Generation of multigroup angularly dependent group constants
Abstract
Strict conversion of the neutral particle Boltzmann transport equation to a multigroup formalism leads directly to nuclear group constants that depend upon angle. It has been common practice to disregard the complexity introduced by such group constants as current core-equilibrium group constant methodologies do not retain angular effects. However, it has recently come to light that such group constants play an important role in transmission problems or problems where the neutron flux is transitional in nature. This work derives a closed analytical expression to generate angularly dependent group constants based upon a P$\sb1$ expansion of the angular flux from continuous energy nuclear cross section data. By tabulating these "transport-extensions" as a function of background cross section and temperature they are analogous to classical self-shielding factors. These angularly dependent group constants or "transport-theory" group constants are completely general in that they could be applied in a modified diffusion theory or in a modified transport theory code. It is believed that the worldwide C/E discrepancy observed in fast reactor transition problems is the result of neglecting transitional effects in resonance self-shielding and directional effects in the group constants. To investigate the gains that could be realized through angularly dependent groups constants, they were applied in an iterated diffusion theory based upon DIF3D to analyze blanket 2SS of the Purdue University Fast Breeder Blanket Facility which has an accurately quantified C/E drop-off. Some enhancement of the drop-off was observed but the overall effect was insufficient to alleviate the entire drop-off. Through this work it has become apparent that diffusion theory is inadequate in non-equilibrium problems even with the benefit of angularly dependent group constants. The distinction between forward and backward directed fluxes must be maintained through the flux calculation as well as through the group constant generation phase. However, it is believed that the use of angularly dependent group constants in a discrete ordinates or Monte Carlo code should yield enhanced accuracy in reaction rate predictions for non-equilibrium problems.
Degree
Ph.D.
Advisors
Ott, Purdue University.
Subject Area
Nuclear physics
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