Temperature adiabatic saturation

In the system just considered, neither the humidity nor the temperature of the gas is appreciably changed. If the gas is passed over the liquid at such a rate that the time of contaci is sulficient for equilibrium to be established, the gas will become saturated and both phases will be brought to the same temperature. In a fhermally insulated system, the total sensible heat falls by an amount equal to the latent tost of die liquid evaporated. As a result of continued passage of the gas, the temperature of the liquid gradually approaches an equilibrium value which is known as the adiabatic samration temperature. 

These conditions are achieved in an infinitely tall thermally insulated humidification column through which gas of a given initial temperature and humidity flows 

Making a heat balance over the column, it is seen that the heat of vaporisation of the liquid must come from the sensible heat in the gas. The temperature of the gas falls from d to the adiabatic saturation temperature 0s, and its humidity increases from to Jf s (the saturation value at 0s). Then working on the basis of unit mass of dry gas  

In Chapter 12 it is shown teat when the Schmidt and Brandd numbers for a mixture of gas anri apour are approximately equal to unity, the Lewis relation applies, or  

For systems containing vapour other than that of water, s is only approximately equal to h/hoPA and the difference between the two quantities may be as high as 50 per cent. 

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Adiabatic-Saturation Temperature, or Constant-Entlialpy Lines.. . . 12-3... 

Relation between Wet-Bulb and Adiabatic-Saturation Temperatures.. 12-4... 

Adiabatic-Saturation Temperature, or Constant-Enthalpy Lines If a stream of air is intimately mixed with a quantity of water at a temperature t, in an adiabatic system, the temperature of the air will drop and its humidity will increase. If t, is such that the air leaving the system is in equihbrium with the water, t, will be the adiabatic-saturation temperature, and the line relating the temperature and humidity of the air is the adiabatic-saturation line. The equation for the adiabatic-saturation line is... 

RELATION BETWEEN WET-BULB AND ADIABATIC-SATURATION TEMPERATURES... 

Experimentally it has been shown that for air-water systems the value of Tj /Zc c, the psychrometric ratio, is approximately equal to 1. Under these conditions the wet-bulb temperatures and adiabatic-saturation temperatures are substantially equal and can be used interchangeably. The difference between adiabatic-saturation temperature and wet-bulb temperature increases with increasing humidity, but this effect is unimportant for most engineering calculations. An empirical formula for wet-bulb temperature determination of moist air at atmospheric pressure is presented by Liley [Jnt. J. of Mechanical Engineering Education, vol. 21, No. 2 (1993)]. 

For systems other than air-water vapor, the value of h /k c, may differ appreciably from unity, and the wet-bulb and adiabatic-saturation temperatures are no longer equal. For these systems the psychrometric ratio may be obtained by determining h /k from heat- and mass-transfer an ogies such as the Chilton-Colburn analogy [Ind. Eng. Chem., 26, 1183 (1934)]. For low humidities this analogy gives... 

Example 1 Compare Wet-Bulb and Adiabatic-Saturation Temperatures For tne air-water system at atmospheric pressure, the measured values of dry-bulh and wet-hulh temperatures are 85 and 72 F respectively. Determine the absolute humidity and compare the wet-bulb temperature and adiabatic-saturation temperature. Assume that h /k is given by Eq. (12-4). 

Values of andt, are given by the saturation curve of the psychrometric chart, such as Fig. 12-2. By trial and error, = 72.1 F, or the adiabatic-saturation temperature is 0.1 F higher than the wet-bulb temperature. 

Since the Schmidt number, Prandtl number, latent heat of vaporization, and humid heat are all essentially independent of pressure, the adiabatic-saturation-temperature and wet-bulb-temperature hues will be substantially equal at pressures different from atmospheric. 

Humidity charts for other solvent vapors may be prepared in an analogous manner. There is one important difference involved, however, in that the wet-bulb temperature differs considerably from the adiabatic-saturation temperatures for vapors other than water. 

The temperature driving force for drying is the difference between the drying-gas outlet temperature and, in the case of pure water, the gas wet-bulb temperature. In the case of a solution, the adiabatic saturation temperature of the pure saturated solution is employed rather than the wet-bulb temperature. 

Adiabatic saturation temperature The temperature attained after an adiabatic process. 

In order that hot condenser water may be re-used in a plant, it is normally cooled by contact with an air stream. The equipment usually takes the form of a tower in which the hot water is run in at the top and allowed to flow downwards over a packing against a countercurrent flow of air which enters at the bottom of the cooling tower. The design of such towers forms an important part of the present chapter, though at the outset it is necessary to consider basic definitions of the various quantities involved in humidification, in particular wet-bulb and adiabatic saturation temperatures, and the way in which humidity data are presented on charts and graphs. While the present discussion is devoted to the very important air-water system, which is in some ways unique, the same principles may be applied to other liquids and gases, and this topic is covered in a final section. 

