. Wind tunnel and model Fig. 1 shows the model installed in one of the environmental wind tunnels at TPU. Descriptions of the TPU and UNott tunnels can be found respectively in Refs. [11] and [12]. For the TPU tunnel, the mean velocity profile(streamwise component) followed a power law with an index of 0.32. The turbulence intensity had a maximum of 0.27, decreasing to 0.09 at the top of the boundary layer. The corresponding values for the UNott tunnel were 0.23. 0.24 and 0.1 (these values are for the resultant velocity component, since they were obtained with a single hot-wire). The model and measuring equipment were developed at UNott. The model was equipped with four identical stacks on the roof, and four sharp-edged orifices (one on each of the four walls), as shown in the sketch in Fig. 1. A dual hot-wire probe in each of the stacks, allowed simultaneous measurement of the instantaneous flow rate of the stacks. At the same time, the external pressures at the stacks and the orifices and the internal pressure could be measured. The dimensions of the rectangular box are 500 250 200 mm. There are four identical circular stacks fixed on each corner of the roof. Fig. 2 shows details of the stack. The total length of the stack is 188 mm, the diameter is 16.8 mm and the venturi diameter is 10 mm. The dual hot-wire is fixed in the center of the venturi area. The diameter of the sharp-edged orifice is the same as the stack. A plan view of stack and orifice positions relative to the wind directionf, is shown in Fig. 3. In some of the following Figures, a shorthand notation is used to identify the opening configuration e.g. “S34 O12” denotes that stacks 3 and 4 and orifices 1 and 2 were open.
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Pressure measurement has the distinct advantage that external surface pressures due to wind should be nominally independent of building Reynolds number, Reb, unless the building has a streamline form and even then the high turbulence levels associated with flows around buildings should reduce the dependency. It is generally accepted that surface pressure coefficients determined from scale models of sharp-edged buildings are applicable to fullscale Reb. In contrast, the internal pressure coefficient CpI , depends on the flow through the openings and may therefore be dependent on Reb, partly due to the dependency of q on Re0 for certain types of opening. It is also to be expected that the external pressure distribution is unchanged by the presence of small openings, and the openings used here are small in relation to the surface in which they lie. This expectation is discussed in Section 5, where it will be seen that the expectation was not always fulfilled. 2.3. Direct flow rate measurement
Fig. 2. Stack geometry and hot-wire probe.
2.2. Pressure measurement Nine pressure tappings were used on the model i.e. one for each of the stacks and the orifices and one internal tapping. Each tapping could be connected to its own pressure transducer (Furness FC044), with the other side of the transducer connected to a reference pressure. The reference pressure was taken within an empty box in the still air of the wind-tunnel laboratory. Fig. 4 shows the connections for one stack and the internal pressure. A pitot-static tube was mounted in the freestream of the wind tunnel to measure the dynamic pressure, from which the reference wind speed Uref was obtained.
Since the interest here is with stacks, it is necessary to determine the direction as well as the magnitude of the flow through each stack. The concept of a time-averaged flow direction is valid e.g. it is defined as upward flow when this occurs for more than 50% of the time and vice versa. But it is not very meaningful in the sense that a stack that has reversed flow for 49% of the time clearly is not performing satisfactorily. It is therefore necessary to consider the reversal percentage, r %. To determine r it is necessary to record instantaneous flow rates and the hot-wire technique was developed for this purpose. The basic equipment is inexpensive and compact, so that simultaneous measurements in multiple stacks can easily be made. A description of the measurement technique and the calibration technique can be found in Ref. [12]. As shown in Fig. 2, a hot-wire probe (Dantec 55P71s) is mounted in the middle of each stack. The standard 55P71 probe consists of two parallel hot-wires, but the probes were specially modified so that the two wires were 5 out of parallel in one plane [2]. Each hotwire was connected to a Dantec MiniCTA anemometer. The instantaneous direction of the flow in a stack is determined by comparing the instantaneous voltage outputs of the two hot-wires. The upstream wire is the one with the higher voltage output. The magnitude of the volume flow rate is then obtained from the calibration of the upstream wire. Unsteady calibration of each wire is carried out in situ using an oscillating piston. A steady calibration at the higher flow rates is carried out using a positive displacement meter (as shown in Fig. 4). The final calibration curve is obtained from a combination of these results. It is recognized that errors will arise due to the changing relationship between volume flow rate and the velocity recorded by the wire (due to changes in the shape of the velocity profile associated with unsteady flow). Prior to each measurement, the zero flow voltage is measured and this is used to account for any changes in tunnel air temperature. 2.4. Determination of still-air Cz The still-air discharge coefficient Cz of an opening is defined in terms of the time-averaged values of the volume flow rate and the pressure difference across the opening:
Cz h
Fig. 3. Plan view of stack and orifice positions, with wind direction.
