Research on the stratification characteristics of binary inert gas mixture

1 Introduction

He–Xe and He–Ar gas mixtures have attracted considerable attention in reactor cooling, space nuclear power systems, and other high-temperature and high-pressure applications because of their favorable physical and chemical properties (Ouyang, 2007). Helium is an inert gas with excellent chemical stability, high specific heat capacity at constant pressure, high thermal conductivity, and superior heat transfer performance (Chen et al., 2023). Xenon and argon also possess good chemical stability and desirable thermophysical properties (Chen et al., 2023). By mixing helium with xenon or argon, a working fluid with a higher molecular weight can be obtained while maintaining favorable heat transfer characteristics and improving compressibility. The use of such gas mixtures in nuclear systems can significantly enhance system safety and thermal efficiency. In particular, He–Xe mixtures have shown outstanding potential in space nuclear reactors (Liu et al., 2023)^, where they are widely used as working fluids in Brayton cycles (Chen et al., 2023) because of their high cycle efficiency, high power-to-mass ratio, and reliable operation.

Research on He–Xe and He–Ar gas mixtures is important not only for addressing practical issues in current nuclear reactors and space nuclear power systems, but also for advancing the development of nuclear technology (Yang and Shi, 2018). Investigating the distribution and evolution characteristics of these binary gas mixtures in enclosed vessels can improve the understanding of gas flow and heat transfer behavior in reactor systems. Such knowledge is essential for reactor design optimization and for improving the thermal efficiency and power output of nuclear energy systems (Hasan Tusar et al., 2025).

A number of studies have been conducted on the distribution behavior of mixed gases under different conditions. Liu et al. (2021) investigated helium-containing gas mixtures with different concentrations in a containment atmosphere and examined helium concentration stratification and thermal stratification in the gravity direction under steam condensation conditions. Ning et al. (2024) performed numerical simulations of He–Xe gas mixtures and analyzed thermal stratification in horizontal flow under gravity. Wang et al. (2024) studied a natural circulation loop using a helium–xenon mixture and evaluated the effect of the horizontal-section temperature on the gas distribution. Dong et al. (2022) investigated the flow and heat-transfer characteristics of He‐Xe mixtures under flow-blockage conditions. Sharipov and Kalempa (2005) assumed a specified pressure at the pipe inlet and consequently found that the concentration of the lighter component at the pipe outlet was lower than that at the inlet, indicating the occurrence of a separation phenomenon. Punetha et al. (Punetha et al., 2018) carried out experiments on helium distribution and its mixing with air in a confined rectangular enclosure, focusing on the influence of the injection location on helium stratification. Park (Park et al., 2023) investigated a ternary steam–air–helium mixture experimentally, mainly addressing the effect of mixture composition on condensation heat transfer characteristics. Naris (Naris et al., 2003) numerically analyzed binary inert-gas mixtures with different molar concentrations, including Ne–Ar and He–Xe, and suggested that intermolecular interaction forces can affect flow coefficients. Yun et al. (2009) studied the diffusion behavior of He and Xe in UO₂, showing that the strain energy associated with differences in atomic radius plays a key role in diffusion. Kljenak et al. (2006) conducted simulations of the French TOSQAN facility, in which steam, air, and helium were injected into a cylindrical containment vessel, revealing the heterogeneous distribution of the atmosphere. Fernández et al. (2004) determined the self-diffusion coefficients of argon and methane using the Green–Kubo method, and the results exhibited minor deviations and good agreement when compared with experimental data. Ohwada and Sone (Ohwada and Sone, 2003) numerically analyzed the flow behavior of binary gas mixtures under thermal creep and diffusion slip conditions based on the linearized Boltzmann equation. Xiao et al. (2019) proposed the unified gas-kinetic scheme (UGKS) for simulating nonequilibrium flows of multicomponent gases across different scales. Although extensive efforts have been devoted to the distribution behavior of various gas mixtures under different conditions (Sommerfeld and Taborda, 2024), the behavior of mixed gases in enclosed spaces remains a rapid and complex process, and experimental investigations are often subject to significant limitations. Moreover, the concentration distribution of mixed gases is influenced by multiple factors, including composition, pressure, geometry, and temperature. At present, studies on the distribution characteristics of He–Ar gas mixtures in confined spaces are still limited, the relative contributions of thermal, compositional, operating, and geometric parameters have not been sufficiently quantified within a unified framework, and further investigation is particularly needed on the stratification behavior of He–Ar mixtures under gravity.

