J. T. Mihalczo. P. 0. Box 2008

Transcription

1 nstrumentation and Controls Division MONTE CARLO VERFCATON OF PONT KENETCS FOR SAFETY ANALYSS OF NUCLEAR REACTORS T. E. Valentine J. T. Mihalczo Oak Ridge National Laboratory* P. 0. Box 2008 Oak Ridge, TN Paper t o be presented at the 7th Symposium on Nuclear Reactor Surveillance and Diagnostics Avignon, France June 19-23,1995 "hsubmtted lmmmcrpt hsr bea, authored by a contracts of ms U.S. Govsmment under contnct No. DEAC05-840R Accabg)v, the U.S Government retans a nmxdltyyo. ~ovsnv-freekcmrs to plblah a reqmthn the wbkshsd form Of ms cam&mon.q auow o m s to do so. for Govarrnant PXPGees- u.s *Research sponsored by the U. S. Department of Energy and performed at Oak Ridge National Laboratory, managed by Martin Marietta Energy Systems, nc., for the U.S. Department of Energy under contract DE-AC05-840R21400.

2 Monte Carlo Verification of Point Kinetics for Safety Analysis of Nuclear Reactors T. E. Valentine J. T. Mihalczo nstrumentation and Controls Division Oak Ridge National Laboratory (USA) Abstract Monte Carlo neutron transport methods can be used to verify the applicability of point kinetics for safety analysis of nuclear reactors. KENO-NR was used to obtain the transfer function of the Advanced Neutron Source reactor and the time delay between the core power production and the external detectors, a parameter of interest to the safety systems design. The good agreement between the Monte Carlo generated transfer function and the point kinetics transfer function validates that the uncommon ANS geometry does not -..o l>.rlm plyyulc. +LA Llr use of poirir kinetics in the frequency range that was investigated. Various features of the power spectral densities also demonstrated the applicability of point kinetics. The time delay was obtained from the CPSD and is -15 ms. These analyses show that frequency analysis can be used experimentally to investigate the validity of the use of point kinetics models in critical experiments or zero power testing of reactors. DSCLAMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

3 DSCLAMER Portions of this document may be illegible in electronic image products. mages are produced from the best available original document.

4 ntroduction The point kinetics equations are commonly used to evaluate certain accident scenarios for nuclear reactors. These safety analyses provide the basis for the design of the control and safety systems of the reactor. The validity of the point kinetics formalism is a very relevant question if the results of these safety analyses are to be credible. Monte Carlo neutron transport calculations are used to verify the validity of this formulation and they show that frequency analysis measurements can confirm the validity of the use of point kinetics. Rod oscillator experiments' have been used in the past to determine reactor kinetics parameters; however, these experiments require a perturbation of the reactor. Noise analysis measurements of the cross-power spectral density (CPSD) between a source in or near the reactor core and a detector in or outside the reactor core could be used to validate the assumptions of point kinetics for the safety analysis. The CPSD has functional dependencies that can be used to verify the applicability of point kinetics. f point kinetics are not applicable, this measurement could provide the basis for a more complicated kinetics model that can the be used for the safety analysis. To illustrate this method, Monte Carlo calculations of the various power spectral densities have been performed using KFiNO-NR2 with a model of the Advanced Neutron Source (ANS) Reactop. These spectral densities were used to obtain the reactor transfer function and the time delay between the core and the external detectors. KENO-NR is an analog Monte Carlo code with "natural" tracking except for the use of group cross sections. n the code, fission chains are started with a source fission and the subsequent fission neutrons are followed until extinction. This code cannot be used for a critical system because the fission chain multiplication process does not terminate. The time distribution of the source events is stored, and the source is treated as a detector. This simulates a 252Cf source that is contained in an ionization chamber that produces a pulse every time 252Cf spontaneously fission^.^ The source particles and their progeny are tracked throughout the system. The time ordered sequences of pulses at the detectors are then obtained for each source fission. The sequence of pulses from the various fission chains are superimposed in a manner consistent with the random distribution of 252Cfission to form the data block of the detector response. A data block is a sample of the detector response for a time period which is determined from the sampling rate and the number of points sampled. These blocks of data are then Fourier transformed and complex multiplied to obtain the various auto-and cross-power spectral densities. The Advanced Neutron Source Reactor The conceptual design of the ANS reactor consisted of a variety of experimental facilities for neutron research. Figure 1 is a sketch of the conceptual design of the ANS reactor. The design model analyzed in this study consisted of two different diameter annular fuel elements that were vertically displaced. There were three hafnium control rods located in the inner region of the amular FC elements. The core pressure boundary tube separated

