Towards the Direct Numerical Simulation of a Nuclear Pebble Bed Flow - PowerPoint PPT Presentation

Towards the Direct Numerical Simulation of a Nuclear Pebble Bed Flow Star-CD User Conference 22-23 March, 2011 Amsterdam A. Shams, F. Roelofs, E.M.J. Komen shams@nrg.eu

Presentation Plan • Introduction: Problem Description • Strategies adopted • Numerical Tools • Results • Conclusions & Perspectives 2

INTRODUCTION 3

Introduction Overview The nuclear core of High Temperature Reactor (HTR) with pebble bed type has been investigated intensively due to its benefits in management.  Among them flow through the randomly distributed pebble has been a challenge.  This type of flow has distinctive features:  Pressure gradient strongly One needs to master the flow ! affects the boundary layer behaviour.  Transition from a laminar to turbulent flow occurs at different Re numbers. Pebble bed  Flow induced local heat HTR-PM (INET, China) transfer … 4

Introduction Aims of Present Study  Detailed analysis of the flow-field by employing LES and/or RANS and its validation with the experimental or DNS database.  Generate reference DNS database . Experimental studies provided limited information of flow because of the complex geometric configuration.  RANS study of pebble bed geometry. – Previous Experimental Studies: Pre-requisites • Hassan et al. (2008), performed PTV & PIV measurements for randomly distributed pebble stacking. • Geometry selection (i.e. pebble stacking). • Selection of computational domain (RANS study). • Lee et al. (2008), performed PIV measurement of Face Centered • Mesh generation (for RANS and DNS). Cubic (FCC) distribution. • Calibration of boundary conditions (RANS study). • Initial field (RANS study) for DNS • Problem: flow behaviour unknown  Solution: DNS • … 5

STRATEGIES ADOPTED FOR THE PRESENT STUDY 6

Strategies Adopted (FCC) Geometry Selection (pebble stacking) • Different Cubic Arrangment Selected Also considered by Lee et al. (2008), experimental study 7

Strategies Adopted (FCC, 5mm gap) Geometry Selection (pebble stacking) • Face-Centered Cubic (FCC) pebble distribution Point contact ? Not feasible for DNS ! (i) with inter-pebble gap (ii) without inter-pebble gap 5 mm Point contact Area contact Keeping the porosity level close to the experiments 8 8

Strategies Adopted (FCC, 5mm gap, 1 & 8 Cubic) Selection of Computational Domain ( for RANS Study ) D pebble = 0.06 m L single cube = 0.09192 m single cube, 4 pebbles eight cube, 32 pebbles 9 9

Strategies Adopted (FCC, 5mm gap, 1 & 8 Cubic, Polyhedral mesh) Mesh Generation (for RANS Study) • Star-CCM+ is used for the mesh generation. – Polyhedral • ~0.15 M (ii) ~ 0.36 M (iii) ~ 0.71 M (for eight cubic domain) – Refined Mesh, ~2.4 M Polyhedral (for eight cubic domain) – Mesh, ~0.3 M Polyhedral (for single cubic domain) 10 10

Strategies Adopted (FCC, 5mm gap, 1 Cubic, Polyhedral mesh) Mesh Generation (for RANS Study) 11 11

NUMERICAL TOOLS 12

Turbulence Modelling & Numerical Schemes Code Star-CCM+ Flow Configuration Incompressible Solver Segregated flow solver RANS STUDY Turbulence Model K-Epsilon (Standard) Numerical Scheme Second order upwind scheme DNS STUDY Initial Turbulence Field Synthetic Eddy Method Space Discretization Second order Central (5% boundedness) Time Discretization Second order implicit 13 13

Boundary Conditions (RANS study for the calibration of computational domain & BC) • Working fluid is Helium gas . inlet • Mass flow rate (following PBMR-250 MWth) – 0.1124 kg/s for single cube case – 0.4496 kg/s for eight cubic case symmetry • Density = 5.36 Kg/m 3 3.69 × 10 -5 N.s/m 2 • Viscosity = outlet • Turbulence level at inlet and outlet ~ 5 % (Lee, 2007) • Symmetry / Periodic boundary conditions. • No-slip condition on pebbles (solid wall). (i) inlet & outlet (ii) periodic boundary conditions 14 14

