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Laminar Separation Bubble

Mohsen Jahanmiri

Dept. of Mech. and Aerospace Engineering, Shiraz University of Technology, Shiraz, Iran

Abstract

Due to the importance of drag reduction in various air and ground vehicles, gas turbines, etc., and since presence of separation bubbles play the key role in this context, the main aim of this review work is to uncover the major research activities on different aspects of laminar separation bubble (LSB) which have been carried out theoretically and experimentally for past few decades. These research studies are majorly concentrated on: structure, characteristics and dynamics of LSB; instability of LSB; and most important issue of controlling LSB passively and actively, along with few research examples on low Reynolds number airfoils. Introduction

For conventional aircraft wings, whose Reynolds number exceeds a million,

the flow is typically turbulent with the boundary layer able to strengthen

itself by ‘mixing’. Consequently flow doesn’t separate until high angles of

attack are encountered. For lower Reynolds numbers, the flow is initially

laminar and is prone to separate even under mild adverse pressure

gradient. Under certain flow conditions, the separated flow reattaches and

forms a Laminar Separation Bubble (LSB) while transitioning from laminar

to turbulent state. Laminar separation bubble could modify the effective

shape of the airfoil and consequently influence the aerodynamic

performance, generally in a negative manner.

The need to understand low Reynolds number (104 to 106) aerodynamics is

driven by variety of applications from windmills to aircrafts. High Altitude

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Long Endurance (HALE) Reconnaissance aircrafts, Micro Aerial Vehicles,

insect and bird’s flight fall in this Reynolds number range (Saxena, 2009).

Usually, under the influence of an adverse pressure gradient, a laminar

boundary layer separates from the surface, becomes transitional and

ultimately the separated shear layer reattaches to form a ‘laminar

separation bubble’. Such bubbles are typically observed close to the

leading edges of thin aerofoils, on gas turbine blades and on low Reynolds

number micro-aero-vehicle wings (Diwan and Ramesh, 2007). Presence of

bubbles has a deteriorating effect on the performance of the device. The

understanding of the physics of the laminar separation bubble and possible

ways to control it thus are essential prerequisites for efficient design of

these aerodynamic devices.

One of the earliest surveys of the literature was that of Tani (1964). Most of

the work reported therein was done on the suction surface of a variety of

aerofoil configurations at different angles of attack. It was observed that at

relatively small angles of attack, the length of the separation bubble

reduced with an increase in angle of attack till a critical condition was

reached when there was a sudden increase in the length of the bubble.

This phenomenon was termed ‘bursting’ of the bubble, and most of the

early work was done towards devising empirical criteria to predict bursting,

since it was seen to be directly related to the stalling of the aerofoil (Diwan

and Ramesh, 2009).

Gaster (1969) was the first to systematically explore the stability

characteristics associated with the transition taking place in separation

bubble. Many recent studies have been directed towards exploring the

dynamics of separation bubbles (see Watmuff, 1999; Pauley et al., 1990;

Marxen et al., 2003). The bubble constitutes, at the same time, laminar

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separation, transition to turbulence and aspects of both the attached as

well as free shear layer. Even though there is a fair amount of

understanding of the individual aspects, the interplay amongst them is far

from being understood (Diwan and Ramesh, 2007).

Separation bubbles are important due to the controlling influence that they

can have on the overall performance of aerofoils. Leading edge separation

bubbles do not greatly influence the pressure distribution but effectively fix

the location of transition to turbulence (Sandham, 2008). Additionally, short

bubbles may undergo a bursting process which fixes the maximum lift that

can be generated by an aerofoil. Since the early observations of Jones

(1934), much work has been done to study transitional separation bubbles

in the laboratory and more recently by direct numerical simulation, with a

result that much of the flow physics has been identified, if not yet fully

incorporated into prediction methods. The pioneering experiments covered

in the PhD theses of McGregor (1954), Gaster (1963), Young and Horton

(1996), Horton (1968), Woodward (1970) and the more recent direct

numerical simulations (DNS) of Alam (1999) have discovered a lot of

unknown aspects of separation bubbles.

In this report, an effort is made to make a review on earlier works with

emphasis on dynamics and control of separation bubbles. But, before

discussing experimental and modelling techniques in this regard, the

physical concept of LSB is explained.

Basic concepts

A laminar separation bubble is formed when the previously attached

laminar boundary layer encounters an adverse pressure gradient of

sufficient magnitude to cause the flow to separate. Downstream of the point

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of separation, denoted by S in Figure 1 (O'Meara and Mueller, 1987), the

flow can be roughly divided into two main regions. The first region is

bounded by the mean dividing streamline ST’R and the airfoil surface. The

mean dividing streamline is generally regarded as the collection of points

across each velocity profile at which the integrated mass flow is zero. This

first region represents the relatively slow re-circulatory flow forming the

bubble.

Figure 1: Laminar Separation Bubble. Figure 2: CP distribution on top surface.

The second region of flow consists of the free shear layer contained

between the outer edge of the boundary layer S”T”R” and the dividing

streamline. This separated shear layer undergoes transition at a location

denoted by T due to disturbance amplification occurring in the unstable

laminar layer. Momentum transfer due to turbulent mixing eventually

eliminates the reverse flow near the wall and the flow reattaches at point R.

This process of separation, transition and reattachment results in a laminar

separation bubble that has a predominate effect on the entire airfoil flow

field. As the Reynolds number decreases, the viscous damping effect

increases, and it tends to suppress the transition process or delay

reattachment ( Saxena, 2009).

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In other words, after laminar boundary layer separation a highly unstable

detached shear layer forms and transition to turbulence takes place in the

detached shear layer. The enhanced momentum transport in the turbulent

flow usually enables reattachment and a turbulent boundary layer develops

downstream. In the time-averaged picture there is a ‘deadair’ region under

the detached shear layer immediately after separation and a strong

recirculation zone near the rear of the bubble (Sandham, 2008).