sffiffiffiffiffiffiffiffiffiffi r q A 2:Dp
(3)
where q is the time-averaged value of flow rate, Dp is the timeaveraged pressure difference across the opening and (for a stack).
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B. Wang et al. / Building and Environment 46 (2011) 1380e1392
Fig. 4. Arrangement for steady calibration and determination of Cz.
Dp ¼ pst pI
(4)
drI V ¼ r1 q1 þ r2 q2 þ r3 q3 þ r4 q4 dt
(5)
The measurement of still-air Cz is carried out at the same time as the steady calibration, by measuring the pressure difference across the opening. Fig. 4 shows the arrangement, which employs a domestic gas meter (U6 type) and a fan. The gas meter was used to measure the time-averaged volume flow rate q, and the fan and valve were used to provide a nominally constant flow. Since the ends of the stacks are not identical, Cz will depend on flow direction. The time-averaged value of pressure difference across the stack, Dp (Dp ¼ pst pI ), was measured simultaneously using the pressure transducers. By adjusting the valve, a range of volume flow rates can be generated, thereby values of Cz with different volume flow rates can be obtained.
Since the flow is steady in the mean, each variable can be expressed as the sum of a mean and fluctuating part i.e.
2.5. Mean flow balance
Since the pressure fluctuations are small compared to atmospheric pressure, the errors associated with the r0 q0 terms on the right-hand side should be much less than 1%. Similarly, the mean pressure differences are less than 100 Pa, so any differences between the densities in the terms on the left-hand side should be less than 0.1%. Hence, if V is constant (V0 ¼ 0), equation (7) indicates that the mean
(6)
Substituting Equation (5) into Equation (4) and taking the timeaverage leads to the following equation (the time-average of the product of a mean value and a fluctuating value is zero).
dr0 dV 0 þ V 0 I r01 q01 r02 q02 dt dt r03 q03 r04 q04
r1 q1 þ r2 q2 þ r3 q3 þ r4 q4 ¼ r0I
0.0003
(7)
Stack 1 Stack 2
0.0002 0.0002
Stack 3 Stack 4
0.0001
Sum
0.0001
q (m3/s)
Simultaneous hot-wire measurements on multiple stacks with no other openings, provides a stringent and unique check on the overall accuracy of the technique, in the sense that the measured volume flow rates should satisfy the continuity equation (conservation of mass). Fig. 5 shows results for a symmetrical configuration, where the flows through stacks 1 and 4 were inward at all times (and virtually equal in magnitude). Similarly for stacks 2 and 3, except the flows were outward. The sum of the flow rates is also shown. Relative to the total outflow, the sum ranges from 5% to 8% of the total ventilation rate. In a truly steady flow the sum should be equal to zero and this is clearly not so. However, an error less than 10% in the measurement of ventilation rate is not bad. It compares favorably with other techniques, such as tracer gas techniques. The most likely cause of the error lies in the calibration of the hotwires. The systematic nature of the error (increasing with Uref ) is consistent with this. On this basis, an uncertainty of 10% in the mean flow rates is probably a reasonable estimate of the accuracy of the technique. It is also possible that the difference between the inflow and outflow rates is associated with the unsteady nature of the flow. To examine this it is necessary to consider the unsteady form of the mass conservation equation:
r ¼ r þ r0 ; q ¼ q þ q 0 ; V ¼ V þ V 0
0.0000 -0.0001 -0.0001 -0.0002 -0.0002 -0.0003 -0.0003 0
1
2
3
4
5
6
Uref (m/s)
Fig. 5. Mean flow rate balance (four stacks, no orifice), f ¼ 0.