Therefore, the transient stratification of a He–Ar binary mixture in a closed vessel is investigated by considering both ordinary species diffusion and thermal diffusion in this study. The effects of initial composition, pressure, initial temperature, aspect ratio, and imposed temperature difference are examined within a unified numerical framework. The novelty of this work lies in quantitatively separating the effects of these operating and geometric parameters on the axial concentration difference, transient evolution, and stabilization characteristics of gas stratification. The present work is of both theoretical and practical significance for improving reactor safety, optimizing reactor design, enhancing the performance of nuclear power systems, and promoting the development of nuclear technology.

2 Materials and methods

To clarify the density stratification characteristics of the He–Ar gas mixture under the combined effects of the temperature field and gravity, the following assumptions are adopted in this study: the gas mixture is treated as a continuum; no chemical reaction occurs in the system; the fluid satisfies the Newtonian fluid assumption; the gas mixture is regarded as an ideal-gas mixture; the thermophysical properties vary with the local temperature and species composition; and the gravitational acceleration remains constant. Owing to the significant difference in molecular weight between helium and argon, the density of the gas mixture is governed not only by temperature but also by the local species distribution. As a result, the mixture exhibits pronounced buoyancy-driven flow and stratification behavior in the gravitational field.

2.1 Governing equations

The flow, heat transfer, and mass transfer processes of the He–Ar binary gas mixture are described by the continuity equation, momentum equation, energy equation, and species transport equation.

2.1.1 Continuity equation

The gas mixture satisfies mass conservation, and the continuity equation can be written as Equation 1: where ρ is the density of the gas mixture, and u is the velocity vector.

∂ ρ ∂ t + ∇ · ρ u = 0 (1)

2.1.2 Momentum equation

The momentum conservation equation is given by Equation 2: where p is the static pressure, μ is the dynamic viscosity, and g is the gravitational acceleration vector.

∂ ρ u ∂ t + ∇ · ρ uu = − ∇ p + ∇ · μ ∇ u + ∇ u T − 2 3 ∇ · u I + ρ g (2)

2.1.3 Energy equation

The energy conservation equation can be expressed as Equation 3: where h is the specific enthalpy of the mixture, k is the thermal conductivity, T is the temperature, h i is the specific enthalpy of species i, J i is the diffusion flux of species i, and S h is the volumetric heat source term. In the absence of an internal heat source, S h = 0.

∂ ρ h ∂ t + ∇ · ρ u h = ∇ · k ∇ T − ∇ · ∑ i h i J i + S h (3)

The mixture enthalpy can be expressed as Equation 4: where Y i is the mass fraction of species i.

h = ∑ i Y i h i (4)

2.1.4 Species transport equation

For species i, the conservation equation for the mass fraction is written as Equation 5:

∂ ρ Y i ∂ t + ∇ · ρ u Y i = − ∇ · J i (5)

Since the present system is a non-reactive He–Ar binary gas mixture, neither chemical reaction source terms nor additional volumetric source terms are considered. Because the binary system satisfies Equation 6, only one independent species mass fraction equation needs to be solved, while the mass fraction of the other species can be directly obtained from the conservation relation. only one independent species mass fraction equation needs to be solved, while the mass fraction of the other species can be directly obtained from the conservation relation.

Y He + Y Ar = 1 (6)

2.1.5 Diffusion flux model

Species transport in the He–Ar binary mixture was described using the mixture-averaged Fickian diffusion model implemented in ANSYS Fluent 2022 R¹. No chemical reactions or volumetric species source terms were considered (ANSYS and Inc, 2022). Considering both ordinary molecular diffusion and thermal diffusion, the diffusive mass flux of species i is expressed as Equation 7: where J i is the diffusive mass flux of species i, ρ is the mixture density, Y i is the mass fraction of species i, D i , m is the mixture-averaged mass diffusion coefficient, D T , i is the thermal diffusion coefficient, and T is the local absolute temperature. The first term represents ordinary molecular diffusion driven by the species concentration gradient, whereas the second term represents thermal diffusion induced by the temperature gradient, commonly known as the Soret effect.

