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Computer modeling of displacement ventilation systems based on plume rise in stratified environment
Energy and Buildings 39 (2007) 427–436 www.elsevier.com/locate/enbuild
Computer modeling of displacement ventilation systems based on plume rise in stratified environment C.K. Lee *, H.N. Lam Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong Received 27 February 2006; received in revised form 1 August 2006; accepted 8 August 2006
Abstract A model for displacement ventilation system based on plume rise of single point heat source was developed. The errors for temperature gradient ratio were less than 6% in most cases. Errors for temperature gradient and displacement zone height were relatively higher (up to 28.1%) which might be due to the derivation of the parameters from experimental data. Still, the errors were lower than those from design model/method of some other workers (68.5% for the temperature gradient ratio and 15.7% for the temperature difference between the supply air and at 0.1 m above floor level). With a room height of 2.4 m (common for office in Hong Kong) and design room temperature 25.5 8C defined at 1.1 m above floor level under the normal load to air flow ratio of 12,000 W/m3/s (typical values for sub-tropical region) and minimum supply temperature of 18 8C, there existed a zone capacity range from 1000 to 5000 W that stand alone operation displacement ventilation system was feasible and that the displacement zone height (minimum 2.2 m) was above normal breathing level. The feasible zone capacity range diminished with decrease in design room temperature and/or room height. In this case, the load to air flow ratio had to be reduced, resulting in a higher flow rate when compared to a mixing ventilation system, or an auxiliary cooling facility such as a chilled ceiling had to be used. # 2006 Elsevier B.V. All rights reserved. Keywords: Displacement ventilation; Displacement zone height; Plume; Temperature gradient; Temperature gradient ratio
1. Literature review 1.1. Performance of displacement ventilation system Displacement ventilation systems have become a popular topic since the early 1980s, especially in the Scandinavian region. Air is supplied close to the floor and exhausted at ceiling level. According to previous studies from Skistad [1] and Jackman [2], heat sources inside the room generate convective plumes moving upward. The induced convective air flow of the plumes increases with height up to a level (displacement zone height) where it equals the supply air flow. Above this level, recirculation of air around the convective plumes occurs, and the room air becomes fully mixed above the displacement zone height (mixing zone). The air temperature is the same within the mixing zone. Below this mixing zone (displacement zone), the temperature increases with height. The supply air velocity decreases up to some distance from the supply terminal (near
* Corresponding author. Tel.: +852 2859 2635; fax: +852 2858 5415. E-mail address: [email protected] (C.K. Lee). 0378-7788/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2006.08.007
zone) where the envelope of the supply air stream drops to a height of around 100 mm from floor. Beyond this distance, the flow pattern is similar regardless the supply terminal characteristics. Fig. 1 shows the location of the various zones. To maintain thermal comfort, a high vertical temperature gradient should be avoided as stipulated in the ASHRAE [3] and ISO [4] standard. This limits the cooling load per unit air flow, and is easier to achieve for low cooling load situation (as in the Scandinavian region). According to Skaret [5], stratified displacement air flow can be upward or downward. Downward displacement flow is beneficial only if the contaminant sources are denser than the room air. In most cases, the contaminant sources are lighter than the room air, and upward displacement flow predominates. Many studies had covered the various aspects of displacement ventilation systems. The design guide from REHVA [6] summarized the work from Skistad [1], Mundt [7] and several other researchers. Fitzner [8] investigated the improvement of indoor air quality in terms of the ventilation effectiveness (defined as the ratio of pollutant concentration of exhaust air to that of the air at breathing zone) by applying a displacement ventilation system. He found that the ventilation effectiveness
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Nomenclature A B cp ET 1 F g Q0 Qac R S T Te Tgrad T1.1 U Vs Z Zoc
R2U (m3/s) RU (m2/s) specific heat capacity of air (W/kg K) temperature gradient ratio referring to T1 specific buoyancy flux of plume air (m4/s3) acceleration due to gravity (9.81 m/s2) convective heat load at plume source (W) heat load transferred to air conditioning system (W) plume radius (m) degree of stratification (s2) air temperature (8C) exhaust air temperature (8C) temperature gradient (8C/m) room temperature at 1.1 m above floor (8C) mean plume air velocity (m/s) supply air volume flow rate (m3/s) height above plume source (m) displacement zone height (m)
Greek letters a plume entrainment constant (0.109 according to Jin [24]) g Q0/Qac r air density (kg/m3) Suffixes a s 0 1
ambient outside heat plume supply air plume source ambient outside heat plume at reference height (taken as 0.1 m above floor according to Lee [30])
was greater than unity, meaning that indoor air quality was improved with displacement ventilation system. Breum et al. [9] compared the performance of displacement ventilation system with conventional system by site measurement using tracer gas techniques and found that displacement ventilation system yielded a better indoor air quality by a factor ranging from 1.6 to 6.6 over the conventional system. Holmberg et al. [10] explored the limitation of displacement ventilation system in improving the indoor air quality. They commented that with air flow rate of 10 l/s per person, the air quality in the breathing zone with occupants sitting still was better than that of conventional system even though the displacement zone height was slightly below the head height of the seated persons. However, this improvement in air quality was reduced by the natural movement of occupants. With air flow rate down to 5 l/s per person, there was no appreciable improvement in the quality of the inhaled air, since the displacement zone height was far below the breathing height. Skaret [5] discussed the various design implications of displacement ventilation such as the displacement flow principle (piston flow or thermally stratified flow), method of
Fig. 1. Location of various zones in displacement ventilation system.
air supply (through porous floor, jet type supply nozzles in the floor or diffuse air supply terminals with horizontal air outflow located at floor level) and evaluation model for displacement ventilation system (two-zone model). Mathisen [11] recorded the results of four installed displacement ventilation systems in some typical and relatively large ventilated space by means of field measurements of the air temperatures and CO2 concentration. He found that the air quality and temperature efficiency for most of the space was better than that obtainable with a complete mixing system. The only exception was in the CO2 concentration and temperature at the back part of the premises, which were higher than the rest of the room. Each displacement ventilation system also seemed to give satisfactory thermal comfort. Svensson [12] summarized the results of application of displacement ventilation systems in Nordic countries. He concluded that displacement ventilation was better than conventional ventilation in terms of ventilation efficiency (defined as the ratio of pollutant concentration difference between exhaust and supply air and that between room and supply air). As the pollutant concentration is lower in the displacement zone than at the exhaust, higher ventilation efficiency (greater than one) can be achieved. This is extremely important if the activity inside the room will generate substantial amount of pollutants as in some manufacturing plant. In fact, more than half of the factories in the Scandinavian region have now employed displacement ventilation system, and the results from field measurements [9] had demonstrated the improvement of indoor air quality. Sandberg and Blomqvist [13] measured the contaminant concentration, temperature and air velocity within the near zone, and temperature and contaminant gradient inside typical office room using several kinds of diffusers. They commented that applying the same supply air flow rate as that used in mixing ventilation would not much improve the air quality within the breathing zone. Cheong et al. [14–16] studied the perceived air quality, sick building syndrome, local thermal sensation, local thermal comfort and thermal effect of temperature gradient on tropically acclimatized occupants inside test chamber served by displacement ventilation system. They commented that
C.K. Lee, H.N. Lam / Energy and Buildings 39 (2007) 427–436
