Particle Transport in Low-Energy Ventilation Systems. Part 1: Theory of Steady States

Particle transport in low-energy ventilation systems. Part 1: theory of steady states

Abstract Many modern low-energy ventilation schemes, such as displacement or D. T. Bolster, P. F. Linden natural ventilation, take advantage of temperature stratification in a space, extracting the warmest air from the top of the room. The adoption of these Department of Mechanical and Aerospace Engineering, energy-efficient ventilation systems still requires the provision of acceptable University of California, San Diego, La Jolla, CA, USA indoor air quality. In this work we study the steady state transport of particulate contaminants in a displacement-ventilated space. Representing heat sources as ideal sources of buoyancy, analytical models are developed that allow us to compare the average efficiency of contaminant removal between traditional and modern low-energy systems. We found that on average traditional and low- Key words: Low-energy ventilation; Contaminant; energy systems are similar in overall pollutant removal efficiency, although Particles. quite different vertical distributions of contaminant can exist, thus affecting Diogo T. Bolster individual exposure. While the main focus of this work is on particles where the Department of Geo-Engineering dominant mode of deposition is by gravitational settling, we also discuss Technical University Catalunya (UPC) additional deposition mechanisms and show that the qualitative observations we Campus Nord, 08034 Barcelona make carry over to cases where such mechanisms must be included. Spain Tel.: +34 655 039 065 Fax: +34 93 401 6890 e-mail: [email protected]

Received for review 21 January 2008. Accepted for publication 4 August 2008. Indoor Air (2008)

Practical Implications We illustrate that while average concentration of particles for traditional mixing systems and low energy displacement systems are similar, local concentrations can vary signiﬁcantly with displacement systems. Depending on the source of the particles this can be better or worse in terms of occupant exposure and engineers should take due diligence accordingly when designing ventilation systems.

To reduce energy consumption various low-energy Introduction systems such as displacement-ventilation, underfloor air We live in world where Ôenergy consumption defines the distribution, operable windows, night cooling, radiant quality of urban lifeÕ (Santamouris, 2005). Developed and evaporative cooling are under consideration. countries consume massive amounts of energy while Underlying all these systems is the idea that free cooling only accounting for a small fraction of the global is possible. Traditional ventilation, such as that pro- population. According to the Energy Information vided by a conventional overhead heating, ventilating Administration (http://www.eia.doe.gov/) the US and air-conditioning system, is mixing ventilation, alone produces 25% of the worldÕs total anthropogenic where incoming air is mixed with the air in the room CO2, while accounting for <5% of the worldÕs and diluted. This typically results in a relatively uniform population. A major fraction is produced by modern interior temperature distribution. In contrast, many buildings, which consume approximately 40% of the modern low-energy ventilation schemes require the use worldÕs energy and are responsible for 50% of global of temperature stratification in a space, with a bottom anthropogenic CO2 emissions. A significant fraction of layer of cooler comfortable air where occupants are this energy is spent on ventilation of buildings with located, and an unoccupied upper layer that is compar- summer time cooling account for almost 10% of the atively warm (Linden, 1999). The ability to extract air at US total energy budget. elevated temperatures is necessary for energy-efficiency