J i = − ρ D i , m ∇ Y i − D T , i ∇ T T (7)

The binary mass diffusion coefficient between helium and argon was evaluated using the kinetic-theory model available in Fluent. Based on the modified Chapman–Enskog relation (Hirschfelder et al., 1954), the binary diffusion coefficient is calculated using Equation 8: where D i j is the binary coefficient between species i and j, M i and M j are the corresponding molar masses, p abs is the local absolute pressure, σ i j is the binary collision diameter, and Ω D , i j is the diffusion collision integral. The local absolute pressure was obtained as the sum of the operating pressure and gauge pressure. The collision diameter and diffusion collision integral were determined from the Lennard–Jones parameters of helium and argon using the kinetic-theory model implemented in Fluent.

D i j = 0.00188 T 3 / 2 1 M i + 1 M j 1 / 2 p abs σ i j 2 Ω D , i j (8)

For the He–Ar binary mixture considered in this study, the mixture-averaged diffusion coefficient reduces to the He–Ar binary diffusion coefficient. Therefore, the ordinary molecular diffusion coefficient varies mainly with the local temperature and absolute pressure. In general, it increases with increasing temperature and decreases with increasing pressure. The thermal diffusion option was enabled to account for the Soret effect. The thermal diffusion coefficient was evaluated using the kinetic-theory correlation implemented in Fluent, as shown in Equation 9: where X_i and Y_i are the local mole fraction and mass fraction of species i, respectively. Thus, the local species composition affects the diffusion process through both the concentration gradient in the ordinary diffusion term and the composition dependence of the thermal diffusion coefficient.

D T , i = − 2.59 × 10 − 7 T 0.659 M i 0.511 X i ∑ j = 1 N M j 0.511 X j − Y i ∑ j = 1 N M j 0.511 X j ∑ j = 1 N M j 0.489 X j (9)

2.1.6 Numerical method

The governing equations described above are discretized using the finite volume method. For an arbitrary control volume V, the general transport equation can be written as Equation 10: where ϕ denotes the general transported variable, which may represent a velocity component, temperature, or species mass fraction; Γ ϕ is the corresponding diffusion coefficient; and S ϕ is the source term.

∂ ∂ t ∫ V ρ ϕ d V + ∫ A ρ u ϕ · d A = ∫ A Γ ϕ ∇ ϕ · d A + ∫ V S ϕ d V (10)

2.2 Geometries and mesh of the numerical model

The geometries of the cylindrical vessels used in this study are shown in Figures 1a–c. The length-to-diameter ratios of these geometries are 2:1, 3.6:1 and 5:1 respectively. An example of the computational mesh is shown in Figure 1d. An unstructured tetrahedral mesh was employed to solve the governing equations. The primary advantage of using an unstructured mesh lies in its ability to generate high-quality computational grids for complex geometries.

The system under investigation is a cylindrical closed vessel filled with a He–Ar gas mixture, with an initial volume fraction of 6:4. All boundaries were treated as stationary, impermeable, and no-slip walls, and no species mass flux was allowed through the vessel surfaces. The gravitational direction is aligned with the axial direction of the vessel. For the isothermal cases, the upper wall, lower wall, and cylindrical sidewall were all treated as adiabatic. For the non-isothermal cases, the lower wall was maintained at 300 K, while the upper wall was prescribed at 350, 400, or 450 K, corresponding to temperature differences of 50, 100, and 150 K, respectively. The density of the He–Ar mixture was calculated using the volume-weighted mixing law. Heat conduction through the vessel wall and external convective heat losses were not considered. Radiative heat transfer within the gas mixture was also neglected because helium and argon were treated as non-participating monatomic gases. Under isothermal conditions (without temperature difference), the vessel walls are treated as adiabatic boundaries. In contrast, under non-isothermal conditions, constant temperatures are imposed on the upper and lower end surfaces to establish a temperature gradient. The boundary and initial conditions are summarized in Table 1.

TABLE 1. Boundary and initial conditions.

The numerical simulations were performed using ANSYS Fluent 2022 R¹. The governing equations for mass, momentum, energy, and species transport were discretized using the finite volume method. A transient pressure-based solver was employed, and pressure–velocity coupling was achieved using the Pressure-Implicit with Splitting of Operators (PISO) algorithm.