thermal gradient had insignificant impact on perceived air quality and sick building syndrome and a temperature gradient of up to 5 8C/m could be tolerated. Local thermal discomfort reduced with increase in room temperature, and the lower body segment was more susceptible to thermal discomfort. The percentage dissatisfied was not significantly affected by temperature gradient, but varied widely at different room temperature and overall thermal sensations. The air movement inside the room also affects the performance of displacement ventilation system. Melikov et al. [17] studied the air flow characteristics in the occupied zone. Flow visualization indicated the convective flow generated above the heat sources and the development of the stratified layer. Linden et al. [18] studied the natural ventilation inside a room by using the ‘‘emptying filling boxes method’’ to investigate the plume spreading in a density stratified flowing fluid (brine). They compared the flow pattern of mixing ventilation and displacement ventilation under various loading conditions. They also proposed a formula to estimate the height of the displacement zone. The variation of temperature and air velocity within the near zone around the supply terminal is closely related to the problem of cold draught. Skistad [1] gave a brief account of the flow properties inside the near zone. He commented on the performance of different types of supply terminals in term of the size of the cold draught region. He also derived equations for the estimation of the velocity profile inside the near zone. Skistad [1] argued that the supply terminals would only influence the temperature gradient below the height of the terminals and played no part on the air flow above the terminals. Melikov [19] gave a brief account of the problem of thermal discomfort due to draft and vertical temperature difference for displacement ventilation system. He compared the temperature and air velocity variation with that of the international standard for thermal comfort [3,4] which specified that the temperature difference between 1.1 and 0.1 m above floor should not exceed 3 8C. The studies of the displacement zone are mostly concentrated on the behavior of the buoyant plumes generated by various types of heat sources inside the space. Skaret [20] gave the formulae for the convective flow from various types of heat sources. However, they were only applicable in an isothermal quiescent environment. Investigation of buoyant plumes in stratified but still quiescent environment had also been made. Morton et al. [21] analyzed the plume rise from a point source in a density stratified fluid and developed equations which were solved numerically. The simulated results were compared with experimental data. Crawford and Leonard [22] observed the buoyant plumes in calm stably stratified air and compared the results with those of Priestley and Ball [23] and Morton et al. [21]. Jin [24] studied the plume rise in stratified environment, and modified the constant in the plume rise formula developed by Morton et al. [21] based on experimental data. Chen [25] developed an analytical solution for the maximum plume rise height based on theory of Priestley and Ball [23]. Madni and Pletcher [26] modeled the behavior of buoyant jets discharged
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into uniform and stratified quiescent ambient by mean of finite difference method with a simple turbulence model. They found that the influence of buoyancy on the turbulent transport was of secondary importance for vertically discharged buoyant jets. Ogino et al. [27] derived equations for the variation of centerline velocity and temperature, zero momentum and zero buoyancy heights of buoyant jets discharged into a linearly stratified ambient environment. He found that zero momentum and zero buoyancy heights were correlated with the product of discharge Froude number and the vertical temperature gradient of the ambient fluid. In designing displacement ventilation systems, thermal comfort and indoor air quality are the main factors of concerns. However, in certain cases, it is not possible to satisfy requirements in both of these factors. Skistad [1] commented that if the pollutants or contaminants were not delivered from the warmest source, the pollutants or contaminants concentration might be higher at some location than at the exhaust. This also applied to passive contaminants, i.e. non-buoyant gases. Moreover, Skistad [1] pointed out that sometimes mixing might be necessary in order to reduce the draught zone. This was achieved by having a perforated supply terminal surface. The smaller the proportion of free area of the perforated surface, the greater the mixing would be. However, this would deteriorate the indoor air quality, as the pollutant concentration within the occupied zone would be evened out when mixing occurred. 1.2. Design method of displacement ventilation system As the performance of displacement ventilation is related to the thermal plumes developed from various kinds of heat sources, an exact analytical formulation is impossible. Danielsson [28] proposed a design method based on extensive experimental data. He related the temperature difference between the supply air and the occupied zone (mid height of displacement zone) to the load/air flow ratio (Qac/Vs) in a graph at various room height range (see Fig. 2). From the graph, the temperature gradient could be read. Skistad [1] postulated that the temperature difference between supply and exhaust was double that of the temperature difference between the supply and that at 0.1 m above ground far enough downstream of the supply terminals (ET 1 ¼ 0:5). He supposed that the temperature would increase steadily from the floor up to the ceiling level with a nearly constant temperature gradient (displacement zone height was the same as the room height). Cheong [29] empirically related T1 to Ts, T1.1, sensible heat load per unit area and the room height. The exhaust air temperature was then calculated based on given supply flow rate and assuming that the room temperature increased linearly from floor to ceiling. Mundt [7] devised an equation to calculate the dimensionless temperature difference at floor level under different supply flow rate. She also presumed that the temperature increased steadily from the floor to ceiling. However, Lee [30] found that across the displacement zone height, the temperature gradient changed substantially, and the displacement zone height might not be the same as the room height.
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conservation equations for specific volume, momentum, and buoyancy flux was quoted from Jin [24] as d 2 ðR UÞ ¼ 2aRU dZ
(1)
d 2 2 r r ðR U Þ ¼ R2 g a dZ r1
(2)
d ra r g dra 2 R Ug ¼ R2 U dZ r1 r1 dZ
(3)
By setting A = R2U, B = RU, F = R2Ug(ra r)/r1 and applying ideal gas law as done by Jin [24], Eqs. (1)–(3) were rewritten as
Fig. 2. Performance graph for displacement ventilation system by Danielsson [28].
dA ¼ 2aB dZ
(4)
dB4 ¼ 2FA dZ
(5)
dF ¼ AS dZ
(6)
where S¼
Auban et al. [31] studied the convection of thermal plume in a confined stratified environment by hydraulic solutal simulation. They related the stratified height to the supply flow rate, buoyancy flux at source and source diameter but without the stratification level. Zhao and Li [32] proposed formulae for the displacement zone height based on a plate heat source. Xing and Awbi [33] measured the displacement zone height in a room and compared the results with models proposed by Mundt [34], showing good agreement. Bouzinaoui et al. [35] extended the work of Auban et al. [31] by measuring the displacement zone height in a room and compared results with equations proposed by the latter. However, they did not propose any formula for the temperature gradient ratio. In this study, the total air conditioning load is simplified by a single point source located at floor level. The temperature gradient ratio and displacement zone height was calculated using the plume rise equation and empirical correlation determined from the test results of Lee [30]. The new model provides a rough picture of the temperature variation inside the room and simple tool for designing displacement ventilation systems. 2. Theory 2.1. Thermal plume from point source in stratified environment Fig. 3 illustrated the definition of various parameters. As stated by Jin [24], the velocity and temperature deficit of a thermal plume from a point heat source could be approximated by a ‘‘top hat’’ profile suggested by Morton et al. [21]. The
g T grad T 1 þ 273:13
(7)
as defined by Jin [24]. The volume flow rate of the plume air became pA. Eqs. (4)–(6) were solved numerically using the fully implicit finite difference method. The boundary conditions at Z = 0 were A = 0, B = 0 and F = F 0, where F0 ¼
gQ0 pcp0 r0 ðT 0 þ 273:13Þ
(8)
according to Jin [24]. 2.2. Displacement ventilation system Defining T1 as the temperature of ambient air at 0.1 m above floor (to cohere with measured data from Lee [30]), then T grad ¼
Te T1 Z oc 0:1
(9)
Also, Qac ¼ rs V s cps ðT e T s Þ
(10)
where Qac was the loading transferred to the air conditioning system. Defining the temperature gradient ratio as ET 1 ¼
Te T1 Te Ts
(11)
The heat delivered from the source was only partially transferred by convection to the room (hence the air conditioning system), and Q0 ¼ gQac
(12)
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431
Fig. 3. (a) Temperature variation in displacement ventilation system and (b) thermal plume generated by a point heat source.
where 0 < g < 1. g was determined from experimental data of Lee [30]. From Eqs. (7) and (9), T1 ¼
T e þ 273:13 273:13 1 þ ððZ oc 0:1ÞS=gÞ
(13)
The room temperature was usually defined as the temperature at certain preset height (say 1.1 m above floor), and T 1:1 ¼ T 1 þ T grad
(14)
2.3. Solution methodology In designing a displacement ventilation system, Vs, Qac, Ts and Te were defined. The remaining variables were T1, Zoc and Tgrad. At displacement zone height, the plume buoyancy flux vanished and the convective plume flow balanced the supply air flow. Hence, F ¼ 0 and
pA ¼ V s
(15)
With known g, F 0 was determined. The variation of buoyancy flux and convective flow above the source plume were then calculated from Eqs. (4)–(6) using fully implicit finite difference method if Tgrad was set. By adjusting Tgrad iteratively, the conditions stated by Eq. (15) were met at a particular height. Hence, Tgrad and Zoc were solved. With Eqs. (13) and (14), T1 and T1.1 were found and ET 1 calculated using Eq. (11). 3. Analysis The coupled equations were solved using Engineering Equation Solver (EES). In solving Eqs. (4)–(6), a height step of 0.01 m was used for the finite difference scheme. The test results from Lee [30] were used to justify the model. To investigate the variation of g from the test results, Vs, Ts and Qac were used as input parameters and g adjusted so that the calculated ET 1 matched with the test data. Qac was calculated from measured temperatures and flow rate, while ET 1 was calculated from the measured temperatures. As all the air conditioning loads were represented by a single point source, T0 was considered as the average source temperature, and a value of 50 8C was chosen.
