- Email: [email protected]
Pollutant dilution in displacement natural ventilation rooms with inner sources
Building and Environment 56 (2012) 108e117
Contents lists available at SciVerse ScienceDirect
Building and Environment journal homepage: www.elsevier.com/locate/buildenv
Pollutant dilution in displacement natural ventilation rooms with inner sources Ke Zhong, Xiufeng Yang, Wei Feng, Yanming Kang* School of Environmental Science and Engineering, Donghua University, 2999 North Renmin Road, Shanghai 201620, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 11 December 2011 Received in revised form 23 February 2012 Accepted 24 February 2012
Indoor air quality and pollutant dispersion in natural ventilation rooms have received considerable attention in recent years. In order to evaluate the pollutant concentration levels in the occupant zone in a displacement natural ventilation (DNV) room, the mathematical model in previous studies are employed and extended to estimate pollutant transportation in a DNV room with the consideration of both the incoming air concentration and indoor pollutant source, resulting in exponential type expressions in time for the concentration in the lower zone and the mean concentration in DNV rooms. The results show that for reducing the concentration in the lower zone to a certain value, the concentration of inflow air and indoor emission rate should be less than their critical values for a given effective opening area of the window. The effect of thermal radiation of the inner surface on the reduction of pollutant concentration in the upper zone is greater than that in the lower zone of a DNV room. In addition, the effective opening area of the window primarily influences the final concentration level in the DNV room, and only affects the decay rate of indoor pollutant concentration when the pollutant concentration of incoming air or the strength of the indoor source approach their critical values. 2012 Elsevier Ltd. All rights reserved.
Keywords: Displacement natural ventilation room Pollutant Source Concentration Dilution Decay rate
1. Introduction Ventilation is necessary for indoor environments to supply fresh air for the metabolism process, to provide good indoor air quality and to maintain a comfortable thermal environment. Building ventilation has become more important because people spend most of their time indoors [1e3], and more and more high rise buildings with high air tightness appear in cities. Although mechanical ventilation in buildings is nowadays a common way to maintain a steady indoor air environment, the energy consumption related to the operation of heating, ventilation and air-conditioning systems (HVAC) is considerable. According to recent studies, more than half of the total energy used in service and residential buildings is attributable to HVAC systems [4e8]. Studies have shown that in Europe and USA about 40% of final energy consumption is in the buildings sector [5,6]. Also in the past two decades, building energy consumption in China has been increasing at more than 10% a year. In the year 2004, building energy consumption alone constituted 20.7% of the total national energy consumption [7,8], and now it has increased to 30% [9]. Natural ventilation can be used as a passive cooling technique for reducing building energy consumption, and it has been the subject of much research over recent decades due to its potential for offering good indoor air quality for occupants and relatively low
* Corresponding author. Tel.: þ86 21 67792159; fax: þ86 21 67792522. E-mail address: [email protected] (Y. Kang). 0360-1323/$ e see front matter 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2012.02.028
energy usage compared with mechanical ventilation. Natural ventilation of buildings is the flow generated by temperature differences, i.e. thermal buoyancy, and by the wind [10]. Many investigations have been carried out to explore the temperature distribution, thermal comfort and air exchange rate of naturally ventilated rooms/buildings driven by thermal force [11e15]. In a building with displacement natural ventilation, dense ambient air flows through low-level openings by thermal buoyancy sources (generally, heating elements) and displaces the lighter air in the building out through high-level openings. Since the incoming air is essentially at the low level, a thermal stratification develops between the air intake and the air previously in the building. Linden et al. [11] investigated DNV in a single-zone building with two-level openings. Theoretical expressions were obtained for the airflow rate through the openings and the stratification interfacial position induced by a single point source and a single line source, respectively. The results show that while the airflow rate does depend on the source strength, the location of the stratification is exclusively determined by the geometrical parameters of the building and independent of the source strength. Kaye and Hunt [16] studied and compared the process of the flow developed to the steady displacement flow modeled by Linden et al. [11] in an enclosure with low and high level openings. They identified the time scales which characterize the development of the plume-driven flow to steady state. Hunt and Kaye [17] extended the transient model of Kaye and Hunt [16] to examine the flushing of a neutrally-buoyant pollutant from a naturally ventilated
K. Zhong et al. / Building and Environment 56 (2012) 108e117
enclosure. Their model demonstrates that the concentration of the pollutant will decay exponentially with time, and the decay rate is a function of the room geometry, outlet areas and the distribution, number and strength of the heat sources. Without the consideration of the effect of thermal radiation of the inner surface of the building, Hunt and Kaye [17] also investigated the dilution process of indoor pollutants for the case of no source but an initial pollutant concentration, with the concentration of the inflow air from outdoors being zero. In an attempt to give a more realistic model of the practical problems, Li [18] incorporated the surface thermal radiation effect in the building and obtained more general expressions for the airflow rate and stratification interface position for DNV in a singlezone building with two-level openings. The results showed that when the thermal radiation effect is considered, the airflow rate is affected by the strength of the buoyancy source. However, pollutant sources (for example, CO2) may exist in a room and the inflow air from outdoors contains a certain amount of pollutants for practical cases. In addition, indoor air quality can be influenced by outdoor air in the absence of indoor pollutant sources, i.e., intake of outdoor air constitutes the main source of pollutants in the indoor environment. The main purpose of the present study is to obtain expressions for predicting the dilution processes of pollutants in a DNV room by employing and extending the results from previous investigations [11,16e20]. Furthermore, the relationships between indoor concentrations and the thermal radiation effects of the inner surface and the window opening area, etc., are analyzed and the dilution of indoor pollutant in the DNV room is discussed and evaluated.
109
2. Mathematical models and thermal stratification height of natural ventilation flows induced by thermal forces In order to put this work in context, the existing DNV flow theory and the models employed in the previous investigations are reviewed and discussed in this section. 2.1. Mathematical models When outdoor air enters an indoor environment from the bottom of the room with a relatively low speed, and a central heat source exists near the floor, a specific flow pattern forms in the room that is largely influenced by a thermal plume emanating from the heat source. The fully mixed model developed by Andersen [19] considered that the air temperature distributes uniformly in the room, as shown in Fig. 1(a). According to the “emptying waterfilling box model” given by Linden et al. [10e12], the distribution of air temperature in the room can be divided into two zones by the thermal stratification interface, while the air temperature in each zone is uniform, and the temperature in the upper zone is higher than that of the lower zone, which shares the same air temperature with the supply air, see Fig. 1(b). Considering the effect of thermal radiation between the ceiling and floor of the room on the temperature distribution, Li [18] improved Linden’s “emptying water-filling box” models and Andersen’s “fully-mixed” model and derived two new ones, i.e., the “emptying air-filling box” model I and model II, for predicting a single-zone building with buoyancy-driven ventilation. The difference between the “emptying air-filling box” model I and
Fig. 1. Airflow models of natural ventilation induced by thermal forces. (a) Fully mixed model (b) Emptying water-filling box model. (c) Emptying air-filling box model I (d) Emptying air-filling box model II.
110
K. Zhong et al. / Building and Environment 56 (2012) 108e117
“emptying water-filling box” model is that in the former the air temperature at the bottom of the lower zone is higher than the supply air temperature due to the thermal radiation effect of the inner surface of the building, as shown in Fig. 1(c). And the “emptying air-filling box” model II is modified from model I with an assumption of a linear temperature profile in the room, see Fig. 1(d). Li [18] also found that the “fully-mixed” model overestimates the clean zone (lower zone) height and the incoming airflow rate, while the “emptying water-filling box” model underpredicts the magnitudes of these two parameters. In order to compare the effect of thermal radiation of the inner surface of the building on the distribution of pollutant concentration, the “emptying air-filling box” model I is adopted to analyze the changes of pollutant concentration in a naturally ventilated room in the present study. 2.2. Thermal stratification height Stratification height is an essential parameter for DNV flows formed by a central heat source (including point and line heat sources). When the thermal radiation in a building is negligible, Linden et al. [10,11] derived an expression of the dimensionless depth of the cool ambient layer, x, which is defined as the ratio of the thermal stratification height h and the room height H from the “emptying water-filling box” model, i.e. x ¼ h/H, and it can be given by
A* ¼ C 3=2 nH 2
sffiffiffiffiffiffiffiffiffiffiffi
x5
(1a)
1x
where A*, which represents the effective opening (vent) area, can be expressed by
A* ¼
.qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi A2t þ A2b 2At Ab
(1b)
where At and Ab are the effective areas of the pffiffiffioutlet/top and pffiffiffiinlet/ bottom openings, respectively, and At ¼ 2ct at , Ab ¼ 2cb ab . Here ct and cb are the discharge coefficients of the outlet/top and inlet/bottom openings, respectively. And at and ab are the outlet and inlet opening areas, respectively. n is the number of individual sources; C is an entrainment constant, where for a point heat source, C ¼ (6pa/5)(9a/10p)1/3, and for a line heat source, C ¼ (2a)2/3; while a, with a value of 0.102, is a turbulent flow entrainment constant of the heat source, see Refs. [17,21]. When the thermal radiation effect in the building is taken into consideration, x obtained from the “emptying air-filling box” model I by Li [18] can be written as
A* Cd 3k=2 ð3j1Þ=2 ¼ C 3=2 L H
(A*)/(L3k/2H(3j1)/2) is the dimensionless opening area of the central heat source, and when substituting the value of j and k into Eq. (2), one can obtain the specific expression of A*/H2 for a point heat source and A*L/H for a line heat source. Here A*L ¼ A*/L. The previous studies show that the strength of the inner heat source mainly influences the airflow rate but seems to have no effect on the thermal stratification height of a DNV room, as shown by Linden [11] and Li [18]. As the most important parameter is the pollutant concentration in the occupied zone for evaluating indoor air quality, the following discussion will focus on the parameters which affect the thermal stratification height. The influence of the strength of the heat source on the decay of pollutant concentration in the room will not be considered. 3. Changes of pollutant concentration in naturally ventilated rooms driven by thermal forces Many investigations on the flushing of a neutrally-buoyant nonreactive pollutant (i.e., a passive tracer) from ventilated rooms have been conducted both experimentally and theoretically, for example see Ref. [22]. The tracer gas removal technique has been widely used for estimating airflow rates and ventilation efficiency in enclosures. However, in contrast to forced ventilation, studies on pollutant flushing using natural ventilation are still lacking in the literature. In a DNV room, localized buoyancy sources giving rise to turbulent plumes induce outside air into the room through the lower opening, which mixes with the polluted indoor air. This air is then entrained into the plumes and finally is flushed out through the upper vent(s). A schematic of this process is shown in Fig. 2. By employing the “emptying water-filling box”, Hunt [17] analyzed the dilution process of indoor pollutants with the assumptions that there is an initial pollutant concentration in the room, and the concentration of the incoming air is zero. In fact, pollutant sources, for example, CO2 and VOCs, may exist in a room and the incoming air from outdoors also contains a certain amount of the pollutants. Thus the “emptying air-filling box” model I [18] can be extended to establish a dilution model of pollutant concentration in a DNV room. To simplify the analysis, see Fig. 2, we assume that the ventilation flow has reached a steady state prior to contaminant release, and the initial indoor concentration is assumed to be K0 (kg/m3).
