Differential Reynolds Stress Modeling For Separating Flows In Industrial Aerodynamics PDF Download

This work seeks to improve the prediction of turbulent boundary layer flows under adverse pressure gradients (APG) encountered in the aeronautical industry, especially towards the trailing edge of wings. Indeed, the inaccurate prediction of such flows results in inaccurate predictions of aircraft performance and of the limits of the flight domain. To reduce the design margins and enable optimal aircraft geometries, the reliability of turbulence models in APG boundary layers has to be improved.The relevance of second-moment closures of the RANS equations, also called Reynolds-stress models (RSM), aiming at reproducing more accurately the physics of the flow, is therefore assessed for industrial use. Three Reynolds-stress models that differ in their near-wall modelling and in their length-scale providing equation, namely the EB-RSM, the SSG/LRR-omega RSM and the SSG-omega ATAAC RSM, are first benchmarked on two academic test cases, a flat plate and the APG boundary layer at equilibrium of the Skåre & Krogstad experiment, against the Spalart-Allmaras model and the reference data. These academic cases highlight the fundamental differences between the models and their impact on the profiles and integral quantities of the boundary layer. In particular, the Reynolds-stress profiles and the turbulence budgets in the flat plate test case demonstrate the effectiveness of near-wall modelling. However, the Skåre & Krogstad test case shows the necessity to improve the prediction of velocity profiles in the log region and of skin friction in strong APG flows, despite an excellent prediction of the boundary layer growth.A correction for the log-law region, corresponding to a local recalibration of the model constants in APG regions, is first explored to ensure the correct velocity gradient in APG log layers. The correction is investigated with the Spalart-Allmaras model using a NACA 4412 test case. Despite satisfactory results, the correction is shown to be difficult to generalise to other models and that its impact on the flow prediction is limited to low-Reynolds-number cases, thus restricting its relevance for the aeronautical industry.The two-equation eddy-viscosity models and RSMs are shown to be incompatible with the square-root layer, which progressively grows at the outer end of the log layer in APG boundary layers. A correction locally introducing a pressure-diffusion term is therefore investigated analytically and assessed on the RSMs considered using the Skåre & Krogstad test case. A new model, the EB-RSM-dP, is here defined as a corrected version of the EB-RSM and exhibits improved predictions regarding the velocity and Reynolds-stress profiles and the boundary layer quantities.The standard and corrected RSMs are compared to the Spalart-Allmaras model on an application case, the Common Research Model, representative of a commercial aircraft, and demonstrate the relevance of such models for the aeronautical industry with improved pressure distribution on the wing and reduced errors in the drag-due-to-lift predictions. The square-root-law correction is here validated with the SSG/LRR-omega-dP of Knopp et al. (2018) and the newly developed EB-RSM-dP, and shows significant improvement of the aerodynamic load on the wing, and of both the lift and drag predictions for the highest Reynolds number configuration, compared to the uncorrected models. This study also highlights the strong impact of the activation region of the correction on the results.