Three-dimensional linear stability analysis of incompressible viscous flows using the finite element method

Ding, Yan; Kawahara, Mutsuto

doi:10.1002/(sici)1097-0363(19990930)31:2<451::aid-fld885>3.0.co;2-o

Cited by 69 publications

(34 citation statements)

References 36 publications

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“…The uncertainty of the critical Reynolds number was of the order of magnitude of 1%. Despite the sparseness of reliable stability data, our results were validated by comparison with neutral-stability data of Ding and Kawahara [16,17] and by critical Reynolds numbers of Kuhlmann et al [33]. Additional confidence was gained from our own experimental results [2] and from the numerical work of Spasov et al [46] and Shatrov et al [43].…”

Section: Introductionsupporting

confidence: 93%

Accurate three-dimensional lid-driven cavity flow

Albensoeder

Kuhlmann

2005

Journal of Computational Physics

195

165

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Section: Introductionsupporting

confidence: 93%

Accurate three-dimensional lid-driven cavity flow

Albensoeder

Kuhlmann

2005

Journal of Computational Physics

195

165

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“…The symbols represent data from: Norberg, 1994 [20] (Q), Zebib, 1987 [21] (E), Pier, [22] 2001, (×), Williamson, [23] 1989 (P), Leweke and Provansal, [24] 1995 (+), Strykowski and Sreenivasan, [25] 1990 ( * ), Coutanceau and Bouard, [26] 1977 (! ), Elsenlhor and Eckelmann, [27] 1989 ("), Hammache and Gharib, [28] 1989 (2), Jackson, [29] 1987 (1), Ding and Kawahara, [30] 1999 (F), Morzynski et al, [31] 1999 (e), Kumar and Mittal, [32] 2006 (a). The solid line in parts (b) and (d) indicates the median value (R cr ≈ 46.6) of these data.…”

Section: Discussionsupporting

confidence: 86%

The first as a possible measure of the entrainment length in a 2D steady wake

Tordella

Scarsoglio

2009

Physics Letters A

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At a fixed distance from the body which creates the wake, entrainment is only seen to increase with the Reynolds number (R) up to a distance of almost 20 body scales. This increase levels up to a Reynolds number close to the critical value for the onset of the first instability. The entrainment is observed to be almost extinguished at a distance which is nearly the same for all the steady wakes within the R range here considered, i.e. , which indicates that supercritical steady wakes have the same entrainment length as the subcritiacal ones. It is observed that this distance is equal to a number of body lengths that is equal to the value of the critical Reynolds number (∼ 47), as indicated by a large compilation of experimental results. A fortiori of these findings, we propose to interpret the unsteady bifurcation as a process that allows a smooth increase-redistribution of the entrainment along the wake according to the weight of the convection over the diffusion. The entrainment variation along the steady wake has been determined using a matched asymptotic expansion of the Navier-Stokes velocity field [D. Tordella, M. Belan, Phys. Fluids 15 (7) (2003) 1897] built on criteria that include the matching of the transversal velocity produced by the entrainment process.

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“…The latter scales linearly with the Krylov subspace dimension. As experienced in previous studies [18], only eigenvalues with large modules can be obtained by a straightforward application of the algorithm. A shift-invert transformation in the Arnoldi algorithm is required to accurately capture the region of the complex plane where the unstable eigenvalues live.…”

Section: Direct Problemmentioning

confidence: 99%

“…A full LU factorization is performed for the Jacobian matrix A. This strategy, used here in a compressible finite volume context, has also been followed in Biglobal computations of incompressible flows in finite elements discretizations [18,19] and in the context of spectral methods [20,21]. The full LU decomposition consumes a large amount of RAM memory.…”

Section: Direct Problemmentioning

confidence: 99%

Direct and adjoint global stability analysis of turbulent transonic flows over a NACA0012 profile

Iorio

González

Ferrer

2014

Numerical Methods in Fluids

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SUMMARYIn this work, various turbulent solutions of the two-dimensional (2D) and three-dimensional compressible Reynolds averaged Navier-Stokes equations are analyzed using global stability theory. This analysis is motivated by the onset of flow unsteadiness (Hopf bifurcation) for transonic buffet conditions where moderately high Reynolds numbers and compressible effects must be considered. The buffet phenomenon involves a complex interaction between the separated flow and a shock wave. The efficient numerical methodology presented in this paper predicts the critical parameters, namely, the angle of attack and Mach and Reynolds numbers beyond which the onset of flow unsteadiness appears. The geometry, a NACA0012 profile, and flow parameters selected reproduce situations of practical interest for aeronautical applications.The numerical computation is performed in three steps. First, a steady baseflow solution is obtained; second, the Jacobian matrix for the RANS equations based on a finite volume discretization is computed; and finally, the generalized eigenvalue problem is derived when the baseflow is linearly perturbed. The methodology is validated predicting the 2D Hopf bifurcation for a circular cylinder under laminar flow condition. This benchmark shows good agreement with the previous published computations and experimental data.In the transonic buffet case, the baseflow is computed using the Spalart-Allmaras turbulence model and represents a mean flow where the high frequency content and length scales of the order of the shear-layer thickness have been averaged. The lower frequency content is assumed to be decoupled from the high frequencies, thus allowing a stability analysis to be performed on the low frequency range. In addition, results of the corresponding adjoint problem and the sensitivity map are provided for the first time for the buffet problem. Finally, an extruded three-dimensional geometry of the NACA0012 airfoil, where all velocity components are considered, was also analyzed as a Triglobal stability case, and the outcoming results were compared to the previous 2D limited model, confirming that the buffet onset is well detected.

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Three-dimensional linear stability analysis of incompressible viscous flows using the finite element method

Cited by 69 publications

References 36 publications

Accurate three-dimensional lid-driven cavity flow

Accurate three-dimensional lid-driven cavity flow

The first as a possible measure of the entrainment length in a 2D steady wake

Direct and adjoint global stability analysis of turbulent transonic flows over a NACA0012 profile

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