Data-driven discovery of dimensionless numbers and governing laws: A scaling technique for nuclear test facility design

Abstract

New designs of water-cooled reactors that include thermal-hydraulics systems undergo safety analysis during the licensing process. For economic reasons and safety concerns, systems are firstly tested on reduced scale test facilities. A proper scaling ensures that dominant thermalhydraulics safety-related phenomena are captured, even though unavoidable scale distortions occur. Some existing scaling methods, based on prior knowledge of the physical phenomena at stake, can quantify such distortions. They are however limited when the phenomena are non-linear and coupled, or even not formalized as an equation. Dimensionless numbers play a central role in scaling techniques as their scale invariant properties help preserve similarities between reactor and test facilities. Building on this principle, this paper proposes a data driven alternative to traditional scaling techniques. From a dataset of physical variables describing the phenomenon of interest, the method identifies a governing law that captures the dominant safety related phenomenon. This governing law is expressed in terms of dimensionless numbers, which are physically meaningful combinations of dimensional variables and are automatically inferred by the algorithm. Based on a clear mathematical formulation, the proposed data driven method combines advanced regression analysis with the constrained optimization of a cross validation based objective function. Two variants are presented: one assuming that the output of the nondimensional governing law is known, and an extension in which this output is estimated. Both variants identify the dominant input dimensionless number as well as the explicit form of the governing law. As a proof of concept, the method is tested on a simulated dataset representative of single-phase natural circulation in a passive heat removal system.