Data-Driven Discovery of Dimensionless Numbers and Governing Laws: A Scaling Technique for Nuclear Test Facility Design

New designs of water-cooled reactors that include thermal-hydraulic systems undergo safety analysis during the licensing process. For economic reasons and safety concerns, the systems are first tested at reduced-scale test facilities. A proper scaling ensures that dominant thermal-hydraulic 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 limited, however, when the phenomena are nonlinear and coupled, or even not formalized as an equation. Dimensionless numbers play a central role in the scaling techniques, as their scale invariant properties help preserve the similarities between the 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 was tested on a simulated dataset representative of single-phase natural circulation in a passive heat removal system.