- Email: [email protected]
Interaction between the mixing and displacement modes in a naturally ventilated enclosure
ARTICLE IN PRESS
Building and Environment 41 (2006) 1755–1761 www.elsevier.com/locate/buildenv
Interaction between the mixing and displacement modes in a naturally ventilated enclosure Vitaly Haslavskya, Josef Tannya,, Meir Teitelb a
Institute of Soil, Water & Environmental Sciences, Agricultural Research Organization, The Volcani Center, P.O. Box 6, Bet Dagan 50250, Israel b Institute of Agricultural Engineering, Agricultural Research Organization, The Volcani Center, P.O. Box 6, Bet Dagan 50250, Israel Received 10 March 2005; received in revised form 17 June 2005; accepted 7 July 2005
Abstract Experiments are carried out to study for the first time interactive phenomena in buoyancy-induced natural ventilation in a fullscale enclosure with upper and lower openings on one of the sidewalls. The interaction between the mixing and the displacement ventilation modes is revealed by opening the lower vent to different heights while the upper vent is kept fully open. Both the transient process and steady state interaction are explored. Measurements include temperature differences between inside and outside and air velocity through the upper opening. The level of the neutral plane at the upper vent, defined here as the plane separating between inflow and outflow, decreases with R , the ratio between the opening heights (and areas) of the lower and upper vents. Experiments show that when 0oR o0:27 the mixing and displacement modes interact through a new combined ventilation mode. For 0:53oR p1, the displacement mode dominates whereas in the intermediate range, 0:27pR p0:53, either the combined or the pure displacement mode takes place. The experiments are in qualitative agreement with a previous theoretical model. r 2005 Elsevier Ltd. All rights reserved. Keywords: Buoyancy-induced ventilation; Neutral plane; Velocity; Temperature
1. Introduction There are two fundamentally different modes of buoyancy-driven natural ventilation: displacement and mixing. Displacement ventilation (Fig. 1a) occurs in enclosures with upper and lower vents. Outside air enters through low-level openings and displaces warm air from the space through openings at higher levels. Thus inflow and outflow are separated and take place through the lower and upper vents, respectively. The neutral plane, defined as the vertical level where the internal and outside pressures are equal, is located in between the upper and lower vents. On the other hand, mixing ventilation occurs when only one high-level vent is opened so that inflow and outflow take place through different regions of the same opening (Fig. 1b). The plume of the incoming cool Corresponding author. Tel.: +972 3 9683410; fax: 972 3 9604017.
E-mail address: [email protected] (J. Tanny). 0360-1323/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2005.07.013
outside air mixes with the fluid within the space, while warmer air leaves the space through the upper region of the same upper vent. In mixing ventilation the neutral plane is approximately at the mid-height of the upper vent, separating inflow from outflow. The above two ventilation modes are well defined and were documented by theoretical analyses and experiments in small-scale laboratory models by Linden [1]. In full-scale enclosures, experiments were reported on displacement ventilation by, e.g., Howell and Potts [2] and Xing and Awbi [3]. Internal density profile measurements showed that in displacement ventilation with a localized buoyancy source, a two-layer stable stratification with a density interface is established within the enclosure. On the other hand, in mixing ventilation the density gradient is usually weaker due to the mixing between the descending plume of the incoming air and the plume rising from the heat source within the enclosure.
ARTICLE IN PRESS V. Haslavsky et al. / Building and Environment 41 (2006) 1755–1761
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Nomenclature A opening area B buoyancy flux g acceleration due to gravity hL opening height of the lower vent hU opening height of the upper vent HE total height of enclosure HV height of upper vent k coefficient; for a vertical opening k ¼ 0:25 R ¼ hL =hU ratio between opening height of lower and upper vents t time
(a)
(b)
(c) Fig. 1. A schematic presentation of the different ventilation modes in an enclosure with openings on one side wall. (a) Displacement ventilation; (b) mixing ventilation; (c) combined ventilation mode— displacement and mixing. (In case (c) the height of the lower vent is smaller than the height of the upper vent.)
In many situations, the area of the upper and lower vents may not be the same and previous works [4] studied the effect of the ratio between the areas of the upper and lower vents on the interface level. Recently, Fitzgerald and Woods [5] extended these works by investigating the effect of this area ratio on the level of the neutral plane. A reduction in the area of the lower vent with comparison to that of the upper vent caused a decrease in the level of the neutral plane. It was also shown [5] how introducing a third shallow opening at an intermediate level affects the levels of the interface and the neutral plane. Openings were restricted to shallow vertical extent such that they generally act as pure outlets or inlets. Good agreement between experiments and modeling was obtained [5].
time of opening of the lower vent ts U c ¼ ðgaDTH E Þ0:5 characteristic velocity V enclosure’s volume Z np neutral plane level measured from the lower edge of the upper vent ZV coordinate along the height of the upper vent Greek letters a DT tm
coefficient of thermal expansion temperature difference between inside and outside mixing timescale
Most of the above studies considered upper and lower vents of the same opening height, i.e., a height ratio, R ¼ hL =hU ¼ 1, where h is the opening height and subscripts L and U designate lower and upper openings, respectively. In many cases, however, the opening heights are not the same, i.e., R a1. In this paper, we study the effect of R on the ventilation process. Since the two vents have the same constant width, the ratio R also represents the ratio between the areas of the two openings. In particular, we report for the first time on natural ventilation driven by a combined mode of mixing and displacement. The upper vent is always fully opened while the lower vent height is variable such that R is changed within the range 0pR p1. The limits R ¼ 0 and 1 correspond, respectively, to the mixing and displacement modes of ventilation. For example, consider a large vertical window opened at a high level while the lower vent is closed. With a continuous buoyancy source, the enclosure is ventilated by the mixing ventilation mode under steady state. If the lower vent is instantaneously opened to a certain height, a transition process will take place during which the internal density and the flow through the vents would adjust to the new steady state. If the opening height of the lower vent is relatively small, inflow may take place through both the lower and upper openings [4] as shown schematically in Fig. 1c. The present paper shows that this may lead to interactions between the two ventilation modes. Here we experimentally explore the transition process and the steady state interactions using temperature and velocity measurements in a full-scale, buoyancy-induced naturally ventilated enclosure.
