Lamarsh, "Introduction to Nuclear Reactor Theory", Addison Wesley (1972), Ch. 12 & 13

Transcription

1 NEEP 428 REACTOR PULSING Page 1 April 2003 References: Lamarsh, "Introduction to Nuclear Reactor Theory", Addison Wesley (1972), Ch. 12 & 13 Notation: Lamarsh (2), "Introduction to Nuclear Engineering",(1975), Ch. 7. Hetrick, Ch. 3. (Useful for reactivity kinetics; different notation.) Duderstadt & L. J. Hamilton, "Nuclear Reactor Analysis", J. Wiley & Sons, New York (1976), Ch. 6. Lamarsh's notation shall be used, with additional symbols and definitions consistent with this notation: C p = specific heat capacity per cm 3 of the reactor core. 0 = step input reactivity. = intrinsic feedback reactivity T 0 = reference temperature ( Kelvin, such that f = 0. t = magnitude of the negative temperature coefficient of reactivity = - T W(t) = total energy release per cm 3, on the time n(t) = P(t) = interval(t 0,t)(assuming dp/dt = 0 at t = t 0 thermal neutron density. power The Experiment: 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

2 NEEP 428 REACTOR PULSING Page 2 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. TRIGA-FLIP fuel is designed with a large prompt negative temperature coefficient. Most of this temperature coefficient is due to the presence of erbium oxide which is added to the fuel material. Erbium has a very large resonance absorption peak at about 0.4 ev plus a number of other large resonances from 1 to 100 ev. It, therefore, provides some Doppler coefficient but, more importantly, it has a large effect on the upper end of the Maxwellian neutron distribution as neutron energy increases. Most of the moderation in the core is provided by the hydrogen in the zirconium hydride-uranium fuel matrix. The energy release from fission immediately causes an increase in the motion of the hydrogen which raises the neutron energy enough to cause a significant increase in absorption by the erbium, thus reducing reactivity. If the reactor is properly designed, this effect can be used to allow the reactor to be pulsed. To do this the fuel elements are made large enough so that, over the short period of time corresponding to a pulse, the heat release from the fuel is negligible. The power produced in the reactor then heats the fuel, thereby reducing the reactivity to make the reactor subcritical and terminate the pulse. After the pulse is over, control rods are inserted to hold the reactor sub-critical while the fuel cools and the K eff of the core increases.

3 NEEP 428 REACTOR PULSING Page 3 The purpose of the experiment is to determine two significant parameters: the prompt neutron lifetime ( p ) and energy coefficient of feedback reactivity ( /C p ) for this reactor. In order to extract these reactor parameters from the recorded data, some approximations must be made which are applicable when a self-limiting power excursion takes place in a short period of time. The principal approximation is to neglect all neutron sources except the production of prompt neutrons. This can be assumed only if the reactivity is sufficiently large, so that the power and its rate of change are so large that we may neglect entirely the production of delayed neutrons and other neutron sources. This simplified model for studying power transients is referred to as the Fuchs-Nordheim model. It is valid only for short times, and applicable when a power excursion is selflimiting by negative reactivity feedback. The predictions of the Fuchs-Nordheim model can be compared with these results, and a determination of the prompt neutron lifetime ( p ) and energy coefficient of feedback reactivity ( /C p ) for this reactor can be made. TRIGA Kinetics By Lamarsh's definition, the magnitude of the negative temperature coefficient is: We shall use a coefficient = - T. A simple temperature feedback implies = (T - T 0 ). During a large, fast step input reactivity 0, if we assume all heat loss is negligible (the adiabatic approximation), we may write:

4 NEEP 428 REACTOR PULSING Page 4 For a change in reactivity, In the absence of delayed neutrons, the kinetic equations in the Fuchs-Nordheim model are: (1) (2) (3) We will measure the change in power as a function of feedback reactivity, so it is convenient to write: Integrating for a step input of positive reactivity 0, assuming constant and Cp we get: (4)

5 NEEP 428 REACTOR PULSING Page 5 The power will increase until the increment of reactivity above prompt critical ( = ) is offset by the feedback. Before the feedback becomes significant, power will rise exponentially with a short period which can be measured from the initial rise of the pulse. The reciprocal of this initial period,, is related to the initial reactivity, 0, by the point kinetics equations as From equation (4) we see that the power is a maximum when =. This is also the point where dp/dt = 0. Denoting the peak power as we see that (5) After the peak, the power falls rapidly, returning to P 0, with the amount of feedback reactivity at the end of the pulse given by: The temperature rise is The approximate energy released is:

6 NEEP 428 REACTOR PULSING Page 6 Combining the equations for P and W: The pulse full width at half maximum and the energy release are other useful parameters which may be determined from the pulse power vs. time data. Refer to equation (5). but so or Now substitute this in equation (4) and we find (6) Which is an equation relating power and reactivity.

