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

Transcription

1 Indoor Air Printed in Singapore. A rights reserved Ó 2008 The Authors Journa compiation Ó Backwe Munksgaard 2008 INDOOR AIR doi:0./j x Partice transport in ow-energy ventiation systems. Part : theory of steady states Abstract Many modern ow-energy ventiation schemes, such as dispacement or natura ventiation, take advantage of temperature stratification in a space, extracting the warmest air from the top of the room. The adoption of these energy-efficient ventiation systems sti requires the provision of acceptabe indoor air quaity. In this work we study the steady state transport of particuate contaminants in a dispacement-ventiated space. Representing heat sources as idea sources of buoyancy, anaytica modes are deveoped that aow us to compare the average efficiency of contaminant remova between traditiona and modern ow-energy systems. We found that on average traditiona and owenergy systems are simiar in overa poutant remova efficiency, athough quite different vertica distributions of contaminant can exist, thus affecting individua exposure. Whie the main focus of this work is on partices where the dominant mode of deposition is by gravitationa setting, we aso discuss additiona deposition mechanisms and show that the quaitative observations we make carry over to cases where such mechanisms must be incuded. D. T. Boster, P. F. Linden Department of Mechanica and Aerospace Engineering, University of Caifornia, San Diego, La Joa, CA, USA Key words: Low-energy ventiation; Contaminant; Partices. Diogo T. Boster Department of Geo-Engineering Technica University Cataunya (UPC) Campus Nord, Barceona Spain Te.: Fax: e-mai: diogoboster@gmai.com Received for review 2 January Accepted for pubication 4 August Ó Indoor Air (2008) Practica Impications We iustrate that whie average concentration of partices for traditiona mixing systems and ow energy dispacement systems are simiar, oca concentrations can vary significanty with dispacement systems. Depending on the source of the partices this can be better or worse in terms of occupant exposure and engineers shoud take due diigence accordingy when designing ventiation systems. Introduction We ive in word where Ôenergy consumption defines the quaity of urban ifeõ (Santamouris, 2005). Deveoped countries consume massive amounts of energy whie ony accounting for a sma fraction of the goba popuation. According to the Energy Information Administration ( the US aone produces 25% of the wordõs tota anthropogenic CO 2, whie accounting for <5% of the wordõs popuation. A major fraction is produced by modern buidings, which consume approximatey 40% of the wordõs energy and are responsibe for 50% of goba anthropogenic CO 2 emissions. A significant fraction of this energy is spent on ventiation of buidings with summer time cooing account for amost 0% of the US tota energy budget. To reduce energy consumption various ow-energy systems such as dispacement-ventiation, underfoor air distribution, operabe windows, night cooing, radiant and evaporative cooing are under consideration. Underying a these systems is the idea that free cooing is possibe. Traditiona ventiation, such as that provided by a conventiona overhead heating, ventiating and air-conditioning system, is mixing ventiation, where incoming air is mixed with the air in the room and diuted. This typicay resuts in a reativey uniform interior temperature distribution. In contrast, many modern ow-energy ventiation schemes require the use of temperature stratification in a space, with a bottom ayer of cooer comfortabe air where occupants are ocated, and an unoccupied upper ayer that is comparativey warm (Linden, 999). The abiity to extract air at eevated temperatures is necessary for energy-efficiency

2 Boster & Linden and free cooing. This can be achieved, for exampe, by dispacement-ventiation, underfoor air distribution or natura ventiation. Hence, stratification is an important feature in modern ventiation design. This is particuary true for ta spaces, where temperature differences can be quite significant. Peope spend substantia amounts of time indoors, in many cases up to as much as 90% (Jenkins et a., 992) and, therefore, the provision of a thermay comfortabe environment in an energy-efficient manner is ony one requirement of a ventiation system. It is aso important to understand the detais of the indoor environment regarding indoor air quaity (IAQ). It is often stated that such dispacement-ventiation systems can be more effective at removing contaminants (e.g. Brohus and Niesen, 996; Lin et a., 2005; Xinga et a., 200). In a previous study (Boster and Linden, 2007), the authors showed that this may in fact not aways be true and that the average rate of contaminant remova for passive contaminants is quite simiar for traditiona and modern ow-energy