Comparing equations 13.8 and 13.9, it is seen that the adiabatic saturation temperature i > equal to the wet-bulb temperature when s = h/hDpA. This is the case for most water vapour systems and accurately so when Jf = 0.047. The ratio (h/hopAs) = b is sometimes known as the psychrometric ratio and, as indicated, b is approximately unity for the air-water system. For most systems involving air and an organic liquid, b = 1.3 - 2.5 and the wet-bulb temperature is higher than the adiabatic saturation temperature. This was confirmed in 1932 by SHERWOOD and COMINGS 2 who worked with water, ethanol, n-propanol, n-butanol, benzene, toluene, carbon tetrachloride, and n-propyl acetate, and found that the wet-bulb temperature was always higher than the adiabatic saturation temperature except in the case of water. 

If an unsaturated gas is brought into contact with a liquid which is at the adiabatic saturation temperature of the gas, a simultaneous transfer of heat and mass takes place. The temperature of the gas falls and its humidity increases (Figure 13.2). The temperature of the liquid at any instant tends to change and approach the wet-bulb temperature corresponding to the particular condition of the gas at that moment. For a liquid other than water, the adiabatic saturation temperature is less than the wet-bulb temperature and therefore in the initial stages, the temperature of the liquid rises. As the gas becomes humidified, however, its wet-bulb temperature falls and consequently the temperature to... 

Figure 13.2. Saturation of gas with liquid other than water at the adiabatic saturation temperature...

When humidification is carried out in a packed column, the water which is not evaporated can be recirculated so as to reduce the requirements of fresh water. As a result of continued recirculation, the temperature of the water will approach the adiabatic saturation temperature of the air, and the air leaving the column will be cooled — in some cases to within 1 deg K of the temperature of the water. If the temperature of the air is to be maintained constant, or raised, the water must be heated. 

Two methods of changing the humidity and temperature of a gas from Aidj. JP x i to B(()2. J 2) may be traced on the humidity chart as shown in Figure 13.11. The first method consists of saturating the air by water artificially maintained at the dew point of air of humidity (line AC) and then heating at constant humidity to 82 (line CB). In the second method, the air is heated (line AD) so that its adiabatic saturation temperature corresponds with the dew point of air of humidity JP2- It is then saturated by water at the adiabatic saturation temperature (line DC) and heated at constant humidity to 82 (line CB). In this second method, an additional operation — the preliminary heating—is carried out on the air, hut the water temperature automatically adjusts itself to the required value. 

In a humidifier in which the make-up liquid is only a small proportion of the total liquid circulating, its temperature approaches the adiabatic saturation temperature 0S, and remains constant, so that there is no temperature gradient in the liquid. The gas in contact with the liquid surface is approximately saturated and has a humidity Jf... 

Calculations involving to systems where the Lewis relation is not applicable are very much more complicated because the adiabatic saturation temperature and the wet-bulb temperature do not coincide. Thus the significance of the adiabatic cooling lines on the psychrometric chart is very much restricted. They no longer represent the changes which take place in a gas as it is humidified by contact with liquid initially at the adiabatic saturation temperature of the gas, but simply give the compositions of all gases with the same adiabatic saturation temperature. 

For water, numerically C — hfk, so that the wet bulb and adiabatic saturation temperatures are identical. For other vapors this conclusion is not correct. 

The wet bulb temperature Tw is attained by measurement under standardized conditions. For water, Tw is numerically nearly the same as the adiabatic saturation temperature Ts. 

The adiabatic saturation temperature Ts is the temperature attained if the gas were saturated by an adiabatic process. 

Similarly, if the gas enters at 120°C, at the exit we would find 10 percent of the differential above the adiabatic saturation temperature. For an adiabatic saturation temperature of 70°C, the exit gas temperature would be... 

For an entry temperature of 120°C and an adiabatic saturation temperature of 70°C, the expected outlet temperature would be... 

Parametric studies in spray dryer pilot plants have demonstrated that the main variable affecting S02 removal in the bag filters, besides the stoichiometric ratio of Ca(0H>2 to SO2, is the approach to the adiabatic saturation temperature of the flue gases... 

The approach to the adiabatic saturation temperature in turn is correlated with the moisture content of the solids. Additives that will modify the moisture content of the Ca(0H)2 solids in equilibrium with a gas phase of a given relative humidity would then be expected to change the reactivity of the Ca(0H)2 towards S02. 

As shown in the results section, the relative humidity of the gaseous phase is the most important variable in the reaction of SO2 with dry Ca(0H)2 solids. These results are in agreement with results reported in the literature for SO2 removal in the bag filters of spray dryer pilot and commercial plants C3, 5-9). In the spray dryer plants, the moisture content of the gases is normally indicated as approach to the adiabatic saturation temperature (difference between the temperature of the gas and the adiabatic saturation temperature) rather than relative humidity. 

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