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
x3j
1 ð1 lÞx
(2)
where Cd is the discharge coefficient with a value of 0.6, which is assumed equal for the outlet and inlet vent [18]; L is the length of the line heat source, with L ¼ 1 for a point source; for a point heat source, j ¼ 5/3, and for a line heat source, j ¼ 1, k ¼ 5/3 j, see Ref. [17]. l ¼ ½ðrcp Q =Af Þð1=ar þ 1=ac þ 1=af Þ þ 11 is the dimensionless temperature with consideration of the thermal radiation of the inner surface of the building, Q is the ventilation airflow rate, m3/s; cp is the heat capacity of air, J/(kg K); r is the air density, kg/m3; Af is the floor area, m2; ar, ac and af are the radiant heat transfer coefficient of the inner surface of the room, convective heat transfer coefficient at the ceiling and floor of the room, respectively, W/ (m2 K). l is a function of the heat transfer coefficients and ventilation airflow rate Q, and its value is in the range 0 < l < 1.
Fig. 2. Dilution model of pollutant concentration in a displacement natural ventilation room.
K. Zhong et al. / Building and Environment 56 (2012) 108e117
The strength of the source is M (kg/s) in both the upper and lower zones, respectively, and the outdoor airflow with a concentration Kin (kg/m3) enters the room from the bottom opening and finally is flushed out of the room through the top opening by thermal forces. According to the previous discussion, the flow patterns in the upper and lower zones are different in a DNV room [23,24], resulting in a significant difference of pollutant distributions between the two zones of the room. To analyze the distribution of pollutant concentration in the room, the pollutant conservation equations (i.e. the mass balance equations) should to be satisfied separately in the two zones.
3.1. The variations of pollutant concentrations in the lower zone of a DNV room Assuming that the pollutants distribute uniformly in the lower zone of a DNV room, the concentration in the zone, Klo (t) (kg/m3), satisfies the following mass balance equation (See Fig. 2)
d K hA ¼ Kin Qin þ M Klo Qp d¼h dt lo f
(3)
with the initial condition t ¼ 0, Klo ¼ K0. Qin is the airflow rate which enters the room through the lower opening, m3/s; Qp is the airflow rate (which is entrained by the thermal plume) enters the upper zone through the stratification interface, m3/s; and d is the height of the thermal stratification interface, m. At the height of the stratification interface, the airflow rate entrained by the thermal plume equals that of the inflow from outdoors, i.e. Qin ¼ Qp jd¼h . Kaye and Hunt [16] showed that the airflow rate of a thermal plume induced by a single central heat source at the height of d can be written by j
Qp ¼ CB1=3 d Lk
j j mx ¼ M= K0 CB1=3 Lk Hj ¼ M x = K0 Qp ¼ m$x
(5)
where m ¼ M/(K0Qp). Obviously, mx is related to strength of the heat source, height of the room and initial indoor pollutant concentration. It is not affected by the area of the opening. The dimensionless time should be given properly for solving Eq. (3). In order to show the relationship of the variation of pollutant concentration with the ratio of the times of emptying and filling, Hunt and Kaye [17] defined a dimensionless time, s, as follows
t
s ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A2f =C 1=2 A* B2=3 Lk=2 Hðj3Þ=2
t Af =CB1=3 Lk H j1
Substituting Eqs. (4), (5) and (6b) into Eq. (3), yields
(7)
and the initial condition at s ¼ 0 is klo ¼ 1. The dimensionless pollutant concentration in the lower zone of a DNV room with a central heat source can thus be obtained
klo ¼ ðkin þ mÞ ðkin þ m 1Þeflo s where flo ¼ x
j1
(8)
.
3.2. The variations of averaged concentrations in a DNV room Similarly, in the upper zone of a DNV room, the mass balance equation for the pollutant concentration, Kup(t), can be written as
d Kup ðH hÞAf ¼ Klo Qp d¼h þ M Kup Qout dt
(9)
and the initial condition at t ¼ 0 is Kup ¼ K0.where Qout is the airflow rate discharged from the upper opening, m3/s; and Qout ¼ Qin ¼ Qp jd¼h . Substituting Kup with the dimensionless form kup ¼ Kup/K0, Eq. (9) can be simplified as the follows
xj d kup ¼ klo þ m kup ds 1x
(10)
with the initial condition s ¼ 0, kup ¼ 1. Then the pollutant concentration in the upper zone of a DNV room with a central heat source is
kup ¼ ðkin þ 2mÞ ðkin þ m 1Þ
fup eflo s flo efup s fup flo
mefup s
(11)
j
where fup ¼ x =ð1 xÞ And the averaged dimensionless pollutant concentration, ktot, in the room at any time can be calculated by
ktot
#, " Klo hAf þ Kup ðH hÞAf K0 ¼ klo x þ kup ð1 xÞ ¼ HAf
(12)
Substituting Eqs. (8) and (11) into Eq. (12), ktot can be given by
x2
ktot ¼ ðkin þ 2m mxÞ ðk þ m 1Þeflo s 2x 1 in ð1 xÞx þ ðkin þ m 1Þ ð1 xÞðkin þ 2m 1Þ efup s 2x 1 (13) The results for the concentration calculation and the main parameters used for the derivations above are summarized in Table 1.
(6a)
If the effects of indoor pollutant source and outdoor pollutant on the indoor air quality are considered, and the definition of Eq. (6a) is adopted, the analytical solution of Eq. (3) cannot be obtained. Therefore a new dimensionless time is defined here
s ¼
d j1 k ¼ ðkin þ m klo Þx ds lo
(4)
where B is the buoyancy flux, m4/s3; B ¼ Eg/(CprT0). Here E is the heat flux produced by an inner heating source, W; T0 is the ambient air temperature, K; and g is the gravitational acceleration, m/s2. To obtain the analytical solution for Eq. (3), the dimensionless concentrations are introduced and defined as klo ¼ Klo/K0, and kin ¼ Kin/K0, respectively. Also a dimensionless strength of the pollutant source, mx, is defined as
111
(6b)
4. Necessary conditions for the decay of pollutant concentration in DNV rooms In a naturally ventilated room driven by thermal buoyancy forces, the inflow air from outdoors has two primary effects on the indoor pollutant concentration. On the one hand, indoor air quality can be improved as the indoor pollutant is flushed out by the natural ventilation airflow; on the other hand, when the pollutant concentration contained in the inflow air is higher than that indoors, the indoor concentration would be increased. In order to
112
K. Zhong et al. / Building and Environment 56 (2012) 108e117
Table 1 Calculated concentrations and the definitions of main parameters for the derivations. Variables
Point heat source sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x5 Cd A* 3=2 ¼ C 1 ð1 lÞx H2
x
Line heat source sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Cd A*L x3 ¼ C 3=2 H 1 ð1 lÞx 1 x/(1 x)
x2/3 x5/3/(1 x)
flo fup s
t Af =CB1=3 Lk H j1 ðkin þ mÞ ðkin þ m 1Þeflo s
klo(s) kup(s)
ðkin þ 2mÞ ðkin þ m 1Þ
fup eflo s flo efup s mefup s fup flo
ktot(s)
ðkin þ 2m mxÞ
reduce the indoor concentration with ventilation time, it is necessary to explore the factors which directly affect the decay of indoor pollutant concentration. 4.1. Cases of the lower zone In practice, the final concentration level in a room is one of the main parameters for characterizing the ventilation effectiveness, therefore, it is important to obtain some conditions for reducing the pollutant concentration to a certain level in the lower zone of the room. For example, the necessary conditions for reducing the concentration to 50% or 10% of the initial concentration in the lower zone. Assuming klo jx ¼ klo ðsÞjs¼0 x%, where x ranges from 0 to 100, if the concentration in a DNV room should be reduced to a certain value after the room has been ventilated for a long time, klo(s) needs to satisfy
lim k ðsÞ klo jx s/þN lo
(14)
Combining Eqs. (8) and (14), we have
lim k ðsÞ ¼ kin þ m klo jx s/þN lo
(15a)
i.e.
kin þ
x2 ð1 xÞx ðk þ m 1Þeflo s þ ðk þ m 1Þ ð1 xÞðkin þ 2m 1Þ efup s 2x 1 in 2x 1 in
1 M klo jx CB1=3 Lk hj K0
(15b)
Eq. (15) gives the restriction between the pollutant concentration of inflow air from outdoors and the strength of indoor pollutant sources when the indoor pollutant concentration in the lower zone of a DNV room needs to be reduced to a certain level. Table 2 shows the cases for the following discussion. By using Eq. (15) under the conditions listed in Table 2, the following results can be obtained for the four possible cases in a DNV room:
a similar situation without considering the inner thermal radiation effect; (2) Case B: to reduce the pollutant concentration to a certain value in the lower zone, Eq. (15) only requires kin klo jx ; (3) Case C: conditions required for the reduction of pollutant concentration in the lower zone to different levels can also be derived from Eqs. (15) and (5) j
ð1=xÞ mx klo jx
To ensure that the concentration in the lower zone can be reduced to klo jx , the upper limit of mx,max is j mx;max ¼ x klo jx
(4) Case D: the requirement for this case can be readily obtained from Eq. (15) as j
kin þ ð1=xÞ mx klo jx
Table 2 Possible cases of inflow air and inner sources in the lower zone of the DNV room.
j mx;max ¼ x klo jx kin
A B C D
Mode of pollutant in air Incoming air
Indoor air
contains contains contains contains
no indoor pollutant source no indoor pollutant source indoor pollutant source exists indoor pollutant source exists
no pollutant pollutant no pollutant pollutant
(17)
Because the dimensionless thermal stratification height x of a DNV room mainly depends on the effective window opening area A*, the height of the room and the type of inner heat source, the upper limit of strengths of indoor pollutant sources (mx,max) are different for different rooms for reducing the indoor concentration to the same level. Fig. 3 shows the effect of window opening area on the upper limit of dimensionless strength of point and line pollutant sources when klo jx ¼ klo ð0Þ, 0.5klo (0) and 0.1klo (0), respectively, where klo jx ¼ klo ð0Þ represents the critical value of the decay of indoor pollutant concentration. It can be seen from Fig. 3 that mx,max increases with the increase of window opening area if the concentration decreases with a same percentage from its initial value. However, when the indoor concentration should be reduced to a very low level (for example, klo jx ¼ 0:1klo ð0Þ), mx,max should be quite low even if the window opening area can be increased to a very large value. This means that the increase of the window opening area is effective for increasing the upper limit of the source strength only if the klo jx is large.