systems. Additionay, experimenta studies (Mundt, 200) have shown that the ventiation effectiveness of a dispacement system is sensitive the ocation and type of the contaminant source invoved. Dispacement systems typicay resut in different vertica concentration gradients and in some cases can ead to arger exposure of occupants to contaminants. Whie the study of passive tracer contaminants is important in understanding ventiation system efficiency, there is another type of contaminant that must aso be considered - particuates. The concentration and composition of indoor partices are major determinants of environmenta quaity, as inhaation exposure poses potentiay adverse effects on peopeõs heath. Such partices can penetrate into buidings from the outdoors or can be emitted from indoor sources such as smoking, cooking, occupants, buiding materias or even during a deiberate maicious reease. The study of particuate matter is more compicated than that of passive contaminants. With partices there are various other phenomena that can occur deposition, resuspension, coaguation, and fitration, which are a difficut to mode and quantify. In particuar, gravitationa setting raises the concern that partices may not be removed as efficienty from a system that is extracting air from the top of a room, which is typica of ow-energy ventiation systems. Mathematica modes To understand the fate of partices in a ventiated space, it is necessary to understand the fow within the space. As mentioned previousy, many modern ow-energy ventiation schemes, such as dispacement or natura ventiation, expoit vertica temperature stratification in a space. So it is critica to understand how heat sources within a ventiated encosure stratify that space. Many heat sources within a buiding can be regarded as ocaized and can often be modeed as pure sources of buoyancy. Using the pume equations deveoped by Morton et a., 956 aong with the ÔfiingÕ (Baines and Turner, 969) and Ôemptying-fiingÕ box modes (Linden et a., 990) we can mode the fow in such ow energy buidings, and cacuate the transport of particuate contaminants within the interior space. Figure shows a schematic of the two modes that we consider. We anayze one ow-energy ventiation mode and one traditiona mixing mode. In the owenergy modes we consider the space either mechanicay or naturay ventiated with fresh air entering through a ow eve vent and hot buoyant air eaving via a vent at high eve. Heat sources in the space are represented by idea pumes. As we are ony considering steady states in this particuar paper, we are not concerned with the detaied vertica contaminant distribution in the two ayer mode (see Boster and Linden, 2007) as the simpest mode with two we mixed ayers resuts in the same steady state as other two ayer modes. Figure 2 iustrates the transport processes for the contaminant for both the we mixed and two-ayer cases. In part 2 of this work we consider a mode where vertica gradients of contaminant can exist. Contamination scenarios considered For each of the modes depicted in Figure, we consider two types of contamination situations:. Externa contaminant (Step up): Here we consider a case where contaminant is introduced in through the ventiation system. This can aso be thought of as a contaminant that is ocated in the ower ayer of the two-ayer ventiation system. In terms of Figure 2 this corresponds to K in being non-zero and K s =0. 2. Interna contaminant (Isoated source in pume): Here contaminant is introduced as a point source ocated within the pume. We choose this ocation because peope are often the source of heat as we as the source of contaminants in buidings. This can aso be thought of as a contaminant ocated in the upper ayer of the dispacement-ventiation system. In terms of Figure 2 this corresponds to K s being non-zero and K in =0. Mode - entirey we mixed space In this mode we treat the entire room as we mixed (Figure a). The reason for this is twofod. First, it aows us to compare ow-energy ventiation systems to traditiona mixing systems, which minimize stratification by mixing the space. Second, many buiding software packages treat buidings as networks of spaces that are each assumed to be we mixed. As many 2

