Chapter 2 Psychrometry and Air-conditioning 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 proc esses are to be carried carr ied out, or to provi p rovide de air-condi air-c ondition tioning ing in private priv ate and public publ ic buildings. build ings. The properties of atmospheric air have to be considered in these problems, and this is a subject which is receiving an increasing amount of attention and application. Another topic which will be considered is that of the cooling tower by means of which large quantities of cooling water are cooled for recirculation. These topics come under the title of psychrometry (sometimes called hygrometry).
2.1
Psychrometric mixtures
Consider atmospheric air at P a = 1.013bar and Ta = 15 ºC For the water vapour, Psat = 0.01704bar and T= 15ºC
Figure 2.1 Vapourisation at atmospheric pressure According to Gibbs-Dalton law, at low vapour p ressures the vapour can be assumed as a perfect gas. Assume: P sat = 0.01bar at T= 15ºC
P = Pa + Ps
, where
P a = partial pressure of dry air P s = partial pressure of superheated vapour
Or Pa
=
P − Ps = 1.013 - 0.01= 1.003bar
Degree of superheat = 15 – 7 = 8K The saturation temperature corresponding to 0.01bar is 7ºC
Figure 2.2 T-s diagram
Consider: Dew point, Td = temperature to which unsaturated mixture must be cooled in order to become just saturated
2.2 Specific Humidity, Relative Humidity and Percentage Saturation
ω =
Specific humidity (moisture content),
∴ω =
ms ma
=
ms
(2.1)
ma
ms / V ma / V
=
ρ s ρ a
Assumed vapour and dry air are perfect gases. Thus, ms =
PsV RsT
Where
and
Rs =
ℜ Μs
ma =
,
Substitute (2.2) in (2.1):
PaV RaT Ra =
ℜ Μa
(2.2)
=
ν a ν s
ω =
PsV Μ s
ℜT
However,
×
P P ℜT 18 = × s = 0.622 s PaV Μ a 28.96 Pa Pa
P = Pa + Ps
or
Pa = P − Ps
Ps P P − s
Thus, specific humidity, ω = 0.622
Relative humidity, φ =
ms =
PsV RsT
and
(2.3)
ms
(ms )sat (ms )sat =
PgV Rs T
Where P g = saturation pressure at the temperature of mixture Thus;
Ps Pg
φ =
Percentage saturation, ψ = ratio of the specific humidity of mixture to the specific humidity of mixture when saturated at same temperature
∴ψ =
ω
(2.4)
ω g
Or also known as relative saturation or degree o f saturation. Thus,
P − Pg P P − s
ψ = 100φ
(2.5)
In air-conditioning practice the percentage difference between ψ and φ in approximation in the range of 0.5 to 2%.
Example 2.1:
The air supplied to a room of a building in winter is to be at 7ºC and have a percentage relative humidity of 60%. If the barometric pressure is 1.01326 bar, calculate the specific humidity. What would be the dew point under these conditions? Solutions From the steam table, at 7ºC
∴φ =
Ps Pg
or
∴ Pg = 0.01936bar 0.6 =
Ps
0.01936
;
Thus,
P s = 0.012bar
P 0.012 ∴ω = 0.622 s = 0.622 = 0.0072 P P 1 . 01326 0 . 012 − − s
Thus, the dew point;
0.011616 − 0.01147 = 9.18°C 0 . 01227 − 0 . 01147
T d = 9 + (10 − 9)
Measurement of relative humidity An instrument used to measure relative humidity is called a psychrometer, or a hygrometer. Another method is by the determination of wet and dry bulb temperatures.
Figure 2.3 Two thermometer situated in a stream of unsaturated air are separated by a radiation screen. One of them indicates the air temperature and is called the dry bulb temperature. The bulb of the second is surrounded by a wick which dips into a small reservoir of water and the temperature indicated is called the wet bulb temperature. As the air stream passes the wet wick, some of the water evaporates and this produces a cooling effect at the bulb. The amount 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 wick is high, and hence the wet bulb depression is high.
Psychrometer Chart
Figure 2.3 Psychrometric chart The zero specific enthalpy of the mixture for the vapour is taken at 0°C. For the dry air the zero for enthalpy is also taken at 0°C.
Figure 2.4 Property line in psychrometric chart From equation (2.3),
ω =
0.622 Pg ( P − Pg )
Combining this with equation (2.4), we have ψ =
100ω ω g
=
100ω ( P − Pg ) 0.622 Pg
For a given barometric pressure, P, the percentage saturation is a function of ω and P g . The barometric pressures are in the range 0.95 – 1.05bar.
