Session E20: Instability in Jets and Wakes I

Competition between single and double helical vortex breakdown

The spiral vortex breakdown of nominally axisymmetric, swirling flows observed in the three-dimensional direct numerical simulations of Ruith, Chen, Meiburg {\&} Maxworthy [JFM 2003, 486, p 331--378] is revisited and interpreted in terms of linearly unstable global modes. We show that increasing the swirl number, which compares the magnitude of the azimuthal and axial velocity components, results in successive Hopf bifurcations involving helical modes of azimuthal wave numbers $m =-$1 and $m =-$2. These modes develop in the lee of the axisymmetric bubble, and correspond to spiral perturbations rotating in time in the same direction as the swirling flow, but winding in space in the opposite direction. The global stability analysis is shown to yield an accurate frequency prediction. We further extend the range of swirl considered in the DNS, and show that the $m =-$1 and $m =-$2 Hopf bifurcations can occur simultaneously, both modes approaching a strong 2:1 resonance. We compute the normal form describing the leading-order nonlinear interaction between modes, and show that it accurately predicts the pattern and symmetries of the solutions observed in the DNS calculations, with satisfactory agreement on the bifurcation thresholds.   

Experimental study of axial forcing of a swirling jet

Swirling jets enhance mixing of fluids. This leads to more complete combustion, chemical process mixings, lower plume temperatures, and reduced pollutant emissions. Mixing can be improved further by forcing instabilities in the jet and was tested on both non-swirling and swirling jets. These imposed disturbances are either axial, which generates vortex rings or angular, which create more complex structures. In this study, the effects of axial forcing on a swirling jet are experimentally investigated for Reynolds number ranging from 1,000 to 10,000, Swirl number from 0 to 1.3, and a Strouhal number from 0 to 15, where limited past experimental data exists within these flow regimes. This experiment offers insight into the flow structure of the swirling jet in the vortex breakdown region, as observed using PLIF with dye injected azimuthally on the jet periphery.   

Characterization of hydrodynamic instabilities in non- premixed flames by combining detailed simulations and linear stability analysis

Numerical simulations and linear stability analysis are invaluable tools in complementing experiments to obtain improved understanding about instability mechanisms in non-premixed and premixed flames. By utilizing the experiments of F\"uri et al., the objective of this study is to characterize hydrodynamic instability mechanisms in methane/air diffusion flames. To this end, detailed simulations are performed to obtain the reactive mean flow, which is used as input to the linear stability analysis. In order to account for the detailed reaction chemistry and variations in thermo-viscous properties, a flamelet-representation is introduced in the linear stability method. Model predictions for growth rate and phase velocity are compared with experimental data, and parametric studies are performed to quantify effects of heat-release and detailed chemistry in controlling hydrodynamic instabilities.   

Dynamics of a laminar flow past a rotating bullet-shaped body

Numerical simulations are performed for laminar flow past a rotating bullet-shaped body of length-to-diameter ratio $L/D=2$, ranging the non-dimensional angular rotation velocity, $\Omega=\omega R/u_{\infty}$, from $0$ to $0.6$, and covering the Reynolds number range $3200.5$ there are also two transitions, both leading to different swirling flows.   

Oblique and Parallel Vortex Shedding in the Wake of a Circular Cylinder at Subcritical Flow Regime

Parallel/oblique shedding of vortices in the wake of a cylinder at subcritical Reynolds numbers are investigated experimentally in a water channel. Experiments involved a cylinder with various combinations of free-surface, channel-floor, endplate boundaries, such as, a free-surface on one end and the channel floor on the other end of the cylinder. The cylinder aspect ratios (L/D) ranged between 12.3 to 13.5. Flow visualization via PIV is conducted along the spanwise flow field on a plane that is tangent to the cylinder surface and is oriented in the free-stream direction. As the vortices are shed behind this plane of visualization from sides of the cylinder, distinct spanwise regions with increased or decreased levels of streamwise velocity contours are alternately induced. These regions can be used to estimate the spanwise orientation of the vortices. Our preliminary results showed an unsteady character in the degree of obliqueness of the shed vortices. Vortices shed out of phase between two neighboring regions of the span led to the formation of dislocations.   

