Temperature of adiabatic saturation

An adiabatic process is one in which no heat is supplied to or rejected from the gas during the change of state it undergoes.

Consider the flow of a mixture of air and water vapour through a perfectly insulated chamber. The chamber contains a large wetted surface, and water is evaporated from the surface to the stream of moist air flowing over it, provided the moist air is not already saturated. Feed-water is supplied to the chamber to make good that evaporated. Figure 2.8 shows such a situation.

1 kg/s dry air

1 kg/s dry air

G, kg steam

G2 kg steam


H2 enthalpy

F, temperature

T2 temperature


(92 ~ Si) kg

Tw temperature

Hw enthalpy

Fig. 2.8 Airflow through a perfectly insulated humidification chamber.

A heat balance may be established:

CaOl — h) + csgi(ti — t2) = (g2 — g)[(h — tw) + hfg]

This equation expresses the physical changes that have taken place:

(i) g2 — gi kg of feed-water are sensibly heated from a temperature of? w to a temperature


(ii) g2~ g kg of water are evaporated from the wetted surface within the chamber, at a temperature t2. The latent heat required for this is h{g kJ kg-1 at temperature t2.

(iii) 1 kg of dry air is cooled from a temperature t to a temperature t2.

(iv) g) kg of steam are cooled from tx to t2.

The left-hand side of the equation may be simplified by using a combined specific heat, c, for moist air:

C(t — t2) = (g2 — g{){(t2 — tj + hig}

In due course, if the chamber is infinitely long, the moist air will become saturated and will have a moisture content gss and a temperature tss.

The equation then becomes

C(h — ^ss) ~ (gss ~ <?l){(^ss — ^w) ^fg)

If the feed-water is supplied to the chamber at a temperature tss, then a further simplification results:

C(t i — tss) — (gss — §i)hfg

From this we can write an equation representing an adiabatic saturation process:

_ C /л q i


This equation should be compared with equation (2.30). Both give a value for the slope of a line in a moisture content-temperature, co-ordinate system, which is shown in Figure 2.9. It can also be seen that if the air is saturated by passing it through an adiabatic saturation chamber, its wet-bulb temperature will fall, if as illustrated, the value of the Lewis number is greater than one. At the saturated condition, the temperature of adiabatic saturation, t*, the wet-bulb temperature, t’2, and the dry-bulb temperature, t2, are all equal and may be denoted by fss.

Temperature of adiabatic saturation

Fig. 2.9 A humidification process along a line of constant adiabatic saturation temperature has a different slope from that of a process along a line of constant wet-bulb temperature.

An illustration of a Lewis number being greater than one is that of moist air, initially at 21 °C dry-bulb, 15°C wet-bulb (sling) and 101.325 kPa barometric pressure which is flowing over a wet-bulb thermometer or through an adiabatic saturation chamber at a velocity of 1 m s_1. The lewis number is 1.05. If the velocity exceeded about 1 ms-1, then the Lewis number would become less than unity and the wet-bulb temperature would increase as the moist air was humidified by a process of adiabatic saturation.

Outside the field of air conditioning, if toluene is evaporated into dry air by a process of adiabatic saturation, it can be observed that the wet-bulb temperature is very much more than the temperature of adiabatic saturation. This is because, at the temperatures and pressures considered here, the Lewis number equals about 1.8, instead of unity.

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