Formation Of Hairpin Vortices Research Articles

Coherent structures in bypass transition induced by a cylinder wake

Flat-plate boundary layer transition induced by the wake vortex of a two-dimensional circular cylinder is experimentally investigated. Combined visualization and velocity measurements show a different transition route from the Klebanoff mode in free-stream turbulence-induced transition. This transition scenario is mainly characterized as: (i) generation of secondary transverse vortical structures near the flat plate surface in response to the von Kármán vortex street of the cylinder; (ii) formation of hairpin vortices due to the secondary instability of secondary vortical structures; (iii) growth of hairpins which is accelerated by wake-vortex induction; (iv) formation of hairpin packets and the associated streaky structures. Detailed investigation shows that during transition the evolution dynamics and self-sustaining mechanisms of hairpins, hairpin packets and streaks are consistent with those in a turbulent boundary layer. The wake vortex mainly plays the role of generating and destabilizing secondary transverse vortices. After that, the internal mechanisms become dominant and lead to the setting up of a self-sustained turbulent boundary layer.

Evolution of a localized vortex in plane nonparallel viscous flows with constant velocity shear. I. Hyperbolic flow

The framework of the linear theory is employed to study the evolution of an initial compact vortical disturbance in unbounded plane nonparallel viscous incompressible flows with constant velocity gradients. Two types of such flows are known to be possible: hyperbolical and elliptical (as well as an intermediate case of the well-studied parallel Couette flow). The results presented here are obtained for a hyperbolical flow. (Results concerning the elliptical flow are to be issued in a separate publication.) This paper is a development of earlier work by R. R. Lagnado, N. Phan-Thien, and L. G. Leal [Phys. Fluids 27, 1094 (1984)] studying the stability of a hyperbolical flow relative to the simplest perturbations in the form of plane waves with a time-dependent wave vector. The dynamics of vortex intensity is investigated as well as the evolution of its geometrical form and orientation. The results are discussed in the context of the problem of hairpin vortex formation.

Characteristics of laminar flow past a sphere in uniform shear

Numerical simulations are performed to investigate the characteristics of laminar flow past a sphere in uniform shear. The Reynolds numbers considered are Re=300, 425, and 480 based on the inlet center velocity uc and sphere diameter d. The nondimensional shear rate K of inlet uniform shear is varied from 0 to 0.15, where K=∣∇u∣d∕uc (∣∇u∣) and ∣∇u∣ is the shear rate at inlet. For all Reynolds numbers investigated, the head of the hairpin vortex loop is always located on the high-velocity side in uniform shear. The flow maintains planar symmetry at Re=300. At Re=425 and 480, the temporal variation in the azimuthal angle of the hairpin vortex formation appearing in the uniform inlet flow is greatly reduced in uniform shear, but the flows still keep asymmetry for most inlet shear rates. However, in the cases of K=0.075 and 0.1, at Re=425, the flows become planar symmetric and their characteristics of formation and evolution of the hairpin vortex loops are different from those of asymmetric flows. In most cases, except the instances showing planar symmetry at Re=425, the Strouhal number and time-averaged drag and lift coefficients increase with increasing inlet shear rate. On the other hand, for K=0.075 and 0.1, showing planar symmetry at Re=425, three different vortices are shed in the wake, resulting in three distinct peak frequencies. Finally, a hysteresis phenomenon switching from planar symmetry to asymmetry (or vice versa) depending on the initial condition is observed at Re=425 and 450, implying that small variations in the flow or initial conditions change the flow field at these Reynolds numbers.

