Predicting the onset of flow unsteadiness based on global instability

Crouch, J. D.; Garbaruk, A. V.; Magidov, D.

doi:10.1016/j.jcp.2006.10.035

Cited by 232 publications

(200 citation statements)

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“…The frozen eddy viscosity performed almost as well as the fully linearized turbulent viscosity for a cavity flow (Crouch et al 2007). It has also performed well in swirling flow studies using local spatio-temporal techniques in injector flows (Oberleithner et al 2015).…”

Section: Introductionmentioning

confidence: 79%

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Coherent structures in a swirl injector at Re = 4800 by nonlinear simulations and linear global modes

2016

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The large-scale coherent motions in a realistic swirl fuel injector geometry are analysed by direct numerical simulations (DNS), proper orthogonal decomposition (POD), and linear global modes. The aim is to identify the origin of instability in this turbulent flow in a complex internal geometry.The flow field in the nonlinear simulation is highly turbulent, but with a distinguishable coherent structure: the precessing vortex core (a spiraling mode).The most energetic POD mode pair is identified as the precessing vortex core. By analysing the FFT of the time coefficients of the POD modes, we conclude that the first four POD modes contain the coherent fluctuations. The remaining POD modes (incoherent fluctuations) are used to form a turbulent viscosity field, using the Newtonian eddy model.The turbulence sets in from convective shear layer instabilities even before the nonlinear flow reaches the other end of the domain, indicating that equilibrium solutions of the Navier-Stokes are never observed. Linear global modes are computed around the mean flow from DNS, applying the turbulent viscosity extracted from POD modes. A slightly stable discrete m = 1 eigenmode is found, well separated from the continuous spectrum, in very good agreement with the POD mode shape and frequency. The structural sensitivity of the precessing vortex core is located upstream of the central recirculation zone, identifying it as a spiral vortex breakdown instability in the nozzle. Furthermore, the structural sensitivity indicates that the dominant instability mechanism is the KelvinHelmholtz instability at the inflection point forming near vortex breakdown. Adjoint modes are strong in the shear layer along the whole extent of the nozzle, showing that the optimal initial condition for the global mode is localized in the shear layer.We analyse the qualitative influence of turbulent dissipation in the stability problem (eddy viscosity) on the eigenmodes by comparing them to eigenmodes computed without eddy viscosity. The results show that the eddy viscosity improves the complex frequency and shape of global modes around the fuel injector mean flow, while a qualitative wavemaker position can be obtained with or without turbulent dissipation, in agreement with previous studies.This study shows how sensitivity analysis can identify which parts of the flow in a complex geometry need to be altered in order to change its hydrodynamic stability characteristics.Key Words: † Email address for correspondence: outi-leena.tammisola@nottingham.ac.uk , and the exit velocity from the swirler (U E ). The coordinate system is also defined: the origin is at the centerline at the swirler exit location. The relative dimensions of the geometry are the same as in the numerical simulation, except that the numerical domain is longer in the downstream direction.

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Section: Introductionmentioning

confidence: 79%

“…The most sensitive region for passive control was successfully matched against experiments. Other successful studies include Mettot et al (2014a); Crouch et al (2007). The base flow approach is mathematically fully consistent.…”

Section: Introductionmentioning

confidence: 95%

Coherent structures in a swirl injector at Re = 4800 by nonlinear simulations and linear global modes

2016

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“…It means that the feedback model (4.2) may reliably predict the shock motion. Moreover, Crouch et al (2007Crouch et al ( , 2009) advocated that transonic buffet results from the global instability, where the unsteadiness is characterized by phase-locked oscillations of the shock and the separated shear layer. In this situation, both the upper and lower surfaces of the aerofoil are responsible for the instability, consistent with the present model.…”

