Investigation of Gas-Liquid Mass Transfer in the Fuel Scrubbing Inerting Process Using Mixed Inert Gas

Abstract

This study investigates the dynamics of mass transfer between gas and liquid during the fuel scrubbing inerting process, utilizing a mixed inert gas (MIG) composed of CO₂, N₂, and trace amounts of O₂. The goal is to lower oxygen concentrations in aircraft fuel tanks, thereby reducing the risk of explosions. The experiments were conducted on a fuel scrubbing inerting platform, where an MIG was utilized to deoxygenate aviation fuel. Changes in the oxygen concentration in the ullage (OCU) and the dissolved oxygen concentration in the fuel (DOCF) were measured during the scrubbing process. Validated by these experimental data, Computational Fluid Dynamics (CFD) simulations demonstrated the reliability of the model. The discrepancies between CFD predictions and experimental measurements were 4.11% for OCU and 5.23% for DOCF. The influence of the MIG bubble diameter, MIG flow rate, and fuel loading rate on DOCF, gas holdup (GH), and the oxygen volumetric mass transfer coefficient (OVMTC) was comprehensively examined. The results reveal that larger MIG bubble diameters lead to an increased DOCF but reduced GH and OVMTC. In contrast, a higher MIG flow rate decreases DOCF while boosting GH and OVMTC. Additionally, a greater fuel loading rate increases DOCF but decreases GH and OVMTC. These findings offer important insights for optimizing fuel scrubbing inerting systems, underscoring the necessity of selecting suitable operating parameters to enhance oxygen displacement and ensure aircraft safety.

1. Introduction

Ensuring the safety of aircraft fuel tanks is a paramount concern in aviation engineering, as the presence of flammable vapors poses a significant risk of explosion. This risk is particularly pronounced when the OCU of a fuel tank reaches the minimum oxygen concentration to support fuel combustion [1,2]. To mitigate this danger, fuel tank inerting systems have been developed and implemented. These systems reduce the oxygen concentration to non-flammable levels by injecting inert gas into the ullage [3]. Traditionally, the inert gas used is nitrogen-enriched air (NEA), produced by a hollow fiber membrane air separation device.

However, recent studies have shown that oxygen consumption inerting systems offer more advantages compared to hollow fiber membrane nitrogen production systems [4,5]. In oxygen consumption inerting systems, the inert gas is a mixture of CO₂, N₂, and residual O₂, known as MIG.

During the flight, changes in boundary conditions such as temperature and pressure can cause dissolved gasses to escape from the fuel, adversely affecting the oxygen concentration in the ullage and consequently the effectiveness of the inerting system [6,7]. Fuel scrubbing is a proven and effective method to reduce the effect of dissolved oxygen escaping by displacing most of the oxygen in the fuel with inert gas [8]. The gas–liquid mass transfer rate directly influences the OCU during fuel scrubbing, making it crucial to study the mass transfer rate between gas and liquid during this process.

The process of fuel scrubbing with inert gas involves complex gas–liquid mass transfer dynamics. The efficiency of oxygen displacement from the fuel via these inert gasses is influenced by several factors, such as bubble diameter, gas flow rate, and fuel loading rate [9,10]. Understanding these dynamics is crucial for optimizing the configuration and functionality of fuel scrubbing inerting systems. The use of CO₂, in particular, offers potential advantages due to its higher solubility in aviation fuel compared to nitrogen, which may improve the efficiency of oxygen displacement [11,12]. This is because the MIG is derived from the airborne oxygen-consuming inerting system, which uses the oxygen in the ullage of the tank and fuel vapor to react and generate carbon dioxide in the presence of a catalyst. Then, MIG is sent to the bottom of the fuel tank through the pipeline to scrub and inert the fuel. The oxygen content in the MIG is extremely low, while the carbon dioxide content increases. As a result, the partial pressure of oxygen in the MIG decreases, enhancing the driving force for the mass transfer of dissolved oxygen from the fuel and thus facilitating the release of dissolved oxygen. Furthermore, due to the relatively high solubility of carbon dioxide in the fuel, the release of carbon dioxide can prevent the increase in oxygen concentration in the ullage of the tank caused by the escape of oxygen. Additionally, the controlled presence of residual oxygen in the mixture can help maintain the effectiveness of inerting while optimizing overall gas utilization [13].

