7. Effect of the wall temperature TW

The effect of the wall temperature TW on the liquid film thickness and the condensing mass flux is presented in Figure 11. It is noted that the thickness of the liquid film varies inversely with the imposed temperature of the wall. Clearly, there is a significant growth of the liquid film thickness when TW reduces from 35C to 5C because the amount of the condensed vapour is enhanced along the tube by the increase of the heat transfer and hence the thickness of the

Computational Study of Liquid Film Condensation with the Presence of Non-Condensable Gas in a Vertical Tube http://dx.doi.org/10.5772/intechopen.76753 71

Figure 11. Effect of TW on the evolution of the liquid film thickness and the condensing mass flux at the interface.

Figure 12. Effect of TW on the accumulated condensation along the tube.

This result is confirmed in Figure 10, which shows that the thickness of the film increases considerably from the inlet to the exit of the tube. It is also observed that the increase in the mass fraction of water vapour w0 considerably improves the condensation mechanism along the tube. Indeed, for a constant T0, an increase of w0 affects the thermo-physical properties of the gas mixture at the inlet, which leads to an augmentation of the vapour partial pressure and the temperature at the vapour-liquid interface. Consequently, the condensing mass flux at the interface J" increases significantly with w0 leading to an increase in the rate of condensation, which improves the thickness of the liquid film. On the other hand, a small amount of w0 (inversely proportional to the mass fraction of the non-condensable gas) causes a remarkable reduction of the condensed mass flux rate and the axial variation of the thickness of the film along the tube. This is due to the presence of air, which plays the role of thermal and mass

Figure 10. Effect of the inlet vapour mass fraction on the variation of the liquid film thickness and the condensing mass

The effect of the wall temperature TW on the liquid film thickness and the condensing mass flux is presented in Figure 11. It is noted that the thickness of the liquid film varies inversely with the imposed temperature of the wall. Clearly, there is a significant growth of the liquid film thickness when TW reduces from 35C to 5C because the amount of the condensed vapour is enhanced along the tube by the increase of the heat transfer and hence the thickness of the

transfer resistance at the vapour-liquid interface.

flux at the interface.

70 Desalination and Water Treatment

7. Effect of the wall temperature TW

liquid film becomes thicker. From this figure, it is also observed that the condensing mass flux is important for a large value of the inlet-to-wall temperature difference and then decreases along the tube. The results indicate that J" decreases as the gas flow progresses along the tube because the condensation is accompanied by a diminution in the temperature of the vapour phase and the heat transferred by the latent mode during the condensation to the liquid film. The effect of wall temperature on the accumulated condensation mcd is illustrated in Figure 12. It can be seen that mcd becomes important for low temperatures. When the temperature difference (T0 - TW) increases, the heat transfer increases, and consequently the density of the condensed flux increases. This explains why the condensation process is favoured for a highertemperature difference.

tube. For a fixed w0, P0 and Re0, an increase in the molar mass of the gas leads to a growth in the density of the gas mixture, the temperature of the gas mixture, as well as a decrease in the saturation concentration especially for water-oxygen mixture. This causes a strong vapour concentration gradient and condensing mass flux at the vapour-liquid interface. The results obtained show that the evolution of the film thickness and condensing mass flux in the wateroxygen mixture are significantly greater than those of the other mixtures. In addition, the condensing mass flux decreases along the tube and tends to a lower value especially near to

Computational Study of Liquid Film Condensation with the Presence of Non-Condensable Gas in a Vertical Tube

http://dx.doi.org/10.5772/intechopen.76753

73

A numerical analysis has been carried out to investigate the liquid film condensation of the water vapour with the presence of non-condensable gas inside a vertical tube. The main

1. The efficiency of the system is enhanced by increasing the tube length and decreasing the

3. Decreasing the wall temperature enhances the liquid film thickness and the accumulated

radius, which allows condensing the maximum of the water vapour.

2. A small amount of non-condensable gas improves the heat and mass exchanges.

4. The non-condensable gas type has a great effect on the condensation process.

)

the tube exit, which means the end of the condensation process.

conclusions drawn from this study are as follows:

. K<sup>1</sup> )

)

. s<sup>1</sup> )

9. Conclusion

condensation.

Nomenclature

Cp specific heat (J. kg<sup>1</sup>

L tube length (m)

T temperature (C) u axial velocity (m. s<sup>1</sup>

D diffusion coefficient (m<sup>2</sup>

d diameter of the tube (m)

Nus sensible Nusselt number

mcd accumulated condensation P atmospheric pressure (Pa)

R radius of the tube (d/2) (m)

g gravitational acceleration (m. s<sup>2</sup>

#### 8. Effect of the non-condensable gas type

In thermal desalination units, when the water vapour condenses, the presence of a noncondensable gas hinders this phenomenon. The accumulation of non-condensable components at the vapour-liquid interface plays the role of an obstacle for heat and mass transfer. This causes a reduction in the efficiency of the system and therefore an increase in costs in most desalination units using phase change.

In this section, we analyse the influence of the non-condensable gas type during water vapour condensation. We considered mixed mixtures of water-oxygen, water-air and water- nitrogen. The molar mass of oxygen, air and nitrogen are equal to 31.99, 28.95 and 28.01 g/mol, respectively. Since the liquid film thickness δ and the condensing mass flux at the interface J" determine the condensation efficiency, Figure 13 illustrates the variation of δ and J" along the

Figure 13. Effect of the type of non-condensable gas on the evolution of the liquid film thickness and the condensing mass flux at the interface along the tube.

tube. For a fixed w0, P0 and Re0, an increase in the molar mass of the gas leads to a growth in the density of the gas mixture, the temperature of the gas mixture, as well as a decrease in the saturation concentration especially for water-oxygen mixture. This causes a strong vapour concentration gradient and condensing mass flux at the vapour-liquid interface. The results obtained show that the evolution of the film thickness and condensing mass flux in the wateroxygen mixture are significantly greater than those of the other mixtures. In addition, the condensing mass flux decreases along the tube and tends to a lower value especially near to the tube exit, which means the end of the condensation process.
