Speculation in the feasibility of evaporative cooling

Building and Environment 44 (2009) 826–838

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Speculation in the feasibility of evaporative cooling M.F. El-Refaie*, S. Kaseb Mechanical Power Engineering Department, Cairo University, Cairo, Egypt

a r t i c l e i n f o

a b s t r a c t

Article history: Received 21 March 2008 Received in revised form 12 May 2008 Accepted 27 May 2008

The use of evaporative air cooling, for residential air conditioning, cannot be taken for granted in all situations. It depends on the climatic conditions and the specific nature of application. This work establishes a general foundation for judging the feasibility of evaporative cooling with different evaporative-system configurations, under different climatic conditions and for different applications. Two feasibility criteria were stipulated; the rate of air supply to space and the indoor relative humidity. Systematic procedures are presented for evaluating the required air-flow rate and predicting the achievable indoor condition. Explicit mathematical expressions are derived to define the limitations on outdoor conditions for any allowable specific air flow. The impacts of various pertinent factors are investigated. These include the required indoor temperature, the quality of space load represented by its SHF and the performance index of the system. Computer programs were devised to automate, hence facilitate, the repetitive computations and to evade the graphical work on the psychrometric chart. Samples of program results are graphically displayed. Ó 2008 Elsevier Ltd. All rights reserved.

Keywords: Evaporative cooling Air conditioning Feasibility Air-flow rate Indoor relative humidity

1. Introduction Due to its simplicity, evaporative cooling of air was the oldest method adopted by man to realize, or improve, human comfort through reducing the temperature [1–3]. However, it has been relatively renounced, for a long period since the commercial onset of the air-conditioning trade, in favor of mechanically-refrigerated systems. Its use had been generally limited to some nonresidential applications or small residential applications in hot arid regions only. Nowadays, the interest in evaporative cooling has revived because of the pending energy shortage, the increasing energy cost and the recently recognized environmental issues. In these respects, evaporative cooling is advantageous because of its relatively low specific energy consumption and the absence of environmentally aggressive refrigerants. Moreover, evaporative-cooling systems will certainly have lower running charges and may also have less initial cost than a comparable mechanical system [4]. The results of the renewed worldwide interest in evaporative cooling manifested in a considerable number of systems designed and installed at different locations [5,6]. Energy savings as high as 79% could be realized at some places [6]; and satisfactory indoor conditions could be achieved in different buildings and under different climatic conditions [7].

* Corresponding author. Tel.: þ20 237483506; fax: þ20 235714185. E-mail address: [email protected] (M.F. El-Refaie). 0360-1323/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2008.05.020

However, the evaporative-cooling systems are, by their very nature, more dependent on climatic conditions than mechanically cooled systems. Accordingly, a success achieved at one particular location cannot be offhand guaranteed or readily copied elsewhere. The feasibility of evaporative cooling should be investigated at each location individually. The main objective of this work is to establish a systematic method to explore the possibility of using evaporative cooling in any particular situation; and to determine the required air-flow rate and the condition that can be realized inside the conditioned space. 2. Building blocks Evaporative-cooling systems can be built in a variety of configurations. All possible configurations are, in fact, constructed using two basic building blocks. These two blocks are shown in Fig. 1. 2.1. Direct unit In this unit, shown symbolically in Fig. 1a, the air supplied to the space, known as ‘‘Primary Air’’, is cooled through direct evaporation of water in the air stream. Water is continuously recirculated and replenished to make up for the water removed by the air. As such, the process approximates the adiabatic-saturation process and the path, shown in Fig. 1b, lies on a constant wet-bulb temperature which is, approximately, a constant-enthalpy line. In practice, different types of hardware may be used for the direct evaporative cooling of air [8].

M.F. El-Refaie, S. Kaseb / Building and Environment 44 (2009) 826–838

in

out

out

in

twb tout

C

P Primary (outdoor)

Space R

S1

Exhaust

S

R C

S

Exhaust

S

out

R S1

E

E S1

Secondary air

HE

Space R

C

Primary (outdoor)

Swb

CR is the space condition line

(a) Single-stage direct system.

Out

E

R c

R room condition C conditioned (supply) air O outdoor air

tin

P

P

R

O (P)

(a) Symbolic flow diagram (b) Psychrometric process Direct evaporative-cooling unit. Primary air

827

S1

O (P&S)

Secondary (outdoor)

HE

E

P (b) Single-stage indirect system.

Primary Secondary

(c) Symbolic flow diagram (d) Psychrometric processes Indirect evaporative-cooling unit.

C

P Primary (outdoor)

S1

The theoretical minimum air-delivery temperature is the wetbulb temperature of incoming air; if air is completely brought to full saturation. But, in an actual unit, such perfect cooling cannot be achieved. The performance of the direct unit will be expressed in terms of a ‘‘Performance Factor PFD’’ defined as the ratio of the actual temperature drop to the theoretical maximum drop. Thus,

Secondary (return)

(c) Single-stage indirect regenerative system. Fig. 3. Single-stage systems.

The theoretical minimum temperature, to be sought in the indirect unit, is the wet-bulb temperature of the incoming secondary air ts,wb. Accordingly, the performance factor of the indirect unit PFI will be defined as

2.2. Indirect unit

PFI ¼ tp  tout

This unit is symbolized in Fig. 1c. Primary air is indirectly and sensibly cooled, without any addition of moisture, in a heat exchanger by another stream of air, known as the ‘‘Secondary Air’’, which has been evaporatively cooled in a direct unit. The psychrometric plot will generally look like that displayed in Fig. 1d. Several types of devices can be used to fulfill the heat-exchange function in an indirect unit [9,10].




P1

P Primary (outdoor) E

C Space R

(2)

R E

R

C

Secondary (outdoor)

O (P&S)

P1

(a) Two-stage (indirect/direct) system

Exhaust Makeup water

P1

P Primary (outdoor)

S out

HE Primary air ts,wb

tw,c

AP

Fig. 2. Indirect unit using evaporative cooling of water.

C Space R

R S1

S1

E

Out

P




S1

HE

tw,c

tp  ts;wb

S S1

Secondary air

R&S O (P)

C

(1)

where D is the wet-bulb depression of incoming air.

