Keywords

1 Introduction

Heavy Liquid Metals (HLM) such as liquid lead (Pb) and lead-bismuth eutectic (LBE) are considered as candidate coolants in Generation IV Nuclear Reactors thanks to their suitable thermo-physical and chemical properties. However, the oxidation of HLM and corrosion of structural steels have become major issue in the development of HLM-cooled nuclear reactors. One of the most viable methods for protection of HLM-cooled nuclear reactors is to control the oxygen content dissolved in the HLM among an appropriate range, which could guarantee the structural steels and avoid the HLM oxidation at the same time.

Several researchers have studied the characteristics of oxygen control technics based on different facilities [1,2,3,4,5]. Schroer et al. [1] investigated the oxygen-transfer to flowing lead alloys inside a gas/liquid transfer device in the CORRIDA loop. Marino et al. [2] acquired a mass transfer correlation for the lead oxide mass exchanger and the model was validated using experimental data from the CRAFT loop. Chen et al. [3] explored the LBE flow and oxygen transport in a simplified container under the gas oxygen control using a lattice Boltzmann simulation. However, the mechanisms and characteristics of oxygen diffusion during oxygen control are still not well understood.

In this study, a CFD model in the specific oxygen transfer device has been developed to determine the oxygen transport and distribution in flowing LBE. A mass transfer correlation for oxygen transport was obtained in terms of the Sherwood with simulation results. The numerical data presented in this study represents an essential step to reveal the mechanism of oxygen transport in flowing LBE and provides the theoretical basis for guiding the design of oxygen transfer device in HLM-cooled nuclear reactors.

2 Numerical Modeling

2.1 Geometry and Mesh

The simulated oxygen transfer device has a similar geometry with that in the CORRIDA loop [6], which has a specific inner diameter of 400 mm and a length of 1300 mm. As shown in Fig. 1, the LBE flows through vessels with a liquid level of 1/3 diameter. The control gas is pumped into the oxygen transfer device in the opposite direction through top vessels. The computational domain is simplified and depicted in Fig. 2. The minimum mesh size is set as 5 ⋅ 10–3 m and the total number of the elements is about 2150977 after the mesh independence analysis [7].

Fig. 1.
figure 1

Schematic diagram of the gas control apparatus

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Fig. 2.
figure 2

Geometry of the simulated oxygen transfer device

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2.2 Governing Equations and Boundary Conditions

The transport of oxygen obeys the Reynolds-averaged transport equation for turbulent flow:

$$ \frac{{\partial C_{o} }}{\partial t} + \overrightarrow {u} \cdot \nabla C_{o} = \nabla \cdot (D + \frac{{\mu_{t} }}{{Sc_{t} }})\nabla C_{o} + q_{o} $$
(1)

where Co is the oxygen concentration, u is the velocity of LBE, μt is the eddy viscosity, Sct is the turbulent Schmidt number, and qo is the oxygen source, D is the diffusion coefficient of oxygen. D (cm2·s−1) is given by the following equation [8]:

$$ \begin{array}{*{20}c} {D{ = 0}{\text{.0239e}}^{{ - \frac{43073}{{RT}}}} } & {473K} \\ \end{array} < T < 1273K $$
(2)

where R is the molar gas constant.

Based on the research in [9], the gas/liquid interface is simulated as a free-surface boundary with constant oxygen concentration.

The average dissolution rate q (kg·s−1) of oxygen in the flowing LBE is described by:

$$ q = m{(}C_{out} - C_{in} {)} $$
(3)

where Cout and Cin are the oxygen concentration at the outlet and inlet of oxygen transfer device (wt%), respectively. m is the mass flow rate.

The average mass transfer coefficient k (kg·m−2·s−1) of oxygen in the flowing LBE is calculated by:

$$ k = \frac{q}{{A{(}C_{g/l} - C_{ave} {)}}} $$
(4)

where A is the area of gas/liquid interface (m2), Cg/l is the oxygen concentration at the gas/liquid interface (wt%), Cave is the average oxygen concentration of inlet and outlet (wt%).

The Sherwood number (Sh) representing the dimensionless form of the average mass transfer coefficient is defined by:

$$ Sh = \frac{k \cdot l}{{\rho \cdot D}} $$
(5)

where l is a characteristic length and ρ is the density of LBE.