The effect of a laminar separation bubble on an airfoil pressure distribution

is demonstrated in Figure 2 which shows an experimentally measured

distribution plus a pair of theoretically predicted distributions: one with and

one without the bubble (Lee et al., 2006). Once the flow separates, the

edge of the bubble becomes a zero pressure gradient streamline which is

evidenced by the plateau in the pressure distribution (Saxena, 2009). Note

that downstream of the bubble (after re-attachment) the flow appears to

proceed normally and fully attached to the trailing edge.

Another interpretation on creation of separation bubble made by Gaster

(1969) is that, the laminar boundary layer over the nose of a thin aerofoil at

high incidence fails to remain attached to the upper surface in the region of

high adverse pressure gradient that occurs just downstream of the suction

peak. The separated shear layer which is formed may curve back to the

aerofoil surface to form a shallow region of reverse flow known as a

separation bubble. The fluid is static in the forward region of the bubble and

a constant pressure region results. At high Reynolds numbers the extent of

such a bubble is exceedingly small, of the order of 1 per cent chord, and

the slight step in the pressure distribution produced by the dead air region

has a negligible effect on the forces acting on the aerofoil. However, with a

change in incidence or speed (usually an increase of incidence or a

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reduction in speed) the shear layer may fail to reattach and the 'short'

bubble may 'burst' to form either a 'long' bubble, or an unattached free

shear layer. This change in mode of reattachment can occur gradually or

quite sharply, depending on the type of aerofoil. The pressure-distribution

association with a long bubble is quite different from that of inviscid flow,

and the forces acting on the aerofoil are therefore modified, sometimes

quite drastically, by the change in mode of reattachment. In particular,

bubble bursting creates an increase in drag and an undesirable change in

pitching moment. If a very large bubble is formed on bursting, or if the

shear layer fails to reattach, there is also an appreciable fall in lift. This is

one type of stall the thin aerofoil nose stall.

General characteristics of separation bubble

From experimental data it is found out that, variables that significantly affect

the physical dimensions of the separation bubble are Reynolds number,

external disturbance and the angle of attack (Shyy et al., 2008). Figure 3

shows the effect of Reynolds number for various levels of freestream

disturbances (O'Meara and Mueller, 1987). The length of the bubble

decreases as the Reynolds number is increased. The effect of freestream

disturbance on the bubble length is that, as the disturbance level is

increased, the bubble is reduced in length and the suction peak grows in

magnitude. This phenomenon closely resembles the effects observed by

increasing the Reynolds number and are often equated. The effect of angle

of attack variation is summarized in Figure 4 (O'Meara and Mueller, 1987).

As the angle of attack is increased, the point of laminar separation moved

forward but there is no significant change in the length of the bubble. The

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forward movement of the separation point with increase in angle of attack is

due to more severe pressure gradient occurring at higher incidences.

Figure 3: Total bubble length versus chord Reynolds Number.

In addition to overall length, the thickness of the bubble is also influenced

by these parameters and Figure 5 shows the variation of bubble height with

Reynolds number (O'Meara and Mueller, 1987). The figure indicates sharp

reduction in bubble thickness with increase in chord Reynolds number.

Figure 4: Total bubble length versus angle of attack . Figure 5: Bubble height variation.

Experiments carried out by Diwan and Ramesh (2007) showing that both

length and height of the bubble increase with decrease in speed. However,

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further analysis shows that the height increases at a greater rate than the

length. This feature could be useful in characterising separation bubbles,

especially from the point of view of low Reynolds number aerofoil design.

Figure 6 shows a typical smoke flow visualisation picture of their

experiments. The Reynolds number based on the freestream velocity and

the momentum thickness at separation was calculated to be 551·4.

Figure 6: A typical smoke flow visualization picture depicting the separation bubble. The flow is from left to right. Also visible is the reflection of the bubble in the polished surface of the plate.

An investigation into the laminar separation bubble that frequently plagues

airborne vehicles operating in the low Reynolds number regime is made by

Swift (2009). A basic generic model was chosen for this investigation: a

circular arc (section of 16 inch diameter PVC pipe) with sharp leading and

trailing edges having a chord length of 9.3 inches and height of 1.5 inches

(see Figure 7). Small diameter cylinders were then statically placed

upstream of the model to determine their interaction with the laminar

separation bubble and its effects on the boundary layer downstream over

the airfoil model. The length and height of the laminar separation bubble

(Figure 8) was found to be impacted with a small cylindrical wire placed

upstream at all Reynolds numbers and angles of attack with the exception

of an 18 degree angle of attack at the higher Reynolds number. However,

these changes did not result in a substantial or distinguishable

improvement in the downstream separation point. The laminar separation

bubble was found to be nearly or completely eliminated when a

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thermocouple wire was placed upstream of the leading edge. Although the

elimination of the bubble would result in only a minor decrease in drag and

increase in lift, there would be a possible improvement in the stability of the

leading edge stall and possible reduction or elimination in the hysteresis

associated with stall.

Figure 7: Two Dimensional View of Model with Endplates and Mounting Mechanism.

Figure 8: Measurement Details of the Laminar Separation Bubble.

In fact the dependency of separation bubble on Reynolds number was first

found by Gaster (1969). The study has been made of laminar separation

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bubbles formed over a wide range of Reynolds numbers and in a variety of

pressure distributions. His final conclusion was that, the structure of the

bubble depended on the value of the Reynolds number of the separating

boundary layer and a parameter based on the pressure rise over the region

occupied by the bubble. Conditions for the bursting of 'short' bubbles were

determined by a unique relationship between these two parameters.

Instability of laminar separation bubble

Investigations of disturbances developing in a laminar separation bubble

flow has been studied by Häggmar (2000) in wind tunnel experiments using

controlled forcing of low-amplitude instability waves. A region with

exponential disturbance growth is observed in the separated shear layer

associated with a highly two-dimensional flow. A local maximum in the

disturbance amplitude develops at the inflection point in the mean velocity

profile, indicating an inviscid type of instability. Further downstream, in the

reattachment region, a complex three-dimensional flows structure develops

including reverse flown ear the wall.