3 Partice transport in ow energy ventiation systems WM WM Q out Q out H veocity, assumed here to be the Stokes setting veocity, K in is the concentration of contaminant in the incoming air, K s is the concentration associated with a point source (defined in greater detai in appendix A), S is the room cross sectiona area and H is the height of the room. As outined in appendix A we take Q s =Q p, where Q p is the voume fux associated with the pume across the interface for the two-ayer case. At steady state =Q out = Q p (see Linden et a., 990). Q fa quantifies the amount of deposition that wi take pace. We negect deposition of partices to the ceiing and sidewas and assume that partices sette out of the ower and upper ayers at this setting veocity. This is a reasonabe assumption for arger partices (>O(0. )m), where the predominant mechanism of deposition is gravitationa setting and Brownian effects are negigibe (Lai and Nazaroff, 2000). For utrafine partices (<O(0. )m) deposition wi aso be driven by Brownian effects. Deposition due to Brownian effects is strongy dependent on the turbuent friction veocity at the boundaries of the room. As for dispacement-ventiation, characteristic veocities are typicay an order of magnitude smaer than for traditiona mixing systems (Jiang et a.,992), it is reasonabe to assume that deposition effects driven by Brownian setting wi aso be much smaer and ony become significant for smaer partices (<O(0.)m). WM Q p Fig. Modes of dispacement-ventiation systems. singe we mixed ayer, two-ayer system researchers have previousy pointed out (e.g. Baughman et a., 994; Kepeis, 999), this assumption is questionabe and so we test it here. At steady state the concentration in a we mixed space, K wm, satisfies the conservation equation ðq out þ Q fa ÞK wm K in þ Q s K s ; ðþ where is the fow rate into the space, Q out is the fow rate into the space, Q s is the fow rate associated with an interna contaminant source, Q fa =v fa S is defined as the setting fow rate, v fa is the setting H h Mode - we mixed two ayer mode In this section we consider mode from Figure. We take an approach simiar to that of Hunt and Kaye (2006) and assume that the upper and ower ayers are aways we mixed. The justification for this assumption is that the pume wi cause some mixing in the upper ayer. However, in a previous study on passive contaminants (Boster and Linden, 2007) we found that this assumption does not describe the compete dynamics of the system. None the ess, at east for passive contaminants, it has been shown to be an adequate mode (Hunt and Kaye, 2006) and is very appeaing because of its simpicity. We aso assume that the ower ayer is we mixed. As the incoming fow wi have a finite amount of momentum, a certain amount of mixing wi be inevitabe and in our previous work on passive contaminants we showed that this is a reasonabe assumption. Thus the governing equations for conservation of contaminant in each of the ayers are ðq p þ Q fa ÞK Q fa K u þ K in ðq fa þ Q p ÞK u Q p K þ Q p K s ð2þ where K and K u are the concentrations of contaminant in the ower and upper ayers, respectivey, h is the height of the ower ayer and Q p is the pume fow rate across the interface and at steady state Q p =. 3

4 Boster & Linden Q out K wm Q out K out Q s K s Contaminant source (K s +K ) Q p K u Q fa Q fa K wm K Q fa K in K in Fig. 2 A schematic iustrating the contaminant transport processes taking pace in the we mixed and two-ayer cases Non-dimensionaization We non-dimensionaize as foows: K K ref j; h Hf; ð3þ where K ref is a reference concentration, which wi be different for each of the three situations considered. For the step-up system it is the concentration of contaminant entering the spaces (K ref =K in ) and for the point source case it is the concentration of the source (K ref =K s ). This resuts in the foowing dimensioness equations: ð þ aþj j in þ j s ; ð4þ ð þ aþj aj u þ j in ; ð þ aþj u j þ j s ; ð5þ where a Q fa Q p, which is a dimensioness representation of the partice setting veocity. Resuts Externa contaminant We consider the situation where contaminant is introduced via the ventiation system. This can correspond to a number of scenarios, such as a eak in a ventiation system, a maicious reease, or an externa contaminant entering the buiding though natura ventiation. Here j in = and j s = 0, which shoud be substituted in to the equations presented in the previous section. For a passive contaminant this steady state corresponds to a uniformy distributed concentration of contaminant equa to that of the source. However, the infuence of gravitationa setting eads to nontrivia steady state distributions. From (4) we predict that the we mixed space in mode tends to a uniform contaminant concentration of j ðaþ þ a : ð6þ This is ower than the concentration of fuid entering the space, because there is an additiona sink in the deposition term that does not extract fuid, but does extract contaminant. For the two-ayer case it can be shown from (5) that for such a system u ða þ Þ 2 a ; ð þ aþ jðbþ ða þ Þ 2 a : ð7þ Therefore, at steady state, the concentration in the ower ayer is aways greater than that in the upper ayer and occupants, assumed to be ocated in the ower ayer, are exposed to the highest concentrations in the space. Interestingy, this steady state is aso independent of f, the interface height. We can compare the steady state vaue of the concentration of ower ayer for mode to the we mixed case, which resuts in j ð þ aþ2 ðaþ ð þ aþ 2 a >: ð8þ This ratio is aso independent of f the interface height. It is potted in Figure 3. Additionay, regardess of the vaue of a the ower ayer aways has a higher eve of contaminant than the we mixed case. Thus peope are aways exposed to a higher concentration in the ow-energy ventiation system. It is worth noting that there is a maximum vaue for the ratio jðbþ :33 j ðaþ at a =, which means that this corresponds to the 4

