## 1. Introduction

Falling film exchangers are commonly employed in ammonia (NH

_{3})- and lithium bromide (LiBr)-based absorption refrigeration systems [

1,

2,

3,

4,

5,

6]. In falling film exchangers, a thin layer of liquid film is formed around the tube and heat is transferred to/from the fluid flowing inside the tube. The heat and mass transfer coefficients strongly depend on the film hydrodynamics. Extensive experimental, analytical, and numerical works were performed to describe the falling film flow on bare and enhanced tubes [

7,

8]. The falling film characterization comprises of (a) film thickness, (b) wave formation, (c) wettability, (d) flow development regions, such as stagnation, (e) impingement, (f) developing, developed detachment, and necking zones, (g) flow modes, such as droplet, jet, and sheet, and (h) flow regimes, which include laminar, wavy laminar, and turbulent [

7,

9,

10,

11,

12,

13].

The falling film modes were experimentally distinguished: droplet, droplet-jet, jet, jet-sheet, and sheet modes. Researchers have developed empirical correlations based on films’ Reynolds number

Re_{f} and modified Galileo number

Ga for flow mode recognition and transition [

14,

15,

16,

17]. The correlations developed by Roques et al. [

16] are as follows:

Droplet to droplet-jet mode:

Re_{f} and

Ga are defined as:

where

Γ_{1/2} represents the liquid load on one side of the tube,

μ is the viscosity,

g is the acceleration due to gravity,

ρ is the density, and

σ is the surface tension. In 1916, Nusselt established the film thickness

δ correlation as a function of angular position

θ, liquid load

Γ_{1/2}, and thermophysical properties [

18]. The Nusselt solution, as shown in Equation (7), is widely used for thickness estimation and comparison purposes [

9,

19,

20,

21]:

Rogers and Goindi [

22] measured the film thickness on an aluminum tube of 132 mm outer tube diameter

D at three different angular positions,

θ = 45°, 90°, and 135°. They found a 30% deviation on averaged when compared with Equation (7). Gstoehl et al. [

23] applied the laser method to analyze the film thickness around the tube. The film thicknesses

θ = 22°–62° and 112°–152° on a 19.05-mm copper tube were recorded for different intertube spacing

s. They concluded that Equation (7) predicts the film thickness well for the upper region (

θ = 0°–90°), but overestimates the thickness for the lower region (

θ > 90°). Hou et al. [

24] conducted experiments to measure film thickness using a displacement micrometer from

θ = 15°–165° for

D = 20–32 mm,

s = 10–40 mm, and

Re_{f} = 150–800. They reached a similar conclusion, that Equation (7) overestimates the film thickness in the lower portion, and proposed a modified version of Equation (7) by incorporating intertube spacing in the tube diameter ratio (

s/

D). In addition, it was observed that the minimum film thickness lies in the range of 90°–110° instead of at a fixed location, i.e.,

θ = 90° as per Equation (7). Chen et al. [

25] used the laser technique to capture film thickness in the longitudinal and circumferential directions. In their findings, the maximum film thickness was found to be at the crest location, where it was twice the minimum film thickness in the axial direction. Furthermore, higher film thickness for seawater was recorded as compared to water.

Since there are limitations in experimental procedures covering the entire parameters and capturing other details such as operating conditions, velocity, and temperature profiles within the film, computational fluid dynamics (CFD) has become an important tool for in-depth analysis to design optimal conditions for various applications. Tahir et al. [

11] analyzed the liquid load distribution for each column and concluded that the triangular pitch configuration exhibits more maldistribution than a square pitch arrangement. Ji et al. [

19] performed CFD simulations by implementing a volume of fluid (VOF) model to track the liquid/gas interface, with LiBr solution as the working fluid. They found the minimum thickness near 120°, so adjusted Equation (7) by replacing sin(

θ) with sin(3/4

θ), such that it predicts the minimum thickness at 120°. Lin et al. [

26] performed experiments and numerical calculations for a three-dimensional geometry, to examine the film distribution. They validated their VOF model with the experimental data and observed the minimum thickness to lie in the valley area, in which the heat transfer performance was found to poor. Wang et al. [

27] also studied film thickness numerically, with a three-dimensional geometry of two 25.4-mm diameter tubes. They found that the minimum film thickness location depends on both the angular position and the axial displacement. Based on their CFD results, they proposed a film thickness correlation similar to Hou et al. [

24], but with different parameters for three sections, namely impingement, transition, and departure regions. Hosseinnia et al. [

20] carried out a numerical analysis for mass transfer mechanism in the LiBr-based absorber. The VOF model and h-refinement (a mesh adaptation technique) were implemented in order to solve conservation of mass, momentum, and energy equations. Their analysis showed that the mass transfer mechanism is greatly affected by the flow mode, as the absorption rate was decreased more than 10-fold when the flow mode was changed from droplet to jet. For this reason, most of the absorber operates under droplet, droplet-jet, and modes or low liquid load [

9,

20].

The film distribution around the tube can be divided into stagnation, impingement, developing, developed, detachment, and necking regions. The majority of the heat and mass transfer takes place in the first three regions [

9], thus the film distribution affects the heat and mass transfer mechanisms. In this study, a 2D CFD model for an aqueous LiBr solution falling over a horizontal tube was modeled, which is used in the refrigeration and multi-effect desalination industries [

28,

29,

30,

31].The LiBr concentration changes in an absorber and generator due to vapor absorption and evaporation. As the concentration varies, the thermophysical properties differ and alter the magnitude of forces and hence the film hydrodynamics. The influence of LiBr concentration on the film hydrodynamics and conduction thermal resistance (which is often neglected) is lacking in the literature. Therefore, the effects of LiBr concentration, with corresponding liquid loads for droplet and jet mode, on film distribution were analyzed. First, the CFD model was validated using experimental data from the literature. Then, the transient behavior of falling film, film thickness distribution, average film thickness, and residence time were quantified and discussed. Afterwards, the tangential and normal velocities distribution for impingement and developing regions for low and high LiBr concentrations C were examined.

## 5. Conclusions

The CFD model of an aqueous LiBr solution falling over a horizontal tube was developed in this work. The effects of LiBr concentration and liquid load on falling film distribution were analyzed. It was found that jet mode, corresponding to 0.05 kg/(m·s), was more stable at a higher concentration, i.e., C = 0.65, with small fluctuations of +0.5%. In contrast, low concentration (C = 0.45) flow with 0.05 kg/(m·s) had maximum fluctuations of 14.1%. The film thickness increased with concentration and liquid load, and the residence time increased with higher concentration and lower liquid loads. The average film thickness and residence time at 0.05 kg/(m·s) and C = 0.65 were found to be 44% and 76% higher than for C = 0.45, respectively. Weak recirculation was observed for higher concentration; the recirculation exists until 5° for C = 0.65 and 10° for C = 0.45. In addition, the maximum tangential velocity when the flow was developed was 0.108 m/s for C = 0.65, vs. 0.189 m/s for C = 0.45. The flow was fully developed at θ = 40° for both concentrations. The thermal resistance analysis demonstrated that the thermal resistance rises with the concentration and liquid load. For Γ_{1/2} = 0.05 kg/(m·s), the thermal resistance for C = 0.65 was 72.9% higher than that of C = 0.45. It may be deduced from this hydrodynamics study that the heat transfer performance is expected to be better at lower concentrations because of the lower film thickness, more recirculation, higher velocity, and lower thermal resistance. In practical applications, such as refrigeration and desalination, this implies that regions in falling film evaporators with low concentration would have better thermal performance as compared to high concentration regions.