1 Bolster & Linden and free cooling. This can be achieved, for example, by within a ventilated enclosure stratify that space. Many displacement-ventilation, underfloor air distribution or heat sources within a building can be regarded as natural ventilation. Hence, stratification is an important localized and can often be modeled as pure sources of feature in modern ventilation design. This is particularly buoyancy. Using the plume equations developed by true for tall spaces, where temperature differences can be Morton et al., 1956 along with the ÔfillingÕ (Baines and quite significant. Turner, 1969) and Ôemptying-fillingÕ box models (Linden People spend substantial amounts of time indoors, in et al., 1990) we can model the flow in such low energy many cases up to as much as 90% (Jenkins et al., 1992) buildings, and calculate the transport of particulate and, therefore, the provision of a thermally comfort- contaminants within the interior space. able environment in an energy-efficient manner is only Figure 1 shows a schematic of the two models that we one requirement of a ventilation system. It is also consider. We analyze one low-energy ventilation model important to understand the details of the indoor (b) and one traditional mixing model (a). In the low- environment regarding indoor air quality (IAQ). It is energy models we consider the space either mechani- often stated that such displacement-ventilation systems cally or naturally ventilated with fresh air entering can be more effective at removing contaminants (e.g. through a low level vent and hot buoyant air leaving via Brohus and Nielsen, 1996; Lin et al., 2005; Xinga a vent at high level. Heat sources in the space are et al., 2001). In a previous study (Bolster and Linden, represented by ideal plumes. As we are only considering 2007), the authors showed that this may in fact not steady states in this particular paper, we are not always be true and that the average rate of contam- concerned with the detailed vertical contaminant dis- inant removal for passive contaminants is quite similar tribution in the two layer model (see Bolster and for traditional and modern low-energy systems. Addi- Linden, 2007) as the simplest model with two well mixed tionally, experimental studies (Mundt, 2001) have layers results in the same steady state as other two layer shown that the ventilation effectiveness of a displace- models. Figure 2 illustrates the transport processes for ment system is sensitive the location and type of the the contaminant for both the well mixed and two-layer contaminant source involved. Displacement systems cases. In part 2 of this work we consider a model where typically result in different vertical concentration gra- vertical gradients of contaminant can exist. dients and in some cases can lead to larger exposure of occupants to contaminants. Contamination scenarios considered While the study of passive tracer contaminants is important in understanding ventilation system effi- For each of the models depicted in Figure 1, we ciency, there is another type of contaminant that must consider two types of contamination situations: also be considered - particulates. The concentration 1. External contaminant (Step up): Here we consider a and composition of indoor particles are major deter- case where contaminant is introduced in through the minants of environmental quality, as inhalation expo- ventilation system. This can also be thought of as a sure poses potentially adverse effects on peopleÕs contaminant that is located in the lower layer of the health. Such particles can penetrate into buildings two-layer ventilation system. In terms of Figure 2 from the outdoors or can be emitted from indoor this corresponds to K being non-zero and K =0. sources such as smoking, cooking, occupants, building in s 2. Internal contaminant (Isolated source in plume): materials or even during a deliberate malicious release. Here contaminant is introduced as a point source The study of particulate matter is more complicated located within the plume. We choose this location than that of passive contaminants. With particles there because people are often the source of heat as well as are various other phenomena that can occur – depo- the source of contaminants in buildings. This can sition, resuspension, coagulation, and filtration, which also be thought of as a contaminant located in the are all difficult to model and quantify. In particular, upper layer of the displacement-ventilation system. gravitational settling raises the concern that particles In terms of Figure 2 this corresponds to K being may not be removed as efficiently from a system that is s non-zero and K =0. extracting air from the top of a room, which is typical in of low-energy ventilation systems. Model (a) - entirely well mixed space Mathematical models In this model we treat the entire room as well mixed To understand the fate of particles in a ventilated space, (Figure 1a). The reason for this is twofold. First, it it is necessary to understand the flow within the space. allows us to compare low-energy ventilation systems to As mentioned previously, many modern low-energy traditional mixing systems, which minimize stratifica- ventilation schemes, such as displacement or natural tion by mixing the space. Second, many building ventilation, exploit vertical temperature stratification in software packages treat buildings as networks of spaces a space. So it is critical to understand how heat sources that are each assumed to be well mixed. As many

2 Particle transport in low energy ventilation systems

Q velocity, assumed here to be the Stokes settling (a) out velocity, Kin is the concentration of contaminant in the incoming air, Ks is the concentration associated with a point source (defined in greater detail in appendix A), S is the room cross sectional area and H is the height of the room. As outlined in appendix A we take Qs =Qp, where Qp is the volume flux associated with the plume across the interface for the two-layer case. At steady state Qin =Qout = Qp (see Linden et al., 1990). Qfall quantifies the amount of WM H deposition that will take place. We neglect deposition of particles to the ceiling and sidewalls and assume that particles settle out of the lower and upper layers at this settling velocity. This is a reasonable assumption for larger particles (>O(0.1–1)lm), where the predomi- nant mechanism of deposition is gravitational settling and Brownian effects are negligible (Lai and Nazaroff, 2000). For ultrafine particles (

Q p Model (b) - well mixed two layer model H In this section we consider model (b) from Figure 1. We take an approach similar to that of Hunt and Kaye (2006) and assume that the upper and lower layers are always well mixed. The justification for this assumption WM h is that the plume will cause some mixing in the upper layer. However, in a previous study on passive contaminants (Bolster and Linden, 2007) we found that this assumption does not describe the complete dynamics of the system. None the less, at least for passive contam- Q inants, it has been shown to be an adequate model (Hunt in and Kaye, 2006) and is very appealing because of its Fig. 1 Models of displacement-ventilation systems. (a) single simplicity. We also assume that the lower layer is well well mixed layer, (b) two-layer system mixed. As the incoming flow will have a finite amount of momentum, a certain amount of mixing will be inevi- table and in our previous work on passive contaminants researchers have previously pointed out (e.g. Baugh- we showed that this is a reasonable assumption. Thus man et al., 1994; Klepeis, 1999), this assumption is the governing equations for conservation of contami- questionable and so we test it here. At steady state the nant in each of the layers are concentration in a well mixed space, Kwm, satisfies the conservation equation ðQp þ QfallÞKl ¼ QfallKu þ QinKin

