Session Q15: Flow Instability: Global Modes

Spatiotemporal Analysis of a Low-Viscosity Jet

The effect of viscosity contrast between a jet and its surrounding is experimentally investigated using density-matched fluids. A gravity-driven flow is established, with a saltwater jet of relatively low-viscosity emerging into an ambient composed of high-viscosity propylene glycol. Jet Reynolds numbers, Re, ranging from 1600 to 3400 are studied for ambient-to-jet viscosity ratios, M, ranging from 1 to 45. Flow visualization suggests that at low values of viscosity ratios, the jet breakdown is axisymmetric, while helical modes develop at high values of M. High-speed imaging with a fluorescent dye in the jet is used to enhance contrast and identify the interface. Temporal analysis is performed to determine the frequency of the jet while spatial analysis yields the wavelength of perturbations. Proper Orthogonal Decomposition (POD) is performed to find the eigenvalues associated with axisymmetric and helical modes.   

Effect of nozzle on the global eigenfunctions of a Ma=1 jet

The effect of the nozzle on instability mechanisms in perfectly expanded Ma=1 jets is assessed by means of global stability analysis. The first considered configuration represents the geometry of the nozzle within the computational domain. A second setup replaces the flow through the nozzle with a parallel jet. In both cases, a globally unstable eigenfunction is computed, indicating of absolute instability. The origin of the instability is identified as the sharp streamwise gradient in the base flow immediately downstream of the nozzle exit location. The destabilizing role of the nozzle is attributed to the generation of the steep streamwise gradient while the constraining effect of the nozzle walls leads to a reduction of the instability growth rate. Finally, the vortical, acoustic and thermal components of the eigenfunctions are assessed using the momentum potential theory by Doak (1989).   

Linear stability of curved pipe flow approaching zero curvature

This study investigates the linear stability of the flow in a torus for very low curvatures, approaching the limit of a straight pipe, i.e. zero curvature. An in-house developed method is employed for both computing the base flow and the stability analysis. The equations are solved on a 2D domain with three components, employing a spectral collocation method based on Chebychev and Fourier nodes in the radial and azimuthal direction, respectively. The linear stability analysis is carried out for curvatures ?? < 10^-2 approaching zero. Inhomogeneous disturbances are considered in both the radial and azimuthal directions, whereas normal modes are assumed in the streamwise direction. The Navier-Stokes equations are linearised with respect to both the computed base flow and the parabolic Poiseuille velocity profile. In the latter case, perturbations are allowed to have non-zero curvature. In this way, one can assess for which parameters (??, Re) the base flow is indistinguishable from the parabolic velocity profile regarding the stability properties. For the curvatures here investigated, the critical Reynolds number increases monotonically as the curvature decreases, going asymptotically to infinity as ?? → 0, i.e. approaching the straight pipe which is known to be linearly stable.   

Triglobal resolvent analysis of finite-aspect-ratio swept wing wakes

We perform triglobal resolvent analysis for laminar flows over finite-aspect-ratio swept wings. Base flows are obtained from direct numerical simulations at a chord-based Reynolds number 400 and a freestream Mach number 0.1 over NACA 0015 wings with an aspect ratio 4 at different post-stall angles of attack and angles of sweep. For the unswept wings, the wake is dominated by the interaction of mid-span vortex shedding, tip vortex and an interaction zone. As we increase the sweep angle, the wake oscillations are stabilized and finger-like structures appear. Through resolvent analysis we are able to identify these phenomena through mode switching over varied frequencies. For wings with sweep angles less than 15 degrees, the mid-span shedding structures are the primary response modes at the vortex shedding frequency. As frequency increases, these modes become secondary while the primary modes develop from the wing tip. For higher sweep angles, the tip modes dominate the response mechanisms for all frequencies. These studies provide fundamental insights on the complex wake dynamics behind finite-aspect-ratio swept wings.   

Hypersonic Boundary-Layer Instabilities over Cone-Flare Models

Cone-flare geometries exhibit a shock-wave/boundary-layer interaction with high surface heating in the reattachement region. Computational investigations of a cone-flare geometry with varying nosetip radii and flare angle at zero degrees angle of attack are presented. The model geometry and conditions are selected to match the experiments conducted in the Air Force Research Laboratory (AFRL) Mach 6 Ludwieg Tube. Four nosetip radii of interest are used for the computational studies herein: 0.1, 0.5, 5.1, and 10.2 mm. These nosetips are attached to a 7-degree half-angle circular cone which is followed by a flare with angle varying from 34, 37, 40, and 43-degrees. Peak surface heating was measured at the reattachement location, which is located slightly past the cone-flare junction. Streamwise heat flux streaks were measured at the reattachement location on the flare and the azimuthal spacing was reported for all conditions. The laminar boundary layer solution is computed using the VULCAN-CFD solver on a single-block structured grid, with the built-in options for shock alignment and boundary-layer grid adaptation enabled. Global instability analysis is performed to identify possible correlations between global mode wavelength and the spacing of heat flux streaks observed experimentally.   