Currently, there are very few studies on the deoxygenation of inert gas in fuel scrubbing, resulting in limited reference data on the mass transfer rate between MIG and fuel. Most research has focused on the application of industrial bubble column reactors, which can serve as a valuable reference for investigating the mass transfer behavior in fuel scrubbing inerting processes. Shao [14] experimentally studied the relationship between the diameter of scrubbing bubbles and scrubbing efficiency, showing that scrubbing efficiency decreases rapidly with an increase in bubble diameter. Saad [15] employed CFD software to analyze flow patterns between gas and liquid within a bubble column. By simulating the ascent velocity of bubbles, bubble size, and gas holdup across varying superficial gas velocities and locations, the study enhances the understanding of gas and liquid flow dynamics in bubble columns, aligning closely with experimental findings.

This study will employ the CFD method to analyze the mass transfer characteristics of MIG in fuel scrubbing. Key parameters such as MIG bubble diameter, gas flow rate, and fuel loading rate will be systematically varied to understand their impact on the oxygen displacement process.

2. Theory and Model

2.1. Physical Model

In this research, a scaled-down physical model of the fuel tank, measuring 300 × 100 × 200 mm³, was utilized to illustrate the process of fuel scrubbing. The fuel tank model is shown in Figure 1. The model is equipped with a 10 mm × 10 mm MIG inlet at the bottom and a 10 mm × 10 mm vent at the upper right. The vent is normally open and connected to the external environment. When the pressure inside the tank exceeds the external environmental pressure, the gas inside the tank is automatically discharged without the need for manual operation. The fuel used is domestic RP-3 fuel.

2.2. Mathematical Model

Numerical methods for addressing gas–liquid two-phase flow are generally classified into two main categories: the Euler–Lagrange method and the Euler–Euler method. The Euler–Lagrange method treats the liquid phase as a continuous fluid while modeling the gas phase as discrete Lagrangian particles. By solving the motion differential equations for these particles, it captures the motion and state of the discrete gas phase in the flow field, as well as any size changes due to external forces. A key strength of this method lies in its ability to obtain detailed motion information for the discrete bubbles. However, it is only practical for multiphase flows with a low volume fraction of the discrete phase and typically demands substantial computational power. On the other hand, the Euler–Euler method employs the concept of volume fraction, treating both phases as interpenetrating continuous media. Each phase is characterized by its own independent pressure, velocity, temperature, and other physical fields. While this method reduces computational costs compared to the Euler–Lagrange approach, it still provides a reasonable level of accuracy, and is therefore widely adopted in multiphase flow simulations.

MIG was used for fuel scrubbing, and the MIG–liquid mass transfer process was simulated and solved using the Euler–Euler approach [16,17]. In this multiphase flow model, each phase is solved using the momentum equation and the continuity equation.

The equation for mass conservation can be formulated as follows:

$${\displaystyle \frac{\partial }{\partial t}}({\rho }_{\mathrm{i}}{\alpha }_{\mathrm{i}})+\nabla ({\rho }_{\mathrm{i}}{\alpha }_{\mathrm{i}}{u}_{\mathrm{i}})=0$$

(1)

where ρ_i is the density of phase i, kg/m³; α_i is the volume fraction of phase i; u is the velocity of phase i, m/s; t is the time, s.

