CHAPTER 2 Psychrometry and Air-conditioning

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Chapter 2

Psychrometry and Air-conditioning

2.0 Introduction

Mixtures of air and water vapour are considered moist atmospheric air (i.e. a mixture of dry

air and water vapour).It is often necessary to provide a controlled atmosphere in buildings where industrial

processes are to be carried out, or to provide air-conditioning in private, public and industry

buildings. The properties of atmospheric air have to be considered in these problems, and thisis a subect which is receiving an increasing amount of attention and application. !nother

topic which will be considered is that of the cooling tower by means of which large

"uantities of cooling water are cooled for recirculation. These topics come under the title of psychrometry (sometimes called hygrometry).

2.1 Psychrometric mixtures

#onsider atmospheric air at $a% &.'&bar and Ta% & *#

+or the water vapour, $sat% '.'&'bar and T% &*#

+igure .& /apourisation at atmospheric pressure

!ccording to 0ibbs-1alton law, at low vapour pressures the vapour can be assumed as a perfectgas.

!ssume2 $sat% '.'&bar at T% &*#

sa P P P += , where $a% partial pressure of dry air

$s% partial pressure of superheated vapour



3r sa P P P −= % &.'& - '.'&% &.''bar

1egree of superheat % & 4 % 56

The saturation temperature corresponding to '.'&bar is *#

+igure . T-s diagram

Consider:

1ew point, Td % temperature to which unsaturated mixture must be cooled in order to become

ust saturated

2.2 Specific Humidity !e"ati#e Humidity and Percentage Saturation

7pecific humidity (moisture content), a

s

m

m

=ω (.&)

s

a

a

s

a

s

a

s

V m

V m

m

m

ν

ν

ρ

ρ ω ====∴

8

8

!ssumed vapour and dry air are perfect gases.

Thus,

T R

V P m

s

s s =

and T R

V P m

a

a

a

=

9here s

s RΜℜ

= ,a

a RΜℜ

= (.)

7ubstitute (.) in (.&)2



a

s

a

s

aa

s s

P

P

P

P

V P

T

T

V P :.'

;:.5

&5=×=

Μℜ

×ℜΜ

=ω

<owever, sa P P P += or sa P P P −=

Thus, specific humidity,

−

= s

s

P P

P :.'ω (.)

=elative humidity, ( ) sat s

s

m

m=φ

T R

V P m

s

s s = and ( )

T R

V P m

s

g

sat s =

9here $g% saturation pressure at the temperature of mixture

Thus>

=

g

s

P

P φ

$ercentage saturation, ? % ratio of the specific humidity of mixture to the specific humidity ofmixture when saturated at same temperature

g ω

ω ψ =∴ (.)

3r also @nown as relative saturation or degree of saturation.

Thus,

−

−=

s

g

P P

P P φ ψ &'' (.)

In air-conditioning practice the percentage difference between ? and A in approximation in therange of '. to B.

$xamp"e 2.1:

The air supplied to a room of a building in winter is to be at &*# and have a percentage relative

humidity of :'B. If the barometric pressure is &.'&:bar, calculate the specific humidity. 9hatwould be the dew point under these conditionsC



So"utions

+rom the steam table, at &*# bar P g '&;(:.'=∴

g

s

P

P =∴φ

or '&;:.':.' s P

= > Thus, $s% '.'&bar

'',.''&.''&:.&

'&.':.':.' =

−=

−

=∴ s

s

P P

P ω

Thus, the dew point> C T d °=

−−

−+= ':.;5,&.',:.&

5,&.'.&)&'(

%easurement of re"ati#e humidity!n instrument used to measure relative humidity is called a psychrometer, or a hygrometer.

!nother method is by the determination of wet and dry bulb temperatures.

+igure .

Two thermometer situated in a stream of unsaturated air are separated by a radiation screen.

3ne of them indicates the air temperature and is called the dry bulb temperature. The bulb of the second is surrounded by a wic@ which dips into a small reservoir of water and the

temperature indicated is called the wet bulb temperature. !s the air stream passes the wet

wic@, some of the water evaporates and this produces a cooling effect at the bulb. Theamount of this wet bulb depression depends on the relatives humidity of the air. If the

relative humidity is low, then the rate of evaporation at the wic@ is high, and hence the wet

bulb depression is high.

