Statistical algorithm verification

for high concentration microfuel M.I. Gurevich, B.K. Chukbar

The pebble-bed reactor is a graphite-moderated, gas-cooled, nuclear reactor. The basic design of pebble-bed reactors features spherical fuel elements called pebbles. These pebbles contain thousands of micro-fuel particles.

TRISO coated particle

Fuel kernel consists of UO2 coated with four layers:

1-st layers is a porous buffer layer made of carbon,

2-d layer is pyrolytic carbon (PyC);

3-d layer is ceramic layer of SiC (silicon carbide)

4-th is dense outer layer of PyC.

Covering layers mostly consist of carbon, its cross section doesn’t have resonances, and therefore it can be homogenized with matrix material. Fuel particles can’t be homogenized with matrix material due to resonances.

Designations

• ∑m – real macroscopic cross section of matrix

• ∑i – real macroscopic cross section of fuel

• N – mean number of fuel particles in sm3

• Δ – mean length of chord Δ=(4/3)•r

• ∑k – cross section of the enter to fuel particle

∑k = πr2 N,

Vk = N (4π/3)r3 = ∑k Δ – volume of particles

ASTRA

(RRS Kurchatov Institute, Russia)

• N≈60 sm3 • Øfuel = 5 sm • Øpebble = 6 sm • Core consists only from

fuel pebbles. • Dummy pebbles form

the top reflector.

PROTEUS

( Paul Scherrer Institute, Würenlingen, Switzerland)

• N≈173 sm3 • Øfuel = 4.7 sm • Øpebble = 6 sm • Core consists of

randomly mixed fuel and dummy pebbles.

Two benchmarks

The MCU Project

Codes of the MCU family are intended for modeling of transport

of neutrons, photons, electrons and positrons by analog and not

analog Monte Carlo methods on the basis of the evaluated nuclear

data in systems with three-dimensional geometry.

The MCU code uses

• continuous particle energy;

• the evaluated nuclear data;

• universal combinatorial three-dimensional geometry;

• calculation of resonance cross sections according to the formula;

• combinatorial source;

• CORN algorithm

Real situation if Vk <<1

P(x, x+dx)=exp(-∑ef x)∑ k dx ∑ef =∑m + ∑k

Enter to corn

Exit from corn

CORN model

P(x, x+dx)=exp(-∑ef x)∑ k dx ∑ef =∑mm + ∑k

∑mm = ∑m (1 – Δ∑k ) preserves mass of matrix material

Enter

Exit

Main space

Corn space

Two models were compared. Co

Single pebble simulation

• The albedo boundary condition simulates leakage.

• All layers were considered for the cubic lattice model.

The result for all cases was just the same

0.163

PROTEUS

The assembly includes :

• fuel pebbles;

• dummy pebbles (carbon only).

All pebbles were mixed randomly.

So, the model randomly selected positions for dummy pebbles.

PROTEUS results

• keff = 1.0194 • keff = 1.0179 (another • position of dummy pebbles)

CORN model

MCU

• keff = 1.0196 Cubic model

MCU

• keff = 1.0176

Cubic model

MCNP

(other author)

Conclusions:

1. CORN algorithm can be used in wide range of particle concentrations

2. PROTEUS benchmark’s specifications contain inaccuracy, which results in keff higher than 1

3. Relative position of fuel and dummy pebbles has significant impact on keff

Literature

1. John D. Bess, James W. Sterbentz, Luka Snoj, Igor Lengar,

Oliver Köberl “HTR-Proteus Pebble Bed Experimental Program Cores 9 & 10: Columnar Hexagonal Point-on-Point Packing with a 1:1 Moderator-to-Fuel Pebble Ratio” // NEA/NSC/DOC(2006)

2. N.N.Ponomarev-Stepnoy, V.I Bryzgalov, E.S. Glushkov, E.A. Gomin, V.E. Demin, G.V. Companeec, V.A. Lobyncev, V.I. Nosov, D.N. Polyakov, M.I Gurevich, O.N. Smirnov, O.V. Telkvoskaya “Using the MCU to analyze the results of the critical experiment with pebble bed HTGR on the “ASTRA” benchmark” // Атомная энергия, Том 97, вып. 4, Октябрь 2004, сс 243 – 252.

3. V.I.Brizgalov, M.I.Gurevich, “The neutrons flux density calculations by Monte-Carlo code for the double geterogeneity fuel” // Proc.of the Int. Conf.on Reactor Phys. and Reactor Comp. Tel-Aviv, Jan 23-26, 1994, p.190

•Thank you for your attention