S

E

S

HE

PFD ¼ ðtin  tout Þ=ðtin  twb Þ ¼ ðtin  tout Þ=D

R S1

E

Fig. 1. Building blocks of evaporative systems.

Space R

P HE

S Secondary (return)

E R&S

C P1

(b) Two-stage (indirect/direct) regenerative system Fig. 4. Two-stage systems.

O (P)

828

M.F. El-Refaie, S. Kaseb / Building and Environment 44 (2009) 826–838 Table 1 Performance factors of multi-stage systems

P1

P Primary (outdoor) S Secondary (outdoor)

P2

C Space R

R Two stage (indirect/direct) P and S are the same

P1 PF ¼ tp  tc

S1




ðD1 þ D2 Þ

c

P&S

S2 HE

E2 HE Exhaust

E1 Exhaust

S1

(6)

where tp1 ¼ tp  PFI D1

(7)

P1 D2

E2

PF ¼ tp  tc




ðD þ D1 þ D2 Þ

c

R P2

P1

D1

Two stage (indirect/direct) P and S are different

E1

S2 C

PFI D1 þ PFD DP1 PF ¼ D1 þ D2

O (P&S)

PF ¼

PFI ðD þ D1 Þ þ PFD DP1 D þ D1 þ D2

P P1

(8)

D2 Fig. 5. Three-stage (indirect/indirect/direct) system.

¼ 3½ðDs PFD þ DÞ=ðDs þ DÞ

where tp1 ¼ tp  PFI ðD þ D1 Þ

(3)

where

If both primary and secondary streams are taken from the same source, the two state points (P) and (S), in Fig. 1d, will coincide and Eq. (3) will reduce to

PFI ¼ PFD 3

(4)

Another version of the indirect unit may also be used. This one utilizes the evaporative cooling of water rather than air; as illustrated in Fig. 2 [4,6,11]. The primary air is sensibly cooled by water which has been evaporatively cooled by secondary air. The evaporative device may be perceived, in this case, as a water-cooling tower. Accordingly, the theoretical minimum temperature of outgoing cooled water tw,c is the wet-bulb temperature of the incoming secondary air; and, hence, Eq. (2) can still be used. However, and in practice, the temperature of cooled water will be slightly higher than the wet-bulb temperature. The difference may be regarded as the ‘‘Approach’’ of the tower. Eq. (2) may be manipulated to the form

PFI ¼ 3½1  AP=ðDs þ DÞ

Δ

D1

(9)

Three stage (indirect/indirect/direct) P and S are the same PF ¼ tp  tc

PFD is the performance factor of the direct secondary-air-cooling unit ¼ (ts  ts1)/(ts  ts,wb); and ts1 is the temperature of cooled secondary air. 3 is the effectiveness of heat exchanger ¼ (tp  tout)/(tp  ts1); based on the practically logical assumption that the flow rate of secondary air is higher than that of the primary air. Ds is the wet-bulb depression of the incoming secondary air ¼ ts  ts,wb D is the temperature difference (tp  ts).

S

PF ¼




ðD1 þ D2 þ D3 Þ

PFI D1 þ PFI DP1 þ PFD DP2 D1 þ D2 þ D3

c (10)

P2 D3 D2

where tp1 ¼ tp  PFI D1

(11)

tp2 ¼ tp1  PFI DP1

(12)

P&S P1 D1

Three stage (indirect/indirect/direct) P and S are different PF ¼ tp  tc

PF¼




ðD þ D1 þ D2 þ D3 Þ

PFI ðD þD1 ÞþPFI DP1 þPFD DP2 D þD1 þD2 þD3

S

c (13)

P2 D3 D2

where tp1 ¼ tp  PFI ðD þ D1 Þ

(14)

tp2 ¼ tp1  PFI Dp1

(15)

P

P1 D1

Δ

P incoming primary air, P1 primary air after being cooled in first stage, P2 primary air after being cooled in second stage, C conditioned air delivered by the system, S incoming secondary air, Dp1 and Dp2 welt-bulb depressions of states P1 and P2, Performance factors of direct and indirect single stage, PFD and PFI, are given by Eqs. (1) and (3) or (4). In three-stage systems, PFI may not be the same for first and second stages.

performance factor fall usually in the range 80–90% for direct units and 55–65% for indirect units [1,4,12].

(5)

where the approach AP ¼ tw,c  ts,wb. The cooled-water temperature tw,c should replace ts1 in the expression, given above, for the heat-exchanger effectiveness 3. 2.3. Practical performance indices The performance factor of an evaporative-cooling unit depends on how sophisticated the design is. Current practical values of the

3. Survey of system configurations Different configurations of evaporative-cooling systems are briefly surveyed [3,4,12]. The common practice with evaporative systems is to use total outdoor air. Accordingly, the less-common systems with air recirculation are not included in the survey. Also, the systems employing indirect units with evaporative cooling of water (as mentioned hereinbefore) are not addressed separately; they can be readily understood from the displayed configurations.

M.F. El-Refaie, S. Kaseb / Building and Environment 44 (2009) 826–838

tc,db

829

tc,db Slope = (1-PFD)

Slope = PFD

PFD.to,wb (1-PFD).to,db to,db at W=0 to,db

0 to,wb

(a) Fixed outdoor wet-bulb temperature

to,db

0 to,wb at W=0

to,wb

(b) Fixed outdoor dry-bulb temperature

Variation of supply temperature with the outdoor temperatures

to,wb,3

tc,db

PFD,2

to,wb,2 to,wb,1

PFD,1

to,wb,3 to,wb,2

to,wb,1

PFD,1

PFD,2

to,wb,3

to,wb,2

to,wb,1

to,db (c) Variation of the supply temperature with to,db, to,wb and PFD

Fig. 6. Factors affecting the supply temperature.

