A multi-scale and multi-physics approach to main steam line break accidents using coupled MASTER/CUPID/MARS code

One-dimensional system analysis codes such as RELAP5, TRACE, CATHARE-3, and SPACE are generally used to address nuclear safety issues with an umbrella of conservativeness. The three-dimensional (3-D) approach for 3-D components like reactor vessels, however, is always of concern in nuclear safety analysis.

A simplified 3-D approach by which the “cross-flow junctions” between 1-D modules represented some multi-dimensional flow features, was first developed in system codes like RELAP (The RELAP5-3-D Code Development Team, 2001) and ATHLET (Burell et al., 1989). This may be sufficient in some cases particularly for a porous body like a reactor core when only small cross flows exist due to high resistance to transverse velocity. Explicit 3-D modules exist as an option in the codes TRACE (Bajorek et al., 2015) and CATHARE-3 (Barre and Bernard, 1990) for the reactor pressure vessel. In this case, the main objective is the modelling of large scale 3-D effects in a pressure vessel during Large Break Loss of Coolant Accidents (LBLOCAs) such as ECCS water reflooding of the core with transverse power profile effects. The 3-D modules are straight forward extensions of the 1-D modules for cylindrical or Cartesian coordinates. A multiscale software platform, including a CFD module and CATHARE-3 as a system code, were developed to model reactor pressure vessels effectively. Development of a 3-D reactor core module using 1000 or fewer cells was also started using SPACE code (Ha et al., 2010).

Main steam line breaks (MSLBs) in pressurized water reactors (PWRs) is another issue for which the 3-D approach has been raised. This event is characterized by significant space-time effects in the core caused by asymmetric cooling and an assumed stuck-out control rod after the reactor trip. Major concerns for main steam line break (MSLB) accidents include the return-to-power and criticality. The coupled 3-D kinetics/core thermal-hydraulic (T/H) code was used to address these in the best-estimate manner because the T/H system analysis code with point kinetics did not provide reliable solutions (Todorova et al., 2003). A DNB, another primary concern in MSLB accidents, is, however, a local phenomenon, and thus the accuracy of the calculated Departure Nucleate Boiling Ratio (DNBR) depends on the accuracy of the power distribution as well as the global core power level (Joo et al., 2003). In this regard, the refined core T/H nodalization feature is desirable because incorporation of the detailed thermal feedback is crucial in producing accurate power distribution. Pressurized Thermal Shock (PTS) also becomes a primary concern with MSLB accidents from the point of view of ageing mechanisms. MSLB analysis for PTS has two main objectives: to support the transient selection process and to provide fluid temperatures in the down comer for the structural analyses of the RPV. The 1-D nuclear system code and the integral test experimental data must have some limitation for achieving the latter objective.

Expansion of the 1-D system analysis codes has some technical and economic limitations; therefore, code coupling was adopted as another strategy for multi-scale and multi-physics safety analysis. Thus, a coupled code of 3-D reactor kinetics and 3-D thermal-hydraulics was consolidated into a one-dimensional system analysis code in the MASTER/COBRA-TF/RELAP5 or MARS, which was applied to simulation of a main steam line break accident (Jeong et al., 2006). The capability of coupled codes has been enhanced considerably according to improvement of the separate codes and to the computational environment. CFD codes used to conduct huge amounts of calculation are coupled with 1-D system analysis code (Martelli et al., 2017), and coupled 3-D thermal-hydraulics and 3-D neutronics codes can handle full core modeling for all the fuel (Brown et al., 2016).