7 NEEP 428 REACTOR PULSING Page 7 Our basic feedback equation was which upon substituting equation (6) gives i.e. a differential equation involving only and t. The variables in this equation can be separated and the equation integrated. If we do this and define t = 0 being where, we find the following result after some algebra: Remembering that and using equation (6) we finally get The energy release W(t) is: At the time the power peaks,

8 NEEP 428 REACTOR PULSING Page 8 The total energy release W( ) = 2W. The fwhm of the power pulse can be obtained by setting P = P/2, t = /2 in the equation for P(t). Experimental Procedure The reactor will be pulsed with reactivity insertions from 1% to 1.4%(or the maximum available) in 0.1% increments. Calculate the transient rod fired position to obtain the desired reactivity insertions. One pulse will be fired for each reactivity step. A second pulse will be fired for one of the steps to provide an indication of the reproducibility of the measurements. The signal from the gamma ion chamber is sampled at one millisecond intervals and stored in the TestLab. The TestLab internal program calculates the information needed for the reactor log and records two channels of power-level data derived from the gamma-ray dose from the reactor core. The first channel, labeled "pulsetrace", records the full pulse. The second, labeled "pulserise", uses a smaller range and thus records the early part of the pulse most useful for reactor period measurements. In both cases the raw data is normalized such that the output is in MW. The data should be analyzed for period, pulse full width at half maximum, peak power, and total energy release.

9 NEEP 428 REACTOR PULSING Page 9 Pre-Laboratory Exercise Calculate and plot the time for the transient rod to move from its initial position to full out for a withdrawal range of 0 to 8 inches. The effective weight of the transient rod and drive is 8.3 lbs. The driving piston is 1 inch in diameter with a 5/16 inch rod in the center. The air pressure on the piston is 75 psi. You may ignore drag forces. Data Analysis and Report The object of the data analysis in this report is twofold: To determine if the reactor pulsing is adequately described by the Fuchs-Nordheim model and to measure some parameters (the prompt neutron lifetime ( p) and the energy coefficient of feedback reactivity ( /C p )) of the reactor if it is. There are several possible sources of difficulty in this analysis. There may be a problem with a systematic error in one or more of the measured parameters. The reactor may not follow the Fuchs Nordheim model. The values of certain input parameters may be incorrect. The physical state of the reactor during a given pulse may not be consistent with the assumptions made in our derivation. Therefore the analysis should be made in such a manner as to satisfy the object of the experiment and to determine which, if any, of the possible problems are present. One assumption basic to the analysis above is that all of the positive reactivity is inserted in the reactor before fuel temperature inserts negative reactivity to begin terminating the pulse. If a constant period is not reached on the rise of the pulse you may be sure that the reactivity predicted for the pulse is not the actual reactivity selected for the pulse. If one knows what amount of reactivity has been inserted before the rapid fuel heat-up begins, using

10 NEEP 428 REACTOR PULSING Page 10 this amount of reactivity when plotting curves or calculating values might indicate better values of the measured parameters. 1. The Fuchs-Nordheim model predicts a certain form for the pulse. Since we have not measured the pulse directly we can only use some of the properties of the pulse. Develop a relation between the peak power and the energy release and graph your data in a form that will result in a straight line. In this graph and the succeeding ones you should evaluate how well the data fits the model and find the values of those parameters which could be obtained from the data (Remember that the values at intercepts or the origin may be set by definite physical conditions. Here, for example, we know that when P = 0, W must equal zero. 2. The other parameter that relates directly to the pulse shape is the full width at half maximum (fwhm). It may be related to either the peak power or the energy. Since the peak power is somewhat more likely to be measured correctly, develop a relation between peak power and the fwhm and plot such that the result would be a straight line. As before, evaluate the fit, obtain the value of the desired parameters, and discuss the suitability of the Fuchs- Nordheim model. 3. The Fuchs-Nordheim model indicates that the fwhm is related to the initial period of the transient which is in turn related to the reactivity inserted using simple kinetics equations. Find the relation between the fwhm and the reactivity and plot to give a straight line. Evaluate the fit, determine the appropriate parameters and discuss possible reasons for deviations from expected results.

11 NEEP 428 REACTOR PULSING Page All of the previous analysis has relied on the Fuchs- Nordheim model. The relationship between the initial period and the reactivity is obtained using basic reactor kinetics only. Therefore, this relationship can be used to determine certain parameters -- specifically the prompt neutron lifetime and the delayed neutron fraction -- if both the period and the reactivity are known. Using expressions for period as a function of reactivity, plot your data such that a straight line would be expected and analyze as above. 5. From the data analysis above: a. Summarize the applicability of the Fuchs-Nordheim model to the UWNR, b. Summarize possible reasons why any of the results of the experiment do not go as expected. 6. Obtain your best estimate of the prompt neutron lifetime and the energy coefficient of feedback reactivity. Provide the uncertainties in these quantities based on the experimental accuracy of the data. 7. Indicate radiation dose rates and dose to individuals in the laboratory. 8. The heat capacity of the core is watt-seconds/ C, and the fuel temperature rise during a pulse as measured on the instrumented element is 1.39 times the average temperature rise in fuel. Calculate the prompt temperature coefficient of reactivity of the core. Values for UWNR p = 22 x 10-6 sec eff = 0.007

12 Page 12