**4. Modeling and simulation of NTPs**

In this section, we focus on the modeling and simulation (M&S) needs for NTP systems from a nuclear reactor perspective, with a particular emphasis on transient modeling. INL leads the development of the multiphysics object oriented simulation environment (MOOSE) [52] that provides a cohesive framework for multiphysics analysis; MOOSE is introduced first. The needs of a transient reactor-centric M&S are introduced next, and then MOOSE applications performing transient simulations are introduced. Finally, we present the capabilities of MOOSE for a PID controlled startup transient.

#### **4.1 Multiphysics object oriented simulation environment**

MOOSE is a C++ based framework for a finite element and finite volume-based solution of partial differential equations. Its goal is to provide high-level access to the powerful finite element capabilities implemented in the libMesh library [53] and the linear and nonlinear solver technologies in PETSc [54] without having to understand multiple interfaces, manage parallel execution, or handle input/output. MOOSE is structured such that code can be reused among different research groups, facilitating the development of a multiphysics ecosystem referred to as the MOOSE herd.

The MOOSE framework provides: (1) extensible systems that perform tasks in a partial differential equation (PDE) solver and can be inherited from and used by physics applications; (2) an input/output handling system; and (3) specific internal data structures like the finite element mesh and finite element variables. Physics applications are developed on top of the framework. To date, the MOOSE repository comes with 21 modules (i.e., open-source physics implementations that are general enough to be packaged with MOOSE) including heat conduction, Navier– Stokes, and phase field. Many physics applications have been created based on MOOSE that contain either export-controlled, proprietary, or very specialized physics and require user approval and licensing.

The difference between MOOSE and traditional multiphysics nuclear engineering applications is that MOOSE is not a collection of single-physics codes connected with *glue code* [55]. MOOSE-based software applications are built using interfaces provided by the framework that are extended and specialized using inheritance. This paradigm shift away from using glue code provides many advantages, including reduction in data storage duplication, increased robustness against future compatibility issues, shared representation of geometry precludes developing a significant number of translation routines [56].

#### **4.2 Relevant physics and simulation capability within MOOSE**

#### *4.2.1 Neutronics*

Neutronics is at the heart of a reactor-centric viewpoint of NTP M&S. The neutron distribution drives the power distribution, which in turn drives temperatures and stresses in the core. In addition, the dynamic behavior of NTPs is to a significant degree driven by the neutronics feedback behavior. In contrast to most terrestrial reactors, NTPs spend a large fraction of their operating life in transient operation. Therefore, neutronics M&S for NTPs should provide a strong transient simulation capability. Traditionally, many neutronics tools are developed for steady-state (i.e., *k*-eigenmode calculations) or very slow transients (i.e., depletion

### *Nuclear Thermal Propulsion DOI: http://dx.doi.org/10.5772/intechopen.103895*

calculations). During a transient, temperature and thermal-fluids conditions can vary rapidly, making a tight coupling of neutronics and heat conduction mandatory. Finally, one of the control mechanisms for the ramp up to power is the rotation of the control drums. During a startup transient, the neutronics code must be able to accurately model the behavior of the control drums rotated to an arbitrary angle.

Griffin is the MOOSE-based reactor multiphysics application [57]. It is a superset of the capabilities previously implemented in Rattlesnake [56] and Proteus [58]. In the near-term, it will also provide an interface to the MC2–3 cross-section preparation capability [59]. The main distinction between Griffin and traditional radiation transport solvers is that it is designed for transient multiphysics simulations, making it an ideal candidate for NTP simulation. Griffin is a deterministic radiation transport application that provides the user with a variety of solvers for the linear Boltzmann transport equation. These solvers provide a variety of different fidelity levels ranging from zero-dimensional point-kinetics models over neutron diffusion with equivalence correction to high-fidelity *S*<sup>N</sup> models [56, 57] with spatial kinetics.

Griffin is an ideal candidate for transient analysis of NTPs. It naturally couples to MOOSE's heat conduction capability, described later in Section 4.2.2, and can be either connected via a Newton scheme (full coupling) or a Picard iterative scheme (tight coupling). It provides several radiation transport methods that can be used in steady-state and transient analysis with general cross-section and geometric feedback. For transient simulations, cross sections are usually pre-tabulated and then interpolated during the transient. Griffin provides a control-drum decusping method that allows an accurate modeling of control drum motion during a transient simulation [60].
