Implementation of a high-order spatial discretization into a finite volume solver: Applications to turbomachinery test cases using an eddy-viscosity turbulence closure

In this study, the implementation of a high-order spatial discretization method into a Finite Volume solver is presented. Specific emphasis is put on the analysis of the performance over selected turbomachinery test cases. High-order numerical discretization is achieved by adopting the cell-centered Least-Square reconstruction, which is implemented in the in-house solver HybFlow. The validation of the adopted methodology is performed by assessing the solution of a turbulent flat plate with zero pressure gradient, using a eddy-viscosity transitional model. The test case also evidences the effect of the discretization of gradient-based source terms when a high-order reconstruction methodology is used. In the second part of the paper, the solver is used for the solution of relevant two-dimensional turbomachinery test cases, assessing the impact of 2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow></mml:mrow> <mml:mrow><mml:mi>n</mml:mi> <mml:mi>d</mml:mi></mml:mrow> </mml:msup> </mml:math> and 3 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow></mml:mrow> <mml:mrow><mml:mi>r</mml:mi> <mml:mi>d</mml:mi></mml:mrow> </mml:msup> </mml:math> order reconstruction on the prediction of the aerodynamics and the heat transfer for respectively a low-pressure blade and a high-pressure turbine vane. It is shown how a high-order reconstruction allows for obtaining a better prediction of turbomachinery aerodynamics, with lower number of elements. The benefits over heat transfer predictions in high Reynolds number conditions are instead limited to the reduction of heat transfer coefficient spikes in under-resolved regions of the blade. Eventually, the methodology is validated for a three-dimensional low-pressure turbine cascade with realistic boundary layer inflow conditions.