Reactivity asymptotic-period

This section presents [after references (j) and ( )] perturbation expressions for several definitions of reactivity, as well as the equivalent expressions required for the experimental determination of reactivities of exactly the same definition. The reactivities considered are the static reactivity (the reactivity most commonly calculated) and three special cases of Henry s time-dependent reactivity (5) the asymptotic-period reactivity, the promptmode reactivity, and the source-multiplication reactivity. 

The asymptotic period is one of the most commonly used methods for reactivity determination, whereby the measured asymptotic period is related to reactivity via the Inhour equation (7, 8). The definition of reactivity inferred from the Inhour equation depends on the definition of the reactor s effective kinetic parameters. 

The Inhour equation relating the asymptotic period to the static reactivity is... 

The asymptotic period and the prompt mode decay constant can be related more naturally to reactivities other than the static reactivity. The natural reactivities are related to real flux distributions in the subcritical reactor and to the importance function in the reference critical reactor. 

Consider a source-free reactor that runs on an asymptotic period. The neutron flux for this reactor is described by Eqs. (16) and (17). With this flux, Henry s reactivity becomes... 

We shall refer to as the asymptotic-period reactivity. The Inhour equation for this reactivity can be obtained by multiplying Eq. (19) by 0q, integrating over phase space and rearranging ... 

The calculation of the effective kinetic parameters of the Inhour equation for the asymptotic-period reactivity requires only one distribution 0, for each subcritical configuration. The effective kinetic parameters for the... 

Inhour equation for the static reactivity [Eq. (13)] are functions of two such distributions, (f), and 4>. The asymptotic-period reactivity is, therefore, the natural reactivity to infer from the Inhour equation. 

B. J, Toppel, Sources of Error in Reactivity Determinations by Means of Asymptotic Period Measurements, Nucl. Scl. and Eng. 5, 88 (1959). 

The foregoing tells us that to determine the reactivity associated with the blade movement h, the resultant asymptotic period of the reactor must be measured. can then be calculated from the inhour equation. Point 2 says that after the withdrawal of the element, the power rise will not be a simple exponential and that there will be a waiting period while the transient terms did out. 

This experiment is designed to study the temperature effects on reactivity. The UW reactor will be pulsed with various reactivity insertions up to the license limit. A computer-based data acquisition system will record a pulse power trace (power as a function of time), while the console recorder will record the maximum fuel temperature reached during the pulse. From the power trace data, measurements will be made of the asymptotic period, pulse width, peak power, and total energy release. 

Measurements of subcriticality relative to the effective delayed neutron fraction can be made by calibrating a reference fine control rod by means of asymptotic period measurements following rod withdrawal, or by inverse kinetics analysis of the reactor power response following rod drop or rod withdrawal (fitting the response using the delayed neutron kinetics equations).There are imcertainties in total delayed neutron yields and in the time dependence of delayed neutron emission, the accuracy of this reactivity scale being estimated to be 5%. 

The fact that, after the transients have decayed, the reactor flux rises or falls with an asymptotic period which is a function of the imposed reactivity change provides a useful method of measuring the reactivity values associated with the control system of the reactor. For example, a standard method of calibrating a control rod, in terms of the reactivity change produced by a given movement of the rod, is to raise the rod out of the critical reactor by the amount required to set the reactor flux diverging with a conveniently measurable period. The determination of the period then leads immediately to a knowledge of the reactivity value associated with the section of rod removed from the reactor. 

Fig. 3.5. Positive Reactivity p Dollars Versus Positive Asymptotic Period t Seconds... 

In this experiment the basic concepts of control rod calibration of a nuclear reactor are considered. Reactivity changes are measured by observing positive asymptotic periods of the reactor. These asymptotic periods are related to reactivity by the reactor kinetic equations and the usual inhour equation. Several examples of kinetic behavior in response to changes in reactivity are qualitatively observed so that operating skill and safe attitudes pertaining to reactor operation may be developed. 

The fine control rod of the AGN-201 reactor will be calibrated in this experiment. The technique used to measure reactivity changes at different rod positions in the core will be measurements of positive asymptotic periods. The reactivity of the assembly corresponding to a measured stable period will be determined from the basic inhour equation, which is derived below. 

The quantity odq is the reciprocal of the stable asymptotic period T. If a measurement of this stable period is made when a reactor is supercritical, the reactivity corresponding to the period can be determined from Eq. (10). Substituting CJO = i/t into the basic inhour equation gives... 

For each asymptotic period observed the reactivity of the reactor may be found from a chart of reactivity versus period which will be available. The net reactivity worth... 

At an arbitrarily chosen time zero, mark the recorder chart and close the switch to fill the empty void holder. Shortly after the void holder is full ( 30 sec) the transient periods will disappear, and a steady asymptotic period will be established. From the power level versus time data given on the power level recorder chart, the reactor period can be determined in several ways perhaps the most instructive is to plot the power level versus time data on semilog paper. What does the straight-line portion of the graph indicate From this graph, measure the period, A calculated curve is available to convert the measured asymptotic period to reactivity. 

This test can be used to eliminate the two most Important sources systematic error in the experiment. When the reactivity is changed, transient effects dominate for some time while the instantaneous period approaches an asymptotic value. Since the data are assumed to fit a true exponential, the effect of the transient shows up as a systematic error, easily detected, by the g oodness-of-fit tysts. An experimental plot, similar to the calculated curves of Toppel, can then be constructed showing the necessary wait time for an arbitrary acceptable error as a function of the period for the given reactor and experimental condiffons. 

Note the behavior shown on Figure 1 for negative periods and reactivities -- you can see the approach to the asymptotic -80 sec. period. These subjects will be discussed again when we do the control rod calibration laboratory that is part of this section. 

The reactivity changes that occur in the reactor when an absorber is placed at its center will be measured in terms of asymptotic positive periods. The stable period of a supercritical reactor is related to the reactivity through the basic inhour equation. This expression involves the prompt neutron lifetime and the delayed neutron parameters (see Appendix B). 

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