An empirical correlation for g was exploited. With the correlation for g determined, the complete model was used to simulate data and compared with test results from Lee [30]. For the test results, Tgrad was derived from measured temperatures using Eq. (14) and Zoc from the method stated in Lee [30] (adopting the definition of Tgrad from Eq. (14) and extending the temperature profile upward to a height where the room temperature equaled the exhaust temperature). Finally, the developed model was used to investigate the performance of displacement system applied to sub-tropical regions. A comparison was also made with other design models/methods. 4. Results and discussion 4.1. Evaluation of g The key test results from Lee [30] and required g to match ET 1 were summarized in Table 1. Ts affected the amount of heat dissipated from the heat source to the room but generally it would not influence the way the load was transferred. Hence, its effect on g was insignificant. Upon inspection of Table 1, a new parameter (Qac/Vs) was selected to investigate its effect on g, where 0 < g < 1 when 1 > (Qac/Vs) > 0. This parameter was also used by Danielsson [28] in his displacement ventilation system design method. One possible form of the relation is Table 1 Summarized key test data from Lee [30] and required g Vs
Ts
T1
Te
Qac
ET 1
Zoc
Tgrad
Required g
0.04129 0.04129 0.03805 0.03805 0.04129 0.04129 0.04129 0.04129 0.04129 0.04129 0.05425 0.05425 0.05425 0.05425
20.27 17.10 19.73 17.33 20.59 16.94 20.00 17.17 19.34 17.14 23.22 21.86 20.96 19.09
22.31 21.33 22.11 21.43 22.31 20.96 22.41 21.10 21.91 21.00 23.48 23.38 22.96 22.06
25.41 26.17 25.24 26.35 25.41 25.94 25.7 25.64 25.47 25.41 25.18 25.64 25.70 25.64
256.03 452.00 252.55 414.09 240.19 447.83 283.89 421.67 305.03 412.04 128.26 247.34 310.4 429.03
0.604 0.533 0.569 0.546 0.644 0.554 0.578 0.537 0.581 0.533 0.867 0.599 0.577 0.547
1.92 1.44 1.89 1.43 1.86 1.44 1.90 1.52 1.93 1.54 2.08 1.85 1.7 1.53
1.71 3.62 1.75 3.70 1.76 3.72 1.83 3.19 1.94 3.07 0.86 1.3 1.71 2.5
0.2490 0.2223 0.2354 0.2291 0.2669 0.2319 0.2391 0.2205 0.2403 0.2200 0.3515 0.2447 0.2363 0.2241
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C.K. Lee, H.N. Lam / Energy and Buildings 39 (2007) 427–436 Table 2 Errors of simulated data based on present model
Fig. 4. Comparison between required g and computed g.
g = 1/a(Qac/Vs), where a was positive and determined from Table 1. This relation required that the line for ln(g) versus (Qac/ Vs) should pass the origin, which was not found using the data in Table 1. Hence, this choice was not appropriate. Another form g = 1/[1 + a(Qac/Vs)b] was adopted. This form was similar to the relation between the dimensionless temperature difference at floor and supply flow rate (with b equal 1) as proposed by Mundt [7]. a and b were found by applying linear regression to ln(1/g 1) versus ln(Qac/Vs), where a = 0.1429 and b = 0.348. Hence, g¼
1 1 þ 0:1429ðQac =V s Þ0:348
(16)
Comparison was made between the required g from test data and the computed g from Eq. (16) as shown in Fig. 4. The root-meansquare value for the errors is 5.35% and Eq. (16) was justified. 4.2. Model simulation and comparison with test data With Eq. (16) established, the complete model was used to simulate results using the data in Table 1 as inputs and compared with experimental values from Lee [30], with the errors for the simulated data shown in Table 2. The errors for ET 1 were less than 6% except for results from three tests which corresponded to the three points where the required g and computed g deviated most as shown in Fig. 4 (leftmost three points). The errors for the temperature difference were below 8% except for the last four sets of data. The reason was similar to above. Errors for Zoc and Tgrad were remarkably higher (up to 28.1%). This could be explained by the fact that Zoc and Tgrad were derived from the experimental data. Avery clear change of temperature gradient at particular height was not easily found from the measured vertical temperature profiles (see Appendix A), and the adopted derivation of Zoc and Tgrad might not be the best one in every case. Nevertheless, the range of errors was still acceptable. 4.3. System simulation using the developed model The performance of displacement ventilation was studied using the established model with emphasis on application to sub-tropical region like Hong Kong. Generally, the design temperature difference between exhaust and supply temperature was about 10 8C, corresponding to a value of 12,000 for (Qac/Vs). The minimum supply temperature for displacement
T1 Ts
T1.1 Ts
ET 1
Zoc
Tgrad
0.00 2.13 5.46 5.85 7.56 6.47 2.90 1.53 1.17 0.78 69.23 14.47 10.00 6.06
3.20 6.75 3.16 5.26 3.16 6.21 2.84 4.49 4.66 4.76 0.89 9.25 10.24 11.52
0.50 1.88 4.39 4.95 3.73 5.6 2.42 1.68 0.34 0.75 9.80 10.52 8.32 5.30
5.21 16.67 7.41 14.69 1.08 16.67 5.26 11.18 7.77 10.39 13.46 15.14 21.18 28.10
7.02 17.13 14.29 17.84 1.14 20.16 9.29 11.91 9.28 9.77 19.77 3.85 10.53 18.40
Percentage error (100 (simulated data-test result)/test result).
ventilation system was taken as 18 8C (in consideration of the risk of draught). For a room height of 2.4 m (typical office ceiling height in Hong Kong), the simulated results were shown in Table 3. At small Qac (and consequently small Vs), the temperature gradient and reference room temperature were high. When Qac was increased, both Tgrad and T1.1 decreased and Zoc increased. This could be explained by using the plume rise equations since the induced plume air flow increased at a rate lower than that of the source heat flux. Auban et al. [31] stated that the induced plume air flow was proportional to (specific source buoyancy flux)1/3. As specific source buoyancy flux is proportional to the source heat flux according to Eq. (8), the induced plume air flow would be proportional to (source heat flux)1/3. Hence, to maintain a fixed (Qac/Vs), Zoc should be increased. Jin [24], Chen [25] and Crawford and Leonard [22] also reported that the maximum plume rise in stably stratified ambient was proportional to (source heat flux)1/4. When Qac continued to increase until the displacement zone height reached the ceiling, T1.1 would decrease a little bit further and reached a minimum value. Beyond that, T1.1 would increase. From Table 3, the minimum T1.1 was 24.63 8C. If the design room temperature was 25.5 8C, there would exist a range of Qac where displacement ventilation system alone could be used even in sub-tropical region (different from previous study Table 3 Simulated results based on (Qac/Vs) = 12,000 Qac
Vs
ET 1
T1
T1.1
Tgrad
Zoc
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000
0.04167 0.08333 0.125 0.1667 0.2083 0.25 0.2917 0.3333 0.375 0.4167 0.4583 0.5
0.5031 0.5208 0.5383 0.5923 0.5531 0.5227 0.4981 0.4776 0.4601 0.445 0.4317 0.4199
22.95 22.77 22.6 22.06 22.45 22.76 23 23.2 23.38 23.53 23.66 23.78
26.14 25.24 24.93 24.63 24.85 25.02 25.16 25.27 25.37 25.46 25.53 25.6
3.192 2.471 2.332 2.565 2.396 2.264 2.157 2.069 1.993 1.927 1.87 1.819
1.67 2.2 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4
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that displacement ventilation system could not be used alone in sub-tropical region). Besides, the displacement zone height (minimum 2.2 m) would be above the normal breathing level, indicating an improvement in indoor air quality. Of course, if the ceiling height was lower, the simulated reference room temperature might always be higher than the design room temperature. In this case, (Qac/Vs) should decrease, meaning that a higher flow rate should be chosen when compared to a mixing ventilation system, or auxiliary cooling facility (like chilled ceiling) had to be used. Based on Table 3, with a zone capacity of 1000–5000 W, a displacement ventilation system can work alone in a room with 2.4 m ceiling height and 25.5 8C design room temperature taken at 1.1 m above floor. A higher ceiling height would definitely be beneficial, as the feasible zone capacity range for stand alone operation of displacement ventilation system would be larger. 4.4. Comparison with other design models/methods A comparison was made for the simulated ET 1 and (T1 Ts) with those calculated using the design models/ methods from Mundt [7], Danielsson [28] and Cheong [29] based on test conditions of Lee [30]. The percentage errors for the simulated data were shown in Table 4. As compared with Table 2, it could be found that with the exception of results from Test 11 (reason already mentioned in Section 4.2), the percentage errors of the present model (0.46–10.48 for ET 1 and 0–14.47 for (T1 Ts)) were much lower than those from other design models/methods. Even including Test 11, the root-mean-square values of percentage errors was 5.39 for ET 1 and 19.49 for (T1 Ts). The corresponding values for simulated data from design model of Mundt [7] was 26.49 for ET 1 and 39.9 for (T1 Ts), those from design method of Danielsson [28] being 19.12 for ET 1 and 36.48 for (T1 Ts), and those from design model of Cheong [29] being 17.13 for ET 1 and 23.12 for (T1 Ts). This implied that the root-meansquare values of percentage errors in ET 1 and (T1 Ts) for the Table 4 Comparison of errors for simulated ET 1 and (T1 Ts) using other design model/ method based on test conditions of Lee [30] Percentage error for (T1 Ts)
