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Cooling coil selection using apparatus dewpoint charts K. O. Kessey Mechanical Engineering Department, Ahmadu Bello University, Zaria, Nigeria Received

This Paper presents apparatus dewpoint charts for selecting cooling and dehumidifying coils in the design of air conditioning plants. The apparatus dewpoint parameter has become one of the common methods for selecting cooling coils. With the aid of a digital computer, values for the apparatus dewpoint were computed for several ambient conditions and effective sensible heat factors. The computations reveal that, for any set of ambient conditions, there is a corresponding minimum value of the effective sensible heat factor below which no unique apparatus dewpoint exists. This fact is borne out by the apparent asymptotic trend of the graphs produced.

(Keywords:dewpoint;apparatusdewpointcharts;coolingcoils)

Choix des 6vaporateurs frigorifiques & l'aide de diagrammes du point de ros6e des appareils Cet article pr~sente des diagrammes du point de ros~e des appareils pour le choix des ~vaporateurs frigorifiques et de d~shumidification dans la conception des installations de conditionnement d'air. Le paramdtre du point de ros~e de l'appareil est devenu l'une des m~thodes les plus courantes de choix des ~vaporateurs frigorifiques. A raide d'un ordinateur on a calcul~ les points de ros~e de rappareil pour plusieurs conditions ambiantes et plusieurs facteurs de la chaleur sensible effective. Les calculs r~v~lent que, pour tout ensemble de conditions ambiantes, il existe une valeur mimimale du facteur de la chaleur sensible effective au-dessous de laquelle il n'y a pas de point unique de fosse de l'appareil. Ce fait est confirm~ par la tendance asymptotique des courbes obtenues.

(Mots cl6s: point de rosbe;diagramme du point de ros6e des appareils; 6vaporateur frigorifique)

The air conditioning engineer engaged with the design of a plant with comfort applications is frequently concerned with the selection of appropriate cooling and dehumidifying coils. The simplest method currently in wide use is based on the determination of the apparatus dewpoint. For convenience, this method has been called the apparatus dewpoint method in this Paper. The method presupposes a value for the bypass factor (BF) and uses this value in conjunction with outdoor and room conditions and heat loads to evaluate the effective sensible heat factor (ESHF). It then seeks to obtain the apparatus dewpoint (ADP) by making use of the psychrometric chart or tables based on imperial units 1. Using the psychrometric chart may entail a lengthy graphical approach, particularly if several coils are to be selected, and interpolation is often necessary when using tables. In this Paper apparatus dewpoint charts are presented in SI units to allow quick determination of the apparatus dewpoint from which the required air quantity may be obtained from an appropriate equation. This approach eliminates the human errors inherent in the graphical approach as well as the need for interpolation when using tables.

Equations used It is customary in air conditioning design to relate the design parameters to standard conditions of a dry-bulb temperature of 21 °C and relative humidity of 50~. Under 0140-7007/85/060360~)7503.00 • ) 1985 Butterworth & Co (Publishers) Ltd and IIR

360

Int. J. Refrig. 1985 Vol 8 November

these conditions the constant pressure specific heat capacity of moist air, c_ = 1.019 kJ kg- 1 K - 1, the specific volume, v=0.8425 m 5 kg-1, and the latent heat of water vapour, h1=2502 kJ kg -1. With these standard conditions as a reference point, if moist air undergoes a psychrometric change from reference state 1 to state 2 its sensible heat (SH) may be expressed as: SH = rh(h2 - h 1) = (~/v)(cp)(t~

- t, )

= (0.02015)(f/)(t 2 - t I ) in kW

(1)

having substituted the above values for v and Cp; and its latent heat (LH) may be expressed as: LH = rfihl(w 2 - w l ) = ( l//v)(h.)(w 2 - w 1)

= (49.5)( ~')(w2 - w 1) in kW

(2)

where n~, h, t/, t and w denote, respectively, the air mass flow rate, enthalpy, volumetric flow rate, dry-bulb temperature and humidity ratio. Equations (1) and (2) can be used to establish relationships between certain design parameters, specifically for the combined cooling and dehumidifying process. Various concepts have been enunciated to relate this psychrometric process to the characteristics of the cooling

Cooling coil selection: K. O. Kessey Nomenclature Constant pressure specific heat capacity Enthalpy h Latent heat of water vapour hi ni Mass flow rate of moist air Barometric pressure P Saturation water vapour pressure Pss t Dry-bulb temperature T Absolute dry-bulb temperature Specific volume of moist air V P Volumetric flow rate of moist air W Humidity ratio Relative humidity