The equation for momentum conservation can be formulated as follows:

$${\displaystyle \frac{\partial }{\partial t}}({\rho }_{\mathrm{i}}{\alpha }_{\mathrm{i}}{u}_{\mathrm{i}})+\nabla \cdot ({\rho }_{\mathrm{i}}{\alpha }_{\mathrm{i}}{u}_{\mathrm{i}}{u}_{\mathrm{i}})=-{\alpha }_i\nabla p+\nabla \cdot [{\alpha }_{\mathrm{i}}{\mu }_{\mathrm{i}}(\nabla u_{\mathrm{i}}+\nabla {u_{\mathrm{i}}}^{\mathrm{T}})]+{\alpha }_{\mathrm{i}}{\rho }_{\mathrm{i}}g+R_{\mathrm{i}\mathrm{j}}$$

(2)

where p is the pressure, Pa; μ_i is the dynamic viscosity of phase i, Pa·s; g is gravitational acceleration, m/s²; R_ij is the force between the i and j phases’ interfacial, N/m.

In the Euler–Euler approach, the interaction force between the gas and liquid phases is crucial for accurately solving each phase. These interaction forces mainly include drag force, lift force, and virtual mass force. Since the actions on the gas and liquid phases are reciprocal

$$R_{\mathrm{l}}=-R_{\mathrm{g}}=R_{\mathrm{l}}^{\mathrm{DF}}+R_{\mathrm{l}}^{\mathrm{LF}}+R_{\mathrm{l}}^{\mathrm{VMF}}$$

(3)

where R_l is the interfacial force of the liquid, N/m; R_g is the interfacial force of the gas, N/m; R_l^DF is the interfacial drag force of the liquid, N/m; R_l^LF is the interfacial lift force of the liquid, N/m; R_l^VMF is the interfacial virtual mass force of the liquid, N/m.

The drag force represents the frictional resistance encountered by the bubble as it moves through the liquid during the gas–liquid flow process. It can be formulated as follows:

$$R_{\mathrm{l}}^{\mathrm{DF}}={\displaystyle \frac{3}{4}}{\rho }_l{\alpha }_g{\displaystyle \frac{C_{\mathrm{D}}}{d_{\mathrm{B}}}}(u_{\mathrm{g}}-u_{\mathrm{l}})|u_{\mathrm{g}}-u_{\mathrm{l}}|$$

(4)

where ρ_l is the density of the liquid, kg/m³; α_g is the volume fraction of the gas; C_D is the drag coefficient; d_B is the diameter of the gas bubble, m; u_g is the velocity of the gas, m/s; u_l is the velocity of the liquid, m/s.

The drag coefficient C_D is associated with the Reynolds number and Eotvos number. According to Buwa and Ranade [18], the drag coefficient can be expressed in relation to these two numbers as follows:

$$C_{\mathrm{D}}=\max \left(\min \left({\displaystyle \frac{24}{R\mathrm{e}}}(1+0.15R{\mathrm{e}}^{0.687}),{\displaystyle \frac{72}{R\mathrm{e}}}\right),{\displaystyle \frac{8}{3}}{\displaystyle \frac{Eo}{Eo+4}})\right)$$

(5)

$$R\mathrm{e}={\displaystyle \frac{d_{\mathrm{B}}|u_{\mathrm{g}}-u_{\mathrm{l}}|}{{\mu }_{\mathrm{g}}}}$$

(6)

$$Eo={\displaystyle \frac{|{\rho }_{\mathrm{g}}-{\rho }_{\mathrm{l}}|\mathrm{g}{d}_B^2}{8\omega }}$$

(7)

where Re is the Reynold number; Eo is the Eotvos number; ω is the coefficient of surface tension.

The momentum transfer between the bubbles induced by aerodynamic lift and the liquid flow field in a gas–liquid two-phase system can be described in terms of lift:

$$R_{\mathrm{l}}^{\mathrm{FL}}={\alpha }_{\mathrm{g}}{\rho }_{\mathrm{l}}{C}_{\mathrm{L}}(u_{\mathrm{g}}-u_{\mathrm{l}})\times \nabla \times u_{\mathrm{l}}$$

(8)

where C_L is the lift coefficient.

