Mass Transfer Correlation for Tubular Membrane-Based Liquid Desiccant Air-Conditioning System

Abstract

In this study, a tubular membrane-based liquid desiccant air-conditioning system was numerically simulated to obtain mass transfer correlation. The design parameters for the membrane-based liquid desiccant system (Re numbers and aspect ratio, L/D) were also optimized using the numerically obtained results. The mass transfer correlation was developed as a function of Reynolds numbers, Schmidt numbers and aspect ratio which indicates a ratio of the length to the diameter of the membrane tube. The effect of the aspect ratio and airflow velocity on the efficiency of the membrane-based liquid desiccant system was also investigated. COMSOL Multiphysics modules of this study were validated with the literature results. The maximum efficiency was obtained as 50% with an aspect ratio of 40 at low Re number of 50.

Appendix

Vapor pressure of LiCl solution, at a specific temperature and concentration, is given by Conde [15] as shown in Eq. A1.

$$ \frac{{P_{\text{s}} }}{{P_{\text{w}}^{\text{sat}} }} = \left( { + \frac{T}{647.096}} \right) $$

(A1a)

$$ = 2 - \left[ {1 + \left( {\frac{\xi }{{\pi_{0} }}} \right)^{{\pi_{1} }} } \right]^{{\pi_{2} }} $$

(A1b)

$$ = \left[ {1 + \left( {\frac{\xi }{{\pi_{3} }}} \right)^{{\pi_{4} }} } \right]^{{\pi_{5} }} - 1 $$

(A1c)

$$ = 1 - \left[ {1 + \left( {\frac{\xi }{{\pi_{6} }}} \right)^{{\pi_{7} }} } \right]^{{\pi_{8} }} - \pi_{9} e^{{\frac{{ - (\xi - 0.1)^{2} }}{0.005}}} $$

(A1d)

$$ \xi = \frac{{m_{\text{LiCl}} }}{{m_{\text{LiCl}} + m_{\text{w}} + \Delta m_{\text{v}} }} $$

(A1e)

The vapor pressure of LiCl–water solution was calculated by the saturation pressure of pure water. The constants π₀, π₁, π₂, π₃, π₄, π₅, π₆, π₇, π₈ and π₉ are given in Table 3.

Table 3 Constants for vapor pressure of LiCl–water desiccant solution (Conde 2012)

The density of LiCl–water desiccant solution varied according to the concentration of LiCl in solution. Thus, the density of LiCl–water solution depends on temperature and concentration of LiCl in solution and was defined by the density of pure water. Conde [15] was modeled density of LiCl–water solution as the following equations. The constants Bi and ρ_i are listed in Table 4.

$$ \rho_{\text{s}} = \rho_{\text{w}} \mathop \sum \limits_{i = 0}^{3} \rho_{i} \left( {\frac{\xi }{1 - \xi }} \right)^{i} $$

(A2a)

$$ \rho_{\text{w}} = 322\left( {1 + B_{0} \theta^{{\frac{1}{3}}} + B_{1} \theta^{{\frac{2}{3}}} + B_{2} \theta^{{\frac{5}{3}}} + B_{3} \theta^{{\frac{16}{3}}} + B_{4} \theta^{{\frac{43}{3}}} + B_{5} \theta^{{\frac{110}{3}}} } \right) $$

(A2b)

$$ \theta = 1 - T /T_{\text{c}} $$

(A2c)

Table 4 Constants for density of LiCl–water desiccant solution and pure water (Conde 2012)

The dynamic viscosity of LiCl–water desiccant solution was calculated by Eq. (A3). Table 5 lists the constants of dynamic viscosity of LiCl–water desiccant solution.

$$ \mu_{\text{s}} = \mu_{\text{w}} e^{{\mu_{1} \zeta^{3.6} + \mu_{2} \zeta^{{}} + \mu_{3} \frac{\zeta }{\theta } + \mu_{4} \zeta^{2} }} $$

(A3a)

$$ \zeta = \frac{\xi }{{\left( {1 - \xi } \right)^{{\frac{1}{0.6}}} }} $$

(A3b)

$$ \mu_{\text{w}} = 1.787 \times 10^{ - 6} (1.0261862 + 12481.702\theta^{0.02} - 19510.923\theta^{0.04} + 7065.286\theta^{0.08} - 395.561\theta^{2.85} + 143922.996\theta^{8} ) $$

(A3c)

Table 5 Constants for viscosity of LiCl–water desiccant solution (Conde 2012)