Stefano Riva

The Empirical Interpolation Method (EIM), and its generalized version (GEIM), are non-intrusive, reduced-basis model order reduction methods hereby adopted and modified to address the problem of optimal placement of sensors and real-time estimation in thermo-hydraulics systems. These techniques have been used to extract the characteristic spatial modes of the system and select a set of points (or functionals) corresponding to the optimal locations for the sensors. Collecting experimental measurements in the available points allows the construction of an empirical interpolation of the fields employed to estimate the variable of interest. However, when these data are affected by noise, the (G)EIM loses its good convergence properties. In this context, stabilization techniques allow good field reconstruction even with noisy data. This work provides an alternative and effective solution to the problem of reconstructing the system state in the presence of experimental data affected by random noise by using the Tikhonov regularization technique. The developed methods have been tested on a simple thermo-fluid dynamics problem known as “two-sided lid-driven differentially heated square cavity”.

As first proposed by Madelung in 1926, the analogy between quantum mechanics and hydrodynamics has been known for a long time; however, its potentialities and the possibility of using the characteristic equations of quantum mechanics to simulate the behavior of inviscid fluids have not been thoroughly investigated in the past. In this methodology, the incompressible Euler equations are thus substituted by the Schrödinger equation, turning a quasi-linear Partial Differential Equation into a linear one, an algorithm known in the literature as Incompressible Schrödinger Flow. Previous works on the subject used the Fast Fourier Transform method to solve this problem, obtaining promising results, especially in predicting vortex dynamics; this paper aims to implement this novel approach into a Finite Element framework to find a more general formulation better suited for future application on complex geometries and on test cases closer to real-world applications. Simple case studies are presented in this work to analyze the potentialities of this method: the results obtained confirm that this method could potentially have some advantages over traditional Computational Fluid Dynamics method, especially for what concerns computational savings related to the required time discretization, whilst also introducing new aspects of the algorithm, mainly related to boundary conditions, not addressed in previous works.

Due to the multiple physics involved and their mutual and complex interactions, nuclear engineers and researchers are constantly working on developing highly accurate Multi-Physics models, focusing in particular on the core coupling of Neutronics and Thermal-Hydraulics. Nevertheless, the development of accurate and stable models remains a challenging task despite the advancements in computational hardware and software. This work investigates the possibility of combining the available mathematical model with data collected on physical systems, with a two-fold goal: improvement of the performance of the former from the computational point of view without sacrificing accuracy and performing model bias correction with the knowledge coming in real-time from the system. In particular, two Data-Driven Reduced Order Modelling techniques, the Generalised Empirical Interpolation Method and the Parametrised-Background Data-Weak formulation, are applied to literature benchmark nuclear case studies, as they were observed to be quite well suited for the chosen cases. The main goal of this work is to assess the possibility of using external data to perform model bias correction: starting from a purposefully less accurate, but computationally cheaper base model, then using high-fidelity data to update and correct the model efficiently. Indeed, the numerical results obtained in this paper are promising, confirming the feasibility of this approach to develop computationally cheap and accurate multi-physics models; furthermore, investigation of Data-Driven Reduced Order Modelling approach to nuclear industrial cases, in the context of model bias correction, is foreseen.

Reliable, real-time state estimation in nuclear reactors is of critical importance for monitoring, control and safety. It further empowers the development of digital twins that are sufficiently accurate for real-world deployment. As nuclear engineering systems are typically characterised by extreme environments, their in-core sensing is a challenging task, even more so in Generation-IV reactor concepts, which feature molten salt or liquid metals as thermal carriers. The emergence of data-driven methods allows for new techniques for accurate and robust estimation of the full state space vector characterising the reactor (mainly composed by neutron fluxes and the thermal-hydraulics fields). These techniques can combine different sources of information, including computational proxy models and local noisy measurements on the system, in order to robustly estimate the state. This work leverages the Shallow Recurrent Decoder (SHRED) architecture to estimate the entire state vector of a reactor from three, out-of-core time-series neutron flux measurements alone. Specifically, the Molten Salt Fast Reactor, in the EVOL geometry (Evaluation and Viability of Liquid Fuel Fast Reactor System project), is demonstrated as a test case, with neutron flux measurements alone allowing for reconstruction of the 20 coupled field variables of the dynamics. This approach can further quantify the uncertainty associated with the state estimation due to its considerably low training cost on compressed data. The accurate reconstruction of every characteristic field in real-time makes this approach suitable for monitoring and control purposes in the framework of a reactor digital twin.