Optimal suppression of a separation bubble in a laminar boundary layer

Separation bubbles in high-camber blades under part-load conditions have been addressed via continuous and pulsed jets, and also via plasma actuators. Numerous passive techniques have been employed as well. In this type of blades, the laminar boundary layer cannot overcome the adverse pressure gradient arising along the suction side, resulting on a separation bubble. When separation is abated, a common explanation is that kinetic energy added to the laminar boundary layer speeds up its transition to turbulent. In the present study, a plasma actuator installed in the trailing edge (i.e. “wake filling configuration”) of a cascade blade is used to excite the flow in pulsed and continuous ways. The pulsed excitation can be directed to the frequencies of the large coherent structures (LCS) of the flow, as obtained via a hot-film anemometer, or to much higher frequencies present in the suction-side boundary layer, as given in the literature. It is found that pulsed frequencies much higher than that of LCS reduce losses and improve turning angles further than frequencies close to those of LCS. With the plasma actuator 50% on time, good loss abatement is obtained. Larger “on time” values yield improvements, but with decreasing returns. Continuous high-frequency activation results in the largest loss reduction, at increased power cost. The effectiveness of high frequencies may be due to separation abatement via boundary layer excitation into transition, or may simply be due to the creation of a favorable pressure gradient that averts separation as the actuator ejects fluid downstream. Both possibilities are discussed in light of the experimental evidence.

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Development of a laminar boundary layer under conditions of continuous incipient separation

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s030821050001948x ◽

1976 ◽

Vol 76 (1) ◽

pp. 55-66 ◽

Cited By ~ 2

Author(s):

N. Curle

Keyword(s):

Boundary Layer ◽

Pressure Distribution ◽

Laminar Boundary Layer ◽

Shape Parameter ◽

Uniform Pressure ◽

Continuous Change ◽

Similar Series ◽

Image Position ◽

Incipient Separation

SynopsisThis paper, extending the work of Stratford [6] considers a boundary layer with uniform pressure when x < x0, and with the pressure in x > x0 so chosen that the layer is just on the point of separation for all x >x0. The required pressure distribution is shown to beThe displacement and momentum thicknesses are also derived as series in powers of ξ (and log ξ), and the shape parameter H then obtained as a similar series. The continuous change in H from the Blasius value (when ξ = 0) towards the Falkner-Skan [3] separation value is convincingly demonstrated, with the aid of the leading terms of an asymptomatic expansion for large ξ.

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The impact of dynamic roughness elements on marginally separated boundary layers

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.589 ◽

2018 ◽

Vol 855 ◽

pp. 351-370

Author(s):

P. Servini ◽

F. T. Smith ◽

A. P. Rothmayer

Keyword(s):

Boundary Layer ◽

Laminar Boundary Layer ◽

Separation Bubble ◽

Roughness Element ◽

Angle Of Attack ◽

Dynamic Roughness ◽

Separation Theory ◽

Roughness Elements ◽

Maximum Angle ◽

The Impact

It has been shown experimentally that dynamic roughness elements – small bumps embedded within a boundary layer, oscillating at a fixed frequency – are able to increase the angle of attack at which a laminar boundary layer will separate from the leading edge of an airfoil (Grager et al., in 6th AIAA Flow Control Conference, 2012, pp. 25–28). In this paper, we attempt to verify that such an increase is possible by considering a two-dimensional dynamic roughness element in the context of marginal separation theory, and suggest the mechanisms through which any increase may come about. We will show that a dynamic roughness element can increase the value of $\unicode[STIX]{x1D6E4}_{c}$ as compared to the clean airfoil case; $\unicode[STIX]{x1D6E4}_{c}$ represents, mathematically, the critical value of the parameter $\unicode[STIX]{x1D6E4}$ below which a solution exists in the governing equations and, physically, the maximum angle of attack possible below which a laminar boundary layer will remain predominantly attached to the surface. Furthermore, we find that the dynamic roughness element impacts on the perturbation pressure gradient in two possible ways: either by decreasing the magnitude of the adverse pressure peak or by increasing the streamwise extent in which favourable pressure perturbations exist. Finally, we discover that the marginal separation bubble does not necessarily have to exist at $\unicode[STIX]{x1D6E4}=\unicode[STIX]{x1D6E4}_{c}$ in the time-averaged flow and that full breakaway separation can therefore occur as a result of the bursting of transient bubbles existing within the length scale of marginal separation theory.

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Heat and momentum transfer to a particle in a laminar boundary layer

Journal of Fluid Mechanics ◽

10.1017/jfm.2020.45 ◽

2020 ◽

Vol 889 ◽

Cited By ~ 1

Author(s):

Aaron M. Lattanzi ◽

Xiaolong Yin ◽

Christine M. Hrenya

Keyword(s):

Boundary Layer ◽

Momentum Transfer ◽

Laminar Boundary Layer ◽

Image Position ◽

Heat And Momentum Transfer

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An Experimental Study of the Laminar Flow Separation on a Low-Reynolds-Number Airfoil

Journal of Fluids Engineering ◽

10.1115/1.2907416 ◽

2008 ◽

Vol 130 (5) ◽

Cited By ~ 56

Author(s):

Hui Hu ◽

Zifeng Yang

Keyword(s):