5 the heavy water core coolant flow from the heavy water reflector. There were eight shutdown rods that were located outside the core pressure boundary tube. There were 7 beam tubes, a thru-tube, 2 cold neutron source facilities, and a hot neutron source facility in the heavy water reflector. The heavy water reflector tank was contained within a light water pool. The fission detectors, located in the light water pool, were used for the control and safety systems of the reactor. The Monte Carlo model in this analysis consisted of the annular fuel elements with three hafnium control rods, the heavy water reflector, and the light water pool. The beam tubes and the cold and hot neutron source facilities were not modeled in these calculations. n the calculations, a 252Cf source was positioned at the midplane on the axis of the reactor core to initiate the fission process. Part of the upper fuel element and part of the lower fuel element were treated as fission detectors. The radial position of the external detectors was varied from -400 mm to 2500 mm, the latter being the location of the external fission detectors. To increase the statistical accuracy, the external detector was modeled as an annular ring of the relevant moderator (D,O or H,O) for a given radial position. n the model, these detectors were 10 mm wide and 1080 mm high. Neutron scattering was the event scored as a detection. Modeling the detectors in this fashion decreased the calculation time in that the efficiency was increased over that of a point detector. The tip of the control rods were positioned at the midplane of the reactor. The presence of the components in the heavy water reflector (Fig. 1) will reduce the core reactivity. To accoiint for this negative reactivity, the neutron emission probabilities were arbitrarily reduced by 2% to produce a subcritical configuration rather than changing the control rod positions. This reduced the average number of neutrons from fission and resulted in a subcritical configuration. t was later determined that the components in the heavy water reflector have a larger effect on the core reactivity than initially thought. The critical control rod position was changed from the midplane to 100 mm above the midplane of the reactor. However, this change in the control rod position is not expected to impact the results of this analysis. Discussion and Results of Calculations The KENO-NR model can be considered as a single-input multiple-output system. The input is the 252Cf source and the outputs are the core power (the response of the fuel elements as fission detectors) and the external detector responses. The transfer function can be determined by computing the auto-power spectral density (APSD) of the source and the cross-power spectral density (CPSD) between the source and the core power production. The calculated source transfer function for a slightly subcritical system can be expressed as where G,l( o) is the APSD of the source and Gi( a) is the CPSD between the source and fuel element fission detector i. This transfer function can be directly compared to the point kinetics transfer function for prompt neutrons. The reactivity of the reactor was determined

6 from a Monte Carlo calculation, and the neutron generation time was obtained from other calculations. These parameters were then used to obtain the point kinetics transfer function. As can be seen in Fig. 2, there is good agreement between the point kinetics transfer function and the Monte Carlo generated transfer functions for the frequency range that was considered in this analysis. There is also good agreement between the Monte Carlo generated transfer functions between the source and the two fuel elements. The validityof point kinetics can also be examined by analyzing known functional dependencies of the CPSDs. For point kinetics to be applicable, the real part of the CPSD between the, source and the fuel element fission detector must be positive. As can be seen in Fig. 3, the real part of the CPSD between the source and the fuel element fission detector is positive. Because the upper fuel element has a higher 235Uconcentration than the lower fuel element, the CPSD for the upper fuel element will have a greater value than the CPSD for the lower fuel element. f point kinetics is applicable, the phase of the CPSD between the fuel element fission detectors must be zero. f the phase is zero, then the detected neutrons represent those of the fundamental mode, and the two elements behave as one element. The phase of the CPSD between the two fuel elements is approximately zero as shown in Fig. 4. These properties of the power spectral densities show that point kinetics is applicable for this geometrical configuration of the ANS reactor. The time delay between the core power production and the external detectors can be determined from the phase of the CPSD between the fuel element fission detector and the external detectors. f the phase is linear with frequency, the response of the external detectors is just a time lag of the core power production. The time delay is related to the phase in the following manner where e(f) is the phase in degrees, and f is the frequency in Hz. The phases of the CPSDs between the fuel element fission detectors and the external scattering detectors are linear with frequency. Figure 5 is a plot of the time delay as a function of the radial position of the external scattering detectors. The time delay increases as a function of distance from the core until it reaches a saturation value in the light water pool. The time delay has a maximum (-18 ms) inside the D20 reflector and then decreases to 15 ms in the H20 tank. This decrease is due to the fact that once a slowed-down neutron gets into the light water tank it is absorbed locally and disappears by hydrogen capture. The flight path of a neutron to a radial point is not a direct path but consists of many scattering paths in all directions while diffusing to the radial point. Therefore, the calculated time delay is the average flight time of thermal neutrons diffusing to each radial point. Since more neutron scattering occurs in the D20, the average flight path willbe longer in the D20; hence, the average flight time will be longer. Neutrons that have numerous scattering collisions in the D20 may be scattered back into the reactor core and would not contribute to the detector response in the light water reflector. To evaluate further the understanding of this decrease in the time delay, a ca:cdation was performed with the light water replaced by heavy water. For the all-d20 case,