Percentage error for ET 1 Mundt [7]
Danielsson [28]
Cheong [29]
Mundt [7]
Danielsson [28]
Cheong [29]
16.89 32.89 21.12 26.54 9.60 27.87 22.18 31.88 21.64 32.87 12.63 26.61 31.53 38.96
20.50 14.32 16.87 18.42 12.97 15.56 17.23 16.93 15.16 20.84 15.21 24.94 29.90 21.50
16.80 18.44 22.99 17.29 10.71 14.08 20.50 19.09 18.97 20.15 3.15 17.35 16.14 14.94
25.00 37.59 27.73 31.95 16.86 34.83 29.88 37.15 25.68 37.56 84.62 38.82 42.00 46.80
30.88 16.31 21.85 22.20 22.67 19.65 23.24 19.85 20.62 23.83 100.00 36.84 40.00 25.59
25.00 21.04 30.25 20.98 18.60 17.91 27.80 22.39 26.07 23.06 23.08 25.00 21.00 17.51
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present model were at least 68.5 and 15.7%, respectively, lower than those from other models/methods. 5. Recommendations and conclusions 5.1. Recommendations for further work The higher supply temperature for displacement ventilation system compared to a mixing ventilation system means that the latent load in the room should be low. Hence, if displacement ventilation system is to be used in sub-tropical region like Hong Kong, auxiliary facility will be needed to handle to latent load. One possible solution is to supply air with a desiccant or heat pipe type dehumidifier which can supply cool air at a low relative humidity. The resulting room relative humidity might be kept at a level (lower than the usual design value) such that the comfort room temperature (according to the comfort chart) can be higher, thus reducing the room cooling load. Moreover, the coupling of the dehumidifier with ground heat exchanger provides extra potential for energy saving. Further research will be needed to investigate this possibility. 5.2. Conclusions A model for displacement ventilation system based on plume rise of single point heat source was developed from the test results of Lee [30]. The difference between the simulated data and the test results for temperature gradient ratio (ET 1 ) were less than 6% in most cases. Differences for temperature gradient (Tgrad) and displacement zone height (Zoc) were relatively higher (up to 28.1%). The reason might be that the ways of deriving the parameters from experimental data was not the best in every case. Nevertheless, the prediction of temperature gradient ratio (ET 1 ) and temperature difference (T1 Ts) between the supply air and at 0.1 m above floor level based on present model were in most cases much better than those obtained from design models/methods of some other workers. The root-mean-square values of percentage errors in ET 1 and (T1 Ts) were at least 68.5 and 15.7%, respectively, lower than those from other models/methods. The feasibility of applying displacement ventilation system alone in sub-tropical region depended on the ceiling height, height for reference room temperature and the design room temperature. With a room height of 2.4 m and design room temperature of 25.5 8C defined at 1.1 m above floor level under the normal load to air flow ratio (Qac/Vs) of 12,000 W/ m3/s and minimum supply temperature of 18 8C, there existed a zone capacity range from 1000 to 5000 W that stand alone operation displacement ventilation system was feasible and that the displacement zone height (minimum 2.2 m) was above normal breathing level. A higher ceiling height was beneficial as the feasible zone capacity range would be greater. With lower ceiling heights and/or lower design room temperatures, the load to air flow ratio (Qac/Vs) should be reduced, resulting in a higher flow rate when compared to a mixing ventilation system, or auxiliary cooling facility (like chilled ceiling) had to be used.
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Appendix A See Figs. A.1–A.6.
Fig. A.1. Measured room temperature profiles from Lee [30] (Tests 1 and 2).
Fig. A.2. Measured room temperature profiles from Lee [30] (Tests 3 and 4).
Fig. A.3. Measured room temperature profiles from Lee [30] (Tests 5 and 6).
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Fig. A.4. Measured room temperature profiles from Lee [30] (Tests 7 and 8).
Fig. A.5. Measured room temperature profiles from Lee [30] (Tests 9 and 10).
Fig. A.6. Measured room temperature profiles from Lee [30] (Tests 11–14).
References [1] H. Skistad, Displacement Ventilation, Research Studies Press Ltd., Taunton, 1994. [2] P. Jackman, Displacement Ventilation, Technical Memorandum 2/90, BSRIA, 1990. [3] Thermal Environmental Conditions-human Occupancy, ANSI/ASHRAE Standard 55-1981, Altanta, 1981. [4] Moderate Thermal Environments-determination of the PMV and PPD Indices and Specification of the Conditions for Thermal Comfort, ISO Standard 7730, Geneva, 1984.
[5] E. Skaret, in: H.D. Goodfellow (Ed.), Ventilation by displacement-characterization and implications, Ventilation ’85, Elsevier Science Publishers B.V., Amsterdam, 1986. [6] H. Skistad, E. Mundt, P.V. Nielsen, K. Hagstrom, J. Railio, Displacement ventilation in non-industrial premises, in: Guidebook No. 1, REHVA, 2002. [7] E. Mundt, The performance of displacement ventilation system, Ph.D. Thesis, Royal Institute of Technology, Sweden, 1996. [8] F. Fitzner, Displacement flow-one possibility to improve air quality by better ventilation effectiveness, in: Proc Sick Building and Related Illness Symposium, Hong Kong, (1991), pp. 6.1–6.17.
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[9] N.O. Breum, F. Helbo, O. Lausten, Dilution versus displacement ventilation—an intervention study, The Annals of Occupational Hygiene 33 (3) (1989) 321–329. [10] R.B. Holmberg, L. Eliason, K. Folkesson, O. Strindehag, Inhalation-zone air quality provided by displacement ventilation, in: Proc., ROOMVENT 90 Second Intl. Conf., 1990. [11] H.M. Mathisen, Case studies of displacement ventilation in public halls, ASHRAE Transactions 95 (Part 2) (1989) 1018–1027. [12] A.G.L. Svensson, Nordic experiences of displacement ventilation systems, ASHRAE Transactions 95 (Part 2) (1989) 1013–1017. [13] M. Sandberg, C. Blomqvist, Displacement ventilation systems in office rooms, ASHRAE Transactions 95 (Part 2) (1989) 1041–1049. [14] K.W.D. Cheong, W.J. Yu, K.W. Tham, S.C. Sekhar, R. Kosenen, A study of perceived air quality and sick building syndrome in a field environment chamber served by displacement ventilation system in the tropics, Building and Environment 41 (11) (2006) 1530–1539. [15] K.W.D. Cheong, W.J. Yu, K.W. Tham, S.C. Sekharm, R. Kosenen, Local thermal sensation and comfort study in a field environment chamber served by displacement ventilation system in the tropics, Building and Environment 42 (2) (2007) 525–533. [16] K.W.D. Cheong, W.J. Yu, K.W. Tham, S.C. Sekhar, R. Kosenen, Thermal effect of temperature gradient in a field environment chamber served by displacement ventilation system in the tropics, Building and Environment 42 (1) (2007) 516–524. [17] A.K. Melikov, G. Langkilde, B. Derbiszewaki, Airflow characteristics in the occupied zone of rooms with displacement ventilation, ASHRAE Transactions 96 (Part 1) (1990) 1050–1057. [18] P.F. Linden, G.F. Lane-Serff, D.A. Smeed, Emptying filling boxes: the fluid mechanics of natural ventilation, Journal of Fluid Mechanics 212 (1990) 309–335. [19] A.K. Melikov, Local thermal discomfort due to draft and vertical temperature difference in rooms with displacement ventilation, ASHRAE Transactions 95 (Part 2) (1989) 1050–1057. [20] E. Skaret, VENTILASJONSTEKNIKK, Inst. of Heating, Ventilation and Sanitary Techniques, NTH, Trondheim, 1986. [21] B.R. Morton, G.I. Taylor, J.S. Turner, Turbulent gravitational convection from mainland and instantaneous sources, Proceedings of the Royal Society of London Series A 4 (1956) 1–23. [22] T.V. Crawford, A.S. Leonard, Observation of buoyant plumes in calm stably stratified air, Journal of Applied Meteorology 1 (1962) 251–256.