2. Experimental setup and procedures The experiments were conducted in an enclosure with length, width and height of 243, 242 and 235 cm, respectively, made of 1 cm thick wooden sheets and
ARTICLE IN PRESS V. Haslavsky et al. / Building and Environment 41 (2006) 1755–1761
150 cm Upper opening
30 cm
30 cm 235 cm 106 cm
106 cm H.S.
150 cm Lower opening
242 cm 30 cm
243 cm
(a)
S.A.
HV
ZV XV
YV
23.5 cm H.S. 121 cm
121 cm
(b)
5.8 cm
Vertical path length
insulated by 5 cm thick Styrofoam plates (Fig. 2a). Vertical openings were cut at low and high levels of one sidewall. The vents were 150 cm wide and their height was adjustable from 0 (closed) up to a maximum of 30 cm. The enclosure was located on an elevated stage, about 20 cm above the floor, such that undisturbed airflow was possible in and out of both the lower and upper openings. It was placed in a large hall ð15 m 13 m 5 m highÞ that allowed undisturbed exchange of air between the compartment and its environment, while preventing undesired wind and solar radiation effects. A localized electrical heater was installed in the compartment. It was a U-shaped tube, 33 cm high and 0.8 cm in diameter, located in an upright position on the enclosure’s floor, about 210 cm away from the centerline of the sidewall with openings (Fig. 2a). The heater was capable of supplying variable heat flux of up to 600 W, corresponding to a buoyancy flux of about 0:0167 m4 s3 (for air in 20 CÞ. A rake of 11 copper-constantan thermocouples (type T, accuracy: 0:75 C, junction diameter 0:25 mm, time constant 1:5 s) measured the vertical temperature distribution at the center of the enclosure (Fig. 2b). Outside temperature was measured by 6 additional similar thermocouples (type T) installed at the two outside corners of the front side of the enclosure. At each corner 3 sensors were distributed vertically along the enclosure’s height. A data logger (model CR21X, Campbell Sci., USA) recorded the output of all thermocouples every 2 s. The temperature difference between the inside and the outside was calculated by averaging the readings of the 6 external thermocouples and subtracting this average outside temperature from the reading of each internal thermocouple. Air velocity measurements at the upper vent were carried out by a three-dimensional sonic anemometer (model CSAT3, Campbell Sci., USA; resolution: 1 mm/s; accuracy smaller than 4 cm=s; vertical path length: 5.8 cm, measurement rate: up to 60 Hz). The sonic anemometer measured vertical profiles of the 3 air velocity components at the mid-span of the upper opening (Figs. 2b and c). Each profile consisted of 11 measurement points, separated a uniform vertical distance of 3 cm. At each point the sonic anemometer measured at a sampling rate of 10 Hz during a period of 2 min. To study the transient response of the air flow through the upper vent, in some experiments the anemometer was positioned at a fixed point in the lower region of the vent and the velocity was measured continuously before and after the opening of the lower vent. To prevent radiative heating effects, all inner surfaces within the enclosure were covered with aluminum foil, including the electrical wires, the thermocouple wires and the heating element. The thermocouple tips were gold plated to prevent radiation effects on the temperature readings.
1757
ZV
XV
YV
(c) Fig. 2. (a) A schematic view of the experimental setup. H.S. is the heat source; (b) side view of the enclosure showing the distribution of thermocouples (denoted by ) and the position of the sonic anemometer (denoted by S. A.) at the upper vent; H.S. is the heat source. (c) A view of the three-dimensional sonic anemometer (model CSAT3, Campbell Sci. Inc., USA). The vertical path length is 5.8 cm.
Three series of experiments were conducted, with the source supplying a heat flux of 100, 300 and 500 W. Using smoke visualization (not presented here) it was verified that for these fluxes the buoyancy-driven flow above the source is turbulent. It should be noted that for turbulent plumes, the buoyancy flux does not affect the
ARTICLE IN PRESS V. Haslavsky et al. / Building and Environment 41 (2006) 1755–1761
form of the internal stratification established within the enclosure. However, the strength of the stratification and the velocities do depend on the source strength [5]. In the 100, 300 and 500 W heat fluxes, 18, 18 and 17 values of R were studied, respectively. Many experiments were repeated and their total number reached 121. Each series of experiments started by operating the heating element during at least 5 h with the upper vent fully opened. This allowed the system to reach quasiequilibrium. Then, in each experiment the lower vent was opened to the prescribed height ðR Þ and measurements of the transition process were conducted. The steady state data were collected at least 30 min after the change in the opening height. Results show (see Section 3) that in practice the enclosure adjusted to the new steady state during a shorter time period. The 30 min time period is also larger than the mixing timescale [4] estimated to be between 12 and 21 min for the heat fluxes (between 100 and 500 W) supplied in this study. The mixing timescale, tm , is calculated using the expressions in [4] by 2V , tm ¼ 1=3 pffiffiffiffiffiffiffi B ðkA H V Þ2=3 where V is the enclosure’s volume, B is the buoyancy flux, k is a constant (¼ 0:25 for a vertical opening) and A and H V are the opening’s area and height, respectively. The 30 min time period is certainly larger than the displacement timescale which is always smaller than the mixing timescale.
steady state (mixing) to the other (displacement) is approximately 30 s. Fig. 4 shows the response with time of the temperature difference between inside and outside at different levels within the enclosure. Each symbol represents the level of the sensor normalized with respect to the total height of the enclosure (235 cm). It is generally observed that, as expected, the temperature difference increases with height. In this figure, at t ¼ 0 the lower vent is instantaneously fully opened to R ¼ 1 and the response up to t ¼ 11 min is presented. The results show that in most levels, up to about t ¼ 5 min the temperature difference is reduced due to the enhanced ventilation; this is the approximate duration of the temperature transition process. However, for tX6 min, a new steady state is established at which the temperature difference is essentially constant with time. Qualitatively similar results were obtained for transitions to other values of R (i.e., other opening heights of the lower vent).
