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Wind tunnel investigation of natural ventilation through multiple stacks. Part 2: Instantaneous values
Building and Environment 46 (2011) 1393e1402
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Wind tunnel investigation of natural ventilation through multiple stacks. Part 2: Instantaneous 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. Part 1 of the paper [1] concentrated on the characteristics of the mean flows. Part 2 concentrates on the instantaneous characteristics of the flows, both in terms of the experimental measurements and in terms of an unsteady envelope flow model. Further investigations into the experimental measurement techniques are described. These relate to improving the hot-wire calibration, to the instantaneous flow balance with multiple stacks (and the importance of model rigidity) and to the increased importance of internal air motion with the higher flow rates associated with multiple openings. The experimental measurements of stack reversal percentage are examined in some detail, regarding the effects of wind direction and Reynolds number and how the reversal percentage relates to a simple pressure parameter. Following on from Part 1, the effect of opening configuration on the instantaneous properties of the external wind pressures is investigated by examining their correlations. As with the mean values it is found that the correlations are not entirely independent of opening configuration. The experimental data is used to assess the performance of an unsteady envelope flow model, both in terms of calculating instantaneous values and mean values such as reversal percentage. The model is shown to perform well with multiple stacks. It is then used to estimate the effect of Reynolds number on the reversal percentage at model-scale and full-scale. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Wind tunnel Hot-wire technique Natural ventilation Stacks Reynolds number Unsteady flow
1. Introduction Part 1 [1] of the companion paper dealt with mean flow properties such as mean pressure coefficient and mean flow rate. As mentioned in Part 1, the special feature of the experimental technique is that measurements of the instantaneous flow and pressure in multiple stacks can be made simultaneously. In Part 2, the emphasis is on instantaneous values. The objectives are: (i) to describe further work that has been done on the experimental technique, namely improving the hot-wire calibration technique (Section 2.1), investigating the instantaneous flow balance (Section 2.2) and improving the measurement of internal pressure (Section 4.1). (ii) to present the observed effects of Reynolds number, wind direction and stack geometry on instantaneous flow properties (Sections 3 and 4). * Corresponding author. Tel.: þ44 115 951 3171; fax: þ44 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.2011.01.011
(iii) to compare the instantaneous measurements with a theoretical unsteady model (Section 5.l). Again the underlying philosophy is to use the wind tunnel results to assess the theoretical model. If the model performs well at low Reynolds numbers, there is reason to be optimistic about its performance at full-scale. 2. Experimental techniques 2.1. Unsteady calibration of hot-wires The calibration procedure for the hot-wires has been described in earlier papers [2,3],. Basically each wire is calibrated in terms of volume flow rate rather than velocity. It is recognized that the relation between the local velocity and the volume flow rate will depend on the instantaneous velocity profile in the stack, due to unsteady effects, and for this reason each wire is calibrated with steady and unsteady flow. Both the steady and unsteady calibrations are carried out in-situ, using different devices: a fan with a flow meter for steady calibration; a specially designed piston
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calibrator for unsteady calibration. With the original piston calibrator, the rotational speed was assumed to be constant and it was determined by measuring the time for one complete cycle. Knowing the rotational speed, the velocity of the piston can be calculated from the known geometry (bore, stroke and length of connecting rod). There was some evidence that the assumption of constant speed was introducing avoidable errors into the calibration. Thus an improved version of the calibrator was developed, to measure the instantaneous rotational speed of the motor, rather than the overall value. For this purpose a disc was attached to the drive shaft, of the original calibrator, as shown in Fig. 1. The disc contains one hundred laser-cut slots, through which an LED sensor generates a constant voltage pulse each time a slot passes. In terms of data acquisition, the sampling frequency is set high enough (5000 Hz) to detect the passage of each slot to within 0.2 ms. Thereby, one can evaluate 100 instantaneous rotational speeds per cycle, and hence the instantaneous flow rate of the piston. The frequencies (and corresponding velocity ranges) obtained were 1.39 Hz (0.55 m/s), 2.11 Hz (0.85 m/s), 2.95 Hz (1.2 m/s) and 4.86 Hz (2.0 m/s). Fig. 2 shows the unsteady calibration curves obtained for one wire at two of the four frequencies i.e. 1.39 and 2.11 Hz. The different calibrations for the acceleration and deceleration phases can be seen and these lead to calibration errors. The differences are larger at the higher frequencies, but they are not representative of the calibration errors that occur in the measurements. A frequency of 4.86 Hz corresponds to 9.72 zero crossings per second. The flow produced by the piston is a nominally sinusoidal oscillation (zero mean). In the model tests, this corresponds to a reversal percentage of 50%. Fig. 3 shows a stack velocity record with r ¼ 53.9% obtained at a high wind speed of 5 m/s, with consequently high frequencies. The number of zero crossings is 175 over the measurement period i.e. 5.15 per second. On this basis, a calibration frequency of 2.67 Hz would be representative. In fact the situation is probably better than this, because many of the zero crossings are probably associated with small-scale turbulence. On this basis the calibration frequency of 1.39 Hz is probably more appropriate (at lower wind
Fig. 2. Calibration results at two frequencies (a) 1.39 Hz and (b) 2.11 Hz.
speeds, this is more likely). The final calibration was in fact obtained by combining the unsteady calibration for 1.39 Hz and the steady calibration, in the same way as in [2] and [3]. 2.2. Instantaneous flow balance In Part 1, the mean flow balance was examined for the four-stack case with no orifices. In the following the instantaneous flow balance for the four-stack case is considered. It is of course to be
Fig. 1. Original piston calibrator fitted with slotted disc.
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Fig. 3. Velocity record for a stack (velocity 1) with nominally oscillating flow (zero mean) (stacks 1 and 4, orifices 3 and 4, wind direction 90 ).
Fig. 5. Spectral analysis of velocity sum with wind speeds of 5 m/s and 2 m/s (four stacks, no orifice).
expected that that the instantaneous imbalance will at times be greater than the mean imbalance. However, tests on an earlier wind tunnel model [4] indicated that vibration of the walls of the model could lead to significant changes in the volume of the model. Such changes would lead to spurious contributions to the instantaneous flow rates. As a result, the four-stack model was made more rigid. First, the wall thickness was increased from 5 to 8 mm. Second, and more important, the base plate was rigidly screwed to the side walls. In the earlier model the base plate was taped to the side walls. Fig. 4 displays instantaneous velocities of the four stacks over a period of 6 s, for a high wind speed of 5 m/s and a wind direction equal to zero. The flows through stacks 1 and 4 were inward at all times and outward for stacks 2 and 3. The important point to note is that the instantaneous sum of the velocities has a discrete frequency component. This can also be clearly seen in the power spectrum of the velocity sum, as shown in Fig. 5, and in the spectra of the stack velocities (Fig. 6). Figs. 5 and 6 show results for a wind speed Uref ¼ 5 m/s, but Fig. 5 also shows results for Uref ¼ 2 m/s. (NB The power spectra were generated using the Fourier Analysis tool in MS Excel and are not normalized. The aim was simply to identify any peaks in the spectra.) The fact that a frequency of around 22 Hz is clearly apparent in both results shown in Fig. 5 implies that the phenomenon is independent of wind speed. In which case, a likely explanation is that a resonant frequency of the box structure is excited. However,
at the low wind speed, there is also evidence of resonance around 11 Hz. Fig. 7 shows the spectra for the pressure difference across stack 4 (ps4 e pin) and the external stack pressure (ps4 e pref). It can be seen that the resonance is evident in the former, but not the latter. Although not shown here, the resonance is clearly evident in the internal pressure (pin e pref). This indicates that the hot-wire results are due to a flow phenomenon rather than, say, mechanical vibration of the wire. Furthermore, the fact that a frequency of around 22 Hz is clearly apparent in both results shown in Fig. 5 implies that the phenomenon is to some extent independent of wind speed. In which case, a likely explanation is that a resonant frequency of the box structure is excited. However, this may not be the full explanation, because at the low wind speed, there is also evidence of resonance around 11 Hz. Another reason for caution about this explanation is that resonant peaks were observed in the orifice external pressures (but not in the stack pressures), which do show a dependence on wind speed. This could conceivably be due to vibration of the orifice pressure tubing, which passed through the model. In summary, the above results indicate that when recording instantaneous pressures, care must be taken to minimise volume changes due to vibration of the model walls. The deflections of the walls may be very small, but the associated volume changes can be significant. Despite the measures taken, the effect was not entirely eliminated, and this could be responsible for some of the differences observed in the comparisons with the theoretical model in Section 5.
