This paper highlights two novel features that have been implemented into the coupled RELAP5/PANBOX2/COBRA3 (R/P/C) code system. On the one hand, the R/P/C code system has been extended to include a dimensionally adaptive algorithm that uses the underlying physical phenomena to switch dynamically between three-dimensional (3D), one-dimensional (1D), and point-kinetics models, thereby reducing computational times up to a factor of five while preserving the accuracy, within user-defined error criteria, of the 3D reference calculation. On the other hand, the R/P/C system has also been extended to include the Adjoint Sensitivity Analysis Procedure (ASAP) for the RELAP5/MOD3.2 two-fluid model with non-condensables, thus enabling the efficient calculation of local sensitivities of RELAP5 results to various parameters in the RELAP5 code.
The coupled RELAP5/PANBOX2/COBRA3 (R/P/C) code system (Knoll and Müller, 1994) is used for detailed numerical simulations and analyses of light-water reactor (LWR) plant transients, both for normal operating conditions and for postulated accident scenarios. Within the R/P/C code system, the RELAP5 (Ransom et al., 1987) code simulates the thermal-hydraulic characteristics of LWRs by using a non-equilibrium, non-homogeneous two-phase flow model together with conservation equations for boron concentration and non-condensable gases; the PANBOX code solves the diffusion-theory-based neutron kinetics equations in three-, one-, or zero (point)-dimensions using the nodal expansion method; the COBRA code computes the flow and enthalpy in the sub-channels of rod bundles for boiling and non-boiling conditions.
On the one hand, the coupling of three-dimensional (3D) neutron kinetics models with system thermal-hydraulics codes leads to a very high computational overhead, which prohibits their routine use. On the other hand, most of the postulated accident scenarios are characterized by relatively large time intervals during which a point-kinetics (PK) or a one-dimensional (1D) neutron kinetics model would suffice. Thus, an efficient code system would activate the 3D neutron kinetics model only when called for by the physical phenomena occurring in the respective portions of the transient, but would use a correspondingly lower dimensional model at other times. The R/P/C code system has been recently extended (Jackson et al., 1999a and Jackson et al., 1999b) to include a dimensionally adaptive, automatic algorithm that switches dynamically, using the underlying physical phenomena, between the 3D, 1D, and PK models, as required by the physical phenomena underlying the transient scenario under investigation. This algorithm is described qualitatively in Section 2; specifically, Section 2.1 highlights the criteria for dynamic switching from lower-to-higher dimensional neutron kinetics models, while Section 2.2 highlights the criteria for dynamic switching from higher-to-lower dimensional neutron kinetics models. Section 2.3 presents illustrative results for the dimensionally adaptive calculation of the Control Rod Ejection NSC Benchmark Problem (Finnemann et al., 1993 and Fraikin, 1996).
The implementation of efficient methods to analyze the sensitivity of results (responses) calculated with the R/P/C code system would represent a major development towards establishing a general-purpose code system for the analysis of postulated accident scenarios. As an important first step in this direction, work is currently in progress (Cacuci and Ionescu-Bujor, 2000, Ionescu-Bujor and Cacuci, 1999 and Ionescu-Bujor and Cacuci, 2000) to implement the Adjoint Sensitivity Analysis Procedure (ASAP) for Nonlinear Systems, originally developed by Cacuci et al., 1980, Cacuci, 1981a and Cacuci, 1981b, into the RELAP5/MOD3.2 code. The salient features of this work are briefly described in Section 3. Finally, Section 4 summarizes the results obtained thus far and outlines developments aimed at establishing a multipurpose code for comprehensive analyses of reactor plant transients
This work has illustrated novel features of the R/P/C coupled neutron kinetics/thermal-hydraulics “best estimate” code system for performing transient reactor safety calculations. On the one hand, the dimensionally adaptive, dynamic neutron kinetics algorithm described in this work can greatly increase the efficiency of coupled thermal-hydraulic/neutron kinetics reactor safety transient calculations while preserving the accuracy of reference 3D-kinetics calculations. This efficiency is reached by using the 3D neutron kinetics model only when necessary, and by activating 1D or PK models during the time intervals in which their accuracy is within a user-specified error criterion from the accuracy of the full 3D-kinetics model.
On the other, we have implemented the ASAP for the two-fluid model with non-condensable(s) used in RELAP5/MOD3.2. Underlying the ASAP is the ASM, which comprises nine coupled differential equations that are linear in the adjoint function. The solution of the ASM has been verified for the single-phase sub-model by using the “Two Loops with Pumps Problem” supplied with RELAP5/MOD3.2. The presented results depict typical sensitivities of junction velocities and volume-averaged pressures to perturbations in initial velocities. The good agreement between the adjoint calculations and the exact recalculations indicates that the adjoint solution for the single-phase sub-model is as robust, stable, and accurate as the original RELAP5/MOD3.2 calculations.
Our ongoing research emphasizes simultaneously the analysis of international benchmarks with the R/P/C code system, as well as the continuing validation of the two-phase flow segment of the Adjoint Sensitivity System for the two-fluid model in RELAP5/MOD3.2. Longer-range research is envisaged towards developing a 3D adjoint neutron kinetics model in PANBOX, and coupling it to the ASM of RELAP5/MOD3.2. At that stage, the adjoint sensitivity analysis capability will be combined with the dimensionally adaptive dynamic switching algorithm for neutron-kinetics. The resulting multipurpose code system is expected to provide an efficient tool for performing comprehensive sensitivity/uncertainty analyses for reactor safety transients.
