Geometrical properties of the vorticity vector derived using large-eddy simulation

Abstract

In this paper, the geometrical properties of the resolved vorticity vector ¯ derived from large-eddy simulation are investigated using a statistical method. Numerical tests have been performed based on a turbulent Couette channel flow using three different dynamic linear and nonlinear subgrid-scale stress models. The geometrical properties of ¯ have a significant impact on various physical quantities and processes of the flow. To demonstrate, we examined helicity and helical structure, the attitude of ¯ with respect to the eigenframes of the resolved strain rate tensor Sij and negative subgrid-scale stress tensor − ij , enstrophy generation, and local vortex stretching and compression. It is observed that the presence of the wall has a strong anisotropic influence on the alignment patterns between ¯ and the eigenvectors of Sij , and between ¯ and the resolved vortex stretching vector. Some interesting wall-limiting geometrical alignment patterns and probability density distributions in the form of Dirac delta functions associated with these alignment patterns are reported. To quantify the subgrid-scale modelling effects, the attitude of ¯ with respect to the eigenframe of − ij is studied, and the geometrical alignment between ¯ and the Euler axis is also investigated. The Euler axis and angle for describing the relative rotation between the eigenframes of − ij and Sij are natural invariants of the rotation matrix, and are found to be effective for characterizing a subgrid-scale stress model and for quantifying the associated subgrid-scale modelling effects on the geometrical properties of ¯ .

Geometrical Properties of the Resolved-Scale Velocity and Temperature Fields Predicted using Large-Eddy Simulation

“…Prototypical geometrical patterns have been reproduced and compared with the reported DNS, experimental and a priori LES results. The present research together with some recently reported LES studies [13,14,16,21,28,58] confirms that LES is an effective tool for investigating the geometrical property of a turbulent field at the resolved-scales.…”

“…Since then, this subject has been extensively studied based on a variety of analytical, experimental and numerical methodologies. A detailed review of the subject can found in the recent work of Wang et al [21]. To date, research on the alignment betweenω and e Sβ has been restricted primarily to isotropic isothermal flows [3,4,13,14,54].…”

“…In this regard, investigations of wall-bounded flows and non-isothermal flows are still very limited. Reports of the wall anisotropic effect on the preferred alignment betweenω and e Sβ are only found in the previously mentioned DNS studies by Blackburn et al [10], experimental investigations by Honkan and Andreopoulos [5], and LES studies by Higgins et al [16] and Wang et al [20,21]. In the remainder of this subsection, we provide a numerical and analytical analysis of the near-wall anisotropic effect on the observed alignment pattern betweenω and the eigenframe [e Sα , e Sβ , e Sγ ] of the resolved strain rate tensorS ij in the context of a non-isothermal flow.…”

“…In contrast to the above mentioned advancements in the a priori LES study of the geometrical properties of fluid tensors and vectors, the a posteriori LES approach (based on numerical simulations) has also been recently applied for this type of study, which includes the work of Fureby and Grinstein [18] who investigated the resolved-scale vorticity magnitude and vortex stretching rate using numerical simulations based on a promising monotonically integrated LES (MILES) method; and the works of Wang et al [19][20][21] who studied the geometrical property of the SGS stress tensor and resolved vorticity, and the near-wall anisotropic effect on vortex stretching patterns based on LES of turbulent Couette flows. In comparison with DNS, study of turbulence geometrical statistics using an LES approach is beneficial in that it provides a reduction in the computational cost, and more importantly, the results of the analysis can potentially lead to development of improved SGS modelling strategies.…”

“…According to DNS studies of iso-thermal wall-bounded flows [7,10,11] and recent LES studies of turbulent iso-thermal Couette flows [20,21], the presence of the wall in a flow field has a significant anisotropic impact on the geometrical properties of quantities such as enstrophy generation, the alignment pattern of the vorticity vector with respect to the eigenframe of the resolved strain rate tensor, and the ratio of the eigenvalues (or, principal values) of the resolved strain rate tensor. In contrast to previous investigations based on LES of iso-thermal flows, in the present research, we aim at addressing the influence of wall-imposed anisotropy in conjunction with buoyancy on the geometrical properties of the temperature and velocity fields of a non-isothermal vertical channel flow.…”