Nonlinear sinusoidal and varicose instability in a boundary layer

It is well known [1] that the laminar‐turbulent transition at a low turbulence level of the free flow is associated with the development of instability waves, the so-called Tollmien‐Schlichting waves. When a twodimensional Tollmien‐Schlichting wave reaches a certain amplitude at the nonlinear stage of its development, it undergoes three-dimensional distortion and, as a result, characteristic three-dimensional Λ structures arise [1]. Owing to certain features of the appearance and development of these structures, they are not only typical for the classical laminar‐turbulent transition, but are also inevitable attributes of a transition to more complex flows, e.g., flows modulated with longitudinal streaky structures, such as Hertler vortices, transverseflow vortices on sliding wings, etc., as well as flows in the viscous sublayer of a turbulent boundary layer. In these cases, they arise in particular due to the secondary high-frequency instability of such flows and may be manifested not only as Λ structures, but also in the form of horseshoe vortices ( Ω structures), hairpin vortices, etc. A characteristic feature of the development of such structures, e.g., on a sliding wing, is the disappearance of one of the counter-rotating vortices due to the transverse flow, whereas the development of a classical Λ structure can be observed on a straight wing [1]. The high-frequency secondary instability of transition and turbulent near-wall flows in the presence of streaky structures is often attributed to so-called sinusoidal and varicose instability. Both instability modes were investigated under controlled conditions at the linear and initial stages of nonlinear development. When the transverse size of the streaky structure was larger than the thickness of the shear layer, growth of varicose instability was observed. At the same time, when the transverse size of the streaky structure was comparable to or smaller than the thickness of the shear layer, it became more instable with respect to antisymmetric (sinusoidal) modes than to symmetric (varicose) modes. The experiment reported in [2] clearly shows that the growth of the symmetric mode leads to the formation of hairpin vortices, which are a pair of counterrotating longitudinal vortices that are connected by a head, i.e., a Λ vortex, while an antisymmetric mode is developed to a train of quasi-longitudinal vortices with alternating-sign vorticity. Unfortunately, the experiments reported in [2] concerned only the initial stage of the nonlinear development of disturbances, and spatial resolution was insufficiently high to reveal the structure of the flow in more detail. In this paper, we report on our experimental investigations of the nonlinear stage of the varicose and sinusoidal instability of the streaky structure in the Blasius boundary layer. In contrast to the experiment reported in [2], the study is more detailed (thermal anemometer measurements of the longitudinal velocity component and velocity pulsations in space ( xyz ) at 5 × 10 4 points) in order to reveal the features of the dynamics of the appearance, development, and internal structure of coherent formations up to the later stages of their nonlinear development. The experiments were carried out under controlled conditions in a low-turbulent wind tunnel. A plane plate 14 mm in thickness, 1000 mm in width, and 2000 mm in length was placed in parallel in the operation part of the tunnel. The streaky structure was generated by means of a cylindrical roughness element, which had a height of 1.1 mm and a diameter of 5.8 mm and was placed in the center of the plate at a distance of x 0 = 438 mm from the fore. The velocity of the flow was equal to U ∞ = 7.8 m/s, and the turbulence level was no higher than 0.04%. In the absence of the roughness element, the laminar boundary layer was developed without any waves and the velocity profile was close to the Blasius profile. A roughness-element height of h = 1.1 mm is close to the thickness of the displacement of

Numerical simulation of nonlinear structures in channel flow transition

Introduction T HE objective of this computational study is to investigate the development of nonlinear vortical structures in plane channel flow transition by the visualization of threedimensional vortex lines. It has long been recognized that transition may be viewed as a sequence of events that is triggered by two-dimensional Tollmien-Schlichting waves that become three-dimensional, leading to nonlinear wave interactions. In a recent experiment, Williams used hot film probes in a water channel boundary layer to create a data base containing three-dimensional instantaneous velocity and vorticity components documenting the evolution of the high shear layer and the formation of hairpin vortices. He then used this data base to obtain three-dimensional vortex lines. In this work, a similar technique is used to visualize the flowfield structures. In order to extract information from the computational data base, which provides the three-dimensional instantaneous velocity/vorticity field in over a quarter million grid points, vortex lines were calculated at time intervals that can be viewed sequentially. In addition, vorticity contours and velocity vector plots for the secondary flow are presented for a comparison with the findings inferred from the vortex line plots. Although flow visualization by vortex lines have been utilized in other numerical studies,' the present results effectively capture the continuous evolution of the flow, enabling the identification of various vortical structures.