scholarly journals Three-dimensional wake transition behind an elliptic cylinder near a moving wall

2021 ◽  
Vol 33 (4) ◽  
pp. 043606
Author(s):  
Jianxun Zhu ◽  
Fengjian Jiang ◽  
Lars Erik Holmedal
Keyword(s):  
Three Dimensional ◽  
Elliptic Cylinder ◽  
Moving Wall ◽  
Wake Transition

scholarly journals Three-dimensional wake transition for a circular cylinder near a moving wall

2017 ◽  
Vol 818 ◽  
pp. 260-287 ◽  
Author(s):  
Hongyi Jiang ◽  
Liang Cheng ◽  
Scott Draper ◽  
Hongwei An
Keyword(s):  
Circular Cylinder ◽  
Parameter Space ◽  
Large Scale ◽  
Three Dimensional ◽  
Scale Structure ◽  
Moving Wall ◽  
Local Reduction ◽  
Gap Ratio ◽  
Wake Transition ◽  
Mode A

Three-dimensional (3D) wake transition for a circular cylinder placed near to a moving wall is investigated using direct numerical simulation (DNS). The study covers a parameter space spanning a gap ratio $(G/D)\geqslant 0.3$ and Reynolds number ($Re$) up to 325. The wake transition regimes in the parameter space are mapped out. It is found that vortex dislocation associated with Mode A is completely suppressed at $G/D$ smaller than approximately 1.0. The suppression of vortex dislocation is believed to be due to the confinement of the Mode A streamwise vortices by the plane wall, which suppresses the excess growth and local dislocation of any Mode A vortex loop. Detailed wake transition is examined at $G/D=0.4$, where the wake transition sequence is ‘two-dimensional (2D) $\rightarrow$ ordered Mode A $\rightarrow$ mode swapping (without dislocations) $\rightarrow$ Mode B’. Relatively strong three-dimensionality is found at $Re=160{-}220$ as the wake is dominated by large-scale structure of ordered Mode A, and also at $Re\geqslant 285$, where Mode B becomes increasingly disordered. A local reduction in three-dimensionality is observed at $Re=225{-}275$, where the wake is dominated by finer-scale structure of a mixture of ordered Modes A and B. Corresponding variations in the vortex shedding frequency and hydrodynamic forces are also investigated.

Three-dimensional wake transition

1996 ◽  
Vol 328 ◽  
pp. 345-407 ◽  
Author(s):  
C. H. K. Williamson
Keyword(s):  
Shear Layer ◽  
Three Dimensional ◽  
Streamwise Vortex ◽  
Physical Structure ◽  
Small Scale ◽  
Half Cycle ◽  
Vortex Loops ◽  
Wake Transition ◽  
Mode A ◽  
Flow States

It is now well-known that the wake transition regime for a circular cylinder involves two modes of small-scale three-dimensional instability (modes A and B), depending on the regime of Reynolds number (Re), although almost no understanding of the physical origins of these instabilities, or indeed their effects on near-wake formation, have hitherto been made clear. We address these questions in this paper. In particular, it is found that the two different modes A and B scale on different physical features of the flow. Mode A has a larger spanwise wavelength of around 3–4 diameters, and scales on the larger physical structure in the flow, namely the primary vortex core. The wavelength for mode A is shown to be the result of an ‘elliptic instability’ in the nearwake vortex cores. The subsequent nonlinear growth of vortex loops is due to a feedback from one vortex to the next, involving spanwise-periodic deformation of core vorticity, which is then subject to streamwise stretching in the braid regios. This mode gives an out-of-phase streamwise vortex pattern.In contrast, mode-B instability has a distinctly smaller wavelength (1 diameter) which scales on the smaller physical structure in the flow, the braid shear layer. It is a manifestation of an instability in a region of hyperbolic flow. It is quite distinct from other shear flows, in that it depends on the reverse flow of the bluff-body wake; the presence of a fully formed streamwise vortex system, brought upstream from a previous half-cycle, in proximity to the newly evolving braid shear layer, leads to an in-phase stream-wise vortex array, in strong analogy with the ‘Mode 1’ of Meiburg & Lasheras (1988) for a forced unseparated wake. In mode B, we also observe amalgamation of streamwise vortices from a previous braid with like-sign vortices in the subsequent braid.It is deduced that the large scatter in previous measurements concerning mode A is due to the presence of vortex dislocations. Dislocations are triggered at the sites of some vortex loops of mode A, and represent a natural breakdown of the periodicity of mode A instability. By minimizing or avoiding the dislocations which occur from end contamination or which occur during wake transition, we find an excellent agreement of both critical Re and spanwise wavelength of mode A with the recent secondary stability analysis of Barkley & Henderson (1996).Wake transition is further characterized by velocity and pressure measurements. It is consistent that, when mode-A instability and large-scale dislocations appear, one finds a reduction of base suction, a reduction of (two-dimensional) Reynolds stress level, a growth in size of the formation region, and a corresponding drop in Strouhal frequency. Finally, the present work leads us to a new clarification of the possible flow states through transition. Right through this regime of Re, there exist two distinct and continuous Strouhal frequency curves: the upper one corresponds with purley small- scale instabilities (e.g. denoted as mode A), while the lower curve corresponds with a combination of small-scale plus dislocation structures (e.g. mode A*). However, some of the flow states are transient or ‘unstable’, and the natural transitioning wake appears to follow the scenario: (2D→A*→B).

scholarly journals A Moving Frame Trajectory Tracking Method of a Flying-Wing UAV Using the Differential Geometry