The virtual mass force refers to the force exerted on the adjacent liquid when the bubble accelerates and can be expressed as follows [19]:

$$R_{\mathrm{l}}^{\mathrm{VMF}}=C_{\mathrm{VM}}{\rho }_{\mathrm{l}}{\alpha }_{\mathrm{g}}\left({\displaystyle \frac{\mathrm{d}{u}_{\mathrm{g}}}{\mathrm{d}t}}-{\displaystyle \frac{d{u}_{\mathrm{l}}}{\mathrm{d}t}}\right)$$

(9)

where C_VM is the coefficient of virtual mass.

In Eulerian–Eulerian multiphase simulations, turbulence in the liquid phase is represented by a turbulence model. Among the options, the standard k-ε model is frequently used to predict liquid flow patterns and GH at a low gas flow rate, thanks to its uncomplicated algorithm and lower computational demands.

Turbulent kinetic energy k:

$${\displaystyle \frac{\partial }{\partial t}}(\rho k)+{\displaystyle \frac{\partial }{\partial x_i}}(\rho k{u}_i)={\displaystyle \frac{\partial }{\partial x_j}}(P_k{\mu }_{\mathrm{eff}}{\displaystyle \frac{\partial k}{\partial x_j}})+G_k+G_{\mathrm{b}}-\rho \epsilon -Y_{\mathrm{M}}+S_k$$

(10)

where k is the turbulence kinetic energy, m²/s²; P is the Prandtl number; G_k is the turbulent energy due to the velocity gradient, kg/(m∙s³); G_b is turbulent energy caused by buoyancy, kg/(m∙s³); ε is turbulent dissipation; Y_M is turbulent energy generated by fluid expansion in compressible turbulence, kg/(m∙s³); S_k is customized turbulent energy terms kg/(m∙s³).

Turbulent dissipation ε:

$${\displaystyle \frac{\partial }{\partial t}}(\rho \epsilon )+{\displaystyle \frac{\partial }{\partial x_i}}(\rho \epsilon u_i)={\displaystyle \frac{\partial }{\partial x_j}}(P_{\epsilon }{\mu }_{\mathrm{eff}}{\displaystyle \frac{\partial \epsilon }{\partial x_j}})+C_{\epsilon 1}{\displaystyle \frac{\epsilon }{k}}(G_k+C_{\epsilon 3}{G}_{\mathrm{b}})-C_{\epsilon 2}\rho {\displaystyle \frac{{\epsilon }^2}{k}}-R_{\epsilon }+S_{\epsilon }$$

(11)

where C_ε1, C_ε2, and C_ε3 are constants; R_ε is additional value, kg/(m∙s³); S_ε is customized turbulent energy terms, kg/(m∙s³).

Component transport equation:

$${\displaystyle \frac{\partial }{\partial t}}({\alpha }_i{\rho }_i{x}_{i,n})+\nabla \cdot ({\alpha }_i{\rho }_{i}u{x}_{i,n}-{\alpha }_{i}D\nabla x_{i,n})=S_{i,n}$$

(12)

where x_i,n is the mass fraction of component n in phase i; S_i,n is the mass source term of component n in phase i, kg/m³.

Introducing a mass source term at the MIG–liquid interface allows for the calculation of mass transfer between the MIG and the liquid. The mass transfer equation can be integrated into CFD software through the user-defined function (UDF) method. If the bubble size is assumed to be a rigid oval, the equivalent diameter of the sphere can be expressed as follows:

$$d_{\mathrm{b}i}={(h_{\mathrm{b}i}{l_{\mathrm{b}i}}^2)}^{{\displaystyle \frac{1}{3}}}$$

(13)

where d_bi is the equivalent bubble diameter, m; h_bi is the bubble’s long axis length, m; l_bi is the bubble’s short axis length, m.