0.25 0.2 Air velocity [m/s]
1758
0.15 0.1 0.05 0 -0.05 -0.1
t=ts
-0.15 0
3.1. Transition process Fig. 3 shows the velocity normal to the opening plane as measured by the sonic anemometer, 3 cm above the lower edge of the upper vent. The enclosure was initially operating under the mixing ventilation mode with a continuous heat flux of 100 W. In this mode there is bidirectional flow with inflow and outflow through the lower and upper regions of the upper vent, respectively. This is illustrated in Fig. 3 by the negative inwards velocity measured at the lower region of the upper vent for tots . At t ¼ ts the lower vent is instantaneously fully opened such that transition to displacement ventilation commences. A jump in the measured velocity is observed at t ¼ ts , which is followed by a relatively fast adjustment to a new velocity whose average is constant with time and has a value close to zero. Such a velocity is typical of displacement ventilation where there is no inflow through the upper vent. Fig. 3 suggests that the duration of the velocity transition process from one
4
6
8 10 Time [min]
12
14
16
Fig. 3. The response with time of the air velocity normal to the opening plane measured at the lower region of the upper vent to an instantaneous opening of the lower vent from R ¼ 0 to R ¼ 1. Heat flux is 100 W.
4 Temperature difference [K]
3. Results
2
0.995 0.4
0.9 0.3
0.8 0.2
0.7 0.1
0.6 0.005
0.5
3 2 1 0 -1 0
1
2
3
4
5 6 Time [min]
7
8
9
10
11
Fig. 4. The response with time of the temperature difference between inside and outside to an instantaneous opening of the lower vent from R ¼ 0 to R ¼ 1. Heat flux is 100 W. The number of each symbol represents the level of the thermocouple sensor normalized by the total height of the enclosure (235 cm).
ARTICLE IN PRESS V. Haslavsky et al. / Building and Environment 41 (2006) 1755–1761
3.2. Steady state interaction At each R , the temperature difference between the internal sensors and the outside was averaged over the enclosure’s height and the results are plotted in Fig. 5. For illustrative purposes exponential curves are fitted to the data points by the least-square technique. The figure shows that as R is increased, by increasing the opening height (and area) of the lower vent, the average temperature difference between inside and outside is decreased due to the enhanced ventilation. Equilibrium temperature differences for 500 W are larger than those for 300 and 100 W, as expected. The air exchange between inside and outside is represented by the velocity normal to the opening plane. Vertical profiles of the normal component of the air velocity at the mid span of the upper opening are shown in Fig. 6 for a heat flux of 500 W. Each data point is measured after the enclosure reached equilibrium at a different value of R . The velocity is normalized by a characteristic free convection velocity, defined as: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi U c ¼ gaDTH E where g is the acceleration due to gravity, a is the coefficient of thermal expansion and DT is the temperature difference between inside and outside, averaged over the enclosure’s height, H E . Qualitatively similar results are obtained for heat fluxes of 100 and 300 W. Considering the instrument’s vertical path length (5.8 cm), each data point represents the average velocity over a vertical distance of 2:9 cm. Fig. 6 shows that in the mixing ventilation mode (R ¼ 0, full diamonds) outflow takes place through the upper part of the vent while inflow (negative velocity) through its lower part. The level where the velocity changes sign is identified as the neutral plane and for R ¼ 0 it is located at Z V =H V 0:62 where ZV is the vertical coordinate along the vent and H V is the vent height (¼ 30 cm). It is noticed that the profile is asymmetric around the neutral plane. When the lower vent is slightly opened to 4 cm height (R ¼ 0:133, full
Average ∆T [K]
7.0 100W (N=64)
y = 1.70e -1.87x , r 2 = 0.65
6.0
300W (N=26)
y = 4.05e -2.41x , r 2 = 0.69
5.0
500W (N=20)
y = 5.73e -1.74x , r 2 = 0.89
4.0 3.0 2.0 1.0 0.0 0
0.2
0.4
0.6
0.8
1
R*
Fig. 5. The temperature difference between inside and outside averaged over the enclosure’s height as a function of R for heat fluxes of 100, 300 and 500 W. N is the number of data points. The lines represent best fit regressions, with the specified coefficients of determination (r-squared values).
1 0.8 zv /Hv
The results in Figs. 3 and 4 suggest that the response with time of the air velocity at the upper vent to instantaneous changes in the height of the lower vent is much faster than the corresponding response of the temperature difference between inside and outside. It appears that opening of the lower vent modifies almost immediately the local pressure distribution at the openings which results in a fast change of the flow pattern there. Then, this flow pattern gradually adjusts the internal temperature field to the new steady state. The latter process (temperature adjustment) is associated with the entire enclosure’s volume and therefore it is considerably slower than the former (velocity adjustment) which occurs locally at the openings.
