Comparison of experimental and analytic simulations of reactor structural response to a hypothetical core disruptive accident

Nuclear Engineering and Design 60 (1980) 257-266 © North-Holland Publishing Company

COMPARISON OF EXPERIMENTAL AND ANALYTIC SIMULATIONS OF REACTOR STRUCTURAL RESPONSE TO A HYPOTHETICAL CORE DISRUPTIVE ACCIDENT A.M. CHRISTIE Westinghouse Electric Corporation, Advanced Reactors Division, Madison, PA 15663, USA

N.W. BROWN and B.W. JOE General Electric Company, General Electric Fast Breeder Reactor Department, Sunnyvale, CA 94086, USA

Received 3 April 1980

A series of scale model tests assessing the ability of the Clinch River Breeder Reactor to withstand the loads resulting from a hypothetical core disruptive accident have been performed. Supporting analytic simulations of these tests using the REXCO-HEP code were also performed. Comparisons of the analytic and experimental results are described inthis paper. As a general conclusion, the analytically predicted loads on the coolant boundary and resulting structural deformations were greater than the corresponding experimental loads and deformations.

1. Introduction

used to derive the SMBDB loads. As discussed in the previous paper, five tests, SM-1 through SM-5, were run. In the first test, a 1/20th scale model of the three-plug vessel head was loaded hydrostatically on its lower face to determine its elastic-plastic response. This preliminary component test was not analyzed in any detail and will not be discussed further in this paper. Tests SM-2 through SM-5 consisted of 1/20th scale models of the CRBRP vessel, vessel head and internals, SM-2 being the simplest, SM-4 and SM-5 being the most complex. The models for tests SM-2 through SM-5 are shown in fig. 1.

In the previous paper, experimental results from a set of scale model tests were presented. These tests assessed the ability of 1/20th scale models of the Clinch River Breeder Reactor Plant (CRBRP) reactor enclosure assembly to withstand the loads from a simulated hypothetical core disruptive accident (HCDA). This paper describes the analyses supporting these tests and compares the analytic and experimental results. Details of these analyses and experiments are discussed by Romander [1]. To assure that CRBRP has adequate structural margin to withstand the loadings from an HCDA, structural requirements have been imposed on and within the primary coolant boundary of CRBRP [2]. These Structural Margin Beyond the Design Base (SMBDB) requirements are based on the pressurevolume relationship which defines a 661 MJ energy source, and on analytic simulations of the responses of the coolant and structures to that energy source. In deriving the loads upon which the SMBDB requirements are based, the REXCO-HEP code [3] was used. Thus, in addition to providing direct information about the adequacy of CRBRP structural response, the tests provided data to assess the analysis approach

2. The REXCO-HEP models Two sets of reactor system simulations with the REXCO-HEP code were performed. First, a pre-test set of calculations was performed for tests SM-2, SMSM-3, and SM-4/SM-5. Only one calculation was performed for tests SM-4 and SM-5 since, with respect to code modelling, these two tests were identical. Second, a set of post-test calculations was performed for tests SM-2 and SM-4/SM-5. The pre-test analyses were performed to support test planning and allow 257

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A.M, Christie et al. / Comparison o f reactor structural response to atl HCDA ACCELEROMETERS

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an assessment of the adequacy of the numerical modeling techniques to be determined without a prior knowledge of the test results. The post-test analyses were then performed to determine if reasonable improvements to the modeling could be made using the insight gained from the experiments. The SM-2 and SM-4/SM-5 analyses will be discussed in more detail than the SM-3 analysis which will be reviewed either when results from this calculation are of particular importance or to amplify important conclusions drawn from the other analyses. Figs. 2 and 3 show the REXCO-HEP models used to simulate tests SM-2 and SM-4/SM-5, respectively. The SM-3 model is identical to that of SM-2 except that the upper internals structure (UIS) is modeled as a dense hydrodynamic, non-structural fluid. The superimposed grid regions represent Lagrangian zones which move and distort with the simulant coolant (water). The major difference between the pre- and post-test analyses lay in the material property representation of the Nickel 200 (simulating the 304 stainless steel). In the pre-test analysis, no consideration was given to potential strain-rate effects while in the post-test analysis, a stress-strain curve representing the material proper-

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The most meaningful and direct comparison between the experiments and calculations can be made using the reactor vessel and core barrel ffmal hoop strains and relating these strains to the applied loadings. Figs. 6 and 7 compare the calculated and measured SM-2 and SM-4/SM-5 vessel and core barrel strain profdes, respectively. As a result of conservative assumptions in the REXCO-HEP code (for example, lack of energy dissipating mechanisms), the predicted strain profiles generally envelope the corresponding experimental profiles. The differences

