Paris, 9 February 2018 Thermohydraulic of nuclear core reactor: construction, study and dicretisation of models Asymptotic vs compressible models LMNC projects (2014-2017) Team Needs-2018 Gloria Faccanoni, Cédric Galusinski, Mehmet Ersoy, Moustoifa Rafiou Team ❶ Bérénice Grec, Samuel Kokh, Olivier Lafitte, Yohan Penel, (Stéphane Dellacherie) Team ❷ Jean-Marc Hérard, Olivier Hurisse, Lucie Quibel Team ❸ Hélène Mathis, Hala Ghazi, Nicolas Seguin, Benjamin Boutin, Thuong Nguyen, Jonathan Jung Team ❹ Olivier Doche, Pablo Rubiolo Team ❺
1. Context 2. Past 3. 2018. . . Outline Context 1 Needs 2014-2017 2 Needs 2018. . . 3 LMNC projects (2014-2017) Thermohydraulic: LOFA, LOCA, vapor explosion 2 / 23 :
1. Context 2. Past 3. 2018. . . Section 1 Context LMNC projects (2014-2017) Thermohydraulic: LOFA, LOCA, vapor explosion 3 / 23 :
1. Context 2. Past 3. 2018. . . Context Modelisation and numerical simulation of heat transfers in a core of a nuclear reactor (or steam generator) where the coolant is water (or sodium or molten salt) with or without phase transition. LMNC projects (2014-2017) Thermohydraulic: LOFA, LOCA, vapor explosion 4 / 23 :
1. Context 2. Past 3. 2018. . . Core of a Pressurized Water Reactor Mixture liquid-steam (330 ◦ C) Control Rods Φ ≃ 170 MW Fuel Elements Water : coolant and moderator p 0 ≃ 155 bar Liquid Water (290 ◦ C and 5 m · s − 1 ) LMNC projects (2014-2017) Thermohydraulic: LOFA, LOCA, vapor explosion 5 / 23 :
1. Context 2. Past 3. 2018. . . Core of a Pressurized Water Reactor Nominal regime Inlet velocity : | u | ≃ 5 m · s − 1 ℓ ≃ 1 . 0 × 10 3 m · s − 1 Speed of sound at p 0 = 155 bar and T = 300 ◦ C : c ∗ Mach number M = | u | ≃ 5 × 10 − 3 ≪ 1 c ∗ ℓ LOFA The Loss of Flow Accident is an accidental scenario induced by a coolant pump trip event with phase change Acoustics negligible (no shock waves) BUT high heat transfers : div u � = 0 LOCA This is not the case for very fast depressurizations such as a Loss of Coolant Accident LMNC projects (2014-2017) Thermohydraulic: LOFA, LOCA, vapor explosion 6 / 23 :
1. Context 2. Past 3. 2018. . . Core of a Pressurized Water Reactor Nominal regime Inlet velocity : | u | ≃ 5 m · s − 1 ℓ ≃ 1 . 0 × 10 3 m · s − 1 Speed of sound at p 0 = 155 bar and T = 300 ◦ C : c ∗ Mach number M = | u | ≃ 5 × 10 − 3 ≪ 1 c ∗ ℓ LOFA The Loss of Flow Accident is an accidental scenario induced by a coolant pump trip event with phase change Acoustics negligible (no shock waves) BUT high heat transfers : div u � = 0 LOCA This is not the case for very fast depressurizations such as a Loss of Coolant Accident LMNC projects (2014-2017) Thermohydraulic: LOFA, LOCA, vapor explosion 6 / 23 :
1. Context 2. Past 3. 2018. . . Core of a Pressurized Water Reactor Nominal regime Inlet velocity : | u | ≃ 5 m · s − 1 ℓ ≃ 1 . 0 × 10 3 m · s − 1 Speed of sound at p 0 = 155 bar and T = 300 ◦ C : c ∗ Mach number M = | u | ≃ 5 × 10 − 3 ≪ 1 c ∗ ℓ LOFA The Loss of Flow Accident is an accidental scenario induced by a coolant pump trip event with phase change Acoustics negligible (no shock waves) BUT high heat transfers : div u � = 0 LOCA This is not the case for very fast depressurizations such as a Loss of Coolant Accident LMNC projects (2014-2017) Thermohydraulic: LOFA, LOCA, vapor explosion 6 / 23 :
1. Context 2. Past 3. 2018. . . Core of a Pressurized Water Reactor Nominal regime Inlet velocity : | u | ≃ 5 m · s − 1 ℓ ≃ 1 . 0 × 10 3 m · s − 1 Speed of sound at p 0 = 155 bar and T = 300 ◦ C : c ∗ Mach number M = | u | ≃ 5 × 10 − 3 ≪ 1 c ∗ ℓ LOFA The Loss of Flow Accident is an accidental scenario induced by a coolant pump trip event with phase change Acoustics negligible (no shock waves) BUT high heat transfers : div u � = 0 LOCA This is not the case for very fast depressurizations such as a Loss of Coolant Accident LMNC projects (2014-2017) Thermohydraulic: LOFA, LOCA, vapor explosion 6 / 23 :
1. Context 2. Past 3. 2018. . . All Mach number flow : Compressible vs incompressible Large Mach number Compressible flow : hyperbolic systems of conservation laws Shock discontinuities are generic Conservation schemes necessary in order to guarantee consistency for weak solutions CFL restriction physiological (we are in general interested in acoustic waves) Small Mach number Quasi-incompressible flow Often one is not interested in resolving acoustic waves Material shocks do not form from smooth initial data and acoustic shocks have negligible amplitude Classical CFL restriction is pathological : it is due to the stiffness of the problem and should be avoided Zero Mach number Incompressible flow No acoustic waves Compressible and incompressible flows are usually treated by different techniques. Not obvious how to unify the treatment. Goal : design numerical method for compressible flows that can handle both the compressible regime and the incompressible limit LMNC projects (2014-2017) Thermohydraulic: LOFA, LOCA, vapor explosion 7 / 23 :