An Immersed Boundary technique for the linear stability analysis of fluid-structure interactions

To date, the global stability analysis of three-dimensional elastic structures interacting with incompressible flows remains a prohibitive task due to the high computational costs. Here we present a Jacobian-free strategy to perform global stability analyses of interacting fluid-structure systems, which is incorporated into a validated FSI solver based on a Moving-Least-Squares Immersed Boundary. The linear stability analysis is carried out using the fluid-structure interaction solver as a black box to be interfaced with a matrix-free eigenvalue solver. The process consists of three different stages: 1) Determination of the equilibrium solution through the use of BoostConv, a stabilization procedure which numerically suppresses the instabilities and forces the simulation to converge towards the steady state; 2) Retrieval of the linear dynamics around the base state by numerically approximating the Jacobian-vector product; 3) Computation of the leading eigenvalues by supplying the matrix-vector product to an iterative eigenvalue solver. The procedure will be described in details and results on simple configurations will be compared with those obtained with mesh-deforming techniques. The efficiency and limitations of the proposed methodology will be discussed.   

Global Stability Analysis of Eccentric Taylor Couette Flow

Stability analysis of a flow studies the transition of a simple laminar base flow to a bifurcated complex system of flow, or later to a turbulent flow. Hydrodynamic stability analysis deals with the transition region of any flow. Linear bi-global stability analysis of eccentric Taylor-Couette(TC) flow is slightly complicated compared to the simple TC system, for the eccentric system is hard to solve in a traditional radial coordinate system. Simple TC system can be solved using a pseudo - parallel flow assumption and solving the Orr-Squire system of governing equations, while eccentric TC flow is completely non-parallel and complex. The work around authors employed here is to use a bipolar coordinate system for representing the governing equations. Base flow is solved using a Finite Volume Method to numerically approximate the solution of governing Navier Stokes equations and then interpolated to the points required in the bipolar coordinates to solve for stability. Chebyshev-Fourier collocation spectral method is used to solve for the governing stability equations, since the angular flow is to be periodic. The biglobal stability analysis reveals modes of instability in the plane of rotation of the inner cylinder. The axial coordinate is assumed to be periodic. The stability code which is validated with the simple TC system, revealed that the eccentric system is stable for higher Reynolds number than the concentric system. It also revealed formation of Taylor vortices as its first instability.   

Linear stability analysis of a low-viscosity jet emerging into a high-viscosity ambient fluid

Recent experiments with low-viscosity jets emerging into a high viscosity ambient medium have documented a transition from axisymmetric instabilities to helical instabilities, as the viscosity ratio M between the ambient and jet is increased. A single dominant frequency is observed in the near-field of the jet, suggesting that this may be a global mode. Global modes have been linked in other flows such as low-density jets and countercurrent shear layers to the presence of local absolutely unstable profiles. Accordingly, in this study, linear stability calculations of a low-viscosity jet emerging into a high-viscosity ambient are performed. We conduct a systematic study of the effect of ambient-to-jet viscosity ratio, jet Reynolds number, and the velocity profile specified by the shear layer thickness and inflection point location, on the growth of axisymmetric and helical modes. Spatio-temporal analysis in the complex wavenumber plane suggests that beyond a critical viscosity ratio, the flow becomes absolutely unstable, with the helical mode being dominant. The shear layer thickness, as well as the location of the inflection point, which is determined by the viscosity ratio in experiments, are shown to be critical factors in determining this critical value of viscosity ratio.   

Approximating the resolvent operator with hierarchically semi-separable matrix representation and randomized sketching

Resolvent analysis has become an indispensable technique to understand the dynamics of turbulent flows.  Computational challenges with resolvent analysis remain in tackling large-scale problems arising from high Reynolds numbers and multi-dimensional external flows.  Here, we consider the use of a hierarchically semi-separable (HSS) matrix representation for the linear operator with randomized sketching to extend the applicability of resolvent analysis. The HSS representation considers a binary index tree to extract a hierarchical series of diagonal and off-diagonal blocks from the linear operator.  The off-diagonal blocks can be compressed with their low-rank approximations, resulting in a `sketched' linear operator inside-out. To construct the resolvent operator for different frequencies, only the diagonal blocks at the lowest hierarchy level need to be modified.  Consequently, the matrix inversion can be achieved via a series of rank-k updates by tracking the hierarchy bottom-up, significantly reducing the resources needed for the matrix inverse. We demonstrate the use of this approach on a 2D channel flow and a turbulent airfoil wake.   

Experimental study on airborne contaminant release from the impact of a liquid on a horizontal solid surface.

 

The airborne release of dry contamination residues resulting from a liquid jet impinging a surface is an important mechanism by which Codiv-19 virus or radioactive contamination can reach human respiratory airways. The very fine evaporable droplets responsible for this threat are hard to quantify due both to their small size and short lifespan. We developed an experimental bench, which is able of quantifying in very accurate way, the evaporated dry contamination using a tracer. We evaluate the aerosol release fraction (ARF), corresponding to the ratio between the mass of airborne particles and the mass of dispersible tracer dissolved in the impinging liquid jet, in relation with the jet dynamic. The purpose of this present work is to present our measurements of aerosols release when a broken circular liquid jet, due the capillary instability, impacts a solid surface.

It was found that, when the liquid jet is in the Rayleigh regime, the Airborne Release Fraction increase with the jet velocity for the same jet diameter. In this regime, the ARF is around 10^-5. The airborne aerosol size distribution reveals particles of aerodynamic diameter within the respirable range (below 10 µm). The distribution exhibits features, which characteristics seem to indicate competing aerosol generation mechanisms in relation with the jet diameter and velocity. The particle size distribution of the 2 mm diameter liquid jet looks like unimodal whereas the 1 mm seems trimodal. The Rayleigh Plateau instabilities seem to be the origin of this difference.  Indeed, high speed camera visualization pointed out the fact that there are several mechanisms at the origin of the airborne release aerosols and we are trying to determine which one lead the ARF.