RESULTS 15

Results (RANS, 8 Cubic, in-out flow) Eight Cubic Configuration No Periodic B.C 16

Results (RANS, 8 Cubic, in-out flow) Eight Cubic Configuration Wake region Stagnation region No Periodic B.C 17

Results (RANS, 1 Cubic, periodic) Single Cubic Configuration 18

Results (RANS, 1 & 8 Cubic, periodic) Velocity Comparison, 1 & 8 domain Line A Line B Line C

Results (RANS, 8 Cubic, periodic) Boundary Condition Influence All periodic In-out periodic, sides-symmetry 20

Results (RANS, 1 Cubic, periodic) Mass flow rate calibration for DNS  Wall shear stress corresponding to calibrated mass flow rate has been calculated (via RANS study) in order to check the friction velocity scales.  The computed friction velocity corresponding to the original mass flow rate (i.e. M) gives an estimate of a huge mesh requirement for DNS, i.e. around 73 M grid points.  Hence this original mass flow rate has been scaled in order to obtain the a feasible meshing requirement providing the flow regimes behaves in the same manner as of the original M => Re=21614 (based on pebble diameter)

Results (RANS, 1 Cubic, periodic, M, M/5, M/7, M/10) Mass Flow Rate Calibration M7 M7 is Selected !, Mesh Requirement ~ 12.5 M 22

Results (RANS, 1 Cubic, periodic, M/7, Heat input) Calibration of Heat Input • Addition of heat source into the pebbles. • Check either heat input is active or passive scalar. • Q is calculated from the original configuration. • Corresponding to scaled mass flow rate, heat flux is also scaled to the order of 7, i.e. Q7

Results (RANS, 1 Cubic, periodic, M/7, Heat input: Q7) Scaled Heat Input Q/7 = 8,317 W/m 2 , M7 Line A T ave = 783 K Line B 24

Results (DNS, 1 Cube) Meshing for DNS • Polyhedral mesh with an off-set layer. • Integrity of such meshes with the available numerical schemes within Star-CCM+ is checked for DNS type simulations. • DNS of pipe has been perforemd and compared with Kasagi DNS data.

Results (DNS, Pipe Flow, Re Ʈ = 180) Behaviour of Polyhedral for DNS cases Pipe Flow Re Ʈ = 180 Radius=1 m Length~6 m 3.7 Million Points ∆ r + ~ 0.4-11 ∆ x+ ~ 7-8 ∆θ + ~ 5 26

Results (DNS, Pipe Flow, Re Ʈ = 180) Re Ʈ = 180 Behaviour of Polyhedral for DNS cases Transition in mesh from Off-set layer to polys 27

Results (DNS, 1 Cubic, M/7) Mesh Generation for Pebble Bed Number of grid point = ~ 13.5 M Computational domain = 0.092*0.092*0.092 m3 wall normal direction < 1 azimuthal direction ~ 5 cross-sectional directions ~ 5-7 Number of grid point ~ 15 M 28 28

Results (DNS, 1 Cubic, M/7) Prelimenary Results of On-Going DNS Iso-surfaces of Q-criterion coloured with velocity contours 29

Results (DNS, 1 Cubic, M/7) Computational Domain Check via On-going DNS P1,P2,P2,P4 P5,P6,P7,P8 P9,P10,P11,P12,P13,P14,P15 Two-Point Correlations

CONCLUSIONS & PERSPECTIVES 31

Conclusions / Summary  Face Cubic Centered (FCC) configuration has been selected for pebble distribution.  (i) inter-pebble gap of 5 mm (ii) RANS calculations  Periodic BC’s are used, show good qualitative results, and are considered the preferred option for DNS in generating sustained turbulent simulation.  Quantitative comparison of velocity distribution between 8 & 1- cubic arrangement have shown good agreement.  Scaled Heat input (Q7) → T can be used as a passive scalar.  Single cube arrangement is selected for the computational domain of DNS. 32

Conclusions / Summary  Performance of polyhedral mesh was check via pipe flow DNS .  Results support the ability of polyhedral mesh + used numerical strategies used to perform DNS.  … 33

Thank-You 34