Author details

Alberto M. Pernía\*, Miguel J. Prieto, Juan A. Martín-Ramos, Pedro J. Villegas and Francisco J. Álvarez-González

\*Address all correspondence to: amartinp@uniovi.es

University of Oviedo, Gijón, Spain

## References

The green plot determines the average of the optimal current during the whole energy trans-

Figure 18. System efficiency operating at optimum current (red) and average optimum current during the energy

The efficiency improvement depends on the CDI cell geometry and the salt concentration (M) because these magnitudes condition the values of the parameters that define the electrical model of the cell. Actual measurements confirmed that, by applying this control strategy, the efficiency was improved by 10% in most of the cases as compared to that obtained when using

The method presented allows the electrical characterization of the CDI cell in terms of salt concentration in the water and cell geometry. A model proposed is based only on three parameters RP, RS, C, which simplifies mathematical calculations. Using this electrical model

ference process (right-hand scale).

Figure 17. Optimum current iLmax estimated.

52 Desalination and Water Treatment

6. Conclusions

transference (green).

a constant current value during the charge/discharge process.


[8] Li H, Zou L. Ion-exchange membrane capacitive deionization: A new strategy for brackish water desalination. Desalination. 2011;275(1-3):62-66

**Chapter 4**

Provisional chapter

**Computational Study of Liquid Film Condensation with**

DOI: 10.5772/intechopen.76753

Computational Study of Liquid Film Condensation with

the Presence of Non-Condensable Gas in a Vertical Tube

The main objective of this chapter is to study the liquid film condensation in a thermal desalination process, which is based on the phase change phenomenon. The external tube wall is subjected to a constant temperature. The set of the non-linear and coupled equations expressing the conservation of mass, momentum and energy in the liquid and gas mixtures is solved numerically. An implicit finite difference method is employed to solve the coupled governing equations for liquid film and gas flow together with the interfacial matching conditions. Results include radial direction profiles of axial velocity, temperature and vapour mass fraction, as well as axial variation of the liquid film thickness. Additionally, the effects of varying the inlet conditions on the phase change phenomena are examined. It was found that increasing the inlet-to-wall temperature difference improves the condensate film thickness. Decreasing the radius of the tube increased the condensation process. Additionally, non-condensable gas is a decisive factor in reducing the efficiency of the heat and mass exchanges. Overall, these parameters are relevant

Keywords: thermal process, vapour-gas mixtures, condensation, heat and mass transfer,

The demand of fresh water supply is increasing due to the economic development and the fast population growth. With limited resources of fresh water, desalination of seawater and brackish water offers the potential to encounter the increasing water demands around the world. Generally, the reverse osmosis has about the great part of the market share in the world

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

factors to improve the effectiveness of the thermal desalination units.

**the Presence of Non-Condensable Gas in a Vertical**

**Tube**

Adil Charef, M'barek Feddaoui,

Adil Charef, M'barek Feddaoui,

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

Abstract

phase change

1. Introduction

Abderrahman Nait Alla and Monssif Najim

Additional information is available at the end of the chapter

Abderrahman Nait Alla and Monssif Najim

Additional information is available at the end of the chapter


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

DOI: 10.5772/intechopen.76753

Adil Charef, M'barek Feddaoui, Abderrahman Nait Alla and Monssif Najim Abderrahman Nait Alla and Monssif Najim Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

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

Adil Charef, M'barek Feddaoui,

#### Abstract

[8] Li H, Zou L. Ion-exchange membrane capacitive deionization: A new strategy for brack-

[9] Hassanvanda A, Chenb GQ, Webleya PA, Sandra E. Kentish improvement of MCDI operation and design through experiment and modelling: Regeneration with brine and

[10] Niu R, Yang H. Modeling and identification of electric double-layer supercapacitors. ICRA

[11] Spyker RL, Nelms RM. Classical equivalent circuit parameters for a double-layer capacitor. IEEE Transactions on Aerospace and Electronic Systems. Jul. 2000;36(3):829-836 [12] Hemmatifar A, Stadermann M, Santiago JG. Two-dimensional porous electrode model for capacitive deionization. The Journal of Physical Chemistry C. 2015;119(44):24681-

[13] Pernia AM, Norniella JG, Martin-Ramos JA, Diaz J, Martinez JA. Up-down converter for energy recovery in a CDI desalination system. IEEE Transactions on Power Electronics.