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between the predicted and experimental profiles can be explained by examining the loadings within the reactor vessel. In the paragraphs below, the pressure loads causing the strains in the core barrel and in the different sections of the vessel wall are discussed. From figs. 6 and 7, it is evident that REXCO-HEP tends to overpredict core barrel strains. This results from four known effects. First, REXCO-HEP (Release 2) models the core shielding as a hydrodynamic medium having no structural resistance. Thus the loads are transmitted to the core barrel more readily than in the experiment and greater core barrel expansion results. The more rapid initial expansion of the core barrel was observed to lead to more rapid decay o f the core region pressure. Second, because o f the particular Lagrangian mesh formulation used in the Release 2 version of REXCOHEP, there is a coupling between the shielding and core region zones which resists upward movement of the bubble-liquid interface. This resistance to upward fluid movement tends to retard bubble expansion and thus adds to the overprediction of core barrel deformation. Overall bubble expansion is, however, dominated by the first o f the two effects above and hence the predicted core pressure still decays more rapidly than in the test. Third, while no experimental strain histories of the core barrel are available, REXCO-HEP pre-test calculations indicate core barrel strain rates o f up to 95 in/in/s. Thus the strain rate effect is likely to strain harden the core barrel material as a result o f its rapid dynamic response. This effect was not accounted for in the pre-test analysis. Fourth, the computed core barrel deformations are influenced by the wave reflected after slug impact. Because o f the lack o f energy dissipating effects in REXCO-HEP, such as turbulence, the reflected wave, which travels into the annulus between the vessel wall and core barrel, is more intense in the calculations than in the experiments. The differences between the analytic and experimental post-impact pressures (i.e., beyond three milliseconds) can be seen in figs. 8 and 9. These differences result in the analysis predicting some reverse deformation o f the core barrel while no reverse deformation occurs in the tests. Consider now the reactor vessel mid-wall response (i.e., from the core support cone to the elevation mid-

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way between the upper core barrel and the vessel head) and the associated loadings. From fig. 6, it can be seen that the SM-2 pre-test prediction significantly underestimated the vessel strain around the elevation of the outlet nozzle, but this situation is reversed in SM-4 (fig. 7). The relative magnitudes of these deformations are seen to be consistent with the relative magnitude of the corresponding vessel wall pressure loads before 2 ms, as shown in figs. 8 and 9. The early loading on the SM-2 vessel is considerably more severe than in the pre-test prediction. As discussed below, this results from the same considerations as those affecting the core barrel response. 800

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Because of a more rapid expansion of the core barrel in the pre-test analyses, less liquid is initially ejected upwards than in the test. Also the non-prototypic coupling between the shielding and the upward moving fluid tends to retard the fluid movement. A similar coupling is also present between the inner and outer fluid zones above the core barrel and helps retard the rapid upward movement of the liquid ejected from the core barrel. Fig. 9 compares the predicted and experimental mid-vessel pressures for SM-4. Early in the transient, the predicted and experimental results are in closer agreement than the predicted and experimental SM-2 results. This agreement results in the favorable vessel wall strain comparison at the mid-vessel elevation. Since REXCO-HEP does not model the energy dissipating mechanisms in the liquid, the longer term calculated pressures (i.e., from 3 to 6 ms) tend to be higher than the experimental values. These later loadings produce little additional vessel strain, since the early loadings have a strain hardening effect on the structures. In the SM-4 and SM-5 tests, the UIS plays a major role in dissipating energy through the creation of fluid turbulence and produces the significant reduction in the early vessel wall loadings. The addition of the hydrodynamic UIS in the SM-4/SM-5 analytic model, however, does little to change the calculated fluid response. The final effect of the above competing processes (i.e., bubble retardation in the analysis and US-created energy dissipation in the tests) is that remarkably good agreement between test and calculated early mid-vessel loadings occurs when the UIS structure is included. The predicted upper vessel wall hoop strains are all greater than the corresponding test values. Specifically, the experimental peak vessel hoop strains for SM-2, SM-3 and SM-4 are 4.4, 2.8 and 1.7 percent, respectively, while the corresponding predicted peak vessel hoop strains are 6.4, 6.8 and 4.0 percent, respectively. The overpredictions are partly due, in SM-2 and SM-3, to the higher predicted upper vessel wall loads as reflected by the SM-2 loadings shown in fig. 10, and to the fact that the REXCO-HEP models did not account for material strain rate effects. However, the SM-4 predicted and experimental upper vessel wall loads are comparable (see fig. 11) and it is unlikely that the tack of strain rate effects in the anal-