According to the Sauter mean diameter [20], the assumed sphere can be converted into a sphere of equal volume. The Sauter mean diameter d_bs can be expressed as follows:

$$d_{\mathrm{bs}}={\displaystyle \frac{{\displaystyle \sum n_i{d}_{\mathrm{b}i}^3}}{{\displaystyle \sum n_i{d}_{\mathrm{b}i}^2}}}$$

(14)

The MIG bubble surface area is defined as follows:

$$a={\displaystyle \frac{6}{d_{\mathrm{bs}}}}{\displaystyle \frac{{\alpha }_{\mathrm{g}}}{1-{\alpha }_{\mathrm{g}}}}$$

(15)

where a is the interface area between the gas and liquid, m²/m³.

The MIG–liquid contact time between the gas and liquid can be expressed as follows:

$$t={\displaystyle \frac{d_{\mathrm{bs}}}{v_{\mathrm{r}}}}$$

(16)

where v_r is relative velocity, m/s.

According to the Higbie mass transfer theory [21], the source terms of the CO₂, O₂, and N₂ mass transfer rates at the contact interface of MIG and fuel can be expressed as follows:

$$S_{\mathrm{C}}=K_{\mathrm{C}}a(c_{\mathrm{C}}^{*}-c_{\mathrm{C}})=2\sqrt{{\displaystyle \frac{D_{\mathrm{C}}{v}_r}{\pi d_{\mathrm{bs}}}}}\cdot {\displaystyle \frac{6}{d_{\mathrm{bs}}}}{\displaystyle \frac{{\alpha }_{\mathrm{g}}}{1-{\alpha }_{\mathrm{g}}}}(c_{\mathrm{C}}^{*}-c_{\mathrm{C}})$$

(17)

$$S_{\mathrm{O}}=K_{\mathrm{O}}a(c_{\mathrm{O}}^{*}-c_{\mathrm{O}})=2\sqrt{{\displaystyle \frac{D_{\mathrm{O}}{v}_r}{\pi d_{\mathrm{bs}}}}}\cdot {\displaystyle \frac{6}{d_{\mathrm{bs}}}}{\displaystyle \frac{{\alpha }_{\mathrm{g}}}{1-{\alpha }_{\mathrm{g}}}}(c_{\mathrm{O}}^{*}-c_{\mathrm{O}})$$

(18)

$$S_{\mathrm{N}}=K_{\mathrm{N}}a(c_{\mathrm{N}}^{*}-c_{\mathrm{N}})=2\sqrt{{\displaystyle \frac{D_{\mathrm{N}}{v}_r}{\pi d_{\mathrm{bs}}}}}\cdot {\displaystyle \frac{6}{d_{\mathrm{bs}}}}{\displaystyle \frac{{\alpha }_{\mathrm{g}}}{1-{\alpha }_{\mathrm{g}}}}(c_{\mathrm{N}}^{*}-c_{\mathrm{N}})$$

(19)

where S_C, S_O, and S_N are the mass transfer of carbon dioxide, oxygen, and nitrogen at the gas–liquid interface respectively, kg/(m³∙s); K is the mass transfer coefficient, m/s; c* is saturation solubility, kg/m³; c is actual solubility, kg/m³; D is the mass diffusion coefficient, m²/s.

The values of the mass diffusion coefficients for CO₂, O₂, and N₂ can be found in the author’s previous experimental research [22,23]. The saturation solubility of the fuel was calculated based on the Ostwald coefficient with the calculation method referenced in the Standard Test Method for Estimation of Solubility of Gases in Petroleum Liquids (D 2779-92) [11].

3. CFD Simulation Calculation

The study is predicated on several fundamental assumptions to simplify the computational frameworks. The MIG was modeled as a compressible ideal gas, disregarding deviations from ideal behavior. Bubbles within the fuel were presumed to maintain a rigid oval shape, despite the likelihood of more complex and variable geometries in practice.