[14] Álvarez-González FJ, Martín-Ramos JA, Díaz J, Martínez JA, Pernía AM. Energy-recovery optimization of an experimental CDI desalination system. IEEE Transactions on Indus-

ish water desalination. Desalination. 2011;275(1-3):62-66

Communications. Feb. 2011:1-4

July 2012;27(7):3257-3265

trial Electronics. March 2016;63(3):1586-1597

24694

54 Desalination and Water Treatment

optimum residence time. Desalination. September 2017;417(1):36-51

The main objective of this chapter is to study the liquid film condensation in a thermal desalination process, which is based on the phase change phenomenon. The external tube wall is subjected to a constant temperature. The set of the non-linear and coupled equations expressing the conservation of mass, momentum and energy in the liquid and gas mixtures is solved numerically. An implicit finite difference method is employed to solve the coupled governing equations for liquid film and gas flow together with the interfacial matching conditions. Results include radial direction profiles of axial velocity, temperature and vapour mass fraction, as well as axial variation of the liquid film thickness. Additionally, the effects of varying the inlet conditions on the phase change phenomena are examined. It was found that increasing the inlet-to-wall temperature difference improves the condensate film thickness. Decreasing the radius of the tube increased the condensation process. Additionally, non-condensable gas is a decisive factor in reducing the efficiency of the heat and mass exchanges. Overall, these parameters are relevant factors to improve the effectiveness of the thermal desalination units.

Keywords: thermal process, vapour-gas mixtures, condensation, heat and mass transfer, phase change

#### 1. Introduction

The demand of fresh water supply is increasing due to the economic development and the fast population growth. With limited resources of fresh water, desalination of seawater and brackish water offers the potential to encounter the increasing water demands around the world. Generally, the reverse osmosis has about the great part of the market share in the world

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

compared to thermal desalination technologies. Consequently, the necessity to improve the thermal processes, which are based on the phase change phenomenon of evaporation and condensation, continues to receive a high interest. Condensation on the cooling surfaces is a phenomenon of major significance in the chemical industries, refrigeration, heat exchangers and desalination units, including thermal desalination.

Merouani et al. [12] presented a numerical analysis during the condensation of steam-gas mixtures between two coaxial cylinders. They observed that a higher vapour concentration at the inlet and molar mass of the non-condensable gas increases the heat flux at the inner wall. Qiujie et al. [13] presented a numerical study in the case of steam-air condensation on isothermal vertical plate by using volume of fluid (VOF) method. Their results indicate that the mass fraction variation of the non-condensable gas directly affects the liquid film condensation and

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

57

In the thermal desalination unit, the condenser is used for producing freshwater from the saline water sources. In fact, in order to enhance the condensation process with the presence of non-condensable gas in thermal seawater desalination processes, many studies have been conducted. Semiat and Galperin [14] found from steam condensation that even a small air mass fraction decreases the heat transfer coefficient in seawater desalination plant. Al-Shammari et al. [15] have shown from an experimental study that non-condensable gas has a negative effect on the heat transfer. An experimental study on the role of non-condensable gases in the condensation of steam inside slightly inclined tubes was presented by Caruso et al. [16]. The experiments were carried out under the following conditions: inner diameter of the tube 12.6 and 26.8 mm, inclination of the tube 7, mass fraction of the non-condensable gas between 5 and 42%, and vapour saturated at atmospheric pressure. Due to the gravity, the condensate is collected mainly in the lower part of the tube. They also developed a correlation to calculate the local condensation heat transfer coefficient. Hassaninejadfarahani et al. [17] investigated numerically a liquid film condensation with high amount of non-condensable gas inside vertical tube. They examined the effects of varying the inlet air mass fraction, the inlet relative humidity, the inlet Reynolds number and the radius of the tube on the simultaneous heat and mass transfer during condensation. Recently, Charef et al. [18] investigated the condensation process of water vapour-air into liquid film inside a vertical tube under two different boundary conditions: imposed temperature and imposed heat flux. The results indicated a better condensation process under imposed heat flux. It was found that the presence of

The purpose of this study is to numerically develop and investigate the problem of water vapour condensation in the presence of non-condensable gas in a vertical tube. In order to improve the effectiveness of the steam condensation in desalination process, special attention is addressed to examine the effects of the tube geometry and the inlet conditions on the condensation process. In the following, we present the studied problem, the numerical method

The geometry under consideration is a vertical tube with length L and radius R (Figure 1). The tube wall is subjected to a constant temperature. A mixture of water vapour and non-

then influences the heat transfer.

and the main results.

2. Mathematical model

2.1. Physical model and assumptions

non-condensable gas affects negatively the system efficiency.

