Turbulence modeling within the RANS equations' framework is essential in
engineering due to its high efficiency. Field inversion and machine learning
(FIML) techniques have improved RANS models' predictive capabilities for
separated flows. However, FIML-generated models often lack interpretability,
limiting physical understanding and manual improvements based on prior
knowledge. Additionally, these models may struggle with generalization in flow
fields distinct from the training set. This study addresses these issues by
employing symbolic regression (SR) to derive an analytical relationship between
the correction factor of the baseline turbulence model and local flow
variables, enhancing the baseline model's ability to predict separated flow
across diverse test cases. The shear-stress-transport (SST) model undergoes
field inversion on a curved backward-facing step (CBFS) case to obtain the
corrective factor field beta, and SR is used to derive a symbolic map between
local flow features and beata. The SR-derived analytical function is integrated
into the original SST model, resulting in the SST-SR model. The SST-SR model's
generalization capabilities are demonstrated by its successful predictions of
separated flow on various test cases, including 2D-bump cases with varying
heights, periodic hill case where separation is dominated by geometric
features, and the three-dimensional Ahmed-body case. In these tests, the model
accurately predicts flow fields, showing its effectiveness in cases completely
different from the training set. The Ahmed-body case, in particular, highlights
the model's ability to predict the three-dimensional massively separated flows.
When applied to a turbulent boundary layer with Re_L=1.0E7, the SST-SR model
predicts wall friction coefficient and log layer comparably to the original SST
model, maintaining the attached boundary layer prediction performance.Comment: 37 pages, 46 figure