Section: Feedback Model Of Shock Wave Motionmentioning

confidence: 99%

Numerical investigation of the compressible flow past an aerofoil

Chen

2009

J. Fluid Mech.

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Numerical investigation of the compressible flow past an 18% thick circular-arc aerofoil was carried out using detached-eddy simulation for a free-stream Mach number M∞ = 0.76 and a Reynolds number Re = 1.1 × 107. Results have been validated carefully against experimental data. Various fundamental mechanisms dictating the intricate flow phenomena, including moving shock wave behaviours, turbulent boundary layer characteristics, kinematics of coherent structures and dynamical processes in flow evolution, have been studied systematically. A feedback model is developed to predict the self-sustained shock wave motions repeated alternately along the upper and lower surfaces of the aerofoil, which is a key issue associated with the complex flow phenomena. Based on the moving shock wave characteristics, three typical flow regimes are classified as attached boundary layer, moving shock wave/turbulent boundary layer interaction and intermittent boundary layer separation. The turbulent statistical quantities have been analysed in detail, and different behaviours are found in the three flow regimes. Some quantities, e.g. pressure-dilatation correlation and dilatational dissipation, have exhibited that the compressibility effect is enhanced because of the shock wave/boundary layer interaction. Further, the kinematics of coherent vortical structures and the dynamical processes in flow evolution are analysed. The speed of downstream-propagating pressure waves in the separated boundary layer is consistent with the convection speed of the coherent vortical structures. The multi-layer structures of the separated shear layer and the moving shock wave are reasonably captured using the instantaneous Lamb vector divergence and curl, and the underlying dynamical processes are clarified. In addition, the proper orthogonal decomposition analysis of the fluctuating pressure field illustrates that the dominated modes are associated with the moving shock waves and the separated shear layers in the trailing-edge region. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to this complex flow.

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“…In the last decade instability analyses based on solutions of partial-derivative eigenvalue problems (often referred to as BiGlobal analyses, Theofilis 2003) and/or DNS have elucidated global instability mechanisms in a variety of LSB flows, including the aforementioned adverse-pressure-gradient flat-plate flow , backward-facing step flow , as well as geometry-induced separation (Marquillie & Ehrenstein 2003;Gallaire, Marquillie & Ehrenstein 2007), NACA 0012 airfoil in incompressible (Theofilis, Barkley & Sherwin 2002) and compressible flow (Crouch, Garbaruk & Magidov 2007), low-pressure-turbine flow (Abdessemed, Sherwin & Theofilis 2004, 2009), shock-induced separation (Boin et al 2006;Robinet 2007), open cavity (Akervik et al 2007) and S-shaped duct flows (Marquet et al 2008(Marquet et al , 2009. In all configurations examined consensus has been built that two different primary instability mechanisms coexist.…”

Section: Introductionmentioning

confidence: 99%

Structural changes of laminar separation bubbles induced by global linear instability

Rodríguez

Theofilis

2010

J. Fluid Mech.

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The topology of the composite flow fields reconstructed by linear superposition of a two-dimensional boundary layer flow with an embedded laminar separation bubble and its leading three-dimensional global eigenmodes has been studied. According to critical point theory, the basic flow is structurally unstable; it is shown that in the presence of three-dimensional disturbances the degenerate basic flow topology is replaced by a fully three-dimensional pattern, regardless of the amplitude of the superposed linear perturbations. Attention has been focused on the leading stationary eigenmode of the laminar separation bubble discovered by Theofilis et al. (Phil. Trans. R. Soc. Lond. A, vol. 358, 2000, pp. 3229-3324); the composite flow fields have been fully characterized with respect to the generation and evolution of their critical points. The stationary global mode is shown to give rise to a three-dimensional flow field which is equivalent to the classical U-shaped separation, defined by Hornung & Perry (Z. Flugwiss. Weltraumforsch., vol. 8, 1984, pp. 77-87), and induces topologies on the surface streamlines that are resemblant to the characteristic stall cells observed experimentally. IntroductionThe instability of a laminar separation bubble (LSB), embedded inside a boundary layer and arising as a consequence of an adverse free-stream pressure gradient on a flat surface, or induced by changes of the surface curvature, constitutes a problem of prime technological significance: in an aeronautical context related applications include lifting surfaces, low-pressure turbines and wind-turbine blades. The presence of a separated shear layer as an integral part of the LSB suggests that the instability properties of the shear layer should play a decisive role in the reattachment of the separated boundary layer. The one-dimensionality of the model shear-layer profile and its resulting amenability to classic, ordinary-differential-equation-based analysis (Michalke 1964; Blumen 1970 and subsequent work in this 'local' vein) has generated a wealth of knowledge on the problem of shear-layer instability perse and as applied to the LSB flow. On the other hand, Gaster postulated (H. Fasel, private communication November 2004) that, besides paying attention to the amplification of incoming disturbances by solution of the local instability problem, analysis of LSB flows 'in the true sense' should also be performed, by which a global instability analysis of the entire separated boundary layer flow is implied.

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Predicting the onset of flow unsteadiness based on global instability

Cited by 232 publications

References 17 publications

Coherent structures in a swirl injector at Re = 4800 by nonlinear simulations and linear global modes

Coherent structures in a swirl injector at Re = 4800 by nonlinear simulations and linear global modes

Numerical investigation of the compressible flow past an aerofoil

Structural changes of laminar separation bubbles induced by global linear instability

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