The occurrence of temporally growing unstable disturbances is investigated

by Rist and Maucher (2002) based on eigenvalues with zero group velocity

from linear stability theory (LST) and compared with observations of

upstream travelling disturbances obtained in a two-dimensional direct

numerical simulation (DNS) of an unsteady laminar separation bubble. For

large wall distances two unstable modes are found. Apart from a low-

frequency motion of the bubble the DNS exhibit high-frequency oscillations

which periodically appear and disappear. Part of these disturbances travel

upstream and amplify with respect to time. Their initial occurrence and their

frequency are in excellent agreement with the results of the parameter

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study based on LST and a closer examination of the disturbances yields

insight into their spatial structure. Figure 9 shows integration domain and

free-stream velocity for their DNS calculation.

Figure 9: Integration domain (a) and free-stream velocity (b) for the DNS of a laminar separation bubble. S = separation point, R = reattachment point; experimental measurements with tripped boundary layer (+) for comparison.

Recently, a detailed experimental and theoretical investigation of the linear

instability mechanisms associated with a laminar separation bubble has

been performed by Diwan and Ramesh (2009). It has been shown that the

primary instability mechanism in a separation bubble, in the form of two-

dimensional waves, is inviscid inflectional in nature, and its origin can be

traced back to the region upstream of separation. In other words, the

inviscid inflectional instability associated with the separated shear layer

should be logically seen as an extension of the instability of the upstream

attached adverse-pressure-gradient boundary layer. This modifies the

traditional view that connects the origin of the inviscid instability in a bubble

to the detached shear layer outside the bubble with its associated Kelvin–

Helmholtz mechanism. Also, a scaling principle for the most amplified

frequency in terms of the height of the inflection point from the wall (yin) and

the vorticity thickness (δω) is obtained and shown it to be universal,

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independent of the precise shape of the velocity profile. This was motivated

by the linear inviscid spatial stability analysis of a piecewise linear profile

adjoining a solid wall. It is shown that only when the separated shear layer

has moved considerably away from the wall (and this happens near the

maximum-height location of the mean bubble), a description by the Kelvin–

Helmholtz instability paradigm, with its associated scaling principles (such

as ω∗=0.21), could become relevant.

Figure 10: Evolution of the wave packet in the downstream direction. The disturbance is introduced at x=340mm; S, M and R indicate separation, maximum-height and reattachment locations for the unexcited case respectively; Uref =2.78ms−1.

The evolution of wave packet in the downstream direction is shown in

Figure 10 (Diwan and Ramesh, 2009). This figure suggests that the

inflectional instability does indeed originate upstream of the separation

location, and it is advected downstream to manifest as the inviscid

instability of the inflectional profile associated with the separation bubble.

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BiGlobal linear analysis provides a unified means of addressing instability

phenomena of separated flows in complex configurations. It has been

demonstrated (Theofilis et al., 2004)) that, closed separation bubbles

sustain global eigenmodes distinct from the known inflectional instability of

the shear-layer in three case-studies of canonical flat-plate and complex

airfoil and low-pressure turbine flows. In all three applications and

parameter ranges studied, a consistent picture emerges regarding the

characteristics of the respective most amplified/least damped global mode;

the latter is found to have analogous characteristics in terms of frequency

and spatial structure of the respective disturbance eigenfunctions in the

different applications. The dominant global mode of laminar separation

remains less significant than other types of linear instabilities in all three

applications, but its omission would result in an incomplete description of

the phenomenon of laminar separated flow instability or efforts to

reconstruct and control the respective flow fields using reduced-order

models.

Figure 11: Basic flow vorticity in (a) the flat plate (Theofilis et al., 2000), (b) the NACA 0012 airfoil at an angle of attach (Theofilis and Sherwin, 2001; Theofilis et al., 2002) and (c) the T-106/300 Low Pressure Turbine blade (Abdessemed et al., 2004).

In case studies of separated flows carried out by Theofilis et al., (2004), it is

seen that, despite the different means of producing separation, in all three

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cases steady closed separation bubbles have been obtained (see Figure

11).

The instability of nominally laminar steady two-dimensional closed

separation bubbles is investigated using direct numerical simulations and

BiGlobal instability analysis (Simens et al., 2006). They demonstrate that

large steady two-dimensional bubbles may become unsteady and

shortened in the mean upon applying periodic forcing. Using BiGlobal

instability analysis, it is shown that, the generation of Kelvin-Helmholtz

instabilities as solutions of the pertinent partial-derivative eigenvalue

problem, without resorting to the simplifying assumptions on the form of the

underlying basic state is possible.

Another research studies on instability of laminar separation bubbles is

carried out by a team from School of Aeronautics, Universidad Politécnica

de Madrid. Global linear modal instability analysis of laminar separation

bubble flows has been performed (Rodríguez et al., 2010). The pertinent

direct and adjoint eigenvalue problems have been solved in order to

understand receptivity, sensitivity and instability of the global mode

associated with adverse-pressure-gradient-generated LSB, as well as that

formed by shock/boundary-layer-interaction (SBLI) and over a finite angle

wedge in supersonic flow (see Figure 12). In incompressible flow the global

mode of LSB has been found to be at the origin of the experimentally-

observed phenomena of U-separation and stall-cell formation. Qualitatively

analogous results have been obtained in compressible subsonic flow, but

convergence of the corresponding eigenspectra in supersonic flow

continues posing computational challenges, despite use of state-of-the-art

algorithms and the largest European supercomputing facility.

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Figure 12: Isolines of stream function in incompressible LSB flow (Rodríguez and Theofilis, 2010) (left). Isolines of density for compressible LSB flows generated by SBLI (middle) and a 45 degree wedge (Ekaterinaris, 2004) (right).

Same research group at Madrid, Spain (Theofilis et al., 2010) somewhere

else on global instability of laminar separation bubbles concluded the

followings:

1. In the past few years, global linear instability of LSB has been revisited,

using state-of-the-art hardware and algorithms.

2. Eigenspectra of LSB flows have been understood and classified in

branches of known and newly-discovered eigenmodes.

3. Major achievements:

• World-largest numerical solutions of global eigenvalue problems (EVP)

are routinely performed.

• Key aerodynamic phenomena have been explained via critical point

theory, applied to global mode results.