(1) Case A: from Eq. (15) it can be easily known that indoor pollutant concentration in the lower zone can certainly decrease to any level required. Hunt and Kaye [17] discussed
Case
(16)
(18)
To reduce the concentration in the lower zone to klo jx , the upper limit of mx,max is
(19)
The relationship between kin and mx,max can be obtained from Eq. (19) for reducing the indoor pollutant concentration to a certain level klo jx in the lower zone of the DNV room. The curves in Fig. 4 show that if the dimensionless window opening area is given (therefore the stratification height is determined), the concentration indoors can be reduced to the required level only when the
K. Zhong et al. / Building and Environment 56 (2012) 108e117
113
Fig. 4. Conditions required by Case D for reducing pollutant concentration in the lower zone. (a) Point heat source (b) Line heat source.
Fig. 3. Conditions required by Case C for reducing pollutant concentration in the lower zone (a) Point heat source (b) Line heat source.
explore the conditions for the decay of the averaged indoor concentration with time. Letting vktot ðsÞ=vsjs¼s0 ¼ 0, it can be obtained from Eq. (13) that
pollutant concentration of the incoming air and the strength of indoor pollutant source are restricted in certain ranges, i.e., kin and mx must fall into the range below the curves shown in Fig. 4. Fig. 4 shows that mx,max decreases with the decrease of the window opening area and also decreases with the increase of pollutant concentration of the inflow air from outdoors. In addition, the influence of the window opening area on mx,max is large for small kin; when kin approaches klo jx , this influence becomes weak and thus can be ignored.
s0 ¼
4.2. Cases of the whole room In the initial stage of the pollutant emission in a DNV room, the thermal plume brings the pollutant from the lower zone to the upper zone. The pollutant concentration may increase in the upper zone and even in the whole room because the exhaust openings cannot removal the pollutant air quickly enough. But with the increase of the concentration near the exhaust, the effectiveness of ventilation is also increased, which results in the reduction of the concentration in the upper zone and the whole room. Thus it is necessary to analyze the monotonic characteristics of ktot (s) to
1x ðkin þ m 1Þx=ð2x 1Þ ln x2=3 ð1 2xÞ ðkin þ m 1Þx=ð2x 1Þ ðkin þ 2m 1Þ (20)
Then the monotone intervals of ktot (s) can be determined by Eq. (20), with the results given in Table 3. The results in Table 3 show some characteristics of the variation of ktot (s) in a DNV room: (1) If kin þ 2m 1 < 0, the averaged indoor concentration ktot (s) decreases monotonically with time for any value of the thermal stratification height of the room. Curve 1 in Fig. 5 shows such a case. (2) If kin þ 2m 1 > 0, ktot (s) increases with time in the time internal s˛ð0; s0 Þ. When s˛ðs0 ; þNÞ, the necessary conditions for the decay of ktot (s) depends on the dimensionless thermal stratification height x of the room. For x 0.5, to ensure ktot (s) decreases monotonically with time in a DNV room, another necessary condition, kin þ m 1 < 0, is required. For x < 0.5, the additional necessary condition for the monotonic decay is (x/2x 1)(kin þ m 1) > kin þ 2m 1. The time
114
K. Zhong et al. / Building and Environment 56 (2012) 108e117
Table 3 Monotone intervals of ktot (s).
x
Main terms in Eq. (20)
x 0.5 kin þ 2m 1 < 0
kin þ 2m 1 > 0 kin þ m 1 < 0 x < 0.5 kin þ 2m 1 < 0 8 > kin þ 2m 1 > 0 < 2x 1 > ðkin þ 2m 1Þ < 0 : kin þ m 1
x
Monotone interval decrease when s˛ð0; þNÞ increase when s˛ð0; s0 Þ decrease when s˛ðs0 ; þNÞ decrease when s˛ð0; þNÞ increase when s˛ð0; s0 Þ decrease when s˛ðs0 ; þNÞ
dependent characteristic line for the two cases is shown as Curve 2 in Fig. 5. If kin and m do not satisfy the conditions mentioned above, ktot (s) will not decrease with time but increase exponentially in the range s˛ð0; þNÞ. In order to reduce ktot (s) to a target level ktot jx ¼ ktot ðsÞjs¼0 x%; let lim ktot ðsÞ ktot jx , also from Eq. s/þN (13), we have
kin þ 2m mx ktot jx
(21)
Which means that beside the necessary conditions in Table 3, Eq. (21) is required for ktot (s) to reduce to x% of the initial concentration when kin þ 2m 1 > 0.
radiation of the inner surface only affects the decay rate of concentration in the upper zone of a room. If a point heat source exists in the room, to simplify the analysis, it can be assumed that kin ¼ 0.1, x ¼ 0.6 and mx ¼ 0.043 (i.e. m ¼ 0.1). l ¼ 0e1, where l ¼ 0 means no thermal radiation in the room. Figs. 6 and 7 show the variations of pollutant concentration in the lower zone and averaged concentration of the room for different values of l with a point or line heat source. For small opening area of the window (e.g., A*/H2 ¼ 0.005), Fig. 6(a) shows that the differences of klo between the three curves (with different values of l) are negligible. This difference increases slightly with the increasing of the opening area, which indicates that the effect of l on the decay rate of concentration is weak in the lower zone. Fig. 6(b) and Fig. 7 show the variations of averaged concentrations of the room with point and line heat sources, respectively. It can be found that the impact of l on the decay rate of averaged indoor concentration is much larger than that of the lower zone, which implies that thermal radiation of the inner surface of a building mainly affects the reduction of concentration in the upper zone. In addition, the thermal radiation effect of the inner surface on the decay rate of concentration at the later stages is more obvious than that of the initial stage. Taking the line heat source
5. Analysis of the decay rate of indoor pollutant concentration As has been discussed in the previous sections, indoor concentration decays with time if kin and m satisfy certain conditions in a DNV room. Eqs. (8) and (13) indicate that when the room height is given, the decay rate primarily depends on the stratification height (determined by the dimensionless area of the opening), x, the thermal radiation coefficient of the inner surface, l, the concentration of the incoming air from outdoor, kin, and the strength of the indoor source mx. 5.1. Effect of thermal radiation of the inner surface on the concentration decay rate It can be found from Table 1 that when a line heat source exists in the room, the decay coefficient of concentration in the lower zone is flo ¼ 1, which is independent of the parameter l, i.e. thermal
Fig. 5. Variations of averaged indoor pollutant concentration with time.
Fig. 6. Effect of thermal radiation of the inner surface on indoor pollutant concentration when a point heat source exists in a DNV room. (a) Cases of the lower zone (b) Cases of the whole room.
K. Zhong et al. / Building and Environment 56 (2012) 108e117
Fig. 7. Effect of thermal radiation of the inner surface on indoor pollutant concentration when a line heat source exists in a DNV room.
115
Fig. 8. Variations of s50 vs kin in the lower zone with different window opening areas for Case B.
with A*L =H ¼ 0:22 as an example, when the pollutant concentration reduces to 70% and 30% of the initial value, respectively, the corresponding dimensionless time for the three different cases (i.e. l ¼ 0.0, 0.4 and 0.8, respectively) are 0.70, 0.79, 0.88 and 2.7, 3.1, 3.4, respectively.
5.2. Effect of window opening area on the concentration decay rate in the lower zone People usually concern more about indoor air quality of the occupied zone. Thus it is important to analyze the variation of concentration and the factors influencing pollutant dispersion in the lower zone of a DNV room. Since, as previously shown, the thermal radiation of the inner surface has no significant influence on the decay of concentration in the lower zone, the following discussion will focus on l ¼ 0. To analyze the effect of the window opening area on the decay of concentration in the lower zone, here we define the time required to reduce the pollutant concentration to 50% of its initial value in the lower zone as s50. From Eq. (8) we have
i h h i j j 0:5 ¼ kin þ ð1=xÞ mx kin þ ð1=xÞ mx 1 eflo s50 i.e.
s50 ¼
1
flo
j
ln
0:5 kin ð1=xÞ mx j
1 kin ð1=xÞ mx
(22)
(1) For Case A (kin ¼ 0, mx ¼ 0), from Eq. (22) we have
s50 ¼
1
flo
ln0:5 ¼ x
1j
ln0:5
(23)
Eq. (23) means that for a point heat source, s50 decreases with the increase of x2/3, i.e. decreases with the increase of the window opening area (A*/H2); for a line heat source, the value of s50 is fixed because j ¼ 1, and A*L/H has no effect on the reduction of concentration in the lower zone.
Fig. 9. Variations of s50 vs mx in the lower zone with different window opening areas for Case C. (a) Point heat source (b) Line heat source.