Spatial gradients were evaluated using the least-squares cell-based method. The PRESTO! scheme was adopted for pressure interpolation, whereas the momentum, energy, and species transport equations were discretized using the second-order upwind scheme. The transient terms were discretized using the first-order implicit scheme. All residuals remained bounded without a progressive increase during the calculation, indicating stable iterative convergence of the transient solution.

2.3 Mesh independence study

A mesh independence study was carried out to ensure that the predicted species stratification was not affected by the mesh resolution. The representative non-isothermal case was selected for this test, with a vessel height of 1 m, a vessel diameter of 0.5 m, an initial He/Ar volume ratio of 80/20, an initial pressure of 0.1 MPa, a bottom-wall temperature of 300 K, and a top-wall temperature of 400 K. Four unstructured tetrahedral meshes with different cell numbers were tested. For all mesh cases, the physical model, boundary conditions, numerical schemes, and time-step size were kept identical.

The Ar volume fractions at the bottom and top monitoring points were selected as the main quantities for evaluating mesh sensitivity. As shown in Figure 2, the predicted Ar volume fraction at the bottom remained nearly unchanged with mesh refinement, staying close to 20.01%. The Ar volume fraction at the top increased slightly when the mesh was refined from the coarsest mesh to the medium mesh, but the variation became negligible when the number of cells exceeded approximately 1,015,178. Further increasing the cell number to about 2,077,000 produced almost no visible change in either the bottom or top Ar volume fraction.

2.4 Model validation

Figure 3 shows the model validation that takes experimental data provided by methane-air mixture as the research object (Ren and Qi, 2015). Gas stratification occurs under the action of gravity, and the numerical simulation is in good agreement with the experimental results. The maximum error is 4.5% and the average error is less than 3.7%, which verifies the computational reliability of this model.

The present study established a theoretical relationship based on the balance between Soret thermodiffusion and ordinary molecular diffusion, and compared the theoretical predictions with the numerical results under temperature differences of 50 K, 100 K, and 150 K. The theoretically predicted Ar concentration differences were 0.338, 0.631, and 0.890 percentage points, respectively, while the corresponding simulated values were 0.338, 0.633, and 0.892 percentage points. The relative deviations were 0.05%, 0.30%, and 0.28%, respectively, all below 0.3%. This close agreement indicates that the simulated He–Ar stratification behavior is consistent with the theoretical prediction based on the coupled effects of Soret thermodiffusion and ordinary molecular diffusion.

3 Parametric analysis

3.1 Effect of gas mixture composition

A cylindrical vessel with a height of 2.5 m and a diameter of 0.5 m was selected for the analysis. Two initial gas compositions were considered, namely 60% He–40% Ar and 80% He–20% Ar by volume. The gas mixture was treated as a compressible ideal gas, with an initial pressure of 0.1 MPa and an initial temperature of 300 K. Several monitoring points were arranged along the axial direction of the vessel. The five monitoring points were located at S₁ (h = 0.30 m), S₂ (h = 0.80 m), S₃ (h = 1.25 m), S₄ (h = 1.70 m), S₅ (h = 2.20 m).

To compare the concentration distribution of the He–Ar mixture during long-term quiescent conditions, Figure 4 presents the temporal evolution of the argon volume fraction and its relative deviation for the case with a macroscopic argon concentration of 40% over a time period of 5–30 min. The relative deviation is defined by Equation 11: where ϕ A r , i is the argon volume fraction at a given monitoring point, and ϕ ¯ A r is the macroscopic average argon concentration in the vessel.

δ i = ϕ A r , i − ϕ ¯ A r ϕ ¯ A r × 100 % (11)

After 10 min of quiescent evolution, for the 60%He–40%Ar case, the argon volume fractions at the bottom, center, and top of the vessel were 40.00%, 40.00%, and 39.99%, respectively. For the 80%He–20%Ar case, the corresponding argon volume fractions were 20.00%, 20.00%, and 19.99%, respectively. Because helium and argon exhibit good mutual miscibility, the He–Ar mixtures with the two different volume ratios showed nearly identical distribution characteristics. Both the volume fraction profiles and the relative deviations remained stable without noticeable fluctuations. The small differences between the monitoring points are within the numerical uncertainty range and are therefore not interpreted as physically significant stratification. These results indicate that the He–Ar mixture remains essentially uniform under the investigated isothermal composition conditions.

