Inverse Estimation of the Centerline Boundary Conditions in Confined Planar Mixing Layers
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Similarity solutions of planar mixing layers have long been fundamental in the study of free shear layers, offering reduced computational costs compared to full computational fluid dynamics (CFD) simulations. These solutions provide valuable insights into shear flow dynamics while minimizing computational overhead. However, a major challenge arises in applying similarity theory to planar mixing layers: determining the location of the separating streamline, which remains unknown in low-order boundary layer models. Typically, this issue is addressed through approximations, with the most common assumption being that the separating streamline lies at the geometrical centerline. While this assumption simplifies analysis, it contradicts experimental observations and high-fidelity simulations, which show the streamline displaced toward the lower-speed stream. This displacement impacts the predicted entrainment, leading to mismatches with real-world behavior. To address this, an inverse problem framework based on parameter estimation is used to determine the streamline’s correct position. A generic formulation for the streamline location consistent with similarity principles is introduced, and nonlinear parameters are identified using the Gauss-Newton Method (GNM), minimizing entrainment prediction errors compared to direct numerical simulations (DNS) and experiments. We also offer a parametrization of the centerline position obtained via genetic algorithms. Additionally, the study incorporates DNS simulations mimicking wind tunnel effects, refining the model by considering the influence of tunnel height on velocity profiles. This aims to better represent real-world confined flows by accounting for the tunnel’s effect on the vertical velocity distribution, improving the accuracy of the similarity solutions.
