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

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Presentation Plan

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

INTRODUCTION

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Overview

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Introduction

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

affects the boundary layer behaviour.

• Transition from a laminar

to turbulent flow occurs at different Re numbers.

• Flow induced local heat

transfer … One needs to master the flow !

HTR-PM (INET, China) Pebble bed

Experimental studies provided limited information of flow because of the complex geometric configuration.

– Previous Experimental Studies:

• Hassan et al. (2008), performed PTV & PIV measurements for

randomly distributed pebble stacking.

• Lee et al. (2008), performed PIV measurement of Face Centered

Cubic (FCC) distribution.

• Problem: flow behaviour unknown  Solution: DNS

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.  RANS study of pebble bed geometry. Pre-requisites

• Geometry selection (i.e. pebble stacking).
• Selection of computational domain (RANS study).
• Mesh generation (for RANS and DNS).
• Calibration of boundary conditions (RANS study).
• Initial field (RANS study) for DNS
• …

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Introduction

STRATEGIES ADOPTED FOR THE PRESENT STUDY

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Geometry Selection (pebble stacking)

• Different Cubic Arrangment

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Also considered by Lee et al. (2008), experimental study

Selected

Strategies Adopted (FCC)

• Face-Centered Cubic (FCC) pebble distribution

(i) with inter-pebble gap

(ii) without inter-pebble gap

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5 mm Point contact Area contact

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Point contact ? Not feasible for DNS ! Keeping the porosity level close to the experiments

Geometry Selection (pebble stacking)

Strategies Adopted (FCC, 5mm gap)

Selection of Computational Domain (for RANS Study)

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Dpebble = 0.06 m Lsingle cube = 0.09192 m

single cube, 4 pebbles eight cube, 32 pebbles Strategies Adopted (FCC, 5mm gap, 1 & 8 Cubic)

Mesh Generation (for RANS Study)

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• 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)

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Strategies Adopted (FCC, 5mm gap, 1 & 8 Cubic, Polyhedral mesh)

Mesh Generation (for RANS Study)

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Strategies Adopted (FCC, 5mm gap, 1 Cubic, Polyhedral mesh)

NUMERICAL TOOLS

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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

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Boundary Conditions (RANS study for the calibration of

computational domain & BC)

inlet

• utlet

symmetry 14

• Working fluid is Helium gas.
• Mass flow rate (following PBMR-250 MWth)

– 0.1124 kg/s for single cube case – 0.4496 kg/s for eight cubic case

• Density

= 5.36 Kg/m3

• Viscosity

= 3.69×10-5 N.s/m2

• 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

RESULTS

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Eight Cubic Configuration

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

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Eight Cubic Configuration

No Periodic B.C

Wake region Stagnation region

Results (RANS, 8 Cubic, in-out flow)

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Single Cubic Configuration

Results (RANS, 1 Cubic, periodic)

Velocity Comparison, 1 & 8 domain

Results (RANS, 1 & 8 Cubic, periodic)

Line C Line A Line B

Boundary Condition Influence

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Results (RANS, 8 Cubic, periodic) In-out periodic, sides-symmetry All 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

• btain the a feasible meshing requirement providing the flow regimes

behaves in the same manner as of the original M => Re=21614 (based

• n pebble diameter)

Results (RANS, 1 Cubic, periodic)

Mass Flow Rate Calibration

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

• 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

Calibration of Heat Input

Results (RANS, 1 Cubic, periodic, M/7, Heat input)

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Scaled Heat Input

Q/7 = 8,317 W/m2, M7 Tave= 783 K Results (RANS, 1 Cubic, periodic, M/7, Heat input: Q7)

Line A Line B

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, 1 Cube)

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Pipe Flow

Radius=1 m Length~6 m ∆r+ ~ 0.4-11 ∆x+ ~ 7-8 ∆θ+ ~ 5

3.7 Million Points ReƮ = 180

Behaviour of Polyhedral for DNS cases

Results (DNS, Pipe Flow, ReƮ = 180)

27 Transition in mesh from Off-set layer to polys

ReƮ = 180

Behaviour of Polyhedral for DNS cases

Results (DNS, Pipe Flow, ReƮ = 180)

Mesh Generation for Pebble Bed

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Number of grid point ~ 15 M

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Results (DNS, 1 Cubic, M/7)

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

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Iso-surfaces

• f

Q-criterion coloured with velocity contours

Prelimenary Results of On-Going DNS

Results (DNS, 1 Cubic, M/7)

P1,P2,P2,P4

P9,P10,P11,P12,P13,P14,P15

P5,P6,P7,P8

Computational Domain Check via On-going DNS

Two-Point Correlations Results (DNS, 1 Cubic, M/7)

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CONCLUSIONS & PERSPECTIVES

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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

• f DNS.

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

Conclusions / Summary

Thank-You

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