3.2 Effect of initial pressure

When the initial pressure was set to 0.1 MPa, 0.2 MPa, and 0.4 MPa, respectively, with the gas mixture composition fixed at 60% He and 40% Ar by volume, both the volume fraction and the relative deviation of the mixed gas inside the vessel remained stable. The variations in argon volume fraction and relative deviation at different locations with initial pressure are shown in Figure 5. After 5 min of quiescent evolution, no significant change in the argon volume fraction was observed at different positions as the initial pressure increased, and the overall argon volume fraction remained within the range of 39.99%–40.01%.

Previous studies on the thermophysical properties of He–Xe and He–Ar mixtures have shown that a pressure of 2 MPa is favorable for the performance of He–Xe mixtures and can effectively improve Brayton cycle performance. Therefore, under otherwise identical initial conditions, the initial pressure was further increased to 1 MPa and 2 MPa, and the argon volume fraction inside the vessel was monitored. The argon concentration at the center of the vessel remained 40.00% for both cases.

A comparison of the argon volume fraction distributions near the wall at 0.1 MPa, 1 MPa, and 2 MPa indicates that the local flow behavior in the near-wall region changes slightly with increasing initial pressure. Figure 6 shows the calculated Ar volume-fraction contours at 0.1, 1, and 2 MPa. As the pressure increases, the compressibility of the gas mixture becomes more pronounced, which affects the velocity gradient near the wall and leads to a slight variation in the local argon volume fraction. Specifically, the argon concentration at the top of the vessel decreased from 39.97% to 39.93%, while that at the bottom increased from 40.02% to 40.06%. Nevertheless, after a sufficiently long quiescent period, the argon concentration distribution remained stable under different initial pressures, and the overall variation did not exceed 0.1%.

Both helium and argon are noble gases with large intermolecular spacing and continuous thermal motion inside the vessel. Increasing the initial pressure does not alter the essential thermal motion characteristics of helium and argon or their favorable mutual miscibility. As a result, the two gases remain uniformly mixed even under elevated initial pressure conditions. The temporal variations in Ar volume fraction and the corresponding relative deviation at 1 and 2 MPa are presented in Figures 7, 8, respectively.

3.3 Effect of vessel size

To investigate the influence of vessel geometry on the gas distribution, only the vessel height was varied while the diameter was kept constant. The aspect ratios considered in this study were 2, 3.6, and 5. Figure 9 presents the argon volume fraction contours after 10 min of quiescent evolution for the three aspect ratios. The quantitative profiles of Ar volume fraction and relative deviation for different L/D ratios are shown in Figure 10. As can be seen from the contours, the argon volume fraction remained relatively uniform and stable throughout the vessel, with no significant variation.

The relative deviation near the upper and lower regions of the vessel was slightly larger than that in the central region. However, the maximum difference between the actual argon volume fraction and the theoretical value was only 0.09%, and the maximum relative deviation was merely 0.23%. Overall, the argon volume fraction remained within the range of 39.9%–40.1%, and the relative deviation was within an acceptable range. These results indicate that the variation in vessel aspect ratio has no significant effect on the argon distribution at different locations inside the vessel. Therefore, within the investigated aspect-ratio range, the vessel aspect ratio does not produce appreciable concentration stratification under isothermal conditions.

3.4 Effect of initial temperature

The effect of initial temperature on the distribution of the He–Ar gas mixture was analyzed under three conditions, with the initial temperature set to 300 K, 320 K, and 340 K, respectively. After 10 min of quiescent evolution, the argon volume fractions at the top of the vessel were 39.9988% and 39.9987% for the cases with initial temperatures of 320 K and 340 K, respectively. Figure 11 shows the Ar volume fraction and relative deviation at different initial temperatures. At the center and bottom of the vessel, the argon volume fraction remained 40.00% for both cases. The maximum difference in argon volume fraction among the investigated initial temperatures was only 0.0026%.

These results indicate that, under different initial temperatures and gravitational effects, the concentration distribution of the He–Ar gas mixture gradually stabilizes with increasing quiescent time. As the initial temperature increases, no significant variation is observed in the argon volume fraction distribution. The gas mixture inside the vessel remains uniformly and stably distributed, showing behavior similar to that under ambient pressure conditions, it indicates that changing the uniform initial temperature has a negligible influence on the gas distribution in the absence of an imposed axial temperature gradient.