Psychrometer Chart



+igure . $sychrometric chart

The Dero specific enthalpy of the mixture for the vapour is ta@en at 'E#. +or the dry air theDero for enthalpy is also ta@en at 'E#.



+igure . $roperty line in psychrometric chart

+rom e"uation (.),

)(

:.'

g

g

P P

P

−=ω

#ombining this with e"uation (.), we have

g

g

g P

P P

:.'

)(&''&'' −== ω

ω

ω ψ

+or a given barometric pressure, $, the percentage saturation is a function of F and $ g. The

barometric pressures are in the range '.; 4 &.'bar.



+igure . 7ensible heating and cooling process

+igure .: <umidification and dehumidification process

+igure . #ombination process of humidification and heat transfer



+igure .5 Gffect of heating process

+igure .; Gffect of humidifying process

2.& Specific $ntha"py Specific heat capacity and specific #o"ume of moist air

7pecific enthalpy of moist air

The enthalpy of a mixture is the sum of the enthalpies of the individual constituents,

s saa hmhmmh +=

Gnthalpy of mixture per unit mass of dry air aa mmh 8=

a

s sa

mhmh +=

sa hh ω +=

!t low partial pressure, the enthalpy of water vapour can be expressed as



) H H() H H( s g ps s g s PatttC Pathh −+=

9here the mean specific heat of superheated water vapour, # ps% &.55@8@g6 (approximately).

The specific enthalpy of dry air in the mixture,

t C h paa =

9here # pa% &.''@8@g6

Thus, enthalpy of the mixture per unit mass of dry air>

ω ))HH(HH( s g pss g pa PatttC PathtCh −++=

7ince for low pressures the enthalpy of superheated vapour is approximately e"ual to the

saturation

Gnthalpy of mixture per unit mass of dry air, h

) H H( t at ht C h g pa ω +=

+or specific heat capacity of moist air, # p

m

C m

m

C mC

ps s paa

p +=

Then, the specific heat capacity of mixture per unit mass of dry air,

ps pa p C C C ω +=

+or specific volume of the mixture per unit dry air is convenient to use the specific volume of dry air, Ja



a

aa

P

T R=ν

2.' Summer Air-Conditioning

The air conditioning load on a room8space may be considered in two parts2

(i) The sensible heat load 4 the energy added per unit time which increases the dry

bulb temperature(ii) The latent heat load 4 the energy added per unit time due to the enthalpy of the

moisture added plus the heat re"uired to evaporate the moisture added

The 7ensible <eat 0ain

• 1ue to heat transfer through the fabric, including solar radiation, plus internal

gains from people, lighting, machineries etc.

The Katent <eat 0ains

• 1ue to the occupants of the room

Consider2

+igure .&' $sychrometry chart

$oint & 2 The moist air from the air conditioning plant entering the room

$oint 2 The moist air from the air conditioning

!t point x 2

xω ω =& and xt t =

Thus, sensible heat load % ))(()()( &&& t t C C mt t C mhhm x Ps Pmaa x Pmaa xa −+=−=− ω



Katent heat load % ) H H)(()( .&.. t at hmhhm g a xa ω ω −=−

The room ratio line &-2

load heat Total

load heat Sensible

hh

hh x

H H

H H

&.

&=

−

−

Low, consider a typical conventional air conditioning system2

+igure .&& !ir-conditioning plant and psychrometry chart

In mixing box, assume that the mixing is adiabatic, the mass balance of the mixture are2

Mass of dry air2 - aaa mmm =+

Mass of vapour2 -- aaa mmm ω ω ω =+

Gnergy balance2 -- hmhmhm aaa =+

Glimination of ma from the relations above results in

r hh

hh

m

m

a

a =−−

=−−

=

-

-

-

ω ω

ω ω

- )&( hhr rh =−+

9here r is the mass flow of dry re-circulated air per unit mass flow of dry air supplied to theroom. Thus,

-

hh

hhr

−−

=



Thus, gives2

- )&( ω ω ω =−+ r r

Therefore>

.( H

-( H

.(

-(

.(

-(

−

−

=

−

−

=

−

−

=

line

line

hh

hhr

ω ω

ω ω

If the air undergoes sensible cooling in the cooling coil and dehumidification. $oint ! is

called the apparatus dew point.