1759
0.6
R=0 R=0.133 R=0.267 R=0.333 R=0.533 R=1
0.4 0.2 0 -0.2
0
0.2
0.4 u/Uc
0.6
0.8
1
Fig. 6. Vertical profiles of the normal component of air velocity through the upper vent for different values of R at a heat flux of 500 W. Negative values indicate inflow.
squares) the velocity profile is qualitatively similar to that at R ¼ 0 with a somewhat lower level of the neutral plane, Z V =H V 0:43. Thus, although the lower vent is opened and the situation is conducive to displacement ventilation, there is inflow also through the upper vent. At this value of R ventilation takes place through a combined mode of mixing and displacement. As the lower vent is further opened to larger opening heights, the height of the neutral plane continues to drop. At a lower vent opening height of 8 cm (R ¼ 0:267, full triangles) outflow occupies most of the upper vent, with a small region at the bottom of the upper vent ðZ V =H V o0:15Þ where inflow takes place. For R X0:333 only outflow takes place through the upper vent suggesting that displacement ventilation dominates the process. Inflow takes place through the lower vent only. The level of the neutral plane at different values of R was deduced from vertical velocity profiles, like those
ARTICLE IN PRESS V. Haslavsky et al. / Building and Environment 41 (2006) 1755–1761
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shown in Fig. 6. Fig. 7 shows the normalized level of the neutral plane at the upper vent, Z np =H V , as a function of R deduced from 121 velocity profiles with heat fluxes of 100, 300 and 500 W. Few exceptional data points were discarded from Fig. 7; they were obtained in experiments where the outside temperature was significantly larger than the average outside temperature of all the experiments conducted here. When R ¼ 0 mixing ventilation takes place and Znp =H V 0:6 for all heat fluxes. However, as the lower vent is opened and R is increased, the level of the neutral plane decreases roughly linearly with R . At these intermediate values of R , although there is inflow through the lower vent (as was observed by smoke flow visualization, not shown here), there is also inflow through the lower region of the upper vent. Thus, interaction between the mixing and displacement modes takes place and ventilation is through a combined mode. Fig. 7 suggests that there is a range of critical R above which there is no inflow through the upper vent, such that the height of the neutral plane is Z np =H V ¼ 0. According to Fig. 7 the upper limit of this range is R ffi 0:53. The lower limit of this range, R ffi 0:27, is the value below which either the pure mixing ventilation ðR ¼ 0Þ or the new combined mode prevail. It is therefore suggested that for 0oR o0:27 the mixing and displacement modes interact through a new combined ventilation mode. For 0:53oR p1, the displacement mode dominates whereas in the intermediate range, 0:27pR p0:53, either the combined or the pure displacement mode takes place. A weak dependence of the neutral plane level on the source buoyancy flux is observed in this intermediate range. The dashed-dot and dotted lines in Fig. 7 are the theoretical predictions of the neutral plane level based on the two-vent and three-vent models of Fitzgerald and Woods [5], respectively. A discharge coefficient of 0.5,
typical of the sharp-edge [4] opening of this enclosure, and an entrainment coefficient of 0.102 were used in the model calculation. The two-vent model assumes lower and upper openings with corresponding inflow and outflow. However, in the three-vent model an additional intermediate inflow vent is introduced below the level of the neutral plane. In the present experiment, this vent is represented by the lower region of the upper vent through which inflow takes place. Qualitative agreement is observed between the experimental data and the two theoretical models, supporting the existence of the combined ventilation mode. Moreover, both model curves intersect the abscissa of Fig. 7 at about R ffi 0:57 which is in agreement with the upper limit of the range of critical R ðffi 0:53Þ mentioned above. The quantitative differences between the experiment and models are mainly attributed to the fact that the models consider very shallow vents with unidirectional flow in each of them, while in the experiment bi-directional flow takes place through the upper vent with a shear between the two air streams.
4. Conclusions The following conclusions can be drawn from this experimental study:
0.7 100W (N=78)
0.6
300W (N=24)
Znp / Hv
500W (N=19)
0.5
Two-opening model
0.4
Three-opening model
0.3
When 0oR o0:27 the mixing and displacement modes interact through a new combined ventilation mode. For 0:53oR p1, the displacement mode prevails whereas in the intermediate range, 0:27pR p0:53, either the combined or the pure displacement mode takes place. Mixing ventilation is associated with higher temperature differences between inside and outside than displacement ventilation. The temperature difference between inside and outside averaged over the enclosure’s height decreases monotonically with increasing R . Larger temperature differences are associated with higher heat fluxes, as expected. The transient response of the velocity at the upper vent is much faster than the corresponding response of the temperature difference between inside and outside.
0.2
Acknowledgements
0.1 0 0
0.2
0.4
0.6
0.8
1
R*
Fig. 7. The normalized height of the neutral plane at the upper vent as a function of R . The dashed-dot and dotted lines are, respectively, the theoretical predictions for the two- and three-opening models by Fitzgerald and Woods [5]. N is the number of data points.
This research was funded by the Israeli Ministry of Science and Technology. We acknowledge very useful discussions with Prof. P. F. Linden during the initial stages of this research. We thank Mr. R. Regev and Mr. M. Barak for the construction of the apparatus and technical support.
ARTICLE IN PRESS V. Haslavsky et al. / Building and Environment 41 (2006) 1755–1761
References [1] Linden PF. The fluid mechanics of natural ventilation. Annual Review of Fluid Mechanics 1999;31:201–38. [2] Howell SA, Potts I. On the natural displacement flow through a full-scale enclosure, and the importance of the radiative participation of the water vapor content of the ambient air. Building and Environment 2002;37:817–23.
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[3] Xing H, Awbi HB. Measurement and calculation of the neutral height in a room with displacement ventilation. Building and Environment 2002;37:961–7. [4] Linden PF, Lane-Serff GP, Smeed DA. Emptying filling boxes: the fluid mechanics of natural ventilation. Journal of Fluid Mechanics 1990;212:309–35. [5] Fitzgerald SD, Woods AW. Natural ventilation of a room with vents at multiple levels. Building and Environment 2004;39:505–21.
