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Study of a low Mach nuclear core model for single-phase flows. (English. French summary) Zbl 1329.76248
Summary: This paper deals with the modelling of the coolant (water) in a nuclear reactor core. This study is based on a monophasic low Mach number model (Lmnc model) coupled to the stiffened gas law for a single-phase flow. Some analytical steady and unsteady solutions are presented for the 1D case. We then introduce a numerical scheme to simulate the 1D model in order to assess its relevance. Finally, we carry out a normal mode perturbation analysis in order to approximate 2D solutions around the 1D steady solutions.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76Dxx Incompressible viscous fluids
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
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[12] N. Todreas & M. Kazimi. Nuclear Systems I: Thermal Hydraulic Fundamentals. Taylor & Francis Group, 2nd edition, (2011). ESAIM: PROCEEDINGS131 Figure 5. Linear case. Above: numerical (red dashed line), exact (black circles) and asymptotic (blue solid line) solutions to Eq. (5b) at different times. Below : relative error between numerical and exact solutions (black circles) and between numerical and asymptotic solutions (blue solid line) at different times. Figure 6. Linear case. Convergence rate (logarithmic scale) in norms L\inftyand L2. Figure 7. Linear case. Comparison at time t = 1 s between numerical (red dashed line) and asymptotic solutions (blue solid line) to Syst. (5). Figure 8. Linear case (with singular charge loss). Comparison at time t = 1 s between numerical (red dashed line) solutions to Syst. (5) with (5c) replaced by (5c’) and asymptotic solutions (blue solid line) to Syst. (5). ESAIM: PROCEEDINGS133 Figure 9. Negative {\(\Phi\)} case. Comparison at time t = 1 s between numerical (red dashed line) and asymptotic solutions (blue solid line) to Syst. (5). Figure 10. Sine case. Numerical (red dashed line) and asymptotic (blue solid line) solutions to Eq. (5b) at different times. Figure 11. Alternating {\(\Phi\)} case. Numerical (red dashed line) and asymptotic (associated to {\(\Phi\)}0– blue dotted line and to {\(\Phi\)}0/5 – black dotted line) solutions to Eq. (5b) at different times. Figure 12. Alternating {\(\Phi\)} case. Evolution with respect to time of the error between numerical solution to Eq. (5b) and asymptotic solution associated to {\(\Phi\)}0/5.
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