chapter 8 - psychrometry

8/22/2019 Chapter 8 - Psychrometry

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Chapter 8: Psychrometry1

psychrometry is the study of air-water vapour mixtures. It is also sometimesreferred to as hygrometry. Many mechanical engineering devices exploitpsychrometric processes, such as air conditioning systems and cooling towers.

some remarkable facts that underline the importance of psychrometry.

1. In 1999, Australian heating, ventilation and air conditioning (HVAC) andrefrigeration accounted for 11% and 4% of total greenhouse emissionsrespectively. Such figures are representative of the industrialised world, andcontinue to grow strongly.

2. Between 1-2 kg of water evaporates from the cooling towers of coal firedpower stations per kWhr of electricity they produce. This translates to roughly20% of Melbournes daily fresh water consumption being evaporated by thepower stations that generate our electricity.

so, if you want to make big reductions in CO2 emissions and water consumption,then psychrometry has a major part to play.

8.1 The psychrometric chart and definitions

for an n component mixture in general, we need to specify 1n + properties to

specify the thermodynamic state at equilibrium.

1. we are not considering pure substances here, but rather a 2 componentmixture (water and air). Thus, we need to specify at least 3 properties todetermine the thermodynamic state. In psychrometry, 1 of these properties isoften a measure of the amount of water in the mixture (e.g. the relativehumidity or the humidity ratio, both of which are defined later).

2. in the case of a combustible mixture, we typically specify the temperature andpressure of the mixture as well as the air-fuel ratio (or an analogous quantitysuch as the equivalence ratio or lambda).

the psychrometric chart is a thermodynamic chart like any other. However, it isnormally presented at atmospheric pressure only, as most applications are at thispressure. Thus, we need only 2 more properties to determine the thermodynamicstate the pressure is already given.

thus, if we have a psychrometric problem at non-atmospheric pressure, theatmospheric psychrometric chart cannot be used.

1These lecture notes are strongly based on those given previously in this subject by Dr. Kandadai

Srinivasan.


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major features of the psychrometric chart:

1. the saturation line: this is the line of 100% relative humidity, and representsthe locus of thermodynamic states that can hold the maximum amount ofwater in purely vapour form. DO NOT CONFUSE THIS LINE WITH THESATURATED LIQUID OR VAPOUR LINES IN STEAM TABLES.

2. the dry bulb temperature: is the temperature of the mixture as measured by astandard thermometer. The word dry is used to imply that the the sensor isexposed to the vapour mixture without any liquid present.

3. the enthalpy: as commonly used, but with units of J oules per kilogram of the

dry airin the mixture.

4. the humidity ratio w : the mass of water vapour in the mixture per unit massof dry air, i.e.

w

a

mw

m=

5. the wet bulb temperature *T (or the saturation temperature): is thetemperature at which water evaporating into moist air at a given dry-bulbtemperature and humidity ratio can bring air to saturation adiabatically at the

same pressure p .


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6. the relative humidity : is the ratio of the mole fraction of water vapour in a

given sample of moist air to the mole fraction of water vapour in air saturatedat the same temperature and pressure. It is also the ratio of the partialpressure of water vapour to the partial pressure of water vapour in airsaturated at the same temperature and pressure. The relative humidity is the

colloquial way of expressing moisture content.w w

ws ws

x p

x p= =

7. the specific volume v : as commonly used, but with units of mixture volumeper kilogram of the dry air.

other important terms:

8. the dew point temperature dT : is the temperature of moist air saturated at the

same pressure and humidity ratio as a given specimen of humid air. If we coolit further, water will start condensing and separates out as fog/dew, hence thename.

9. the absolute humidity: exactly the same as the humidity ratio.

10. the specific humidity q : the mass of water vapour per unit mass of the

mixture, i.e.

w

w a

mq

m m=

+

11. the saturation humidity ratio: is the humidity ratio of moist air that is saturatedwith water vapour at the same temperature and pressure.


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8.2 The wet bulb temperature

consider a stream of unsaturated air-water mixture flowing through a tunnel intowhich water is sprayed.

since the air-water mixture is not saturated, it is capable of taking in more ofwater vapour. Some of the water from the spray will therefore evaporate and mixwith the air. Of course, w keeps increasing and at some point the mixture

becomes saturated with water.

during this adiabatic process, the temperature of the air-water mixture willdecrease because the heat required to vaporise the liquid water is provided byair-water vapour mixture. When saturated, the air-water mixture will then be at

the wet bulb temperature *T .

thus, in general, for some non-saturated vapour mixture, the dry bulb temperature*

T T> and ( )*T T is called the wet bulb depression.

the wet bulb temperature is measured by a thermometer that has its bulbenclosed in a wet wick. The wet wick thermometer is cooled down by theevaporation on the wick. The amount of evaporation is a direct indication of themoisture carrying capacity of the atmospheric air at that temperature. When theair is saturated, there is no evaporation and thus the dry bulb and wet bulbtemperatures are the same.

thus, we can determine the thermodynamic state of air at atmospheric pressureby simultaneously taking the dry and wet bulb temperatures. Such a device iscalled a hygrometer. Recourse to the psychrometric chart then allows us tomeasure other quantities.

8.3 Air-water mixtures as perfect gases

if air and water vapour can be treated as perfect gases, then it follows that

&a w

a w

ra rw

m RT m RT p V p V

M M= = (8.1)

where 28.84raM = and 18rwM = are the molecular masses of air and water

respectively.

since the humidity ratio w can be expressed in terms of partial pressures or molefractions, it follows that


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0.624

0.624w rw w w

a ra a a

m M p xw

m M p x

=

= = =

(8.2)

8.4 Psychrometric processes

just as we have several commonly used processes in the thermodynamics ofpure substances (isobars, isotherms, isochores), there are several commonprocesses for air+water vapour mixtures.