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Yi Zhu ◽  
Xin Chen ◽  
Chuntao Li
Keyword(s):  
Flight Control ◽  
Trajectory Tracking ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Elliptic Cylinder ◽  
Dynamic Equations ◽  
Moving Frame ◽  
Moving Frames ◽  
Tracking Method ◽  
Tracking Process

The problem of UAV trajectory tracking is a difficult issue for scholars and engineers, especially when the target curve is a complex curve in the three-dimensional space. In this paper, the coordinate frames during the tracking process are transformed to improve the tracking result. Firstly, the basic concepts of the moving frame are given. Secondly the transfer principles of various moving frames are formulated and the Bishop frame is selected as a final choice for its flexibility. Thirdly, the detailed dynamic equations of the moving frame tracking method are formulated. In simulation, a moving frame of an elliptic cylinder helix is formulated precisely. Then, the devised tracking method on the basis of the dynamic equations is tested in a complete flight control system with 6 DOF nonlinear equations of the UAV. The simulation result shows a satisfactory trajectory tracking performance so that the effectiveness and efficiency of the devised tracking method is proved.

scholarly journals Three-dimensional wake transition in the flow over four square cylinders at low Reynolds numbers

AIP Advances ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 015142
Author(s):  
Yuhang Zhang ◽  
Rui Wang ◽  
Yaoran Chen ◽  
Yan Bao ◽  
Zhaolong Han ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Square Cylinders ◽  
Low Reynolds ◽  
Four Square ◽  
Wake Transition

Boundary-layer-induced potential flow on an elliptic cylinder

1974 ◽  
Vol 66 (1) ◽  
pp. 145-157 ◽  
Author(s):  
Stanley G. Rubin ◽  
Frank J. Mummolo
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Elliptic Cylinder ◽  
Analytic Form ◽  
Slender Body ◽  
Dimensional Solution ◽  
Slender Body Theory ◽  
Simple Analytic Form ◽  
Body Theory

The application of slender-body theory to the evaluation of the three-dimensional surface velocities induced by a boundary layer on an elliptic cylinder is considered. The method is applicable when the Reynolds number is sufficiently large so that the thin-boundary-layer approximation is valid. The resulting potential problem is reduced to a two-dimensional consideration of the flow over an expanding cylinder with porous boundary conditions. The limiting solutions for a flat plate of finite span and a nearly circular cross-section are obtained in a simple analytic form. In the former case, within the limitations of slender-body theory, the results are in exact agreement with the complete three-dimensional solution for this geometry.

Three-dimensional wake transition behind an inclined flat plate

2012 ◽  
Vol 24 (9) ◽  
pp. 094107 ◽  
Author(s):  
Dan Yang ◽  
Vagesh D. Narasimhamurthy ◽  
Bjørnar Pettersen ◽  
Helge I. Andersson
Keyword(s):  
Flat Plate ◽  
Three Dimensional ◽  
Wake Transition

scholarly journals Stability analysis of the elliptic cylinder wake

2014 ◽  
Vol 763 ◽  
pp. 302-321 ◽  
Author(s):  
Justin S. Leontini ◽  
David Lo Jacono ◽  
Mark C. Thompson
Keyword(s):  
Stability Analysis ◽  
Aspect Ratio ◽  
Three Dimensional ◽  
Elliptic Cylinder ◽  
Cylinder Wake ◽  
Long Wavelength ◽  
Aspect Ratios ◽  
Numerical Stability Analysis ◽  
Spatiotemporal Symmetries ◽  
Three Dimensional Simulations

AbstractThis paper presents the results of numerical stability analysis of the wake of an elliptical cylinder. Aspect ratios where the ellipse is longer in the streamwise direction than in the transverse direction are considered. The focus is on the dependence on the aspect ratio of the ellipse of the various bifurcations to three-dimensional flow from the two-dimensional Kármán vortex street. It is shown that the three modes present in the wake of a circular cylinder (modes A, B and QP) are present in the ellipse wake, and that in general they are all stabilized by increasing the aspect ratio of the ellipse. Two new pertinent modes are found: one long-wavelength mode with similarities to mode A, and a second that is only unstable for aspect ratios greater than approximately 1.75, which has similar spatiotemporal symmetries to mode B but has a distinct spatial structure. Results from fully three-dimensional simulations are also presented confirming the existence and growth of these two new modes in the saturated wakes.

Pohlhausen's Method for Three-Dimensional Laminar Boundary Layers

1951 ◽  
Vol 3 (1) ◽  
pp. 51-60 ◽  
Author(s):  
J. C. Cooke
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Elliptic Cylinder ◽  
Three Dimensions ◽  
Momentum Thickness ◽  
Laminar Boundary Layers ◽  
Displacement Thickness ◽  
Good For ◽  
Layer Flow ◽  
Accelerated Flow

SummaryWild has extended to three dimensions the von Kármán-Pohlhausen method for the laminar boundary layer flow over a fixed obstacle and used the method for an infinite yawed elliptic cylinder in a stream. In this paper the method is tested in two ways (which may be called full-Pohlhausen and semi-Pohlhausen) for the case of an infinite yawed cylinder when the velocity outside the boundary layer over the surface normal to the generators is of the form U=cxm. The exact solution is known in this case.A table of the skin friction, displacement thickness and momentum thickness is given for various values of β [=2m/(m + 1)], and the agreement is found to be fairly good for β>0 (accelerated flow) but not so good for β<0 (retarded flow).)

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