7
B. Wang et al. / Building and Environment 46 (2011) 1380e1392
0.20 0.15 Stack Stack Stack Stack
0.10 us t/Uref
volume flow rates should sum to zero. The possible effect of the terms containing V0 has been estimated by assuming that V0 and r0I vary sinusoidally with a phase difference that maximizes the terms. With amplitudes for V0 and r0I of 5% and 1% of their mean values, and a frequency of 5 Hz, the effective volume flow rates from the two terms are both approximately 2 107 m3/s. This is less than 1% of the smallest observed sum, so it would seem that the calibrations are the main reasons for the non-zero sums. In passing it should be noted that for instantaneous flow rates, unsteady effects can be larger, because there is no time averaging (see Part 2).
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0.05
1 2 3 4
0.00 -0.05 -0.10
3. Effect of Reynolds number on Cp, q and r
-0.15
Ideally the nondimensional results should be independent of Reynolds number. The two relevant Reynolds numbers, namely building Reynolds number and opening Reynolds number, are defined as follows:
rUref H Reb h m Re0 h
-0.20 0
1
2
3 4 Uref (m/s)
5
6
7
Fig. 7. Variation of ust/Uref with Uref (four stacks, no orifice).
(8)
rud m
(9)
where r denotes the density of air (kg/m3), H the height of the building (m), d the diameter of the opening (m), u the mean velocity in the stack (uhq=A) and m the viscosity (Ns/m2). A dependence of envelope flow rates on Reb can be considered in two parts i.e. dependence of the external pressure coefficient, Cp (and the external velocity field) on wind tunnel speed (Reb) and dependence of the discharge coefficient on flow rate (Re0). The latter is discussed in Section 7. Fig. 6 illustrates the dependence of Cp on reference wind speed for the case of four stacks and no orifices. Independence of Cp on Reb can be seen for Uref higher than about 4 m/s. Figs. 7 and 8 illustrate the observed dependence of dimensionless flow rate u/Uref on wind speed for two cases i.e. four stacks alone and four stacks with two orifices. Flow into the box (downward stack flow) is defined as positive. When the Cp is independent of wind speed, one would still expect to see a dependence of u/Uref , due the dependence of Cz on Re0. Rather surprisingly this is more evident in Fig. 8 than in Fig. 7. Fig. 7 corresponds to the case where there are no sharp-edged orifices, so one would expect Re effects to be greater. However there is another factor at work, namely that Cz is also a function of Vc/u, particularly with sharp-edged orifices [2].
This can lead to misleading indications of the effect of building Reynolds number Reb. The quantity Vc is the crossflow velocity in the external flow close to the opening. The results in Figs. 7 and 8 were obtained with a fixed wind direction, so Vc/Uref should be nominally constant. However, Vc/Uref could vary with Reb, and the effect on u/Uref could be different to the effect of Cp variations. Unfortunately it was not possible to measure Vc. Previous investigations with a single stack and orifice have shown that the degree of flow reversal r is closely related to the properties (mean and standard deviation) of the instantaneous pressure difference across the two openings. The fact that there were only two openings for those investigations makes interpretation and analysis of results easier. The present investigation is concerned with flow reversal with multiple stacks. Fig. 9 shows the dependence of r on Reb of two opening configurations, i.e. two stacks with two orifices and four stacks with two orifices. One can see a dependence of r on Reb, which indicates that higher r is expected at full scale. Calculations of this effect using the unsteady QT model are given in Part 2. 4. Effect of wind direction Fig. 10 shows Cp variation with wind direction for two stacks and four orifices. Fig. 11 shows the corresponding variation of r with
0.00
0.4 Internal
-0.05
stack 1
0.2
stack 2 stack 3
0
-0.10
stack 4
u/Uref
Stack 1
Cp
Orifice 1 Orifice 2
-0.2
Stack 2 -0.15
Stack 3 Stack 4
-0.4
-0.20
-0.6
-0.25
-0.8
-0.30
0
1
2
3
4
5
6
Uref (m/s) Fig. 6. Variation of Cp with Uref (four stacks, orifice 1 and 2).
7
0
1
2
3 Uref (m/s)
4
5
6
Fig. 8. Variation of ust/Uref with Uref (four stacks, orifice 1 and 2).