ðQout þ QfallÞKwm ¼ QinKin þ QsKs; ð1Þ ðQfall þ QpÞKu ¼ QpKl þ QpKs ð2Þ where Qin is the flow rate into the space, Qout is the flow where Kl and Ku are the concentrations of contaminant rate into the space, Qs is the flow rate associated with in the lower and upper layers, respectively, h is the an internal contaminant source, Qfall =vfall S is height of the lower layer and Qp is the plume flow rate defined as the settling flow rate, vfall is the settling across the interface and at steady state Qp =Qin.

3 Bolster & Linden

QoutKwm QoutKout

QsKs (Ks+Kl) Qp KuQfall Contaminant source

QfallKwm KlQfall

QinKin QinKin

Fig. 2 A schematic illustrating the contaminant transport processes taking place in the well mixed and two-layer cases

equal to that of the source. However, the influence of Non-dimensionalization gravitational settling leads to nontrivial steady state We non-dimensionalize as follows: distributions. From (4) we predict that the well mixed space in model K K j; h Hf; 3 ¼ ref ¼ ð Þ (a) tends to a uniform contaminant concentration of where Kref is a reference concentration, which will be 1 different for each of the three situations considered. jðaÞ ¼ : ð6Þ 1 a For the step-up system it is the concentration of þ contaminant entering the spaces (Kref =Kin) and for This is lower than the concentration of fluid entering the point source case it is the concentration of the the space, because there is an additional sink in the source (Kref =Ks). This results in the following deposition term that does not extract fluid, but does dimensionless equations: extract contaminant. For the two-layer case it can be (a) shown from (5) that for such a system 1 ð1 þ aÞ ð1 þ aÞj ¼ jin þ js; ð4Þ ðbÞ ðbÞ ju ¼ ; j ¼ : ð7Þ ða þ 1Þ2 a l ða þ 1Þ2 a (b) Therefore, at steady state, the concentration in the lower layer is always greater than that in the upper ð1 þ aÞj ¼ aj þ j ; l u in layer and occupants, assumed to be located in the lower layer, are exposed to the highest concentrations ð1 þ aÞju ¼ jl þ js; ð5Þ in the space. Interestingly, this steady state is also where a ¼ Qfall, which is a dimensionless representation independent of f, the interface height. Qp of the particle settling velocity. We can compare the steady state value of the concentration of lower layer for model (b) to the well mixed case, which results in

Results b jð Þ ð1 þ aÞ2 l ¼ >1: ð8Þ External contaminant jðaÞ ð1 þ aÞ2 a We consider the situation where contaminant is intro- This ratio is also independent of f the interface height. duced via the ventilation system. This can correspond It is plotted in Figure 3(b). Additionally, regardless of to a number of scenarios, such as a leak in a ventilation the value of a the lower layer always has a higher level system, a malicious release, or an external contaminant of contaminant than the well mixed case. Thus people entering the building though natural ventilation. Here are always exposed to a higher concentration in the j = 1 and j = 0, which should be substituted in to in s low-energy ventilation system. It is worth noting the equations presented in the previous section. For a ðbÞ jl passive contaminant this steady state corresponds to a that there is a maximum value for the ratio jðaÞ ¼ 1:33 uniformly distributed concentration of contaminant at a = 1, which means that this corresponds to the