4 Effect of the temperature difference between the upper and lower vessel sections

To clarify the influence of the temperature difference between the upper and lower sections of the vessel on the distribution and evolution characteristics of the gas mixture, different temperatures were imposed at the top and bottom boundaries to establish a prescribed axial temperature difference. The bottom of the vessel was maintained as a cold end at 300 K, and the top of the vessel was specified as a hot end with three different temperature conditions: 350 K, 400 K, and 450 K. A cylindrical vessel with a height of 1 m and a diameter of 0.5 m was considered, corresponding to an aspect ratio of 2. The boundary conditions, numerical model, and grid system were kept identical for all cases. The vessel was initially filled with a uniformly mixed He–Ar gas mixture with a He/Ar volume ratio of 8:2. Several monitoring points were arranged along the axial direction of the vessel, namely Y₁ (h = 0.05 m), Y₂ (h = 0.25 m), Y₃ (h = 0.50 m), Y₄ (h = 0.75 m), Y₅ (h = 0.95 m). The distribution characteristics of the gas mixture were then investigated under temperature differences of 50 K, 100 K, and 150 K.

Under all temperature-difference conditions, as the quiescent time increased, the influence of the imposed temperature difference on the axial species distribution became progressively more pronounced. After 30 min of quiescent evolution, when the temperature difference between the upper and lower sections of the vessel increased from 50 K to 100 K and 150 K, the argon volume fraction at the bottom increased from 20.046% to 20.097% and 20.155%, respectively, while that at the top decreased from 19.811% to 19.642% and 19.493%, respectively. This indicates that argon gradually accumulated in the lower region and was progressively depleted in the upper region, demonstrating an increasingly pronounced stratification tendency.

With further quiescent evolution, all cases reached a stable distribution after approximately 2 h. The temporal evolution of Ar volume fraction under different temperature differences is shown in Figure 12, and the corresponding relative deviation is shown in Figure 13. Under the stabilized condition, the argon volume fraction at the bottom was 20.155%, 20.303%, and 20.438% for temperature differences of 50 K, 100 K, and 150 K, respectively, whereas the corresponding values at the top were 19.817%, 19.670%, and 19.546%. Meanwhile, the argon volume fraction in the central region remained close to the macroscopic average concentration throughout. These results demonstrate that increasing the temperature difference significantly enhances the axial concentration non-uniformity inside the vessel and promotes the formation of a stable stratified structure. Figure 14 presents the calculated Ar volume-fraction and temperature contours under different temperature differences.

The temperature field inside the vessel exhibits a clear axial gradient distribution, ranging from 350 to 300 K, 400–300 K, and 450–300 K under different temperature-difference conditions. Heat from the upper wall is gradually transferred toward the lower region through thermal conduction within the gas mixture, resulting in a continuous temperature gradient along the axial direction. Overall, the temperature distribution inside the vessel remains relatively smooth and uniform. However, a more pronounced temperature variation is observed near the wall regions, whereas the temperature variation in the central region of the vessel is comparatively moderate. This indicates that wall effects play a more significant role in shaping the local temperature field, while the core region maintains a relatively stable thermal gradient. The maximum relative deviations of the argon volume fraction for temperature differences of 50 K, 100 K, and 150 K are 0.975%, 1.82%, and 2.535%, respectively, and all occur at the top of the vessel.

The bottom-to-top difference in Ar volume fraction is defined by Equation 12: where X Ar , bottom is the Ar volume fraction at the bottom of the vessel, and X Ar , top is the Ar volume fraction at the top of the vessel.

Δ X Ar = X Ar , bottom − X Ar , top (12)

As the imposed temperature difference increased from 50 to 150 K, the bottom-to-top Ar volume-fraction difference increased from 0.338 to 0.892 percentage points, corresponding to an increase of 0.554 percentage points. Meanwhile, the concentration profiles developed more rapidly and approached a stable state after approximately 2 h. These results demonstrate that the imposed temperature difference controls both the magnitude and temporal evolution of stratification.