After developing the method of multi-physics safety analysis tools using MARS (RELAP5/COBRA-TF)/MASTER (Jeong et al., 1999), researchers at the Korea Atomic Energy Research Institute (KAERI) started to develop the CUPID code (Jeong et al., 2010), which addresses the need for high-resolution multi-dimensional analysis, which is being increased by advanced design features, such as direct vessel injection (DVI) systems, gravity-driven safety injection systems, and passive secondary cooling systems. The CUPID code is designed to address features of both open and porous media. In two-phase momentum equations, non-drag forces such as lift, wall lubrication, and turbulent dispersion forces are modeled in addition to the interfacial drag forces and these non-drag forces are selectively activated. These features with the capacity to deal with huge body-fitting, unstructured mesh with over 10,000,000 cells may categorize CUPID as a CMFD distinct from traditional system analysis codes. The flow or heat structure coupling methods with the MARS system code, a reactor vessel module, and a steam generator module have also been developed to extend the application of CUPID as a 3-D model of a nuclear reactor. A new module of CUPID is being developed at KAERI, which includes such a package of interfacial heat and momentum transfer model, wall friction and wall-to-fluid heat transfer model, and a CUPID-RV (Reactor Vessel) model, for the analysis of reactor thermal hydraulics, especially during a LBLOCA.

During the CUPID development, the code coupling efforts for multi-scale or multi-physics with the 3-D neutron diffusion analysis code (MASTER) and 1-D system analysis code (MARS) resulted in MASTER/CUPID (Lee and Yoon, 2017) and CUPID/MARS (Park et al., 2013, Park et al., 2018), respectively. The multi-physics code, MASTER/CUPID, was developed by linking the MASTER dynamic link library (DLL) to the CUPID code. The OPR1000 Korean PWR reactor core was taken into account by adopting a porous media approach. Two hypothetical accident scenarios for malfunction of the control element assembly (CEA), a CEA drop and a CEA ejection accidents, were numerically simulated. The coupled simulation shows a reasonable and consistent thermal hydraulic behavior. The multi-dimensional thermal hydraulics results show an asymmetric temperature distribution, which was a result that was not obtained by the best-estimated thermal hydraulics code before.

A multi-scale thermal–hydraulic system code, CUPID/MARS, was also developed by consolidating CUPID with MARS (Park et al., 2013). The validation calculation for the ROCOM (Rossendorf Core Mixing) test (Kliem et al., 2008) shows that the multi-scale approach is cheap and convenient. Where the pressure vessel is simulated by CUPID, and the other components such as four hot legs, four cold legs, and four pumps are simulated by MARS in an individual component analysis with complicated boundary conditions like ROCOM vessel, the CUPID code can use the thermal–hydraulics component of MARS as its boundary conditions. A validation calculation (Park et al., 2018) of CUPID/MARS was conducted in comparison with the MSLB integral test in the ATLAS facilities (Baek et al., 2005, Kim et al., 2008). These facilities were built to provide experimental data for the Korean advanced nuclear power plant, APR1400 (Korea Electric Power Corp, 1999). In the simulation, CUPID covers RPV, and MARS covers all the other reactor components, including the two steam generators. In this manner, multi-scale MSLB transients could be simulated successfully for a 1-D and 3-D consolidated reactor system. Moreover the calculations needed to fit 1-D results show that the calculated three-dimensional temperature distributions agree with the measured data quantitatively and qualitatively in absolute values and that the asymmetric cooling behaviors through the heat structure model should be implemented in the CUPID part. Thus, the ATLAS-MSLB simulation indicates that the newly developed CUPID/MARS method could be applied to obtain 3-D calculation results for such as a PWR MSLB after being equipped with the core neutronics model.

This paper presents an application that combines the calculations of a multi-scale and multi-physics analysis code, MASTER/CUPID/MARS, which combines MASTER/CUPID and CUPID/MARS, as mentioned above. In the simulation, CUPID covers the reactor pressure vessel and reactor core, MASTER covers the reactor core power, and MARS covers all the other reactor components. The concept behind the coupling of MASTER/CUPID, CUPID/MARS, and MASTER/CUPID/MARS is briefly described in Section 2. The coupled safety analysis concept and the coupled MSLB calculation are discussed in Section 3.