CFD simulation method was used to study the mass transfer during fuel scrubbing. The commercial CFD software ANSYS Fluent was used for the numerical simulation of this study. A Eulerian–Eulerian two-phase flow model was selected. In the scrubbing calculations, the liquid phase fuel was considered the primary phase, while MIG was treated as the secondary phase. The direction of gravitational acceleration was set along the negative y-axis, with a magnitude of −9.8 m/s². The gas was modeled as a compressible ideal gas with a reference pressure of 0 Pa. The wall of the tank was defined as a no-slip boundary, while the vent hole was treated as a pressure outlet boundary. The external gas oxygen concentration was set at 21%. During the calculations, the species transport equations and energy equation models were activated. The turbulence model employed was the standard k-ε model, and the pressure–velocity coupling utilized the PISO method. The pressure spatial discretization was performed using the widely adopted PRESTO! method. To minimize computational load while ensuring accuracy, the discretization schemes for momentum, turbulent kinetic energy, and turbulent dissipation rate were all implemented using the First-Order Upwind scheme.

In the MIG, the fractions of CO₂, O₂, and N₂ by volume are 10%, 5%, and 85%, respectively. The concentrations of dissolved CO₂, O₂, and N₂ at the outset in the fuel corresponded to their saturated levels at normal temperature and pressure.

3.1. Grid Independence Verification

To reduce the impact of grid resolution on the simulation outcomes, the grid independence of the fuel tank model was initially confirmed. The fuel tank used in this study is regular in shape, allowing for the use of a structured grid for calculations. Since the regions of intense gas–liquid interactions were concentrated near the MIG inlet and the vent, the grid was refined in these areas during the meshing process. Four different grid models were created, with the number of cells being 8000, 15,000, 30,000, and 56,000, respectively.

The four grid models were used to calculate and compare the MIG–liquid flow and mass transfer. The fuel load was set to 80%, the MIG inlet flow rate was 0.04 m/s, and the average bubble diameter was 2 mm. During the calculation process, the DOCF and the OVMTC were compared between two points, (150, 50, 0) and (150, 50, 140), in the fuel tank for the four grid resolutions, as illustrated in Figure 2.

When the grid count was 8000, the DOCF and the OVMTC in the fuel showed significant differences compared to those obtained with higher grid resolutions, indicating that the coarser grid resulted in larger discrepancies. As the number of grids increased from 8000 to 56,000, the deviation in the calculation results for each parameter gradually decreased. The maximum deviation in the DOCF was 0.21%, and the maximum deviation in the OVMTC was 1.59%. Thus, a grid resolution of 30,000 provides accurate calculation results, and considering the computational cost, the model with 30,000 grids is recommended for subsequent calculations.

3.2. CFD Simulation Calculation Correctness Verification

To verify the correctness of the Eulerian–Eulerian two-fluid model for calculating MIG–liquid mass transfer in fuel scrubbing inerting, an experimental verification platform was constructed. Scrubbing the fuel in the tank with MIG allowed for the comparison and analysis of the relative discrepancies between CFD calculations and experimental measurements during the process, validating the theoretical model.

Figure 3 shows the experimental setup for fuel scrubbing inerting. The constructed experimental platform is presented in Figure 4. The fuel scrubbing inerting experimental system comprises several components: the MIG configuration, sensors, fuel pre-washing, experimental measurement, and data processing and analysis. Different bubble sizes were obtained by placing stainless steel meshes of varying sizes at the inlet of the MIG. The oxygen concentration in the ullage was measured using the Figaro KE-25 oxygen sensor, which has a range of 0–100% and an accuracy of ±1%. The dissolved oxygen concentration in the fuel was measured with the Figaro KDS-25B oxygen sensor, with a range of 0–80 mg/L and an accuracy of ±5%. Details of the experimental procedure and test device parameters can be found in the author’s previous research [24,25].