[23] C.H.B. Priestley, F.K. Ball, Continuous convection from an isolated source of heat, Quarterly Journal of Royal Meteorology Society 80 (1955) 144– 157. [24] Y.H. Jin, Experimental study of plume rise in a stably stratified environment, ASHRAE Transaction 97 (Part 2) (1991) 340–346. [25] J.C. Chen, Buoyant jet rise in a calm, linearly stratified environment, in: Proc. Int. Symposium on Environmental Hydraulics, Hong Kong, (1991), pp. 77–83. [26] I.K. Madni, R.H. Pletcher, Prediction of turbulent forced plumes issuing vertically into stratified or uniform ambients, Transactions ASME Journal of Heat Transfer 99 (February) (1977) 99–104. [27] F. Ogino, H. Takechi, I. Kudo, T. Mizushina, Heated jet discharged vertically into ambients of uniform and linear temperature profiles, International Journal of Heat and Mass Transfer 23 (November) (1980) 1581–1588. [28] P.O. Danielsson, Displacement ventilation—a spreading disease or a blessing? in: Ventilation 1988 BOHS, London, (1988), pp. 471– 480. [29] K.W.D. Cheong, Handbook on Design Guidelines for Displacement Ventilation system in the Tropics, Department of Building, University of Singapore, 2005. [30] C.K. Lee, A study of displacement ventilation systems for use in Hong Kong, M.Ph. Thesis, Dept. of Mech. Engg., University of Hong Kong, 1998. [31] O. Auban, F. Lemoine, P. Vallette, J.R. Fontaine, Simulation by solutal convection of a thermal plume in a confined stratified environment: application to displacement ventilation, International Journal of Heat and Mass Transfer 44 (24) (2001) 4679–4691. [32] H.Z. Zhao, A.G. Li, A method for prediction of room temperature distribution, in: Proc. ROOMVENT ’98, Stockholm, Sweden, (1998), pp. 445–449. [33] H.J. Xing, A.B. Awbi, Measurement and calculation of the neutral height in a room with displacement ventilation, Building and Environment 37 (10) (2002) 961–967. [34] E. Mundt, The Performance of Displacement Ventilation System, Report for BFR Project No. 920937-0, 1996. [35] A. Bouzinaoui, P. Vallette, F. Lemoine, J.R. Fontaine, R. Devienne, Experimental study of thermal stratification in ventilated confined spaces, International Journal of Heat and Mass Transfer 48 (19–20) (2005) 4121– 4131.
Computer modeling of displacement ventilation systems based on plume rise in stratified environment C.K. Lee *, H.N. Lam Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong Received 27 February 2006; received in revised form 1 August 2006; accepted 8 August 2006
Abstract A model for displacement ventilation system based on plume rise of single point heat source was developed. The errors for temperature gradient ratio were less than 6% in most cases. Errors for temperature gradient and displacement zone height were relatively higher (up to 28.1%) which might be due to the derivation of the parameters from experimental data. Still, the errors were lower than those from design model/method of some other workers (68.5% for the temperature gradient ratio and 15.7% for the temperature difference between the supply air and at 0.1 m above floor level). With a room height of 2.4 m (common for office in Hong Kong) and design room temperature 25.5 8C defined at 1.1 m above floor level under the normal load to air flow ratio of 12,000 W/m3/s (typical values for sub-tropical region) and minimum supply temperature of 18 8C, there existed a zone capacity range from 1000 to 5000 W that stand alone operation displacement ventilation system was feasible and that the displacement zone height (minimum 2.2 m) was above normal breathing level. The feasible zone capacity range diminished with decrease in design room temperature and/or room height. In this case, the load to air flow ratio had to be reduced, resulting in a higher flow rate when compared to a mixing ventilation system, or an auxiliary cooling facility such as a chilled ceiling had to be used. # 2006 Elsevier B.V. All rights reserved. Keywords: Displacement ventilation; Displacement zone height; Plume; Temperature gradient; Temperature gradient ratio
1. Literature review 1.1. Performance of displacement ventilation system Displacement ventilation systems have become a popular topic since the early 1980s, especially in the Scandinavian region. Air is supplied close to the floor and exhausted at ceiling level. According to previous studies from Skistad [1] and Jackman [2], heat sources inside the room generate convective plumes moving upward. The induced convective air flow of the plumes increases with height up to a level (displacement zone height) where it equals the supply air flow. Above this level, recirculation of air around the convective plumes occurs, and the room air becomes fully mixed above the displacement zone height (mixing zone). The air temperature is the same within the mixing zone. Below this mixing zone (displacement zone), the temperature increases with height. The supply air velocity decreases up to some distance from the supply terminal (near
* Corresponding author. Tel.: +852 2859 2635; fax: +852 2858 5415. E-mail address: [email protected] (C.K. Lee). 0378-7788/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2006.08.007
zone) where the envelope of the supply air stream drops to a height of around 100 mm from floor. Beyond this distance, the flow pattern is similar regardless the supply terminal characteristics. Fig. 1 shows the location of the various zones. To maintain thermal comfort, a high vertical temperature gradient should be avoided as stipulated in the ASHRAE [3] and ISO [4] standard. This limits the cooling load per unit air flow, and is easier to achieve for low cooling load situation (as in the Scandinavian region). According to Skaret [5], stratified displacement air flow can be upward or downward. Downward displacement flow is beneficial only if the contaminant sources are denser than the room air. In most cases, the contaminant sources are lighter than the room air, and upward displacement flow predominates. Many studies had covered the various aspects of displacement ventilation systems. The design guide from REHVA [6] summarized the work from Skistad [1], Mundt [7] and several other researchers. Fitzner [8] investigated the improvement of indoor air quality in terms of the ventilation effectiveness (defined as the ratio of pollutant concentration of exhaust air to that of the air at breathing zone) by applying a displacement ventilation system. He found that the ventilation effectiveness
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Nomenclature A B cp ET 1 F g Q0 Qac R S T Te Tgrad T1.1 U Vs Z Zoc
R2U (m3/s) RU (m2/s) specific heat capacity of air (W/kg K) temperature gradient ratio referring to T1 specific buoyancy flux of plume air (m4/s3) acceleration due to gravity (9.81 m/s2) convective heat load at plume source (W) heat load transferred to air conditioning system (W) plume radius (m) degree of stratification (s2) air temperature (8C) exhaust air temperature (8C) temperature gradient (8C/m) room temperature at 1.1 m above floor (8C) mean plume air velocity (m/s) supply air volume flow rate (m3/s) height above plume source (m) displacement zone height (m)
Greek letters a plume entrainment constant (0.109 according to Jin [24]) g Q0/Qac r air density (kg/m3) Suffixes a s 0 1
ambient outside heat plume supply air plume source ambient outside heat plume at reference height (taken as 0.1 m above floor according to Lee [30])
was greater than unity, meaning that indoor air quality was improved with displacement ventilation system. Breum et al. [9] compared the performance of displacement ventilation system with conventional system by site measurement using tracer gas techniques and found that displacement ventilation system yielded a better indoor air quality by a factor ranging from 1.6 to 6.6 over the conventional system. Holmberg et al. [10] explored the limitation of displacement ventilation system in improving the indoor air quality. They commented that with air flow rate of 10 l/s per person, the air quality in the breathing zone with occupants sitting still was better than that of conventional system even though the displacement zone height was slightly below the head height of the seated persons. However, this improvement in air quality was reduced by the natural movement of occupants. With air flow rate down to 5 l/s per person, there was no appreciable improvement in the quality of the inhaled air, since the displacement zone height was far below the breathing height. Skaret [5] discussed the various design implications of displacement ventilation such as the displacement flow principle (piston flow or thermally stratified flow), method of
Fig. 1. Location of various zones in displacement ventilation system.
