C. del Pino

Structure of trailing vortices: Comparison between particle image velocimetry measurements and theoretical models

The velocity field of the trailing vortex behind a wing at different angles of attack has been measured through the stereo particle image velocimetry technique in a water tunnel for Reynolds numbers between 20 000 and 40 000, and for several distances to the wing tip. After filtering out the vortex meandering, the radial profiles of the axial and the azimuthal velocity components and of the radial profiles of the vorticity were compared to the theoretical models for trailing vortices by [G. K. Batchelor, J. Fluid Mech. 20, 645 (1964)] and by [D. W. Moore and P. G. Saffman, Proc. R. Soc. London, Ser. A 333, 491 (1973)], whose main features are conveniently summarized. We take into account the downstream evolution of these profiles from just a fraction of the wing chord to more than ten chords. The radial profiles of the vorticity and the azimuthal velocity are shown to fit quite well to Moore and Saffman’s trailing vortex model, while Batchelor’s model does not fit so well, especially in the tails of the p...

The onset of absolute instability of rotating Hagen–Poiseuille flow: A spatial stability analysis

A spatial, viscous stability analysis of Poiseuille pipe flow with superimposed solid body rotation is considered. For each value of the swirl parameter (inverse Rossby number) L>0, there exists a critical Reynolds number Rec(L) above which the flow first becomes convectively unstable to nonaxisymmetric disturbances with azimuthal wave number n=−1. This neutral stability curve confirms previous temporal stability analyses. From this spatial stability analysis, we propose here a relatively simple procedure to look for the onset of absolute instability that satisfies the so-called Briggs–Bers criterion. We find that, for perturbations with n=−1, the flow first becomes absolutely unstable above another critical Reynolds number Ret(L)>Rec(L), provided that L>0.38, with Ret→Rec as L→∞. Other values of the azimuthal wave number n are also considered. For Re>Ret(L), the disturbances grow both upstream and downstream of the source, and the spatial stability analysis becomes inappropriate. However, for Re

Dynamics of the wing-tip vortex in the near field of a NACA 0012 aerofoil

Vortex meandering (or wandering) is a typical feature of wing-tip vortices that consists in a random fluctuation of its vortex centreline. This meandering of the vortex is quite significant a few chords downstream the wing, and was originally thought to be due to free stream turbulence [1], then to instabilities of the vortex core [2]. But, independently of the controversy about its origin [3], the quantitative characterization of the vortex wandering phenomenon is a subject of current research [4]-[6]. In this work we have undertaken a systematic visualization of the trailing vortex behind a NACA0012 airfoil at several distances near the wing tip for different angles of attack and different Reynolds numbers to characterize the structure of the vortex meandering phenomenon as well as its frequency, wavelength, and amplitude. The technique is similar to that used by Roy and Leweke [5], but we characterize the downstream evolution of these vortex meandering characteristics and, therefore, the dynamics of the wing-tip vortex in the near field.

Global mode analysis of a pipe flow through a 1:2 axisymmetric sudden expansion

We report the results of the global mode analysis to characterize the onset of unsteadiness in a circular pipe flow through an axisymmetric sudden expansion of inlet-to-outlet diameter ratio of d/D=0.5. We find that the axisymmetric state becomes linearly unstable at a significantly higher critical Reynolds number than the one reported in previous experimental works. This unstable global mode corresponds to an oscillatory bifurcation with wavenumber |m|=1 located at the end of the recirculation region.

The motion of a rough particle in a Stokes flow adjacent to a boundary

Results are presented of experimental investigations into the motion of a heavy sphere in a rotating cylinder which is completely fllled with highly viscous ∞uid. For a given cylinder rotation rate, the sphere adopts a flxed position and rotates adjacent to the cylinder wall. For the case of a smooth sphere the motion is consistent with that predicted by a Stokes ∞ow model. Artiflcially roughened spheres exhibit particle-boundary contact caused by impacts of surface asperities with the boundary for low cylinder speeds. For higher cylinder speeds the behaviour of the roughened spheres crosses smoothly from the particle-boundary contact regime to motion with hydrodynamically lubricated ∞ow.

