Data-Driven Dimensional Analysis

Abstract

The study of thermal radiation interacting with particle-laden turbulence is of great importance in a wide range of scientific and engineering applications. The fundamental and applied study of such systems is challenging as a result of the large number of thermo-fluid mechanisms governing the underlying physics. This complexity is significantly reduced by transforming the problem of interest into its scale-free form by means of dimensional analysis techniques. However, the theoretical framework of classical dimensional analysis presents the limitations of not providing a unique set of dimensionless groups, and no support for measuring the relative importance between them. In the interest of addressing these shortfalls for multiphysics turbulent flow applications, we present a semi-empirical dimensional analysis approach to efficiently extract important dimensionless groups from data obtained by means of computational (or laboratory) experiments. The methodology presented is then used to characterize important dimensionless groups in irradiated particle-laden turbulence. The study concludes that two dimensionless groups are responsible for most of the variation in the system’s thermal response, with the absorption of radiation by particles, the radiative energy deposition rate and the turbulent flow mixing the most important thermo-fluid mechanisms. The generality of the results obtained can be leveraged to effectively reduce the dimensionality of irradiated particle-laden turbulent flows in research studies and in the design and optimization of similar systems.