Figs. 3–5 illustrate various evaporative-cooling system configurations. Each system is shown coupled to the served space. In all figures, the space is assumed to have positive sensible and latent load components; which is typical of most residential spaces in summer. However, the figures can be easily modified for other cases. In fact, the air-conditioned ‘‘space’’, as shown in Figs. 3–5, may not necessarily be a physically-existing building space. Evaporative-cooling systems are sometimes used for localized thermal relief or spot cooling rather than area cooling. The single-stage direct system or the simple system, shown in Fig. 3a, is the most basic or elementary one. It is nothing but a direct unit similar to that presented hereinbefore; in Fig. 1. The

1/VS

single-stage indirect system, shown in Fig. 3b, employs an indirect unit similar to that explained in Fig. 1. The only-sensible cooling of primary air can be useful in cases where low indoor relative humidity is required. This system presents a good solution when the indoor-to-outdoor enthalpic difference (hR  ho) is low or even negative. In Fig. 3b, the secondary air is taken from outdoors. The system displayed in Fig. 3c is basically the same as that of Fig. 3b. But, it makes use of the, generally expected, low wet-bulb temperature of the air exhausted from the space. Air returned from the space is used as the secondary air in the indirect unit. This makes way for a wider sensible cooling of the primary air. Systems

1/VS Slope = -G PFD

Slope = -G(1-PFD) G[tR–(1-PFD)to,db]

G(tR–PFD to,wb)

0

to,db

(a) Fixed outdoor wet-bulb temperature

0

to,wb

(b) Fixed outdoor dry-bulb temperature

Fig. 7. Dependence of the specific flow rate VS on the outdoor condition.

830

M.F. El-Refaie, S. Kaseb / Building and Environment 44 (2009) 826–838

td,max,th

tw,max,th

Slope = -PFD / (1-PFD) Slope = -(1-PFD) / PFD tR / PFD

tR / (1-PFD)

0 to,db 0 to,wb Theoretical maximum wet-bulb temperature Theoretical maximum dry-bulb temperature (a) Theoretical limits on outdoor temperatures

tw,max,V

td,max,V

Slope = -PFD / (1-PFD) Slope = -(1-PFD) / PFD [tR-(vstand./c). (SHF/ VS,max)] / PFD

[tR-(vstand./c). (SHF/ VS,max)] / (1-PFD)

0 to,db 0 to,wb Maximum limit of wet-bulb temperature Maximum limit of dry-bulb temperature (b) Limits on outdoor temperatures ; imposed by restricting the flow rate Fig. 8. Limitations on outdoor temperatures.

a 0.9

0.9

0.8

0.8

0.7

22

0.6 0.5 0.4 0.3

20 18

0.2

25

30

35

40

0.6 0.5 0.4

22

0.3

20

0.1

14

0

0.7

0.2

16

0.1

to,wb = 24°C

1

Vs, m3/kW.s

Vs, m3/kW.s

b

to,wb = 24°C

1

14

0 45

25

50

30

to,db°C

c to,wb = 24°C

0.8 0.7

22

0.4 0.3 0.2 0.1 14

0 25

30

35

40

20 18 16

45

22

20

0.9

Vs, m3/kW.s

Vs, m3/kW.s

to,wb = 24°C

0.7 0.5

50

1

0.8 0.6

45

PFD = 0.9, tR = 27°C and SHF = 0.9

d 0.9

40

to,db°C

PFD= 0.9, tR = 26°C and SHF = 0.9

1

35

18

16

0.6 0.5 0.4

18

0.3 0.2

16 14

0.1 0 50

to,db°C PFD= 0.9, tR = 26°C and SHF = 0.8

25

30

35

40

45

50

to,db°C PFD = 0.8, tR = 26°C and SHF = 0.9

Fig. 9. Specific flow rate for a single-stage direct system.

M.F. El-Refaie, S. Kaseb / Building and Environment 44 (2009) 826–838

a

b

to,wb = 24°C 1

0.7 18

0.6 0.5

16

0.4 0.3

22

0.8

20

Vs, m3/kW.s

Vs, m3/kW.s

0.9

22

0.8

20

0.7

18

0.6

16

0.5 0.4

14

0.3

14

0.2

0.2

0.1

0.1

0

0 25

30

35

40

45

50

25

30

35

40

45

50

to,db°C

to,db°C

PFI =0.6, tR = 26°C and SHF = 0.9

PFI = 0.6, tR = 27°C and SHF = 0.9

d

to,wb = 24°C

1

to,wb = 24°C

0.9

22

0.8 0.7 0.6

16

0.4 0.3

20

0.7

18

0.5

22

0.8

20

Vs, m3/kW.s

1 0.9

Vs, m3/kW.s

to,wb = 24°C 1

0.9

c

831

18

0.6

16

0.5

14

0.4 0.3

14

0.2

0.2

0.1

0.1

0

0 25

30

35

40

45

50

25

30

35

40

45

50

to,db°C

to,db°C

PFI =0.6, tR = 26°C and SHF = 0.8

PFI =0.5, tR = 26°C and SHF = 0.9

Fig. 10. Specific flow rate for a single-stage indirect system.

recycling the primary air to be the secondary stream are known as ‘‘Regenerative’’ systems. Fig. 4 illustrates two-stage systems. These are realized by adding a direct unit in the primary-air stream of Fig. 3b and c. This adds further cooling of the primary air; but, of course, this extra cooling will be associated with increased humidity. The three-stage system, shown in Fig. 5, comprises two indirect units followed by a direct one. A fraction of the primary air cooled in the first indirect unit is used as the secondary stream for the second indirect unit. The remaining primary air is finally cooled in the direct unit right before being admitted to the space. 3.1. Performance factors of different configurations The performance factors of single-stage systems were implicitly presented in the previous section; on building blocks of evaporative systems. For the systems shown in Fig. 3a, b and c, the performance factors are given by Eqs. (1), (4) and (3), respectively. When using Eq. (3) for the regenerative system shown in Fig. 3c, the return-air state R should replace the secondary-air state S. The theoretical minimum temperature in a multi-stage system is the wet-bulb temperature of the last stage; provided that all components will show ideal performance. Accordingly, and if the primary and secondary air are taken from the same source, the theoretical maximum temperature drop will be equal to the sum of the wet-bulb depressions of the different stages. If the secondary air is to be taken from a different source, such as in a regenerative