2.5 velocity1 velocity2 velocity3 velocity4 velocity sum
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v eloc ity (m/ s )
1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 0
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Fig. 4. Instantaneous velocities of four-stack tests and their sum (four stacks, no orifice, Uref ¼ 5 m/s).
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Fig. 6. Spectral analysis of velocities of stack 1 and 2 with a wind speed of 5 m/s (four stacks, no orifice).
3. Flow reversal A simple parameter is used to characterize flow reversal of the stacks i.e. the percentage of time that the flow is reversed, r. The results are presented below in the form that might be appropriate when the technique is used as part of a building design exercise i.e. as plots of r against wind direction, 4. The comments are based on the assumption that, when orifices are present, upward flow is to be maintained in the stacks. Results for several different stack and orifice configurations are presented. Where the opening configuration has symmetry, it has been assumed that symmetry with wind direction applies, so some results are repeated. 3.1. Effect of wind direction, opening distribution Fig. 8 shows the results for four stacks and two orifices (orifices 1 and 2) for the complete range of wind directions in steps of 45 . This is the sort of information that is of potential use for design. It can be seen that flow reversal occurs in at least one of the stacks for all wind directions. This is in contrast to the single stack investigated in [5], where flow reversal scarcely occurred. The results in Fig. 8 can be compared with those in Fig. 9, which are for four stacks and four orifices. The effective area of an orifice (CdA) is about twice that of a stack and one would expect to see some effect on the reversal percentages. Despite this, it can be seen that the effects are quite small. This presumably reflects the fact that the effect also depends on the external pressure at the orifice, relative to the stack pressures.
Fig. 8. Flow reversal percentage for stacks 1, 2, 3 and 4, as a function of wind direction (four stacks, orifices 1 and 2).
Fig. 10 shows the effect of the changes to the opening configuration for just one of the stacks (stack 3). The configurations are 2 stacks and 2 openings, 4 stacks and 2 openings and 4 stacks and 4 openings. Also shown is a case where the boxes enclosing the stacks were removed. This shows some reduction in reversal percentages. In summary, the above results illustrate the importance of the external pressure distribution (wind direction) on flow reversal. It is worth noting that, for all the opening configurations tested, significant flow reversal occurred for at least one wind direction. The presence of buoyancy could of course change this situation. Nevertheless, it is clear that wind effects need to be considered in the design of buildings with natural ventilation stacks, particularly for summer cooling when temperature differences are likely to be relatively small. 3.2. Effect of Reynolds number Ideally the reversal percentage would be independent of building Reynolds number, but some effects are expected, due to the facts that the stacks are long openings and the external velocity depends to some extent on Reynolds number. Fig. 9 in Part 1 shows examples of the variation. The primary cause of this variation is the fact that the mean internal pressure is determined partly by the stack flows. In Section 5.3, the QT model is used to extrapolate the model-scale results to full-scale Reynolds numbers. 100 90 Stack 1
80 Stack 2
70 r (%)
Stack 3
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50 40 30 20 10 0 0
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Wind direction
Fig. 7. Spectra of external stack pressure and stack pressure difference for stack 4 with a wind speed of 5 m/s (four stacks, no orifice).
Fig. 9. Flow reversal percentage for stacks 1, 2, 3 and 4 as a function of wind direction (four stacks, four orifices).
B. Wang et al. / Building and Environment 46 (2011) 1393e1402
There are two possible reasons for the behavior, relating respectively to the measured stack outlet pressure, Pst , and the measured internal pressure, Pin .
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Fig. 10. Flow reversal percentage for stack 3 for different opening configurations and wind directions.
4. Instantaneous pressures and flow rates 4.1. Reversal and DCp =sDCp An important parameter in terms of flow reversal is the ratio between the mean of the instantaneous pressure difference across the stack, DCp , and the standard deviation, sDCp . This pressure parameter is equivalent to that used for describing the effect of wind turbulence on ventilation rates, as described in [6] and in Section 4.3.1 of [7]. The instantaneous pressure difference DCp is defined by
DCp ¼
Pst Pin 2 0:5rUref
(1)
where Pst is the stack pressure and Pin is the internal pressure. In previous work, [3,5], and [8], a well-defined relationship between r and DCp =sDCp was found. Fig. 11 shows r against DCp =sDCp for the tests carried out at TPU (divided into two-stack and four-stack results), compared with results from [8] for a single stack. There is clearly more scatter in the TPU results. In particular, for many of the downward flow results (50 < r < 100%) the value of DCp =sDCp is negative, whereas one would expect it to be positive. This behaviour was not apparent until after the TPU tests were completed, and so it was investigated at UNott.
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(i) The use of one pressure tapping at the stack outlet may not give an appropriate measure of the average static pressure at the outlet. This effect is thought unlikely to be significant, because it was briefly investigated [2] and found to be small. Moreover, one would expect the effect to be apparent in the earlier results. (ii) The internal pressure was measured using a tapping in the base plate (see Fig. 4 in Part 1). It is assumed that the (piezometric) pressure is uniform, so that the measured value can be used to evaluate the pressure differences across the openings. For certain opening configurations and wind directions, this assumption may not be valid, because of pressure changes due to internal air motion (see [9] for a recent discussion of this effect). The effect would be more apparent in the TPU tests than in the others, because the number of openings was larger (up to four times as many) and hence the internal velocities would be higher. Basically the internal pressure measurement may not be representative of the pressure at the base of the stack,P2 . It should be noted that under reversing flow conditions the pressure differences are small (e.g. < 0.3 Pa), so very small pressure changes due to internal air motion can be significant in the evaluation of DCp . To assess the importance of (ii), CFD simulation was carried out to investigate the flow field within the box. In order to model the upstream and downstream flows and the internal flow, it was necessary to use a two-dimensional simulation, due to limitations on the number of cells that could be used. Furthermore, only two openings were used in the box. These are clearly serious limitations (e.g. the effect of a two-dimensional slit will be greater than that of a circular opening), but it was felt that CFD simulation might still prove helpful and this proved to be the case. It revealed a downward component to the flow around the internal pressure tapping, which would tend to increase Pin . It also revealed that the downward component could be eliminated by placing a barrier around the pressure tapping. On this basis It was decided to shield the internal pressure tapping by means of a cylindrical barrier (a plastic cup with its base removed), as shown in Fig. 12. In addition, to minimise the possible effect of (i) above, the average pressure was measured at the stack outlet by connecting the transducer to the four available tappings, to give an average value. Fig. 13 shows results obtained using the cup at UNott. The configuration of four stacks and two orifices was tested over a range of wind directions. It can be seen that there is much less scatter in the results, compared to the TPU results (with the same opening configuration). From Figs. 13 and 11, one can see that to prevent flow reversal (r > 0%), DCp =sCp needs to be greater than 2. In other words, a negative DCp can not guarantee an upward flow, For example, with sDCp ¼ 0:1 , the requirement to maintain upward flow is sDCp < 0:2 (in the absence of buoyancy). This corresponds to the fifth method in Part 1, Section 1.2. It could be incorporated in Methods 1, 2 and 3 to make an approximate allowance for the effect of wind pressure fluctuations, as discussed in [6].
