Advanced Framework for Assessment and Reduction for Model Form Uncertainty of the Closure Laws in Thermal Hydraulics Codes
Abstract: Accurate modeling of the two-phase flow phenomena is important for the safety analysis of light water reactors. The modeling approach must balance model resolution with computational feasibility. The direct implementation of local instant formulation is not practical for most engineering applications. Two-phase two-fluid model is a time average formulation, where each phase is governed by separate set of conservation equations. The interactions between phases are modeled with interfacial terms present in the governing equations. The two-phase two-fluid model is a basis of many nuclear thermal-hydraulics codes used in design, licensing, and safety analysis of nuclear reactors. However, the averaging process introduces new turbulent and interfacial terms that require sub-grid models to close the system of equations. These closure laws describe the steady-state and dynamic characteristics of multi-phase media in terms of averaged field equations. The resolution required to model such terms is no longer a part of the system of equations, hence these closure laws must be derived by separate analysis. In classical approach, semi-empirical correlations are derived based on direct observations from experimental investigation. However, with recent advances in data-driven techniques a lot of attention was placed on using indirect experimental observations to improve the predictive capabilities of the closure laws.
This work introduces a new methodology investigating modeling deficiencies using data-driven and statistical methods. Physics-discovered data-driven model form (P3DM) methodology uses a combination of reduced dimensionality modeling, data analysis and machine learning that aims at combining data-driven approaches with physics-based modeling. Model optimization is coupled to the solution of governing equations allowing model determination based on indirect observations of system response. The flexibility of the model form allows investigation of a large set of alternative models that are used to assess model form uncertainty. The methodology considers all limitations associated with the available data constrains encountered in nuclear industry. The methodology uses best features of calibration and machine learning type approaches, while avoiding their limitations.
Closure laws are associated with significant model form uncertainty. This uncertainty represents the lack of knowledge about modeled phenomena and is difficult to quantify. Bayesian model averaging is often used to assess model form uncertainty using competing, well-established models. However, alternative models suffer from similar assumptions, giving biased estimate of model form uncertainty. The P3DM methodology provides many alternative model forms. This set of possible models does not suffer from similar assumptions, giving unbiased estimate of model form uncertainty.
