1. The PMBR steady-state and Coupled kinetics core thermal-hydraulics benchmark test problems PBMR (Pty) Ltd. – NRG – Penn State Univ. – Purdeu Univ. - INL 1 Resumed from Nuclear Engineering and Design 236 (2006) 657 - 668

2. Review : Introduction Benchmark philosophy and assumptions Geometrical description Materials, properties and cross section Steady-state test case Transient test case Code description Resumed from Nuclear Engineering and Design 236 (2006) 657 - 668 2

3. Introduction In support of the PBMR Verification and Validation (V&V) effort, a set of bencmark test problem has been defined that focus on coupled core neturonics and thermal-hydraulics code-to-code comparisons. The motivation are – to test the existing methods or codes available for HTGR – to serve as a basis for the development of more accurate and efficient tools to analyse the neutronics and thermal-hydraulic behaviour for design and safety evaluations in future. The reference design for the PBMR268 benchmark problem is derived from the 268 MW PBMR design with a dynamic central columns containing only graphite spheres. The PBMR design applies a continues reloading scheme where unloaded fuel spheres, which have not reached the target burnup, are returned to the top of the core. Based on the work performed in this benchmark the PBMR 400 MW design with fixed central reflector has been accepted as ana OECD benchmark problem and work already started. Resumed from Nuclear Engineering and Design 236 (2006) 657 - 668 3

4. Benchmark Philosophy and Assumptions The focus of the current benchmark test cases is on establishing well-defined transient benchmark cases. Also on developing coupled kinetics/core thermal-hydraulics test problem that include fast (reactivity insertions) and slow (thermal heat-up due to decay heat) transient. Several simplifications were made to the design specification so that the need for any further approximations is limited. Number densities and macroscopic cross-sections are given for reference equilibrium core. Multi-dimensional cross-section library and interpolation routines are supplied to participants as the basis for all transient studies. Although this requires source code changes, it circumvents differences due to different sources of cross-section data and preparation. Core design essentially two-dimensional (r,z). Flow channels within the pebble bed have been simplified to be parallel and at equal speed while the dynamic central column and mixing zone widths were defined to be constant over the total axial height. Control rods in the side reflector are modelled as a cylindrical skirt with a given B10 concentration. A multi-pass fuel circulation and vertical pebble flow are assumed. All heat sources (from fission) will be deposited locally in the fuel, and that no other eat sources exist outside the core. Resumed from Nuclear Engineering and Design 236 (2006) 657 - 668

5. Geometrical Description (1) Resumed from Nuclear Engineering and Design 236 (2006) 657 - 668 5

6. Geometrical Description (2) Resumed from Nuclear Engineering and Design 236 (2006) 657 - 668 6

7. Geometrical Description (3) Resumed from Nuclear Engineering and Design 236 (2006) 657 - 668 7

8. Materials: properties and cross-sections Resumed from Nuclear Engineering and Design 236 (2006) 657 - 668 8 Pebble fuel spheres with low enriched (8%) uranium-oxide triso-coated particles and with a loading of 9 g per fule sphere are used in the benchmark. A pebble packing fraction of 0.61 is assumed In the diffusion calculation, directional dependent diffusion coefficients are used to represent the neutron streaming effects.

9. Resumed from Nuclear Engineering and Design 236 (2006) 657 - 668 9 Materials: properties and cross-sections The properties were simplified to removed temperature and fast-fluence dependence to allow straightforward implementation and comparison. The thermal conductivity of the pebble-bed and reflector graphite is dependent on irradiation damage and temperature (history and instantaneous), and this effect must be included if core design calculations are to be performed

10. Steady-state Case (1) Case N-1 : fresh fuel and cold conditions The steady-state solution is to be found for the model description and the following conditions : -All fuel is fresh (9 g heavy metal (HM) and 8 w/o enriched) -Cold conditions (300K) for all materials -Cross section to be generated by participants. Resumed from Nuclear Engineering and Design 236 (2006) 657 - 668 10 In all cases, results such as power, flux and temperature profiles are to be presented on a given mesh for easy comparisons. A two=group energy structure with a thermal cut off at 2.1 eV was selected

11. Steady-state Case (2) Case N-3 : fresh fuel with given cross-section The steady-state solution is to be found for the model description and the following conditions : -Constant temperature conditions 600 and 900 K. -Make use of a single set of tabulated set of cross- section (at the appropriate temperature) -Cross-section for 300-1500 K in 300 K steps are provided as part of the detailed benchmark definition for all materials. Resumed from Nuclear Engineering and Design 236 (2006) 657 - 668 11

12. Steady-state Case (2) Resumed from Nuclear Engineering and Design 236 (2006) 657 - 668 12 Case N-2 : equlibrium cycle with given number densities The steady-state solution is to be found for the model description and the following conditions : -The given equilibrium uranium, graphite and structural number densities are used (no fission product or higher elements) -Constant temperature conditions (600 and 900 K) for all materials -Cross-section to be generated by participants.