A new vortex identification criterion called W-method is proposed based on the ideas that vorticity overtakes deformation in vortex.The comparison with other vortex identification methods like Q-criterion and l2-method is conducted and the advantages of the new method can be summarized as follows: (1) the method is able to capture vortex well and very easy to perform; (2) the physical meaning of W is clear while the interpretations of iso-surface values of Q and l2 chosen to visualize vortices are obscure; (3) being different from Q and l2 iso-surface visualization which requires wildly various thresholds to capture the vortex structure properly, W is pretty universal and does not need much adjustment in different cases and the iso-surfaces of W=0.52 can always capture the vortices properly in all the cases at different time steps, which we investigated; (4) both strong and weak vortices can be captured well simultaneously while improper Q and l2 threshold may lead to strong vortex capture while weak vortices are lost or weak vortices are captured but strong vortices are smeared; (5) W=0.52 is a quantity to approximately define the vortex boundary. Note that, to calculate W, the length and velocity must be used in the non-dimensional form. From our direct numerical simulation, it is found that the vorticity direction is very different from the vortex rotation direction in general 3-D vortical flow, the Helmholtz velocity decomposition is reviewed and vorticity is proposed to be further decomposed to vortical vorticity and non-vortical vorticity. vorticity, vortex, vortex identification, turbulencePACS number(s): 47.55.nb, 47.20.Ky, 47.11.Fg
Vortex and vorticity are two correlated but fundamentally different concepts which have been the central issues in fluid mechanics research. Vorticity has rigorous mathematical definition (curl of velocity), but no clear physical meaning. Vortex has clear physical meaning (rotation) but no rigorous mathematical definition. For a long time, many people treat them as a same thing. However, based on our high-order direct numerical simulation (DNS), we found that first, “vortex” is not “vorticity tube” or “vortex tube” which is widely defined as a bundle of vorticity lines without any vorticity line leak. Actually, vortex is an open area for vorticity line penetration. Second, vortex is not necessarily congregation of vorticity lines, but dispersion in many 3-dimensional cases. Some textbooks say that vortex cannot end inside the flow field but must end on the solid wall (and/or boundaries). Our DNS observation and many other numerical results show almost all vortices are ended inside the flow field. Finally, a more theoretical study shows that neither vortex nor vorticity line can attach to the solid wall and they must be detached from the wall.
Vorticity, vorticity line and vorticity tube have rigorous definitions, but vortex has not been mathematically defined yet. It is realized that vortex is not vorticity tube and must be given a more rigorous definition, at least by some accurate identification methods. The current paper comperes two popular vortex identification methods, Q-criterion and Lambda 2 with the new Omega vortex identification method by visualization of several examples studied by direct numerical simulation and large eddy simulation for flows with different speeds. The comparisons show the Omega method is more close to give a mathematical definition of vortex and better visualization for vortex structures. Additional advantages include clear physical meaning and no need to adjust threshold, which make Omega the most effective and efficient tool in vortex identification.
Shock-boundary layer interaction (SBLI) is a kind of problem which is frequently met in supersonic engine inlet flow and external flow. A detail study on mechanism of reduction of shock induced flow separation by MVG is carried out by high order implicit large eddy simulation (LES). To generate the fully developed turbulent flow, a series of turbulent profiles are given by previous DNS simulation results. The mechanism of reduction of shock induced flow separation was originally considered as a result of plump velocity profile caused by turbulent kinetic energy. It was acclaimed that turbulent flow has so stronger kinetic energy that the velocity profile is changed to be plump, which lead to reduction of shock induced flow separation. However, according to our detail study in this paper, the shock wave breaks down when ring-like vortices generated by MVG are passing through it, while the vortex structure never breaks down and is even little influenced. Therefore, the flow separation induced by shock is reduced by break-down of shock wave, not plump velocity profile. More details of the investigation on the mechanism are reported in this paper.
A floating shock platform (FSP) is important experimental equipment for the antishock assessment of large-scale shipborne equipment. Generally speaking, the FSP is a square barge structure with a flat bottom. In order to satisfy the key index of the horizontal-to-vertical ratio of the impact environment, a special added structure is mounted to the bottom of the platform, and the impact environment is more complicated due to the added structure. Therefore, the spherical shock factor theory is proposed to analyze the impact environment, and the validity of the theory is proved by numerical experiments. The results show that the average impact spectrum response of the platform is essentially consistent under the same shock factor. Meanwhile, the spherical shock factor builds a linear relationship between the input parameters and structural response, which is convenient for the prediction of impact response.
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