Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session G33: Flow Instability: Global Modes |
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Chair: Nils Tilton, Colorado School of Mines Room: 615 |
Sunday, November 24, 2019 3:48PM - 4:01PM |
G33.00001: Global modes in Taylor--Couette--Poiseuille Flow with a permeable inner cylinder Denis Martinand, Nils Tilton The addition to a Taylor--Couette cell of an axial Poiseuille flow and a radial flow associated with a weakly permeable inner cylinder results, at a given rotation rate of the inner cylinder, in adjacent regions of the flow that are simultaneously stable, convectively unstable, and absolutely unstable, making this system fit for obtaining global modes of centrifugal instability. Critical conditions of the instabilities are obtained using the analytical frameworks of linear and non-linear global modes. Besides, dedicated Direct Numerical Simulations implementing the Darcy's condition on the permeable cylinder are performed to assess the validity of these analyses. Three different set-ups are considered. Fluid injection, in the first set-up, or extraction, in the second, occur along the full length of the inner cylinder. In the third, fluid flux through the inner cylinder evolves from extraction to injection as cross flow reversal occurs. Though correctly predicting the nature and location of the wavemakers governing the global instability, and their critical conditions, the analyses do not explain, however, that the instabilities observed in the numerical simulations take the form of axial stacks of wave-packets characterized by step-ups and step-downs of the temporal frequency. [Preview Abstract] |
Sunday, November 24, 2019 4:01PM - 4:14PM |
G33.00002: Randomized Resolvent Analysis of Turbulent Separated Flow over a NACA0012 Airfoil Jean Helder Marques Ribeiro, Chi-An Yeh, Kunihiko Taira Singular value decomposition of a large resolvent operator for high-Reynolds number fluid flow is computationally and memory intensive. For this reason, the applications of resolvent analysis has generally been limited to 1D or laminar flow problems. We consider randomized analysis for fast computation of the dominant resolvent modes by passing a tall and skinny random test matrix to sketch the large resolvent operator. The operator is then projected onto the low-dimensional subspace spanned by the sketch. By performing SVD on this reduced resolvent matrix, we achieve significant reduction in computational and memory requirements compared to traditional techniques. We apply this randomized approach for a bi-global resolvent analysis on a turbulent mean flow over a NACA0012 airfoil at chord-based Reynolds number of 23,000. While the full resolvent operator is projected using only 10 out of the 750,000 bases, the leading gain, forcing and response modes are accurately captured. We also provide discussions on incorporating physical insights into the randomized algorithm for further computational alleviation. [Preview Abstract] |
Sunday, November 24, 2019 4:14PM - 4:27PM |
G33.00003: Global instability mode in a baffled Von Karman flow Pawel Baj, Nicholas Worth, James Dawson A low-frequency spectral peak is identified in velocity spectra measured close to the stagnation point of a baffled turbulent Von Karman swirling flow. This observation is consistent across a range of studied experimental datasets (3D3C Scanning-PIV and 2D3C Stereo-PIV measurements) acquired in two different facilities. An attempt is made to recognise the underlying velocity structure through an application of conditional averaging and Proper Orthogonal Decomposition. The structure that emerges takes a form of a spheroidal zone located near the tank's centre of accelerated, unidirectional flow perpendicular to the axial direction. This structure is then observed to precess around the tank's axis with the frequency of the spectral peak. The dynamics of the recognised feature is then studied via POD-Galerkin projection of the Navier-Stokes equations. This ultimately allows us to track origins of the structure down to the linear term of the projected equations, which is characterised by a pair of unstable eigenvalues. The structure can be, therefore, classified as a global instability mode. A simple sensitivity analysis shows that the characteristic frequency can be controlled via the mean shear in the radial plane. [Preview Abstract] |
Sunday, November 24, 2019 4:27PM - 4:40PM |
G33.00004: Flow Visualization and Velocity Spectra in a Low Viscosity Round Jet. Vinod Srinivasan, Ian Wright Low-density jets are known to exhibit strong nonlinear global modes, whose frequency is dependent on the density ration, boundary layer thickness with a weak dependence on viscosity. The separate role of viscosity gradients has not been investigated experimentally for free shear flows such as round jets. The present research documents the unstable response of a circular jet issuing into an ambient fluid of higher viscosity. Viscosity ratios (ambient-to-jet) of 1 to 40 and jet Reynolds numbers of 500 to 2000 are studied in density-matched, miscible fluids. The mode of breakdown is visualized using fluorescent dye and hydrogen bubble techniques, while the wavelength of the dominant mode is measured through hot-film anemometry. The spatial and temporal growth of instabilities is reported as dependent on viscosity ratio, Reynolds number, and jet shear layer inlet condition. The breakdown process is marked by the emergence of a sharp peak in the frequency spectrum at a distance of half a jet diameter downstream of the exit plane. This peak persists for about 5 diameters downstream, gradually decreasing in magnitude until indistinguishable from the background. The frequency of the peak depends on the viscosity ratio, for any fixed jet Reynolds number. [Preview Abstract] |
