Bi-global Linear Stability Analysis of Laminar Separation Bubble for Helicopter Blade Section Undergoing Dynamic Stall

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

Journal of Fluid Mechanics ◽

10.1017/jfm.2016.297 ◽

2016 ◽

Vol 798 ◽

pp. 5-26 ◽

Cited By ~ 16

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.

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Numerical investigation of the flow over a model transonic turbine blade tip

Journal of Fluid Mechanics ◽

10.1017/jfm.2016.478 ◽

2016 ◽

Vol 803 ◽

pp. 119-143 ◽

Cited By ~ 5

Author(s):

Andrew P. S. Wheeler ◽

Richard D. Sandberg

Keyword(s):

Stability Analysis ◽

Linear Stability ◽

Turbine Blade ◽

Linear Stability Analysis ◽

Free Stream ◽

Separation Bubble ◽

Pressure Side ◽

Blade Tip ◽

Gap Height ◽

Flow Reattachment

Direct numerical simulations (DNS) are used to investigate the unsteady flow over a model turbine blade tip at engine-scale Reynolds and Mach numbers. The DNS are performed with an in-house multiblock structured compressible Navier–Stokes solver. The particular case of a transonic tip flow is studied since previous work has suggested that compressibility has an important effect on the turbulent nature of the separation bubble at the inlet to the tip–casing gap and subsequent flow reattachment. The flow is simulated over an idealized tip geometry where the tip gap is represented by a constant-area channel with a sharp inlet corner to represent the pressure side edge of the turbine blade. The effects of free-stream disturbances, cross-flow and the pressure side boundary layer on the tip flow aerodynamics and heat transfer are studied. For ‘clean’ inflow cases we find that even at engine-scale Reynolds numbers the tip flow is intermittent in nature, i.e. neither laminar nor fully turbulent. The breakdown to turbulence occurs through the development of spanwise streaks with wavelengths of approximately 15 %–20 % of the gap height. Multidimensional linear stability analysis confirms the two-dimensional base state to be most unstable with respect to spanwise wavelengths of 25 % of the gap height. The linear stability analysis also shows that the addition of cross-flows with 25 % of the streamwise gap exit velocity increases the stability of the tip flow. This is confirmed by the DNS, which also show that the turbulence production is significantly reduced in the separation bubble. For the case when free-stream disturbances are added to the inlet flow, viscous dissipation and the rapid acceleration of the flow at the inlet to the tip–casing gap cause significant distortion of the vorticity field and reductions of turbulence intensity as the flow enters the tip gap. The DNS results also suggest that the assumption of the Reynolds analogy and a constant recovery factor are not accurate, in particular in regions where the skin friction approaches zero while significant temperature gradients remain, such as in the vicinity of flow reattachment.

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Modeling and Control of Dynamic Stall Loads on a Smart Airfoil at Low Reynolds Number

Energies ◽

10.3390/en14164958 ◽

2021 ◽

Vol 14 (16) ◽

pp. 4958

Author(s):

Ayman Mohamed ◽

David Wood ◽

Jeffery Pieper

Keyword(s):

Reynolds Number ◽

Separation Bubble ◽

Separated Flow ◽

Dynamic Stall ◽

Laminar Separation Bubble ◽

Real Time Control ◽

Trailing Edge ◽

Laminar Separation ◽

Modeling And Control ◽

Trailing Edge Flap

This article describes the development and testing of a modified, semi-empirical ONERA dynamic stall model for an airfoil with a trailing edge flap—a “smart airfoil”—pitching at reduced frequencies up to 0.1. The Reynolds number is 105. The model reconstructs the load fluctuations associated with the shedding of multiple dynamic stall vortices (DSVs) in a time-marching solution, which makes it suitable for real-time control of a trailing edge flap (TEF). No other model captures the effect of the DSVs on the aerodynamic loads on smart airfoils. The model was refined and tuned for force measurements on a smart NACA 643-618 airfoil model that was pitching with an inactive TEF and was validated against the measurements when the TEF was activated. A substantial laminar separation bubble can develop on this airfoil, which is challenging for modelers of the unsteady response. A closed-loop controller was designed offline in SIMULINK, and the output of the controller was applied to the TEF in a wind tunnel. The results indicated that the model has a comparable accuracy for predicting loads with the active TEF compared to inactive TEF loads. In the fully separated flow regime, the controller performed worse when dealing with the development of the laminar separation bubble and DSVs.

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

Lecture Notes in Engineering - Low Reynolds Number Aerodynamics ◽

10.1007/978-3-642-84010-4_15 ◽

1989 ◽

pp. 189-205 ◽

Cited By ~ 12

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

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Response of a laminar separation bubble to impulsive forcing

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.217 ◽

2017 ◽

Vol 820 ◽

pp. 633-666 ◽

Cited By ~ 17

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.

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