system, the sum of depressions should be augmented, or reduced, by the temperature difference D between primary and secondary sources; depending on whether D is positive or negative. Knowing the theoretical maximum temperature drop for any system and based on the definition of the performance factor, it is possible to derive an expression for the performance factor of any multi-stage system in terms of the factors of its components. The equations expressing the performance factors of various two and three-stage arrangements are summarized, together with typical psychrometric plots, in Table 1. The performance factors of the systems shown in Figs. 4 and 5 can be readily obtained using the appropriate equations from Table 1. For regenerative systems, the return-air state R should be used in place of the secondary-air state S. An important fact can be concluded from Eqs. (6)–(15). No fixed value can be assigned to the performance factor of a multi-stage system; even if the performance factors of the components, PFI and PFD, are constant. The wet-bulb depressions, shown in the equations and in the accompanying diagrams, depend on the states of primary and secondary air. Accordingly, the collective performance factor will vary with the state of air admitted to the primary and/or secondary streams. 4. Assessment of feasibility Unlike mechanically-cooled systems, the employment of evaporative cooling cannot be taken for granted in all situations.

832

a

M.F. El-Refaie, S. Kaseb / Building and Environment 44 (2009) 826–838

a close psychrometric vicinity. Evaporative cooling may not be feasible if wide deviation of the inside condition is unavoidable.

25

5. Analysis

tw,max,V

20

Vs,max=.12 - PF=.9

The analysis presented hereinafter will cover single-stage and non-regenerative two-stage systems. However, the results and conclusions can be expanded to accommodate other configurations.

15 Vs,max=.09 - PF=.9 Vs,max=.12 - PF=.6

10

Vs,max=.09 - PF=.6

5

5.1. Single-stage direct system

0 25

30

35

40

45

5.1.1. Supply temperature For the system illustrated in Fig. 3a and from Eq. (1), it can be shown that the dry-bulb temperature of the conditioned air, supplied to space, tc,db is related to the outdoor dry and wet-bulb temperatures to,db and to,wb, through

50

to,db°C tR = 26°C and SHF = 0.9

b

25

tc;db ¼ ð1  PFD Þto;db þ PFD to;wb ¼ to;db  PFD Do

24 23

tw,max,V

22 21 20

tR = 28°C – SHF = 0.7

19

tR = 28°C – SHF = 0.8 tR = 27°C – SHF = 0.7

18 17

tR = 27°C – SHF = 0.8

16 15 25

30

35

40

45

50

to,db°C Vs,max = 0.09 m3/kW.s and PF = 0.9 Fig. 11. Maximum limit of outdoor wet-bulb temperature.

A ‘‘situation’’ means a combination of prevailing outdoor condition, required indoor condition together with the magnitude and quality of the space-cooling load; where the load quality is represented by the space sensible-heat factor SHF. The state of the air delivered by an evaporative-cooling system, within the frame of its performance capabilities, depends on the outdoor condition. In regenerative systems, it depends also on the indoor condition. In some situations, some or all of the evaporativecooling system configurations may be offhand ruled out; because the delivered air would impose additional load on the space rather than removing the original load. Such situations represent clear cases of impossibility of using evaporative cooling. In other, marginal, situations, the conclusion may not be that obvious. The delivered air may be, in principle, capable of removing load from the space; i.e. the use of evaporative cooling is theoretically possible. But, still, this tentative possibility has to be supported by practicability to achieve complete feasibility. Accordingly, two other points have to be further investigated. In general, when using evaporative cooling, the supply to space enthalpic difference is logically expected to be less than that achieved with mechanical systems (i.e. less air load-carrying capacity). Hence, higher air-flow rates have to be tolerated [5]. However, the flow rate necessary for any situation must be checked to make sure that it does not reach to technically or economically prohibitive levels. The relative positions of the psychrometric states of supply and indoor air (the space condition line) will determine the quality of the load that can be removed. This must be well matched with the intrinsic space SHF in order to realize the stipulated indoor condition or, at least, a readjusted sub-ideal acceptable condition in

(16)

where Do is the wet-bulb depression at the outdoor condition. This reveals that, for a fixed value of the performance factor PFD, the supply temperature increases linearly with either of the outdoor dry-bulb or wet-bulb temperature if the other remains constant. More details are given in Fig. 6; based on Eq. (16). The dotted parts of the straight lines, shown in Fig. 6a and b, have no physical significance; they are shown in figure just to complete the trend. For all states of moist air, we have to,db  to,wb. This condition sets the left-hand limit in Fig. 6a and the right-hand limit in Fig. 6b. Moreover, for fixed outdoor wet-bulb temperature to,wb, the drybulb temperature to,db cannot exceed the maximum value for dry air where the humidity ratio W ¼ 0; and for fixed to,db the wet-bulb temperature to,wb cannot decrease below the minimum value at W ¼ 0. These two conditions define the right-hand limit in Fig. 6a and the left-hand limit in Fig. 6b. As a further explanation, the effects of the three parameters PFD, to,db and to,wb are recapitulated in Fig. 6c. The left and right boundaries, marked in this figure, are imposed by the limits, on to,db, shown in Fig. 6a. 5.1.2. Rate of air flow to space In most of the residential, or comfort, applications, the space is thermostatically controlled; based on the fact that the influence of the dry-bulb temperature on human thermal comfort is more profound than that of the relative humidity [13]. Accordingly, the analysis presented in what follows will be based on a constant inside temperature tR. The mass-flow rate of supply air (m), required to offset the load, can be calculated from

m ¼ QS =c tR  tc;db




Kg dry air=s

(17)

where QS is the space sensible load, kW, and c is the average specific heat of moist air; taken to be 1.02415 kJ/kg dry air K [14]. The righthand side of Eq. (17) can be put in terms of the space total load; in the form

m ¼ SHFQT =c tR  tc;db




kg dry air=s

(18)

where QT is the space total load, kW, and SHF is the space sensibleheat factor. The volumetric flow rate of air (V) is usually expressed in cubic meters of ‘‘Standard Air’’ per second. Thus,

V ¼ mvstand

m3 =s

(19)

where vstand is the specific volume of standard air; taken to be 0.83 m3/kg dry air [15].

