**3. Results**

Since the active desiccant dehumidification is an isenthalpic process, it is not possible to establish a definition for the efficiency based on enthalpy. Accordingly, it is usual do define a dehumidification effectiveness as

*dw*

*ci co*

*Y Y*

Fig. 9. Effectiveness-NTU chart, P\*=10.0

The non-dimensional position defined by Eq. (5) has a remarkable similarity to the NTU parameter, commonly found in heat exchanger analysis. Accordingly, Figure (9) shows the influence of the micro-channel lentgh over the dehumidification effectiveness. It can be seen that the regeneration temperature has a significant influence over the moisture removal. Figure (9) shows the existence of an optimum micro-channel length, which can be explained by observing that the regeneration stream is admitted at x\* = 0. Accordingly, the closer the position is to the end of the channel (x\* =10.0), the lower will be the temperature, allowing for some of the moisture to be re-sorbed by the desiccant felt (Zhang et al., 2003). Figure (10) shows that, for higher non-dimesional periods of revolution P\*, the optimum length is higher, due to the longer exposure to to regeneration stream and consequential higher average temperatures along the desiccant felt. Figure (11) shows the influence of the nondimensional period of revolution over the effectiveness as a function of the regeneration temperature. It can be seen that for a moderate value for the non-dimensional period (P\* = 10.0), the effectiveness is oblivious to an increase in regeneration temperature, due to an

Since the active desiccant dehumidification is an isenthalpic process, it is not possible to establish a definition for the efficiency based on enthalpy. Accordingly, it is usual do define

*dw*

*ci co*

*ci Y Y Y* 

0 2 4 6 810 non-dimensional position, x\*

The non-dimensional position defined by Eq. (5) has a remarkable similarity to the NTU parameter, commonly found in heat exchanger analysis. Accordingly, Figure (9) shows the influence of the micro-channel lentgh over the dehumidification effectiveness. It can be seen that the regeneration temperature has a significant influence over the moisture removal. Figure (9) shows the existence of an optimum micro-channel length, which can be explained by observing that the regeneration stream is admitted at x\* = 0. Accordingly, the closer the position is to the end of the channel (x\* =10.0), the lower will be the temperature, allowing for some of the moisture to be re-sorbed by the desiccant felt (Zhang et al., 2003). Figure (10) shows that, for higher non-dimesional periods of revolution P\*, the optimum length is higher, due to the longer exposure to to regeneration stream and consequential higher average temperatures along the desiccant felt. Figure (11) shows the influence of the nondimensional period of revolution over the effectiveness as a function of the regeneration temperature. It can be seen that for a moderate value for the non-dimensional period (P\* = 10.0), the effectiveness is oblivious to an increase in regeneration temperature, due to an

Treg = 80C

Treg = 100C

Treg = 120C

Treg = 60C

**3. Results** 

a dehumidification effectiveness as

0

Fig. 9. Effectiveness-NTU chart, P\*=10.0

0.2

0.4

dw

0.6

Fig. 10. Effectiveness-NTU chart, P\*=80.0

Fig. 11. Influence of P\*, NTU=10.0, Thi = 100°C

Mathematical Modelling of Air Drying by Adiabatic Adsorption 81

Thi = 50<sup>C</sup>

Fig. 13. Influence of Thi on the Humidity Distribution, NTU=16.0, P\* = 40.0

0 0.2 0.4 0.6 0.8 1 Non-Dimensional Position, X\*

P\* = 10.0

0 0.2 0.4 0.6 0.8 1 Non-Dimensional Position, x\*

Fig. 14. Influence of P\* on the Humidity Distribution, NTU=10.0, Thi = 100°C

Thi = 90<sup>C</sup>

P\* = 40.0

0

0

0.1

Solid Humidity 0.2

 Content,

 W(x\*)

0.3

0.4

0.2

Solid Humidity

 Content,

 W(x\*)

0.4

0.6

insufficient exposure to the hot source. Accordingly, larger values for P\* will benefit from increased regeneration temperatures. Figure (12), however, shows that the dehumidification effectiveness will decrease after it reaches a maximum value, since for an infinite value for P\* there would be no rotation and the heat and mass transport would completely cease.

Figure (13) shows the humidity distribution within the desiccant felt at the onset and at the end of the adsorptive process, for different regeneration temperatures. The area enclosed by these curves is a measure of the dehumidifying capacity of the equipment. It can be seen that the higher temperature enables a thorough drying of the material, resulting in a enhaced dehumidification capacity. Interesting to observe that different shapes for the moisture distribution arise, depending on the case. For the mild regeneration temperature, the moisture uptake is almost uniform aling x\*, resulting in a smooth curve. Conversely, for the higher temperature, the moisture uptake is much more significant at the second half of the total length, as compared to the first half, resulting in an curve with exponential characteristic.

