Please cite this article in press as: M.S. Campobasso et al., Low-speed preconditioning for strongly coupled integration of Reynolds-averaged Navier-Stokes equations and two-equation turbulence models, Aerosp. Sci. Technol. (2018), https://doi. AbstractComputational fluid dynamics codes using the density-based compressible flow formulation of the Navier-Stokes equations have proven to be very successful for the analysis of high-speed flows. However, solution accuracy degradation and, for explicit solvers, reduction of the residual convergence rates occur as the local Mach number decreases below the threshold of 0.1. This performance impairment worsens remarkably in the presence of flow reversals at wall boundaries and unbounded high-vorticity flow regions. These issues can be resolved using low-speed preconditioning, but there exists an outstanding problem regarding the use of this technology in the strongly coupled integration of the Reynoldsaveraged Navier-Stokes equations and two-equation turbulence models, such as the k − ω shear stress transport model. It is not possible to precondition only the RANS equations without altering parts of the governing equations, and * Corresponding author Email addresses: m.s.campobasso@lancaster.ac.uk (M.S. Campobasso), m.yan@lancaster.ac.uk (M. Yan), aldo.bonfiglioli@unibas.it (A. Bonfiglioli), there did not exist an approach for preconditioning both the RANS and the SST equations. This study solves this problem by introducing a turbulent lowspeed preconditioner of the RANS and SST equations that does not require any alteration of the governing equations. The approach has recently been shown to significantly improve convergence rates in the case of a one-equation turbulence model. The study focuses on the explicit multigrid integration of the governing equations, but most algorithms are applicable also to implicit integration methods. The paper provides all algorithms required for implementing the presented turbulent preconditioner in other computational fluid dynamics codes. The new method is applicable to all low-and mixed-speed aeronautical and propulsion flow problems, and is demonstrated by analyzing the flow field of a Darrieus wind turbine rotor section at two operating conditions, one of which is characterized by significant blade/vortex interaction. Verification and further validation of the new method is also based on the comparison of the results obtained with the developed density-based code and those obtained with a commercial pressure-based code.

The high-fidelity aeromechanical analysis and design of multi-megawatt horizontal axis wind turbines can be performed by means of Reynolds-averaged Navier-Stokes codes. The compressible or incompressible formulation of the fluid equations can be used. One of the objectives of the paper is to quantify the effects of flow compressibility on the aerodynamics of large turbine rotors with particular attention to the tip region of a 82 m rotor blade featuring a relative Mach number of about 0.3 near rated conditions. Noticeable local static pressure variations due to compressibility are observed. Such variations point to the better suitability of compressible solvers for turbine aerodynamics, not only when the solver is used for direct aeroacoustic simulation of the near field noise propagation, but also when it is used to provide the surface static pressure to be used as input for acoustic analogy noise propagation codes. On the numerical side, a novel numerical approach to low-speed preconditioning of the mean flow and turbulence model equations for the fully coupled integration of the flow equations coupled to a two-equation turbulence model is presented and implemented in a compressible Navier-Stokes research code for the steady and yawed wind-induced time-dependent flows analyzed herein.