Update and Progress on Deterministic-Based Neutronics

Comparison of Recently Developed Deterministic Codes with Applications

Mahmoud Z Youssef

UCLA

FNST/PFC/MASCO Meetings, August 2-6, 2010, University of California, Los Angeles

Outlines

-Backgroud information

- Method of Discrete Ordinates (discretization in energy, angle and space)

- History of of issuance of deterministic codes

-Recently developed deterministic codes and comparison

- Denovo - PARTISN - ATTILA

-Applications (Capabilities and Limitations) – Emphasize on Attila

-Comments

Calculation Methods for Neutron and Photon Transport

The methods can be broken down into two broad groups

Deterministic method: Directly solves the equation using numerical techniques for solving a system of ordinary and partial differential equations

Monte Carlo method: Solves the equation using probabilistic and statistical techniques (Stochastic Approach)

Each method has its strengths and weaknesses

Deterministic Method:Linear Boltzmann Transport Equation (LBTE)

extscatt QQ

ˆ

0 4

ˆˆ,,ˆ

EErdEdQ sscat

where,

streaming collision sources

• Represents a particle balance over a differential control volume:

– Streaming + Collision = Scattering Source + Fixed Source

– No particles lost

Abdou Lecture 5

Angular Discretization

0.5 cm Element Size

• Angular Differencing – Discrete Ordinates (SN)

– Solves the transport equation by sweeping the mesh on discrete angles defined by a quadrature set which integrates the scattering source

– Sweeps the mesh for each angle in the quadrature set

Ωi

SN=Quadrature set of order N Number of angles in level-symmetric set= N(N+2)

Abdou Lecture 5

• Scattering cross section is represented by expansion in Legendre Polynomials

• The angular flux appearing in the scattering source is expanded in Spherical Harmonics

• The degree of the expansion of the resulting scattering source is referred to as the PN expansion order

0

0, ,4

2ˆˆ,,

PEErEEr ss

0

ˆ,,ˆ,

m

m

m YErEr

L

m

G

g

mmgggls

scatg YrrQ

0 1,,,

ˆˆ,

Scattering Source Expansion

Flux moments

Spherical Harmonics

PN=Harmonics expansion approximation number of moments=(N+1)2

• Division of energy range into discrete groups (Muti-groups):

• Multigroup constants are obtained by flux weighting, such as

• This is exact if is known a priori

• Highly accurate solutions can be obtained with approximations for by a spectral weighting function

0 1

G

g

dE

1

1

,

,,,

, g

g

g

g

E

E

E

E gt

gt

dEEr

dEErErr

Er ,

Er ,

Energy Discretization

Spatial Discretization• Traditional SN approaches use regular

orthogonal structured grid (2D,3D)

– Regular Cartesian or polar grids

– Cell size driven by smallest solution feature requiring resolution

• Many elements are required (several millions)

• curved boundaries are approximated by orthogonal grid

0.5 cm Element Size

Orthogonal structured Grid Unstructured grid

• Advanced SN approaches use unstrctured tetrahedral cells (3D)

– Cell sized can be controlled at pre-selected locations.

– Highly localized refinement for capturing critical solution regions

• Much fewer elements needed for accurate solution

• curved boundaries are accurately represented

Number of the Unknowns in Discrete Ordinates Method

NT= Nc x n x t x Nu x NgNumber of spatial cells

Number of angles =N(N+2) (SN )

Number of Energy groups

Number of moments= (L+1)2 (PL )

number of unknowns per cell

For a typical of Ni=Nj=Nk=400, S32, P3 , Ng=67 (orthogonal grid)

NT 5.23 x 1014 unknown

In unstructured tetrahedral grid

NT= ~5 x 1012 ( 2 orders of magnidude less)

10

History of Deterministic Discrete Ordinates Codes

Development of the deterministic methods for nuclear analysis goes back to the early 1960:

OakRidge National Laboratory (ORNL):

(1D) W. Engle: ANISN (1967)

(2D) R.J. Rogers , W.W. Engle, F.R. Mynatt, W.A. Rhoades, D.B. Simpson, R.L. Childs, T Evans: DOT (1965), DOT II (1967), DOT III (1969), DOT3.5 (1975), DOT IV (1976)……… DORT (~1997)

(3D) TORT (~1997))…….DOORS (early 2000)… DENOVO ~2007-to date)

Los Alamos National Laboratory (LANL):

K.D. Lathrop, F.W. Brinkley, W.H. Reed, G.I. Bell, B.G. Carlson, R. E. Alcouffe, R. S. Baker, J. A. Dahl: TWOTRAN (1970), TWOTRAN II (1977) ….THREETRAN…… …TRIDENT-CTR(~1980)……DANTSYS (1995)…PARTISN (2005)

ATTILA: 3D-FEM-unstrctured tetrahedral cells (1995). Now Transpire/UC

Spatial Descritization:

Orthogonal and structured:

- Weighted diamond differencing (Denovo, PARTISN)

- Weighted diamond differencing with linear-zero fixup (Denovo, PARTISN)- Adaptive weighted diamond Differencing (PATISN)

- Linear discontinuous Galerkin finite element (Denovo, PRTISN)- Trilinear-discontinuous Galerkin finite element (Denovo)- Exponential discontinuous finite element (PARTISN) - Step characteristics, slice balance (Denovo)

Arbitrary and Unstructured:

- Tri-linear discontinuous Finite Element (DFEM) on an arbitrary tetrahedral mesh (ATTILA)

