Study on the particle deposition characteristics in the boundary layer of LBE medium based on the Eulerian deposition model

Xianmin DONG; Ruifeng TIAN; Jiming LIN; Xiaochang LI; Puzhen GAO; Desheng JIN; Bin QIU; Yulong MAO

doi:10.11889/j.0253-3219.2025.hjs.48.250024

NUCLEAR TECHNIQUES, Volume. 48, Issue 7, 070026(2025)

Study on the particle deposition characteristics in the boundary layer of LBE medium based on the Eulerian deposition model

Xianmin DONG^1,2, Ruifeng TIAN^1、*, Jiming LIN^2、**, Xiaochang LI¹, Puzhen GAO¹, Desheng JIN², Bin QIU², and Yulong MAO²

Author Affiliations

¹Harbin Engineering University, Harbin 150001, China

²China Nuclear Power Technology Research Institute Co., Ltd., Shenzhen 518000, China

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Figures & Tables(22)

Fig. 1. Diagram of geometric model

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Fig. 2. Schematic diagram of velocity vectors in the fully developed section

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Fig. 3. Comparison and verification of dimensionless velocity within the boundary layer (color online)

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Fig. 4. Schematic diagram of the time-advancing finite difference method for solution (color online)

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Fig. 5. Diagram of lower boundary conditions and roughness model (color online)

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Fig. 6. Comparison results of different convergence factors (color online)

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Fig. 7. Mesh sensitivity analysis of convergence factors (color online)

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Fig. 8. Convergence analysis of convergence factors (color online)

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Fig. 9. Verification of the computational model for convergence factors (color online)

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Fig. 10. Comparison of particle deposition velocities in LBE and air media with U_air=11.84 m∙s^-1 and U_LBE=1 m∙s^-1 (color online)

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Fig. 11. Comparison of Stokes number of particles in LBE and air media (color online)

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Fig. 12. Comparison of particle deposition velocity at different roughness levels with U=1 m∙s^-1 (color online)

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Fig. 13. Variation of r_p⁺/F⁺ with particle diameter (color online)

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Fig. 14. Comparison of particle deposition velocity at different fluid velocities with F⁺=0 (color online)

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Fig. 15. Comparison of particle deposition velocity at different fluid temperatures with U=1 m∙s^-1 and F⁺=0 (color online)

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Fig. 16. Comparison of particle deposition velocity for different particle types with U=1 m∙s^-1 and F⁺=0 (color online)

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Fig. 17. The influence of virtual mass force on deposition velocity (color online)

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Table 1. Dimensionless parameters
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Table 1. Dimensionless parameters
$V_{d e p}^{+}$ $ρ_{p}^{+}$ ${\bar{V}}_{p y}^{c +}$ $\bar{V_{p y}^{' 2 +}}$ $\bar{V_{f y}^{' 2 +}}$ $y^{+}$ $τ_{p}^{+}$ $r_{p}^{+}$
$\frac{J}{ρ_{p}^{0} u^{*}}$ $\frac{{\bar{ρ}}_{p}}{ρ_{p}^{0}}$ $\frac{{\bar{V}}_{p y}^{c}}{u^{*}}$ $\frac{V_{p y}^{' 2}}{u^{* 2}}$ $\frac{\bar{V_{p y}^{' 2}}}{u^{* 2}}$ $\frac{y u^{*}}{ν}$ $\frac{τ_{p} u^{* 2}}{ν}$ $\frac{r_{p} u^{*}}{ν}$

Table 2. Boundary conditions
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Table 2. Boundary conditions
边界Boundary y⁺ 式（19）Eq.(19) 式（18）Eq.(18)
下边界Lower boundary $y^{+} = r_{^{p}}^{+} + k^{+} - e^{+}$ $ρ_{p}^{+} = 0$ ——
上边界Upper boundary $y^{+} = 60$ $ρ_{p}^{+} = 1$ ${\bar{V}}_{p y}^{c +} = 0$