116
K. Zhong et al. / Building and Environment 56 (2012) 108e117
(2) For Case B (kin s 0, mx ¼ 0), s50 in the lower zone obtained from Eq. (22) can be written as
(3) For Case C (kin ¼ 0, mx s 0), according to Eq. (22) we get j
s50 ¼ xj1 ln
0:5 kin 1 kin
s50 ¼ xj1 ln
0:5 ð1=xÞ mx
(24)
The variations of s50 with kin can be calculated from Eqs. (24) and (2) and are shown in Fig. 8. From Fig. 8 one can find that if no pollutant source exists in the room, s50 increases with kin and approaches to infinite if kin ¼ 0.5. The decay rate increases when the opening area increases, while s50 decreases. In addition, the differences between the decay rates for different opening areas also reduce with the increase of the opening area, meaning that a larger opening area can result in rapid decay of the concentration in the lower zone. But when the opening area increases to a certain extent, the influence on the decay rate becomes weak. As has been discussed in the previous section, j ¼ 1 (i.e. flo ¼ 1) in the lower zone when a line heat source exists in the DNV room. Therefore the opening area has no effect on the decay rate of the concentration for such situations. Comparing the values of s50 for line and point heat sources in Fig. 8, the concentration decay rate for the former is faster than that for the later when no pollutant source exists in the room.
j
1 ð1=xÞ mx
(25)
The variations of s50 with mx which characterizes the emission amount of indoor pollutant with different window opening areas can be found from Eq. (25), and are shown in Fig. 9. It can be seen from Fig. 9 that when mx reaches a certain critical value, s50 approaches infinity for reducing indoor concentration to 50% of its initial value in the lower zone of the room. This value is the upper limit m,xmax of Case C for reducing the concentration to half of its initial value in the lower zone. The calculated curves in Fig. 9 indicate that when the strength of the indoor pollutant source is low, the effect of window opening area on the decay of pollutant concentration in the lower zone of a DNV room is relatively weak. Only when the strength of indoor pollutants is relatively large can the effect of the opening area become significant. (4) For Case D (kin s 0, mx s 0), also from Eq. (22) it can be found that j 1 0:5 kin ð1=xÞ mx s50 ¼ ln flo 1 kin ð1=xÞj mx
(26)
The changes of s50 with kin for different window opening areas and the emission rates of indoor pollutants can be calculated from Eq. (26), and are shown in Fig. 10. Fig. 10 shows when kin increases to a critical value, s50 increases to infinity for reducing concentration to 50% of its initial value in the lower zone of the DNV room. This critical value is the upper limit of Case D for reducing indoor concentration to 50% of the initial value in the lower zone. Fig. 10 also shows that only when kin approaches the critical value can the effective opening area affect the decay rate of pollutant concentration in the lower zone. 6. Conclusions
Fig. 10. Variations of s50 vs kin in the lower zone with different window opening areas for Case D. (a) Point heat source (b) Line heat source.
For the proper design of a DNV system, it is essential to ensure good indoor air quality and maintain the stratification interface above the level of the human breathing zone. Therefore, insight into the important physical mechanisms is necessary for the optimization of the design and operation of natural ventilation systems. Considering both the influences of concentration of incoming air and indoor pollutant sources, mathematical models for predicting airflow in natural ventilation rooms, which were obtained in the previous investigations, are employed to establish the mass conservation equations of pollutant transportation in the upper and lower zones in a DNV room. The variations of indoor concentrations with time were obtained from these equations. The conditions for reducing indoor concentration to certain levels and factors affecting the decay rate of concentration indoors were analyzed and discussed, and conclusions were made. The time variation of the concentration in the lower zone is different from the indoor averaged concentration mathematically in DNV rooms, although both of the variations can be expressed in exponential forms. In order to reduce the concentration in the lower zone to an expected level, both the concentration of incoming air and indoor emission rate should be less than their critical values for a given effective opening area of the window. The influence of thermal radiation of the inner surface on the reduction of pollutant concentration in the upper zone is greater than that in the lower zone of a DNV room. Thus the thermal radiation effect of the inner surface can be ignored for roughly
K. Zhong et al. / Building and Environment 56 (2012) 108e117
estimating the variation of the concentration in the occupant zone of the DNV room. In addition, the decay rate of indoor pollutant concentrations increases with the increase of the effective opening area of the window, but the opening area mainly affects the final indoor concentration level. Only when the concentration of incoming air or the strength of the indoor source approaches their critical values can the opening area influence the decay rate of indoor pollutant concentration in the DNV room.
Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 40975093). The authors would like to thank Dr. D. Gottfried for his helpful discussions and recommendations.
Nomenclature A* Ab Af At ab at B C Cd Cp cb ct E G H H K0 Kin Klo klo jx Kup kin klo ktot ktot jx kup L M mx Q Qin Qp T0 t
effective opening (vent) area of a room pffiffiffi effective area of the inlet/bottom opening, Ab ¼ 2cb ab floor area of a room pffiffiffi effective area of the outlet/top opening, At ¼ 2ct at inlet opening area of a room outlet opening area of a room buoyancy flux entrainment constant discharge coefficient of the opening heat capacity of air discharge coefficient of the inlet opening discharge coefficient of the outlet opening heat flux produced by an inner heating source gravitational acceleration room height thermal stratification height initial indoor pollutant concentration outdoor pollutant concentration pollutant concentration in the lower zone a target level of klo (s), defined as klo jx ¼ klo ðsÞjs¼0 x% pollutant concentration in the upper zone dimensionless concentration of incoming air, kin ¼ Kin/K0 dimensionless concentration in the lower zone, klo ¼ Klo/K0 averaged dimensionless pollutant concentration in a room a target level of ktot (s), defined as ktot jx ¼ ktot ðsÞjs¼0 x% dimensionless concentration in the upper zone, kup ¼ Kup/K0 length of the line heat source strength of indoor pollutant source dimensionless strength of indoor pollutant source ventilation airflow rate airflow rate through the lower opening airflow rate (which is entrained by the thermal plume) enters the upper zone air temperature outdoors time
117
Greek symbols convective heat transfer coefficient at the ceiling convective heat transfer coefficient at the floor radiant heat transfer coefficient of the inner surface of a room d height of the thermal stratification interface l dimensionless temperature with consideration of the thermal radiation of the inner surface x dimensionless thermal stratification height r air density s dimensionless time s50 time required to reduce pollutant concentration to 50% of its initial level in the lower zone
ac af ar
References [1] Jenkins PL, Phillips TJ, Mulberg EJ, Hui SP. Activity patterns of Californians: use and proximity to indoor pollutant sources. Atmos Environ 1992;26A(12): 2141e8. [2] Klepeis NE, Nelson WC, Ott WR, Robinson JP, Tsang AM, Switzer P, et al. The national human activity pattern survey (NHAPS): a resource for assessing exposure to environmental pollutants. J Expo Anal Environ Epidemiol 2001; 11(3):231e52. [3] Kousa A, Kukkonen J, Karppinen A, Aarnio P, Koskentalo T. A model for evaluating the population exposure to ambient air pollution in an urban area. Atmos Environ 2002;36(13):2109e19. [4] Orme M. Estimates of the energy impact of ventilation and associated financial expenditures. Energ Build 2001;33(3):199e205. [5] Perez-Lombard L, Ortiz J, Pout C. A review on buildings energy consumption information. Energ Build 2008;40(3):394e8. [6] Balaras CA, Gaglia AG, Georgopoulou E, Mirasgedis S, Sarafidis Y, Lalas DP. European residential buildings and empirical assessment of the Hellenic building stock, energy consumption, emissions and potential energy savings. Build Environ 2007;42(3):1298e314. [7] Jiang Y. Current building energy consumption in China and effective energy efficiency measures. HV&AC 2005;35(5):30e40 [in Chinese]. [8] Jiang Y, Yang X. China building energy consumption situation and the problems exist in the energy conservation works. China Construct 2006;2:12e7 [in Chinese]. [9] Li B, Yao R. Urbanisation and its impact on building energy consumption and efficiency in China. Renew Energ 2009;34(9):1994e8. [10] Linden PF. The fluid mechanics of natural ventilation. Annu Rev Fluid Mech 1999;31:201e38. [11] Linden PF, Lane-Serff GF, Smeed DA. Empting filling boxes: the fluid mechanics of natural ventilation. J Fluid Mech 1990;212:309e35. [12] Linden PF, Cooper P. Multiple sources of buoyancy in a naturally ventilated enclosure. J Fluid Mech 1996;311:177e92. [13] Gladstone C, Woods AW. On buoyancy-driven natural ventilation of a room with a heated floor. J Fluid Mech 2001;441:293e314. [14] Fitzgerald SD, Woods AW. Natural ventilation of a room with vents at multiple levels. Build Environ 2004;39(5):505e21. [15] Jiang Y, Chen Q. Buoyancy-driven single-sided natural ventilation in buildings with large openings. Int J Heat Mass Tran 2003;46(6):973e88. [16] Kaye NB, Hunt GR. Time-dependent flows in an emptying filling box. J Fluid Mech 2004;520:135e56. [17] Hunt GR, Kaye NB. Pollutant flushing with natural displacement ventilation. Build Environ 2006;41(9):1190e7. [18] Li Y. Buoyancy-driven natural ventilation in a thermally stratified one-zone building. Build Environ 2000;35(3):207e14. [19] Andersen KT. Theoretical considerations on natural ventilation by thermal buoyancy. ASHRAE Trans 1995;101(2):1103e17. [20] Li Y, Delsante A, Symons J. Prediction of natural ventilation in buildings with large openings. Build Environ 2000;35(3):191e206. [21] Jin Y. Particle transport in turbulent buoyant plumes rising in a stably stratified environment. Ph.D. theses, Department of Building Services Engineering, KTH, Stockholm, Sweden; 1993. [22] Yuan X, Chen Q, Glicksman LR, Hu Y, Yang X. Measurements and computations of room airflow with displacement ventilation. ASHRAE Trans 1999; 105(1):340e532. [23] Cooper P, Linden PF. Natural ventilation of an enclosure containing two buoyancy sources. J Fluid Mech 1996;311:153e76. [24] Ji Y, Cook MJ, Hanby V. CFD modelling of natural displacement ventilation in an enclosure connected to an atrium. Build Environ 2007;42(3):1158e72.