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4.2. Correlations between external pressures
10 0 -4
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1
2
Fig. 11. Variation of r with DCp =sDCp (“Ref” denotes [4]).
3
4
Correlations between the external wind pressure coefficients can be important, because they lead to significant errors in steady flow envelope models, particularly when mean pressure differences are small [6].
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Fig. 12. Model with the cup placed around the internal pressure tapping.
The correlation coefficient between Cp1 and Cp4, say, is given by
P
Cp1 Cp1 Cp4 Cp4 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 P 2 P Cp4 Cp4 Cp1 Cp1
(2)
and is identified using the notation P1&P4. Fig. 14 defines the numbering system for the openings in relation to wind direction. The length of the line between stacks (the separation distance) does not of course change with f , but the angle of the line relative to the freestream wind velocity does change. Furthermore, the separation distance for stacks 1 and 2 is greater than that for stacks 1 and 4. These properties of the model configuration presumably have some influence on the observed correlations, but it is not possible to anticipate what this influence is. The observed influence of wind speed (Reynolds number), wind direction and opening configurations on the correlation between selected stack pressures are described in the following.
Fig. 15 shows the correlations coefficients for the case of four stacks alone, f ¼ 0 , with increasing wind speed from 1 m/s to 5 m/s. The correlations show no strong influence of wind speed. Fig. 16 shows the effect of wind direction on selected correlations. As a result of symmetry, one would expect the correlations P1&P2 and P3&P4 to be the same, with f ¼ 0 . Similarly, for the case with f ¼ 90 , the correlations P1&P4 and P2&P3 should be equal. The results are in reasonable agreement with this expectation. The large difference between the correlations P1&P2 and P3&P4 with f ¼ 90 is not apparent in the correlations P1&P4 and P2&P3 with f ¼ 0 . This is presumably connected with the asymmetry of the model (it is rectangular in plan, rather than square). As with the mean pressures (see Part 1, Section 5), one might expect the correlations to be independent of the opening configuration. Unsteady envelope models rely on this assumption. Fig. 17 shows that increasing the number of orifices has some effect on the pressure correlations for f ¼ 90 . From symmetry, correlations P1&P4 and P2&P3 should be the same and this is apparent in the results. There is an obvious difference between the magnitudes of the correlations P1&P2 and P3&P4, presumably reflecting the fact
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Fig. 13. Observed variation of r with DCp =sDCp with (UNott) and without (TPU) cup.
Fig. 14. Definition of wind direction and positions of openings.
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0 Fig. 15. Variation of stack pressure correlations with Reb for 4 ¼ 0 (four stacks, no orifice).
that stacks 3 and 4 lie in a different flow regime (at this wind direction, stacks 1 and 2 are on the windward side of the roof). Fig. 18 shows the correlations corresponding to Table 1of Part 1 for the mean pressures with f ¼ 0 . The mean pressures Cp2 and Cp3 were unaffected by the opening configuration, whereas Cp1 and Cp4 were affected. The results in Fig. 18 are consistent with this, in that P2&P3 is not affected, whereas the remaining three correlations that involve P1 and/or P4 are affected. The results for P3&P4 and P1&P2 are also consistent with symmetry. As with the effect of opening configuration on the mean pressures, it is difficult to explain the observed behaviour. However, the veracity of the observations is supported by the fact that they are consistent with what is expected from symmetry. The results therefore reinforce the conclusion in Part 1, namely that external pressure distributions (mean and instantaneous) are best measured with some simulation of the expected openings in the model. 5. Comparisons with QT model The QT model is an unsteady envelope flow model. The basic model is described in [6] and references cited therein. It relies on a quasi-steady assumption about the flows, but takes account of inertia and compressibility. In truly steady flow the pressure difference across an opening is directly related to the flow rate by some function f
Dp ¼ f ðqÞ
(3)
S1234_90
S1234_O12_90
S1234_O1234_90
Opening configuration Fig. 17. Pressure correlation among stacks for different opening configurations, with 4 ¼ 90.
Dpi ðtÞ ¼ fi ðqi ðtÞÞ þ Ci
dqi dt
(4)
The coefficient C is determined by the geometry of the opening (essentially the volume) and the air density. The function f is assumed to be the same as for steady flow i.e. the quasi-steady assumption. Compressibility is accounted for in the mass conservation equation for the envelope, by including the rate of change of density of the enclosed air due to fluctuations of the internal pressure i.e.
V
dPin
gPin dt
¼ q1 þ q2 þ ...
(5)
Isentropic compression is assumed and g and Pin denote the ratio of specific heats and the time-averaged internal pressure. In this way the QT model takes the form of a set of simultaneous differential equations, one for each opening flow rate and one for the internal pressure. For given simultaneous records of the external wind pressures and given steady flow characteristics of the openings, the model calculates the instantaneous flow rate of each opening and the internal pressure. All previous comparisons between the model and experiment have been made for a single stack and a single opening. In the following, comparisons are shown for the case of six openings (four stacks and two orifices).
With unsteady flow an inertia term appears in the momentum equation for each opening. For opening i the equation is
0.8 0.7
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P1 & P4 P2 & P3
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45 wind direction
90
Fig. 16. Variation of stack pressure correlations with wind direction (four stacks, no orifice).
4S
4S 2O
4S 4O
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Fig. 18. Pressure correlations for increasing number of orifices, with 4 ¼ 0 and Uref ¼ 5 m/s.
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Fig. 19. Comparison between QT model and measurements of stack 1 flow rate (four stacks, orifices 1 and 2).
Fig. 21. Comparison between QT model and measurements of internal pressure (four stacks, orifices 1 and 2).
5.1. Flow rates and internal pressures
the lower wind speeds, but there are significant differences at the higher speeds. A likely explanation for this is that the relationship for Cz used in the QT model becomes increasingly less appropriate when the flow is reversing. However, experimental calibration errors can not be discounted, particularly at the higher wind speeds (and higher frequencies). For design purposes, the interest lies in using the QT model to determine reversal at full-scale Reynolds numbers. Calculations have been carried out for a 20 m high full-scale building, which is 100 times the model-scale. A range of wind speeds were used, from
The results given in Figs. 19, 20 and 21 are for 4 ¼ 0 and Uref ¼ 6.5 m/s. Fig. 19 shows the flow rate for stack 1, which has a measured reversal percentage of 35.5%. Fig. 20 shows the flow rate for stack 2, which has unidirectional upward flow (flow sign negative). Fig. 21 shows the results for the internal pressure. The closest agreement is seen in Fig. 20 i.e. for the flow rate of stack 2. The agreement for stack 1 is not as good, but this is not surprising, because the flow rates are much smaller and reversal is present.
