Identification and Analysis of Nonlinear Transition Scenarios using NOLOT/PSE

Hein, Stefan; Stolte, A.; Dallmann, U.

doi:10.1002/zamm.19990791329

Cited by 3 publications

(3 citation statements)

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“…The respective theoretical concepts are referred to as biglobal, triglobal, and parabolized stability equation three-dimensional (PSE-3D) analyses. Table 1 classifies and refines the different kinds of linear stability theory, demarcating the boundaries between local analysis based on variants of the Orr-Sommerfeld equation (OSE), nonlocal analysis based on the standard PSEs [26][27][28], which represent a generalization of the parallel-flow LST for flows with a mild variation on the streamwise direction, and the three aforementioned versions of global linear theory; symbols appearing will be defined shortly.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

Four Decades of Studying Global Linear Instability: Progress and Challenges

et al. 2012

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Global linear instability theory is concerned with the temporal or spatial development of small-amplitude perturbations superposed upon laminar steady or time-periodic three-dimensional flows, which are inhomogeneous in two (and periodic in one) or all three spatial directions. After a brief exposition of the theory, some recent advances are reported. First, results are presented on the implementation of a Jacobian-free Newton-Krylov time-stepping method into a standard finite-volume aerodynamic code to obtain global linear instability results in flows of industrial interest Second, connections are sought between established and more-modern approaches for structure identification in flows, such as proper orthogonal decomposition and Koopman modes analysis (dynamic mode decomposition), and the possibility to connect solutions of the eigenvalue problem obtained by matrix formation or time-stepping with those delivered by dynamic mode decomposition, residual algorithm, and proper orthogonal decomposition analysis is highlighted in the laminar regime; turbulent and three-dimensional flows are identified as open areas for future research. Finally, a new stable very-high-order finite-difference method is implemented for the spatial discretization of the operators describing the spatial biglobal eigenvalue problem, parabolized stability equation three-dimensional analysis, and the triglobal eigenvalue problem; it is shown that, combined with sparse matrix treatment, all these problems may now be solved on standard desktop computers.

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Section: Theoretical Considerationsmentioning

confidence: 99%

Four Decades of Studying Global Linear Instability: Progress and Challenges

et al. 2012

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“…In both cases the overall growth n-factors are very small ͑corresponding to only a factor of 10 growth in amplitude͒ even though the second modes are locally the most unstable modes. Nonparallel effects are important in the current problem and simulations have therefore been made using the parabolized stability equations ͑see Herbert, 10 Hein et al 11 ͒. The equation set in this case is given by…”

Section: -11mentioning

confidence: 99%

“…The parabolized stability equations ͑PSE; see Herbert, 10 Hein et al 11 ͒ approach improves on the e n method ͑Arnal and Casalis, 12 Stock 13 ͒ by including nonparallel terms and allowing for the streamwise evolution of disturbance shape functions. The method is applicable to convectively unstable flow but, although widely used for transition prediction on wings, it does not appear to have been applied to SBLI until now.…”

Section: Introductionmentioning

confidence: 99%

The effect of Mach number on unstable disturbances in shock/boundary-layer interactions

et al. 2007

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The effect of Mach number on the growth of unstable disturbances in a boundary layer undergoing a strong interaction with an impinging oblique shock wave is studied by direct numerical simulation and linear stability theory ͑LST͒. To reduce the number of independent parameters, test cases are arranged so that both the interaction location Reynolds number ͑based on the distance from the plate leading edge to the shock impingement location for a corresponding inviscid flow͒ and the separation bubble length Reynolds number are held fixed. Small-amplitude disturbances are introduced via both white-noise and harmonic forcing and, after verification that the disturbances are convective in nature, linear growth rates are extracted from the simulations for comparison with parallel flow LST and solutions of the parabolized stability equations ͑PSE͒. At Mach 2.0, the oblique modes are dominant and consistent results are obtained from simulation and theory. At Mach 4.5 and Mach 6.85, the linear Navier-Stokes results show large reductions in disturbance energy at the point where the shock impinges on the top of the separated shear layer. The most unstable second mode has only weak growth over the bubble region, which instead shows significant growth of streamwise structures. The two higher Mach number cases are not well predicted by parallel flow LST, which gives frequencies and spanwise wavenumbers that are significantly different from the simulations. The PSE approach leads to good qualitative predictions of the dominant frequency and wavenumber at Mach 2.0 and 4.5, but suffers from reduced accuracy in the region immediately after the shock impingement. Three-dimensional Navier-Stokes simulations are used to demonstrate that at finite amplitudes the flow structures undergo a nonlinear breakdown to turbulence. This breakdown is enhanced when the oblique-mode disturbances are supplemented with unstable Mack modes.

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Exponential vs Algebraic Growth and Transition Prediction in Boundary Layer Flow

Levin

Henningson

2003

Flow, Turbulence and Combustion

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Identification and Analysis of Nonlinear Transition Scenarios using NOLOT/PSE

Cited by 3 publications

References 1 publication

Four Decades of Studying Global Linear Instability: Progress and Challenges

Four Decades of Studying Global Linear Instability: Progress and Challenges

The effect of Mach number on unstable disturbances in shock/boundary-layer interactions

Exponential vs Algebraic Growth and Transition Prediction in Boundary Layer Flow

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