7
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100
100
S34_O12 Stack 3 90
S34_O12 Stack 4
90
S1234_O12 Stack 1 80
80
S1234_O12 Stack 4
Stack 1
70
70
60
60
r (%)
r (%)
Stack 3
50
50
40
40
30
30
20
20
10
10 0
0 0
20000
40000
60000
80000
0
100000
45
90
180
Fig. 11. Variation of r with wind direction (stack 1 and 3, four orifices).
Fig. 9. Variation of r with Reb.
wind direction for the two stacks. Whether or not flow reversal occurs depends primarily on the relative values of Cp at the openings and on the relative sizes of the openings. For the wind-alone case, it is a relatively simple matter to calculate the flows with an envelope flow model. When buoyancy is involved, the problem is more difficult, since account needs to be taken of the dependence of stack temperature on flow direction. However, the effects of buoyancy are not considered here. Simply using the values Cp of can be misleading, as shown by the fact that flow reversal was observed for f ¼ 0, 90 and 180, but no flow reversal was observed for f ¼ 45 and 135. The stack Cp values are close to the orifice values for the first three wind directions, whereas the most negative stack Cp values were observed for the second two directions. Flow reversal always occurred at some wind directions for all opening configurations tested. 5. Effect of opening configuration on Cp In principle one would expect the opening configuration to have little effect on the mean wind pressures, because the openings are flush and their areas are small in relation to the areas of the surfaces in which they lie. This expectation is a basic assumption in
0.4
0.2
0.0
Cp
135
Wind direction
Reb
conventional envelope flow models. Most of the results satisfy this expectation, but not all Table 1 shows values of stack Cp obtained with different opening configurations at two wind directions. For f ¼ 0, it can be seen that Cp1 and Cp4 change considerably when two orifices are added, but not when a further two orifices are added. At this wind direction, stacks 1 and 4 are located at the leeward side. For f ¼ 180, stacks 2 and 3 become the leeward ones. When the number of orifices increases from two to four, the decrease of stack outlet pressure is less obvious than that when it increases from zero to two, indicating that the stack outlet pressure located in the leeward zone is more sensitive to the change of number of orifices. Results for f ¼ 90 are given in Fig. 12, for two stacks alone and two stacks with four orifices. It can be seen that none of the orifice Cp are affected, and only one of the two stacks (only two stacks were open). Results for f ¼ 0 are given in Fig. 13, for the same opening configurations. It can be seen that none of the Cp are affected. There is a clear indication in the above results (and in others that are not presented) that the orifice Cp are not affected by the opening configuration, but the stack Cp can be affected. The results for the orifices display very good repeatability, and any changes that occur are so small that they can be ignored in the design process (at least for the configurations tested here). The changes that have been observed for the stacks are significant, in the sense that they are not due to poor repeatability. Two possible explanations are as follows. In terms of the flow around the exterior of the model, the presence of an opening corresponds to a source (outward flow) or a sink (inward flow). If the opening lies in an attached boundary layer, the flow through the opening will lead to a change in the local displacement thickness of the layer. The disturbance to the pressure
-0.2
-0.4
Table 1 External pressure coefficients of stacks with different numbers of open orifices. NB “4S” denotes 4 stacks, no orifices, “4S 2O” denotes 4 stacks, 2 orifices.
Stack 1 Stack 3 Orifice 1 Orifice 2 Orifice 3 Orifice 4
-0.6
-0.8 0
45
90 wind direction
135
Fig. 10. Cp variation with wind direction (stacks 1 and 3, four orifices).
180
Wind direction
0
0
0
180
Openings
4S
4S 2O
4S 4O
4S 2O
180 4S 4O
Cp1 Cp2 Cp3 Cp4
0.32 0.54 0.55 0.30
0.17 0.53 0.55 0.17
0.16 0.54 0.56 0.16
0.55 0.18 0.18 0.52
0.52 0.16 0.15 0.50
B. Wang et al. / Building and Environment 46 (2011) 1380e1392
0.7
0.4 0.3
0.6
Cps1 Cps3 Cpo1 Cpo2 Cpo3 Cpo4
0.1 0
0.5
Cz
0.2
Cps
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-0.1
0.4 0.3 Stack 1
-0.2
Stack 2
0.2
-0.3 -0.4
Stack 3 Stack 4
0.1
-0.5
0.0 0
-0.6 S13
500
1000
1500
Rest
S13_O1234
Fig. 14. Variation of Cz with Rest with external flow (four stacks, no orifices).
