THERMODYNAMIC WET BULB TEMPERATURE OR ADIABATIC SATURATION TEMPERATURE (AST)

The thermodynamic wet bulb temperature or AST is the temperature at which the air can be brought to saturation state adiabatically by the evaporation of water in the flowing air. A schematic representation of this process, called the adiabatic saturation process, is shown in Fig. 20.3. It consists of an adiabatic enclosure containing adequate quantity of water. There is also an arrangement for feed water from the top.

The unsaturated air enters the enclosure at section 1. As the air flows through the enclosure water evaporates which is carried by the flowing stream of air. Thus the specific humidity of air increases. The water level in the enclosure is maintained by the feed water. Both the air and water are cooled as the evaporation takes place. The process continues until the energy transferred from the air to water is equal to the energy required to vaporise water. When steady conditions are reached, the air flowing at section 2 becomes saturated with water vapour. The temperature of the saturated air at section 2 is known as thermodynamic wet bulb temperature or adiabatic saturation temperature. The adiabatic saturation process is represented on T-s diagram as shown by the curve 1-2 in Fig. 20.4. The adiabatic saturation temperature is taken equal to the wet bulb temperature.

Let   t_d1 = DBT of initial unsaturated air

t_d2 = DBT of saturated air

     = adiabatic saturation temperature, t_w

h₁, h₂ = enthalpy of unsaturated and saturated air respectively

w₁, w₂ = specific humidity of air at sections 1 and 2 respectively

h_fw = sensible heat of water at adiabatic saturation temperature

For energy balance of air at inlet and outlet, we have

h₁ + (w₂ − w₁)h_fw = h₂

or   h₁ + wh_fw1 = h₂ + wh_fw1

Now   h₁ = h_a1 + w₁ h_s1

and  h₂ = h_a2 + w₂ h_s2

where  h_a1 = enthalpy of 1 kg dry air at DBT = t_d1 = c_pa t_d1

h_s1 = enthalpy of superheated vapour at t_d1 per kg of vapour

h_a2 = enthalpy of 1 kg dry air at WBT = t_w = c_pa t_d2

h_s2 = enthalpy of saturated vapour at WBT = t_w per kg of vapour

Thus, we get

(h_a1 + w₁h_s1) − w₁h_fw = (h_a2 + w₂h_s2) − w₂h_fw

w₁(h_s1 + h_fw) = w₂ (h_s2 + h_fw) + (h_a2 − h_a1)

Also  h₁ = c_pat_d1 + w₁h_s1

h₂ = c_pat_d2 + w₂h_s2

Figure 20.3 Adiabatic saturator

Figure 20.4 T-s diagram for adiabatic saturation process

where  h_s2 = h_f2 + h_fg2

h_s1 = h_s2 + c_pv (t_d1 − t_d2) = h_f2 + h_fg2 + c_pv (t_d1 − t_d2)

From the energy balance, we get

c_pat_d1 + w₁[h_f2 + h_fg2 + c_pv (t_d1 − t_d2)]+ (w₂ − w₁) h_f2

= c_pat_d2 + w₂ (h_f2 + h_fg2)

or  (c_pa + w₁ c_pv)t_d1 − (c_pa + w₂ c_pv)t_d2 = h_fg2 (w₂ − w₁)

where c_p1 and c_p2 are humid specific heats

If c_p1 = c_p2 = c_p, then

c_p (t_d1 − t_d2) = h_fg2 (w₂ − w₁)

Example 20.4

Atmospheric air at 1 bar enters the adiabatic saturator. The dry bulb temperature is 30°C and wet bulb temperature 20°C during adiabatic saturation process. Calculate the following:

1. Humidity ratio of entering air,
2. Vapour pressure and relative humidity at 30°C, and
3. Dew point temperature.

Solution

Given: p_b = 1 bar, t_d = 30°C, t_w = 20°C

1. Saturation pressure of vapour at 20°C, from steam tables is,p_v2 = 2.34 kPa or 0.0234 barEnthalpy of saturated vapour at 20°C, h_s2 = h_g2 = 2538.2 kJ/kgSensible heat of water at 20°C, h_fw = 83.9 kJ/kgEnthalpy of saturated vapour at 30°C, h_s1 = h_g1 = 2556.4 kJ/kgEnthalpy of 1 kg unsaturated air at t_d = 30°C,h_a1 =mc_pat_d =1×1.005×30 = 30.15kJ/kgEnthalpy of 1 kg saturated air at t_w = 20°C,h_a2 =mc_pat_w =1×1.005× 20 = 20.10 kJ/kg
2. Now  0.0107 − 0.0107 p_v1 = 0.622 p_v1p_v1 = 0.0169 barSaturation pressure corresponding to 30°C from steam tables is,p_s = 4.246 kPa or 0.04246 barRelative humidity,
3. Dew point temperature is the saturation temperature corresponding to the partial pressure of water vapour, p_v1 = 0.0169 bar or 1.69 kPaFrom steam tables, we havet_dp = 14.85°C