The breeding blanket in a nuclear fusion reactor generates tritium through capture reaction between lithium and neutrons. Lithium is in a liquid PbLi alloy and the helium formed as reaction by-product can coalesce into bubbles, generating a two-phase mixture with a high-density ratio (η_ρ~O(10^5)). These bubbles can accumulate and stagnate within the blanket channels with potentially harmful consequences [1]. In this paper, the interIsoFoam (iIF) solver of OpenFoam v2012 is used to simulate bubble motion for a two-phase mixture representative of the PbLi-He to test its potential for future developments in the field of fusion.
The first part of the study analyses the performance of the code using several benchmarks: 2D [2] and 3D rising bubble [3], 2D stationary drop [4] and the coaxial coalescence of two bubbles [3]. For almost all the cases, the two variants of the VOF method implemented in iIF, isoAdvector and plicRDF [5], were tested. The code is found in excellent agreement (≤2.1%) with the reference data for minimum circularity/sphericity and maximum rise velocity at a given simulation time for the 2D and 3D rising bubbles. The pressure jump for the stationary drop is underestimated by about 10%, while the index that quantifies the spurious velocities is L_1 (v)~〖O(10〗^(-7)). Excellent agreement is found for the coalescence of two bubbles (Figure 1A).
Subsequently, a parametric analysis for a 2D rising bubble is performed to investigate the performances of the code for a fusion relevant scenario, up to η_ρ≈5∙10^4, where we found a consistent dynamic with the expected regime. Afterwards, He bubbles of different diameters rising in liquid PbLi (η_ρ=〖1.2∙10〗^5) were analysed to investigate regimes for 8∙10^(-3)≤Eo≤2∙10^3 and 44≤Ga≤2∙〖5∙10〗^5, where Eo and Ga are the Eötvös and Galilei numbers. For Eo>10, we were able to recreate the axisymmetric, skirted, oscillatory regimes and the peripheral and central breakup regimes (Figure 1B). For Eo<10, non-physical deformations of the interface are observed, probably generated by spurious velocities that have a greater impact on the solution for very small bubbles and rising velocities.
Overall, iIF is able to reliably simulate the bubble motion in a two-phase flow with η_p≤1.2∙10^5 and Eo>10. The solver will be used as a foundation for developing a multi-phase magnetohydrodynamics model to investigate the bubble motion in a liquid metal subjected to the magnetic field present in a fusion reactor.
[1] M. Kordač and L. Košek, “Helium bubble formation in Pb-16Li within the breeding blanket,” Fusion Eng. Des., vol. 124, pp. 700–704, Nov. 2017, doi: 10.1016/j.fusengdes.2017.05.100.
[2] S. Hysing et al., “Quantitative benchmark computations of two-dimensional bubble dynamics,” Int. J. Numer. Methods Fluids, vol. 60, no. 11, pp. 1259–1288, Aug. 2009, doi: 10.1002/fld.1934.
[3] N. Balcázar, O. Lehmkuhl, L. Jofre, J. Rigola, and A. Oliva, “A coupled volume-of-fluid/level-set method for simulation of two-phase flows on unstructured meshes,” Comput. Fluids, vol. 124, pp. 12–29, Jan. 2016, doi: 10.1016/j.compfluid.2015.10.005.
[4] S. Hysing, “Mixed element FEM level set method for numerical simulation of immiscible fluids,” J. Comput. Phys., vol. 231, no. 6, pp. 2449–2465, 2012, doi: 10.1016/j.jcp.2011.11.035.
[5] L. Gamet, M. Scala, J. Roenby, H. Scheufler, and J. Lou Pierson, “Validation of volume-of-fluid OpenFOAM® isoAdvector solvers using single bubble benchmarks,” Comput. Fluids, vol. 213, p. 104722, Dec. 2020, doi: 10.1016/j.compfluid.2020.104722