Figure 2.5 Sensible heating and cooling process
Figure 2.6 Humidification and dehumidification process
Figure 2.7 Combination process of humidification and heat transfer
Figure 2.8 Effect of heating process
Figure 2.9 Effect of humidifying process
2.3 Specific Enthalpy, Specific heat capacity, and specific volume of moist air
Specific enthalpy of moist air
The enthalpy of a mixture is the sum of the enthalpies of the individual constituents, mh = ma ha
+
ms hs
Enthalpy of mixture per unit mass of dry air = mha / ma
= ha +
ms hs ma
= ha + ω hs At low partial pressure, the enthalpy of water vap our can be expressed as hs = (hg _ at _ Ps ) + C ps (t − t g _ at _ Ps )
Where the mean (approximately).
specific
heat
of
superheated
water
vapour,
C ps =
1.88kJ/kgK
The specific enthalpy of dry air in the mixture, ha = C pa t
Where C pa = 1.005kJ/kgK Thus, enthalpy of the mixture per unit mass of dry air; h = C pa t + (hg _ at _ Ps + C ps (t − t g _ at _ Ps ))ω
Since for low pressures the enthalpy of superheated vapour is approximately equal to the saturation Enthalpy of mixture per unit mass of dry air, h h = C pa t + ω (hg _ at _ t )
For specific heat capacity of moist air, C p C p
=
ma C pa m
+
ms C ps m
Then, the specific heat capacity of mixture per unit mass of dry air, C p = C pa + ω C ps
For specific volume of the mixture per unit dry air is convenient to use the specific volume of dry air, ν a ν a =
RaT Pa
2.4 Summer Air-Conditioning
The air conditioning load on a room/space may be considered in two parts: (i) (ii)
The sensible heat load – the energy added per unit time which increases the dry bulb temperature The latent heat load – the energy added per unit time due to the enthalpy of the moisture added plus the heat required to evaporate the moisture added
The Sensible Heat Gain Due to heat transfer through the fabric, including solar radiation, plus internal • gains from people, lighting, machineries etc. The Latent Heat Gains Due to the occupants of the room •
Consider:
Figure 2.10 Psychrometry chart Point 1 : The moist air from the air conditioning plant entering the room Point 2 : The moist air from the air conditioning At point x : ω 1
=
ω x
and
t 2
t
= x
Thus, sensible heat load = ma (h x
−
h1 ) = ma C Pma (t x
t ) = ma (C Pma
− 1
+
ω C Ps )(t x
t )
− 1
Latent heat load = ma (h2 − h x ) = ma (ω 2 − ω 1 )(hg _ at _ t 2 ) The room ratio line 1-2: h x − h1 h2 − h1
=
Sensible _ heat _ load Total _ heat _ load
Now, consider a typical conventional air conditioning system:
Figure 2.11 Air-conditioning plant and psychrometry chart
In mixing box, assume that the mixing is adiabatic, the mass balance of the mixture are: Mass of dry air:
ma 2 + ma 3 = ma 4
Mass of vapour:
ω 2 ma 2 + ω 3 ma 3 = ω 4 ma 4
Energy balance:
ma 2 h2
+
ma 3 h3
=
ma 4 h4
Elimination of m a4 from the relations above results in ma 2 ma 4
=
ω 3 − ω 4 ω 3 − ω 2
=
h3 − h4 h3 − h2
= r
rh2 + (1 − r ) h3 = h4
Where r is the mass flow of dry re-circulated air per unit mass flow of dry air supplied to the room. Thus,
r =
h3 − h4 h3 − h2
Thus, gives: r ω 2 + (1 − r )ω 3 = ω 4
Therefore; r =
ω 3 − ω 4 ω 3 − ω 2
=
h3 − h4 h3 − h2
=
line _ 3 − 4 line _ 3 − 2
If the air undergoes sensible cooling in the cooling coil and dehumidification. Point A is called the apparatus dew point. The efficiency of the cooler: Coil bypass factor =
line _ 5 − A line _ 4 − A
Or normally defined as contact factor: Contact factor =
line _ 4 − 5 line _ 4 − A
Dehumidification 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.
2.5 Winter Air-Conditioning
A typical conventional type air-conditioning system for winter use is shown in Figure 2.12 and the corresponding state points are shown on Figure 2.12b. The various parts of the system are similar to summer air-conditioning system except for the humidifier. The humidification process 5-6 in the case shown is assumed to be adiabatic and take place at constant wet bulb if pumped recirculation of the water is used as shown in Figure 2.12a.
Figure 2.12 Air-conditioning plant and psychrometry chart In general, direct contact air washers and humidifiers may be classified as follows: (a) pump recirculation (b) (i) no circulation, with a water spray which (ii) no recirculation, with steam blown into the air stream For (a) the process is assumed adiabatic and the process occurs at a constant thermodynamic wet bulb temperature. For cases (b) (i) and (b) (ii), assuming that the process chan ges from state 5 to state 6, we have
s = m a (ω 6 − ω 5 ) Mass of water or steam added, m Also
a (h6 − h5 ) = m s hs m a (h6 − h5 ) = m a (ω 6 − ω 5 )hs i.e. m hs =
h6 − h5
ω 6 − ω 5
2.6 Cooling Towers
The cooling tower is to cool water passing through it by means of a heat exchanger.
Induced draught Natural draught Figure 2.13 Cooling 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 8K above the wet bulb temperature. Induced and natural draught cooling towers are shown in Figure 2.13. The cooling effect is greater with an induced draught compare to a natural draught cooling tower due to the increase flow of air. Example 2.2 : o
o
Water at 40 C enters a cooling tower at a rate of 200kg/s. The water is cooled to 25 C in the o cooling tower by the air which enters the tower at 1 atm, 20 C, 60% relative humidity and o leaves saturated at 25 C. Determine: (a) The volume flow rate of the air entering the cooling tower (b) The required mass flow rate of the make-up water