Building and Environment 41 (2006) 1755–1761 www.elsevier.com/locate/buildenv
Interaction between the mixing and displacement modes in a naturally ventilated enclosure Vitaly Haslavskya, Josef Tannya,, Meir Teitelb a
Institute of Soil, Water & Environmental Sciences, Agricultural Research Organization, The Volcani Center, P.O. Box 6, Bet Dagan 50250, Israel b Institute of Agricultural Engineering, Agricultural Research Organization, The Volcani Center, P.O. Box 6, Bet Dagan 50250, Israel Received 10 March 2005; received in revised form 17 June 2005; accepted 7 July 2005
Abstract Experiments are carried out to study for the first time interactive phenomena in buoyancy-induced natural ventilation in a fullscale enclosure with upper and lower openings on one of the sidewalls. The interaction between the mixing and the displacement ventilation modes is revealed by opening the lower vent to different heights while the upper vent is kept fully open. Both the transient process and steady state interaction are explored. Measurements include temperature differences between inside and outside and air velocity through the upper opening. The level of the neutral plane at the upper vent, defined here as the plane separating between inflow and outflow, decreases with R , the ratio between the opening heights (and areas) of the lower and upper vents. Experiments show that when 0oR o0:27 the mixing and displacement modes interact through a new combined ventilation mode. For 0:53oR p1, the displacement mode dominates whereas in the intermediate range, 0:27pR p0:53, either the combined or the pure displacement mode takes place. The experiments are in qualitative agreement with a previous theoretical model. r 2005 Elsevier Ltd. All rights reserved. Keywords: Buoyancy-induced ventilation; Neutral plane; Velocity; Temperature
1. Introduction There are two fundamentally different modes of buoyancy-driven natural ventilation: displacement and mixing. Displacement ventilation (Fig. 1a) occurs in enclosures with upper and lower vents. Outside air enters through low-level openings and displaces warm air from the space through openings at higher levels. Thus inflow and outflow are separated and take place through the lower and upper vents, respectively. The neutral plane, defined as the vertical level where the internal and outside pressures are equal, is located in between the upper and lower vents. On the other hand, mixing ventilation occurs when only one high-level vent is opened so that inflow and outflow take place through different regions of the same opening (Fig. 1b). The plume of the incoming cool Corresponding author. Tel.: +972 3 9683410; fax: 972 3 9604017.
E-mail address: [email protected] (J. Tanny). 0360-1323/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2005.07.013
outside air mixes with the fluid within the space, while warmer air leaves the space through the upper region of the same upper vent. In mixing ventilation the neutral plane is approximately at the mid-height of the upper vent, separating inflow from outflow. The above two ventilation modes are well defined and were documented by theoretical analyses and experiments in small-scale laboratory models by Linden [1]. In full-scale enclosures, experiments were reported on displacement ventilation by, e.g., Howell and Potts [2] and Xing and Awbi [3]. Internal density profile measurements showed that in displacement ventilation with a localized buoyancy source, a two-layer stable stratification with a density interface is established within the enclosure. On the other hand, in mixing ventilation the density gradient is usually weaker due to the mixing between the descending plume of the incoming air and the plume rising from the heat source within the enclosure.
ARTICLE IN PRESS V. Haslavsky et al. / Building and Environment 41 (2006) 1755–1761
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Nomenclature A opening area B buoyancy flux g acceleration due to gravity hL opening height of the lower vent hU opening height of the upper vent HE total height of enclosure HV height of upper vent k coefficient; for a vertical opening k ¼ 0:25 R ¼ hL =hU ratio between opening height of lower and upper vents t time
(a)
(b)
(c) Fig. 1. A schematic presentation of the different ventilation modes in an enclosure with openings on one side wall. (a) Displacement ventilation; (b) mixing ventilation; (c) combined ventilation mode— displacement and mixing. (In case (c) the height of the lower vent is smaller than the height of the upper vent.)
In many situations, the area of the upper and lower vents may not be the same and previous works [4] studied the effect of the ratio between the areas of the upper and lower vents on the interface level. Recently, Fitzgerald and Woods [5] extended these works by investigating the effect of this area ratio on the level of the neutral plane. A reduction in the area of the lower vent with comparison to that of the upper vent caused a decrease in the level of the neutral plane. It was also shown [5] how introducing a third shallow opening at an intermediate level affects the levels of the interface and the neutral plane. Openings were restricted to shallow vertical extent such that they generally act as pure outlets or inlets. Good agreement between experiments and modeling was obtained [5].
time of opening of the lower vent ts U c ¼ ðgaDTH E Þ0:5 characteristic velocity V enclosure’s volume Z np neutral plane level measured from the lower edge of the upper vent ZV coordinate along the height of the upper vent Greek letters a DT tm
coefficient of thermal expansion temperature difference between inside and outside mixing timescale
Most of the above studies considered upper and lower vents of the same opening height, i.e., a height ratio, R ¼ hL =hU ¼ 1, where h is the opening height and subscripts L and U designate lower and upper openings, respectively. In many cases, however, the opening heights are not the same, i.e., R a1. In this paper, we study the effect of R on the ventilation process. Since the two vents have the same constant width, the ratio R also represents the ratio between the areas of the two openings. In particular, we report for the first time on natural ventilation driven by a combined mode of mixing and displacement. The upper vent is always fully opened while the lower vent height is variable such that R is changed within the range 0pR p1. The limits R ¼ 0 and 1 correspond, respectively, to the mixing and displacement modes of ventilation. For example, consider a large vertical window opened at a high level while the lower vent is closed. With a continuous buoyancy source, the enclosure is ventilated by the mixing ventilation mode under steady state. If the lower vent is instantaneously opened to a certain height, a transition process will take place during which the internal density and the flow through the vents would adjust to the new steady state. If the opening height of the lower vent is relatively small, inflow may take place through both the lower and upper openings [4] as shown schematically in Fig. 1c. The present paper shows that this may lead to interactions between the two ventilation modes. Here we experimentally explore the transition process and the steady state interactions using temperature and velocity measurements in a full-scale, buoyancy-induced naturally ventilated enclosure.