5 Partice transport in ow energy ventiation systems worst case scenario regarding a comparison between traditiona and ow-energy ventiation systems. However, if we ony consider the overa average concentration at steady state of mode vs. mode we find j fj þð fþju ðaþ þa ð þ faþð þ aþ : ð9þ a 2 þ a þ Figure 3 depicts the ranges of a and f where the average concentration for the traditiona mixing system is higher than the ow-energy two-ayer systems. Interna source As for the externa case, the utimate steady state that the system reaches wi differ for the traditiona and ow energy systems. Here j in = 0 and j s =, which shoud be substituted in to the equations presented in section 3. The we mixed space in mode tends to a uniform contaminant concentration of (this is cacuated by assuming a source of j s in the space as is perceived in the upper ayer equation above - see appendix A for detais) j ðaþ þ a : ð0þ This is ower than the concentration of fuid entering the space, because of the sink effect of deposition that does not extract fuid, but does extract contaminant. For the two-ayer cases both systems tend to the same steady state where both ayers are we mixed. For this situation the upper and ower ayer concentration fieds are u þ a ða þ Þ 2 a ; jðbþ a ða þ Þ 2 a ðþ respectivey. At steady state, the concentration in the upper ayer is aways greater than that in the ower ayer and peope, who ony occupy the ower ayer, are ony exposed to the owest concentrations in the space. Again, these steady state vaues are independent of f. Comparing the concentration of the ower ayer for modes and we obtain j a2 þ a ðaþ a 2 þ a þ <; ð2þ which indicates that for this type of point source the ow-energy system aways does a better job removing contaminants than the traditiona system, regardess of the interface ocation or partice size. This ratio is zero for a = 0, which corresponds to a passive contaminant, and approaches as a fi. This is reasonabe because the source is effectivey in the upper ayer and for a = 0, no contaminant can fa back into the ower ayer. However, as a increases, more contaminant can fa through, thus increasing the concentration of the ower ayer. On the other hand, if we ony consider the average contaminant remova, we can see from Figure 4 that there are regions, particuary as the partice size increases, where the two-ayer system is worse (grey region) at removing contaminants than the one-ayer we-mixed system. However, since from a practica perspective we ony care about concentrations in the ower ayer, this is not reay the point of interest and is merey shown here to iustrate that an average contaminant concentration vaue is deceptive in predicting an individuaõs exposure as iustrated in the experiments by Ozkaynak et a. (982). Additiona mechanisms of deposition Whie gravitationa effects dominate the deposition mechanisms for arge partices (typicay >m, athough this is dependent on the friction veocity at a boundary, which for a dispacement system shoud be ess than for traditiona mixing system), the deposition of partices smaer than this can be strongy driven by Brownian diffusion (Lai and Nazaroff, 2000). Therefore, for such partices the governing equations (4) (5).4.3 ζ 0.5 κ > κ / κ κ α 0 0 α Fig. 3 Comparison of the steady state average concentration across the entire height of the space for the singe ayer vs. two ayer modes Ratio of the steady state concentrations of the ower ayer in the two ayer modes to the singe ayer concentration (j /j >) 5

6 Boster & Linden must be modified to account for this. As the utimate steady state for both two ayer modes is the same we focus on mode here. Accounting for additiona setting to a surfaces the governing equations become ð þ Q dw ÞK wm K in þ K s ; ð3þ ðq p þ Q d ÞK Q df K u þ K in ðq du þ Q p ÞK u ðq p þ Q dr ÞK þ Q p K s ð4þ where Q dw is the fow rate at which partices sette out of the we mixed space, Q d is the fow rate at which partices sette out of the ower ayer, Q df is the fow rate of partices that fow from the upper to ower ayer across the interface, Q du is the fow rate at which partices sette out the upper ayer and Q dr is the fow rate at which partices cross the interface from the ower to upper ayers. These quantities are evauated as foows: Q dw v v A v þ v d A d þ v u A u þ v u A u Q df v u A u Q d v v A v þ v da d Q du v v A u v þ v da d þ v u A u Q dr v d A d ð5þ where v v is the deposition veocity of a partice depositing on to a vertica surface, v d is the deposition veocity of a partice