7 ~ the time delay increased with distance (Fig. 4), thus confirming the effects of neutron absorption in the light water. Since the experimental facilities in the D,O reflector were not modeled, these time deiays are overpredicted. f the reflector components were present, neutrons that stay in the reflector long enough will be absorbed by the reflector components. Thus, the addition of the experimental facilities in the heavy water reflector in the model should significantly reduce the time delays. The actual impact of the experimental facilities in the heavy water reflector on the time delays has not been evaluated and could be significant because the presence of the experimental facilities reduces the flux at the detectors by a factor of 4. Conclusions The Monte Carlo analysis provided the means to verify the applicability of point kinetics for the Advanced Neutron Source reactor and provides a means to determine the time delay between the core power production and the external detector response. The results of the calculations show that the point kinetics transfer function is in good agreement with the Monte Carlo calculated transfer functions over the frequency range that was analyzed. The functional dependencies of the power spectral densities further indicate that point kinetics is applicable. The agreement between Monte Carlo generated transfer function and the point kinetics transfer function is necessary for point kinetics to hold for this particular reactor configuration but it is not sufficient to determine if point kinetics holds for reactor transients. The time delay between the core and the external detector response is -15 ms. The time delay was obtained with the omission of the experimental facilities in the heavy water reflector and is considered conservative because the presence of the experimental facilities in the heavy water reflector should significantly reduce the time delays. These calculations also suggested a measurement method to experimentally validate the applicability of point kinetics by measuring the APSD of a source placed in or near the reactor core and the CPSD between the source and a detector placed in or near the reactor core. The time delay for the response of an external detector could be obtained by measuring the CPSD between the detector near the core and the detector in the light water reactor tank. Although the ANS reactor was used for this study, this method could be used to verify the applicability of point kinetics for other types of reactors both theoretically and experimentally in critical experiments or zero power testing of the reactors.

8 References M. N. Moore, TheDetermination of Reactor Transfer Functions from Measurements at Steady Operation, Nucl. Sci. Eng. 3, 387 (1958). E. P. Ficaro and D. K. Wehe, Monte Carlo Simulations of the 252Cf-Source-Driven Noise Analysis Measurements for Determining Subcriticality, Proceedingslnternational Topical Meeting Advances in Mathematics, Computations and Reactor Physics, Pittsburgh, Pennsylvania, April 28-May 2, 1991, Vol. 1, p ,American Nuclear Society, D. L. Selby, R. M. Harrington, and P. B. Thompson, The Advanced Neutron Source Project ProgressReport, FY 199,ORNL-6695, Oak Ridge National Laboratory, Oak Ridge, TN, January J. T. Mihalczo, V. K. Pare, G. E. Ragan, M. V. Mathis, and G. C. Tillet, Determination of Reactivity from Power Spectral Density Measurements with Californium-252, Nucl. Sci. Eng., 66,29 (1978).

9 / Cold Sources, Fission,Neutrcm, &Gamma Mectortl. Pneumatic Faaliies ' Outer Shutdown Rods Rafledor 'V9SSd c Upper Fud E l ment Lower Fuel Element Hot Source Through Tube / Figure 1. Conceptual design of the Advanced Neutron Source reactor

10 1.oo 0.80 z 0.60 N ' Frequency (Hz) Figure 2. Calculated source transfer functions of the reactor t loo 10" 1 o Lower Fuel Element + % loo Frequency (Hz) lo1 Figure 3. Calculated real part of cpsd between source and fuel element fission detector lo2

11 15 L '' Frequency (Hz) Figure 4. Calculated phase of cpsd between fuel element fission detectors O' loo i Upper Element All D,O 0 Lower Element All D,O _.._ _--o Upper Element o.._._..._._~ lower Element O Distance from Core Centerline (mm) Figure 5. Calculated neutron time delays as a function of the radial position from the core centerline 2500