opening configuration Fig. 12. Stack and orifice Cp with two open stacks and increasing number of orifices for f ¼ 90.
distribution will be localized. However, if the opening lies in a separated flow region, with reattachment, the presence of the opening flows could change the shape of the separated region (and the nature of reattachment). A change in shape of a separation region is effectively a change in shape of the model, so the effects could be more far-reaching. Another possibility lies in the position of the tapping used for the stack Cp. This is discussed in Part 2.
present results for multiple stacks are examined in the light of the earlier findings and it will be seen that they are in agreement. 6.1. Still-air values The still-air discharge coefficient is a major parameter in design calculations. The values obtained from the still-air calibration are included in Fig. 16, in the form of Cz against Rest. The results are very close to the earlier results. In particular, Cz with inward flow is greater than that with outward flow, due to the fact that DCp is obtained with one pressure tapping inside the stack. 6.2. Effect of external flow
6. Discharge coefficient of stacks Envelope flow models (steady and unsteady) make use of the still-air discharge coefficients of openings. In previous work Ref. [1] and [3], it was found that the discharge coefficient in the presence of flow can differ from the still-air value, depending on the external flow conditions. For a stack it was found that the external flow has little effect on stack Cz for upward flow, and a significant effect for reversed flow. The basic reason for this is that with upward flow, the external flow only affects the outlet boundary condition. The
Figs. 14 and 15 show the observed variation of stack Cz with Rest for two opening configurations in the presence of wind; the first configuration has four stacks alone and the second has four stacks and two orifices. In Fig. 14 stacks 2 and 3 have outward flow and there is close agreement between them and with the still-air case (Fig. 16). (NB In Fig. 15 of [1], the stacks were incorrectly identified). This reflects the fact that the outlet conditions have little effect on the upstream flow in the stack (except that the outlet pressure determines the flow rate). Stacks 1 and 4 have inward flow and their curves lie above the corresponding still-air curve. The high Cz
0.4
0.7 0.2
Cps1 Cps3 Cpo1 Cpo2 Cpo3 Cpo4
Cps
0
0.6 0.5 0.4
Czst
-0.2
0.3
Stack 1
-0.4
Stack 2 0.2
Stack 3
-0.6
Stack 4
0.1 -0.8 S13
S13_O1234 opening configuration
0.0 0
500
1000
1500
2000
Rest Fig. 13. Stack and orifice Cp with two open stacks and increasing number of orifices for f ¼ 0.
Fig. 15. Variation of Cz with Rest, outward flow (four stacks, orifice 1 and 2).
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0.7
Stack 3 0.2 estimated Cpint
0.6 0.1
u/Uref
0.5
measured Cpint
DelCp and u/U
Cz
0
0.4 Inward steady cal 0.3
Outward steady cal Outward Unsteady
0.2
-0.1
-0.2
Inward Unsteady Stack1 Inward Unsteady Stack4
0.1
-0.3 0
45
90
135
180
0 0
500
1000
1500 Rest
2000
2500
-0.4
3000
Fig. 16. Cz variation with Rest compared with still-air results (four stacks, no orifice).
Fig. 18. Calculated DCp and measured u/Uref of Stack 3 (four stacks, four orifices).
values suggest that there is a downward momentum component in the external flow that contributes to the total driving force of the flow in the stacks. For these two points a different definition of Cz would probably be appropriate i.e. one based on a total pressure containing 0:5rVc2 so that Equation (4) is replaced by:
Dp ¼ pst þ 0:5rVc2 pI
wind direction
calculated 0.2
(10) 0.1
0
q/AUref
In practice, it is not possible to use this definition, because Vc is not known. The results for stacks 1 and 3 are not identical. This can probably be explained by differences between the external flow conditions at the stacks, although calibration errors may play a role. In Fig. 15, all the stacks have outward flow, with reversal percentages less than 50%. There is some scatter, probably reflecting the fact that r is non-zero in some cases. Fig. 16 compares the results in Fig. 14 with the still-air results. An underlying for calculation methods can be seen i.e. the good agreement between the unsteady and steady (still-air) results for outward flow, and the poor agreement that occurs when the flow is inward. The significant differences between the Cz values of stacks 1 and 4 are not due to differences in the stack Reynolds numbers. They are probably caused by asymmetry of the external flow field,
-0.1 q st 1/A Uref q st 2/A Uref
-0.2
q st 3/A Uref q st 4/A Uref
-0.3 0
45 wind direction
90
Measured 0.2
Stack 1 0.2 0.1 estimated Cpint
0.1
q/AUref
DelCp and u/U
u/Uref
0
measured Cpint
0
-0.1 -0.1
-0.2
q st 1/A Uref q st 2/A Uref
-0.2
-0.3
q st 3/A Uref q st 4/A Uref
-0.4 0
45
90
135
180
-0.3 0
wind direction
Fig. 17. Calculated DCp and measured u/Uref of Stack 1 (four stacks, four orifices).