4. Theoretical foundation for control of LSB flows has been laid.

5. Global mode of LSB at the origin of observable phenomena:

• U-separation on semi-infinite plate

• Stall cells on (stalled) airfoil

6. Receptivity/Sensitivity/AFC feasible (practical?) via:

• Adjoint EVP solution

• Direct/adjoint coupling (the Crete connection)

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7. Minor effect of compressibility on global instability in the subsonic

compressible regime.

8. Global instability analysis of LSB in realistic supersonic flows apparently

quite some way down the horizon.

Laminar separation bubble control

LSBs are widely regarded as parasitic because they typically have the

effect of increasing drag, thus reducing aerodynamic efficiency (Aholt,

2009). Additionally, LSBs are characteristically sensitive to small

fluctuations in upstream flow characteristics, and are consequently prone to

instability (Rist and Augustin, 2006; Zaman and McKinzie 1989; Bak et al.,

1999). This instability results in design uncertainty, and has been

experimentally observed to reduce aerodynamic performance as well as

result in potentially dangerous dynamic structural loading in aerospace

structures (Bak et al., 1999; Schreck and Robinson, 2007). Consequently,

methods of controlling or eliminating LSBs are a priority of many

aerodynamicists. The most effective methods of LSB elimination currently

in use involve forcing premature turbulent transition of the boundary layer,

making it less likely to separate; e.g. careful airfoil selection or the

placement of mechanical turbulators upstream of the laminar separation

point (Rist and Augustin, 2006; Bak et al., 1999). However, such methods

are typically passive, generating turbulence regardless of necessity. In

applications where a system must perform under a wide range of operating

conditions (such as a UAV or wind turbine), an active control system is

desirable. It is for this reason that flow control systems such as pneumatic

turbulators and plasma actuators are of current research interest (Aholt and

Finaish, 2011).

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As mentioned by Augustin et al., (2004), existing systems to avoid the

formation of LSBs involve the generation of turbulence upstream of the

separation. Most often used turbulators apply zigzag or dimple tape

mounted on the surface of the airfoil. Other devices use vortex generators

(Kerho et al., 1993) or constant blowing of air through holes in the surface

of the airfoil (Horstmann et al., 1984) to generate-large scale streamwise

vortices. For such active blowing devices a complicated system to provide

the necessary bleed air might be necessary. All these systems have in

common that they have to be developed for an optimum design point.

Therefore, these systems cannot capture off-design conditions like different

speed tasks of sail planes optimized for thermal flights. Active-blowing

devices can be switched off at off-design conditions, but nevertheless

additional disturbances may be generated by secondary flow through the

holes in the presence of pressure gradients in the spanwise direction of the

airfoil. Active systems which deform the surface of the airfoil to introduce

disturbances into the flow represent a solution to these problems. Switched

off, these systems would no longer be a source of additional drag. As a

drawback these systems only provide very small deformation amplitudes

and imply electric driving and control devices. Moreover, a complex

integrated sensor, controller and actuator system becomes desirable to

become independent of any external interference with the system by the

pilot. As maximum efficiency is the aim, according active turbulators have

to be low-energy consuming and thin layered to fit into the limited space

available on an airfoil besides the required supporting structural

components. Nevertheless, such surface-mounted active devices can

generate high-frequency perturbations which are necessary to introduce

Tollmien-Schlichting-type boundary-layer disturbances into the flow. Due to

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hydrodynamic instability of the LSB flow, these boundary-layer

disturbances become strongly amplified which leads to laminar-turbulent

transition despite of their low initial disturbance amplitude. By introducing

boundary-layer perturbations at a disturbance strip upstream of the

separation into the laminar flow, transition can be triggered and therefore

the size of the LSB be influenced.

In the work carried out by Augustin et al., (2004), LSB flows are

investigated in detail by means of linear stability theory (Reed et al., 1996)

and direct numerical simulations (DNS) to evaluate methods using

disturbance modes with different excitation parameters with respect to their

impact on the size of typical mid-chord LSBs under different adverse

pressure gradients. Their results show the advantages of the excitation of

unsteady 2-D or 3-D disturbances rather than steady disturbances in

separation control scenarios. In order to provide the necessary unsteady

disturbance amplitude, a possible control system for LSBs would consist of

a frequency generator, an amplifier and an actuator (see Figure 13), as

already discussed in (Augustin et al., 2003), mainly because it suffices to

provoke laminar-turbulent transition by some appropriate means without an

urgent need for some highly sophisticated controller. In fact, a simple

switch that turns LSB control on or off when appropriate could be sufficient,

once the different flow situations are understood well enough. As already

shown in (Augustin et al., 2003) the frequency generator could be replaced

by a feed-back of instantaneous skin friction signals obtained from a

position downstream of the separation bubble. The broad band of

frequencies in the most unstable frequency range due to hydrodynamic

instability then provides a robust signal source for the actuator, after an

appropriate reduction to lower amplitudes.

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Figure 13: Sensor (S)-actuator (A) concept with controller (C) and signal generator (~).

In another attempt, control of flow over a NACA2415 aerofoil which

experiences a laminar separation bubble at a transitional Reynolds number

of 2×105 is computationally investigated using blowing or suction (Genç and

Kaynak, 2009). In the computational results, the blowing/suction control

mechanism appears to be the suppression of the separation bubble and

the reduction of the upper surface pressure coefficients to increase lift and

decrease the drag (see Figure 14). Furthermore, the smallest blowing

results are better larger blowing velocity ratios independent of the blowing

locations while the largest suction results are better smaller suction velocity

ratios independent of the suction jet locations.

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Figure 14: Comparison of numerical and experimental Cf for the NACA 2415 aerofoil without and with blowing/suction at α = 8°.

Control of trailing-edge separation by tangential blowing inside the bubble

has been investigated by Viswanath and Madhavan (2004).

In the classical boundary layer control approach, the boundary layer is

energized upstream or ahead of the separation location (Figure 15a).

Viswanath et al., (2000) demonstrated recently through detailed flow-field

measurements in an axisymmetric separated flow that injection or blowing

downstream of separation, but inside the bubble (Figure 15b) can be an

effective means of separation control.