M.F. El-Refaie, S. Kaseb / Building and Environment 44 (2009) 826–838

a

b

1

0.8 0.7

0.8

to,wb = 24°C

22

0.7

22

20

0.6

20 18

0.6

18

0.5

16

0.5

øR

øR

0.9

to,wb = 24°C

0.9

14

0.4

0.2

0.2

0.1

0.1

14

0

0 25

30

35

40

45

50

25

30

35

40

45

50

to,db°C

to,db°C

PFD= 0.9, tR = 26°C and SHF = 0.9

PFD= 0.9, tR = 28°C and SHF = 0.9

d

0.9

0.9

to,wb = 24°C

0.8 0.7

0.7

18

0.5

øR

16

14

0.4

22 20 18

0.6

20

0.5

to,wb = 24°C

0.8

22

0.6

øR

16

0.4 0.3

0.3

c

833

14

0.4

0.3

0.3

0.2

0.2

0.1

0.1

16

0

0 25

30

35

40

45

50

25

30

35

40

45

50

to,db°C

to,db°C

PFD= 0.9, tR = 26°C and SHF = 0.7

PFD= 0.8, tR = 26°C and SHF = 0.9

Fig. 12. Indoor relative humidity for a single-stage direct system.

The ‘‘Specific Flow Rate’’ of air (VS) is the volumetric flow rate per unit of space total load. This index is an indicative figure; practically used to size the air moving system for any application. It can be found, from Eqs. (18), (19) and (16), to be

VS ¼ ðvstand =cÞSHF= tR  tc;db ¼






m3 =kWs

G½tR  PFD to;wb  ð1  PFD Þto;db 

1

m3 =kWs

(20)

kJ=m3 K

  tw;max;th ¼ tR  ð1  PFD Þto;db PFD

(23)

(21)

From a reciprocal perspective, the theoretical maximum outdoor dry-bulb temperature td,max,th corresponding to any wet-bulb temperature will be

(22)

td;max;th ¼ tR  PFD to;wb

where

G ¼ c=ðvstand SHFÞ

The specific flow rate tends to infinity when the supply temperature tc,db becomes equal to the room temperature tR. Thus, it can be shown that the theoretical maximum outdoor wet-bulb temperature tw,max,th, for any value of outdoor dry-bulb temperature is given by

Eq. (21) has important implications concerning the dependence of the specific flow rate on the outdoor condition. If a space is to be maintained at a fixed temperature tR and is characterized by a known sensible-heat factor SHF, the equation reveals a straightline relationship between the reciprocal of VS and either of to,db or to,wb if the other is unchanged. This is further illustrated in Fig. 7. 5.1.3. Limitation on outdoor condition It has been shown that the specific flow rate increases, monotonically, with the increase of outdoor dry-bulb and/or wet-bulb temperature. There will be a point at which the required flow rate will jump to an infinitely large value. This defines the theoretical limit for the possibility of using the single-stage direct evaporativecooling system.




ð1  PFD Þ

(24)

The inference from these two equations is pictorially illustrated in Fig. 8a. When either the outdoor dry-bulb or wet-bulb temperature increases, the theoretical ceiling of the other will become lower. For fixed values of the required room temperature tR and the achievable performance factor PFD, any of the two Eqs. (23) or (24), can be used to map a border on the psychrometric chart to mark a domain encompassing all outdoor states for which the system, under consideration, will be theoretically feasible. However, reasonable values of flow rates which can be accepted in actual practice will tighten this border to yield a much narrower feasibility domain of outdoor conditions. For any particular application, there will always be a practical limitation on the maximum allowable air-flow rate. If the maximum acceptable value of the specific flow rate is VS,max, then

834

M.F. El-Refaie, S. Kaseb / Building and Environment 44 (2009) 826–838

a

b

1

0.9

to,wb = 24°C

0.9

0.8

0.8

to,wb = 24°C

0.7

0.7

22

0.6

øR

øR

0.6

20

0.5

0.4

0.4

18

20

0.3

0.3

18

0.2

0.2

16

0.1

0.1 0 25

30

35

14 40

14

16

0 45

50

25

30

35

40

45

50

to,db°C

to,db°C

PFI= 0.6, tR = 26°C and SHF = 0.9

PFI= 0.6, tR = 28°C and SHF = 0.9

d

c

1

1

0.9

0.9

to,wb = 24°C

0.8

to,wb = 24°C

0.8 0.7

0.7

22

0.5

22

0.6

øR

0.6

øR

22

0.5

20

20

0.5 0.4

0.4

18

0.3

0.3

18 16

0.2

16

0.2 0.1

0.1

14

0 25

30

35

40

14

0 45

50

25

30

35

40

45

50

to,db°C

to,db°C

PFI= 0.6, tR = 26°C and SHF = 0.7

PFI= 0.5, tR = 26°C and SHF = 0.9

Fig. 13. Indoor relative humidity for a single-stage indirect system.

the maximum practical limits of the outdoor wet-bulb or dry-bulb temperature will be denoted by tw,max,V or td,max,V; where the subscript (V) signifies a fixed, or pre-specified, flow rate. These can be derived by substituting VS,max in Eq. (21); and the limits will be given by


 tw;max;V ¼ tR ðvstand =cÞ SHF=VS;max ð1PFD Þto;db PFD

(25)

and



td;max;V ¼ tR ðvstand =cÞ SHF=VS;max




 PFD to;wb ð1PFD Þ

These will be detailed hereinafter; in a later section. Special computer programs will be specially developed for the purpose. The state of the treated air, supplied to the space, is completely determined. Its dry-bulb temperature tc,db can be found from Eq. (16); and its wet-bulb temperature is equal to that of the outside air to,wb. Hence, its enthalpy hc can be evaluated. The air-enthalpy change, during load removal from space, is given by

hR  hc ¼ QT =m (26)

