• Numerical methods for reactor thermal-hydraulics: high order, low diffusion, low dispersion, implicit, unconditionally stable numerical method

• Physical model uncertainty: quantification of input models probability density functions and output uncertainties

• Multi-physics coupling: verification and validation of multi-physics coupling for nuclear reactor safety analysis, advanced coupling methods and coupling uncertainty

Analysis of the hyperbolicity of the two-phase two-fluid model, resulting in the analytic solution to the hyperbolicity boundary of the two-fluid model.

• High order numerical solver for two-phase two-fluid model.

Our work resulted in a new 3rd order in space, up to 6th order in time, unconditionally stable method for two-phase two-fluid model. This is the first time such a high order and numerically stable method was derived and implemented for two-phase two-fluid model. For details see PhD thesis of Rabie Abu Saleem.

My research aims at simulating two-phase flows in nuclear reactors. The ultimate goal is accurate and stable numerical solver for the one-dimensional two-fluid two-phase model. This problem poses several challenges that require a thorough understanding of the mathematical model and properties of different numerical schemes. Steps towards building the solver involve:<

- Conducting a numerical analysis to study the dispersive and dissipative properties of different linear numerical schemes and design a new scheme for hyperbolic equations.
- Developing high-order, Total Variation Diminishing (TVD) numerical scheme based on the hybridization of the 1
^{st}-Order Upwind scheme and the Quadratic Upstream scheme (QUICK). Analyzing the accuracy and stability of the scheme for smooth and discontinuous solutions. - Developing a solver for the one-dimensional two-phase two-fluid model based on the proposed scheme. Implementing the solver for different benchmark problems and comparing results to those of existing thermo hydraulic codes (TRACE, RELAP5).

One current area of research includes working on coating for Accident Tolerant Fuel (IRP-ATF). our main focus in evaluation of fuel-cladding-coating-coolant behavior in operating and accident conditions. This work utilizes integrated and comprehensive multi-physics simulation capability for reactor components (fuel, cladding, coating, coolant), with thermal-hydraulics, reactor physics, fuel performance, chemistry and solid mechanics. The codes being used include: Serpent, RELAP5, MOOSE and BISON. The aim is to couple fuel structural degradation with two-phase flow and heat transfer. To accomplish this goal, A new coupling needs to be developed to enhance current BISON coupling to other MOOSE codes and other physical models, for example:

1: peeling/adhesion of coating/cladding

2: neutron transport with neutron damage, neutron activation, particularly (n,p) and (n,alpha), which will cause H/He gases in the cladding and coating

3: oxygen diffusion, fission product generation and migration, porosity migration

4: chemical reactions between cladding/coating/coolant

5: material diffusion between coating/cladding

• Coupling

We implement more advanced and innovative coupling of Monte Carlo and system thermal-hydraulics (Serpent/RELAP5). This work resulted in a new coupling convergence criteria based directly on the accuracy of the solution, without the need for ad-hoc convergence coefficients.

# Rossi Alpha

Current work being performed using physical models includes the research being performed by George McKenzie on the Rossi Alpha method. His research includes development of experiments capable of measuring the value of Alpha on systems near critical. The experiment has primarily been designed for the various critical assemblies in the NCERC facility operated by Los Alamos National Lab. The Rossi Alpha experiment modernizes an experiment designed by Bruno Rossi in the 1940s. The experiment utilizes the fact that neutrons in a fission system occur in chains and not as single entities. The experiment is designed to measure the correlation between neutron counts. Feynman’s equation statistically separates the neutron counts into accidental or correlated neutron pairs based on the time of arrival after an initiating event. The classical method for the Rossi experiment used gated circuitry to track when a neutron was incident upon a system. The downside of this method is that the circuitry was complex and only one single fission chain could be measured at once. The modern method allows many chains to be simultaneously measured by a time tagging system such as the LANL custom designed List-mode module (PATRM systems, etc.). The List-mode module allows for custom time binning to take place and the ability to modify the size of the bins post data collection. Then using software designed by George McKenzie, the useful information can be manipulated from the data.

• Inverse uncertainty of physical models in system thermal-hydraulics codes.

The work resulted in a new Bayesian method based on Maximum a Posteriori (MAP) estimation of Probability Density Function (PDF) for inverse (input parameter) uncertainty. This method quantifies the PDF of the physical models, making it possible to derive PDF for any two-phase flow model for which relevant experimental data exists. This is the first time such method has been derived and implemented for two-phase physical models, and the first time PDFs have been calculated for TRACE physical models. For details see PhD thesis of Rijan Shrestha.

Current work focuses on uncertainty quantification for Boiling Water Reactor (BWR) stability analysis and prediction. This work evaluates the coupled reactor physics-thermal hydraulics behavior modeling of the Oshkarshamn-2 NPP stability event. The primary codes used in this analysis are TRACE (thermal hydraulic modeling) and PARCS (neutronics analysis). The aim is to evaluate the uncertainty of different fluid flow models on reliable stability prediction.

** Contact **: txk (at) illinois.edu