Improved P₁ Approximation for Radiative Transfer Problems

Conference · Sun Jun 07 00:00:00 EDT 1992 · Transactions of the American Nuclear Society

OSTI ID:7232301

Theoretical studies of thermal radiation transfer require solving the radiative transfer equation in which the radiation field is described by an integrodifferential equation involving six phase-space variables and time. Advanced numerical techniques, such as the spherical harmonics method, the discrete ordinates method, and the Monte Carlo method, have been employed in the past to provide accurate solutions. However, these methods demand tremendous computer resources to the extent that their usages are often infeasible for routine engineering calculations. Consequently, approximate solution methods have been proposed, namely, the two- and six-flux methods and the diffusion of P₁ approximation. These methods are characterized by their simplicity, but they often exhibit poor accuracy, especially when the medium is optically thin. The present method adopts the classic P₁ approximation as a base solution. This solution is then improved by the so-called shape and boundary correction factors, which are derived via a known solution to the transfer equation. Through these correction limitations in the P₁ approximation, most notably, the optically thin limit and discontinuities in the transport medium are greatly reduced, and high accuracy can therefore be achieved. In this paper, the authors summarize the application of the improved P₁ method to a radiative transfer problem and to a slab criticality problem and then compare its results with those of other methods.

• Research Organization: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Motorola, Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA), Nuclear Criticality Safety Program (NCSP)
• OSTI ID: 7232301
• Report Number(s): CONF-920606-; CODEN: TANSA
• Journal Information: Transactions of the American Nuclear Society, Vol. 65; Conference: American Nuclear Society Annual Meeting, Boston, MA (United States), 7-12 Jun 1992; ISSN 0003-018X
• Publisher: American Nuclear Society
• Country of Publication: United States
• Language: English

Related Subjects

22 GENERAL STUDIES OF NUCLEAR REACTORS
42 ENGINEERING
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
97 MATHEMATICS AND COMPUTING
HEAT TRANSFER
THERMAL DIFFUSION
CALCULATION METHODS
ACCURACY
BOUNDARY CONDITIONS
COMPUTER CALCULATIONS
CRITICALITY
DIFFERENTIAL EQUATIONS
ERRORS
MONTE CARLO METHOD
NEUTRON DIFFUSION EQUATION
REACTOR PHYSICS
SPACE DEPENDENCE
THERMAL RADIATION
TIME DEPENDENCE
DIFFUSION
ELECTROMAGNETIC RADIATION
ENERGY TRANSFER
EQUATIONS
PHYSICS
RADIATIONS
Nuclear Criticality Safety Program (NCSP)
Theoretical Studies
Thermal Radiation Transfer
Monte Carlo Method
Radiative Transfer Problem
Slab Criticality Problem
220100* - Nuclear Reactor Technology- Theory & Calculation
420203 - Engineering- Handling Equipment & Procedures
665000 - Physics of Condensed Matter- (1992-)