The relations expressed by Eqs. (25) and (26) are depicted in Fig. 8b. As the limitation on the air flow is relaxed, i.e. a higher value of VS,max is allowed, the maximum-border limit of the outdoor wetbulb or dry-bulb temperature will slide upward. This will result in widening of the outdoor-condition feasibility zone on the psychrometric chart. 5.1.4. Indoor relative humidity In order to make a complete assessment, it is important to know the room condition that can be achieved in any situation. A procedure for evaluating the indoor relative humidity is briefly explained in what follows. This explanation proceeds as if we are graphically working on the psychrometric chart. But, the use of the chart cannot be integrated in computational automation; which is mandatory for accurate repetitive calculations. Therefore, it will be replaced by the appropriate relevant equations. In fact, some of the required computational steps will be rather lengthy and involved.

kJ=kg dry air

(27)

where hR is the enthalpy at the room condition. Substituting for (m) from Eq. (19) and based on the definition of the specific flow rate, the enthalpy hR will be

hR ¼ hc þ vstand =Vs

kJ=kg dry air

(28)

Now, the room condition (R) is fully defined by the two properties tR and hR. Thus, the indoor relative humidity 4R can be readily found. 5.2. Single-stage indirect system The results of the analysis of the single-stage indirect system, shown in Fig. 3b, are very similar to those presented in the previous section for the single-stage direct system. Only two changes have to be made. These are 1. Following the same steps shown before, it can be proven that Eqs. (16)–(28) as well as Figs. 6–8 will still hold for the indirect

M.F. El-Refaie, S. Kaseb / Building and Environment 44 (2009) 826–838

a

b

0.4

0.4

0.35

0.35 0.3

0.25

Vs, m3/kW.s

Vs, m3/kW.s

0.3

0.2

to,wb = 24°C

0.15 0.1

16

14

0.2 0.15

22 20

0.05

18

16

18

14

0

0 25

30

35

40

45

50

25

30

35

40

45

50

to,db°C

to,db°C

PFD = 0.9, PFI = 0.6, tR = 27 °C and SHF = 0.8

PFD = 0.7, PFI = 0.6, tR = 27 °C and SHF = 0.8

d

0.4

0.4

0.35

0.35

0.3

0.3

to,wb = 24°C

0.25

Vs, m3/kW.s

Vs, m3/kW.s

to,wb = 24°C

0.25

0.1

22 20

0.05

c

835

0.2 22

0.15

14

0.15 0.1

18

0.05

to,wb = 24°C

0.2

22

20

0.1

0.25

20

16

18

0.05

16

14

0

0 25

30

35

40

45

50

25

30

35

40

45

50

to,db°C

to,db°C

PFD = 0.8, PFI = 0.4, tR = 27 °C and SHF = 0.8

PFD = 0.85, PFI = 0.6, tR = 26 °C and SHF = 0.8

Fig. 14. Specific flow rate for a two-stage indirect/direct system.

system. Except that the performance factor PFI should replace PFD wherever it appears in any equation or figure. 2. In this case, the conditioned air supplied to space has the same humidity ratio as that of outdoor air. Thus, the two properties defining state (C) will be the dry-bulb temperature and the humidity ratio. This should be taken into consideration when calculating the enthalpy hc; as a steppingstone for determining the indoor relative humidity 4R. 5.3. Two-stage indirect/direct system The key point in visualizing the performance of a two-stage system is to determine the state (C) of the air supplied to space; see Fig. 4a. Once this is done, the evaluation of the air flow and the determination of the realizable indoor condition can be accomplished following the same procedure explained hereinbefore for single-stage systems. But, in this case, the procedure for the determination of state (C) is not a straightforward one. The dependence of the supply temperature tc,db on the outdoor condition is rather intricate; and not as simple and direct as that indicated by Eq. (16) for single-stage systems. Based on the first part of Table 1, the supply temperature will be given by

tc;db ¼ to;db  PFðDo þ D2 Þ

(29)

Since no reliable information about the practical range of the twostage performance factor PF is readily available, it may be more unerring to put Eq. (29) in the form

tc;db ¼ to;db  PFI Do  PFD DPI

(30)

where PFI and PFD are the individual performance factors of the two stages constituting the two-stage system and Do and DP1 are the wet-bulb depressions of outdoor air and inter-stage air at state P1 shown in Table 1. It should be realized that the depression DP1 is in itself dependent on the outdoor condition together with the factor PFI. Accordingly, it will not be possible to derive an explicit direct expression, similar to that in Eq. (16), relating the temperature tc,db to the outdoor temperatures to,db and to,wb. The supply temperature has to be worked out through a procedure which involves the location of the inter-stage state and the determination of the corresponding wet-bulb depression. It is to be pointed out that even if the performance factor PF of the two-stage system as a whole is known, or could be guessed, the problem will not be any simpler. Because, the depression D2, in Eq. (29), is implicitly dependent on the outdoor condition.

836

M.F. El-Refaie, S. Kaseb / Building and Environment 44 (2009) 826–838

e

f

0.4 0.35

0.35

to,wb = 24°C 0.3

0.25

Vs, m3/kW.s

Vs, m3/kW.s

0.3

0.2 22

0.15

20

0.1

18

0.2 0.15

20 18 16 14

0.05

14

0

0 25

30

35

40

45

50

25

30

35

40

45

50

to,db°C

to,db°C

PFD = 0.7, PFI = 0.5, tR = 27 °C and SHF = 0.8

PFD = 0.7, PFI = 0.4, tR = 27 °C and SHF = 0.8

h

0.4

0.4

to,wb = 24°C

0.35

0.35

0.3

0.3

Vs, m3/kW.s

Vs, m3/kW.s

22

0.25

0.1

16

0.05

g

to,wb = 24°C

0.4

0.25 0.2

22

0.15

20

0.1

to,wb = 24°C

0.25 0.2 0.15

22

0.1

0.05

14

16

18

20

0.05

0

14

18

16

0 25

30

35

40

45

25

50

30

35

40

45

50

to,db°C

to,db°C

PFD = 0.85, PFI = 0.6, tR = 26 °C and SHF = 0.95

PFD = 0.85, PFI = 0.6, tR = 25 °C and SHF = 0.8

Fig. 14. (continued).

