Chaoqun Liu

Conventional isosurface-based vortex visualization depends strongly on user-specified vortex-strength thresholds, which may hide weak vortices. Liutex core lines provide a line-based representation of vortex structure that is not dependent on a single global vortex-strength threshold and can display local vortex-strength variation along the vortex skeleton. However, an automatic extraction of Liutex core lines remains challenging in complex three-dimensional flows because real core lines usually pass through sub-grid locations, and redundant seed points may cause repeated or incorrect line generation. In this work, an automatic Liutex core line identification method is developed by combining a Liutex-based predictor–corrector procedure, two criteria for identifying Liutex core points, and a grouping algorithm for assembling these points into continuous core lines. The method is applied to both a micro-vortex-generator wake flow and a flat-plate boundary-layer transition flow. The results show that the method correctly captures the vortex structures in these two cases. Compared with conventional isosurface visualization, Liutex core lines can reveal weak structures that may be lost at a prescribed threshold while maintaining a clear representation of strong vortices. The method also reveals dual-core structures within hairpin vortex ring isosurfaces, providing new insight that the formation of hairpin vortices may be related to Kelvin–Helmholtz instability.

A relative Liutex vortex identification method is proposed in this study, together with its explicit mathematical formulation. The method is designed to identify vortical structures based solely on local flow-field information and is inherently Galilean invariant, ensuring robustness under different reference frames. To validate the proposed approach, a three-dimensional flat-plate boundary-layer transition case is investigated, in which the relative Liutex is systematically compared with conventional vortex identification methods, including the Q-criterion and the original Liutex method. The results show that the relative Liutex is capable of simultaneously capturing both strong and weak vortical structures. Importantly, its behavior cannot be interpreted as a simple superposition of Liutex iso-surfaces obtained using different threshold values. Instead, the relative Liutex provides a more selective and physically coherent identification of weak vortices, particularly in regions above the $Λ$-vortex and in the downstream hairpin-vortex structures, while effectively suppressing spurious and noise-induced features. These advantages arise from its formulation based on local velocity-gradient strength rather than a global vortical-intensity measure. Owing to its ability to consistently identify vortices across a wide range of intensities, the relative Liutex demonstrates strong potential for revealing complex vortex structures and underlying flow mechanisms in vortex-dominated flows.

Objectivity is a fundamental requirement for vortex identification, ensuring that vortex structures observed remain invariant under changes in the reference frame. However, although most conventional vortex identification methods, including Liutex, are Galilean invariant, they are not objective. Since the accelerated motion of the observer does not affect the velocity gradient tensor at an instant of time, the rotational motion is only considered for the non-inertial frame. This paper proposes a method to recover the angular velocity of a rotating observer directly from flow field data measured in the rotating frame. The approach exploits the observation that, in an inertial frame, zero-vorticity points tend to dominate the region with an almost identical nonzero vorticity in the observer’s non-inertial coordinate system. By identifying the most frequently occurring vorticity within the domain, the observer’s angular velocity can be uniquely determined, enabling reconstruction of the objective velocity gradient tensor and, consequently, the objective Liutex. The key issue is to find a reference point (RP). The RP should have zero vorticity in the inertial coordinate system, and then the RP has the same angular speed as the observer. The RP can be found by comparing the vorticity of all points in the computational domain and the RP will correspond to the vorticity vector with the highest percentage in the non-inertial coordinate system. The proposed method is validated using DNS data of the boundary layer transition over a flat plate with an artificially imposed angular velocity. The recovered angular velocity agrees closely with the true value within an acceptable margin of error. Furthermore, the objective Liutex reconstructed from the rotating frame data is visually indistinguishable from the original inertial frame Liutex. These results demonstrate that the method provides a simple and accurate way to restore objectivity for Liutex and other vortex identification techniques. The objective Liutex will be equal to the original Liutex in an inertial coordinate system when the observer does not have rotational motion.

Accurate subgrid-scale (SGS) modeling remains a major challenge in large eddy simulation (LES), particularly for wall-bounded turbulent flows with strong near-wall anisotropy. This study proposes a novel SGS model based on Liutex theory, featuring a dynamically adaptive model coefficient and a physics-based length-scale formulation. The magnitude of the Liutex vector is employed as the characteristic velocity scale, enabling a direct and objective quantification of local vortical intensity. The length scale is determined from local flow properties and reflects the physical nature of turbulent diffusion, which occurs predominantly in directions perpendicular to the rotation axis. The dynamic model coefficient adapts locally to variations in vortical structures and naturally vanishes at the wall. Importantly, this coefficient is free of empirical tuning, as it is derived rigorously from the triple decomposition. The model is validated through LES of turbulent channel flow at the friction Reynolds number of 544. Results show improved predictions of both normal and shear Reynolds stresses, particularly in near-wall regions, compared with other SGS models. The proposed model demonstrates competitive computational efficiency, with only a 4.21% overhead.

This paper proposes a novel convention-based subgrid scale (SGS) model for large eddy simulation (LES) by using the Liutex concept. Conventional SGS models typically rely on the eddy viscosity assumption, which uses the linear eddy viscosity terms to approximate the nonlinear effects of unresolved turbulent eddies, that should be measured by unresolved Liutex. However, the eddy viscosity assumption is empirical but lacks a scientific foundation, which limits its predictive accuracy. The proposed model in this paper directly models the convective terms and demonstrates several key advantages: (1) the new model gets rid of isotropic assumption for the unresolved SGS eddies which are, in general, anisotropic, (2) the new model contains no empirical coefficients which need to be adjusted case by case, (3) the new model explicitly captures nonlinear convective effects by the SGS eddies and (4) the new model is consistent with the physics for boundary layer as the model becomes zero in the laminar sublayer, where Liutex becomes zero automatically. This new model has been applied in the flat plate boundary transition flow, and the results show that it outperforms the popular and widely adopted wall-adapting local eddy (WALE) model. This new model is a conceptual breakthrough in SGS modeling and has the potential to open a new direction for more accurate SGS models and future LES applications.

This paper presents an in-depth analysis of a novel subgrid-scale stress model proposed in 2022, which utilizes the rotational part of the velocity gradient as the velocity scale for computing eddy viscosity. This study investigates the near-wall asymptotic behavior and separation prediction capability of this model for the first time. Two canonical flows--fully-developed turbulent channel flow and periodic hill flow--are selected for analysis. The eddy viscosity predicted by this model correlates well with the visualized vortices and exhibits an asymptotic behavior of O(y) near the walls. The dimensionless eddy viscosity, like that of the Wall-Adapting Local Eddy Viscosity (WALE) subgrid model, remains within a small numerical range of 10^-2 to 10^-4. The power spectral density results reveal the asymptotic behavior of the velocity scale in the dissipation range, following a -10/3 scaling law. Additionally, this model predicts velocity profiles more accurately than the Smagorinsky model, even when using Van Driest damping. For the periodic hill case, this model predicts the reattachment point with only a 6.9% error, compared to 14.0% for the Smagorinsky model and 16.4% for the Smagorinsky model with Van Driest damping. In near-wall regions with separation, this model achieves even greater accuracy in Reynolds stress prediction than the WALE model, demonstrating its superior potential for separated flow simulations.