Contents lists available at SciVerse ScienceDirect
Building and Environment journal homepage: www.elsevier.com/locate/buildenv
Pollutant dilution in displacement natural ventilation rooms with inner sources Ke Zhong, Xiufeng Yang, Wei Feng, Yanming Kang* School of Environmental Science and Engineering, Donghua University, 2999 North Renmin Road, Shanghai 201620, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 11 December 2011 Received in revised form 23 February 2012 Accepted 24 February 2012
Indoor air quality and pollutant dispersion in natural ventilation rooms have received considerable attention in recent years. In order to evaluate the pollutant concentration levels in the occupant zone in a displacement natural ventilation (DNV) room, the mathematical model in previous studies are employed and extended to estimate pollutant transportation in a DNV room with the consideration of both the incoming air concentration and indoor pollutant source, resulting in exponential type expressions in time for the concentration in the lower zone and the mean concentration in DNV rooms. The results show that for reducing the concentration in the lower zone to a certain value, the concentration of inflow air and indoor emission rate should be less than their critical values for a given effective opening area of the window. The effect of thermal radiation of the inner surface on the reduction of pollutant concentration in the upper zone is greater than that in the lower zone of a DNV room. In addition, the effective opening area of the window primarily influences the final concentration level in the DNV room, and only affects the decay rate of indoor pollutant concentration when the pollutant concentration of incoming air or the strength of the indoor source approach their critical values. 2012 Elsevier Ltd. All rights reserved.
Keywords: Displacement natural ventilation room Pollutant Source Concentration Dilution Decay rate
1. Introduction Ventilation is necessary for indoor environments to supply fresh air for the metabolism process, to provide good indoor air quality and to maintain a comfortable thermal environment. Building ventilation has become more important because people spend most of their time indoors [1e3], and more and more high rise buildings with high air tightness appear in cities. Although mechanical ventilation in buildings is nowadays a common way to maintain a steady indoor air environment, the energy consumption related to the operation of heating, ventilation and air-conditioning systems (HVAC) is considerable. According to recent studies, more than half of the total energy used in service and residential buildings is attributable to HVAC systems [4e8]. Studies have shown that in Europe and USA about 40% of final energy consumption is in the buildings sector [5,6]. Also in the past two decades, building energy consumption in China has been increasing at more than 10% a year. In the year 2004, building energy consumption alone constituted 20.7% of the total national energy consumption [7,8], and now it has increased to 30% [9]. Natural ventilation can be used as a passive cooling technique for reducing building energy consumption, and it has been the subject of much research over recent decades due to its potential for offering good indoor air quality for occupants and relatively low
* Corresponding author. Tel.: þ86 21 67792159; fax: þ86 21 67792522. E-mail address: [email protected] (Y. Kang). 0360-1323/$ e see front matter 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2012.02.028
energy usage compared with mechanical ventilation. Natural ventilation of buildings is the flow generated by temperature differences, i.e. thermal buoyancy, and by the wind [10]. Many investigations have been carried out to explore the temperature distribution, thermal comfort and air exchange rate of naturally ventilated rooms/buildings driven by thermal force [11e15]. In a building with displacement natural ventilation, dense ambient air flows through low-level openings by thermal buoyancy sources (generally, heating elements) and displaces the lighter air in the building out through high-level openings. Since the incoming air is essentially at the low level, a thermal stratification develops between the air intake and the air previously in the building. Linden et al. [11] investigated DNV in a single-zone building with two-level openings. Theoretical expressions were obtained for the airflow rate through the openings and the stratification interfacial position induced by a single point source and a single line source, respectively. The results show that while the airflow rate does depend on the source strength, the location of the stratification is exclusively determined by the geometrical parameters of the building and independent of the source strength. Kaye and Hunt [16] studied and compared the process of the flow developed to the steady displacement flow modeled by Linden et al. [11] in an enclosure with low and high level openings. They identified the time scales which characterize the development of the plume-driven flow to steady state. Hunt and Kaye [17] extended the transient model of Kaye and Hunt [16] to examine the flushing of a neutrally-buoyant pollutant from a naturally ventilated
K. Zhong et al. / Building and Environment 56 (2012) 108e117
enclosure. Their model demonstrates that the concentration of the pollutant will decay exponentially with time, and the decay rate is a function of the room geometry, outlet areas and the distribution, number and strength of the heat sources. Without the consideration of the effect of thermal radiation of the inner surface of the building, Hunt and Kaye [17] also investigated the dilution process of indoor pollutants for the case of no source but an initial pollutant concentration, with the concentration of the inflow air from outdoors being zero. In an attempt to give a more realistic model of the practical problems, Li [18] incorporated the surface thermal radiation effect in the building and obtained more general expressions for the airflow rate and stratification interface position for DNV in a singlezone building with two-level openings. The results showed that when the thermal radiation effect is considered, the airflow rate is affected by the strength of the buoyancy source. However, pollutant sources (for example, CO2) may exist in a room and the inflow air from outdoors contains a certain amount of pollutants for practical cases. In addition, indoor air quality can be influenced by outdoor air in the absence of indoor pollutant sources, i.e., intake of outdoor air constitutes the main source of pollutants in the indoor environment. The main purpose of the present study is to obtain expressions for predicting the dilution processes of pollutants in a DNV room by employing and extending the results from previous investigations [11,16e20]. Furthermore, the relationships between indoor concentrations and the thermal radiation effects of the inner surface and the window opening area, etc., are analyzed and the dilution of indoor pollutant in the DNV room is discussed and evaluated.
109
2. Mathematical models and thermal stratification height of natural ventilation flows induced by thermal forces In order to put this work in context, the existing DNV flow theory and the models employed in the previous investigations are reviewed and discussed in this section. 2.1. Mathematical models When outdoor air enters an indoor environment from the bottom of the room with a relatively low speed, and a central heat source exists near the floor, a specific flow pattern forms in the room that is largely influenced by a thermal plume emanating from the heat source. The fully mixed model developed by Andersen [19] considered that the air temperature distributes uniformly in the room, as shown in Fig. 1(a). According to the “emptying waterfilling box model” given by Linden et al. [10e12], the distribution of air temperature in the room can be divided into two zones by the thermal stratification interface, while the air temperature in each zone is uniform, and the temperature in the upper zone is higher than that of the lower zone, which shares the same air temperature with the supply air, see Fig. 1(b). Considering the effect of thermal radiation between the ceiling and floor of the room on the temperature distribution, Li [18] improved Linden’s “emptying water-filling box” models and Andersen’s “fully-mixed” model and derived two new ones, i.e., the “emptying air-filling box” model I and model II, for predicting a single-zone building with buoyancy-driven ventilation. The difference between the “emptying air-filling box” model I and
Fig. 1. Airflow models of natural ventilation induced by thermal forces. (a) Fully mixed model (b) Emptying water-filling box model. (c) Emptying air-filling box model I (d) Emptying air-filling box model II.
110
K. Zhong et al. / Building and Environment 56 (2012) 108e117
“emptying water-filling box” model is that in the former the air temperature at the bottom of the lower zone is higher than the supply air temperature due to the thermal radiation effect of the inner surface of the building, as shown in Fig. 1(c). And the “emptying air-filling box” model II is modified from model I with an assumption of a linear temperature profile in the room, see Fig. 1(d). Li [18] also found that the “fully-mixed” model overestimates the clean zone (lower zone) height and the incoming airflow rate, while the “emptying water-filling box” model underpredicts the magnitudes of these two parameters. In order to compare the effect of thermal radiation of the inner surface of the building on the distribution of pollutant concentration, the “emptying air-filling box” model I is adopted to analyze the changes of pollutant concentration in a naturally ventilated room in the present study. 2.2. Thermal stratification height Stratification height is an essential parameter for DNV flows formed by a central heat source (including point and line heat sources). When the thermal radiation in a building is negligible, Linden et al. [10,11] derived an expression of the dimensionless depth of the cool ambient layer, x, which is defined as the ratio of the thermal stratification height h and the room height H from the “emptying water-filling box” model, i.e. x ¼ h/H, and it can be given by
A* ¼ C 3=2 nH 2
sffiffiffiffiffiffiffiffiffiffiffi
x5
(1a)
1x
where A*, which represents the effective opening (vent) area, can be expressed by
A* ¼
.qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi A2t þ A2b 2At Ab
(1b)
where At and Ab are the effective areas of the pffiffiffioutlet/top and pffiffiffiinlet/ bottom openings, respectively, and At ¼ 2ct at , Ab ¼ 2cb ab . Here ct and cb are the discharge coefficients of the outlet/top and inlet/bottom openings, respectively. And at and ab are the outlet and inlet opening areas, respectively. n is the number of individual sources; C is an entrainment constant, where for a point heat source, C ¼ (6pa/5)(9a/10p)1/3, and for a line heat source, C ¼ (2a)2/3; while a, with a value of 0.102, is a turbulent flow entrainment constant of the heat source, see Refs. [17,21]. When the thermal radiation effect in the building is taken into consideration, x obtained from the “emptying air-filling box” model I by Li [18] can be written as
A* Cd 3k=2 ð3j1Þ=2 ¼ C 3=2 L H
(A*)/(L3k/2H(3j1)/2) is the dimensionless opening area of the central heat source, and when substituting the value of j and k into Eq. (2), one can obtain the specific expression of A*/H2 for a point heat source and A*L/H for a line heat source. Here A*L ¼ A*/L. The previous studies show that the strength of the inner heat source mainly influences the airflow rate but seems to have no effect on the thermal stratification height of a DNV room, as shown by Linden [11] and Li [18]. As the most important parameter is the pollutant concentration in the occupied zone for evaluating indoor air quality, the following discussion will focus on the parameters which affect the thermal stratification height. The influence of the strength of the heat source on the decay of pollutant concentration in the room will not be considered. 3. Changes of pollutant concentration in naturally ventilated rooms driven by thermal forces Many investigations on the flushing of a neutrally-buoyant nonreactive pollutant (i.e., a passive tracer) from ventilated rooms have been conducted both experimentally and theoretically, for example see Ref. [22]. The tracer gas removal technique has been widely used for estimating airflow rates and ventilation efficiency in enclosures. However, in contrast to forced ventilation, studies on pollutant flushing using natural ventilation are still lacking in the literature. In a DNV room, localized buoyancy sources giving rise to turbulent plumes induce outside air into the room through the lower opening, which mixes with the polluted indoor air. This air is then entrained into the plumes and finally is flushed out through the upper vent(s). A schematic of this process is shown in Fig. 2. By employing the “emptying water-filling box”, Hunt [17] analyzed the dilution process of indoor pollutants with the assumptions that there is an initial pollutant concentration in the room, and the concentration of the incoming air is zero. In fact, pollutant sources, for example, CO2 and VOCs, may exist in a room and the incoming air from outdoors also contains a certain amount of the pollutants. Thus the “emptying air-filling box” model I [18] can be extended to establish a dilution model of pollutant concentration in a DNV room. To simplify the analysis, see Fig. 2, we assume that the ventilation flow has reached a steady state prior to contaminant release, and the initial indoor concentration is assumed to be K0 (kg/m3).