45 wind direction
Fig. 19. Variation of q/AUref (four stacks, no orifice).
90
B. Wang et al. / Building and Environment 46 (2011) 1380e1392
but slight differences in the stack box shapes and in the positions of pressure tappings may be contributory factors. 7. Determination of flow directions from pressures Figs. 17 and 18 show the measured values of u/Uref for stacks 1 and 3 respectively from a test with constant Uref and varying wind direction. They also show the calculated DCp using methods 1 and 2. If these methods were reliable, the calculated DCp and measured u/Uref should have the same sign, and one could use the methods to determine flow reversal. Stacks 2 and 4 were sealed, but the four orifices were open. It can be seen that flow reversal (downward flow) was observed at f ¼ 0 for stack 1 and at f ¼ 90 and 180 for stack 3. In each figure, the solid line shows the calculated DCp obtained with method 1, where the value of CpI is taken as the weighted arithmetic mean of the Cpi. The weighting uses the product CzA, where Cz for the stacks has been taken as one-half that for the orifices.
CPI ¼
n X i¼1
C A Cpi Pn zi i i¼0 Czi Ai
(11)
1389
The argument for this weighting is that the internal pressure is determined by the balance of the individual flow rates and that each flow rate is proportional to CzA, rather than Cz or A alone. It can be seen that the reversal for stack 1 is not apparent and neither are the reversals for stack 3 (although the 90 result is close to reversal). Using a weighting based on A (i.e. CpI is the simple arithmetic mean of the Cpi) gives the same result. The calculated DCp for method 2, using the measure internal pressure coefficient, are shown by the dashed line and it can be seen that two of the three reversals are apparent. 8. Comparisons with steady envelope flow model A conventional steady envelope flow model (method 3) has been used to calculate stack flow rates and the results are compared with the measured values. This has been done for the following conditions:(i) a fixed wind speed and varying flow direction; four stacks alone and four stacks with two orifices
calculated
calculated
0.2
0.2 q stack 1 q stack 3
0.1
q/AUref
q/AUref
0.1
0
0
-0.1
-0.1 q st 1/A Uref -0.2
-0.2
q st 2/A Uref q st 3/A Uref q st 4/A Uref
-0.3
-0.3 0
45 wind dirction
0
90
45
135
180
measured
measured 0.2
0.2
0.1
0.1
0
0
q/AUref
q/AUref
90 wind direction
-0.1
-0.1 q st 1/A Uref q st 2/A Uref
-0.2
q stack 1
-0.2
q st 3/A Uref q stack 3
q st 4/A Uref -0.3
-0.3 0
45 wind direction Fig. 20. Variation of q/AUref (four stacks, orifice 1 and 2).
90
0
45
90
135
wind direction Fig. 21. Variation of q/AUref (stacks 1 and 3, four orifices).
180
1390
B. Wang et al. / Building and Environment 46 (2011) 1380e1392
(ii) a fixed direction and varying wind speed; four stacks alone and four stacks with two orifices (iii) a fixed wind speed and varying flow direction; two stacks and four orifices. The flow characteristics of the stacks are taken from a quadratic curve-fit to the still-air measurements i.e.
1=Cz2 ¼ C
L þD Rest d
(12)
where L and d are respectively the length and diameter of the stack. C and D are factors obtained from the steady calibration, which relate to stack geometry and flow directions. For upward flow, C ¼ 153.07 and D ¼ 5.739; for downward flow, C ¼ 140.08 and D ¼ 3.692. Except where stated otherwise, the discharge coefficient of the orifices is taken to be 0.68. 8.1. Variation of non-dimensional flow rate with wind direction Figs. 19, 20 and 21 compare the calculated and measured stack flow rates for the three configurations (four stacks alone; four stacks and two orifices; two stacks and four orifices).
