Drying adiabatic

With an inlet air temperature and humidity of 400 K and 0.01 kg/kg dry air respectively from Figure 13.4 in Volume 1, the inlet wet-bulb temperature = 312 K. If, not unreasonably, it is assumed that the number of transfer units is 1.5, then for adiabatic drying the outlet air temperature, To is given by ... 

There are three parameters in exponential collocation p N and a characteristic time, At. Different values of p have been used, and no difference has been observed p - 0 was used in the simulations that follow. The number of collocation points (N + 1) is equivalent to the reciprocal of the step size in finite difference methods the more points used, the greater is the accuracy, but the more time consuming the solution. The sensitivity of the solution to N and At is shown in Figure 2, which shows the movement of the combustion zone in an adiabatic dry ash gasifier when the throughput is reduced to 80% of full load at constant feed ratios. 

In view of the heat sensitivity of the solids, cocurrent operation will be used. The outlet gas temperature is found from Eq. (24.8) for adiabatic drying. Assume the number of transfer units is 1.5, The inlet wet-bulb temperature from Fig. 23.2, is 102°F. Since T j is 260°F, Eq. (24.8) gives... 

If the adiabatic dry air parcel is always in equilibrium with the atmosphere during its motion from the original position to the surface, the atmosphere by definition is neutral and its temperature profile satisfies (16.8). No matter where the air parcel starts in this atmosphere, it will always attain the same temperature when brought to the surface at pressure po- In other words, the potential temperature of the air parcel will not change during its motion and will always be equal to 0. The equilibrium of the air parcel with the surrounding environment means that the neutral atmosphere (or a neutral atmospheric layer) has the same potential temperature at all heights z and therefore dQ/dz = 0. Plots of altitude versus potential temperature for a neutral (adiabatic) atmosphere are vertical lines at 0 = 7b. 

Equation for falling-rate period. For the situation where unsaturated surface drying occurs, //(V is constant for adiabatic drying, the rate of drying is directly dependent upon X as in Eq. (9.7-9), and Eq. (9.10-32) applies. 

For the case where Y is constant, as for adiabatic drying of water into air, Eq. (12.50) becomes... 

For the special case where the bound moisture is negligible X = 0) and Y is constant (adiabatic drying), substitution of Eq. (12.54) and its differential... 

Fig. 8. Characteristic plume patterns where (--) represents dry-adiabatic lapse rate and (—), air (a) fanning (b) fumigation (c) lofting and (d) looping.

The Dravo hydrate addition at low temperature process involves a two-step injection of water and dry sorbent in a rectangular 19.8-m duct having a cross section of 2 m. In one step water is injected through atomization nozzles to cool the flue gas from 150°C to approximately a 15°C approach to adiabatic saturation. The other step involves the dry injection of hydrated lime, either downstream or upstream of the humidifica tion nozzles. Typical SO2 removals were 50—60% at a Ca S ratio of 2. 

Evaporative efficiency in a direct-heat dryer compares vaporization obtained to that which would be obtained if the drying gas were saturated adiabatically. 

In Figure 2 the lines, volume, m /kg dry air, indicate humid volume, which includes the volume of 1.0 kg of dry gas plus the volume of vapor it carries. Enthalpy at saturation data are accurate only at the saturation temperature and humidity however, for air—water vapor mixtures, the diagonal wet bulb temperature lines are approximately the same as constant-enthalpy adiabatic cooling lines. The latter are based on the relationship ... 

Cg = humid heat for humidity H in units of kj / (kg-K) and = latent heat of vaporization at / in kj /kg. The slope of the constant-enthalpy adiabatic cooling line is —C j which is the relationship between temperature and humidity of gas passing through a totally adiabatic direct-heat dryer. The humid heat of a gas—vapor mixture per unit weight of dry gas includes the specific heat of the vapor... 

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). 

Solution. Figure 12-8 shows the path on a psychrometric chart. The leaving dry-bulb temperature is obtained directly from Fig. 12-2 as 72.2 F. Since the spray water enters at the wet-bulb temperature of 70 F and there is no heat added to or removed from it, this is by definition an adiabatic process and there will be no change in wet-bulb temperature. The only change in enthalpy is that from the heat content of the makeup water. This can be demonstrated as follows ... 

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. 

However, away from the surface, processes frequently are adiabatic. For example, if a volume (parcel) of air is forced upward over a ridge, the upward-moving air will encounter decreased atmospheric pressure and will expand and cool. If the air is not saturated with water vapor, the process is called dry adiabatic. Since no heat is added or subtracted. Ah in Eq. (17-13) can be set equal to zero, and introducing the hydrostatic equation... 

Thus air cools as it rises and warms as it descends. Since we have assumed an adiabatic process, -ATIAz defines the dry adiabatic process lapse rate, a constant equal to 0.0098 K/m, is nearly 1 K/lOO m or 5.4°F/1000 ft. 

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