Abstract
The present work investigates the bifurcation properties of the Navier–Stokes equations using characteristics-based schemes and Riemann solvers to test their suitability to predict non-linear flow phenomena encountered in aerospace applications. We make use of a single- and multi-directional characteristics-based scheme and Rusanov’s Riemann solver to treat the convective term through a Godunov-type method. We use the Artificial Compressibility (AC) method and a unified Fractional-Step, Artificial Compressibility with Pressure-Projection (FSAC-PP) method for all considered schemes in a channel with a sudden expansion which provides highly non-linear flow features at low Reynolds numbers that produces a non-symmetrical flow field. Using the AC method, our results show that the multi-directional characteristics-based scheme is capable of predicting these phenomena while the single-directional counterpart does not predict the correct flow field. Both schemes and also Riemann solver approaches produce accurate results when the FSAC-PP method is used, showing that the incompressible method plays a dominant role in determining the behaviour of the flow. This also means that it is not just the numerical interpolation scheme which is responsible for the overall accuracy. Furthermore, we show that the FSAC-PP method provides faster convergence and higher level of accuracy, making it a prime candidate for aerospace applications.
Highlights
Despite the advances made in the field of computational fluid dynamics over the past decades, predicting flow patterns around aerodynamic shapes remains a challenge for aerospace applications.The flow around a wing can have a transonic behaviour which, at high angles of attack, may be supplemented by flow separation, strong crossflow gradients as well as a hysteresis in the lift slope [1,2].Traub [3] highlighted further that at low Reynolds number flows, laminar separation bubbles exist which have an inherently unsteady behaviour
The FSAC-PP method shows a lower level of grid convergence index (GCI) which is of the order of 10% while the Artificial Compressibility (AC) method produces GCI values which are close to double of that result
We investigated the performance of a non-characteristic-based (CB) scheme, single- and multi-directional characteristics-based scheme (SCB/MCB), as well as the Rusanov Riemann solver (RS) and combinations of these schemes and tested all approaches with the Artificial Compressibility (AC) and Fractional-Step, Artificial Compressibility with Pressure-Projection (FSAC-PP) method
Summary
The flow around a wing can have a transonic behaviour which, at high angles of attack, may be supplemented by flow separation, strong crossflow gradients as well as a hysteresis in the lift slope [1,2]. Traub [3] highlighted further that at low Reynolds number flows, laminar separation bubbles exist which have an inherently unsteady behaviour. These separation bubbles may reattach to the wing or transition into a fully turbulent flow, depending on the pressure gradient. It is important to capture the transition between laminar and turbulent flows as flow separation and reattachment have a strong influence on predicting the lift slope, stall angle and hysteresis. Since RANS models are commonly based on the linear Boussinesq assumption, results may provide only a moderate accuracy while models based on non-linear theories may be more efficient in predicting non-isotropic flow behaviour
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