1. Context 2. Past 3. 2018. . . All Mach number flow : Compressible vs incompressible Large Mach number Compressible flow : hyperbolic systems of conservation laws Shock discontinuities are generic Conservation schemes necessary in order to guarantee consistency for weak solutions CFL restriction physiological (we are in general interested in acoustic waves) Small Mach number Quasi-incompressible flow Often one is not interested in resolving acoustic waves Material shocks do not form from smooth initial data and acoustic shocks have negligible amplitude Classical CFL restriction is pathological : it is due to the stiffness of the problem and should be avoided Zero Mach number Incompressible flow No acoustic waves Compressible and incompressible flows are usually treated by different techniques. Not obvious how to unify the treatment. Goal : design numerical method for compressible flows that can handle both the compressible regime and the incompressible limit LMNC projects (2014-2017) Thermohydraulic: LOFA, LOCA, vapor explosion 7 / 23 :
1. Context 2. Past 3. 2018. . . All Mach number flow : Compressible vs incompressible Large Mach number Compressible flow : hyperbolic systems of conservation laws Shock discontinuities are generic Conservation schemes necessary in order to guarantee consistency for weak solutions CFL restriction physiological (we are in general interested in acoustic waves) Small Mach number Quasi-incompressible flow Often one is not interested in resolving acoustic waves Material shocks do not form from smooth initial data and acoustic shocks have negligible amplitude Classical CFL restriction is pathological : it is due to the stiffness of the problem and should be avoided Zero Mach number Incompressible flow No acoustic waves Compressible and incompressible flows are usually treated by different techniques. Not obvious how to unify the treatment. Goal : design numerical method for compressible flows that can handle both the compressible regime and the incompressible limit LMNC projects (2014-2017) Thermohydraulic: LOFA, LOCA, vapor explosion 7 / 23 :
1. Context 2. Past 3. 2018. . . All Mach number flow : Compressible vs incompressible Large Mach number Compressible flow : hyperbolic systems of conservation laws Shock discontinuities are generic Conservation schemes necessary in order to guarantee consistency for weak solutions CFL restriction physiological (we are in general interested in acoustic waves) Small Mach number Quasi-incompressible flow Often one is not interested in resolving acoustic waves Material shocks do not form from smooth initial data and acoustic shocks have negligible amplitude Classical CFL restriction is pathological : it is due to the stiffness of the problem and should be avoided Zero Mach number Incompressible flow No acoustic waves Compressible and incompressible flows are usually treated by different techniques. Not obvious how to unify the treatment. Goal : design numerical method for compressible flows that can handle both the compressible regime and the incompressible limit LMNC projects (2014-2017) Thermohydraulic: LOFA, LOCA, vapor explosion 7 / 23 :
1. Context 2. Past 3. 2018. . . Which model wrt regime ? Mach number M � = 0 1 Compressible Navier-Stokes system: model with acoustics and with heat transfers, if M ≪ 1 standard FV shock-capturing hyperbolic solvers have difficulties. Mach number M ≪ 1 and high heat transfers div u � = 0 2 Asymptotic low Mach model: model without acoustics but with heat transfers Mach number M ≃ 0 3 Incompressible Navier-Stokes system: model with no acoustics and no heat transfers LMNC projects (2014-2017) Thermohydraulic: LOFA, LOCA, vapor explosion 8 / 23 :
1. Context 2. Past 3. 2018. . . Which model wrt regime ? Mach number M � = 0 1 Compressible Navier-Stokes system: model with acoustics and with heat transfers, if M ≪ 1 standard FV shock-capturing hyperbolic solvers have difficulties. Mach number M ≪ 1 and high heat transfers div u � = 0 2 Asymptotic low Mach model: model without acoustics but with heat transfers Mach number M ≃ 0 3 Incompressible Navier-Stokes system: model with no acoustics and no heat transfers LMNC projects (2014-2017) Thermohydraulic: LOFA, LOCA, vapor explosion 8 / 23 :
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