8.4.1 Heating or cool ing of moist air

the addition or removal of heat, without any change in the moisture content (i.e.

the humidity ratio w ), must result in a change of the dry bulb temperature (DBT).The state will move horizontally left (cooling) or right (heating):

the amount of heat transferred to/from the mixture is of course governed by theSFEE,

( )2 1aq m h h= (8.3)

where it is noted that since the enthalpies are per unit mass of the dry air in themixture, this enthalpy difference is multiplied by the mass of air to obtain the heat

transfer.


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if, as a result of the cooling, the left moving point reaches the saturation line,some condensation will start:

the DBT that corresponds to this point is refereed to as the dew pointtemperature of the original mixture, as this is the first point at which liquid water(i.e. dew, fog or mist) forms. If there is further cooling, the state point movesalong the saturation line and further condensation will occur.

application of the first law to this process yields

( )2 1a w wq m h h m h= + (8.4)

wherewm and wh are the mass and enthalpy of the liquid water present at the

end of the process (this water separates out from the vapour mixture as

condensate, and so is not represented on the chart, but must be considered inthe any mass or energy balance).

the initial and final moisture contents during this process are1a

m w and2a

m w

respectively.

since the water must be conserved,

( )1 2

1 2

a a w

w a

m w m w m

m m w w

= +

=

(8.5)

thus, substituting into the SFEE

( ) ( )2 1 2 1a wq m h h w w h= (8.6)

this cooling process can therefore also reasonably be called dehumidification bycooling since the absolute humidity (i.e. the humidity ratio) decreases.

8.4.2 Adiabatic humidifi cation (or evaporative cool ing)

if water is evaporated into the air-water vapour mixture without any heat additionor removal (i.e. adiabatically), the heat required to evaporate the water is takenfrom the vapour mixture. The DBT is therefore reduced whilst the state point

moves along a line of constant wet bulb temperature (WBT).


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consider a stream of air-water vapour mixture into which a water sprayevaporates,

from the SFEE,

( )2 10 a w wm h h m h= (8.7)

once again, since the mass of water is conserved,

( )1 2

2 1

a w a

w a

m w m m w

m m w w+ =

= (8.8)

and thus

2 1

2 1

w

h hh

w w

=

(8.9)

note:

1. because this process is adiabatic does not infer that2 1

0h h = . This is because

lines of constant WBT are not exactly parallel with lines of constant (mixture)enthalpy. As noted earlier, the enthalpy is defined per unit mass of dry air in themixture.

2. the relative humidity is increased during this process until it hits the saturationline. Further injection of water after this point does not result in any evaporationand therefore no decrease in the DBT. Thus, evaporative cooling is ineffective inhumid atmospheric conditions.

8.4.3 Adiabatic dehumidif ication

if the air-water vapour mixture is passed through a chemical sorbent material

(e.g. a silica gel), some of the moisture is removed and the latent heat ofevaporation is released. Thus, the DBT increases along a line of constant WBT ifthis process is adiabatic.

8.4.4 Adiabatic mixing of two vapour streams

consider the mixing of two air streams,


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applying the SFEE

3 3 1 1 2 20

a a am h m h m h= (8.10)

conservation of air3 1 2a a a

m m m= + (8.11)

conservation of water

3 3 1 1 2 2a a am w m w m w= + (8.12)

combining (8.11) and (8.12) with (8.10) to eliminate3a

m ,

( )1 1 2 2

3

1 2

a a

a a

m h m hh

m m

+=

+

(8.13)

thus, the process is as follows on the psychrometric chart,


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8.5 Air conditioning

in terms of the psychrometric chart, our perception of comfort is roughly asfollows,

air conditioning is the generic term given to use of psychrometric processes that

move the state of the air-water vapour mixture to an intended place on the chart.This is usually to cool or moderate conditions, and may involve both heatingand cooling the mixture.

a simple arrangement of a summer air conditioning cycle,


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a simple arrangement of a winter air conditioning cycle,

8.6 Cooling towers

cooling towers are a very important part of almost all power plants. Theiroperation is in principle very simple. They cool the cooling water by evaporatingsome of it into a passing stream of moist air. Considering a spray of cooling waterdroplets in the tower,

cooling towers are closely adiabatic devices, with the vapour phase representedas follows on the psychrometric chart for the ideal process,


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here the red and pink lines represent the paths taken by the vapour as it cools

and then as the cooling water evaporates.

a typical cooling water circulation system:

hot water from the heat exchangers is sent to the cooling tower. The water(minus that evaporated) is sent back to the heat exchangers for further cooling.

Make-up water is used to replenish water lost to evaporation.

there are essentially 2 types of cooling tower designs: natural and mechanicaldraft.

8.6.1 Natural draft cool ing towers

as the name suggests, natural draft cooling towers exploit natural (or free)convection to move air through the cooling water.

these types of towers are typically very large (~150m high and ~100m basediameter) and are generally used with high water flow rates (~10-20 m3/s)


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often these are used in coal fired power stations. When you see a vapour plume

coming from the top, it is of course not smoke, and means that the tower isperforming as intended!

8.6.2 Mechanical draft cool ing towers

Mechanical draft cooling towers are used for low and moderate water flow rates,especially in central air conditioning and refrigeration plants. Fans force airthrough the circulated water.

there are many configurations of mechanical draft cooling towers, for example,

chapter 8 - psychrometry

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