2. Experimental setup and procedures The experiments were conducted in an enclosure with length, width and height of 243, 242 and 235 cm, respectively, made of 1 cm thick wooden sheets and
ARTICLE IN PRESS V. Haslavsky et al. / Building and Environment 41 (2006) 1755–1761
150 cm Upper opening
30 cm
30 cm 235 cm 106 cm
106 cm H.S.
150 cm Lower opening
242 cm 30 cm
243 cm
(a)
S.A.
HV
ZV XV
YV
23.5 cm H.S. 121 cm
121 cm
(b)
5.8 cm
Vertical path length
insulated by 5 cm thick Styrofoam plates (Fig. 2a). Vertical openings were cut at low and high levels of one sidewall. The vents were 150 cm wide and their height was adjustable from 0 (closed) up to a maximum of 30 cm. The enclosure was located on an elevated stage, about 20 cm above the floor, such that undisturbed airflow was possible in and out of both the lower and upper openings. It was placed in a large hall ð15 m 13 m 5 m highÞ that allowed undisturbed exchange of air between the compartment and its environment, while preventing undesired wind and solar radiation effects. A localized electrical heater was installed in the compartment. It was a U-shaped tube, 33 cm high and 0.8 cm in diameter, located in an upright position on the enclosure’s floor, about 210 cm away from the centerline of the sidewall with openings (Fig. 2a). The heater was capable of supplying variable heat flux of up to 600 W, corresponding to a buoyancy flux of about 0:0167 m4 s3 (for air in 20 CÞ. A rake of 11 copper-constantan thermocouples (type T, accuracy: 0:75 C, junction diameter 0:25 mm, time constant 1:5 s) measured the vertical temperature distribution at the center of the enclosure (Fig. 2b). Outside temperature was measured by 6 additional similar thermocouples (type T) installed at the two outside corners of the front side of the enclosure. At each corner 3 sensors were distributed vertically along the enclosure’s height. A data logger (model CR21X, Campbell Sci., USA) recorded the output of all thermocouples every 2 s. The temperature difference between the inside and the outside was calculated by averaging the readings of the 6 external thermocouples and subtracting this average outside temperature from the reading of each internal thermocouple. Air velocity measurements at the upper vent were carried out by a three-dimensional sonic anemometer (model CSAT3, Campbell Sci., USA; resolution: 1 mm/s; accuracy smaller than 4 cm=s; vertical path length: 5.8 cm, measurement rate: up to 60 Hz). The sonic anemometer measured vertical profiles of the 3 air velocity components at the mid-span of the upper opening (Figs. 2b and c). Each profile consisted of 11 measurement points, separated a uniform vertical distance of 3 cm. At each point the sonic anemometer measured at a sampling rate of 10 Hz during a period of 2 min. To study the transient response of the air flow through the upper vent, in some experiments the anemometer was positioned at a fixed point in the lower region of the vent and the velocity was measured continuously before and after the opening of the lower vent. To prevent radiative heating effects, all inner surfaces within the enclosure were covered with aluminum foil, including the electrical wires, the thermocouple wires and the heating element. The thermocouple tips were gold plated to prevent radiation effects on the temperature readings.
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ZV
XV
YV
(c) Fig. 2. (a) A schematic view of the experimental setup. H.S. is the heat source; (b) side view of the enclosure showing the distribution of thermocouples (denoted by ) and the position of the sonic anemometer (denoted by S. A.) at the upper vent; H.S. is the heat source. (c) A view of the three-dimensional sonic anemometer (model CSAT3, Campbell Sci. Inc., USA). The vertical path length is 5.8 cm.
Three series of experiments were conducted, with the source supplying a heat flux of 100, 300 and 500 W. Using smoke visualization (not presented here) it was verified that for these fluxes the buoyancy-driven flow above the source is turbulent. It should be noted that for turbulent plumes, the buoyancy flux does not affect the
ARTICLE IN PRESS V. Haslavsky et al. / Building and Environment 41 (2006) 1755–1761
form of the internal stratification established within the enclosure. However, the strength of the stratification and the velocities do depend on the source strength [5]. In the 100, 300 and 500 W heat fluxes, 18, 18 and 17 values of R were studied, respectively. Many experiments were repeated and their total number reached 121. Each series of experiments started by operating the heating element during at least 5 h with the upper vent fully opened. This allowed the system to reach quasiequilibrium. Then, in each experiment the lower vent was opened to the prescribed height ðR Þ and measurements of the transition process were conducted. The steady state data were collected at least 30 min after the change in the opening height. Results show (see Section 3) that in practice the enclosure adjusted to the new steady state during a shorter time period. The 30 min time period is also larger than the mixing timescale [4] estimated to be between 12 and 21 min for the heat fluxes (between 100 and 500 W) supplied in this study. The mixing timescale, tm , is calculated using the expressions in [4] by 2V , tm ¼ 1=3 pffiffiffiffiffiffiffi B ðkA H V Þ2=3 where V is the enclosure’s volume, B is the buoyancy flux, k is a constant (¼ 0:25 for a vertical opening) and A and H V are the opening’s area and height, respectively. The 30 min time period is certainly larger than the displacement timescale which is always smaller than the mixing timescale.
steady state (mixing) to the other (displacement) is approximately 30 s. Fig. 4 shows the response with time of the temperature difference between inside and outside at different levels within the enclosure. Each symbol represents the level of the sensor normalized with respect to the total height of the enclosure (235 cm). It is generally observed that, as expected, the temperature difference increases with height. In this figure, at t ¼ 0 the lower vent is instantaneously fully opened to R ¼ 1 and the response up to t ¼ 11 min is presented. The results show that in most levels, up to about t ¼ 5 min the temperature difference is reduced due to the enhanced ventilation; this is the approximate duration of the temperature transition process. However, for tX6 min, a new steady state is established at which the temperature difference is essentially constant with time. Qualitatively similar results were obtained for transitions to other values of R (i.e., other opening heights of the lower vent).