4 Particle transport in low energy ventilation systems worst case scenario regarding a comparison between only exposed to the lowest concentrations in the space. traditional and low-energy ventilation systems. Again, these steady state values are independent of f. However, if we only consider the overall average Comparing the concentration of the lower layer for concentration at steady state of model (a) vs. model (b) models (b) and (a) we obtain we find b jð Þ a2 þ a jðbÞ fj þð1 fÞju ð1 þ faÞð1 þ aÞ l ¼ <1; ð12Þ ¼ l ¼ : ð9Þ jðaÞ a2 þ a þ 1 ðaÞ 1 a2 a 1 j 1þa þ þ which indicates that for this type of point source the Figure 3 (a) depicts the ranges of a and f where the low-energy system always does a better job removing average concentration for the traditional mixing system contaminants than the traditional system, regardless of is higher than the low-energy two-layer systems. the interface location or particle size. This ratio is zero for a = 0, which corresponds to a passive contami- Internal source nant, and approaches 1 as a fi¥. This is reasonable because the source is effectively in the upper layer and As for the external case, the ultimate steady state that for a = 0, no contaminant can fall back into the lower the system reaches will differ for the traditional and layer. However, as a increases, more contaminant can low energy systems. Here jin = 0 and js = 1, which fall through, thus increasing the concentration of the should be substituted in to the equations presented in lower layer. section 3. On the other hand, if we only consider the average The well mixed space in model (a) tends to a uniform contaminant removal, we can see from Figure 4 that contaminant concentration of (this is calculated by there are regions, particularly as the particle size assuming a source of js in the space as is perceived in increases, where the two-layer system is worse (grey the upper layer equation above - see appendix A for region) at removing contaminants than the one-layer details) well-mixed system. However, since from a practical 1 perspective we only care about concentrations in the jðaÞ ¼ : ð10Þ 1 þ a lower layer, this is not really the point of interest and is merely shown here to illustrate that an average This is lower than the concentration of fluid entering contaminant concentration value is deceptive in pre- the space, because of the sink effect of deposition that dicting an individualÕs exposure as illustrated in the does not extract fluid, but does extract contaminant. experiments by Ozkaynak et al. (1982). For the two-layer cases both systems tend to the same steady state where both layers are well mixed. For this situation the upper and lower layer concentration Additional mechanisms of deposition fields are While gravitational effects dominate the deposition mechanisms for large particles (typically >1lm, 1 a a ðbÞ þ ðbÞ although this is dependent on the friction velocity at ju ¼ ; jl ¼ ð11Þ ða þ 1Þ2 a ða þ 1Þ2 a a boundary, which for a displacement system should be less than for traditional mixing system), the deposition respectively. At steady state, the concentration in the of particles smaller than this can be strongly driven by upper layer is always greater than that in the lower Brownian diffusion (Lai and Nazaroff, 2000). There- layer and people, who only occupy the lower layer, are fore, for such particles the governing equations (4)–(5)

(a) (b) 1 1.4

1.3 (a) (b) (a) κ / ζ 0.5 κ >κ 1.2 (b) l

κ 1.1

0 1 10−2 100 100 α α

Fig. 3 (a) Comparison of the steady state average concentration across the entire height of the space for the single layer vs. two layer models (b) Ratio of the steady state concentrations of the lower layer in the two layer models to the single layer concentration (j(b)/j(a)>1)

5 Bolster & Linden must be modified to account for this. As the ultimate in Lai and Nazaroff (2000). We treat the interface in steady state for both two layer models is the same we the two layer model as a ÔfictitiousÕ rigid boundary focus on model (b) here. Accounting for additional through which fluxes can occur. settling to all surfaces the governing equations become In dimensionless terms (13) and (14) become: (a) (a)

ðQin þ QdwÞKwm ¼ QinKin þ QinKs; ð13Þ ð1 þ adwÞj ¼ jin þ js; ð16Þ (b) (b) ð1 þ adlÞjl ¼ adfju þ jin; ðQp þ QdlÞKl ¼ QdfKu þ QinKin ð1 þ aduÞju ¼ð1 þ adrÞjl þ js; ð17Þ ðQdu þ QpÞKu ¼ðQp þ QdrÞKl þ QpKs ð14Þ Qdi where adi ¼ represents the dimensionless forms of Qin where Qdw is the flow rate at which particles settle out of the various deposition flow rates defined in (15). The the well mixed space, Qdl is the flow rate at which par- subscript i can represent the subscripts w, l, f, u or r. By ticles settle out of the lower layer, Qdf is the flow rate of accounting for these additional mechanisms we intro- particles that flow from the upper to lower layer across duce several new dimensionless parameters. In the limit the interface, Qdu is the flow rate at which particles settle of large particles, the deposition velocities to upward out the upper layer and Qdr is the flow rate at which facing surfaces reduces to the settling velocity, while particles cross the interface from the lower to upper the deposition to downward facing and vertical layers. These quantities are evaluated as follows: surfaces reduces to zero and we recover the equation presented in sections 2–4. The steady state concentra- l tions for each of the models are given by Qdw ¼ vvAv þ vdAd þ vuAu Qdl ¼ vvAv þ vdAd þ vuAu Qdf ¼ vuAu ðaÞ jin þ js Q v Au v A v A Q v A j ¼ ; ð18Þ du ¼ v v þ d d þ u u dr ¼ d d ð15Þ 1 þ adw where vv is the deposition velocity of a particle ðbÞ ð1 þ aduÞjin þ adfjs jl ¼ ð19Þ depositing on to a vertical surface, vd is the deposition 1 þ adl þ aduð1 þ adlÞadfð1 þ adrÞ velocity of a particle depositing on to a downward facing horizontal surface, v is the deposition velocity u ð1 þ a Þj þð1 þ a Þj of a particle depositing on to an upward facing jðbÞ ¼ dr in dl s : ð20Þ u 1 þ a þ a ð1 þ a Þa ð1 þ a Þ horizontal surface, Av is the total area of verti- dl du dl df dr l cal boundaries in the space, Av is the area of u vertical boundaries in the lower layer, Av is the area External contaminant case. For the external contami- of vertical boundaries in the upper layer, Au is the area nant situation we considered previously (i.e. jin =1 of the an upward facing boundary and Al is the area of and js = 0) we again compare the upper to lower layer downward facing boundaries. The deposition velocities concentrations in the two-layer system. We also can be evaluated using equations presented in Table 2 compare the lower layer concentration in the two-layer

