Characterization of the three-dimensional instability in a lid-driven cavity by an adjoint based analysis

Giannetti, Flavio; Luchini, Paolo; Marino, Luca

doi:10.1007/978-90-481-3723-7_25

Cited by 6 publications

(5 citation statements)

References 14 publications

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“…The sensitivity, product of the direct and adjoint mode, is largest inside the cavity, with no significant contributions from the regions of strong shear above it. It is interesting to note that the wavemaker is similar to that computed for a lid-driven square cavity (Giannetti, Luchini & Marino 2010;Haque et al 2012).…”

Section: Structural Sensitivity Of the First Bifurcationsupporting

confidence: 55%

Linear three-dimensional global and asymptotic stability analysis of incompressible open cavity flow

et al. 2015

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The viscous and inviscid linear stability of the incompressible flow past a square open cavity is studied numerically. The analysis shows that the flow first undergoes a steady three-dimensional bifurcation at a critical Reynolds number of 1370. The critical mode is localized inside the cavity and has a flat roll structure with a spanwise wavelength of about 0.47 cavity depths. The adjoint global mode reveals that the instability is most efficiently triggered in the thin region close to the upstream tip of the cavity. The structural sensitivity analysis identifies the wavemaker as the region located inside the cavity and spatially concentrated around a closed orbit. As the flow outside the cavity plays no role in the generation mechanisms leading to the bifurcation, we confirm that an appropriate parameter to describe the critical conditions in open cavity flows is the Reynolds number based on the average velocity between the two upper edges. Stabilization is achieved by a decrease of the total momentum inside the shear layer that drives the core vortex within the cavity. The mechanism of instability is then studied by means of a short-wavelength approximation considering pressureless inviscid modes. The closed streamline related to the maximum inviscid growth rate is found to be the same as that around which the global wavemaker is concentrated. The structural sensitivity field based on direct and adjoint eigenmodes, computed at a Reynolds number far higher than that of the base flow, can predict the critical orbit on which the main instabilities inside the cavity arise. Further, we show that the sub-leading unstable time-dependent modes emerging at supercritical conditions are characterized by a period that is a multiple of the revolution time of Lagrangian particles along the orbit of maximum growth rate. The eigenfrequencies of these modes, computed by global stability analysis, are in very good agreement with the asymptotic results

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Section: Structural Sensitivity Of the First Bifurcationsupporting

confidence: 55%

Linear three-dimensional global and asymptotic stability analysis of incompressible open cavity flow

et al. 2015

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“…The flow features developing within this geometry have been studied numerically by other authors and the 2D bifurcations by but to the authors' knowledge, there has not been any 3D instability analysis performed in this geometry, other than the study included in de Vicente's PhD dissertation (second author of this paper). Cavity flows are characterised by 3D instabilities developing at lower Reynolds numbers (on the basis of the geometrical cavity length and the lid velocity) than 2D instabilities . For this reason, they are ideal candidates for testing new tools for analysis of 3D flow structures.…”

Section: Direct Problem: L‐shaped Cavity and Three‐dimensional Instabmentioning

confidence: 99%

Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high‐order numerical tools

Ferrer¹,

Vicente²,

Valero³

2014

Numerical Methods in Fluids

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SUMMARYWe explore the recently developed snapshot-based dynamic mode decomposition (DMD) technique, a matrix-free Arnoldi type method, to predict 3D linear global flow instabilities. We apply the DMD technique to flows confined in an L-shaped cavity and compare the resulting modes to their counterparts issued from classic, matrix forming, linear instability analysis (i.e. BiGlobal approach) and direct numerical simulations. Results show that the DMD technique, which uses snapshots generated by a 3D non-linear incompressible discontinuous Galerkin Navier-Stokes solver, provides very similar results to classical linear instability analysis techniques. In addition, we compare DMD results issued from non-linear and linearised NavierStokes solvers, showing that linearisation is not necessary (i.e. base flow not required) to obtain linear modes, as long as the analysis is restricted to the exponential growth regime, that is, flow regime governed by the linearised Navier-Stokes equations, and showing the potential of this type of analysis based on snapshots to general purpose CFD codes, without need of modifications. Finally, this work shows that the DMD technique can provide three-dimensional direct and adjoint modes through snapshots provided by the linearised and adjoint linearised Navier-Stokes equations advanced in time. Subsequently, these modes are used to provide structural sensitivity maps and sensitivity to base flow modification information for 3D flows and complex geometries, at an affordable computational cost. The information provided by the sensitivity study is used to modify the L-shaped geometry and control the most unstable 3D mode.

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“…Another extensión of the classic lid-driven cavity work is the experimental and numerical study of Humphrey et al (2003), who visualized and computed sheardriven incompressible flow in a toroidal cavity of square cross-section; threedimensional structures were identified, reminiscent of those associated with global three-dimensional instability in the simpler cavity flows, although no analysis was performed in the context of the latter work. The sensitivity of lid-driven cavity flows in rectangular containers driven by motion of one or two opposite lids has been analysed by Giannetti, Luchini & Marino (2010) using adjoint-based analysis (Hill 1992(Hill , 1995, which delivers the región of the flow where the global mode is most sensitive to localized initial perturbations.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional flow instability in a lid-driven isosceles triangular cavity

et al. 2011

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Linear three-dimensional modal instability of steady laminar two-dimensional states developing in a lid-driven cavity of isósceles triangular cross-section is investigated theoretically and experimentally for the case in which the equal sides form a rectangular córner. An asymmetric steady two-dimensional motion is driven by the steady motion of one of the equal sides. If the side moves away from the rectangular córner, a stationary three-dimensional instability is found. If the motion is directed towards the córner, the instability is oscillatory. The respective critical Reynolds numbers are identified both theoretically and experimentally. The neutral curves pertinent to the two configurations and the properties of the respective leading eigenmodes are documented and analogies to instabilities in rectangular lid-driven cavities are discussed.

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Characterization of the three-dimensional instability in a lid-driven cavity by an adjoint based analysis

Cited by 6 publications

References 14 publications

Linear three-dimensional global and asymptotic stability analysis of incompressible open cavity flow

Linear three-dimensional global and asymptotic stability analysis of incompressible open cavity flow

Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high‐order numerical tools

Three-dimensional flow instability in a lid-driven isosceles triangular cavity

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