0.25 0.2 Air velocity [m/s]
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0.15 0.1 0.05 0 -0.05 -0.1
t=ts
-0.15 0
3.1. Transition process Fig. 3 shows the velocity normal to the opening plane as measured by the sonic anemometer, 3 cm above the lower edge of the upper vent. The enclosure was initially operating under the mixing ventilation mode with a continuous heat flux of 100 W. In this mode there is bidirectional flow with inflow and outflow through the lower and upper regions of the upper vent, respectively. This is illustrated in Fig. 3 by the negative inwards velocity measured at the lower region of the upper vent for tots . At t ¼ ts the lower vent is instantaneously fully opened such that transition to displacement ventilation commences. A jump in the measured velocity is observed at t ¼ ts , which is followed by a relatively fast adjustment to a new velocity whose average is constant with time and has a value close to zero. Such a velocity is typical of displacement ventilation where there is no inflow through the upper vent. Fig. 3 suggests that the duration of the velocity transition process from one
4
6
8 10 Time [min]
12
14
16
Fig. 3. The response with time of the air velocity normal to the opening plane measured at the lower region of the upper vent to an instantaneous opening of the lower vent from R ¼ 0 to R ¼ 1. Heat flux is 100 W.
4 Temperature difference [K]
3. Results
2
0.995 0.4
0.9 0.3
0.8 0.2
0.7 0.1
0.6 0.005
0.5
3 2 1 0 -1 0
1
2
3
4
5 6 Time [min]
7
8
9
10
11
Fig. 4. The response with time of the temperature difference between inside and outside to an instantaneous opening of the lower vent from R ¼ 0 to R ¼ 1. Heat flux is 100 W. The number of each symbol represents the level of the thermocouple sensor normalized by the total height of the enclosure (235 cm).
ARTICLE IN PRESS V. Haslavsky et al. / Building and Environment 41 (2006) 1755–1761
3.2. Steady state interaction At each R , the temperature difference between the internal sensors and the outside was averaged over the enclosure’s height and the results are plotted in Fig. 5. For illustrative purposes exponential curves are fitted to the data points by the least-square technique. The figure shows that as R is increased, by increasing the opening height (and area) of the lower vent, the average temperature difference between inside and outside is decreased due to the enhanced ventilation. Equilibrium temperature differences for 500 W are larger than those for 300 and 100 W, as expected. The air exchange between inside and outside is represented by the velocity normal to the opening plane. Vertical profiles of the normal component of the air velocity at the mid span of the upper opening are shown in Fig. 6 for a heat flux of 500 W. Each data point is measured after the enclosure reached equilibrium at a different value of R . The velocity is normalized by a characteristic free convection velocity, defined as: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi U c ¼ gaDTH E where g is the acceleration due to gravity, a is the coefficient of thermal expansion and DT is the temperature difference between inside and outside, averaged over the enclosure’s height, H E . Qualitatively similar results are obtained for heat fluxes of 100 and 300 W. Considering the instrument’s vertical path length (5.8 cm), each data point represents the average velocity over a vertical distance of 2:9 cm. Fig. 6 shows that in the mixing ventilation mode (R ¼ 0, full diamonds) outflow takes place through the upper part of the vent while inflow (negative velocity) through its lower part. The level where the velocity changes sign is identified as the neutral plane and for R ¼ 0 it is located at Z V =H V 0:62 where ZV is the vertical coordinate along the vent and H V is the vent height (¼ 30 cm). It is noticed that the profile is asymmetric around the neutral plane. When the lower vent is slightly opened to 4 cm height (R ¼ 0:133, full
Average ∆T [K]
7.0 100W (N=64)
y = 1.70e -1.87x , r 2 = 0.65
6.0
300W (N=26)
y = 4.05e -2.41x , r 2 = 0.69
5.0
500W (N=20)
y = 5.73e -1.74x , r 2 = 0.89
4.0 3.0 2.0 1.0 0.0 0
0.2
0.4
0.6
0.8
1
R*
Fig. 5. The temperature difference between inside and outside averaged over the enclosure’s height as a function of R for heat fluxes of 100, 300 and 500 W. N is the number of data points. The lines represent best fit regressions, with the specified coefficients of determination (r-squared values).
1 0.8 zv /Hv
The results in Figs. 3 and 4 suggest that the response with time of the air velocity at the upper vent to instantaneous changes in the height of the lower vent is much faster than the corresponding response of the temperature difference between inside and outside. It appears that opening of the lower vent modifies almost immediately the local pressure distribution at the openings which results in a fast change of the flow pattern there. Then, this flow pattern gradually adjusts the internal temperature field to the new steady state. The latter process (temperature adjustment) is associated with the entire enclosure’s volume and therefore it is considerably slower than the former (velocity adjustment) which occurs locally at the openings.