Boundary Layer ◽

Pressure Gradient ◽

Laminar Boundary Layer ◽

Flow Separation ◽

Separation Bubble ◽

Adverse Pressure Gradient ◽

Laminar Separation Bubble ◽

Airfoil Surface ◽

Laminar Separation ◽

Turbulence Transition

An experimental study was conducted to characterize the transient behavior of laminar flow separation on a NASA low-speed GA (W)-1 airfoil at the chord Reynolds number of 70,000. In addition to measuring the surface pressure distribution around the airfoil, a high-resolution particle image velocimetry (PIV) system was used to make detailed flow field measurements to quantify the evolution of unsteady flow structures around the airfoil at various angles of attack (AOAs). The surface pressure and PIV measurements clearly revealed that the laminar boundary layer would separate from the airfoil surface, as the adverse pressure gradient over the airfoil upper surface became severe at AOA≥8.0deg. The separated laminar boundary layer was found to rapidly transit to turbulence by generating unsteady Kelvin–Helmholtz vortex structures. After turbulence transition, the separated boundary layer was found to reattach to the airfoil surface as a turbulent boundary layer when the adverse pressure gradient was adequate at AOA<12.0deg, resulting in the formation of a laminar separation bubble on the airfoil. The turbulence transition process of the separated laminar boundary layer was found to be accompanied by a significant increase of Reynolds stress in the flow field. The reattached turbulent boundary layer was much more energetic, thus more capable of advancing against an adverse pressure gradient without flow separation, compared to the laminar boundary layer upstream of the laminar separation bubble. The laminar separation bubble formed on the airfoil upper surface was found to move upstream, approaching the airfoil leading edge as the AOA increased. While the total length of the laminar separation bubble was found to be almost unchanged (∼20% of the airfoil chord length), the laminar portion of the separation bubble was found to be slightly stretched, and the turbulent portion became slightly shorter with the increasing AOA. After the formation of the separation bubble on the airfoil, the increase rate of the airfoil lift coefficient was found to considerably degrade, and the airfoil drag coefficient increased much faster with increasing AOA. The separation bubble was found to burst suddenly, causing airfoil stall, when the adverse pressure gradient became too significant at AOA>12.0deg.

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Direct numerical simulation of ‘short’ laminar separation bubbles with turbulent reattachment

Journal of Fluid Mechanics ◽

10.1017/s0022112099007119 ◽

2000 ◽

Vol 403 ◽

pp. 223-250 ◽

Cited By ~ 104

Author(s):

M. ALAM ◽

N. D. SANDHAM

Keyword(s):

Numerical Simulation ◽

Boundary Layer ◽

Direct Numerical Simulation ◽

Laminar Boundary Layer ◽

Stokes Equations ◽

Separation Bubble ◽

Three Dimensional ◽

Wall Turbulence ◽

Mean Flow ◽

Laminar Separation

Direct numerical simulation of the incompressible Navier-Stokes equations is used to study flows where laminar boundary-layer separation is followed by turbulent reattachment forming a closed region known as a laminar separation bubble. In the simulations a laminar boundary layer is forced to separate by the action of a suction profile applied as the upper boundary condition. The separated shear layer undergoes transition via oblique modes and Λ-vortex-induced breakdown and reattaches as turbulent flow, slowly recovering to an equilibrium turbulent boundary layer. Compared with classical experiments the computed bubbles may be classified as ‘short’, as the external potential flow is only affected in the immediate vicinity of the bubble. Near reattachment budgets of turbulence kinetic energy are dominated by turbulence events away from the wall. Characteristics of near-wall turbulence only develop several bubble lengths downstream of reattachment. Comparisons are made with two-dimensional simulations which fail to capture many of the detailed features of the full three-dimensional simulations. Stability characteristics of mean flow profiles are computed in the separated flow region for a family of velocity profiles generated using simulation data. Absolute instability is shown to require reverse flows of the order of 15–20%. The three-dimensional bubbles with turbulent reattachment have maximum reverse flows of less than 8% and it is concluded that for these bubbles the basic instability is convective in nature.

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On Similar Solutions of the Boundary Layer Equations for Air in Dissociation Equilibrium

Journal of the Royal Aeronautical Society ◽

10.1017/s0368393100071881 ◽

1960 ◽

Vol 64 (589) ◽

pp. 36-37

Author(s):

R. L. Dommett

Keyword(s):

Boundary Layer ◽

Flat Plate ◽

Laminar Boundary Layer ◽

Specific Heats ◽

Boundary Layer Equations ◽

Dissociation Equilibrium ◽

Image Position ◽

On an equation occurring in Falkner and Skan's approximate treatment of the equations of the boundary layer

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100019575 ◽

1937 ◽

Vol 33 (2) ◽

pp. 223-239 ◽

Cited By ~ 299

Author(s):

D. R. Hartree

Keyword(s):

Boundary Layer ◽

Iterative Method ◽

Boundary Conditions ◽

Unique Solution ◽

Laminar Boundary Layer ◽

Image Position ◽

Approximate Treatment ◽

Limiting Value

The differential analyser has been used to evaluate solutions of the equationwith boundary conditions y = y′ = 0 at x = 0, y′ → 1 as x → ∞, which occurs in Falkner and Skan's approximate treatment of the laminar boundary layer. A numerical iterative method has been used to improve the accuracy of the solutions, and the results show that the accuracy of the machine solutions is about 1 in 1000, or rather better.It is shown that the conditions are insufficient to specify a unique solution for negative values of β a discussion of this situation is given, and it is shown that for the application to be made of the solution the appropriate condition is that y′ → 1 from below, and as rapidly as possible, as x → ∞. The condition that y′ → 1 from below can be satisfied only for values of β0, greater than a limiting value β0, whose value is approximately − 0·199, and which is related to the point at which the laminar boundary layer breaks away from the boundary.

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