For the two configurations shown in Figs. 19 and 20, the sign of the flow is accurately calculated at all wind directions, including 45 where intermittent flow reversal occurs. The overall agreement for the magnitude is reasonably good for the four stacks alone case (Fig. 19), but the agreement deteriorates when two orifices are added (Fig. 20). This deterioration with the number of orifices is more apparent in Fig. 21, where there is poor agreement for the flow direction as well as the magnitude. The observed deterioration of the agreement between calculation and measurement is somewhat surprising, because the simple shape of the orifices and the absence of Reynolds number effects leads one to expect that they should be relatively easy to account for in envelope flow models. However, it is consistent with the finding in [1], namely that the discharge coefficient of an orifice is more affected by installation effects (external crossflow) than a long stack. 8.2. Variation of non-dimensional flow rate with wind speed (building Reynolds number) Figs. 22 and 23 compare the calculated and measured stack flow rates for the two configurations (four stacks alone; four stacks, two orifices).
calculated 0.2
calculated 0.2
0.1 0.1
0
q st 2/A Uref
q/AUref
q/AUref
q st 1/A Uref q st 3/A Uref
0
q st 4/A Uref
q st 1/A Uref q st 2/A Uref
-0.1
q st 3/A Uref q st 4/A Uref
-0.1
-0.2
-0.2
-0.3 0
1
2
3
4
5
6
7
0
1
2
3
Uref (m/s)
4
5
6
7
Uref (m/s)
measured
measured
0.2
0.2
0.1 0.1
q/AUref
q/AUref
q st 1/A Uref q st 2/A Uref q st 3/A Uref
0
q st 4/A Uref
0 q st 1/A Uref q st 2/A Uref q st 3/A Uref
-0.1
q st 4/A Uref
-0.1
-0.2
-0.3
-0.2 0
1
2
3
4
5
6
7
Uref (m/s) Fig. 22. Calculated and measured effects of Reynolds number (four stacks, no orifice).
0
1
2
3
4
5
6
7
Uref (m/s) Fig. 23. Calculated and measured effects of Reynolds number (four stacks, orifice 1 and 2).
B. Wang et al. / Building and Environment 46 (2011) 1380e1392
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Wind
3 2
4 1
3 2
Orifice 2
4 1
Orifice 1
Fig. 24. Flow directions of four stacks, orifices 1 and 2; four stacks alone.
Again it is clear that the agreement is good for the stacks alone case, but relatively poor for the configuration with two orifices. There are two likely reasons for this, one associated with the cross flow effects referred to above and the other with intermittent flow reversal. To appreciate this, Fig. 24 shows the flow directions for the two cases. The evidence from [1] is that Cz can be reduced by 50% or more depending on Vc/u. The flows through orifices 1 and 2 are both inward, so one can expect Cz to be less than the still-air value. The stack Cz is not affected by external flow when the flow is outward, but it can be affected when the flow is inward, and may be increased. Fig. 25 shows the discharge coefficient of the orifice for stillair and wind-on cases. Values of Cz0 for wind-on conditions were calculated from tests with one stack and one orifice, in which the volume flow rates of the orifice and the stack are equal. It can be seen that Cz0 is reduced by the presence of wind. On the basis of Fig. 25, calculations were carried out with (i) Cz of both orifices reduced from 0.68 to 0.5 and (ii) with one Cz0 ¼ 0.61 and the other ¼ 0.5.In both cases, the overall improvement was small. The agreement for stacks 2 and 3 was substantially improved, but it was accompanied by reduced agreement for stacks 1 and 4. There is another possible reason for inaccuracy with stacks 1 and 4. For stacks 1 and 4 the reversal percentage was around 30% and the still-air relationship (equation (12)) may be invalid.
Fig. 25. Discharge coefficients of sharp edged orifice e still-air and wind-on.
