A Galerkin-based reduced-order modeling strategy for unsteady plumes

Buoyant plumes exist in a variety of different contexts, including volcanic eruptions, thermal columns, smokestacks, and high temperature burners. At the base of the plume, large-scale vortices form as the flow rapidly accelerates upwards. These structures have an important effect on the entrainment and mixing properties of the flow, but they are not easily captured using standard models. In this talk, we will discuss reduced-order modeling strategies using a combination of Galerkin projection, proper orthogonal decomposition, and sparse regression to build a reduced-order model (ROM) that accurately capture these large vortical structures in a computationally efficient manner. The ROM construction will be based on direct numerical simulations (DNS) of axisymmetric helium plumes where adaptive mesh refinement was used to supply additional resolution to the local flow structures. We will first compare the ROM and the DNS using a variety of different statistics, including Reynolds and Favre averages, oscillation frequency, streamwise fluxes, and kinetic energy production mechanisms. Using the Navier-Stokes equations, we will then examine the most active terms that contribute to the coefficients in set of ordinary differential equations comprising the ROM.