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A.M. Christie et al, / Comparison o f reactor stnwtural response to an HCDA

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ysis is responsible for the fact that the predicted hoop strain is about 2.5 times the measured strain. In addition, on approaching the vessel flange, the experimental strain profile makes an abrupt change in gradient at the flange. These observations tend to indicate that REXCO-HEP is not fully accounting for the bending stiffness of vessel shells adjacent to structural discontinuities. This conclusion is supported by similar observations of the predicted and experimental strains in the lower vessel section of SM-4. This is discussed later in the section. By comparing the predicted and experimental 3000

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responses of SM-2 through SM-5 at the upper vessel wall, it is evident that the approach used to model the UIS in REXCO-HEP does not fully account for energy dissipating mechanisms introduced by the UIS. While the SM-3 vessel wall hoop strain is about 36 percent less than the SM-2 value, the predicted SM-3 strain increased over that of SM-2 by about 8 percent. This resulted because the hydrodynamically modeled UIS in the SM-3 through SM-5 calculations produced a fluid slug having more impulse than in the case of SM-2 where no UIS was modelled. In addition, dissipative fluid turbulence created by the actual UIS was not generated by the hydrodynamically simulated UIS. Thus, in the REXCOHEP model used to generate the SMBDB loads, considerable conservatism in the system response is built in as a result of not including the dissipative effects associated with the UIS. Figs. 12 and 13 compare the SM-2 and SM-3 experimental and predicted central head loads. The SM-2 comparison shows good agreement in loads although the experimental peaks occur earlier. This results because of the limitation in modeling in-core fluid slippage, which as discussed earlier, is inherent in the version of REXCO-HEP used. The SM-3 predicted peak load is significantly higher than that for SM-2 because of the increased slug impluse associated with the hydrodynamic UIS. From these upper vessel and vessel head predicted responses, it is apparent that the approach used here

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to analytically model the UIS results in greater loads to the head and upper vessel. The test results indicate that a prototypic UIS is likely to have the reverse effect reducing head and upper vessel loads. While thy hydrodynamically modeled UIS increases the slug kinetic energy through the addition of higher density fluid above the core, the prototypic UIS would have the effect of reducing slug axial kinetic energy through generation of fluid turbulence. Where comparisons can be made, the SM-4/SM-5 pre-test analysis shows similar trends to those of the SM-2 and SM-3 pre-test analyses. However, unlike the SM-2 and SM-3 test models, the SM-4 and SM-5 test models included scaled core support plates and bottom heads. For these components, the SM-4/SM-5 pre-test analysis predicted considerably more strain than measured in the experiments. In both the SM-4 and SM-5 tests, residual downward displacement of the centers of the core support plates relative to the edges was approximately 0.1 in. However, in the pretest prediction, the corresponding displacement was 0.31 in. In addition, as shown in fig. 7, the predicted peak residual hoop strain in the vessel wall was about 1.8 percent while the measured strain was only about 0.2 percent. These over-predictions may result from two effects. First, the core support structure was modeled as a solid elastic-plastic nickel plate supported by a cone-shaped shell attached to the reactor vessel. The density and yield stress of the plate were ajusted in an attempt to model the flexibility of the actual core

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support plate, but the resulting stiffness of the analytic model may have been too low. Second, the residual hoop strain of the lower vessel wall (0.2 percent) is much less than would be expected from the applied inlet plenum pressure loading of about 400 psi (see figs. 7 and 14). This conclusion is based on a comparison of similar pressure loadings and corresponding mid-vessel wall hoop strains measured in SM-2 and SM-3. (With the thermal liners of SM-4 and SM-5, mid-wall loading and resulting hoop strains are not represen,tative of the lower vessel wall which has no thermal liner.) For example, with a less severe loading of about 350 psi on the SM-3 mid-vessel wall, the vessel wall hoop strain is about 1.5 percent. This indicates that not only the applied pressure but also the boundary constraints are important in determining the final vessel wall hoop strain. It is thus likely that the added hoop stiffness of the cone-to-vessel junction and the vessel bottom head are partly responsible for the reduced vessel wall strain measured in the SM-4 and SM-5 lower vessel walls. This reduction is not very evident in the REXCO SM-4/SM-5 pre-test prediction and it is possible that the code under-estimates the vessel bending stiffness resulting from the cone-to-vessel junction and the vessel bottom head attachments. This is consistent with the earlier discussion on upper vessel wall response. From a comparison of the pre-test predictions