The route to be followed to define the supply state (C), to evaluate the required air-flow rate and to determine the achievable indoor condition is outlined in what follows: - The wet-bulb depression Do and the humidity ratio Wo, at the outdoor condition, can be readily found knowing the two outdoor temperatures to,db and to,wb - The inter-stage dry-bulb temperature tP1,db will be calculated from

tP1;db ¼ to;db  PFI Do

(31)

hence, the inter-stage state will be completely located by tP1,db and WP1 ¼ Wo. - For the defined inter-stage state, the wet-bulb temperature tP1,wb can be found; hence, the depression DP1. - The supply dry-bulb temperature will be obtained from

tc;db ¼ tP1;db  PFD DP1

(32)

hence, state (C) will be defined by tc,db and tc,wb ¼ tP1,wb. - The rest of the steps are similar to those shown before in previous sections.

6. Results 6.1. Single-stage systems The specific flow rate, for a single-stage direct system, is calculated from Eq. (21). Some samples of results are shown in Fig. 9. It can be seen from figure, or from Eqs. (21) and (22), that higher flow rates are required for lower room temperatures , lower performance factors or higher space sensible-heat factors. Fig. 10 displays a similar sample of results but for a single-stage indirect system as represented by the relatively low performance factor. As expected, the flow rates shown in Fig. 10 are, in general, considerably higher than those in Fig. 9. The maximum allowable limit of outdoor wet-bulb temperature is shown in Fig. 11 against the outdoor dry-bulb temperature for an arbitrarily-set limit of specific air flow. This figure has been produced using Eq. (25). Eight exemplary samples are displayed; characterized by tR, PF, SHF and VS,max. Part (a) of the figure covers both direct and indirect systems. The two lines for the indirect system (where PF ¼ 0.6) in Fig. 11a terminate at the natural upper limit imposed on to,db when W ¼ 0. This is also the reason for truncating the three lower lines in Fig. 11b. Along with Eq. (25), the figure asserts that higher wet-bulb temperatures can be put up with at higher tR, higher PF, lower SHF and/or higher VS,max.

M.F. El-Refaie, S. Kaseb / Building and Environment 44 (2009) 826–838

a

b

0.9 0.8

837

0.9 0.8

to,wb = 24°C

to,wb = 24°C

0.7

0.7 22

0.6 0.5

0.6

0.4

0.5

22

0.4

20

øR

øR

20 18 16 14

0.3

18

0.3

16 14

0.2

0.2

0.1

0.1

0

0 25

c

30

35

40

45

25

50

30

35

40

45

to,db°C

to,db°C

PFD = 0.9, PFI = 0.6, tR = 27°C and SHF = 0.8

PFD = 0.7, PFI = 0.6, tR = 27°C and SHF = 0.8

d

0.9 0.8

0.9 0.8

to,wb = 24°C

50

to,wb = 24°C

0.7

0.7 0.6

0.6

22 20

0.5

18

0.4

0.4 16

0.3

20

øR

øR

0.5

22

18 16

0.3

14

14

0.2

0.2

0.1

0.1

0

0 25

30

35

40

45

50

to,db°C PFD = 0.7, PFI = 0.5, tR = 27°C and SHF = 0.95

25

30

35

40

45

50

to,db°C PFD = 0.85, PFI = 0.6, tR = 26°C and SHF = 0.8

Fig. 15. Indoor relative humidity for a two-stage indirect/direct system.

The limiting boundaries of outdoor conditions, as given by Eqs. (25) or (26), are in general agreement with the information given in some previous works [16,17]. The temperature limits shown in Fig. 11 fall within the region of outdoor conditions marked to be suitable for residential application of evaporative cooling [16]. Based on the analysis presented hereinbefore, no single expression could be derived for the direct calculation of the indoor relative humidity. It has to be worked out through a stepwise algorithm. The steps are founded on the equations relating the different psychrometric properties [18]. Computer programs were specially coded to execute the computational steps terminating at the evaluation of the indoor relative humidity; for both cases of direct and indirect systems. The details of the computations and programs are too long to be accommodated in the present work. A sample of results is displayed in Figs. 12 and 13. Based on the analysis presented hereinbefore, in Sections 5.1 and 5.2, the achieved relative humidity inside the space will be dependent on five factors: the maintained indoor temperature tR, the space SHF, the performance factor of the system PF (PFD or PFI;

whether it is a direct or indirect one) and the outdoor temperatures to,db and to,wb. The trends of variation of 4R with these parameters could be deduced from Figs. 12 and 13 as well as a comprehensive analysis of extensive data obtained by running the computer programs. The following conclusions could be reached. Lower indoor relative humidity can be attained if the room temperature is maintained at a higher value and/or the space has a higher SHF. Also, the relative humidity can be reduced for lower values of the performance factor PF. This last point should not be regarded as a contradiction; the poor system performance will have an adverse effect on the required air-flow rate which must be increased as can be seen from Eq. (21). The effect of the outdoor climatic condition on the indoor relative humidity is clear from Figs. 12 and 13. The value of 4R increases at higher wet-bulb temperatures to,wb and decreases at higher dry-bulb temperatures to,db. Some of the curves, in Figs. 12 and 13, are seen to be curtailed; these are truncated at the points where the outdoor dry-bulb temperature reaches the theoretical maximum limit given by Eq. (24); or when it exceeds the natural upper limit marked in Fig. 6a (the value at W ¼ 0).