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Figure 15: Schematic of tangential blowing concepts for separation control.

Their results show that, with the novel approach of blowing inside the

bubble, it is the flow in the bubble (or dead air zone) which is energised

leading to the eventual removal of shear layer closure, as opposed to

energisation of the boundary-layer upstream of separation point, which is

adopted in classical boundary-layer control (Jahanmiri, 2010). Manipulation

of shear layer reattachment or closure is the ‘Key Principle of Separation

Control’. The flow mechanisms that may be responsible for the

effectiveness of this blowing concept include:

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(a) elimination of wall flow reversal due to the interaction of the injected jet

(having higher total pressure or longitudinal momentum) with the reversed

flow boundary-layer leading to surface pressure recovery;

(b) injection of mass into the bubble causes a strong mass imbalance

affecting the shear layer entrainment characteristics ; and

(c) jet entrainment of the reversed flow in the bubble, a strong factor

promoting increased mixing near the wall.

Correa et al. (2010) used an acoustic source to control the size and

location of the laminar separation bubble on a FX63-137 airfoil. Their

results showed that, acoustic excitations were able to reduce the bubble

size by amplifying KH and TS instabilities, but it was not possible to

achieve a bubble breakdown. However, an acoustic source with localized

effects may be a potential candidate to reduce the bubble size in practical

applications.

As an active flow control strategy of laminar separation bubbles developed

over subsonic airfoils at low Reynolds numbers, Aholt and Finaish (2011)

made a computational parametric study to examine the plausibility of an

external body force generated by active means, such as a plasma actuator

(Figure 16). In this study, the effects of altering the strength and location of

the “actuator” on the size and location of the LSB and on the aerodynamic

performance of the airfoil were observed. It was found that the body force,

when properly located and with sufficient magnitude, could effectively

eliminate the LSB (see Figure 17). Additionally, it was found that by

eliminating the LSB, the aerodynamic efficiency of the airfoil could be

improved by as much as 60%.

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Figure 16: Potential approach of external force generation: Plasma actuator (cross-section).

Figure 17: Comparison between stream traces and pressure coefficient contour plots for control case and optimal performance case.

Control of laminar separation using zero-net-mass-flux (ZNMF) devices for

airfoils operating at low to medium Reynolds numbers is a common

approach in laboratory experiments, in both numerical (e.g., Fasel & Postl,

2006; Rist & Augustin, 2006) and experimental (e.g., Bons et al., 2001)

setups. However, ongoing physical processes in such flows can be diverse,

spanning from convective-type (Kelvin-Helmholtz) instability (Rist &

Augustin, 2006) to vortex-wall interaction (Simens & Jimenez, 2006).

Marxen et al., (2006) made an numerical evaluation of active control of a

laminar separation bubble in terms of local linear stability theory based on

the Orr-Sommerfeld equation. Such an instability corresponds to the

convective-type Kelvin-Helmholtz instability for laminar separation bubbles.

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The general setup (Figure 18) is given by a finite flat plate with an elliptic

nose placed in a channel with slip walls, subject to a uniform incoming free-

stream at the channel inlet. In the rear part of the plate, steady blowing and

suction is applied on the upper (slip) wall of the channel in the interval

0.2<x/c<0.8, which induces an adverse pressure gradient at the top wall of

the at plate and in turn leads to separation of the laminar boundary layer on

that plate. A ZNMF actuator is centered at x/c=0.625. This actuator is used

to diminish boundary layer separation downstream of its location by forcing

at different frequencies, but with a fixed amplitude.

Figure 18: Configuration used for numerical simulations.

Their result indicates that a larger separation bubble corresponds to a

larger region of instability and a higher most-amplified frequency. A

feedback effect of the mean flow deformation, i.e., a change of the mean

flow caused through disturbance input even upstream of transition, could

be observed in accordance with reports in Marxen (2005). A deeper

understanding of flow dynamics for the present case of laminar-separation

control was gained with the help of linear stability theory.

Behavior of the separation bubble on the suction surface of a compressor

or a turbine blade has been attracting attention of researchers and

designers of turbomachines for several decades because the separation is

closely related to efficiency, stability, heat transfer and noise generation

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encountered in turbomachines (see Jahanmiri, 2011). In this regard, much

effort is devoted to studies of a leading edge separation bubble. An attempt

is made by Funazaki et al., (2000) to suppress a blade leading edge

separation bubble by utilizing a stationary bar wake. This study aims at

exploration of a possibility for reducing the aerodynamic loss due to blade

boundary layer that is accompanied with the separation bubble. The test

model used in this study consists of semi-circular leading edge and two

parallel flat plates. It can be tilted against the inlet flow so as to change the

characteristics of the separation bubble. Emphasis in this study is placed

on the effect of bar shifting or bar clocking across the inlet flow in order to

see how the bar-wake position with respect to the test model affects the

separation bubble as well as aerodynamic loss generated within the

boundary layer (see Figure 19). The present study reveals a loss reduction

through the separation bubble control using a properly “clocked” bar wake

by choosing a proper position of the bar against the model.

Figure 19: Schemetic showing the relationship between the wake-generating bar and the test model.

Another method to control and manipulate laminar separation bubble is

used by Choi and Kim (2010). Here, an optimization study of a pulsating

26

jet was performed to manipulate the separation bubble behind the fence.

The experiments were carried out in a circulating water channel and the

vertical fence was submerged in the turbulent boundary layer as shown in

Figure 20. The parameters used for controlling the pulsating jet included

the frequency, speed and velocity profile of jet, and the geometries

including angle and location of nozzle.

Figure 20: Schematic diagram of fence model with coordinate system.

The results of this experiment show that, there was a specific frequency,

distance and angle that achieved the largest reduction of time-mean length

of separation bubble. The maximum reduction appeared when Strouhal

number was 0.05 and the pulsating nozzle distance was 1.75H with -30o

blowing angle of jet flow. The parametric studies of frequency and jet speed

reveals there are universal optimal values. In addition, these values

strongly depend on the upstream velocity condition and the change of jet

profiles is less effective to reduce the separation bubble. It is showed that,

27

the main cause of reduction was the vortex shedding phenomena from the

separation bubble; this separation was governed by the vortex developed

from the pulsating jet. If the vortex was weak and there was no separation

from the bubble, the reduction of the bubble became smaller. The

separation bubble can become even bigger than the uncontrolled fence

flow under specific conditions.