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
x3j
1 ð1 lÞx
(2)
where Cd is the discharge coefficient with a value of 0.6, which is assumed equal for the outlet and inlet vent [18]; L is the length of the line heat source, with L ¼ 1 for a point source; for a point heat source, j ¼ 5/3, and for a line heat source, j ¼ 1, k ¼ 5/3 j, see Ref. [17]. l ¼ ½ðrcp Q =Af Þð1=ar þ 1=ac þ 1=af Þ þ 11 is the dimensionless temperature with consideration of the thermal radiation of the inner surface of the building, Q is the ventilation airflow rate, m3/s; cp is the heat capacity of air, J/(kg K); r is the air density, kg/m3; Af is the floor area, m2; ar, ac and af are the radiant heat transfer coefficient of the inner surface of the room, convective heat transfer coefficient at the ceiling and floor of the room, respectively, W/ (m2 K). l is a function of the heat transfer coefficients and ventilation airflow rate Q, and its value is in the range 0 < l < 1.
Fig. 2. Dilution model of pollutant concentration in a displacement natural ventilation room.
K. Zhong et al. / Building and Environment 56 (2012) 108e117
The strength of the source is M (kg/s) in both the upper and lower zones, respectively, and the outdoor airflow with a concentration Kin (kg/m3) enters the room from the bottom opening and finally is flushed out of the room through the top opening by thermal forces. According to the previous discussion, the flow patterns in the upper and lower zones are different in a DNV room [23,24], resulting in a significant difference of pollutant distributions between the two zones of the room. To analyze the distribution of pollutant concentration in the room, the pollutant conservation equations (i.e. the mass balance equations) should to be satisfied separately in the two zones.
3.1. The variations of pollutant concentrations in the lower zone of a DNV room Assuming that the pollutants distribute uniformly in the lower zone of a DNV room, the concentration in the zone, Klo (t) (kg/m3), satisfies the following mass balance equation (See Fig. 2)
d K hA ¼ Kin Qin þ M Klo Qp d¼h dt lo f
(3)
with the initial condition t ¼ 0, Klo ¼ K0. Qin is the airflow rate which enters the room through the lower opening, m3/s; Qp is the airflow rate (which is entrained by the thermal plume) enters the upper zone through the stratification interface, m3/s; and d is the height of the thermal stratification interface, m. At the height of the stratification interface, the airflow rate entrained by the thermal plume equals that of the inflow from outdoors, i.e. Qin ¼ Qp jd¼h . Kaye and Hunt [16] showed that the airflow rate of a thermal plume induced by a single central heat source at the height of d can be written by j
Qp ¼ CB1=3 d Lk
j j mx ¼ M= K0 CB1=3 Lk Hj ¼ M x = K0 Qp ¼ m$x
(5)
where m ¼ M/(K0Qp). Obviously, mx is related to strength of the heat source, height of the room and initial indoor pollutant concentration. It is not affected by the area of the opening. The dimensionless time should be given properly for solving Eq. (3). In order to show the relationship of the variation of pollutant concentration with the ratio of the times of emptying and filling, Hunt and Kaye [17] defined a dimensionless time, s, as follows
t
s ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A2f =C 1=2 A* B2=3 Lk=2 Hðj3Þ=2
t Af =CB1=3 Lk H j1
Substituting Eqs. (4), (5) and (6b) into Eq. (3), yields
(7)
and the initial condition at s ¼ 0 is klo ¼ 1. The dimensionless pollutant concentration in the lower zone of a DNV room with a central heat source can thus be obtained
klo ¼ ðkin þ mÞ ðkin þ m 1Þeflo s where flo ¼ x
j1
(8)
.
3.2. The variations of averaged concentrations in a DNV room Similarly, in the upper zone of a DNV room, the mass balance equation for the pollutant concentration, Kup(t), can be written as
d Kup ðH hÞAf ¼ Klo Qp d¼h þ M Kup Qout dt
(9)
and the initial condition at t ¼ 0 is Kup ¼ K0.where Qout is the airflow rate discharged from the upper opening, m3/s; and Qout ¼ Qin ¼ Qp jd¼h . Substituting Kup with the dimensionless form kup ¼ Kup/K0, Eq. (9) can be simplified as the follows
xj d kup ¼ klo þ m kup ds 1x
(10)
with the initial condition s ¼ 0, kup ¼ 1. Then the pollutant concentration in the upper zone of a DNV room with a central heat source is
kup ¼ ðkin þ 2mÞ ðkin þ m 1Þ
fup eflo s flo efup s fup flo
mefup s
(11)
j
where fup ¼ x =ð1 xÞ And the averaged dimensionless pollutant concentration, ktot, in the room at any time can be calculated by
ktot
#, " Klo hAf þ Kup ðH hÞAf K0 ¼ klo x þ kup ð1 xÞ ¼ HAf
(12)
Substituting Eqs. (8) and (11) into Eq. (12), ktot can be given by
x2
ktot ¼ ðkin þ 2m mxÞ ðk þ m 1Þeflo s 2x 1 in ð1 xÞx þ ðkin þ m 1Þ ð1 xÞðkin þ 2m 1Þ efup s 2x 1 (13) The results for the concentration calculation and the main parameters used for the derivations above are summarized in Table 1.
(6a)
If the effects of indoor pollutant source and outdoor pollutant on the indoor air quality are considered, and the definition of Eq. (6a) is adopted, the analytical solution of Eq. (3) cannot be obtained. Therefore a new dimensionless time is defined here
s ¼
d j1 k ¼ ðkin þ m klo Þx ds lo
(4)
where B is the buoyancy flux, m4/s3; B ¼ Eg/(CprT0). Here E is the heat flux produced by an inner heating source, W; T0 is the ambient air temperature, K; and g is the gravitational acceleration, m/s2. To obtain the analytical solution for Eq. (3), the dimensionless concentrations are introduced and defined as klo ¼ Klo/K0, and kin ¼ Kin/K0, respectively. Also a dimensionless strength of the pollutant source, mx, is defined as
111
(6b)
4. Necessary conditions for the decay of pollutant concentration in DNV rooms In a naturally ventilated room driven by thermal buoyancy forces, the inflow air from outdoors has two primary effects on the indoor pollutant concentration. On the one hand, indoor air quality can be improved as the indoor pollutant is flushed out by the natural ventilation airflow; on the other hand, when the pollutant concentration contained in the inflow air is higher than that indoors, the indoor concentration would be increased. In order to
112
K. Zhong et al. / Building and Environment 56 (2012) 108e117
Table 1 Calculated concentrations and the definitions of main parameters for the derivations. Variables
Point heat source sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x5 Cd A* 3=2 ¼ C 1 ð1 lÞx H2
x
Line heat source sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Cd A*L x3 ¼ C 3=2 H 1 ð1 lÞx 1 x/(1 x)
x2/3 x5/3/(1 x)
flo fup s
t Af =CB1=3 Lk H j1 ðkin þ mÞ ðkin þ m 1Þeflo s
klo(s) kup(s)
ðkin þ 2mÞ ðkin þ m 1Þ
fup eflo s flo efup s mefup s fup flo
ktot(s)
ðkin þ 2m mxÞ
reduce the indoor concentration with ventilation time, it is necessary to explore the factors which directly affect the decay of indoor pollutant concentration. 4.1. Cases of the lower zone In practice, the final concentration level in a room is one of the main parameters for characterizing the ventilation effectiveness, therefore, it is important to obtain some conditions for reducing the pollutant concentration to a certain level in the lower zone of the room. For example, the necessary conditions for reducing the concentration to 50% or 10% of the initial concentration in the lower zone. Assuming klo jx ¼ klo ðsÞjs¼0 x%, where x ranges from 0 to 100, if the concentration in a DNV room should be reduced to a certain value after the room has been ventilated for a long time, klo(s) needs to satisfy
lim k ðsÞ klo jx s/þN lo
(14)
Combining Eqs. (8) and (14), we have
lim k ðsÞ ¼ kin þ m klo jx s/þN lo
(15a)
i.e.
kin þ
x2 ð1 xÞx ðk þ m 1Þeflo s þ ðk þ m 1Þ ð1 xÞðkin þ 2m 1Þ efup s 2x 1 in 2x 1 in
1 M klo jx CB1=3 Lk hj K0
(15b)
Eq. (15) gives the restriction between the pollutant concentration of inflow air from outdoors and the strength of indoor pollutant sources when the indoor pollutant concentration in the lower zone of a DNV room needs to be reduced to a certain level. Table 2 shows the cases for the following discussion. By using Eq. (15) under the conditions listed in Table 2, the following results can be obtained for the four possible cases in a DNV room:
a similar situation without considering the inner thermal radiation effect; (2) Case B: to reduce the pollutant concentration to a certain value in the lower zone, Eq. (15) only requires kin klo jx ; (3) Case C: conditions required for the reduction of pollutant concentration in the lower zone to different levels can also be derived from Eqs. (15) and (5) j
ð1=xÞ mx klo jx
To ensure that the concentration in the lower zone can be reduced to klo jx , the upper limit of mx,max is j mx;max ¼ x klo jx
(4) Case D: the requirement for this case can be readily obtained from Eq. (15) as j
kin þ ð1=xÞ mx klo jx
Table 2 Possible cases of inflow air and inner sources in the lower zone of the DNV room.
j mx;max ¼ x klo jx kin
A B C D
Mode of pollutant in air Incoming air
Indoor air
contains contains contains contains
no indoor pollutant source no indoor pollutant source indoor pollutant source exists indoor pollutant source exists
no pollutant pollutant no pollutant pollutant
(17)
Because the dimensionless thermal stratification height x of a DNV room mainly depends on the effective window opening area A*, the height of the room and the type of inner heat source, the upper limit of strengths of indoor pollutant sources (mx,max) are different for different rooms for reducing the indoor concentration to the same level. Fig. 3 shows the effect of window opening area on the upper limit of dimensionless strength of point and line pollutant sources when klo jx ¼ klo ð0Þ, 0.5klo (0) and 0.1klo (0), respectively, where klo jx ¼ klo ð0Þ represents the critical value of the decay of indoor pollutant concentration. It can be seen from Fig. 3 that mx,max increases with the increase of window opening area if the concentration decreases with a same percentage from its initial value. However, when the indoor concentration should be reduced to a very low level (for example, klo jx ¼ 0:1klo ð0Þ), mx,max should be quite low even if the window opening area can be increased to a very large value. This means that the increase of the window opening area is effective for increasing the upper limit of the source strength only if the klo jx is large.