Figure (14) shows the humidity distribution within the desiccant felt at the onset and at the end of the adsorptive process, for different non-dimensional periods of revolution. It can be seen that for P\* =10.0, the exposure to the regeneration stream is insufficient, resulting in a diminished dehumidification capacity, as the curves of minimum and maximum moisture content are undistinguishable. For a increased value of P\*, represented by the dashed lines, the dehumidification capacity is enhanced, as illustrated by the greater enclosed area.

Fig. 12. Influence of P\*, NTU=10.0.

insufficient exposure to the hot source. Accordingly, larger values for P\* will benefit from increased regeneration temperatures. Figure (12), however, shows that the dehumidification effectiveness will decrease after it reaches a maximum value, since for an infinite value for P\* there would be no rotation and the heat and mass transport would completely cease. Figure (13) shows the humidity distribution within the desiccant felt at the onset and at the end of the adsorptive process, for different regeneration temperatures. The area enclosed by these curves is a measure of the dehumidifying capacity of the equipment. It can be seen that the higher temperature enables a thorough drying of the material, resulting in a enhaced dehumidification capacity. Interesting to observe that different shapes for the moisture distribution arise, depending on the case. For the mild regeneration temperature, the moisture uptake is almost uniform aling x\*, resulting in a smooth curve. Conversely, for the higher temperature, the moisture uptake is much more significant at the second half of the total length, as compared to the first half, resulting in an curve with exponential

Figure (14) shows the humidity distribution within the desiccant felt at the onset and at the end of the adsorptive process, for different non-dimensional periods of revolution. It can be seen that for P\* =10.0, the exposure to the regeneration stream is insufficient, resulting in a diminished dehumidification capacity, as the curves of minimum and maximum moisture content are undistinguishable. For a increased value of P\*, represented by the dashed lines, the dehumidification capacity is enhanced, as illustrated by the greater enclosed area.

> 0 200 400 600 800 1000 non-dimensional period P\*

Treg = 60C Treg = 100C

characteristic.

0

Fig. 12. Influence of P\*, NTU=10.0.

0.2

0.4

dw

0.6

0.8

Fig. 13. Influence of Thi on the Humidity Distribution, NTU=16.0, P\* = 40.0

Fig. 14. Influence of P\* on the Humidity Distribution, NTU=10.0, Thi = 100°C

Mathematical Modelling of Air Drying by Adiabatic Adsorption 83

greater amount of energy to remove the water vapour during the desorptive period. This could be of vital importance for the economic feasibility of this technology, unless an

inexpensive thermal source is available.

Cwr wall specific heat (kJ/Kg K)

h heat transfer coefficient (KW/m2)

Y air absolute humidity (kg/kg air)

YL adsorbed air layer absolute humidity (kg/kg air)

W desiccant humidity content (kg of moisture/kg of desiccant)

hy convective mass transfer coefficient (kg/m2s)

dh hydraulic diameter (m) f desiccant mass fraction

H enthalpy of air (kJ/kg) L length of the wheel (m) *m*<sup>1</sup> air mass flow rate (kg/s) mw mass of the wall (kg) P period of revolution Patm atmospheric Pressure (Pa) Pws saturation pressure (Pa) Q heat of adsorption (kJ/kg)

**5. Nomenclature**  a constant c constant

d constant

t time (s)

**Greek letters** 

**Subscripts** 

1 air **Superscript** 

T temperature (C) u air flow velocity (m/s)

x coordinate (m)

effectiveness

ci cold inlet co cold outlet hi hot inlet ho hot outlet sat saturation

1 auxiliary parameter 2 auxiliary parameter

w desiccant channel wall

**\*** non-dimensional

w relative humidity of air layer

Bearing in mind that the outside air atmospheric conditions can present a significant variation throughout the day, it is usefull to define a dynamic control for the desiccant rotor operation. For instance, supposing a steady increase of 30% in outside air relative humidity, how much would be the required increase in P\*, so as to obtain a constant humidity at the process air stream outlet? Figure (15) shows the results for different increasing values for the regeneration temperature. It can be seen that for T = 60°C, an increase in 10% of the process air stream inlet will require the period of revolution to double, being unable to respond to a further increase of the relative humidity. Conversely, a higher regeneration temperature such as T = 100°C will only require a small increase in the period P\*, being able to respond to a relative humidity of process air stream inlet as high as 90%.

Fig. 15. Required increase in P\*=10.0

### **4. Conclusion**

A mathematical model for the heat and mass transfer on a hygroscopic material was developed, and resulting set of partial differential equations was solved using the finitevolume technique. The results showed that the process air stream outlet condition is strongly influenced by the regeneration temperature, as well as of the non-dimensional period of revolution. It was also shown that an increase on the outside air humidity can be easily handled by increasing the non-dimensional period of revolution, as long as a temperature of regeneration of at least 100°C is provided. The results for the humidity distribution along the desiccant felt show that the moisture removal capacity of silica-gel is limited, which opens an opportunity for the application of more selective materials. However, it shouldn´t be disregarded that a greater affinity to water vapour also implies a greater amount of energy to remove the water vapour during the desorptive period. This could be of vital importance for the economic feasibility of this technology, unless an inexpensive thermal source is available.