An axial temperature gradient was established inside the vessel. Helium is an inert gas characterized by excellent chemical stability, a high specific heat capacity at constant pressure, and a low molecular weight. Under the action of gravity, the lighter helium tends to accumulate in the upper region, whereas the heavier argon tends to settle toward the lower region. However, Peng et al. (Peng et al., 2024) investigated the effect of height difference on gas distribution and found that significant gas stratification occurs only when the elevation difference is sufficiently large; even at a height difference of 1,500 m, the stratification effect can still be negligible. This indicates that gravity alone is generally insufficient to induce pronounced stratification in the present configuration.

In addition, helium has a much higher thermal conductivity and superior heat transfer capability than argon. Under heating conditions, helium transfers heat more rapidly, thereby enhancing the non-uniformity of the temperature field and further influencing the flow and stratification behavior of the gas mixture. Meanwhile, under condensation conditions, helium may generate buoyancy-driven flow near the condensation surface. When the helium concentration reaches a certain level, a buoyant flow can develop in the vicinity of the condensation surface, promoting helium accumulation in the upper part of the vessel and eventually leading to the formation of a stable helium-rich stratified layer.

The temperature-induced stratification mechanism is schematically illustrated in Figure 15. In binary gas mixtures, a temperature gradient not only drives heat transfer but also induces relative migration between different species, causing an initially uniform mixture to gradually develop a stable composition deviation. This phenomenon is commonly referred to as the Soret effect. Under steady-state conditions, a nonzero heat flux and a nonuniform concentration distribution may coexist within the system, while the net mass flux of each species approaches zero. In essence, the Soret effect represents species separation induced by a temperature gradient, and the steady state is jointly determined by thermodiffusion and ordinary molecular diffusion (Chapman and Cowling, 1990).

In the absence of a temperature gradient, the two species remain uniformly distributed due to the balance of intermolecular interactions, including repulsive and attractive forces as well as van der Waals forces. In the presence of a temperature gradient, the species flux consists of ordinary diffusion and thermodiffusion. At steady state, these two mechanisms balance each other, resulting in a negligible net mass flux while maintaining a stable concentration gradient within the system. At the molecular level, a temperature gradient induces differences in molecular velocity distributions and kinetic energy (Liu and Cai, 2013). Variations in molecular mass, collision cross-section, and intermolecular potential lead to asymmetric momentum and energy exchange during collisions, giving rise to selective species migration. For binary mixtures such as He–Ar, where there is a significant disparity in molecular mass (Berezhnoi and Semenov, 2004), thermodiffusion becomes particularly pronounced (Karimi-Sabet et al., 2023). The resulting composition gradient alters the local mean molar mass and density distribution and, when coupled with gravitational buoyancy, plays a crucial role in the development and evolution of thermal stratification.

For the initial He/Ar volume fraction of 80/20, the corresponding mass fractions are Y_He = 0.2861 and Y_Ar = 0.7139 (Sharipov and Benites, 2015). The thermal diffusion coefficients calculated using the above correlation are summarized in Table 2.

TABLE 2. Thermal diffusion coefficients of the He–Ar mixture at different temperatures.

To examine the consistency between the calculated concentration differences and thermodiffusion theory, an effective thermal diffusion factor was introduced. For a binary mixture, the diffusion flux of Ar can be expressed as Equation 13: where c is the total molar concentration, D Ar is the effective molecular diffusion coefficient, x Ar is the Ar mole fraction, and α T , Ar is the dimensionless thermal diffusion factor, the mole fraction is equivalent to the volume fraction.

J Ar = − c D Ar d x Ar d z + α T , Ar x Ar 1 − x Ar 1 T d T d z (13)

When the species distribution reaches a quasi-steady state, ordinary molecular diffusion approximately balances thermal diffusion, and the net diffusion flux approaches zero. Assuming that the effective thermal diffusion factor remains approximately constant between the bottom and top monitoring locations, integration gives Equation 14: the prescribed upper- and lower-wall temperatures were used as representative temperatures for the theoretical evaluation. The effective thermal diffusion factors calculated from the stabilized concentration distributions are listed in Table 3.

α T , Ar = ln x Ar , b / 1 − x Ar , b − ln x Ar , t / 1 − x Ar , t ln T t / T b . (14)

TABLE 3. Effective thermal diffusion factors calculated from the numerical results.