Sunday, November 24, 2019 4:40PM - 4:53PM |
G33.00005: Global mode induced by a symmetry-breaking in a split cylindrical cavity Jesus O. Rodriguez-Garcia, Soledad Le Clainche, Javier Burguete We study experimentally the flow inside a closed cylinder split in two halves at the equator. When these two parts rotate in exact corotation regime the internal flow is essentially in solid-body rotation at the angular velocity of both sides. When a slight difference between the rotation frequencies is established a secondary flow is created due to the differential rotation between halves and restricted to the boundary layer. The behavior of this boundary layer is compared with theoretical and numerical results finding the ``sandwich'' structure of a Stewartson boundary layer. Time-dependent structures are observed near the cylindrical wall. Their behavior for different values of the Reynolds and the Rossby numbers are presented. A global recirculation mode is also found due to a symmetry-breaking induced between sides that appears because of a slight misalignment of the experimental setup, whose characteristics are compatible with the behavior od a precessing cylinder\footnote{J. O. Rodr\'iguez-Garc\'ia and J. Burguete, \textbf{Phy. Rev. E} 99, 023111.}. A HODMD analysis is performed finding relevant frequencies inside the flow that allow us to reconstruct the global mode\footnote{S. Le Clainche and J. M. Vega, \textbf{SIAM J. Appl. Dyn. Syst.} 16, 882-925.}. [Preview Abstract] |
Sunday, November 24, 2019 4:53PM - 5:06PM |
G33.00006: Localized eigenmodes in a moving frame of reference representing convective instability. Koen Groot, Sebastien Niessen When representing convective instability mechanisms with the streamwise BiGlobal stability approach, results suffer from a sensitivity to the streamwise domain truncation length and boundary conditions. The presently proposed methodology resolves this sensitivity by considering a moving frame of reference. In that frame, the spectrum features discrete eigenvalues whose corresponding eigenfunctions decay exponentially in both the up- and downstream directions. Therefore, the truncation boundaries can be placed far enough that both variations in the domain length and artificial boundary conditions have no impact. The discrete nature of the spectrum enables the use of (non-)local stability methods to perform an independent approximation of the BiGlobal eigenvalues via global mode theory. We demonstrate that retrieving set-up-independent solutions in the stationary frame of reference is likely impossible for the flow case considered. [Preview Abstract] |
Sunday, November 24, 2019 5:06PM - 5:19PM |
G33.00007: Global Analysis of the Convective Instabilities in Laminar Shock-Wave/Boundary-Layer Interactions Sebastien Niessen, Koen Groot, Stefan Hickel, Vincent Terrapon The interaction between a laminar boundary layer and an oblique shock wave is investigated through BiGlobal stability analysis. Previous studies have revealed the presence of a stationary mode (J.-Ph. Boin et al., TCFD 20(3), 2006, and J.-Ch. Robinet, JFM 579, 2007) and a convective instability mechanism (F. Guiho et al., JFM 789, 2016). In the latter analyses, non-localized eigenmodes are obtained that are artificially affected by the finite size of the chosen computational domain. In the present work, we obtain localized wave packets, that are independent of domain size and truncation boundary conditions, by applying the stability analysis in a moving frame of reference. The long-time behavior is subsequently determined by time integration, which results in the propagation of the localized wave packets in the flow. Finally, we highlight the mechanisms constituting the convective instabilities through a Reynolds-Orr energy budget analysis. To obtain the unstable basic state solution to the compressible Navier-Stokes equations, we have coupled Direct Numerical Simulations to the selective frequency damping method. [Preview Abstract] |
Sunday, November 24, 2019 5:19PM - 5:32PM |
G33.00008: Linear Stability of Flow through a Compressor Stage. Miguel Fosas de Pando, Peter J. Schmid Fluid systems of industrial interest often consist of a periodic assembly of identical subunits. For instance, a compressor stage in a jet engine is built by arranging a number of airfoil blades in annular rows, one rotating and one stationary. A typical analysis of these systems attempts to describe the flow dynamics by isolating a single subunit, i.e. a blade passage, and imposing periodic boundary conditions. Although this approach leads to problems that are easier to solve, it cannot account for global large-scale synchronization effects across multiple subunits. In this contribution, we first present a computational framework for the analysis of modal and non-modal stability of the full system, i.e. considering the contribution of each subunit to the global dynamics. This technique relies on the underlying properties of operators that are reminiscent of twisted Toeplitz matrices, which are in turn coupled through a time-dependent sliding interface. This framework will be then used to investigate the dynamics of the response of flow through an idealized compressor stage, consisting of a rotor and a stator, to small amplitude forcing. [Preview Abstract] |
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