Search

The Liutex vector is new quantity introduced to represent the rigid-body rotation part of fluid motion and thus to define and identify vortices in various flows. In this work, the intermittency and power-law similarity of the Liutex vector in homogeneous, isotropic turbulence and a turbulent channel are explored. First, we found that the Liutex vector is more intermittent than the vorticity vector in the considered turbulent flows, which indicates that an iso-surface of a Liutex magnitude with an appropriate threshold could capture the major rotating motions or vortical motions of the flow. Second, the three-dimensional energy spectrums of velocity, vorticity (enstrophy spectrum) and the Liutex vector in homogeneous isotropic turbulence are shown to exhibit power laws of −5/3, 1/3 and 1/3 in the inertial subrange, respectively, whilst the Liutex energy spectrum particularly satisfies an additional −10/3 power law in the viscous subrange. This viscous similarity of the Liutex vector is the only power law that survived from the wall presence and is argued to originate from the fact that the Liutex vector represents the rigid part of fluid motion and is free from any shear contamination. The existence of such a viscous similarity law indicates a certain coherence of the small scales of turbulence and could possibly help understand and model turbulence. [ABSTRACT FROM AUTHOR]

To investigate the mechanism of vortex motion, a pitched synthetic jet is arranged on the bottom of a cross flow and simulated by incompressible Naiver–Stokes equations with large eddy simulation. The Liutex vector identification method is utilized to quantitatively study the rotation strength and the core size of the vortex structures according to various driving frequencies (St = 0.25, 0.5, 0.75, 1.0) and amplitudes (A0 = 1.0, 1.5, 2.0, 2.5) of the synthetic jet during 21 periods. The results show that both the frequency and the amplitude play a significant role in the vortex generation mechanism of the synthetic jet. However, the amplitude makes a positive contribution to the rotation strength and the vortex core size, while the frequency makes a negative contribution. The vortex motion mechanism of a synthetic jet in a cross flow can be summarized as follows: low frequency and small amplitude favor the primary clockwise vortex, while high frequency and large amplitude motivate the anticlockwise vortex generation. [ABSTRACT FROM AUTHOR]

The newly developed vortex-identification method, Liutex, has provided a new systematic description of the local fluid rotation, which includes scalar, vector, and tensor forms. However, the advantages of Liutex over the other widely used vortex-identification methods such as Q, ∆, λ2, and λci have not been realized. These traditional methods count on shearing and stretching as a part of vortex strength. But, in the real flow, shearing and stretching do not contribute to fluid rotation. In this paper, the decomposition of the velocity gradient tensor is conducted in the Principal Coordinate for uniqueness. Then the contamination effects of stretching and shearing of the traditional methods are investigated and compared with the Liutex method in terms of mathematical analysis and numerical calculations. The results show that the Liutex method is the only method that is not affected by either stretching or shear, as it represents only the local fluid rigid rotation. These results provide supporting evidence that Liutex is the superior method over others. [ABSTRACT FROM AUTHOR]

Vortices are a ubiquitous natural phenomenon, and their structure, shape, and characteristics should be independent of the observer, which implies that the vortex identification method or vortex definition should maintain its objectivity. Currently, most of the vortex identification methods rely on velocity gradient tensors. The calculation of the velocity gradient tensor is based on the reference frame of the observer, and the velocity gradient tensor will vary with the observer's motion. By these vortex identification methods, very different vortex structures could be visualized and described in a moving reference frame. Recently, a mathematical definition of the Rortex vortex vector was proposed to represent the local fluid rotation. The definition used velocity gradient tensor to derive the local rigid rotation axis and strength. However, the original definition of the Rortex vector is nonobjective. In order to obtain the objectivity, in this paper, by a definition of a net velocity gradient tensor, an objective Rortex vortex vector is defined which uses a spatially averaged vorticity to offset the impact of the motion frame. Some typical numerical examples, such as an implicit large-eddy simulation result for shock and boundary layer interaction and a direct numerical simulation for boundary layer transition, are provided to show the objectivity of the developed method. [ABSTRACT FROM AUTHOR]

Recently, a vector named Rortex was proposed to represent the local fluid rotation [C. Liu et al., "Rortex—A new vortex vector definition and vorticity tensor and vector decompositions," Phys. Fluids 30, 035103 (2018)]. In this paper, a universal Rortex based velocity gradient tensor decomposition is proposed and the relevant local velocity increment decomposition is provided. Vortex structures in boundary layer transition on a flat plate are analyzed to quantify the local rotational, compression-stretching, and shearing effects. The results demonstrate that vorticity is shearing-dominant, while the rotational part or Rortex in general occupies a small part of vorticity in most areas of this case. In other words, vorticity is a quality representing shearing rather than rotation or vortex in most regions of this case. [ABSTRACT FROM AUTHOR]

