The Simulation of Large Transients in Neutron Reactors

Abstract

The simulation of the reactor kinetics equations on an analog computer presents no difficulties in most applications. However, in situations where the reactor is designed to give large bursts of neutrons, analog computers do not have a great enough range. Fortunately, it is possible to transform the kinetics equations into a form in which the log of neutron flux instead of the flux is the dependent variable. This permits the simulation of pulsed reactors such as TREAT, or certain types of rocket motors.The time-dependent behavior of a reactor is usually described by the reactor kinetics equations.' For computational purposes the following form of these equations is found to be most convenient.2The definitions of nj, C1i, and klex are given in the list of symbols. When the reactor is in equilibrium, kex = 0 and nl = Cli since 2/3, =/3. If k1ex is a constant, the equations (1) and (2) are a system of linear equations with constant coefficients and may therefore be solved analytically. In most practical situations, however, k1ex depends on ni because of the internal reactor feedback; an external control system also makes k1ex a function of ni. Since(1) and (2) are in this case no longer a system of linear equations with constant coefficients, they cannot be solved by standard analytical methods. Analog computers have, therefore, been found extremely useful for their solution in the design of reactor control systems.The usual reactor design problem is concerned with the behavior of the system for small changes in n, such as one would find during the normal operation of most reactors.3 For this type of study, equations (1) and (2) have been used extensively. The Argonne TREAT reactor, however, presents a different situation.4 4The TREAT or transient test reactor was designed to produce large thermal neutron bursts to test reactor materials under extreme conditions for safety evaluation. The air-cooled core consists of micronsized particles of highly enriched uranium oxide embedded in a graphite matrix. The graphite absorbs heat more rapidly than a conventional cooling system, and as it heats it raises the energy of the thermal neutrons, thus increasing the amount of neutron leakage. This has the effect of giving the reactor a large enough negative internal feedback coefficient to prevent the neutron flux from increasing to the point of damaging the structure. The reactor design permits a maximum flux of 10&dquo;' neutrons/cc for a maximum time of 40 ms. Equations (1) and (2) are, of course, not suitable for simulating a reactor of this kind on analog computers, as they are limited to three or four decades at the most. The equations can, however, be transformed into a form which permits simulation of as many decades as desired.5 Let Substituting (3) and (4) in (1) and (2), one has As may be seen from the above equations, when klex is large and positive, q approaches a linear function of time and Oi approaches -1 since the delayed neutrons always lag behind the prompt neutrons. When klx is large and negatives becomes gr...