  Many practical combustion systems such as those in rockets, gas turbines, and
internal combustion engines operate under high pressures that surpass the
thermodynamic critical limit of fuel-oxidizer mixtures. These conditions
require the consideration of complex fluid behaviors that pose challenges for
numerical simulations, casting doubts on the validity of existing subgrid-scale
(SGS) models in large-eddy simulations of these systems. While data-driven
methods have shown high accuracy as closure models in simulations of turbulent
flames, these models are often criticized for lack of physical
interpretability, wherein they provide answers but no insight into their
underlying rationale. The objective of this study is to assess SGS stress
models from conventional physics-driven approaches and an interpretable machine
learning algorithm, i.e., the random forest regressor, in a turbulent
transcritical non-premixed flame. To this end, direct numerical simulations
(DNS) of transcritical liquid-oxygen/gaseous-methane (LOX/GCH4) inert and
reacting flows are performed. Using this data, a priori analysis is performed
on the Favre-filtered DNS data to examine the accuracy of physics-based and
random forest SGS-models under these conditions. SGS stresses calculated with
the gradient model show good agreement with the exact terms extracted from
filtered DNS. The accuracy of the random-forest regressor decreased when
physics-based constraints are applied to the feature set. Results demonstrate
that random forests can perform as effectively as algebraic models when
modeling subgrid stresses, only when trained on a sufficiently representative
database. The employment of random forest feature importance score is shown to
provide insight into discovering subgrid-scale stresses through sparse
regression.
