Sensitivity of 2-D turbulent flow past a D-shaped cylinder using global stability

Méliga, Philippe; Pujals, Grégory; Serre, Éric

doi:10.1063/1.4724211

Cited by 79 publications

(96 citation statements)

References 27 publications

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“…The fact that the numerical results cannot adequately capture the details of the reverse flow region (as frequently occurs for RANS computations around bluff-body geometries) could question the physical relevance of their subsequent stability and sensitivity analyses. However, in the aforementioned work, 25 Meliga, Pujals and Serre have shown that, even if L R is underestimated by ≈30% (as in the present case), the global stability analysis still provides a fairly good prediction of the measured vortex-shedding frequency, and, moreover, a very good qualitative agreement in terms of the experimental frequency sensitivity map obtained by Parezanović and Cadot. 26 The comparison between the experimental and numerical mean flow could probably be improved by means of more advanced and computationally expensive techniques, such as LES or DES, which are, however, still far from the state-of-the-art of many industrial CFD applications.…”

Section: Resultssupporting

confidence: 82%

“…25 In their study, the authors computed the time-averaged solution of the unsteady two-dimensional Reynolds-Averaged Navier-Stokes (RANS) equations for the flow past a D-shaped cylinder at Re = 13 000 and then performed a sensitivity analysis of the obtained mean flow by linearising both the flow and the turbulence model equations. In analogy with the studies of the circular cylinder wake at low Reynolds numbers, the frequency control map computed by the authors for the considered turbulent flow was in close agreement with the one experimentally obtained by Parezanović and Cadot 26 through extensive measurements performed for different positions of the secondary cylinder.…”

Section: Introductionmentioning

confidence: 99%

“…To this purpose, we consider the confined incompressible flow past an elongated D-shaped cylinder at Re = 32 000 by means of both numerical and experimental investigations. In analogy with the aforementioned studies, 25,27 numerical simulations are undertaken in the RANS framework while the experimental measurements are performed by means of Particle Image Velocimetry (PIV) in the near-wake region of the flow. Notwithstanding that the accurate and reliable numerical prediction of turbulent flows over bluff-body geometries still represents a great challenge, RANS computations define a consolidated modelling approach for several industrial applications, whose ability in reproducing basic mean-flow features and turbulence statistics has been assessed over the last decades.…”

Section: Introductionmentioning

confidence: 99%

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Global stability and control of the confined turbulent flow past a thick flat plate

et al. 2017

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This article investigates the structural stability and sensitivity properties of the confined turbulent wake behind an elongated D-shaped cylinder of aspect-ratio 10 at Re = 32 000. The stability analysis is performed by linearising the incompressible Navier-Stokes equations around the numerically computed and the experimentally measured mean flows. We found that the vortex-shedding frequency is very well captured by the leading unstable global mode, especially when the additional turbulent diffusion is modelled in the stability equations by means of a frozen eddy-viscosity approach. The sensitivity maps derived from the computed and the measured mean flows are then compared, showing a good qualitative agreement. The careful inspection of their spatial structure highlights that the highest sensitivity is attained not only across the recirculation bubble but also at the body blunt-edge, where tiny pockets of maximum receptivity are found. The impact of the turbulent diffusion on the obtained results is investigated. Finally, we show how the knowledge of the unstable adjoint global mode of the linearised mean-flow dynamics can be exploited to design an active feedback control of the unsteady turbulent wake, which leads, under the adopted numerical framework, to completely suppress its low-frequency oscillation. Published by AIP Publishing. [http://dx

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Section: Resultssupporting

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Global stability and control of the confined turbulent flow past a thick flat plate

et al. 2017

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“…We note that a different approach could have been applied here, by performing the whole analysis around a turbulence model equation ('base flow approach'), such as Unsteady RANS with the Spalart-Allmaras model as in Meliga et al (2012b). In that case, the base flow would be a fixed point of the URANS equations, which approximates the mean flow within the limit of validity of the turbulence model.…”

Section: Eddy Viscosity Modelmentioning

confidence: 99%

“…Several sensitivity studies of turbulent flows have been performed recently. The base flow approach was used by for example Meliga et al (2012b) to compute the sensitivity of a turbulent (Re = 13000) flow around a D-shaped bluff body, using URANS equations combined with a linearized Spalart-Allmaras model. The most sensitive region for passive control was successfully matched against experiments.…”

Section: Introductionmentioning

confidence: 99%

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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Sensitivity analysis to unsteady perturbations of complex flows: a discrete approach

Browne

Rubio

Ferrer

et al. 2014

Numerical Methods in Fluids

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SUMMARYA discrete framework for computing the global stability and sensitivity analysis to external perturbations for any set of partial differential equations is presented. In particular, a complex‐step approximation is used to achieve near analytical accuracy for the evaluation of the Jacobian matrix. Sensitivity maps for the sensitivity to base flow modifications and to a steady force are computed to identify regions of the flow field where an input could have a stabilising effect. Four test cases are presented: (1) an analytical test case to prove the theory of the discrete framework, (2) a lid‐driven cavity at low Reynolds case to show the improved accuracy in the calculation of the eigenvalues when using the complex‐step approximation, (3) the 2D flow past a circular cylinder at just below the critical Reynolds number used to validate the methodology, and finally, (4) the flow past an open cavity presented to give an example of the discrete method applied to a convectively unstable case. The latter three (2–4) of the aforementioned cases were solved with the 2D compressible Navier–Stokes equations using a Discontinuous Galerkin Spectral Element Method. Good agreement was obtained for the validation test case, (3), with appropriate results in the literature. Furthermore, it is shown that for the calculation of the direct and adjoint eigenmodes and their sensitivity maps to external perturbations, the use of complex variables is paramount for obtaining an accurate prediction. Copyright © 2014 John Wiley & Sons, Ltd.

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Sensitivity of 2-D turbulent flow past a D-shaped cylinder using global stability

Cited by 79 publications

References 27 publications

Global stability and control of the confined turbulent flow past a thick flat plate

Global stability and control of the confined turbulent flow past a thick flat plate

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

Sensitivity analysis to unsteady perturbations of complex flows: a discrete approach

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