A Comparison Between Boundary Layer Measurements in a Laminar Separation Bubble Flow and Linear Stability Theory Calculations

1989 ◽  
pp. 189-205 ◽  
Author(s):  
P. LeBlanc ◽  
R. Blackwelder ◽  
R. Liebeck
Keyword(s):  
Boundary Layer ◽  
Linear Stability ◽  
Stability Theory ◽  
Separation Bubble ◽  
Linear Stability Theory ◽  
Bubble Flow ◽  
Laminar Separation Bubble ◽  
Laminar Separation

scholarly journals Response of a laminar separation bubble to impulsive forcing

2017 ◽  
Vol 820 ◽  
pp. 633-666 ◽  
Author(s):  
Theodoros Michelis ◽  
Serhiy Yarusevych ◽  
Marios Kotsonis
Keyword(s):  
Growth Rate ◽  
Wave Packet ◽  
Linear Stability ◽  
Stability Theory ◽  
Separation Bubble ◽  
Linear Stability Theory ◽  
Laminar Separation Bubble ◽  
Time Resolved ◽  
Laminar Separation ◽  
Response Characteristics

The spatial and temporal response characteristics of a laminar separation bubble to impulsive forcing are investigated by means of time-resolved particle image velocimetry and linear stability theory. A two-dimensional impulsive disturbance is introduced with an alternating current dielectric barrier discharge plasma actuator, exciting pertinent instability modes and ensuring flow development under environmental disturbances. Phase-averaged velocity measurements are employed to analyse the effect of imposed disturbances at different amplitudes on the laminar separation bubble. The impulsive disturbance develops into a wave packet that causes rapid shrinkage of the bubble in both upstream and downstream directions. This is followed by bubble bursting, during which the bubble elongates significantly, while vortex shedding in the aft part ceases. Duration of recovery of the bubble to its unforced state is independent of the forcing amplitude. Quasi-steady linear stability analysis is performed at each individual phase, demonstrating reduction of growth rate and frequency of the most unstable modes with increasing forcing amplitude. Throughout the recovery, amplification rates are directly proportional to the shape factor. This indicates that bursting and flapping mechanisms are driven by altered stability characteristics due to variations in incoming disturbances. The emerging wave packet is characterised in terms of frequency, convective speed and growth rate, with remarkable agreement between linear stability theory predictions and measurements. The wave packet assumes a frequency close to the natural shedding frequency, while its convective speed remains invariant for all forcing amplitudes. The stability of the flow changes only when disturbances interact with the shear layer breakdown and reattachment processes, supporting the notion of a closed feedback loop. The results of this study shed light on the response of laminar separation bubbles to impulsive forcing, providing insight into the attendant changes of flow dynamics and the underlying stability mechanisms.

Instability and low-frequency unsteadiness in a shock-induced laminar separation bubble

2016 ◽  
Vol 798 ◽  
pp. 5-26 ◽  
Author(s):  
Andrea Sansica ◽  
Neil D. Sandham ◽  
Zhiwei Hu
Keyword(s):  
Boundary Layer ◽  
Linear Stability ◽  
Flow Instability ◽  
Separation Bubble ◽  
Low Frequency ◽  
Boundary Layer Transition ◽  
Separation Point ◽  
Oblique Shock Wave ◽  
Laminar Separation Bubble ◽  
Laminar Separation

Three-dimensional direct numerical simulations (DNS) of a shock-induced laminar separation bubble are carried out to investigate the flow instability and origin of any low-frequency unsteadiness. A laminar boundary layer interacting with an oblique shock wave at $M=1.5$ is forced at the inlet with a pair of monochromatic oblique unstable modes, selected according to local linear stability theory (LST) performed within the separation bubble. Linear stability analysis is applied to cases with marginal and large separation, and compared to DNS. While the parabolized stability equations approach accurately reproduces the growth of unstable modes, LST performs less well for strong interactions. When the modes predicted by LST are used to force the separated boundary layer, transition to deterministic turbulence occurs near the reattachment point via an oblique-mode breakdown. Despite the clean upstream condition, broadband low-frequency unsteadiness is found near the separation point with a peak at a Strouhal number of $0.04$, based on the separation bubble length. The appearance of the low-frequency unsteadiness is found to be due to the breakdown of the deterministic turbulence, filling up the spectrum and leading to broadband disturbances that travel upstream in the subsonic region of the boundary layer, with a strong response near the separation point. The existence of the unsteadiness is supported by sensitivity studies on grid resolution and domain size that also identify the region of deterministic breakdown as the source of white noise disturbances. The present contribution confirms the presence of low-frequency response for laminar flows, similarly to that found in fully turbulent interactions.

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.

Stability and Transition Over a Low-Reynolds Number Airfoil

2016 ◽  
Author(s):  
Paul Ziadé ◽  
Pierre E. Sullivan
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Separation Bubble ◽  
Three Dimensional ◽  
Peak Frequency ◽  
Laminar Separation Bubble ◽  
Airfoil Surface ◽  
Laminar Separation

Large-eddy simulation and linear stability analysis were performed on a NACA 0025 airfoil at a chord Reynolds number of 105 and four angles of attack. The computations showed that the initial vortex roll-up quickly breaks down to three-dimensional turbulence. Flow separation was observed at all angles, whereas only the lowest angle of attack formed a laminar separation bubble due to flow transition occuring close to the airfoil surface. A Chebyshev collocation method was employed to solve the viscous and inviscid stability equations. Linear stability analysis demonstrated that high-frequency disturbances occur in the laminar separation bubble case, whereas lower frequencies are present for the fully separated angles of attack. The maximum disturbance growth rates were dampened with the addition of viscosity but negligible change in peak frequency was noted.

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