Laminar separation bubbles generally exist on the suction surface of LPT

(low pressure turbine) blade of gas turbines, with short bubbles slightly and

long bubble notably impacting on the performance of blade (Mayle, 1991).

So, one of the key to maintain the aerodynamic performance of high-lift

LPT blade is to control the laminar separation bubble on the suction

surface. As passive control techniques, the effectiveness of indented

surface treatments such as dimples and v-grooves for laminar separation

control on LPT blades were assessed by experiments (Lake et al., 1999).

The dimples and v-grooves generally serve as vortex-generators that

create streamwise vortex to enhance the mixing between high-energy

freestream and low-energy boundary layer flow (Vincent and Maple, 2006).

Recently, LES (Large-Eddy Simulation) computations were preformed (Luo

et al., 2009) to investigate the mechanisms of a kind of spanwise groove for

the passive control of laminar separation bubble on the suction surface of a

low-speed highly loaded low-pressure turbine blade at Re = 50,000. They

concluded, compared with the smooth suction surface, the numerical

results indicate that: (1) the groove is effective to shorten and thin the

separation bubble, which contributes the flow loss reduction on the groove

surface, by thinning the boundary layer behind the groove and promoting

earlier transition inception in the separation bubble; (2) upstream

movement of the transition inception location on the grooved surface is

28

suggested being the result of the lower frequency at which the highest

amplification rate of instability waves occurs, and the larger initial amplitude

of the disturbance at the most unstable frequency before transition; and (3)

the viscous instability mode is promoted on the grooved surface, due to the

thinning of the boundary layer behind the groove. The latter is justified from

Figure 21. This figure shows the instantaneous velocity contour at mid-

span for the baseline case and groove case, indicating the formation and

shedding of the vortices. It is suggested that in the groove case viscous

instability is accompanied by the inviscid K-H instability, and that the latter

is responsible for the ultimate breakdown to turbulence.

Figure 21: Instantaneous velocity contour at mid-span.

29

To get a better understanding of the physical mechanisms which control

the formation and structure of separation bubbles on rounded edges, an

experimental studies has been performed in a visualization water tunnel

(Figure 22) by Courtine and Spohn (2003). These experiments confirm the

existence of a secondary instability which transforms the two-dimensional

Kelvin-Helmholtz vortices into three-dimensional highly unsteady

streamwise vortices. In addition the visualizations underline the strong

influence of the bubble width on its breakdown length. The influence of the

curvature (non-dimensional radius η) on the structure of the recirculation

bubble is shown in Figure 23. The comparison of Figure 23a and 23b

clearly shows that the separation angle increases with decreasing η.

Figure 22: Experimental arrangement. The model is fixed outside the boundary layer of the working section, 2.5 cm above the tunnel wall.

Figure 23: Influence of the non-dimensional radius η (=R/H) of the rounded front edge on the structure of the separation zone at Re = 4000 and aspect ratio Λ = 8.8 (= L/H).

30

Earlier also, an active control of the leading-edge separation bubble of the

blunt circular cylinder by a sinusoidal forcing in a Reynolds-number range

4,500-9,500 is investigated by Kiya et al., (1993). The forcing was applied

to the separated shear layer in the form of an oscillating jet through a thin

slit along the separation edge. Main results of this study may be

summarized as follows.

(I) Three components of the time-mean and r.m.s, velocities q’ were

presented for unforced flows at a Reynolds number of 6,400. This result

can serve as the database for the validation of turbulence models and

direct numerical simulations.

(2) The unforced separation bubbles included a secondary separation

bubble of the opposite circulation near the leading edge. The size of the

secondary separation bubble decreased with increasing Reynolds number,

disappearing at high Reynolds numbers of the order of 105 .

(3) The secondary separation bubble was not observed in the forced

separation bubbles.

(4) The reattachment length decreased with decreasing forcing frequency

in a range fexd/U∞ =2-9, thus attaining a minimum at a particular non-

dimensional forcing frequency less than 2.

(5) The relation between the reattachment length and the forcing frequency

appears to be only weakly dependent on Reynolds numbers in a range of

7,000-69,000.

The disappearance of the secondary separation bubble is brought about by

the formation of larger and stronger vortices shortly after the separation

edge by the forcing, as demonstrated by the flow-visualization photographs

of Figure 24. This was also accompanied by the decrease of height of the

forced separation bubbles.

31

Figure 24: Visualized patterns of unforced flow and forced flow with q’f/U∞=0.07 and fexd/U∞=3.6 at Re=7,000 (fex is excitation frequency and d is the diameter of cylinder). Flow from right to left.

Few practical examples at low Reynolds number

The research in the field of the low Reynolds number flows is being pushed

by the growing interest of the aerospace industries in unmanned and

micro-aerial vehicles (UAV and MAV). UAV wings typically operate at a

Reynolds number of 104−105. At these Reynolds numbers, the flow cannot

sustain strong adverse pressure gradients and often separates in the

laminar regime. The disturbances present in the laminar region are

amplified inside the separated shear layer and transition to the turbulent

regime occurs. The turbulence developing inside the re-circulation region

enhances the momentum transport and the flow re-attaches. This

phenomenon, the laminar separation bubble, is one of the main critical

aspects of flows at low Reynolds numbers and adversely affects the

performance of an airfoil. Thick bubbles change the effective contour of an

airofil. This results in an increase of the pressure drag. Suction is reduced

32

in the aft part and pressure recovery is decreased in the rear part of the

airfoil. Skin friction drag increases as well due to the rise of the turbulent

momentum. A more significant effect occurs when the turbulent transport

is not sufficient to close the bubble. The separated region extends up to the

trailing edge. This causes a loss of lift and an increase of drag with

hysteresis effects of the force coefficients with the angle of attack. Below

few research works on this context are discussed.