3 Results and Discussion

The simulation parameters (Tlbe, ulbe, Cin, Cg/l) and calculated results (Cout, k, Sh) are summarized in Table 1.

Table 1. Simulated parameters
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Figure 3 depicts the distribution of oxygen concentration and velocity under the typical working condition (Tlbe = 550 ℃, ulbe = 0.5 m/s, Cin = 8 × 10–7 wt%, Cg/l = 1 × 10–5 wt%). In the simulated model, the oxygen concentration at gas/liquid interface is considered as a constant 1 × 10–5 wt%. The oxygen concentration inside oxygen transfer device is set as 8 × 10–7 wt% in the initial condition. It can be seen from Fig. 3(a), after the transport of oxygen, the oxygen concentration inside the device increases from inlet to outlet with the flow of LBE. Especially, the oxygen distributed near inlet and outlet is obviously higher as a result of the reversed flow of LBE, as shown in Fig. 3(b).

Fig. 3.
figure 3

The distribution of oxygen concentration and velocity under the typical working condition (Tlbe = 550 ℃, ulbe = 0.5 m/s, Cin = 8 × 10–7 wt%, Cg/l = 1 × 10–5 wt%)

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Figure 4 shows the effects of the temperature and the velocity of LBE on the average oxygen mass transfer coefficient. It can be obtained that the average oxygen mass transfer coefficient increases with the increase of temperature and velocity of LBE. The reason is that the thermophysical properties such as viscosity and diffusion coefficient change with the LBE temperature and the mass transfer of oxygen is improved with the combined effect of convection and diffusion.

Fig. 4.
figure 4

The effects of the temperature and the velocity of LBE on the average oxygen mass transfer coefficient

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Parameter analysis is performed for comparison of the average oxygen mass transfer coefficient k among different gas/liquid interface oxygen concentrations Cg/l and different inlet oxygen concentrations Cin under different velocities of LBE at LBE temperature of 550 ℃ in Fig. 5(a) and 5(b), respectively. The results demonstrate that there is no obvious difference among average oxygen mass transfer coefficients on interface oxygen concentrations, as shown in Fig. 5(a). However, the average oxygen mass transfer coefficients are slightly smaller related to the higher inlet oxygen concentration (8 × 10−7wt%) when the flow rate ulbe <2 m/s, as shown in Fig. 5(b). Thus, the gas/liquid interface oxygen concentration has little influence on the mass transfer coefficient of oxygen in the oxygen transfer device with specific geometry. On the other hand, the smaller inlet oxygen concentration leads to the larger average oxygen mass transfer coefficient and the effects of inlet oxygen concentration become weaker with the increase of flow rate.

Fig. 5.
figure 5

Comparison of the average oxygen mass transfer coefficient k among different gas/liquid interface oxygen concentrations Cg/l and different inlet oxygen concentrations Cin under different velocities of LBE at temperature of 550 ℃

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Finally, a mass transfer correlation for oxygen transport was obtained in terms of the Sherwood with simulation results, as described by

$$ Sh = A \cdot Pe^{B} $$
(6)

The corresponding coefficients A and B are listed in Table 2.

Table 2. Coefficients in (6)
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The deviations between simulated results and calculated results by (6) are shown in Fig. 6. It can be noted that the predictions of the correlation equation are all in agreement with the simulated Sh numbers in general with the maximum deviation of ± 26%.

Fig. 6.
figure 6

The deviations between simulated results and calculated results by (6)

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4 Conclusions

In this study, the oxygen transport characteristic in flowing LBE has been investigated with a turbulence model coupling species transport model in the specific oxygen transfer device. The following conclusions could be drawn:

  1. 1)

    The mass transfer coefficient of oxygen increases with the increase of temperature and velocity of LBE because of the combined effect of convection and diffusion.

  2. 2)

    The gas/liquid interface oxygen concentration has little influence on the mass transfer coefficient of oxygen in the oxygen transfer device with specific geometry. Comparatively, the smaller inlet oxygen concentration leads to the larger average oxygen mass transfer coefficient and the effects of inlet oxygen concentration become weaker with the increase of flow rate.

  3. 3)

    A mass transfer correlation for oxygen transport is obtained and the calculations of the correlation equation are all in agreement with the simulated results.