Secondary instability in forced wavelength Görtler vortices

Mitsudharmadi, Hatsari; Winoto, S. H.; Shah, D. A.

doi:10.1063/1.1941367

Cited by 17 publications

(17 citation statements)

References 20 publications

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“…This agrees with Schmid and Henningson (2001) who found that once the disturbance has reached a finite amplitude at which the boundary-layer flow is dominated by the mushroom-like structures, it often saturates and transforms the flow into a new possibly steady state in which secondary instabilities can grow. However, the spectrum analysis of the fluctuating component u′ shows that the secondary instabilities arise prior to the non-linear saturation as exhibited by the formation of the peak in the spectrum with a band between 50 to 200 Hz at the streamwise location, where the amplitude of the disturbance is still developing (Mitsudharmadi et al, 2005).…”

Section: Resultsmentioning

confidence: 99%

Visualizing Görtler vortices

Winoto

Mitsudharmadi

Shah

2005

J Vis

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The development of Görtler vortices with pre-set wavelength of 15 mm has been visualized in the boundary-layer on a concave surface of 2.0 m radius of curvature at a free-stream velocity of 3.0 m/s. The wavelength of vortices was pre-set by vertical wires of 0.2 mm diameter located 10 mm upstream of the concave surface leading edge. The velocity contours in the cross-sectional planes at several streamwise locations show the growth and breakdown of the vortices. Three different regions can be identified based on different growth rate of the vortices. The occurrence of a secondary instability mode is indicated by the formation of a small horseshoe eddies generated between the two neighboring vortices traveling streamwise, to form mushroom-like structures as a consequence of the non-linear growth of the Görtler vortices.

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Section: Resultsmentioning

confidence: 99%

Visualizing Görtler vortices

Winoto

Mitsudharmadi

Shah

2005

J Vis

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“…The three global spanwise wavenumbers cover the (quasi-) most amplified Görtler modes in all the five Mach numbers. In the incompressible case, these wavenumbers coincide with the wavelengths 36, 18 and 9 mm considered in Li & Malik (1995 Swearingen & Blackwelder (1987) and Mitsudharmadi, Winoto & Shah (2005), K = −0.94 × 10 −6 and −2.5 × 10 −6 , respectively. The flow parameters of all the cases are listed in table 1.…”

Section: Spatial Development Of Görtler Vorticesmentioning

confidence: 86%

Secondary instabilities of Görtler vortices in high-speed boundary layer flows

Ren

2015

J. Fluid Mech.

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Görtler vortices developed in laminar boundary layer experience remarkable changes when the flow is subjected to compressibility effects. In the present study, five Ma numbers, covering incompressible to hypersonic flows, at Ma = 0.015, 1.5, 3.0, 4.5 and 6.0 are specified to illustrate these effects. Görtler vortices in subsonic and moderate supersonic flows (Ma = 0.015, 1.5 and 3.0) are governed by the conventional wall-layer mode (mode W). In hypersonic flows (Ma = 4.5, 6.0), the trapped-layer mode (mode T) becomes dominant. This difference is maintained and intensifies downstream leading to different scenarios of secondary instabilities. The linear and nonlinear development of Görtler vortices which are governed by dominant modal disturbances are investigated with direct marching of the nonlinear parabolic equations. The secondary instabilities of Görtler vortices set in when the resulting streaks are adequately developed. They are studied with Floquet theory at multiple streamwise locations. The secondary perturbations become unstable downstream following the sequence of sinuous mode type I, varicose mode and sinuous mode type II, indicating an increasing threshold amplitude. Onset conditions are determined for these modes. The above three modes can each have the largest growth rate under the right conditions. In the hypersonic cases, the threshold amplitude A(u) is dramatically reduced, showing the significant impact of the thermal streaks. To investigate the parametric effect of the spanwise wavenumber, three global wavenumbers (B = 0.5, 1.0 and 2.0 × 10 −3 ) are specified. The relationship between the dominant mode (sinuous or varicose) and the spanwise wavenumber of Görtler vortices found in incompressible flows (Li & Malik, J. Fluid Mech., vol. 297, 1995, pp. 77-100) is shown to be not fully applicable in high-speed cases. The sinuous mode becomes the most dangerous, regardless of the spanwise wavelength when Ma > 3.0. The subharmonic type can be the most dangerous mode while the detuned type can be neglected, although some of the sub-dominant secondary modes reach their peak growth rates under detuned states.

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“…2͒ and apparatus used have been described in the previous work of Mitsudharmadi et al 3,16 However, a brief description of the experiment with the spanwise wire spacings of 7.5 and 30.0 mm will be given in the following. Six and thirteen vertical wires of 0.2 mm diameter are positioned at an upstream distance of 10.0 mm from the concave surface leading edge to provide wire spacing of 30.0 and 7.5 mm, respectively.…”

Section: Description Of Experimentsmentioning

confidence: 99%

“…Liu and Domaradzki 13 also found that sinuous waves were observed first, and varicose mode in the form of hairpin vortices appeared later downstream. However, the experimental studies of Bakchinov et al, 14 Swearingen and Blackwelder, 9 Matsson,15 and Mitsudharmadi et al 16 show that a development of fluctuations on the spanwise structure coincide with the region of high shear at the mushroom-like structures to imply that the secondary instability is of varicose type at the onset.…”

Section: Introductionmentioning

confidence: 96%

Splitting and merging of Görtler vortices

2005

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The splitting and merging of Görtler vortices are experimentally studied by varying the spacings of vertical wires located 10 mm upstream of a concave surface leading edge of 2.0 m radius of curvature subjected to a free-stream velocity of 3.0 m / s. The splitting and merging as the result of the linear instability of the vortices with respect to spanwise perturbation ͑Eckhaus instability͒, occurred when the wire spacing was set to respectively twice and half of the dominant or most amplified wavelength of Görtler vortices. These show the susceptibility of Görtler vortices to wavelengths greater and smaller than the most amplified wavelength of the vortices. The spectral study shows that the values of the dimensionless frequency parameter for the wire spacings of 7.5, 15.0, and 30.0 mm are nearly constant ͑of about 0.5͒ for the streamwise locations where the mushroom-like structures dominate the flow. It is also found that the dimensionless wavelength parameter is more sensitive than the Reynolds number of the vertical wires as a threshold identification of transition from one pair to two pairs of vortex configurations.

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Secondary instability in forced wavelength Görtler vortices

Cited by 17 publications

References 20 publications

Visualizing Görtler vortices

Visualizing Görtler vortices

Secondary instabilities of Görtler vortices in high-speed boundary layer flows

Splitting and merging of Görtler vortices

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