264

A.M. Christie

et at. / Cot~q~arison o f reactor stntctural response to an HCDA

with the experimental results, the following conclusions can be made. (a) Because of the general lack of energy dissipating mechanisms in REXCO-HEP, the preducted pressure loads and resulting strains are predominantly conservative, as would be expected. The pressure load with its associated hoop strain at the vessel midelevation from SM-2 is the major exception to this. (b) The hydrodynamic modeling used to simulate the UIS increased upper vessel and vessel head loads. In the tests, fluid turbulence generated by the UIS reduced these loads. Although hydrodynamic modeling of the UIS is thus not recommended, it does result in conservative upper vessel and head loads. (c) REXCO-HEP overpredicted hoop strains in the vicinity of structural discontitmities (e.g., at the upper vessel wall next to the flange and at the lower vessel wall between the bottom head and the core support ring). This may result from insufficient shell bending stiffness as modeled in REXCO-HEP. (d) The 1/20 scale model core barrel and upper vessel wall respond sufficiently rapidly that strain rate effects should be included in the definition of material properties. For the prototypic case, vessel wall and core barrel strain rates are likely to be too low to significantly alter material properties. (e) The material properties and modeling used in the analysis to characterize the core support plate and cone produced too flexible a response in these components (SM-4/SM-5 only). This will lead to higher inlet plenum pressures but will make little difference to upper vessel response. (0 Hydrodynamic modeling of the in-core shielding does not account for the structural resistance of the shield rings and leads to too rapid an expansion of both the shield region and the core barrel. This results first in too rapid decay of in-core pressure and second, in reduced energy being imprated to the liquid slug. (g) In REXCO-HEP, the Langrangian zones associated with the high-pressure vapor source are attached to the hydrodynamically modeled shielding zones. The resulting constraint on the vapor bubble expansion retards the liquid slug, reducing the loading on the mid-vessel wall, and delaying slug impact with the vessel head. The effects discussed in the last two conclusions above both tend to reduce the loading on the mid-

vessel wall, and in this sense are non-conservative. However, other modeling assumptions, such as those associated with the UIS more than compensate in the conservative direction.

4. The post-test analyses Several factors were identified in the previous section as having contributed to the differences between the analyses and experiments. These factors, as associated with REXCO-HEP modeling, were: (1) neglect of strain rate effects, (2) hydrodynamic modeling of the UIS, (3) hydrodynamic modeling of the core barrel shielding, (4) artificially strong coupling between hydrodynamic core barrel shielding and the pressurizing gas, (5) insufficient accounting of shell bending stiffness at geometric discontinuities and (6) limitations in core suport plate modeling. The first factor can be assessed by data modification while the last five primarily involve code limitations. Later in the section, the importance of strain rate effects on the core barrel and vessel wall responses of SM-2 and SM-4/SM-5 are discussed. With respect to the second factor, the Lagrangian formulation of REXCO-HEP code makes modeling of orifice flow through the UIS virtually impossible, and it has thus not been possible to address this assumption through the use of REXCO-HEP. Code modifications are required to address fractors 3 and 4. Assessing these effects is beyond the scope of this work since the analyses are being used to validate the mathematical model in the version of REXCO-HEP which was used to generate the SMBDB loads. However, the effect of these factors is addressed through the use of a modified version of REXCO-HEP as discussed by Chang and Gvildys [4]. This showed, for example, that with improved assumptions with respect to factors 3 and 4, the mid-vessel wall loading and corresponding hoop strain in SM-2 matched the experiment much more closely. Factors 5 and 6 have not as yet been addressed quantitatively in any detail. In the post-test SM-2 and SM-4/SM-5 analyses performed to assess the first factor, some additional minor input changes were also made. These changes, such as minor adjustments in the water surface level and cover-gas volume were made with the objective of making the analysis more consistent with the as-

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A.M. Christie et al. / Comparison o f reactor structural response to an HCDA STRAIN (PERCENT) 5

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Fig. 16. Comparison of SM-4/SM-5 pre- and post-test REXCO-HEP deformation profiles.

deformation profiles.

