1,721,040 research outputs found
WKBJ analysis in the periodic wake of a cylinder
No full textAbstractThe nature of the three-dimensional transition arising in the flow past a cylinder is investigated by applying the Lifschitz–Hameiri theory along special Lagrangian trajectories existing in its wake. Results show that the von Kármán street is unstable with regard to short-wavelength perturbations. The asymptotic analysis predicts the possible existence of both synchronous (as modes A and B) and asynchronous (as mode C) instabilities, each associated to specific Lagrangian orbits. The proposed study provides useful qualitative information on the origin of the different modes but no quantitative agreement between the growth rates predicted by the asymptotic analysis and by a global stability analysis is observed. The reasons for such mismatch are briefly discussed and possible improvements to the present analysis are suggested
Linear Stability and Receptivity analysis of the vortex shedding in flows past confined square cylinders
No full textAnalysis of the inversion of the von Karman street in the wake of a confined square cylinder
No full textThis study considers the incompressible 2D laminar flow around a square cylinder symmetrically positioned in a channel. In this type of flow, even if vortices of opposite sign are alternately shed from the body into the wake as in the unconfined case, an inversion of their position with respect to the flow symmetry line takes place further downstream. Thanks to a dedicated numerical investigation, an interpretation of the inversion is given in terms of interference between the wake and the vorticity of the incoming flow, which is shown to play a dominant role in the phenomenon
Structural sensitivity of the first instability of the cylinder wake
No full textThe stability properties of the flow past an infinitely long circular cylinder are studied in the context of linear theory. An immersed-boundary technique is used to represent the cylinder surface on a Cartesian mesh. The characteristics of both direct and adjoint perturbation modes are studied and the regions of the flow more sensitive to momentum forcing and mass injection are identified. The analysis shows that the maximum of the perturbation envelope amplitude is reached far downstream of the separation bubble, where as the highest receptivity is attained in the near wake of the cylinder, close to the body surface. The large difference between the spatial structure of the two-dimensional direct and adjoint modes suggests that the instability mechanism cannot be identified from the study of either eigenfunctions separately. For this reason a structural stability analysis of the problem is used to analyse the process which gives rise to the self-sustained mode. In particular, the region of maximum coupling among the velocity components is localized by inspecting the spatial distribution of the product between the direct and adjoint modes. Results show that the instability mechanism is located in two lobes placed symmetrically across the separation bubble, confirming the qualitative results obtained through a locally plane- wave analysis. The relevance of this novel technique to the development of effective control strategies for vortex shedding behind bluff bodies is illustrated by comparing the theoretical predictions based on the structural perturbation analysis with the experimental data of Strykowski & Sreenivasan (J. Fluid Mech. vol. 218, 1990, p. 71)
Leading Edge Receptivity by Adjoint Methods
No full textThe properties of adjoint operators and the method of composite expansion are used to study the generation of Tollmien–Schlichting (TS) waves in the leading-edge region of an incompressible, flat-plate boundary layer. Following the classical asymptotic approach, the flow field is divided into an initial receptivity region, where the unsteady motion is governed by the linearized unsteady boundary-layer equation (LUBLE), and a downstream linear amplification area, where the evolution of the unstable mode is described by the classical Orr–Sommerfeld equation (OSE). The large x behaviour of the LUBLE is analysed using a multiple-scale expansion which leads to a set of composite differential equations uniformly valid in the wall-normal direction. These are solved numerically as an eigenvalue problem to determine the local properties
of the Lam and Rott eigensolutions. The receptivity coefficient for an impinging acoustic wave is extracted by projecting the numerical solution of the LUBLE onto
the adjoint of the Lam and Rott eigenfunction which, further downstream, turns into an unstable TS wave. In the linear amplification region, the main characteristics of
the instability are recovered by using a multiple-scale expansion of the Navier–Stokes equations and solving numerically the derived eigenvalue problems. A new matching procedure, based on the properties of the adjoint Orr–Sommerfeld operator, is then used to check the existence and the extent of an overlapping domain between the two asymptotic regions. Results for different frequencies are discussed
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