CMPM ERLH ERSH ESHF GSHF LH OLH OSH RLH RSH SH

Abbreviations

a d o r

Cp

ADP BF

Apparatus dewpoint Bypass factor

Volumetric flow rate of air in m 3 min-1 Effective room latent heat Effective room sensible heat Effective sensible heat factor Grand sensible heat factor Latent heat Outdoor latent heat Outdoor sensible heat Room latent heat Room sensible heat Sensible heat

Subscripts Apparatus dewpoint Dehumidified Outdoor Room

effective room sensible heat (ERSH) or effective room latent heat (ERLH), respectively. Hence, the effective sensible heat factor is defined symbolically by: ESHF = ERSH/(ERSH + ERLH)

w

t

Figure 1

Skeleton psychrometric chart showing the ESHF in relation to other lines, a, Apparatus dewpoint; r, ambient room conditions; d, dehumidified; o, outdoor conditions Figure l Diagramme psychromktrique de principe montrant /e facteur de la chaleur sensible effective en relation avec d'autres courbes, a, Point de fosse de l'appareil; r, conditions ambiantes; d, d~shumidifd; c, conditions ext~rieures

equipment. These include the concepts of bypass factor, embracing effective sensible and latent heats. To give a more full appreciation of the derivations of the relationships, this concept is briefly discussed below. When moist air passes through cooling equipment it is supposed that a portion of it leaves the equipment completely unaltered, whilst the remainder is brought to equilibrium with the coil. This portion or fraction of the airstream which conceptually bypasses the equipment represents the bypass factor of the equipment. In particular, the outdoor or ventilation air which bypasses the cooling equipment in this manner constitutes an additional heat load (both sensible and latent) which must be taken into consideration, together with the room loads, in sizing the equipment. The sum total of the room sensible or latent heat load and the sensible or latent heat load accompanying this bypassed air is termed the

(3)

Figure 1 shows the effective sensible heat factor line between the apparatus dewpoint (state a) and ambient room conditions (state r) in relation to other lines on the skeleton psychrometric chart. It follows from what has been said above that, while the portion ofairstream which bypasses the equipment surface leaves it with its condition completely unaltered, the remaining fraction that literally contacts the surface leaves the equipment with its temperature equal to the effective surface temperature of the equipment, termed the apparatus dewpoint. By definition, the apparatus dewpoint is therefore, the imaginary uniform temperature of the cooling surface at which the water vapour in the moist airstream condenses as the air comes into contact with the surface. Using Equation (1), the effective room sensible heat which must be offset by the contact air leaving at ta, may be expressed by: ERSH = (0.02015)(CMPMa)(1 - BF)(tr - ta)

(4)

since the volumetric flow rate of the airstream that contacts the surface is ~"=CMPMd(1-BF), where CMPMd is the volumetric flow rate of air in m 3 min- 1 delivered by the equipment. The temperature of the contact air changes from t a to tr in picking up the room heat load. Similarly, using Equation (2), the effective room latent heat is given by: ERLH = (49.5)(CMPMo)(1 - BF)(wr - Wa)

(5)

since the humidity ratio of the contact air changes from wa to wr. Substituting the above expressions for ERSH and ERLH into Equation (3), it can be shown by a straightforward algebraic manipulation that: ESHF = 1/[1 + 2456 (wr - -

Wa)/(t r - -

ta)]

(6)

The effective room heat loads may also be expressed by

Rev. Int. Froid 1985 Vol 8 Novernbre

361

Cooling coil selection: K. O. Kessey the following alternate equations based on the above concepts: ERSH = RSH + (BF)(OSH)

(7)

ERLH = RLH + (BF)(OLH)

(8)

in which RSH and RLH are, respectively, room sensible and latent heats and OSH and O L H are outdoor sensible and latent heats. A little reflection regarding the interrelationships between the parameters given in Equations (3), (6), (7) and (8) will reveal that, given appropriate design specifications of outdoor and room conditions and room loads, Equation (6) establishes a corresponding apparatus dewpoint which satisfies the specification. However, determination of the apparatus dewpoint from this Equation requires a trial-and-error approach, since wa is a function of ta, as may be seen from the following considerations. First, the humidity ratio of moist air is given by~ w = (0.622)(~p~s)/[p - (~)(ps~)]

