Instability and transition mechanisms induced by skewed roughness elements in a high-speed laminar boundary layer

2016 ◽  
Vol 805 ◽  
pp. 262-302 ◽  
Author(s):  
Gordon Groskopf ◽  
Markus J. Kloker
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Linear Stability ◽  
Stability Theory ◽  
High Speed ◽  
Roughness Element ◽  
Linear Stability Theory ◽  
Minor Importance ◽  
Roughness Elements ◽  
Second Mode

The disturbance evolution in a Mach-4.8 zero-pressure-gradient flat-plate boundary-layer flow altered by discrete three-dimensional roughness elements is investigated including a laminar breakdown scenario. Direct numerical simulation (DNS), as well as the biglobal linear stability theory based on two-dimensional eigenfunctions in flow cross-sections, are applied. Roughness elements with high ratios of spanwise width to streamwise length are compared at varying height and skewing angles with respect to the oncoming flow. For an oblique roughness, the element’s height is varied between 27 % and 68 % of the undisturbed boundary-layer thickness. Compared to a symmetric roughness element an obliquely placed element generates a more pronounced low-speed streak in the roughness wake. The linear stability analysis reveals the occurrence of eigenmodes that can be associated with the first and second modes in the flat-plate flow. At identical roughness height, larger amplification is found for the eigenmodes of the oblique set-up. The results are confirmed by unsteady DNS showing very good agreement with stability theory; transient-growth behaviour in the near wake of the roughness is of minor importance. The comparison of the results gained for adiabatic wind-tunnel flow conditions with those for atmospheric-flight conditions with wall cooling reveals significant differences in the wake vortex system with subsequent impact on the stability properties of the flow. The hot-flow cases are less unstable at identical roughness Reynolds numbers. A variation of the wall cooling shows that the roughness-wake first- and second-mode behaviour is similar to that of the flat-plate flow: wall cooling stabilizes the first-mode and destabilizes the second-mode instabilities of the roughness wake.

The development of a two-dimensional wavepacket in a growing boundary layer

1982 ◽  
Vol 384 (1787) ◽  
pp. 317-332 ◽  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Linear Stability ◽  
Stability Theory ◽  
Linear Stability Theory ◽  
Two Dimensional ◽  
Displacement Thickness ◽  
Power Comparisons ◽  
The One ◽  
Half Power

The evolution of a two-dimensional wavepacket in a growing boundary layer is discussed in terms of linear stability theory. The wavepacket is represented by an integral of periodic wavetrains, each of which is defined as a series in terms of the inverse of the local displacement thickness Reynolds number to the one half power. Comparisons are made between the waveforms computed directly from the integral, a steepest-descent expansion of the integral, and a global expansion about the peak of the wavepacket.

On the evolution of a wave packet in a laminar boundary layer

1991 ◽  
Vol 225 ◽  
pp. 575-606 ◽  
Author(s):  
Jacob Cohen ◽  
Kenneth S. Breuer ◽  
Joseph H. Haritonidis
Keyword(s):  
Boundary Layer ◽  
Wave Packet ◽  
Linear Stability ◽  
Laminar Boundary Layer ◽  
Stability Theory ◽  
Free Stream ◽  
Linear Stability Theory ◽  
Stream Velocity ◽  
Turbulent Spot ◽  
Second Stage

The transition process of a small-amplitude wave packet, generated by a controlled short-duration air pulse, to the formation of a turbulent spot is traced experimentally in a laminar boundary layer. The vertical and spanwise structures of the flow field are mapped at several downstream locations. The measurements, which include all three velocity components, show three stages of transition. In the first stage, the wave packet can be treated as a superposition of two- and three-dimensional waves according to linear stability theory, and most of the energy is centred around a mode corresponding to the most amplified wave. In the second stage, most of the energy is transferred to oblique waves which are centred around a wave having half the frequency of the most amplified linear mode. During this stage, the amplitude of the wave packet increases from 0.5 % to 5 % of the free-stream velocity. In the final stage, a turbulent spot develops and the amplitude of the disturbance increases to 27 % of the free-stream velocity.Theoretical aspects of the various stages are considered. The amplitude and phase distributions of various modes of all three velocity components are compared with the solutions provided by linear stability theory. The agreement between the theoretical and measured distributions is very good during the first two stages of transition. Based on linear stability theory, it is shown that the two-dimensional mode of the streamwise velocity component is not necessarily the most energetic wave. While linear stability theory fails to predict the generation of the oblique waves in the second stage of transition, it is demonstrated that this stage appears to be governed by Craik-type subharmonic resonances.

Experimental Extraction of Linear Disturbance in a Two-Dimensional Turbulent Jet and Comparison to a Linear Stability Theory

2011 ◽  
Author(s):  
Shun Tazoe ◽  
Ayako Kawanishi ◽  
Masaharu Matsubara
Keyword(s):  
Linear Stability ◽  
Stability Theory ◽  
High Speed ◽  
Large Scale ◽  
Turbulent Jet ◽  
Initial Disturbance ◽  
Linear Stability Theory ◽  
Experimental Result ◽  
Two Dimensional ◽  
Large Scale Disturbance

In a two-dimensional turbulent jet, there exists a lateral vibration of the high-speed jet core. In the present study, a periodic initial disturbance is introduced into fully developed turbulent jet from a slot mounted at a duct exit in order to control this vibration. The streamwise and lateral velocity fluctuations are measured with an anemometer with an X-type probe, and are filtered using a phase ensemble average technique based on the periodic initial disturbance. This vibration enables extraction of the fluctuation of the synchronized disturbance and restruction of its velocity field. The experimental result shows that the streamwise variation of the extracted amplitude draws a characteristic growth curve that has the exponential growth at the upstream and slow decay parts at the downstream. It is worth noticing that within a certain amplitude of the initial disturbance the growth curves are identical as well as the spatial distribution of the extracted fluctuations. Furthermore the disturbance amplitude is directly proportional to the intensity of the initial disturbance. A linear stability theory with parallel flow assumption well captures futures of the lateral disturbance. This apparent linearity of the disturbance keeps until the average velocity and the total velocity fluctuation starts to vary with sufficient amplitude of the disturbance. The existence of the linear mode in the turbulent jet implies that the large-scale disturbance can be regarded as an incoherent set of the linear modes.

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