Comparison of Recent Discrete Ordinates Codes 1/5

Parallelization Method- Koch-Baker-Alcouffe (KBA) parallel-wavefront sweeping algorithm

(Denovo) - 2-D spatial decomposition (and inversion of source iteration equation in a single sweep (PARTISN)

-Spatial decomposition parallelism (ATTILA)

Iteration Method- Krylov method (within-group, non-stationary method)

(Denovo) - Source iteration (stationary) method (PARTISN, ATTILA)

Inner Iteration Method

-Diffusion synthetic acceleration, DSA (All)-Transport synthetic acceleration (TSA) (All)

Comparison of Recent Discrete Ordinates Codes 1/5

Denovo serves as the deterministic solver module in the SCALE MAVRIC sequence

Denovo: Parallel 3-D Discrete Ordinates Code

Consistent Adjoint Driven Importance Sampling

Sn- 3-D Code

Monaco with Automated Variance Reduction using Importance Mapping- Monte Carlo Code

SCALE

MAVRICDenovo

CADIS

Appropriate Weight windows

.Developed to replace TORT as the principal 3-D deterministic transport code for nuclear technology applications at Oak Ridge National Laboratory (ORNL).

Geom. Model

• Denovo is used extensively on the National Center for Computational Sciences (NCCS) Cray XT5 supercomputer (Jaguar).

• The KBA method (direct inversion, parallel sweeping) allows for

good weak-scaling on Jaguar.

This ability to run massive problems in reasonable runtimes

Application of Denovo: PWR

Over 1 Billion meshSlightly more than 1 hr

10 cm mesh size

From: Thomas M. Evans , “Denovo-A New Parallel Discrete Transport Code for Radiation Shielding Applications”Transport Methods Group, Oak Ridge National Laboratory, One Bethel Valley Rd, Oak Ridge, TN 37831

evanstm@ornl.gov

• A finite element Sn neutron, gamma and charged particle transport code using 3D unstructured grids (tetrahedral meshes)

• Geometry input from CAD (Solid Works, ProE)

ATTILA

ATTILA R&D Started at LANL (1995) by CIC-3 Group.

Currently being maintained through an exclusive license agreement between Transpire Inc. and University of California..

Shared memory parallel version SEVERIAN

• Accepted as an ITER design tool in July, 2007

Generic Diagnostic Upper Port Plug Neutronics

W/cm3

Generic Upper Port Nuclear Heating

Total: 316 kWFirst Wall + Diagnostic Shield: 309 kWGUPP Structure: 7 kW

Section Through Upper PortShowing the Visible/IR Camera Labyrinth

Generic Upper Port PlugSolidWorks Analysis Model

Generic Diagnostic Upper Port Plug Neutronics

Thermal Analysis in ANSYSBased on Nuclear HeatingData from ATTILA

ATTILA

ANSYS

VacuumFlange

Simplified representation of the Generic Diagnostic Upper Port Structure

40-degree 1:1 scale CAD model re-centered around the lower RH divertor port.

Contains all components and is fully compliant with the Alite03 and Alite04 Diverter model furnished by ITER IO**

M12 upper port connections from the ATTILA Alite04 model of UKAEA Culham.

Many cleanup and minor modifications suitable for nuclear analysis were performed in SolidWorks and ANSYS.

Meshed by Attila

Alite04-UCLA ITER Reference CAD Model

**This work was carried out using an adaptation of the Alite MCNP model which was developed as a collaborative effort between the FDS team of ASIPP China, ENEA Frascati, JAEA Naka, UKAEA Culham and the ITER Organisation

Model will be sent to ITER IO and made available to neutronics community

Neutron Flux in the Vacuum Vessel

Looking down: Horizontal cut at Mid-plane

Bottom of VV

Neutron Heating

W/cc

Gamma Heating

Total Heating is dominated by gamma heating

1.16E5

1.92E6

1.58E6

4.48E4

2.11E5

5.27E43.67E4

1.67E6

2.01E6

9.02E4

Accumulated Dose (Gy) in the Epoxy Insulator at 0.3 MW.a/m2

Local Insulator Dose: The dose limit to the insulation is 10MGy

Dose (Gy/s) = Heating (W/cc)*1/ρmaterial*1000g/kgLocal Lifetime Limit 10 MGy, Assume Titer_life = 1.7E7 seconds

Diagnostics and Port shield Installed

Diagnostics/shield not installed

PF6

PF5

PF4

PF6PF5

PF4

Magnet Insulator

3E3

•Dose in PF5 reduced by a factor of 100 when divertor port is plugged

•Dose limit of 10 MGy is not reached

Gy

TBM (2) Shield

Cryostat

Bio-shield

Port Inter space area

AEU

Dose rates in the port inters pace and AEU area need

Assessment → acurate ocupational Radiation Exposure (ORE) rates

Youssef Dagher

We have a meashable ITER model with DCLL TBM inserted

Follow upNeed to complete the dose rate assessment for the DCLL TBM

Comments• With the recent advances in computers soft and hardware development, the limitation on disk space requirement is much more relaxed.

• Discrete ordinates codes (e.g. ATTILA/SEVERIAN)are good tools for engineering designs that require frequent design modifications.

• ATTILA is already extensively used in ITER in-vessel component designs (diagnostics, ELM.VS, etc.)

Features Comparison of Recently Developed Discrete Ordinates Codes - 1/4

Features Comparison of Recently Developed Discrete Ordinates Codes - 2/4

Features Comparison of Recently Developed Discrete Ordinates Codes - 3/4

Features Comparison of Recently Developed Discrete Ordinates Codes - 4/4