(9)

in which • and Pss are the relative humidity of moist air and the saturation vapour pressure of the water in moist air at the specified condition, p being the barometric pressure. Second, according to Reference 2, pss (in Pa), at a dry-bulb temperature of T(in K), is given by:

p~=exp[cl/T+c2+c3T+c,,T2+c5T3+c61n T]

ESHF lines for these asymptotic values do not intersect the saturation curve on the psychrometric chart. Hence these asymptotic values of ESHF do not have unique apparatus dewpoints. The use of the apparatus dewpoint charts for design requires the usual specification of room and outdoor conditions, typified by their dry-bulb temperatures and relative humidities, as well as room sensible and latent heat loads. Then the process is as follows. Step 1. Assume a suitable bypass factor (use may be made of recommendations on page 1-127 of Reference 1). Step 2. Calculate the effective room loads from the following Equations (obtained from a combination of Equations (1), (2), (7) and (8)): ERSH = RSH + (0.02015)(BF)(CMPMo)(to - tr)

(11)

ERLH = RLH + (49.5)(BF)(CMPMo)(Wo - Wr)

(12)

in which CMPMo (replacing 17in Equations (1) and (2)) is the outdoor ventilation requirement in m 3 min- 1. Woand Wr (the outdoor and room humidity ratios, respectively) may be determined from the psychrometric chart or suitable tables, or from Equations (9) and (10). Step 3.

Determine the effective sensible heat factor:

ESHF = ERSH/(ERSH + ERLH)

(10) Table 1 Apparatus dewpoint versus ESHF ~ Tableau 1 Point de ros~e de rappareil pat" rapport au jacteur de la

in which:

chaleur sensible effective tr = 20.0°C

c 1 = - 5800.2206 c 2 ~-- 1.3914993 c 3 = -0.04860239 c4=4.764768 x 10 -5 c5 = - 1.4452093 x 10 -8 c6 = 6.5459673

Computations Using a computer Equations (9) and (10) were combined with Equation (6) to evaluate the apparatus dewpoint with their corresponding ESHF values for given room conditions, characterized by the relative humidity, ~r, and dry-bulb temperature, tr. m condensed computer output in Table 1 gives the apparatus dewpoint with the related effective sensible heat factor for room dry-bulb temperatures (in °C) of 20-25 at a relative humidity of 74%.

Using apparatus dewpoint charts Results similar to those shown in Table 1 at regular intervals of relative humidity are presented in Figures 2-4, all assuming a baromatic pressure of 101.325 kPa. The curves for the charts representing ambient room relative humidities of 66-72% are truncated above 4°C. The ESHF values are found to be asymptotic to these truncated points at each set of room conditions. In fact, the

362

Int. J. Refrig. 1985 Vol 8 November

tr = 21.0°C

t r = 22.0°C

ta (°C)

ESHF

ta ('C)

ESHF

ta (°C)

ESHF

10.10 11.80 12.75 13.40 13.85 14.15 14.45 14.55 14.85 15.00 15.15 15.25

0.52 0.56 0.50 0.54 0.58 0.72 0.75 0.80 0.84 0.88 0.92 0.95 1.00

11.80 13.10 13.95 14.50 14.90 15.20 15.45 15.65 15.85 15.00 15.10 15.20

0.52 0.56 0.50 0.54 0.58 0.72 0.76 0.80 0.84 0.88 0.92 0.95 1.00

11.05 13.25 14.35 15.05 15.55 15.95 16.25 16.45 16.55 16.80 16.95 17.10 17.20

0.52 0.56 0.50 0.54 0.58 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00

t r = 23.0°C

t r = 24.0°C

t r = 25.0°C

ta (°C)

ESHF

ta (°C)

ESHF

ta (°C)

ESHF

13.00 14.55 15.60 16.20 16.65 17.00 17.25 17.45 17.65 17.80 17.95 18.05 18.15

0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00

14.65 15.95 16.75 17.30 17.70 18.00 18.25 18.45 18.65 18.80 18.90 19.00 19.10

0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00

13.90 16.10 17.20 17.90 18.40 18.75 19.05 19.25 19.45 19.60 19.75 19.90 20.00 20.05

0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00

" Barometric pressure= 101 kPa, room relative h u m i d i t y = 7 4 %

Cooling coil selection." K. O. Kessey

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