When the fuel load is 80% and the superficial velocity of the MIG is 0.04 m/s, the bubble diameter distribution obtained from digital processing of the bubble images shows that the equivalent diameter is primarily distributed in the range of 3 mm to 4 mm, with an average bubble diameter of 3.44 mm, as shown in Figure 5. The MIG–liquid mass transfer during the scrubbing inerting process was calculated using this bubble diameter as the CFD input condition and compared with the experimental results. The variations in OCU and DOCF are illustrated in Figure 6. The highest relative discrepancies in OCU between the CFD simulation results and experimental measurements is 4.11%, while for the DOCF, the highest discrepancy is 5.23%. The discrepancies may be affected by the accuracy of the oxygen concentration sensor as well as errors in measurement and data processing. Additionally, in the CFD simulation, MIG is treated as a compressible ideal gas, while the non-ideal behavior of gasses in reality may affect mass transfer to a certain extent. Moreover, the bubbles are assumed to be rigidly oval-shaped, but in reality, the shape of the bubbles may be more irregular.

4. Analysis of Influencing Factors in MIG–Liquid Mass Transfer

This paper examines the effects of the MIG bubble diameter, MIG flow rate, and fuel loading rate on the mass transfer between the MIG and RP-3 fuel during the scrubbing inerting.

4.1. Effect of MIG Bubble Diameter on Mass Transfer between MIG and Fuel

When the MIG flow rate is 0.04 m/s, the fuel loading rate is 80%, and the MIG bubble diameter varies between 1 mm and 4 mm, the variations in DOCF are shown in Figure 7.

With the scrubbing process, the DOCF showed a decreasing trend. This is because DOCF is gradually transferred to the ullage due to the difference in gas–liquid concentrations, resulting in a decrease in the DOCF. Additionally, the DOCF decreases as the diameter of the MIG bubble increases. As the MIG bubble diameter varies from 1 mm to 4 mm, the maximum change in DOCF reaches 13.32%. This is because, with smaller MIG bubble diameters, the oxygen mass transfer rate between the fuel and the MIG is higher, leading to a faster escape rate of dissolved oxygen and, consequently, a lower DOCF.

The MIG holdup during the fuel scrubbing process embodies the essential principles of gas–liquid mixed flow. Taking the section at x = 150 mm as an example, the MIG holdup distribution for different bubble diameters is shown in Figure 8. It can be observed that the larger the diameter of the scrubbing bubbles, the lower the MIG holdup in the fuel. At an MIG bubble diameter of 1 mm, the average GH is recorded at 0.896%. In contrast, with a bubble diameter of 4 mm, the average gas holdup decreases to 0.76%, representing a reduction of 15.18% as the bubble diameter increases.

The volumetric transfer coefficient for mass is crucial when evaluating the performance of scrubbing equipment. The distribution of the OVMTC for different MIG bubble diameters is shown in Figure 9. As the MIG bubble diameter increases, the OVMTC in the fuel gradually decreases. When the MIG bubble diameter is 1 mm, the average OVMTC is 0.267 s⁻¹. In contrast, with an MIG bubble diameter of 4 mm, the average OVMTC decreases to 0.041 s⁻¹. This represents an 84.64% reduction in the OVMTC as the MIG bubble diameter increases.

4.2. Effect of MIG Flow Rate on Mass Transfer between MIG and Fuel

Figure 10 shows how the DOCF varies when MIG scrubs the fuel at different MIG flow rates. The MIG flow rates were 0.04 m/s, 0.06 m/s, 0.08 m/s, and 0.1 m/s, respectively, when the bubble diameter was set at 2 mm and the fuel loading rate at 80%. The DOCF varies with the MIG flow rate, showing a decreasing trend as the superficial velocity increases. When the MIG flow rate ranges from 0.04 m/s to 0.10 m/s, the maximum change in DOCF reaches 35.26%. This is because a higher MIG flow rate results in a faster mass transfer rate of oxygen between the fuel and the MIG, leading to the more rapid escape of dissolved oxygen from the fuel and, consequently, a lower DOCF.