(a) (b) 1 1 (a)

κ / ζ 0.5 0.5 (b) l

κ κ(b)>κ (a) 0 0 10−2 100 10−2 100 α α

Fig. 4 (a) Comparison of the steady state average concentration across the entire height of the space for the single layer vs. two layer models (b) Ratio of the steady state concentrations of the lower layer in the two layer models to the single layer concentration (j(b)/ j(a)<1)

6 Particle transport in low energy ventilation systems system to the concentration in the traditional well It is widely believed that low-energy displacement- mixed space. ventilation systems can be better than traditional mixing systems at removing contaminants from a space. This is ðbÞ j 1 þ adu because there is a belief that these systems will use the l ¼ : ð21Þ ðbÞ same mechanism for contaminant removal as they do for ju 1 þ adr heat removal, where they are clearly more efficient. The Because adu includes deposition to vertical and hori- heat extraction problem exploits the natural stratifica- zontal surfaces, while adr only involves deposition to a tion that develops, extracting the warmest air that downward facing horizontal surface, it is readily seen ðb;cÞ ðb;cÞ naturally sits at the top of the room. However, there is no that adu>adr and therefore jl >ju . Once again for physical justification as to why this location should the step-up case the concentration in the lower layer is correspond to the location of maximum contaminant always greater than it is in the upper layer, even with concentration too. In fact many times it does not the additional settling mechanisms for fine and ultra- (Bolster and Linden, 2007). fine particles. Now we compare the lower layer For the external contaminant case, we showed that, concentration in the two-layer system to the concen- at steady state, the concentration in the lower layer is tration in the traditional mixing space greater than that of the upper layer. Further, this lower layer concentration is larger than that for an equivalent jðbÞ ð1 þ a Þð1 þ a Þ l du dw : 22 traditional ventilation system. The largest difference ðaÞ ¼ ð Þ j 1 þ adl þ aduð1 þ adlÞadfð1 þ adrÞ occurs for particles with a = 1, where the lower layer concentration in the displacement system is 33% higher It is relatively straightforward using (15) to show to than that in the traditional system. that the denominator is greater than the numerator On the other hand, when considering the internal in (22). Therefore, as we observed previously, occupants are exposed to higher levels of contaminants in contaminant scenario, we predict a higher steady state the low energy system when a step-up case is concentration in the upper layer compared to the lower considered. layer. The lower layer concentration will always be less than that in an equivalent traditional system, thus reducing occupantsÕ exposure to contaminants. Internal source case. In the same manner we can It is clearly important to consider the types of sources consider the internal source situation (j = 0 and in that are likely to be encountered in a real building. For j = 1), where s example, in a well designed surgical operating theater, ðbÞ the ventilation system typically filters out most contam- j adf l ¼ : ð23Þ inant before introducing air into the room. Therefore, it ðb;cÞ 1 þ a ju dl is unlikely that the step-up scenario is relevant. In an operating theater the most common sources of contam- Now, from (15), we know that adf

7 Bolster & Linden

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Appendix A. point source strength estimation dKl Qp þ Qfall Qfall Qin ¼ð ÞKl þ Ku þ Kin; ðA:3Þ A point source in the plume in the lower layer can be dt Sh Sh Sh thought of as an additional source into the upper layer. dK Q Q þ Q dP 5 u p K K fall p K : A:4 ¼ ðK PÞ; z