3.1.1 Range of applicability……….……….….… 3-2 3.1.2 Code structure……….….….. 3-2 3.1.3 Fluid-dynamics………..… 3-3 3.1.4 Numerical methods………....… 3-4 3.1.5 Heat conduction and heat transfer………...… 3-5 3.1.6 Nuclear heat generation……….……….……... 3-6 3.1.7 Simulation of components………..……... 3-7 3.1.8 Simulation of control and balance of plant………... 3-7

3.2 ATHLET Thermo-Fluid dynamics………...

_3-8

3.2.1 Basic field equations……….……..….. 3-8 3.2.2 The finite-volume approach………..… 3-11

3.3 The time advancement procedure FEBE………..………..….…. 3-12

3.3.1 Main features………..….….. 3-12

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3.3.2 Benefits of FEBE application……….…...…… 3-14

3.4 Nodalization of the Spallation loop with ATHLET code…...………..… 3-16

3.5 Transient simulations………..………...………... 3-21

3.5.1 Test A………...…. 3-22 3.5.2 Test B……….………….….. 3-28 3.5.3 Test C………..….. 3-30 3.5.4 Test D………..……….……. 3-33 3.5.5 Test E………....……. 3-35

Bibliography……….. 3-38

4. The CFD code ANSYS CFX……….…....

4-1

4.1 The governing equations of fluid flow and heat transfer……….………..……... 4-1

4.2 Differential and integral forms of the general transport equations……….….. 4-4

4.2.1 Approximation of surface integrals……….….. 4-6 4.2.2 Approximation of volume integrals………....….. 4-7 4.2.3 Upwind interpolation (UDS)………....……. 4-7 4.2.4 Linear interpolation (CDS)……….…....…... 4-8

4.3 Discretization method implemented in ANSYS CFX………... 4-9

4.3.1 Upwind differencing scheme……….….... 4-10 4.3.2 Specific blend factor……….…….….... 4-10 4.3.3 High resolution scheme……….………....4-11

4.4 Turbulence models………...…. 4-11

4.4.1 k – ε model……….…...…. 4-13 4.4.2 k – ω model………... 4-14 4.4.3 SST k – ω model………..….4-15

4.5 Numerical models for the CFD analysis of target………..……….. 4-17

4.5.1 Multiphase models implemented in ANSYS CFX……….….. 4-17 4.5.2 Inhomogeneous model……….…. 4-19 4.5.3 Homogeneous model………...….. 4-21 4.5.4 Multiphase turbulence models……….……. 4-22 4.5.5 The cavitation model……….….…...4-23

4.6 Hydraulic study of the target………..…….…..… 4-25

4.6.1 Geometry and mesh generation……….………….…... 4-25 4.6.2 Numerical models and simulation setup……….….. 4-28 4.6.3 Simulation results…………...………... 4-32

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5. ATHLET – ANSYS CFX coupled code technique………...

5-1

5.1 Coupled systems classification………...…..… 5-1

5.1.1 Spatial domain……….…....….. 5-2 5.1.2 Coupling execution……….……… 5-3 5.1.3 Code integration………...…. 5-4 5.1.4 Synchronization………..…….……..… 5-4 5.1.5 Information exchange type……….……..…. 5-5 5.1.6 Numerical schemes……….……… 5-5

5.2 State-of-the-art of the coupled code technique….……….... 5-8

5.3 ATHLET – ANSYS CFX coupling scheme………..…... 5-10

5.3.1 Coupling structure………..…………....…... 5-11 5.3.2 Coupling interface code………...… 5-13 5.3.3 Coupling procedure……….…..… 5-14 5.3.4 Code modification and boundary exchange parameters………....….... 5-17 5.3.5 Coupling schemes………...…... 5-19

5.4 ATHLET – ANSYS CFX coupled code test case………..…….. 5-21

5.4.1 Introduction to the coupled code calculations...……….…. 5-21 5.4.2 Challenges in the coupled code simulations……….…. 5-22 5.4.3 Pipe modeling and CFD simulation………..… 5-22 5.4.4 Coupled simulation with ATHLET – ANSYS CFX……….……..….. 5-24

5.5 Coupled code analysis of the MYRRHA spallation loop………...

5-27

5.5.1 First coupling calculation applied to the spallation loop………..………….… 5-27 5.5.2 Extension of the CFD domain……….….…. 5-30 5.5.3 ANSYS CFX stand-alone simulation results with the extended CFD domain……..…... 5-33 5.5.4 ATHLET – ANSYS CFX simulation for the open configuration………..…... 5-36 5.5.5 Transient analyses with ATHLET – ANSYS CFX……….….. 5-39 5.5.5.1 Mass flow increase………..…... 5-39 5.5.5.2 Mass flow decrease………...….. 5-43 5.5.6 ATHLET – ANSYS CFX simulation for the closed configuration………..…

5-47

5.5.7 Transients analyses using the closed configuration……….…..…..….

5-50

5.5.7.1 Mass flow increase………..……... 5-50 5.5.7.2 Mass flow decrease………... 5-52

Table of Contents