2.2.1. Governing Equations and Physical Models
The absorption of water vapor from natural gas by triethylene glycol is a purely physical process without any accompanying chemical reactions, and the same applies to the absorption of water vapor from air [
21,
22]. However, there is currently no accurate description of the mass transfer coefficient or correlation for the triethylene glycol absorption process under a high-gravity field, which makes it impossible for simulation results to directly reflect the absorption extent. As a result, the influence of temperature on the simulation outcomes is negligible, and the thermal effects can be disregarded during the simulation. The energy equation is thus excluded, while the viscosity of triethylene glycol is considered due to its certain impact on the flow dynamics [
23,
24]. Sensitivity analysis conducted on the viscosity variation corresponding to typical ±10 °C fluctuations indicates that the relative change in the UI is less than 2.2%, and the fluctuation in the dehydration equilibrium degree is less than 0.8%.
The physical properties are simplified and characterized by the density and viscosity at the experimentally determined optimal temperature of 40 °C, ensuring better alignment with practical conditions. Therefore, this section only considers the continuity equation and the momentum equation.
Here x, y, z represent the three spatial directions of the flow, while ux, uy, uz denote the corresponding velocity components in each direction. The term Sm stands for the source term in the continuity equation, which is set to zero in the present simulation.
Here , , denote the components of the stress tensor τ, while , , represent the unit body forces acting in the three coordinate directions.
The simulation focused on analyzing gas–liquid flow dynamics and mass transfer mechanisms within the rotating packed bed, addressing both mass and momentum conservation under intense swirling conditions. Given the flow complexity involving rotational shear, jet mixing, and boundary layer separation, turbulence modeling required careful consideration. Based on prior validation studies [
25,
26], the RNG k-ε model was selected over standard k-ε for its demonstrated accuracy in rotating shear flows, free jets, and separation scenarios—key features of RPB hydrodynamics.
Turbulent kinetic energy (k) equation:
Dissipation rate (ε) equation:
Here,
denotes time;
and
represent spatial coordinate directions;
is the mean velocity component; and
stands for fluid density. The turbulent kinetic energy and its dissipation rate are expressed as
and
, respectively.
refers to the generation term of turbulent kinetic energy resulting from mean velocity gradients, while
indicates the effective dynamic viscosity, defined as
, where
is the molecular viscosity and
denotes the turbulent viscosity. The parameters
and
represent the inverse effective Prandtl numbers for
and
, respectively. In the RNG model, these parameters vary with the flow field.
and
are model constants, and
describes the contribution of fluctuating dilatation to the overall dissipation rate in compressible turbulence.
and
denote user-defined source terms.
is a distinctive additional term in the RNG model, serving as a key differentiator from the standard k–ε model. This term is designed to account for the effects of small-scale turbulence and improve predictions in shear flows. It is typically formulated as follows:
where
represents the ratio of the turbulent to mean strain time scales, defined as
with
being the modulus of the mean strain rate tensor. The constants
and
are specific to the RNG model.
As the TEG-water vapor absorption involves no chemical reactions, a multiphase approach treating gas and liquid as interpenetrating continua was adopted. Comparative evaluation confirmed the Mixture model’s superiority for this system, efficiently resolving phase interactions while maintaining computational stability. The presence of both stationary and rotating components necessitated a sliding mesh technique for transient simulation, capturing critical rotor-stator interaction effects absent in steady-state approaches.
2.2.3. Boundary Conditions and Solution Strategy
The gas phase (treated as incompressible) and the liquid TEG phase both employed velocity-inlet and pressure-outlet (atmospheric) boundaries. The gas inlet velocity is 4 m/s, and the liquid inlet velocity is 2 m/s. Turbulence parameters are defined by turbulence intensity and hydraulic diameter: gas phase: 5.2% and 15 mm; liquid phase: 6.8% and 1 mm. The initial gas volume fraction is 1, and liquid is gradually injected from the nozzles until a periodic steady state is reached. A sliding mesh is used between the rotor and the casing; the computational domain is divided into rotating and stationary zones, with flux interpolation at the interface [
27,
28]. Taking into account both computational accuracy and resource consumption, a medium grid is selected for subsequent calculations. The near-wall area is processed using standard wall functions, and after post-processing statistics, the y + values on the wall are mainly distributed in the range of 30–150, which meets the requirements of logarithmic law layers. Both the rotor and the stationary wall are equipped with 5 layers of prismatic mesh (with a first layer height of 0.02 mm and a growth rate of 1.2) to analyze the velocity gradient within the boundary layer.