9. Conclusions The UNott hot-wire technique has been used to measure simultaneously the instantaneous magnitude and direction of flow in multiple (up to four) stacks. As far as is known, such measurements have not been made before. The tests were carried out with up to four other openings (sharp-edged orifices), with simultaneous measurements of external and internal pressures. The tests with no other openings allowed an estimate to be made of the overall uncertainty of the stack flow measurements. In terms of the mean ventilation rate, the results indicate an overall uncertainty of about 10%, which compares favorably with other less comprehensive techniques (e.g. tracer gas). Tests over a range of wind tunnel speeds indicate that the external pressure coefficients can be taken as independent of Reynolds number above about 3 or 4 m/s. As expected, there is some dependency of the dimensionless flow rates over the whole range, due to the presence of the stacks. The reversal percentage shows a similar dependency. Examination of the external pressure coefficients for a range of opening configurations revealed that the values for the orifices were independent of the opening configuration. This is what one expects for small openings. However, some effect of opening configuration was observed for the stacks. Tests over a range of wind directions showed that the external pressure coefficients for the stacks were always negative. It obviously does not follow that the stack flows would be always upwards, since this depends on the overall opening configuration. However, even with four orifices present, flow reversal was observed at some wind directions. It should be noted that the value of CzA for an orifice facing the wind is twice that for a stack, whereas CzA for orifices facing other directions could be much lower. The observed effects of external flow on the discharge coefficients are consistent with previous work on single stacks. The measurements have been used to assess three methods for determining stack flow directions from wind tunnel pressure measurements alone. They differ in the way in which the internal pressure is determined. A conventional envelope flow model (in which the internal pressure is calculated) performed the best. However, the main feature of this investigation is that it revealed that the agreement between calculation and measurement deteriorated as the number of orifice openings was increased. This is consistent with earlier work that showed that the discharge coefficients of orifice openings are more susceptible to external flow effects than long stacks. Compared to methods based on pressure measurements, the advantage of the direct hot-wire technique is that the measurements include (i) the effects of wind turbulence, (ii) the effect of crossflow
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on discharge coefficient and (iii) any effect of opening configuration on pressure coefficient and their correlations. However some means of extending the results to full-scale Reynolds numbers is needed. Acknowledgements The work described has been funded by EPSRC (UK), with support from the COE Program at Tokyo Polytechnic University, and this is gratefully acknowledged. References [1] Chui YH, Etheridge DW. External flow effects on the discharge coefficients of two types of ventilation opening. Jnl Wind Eng Ind Aerod 2007;95:225e352. [2] Costola D, Etheridge DW. Unsteady natural ventilation at model scaleeFlow reversal and discharge coefficients of a short stack and an orifice. Building Environ 2007;43:1491e506. [3] Cooper EW, Etheridge DW. Wind tunnel investigation of unsteady flow in a natural ventilation stack. In: Second WERC International Symposium on Architectural wind Engineering. Tokyo: Wind Engineering Research Center; 2007. p. 191e208.
[4] Claesson L, Etheridge DW. Unsteady flow reversal in a natural ventilation stack e model scale tests. Int J Ventilation 2005;4(1):25e35. [5] Alexander DK, Jenkins HG, Jones PJ. A comparison of wind tunnel and CFD methods applied to natural ventilation design. Proc Building Simulation 1997;97(2):321e6. [6] Ohba M, Kurabuchi T, Endo T, Akamine Y, Kamata M, Kurahashi A. “Local dynamic similarity model of cross-ventilation, Part 2-Application of local dynamic similarity model.” Int Jnl Ventilation 2004;2(4):383e94. [7] Etheridge DW, Ohba M, Wang B. Wind tunnel investigation of natural ventilation through multiple stacks. In: The 4th International Conference on Advances in wind and Structures. Korea: AWS’08; 2008. p. 1117e28. [8] Wang B. Unsteady wind effects on natural ventilation, PhD thesis, University of Nottingham, Nottingham, UK, July 2010. [9] Etheridge DW. Unsteady flow effects due to fluctuating wind pressures in natural ventilation design-mean flow rates. Building Environ 2000;35: 111e33. [10] Etheridge DW, Nolan JA. Ventilation measurements at model scale in a turbulent flow. Building Environ 1979;14:53e64. [11] Ohba M, Irie K, Kurabuchi T. Study on airflow characteristics inside and outside a cross-ventilation model, and ventilation flow rates using wind tunnel experiments. Jnl Wind Eng Ind Aerod 2001;89:1513e24. [12] Chiu YH, Etheridge DW. Experimental technique to determine unsteady flow in natural ventilation stacks at model scale. Jnl Wind Eng Ind Aerod 2004;92:291e313.