The efficiency of the cooler2

#oil bypass factor % Aline

Aline

−

−

- H

) H

3r normally defined as contact factor2

#ontact factor % Aline

line

−

−

- H

)- H

1ehumidification may also be achieved by passing the air through a spray cooler supplied

with chilled water. The apparatus dew point is then the water temperature. In this case the

contact factor is usually renamed the spray cooler, or washer, efficiency and is expressed as a

percentage.

2.( )inter Air-Conditioning

! typical conventional type air-conditioning system for winter use is shown in +igure .&

and the corresponding state points are shown on +igure .&b. The various parts of thesystem are similar to summer air-conditioning system except for the humidifier. The

humidification process -: in the case shown is assumed to be adiabatic and ta@e place at

constant wet bulb if pumped recirculation of the water is used as shown in +igure .&a.



+igure .& !ir-conditioning plant and psychrometry chart

In general, direct contact air washers and humidifiers may be classified as follows2

(a) pump recirculation

(b) (i) no circulation, with a water spray which

(ii) no recirculation, with steam blown into the air stream

+or (a) the process is assumed adiabatic and the process occurs at a constant thermodynamic wet

bulb temperature.

+or cases (b) (i) and (b) (ii), assuming that the process changes from state to state :, we have

Mass of water or steam added, )( : ω ω −= a s mm

!lso

s sa hmhhm =− )( :

i.e. saa hmhhm )()( :: ω ω −=−

:

:

ω ω −−

= hh

h s

2.* Coo"ing +o,ers

The cooling tower is to cool water passing through it by means of a heat exchanger.



Induced draught Latural draught

+igure .& #ooling Tower

This is done by spraying the water into the air over a pond, or into the air passing through a

cooling tower. The cooling water can be theoretically be cooled to the wet bulb temperature

of the incoming air, the figure used in design for cooling water leaving the tower is about 56above the wet bulb temperature. Induced and natural draught cooling towers are shown in

+igure .&. The cooling effect is greater with an induced draught compare to a natural

draught cooling tower due to the increase flow of air.

$xamp"e 2.2 :

9ater at 'o# enters a cooling tower at a rate of ''@g8s. The water is cooled to o# in thecooling tower by the air which enters the tower at & atm, ' o#, :'B relative humidity and

leaves saturated at o#. 1etermine2

(a) The volume flow rate of the air entering the cooling tower

(b) The re"uired mass flow rate of the ma@e-up water

So"utions:

(a) +rom the conservation of mass and energy2

1ry air 2 aaa mmm == &

9ater 2 -&& aa mmmm ω ω +=+

wa mmmm =−=− )( &- ω ω Gnergy 2 iiee hmhmW Q ∑ ∑−=− but %' and 9%'

')()( -& =−−+−∴ hmhmmhhm wa

or-&&

-

)()(

)(

hhh

hhmm

aω ω −−−

−=



+rom the psychrometric chart2

h& % @8@g d.a.

F& % '.''5 @g <38@g d.a.

J& % '.5 m

8@g d.a.h % @8@g d.a.

F % '.' @g <38@g d.a.

+rom the steam table, T% o# and T% o#

h % h f % &:. @8@g <3

h % h f % &'.5; @8@g <3

skg ma 8;.;

5;.&'-)''55.''.'()-,(

)5;.&'-,.&:,(''=

×−−−

−=∴

/olume flow rate, smmq a 8;.')5-.'(;.;

& === ν

(b) The ma@e-up water, mw 2

skg mm aw 8-&.-)''55.''.'(;.;)( & =−=−= ω ω

CHAPTER 2 Psychrometry and Air-conditioning

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Transcript of CHAPTER 2 Psychrometry and Air-conditioning