Laminar-turbulent transition of a low Reynolds number rigid or flexible airfoil

was investigated by Lian and Shyy (2007). They coupled a Navier–Stokes

equation solver with a transition model and a Reynolds-averaged two

equation closure to study the low Reynolds number flow characterized with

laminar separation and transition. The transition model is based on the eN

method, derived from the linear stability analysis and Orr–Sommerfeld

equations. The followings were some of their observations: 1) As expected,

both the separation position and transition position move upstream with

increasing angle of attack. The stronger adverse pressure gradient

amplifies the unstable TS wave and expedites the transition. Before stall,

the laminar separation bubble becomes shorter and thinner with the

increase of angle of attack. 2) Increased freestream turbulence intensity

prompts the transition, resulting in a shorter and thinner separation bubble

(see Figure 25). Increased turbulence intensity also leads to higher

pressure and velocity peak. 3) For the studied airfoil, though increasing the

Reynolds number can shorten the laminar separation bubble, it does not

necessarily increase the lift or decrease the drag.

33

Figure 25: Streamlines and normalized shear stress contours at α=4 deg. for different turbulence

levels.

Hu and Yang (2008) conducted an experiment 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. The interesting outcome of their

experiments were the followings. The separated laminar boundary layer

was found to rapidly change 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<12.0 deg. 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

34

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 (see Figure 26).

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>12.0 deg.

Figure 26: Visualized PIV measurements near the airfoil leading edge with AOA=12.0 deg; (upper) instantaneous velocity vectors, (lower) streamlines of the mean flow.

35

Catalano (2009) presented an aerodynamic analysis of low-Reynolds

number flows with the focus is placed on the laminar separation bubbles, a

peculiar phenomenon of these kind of flows. The simulations techniques

feasible to be applied to complex configurations appeared to be the

methods based on the Reynolds Averaged Navier Stokes equations. A

critical point is the turbulence modeling. In fact, the turbulence models are

calibrated for flows at high Reynolds number with separation in the

turbulent regime. The flow over a flat plate with an imposed pressure

gradient, and around the Selig-Donavan 7003 airfoil is considered. Large

eddy simulations have also been performed and used as reference for the

RANS results. Laminar separation bubbles have been found by the Spalart-

Allmaras and the κ−ω SST turbulence models. The models have been

used without prescribing the transition location and assuming low values of

the free stream turbulence. The main results have been achieved for the

κ−ω SST turbulence model. This model is very reliable for transonic flows

at high Reynolds number, but has shown limits when applied to low-

Reynolds number flows. A modification of the model has been proposed.

The modified model, named as κ−ω SST-LR, has provided a correct

simulation of the boundary layer in the tests performed at low and high

Reynolds numbers. The laminar separation bubble arising of the SD 7003

airfoil has been well captured. The accuracy of the new model is not

reduced in transonic regime. It is concluded that, the κ-ω SST-LR

turbulence model can be used in a wide range of Reynolds numbers to

simulate different flow aspects from the laminar separation bubbles to the

shock-boundary layer interaction.

36

The effects of surface roughness on laminar separation bubble (LSB) over

a wing at a low-Reynolds number studied by Zhou and Wang (2011). It is

found that, by introducing the roughness bumps near the leading edge, the

LSBs are diminished or avoided depending on the bump geometric

parameters. It is found that larger and taller bumps generate larger

disturbances, which trigger the vortex breakdown, and delay or avoid flow

separation. In addition, the flow also transitions into turbulent flow sooner.

Although the friction drag increases slightly, the pressure drag is

significantly reduced resulting in an overall drag reduction. The diminishing

of LSBs by roughness bumps also slightly reduces the lift. However, the lift-

to-drag ratio is significantly increased in the controlled cases. It is also

found that no significant change was observed by doubling the number of

bumps, but the detailed mechanism requires further study. With a fixed

configuration of bumps, the effects of bumps are tested over three AOAs.

In the basic cases, the LSB causes a dramatic increase of the pressure

drag which may decrease the lift-to-drag ratio with the increase of AOA. In

the controlled cases, the aerodynamic performance has been largely

improved with the diminishing of the LSB especially at higher AOAs.

Volumetric three-component velocimerty (V3V) measurements were carried

out on a NACA4412 airfoil at low Reynolds number by Wahidi et al. (2012).

The spanwise normal Reynolds stress predicts the location of onset of

transition with good agreement with the predicted location based on the eN

method. The spanwise and wall-normal Reynolds stresses suggest the

reattachment location. The spanwise normal Reynolds stress indicates that

three-dimensional disturbances exist in the reattachment region as

illustrated by periodic appearance of positive and negative pairs. In addition

to the V3V measurements, particle image velocimerty (PIV) measurements

37

were carried out in the reattachment region. The PIV results are in general

agreement with the V3V results. The V3V and PIV results clearly

demonstrate that the vortices induce pairs of positive and negative wall-

normal velocity (see Figure 27). These pairs play a role in the fluctuations

of the streamwise velocity in the reattachment region.

Figure 27: Contours of (upper) wall-normal velocity (W/U∞) at t0, (lower) W/U∞ at t0+0.04 sec.

38

Another study is a detailed experimental investigation carried out by Serdar

Genç et al. (2012) on aerodynamics of a NACA2415 aerofoil by varying

angle of attack from −12° to 20° at low Reynolds number flight regimes

(0.5× 05 to 3×105). For this investigation, pressure distributions over the

aerofoil were measured using a system including a pitot-static tube, a

scanivalve unit and a pressure transducer. Moreover, time-dependent lift

and drag forces and pitch moment of the aerofoil were obtained by using

an external three-component load-cell system. Velocity measurements at

different points over the aerofoil were carried out by using a hot-wire

anemometer, and oil flow visualization method was used to photograph the

surface flow patterns. The experimental results showed that as the angle of

attack increased, the separation and the transition points moved towards

the leading edge at all Reynolds numbers. Furthermore as the Reynolds

number increased, stall characteristic changed and the mild stall occurred

at higher Reynolds numbers whereas the abrupt stall occurred at lower

Reynolds numbers. The stall angle varied with Re number due to the

viscous effects and decreased with decreasing Re number. By the

decreasing of the Re number, short bubble burst at higher angles of attack,

which caused long bubble to occur.