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From the calculated flow rates, it is a simple matter to evaluate the reversal percentage. Fig. 22 shows the comparison between the QT model (lower plot) and measurements (upper plot) over a range of wind directions. On the basis of Fig. 22, the QT model calculates the presence of reversal for all four stacks to within about 10 percentage points, over the range of wind directions.
50 40 30
5.3. Flow reversal and Reynolds number
20 10
In Section 3 of Part 1, it was noted that the reversal percentage showed a dependence on building Reynolds number. Fig. 23 compares the calculated dependence with the measurements, for stacks 1 and 4. The QT results exhibit the correct trend and range at
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Fig. 20. Comparison between QT model and measurements of stack 2 flow rate (four stacks, orifices 1 and 2).
Fig. 22. Comparison between QT model and measurements of reversal percentage for four stacks. Measurements are given in upper graph, calculations in lower graph (four stacks, orifices 1 and 2).
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Fig. 25. Comparison between tests and QT model (stack 1, orifice 2; four stacks, orifices 1 and 2).
Fig. 23. Effect of Reynolds number on reversal percentage; comparison between measurements and QT model (stacks 3 and 4, orifices 1 and 2).
Uref ¼ 1.5e6.5 m/s, with 4 ¼ 0. The equation used for the full-scale discharge coefficients of the stacks is
1 L ¼ C 0:25 þ D CZZ Rest d
(6)
corresponding to turbulent flow in a long duct (with C ¼ 0.316 and D ¼ 6). For the orifices, the discharge coefficient was taken as 0.68. Fig. 24 shows both model-scale and full-scale calculations in logarithmic form. It shows a trend for r to increase increasing with increasing Reynolds number. The wind tunnel technique gives a reversal percentage of about 35% compared to about 65% for fullscale. Whether this error in the wind tunnel technique is significant for design is open to question. 5.4. Flow reversal and DCp =sDCp Fig. 25 shows the relationship between reversal percentage and pressure parameter DCp =sDCp as obtained from the QT model and measurements. The results cover a range of opening configurations, but with the improved pressure measurements (Section 4.1). It can be seen that there is reasonable agreement. For the purpose of comparison, Fig. 25 also shows the QT results for the single stack and single orifice model, as given in [8]. 100.0 90.0 80.0 70.0 60.0 r (%)
1401
50.0 40.0 30.0
S1 QT
20.0
S4 QT S1 QT High Re
10.0
S4 QT High Re
0.0 4
4.5
5
5.5
6
6.5
7
log(Reb)
Fig. 24. Calculated variation of r with log(Reb) for model-scale and full-scale (stacks 3 and 4, orifices 1 and 2).
In summary, it is reasonable to say that the QT model is capable of calculating instantaneous envelope flow rates to an accuracy that is probably adequate for design purposes. In particular, the model offers a means of investigating flow reversal that is not possible with conventional steady models. 6. Conclusions Due to the nature of unsteady effects of wind on ventilation stacks, both laboratory measurements and theoretical modeling are quite challenging. The hot-wire technique developed at NottinghamUniversity was designed to measure the instantaneous flow rate in stacks at modelscale. The calibration of the device has been improved and its limitations at high frequency have been quantified. Further investigations have been carried out from which the following conclusions have been drawn. Special care has to be taken with the rigidity of the model when measuring instantaneous flow rates and pressures. A small and rapid volume change can significantly affect the mass flow balance. With multiple openings, the internal velocities can lead to pressure changes that can be significant at the very low pressure differences associated with reversing flow. Shielding the internal pressure tapping seems to resolve this problem, although the best way of avoiding it is to use individual internal pressure tappings for each opening. The experimental tests are important in that they have been carried out with multiple stacks and orifices (up to four of each). The following conclusions can be drawn. The results confirm the importance of the external pressure distribution on the occurrence of flow reversal. In particular, for all of the opening configurations tested, flow reversal was observed for at least one wind direction. The reversal percentage measured in the model is dependent on building Reynolds number. Calculations with the QT model indicate that r would be about twice as large at full-scale. This is clearly a disadvantage of the direct measurement technique. The advantages of the direct measurement of flow reversal in a wind tunnel model are that turbulence effects are present in the results and that detailed pressure measurements are not required. Whether these advantages outweigh the Reynolds number effect is open to question. The strong relationship between r and the pressure parameter DCp =sDCp has been confirmed for multiple stacks. The correlation coefficients between the external wind pressures are not always independent of opening configuration. This is consistent with the results for the mean pressures in Part 1.
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The QT model has been shown to perform reasonably well for multiple stacks, for instantaneous quantities as well as mean values. There is evidence that r can be calculated to within about 10 percentage points. Acknowledgements The work described has been funded by EPSRC (UK) and by the COE Program (Japan). This support is gratefully acknowledged. References [1] Wang B, Etheridge DW, Ohba M. Wind tunnel investigation of natural ventilation through multiple stacks. Part 1: mean values. Submitted to Building and Environment; 2011.
[2] Chiu YH, Etheridge DW. Experimental technique to determine unsteady flow in natural ventilation stacks at model scale. Journal of Wind Engineering & Industrial Aerodynamics 2005;92:291e313. [3] Costola D, Etheridge DW. Unsteady natural ventilation at model scale e Flow reversal and discharge coefficients of a short stack and an orifice. Building and Environment 2008;43:1491e506. [4] Wang B , Unsteady wind effects on natural ventilation, PhD thesis, University of Nottingham, Nottingham, 2010, UK, July 2010. [5] Claesson L, Etheridge DW. Unsteady flow reversal in a natural ventilation stack model scale tests. International Journal of Ventilation 2005;4:25e36. [6] Etheridge DW. Unsteady flow effects due to fluctuating wind pressures in natural ventilation design-mean flow rates. Building and Environment 2000;35:111e33. [7] Etheridge DW, Sandberg M. Building ventilation e Theory and measurement. Chichester, UK: Wiley; 1996. [8] 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. 191e208. [9] Karava P, Stathopoulos T, Athienitis A. Impact of internal pressure coefficients on wind-driven ventilation analysis. International Journal of Ventilation 2006;5 (1):53e66.