A robust solution strategy was first implemented. The FLUENT pressure-based solver was employed for transient analysis to accurately capture rotor-stator interactions. A timestep of 0.001 s was selected to ensure Courant number stability, and a total physical time of 10 s (10,000 iterations) was simulated to achieve period-independent solutions. Convergence criteria mandated residual reductions below 10−4 for all parameters per timestep.
To verify grid independence, this study used three sets of schemes: coarse grid (approximately 850,000), medium grid (approximately 1.65 million), and fine grid (approximately 2.8 million) for independence testing. Based on the medium grid, the pressure drop and uniformity index changes in the fine grid are both less than 1%.
2.2.4. Liquid Distribution Uniformity and Its Correlation with Dehydration Performance
Liquid distribution characteristics serve as a fundamental factor influencing mass transfer efficiency in rotating beds. Uniform liquid distribution ensures full wetting of the packing surface, effectively increasing the gas–liquid contact area and thereby significantly enhancing the mass transfer process. In contrast, non-uniform distribution leads to insufficient wetting, reduces the mass transfer area, and diminishes gas–liquid contact efficiency, ultimately impairing overall mass transfer performance [
29,
30]. Research by Zhang [
31] clearly pointed out that “uneven liquid distribution in RPB has a serious impact on mass transfer performance” and employed CFD methods to quantify the maldistribution index. Liao [
32] improved the overall performance of RPB by optimizing the liquid distributor structure. Similarly, Han’s study on the hydrodynamics and liquid-solid mass transfer in micro-packed bed reactors with copper foam packing highlighted the significant influence of liquid distribution on liquid-solid mass transfer. Liu’s work further revealed the impact of initial liquid dispersion on liquid distribution and mass transfer performance in rotating packed beds. Numerous studies support the view that liquid distribution performance can serve as an effective indicator for evaluating mass transfer effectiveness [
33,
34]. Therefore, liquid distribution characteristics can serve as effective simulation outputs for evaluating mass transfer effectiveness. It should be noted that the validity of UI as a surrogate indicator for dehydration performance is based on the premise that physical absorption dominates and the mass transfer resistance is mainly controlled by the gas–liquid interfacial area.
This study established a three-dimensional model that matches the experimental conditions to accurately represent the true flow field characteristics and capture the liquid phase distribution. We employed FLUENT’s built-in uniformity index (UI) calculation to assess distribution quality, which quantifies liquid volume fraction variations across specified surfaces to reflect distribution homogeneity. The UI ranges from 0 to 1 and is calculated using the following equation:
where
represents the face index for a surface discretized into
n computational faces, and
denotes the area-averaged liquid volume fraction across the entire surface.
Where represents the area of the i-th computational face in the surface mesh, and denotes the liquid volume fraction at the i-th face. The index i ranges from 1 to n, where n is the total number of discretized faces comprising the surface domain.
Through experimental and simulation-based multiple correlation analysis of the uniformity index and dehydration equilibrium under different operating conditions, the scatter plot of the fitted curve is shown in
Figure 5. The goodness-of-fit reaches 0.935, indicating an excellent fitting effect. Therefore, based on the relationship established between the distribution uniformity index and the dehydration equilibrium, Equation (11) is used in subsequent calculations to determine the dehydration equilibrium. The limitation of UI as a mass transfer performance indicator lies in that it only characterizes the geometric uniformity of liquid distribution, rather than the actual mass transfer rate of water vapor. Therefore, the UI-performance correlation established in this work is applicable only to dehydration processes dominated by physical absorption; caution is required when applying engineering extrapolation to real natural gas systems involving chemical reactions or complex components.
The correlation between the uniformity index and the dehydration equilibrium degree was fitted as follows:
where
denotes the dehydration equilibrium degree (%);
represents the uniformity index.