(1) Case A: from Eq. (15) it can be easily known that indoor pollutant concentration in the lower zone can certainly decrease to any level required. Hunt and Kaye [17] discussed
Case
(16)
(18)
To reduce the concentration in the lower zone to klo jx , the upper limit of mx,max is
(19)
The relationship between kin and mx,max can be obtained from Eq. (19) for reducing the indoor pollutant concentration to a certain level klo jx in the lower zone of the DNV room. The curves in Fig. 4 show that if the dimensionless window opening area is given (therefore the stratification height is determined), the concentration indoors can be reduced to the required level only when the
K. Zhong et al. / Building and Environment 56 (2012) 108e117
113
Fig. 4. Conditions required by Case D for reducing pollutant concentration in the lower zone. (a) Point heat source (b) Line heat source.
Fig. 3. Conditions required by Case C for reducing pollutant concentration in the lower zone (a) Point heat source (b) Line heat source.
explore the conditions for the decay of the averaged indoor concentration with time. Letting vktot ðsÞ=vsjs¼s0 ¼ 0, it can be obtained from Eq. (13) that
pollutant concentration of the incoming air and the strength of indoor pollutant source are restricted in certain ranges, i.e., kin and mx must fall into the range below the curves shown in Fig. 4. Fig. 4 shows that mx,max decreases with the decrease of the window opening area and also decreases with the increase of pollutant concentration of the inflow air from outdoors. In addition, the influence of the window opening area on mx,max is large for small kin; when kin approaches klo jx , this influence becomes weak and thus can be ignored.
s0 ¼
4.2. Cases of the whole room In the initial stage of the pollutant emission in a DNV room, the thermal plume brings the pollutant from the lower zone to the upper zone. The pollutant concentration may increase in the upper zone and even in the whole room because the exhaust openings cannot removal the pollutant air quickly enough. But with the increase of the concentration near the exhaust, the effectiveness of ventilation is also increased, which results in the reduction of the concentration in the upper zone and the whole room. Thus it is necessary to analyze the monotonic characteristics of ktot (s) to
1x ðkin þ m 1Þx=ð2x 1Þ ln x2=3 ð1 2xÞ ðkin þ m 1Þx=ð2x 1Þ ðkin þ 2m 1Þ (20)
Then the monotone intervals of ktot (s) can be determined by Eq. (20), with the results given in Table 3. The results in Table 3 show some characteristics of the variation of ktot (s) in a DNV room: (1) If kin þ 2m 1 < 0, the averaged indoor concentration ktot (s) decreases monotonically with time for any value of the thermal stratification height of the room. Curve 1 in Fig. 5 shows such a case. (2) If kin þ 2m 1 > 0, ktot (s) increases with time in the time internal s˛ð0; s0 Þ. When s˛ðs0 ; þNÞ, the necessary conditions for the decay of ktot (s) depends on the dimensionless thermal stratification height x of the room. For x 0.5, to ensure ktot (s) decreases monotonically with time in a DNV room, another necessary condition, kin þ m 1 < 0, is required. For x < 0.5, the additional necessary condition for the monotonic decay is (x/2x 1)(kin þ m 1) > kin þ 2m 1. The time
114
K. Zhong et al. / Building and Environment 56 (2012) 108e117
Table 3 Monotone intervals of ktot (s).
x
Main terms in Eq. (20)
x 0.5 kin þ 2m 1 < 0
kin þ 2m 1 > 0 kin þ m 1 < 0 x < 0.5 kin þ 2m 1 < 0 8 > kin þ 2m 1 > 0 < 2x 1 > ðkin þ 2m 1Þ < 0 : kin þ m 1
x
Monotone interval decrease when s˛ð0; þNÞ increase when s˛ð0; s0 Þ decrease when s˛ðs0 ; þNÞ decrease when s˛ð0; þNÞ increase when s˛ð0; s0 Þ decrease when s˛ðs0 ; þNÞ
dependent characteristic line for the two cases is shown as Curve 2 in Fig. 5. If kin and m do not satisfy the conditions mentioned above, ktot (s) will not decrease with time but increase exponentially in the range s˛ð0; þNÞ. In order to reduce ktot (s) to a target level ktot jx ¼ ktot ðsÞjs¼0 x%; let lim ktot ðsÞ ktot jx , also from Eq. s/þN (13), we have
kin þ 2m mx ktot jx
(21)
Which means that beside the necessary conditions in Table 3, Eq. (21) is required for ktot (s) to reduce to x% of the initial concentration when kin þ 2m 1 > 0.
radiation of the inner surface only affects the decay rate of concentration in the upper zone of a room. If a point heat source exists in the room, to simplify the analysis, it can be assumed that kin ¼ 0.1, x ¼ 0.6 and mx ¼ 0.043 (i.e. m ¼ 0.1). l ¼ 0e1, where l ¼ 0 means no thermal radiation in the room. Figs. 6 and 7 show the variations of pollutant concentration in the lower zone and averaged concentration of the room for different values of l with a point or line heat source. For small opening area of the window (e.g., A*/H2 ¼ 0.005), Fig. 6(a) shows that the differences of klo between the three curves (with different values of l) are negligible. This difference increases slightly with the increasing of the opening area, which indicates that the effect of l on the decay rate of concentration is weak in the lower zone. Fig. 6(b) and Fig. 7 show the variations of averaged concentrations of the room with point and line heat sources, respectively. It can be found that the impact of l on the decay rate of averaged indoor concentration is much larger than that of the lower zone, which implies that thermal radiation of the inner surface of a building mainly affects the reduction of concentration in the upper zone. In addition, the thermal radiation effect of the inner surface on the decay rate of concentration at the later stages is more obvious than that of the initial stage. Taking the line heat source
5. Analysis of the decay rate of indoor pollutant concentration As has been discussed in the previous sections, indoor concentration decays with time if kin and m satisfy certain conditions in a DNV room. Eqs. (8) and (13) indicate that when the room height is given, the decay rate primarily depends on the stratification height (determined by the dimensionless area of the opening), x, the thermal radiation coefficient of the inner surface, l, the concentration of the incoming air from outdoor, kin, and the strength of the indoor source mx. 5.1. Effect of thermal radiation of the inner surface on the concentration decay rate It can be found from Table 1 that when a line heat source exists in the room, the decay coefficient of concentration in the lower zone is flo ¼ 1, which is independent of the parameter l, i.e. thermal
Fig. 5. Variations of averaged indoor pollutant concentration with time.
Fig. 6. Effect of thermal radiation of the inner surface on indoor pollutant concentration when a point heat source exists in a DNV room. (a) Cases of the lower zone (b) Cases of the whole room.
K. Zhong et al. / Building and Environment 56 (2012) 108e117
Fig. 7. Effect of thermal radiation of the inner surface on indoor pollutant concentration when a line heat source exists in a DNV room.
115
Fig. 8. Variations of s50 vs kin in the lower zone with different window opening areas for Case B.
with A*L =H ¼ 0:22 as an example, when the pollutant concentration reduces to 70% and 30% of the initial value, respectively, the corresponding dimensionless time for the three different cases (i.e. l ¼ 0.0, 0.4 and 0.8, respectively) are 0.70, 0.79, 0.88 and 2.7, 3.1, 3.4, respectively.
5.2. Effect of window opening area on the concentration decay rate in the lower zone People usually concern more about indoor air quality of the occupied zone. Thus it is important to analyze the variation of concentration and the factors influencing pollutant dispersion in the lower zone of a DNV room. Since, as previously shown, the thermal radiation of the inner surface has no significant influence on the decay of concentration in the lower zone, the following discussion will focus on l ¼ 0. To analyze the effect of the window opening area on the decay of concentration in the lower zone, here we define the time required to reduce the pollutant concentration to 50% of its initial value in the lower zone as s50. From Eq. (8) we have
i h h i j j 0:5 ¼ kin þ ð1=xÞ mx kin þ ð1=xÞ mx 1 eflo s50 i.e.
s50 ¼
1
flo
j
ln
0:5 kin ð1=xÞ mx j
1 kin ð1=xÞ mx
(22)
(1) For Case A (kin ¼ 0, mx ¼ 0), from Eq. (22) we have
s50 ¼
1
flo
ln0:5 ¼ x
1j
ln0:5
(23)
Eq. (23) means that for a point heat source, s50 decreases with the increase of x2/3, i.e. decreases with the increase of the window opening area (A*/H2); for a line heat source, the value of s50 is fixed because j ¼ 1, and A*L/H has no effect on the reduction of concentration in the lower zone.
Fig. 9. Variations of s50 vs mx in the lower zone with different window opening areas for Case C. (a) Point heat source (b) Line heat source.