The mechanism of condensation can be classified by various ways: geometric configurations like tube, channel, internal, external, horizontal or vertical; species of fluid such as steam, refrigerant or mixture with the presence of non-condensable gas; condensing phenomena as filmwise, dropwise or fog; and flow regime like laminar and turbulent. Since the first analysis of Nusselt [1] for film condensation on a vertical plate, a numerous number of studies have been done on improving film condensation modelling and to contribute to the comprehension of this complex phenomenon. Lebedev et al. [2] performed experimentally a combined study of heat and mass transfer from water vapour on a flat plate. They observed an enhancement of the condensation heat transfer with the increase of the inlet relative humidity. Dobran and Thorsen [3] studied the laminar filmwise condensation of a saturated vapour inside a vertical tube. They found that the mechanism of condensation is governed by ratio of vapour to liquid viscosity, Froude number to Reynolds number ratio, subcooling number and Prandtl number of liquid. Siow et al. [4, 5] presented a numerical study of the laminar film condensation with the presence of non-condensable gas in horizontal and then in vertical channels. They analysed the effect of the inlet Reynolds number, the inlet pressure and the inlet-to-wall temperature difference on the condensation mechanism. They studied also the liquid film condensation from steam-air mixtures inside a vertical channel. Results indicate that a higher concentration of non-condensable gas caused substantial reduces in the local Nusselt number, the pressure gradient and the film thickness. Belhadj et al. [6] conducted a numerical analysis to improve the condensation process of water vapour inside a vertical channel. Their results show that the phenomenon of phase change is sensitive to the inlet temperature of liquid film. For different values of the system parameters at the inlet of the tube, Dharma et al. [7] estimated from a numerical study the local and average values of Nusselt number, the pressure drop, the condensate Reynolds number and the gas-liquid interface temperature. Lee and Kim [8] carried out experimental and analytical studies to analyse the effect of the non-condensable gas (nitrogen) on the condensation of water vapour along a vertical tube with a small diameter. The experimental results demonstrate that the heat transfer coefficients become important with a high inlet vapour flow and the reduction of mass fraction of nitrogen. In addition, the authors developed a new correlation to evaluate the heat transfer coefficient regardless the diameter of the condenser tube. Nebuloni and Thome [9] developed a numerical and theoretical model to predict the laminar film condensation inside various channel shapes. They showed that the channel shape strongly affects the overall thermal performance. Chantana and Kumar [10] investigated experimentally and theoretically the heat transfer characteristics of steam-air during condensation inside a vertical tube. They observed that a higher Reynolds number and mass fraction of vapour improve the process of condensation. Dahikar et al. [11] conducted an experimental and CFD studies in the case of the film condensation with downward steam inside a vertical pipe. They found that a larger interfacial shear affects the momentum transfer because of the great velocity gradient especially at the gas-liquid interface. Merouani et al. [12] presented a numerical analysis during the condensation of steam-gas mixtures between two coaxial cylinders. They observed that a higher vapour concentration at the inlet and molar mass of the non-condensable gas increases the heat flux at the inner wall. Qiujie et al. [13] presented a numerical study in the case of steam-air condensation on isothermal vertical plate by using volume of fluid (VOF) method. Their results indicate that the mass fraction variation of the non-condensable gas directly affects the liquid film condensation and then influences the heat transfer.

In the thermal desalination unit, the condenser is used for producing freshwater from the saline water sources. In fact, in order to enhance the condensation process with the presence of non-condensable gas in thermal seawater desalination processes, many studies have been conducted. Semiat and Galperin [14] found from steam condensation that even a small air mass fraction decreases the heat transfer coefficient in seawater desalination plant. Al-Shammari et al. [15] have shown from an experimental study that non-condensable gas has a negative effect on the heat transfer. An experimental study on the role of non-condensable gases in the condensation of steam inside slightly inclined tubes was presented by Caruso et al. [16]. The experiments were carried out under the following conditions: inner diameter of the tube 12.6 and 26.8 mm, inclination of the tube 7, mass fraction of the non-condensable gas between 5 and 42%, and vapour saturated at atmospheric pressure. Due to the gravity, the condensate is collected mainly in the lower part of the tube. They also developed a correlation to calculate the local condensation heat transfer coefficient. Hassaninejadfarahani et al. [17] investigated numerically a liquid film condensation with high amount of non-condensable gas inside vertical tube. They examined the effects of varying the inlet air mass fraction, the inlet relative humidity, the inlet Reynolds number and the radius of the tube on the simultaneous heat and mass transfer during condensation. Recently, Charef et al. [18] investigated the condensation process of water vapour-air into liquid film inside a vertical tube under two different boundary conditions: imposed temperature and imposed heat flux. The results indicated a better condensation process under imposed heat flux. It was found that the presence of non-condensable gas affects negatively the system efficiency.

The purpose of this study is to numerically develop and investigate the problem of water vapour condensation in the presence of non-condensable gas in a vertical tube. In order to improve the effectiveness of the steam condensation in desalination process, special attention is addressed to examine the effects of the tube geometry and the inlet conditions on the condensation process. In the following, we present the studied problem, the numerical method and the main results.