depositing on to a downward facing horizonta surface, v u is the deposition veocity of a partice depositing on to an upward facing horizonta surface, A v is the tota area of vertica boundaries in the space, A v is the area of vertica boundaries in the ower ayer, A u v is the area of vertica boundaries in the upper ayer, A u is the area of the an upward facing boundary and A is the area of downward facing boundaries. The deposition veocities can be evauated using equations presented in Tabe 2 in Lai and Nazaroff (2000). We treat the interface in the two ayer mode as a ÔfictitiousÕ rigid boundary through which fuxes can occur. In dimensioness terms (3) and (4) become: ð þ a dw Þj j in þ j s ; ð6þ ð þ a d Þj a df j u þ j in ; ð þ a du Þj u ð þ a dr Þj þ j s ; ð7þ where a di Q di represents the dimensioness forms of the various deposition fow rates defined in (5). The subscript i can represent the subscripts w,, f, u or r. By accounting for these additiona mechanisms we introduce severa new dimensioness parameters. In the imit of arge partices, the deposition veocities to upward facing surfaces reduces to the setting veocity, whie the deposition to downward facing and vertica surfaces reduces to zero and we recover the equation presented in sections 2 4. The steady state concentrations for each of the modes are given by j ðaþ j in þ j s þ a dw ; ð8þ u ð þ a du Þj in þ a df j s þ a d þ a du ð þ a d Þ a df ð þ a dr Þ ð9þ ð þ a dr Þj in þð þ a d Þj s þ a d þ a du ð þ a d Þ a df ð þ a dr Þ : ð20þ Externa contaminant case. For the externa contaminant situation we considered previousy (i.e. j in = and j s = 0) we again compare the upper to ower ayer concentrations in the two-ayer system. We aso compare the ower ayer concentration in the two-ayer ζ 0.5 κ /κ α κ >κ α Fig. 4 Comparison of the steady state average concentration across the entire height of the space for the singe ayer vs. two ayer modes Ratio of the steady state concentrations of the ower ayer in the two ayer modes to the singe ayer concentration (j / j <) 6

7 Partice transport in ow energy ventiation systems system to the concentration in the traditiona we mixed space. þ a du : ð2þ þ a u dr Because a du incudes deposition to vertica and horizonta surfaces, whie a dr ony invoves deposition to a downward facing horizonta surface, it is readiy seen that a du >a dr and therefore j ðb;cþ >j ðb;cþ u. Once again for the step-up case the concentration in the ower ayer is aways greater than it is in the upper ayer, even with the additiona setting mechanisms for fine and utrafine partices. Now we compare the ower ayer concentration in the two-ayer system to the concentration in the traditiona mixing space j ð þ a du Þð þ a dw Þ ðaþ þ a d þ a du ð þ a d Þ a df ð þ a dr Þ : ð22þ It is reativey straightforward using (5) to show to that the denominator is greater than the numerator in (22). Therefore, as we observed previousy, occupants are exposed to higher eves of contaminants in the ow energy system when a step-up case is considered. Interna source case. In the same manner we can consider the interna source situation (j in = 0 and j s = ), where a df : ð23þ j ðb;cþ þ a u d Now, from (5), we know that a df <a d Therefore, the ower ayer concentration is aways ess than that in the upper ayer. Simiary j a df ð þ a dw Þ ðaþ þ a d þ a du ð þ a d Þ a df ð þ a dr Þ : ð24þ Once again using (5), we can show that the denominator is ess than the numerator in (24). Therefore, as we observed previousy, occupants are exposed to ower eves of contaminants in the ow energy system when a point source is considered. Concusions In this paper we have considered the steady transport of particuate contaminants in a dispacement-ventiated space. We compared two modes, one representing a traditiona ventiation system and the other representing a dispacement-ventiated space. We considered two contamination scenarios, namey an externa and an interna contaminant source. Severa important differences between the traditiona and ow-energy systems were noted. It is widey beieved that ow-energy dispacementventiation systems can be better than traditiona mixing systems at removing contaminants from a space. This is because there is a beief that these systems wi use the same mechanism for contaminant remova as they do for heat remova, where they are ceary more efficient. The heat extraction probem expoits the natura stratification that deveops, extracting the warmest air that naturay sits at the top of the room. However, there is no physica justification as to why this ocation shoud correspond to the ocation of maximum contaminant concentration too. In fact many times it does not (Boster and Linden, 2007). For the externa contaminant case, we showed that, at steady state, the concentration in the ower ayer is greater than that of the upper ayer. Further, this ower ayer concentration is arger than that for