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 2: Instantaneous 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. Part 1 of the paper [1] concentrated on the characteristics of the mean flows. Part 2 concentrates on the instantaneous characteristics of the flows, both in terms of the experimental measurements and in terms of an unsteady envelope flow model. Further investigations into the experimental measurement techniques are described. These relate to improving the hot-wire calibration, to the instantaneous flow balance with multiple stacks (and the importance of model rigidity) and to the increased importance of internal air motion with the higher flow rates associated with multiple openings. The experimental measurements of stack reversal percentage are examined in some detail, regarding the effects of wind direction and Reynolds number and how the reversal percentage relates to a simple pressure parameter. Following on from Part 1, the effect of opening configuration on the instantaneous properties of the external wind pressures is investigated by examining their correlations. As with the mean values it is found that the correlations are not entirely independent of opening configuration. The experimental data is used to assess the performance of an unsteady envelope flow model, both in terms of calculating instantaneous values and mean values such as reversal percentage. The model is shown to perform well with multiple stacks. It is then used to estimate the effect of Reynolds number on the reversal percentage at model-scale and full-scale. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Wind tunnel Hot-wire technique Natural ventilation Stacks Reynolds number Unsteady flow
1. Introduction Part 1 [1] of the companion paper dealt with mean flow properties such as mean pressure coefficient and mean flow rate. As mentioned in Part 1, the special feature of the experimental technique is that measurements of the instantaneous flow and pressure in multiple stacks can be made simultaneously. In Part 2, the emphasis is on instantaneous values. The objectives are: (i) to describe further work that has been done on the experimental technique, namely improving the hot-wire calibration technique (Section 2.1), investigating the instantaneous flow balance (Section 2.2) and improving the measurement of internal pressure (Section 4.1). (ii) to present the observed effects of Reynolds number, wind direction and stack geometry on instantaneous flow properties (Sections 3 and 4). * Corresponding author. Tel.: þ44 115 951 3171; fax: þ44 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.2011.01.011
(iii) to compare the instantaneous measurements with a theoretical unsteady model (Section 5.l). Again the underlying philosophy is to use the wind tunnel results to assess the theoretical model. If the model performs well at low Reynolds numbers, there is reason to be optimistic about its performance at full-scale. 2. Experimental techniques 2.1. Unsteady calibration of hot-wires The calibration procedure for the hot-wires has been described in earlier papers [2,3],. Basically each wire is calibrated in terms of volume flow rate rather than velocity. It is recognized that the relation between the local velocity and the volume flow rate will depend on the instantaneous velocity profile in the stack, due to unsteady effects, and for this reason each wire is calibrated with steady and unsteady flow. Both the steady and unsteady calibrations are carried out in-situ, using different devices: a fan with a flow meter for steady calibration; a specially designed piston
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calibrator for unsteady calibration. With the original piston calibrator, the rotational speed was assumed to be constant and it was determined by measuring the time for one complete cycle. Knowing the rotational speed, the velocity of the piston can be calculated from the known geometry (bore, stroke and length of connecting rod). There was some evidence that the assumption of constant speed was introducing avoidable errors into the calibration. Thus an improved version of the calibrator was developed, to measure the instantaneous rotational speed of the motor, rather than the overall value. For this purpose a disc was attached to the drive shaft, of the original calibrator, as shown in Fig. 1. The disc contains one hundred laser-cut slots, through which an LED sensor generates a constant voltage pulse each time a slot passes. In terms of data acquisition, the sampling frequency is set high enough (5000 Hz) to detect the passage of each slot to within 0.2 ms. Thereby, one can evaluate 100 instantaneous rotational speeds per cycle, and hence the instantaneous flow rate of the piston. The frequencies (and corresponding velocity ranges) obtained were 1.39 Hz (0.55 m/s), 2.11 Hz (0.85 m/s), 2.95 Hz (1.2 m/s) and 4.86 Hz (2.0 m/s). Fig. 2 shows the unsteady calibration curves obtained for one wire at two of the four frequencies i.e. 1.39 and 2.11 Hz. The different calibrations for the acceleration and deceleration phases can be seen and these lead to calibration errors. The differences are larger at the higher frequencies, but they are not representative of the calibration errors that occur in the measurements. A frequency of 4.86 Hz corresponds to 9.72 zero crossings per second. The flow produced by the piston is a nominally sinusoidal oscillation (zero mean). In the model tests, this corresponds to a reversal percentage of 50%. Fig. 3 shows a stack velocity record with r ¼ 53.9% obtained at a high wind speed of 5 m/s, with consequently high frequencies. The number of zero crossings is 175 over the measurement period i.e. 5.15 per second. On this basis, a calibration frequency of 2.67 Hz would be representative. In fact the situation is probably better than this, because many of the zero crossings are probably associated with small-scale turbulence. On this basis the calibration frequency of 1.39 Hz is probably more appropriate (at lower wind
Fig. 2. Calibration results at two frequencies (a) 1.39 Hz and (b) 2.11 Hz.
speeds, this is more likely). The final calibration was in fact obtained by combining the unsteady calibration for 1.39 Hz and the steady calibration, in the same way as in [2] and [3]. 2.2. Instantaneous flow balance In Part 1, the mean flow balance was examined for the four-stack case with no orifices. In the following the instantaneous flow balance for the four-stack case is considered. It is of course to be
Fig. 1. Original piston calibrator fitted with slotted disc.
B. Wang et al. / Building and Environment 46 (2011) 1393e1402 100
0.6
90
power, v eloc ity sum
0.8
velocit y m/s
0.4 0.2 0.0 -0.2
1395
80 70 S1234_U5
60
S1234_U2
50 40 30
-0.4
20 -0.6
10
-0.8
0 0
5
10
15
20
25
30
0
35
10
20
t secs
30
40
50
60
frequency (Hz)
Fig. 3. Velocity record for a stack (velocity 1) with nominally oscillating flow (zero mean) (stacks 1 and 4, orifices 3 and 4, wind direction 90 ).
Fig. 5. Spectral analysis of velocity sum with wind speeds of 5 m/s and 2 m/s (four stacks, no orifice).
expected that that the instantaneous imbalance will at times be greater than the mean imbalance. However, tests on an earlier wind tunnel model [4] indicated that vibration of the walls of the model could lead to significant changes in the volume of the model. Such changes would lead to spurious contributions to the instantaneous flow rates. As a result, the four-stack model was made more rigid. First, the wall thickness was increased from 5 to 8 mm. Second, and more important, the base plate was rigidly screwed to the side walls. In the earlier model the base plate was taped to the side walls. Fig. 4 displays instantaneous velocities of the four stacks over a period of 6 s, for a high wind speed of 5 m/s and a wind direction equal to zero. The flows through stacks 1 and 4 were inward at all times and outward for stacks 2 and 3. The important point to note is that the instantaneous sum of the velocities has a discrete frequency component. This can also be clearly seen in the power spectrum of the velocity sum, as shown in Fig. 5, and in the spectra of the stack velocities (Fig. 6). Figs. 5 and 6 show results for a wind speed Uref ¼ 5 m/s, but Fig. 5 also shows results for Uref ¼ 2 m/s. (NB The power spectra were generated using the Fourier Analysis tool in MS Excel and are not normalized. The aim was simply to identify any peaks in the spectra.) The fact that a frequency of around 22 Hz is clearly apparent in both results shown in Fig. 5 implies that the phenomenon is independent of wind speed. In which case, a likely explanation is that a resonant frequency of the box structure is excited. However,
at the low wind speed, there is also evidence of resonance around 11 Hz. Fig. 7 shows the spectra for the pressure difference across stack 4 (ps4 e pin) and the external stack pressure (ps4 e pref). It can be seen that the resonance is evident in the former, but not the latter. Although not shown here, the resonance is clearly evident in the internal pressure (pin e pref). This indicates that the hot-wire results are due to a flow phenomenon rather than, say, mechanical vibration of the wire. Furthermore, the fact that a frequency of around 22 Hz is clearly apparent in both results shown in Fig. 5 implies that the phenomenon is to some extent independent of wind speed. In which case, a likely explanation is that a resonant frequency of the box structure is excited. However, this may not be the full explanation, because at the low wind speed, there is also evidence of resonance around 11 Hz. Another reason for caution about this explanation is that resonant peaks were observed in the orifice external pressures (but not in the stack pressures), which do show a dependence on wind speed. This could conceivably be due to vibration of the orifice pressure tubing, which passed through the model. In summary, the above results indicate that when recording instantaneous pressures, care must be taken to minimise volume changes due to vibration of the model walls. The deflections of the walls may be very small, but the associated volume changes can be significant. Despite the measures taken, the effect was not entirely eliminated, and this could be responsible for some of the differences observed in the comparisons with the theoretical model in Section 5.