air supply (through porous floor, jet type supply nozzles in the floor or diffuse air supply terminals with horizontal air outflow located at floor level) and evaluation model for displacement ventilation system (two-zone model). Mathisen [11] recorded the results of four installed displacement ventilation systems in some typical and relatively large ventilated space by means of field measurements of the air temperatures and CO2 concentration. He found that the air quality and temperature efficiency for most of the space was better than that obtainable with a complete mixing system. The only exception was in the CO2 concentration and temperature at the back part of the premises, which were higher than the rest of the room. Each displacement ventilation system also seemed to give satisfactory thermal comfort. Svensson [12] summarized the results of application of displacement ventilation systems in Nordic countries. He concluded that displacement ventilation was better than conventional ventilation in terms of ventilation efficiency (defined as the ratio of pollutant concentration difference between exhaust and supply air and that between room and supply air). As the pollutant concentration is lower in the displacement zone than at the exhaust, higher ventilation efficiency (greater than one) can be achieved. This is extremely important if the activity inside the room will generate substantial amount of pollutants as in some manufacturing plant. In fact, more than half of the factories in the Scandinavian region have now employed displacement ventilation system, and the results from field measurements [9] had demonstrated the improvement of indoor air quality. Sandberg and Blomqvist [13] measured the contaminant concentration, temperature and air velocity within the near zone, and temperature and contaminant gradient inside typical office room using several kinds of diffusers. They commented that applying the same supply air flow rate as that used in mixing ventilation would not much improve the air quality within the breathing zone. Cheong et al. [14–16] studied the perceived air quality, sick building syndrome, local thermal sensation, local thermal comfort and thermal effect of temperature gradient on tropically acclimatized occupants inside test chamber served by displacement ventilation system. They commented that
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thermal gradient had insignificant impact on perceived air quality and sick building syndrome and a temperature gradient of up to 5 8C/m could be tolerated. Local thermal discomfort reduced with increase in room temperature, and the lower body segment was more susceptible to thermal discomfort. The percentage dissatisfied was not significantly affected by temperature gradient, but varied widely at different room temperature and overall thermal sensations. The air movement inside the room also affects the performance of displacement ventilation system. Melikov et al. [17] studied the air flow characteristics in the occupied zone. Flow visualization indicated the convective flow generated above the heat sources and the development of the stratified layer. Linden et al. [18] studied the natural ventilation inside a room by using the ‘‘emptying filling boxes method’’ to investigate the plume spreading in a density stratified flowing fluid (brine). They compared the flow pattern of mixing ventilation and displacement ventilation under various loading conditions. They also proposed a formula to estimate the height of the displacement zone. The variation of temperature and air velocity within the near zone around the supply terminal is closely related to the problem of cold draught. Skistad [1] gave a brief account of the flow properties inside the near zone. He commented on the performance of different types of supply terminals in term of the size of the cold draught region. He also derived equations for the estimation of the velocity profile inside the near zone. Skistad [1] argued that the supply terminals would only influence the temperature gradient below the height of the terminals and played no part on the air flow above the terminals. Melikov [19] gave a brief account of the problem of thermal discomfort due to draft and vertical temperature difference for displacement ventilation system. He compared the temperature and air velocity variation with that of the international standard for thermal comfort [3,4] which specified that the temperature difference between 1.1 and 0.1 m above floor should not exceed 3 8C. The studies of the displacement zone are mostly concentrated on the behavior of the buoyant plumes generated by various types of heat sources inside the space. Skaret [20] gave the formulae for the convective flow from various types of heat sources. However, they were only applicable in an isothermal quiescent environment. Investigation of buoyant plumes in stratified but still quiescent environment had also been made. Morton et al. [21] analyzed the plume rise from a point source in a density stratified fluid and developed equations which were solved numerically. The simulated results were compared with experimental data. Crawford and Leonard [22] observed the buoyant plumes in calm stably stratified air and compared the results with those of Priestley and Ball [23] and Morton et al. [21]. Jin [24] studied the plume rise in stratified environment, and modified the constant in the plume rise formula developed by Morton et al. [21] based on experimental data. Chen [25] developed an analytical solution for the maximum plume rise height based on theory of Priestley and Ball [23]. Madni and Pletcher [26] modeled the behavior of buoyant jets discharged
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into uniform and stratified quiescent ambient by mean of finite difference method with a simple turbulence model. They found that the influence of buoyancy on the turbulent transport was of secondary importance for vertically discharged buoyant jets. Ogino et al. [27] derived equations for the variation of centerline velocity and temperature, zero momentum and zero buoyancy heights of buoyant jets discharged into a linearly stratified ambient environment. He found that zero momentum and zero buoyancy heights were correlated with the product of discharge Froude number and the vertical temperature gradient of the ambient fluid. In designing displacement ventilation systems, thermal comfort and indoor air quality are the main factors of concerns. However, in certain cases, it is not possible to satisfy requirements in both of these factors. Skistad [1] commented that if the pollutants or contaminants were not delivered from the warmest source, the pollutants or contaminants concentration might be higher at some location than at the exhaust. This also applied to passive contaminants, i.e. non-buoyant gases. Moreover, Skistad [1] pointed out that sometimes mixing might be necessary in order to reduce the draught zone. This was achieved by having a perforated supply terminal surface. The smaller the proportion of free area of the perforated surface, the greater the mixing would be. However, this would deteriorate the indoor air quality, as the pollutant concentration within the occupied zone would be evened out when mixing occurred. 1.2. Design method of displacement ventilation system As the performance of displacement ventilation is related to the thermal plumes developed from various kinds of heat sources, an exact analytical formulation is impossible. Danielsson [28] proposed a design method based on extensive experimental data. He related the temperature difference between the supply air and the occupied zone (mid height of displacement zone) to the load/air flow ratio (Qac/Vs) in a graph at various room height range (see Fig. 2). From the graph, the temperature gradient could be read. Skistad [1] postulated that the temperature difference between supply and exhaust was double that of the temperature difference between the supply and that at 0.1 m above ground far enough downstream of the supply terminals (ET 1 ¼ 0:5). He supposed that the temperature would increase steadily from the floor up to the ceiling level with a nearly constant temperature gradient (displacement zone height was the same as the room height). Cheong [29] empirically related T1 to Ts, T1.1, sensible heat load per unit area and the room height. The exhaust air temperature was then calculated based on given supply flow rate and assuming that the room temperature increased linearly from floor to ceiling. Mundt [7] devised an equation to calculate the dimensionless temperature difference at floor level under different supply flow rate. She also presumed that the temperature increased steadily from the floor to ceiling. However, Lee [30] found that across the displacement zone height, the temperature gradient changed substantially, and the displacement zone height might not be the same as the room height.
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conservation equations for specific volume, momentum, and buoyancy flux was quoted from Jin [24] as d 2 ðR UÞ ¼ 2aRU dZ
(1)
d 2 2 r r ðR U Þ ¼ R2 g a dZ r1
(2)
d ra r g dra 2 R Ug ¼ R2 U dZ r1 r1 dZ
(3)
By setting A = R2U, B = RU, F = R2Ug(ra r)/r1 and applying ideal gas law as done by Jin [24], Eqs. (1)–(3) were rewritten as
Fig. 2. Performance graph for displacement ventilation system by Danielsson [28].