The theoretical values agree closely with the numerical results, with deviations below 0.3%. Both approaches show that the top-to-bottom Ar concentration difference increases monotonically with the imposed temperature difference. The small deviations arise mainly from the assumptions of a one-dimensional concentration distribution, a constant effective thermal diffusion factor, and the use of wall temperatures as representative temperatures. In the numerical model, the local temperature, density, molecular diffusion coefficient, and thermal diffusion coefficient vary continuously within the vessel. Nevertheless, the agreement in migration direction, variation trend, and concentration-difference magnitude demonstrates that the simulated stratification is consistent with the balance between ordinary molecular diffusion and Soret thermodiffusion. The comparison between the theoretical and simulated Ar concentration differences is summarized in Table 4.

TABLE 4. Comparison between theoretical and simulated Ar concentration differences.

The dimensionless Soret number was introduced to characterize the strength of temperature-gradient-induced species separation, as defined in Equation 15: where S T , i is the Soret coefficient, α T , i is the thermal diffusion factor, and T r e f is the mean temperature of the upper and lower walls. The magnitude of S r i represents the relative strength of thermodiffusion under the imposed temperature difference.

S r i = S T , i Δ T = α T , i Δ T T r e f (15)

For Ar, the calculated Soret number increases from 0.0211 to 0.0393 and 0.0550 as the temperature difference increases from 50 to 100 and 150 K, respectively. This monotonic increase indicates that the thermodiffusion driving force becomes progressively stronger with increasing temperature difference. Correspondingly, the simulated top-to-bottom Ar concentration difference increases from 0.338 to 0.633 and 0.892 percentage points. Therefore, the variation in the Soret number is consistent with the numerical concentration distributions and confirms that the enhanced axial stratification is primarily driven by the increasing thermodiffusion effect.

The present results have several implications for gas-cooled reactor systems. Under non-isothermal conditions, the preferential accumulation of the heavier component in the lower region produces a vertical composition and density gradient. Such a stable stratification may suppress vertical mixing and modify buoyancy-driven flow, which could influence natural circulation and passive decay-heat removal under low-flow or transient conditions. In addition, because argon has a considerably lower thermal conductivity than helium, the local reduction in helium concentration may decrease the heat-transfer capability of the gas mixture and contribute to non-uniform temperature distributions or local thermal gradients.

5 Conclusion

A systematic numerical investigation was conducted to examine the distribution evolution and thermal stratification behavior of He–Ar binary gas mixtures in a closed cylindrical vessel under gravity. Particular attention was given to the effects of the initial composition, initial pressure, vessel aspect ratio, initial temperature, and the temperature difference between the upper and lower sections of the vessel. The main conclusions are summarized as follows:

• In the absence of an axial temperature gradient, the He–Ar mixture remains nearly uniform under the investigated variations in initial composition, pressure, initial temperature, and vessel aspect ratio. The Ar volume-fraction variation remains below 0.1%, indicating that gravity alone is insufficient to produce appreciable species separation over the present vessel height and time scale.
• The imposed axial temperature difference is the dominant parameter governing species stratification. When the temperature difference increases from 50 to 150 K, the stabilized bottom-to-top Ar volume-fraction difference increases from 0.338 to 0.892 percentage points. The corresponding Soret number also increases monotonically, confirming that the enhancement of stratification is directly associated with the increasing thermodiffusion driving force.
• The stratification mechanism is governed by the competition between Soret thermodiffusion and ordinary molecular diffusion. Thermodiffusion drives the lighter He toward the hotter upper region and the heavier Ar toward the colder lower region, whereas ordinary diffusion acts against the developing concentration gradient. A stable composition profile is established when these two diffusion mechanisms approximately balance. The resulting composition gradient further modifies the local mean molecular weight and density, thereby reinforcing the stable vertical density distribution. The close agreement between the theoretical and simulated concentration differences, with deviations below 0.3%, supports this physical interpretation.
• The resulting composition and density gradients may suppress vertical mixing and affect buoyancy-driven transport in confined gas systems. These findings provide useful guidance for evaluating rare-gas mixture stratification in gas-cooled nuclear systems, especially under low-flow or non-isothermal conditions. The conclusions are limited to the investigated geometry, pressure range, temperature range, and prescribed wall-temperature boundary conditions.

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Footnotes

Edited by: Wenxi Tian, Xi’an Jiaotong University, China

Reviewed by: Jamal Al-Zain, Sana’a University, Yemen

Bhuvaneshwar Gera, Bhabha Atomic Research Centre (BARC), India