Adiabatic-Saturation Curves

In the special case where the gas-vapor mixture leaves saturated, and therefore at conditions Tas, YJ, Hj, and the liquid enters at temperature Tas, equation (8-7) can be written as (Treybal, 1980) 

It can be shown (see Problem 8.1) that the quantity in brackets in equation (8-9) is the latent heat of evaporation of the liquid A at the temperature Tas, X. Consequently, 

To solve equation (8-10) for the adiabatic saturation temperature requires a trial-and-error procedure since Y and A are functions of T.  

Air at 356 K, Y = 0.03 kg water/kg dry air, and 1 atm is contacted with water at the adiabatic saturation temperature until it becomes saturated. What are the final temperature and humidity of the air  

To solve equation (8-10), the latent heat of vaporization of water and the absolute humidity of saturated mixtures of air-water vapor must be expressed in terms of the saturation temperature. The method proposed by Watson (Smith et al., 1996) for the latent heat (see Example 2.11) and the Antoine equation combined with equation (8-2) for the humidity are used. The trial-and-error procedure required to solve equation (8-10) for T is easily implemented using the solve block feature of Mathcad as 

---

For problem 3.9 derive the relationship for the adiabatic saturation curve for the system. 

From the psychrometric chart (Figure 2.5), follow the adiabatic saturation curve for tw = 95°F down to the dry-bulb temperature 165°F, where... 

This is the equation of the adiabatic saturation curve, which passes through the points (Mas, Tas) on the 100% saturation curve and (J/i, TGl). Note that... 

The outlet temperature and humidity determined in this manner are represented by a point on the psychrometric chart. If a lower value of Ts is assumed, a higher outlet humidity would be calculated, yielding another point on the chart. The set of ail such points for a specified and m i th defines a curve on the chart, known as the adiabatic saturation curve. If the three stated assumptions are valid, the final state of air undergoing an adiabatic humidification must lie on the adiabatic saturation curve that passes through the inlet state on the psychrometric chart. 

If the outlet temperature is low enough, the air leaves saturated with water. The temperature corresponding to this condition is called the adiabatic saturation temperature and is found at the intersection of the adiabatic saturation curve with the 100% relative humidity curve. 

The psychrometric chart for most gas-liquid systems would show a family of adiabatic saturation curves in addition to the families of curves shown on Figures 8.4-1 and 8.4-2. However, for the air-tvater system at 1 atm, the adiabatic saturation curve through a given state coincides with the constant wet-bulb temperature line through that state, so that Tas = Twb- The simple material and energy balance procedure for adiabatic cooling outlined in this section is possible only because of this coincidence. 

Also plotted on the psychrometric chart are a family of adiabatic saturation curves. The operation of adiabatic saturation is indicated schematically in Figure 1.5. The entering gas is contacted with a liquid and as a result of mass and heat transfer between the gas and liquid the gas leaves at conditions of humidity and temperature different from those at the entrance. The operation is adiabatic as no heat is gained or lost by the surroundings. Doing a mass balance on the vapor results in... 

Equation 1.41 represents the adiabatic saturation curve on the psychrometric chart, which passes through the points A(Fgs, Tqs) on the 100% saturation curve (y/= 1) andB(Fi , TJ, the initial condition. Since the humid heat contains the term Fin, the curve is not straight but is curved slightly concave upward. Knowing the adiabatic saturation temperature and the actual gas temperature, the actual gas humidity can be easily obtained as the absolute humidity from the saturation locus. Equation 1.40 indicates that the sensible heat given up by the gas in cooling equals the latent heat required to evaporate the added vapor. It is important to note that, since Equation 1.41 is derived from the overall mass and energy balances between the initial gas conditions and the adiabatic... 

It is worthwhile pointing out here that, although the adiabatic saturation curve equation does not reveal anything of the enthalpy-humidity path of either the liquid phase or gas phase at various points in the contacting device (except for the air-water vapor system), each point within the system must conform with the wet bulb relation, which requires that the heat transferred be exactly consumed as latent heat of vaporization of the mass of liquid evaporated. The identity of hc/K with CpY was first found empirically by Lewis and hence is called the Lewis relation. The treatment given here on the wet bulb temperature applies only in the limit of very mild drying conditions when the vapor flux becomes directly... 

Lines -----Adiabatic saturation curves (wet bulb temperature)... 

Solution The wet bulb temperature of 29.5°C can be assumed to be the same as the adiabatic saturation temperature 7, as discussed. Following the adiabatic saturation curve of 29.5°C until it reaches the dry bulb temperature of 60°C, the humidity is H = 0.0135 kgHjO/kg dry air. 

Wet-bulb temperature is the equilibrium temperature reached by a small amount of liquid evaporating adiabatically into a large volume of gas. Equilibrium exists when the rate of heat transfer from the gas to the cooler liquid equals that consumed by evaporation. It is affected by heat and mass transfer coefficients as well as humidity, therefore is dependent on maintaining turbulent gas flow around the bulb. Humidity can be determbied from wet-bulb, and dry-bulb, T, temperatures by following the adiabatic-saturation curves on a psychrometric chart, or by... 

As another alternative tine DF is drawn parallel to the adjacent adiabatic-saturation curves. At F, the enthalpy is 134 kJ/kg dry air, or nearly the same as at D. 

The psychrometric chart (Fig. 7.5) for air-water contains a family of adiabatic-saturation curves, as previously noted. Each point on the curve represents a mixture whose adiabatic-saturation temperature is at the intersection of the curve with the 100 percent humidity curve. 

Solution The pjoint representing the original air is located on the psychrometric chart (Fig. 7.5a). The adiabatic-saturation curve through the point reaches the 100% saturation curve at 40 C, the adiabatic-saturation temperature. This is the water temperature. On this curve, 90% saturation occurs at 4I.5°C, Y = 0.0485 kg water/kg air, the outlet-air conditions. 

I The adiabatic-saturation curve is nearly one of constant enthalpy per unit mass of dry gas. As Eq. (7.16) indicates, differs from by the enthalpy of the evaporated liquid at its entering temperature i , but this difference is usually unimportant. 

It will be noted that Eq. (7.26) is identical wth Eq. (7.21) for the adiabatic-saturation temperature, but with replacement of si by ftQ/ky. These are nearly equal for air-water vapor at moderate humidities, and for many practical purposes the adiabatic-saturation curves of Fig, 7,5 can be used instead of Eq. (7.26). This is not the case for most other systems. 

With the same adiabatic-saturation curve as before, tgj = 34.0 C. 

IS An air-water-vapor mixture, 1 std atm, 180 C, flows in a duct (wall temperature 180 Q at 3 m/s average velocity. A wet-bulb temperature, measured with an ordinary, unshielded thermometer covered with a wetted wick (9.5 mm outside diameter) and inserted in the duct at right angles to the duct axis, is-52 C. Under these conditions, the adiabatic-saturation curves of the psychromctric chart do not approximate wet-bulb lines, radiation to the wet bulb and the effect of mass transfer on heat transfer are not negligible, and the k-type (rather than F) mass-transfer coefficients should not be used. 

Prepare a psychromctric chart for the mixture acetone-nitrogen at a pressure of 800 mmHg over the ranges —15 to 60 C, T = 0 to 3 kg vapor/kg diy gas. Include the following curves, all plotted against temperature (a) 100, 75, SO, and 25% humidity (b) dry and saturated humid volumes (c) enthalpy of dry and saturated mixtures expressed as N m/kg dry gas, referred to liquid acetone and nitrogen gas at — 15 C (d) wet-bulb curves for 25 C (e) adiabatic-saturation curves... 

---