dA ¼ 2aB dZ
(4)
dB4 ¼ 2FA dZ
(5)
dF ¼ AS dZ
(6)
where S¼
Auban et al. [31] studied the convection of thermal plume in a confined stratified environment by hydraulic solutal simulation. They related the stratified height to the supply flow rate, buoyancy flux at source and source diameter but without the stratification level. Zhao and Li [32] proposed formulae for the displacement zone height based on a plate heat source. Xing and Awbi [33] measured the displacement zone height in a room and compared the results with models proposed by Mundt [34], showing good agreement. Bouzinaoui et al. [35] extended the work of Auban et al. [31] by measuring the displacement zone height in a room and compared results with equations proposed by the latter. However, they did not propose any formula for the temperature gradient ratio. In this study, the total air conditioning load is simplified by a single point source located at floor level. The temperature gradient ratio and displacement zone height was calculated using the plume rise equation and empirical correlation determined from the test results of Lee [30]. The new model provides a rough picture of the temperature variation inside the room and simple tool for designing displacement ventilation systems. 2. Theory 2.1. Thermal plume from point source in stratified environment Fig. 3 illustrated the definition of various parameters. As stated by Jin [24], the velocity and temperature deficit of a thermal plume from a point heat source could be approximated by a ‘‘top hat’’ profile suggested by Morton et al. [21]. The
g T grad T 1 þ 273:13
(7)
as defined by Jin [24]. The volume flow rate of the plume air became pA. Eqs. (4)–(6) were solved numerically using the fully implicit finite difference method. The boundary conditions at Z = 0 were A = 0, B = 0 and F = F 0, where F0 ¼
gQ0 pcp0 r0 ðT 0 þ 273:13Þ
(8)
according to Jin [24]. 2.2. Displacement ventilation system Defining T1 as the temperature of ambient air at 0.1 m above floor (to cohere with measured data from Lee [30]), then T grad ¼
Te T1 Z oc 0:1
(9)
Also, Qac ¼ rs V s cps ðT e T s Þ
(10)
where Qac was the loading transferred to the air conditioning system. Defining the temperature gradient ratio as ET 1 ¼
Te T1 Te Ts
(11)
The heat delivered from the source was only partially transferred by convection to the room (hence the air conditioning system), and Q0 ¼ gQac
(12)
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Fig. 3. (a) Temperature variation in displacement ventilation system and (b) thermal plume generated by a point heat source.
where 0 < g < 1. g was determined from experimental data of Lee [30]. From Eqs. (7) and (9), T1 ¼
T e þ 273:13 273:13 1 þ ððZ oc 0:1ÞS=gÞ
(13)
The room temperature was usually defined as the temperature at certain preset height (say 1.1 m above floor), and T 1:1 ¼ T 1 þ T grad
(14)
2.3. Solution methodology In designing a displacement ventilation system, Vs, Qac, Ts and Te were defined. The remaining variables were T1, Zoc and Tgrad. At displacement zone height, the plume buoyancy flux vanished and the convective plume flow balanced the supply air flow. Hence, F ¼ 0 and
pA ¼ V s
(15)
With known g, F 0 was determined. The variation of buoyancy flux and convective flow above the source plume were then calculated from Eqs. (4)–(6) using fully implicit finite difference method if Tgrad was set. By adjusting Tgrad iteratively, the conditions stated by Eq. (15) were met at a particular height. Hence, Tgrad and Zoc were solved. With Eqs. (13) and (14), T1 and T1.1 were found and ET 1 calculated using Eq. (11). 3. Analysis The coupled equations were solved using Engineering Equation Solver (EES). In solving Eqs. (4)–(6), a height step of 0.01 m was used for the finite difference scheme. The test results from Lee [30] were used to justify the model. To investigate the variation of g from the test results, Vs, Ts and Qac were used as input parameters and g adjusted so that the calculated ET 1 matched with the test data. Qac was calculated from measured temperatures and flow rate, while ET 1 was calculated from the measured temperatures. As all the air conditioning loads were represented by a single point source, T0 was considered as the average source temperature, and a value of 50 8C was chosen.
An empirical correlation for g was exploited. With the correlation for g determined, the complete model was used to simulate data and compared with test results from Lee [30]. For the test results, Tgrad was derived from measured temperatures using Eq. (14) and Zoc from the method stated in Lee [30] (adopting the definition of Tgrad from Eq. (14) and extending the temperature profile upward to a height where the room temperature equaled the exhaust temperature). Finally, the developed model was used to investigate the performance of displacement system applied to sub-tropical regions. A comparison was also made with other design models/methods. 4. Results and discussion 4.1. Evaluation of g The key test results from Lee [30] and required g to match ET 1 were summarized in Table 1. Ts affected the amount of heat dissipated from the heat source to the room but generally it would not influence the way the load was transferred. Hence, its effect on g was insignificant. Upon inspection of Table 1, a new parameter (Qac/Vs) was selected to investigate its effect on g, where 0 < g < 1 when 1 > (Qac/Vs) > 0. This parameter was also used by Danielsson [28] in his displacement ventilation system design method. One possible form of the relation is Table 1 Summarized key test data from Lee [30] and required g Vs
Ts
T1
Te
Qac
ET 1
Zoc
Tgrad
Required g
0.04129 0.04129 0.03805 0.03805 0.04129 0.04129 0.04129 0.04129 0.04129 0.04129 0.05425 0.05425 0.05425 0.05425
20.27 17.10 19.73 17.33 20.59 16.94 20.00 17.17 19.34 17.14 23.22 21.86 20.96 19.09
22.31 21.33 22.11 21.43 22.31 20.96 22.41 21.10 21.91 21.00 23.48 23.38 22.96 22.06
25.41 26.17 25.24 26.35 25.41 25.94 25.7 25.64 25.47 25.41 25.18 25.64 25.70 25.64
256.03 452.00 252.55 414.09 240.19 447.83 283.89 421.67 305.03 412.04 128.26 247.34 310.4 429.03
0.604 0.533 0.569 0.546 0.644 0.554 0.578 0.537 0.581 0.533 0.867 0.599 0.577 0.547
1.92 1.44 1.89 1.43 1.86 1.44 1.90 1.52 1.93 1.54 2.08 1.85 1.7 1.53
1.71 3.62 1.75 3.70 1.76 3.72 1.83 3.19 1.94 3.07 0.86 1.3 1.71 2.5
0.2490 0.2223 0.2354 0.2291 0.2669 0.2319 0.2391 0.2205 0.2403 0.2200 0.3515 0.2447 0.2363 0.2241
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C.K. Lee, H.N. Lam / Energy and Buildings 39 (2007) 427–436 Table 2 Errors of simulated data based on present model
Fig. 4. Comparison between required g and computed g.
g = 1/a(Qac/Vs), where a was positive and determined from Table 1. This relation required that the line for ln(g) versus (Qac/ Vs) should pass the origin, which was not found using the data in Table 1. Hence, this choice was not appropriate. Another form g = 1/[1 + a(Qac/Vs)b] was adopted. This form was similar to the relation between the dimensionless temperature difference at floor and supply flow rate (with b equal 1) as proposed by Mundt [7]. a and b were found by applying linear regression to ln(1/g 1) versus ln(Qac/Vs), where a = 0.1429 and b = 0.348. Hence, g¼
1 1 þ 0:1429ðQac =V s Þ0:348
(16)
Comparison was made between the required g from test data and the computed g from Eq. (16) as shown in Fig. 4. The root-meansquare value for the errors is 5.35% and Eq. (16) was justified. 4.2. Model simulation and comparison with test data With Eq. (16) established, the complete model was used to simulate results using the data in Table 1 as inputs and compared with experimental values from Lee [30], with the errors for the simulated data shown in Table 2. The errors for ET 1 were less than 6% except for results from three tests which corresponded to the three points where the required g and computed g deviated most as shown in Fig. 4 (leftmost three points). The errors for the temperature difference were below 8% except for the last four sets of data. The reason was similar to above. Errors for Zoc and Tgrad were remarkably higher (up to 28.1%). This could be explained by the fact that Zoc and Tgrad were derived from the experimental data. Avery clear change of temperature gradient at particular height was not easily found from the measured vertical temperature profiles (see Appendix A), and the adopted derivation of Zoc and Tgrad might not be the best one in every case. Nevertheless, the range of errors was still acceptable. 4.3. System simulation using the developed model The performance of displacement ventilation was studied using the established model with emphasis on application to sub-tropical region like Hong Kong. Generally, the design temperature difference between exhaust and supply temperature was about 10 8C, corresponding to a value of 12,000 for (Qac/Vs). The minimum supply temperature for displacement
T1 Ts
T1.1 Ts
ET 1
Zoc
Tgrad
0.00 2.13 5.46 5.85 7.56 6.47 2.90 1.53 1.17 0.78 69.23 14.47 10.00 6.06
3.20 6.75 3.16 5.26 3.16 6.21 2.84 4.49 4.66 4.76 0.89 9.25 10.24 11.52
0.50 1.88 4.39 4.95 3.73 5.6 2.42 1.68 0.34 0.75 9.80 10.52 8.32 5.30
5.21 16.67 7.41 14.69 1.08 16.67 5.26 11.18 7.77 10.39 13.46 15.14 21.18 28.10
7.02 17.13 14.29 17.84 1.14 20.16 9.29 11.91 9.28 9.77 19.77 3.85 10.53 18.40
Percentage error (100 (simulated data-test result)/test result).