Unsteady fronts in the spin-down of a fluid-filled torus

We report the results of an experimental investigation into fluid motion induced by the deceleration to rest of a rigidly rotating fluid-filled torus. Transition to a transient turbulent state is found where the onset of the complicated motion is triggered by a small-scale wavelike instability. The wave forms on a front that propagates from the inner wall of the toroidal container after it is stopped. We reveal the origins of the front through a combination of careful experimental measurements, boundary-layer analysis, and computation of the axisymmetric Navier–Stokes equations.

Three-dimensional structure of confined swirling jets at moderately large Reynolds numbers

We have performed a series of three-dimensional (3D) numerical simulations of the incompressible flow discharging from a rotating pipe into a coaxial static cylindrical container through a sudden expansion. We have considered several values of the Reynolds number based on the pipe flow rate ReQ between 50 and 300, and an expansion diameter ratio of 8, and have analyzed the emerging 3D flow structures in the swirling jet exiting from the rotating pipe as the swirl parameter S is increased. The results are compared to axisymmetric numerical simulations of the same problem. Three-dimensional, nonlinear instabilities are found in the swirling jet when ReQ≳98 above a critical value of S, which depends on ReQ, that obviously do not appear in the axisymmetric simulations. These nonlinear instabilities are initially triggered by the linear instabilities inside the rotating pipe, which are already present in the pipe from a much lower value of S, and are transformed in the jet. As S increases further, there exists...

Confined swirling jet impingement on a flat plate at moderate Reynolds numbers

The behavior of a swirling jet issuing from a pipe and impinging on a flat smooth wall is analyzed numerically by means of axisymmetric simulations. The axial velocity profile at the pipe outlet is assumed flat while the azimuthal velocity profile is a Burger’s vortex characterized by two non-dimensional parameters; a swirl number S and a vortex core length δ. We concentrate on the effects of these two parameters on the mechanical characteristics of the flow at moderate Reynolds numbers. Our results for S=0 are in agreement with Phares et al. [J. Fluid Mech. 418, 351 (2000)], who provide a theoretical determination of the wall shear stress under nonswirling impinging jets at high Reynolds numbers. In addition, we show that the swirl number has an important effect on the jet impact process. For a fixed nozzle-to-plate separation, we found that depending on the value of δ and the Reynolds number Re, there is a critical swirl number, S=S∗(δ,Re), above which recirculating vortex breakdown bubbles are observed...

Stability of the boundary layer flow on a long thin rotating cylinder

The development and stability of the boundary layer flow over a long thin cylinder aligned with the main flow and which rotates around its axis is considered. Numerical results show that the introduction of rotation has an important effect on the behavior of the basic flow. When the swirl increases, the shear stress at the wall also increases due to the changes in the pressure distribution along the cylinder surface. A nonparallel linear stability analysis of the basic flow is performed using parabolized stability equations. Even at moderately low rotation, we find the existence of unstable centrifugal modes, in addition to the shear ones found in previous stability analysis of the boundary layer flow on a cylinder with no rotation. These centrifugal instabilities develop at Reynolds numbers, based on the cylinder radius and external axial velocity, much smaller than those required for the growing of the shear instabilities. Our analysis shows that nonparallel effects play a key role in the onset and deve...

Experimental study of rotating Hagen-Poiseuille flow discharging into a 1:8 sudden expansion

In this paper, we present experimental evidence for the five different states that result from rotating Hagen-Poiseuille flow when it discharges into a 1:8 sudden expansion, namely: stable, convectively unstable, unstable shear layer, stable and unstable vortex breakdowns. Sanmiguel-Rojas et al. [“Three-dimensional structure of confined swirling jets at moderately large Reynolds numbers,” Phys. Fluids 20, 044104 (2008)] numerically predicted four of these five states and mapped the transition from one state to another. Our main objective is to study the onset of instabilities and vortex breakdown in these states experimentally. For this purpose, we visualize the flow at the inlet of the expansion for several values of moderately large Reynolds numbers, Re, and of swirl parameters, S. We analyze the inner region of the state that corresponds to the unstable shear layer in the sudden expansion and find two different states that share the same character, although they have different non-dimensional frequenci...