Spatial Direct Numerical Simulation of Transition in a Three-Dimensional Boundary Layer

Müller, W.; Bestek, H.; Fasel, Hermann F.

doi:10.1007/978-3-642-79765-1_47

Cited by 7 publications

(5 citation statements)

References 5 publications

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“…5(a), and indicate that the steady mode does not change in magnitude in the downstream direction, at least for 0 > 65 °. This saturation of the steady disturbance has already been observed by Bippes et al (1991) at an earlier stage of three-dimensional flate plate boundary layer with a displacement body in an environment with a quite high freestream turbulence; and by Miiller et al (1995) Fig. 6.…”

Section: Development Of Steady Modesupporting

confidence: 64%

Dispersive evolution of crossflow disturbances excited by an airjet column in a three-dimensional boundary layer

Takagi¹,

Itoh²

1998

Fluid Dyn. Res.

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An experimental study is made to show that dispersive properties of disturbances originating from a point source lead to the separate appearance of stationary vortices and travelling waves of the crossflow instability in a three-dimensional boundary layer. The spatial development of disturbances induced by a weak airjet issuing from a small surface hole near the attachment line of a yawed circular cylinder is observed at several downstream stations. Experimental results show that the disturbances evolve into a wedge-shaped distribution, which includes both stationary and nonstationary modes of the crossflow instability. The observed behavior of those disturbances is shown to be in fairly good agreement with recent results of a linear stability theory based on the method of complex characteristics, although there are some incongruities in frequency and growth rate of the most unstable disturbances. The experiment also shows the existence of a new instability due to the curvature of external streamlines, which was simultaneously predicted by the theory.

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Section: Development Of Steady Modesupporting

confidence: 64%

Dispersive evolution of crossflow disturbances excited by an airjet column in a three-dimensional boundary layer

Takagi¹,

Itoh²

1998

Fluid Dyn. Res.

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“…In the DNS analyses of Wagner (1992) and Muller et al (1994), as well as in the nonlinear PSE analysis of Malik & Chang (1994), the same phenomenon is predicted as being due to additional Fourier modes generated from interaction between a primary steady and unsteady modes. This is illustrated in figure 12 which compares the spanwise variation of the r.m.s.…”

Section: Resultsmentioning

confidence: 62%

“…Comparison with Muller's experiment revealed that the secondary theory can explain the features observed in the experiment although the tests were performed in a parameter range which is at the limit of the applicability of the theoretical model. It should be noted that the direct numerical simulations of Meyer & Kleiser (1989), Wagner (1992) and Muller, Bestek & Fasel (1994) (for more details see the thesis of W. Muller 1995) not only reproduce the early beginning of nonlinear development but also the strong dependence upon the initial conditions. The nonlinear parabolized stability equations (PSE) analysis by Malik, Li & Chang (1994) for swept wing flow leads to the same conclusions.…”

Section: Discussion Of Previous Results Motivating the Present Workmentioning

confidence: 98%

Disturbance growth in an unstable three-dimensional boundary layer and its dependence on environmental conditions

1996

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Experimental investigations in the three-dimensional boundary layer of a swept flat plate with the pressure gradient induced from outside are aimed at enhancing knowledge of the transition process in the presence of pure crossflow instability. The development of disturbances is characterized by the occurrence of both stationary and travelling instability modes, by early nonlinear development and by complex dependence upon the environmental conditions. Experiments under natural conditions of transition showed a good correspondence of the identified modes with those predicted by local linear stability theory. The disturbance growth, however, is generally overpredicted. Controlled excitation of crossflow vortices allowing measurements closer to the linear range of amplification confirmed this result. Nonlinear effects such as interaction between stationary disturbances and base flow and between travelling and stationary modes have already been observed when the naturally excited instabilities become of measurable size.The most striking feature of the disturbance development is the complex dependence on initial conditions. Experiments under systematically varied environments showed that surface roughness represents the key parameter responsible for the initiation of stationary crossflow vortices. In contrast to two-dimensional boundary layers, free-stream turbulence influences the transition process indirectly. Only for turbulence levels Tu > 0.2% and smooth surfaces do the travelling instability waves dominate. The location of the final breakdown of laminar flow is clearly determined by the saturation amplitude of crossflow vortices. The receptivity to sound, two-dimensional surface roughness and non-uniformities of the test-section mean flow was found to be very weak.

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“…Meyer & Kleiser (1988) or Meyer (1989), spatial DNS, cf. Joslin & Streett (1994), Müller (1995) or Müller, Bestek & Fasel (1995) and PSE computations, cf. Bertolotti (1996) or Janke & Balakumar (1998a).…”

Section: Laminar Base Flowmentioning

confidence: 99%

Nonlinear equilibrium solutions in a three-dimensional boundary layer and their secondary instability

Koch¹,

Bertolotti²,

Stolte³

et al. 2000

J. Fluid Mech.

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The observed nonlinear saturation of crossflow vortices in the DLR swept-plate transition experiment, followed by the onset of high-frequency signals, motivated us to compute nonlinear equilibrium solutions for this flow and investigate their instability to high-frequency disturbances. The equilibrium solutions are independent of receptivity, i.e. the way crossflow vortices are generated, and thus provide a unique characterization of the nonlinear flow prior to turbulence. Comparisons of these equilibrium solutions with experimental measurements exhibit strong similarities. Additional comparisons with results from the nonlinear parabolized stability equations (PSE) and spatial direct numerical simulations (DNS) reveal that the equilibrium solutions become unstable to steady, spatial oscillations with very long wavelengths following a bifurcation close to the leading edge. Such spatially oscillating solutions have been observed also in critical layer theory computations. The nature of the spatial behaviour is herein clarified and shown to be analogous to that encountered in temporal direct numerical simulations. We then employ Floquet theory to systematically study the dependence of the secondary, high-frequency instabilities on the saturation amplitude of the equilibrium solutions. With increasing amplitude, the most amplified instability mode can be clearly traced to spanwise inflectional shear layers that occur in the wake-like portions of the equilibrium solutions (Malik et al. 1994 call it ‘mode I’ instability). Both the frequency range and the eigenfunctions resemble recent experimental measurements of Kawakami et al. (1999). However, the lack of an explosive growth leads us to believe that additional self-sustaining processes are active at transition, including the possibility of an absolute instability of the high-frequency disturbances.

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Spatial Direct Numerical Simulation of Transition in a Three-Dimensional Boundary Layer

Cited by 7 publications

References 5 publications

Dispersive evolution of crossflow disturbances excited by an airjet column in a three-dimensional boundary layer

Dispersive evolution of crossflow disturbances excited by an airjet column in a three-dimensional boundary layer

Disturbance growth in an unstable three-dimensional boundary layer and its dependence on environmental conditions

Nonlinear equilibrium solutions in a three-dimensional boundary layer and their secondary instability

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