Numerical investigations of the vortex feature-based vorticity confinement models for the assessment in three-dimensional vortex-dominated flows

Abstract

In order to improve the vortex resolution in aerodynamic wakes, a locally normalized vortex feature-based vorticity confinement method is implemented into the multi-block, structured computational fluid dynamics solver (ROSITA). In this method, the second vorticity confinement (VC2) scheme with two well-known vortex feature detection methods (non-dimensional Q criterion, non-dimensional $$\lambda _2$$ λ 2 criterion) is employed to counterbalance the truncation error introduced by the numerical discretization of the convective term. The flow field of two benchmark three-dimensional steady vortex-dominated cases, the NACA0015 wing and the Caradonna–Tung hovering rotor, is simulated with the implemented method. The improvements in aerodynamics prediction, vorticity preservation, computational stability, and efficiency are demonstrated. From the numerical results, the vortex feature-based confinement models significantly improve the computational stability, the aerodynamic loads prediction and vorticity preservation capability, especially for the $$\lambda _2$$ λ 2 –based VC2 model. In addition, it allows the use of higher confinement parameters on a coarse grid with a relatively higher computational efficiency to obtain better results than those of a finer grid.

Assessment of the Vortex Feature-Based Vorticity Confinement Method Applied to Rotor Aerodynamics and Aeroacoustics

“…In this work, the VC2 scheme, which has better numerical properties in conservation and regularity at the vortex center, is used to preserve vorticity in helicopter rotor flows. The implementation of the VC2 scheme relies on the experience of our past studies [8,11], that is, considering the vorticity confinement term as a body force source term f b on the momentum equation alone. This approach is preferred since the treatment that removes the vorticity confinement term from the energy conservation equation could obtain far better results [18].…”

“…The FVC2-Q and FVC2-L2 schemes have been used in 3D flows that are dominated by vortices. Recent studies have shown that the FVC2-L2 scheme performs better than the FVC2-Q scheme in terms of computational stability, aerodynamic prediction, and vorticity preservation [11]. Based on this finding, the threshold function of the non-dimensional λ 2 criterion can be expressed as follows:…”

“…However, an inherent issue of these simulations is that the vortex features are prematurely deformed and dissipated due to the dissipative nature of numerical schemes, this makes the employment of such techniques in helicopter rotor flows unsatisfactory. In recent years, four major classes of numerical methods, including scale-resolving simulation (SRS) [1][2][3], high-order spatial discretization schemes [4][5][6][7], vorticity confinement (VC) method [8][9][10][11], and grid refinement techniques [12][13][14] have emerged to help improve the capability of preserving vortices in CFD simulations. Nevertheless, some of them are often prohibitive for industrial applications due to the substantial computational time and resources.…”

“…To eliminate this issue, some studies [10,34,35] combined the standard VC method with the advanced vortex feature detection techniques, resulting in the vortex feature-based VC (FVC1 or FVC2) approach. In our previous work [11], the benefits of such treatment for 3D vortex-dominated flows in terms of computational stability, aerodynamic prediction, vorticity preservation, and computational efficiency, were explicitly demonstrated by comparing the standard VC2 scheme with two FVC2 formulations combining different vortex feature detection techniques (Q and λ 2 ). Moreover, the λ 2 -based VC2 (FVC2-L2) scheme expressed a higher resolution of the vortical structure, more robust computational procedure, more accurate aerodynamic loads, and almost the same computational time cost if compared to the Q-based VC2 (FVC2-Q) scheme.…”

“…In addition, it is worth mentioning that the application of the λ 2based VC2 formulation to the study of helicopter rotor aerodynamics and aeroacoustics constitutes a further original contribution of this paper. Firstly, the HART-II baseline configuration was simulated to resolve the BVI phenomenon by using ROSITA, a multiblock, structured grid CFD solver that implements the FVC2-L2 scheme [11], and an in-house developed multi-dimensional delta trim procedure. Afterward, together with the permeable surface Ffowcs Williams-Hawkings (PS-FWH) equation, the influence of the FVC2-L2 scheme in rotor noise predictions was assessed via two benchmark test examples.…”