Dähnert et al. (2012) performed a detailed experimental work conducted at

a low speed test facility. Their study describes the transition process in the

presence of a separation bubble with low Reynolds number, low free-

stream turbulence, and steady main flow conditions. A pressure distribution

has been created on a long flat plate by means of a contoured wall

opposite of the plate, matching the suction side of a modern low-pressure

turbine aerofoil. The main flow conditions for four Reynolds numbers,

based on suction surface length and nominal exit velocity, were varied from

39

80,000 to 300,000, which covers the typical range of flight conditions.

Velocity profiles and the overall flow field were acquired in the boundary

layer at several streamwise locations using hot-wire anemometry. The data

plotted in the form of contours for velocity, turbulence intensity, and

turbulent intermittency. The results highlight the effects of Reynolds

number, the mechanisms of separation, transition, and reattachment, which

feature laminar separation-long bubble and laminar separation-short bubble

modes. For each Reynolds number, the onset of transition, the transition

length, and the general characteristics of separated flow are determined.

These findings are compared to the measurement results found in the

literature. Furthermore, the experimental data is compared with two

categories of correlation functions also given in the literature: (1)

correlations predicting the onset of transition and (2) correlations predicting

the mode of separated flow transition. Moreover, it is shown that the type of

instability involved corresponds to the inviscid Kelvin-Helmholtz instability

mode at a dominant frequency that is in agreement with the typical ranges

occurring in published studies of separated and free-shear layers.

Jahanmiri and Zeinali Araghi (2013) through an computational studies on a

reflex airfoil (MH-64) at low Reynolds number found that, by increase of

AOA the formed separation bubble has the tendency to move towards

leading edge on upper surface besides the stretched geometry(see Figure

28). This process will continue till stream lines would not be able to reattach

to the surface and eventually the critical separation stage will occur.

40

Figure 28: Pressure coefficient distribution for MH-64 airfoil at AOA zero and 6 deg., and Reynolds number 10000(upper) and, streamlines pattern (lower).

Three-dimensional laminar-separation bubbles on a cambered thin wing

with an aspect ratio of 6 at a low Reynolds number of 60,000 have been

investigated by solving the Reynolds-averaged Navier–Stokes equations

(Chen et al., 2013). The k-ω shear-stress transport γ-Reθ turbulence-

transition model is used to account for the effect of transition on the laminar

separation-bubble development. The aerodynamic forces are compared

with the experimental data available for validation. The laminar-separation

41

bubble is shown to evolve in its shape and dimension in both chord and

span directions with increasing incidence due to its interaction with the

wing-tip flow and the trailing-edge separation. The strongest three-

dimensional effects are found at a moderate incidence of 6 deg. and at

higher incidences beyond 10 deg. Within the incidence range, the two-

dimensional airfoil results are not reproduced at any of the span locations,

including the symmetry plane, in the three-dimensional wing case.

Generally, the chordwise development of the three-dimensional laminar-

separation-bubble at the symmetry plane is delayed as compared with the

two-dimensional laminar-separation bubble. Another noticeable point is the

association of a sudden increase in lift-curve slope due to abrupt expansion

of the laminar-separation bubble at a certain incidence. This phenomenon

is observed in both the two- and three-dimensional cases, but at different

incidences.

Concluding remarks

This paper showed a few research studies results carried out on different

aspects of laminar separation bubble, majorly on basic concepts and

characteristics, instability and control mechanism of LSB.

The complete understanding of the flow structure and transition

mechanisms in the bubble region is still far from complete. While the

influence of adverse pressure gradients on LSB has been studied

extensively both numerically and experimentally, a better understanding of

the physical mechanisms which control the formation and structure of

separation bubbles is still to be uncovered.

Significant progress has been made so far on various aspects of the linear

stability of a separation bubble, and most of the studies point to the inviscid

42

instability associated with the separated shear layer to be the main

mechanism. However, as shown by Diwan and Ramesh (2009), the

primary instability mechanism in a separation bubble, in the form of two-

dimensional waves, is inviscid inflectional in nature, and its origin can be

traced back to the region upstream of separation.

In complex configurations BiGlobal linear analysis provides a unified means

of addressing instability phenomena of separated flows as has been

demonstrated by Theofilis et al. (2004).

The key of LSB control is to control laminar-turbulent transition since an

earlier transition will move the re-attachment upstream. Gad-el-Hak (2000)

has termed this “the easy task of flow control” (compared to turbulent

separation control). Mainly because it suffices to provoke laminar-turbulent

transition by some appropriate means without an urgent need for some

highly sophisticated controller. In fact, a simple switch that turns LSB

control on or off when appropriate could be sufficient, once the different

flow situations are understood well enough. So the control methods of LSB

discussed above was the main purpose of the present contribution to

illustrate the underlying mechanisms in a rather brief manner.

A good physical understanding is essential in order to control the laminar

flow separations and suppress the burst of the laminar separation bubbles

for better aerodynamic performances of low Reynolds number airfoils. This

requires a detailed knowledge about transient behavior of the separated

laminar boundary layers and the evolution of laminar separation bubbles.

New active control methods are emerging these days, as one proposed by

Yang and Spedding (2013). By external acoustic excitation at Low

Reynolds numbers, separation control, hysteresis elimination, and more

43

than 70% increase in lift–drag ratio are obtained at certain excitation

frequencies and sound pressure levels.

While extensive experimental and numerical studies have been conducted

to investigate laminar flow separation, transition, and reattachment on low-

Reynolds-number airfoils (as discussed above), future research efforts will

seek to integrate experimental results and the existing models to improve

overall predictive capability for different problems such as unmanned aerial

vehicle applications.

Acknowledgements

This work is supported by Dept. of Fluid Dynamics of Chalmers University

(Sweden) and Shiraz University of Technology (Iran). I am thankful to all

scientists whose papers are quoted in this research report.

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