ventilation system was taken as 18 8C (in consideration of the risk of draught). For a room height of 2.4 m (typical office ceiling height in Hong Kong), the simulated results were shown in Table 3. At small Qac (and consequently small Vs), the temperature gradient and reference room temperature were high. When Qac was increased, both Tgrad and T1.1 decreased and Zoc increased. This could be explained by using the plume rise equations since the induced plume air flow increased at a rate lower than that of the source heat flux. Auban et al. [31] stated that the induced plume air flow was proportional to (specific source buoyancy flux)1/3. As specific source buoyancy flux is proportional to the source heat flux according to Eq. (8), the induced plume air flow would be proportional to (source heat flux)1/3. Hence, to maintain a fixed (Qac/Vs), Zoc should be increased. Jin [24], Chen [25] and Crawford and Leonard [22] also reported that the maximum plume rise in stably stratified ambient was proportional to (source heat flux)1/4. When Qac continued to increase until the displacement zone height reached the ceiling, T1.1 would decrease a little bit further and reached a minimum value. Beyond that, T1.1 would increase. From Table 3, the minimum T1.1 was 24.63 8C. If the design room temperature was 25.5 8C, there would exist a range of Qac where displacement ventilation system alone could be used even in sub-tropical region (different from previous study Table 3 Simulated results based on (Qac/Vs) = 12,000 Qac
Vs
ET 1
T1
T1.1
Tgrad
Zoc
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000
0.04167 0.08333 0.125 0.1667 0.2083 0.25 0.2917 0.3333 0.375 0.4167 0.4583 0.5
0.5031 0.5208 0.5383 0.5923 0.5531 0.5227 0.4981 0.4776 0.4601 0.445 0.4317 0.4199
22.95 22.77 22.6 22.06 22.45 22.76 23 23.2 23.38 23.53 23.66 23.78
26.14 25.24 24.93 24.63 24.85 25.02 25.16 25.27 25.37 25.46 25.53 25.6
3.192 2.471 2.332 2.565 2.396 2.264 2.157 2.069 1.993 1.927 1.87 1.819
1.67 2.2 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4
C.K. Lee, H.N. Lam / Energy and Buildings 39 (2007) 427–436
that displacement ventilation system could not be used alone in sub-tropical region). Besides, the displacement zone height (minimum 2.2 m) would be above the normal breathing level, indicating an improvement in indoor air quality. Of course, if the ceiling height was lower, the simulated reference room temperature might always be higher than the design room temperature. In this case, (Qac/Vs) should decrease, meaning that a higher flow rate should be chosen when compared to a mixing ventilation system, or auxiliary cooling facility (like chilled ceiling) had to be used. Based on Table 3, with a zone capacity of 1000–5000 W, a displacement ventilation system can work alone in a room with 2.4 m ceiling height and 25.5 8C design room temperature taken at 1.1 m above floor. A higher ceiling height would definitely be beneficial, as the feasible zone capacity range for stand alone operation of displacement ventilation system would be larger. 4.4. Comparison with other design models/methods A comparison was made for the simulated ET 1 and (T1 Ts) with those calculated using the design models/ methods from Mundt [7], Danielsson [28] and Cheong [29] based on test conditions of Lee [30]. The percentage errors for the simulated data were shown in Table 4. As compared with Table 2, it could be found that with the exception of results from Test 11 (reason already mentioned in Section 4.2), the percentage errors of the present model (0.46–10.48 for ET 1 and 0–14.47 for (T1 Ts)) were much lower than those from other design models/methods. Even including Test 11, the root-mean-square values of percentage errors was 5.39 for ET 1 and 19.49 for (T1 Ts). The corresponding values for simulated data from design model of Mundt [7] was 26.49 for ET 1 and 39.9 for (T1 Ts), those from design method of Danielsson [28] being 19.12 for ET 1 and 36.48 for (T1 Ts), and those from design model of Cheong [29] being 17.13 for ET 1 and 23.12 for (T1 Ts). This implied that the root-meansquare values of percentage errors in ET 1 and (T1 Ts) for the Table 4 Comparison of errors for simulated ET 1 and (T1 Ts) using other design model/ method based on test conditions of Lee [30] Percentage error for (T1 Ts)
Percentage error for ET 1 Mundt [7]
Danielsson [28]
Cheong [29]
Mundt [7]
Danielsson [28]
Cheong [29]
16.89 32.89 21.12 26.54 9.60 27.87 22.18 31.88 21.64 32.87 12.63 26.61 31.53 38.96
20.50 14.32 16.87 18.42 12.97 15.56 17.23 16.93 15.16 20.84 15.21 24.94 29.90 21.50
16.80 18.44 22.99 17.29 10.71 14.08 20.50 19.09 18.97 20.15 3.15 17.35 16.14 14.94
25.00 37.59 27.73 31.95 16.86 34.83 29.88 37.15 25.68 37.56 84.62 38.82 42.00 46.80
30.88 16.31 21.85 22.20 22.67 19.65 23.24 19.85 20.62 23.83 100.00 36.84 40.00 25.59
25.00 21.04 30.25 20.98 18.60 17.91 27.80 22.39 26.07 23.06 23.08 25.00 21.00 17.51
433
present model were at least 68.5 and 15.7%, respectively, lower than those from other models/methods. 5. Recommendations and conclusions 5.1. Recommendations for further work The higher supply temperature for displacement ventilation system compared to a mixing ventilation system means that the latent load in the room should be low. Hence, if displacement ventilation system is to be used in sub-tropical region like Hong Kong, auxiliary facility will be needed to handle to latent load. One possible solution is to supply air with a desiccant or heat pipe type dehumidifier which can supply cool air at a low relative humidity. The resulting room relative humidity might be kept at a level (lower than the usual design value) such that the comfort room temperature (according to the comfort chart) can be higher, thus reducing the room cooling load. Moreover, the coupling of the dehumidifier with ground heat exchanger provides extra potential for energy saving. Further research will be needed to investigate this possibility. 5.2. Conclusions A model for displacement ventilation system based on plume rise of single point heat source was developed from the test results of Lee [30]. The difference between the simulated data and the test results for temperature gradient ratio (ET 1 ) were less than 6% in most cases. Differences for temperature gradient (Tgrad) and displacement zone height (Zoc) were relatively higher (up to 28.1%). The reason might be that the ways of deriving the parameters from experimental data was not the best in every case. Nevertheless, the prediction of temperature gradient ratio (ET 1 ) and temperature difference (T1 Ts) between the supply air and at 0.1 m above floor level based on present model were in most cases much better than those obtained from design models/methods of some other workers. The root-mean-square values of percentage errors in ET 1 and (T1 Ts) were at least 68.5 and 15.7%, respectively, lower than those from other models/methods. The feasibility of applying displacement ventilation system alone in sub-tropical region depended on the ceiling height, height for reference room temperature and the design room temperature. With a room height of 2.4 m and design room temperature of 25.5 8C defined at 1.1 m above floor level under the normal load to air flow ratio (Qac/Vs) of 12,000 W/ m3/s and minimum supply temperature of 18 8C, there existed a zone capacity range from 1000 to 5000 W that stand alone operation displacement ventilation system was feasible and that the displacement zone height (minimum 2.2 m) was above normal breathing level. A higher ceiling height was beneficial as the feasible zone capacity range would be greater. With lower ceiling heights and/or lower design room temperatures, the load to air flow ratio (Qac/Vs) should be reduced, resulting in a higher flow rate when compared to a mixing ventilation system, or auxiliary cooling facility (like chilled ceiling) had to be used.
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Appendix A See Figs. A.1–A.6.
Fig. A.1. Measured room temperature profiles from Lee [30] (Tests 1 and 2).
Fig. A.2. Measured room temperature profiles from Lee [30] (Tests 3 and 4).
Fig. A.3. Measured room temperature profiles from Lee [30] (Tests 5 and 6).
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Fig. A.4. Measured room temperature profiles from Lee [30] (Tests 7 and 8).
Fig. A.5. Measured room temperature profiles from Lee [30] (Tests 9 and 10).
Fig. A.6. Measured room temperature profiles from Lee [30] (Tests 11–14).
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