tested geometry and materials properties of the scale models. Their total effect is not believed to be very significant to the analysis. Fig. 4 shows the stress-strain curve for Nickel 200 used in the reactor vessel at a strain rate of 100 in/in/s and compares it to the low strain rate curve and the piecewise linear curve used in the REXCO-HEP calculation. A similar adjustment to the stress-strain properties for the core barrel material was made in the post-test analysis. The stress-strain properties at the high and low strain rates will bound those properties actually experienced by the Ni 200 (50 to 100 in/in/s). With the limited strain rate data available on this material, this approach was felt to be most appropriate. Fig. 15 compares the deformation profiles of the reactor vessel and core barrel for the SM-2 experiment and pre- and post-test analyses. As can be seen in this figure, calculated peak vessel strain is in much better agreement with the experiment than is the peak strain from the pre-test analysis. A comparison of SM-4/SM-5 pre- and post-test vessel wall and core barrel deformations is then shown with the experi-

mental results in fig. 16. Again improvement in calculated vessel wall peak strain can be seen although it is not marked as with the SM-2 calculations. The SM-4/SM-5 core barrel analytic profile is shown at two times. One is prior to the return of the reflected pressure pulse and the second is after this pulse has acted on the core barrel and corresponds to the time of final reactor vessel deformations. The higher strength resulting from the high strain rate properties is seen to reduce both the maximum core barrel strain early in time and the degree of reverse deformation caused by the computed reflected pressure pulse. As a result, the final strain of the core barrel is greater than in the low strain rate analysis. The correction for material properties does improve the correlation between the analyses and test results, especially in the upper reactor vessel region. However, there are still some differences that result from the other factors discussed, such as those addressed by Chang and Gvildys [4]. However, the lack of proper characterization of the UIS is likely to be most significant (in SM-4/SM-5) and will contri-

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bute to a large share of this continuing difference. Over-prediction of the deformation of the upper reactor vessel is still present in SM-4/SM-5 ; whereas, in SM-2 the change in material properties and the other minor adjustments brought the experiments and analysis into close agreement. This difference is attributed to the limited ability of REXCO-HEP to model the UIS structure and its effects on fluid flow. Thus, changing the material properties in the reactor vessel would not be expected to completely resolve the discrepancy in upper vessel deformation in the SM-4/SM-5 analysis as it did in the SM-2 analysis. Over-prediction of strain in the core barrel and the reactor vessel at the core elevation is still substantial. The failure to properly model the shield region is apparently a major source of this discrepancy and changing the core barrel material properties only produced a small improvement. In summary, the changes in the stress-strain properties for shell structures and correction of other minor discrepancies in the pre-test analysis improve the comparisons of the analytical results with the test results. The apparent causes of the reamining discrepancies have been identified and partially addressed by Chang and Gvildys [4].

5. Summary and conclusions In this paper, we have verified that the REXCOHEP code can provide a conservative representation of the loads on the vessel and head of a reactor such as that in CRBRP having an upper internals structure, and predicts peak vessel strains in excess of the physical system being simulated. The analysis supporting the tests consisted of preand post-test phases for tests SM-2 through SM-5. In the pre-test phase, predictions of the response of the models, unbiased by the tests themselves, were performed. These showed that because of such effects as fluid turbulence, the predicted loads were in general higher than in the tests. In particular, it was found that while hydrodynamic modeling of the upper

internals structure lead to increases in head load, hi reality, the dissipative effects of the upper internals lead to substantially reduced head loads. Other modeling approximations and their effect on loads were examined. For example, it was found that the hydrodynamic modeling of structures inside the core barrel and an unrealistic coupling between in-core liquid and gas zones resulted in an overprediction of core barrel and lower vessel wall deformation. Post-test analyses were performed primarily to assess the effects of high strain rate material properties on the dynamic responses of the vessel wall and core barrel. Introduction of high strain rate material properties did significantly improve the peak calculated vessel wall strain particularly for the test (SM-2) where upper internals were not present but did not improve the response of the core barrel. However, the discrepancy was somewhat greater for the tests with an upper internals structure (SM-4 and SM-5) since the energy dissipating effects of this structure were still not accounted for in the post-test SM-4/ SM-5 analysis.

Acknowledgements The authors wish to thank L.E. Strawbridge (WARD) who gave considerable support in planning and coordination. The tests were performed under a DOE contribution base technology program while the analysis was performed under the CRBRP contract.

References [1] C.M. Romander and D.J. Cagliostro, DOE/TIC-10063 (October 1978). [2] Hypothetical Core Disruptive Accident Considerations in CRBRP, Energetics and structural margin beyond the design base, CRBRP-3, Vol. 1, Rev. 2 (January 1979). [3] Y.W. Chang and J. Gvildys, ANL-75-19 (June 1975). [4] Y.W. Chang and J. Gvildys, ANL-78-18 (Agust 1978).