The MIG GH distributions at different MIG flow rates are shown in Figure 11. It is evident that an increase in MIG flow rate leads to a higher MIG GH in the fuel. When the MIG flow rate is 0.04 m/s, the average MIG GH is 0.84%. In contrast, when the MIG flow rate increases to 0.10 m/s, the average MIG GH rises to 1.33%, representing an increase of 58.33%.

Figure 12 shows the distribution of the OVMTC at different MIG flow rates. It can be observed that as the MIG flow rate increases, the OVFTC in the fuel gradually increases. When the MIG flow rate is 0.04 m/s, the average OVMTC is 0.114 s⁻¹. In contrast, when the MIG flow rate increases to 0.10 m/s, the average OVMTC rises to 0.149 s⁻¹, reflecting an increase of 30.71%.

4.3. Effect of Fuel Loading Rate on Mass Transfer between MIG and Fuel

Figure 13 shows the change in DOCF under the conditions of an MIG bubble diameter of 2 mm, an MIG flow rate of 0.08 m/s, and a fuel loading rate ranging from 35% to 80%. The DOCF varies with the fuel loading rate, decreasing as the fuel loading rate decreases. As the fuel loading rate increases from 35% to 80%, the highest difference in DOCF at any given time reaches 7.92%. This occurs because a lower fuel load means there is less aviation fuel in the tank. With a constant MIG flow, more dissolved oxygen is transferred to the MIG and escapes, resulting in a lower DOCF.

Figure 14 shows the MIG GH distribution in fuel at different fuel loads. With a higher fuel loading rate, the MIG GH in the fuel decreases. At a fuel load of 35%, the average MIG holdup is 1.85%. In contrast, at a fuel load of 80%, the average MIG holdup decreases to 1.22%, representing a reduction of 34.05%.

Figure 15 shows the distribution of the OVMTC at different fuel loading rates. As the fuel loading rate increases, the OVMTC in the fuel gradually decreases. At a fuel loading rate of 35%, the coefficient is 0.173 s⁻¹, whereas at a fuel loading rate of 80%, it decreases to 0.084 s⁻¹, representing a reduction of 51.44%.

5. Conclusions

The mass transfer behavior between the gas and liquid of the fuel scrubbing inerting process using MIG was investigated through CFD numerical simulations. The relative discrepancies between the CFD results and experimental data for the OCU and the DOCF were 4.11% and 5.23%, respectively, validating the accuracy of the CFD simulations. The effects of MIG bubble diameter, MIG flow rate, and fuel loading rate on the DOCF, the MIG GH, and the OVMTC during fuel scrubbing were systematically analyzed using CFD. The findings suggest that as the MIG bubble diameter increases, the DOCF also increases, while the MIG GH and OVMTC decrease. Conversely, as the MIG flow rate increases, the DOCF decreases, and both the MIG GH and OVMTC increase. Additionally, with an increase in fuel loading rate, the DOCF increases, whereas the MIG GH and OVMTC decrease.

Moreover, these findings have significant implications for improving safety and operational efficiency in aviation fuel systems. By optimizing the MIG parameters, such as bubble diameter and flow rate, it is possible to enhance the efficiency of the scrubbing process, thereby minimizing the risk of oxygen buildup, which can lead to potential combustion hazards. This research underscores the importance of effective inerting strategies to aviation safety and can directly inform the design of fuel systems to better mitigate the risks associated with fuel tank vaporization.

In terms of future research, it would be beneficial to investigate the inerting performance of fuel scrubbing under actual flight conditions. This includes analyzing the effects of varying environmental temperatures and pressures throughout the aircraft’s operational envelope, which could provide deeper insights into optimizing fuel scrubbing processes for enhanced safety and efficiency in real-world applications.