Table 3. Experimental verification conditions for particle deposition in air

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Table 3. Experimental verification conditions for particle deposition in air

参数Parameters	空气参数Air parameters	颗粒参数Particle parameters
密度 Density / kg∙m^-3	1.195	920
导热系数 Thermal conductivity / W∙(m·K)^-1	0.026 7	0.190 7
动力黏度 Dynamic viscosity / Pa·S	1.789 4×10^-5	―
普朗特数Prandtl number	0.713	―
分子平均自由程 Mean free path of molecules / m	6.5×10^-8	―
温度 Temperature / K	298	―
流速 Velocity / m∙s^-1	11.84	―
摩擦速度Friction velocity	0.794	―
粗糙度 Roughness / m	0	―

Table 4. Calculation conditions for particle deposition in liquid LBE medium

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Table 4. Calculation conditions for particle deposition in liquid LBE medium

参数Parameters	LBE参数LBE parameters
密度 Density / kg∙m^-3	$ρ_{L B E} = 11 096 - 1.323 6 \times T$
导热系数 Thermal conductivity / W∙(m·K)^-1	$λ_{L B E} = 3.61 + 1.517 \times 10^{- 2} \times T$
动力黏度 Dynamic viscosity / Pa·S	$η_{L B E} = 4.94 \times 10^{- 4} e x p (757.1 / T)$
定压比热容 Specific heat capacity / J∙(kg∙K)^-1	$c_{p, L B E} = 159 - 2.72 \times 10^{- 2} \times T + 7.12 \times 10^{- 6} \times T^{2}$
普朗特数 Prandtl number	0.015
平均自由程 Mean free path of molecules / m	10^-10
速度 Velocity / m∙s^-1	0.2，1.0，3.0
温度 Temperature / K	473.15，500.15，533.15
无量纲粗糙度F Dimensionless roughness / m	0，0.25，0.5

Table 5. Calculation conditions for particle deposition in liquid LBE medium^[21-23]

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Table 5. Calculation conditions for particle deposition in liquid LBE medium^[21-23]

参数Parameters	颗粒参数Particle parameters
颗粒种类Particle type	PbO，Al₂O₃，Fe₃O₄
颗粒直径Particle diameter / μm	0.1~70
密度Density / kg∙m^-3	PbO	8 530
	Al₂O₃	3 900
	Fe₃O₄	5 180
导热系数Thermal conductivity / W∙(m·K)^-1	PbO	3.16
	Al₂O₃	35
	Fe₃O₄	17.65

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Xianmin DONG, Ruifeng TIAN, Jiming LIN, Xiaochang LI, Puzhen GAO, Desheng JIN, Bin QIU, Yulong MAO. Study on the particle deposition characteristics in the boundary layer of LBE medium based on the Eulerian deposition model[J]. NUCLEAR TECHNIQUES, 2025, 48(7): 070026

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Paper Information

Category: Special Issue on The First Academic Annual Conference of the Research Reactor and Innovative Reactor Association of Chinese Nuclear Society and Advanced Nuclear Power System Reactor Engineering

Received: Jan. 17, 2025

Accepted: --

Published Online: Sep. 15, 2025

The Author Email: Ruifeng TIAN (TIANRuifeng), Jiming LIN (LINJiming)

DOI:10.11889/j.0253-3219.2025.hjs.48.250024

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Dimensionless parameters

Table 1. Dimensionless parameters

Table 2. Boundary conditions

Table 2. Boundary conditions

Table 3. Experimental verification conditions for particle deposition in air

Table 3. Experimental verification conditions for particle deposition in air

Table 4. Calculation conditions for particle deposition in liquid LBE medium

Table 4. Calculation conditions for particle deposition in liquid LBE medium

Table 5. Calculation conditions for particle deposition in liquid LBE medium[21-23]

Table 5. Calculation conditions for particle deposition in liquid LBE medium[21-23]

Table 5. Calculation conditions for particle deposition in liquid LBE medium^[21-23]

Table 5. Calculation conditions for particle deposition in liquid LBE medium^[21-23]