Delayed Critical Reactor

Define prompt critical, delayed critical, reactor period, source critical, and decay heat. 

Solve problems for prompt and delayed critical reactors involving reactor period, power, positive and negative reactivity, prompt jump, and prompt drop,... 

Which is the period equation for a delayed critical reactor. 

Defend the statement "On a microsecond time scale, a delay critical reactor is subcritical."... 

Show from all of this that the neutron population of a delayed-critical reactor decays on the microsecond time scale according to exp (-/Bt/l). 

An important consequence of these remarks is that the time behavior of a reactor may possibly be reasonably well represented by considering only the persistent mode including all delayed neutron sub-modes. An important class of problems for which this situation exists is that of an initially critical reactor in which a small local change occurs, such as the motion of a control... 

Some non-linear problems. Consider the problem of a sudden introduction of reactivity into a critical reactor with no source in which the feedback reactivity is proportional to the energy generated, as might be the case for a reactor with no cooling. Assuming that the reactivity is less than j8, the prompt jump approximation may be used, which in the one delay group approximation results in (compare Equation (106))... 

Outside the inner region (D2O) a subcritical assembly of fissile material in the form of a melt of fluorides (LiF/BeF2 containing UF4 or fluorides of other fissile nuclides at a temperature of 500/700° C inlet/outlet) is circulated producing the thermal energy required to drive the turbines. The operation of the core in a subcritical state (k = 0.97) increases the safety of the reactor. As it has been shown before (see Sect. 57.3.6), the reactivity window for safe operation of a critical reactor is given by 1 + (where fl is the fraction of delayed neutrons). 

The spherical critical mass of 93% " ll enriched uranium metal which has teen used as a benchmark problem for verification of calculational methods is based on foe delayed critical mass measurements made on Godiva corrected to standard conditions. A near Spherical mass of U(93.2), recently surplused from an ei erimental program examining fast reactor behavior with an accelerator booster, was re-machined to a spherical radius of 3.466 in. Tte device is to be used in a study of neutron kinetic parameters. The data obtained for the delayed critical configuratian confirm the reevaluated critical parameters recently reported by Man-sen and Paxton. ... 

Critical - The condition existi when t e effective multiplication constant for a reactor is unity (or l) so that a self-supporting fission chain reaction can be maintained is said to be "critical." As commonly used, this means "delayed critical" and the reaction is depezident upon both prompt and delayed neutrons. Prompt critical is capable of sustaining a chain reaction without the aid of delayed neutrons. 

When an amount of positive reactivity equal in magnitude to the average effective delayed neutron fraction is inserted into a critical reactor, the reactor is ... 

Reactor Kinetics involves analysis of the dynamic behavior of a nuclear reactor prompt criticality and supercritical behavior and delayed criticality and supercritical behavior. 

In a normal, critical reactor, the neutron fractions are divided between delayed neutrons and (I Pftff) prompt... 

Figure 4.1 Delayed and Prompt Neutron Fractions in Subcritical Critical, Supercritical, and Prompt Critical Reactors...

Since we are considering a critical reactor, we may assume that there is no primary source present. However, since we are interested in the effects of delayed neutrons, we must consider our source term to be composed of two parts the source of prompt fission neutrons and the source of delayed fission neutrons. If we let represent the fraction of the total number of fission neutrons that are delayed and the fraction that are associated with a single time of delay (a single precursor), then (1 - jS) is the fraction of fission neutrons that are emitted promptly. We can then write our prompt source term as before, except that it must be decreased by a factor (1 - jS). An additional source term must be included for the delay-neutron source. The rate of formation of delayed neutrons of the i h kind is equal to the rate of decay of its precursor, which is... 

This experiment is designed to determine the reactivity worth of the control rods by a pulsed neutron technique. A burst of neutrons is injected into the reactor, and the decay rate of the resultant neutron flux is measured. The decay rate measured is that of the prompt fission neutrons and is proportional to the prompt critical reactivity of the reactor. Measurements will be made with the reactor in subcritical conditions and at delayed critical. The decay rate at delayed critical yields the constant of proportionality between the decay rate of the neutron flux and the reactivity in dollars. This constant is equal to the ratio of the effective delayed-neutron fraction to the prompt-neutron lifetime. 

The three methods for measuring reactivity in a nuclear reactor are the inverse multiplication method, the positive-period and rod-drop methods based on reactor kinetics equations, and the pulsed neutron technique. This experiment will acquaint the participant with the latter technique. The pulsed neutron technique has two advantages over the others. The first is that large negative reactivities can be measured with good accuracy. Secondly, the method obtains its own calibration at delayed critical, relating the prompt-neutron decay constant to the reactivity of the system. 

After a few subcritical runs have been made, the reactor can be brought to delayed critical and pulsed. Care must be taken at this point, since the delayed-neutron background will yield a steady-state neutron level in the reactor. The background will steadily increase each time more neutrons are injected into the system. After enough data have been taken, the pulsing is stopped, and the reactor power level should level off and remain at steady state, since the reactor is in a delayed critical condition. The decay constant calculated for this run will yield the constant of proportionality between the decay constant and the negative reactivity (in dollars) of the system. This constant is equal to jSgff/ip as pointed out in Section II. 

A. In a critical reactor, the neutron population is exactly sustained by the contributions of fission neutrons, which appear promptly upon fission, plus the delayed neutrons which are emitted by the fission fragments and appear second or minutes after the fission event. This condition of neutron balance is called "delayed critical," denoting the fact that prompt and delayed neutrons are needed to balance neutron losses from absorption and leakage and thus to sustain the chain reaction. A "prompt critical" condition is one in which the neutron economy is balanced by the contribution of the prompt neutrons alone, without the need of the delayed neutrons. 

Figure 16.1 shows a typical fluctuation of the neutron population after an initial neutron has caused a fission event and has thus, instantaneously increased the neutron population to, say, three neutrons. Note that the time scale is very short so that delayed neutrons from this fission event have not had time to make their appearance. The reactor, since it is delayed critical so that the delayed-neutron contribution is necessary to sustain the neutron population, will show a behavior which is characteristic of a subcritical pile, until the delayed neutrons appear. Note also that the origin of the figure is shifted in such a way that the average neutron population is omitted. The figure represents one, typical, time development of the fluctuation of the neutron population, triggered by an initial fission event and dying out for need of delayed neutrons. 

Compare the two reactor conditions "delayed critical" and "prompt critical."... 

Semibatch Reactors. Semibatch reactors are the most versatile of reactor types. Thermoplastic injection molds are semibatch reactors in which shaped plastic articles are produced from melts. In mol ding thermoplastics, large clamping forces of up to 5000 metric tons are needed to keep molds together, while highly viscous polymers are forced into their cavities. Heat transfer is critical. If the molds are too cold, polymers soHdify before filling is completed if they are too hot, the time required for cooling delays production. 

Granulation of urea [13] is a complex process that has to be controlled by experienced process operators in order to avoid critical shutdown situations. The parameters most often used for monitoring granulation processes are measured by classical univariate sensors, such as temperature, pressure and flow. However, these standard process measurements carry only little or no relevant information, or are only indirectly related to, for example particle size, clogging of the reactor, or the accumulation of a solids layer on the bottom plate. The response from these sensors often comes with quite a substantial delay time. 

As it is mentioned above 36 reactor reloads have been carried out since the power unit has been put into operation. In general the refuelling system performance during this period of time was sufficiently reliable - in fact no failures which would have caused the delay of making the reactor critical occurred. It is the refuelling system mechanism position indication and control system that has mostly been a trouble contributor. As far as the mechanical part is concerned the following operating results can be noted ... 

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