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0.6
R=0 R=0.133 R=0.267 R=0.333 R=0.533 R=1
0.4 0.2 0 -0.2
0
0.2
0.4 u/Uc
0.6
0.8
1
Fig. 6. Vertical profiles of the normal component of air velocity through the upper vent for different values of R at a heat flux of 500 W. Negative values indicate inflow.
squares) the velocity profile is qualitatively similar to that at R ¼ 0 with a somewhat lower level of the neutral plane, Z V =H V 0:43. Thus, although the lower vent is opened and the situation is conducive to displacement ventilation, there is inflow also through the upper vent. At this value of R ventilation takes place through a combined mode of mixing and displacement. As the lower vent is further opened to larger opening heights, the height of the neutral plane continues to drop. At a lower vent opening height of 8 cm (R ¼ 0:267, full triangles) outflow occupies most of the upper vent, with a small region at the bottom of the upper vent ðZ V =H V o0:15Þ where inflow takes place. For R X0:333 only outflow takes place through the upper vent suggesting that displacement ventilation dominates the process. Inflow takes place through the lower vent only. The level of the neutral plane at different values of R was deduced from vertical velocity profiles, like those
ARTICLE IN PRESS V. Haslavsky et al. / Building and Environment 41 (2006) 1755–1761
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shown in Fig. 6. Fig. 7 shows the normalized level of the neutral plane at the upper vent, Z np =H V , as a function of R deduced from 121 velocity profiles with heat fluxes of 100, 300 and 500 W. Few exceptional data points were discarded from Fig. 7; they were obtained in experiments where the outside temperature was significantly larger than the average outside temperature of all the experiments conducted here. When R ¼ 0 mixing ventilation takes place and Znp =H V 0:6 for all heat fluxes. However, as the lower vent is opened and R is increased, the level of the neutral plane decreases roughly linearly with R . At these intermediate values of R , although there is inflow through the lower vent (as was observed by smoke flow visualization, not shown here), there is also inflow through the lower region of the upper vent. Thus, interaction between the mixing and displacement modes takes place and ventilation is through a combined mode. Fig. 7 suggests that there is a range of critical R above which there is no inflow through the upper vent, such that the height of the neutral plane is Z np =H V ¼ 0. According to Fig. 7 the upper limit of this range is R ffi 0:53. The lower limit of this range, R ffi 0:27, is the value below which either the pure mixing ventilation ðR ¼ 0Þ or the new combined mode prevail. It is therefore suggested that for 0oR o0:27 the mixing and displacement modes interact through a new combined ventilation mode. For 0:53oR p1, the displacement mode dominates whereas in the intermediate range, 0:27pR p0:53, either the combined or the pure displacement mode takes place. A weak dependence of the neutral plane level on the source buoyancy flux is observed in this intermediate range. The dashed-dot and dotted lines in Fig. 7 are the theoretical predictions of the neutral plane level based on the two-vent and three-vent models of Fitzgerald and Woods [5], respectively. A discharge coefficient of 0.5,
typical of the sharp-edge [4] opening of this enclosure, and an entrainment coefficient of 0.102 were used in the model calculation. The two-vent model assumes lower and upper openings with corresponding inflow and outflow. However, in the three-vent model an additional intermediate inflow vent is introduced below the level of the neutral plane. In the present experiment, this vent is represented by the lower region of the upper vent through which inflow takes place. Qualitative agreement is observed between the experimental data and the two theoretical models, supporting the existence of the combined ventilation mode. Moreover, both model curves intersect the abscissa of Fig. 7 at about R ffi 0:57 which is in agreement with the upper limit of the range of critical R ðffi 0:53Þ mentioned above. The quantitative differences between the experiment and models are mainly attributed to the fact that the models consider very shallow vents with unidirectional flow in each of them, while in the experiment bi-directional flow takes place through the upper vent with a shear between the two air streams.
4. Conclusions The following conclusions can be drawn from this experimental study:
0.7 100W (N=78)
0.6
300W (N=24)
Znp / Hv
500W (N=19)
0.5
Two-opening model
0.4
Three-opening model
0.3
When 0oR o0:27 the mixing and displacement modes interact through a new combined ventilation mode. For 0:53oR p1, the displacement mode prevails whereas in the intermediate range, 0:27pR p0:53, either the combined or the pure displacement mode takes place. Mixing ventilation is associated with higher temperature differences between inside and outside than displacement ventilation. The temperature difference between inside and outside averaged over the enclosure’s height decreases monotonically with increasing R . Larger temperature differences are associated with higher heat fluxes, as expected. The transient response of the velocity at the upper vent is much faster than the corresponding response of the temperature difference between inside and outside.
0.2
Acknowledgements
0.1 0 0
0.2
0.4
0.6
0.8
1
R*
Fig. 7. The normalized height of the neutral plane at the upper vent as a function of R . The dashed-dot and dotted lines are, respectively, the theoretical predictions for the two- and three-opening models by Fitzgerald and Woods [5]. N is the number of data points.
This research was funded by the Israeli Ministry of Science and Technology. We acknowledge very useful discussions with Prof. P. F. Linden during the initial stages of this research. We thank Mr. R. Regev and Mr. M. Barak for the construction of the apparatus and technical support.
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References [1] Linden PF. The fluid mechanics of natural ventilation. Annual Review of Fluid Mechanics 1999;31:201–38. [2] Howell SA, Potts I. On the natural displacement flow through a full-scale enclosure, and the importance of the radiative participation of the water vapor content of the ambient air. Building and Environment 2002;37:817–23.
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[3] Xing H, Awbi HB. Measurement and calculation of the neutral height in a room with displacement ventilation. Building and Environment 2002;37:961–7. [4] Linden PF, Lane-Serff GP, Smeed DA. Emptying filling boxes: the fluid mechanics of natural ventilation. Journal of Fluid Mechanics 1990;212:309–35. [5] Fitzgerald SD, Woods AW. Natural ventilation of a room with vents at multiple levels. Building and Environment 2004;39:505–21.