838

M.F. El-Refaie, S. Kaseb / Building and Environment 44 (2009) 826–838

6.2. Two-stage systems The computational work necessary for executing the calculation sequence presented hereinabove, in Section 5.3, was transformed into a computer program. This program culminates in the evaluation of the required specific rate of air flow VS and the determination of the indoor condition for any application described by tR and SHF, for any system capability expressed by PFI and PFD and under any climatic conditions defined by the two temperatures to,db and to,wb. It can be readily understood that both the specific air-flow rate VS and the indoor relative humidity 4R will be affected by the six factors: tR, SHF, PFI, PFD, to,wb and to,db. Due to limitation on paper size, it was not possible to include, herein, fully detailed results which would illustrate the variation trends of VS and 4R with each of these factors individually. Instead, some limited samples of program results are displayed in Fig. 14 for the air-flow rates and Fig. 15 for the indoor relative humidity. These figures together with in-depth analysis of the results of extensive computer runs, representing numerous cases (not included here), led to the following conclusions. The required specific flow rate VS becomes higher for lower values of the performance factors PFI and PFD and lower indoor temperature tR. Higher flow rates are also necessary at higher values of space SHF. The effect of the outdoor wet-bulb temperature, which is readily predictable, is obvious from Fig. 14. The flow rate VS increases monotonically as to,wb gets higher. A point which needs special attention is the variation of VS with the outdoor dry-bulb temperature to,db. This variation does not have a fixed trend; as can be seen from Fig. 14. The cases where VS decreases upon increasing to,db may seem to be rather paradoxical or, at least, unexpected. However, this can be understood based on the fact that, for fixed to,wb, a higher value of to,db means a higher value of the theoretical maximum temperature drop (sum of Do and DP1). If this available drop is thriftily utilized by a well-designed system, having high values of PFI and PFD, low supply temperatures tc,db can be produced and the required flow rate will be reduced. On the other hand, systems having poor performance, represented by low values of PFI and/or PFD, will not benefit from the increased availability of theoretical temperature drop. For such systems, the flow rate VS increases at higher values of to,db; as shown, for some cases, in Fig. 14. As a matter of fact, this point is worth further investigations to assess the relative effects of PFI and PFD and to include the effects of the other factors; tR , SHF and to,wb. But, this cannot be accommodated here; it may be planned for future work. The indoor relative humidity 4R increases as: PFI decreases, PFD increases, tR decreases, SHF decreases, to,wb increases and/or to,db decreases. All these trends are logical; and come in complete agreement with the envision of tracing the processes on the psychrometric chart. 7. Conclusion In this work, the utilization of evaporative air cooling, as a means of maintaining a required indoor environment, was reviewed. The salient advantages and handicaps of the method were outlined. The rudimentary elements of the system were identified; then, different simple and combinative configurations were surveyed. Typical performance indices were defined for the different system configurations. A complete analysis was conducted for single and double-stage systems. This analysis encompassed and interrelated the prevailing outdoor climatic condition, the performance capabilities of the system and the indoor load quality and required temperature. The theoretical maximum limits of outdoor climatic conditions were deduced and mathematically phrased into general expressions

valid for any indoor temperature, any quality of space load and any system performance factor. More realistic, hence more significant, practical limits, based on practically tolerable air-flow rates, were also presented. Such limits enable the designer to decide offhand the suitability of a certain climate for the application of evaporative cooling to serve a certain space; based on a specified level of system performance. Systematic procedures were established for evaluating the required air flow and determining the achievable indoor condition when using different systems in different applications and under different climatic conditions. Useful tools were devised in the form of computer programs where computations are completely automated and the use of the psychrometric chart could be dispensed with. Samples of results obtained by using these programs were presented and analyzed to show the effects of various parameters on system performance. As a bottom line, and in accordance with the bases set hereinbefore for judging the feasibility and practicability, the option of using evaporative cooling, for a specific application and under certain climatic condition, will be a viable one if the following two conditions can be simultaneously satisfied: 1 Limiting the supply-air-flow rate to an acceptable value; taking into consideration space constraints, noise level, energy efficiency and economical factors. 2 Maintaining the indoor relative humidity within a tolerable range commensurate with the application nature or requirements. The realization of these two objectives may, sometimes, necessitate switching from a simple, or basic, configuration to a more sophisticated one; e.g. replacing a single-stage by a twostage system.

References [1] ASHRAE handbook of systems. ASHRAE; 1984 [chapter 36]. [2] ASHRAE handbook of applications. ASHRAE; 1999 [chapter 50]. [3] Mathews EH, Kleingeld M, Grobler LJ. Integrated simulation of buildings and evaporative cooling systems. Building and Environment 1994;29(2):197–206. [4] Fergin RK. A winning combination: heat recovery and evaporative cooling. In: Roose RW, editor. Handbook of energy conservation for mechanical systems in buildings. Van Nostrand Reinhold Company; 1978. p. 167–71. [5] Osbaugh RD, Moore TB. Applying two-stage evaporative cooling. ASHRAE Journal July 1988:26–30. [6] Beaudin D. Evaporative cooling system for remote medical center. ASHRAE Journal 1996;38(5):35–8. [7] Millet JR, Hutter E, Picard P. Evaporative cooling for summer comfort in office buildings. In: 2nd European conference on architecture, France; 1989. p. 108–10. [8] ASHRAE handbook of equipment. ASHRAE; 1979. [9] Fergin RK. Heat recovery devices for air conditioning. In: Roose RW, editor. Handbook of energy conservation for mechanical systems in buildings. Van Nostrand Reinhold Company; 1978. p. 146–50. [10] Pannkoke TE. Air-to-air energy recovery. In: Roose RW, editor. Handbook of energy conservation for mechanical systems in buildings. Van Nostrand Reinhold Company; 1978. p. 151–66. [11] Trott AR. Refrigeration and air conditioning. McGraw-Hill Book Company; 1981. [12] Yilmaz T, Bulut H, Ozgoren M, Buyukalaca O. An alternative cooling system for hot arid regions. In: International conference on energy research and development ICERD, Kuwait; 1998. I. p. 422–32. [13] Threlkeld JL. Thermal environmental engineering. Prentice-Hall Inc.; 1965. [14] ASHRAE handbook of fundamentals. ASHRAE; 1981. [15] Arora CP. Refrigeration and air conditioning. Tata McGraw-Hill Publishing Company; 1983. [16] Stein B, Reynolds JS. Mechanical and electrical equipment for buildings. John Wiley and Sons; 2000. p. 55–7. [17] Visitsak S, Haberl JS. An analysis of design strategies for climate-controlled residences in selected climates. In: SimBuild 2004, IBPSA-USA National conference, USA 2004. p. 1–11. [18] ASHRAE handbook of fundamentals. ASHRAE; 1993.