Instabilities of a cylinder wake in a stratified fluid

The goal of this study is to analyse experimentally, numerically and theoretically how a linear density stratification modifies a cylinder wake, which is well known to exhibit a rich dynamics in a homogeneous fluid. In a first part, we focus on the 2D dynamics of the wake. We show that the von Karman vortex street is stabilised by a moderate stratification for tilted and horizontal cylinders, in agreement with the stabilisation of shear flows at large Richardson numbers. However, it is curious to see that the von Karman vortices reappear for a strong stratification in the case of a tilted cylinder. This new unstable mode can be explained by the presence of tilted vortices with no vertical velocity, i.e. with horizontal streamlines. In a second part, we focus on the 3D instabilities of the cylinder wake. For a vertical cylinder, the well known mode A can be nicely visualised by shadowgraph and seems to be enhanced by a moderate stratification. For a tilted cylinder, the structure of the instability is strongly modified, with the presence of thin undulated dark lines in the shadowgraph images. These structures are similar to the Kelvin-Helmholtz billows which have been observed recently in the critical layer of a tilted stratified vortex.   

Sensitivity Analysis of Spiral Vortex Breakdown

Vortex breakdown occurs in some swirling flows, such as those in gas turbine combustion chambers. Previous studies have established that the initial breakdown is steady and axisymmetric but that an unsteady spiralling breakdown mode develops on top of this, due to a region of absolute instability. We investigate the linear stability of steady axisymmetric vortex breakdown in a semi-infinite domain for an incompressible fluid at Re = 200. We relate the global behaviour of the flow to its local stability properties. We use direct numerical simulation (DNS) of the linearized direct and adjoint Navier--Stokes equations to obtain the linear direct and adjoint global modes. We use these to map the regions of the flow that are most sensitive to external forcing and internal feedback. This enables us to identify the wavemaker region, which causes spiral vortex breakdown. We find that, for low swirls, the wavemaker of the linear global mode lies in the axisymmetric breakdown bubble. Previous studies of the same flow indicate that the wavemaker of the nonlinear global mode lies in the wake of the axisymmetric breakdown bubble. We explain this apparent contradiction by analogy with two coupled Van der Pol oscillators.   

Stability and sensitivity analysis of experimental flow fields measured past a porous cylinder

It is known in the literature that the linear stability analysis of the time-averaged flow field past a circular cylinder, after the primary wake instability, predicts a global mode that is marginally stable with a frequency in time that well approximates the one of the saturated vortex shedding. This behavior has been recently shown to hold up to Reynolds number $Re=600$ by DNS simulations [Leontini et al., JFM 645, pp. 435-446, 2010]. Here we carry out a stability/sensitivity analysis of the PIV velocity fields measured in the wake past a porous circular cylinder at $Re\simeq 8.3\cdot 10^4$ [Fransson et al., JFS 19, pp.1031-1048, 2004]. Different intensities of uniform suction/blowing through the cylinder surface are considered. The objectives of this work are the following. Firstly, we extend the analysis described in [Leontini et al.] at higher values of $Re$. Moreover, the global direct and adjoint modes, derived from the experimental data, are used to locate the core of the instability, to realign the instantaneous flow snapshots in phase and, thus, to help in the analysis of the experimental data. Lastly, it is shown that the sensitivity of the marginally stable eigenvalue to a generic variation of the mean flow provides hints for the control of the vortex-shedding frequency.   

Flow Structure and Stability in Confined, Reacting, Bluff Body Wakes

This paper describes the variation of reacting bluff body wake structure with flame density ratio for a variety of bluff bodies and lip velocities. Previous experiments and computations have shown that the bluff body flow structures at ``high'' and ``low'' flame density ratios are fundamentally different, being dominated by the convectively unstable shear layers and absolutely unstable Von Karman vortex street, respectively. This paper characterizes the transition between these two flow structures, and shows that the bifurcation behavior does not occur abruptly at some density ratio. Rather, there exists a range of transitional density ratios at which the flow exists intermittently in both states. The fraction of time that the flow spends in either state is a monotonic function of density ratio. This paper also shows that local parallel stability analyses developed for confined, variable density, laminar base wake flows captures the qualitative behavior of this transition, demonstrating a successful parameterization of this phenomenon. These results have important implications on the dynamics of high Reynolds number, vitiated, reacting flows, suggesting that such flows exhibit two co-existing dynamical states, intermittently jumping between the two.   

Measurements in a bluff body wake with variable inlet condition

The aim of this project is to experimentally study the instability of wakes behind bluff bodies from a fundamental research point of view, both for the natural case as well with various flow control methods applied. This is realized in an experimental setup specially designed to perform parameter variations, which are most often not possible in usually fixed experimental geometries. The bluff body is a so-called rectangular-based forebody with permeable surfaces on both sides, which enables modulation of the boundary layer through suction or blowing of air through the surfaces. The suction or blowing can either be uniform or local and the two sides can be modulated independently and consequently the inlet condition of the wake is altered. Investigations have been performed by means of pressure measurements, hot-wire anemometry and PIV in order to study how the wake mean flow, the vortex shedding frequency and the vortical structures are affected by the wake initial condition.