A focus is presented on the investigation of vorticity generation and development and the vorticity structures inside/outside of a vortex. A vortex cannot be directly represented only by the vorticity, but is a region where the vorticity overtakes deformation. Except for those vorticity lines which come from and end at side boundaries, another type, self-closed vorticity lines named vorticity rings, is numerously generated inside the domain during flow transition. Vorticity and vortex are two different but closely related concepts, and both new vorticity and new vortices are generated during flow transition. According to our direct numerical simulation result, the generation and growth of the vorticity rings are produced by the buildup of the vortex; on the other hand, the vortex buildup is a consequence of the lengthening (stretching, tilting, and twisting) of the vorticity lines. According to the vorticity flux conservation law, a vorticity line cannot be interrupted, started, or ended inside the flow field; the newly generated vorticity has only one form which is a vorticity ring. In addition, for a single hairpin vortex or a ring-like vortex, it may consist of several types of vorticity lines: some could come from the side boundaries and some could be full of vorticity rings or part of vorticity rings. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we studied the influence of different inflow conditions on the MVG controlled supersonic ramp flow. In front of the MVG, the inflow of three turbulent inflow profiles with different boundary layer thickness is generated. It is found that the generation of ring-like vortical structure is not dominated by the inflow conditions. However, the inflow conditions give significant influences to the ring-like vortex shapes, vorticity origins, momentum deficit zones, streamwise velocity profiles after MVG and vortex organizations. Further, it is seen that the interaction between ring-like vortices and shock waves at the ramp corner is also affected. [Copyright &y& Elsevier]

A high-order direct numerical simulation (DNS) of flow transition over a flat plate at a free stream Mach number 0.5 has been carried out. During the simulation, we cannot find, according to the classical theory of boundary layer transition, the 'hairpin vortex breakdown to smaller structures' in the last stage of flow transition on a flat plate. However, we did discover the so-called spikes as a result of a multibridge or multiring formation. This indicated a large and stable vortex structure which can travel for a long distance. We believe that this is a result of ring heads that are located in an inviscid region. These heads of the 'turbulence spot' never seem to break down and persist as a stable structure. In addition, we discovered that the U-shaped vortex is a part of an existing coherent structure instead of a newly generated one. The U-shaped vortex also provides an additional channel to transfer vorticity to the ring from the wall. During travel, the leading primary ring in the front of the spot is sloped and skewed, causing disappearance of the second sweep. As a consequence, no energy is brought down to the lower boundary layer near the vortex ring head of the spot. Thus, the small length scale structures become damped and the existing U-shaped vortex structure becomes distinguishable. So, the question is where do the turbulent small length scale vortices come from? We will address this with a new theory which states that all of small length scales (turbulence) are generated by high-shear (HS) layers rather than being produced by 'vortex breakdown.' The new DNS shows that the HS layers are produced by strong positive spikes surrounded by low-speed fluids and by the interaction between the secondary and higher-level vortices and the wall surface especially near the ring neck. This multiple ring-like vortex generation also follows the first Helmholtz vortex conservation law. Furthermore, the Λ-shaped vortex is formed and rolling up, and the Λ-vortex is stretched and narrowed, and a new bridge is generated after the neck. The bridge will further become a second ring and so on. Besides the original vortex legs, there are also U-shaped vortex tubes. Finally, the multiple ring vortex structure is formed. From this process, no evidence is found to support that two consequent multiring circles are mixed to generate small vortices. The connection of downdraft/updraft motions is also studied. [ABSTRACT FROM AUTHOR]

Abstract: It has been widely accepted that small length vortices, a key mechanism for late flow transition and turbulence generation, are generated by “large vortex breakdown”. However, according to our recent DNS results, the hairpin vortex structure remains very stable and never breaks down. We also recognize strong multiple level negative and positive spikes and consequent multiple level high shear (HS) layers near the bottom of the boundary layer. From our DNS results, we found a second sweep of the first level rings gathering energy from the inviscid region downdraft and generating positive spikes and consequent HS layers. With the instability of the HS layer, new vortex rings and consequent new sweeps are generated. Then, the second level negative and positive spikes and high shear layers are formed near the laminar sub-layer. According to our observation, all small length scales (turbulence) are found around high shear layers generated by multilevel positive spikes and the wall surface, especially near the bottom of the boundary layer, but no small length vortices are found generated by “large vortex breakdown”. This paper provides detailed description and analysis for the energy transfer paths and small length scale (turbulence) generation and sustenance observed by our DNS. [Copyright &y& Elsevier]

Through our extensive theoretical and numerical study, we present two theorems on vortex tubes and one corollary on ‘vortex breakdown’. First, we addressed that vortex cannot have ends inside the flow field and the only vortex tube that exists inside the flow field is the ring-like vortex with or without legs on the wall. In addition, we found that the widely spread statement vortex breakdown is theoretically impossible and can never happen inside the flow field. Flow transition in a boundary layer is not caused by vortex breakdown, but rather high shear layers near the wall. [ABSTRACT FROM AUTHOR]