116
K. Zhong et al. / Building and Environment 56 (2012) 108e117
(2) For Case B (kin s 0, mx ¼ 0), s50 in the lower zone obtained from Eq. (22) can be written as
(3) For Case C (kin ¼ 0, mx s 0), according to Eq. (22) we get j
s50 ¼ xj1 ln
0:5 kin 1 kin
s50 ¼ xj1 ln
0:5 ð1=xÞ mx
(24)
The variations of s50 with kin can be calculated from Eqs. (24) and (2) and are shown in Fig. 8. From Fig. 8 one can find that if no pollutant source exists in the room, s50 increases with kin and approaches to infinite if kin ¼ 0.5. The decay rate increases when the opening area increases, while s50 decreases. In addition, the differences between the decay rates for different opening areas also reduce with the increase of the opening area, meaning that a larger opening area can result in rapid decay of the concentration in the lower zone. But when the opening area increases to a certain extent, the influence on the decay rate becomes weak. As has been discussed in the previous section, j ¼ 1 (i.e. flo ¼ 1) in the lower zone when a line heat source exists in the DNV room. Therefore the opening area has no effect on the decay rate of the concentration for such situations. Comparing the values of s50 for line and point heat sources in Fig. 8, the concentration decay rate for the former is faster than that for the later when no pollutant source exists in the room.
j
1 ð1=xÞ mx
(25)
The variations of s50 with mx which characterizes the emission amount of indoor pollutant with different window opening areas can be found from Eq. (25), and are shown in Fig. 9. It can be seen from Fig. 9 that when mx reaches a certain critical value, s50 approaches infinity for reducing indoor concentration to 50% of its initial value in the lower zone of the room. This value is the upper limit m,xmax of Case C for reducing the concentration to half of its initial value in the lower zone. The calculated curves in Fig. 9 indicate that when the strength of the indoor pollutant source is low, the effect of window opening area on the decay of pollutant concentration in the lower zone of a DNV room is relatively weak. Only when the strength of indoor pollutants is relatively large can the effect of the opening area become significant. (4) For Case D (kin s 0, mx s 0), also from Eq. (22) it can be found that j 1 0:5 kin ð1=xÞ mx s50 ¼ ln flo 1 kin ð1=xÞj mx
(26)
The changes of s50 with kin for different window opening areas and the emission rates of indoor pollutants can be calculated from Eq. (26), and are shown in Fig. 10. Fig. 10 shows when kin increases to a critical value, s50 increases to infinity for reducing concentration to 50% of its initial value in the lower zone of the DNV room. This critical value is the upper limit of Case D for reducing indoor concentration to 50% of the initial value in the lower zone. Fig. 10 also shows that only when kin approaches the critical value can the effective opening area affect the decay rate of pollutant concentration in the lower zone. 6. Conclusions
Fig. 10. Variations of s50 vs kin in the lower zone with different window opening areas for Case D. (a) Point heat source (b) Line heat source.
For the proper design of a DNV system, it is essential to ensure good indoor air quality and maintain the stratification interface above the level of the human breathing zone. Therefore, insight into the important physical mechanisms is necessary for the optimization of the design and operation of natural ventilation systems. Considering both the influences of concentration of incoming air and indoor pollutant sources, mathematical models for predicting airflow in natural ventilation rooms, which were obtained in the previous investigations, are employed to establish the mass conservation equations of pollutant transportation in the upper and lower zones in a DNV room. The variations of indoor concentrations with time were obtained from these equations. The conditions for reducing indoor concentration to certain levels and factors affecting the decay rate of concentration indoors were analyzed and discussed, and conclusions were made. The time variation of the concentration in the lower zone is different from the indoor averaged concentration mathematically in DNV rooms, although both of the variations can be expressed in exponential forms. In order to reduce the concentration in the lower zone to an expected level, both the concentration of incoming air and indoor emission rate should be less than their critical values for a given effective opening area of the window. The influence of thermal radiation of the inner surface on the reduction of pollutant concentration in the upper zone is greater than that in the lower zone of a DNV room. Thus the thermal radiation effect of the inner surface can be ignored for roughly
K. Zhong et al. / Building and Environment 56 (2012) 108e117
estimating the variation of the concentration in the occupant zone of the DNV room. In addition, the decay rate of indoor pollutant concentrations increases with the increase of the effective opening area of the window, but the opening area mainly affects the final indoor concentration level. Only when the concentration of incoming air or the strength of the indoor source approaches their critical values can the opening area influence the decay rate of indoor pollutant concentration in the DNV room.
Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 40975093). The authors would like to thank Dr. D. Gottfried for his helpful discussions and recommendations.
Nomenclature A* Ab Af At ab at B C Cd Cp cb ct E G H H K0 Kin Klo klo jx Kup kin klo ktot ktot jx kup L M mx Q Qin Qp T0 t
effective opening (vent) area of a room pffiffiffi effective area of the inlet/bottom opening, Ab ¼ 2cb ab floor area of a room pffiffiffi effective area of the outlet/top opening, At ¼ 2ct at inlet opening area of a room outlet opening area of a room buoyancy flux entrainment constant discharge coefficient of the opening heat capacity of air discharge coefficient of the inlet opening discharge coefficient of the outlet opening heat flux produced by an inner heating source gravitational acceleration room height thermal stratification height initial indoor pollutant concentration outdoor pollutant concentration pollutant concentration in the lower zone a target level of klo (s), defined as klo jx ¼ klo ðsÞjs¼0 x% pollutant concentration in the upper zone dimensionless concentration of incoming air, kin ¼ Kin/K0 dimensionless concentration in the lower zone, klo ¼ Klo/K0 averaged dimensionless pollutant concentration in a room a target level of ktot (s), defined as ktot jx ¼ ktot ðsÞjs¼0 x% dimensionless concentration in the upper zone, kup ¼ Kup/K0 length of the line heat source strength of indoor pollutant source dimensionless strength of indoor pollutant source ventilation airflow rate airflow rate through the lower opening airflow rate (which is entrained by the thermal plume) enters the upper zone air temperature outdoors time
117
Greek symbols convective heat transfer coefficient at the ceiling convective heat transfer coefficient at the floor radiant heat transfer coefficient of the inner surface of a room d height of the thermal stratification interface l dimensionless temperature with consideration of the thermal radiation of the inner surface x dimensionless thermal stratification height r air density s dimensionless time s50 time required to reduce pollutant concentration to 50% of its initial level in the lower zone
ac af ar
References [1] Jenkins PL, Phillips TJ, Mulberg EJ, Hui SP. Activity patterns of Californians: use and proximity to indoor pollutant sources. Atmos Environ 1992;26A(12): 2141e8. [2] Klepeis NE, Nelson WC, Ott WR, Robinson JP, Tsang AM, Switzer P, et al. The national human activity pattern survey (NHAPS): a resource for assessing exposure to environmental pollutants. J Expo Anal Environ Epidemiol 2001; 11(3):231e52. [3] Kousa A, Kukkonen J, Karppinen A, Aarnio P, Koskentalo T. A model for evaluating the population exposure to ambient air pollution in an urban area. Atmos Environ 2002;36(13):2109e19. [4] Orme M. Estimates of the energy impact of ventilation and associated financial expenditures. Energ Build 2001;33(3):199e205. [5] Perez-Lombard L, Ortiz J, Pout C. A review on buildings energy consumption information. Energ Build 2008;40(3):394e8. [6] Balaras CA, Gaglia AG, Georgopoulou E, Mirasgedis S, Sarafidis Y, Lalas DP. European residential buildings and empirical assessment of the Hellenic building stock, energy consumption, emissions and potential energy savings. Build Environ 2007;42(3):1298e314. [7] Jiang Y. Current building energy consumption in China and effective energy efficiency measures. HV&AC 2005;35(5):30e40 [in Chinese]. [8] Jiang Y, Yang X. China building energy consumption situation and the problems exist in the energy conservation works. China Construct 2006;2:12e7 [in Chinese]. [9] Li B, Yao R. Urbanisation and its impact on building energy consumption and efficiency in China. Renew Energ 2009;34(9):1994e8. [10] Linden PF. The fluid mechanics of natural ventilation. Annu Rev Fluid Mech 1999;31:201e38. [11] Linden PF, Lane-Serff GF, Smeed DA. Empting filling boxes: the fluid mechanics of natural ventilation. J Fluid Mech 1990;212:309e35. [12] Linden PF, Cooper P. Multiple sources of buoyancy in a naturally ventilated enclosure. J Fluid Mech 1996;311:177e92. [13] Gladstone C, Woods AW. On buoyancy-driven natural ventilation of a room with a heated floor. J Fluid Mech 2001;441:293e314. [14] Fitzgerald SD, Woods AW. Natural ventilation of a room with vents at multiple levels. Build Environ 2004;39(5):505e21. [15] Jiang Y, Chen Q. Buoyancy-driven single-sided natural ventilation in buildings with large openings. Int J Heat Mass Tran 2003;46(6):973e88. [16] Kaye NB, Hunt GR. Time-dependent flows in an emptying filling box. J Fluid Mech 2004;520:135e56. [17] Hunt GR, Kaye NB. Pollutant flushing with natural displacement ventilation. Build Environ 2006;41(9):1190e7. [18] Li Y. Buoyancy-driven natural ventilation in a thermally stratified one-zone building. Build Environ 2000;35(3):207e14. [19] Andersen KT. Theoretical considerations on natural ventilation by thermal buoyancy. ASHRAE Trans 1995;101(2):1103e17. [20] Li Y, Delsante A, Symons J. Prediction of natural ventilation in buildings with large openings. Build Environ 2000;35(3):191e206. [21] Jin Y. Particle transport in turbulent buoyant plumes rising in a stably stratified environment. Ph.D. theses, Department of Building Services Engineering, KTH, Stockholm, Sweden; 1993. [22] Yuan X, Chen Q, Glicksman LR, Hu Y, Yang X. Measurements and computations of room airflow with displacement ventilation. ASHRAE Trans 1999; 105(1):340e532. [23] Cooper P, Linden PF. Natural ventilation of an enclosure containing two buoyancy sources. J Fluid Mech 1996;311:153e76. [24] Ji Y, Cook MJ, Hanby V. CFD modelling of natural displacement ventilation in an enclosure connected to an atrium. Build Environ 2007;42(3):1158e72.