2.5 velocity1 velocity2 velocity3 velocity4 velocity sum
2.0 1.5
v eloc ity (m/ s )
1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 0
1
2
3
4
5
t (s)
Fig. 4. Instantaneous velocities of four-stack tests and their sum (four stacks, no orifice, Uref ¼ 5 m/s).
6
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80
Stack 2 70
Stack 3 Stack 4
r (%)
60 50 40 30 20 10 0 0
45
90
135
180
225
270
315
wind direction
Fig. 6. Spectral analysis of velocities of stack 1 and 2 with a wind speed of 5 m/s (four stacks, no orifice).
3. Flow reversal A simple parameter is used to characterize flow reversal of the stacks i.e. the percentage of time that the flow is reversed, r. The results are presented below in the form that might be appropriate when the technique is used as part of a building design exercise i.e. as plots of r against wind direction, 4. The comments are based on the assumption that, when orifices are present, upward flow is to be maintained in the stacks. Results for several different stack and orifice configurations are presented. Where the opening configuration has symmetry, it has been assumed that symmetry with wind direction applies, so some results are repeated. 3.1. Effect of wind direction, opening distribution Fig. 8 shows the results for four stacks and two orifices (orifices 1 and 2) for the complete range of wind directions in steps of 45 . This is the sort of information that is of potential use for design. It can be seen that flow reversal occurs in at least one of the stacks for all wind directions. This is in contrast to the single stack investigated in [5], where flow reversal scarcely occurred. The results in Fig. 8 can be compared with those in Fig. 9, which are for four stacks and four orifices. The effective area of an orifice (CdA) is about twice that of a stack and one would expect to see some effect on the reversal percentages. Despite this, it can be seen that the effects are quite small. This presumably reflects the fact that the effect also depends on the external pressure at the orifice, relative to the stack pressures.
Fig. 8. Flow reversal percentage for stacks 1, 2, 3 and 4, as a function of wind direction (four stacks, orifices 1 and 2).
Fig. 10 shows the effect of the changes to the opening configuration for just one of the stacks (stack 3). The configurations are 2 stacks and 2 openings, 4 stacks and 2 openings and 4 stacks and 4 openings. Also shown is a case where the boxes enclosing the stacks were removed. This shows some reduction in reversal percentages. In summary, the above results illustrate the importance of the external pressure distribution (wind direction) on flow reversal. It is worth noting that, for all the opening configurations tested, significant flow reversal occurred for at least one wind direction. The presence of buoyancy could of course change this situation. Nevertheless, it is clear that wind effects need to be considered in the design of buildings with natural ventilation stacks, particularly for summer cooling when temperature differences are likely to be relatively small. 3.2. Effect of Reynolds number Ideally the reversal percentage would be independent of building Reynolds number, but some effects are expected, due to the facts that the stacks are long openings and the external velocity depends to some extent on Reynolds number. Fig. 9 in Part 1 shows examples of the variation. The primary cause of this variation is the fact that the mean internal pressure is determined partly by the stack flows. In Section 5.3, the QT model is used to extrapolate the model-scale results to full-scale Reynolds numbers. 100 90 Stack 1
80 Stack 2
70 r (%)
Stack 3
60
Stack 4
50 40 30 20 10 0 0
90
180
270
Wind direction
Fig. 7. Spectra of external stack pressure and stack pressure difference for stack 4 with a wind speed of 5 m/s (four stacks, no orifice).
Fig. 9. Flow reversal percentage for stacks 1, 2, 3 and 4 as a function of wind direction (four stacks, four orifices).
B. Wang et al. / Building and Environment 46 (2011) 1393e1402
There are two possible reasons for the behavior, relating respectively to the measured stack outlet pressure, Pst , and the measured internal pressure, Pin .
100
Rev ersal perc entage (%)
90 80
S34_O12 S34_O12 no box
70
S1234_O12 S1234_O1234
60 50 40 30 20 10 0
0
45
90
135
180
225
270
315
Wind direc tion
Fig. 10. Flow reversal percentage for stack 3 for different opening configurations and wind directions.
4. Instantaneous pressures and flow rates 4.1. Reversal and DCp =sDCp An important parameter in terms of flow reversal is the ratio between the mean of the instantaneous pressure difference across the stack, DCp , and the standard deviation, sDCp . This pressure parameter is equivalent to that used for describing the effect of wind turbulence on ventilation rates, as described in [6] and in Section 4.3.1 of [7]. The instantaneous pressure difference DCp is defined by
DCp ¼
Pst Pin 2 0:5rUref
(1)
where Pst is the stack pressure and Pin is the internal pressure. In previous work, [3,5], and [8], a well-defined relationship between r and DCp =sDCp was found. Fig. 11 shows r against DCp =sDCp for the tests carried out at TPU (divided into two-stack and four-stack results), compared with results from [8] for a single stack. There is clearly more scatter in the TPU results. In particular, for many of the downward flow results (50 < r < 100%) the value of DCp =sDCp is negative, whereas one would expect it to be positive. This behaviour was not apparent until after the TPU tests were completed, and so it was investigated at UNott.
100 90 80 70 r (%)
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Ref
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Two-Stack results
40
Four-Stack results
30
(i) The use of one pressure tapping at the stack outlet may not give an appropriate measure of the average static pressure at the outlet. This effect is thought unlikely to be significant, because it was briefly investigated [2] and found to be small. Moreover, one would expect the effect to be apparent in the earlier results. (ii) The internal pressure was measured using a tapping in the base plate (see Fig. 4 in Part 1). It is assumed that the (piezometric) pressure is uniform, so that the measured value can be used to evaluate the pressure differences across the openings. For certain opening configurations and wind directions, this assumption may not be valid, because of pressure changes due to internal air motion (see [9] for a recent discussion of this effect). The effect would be more apparent in the TPU tests than in the others, because the number of openings was larger (up to four times as many) and hence the internal velocities would be higher. Basically the internal pressure measurement may not be representative of the pressure at the base of the stack,P2 . It should be noted that under reversing flow conditions the pressure differences are small (e.g. < 0.3 Pa), so very small pressure changes due to internal air motion can be significant in the evaluation of DCp . To assess the importance of (ii), CFD simulation was carried out to investigate the flow field within the box. In order to model the upstream and downstream flows and the internal flow, it was necessary to use a two-dimensional simulation, due to limitations on the number of cells that could be used. Furthermore, only two openings were used in the box. These are clearly serious limitations (e.g. the effect of a two-dimensional slit will be greater than that of a circular opening), but it was felt that CFD simulation might still prove helpful and this proved to be the case. It revealed a downward component to the flow around the internal pressure tapping, which would tend to increase Pin . It also revealed that the downward component could be eliminated by placing a barrier around the pressure tapping. On this basis It was decided to shield the internal pressure tapping by means of a cylindrical barrier (a plastic cup with its base removed), as shown in Fig. 12. In addition, to minimise the possible effect of (i) above, the average pressure was measured at the stack outlet by connecting the transducer to the four available tappings, to give an average value. Fig. 13 shows results obtained using the cup at UNott. The configuration of four stacks and two orifices was tested over a range of wind directions. It can be seen that there is much less scatter in the results, compared to the TPU results (with the same opening configuration). From Figs. 13 and 11, one can see that to prevent flow reversal (r > 0%), DCp =sCp needs to be greater than 2. In other words, a negative DCp can not guarantee an upward flow, For example, with sDCp ¼ 0:1 , the requirement to maintain upward flow is sDCp < 0:2 (in the absence of buoyancy). This corresponds to the fifth method in Part 1, Section 1.2. It could be incorporated in Methods 1, 2 and 3 to make an approximate allowance for the effect of wind pressure fluctuations, as discussed in [6].
