Assessment of Turbulence Length Scales in Hybrid RANS-LES Methods

Abstract

Separated flows are common in many scenarios of practical interest. Key examples of these scenarios include static stall over fixed wing aircraft and dynamic stall over rotorcraft blades. During rotor operation at high advance ratio, the stall events lead to loss in performance of the rotorcraft and may cause severe aerodynamic loads. In order to mitigate vibratory loads, it is important to evaluate the involved flow physics as accurately as possible. It is well known that a complex rotor flow field involving separation and reverse flow cannot be numerically predicted reliably by classical RANS model. At the other end, using high-fidelity approaches such as DNS and LES to resolve the rotor flow-field at practical Reynolds number is beyond the current computational capabilities. Therefore, the main objective of this work is to develop a high-fidelity modeling framework for capturing flow features that are important for predicting stall events while remaining computationally affordable. The framework employs and refines DES type hybrid RANS-LES methods along with specialized numerical techniques from literature to accurately resolve incipient separated flows under static and dynamic conditions. A baseline computational framework comprising of well established laminar-turbulent transition model, adverse pressure gradient (APG) correction and a low Mach number correction is selected as a starting point.

By conducting simulations of flow over SC1095 airfoil at near-stall regime using the baseline framework, the importance of regulating eddy viscosity in the outer part of the shear layer is realized. Sub-grid length scales from the literature are implemented into the in-house computational solvers and their sensitivity in generating the eddy viscosity is investigated. A novel length scale called SSM length scale is proposed based on the properties of available length scales and the grid requirements in mildly separated flows. Proposed length scale demonstrated good predictive capabilities in mildly separated flows under static conditions by reducing eddy viscosity levels at the outer region boundary layer. Three-dimensional dynamic stall simulations are also conducted on flow over the modified VR12 airfoil. With SSM length scale, DDES method predictions agreed well with experimental data and captured the cycle-to-cycle variation of integrated aerodynamic quantities.

The undesirable weakening of conventional shielding is observed due to proposed length scale in a highly resolved computational domain. A novel and stronger shielding formulation are proposed based on the properties of available length scales. The combination of new shielding and SSM length scale demonstrated good predictive capabilities in near stall regime without any undesirable effects. The combination also eliminated the need for adverse pressure gradient correction.

The final computational framework proved to be robust towards grid resolution and varying flow separation and provided highly accurate aerodynamic characteristics for rotorcraft airfoils exhibiting stall events in the complete angle of attack range.