an equivaent traditiona ventiation system. The argest difference occurs for partices with a =, where the ower ayer concentration in the dispacement system is 33% higher than that in the traditiona system. On the other hand, when considering the interna contaminant scenario, we predict a higher steady state concentration in the upper ayer compared to the ower ayer. The ower ayer concentration wi aways be ess than that in an equivaent traditiona system, thus reducing occupantsõ exposure to contaminants. It is ceary important to consider the types of sources that are ikey to be encountered in a rea buiding. For exampe, in a we designed surgica operating theater, the ventiation system typicay fiters out most contaminant before introducing air into the room. Therefore, it is unikey that the step-up scenario is reevant. In an operating theater the most common sources of contaminants are the surgeons, nurses and patients (Smith, 975), which woud correspond to the point source probem described herein. As such, a dispacement system may provide better air quaity than a traditiona mixing ventiation system. On the other hand, if we consider a naturay ventiated space, where externa sources can pay an important part in contamination, the step-up scenario may be reevant. Another important point to note is that it is not aways sufficient to estimate the average amount of contaminant within a space. As shown for a three contamination scenarios, computing the average concentrations ony can ead to an overy optimistic picture as oca concentrations can often be significanty higher. In many cases one ventiation system can outperform another based on average concentrations. However, when considering individua exposure this may no onger hod true. Acknowedgement The authors woud ike to thank the Caifornia Energy Commission for their financia support of this project. 7

8 Boster & Linden References Baines, W.D. and Turner, J.S. (969) Turbuent buoyant convection from a source in a confined region, J. Fuid Mech., 37, Baughman, A., Gadgi, A. and Nazaroff, W. (994) Mixing of a point source poutant by natura convection fow within a room, Indoor Air, 4, Boster, D. and Linden, P. (2007) Contaminated ventiated emptying boxes. J. Fuid Mech., 59, Brohus, H. and Niesen, P.V. (996) Persona exposure in dispacement ventiated rooms, Indoor Air, 6, 57. Hunt, G. and Kaye, N. (2006) Poutant fushing with natura dispacement ventiation, Buid. Environ., 4, Jenkins, P., Phiips, T., Muberg, E. and Hui, S. (992) Activity patterns of caifornians: use and proximity to indoor poutant sources, Atmos. Environ., 26A, Jiang, Z., Chen, Q. and Moser Smith, A. (992) Comparison of dispacement & mixing diffusers, Indoor Air, 2, Kepeis, N. (999) Vaidity of the uniform mixing assumption: determining human exposure to environmenta tobacco smoke, Environ. Heath Perspect., 07, Lai, A. and Nazaroff, W. (2000) Modeing indoor partice deposition from turbuent fow onto amooth surfaces, J. Aeroso Sci., 3, Lin, Z., Chow, T.T., Fong, K.F., Tsang, C.F. and Wang, Q., (2005) Comparison of performances of dispacement and mixing ventiations. Part II: Indoor air quaity, Int. J. Refrigeration, 28, Linden, P.F. (999) The fuid mechanics of natura ventiation, Annu. Rev. Fuid Mech., 3, Linden, P.F., Lane-Serff, G.F. and Smeed, D.A. (990) Emptying fiing boxes: the fuid mechanics of natura ventiation, J. Fuid Mech., 22, Morton, B.R., Tayor, G.I. and Turner, J.S. (956) Turbuent gravitationa convection from maintained and instantaneous sources, Proc. R. Soc., A234, 23. Mundt, E. (200) Non-buoyant poutant sources and partices in dispacement ventiation, Buid. Environ., 36, Ozkaynak, H., Ryan, P., Aen, G. and Turner, W. (982) Indoor air quaity modeing: compartmenta approach with reactive chemistry, Environ. Int., 8, Santamouris, M., Buiding Ventiation: The State of the Art. Earthscan, James & James. Smith, C. (975) Hospita operating theatre environment and the assessment of fiters for use in associated ventiating pants, Ann. Occup. Hyg., 7, Xinga, H., Hattonb, A. and Awbi, H.B. (200) A study of the air quaity in the breathing zone in a room with dispacement ventiation, Buid. Environ., 36, Appendix A. point source strength estimation A point source in the pume in the ower ayer can be thought of as an additiona source into the upper ayer. dp dz 5 ðk PÞ; z<h ða:þ 3z dk dt ðq p þ Q fa ÞK þ Q fa Sh Sh K u þ Sh K in; dk u dt Q p SðH hþ ðk þ K s Þ ð Q fa þ Q p SðH hþ ÞK u: ða:3þ ða:4þ which impies that if we have a source of strength ^K s at a height z s in the ower ayer, the concentration being injected into the upper ayer by the pume is Pðz hþ K þ ^K s ð z s h Þ5 3 K þ K s ða:2þ Therefore the conservation equations can be written as To compare equivaent systems the conservation equation for the we mixed room shoud incude a source of the same strength eading to dk wm dt ðk in þ K s Þ SH þ Q fa : ða:5þ SH 8