Large-eddy simulation with filtered-structure-function subgrid model and implicit large-eddy simulation (ILES without explicit subgrid model) using high-order accuracy and high resolution compact scheme have been performed on the tip vortex shedding from a rectangular half-wing with a NACA 0012 airfoil section and a rounded wing tip. The formation of the tip vortex and its initial development in the boundary layer and the near field wake are investigated and analysed in detail. The physics, why the tip vortex, which is originally turbulent in the boundary layer, is re-laminarised and becomes stable and laminar rapidly after shedding in the near field, is revealed by this simulation. The computation also shows the widely used second-order subgrid model is not consistent to six-order compact scheme and would degenerate the six-order LES results to second-order. Therefore, high-order schemes, grid refinement and six-order subgrid models are critical to LES approaches. [ABSTRACT FROM AUTHOR]

ABSTRACT: Large eddy simulation with high-order accuracy and high resolution has been performed on the tip vortex shed from a rectangular half-wing with a NACA 0012 airfoil section and a rounded wing tip. The formation of the tip vortex and its initial development in the near field are studied and analyzed in details. [Copyright &y& Elsevier]

A vortex is intuitively recognized as the rotational/swirling motion of the fluids. However, an unambiguous and universally accepted definition for vortex is yet to be achieved in the field of fluid mechanics, which is probably one of the major obstacles causing considerable confusions and misunderstandings in turbulence research. In our previous work, a new vector quantity that is called vortex vector was proposed to accurately describe the local fluid rotation and clearly display vortical structures. In this paper, the definition of the vortex vector, named Rortex here, is revisited from the mathematical perspective. The existence of the possible rotational axis is proved through real Schur decomposition. Based on real Schur decomposition, a fast algorithm for calculating Rortex is also presented. In addition, new vorticity tensor and vector decompositions are introduced: the vorticity tensor is decomposed to a rigidly rotational part and a non-rotationally anti-symmetric part, and the vorticity vector is decomposed to a rigidly rotational vector which is called the Rortex vector and a non-rotational vector which is called the shear vector. Several cases, including the 2D Couette flow, 2D rigid rotational flow, and 3D boundary layer transition on a flat plate, are studied to demonstrate the justification of the definition of Rortex. It can be observed that Rortex identifies both the precise swirling strength and the rotational axis, and thus it can reasonably represent the local fluid rotation and provide a new powerful tool for vortex dynamics and turbulence research. [ABSTRACT FROM AUTHOR]

In this paper, two functions are introduced to describe the turbulence generation in late flow transition. One is called the volume omega bar (volume Ω ¯ ), which represents the flow rotation or vortex strength. The other is called the volume vorticity, which shows the flow statistical fluctuations. Although they have very different definitions, one is for fluctuation and the other is for rotation, volume Ω ¯ and volume vorticity are found highly correlated with a correlation factor greater than 0.9, which means that there is a very close correlation between flow fluctuation and flow rotation (vortex). While the vorticity flux keeps constant in the late flow transition through the integration over any sections either parallel or perpendicular to the flow direction, the volume Ω ¯ is greatly increased along the flow direction during the flow transition process. This means that the vortex structures are greatly built up and rotation becomes more and more dominant. On the other hand, the total volume vorticity is also quickly increased, which shows that the fluctuation is stronger. The flow transition is a process with significant volume vorticity increase, which is attributed to two of the following crucial factors: the first one is the lengthening of the vorticity tubes from side boundary due to the vorticity line stretching, distortion, and tangling; the second one is the generation of countless self-closed vorticity rings within the domain. Both the increase of the volume vorticity and the volume Ω ¯ can be a significant symbol of the flow transition from the laminar flow to turbulent flow. It also shows that vorticity (tubes or lines) cannot directly represent vortex and should not be simply used as a signal of the turbulent transition process. [ABSTRACT FROM AUTHOR]

In this paper, a new visualization method for vortex structure is presented. Several widely used techniques for local vortex visualization in turbulent flows are reviewed and compared. Among these techniques, lambda2 and Q method are the most prominent and they are considered to be the best methods in visualizing vortical structures. However, as we illustrate, there are some defects in those iso-surface based methods. They may cause fake vortex breakdown since they can only capture the strong rotation centers and may not reveal the true vortex structure, i.e., the λ 2 iso-surface may only represent rotation cores but not necessarily vortex tubes. To better illustrate the real vortical structures and distinguish the vortex, which has a rotation core but vorticity lines can penetrate, from the vortex tubes, which vorticity lines cannot penetrate, we present a new visualization method via a hybrid of lambda2 and vortex filaments. As shown in our examples, the new method enables us to find the accurate vortex structure and well capture the physics. [ABSTRACT FROM AUTHOR]