Improved quadratic constitutive relation via turbulence anisotropy analysis and symbolic regression

Secondary flows widely appear in aerospace engineering, appearing in phenomena such as wing-body junction flows and corner flows in square ducts. These flows are driven by turbulence anisotropy and are characterized by motion perpendicular to the primary flow direction. Accurately capturing the anisotropy of Reynolds stresses is crucial for secondary flows, but existing turbulence models based on the linear constitutive relation perform poorly in this regard. This study investigates the quadratic constitutive relation (QCR) model, which provides a robust framework for Reynolds stress modeling. By integrating the QCR2024 model with anisotropy invariant maps, we propose a modeling approach for the model coefficients to better represent the Reynolds stress anisotropy in secondary flows. Through analytical derivation and feature selection, we obtain Reynolds stress expressions applicable to quasi-two-dimensional flows and use symbolic regression to construct the model. The new model is tested on developed turbulence in square duct and flow in rectangular diffuser, demonstrating higher predictive accuracy compared to existing QCR models (QCR2000 and QCR2024). This approach enables more accurate secondary flow prediction and holds significant promise for improving turbulence simulations in complex aerospace engineering applications.