20
4.2. Correlations between external pressures
10 0 -4
-3
-2
-1
0 DCp/ SD Cp
1
2
Fig. 11. Variation of r with DCp =sDCp (“Ref” denotes [4]).
3
4
Correlations between the external wind pressure coefficients can be important, because they lead to significant errors in steady flow envelope models, particularly when mean pressure differences are small [6].
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Fig. 12. Model with the cup placed around the internal pressure tapping.
The correlation coefficient between Cp1 and Cp4, say, is given by
P
Cp1 Cp1 Cp4 Cp4 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 P 2 P Cp4 Cp4 Cp1 Cp1
(2)
and is identified using the notation P1&P4. Fig. 14 defines the numbering system for the openings in relation to wind direction. The length of the line between stacks (the separation distance) does not of course change with f , but the angle of the line relative to the freestream wind velocity does change. Furthermore, the separation distance for stacks 1 and 2 is greater than that for stacks 1 and 4. These properties of the model configuration presumably have some influence on the observed correlations, but it is not possible to anticipate what this influence is. The observed influence of wind speed (Reynolds number), wind direction and opening configurations on the correlation between selected stack pressures are described in the following.
Fig. 15 shows the correlations coefficients for the case of four stacks alone, f ¼ 0 , with increasing wind speed from 1 m/s to 5 m/s. The correlations show no strong influence of wind speed. Fig. 16 shows the effect of wind direction on selected correlations. As a result of symmetry, one would expect the correlations P1&P2 and P3&P4 to be the same, with f ¼ 0 . Similarly, for the case with f ¼ 90 , the correlations P1&P4 and P2&P3 should be equal. The results are in reasonable agreement with this expectation. The large difference between the correlations P1&P2 and P3&P4 with f ¼ 90 is not apparent in the correlations P1&P4 and P2&P3 with f ¼ 0 . This is presumably connected with the asymmetry of the model (it is rectangular in plan, rather than square). As with the mean pressures (see Part 1, Section 5), one might expect the correlations to be independent of the opening configuration. Unsteady envelope models rely on this assumption. Fig. 17 shows that increasing the number of orifices has some effect on the pressure correlations for f ¼ 90 . From symmetry, correlations P1&P4 and P2&P3 should be the same and this is apparent in the results. There is an obvious difference between the magnitudes of the correlations P1&P2 and P3&P4, presumably reflecting the fact
120
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60 NOTT TPU
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20
0 -2.0
-1.5
-1.0
-0.5
0.0
0.5
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2.0
DCp/ SDCp
Fig. 13. Observed variation of r with DCp =sDCp with (UNott) and without (TPU) cup.
Fig. 14. Definition of wind direction and positions of openings.
B. Wang et al. / Building and Environment 46 (2011) 1393e1402 0.8
0.8
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0.2
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0.2
0 10,000
20,000
30,000
40,000 Reb
50,000
60,000
P2 & P3
P3 & P4
0.1
70,000
0 Fig. 15. Variation of stack pressure correlations with Reb for 4 ¼ 0 (four stacks, no orifice).
that stacks 3 and 4 lie in a different flow regime (at this wind direction, stacks 1 and 2 are on the windward side of the roof). Fig. 18 shows the correlations corresponding to Table 1of Part 1 for the mean pressures with f ¼ 0 . The mean pressures Cp2 and Cp3 were unaffected by the opening configuration, whereas Cp1 and Cp4 were affected. The results in Fig. 18 are consistent with this, in that P2&P3 is not affected, whereas the remaining three correlations that involve P1 and/or P4 are affected. The results for P3&P4 and P1&P2 are also consistent with symmetry. As with the effect of opening configuration on the mean pressures, it is difficult to explain the observed behaviour. However, the veracity of the observations is supported by the fact that they are consistent with what is expected from symmetry. The results therefore reinforce the conclusion in Part 1, namely that external pressure distributions (mean and instantaneous) are best measured with some simulation of the expected openings in the model. 5. Comparisons with QT model The QT model is an unsteady envelope flow model. The basic model is described in [6] and references cited therein. It relies on a quasi-steady assumption about the flows, but takes account of inertia and compressibility. In truly steady flow the pressure difference across an opening is directly related to the flow rate by some function f
Dp ¼ f ðqÞ
(3)
S1234_90
S1234_O12_90
S1234_O1234_90
Opening configuration Fig. 17. Pressure correlation among stacks for different opening configurations, with 4 ¼ 90.
Dpi ðtÞ ¼ fi ðqi ðtÞÞ þ Ci
dqi dt
(4)
The coefficient C is determined by the geometry of the opening (essentially the volume) and the air density. The function f is assumed to be the same as for steady flow i.e. the quasi-steady assumption. Compressibility is accounted for in the mass conservation equation for the envelope, by including the rate of change of density of the enclosed air due to fluctuations of the internal pressure i.e.
V
dPin
gPin dt
¼ q1 þ q2 þ ...
(5)
Isentropic compression is assumed and g and Pin denote the ratio of specific heats and the time-averaged internal pressure. In this way the QT model takes the form of a set of simultaneous differential equations, one for each opening flow rate and one for the internal pressure. For given simultaneous records of the external wind pressures and given steady flow characteristics of the openings, the model calculates the instantaneous flow rate of each opening and the internal pressure. All previous comparisons between the model and experiment have been made for a single stack and a single opening. In the following, comparisons are shown for the case of six openings (four stacks and two orifices).
With unsteady flow an inertia term appears in the momentum equation for each opening. For opening i the equation is
0.8 0.7
0.8 0.6
0.7 0.5
Correl P
0.5
Correl P
0.6
P1 & P4 P2 & P3 P1 & P2 P3 & P4
0.4 0.3
0.4 0.3
P1 & P4 P2 & P3
0.2
0.2
P1 & P2 P3 & P4
0.1
0.1 0
0
0
45 wind direction
90
Fig. 16. Variation of stack pressure correlations with wind direction (four stacks, no orifice).
4S
4S 2O
4S 4O
opening configuration
Fig. 18. Pressure correlations for increasing number of orifices, with 4 ¼ 0 and Uref ¼ 5 m/s.
