The build-up and characterization of nuclear burn-up wave in a fast neutron multiplying medium

Abstract

A study has been carried out on the build-up and characterization of nuclear burn-up wave in fast neutron multiplying media. The focus of the study is more on the transient part of the burn-up wave though the steady state is also studied. The characteristics of the transient part are expressed in terms of new parameters, i.e., Transient Length (TL) and Transient Time (TT) elapsed in establishing the asymptotic burn-up wave. The TT and TL are defined, respectively, as the time and length needed to establish 95% and 99% of the asymptotic neutron flux propagating in the media. From these parameters, the transient wave velocity is determined. The characteristics of asymptotic part of the wave are determined in terms of wave velocity, Full Width at Half Maximum (FWHM) and Full Width at 10% Maximum (FW10M) of neutron flux distribution in the space. A parametric study is also carried out to investigate the sensitivity of these parameters to some of the physical parameters of the ignition zone and the breeder zone of the reactor. The characterization parameters would be very meaningful to understand the transient characteristics of the self-sustaining nuclear burn-up wave and in evaluating the quality of the wave by the researchers working in the field of nuclear burn-up wave build-up and propagation.

Newton’s second law analogy for the traveling wave of nuclear burning

“…These equations are too complicated for the exact analytical solutions being looked for, so one has to seek either for the simplified systems of equations or the numerical simulations. In a number of papers [1,[3][4][5][6][7][8] authors regard significantly simplified expressions for this system. Using it, they try to analyze physical effects and look for the traveling-wave solutions to this problem.…”

“…Using it, they try to analyze physical effects and look for the traveling-wave solutions to this problem. In present work, we consider the system of equations, similar to one from [1] and [8], but we suggest a different way to analyze it. Substantial difference between models of [1,4,7,8] and [3,5,6,9] consists lies in describing the combustion processes.…”

“…In present work, we consider the system of equations, similar to one from [1] and [8], but we suggest a different way to analyze it. Substantial difference between models of [1,4,7,8] and [3,5,6,9] consists lies in describing the combustion processes. In [3] author regards only one differential equation for the neutrons diffusion, what implies that the nonlinearity and nonlocality of the system are regarded as an effect of the fuel's combustion, while the equations which describe these processes are not considered at all.…”

“…Considering these terms makes impossible to apply the methods, similar to that in [5,9]. There is an important difference in [1,8,10] and [5,11] and it is that in the differential equations we have some terms which are not proportional to the neutron flux and are responsible for the β-decay. Considering these terms makes impossible to apply the methods, similar to that in [5,11].…”

“…In [8] the numerical simulation was performed only with time-constant external neutron flux. Since the system is not left to itself in such a mode, one can question the interpretation of these results as autowave.…”