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-2.0 -2.5
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-3.0 -3.5 pI (Pa)
q (m3/ s)
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10 t (s)
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12
13
14
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t (s)
Fig. 19. Comparison between QT model and measurements of stack 1 flow rate (four stacks, orifices 1 and 2).
Fig. 21. Comparison between QT model and measurements of internal pressure (four stacks, orifices 1 and 2).
5.1. Flow rates and internal pressures
the lower wind speeds, but there are significant differences at the higher speeds. A likely explanation for this is that the relationship for Cz used in the QT model becomes increasingly less appropriate when the flow is reversing. However, experimental calibration errors can not be discounted, particularly at the higher wind speeds (and higher frequencies). For design purposes, the interest lies in using the QT model to determine reversal at full-scale Reynolds numbers. Calculations have been carried out for a 20 m high full-scale building, which is 100 times the model-scale. A range of wind speeds were used, from
The results given in Figs. 19, 20 and 21 are for 4 ¼ 0 and Uref ¼ 6.5 m/s. Fig. 19 shows the flow rate for stack 1, which has a measured reversal percentage of 35.5%. Fig. 20 shows the flow rate for stack 2, which has unidirectional upward flow (flow sign negative). Fig. 21 shows the results for the internal pressure. The closest agreement is seen in Fig. 20 i.e. for the flow rate of stack 2. The agreement for stack 1 is not as good, but this is not surprising, because the flow rates are much smaller and reversal is present.
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5.2. Flow reversal and wind direction
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From the calculated flow rates, it is a simple matter to evaluate the reversal percentage. Fig. 22 shows the comparison between the QT model (lower plot) and measurements (upper plot) over a range of wind directions. On the basis of Fig. 22, the QT model calculates the presence of reversal for all four stacks to within about 10 percentage points, over the range of wind directions.
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5.3. Flow reversal and Reynolds number
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In Section 3 of Part 1, it was noted that the reversal percentage showed a dependence on building Reynolds number. Fig. 23 compares the calculated dependence with the measurements, for stacks 1 and 4. The QT results exhibit the correct trend and range at
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Fig. 20. Comparison between QT model and measurements of stack 2 flow rate (four stacks, orifices 1 and 2).
Fig. 22. Comparison between QT model and measurements of reversal percentage for four stacks. Measurements are given in upper graph, calculations in lower graph (four stacks, orifices 1 and 2).
B. Wang et al. / Building and Environment 46 (2011) 1393e1402 100
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Fig. 25. Comparison between tests and QT model (stack 1, orifice 2; four stacks, orifices 1 and 2).
Fig. 23. Effect of Reynolds number on reversal percentage; comparison between measurements and QT model (stacks 3 and 4, orifices 1 and 2).
Uref ¼ 1.5e6.5 m/s, with 4 ¼ 0. The equation used for the full-scale discharge coefficients of the stacks is
1 L ¼ C 0:25 þ D CZZ Rest d
(6)
corresponding to turbulent flow in a long duct (with C ¼ 0.316 and D ¼ 6). For the orifices, the discharge coefficient was taken as 0.68. Fig. 24 shows both model-scale and full-scale calculations in logarithmic form. It shows a trend for r to increase increasing with increasing Reynolds number. The wind tunnel technique gives a reversal percentage of about 35% compared to about 65% for fullscale. Whether this error in the wind tunnel technique is significant for design is open to question. 5.4. Flow reversal and DCp =sDCp Fig. 25 shows the relationship between reversal percentage and pressure parameter DCp =sDCp as obtained from the QT model and measurements. The results cover a range of opening configurations, but with the improved pressure measurements (Section 4.1). It can be seen that there is reasonable agreement. For the purpose of comparison, Fig. 25 also shows the QT results for the single stack and single orifice model, as given in [8]. 100.0 90.0 80.0 70.0 60.0 r (%)
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Fig. 24. Calculated variation of r with log(Reb) for model-scale and full-scale (stacks 3 and 4, orifices 1 and 2).
In summary, it is reasonable to say that the QT model is capable of calculating instantaneous envelope flow rates to an accuracy that is probably adequate for design purposes. In particular, the model offers a means of investigating flow reversal that is not possible with conventional steady models. 6. Conclusions Due to the nature of unsteady effects of wind on ventilation stacks, both laboratory measurements and theoretical modeling are quite challenging. The hot-wire technique developed at NottinghamUniversity was designed to measure the instantaneous flow rate in stacks at modelscale. The calibration of the device has been improved and its limitations at high frequency have been quantified. Further investigations have been carried out from which the following conclusions have been drawn. Special care has to be taken with the rigidity of the model when measuring instantaneous flow rates and pressures. A small and rapid volume change can significantly affect the mass flow balance. With multiple openings, the internal velocities can lead to pressure changes that can be significant at the very low pressure differences associated with reversing flow. Shielding the internal pressure tapping seems to resolve this problem, although the best way of avoiding it is to use individual internal pressure tappings for each opening. The experimental tests are important in that they have been carried out with multiple stacks and orifices (up to four of each). The following conclusions can be drawn. The results confirm the importance of the external pressure distribution on the occurrence of flow reversal. In particular, for all of the opening configurations tested, flow reversal was observed for at least one wind direction. The reversal percentage measured in the model is dependent on building Reynolds number. Calculations with the QT model indicate that r would be about twice as large at full-scale. This is clearly a disadvantage of the direct measurement technique. The advantages of the direct measurement of flow reversal in a wind tunnel model are that turbulence effects are present in the results and that detailed pressure measurements are not required. Whether these advantages outweigh the Reynolds number effect is open to question. The strong relationship between r and the pressure parameter DCp =sDCp has been confirmed for multiple stacks. The correlation coefficients between the external wind pressures are not always independent of opening configuration. This is consistent with the results for the mean pressures in Part 1.
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The QT model has been shown to perform reasonably well for multiple stacks, for instantaneous quantities as well as mean values. There is evidence that r can be calculated to within about 10 percentage points. Acknowledgements The work described has been funded by EPSRC (UK) and by the COE Program (Japan). This support is gratefully acknowledged. References [1] Wang B, Etheridge DW, Ohba M. Wind tunnel investigation of natural ventilation through multiple stacks. Part 1: mean values. Submitted to Building and Environment; 2011.
[2] Chiu YH, Etheridge DW. Experimental technique to determine unsteady flow in natural ventilation stacks at model scale. Journal of Wind Engineering & Industrial Aerodynamics 2005;92:291e313. [3] Costola D, Etheridge DW. Unsteady natural ventilation at model scale e Flow reversal and discharge coefficients of a short stack and an orifice. Building and Environment 2008;43:1491e506. [4] Wang B , Unsteady wind effects on natural ventilation, PhD thesis, University of Nottingham, Nottingham, 2010, UK, July 2010. [5] Claesson L, Etheridge DW. Unsteady flow reversal in a natural ventilation stack model scale tests. International Journal of Ventilation 2005;4:25e36. [6] Etheridge DW. Unsteady flow effects due to fluctuating wind pressures in natural ventilation design-mean flow rates. Building and Environment 2000;35:111e33. [7] Etheridge DW, Sandberg M. Building ventilation e Theory and measurement. Chichester, UK: Wiley; 1996. [8] 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. 191e208. [9] Karava P, Stathopoulos T, Athienitis A. Impact of internal pressure coefficients on wind-driven ventilation analysis. International Journal of Ventilation 2006;5 (1):53e66.