Boundary Layer Control

Boundary-Layer Control

Boundary-Layers

• When a real (viscous) fluid flows past a solid body, a laminar boundary-layer forms.

• Shortly, the boundary-layer transitions from laminar to turbulent.

• The velocity fluctuations near the wall must die out, so there is always a small laminar sub-layer beneath the turbulent boundary-layer.

• Mixing properties cause the gradient in the sub-layer to be much stronger than that in the fully-laminar layer. Thus, transition greatly affects drag.

Boundary-Layer Control

• Passive Methods– Vortex Generators– Flaps/Slats– Absorbant Surfaces– Riblets– MEMS

• Active Methods– Mobile Surfaces– Suction– Blowing– Binary Boundary-Layers– Jet-induced Turbulence– Planform Control– Advanced methods

• Magnetodynamics• Electrodynamics• Feedback Control Systems

No Slip Conditions

• According to the kinetic theory gases– The velocity at the surface is not exactly zero.– There is a velocity of slip proportional to the velocity gradient.

–

• Where ξ has the dimension of length and “may be considered a backward displacement of the wall with the velocity gradient extending effectively right up to the displaced wall where the velocity is zero.”

• Millikan Maxwell has shown that for most surfaces, the coefficient of slip is “very nearly equal to the mean free path of the molecules.”

– At ordinary altitudes this distance is so small that it may be neglected.– At very high altitudes the slip velocity may have large effects.– At extreme altitudes the entire concept of the boundary layer and viscosity

become invalid.

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duvs

Vortex Generators

• Vortex generators are simply small rectangular plates that sit above the wing surface. They look like tiny little wings sitting up perpendicular to the wing itself.

• As air moves past them, vortices are created off the tips of the generators. These vortices interact with the rest of the air moving over the wing to speed it up and help prevent separation.

Vortex Generators

Many early swept wings were found to suffer from separation at transonic speeds because the shocks formed on the wing suddenly slow the flow. Vortex generators on both surfaces serve to dissipate shocks formed at transonic speeds, thereby delaying the effects of separation.

Vortex Generators

• Ineffective control surfaces:– The separation problem becomes

even more significant since control surfaces like ailerons are usually located along the trailing edge of a wing.

– When the flow separates from the wing, these control surfaces have little or no air flowing over them and they become ineffective.

– Thus, not only will the aircraft lose lift when the wing stalls, but the pilot may not be able to control the orientation of the aircraft.

– In this case, vortex generators are often placed shortly before the control surfaces to keep the flow attached.

Vortex Generators

• Short-takeoff and landing aircraft:– These aircraft generally must

operate at low speeds during takeoff and landing, so the flow speed over the wings tends to be low as well.

– Aircraft like the C-17 Globemaster III use vortex generators to energize the flow over the wings and control surfaces at these conditions to improve performance and controllability.

Leading Edge Devices(Nose flaps, Kruger flaps, and Slats)

• “Nose flaps, Kruger flaps, and Slats are several types of leading edge devices used to increase the maximum lift coefficient of the aircraft.

• The system has an opening at the leading edge of the airfoil allowing high pressure air under the airfoil to pass. As a result, the high pressure air mixes with the air at the top surface and increases the energy of the boundary-layer at the surface.

• By increasing the energy of the boundary-layer the wing can sustain higher angles of attack and a higher maximum coefficient of lift.”

Slotted Flaps

Slotted Flaps duct high-energy air from the lower surface to the upper surface and delay separation of the flow over the flap.

Ultrasonically Absorptive Surfaces

• “Recently performed linear stability analyses suggested that transition could be delayed in hypersonic boundary layers by using an ultrasonically absorptive surface that would damp the second mode (Mack mode).”

• The experiments show that the porous surface was highly effective in delaying transition provided that the hole size was significantly smaller than the viscous length scale.

Motion of the Solid Surface

• Boundary-layers are formed due to the velocity difference between the solid surface and the outer flow. The boundary-layer can therefore be eliminated or minimized by removing the velocity difference.

U∞uw=U∞


• An example of a moving surface is a semi-infinite circular cylinder rotating about its center. On the upper side, the separation of the boundary-layer is completely avoided. Because of the difference in velocities on the bottom side, a transverse force is created and separation still occurs. This is called the Magnus effect.


• In 1938, A. Favre applied this moving surface principle to an airfoil. A rotating belt was incorporated into the top surface of the airfoil.

• Maximum lift coefficients of about 3.5 were achieved for large angles of attack (α ≈ 55˚).

• A new separation parameter must be chosen ( is no longer valid).

• The MRS criterion is used to determine separation along a moving surface. Separation happens when:

& occur simultaneously.


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Determining The Separation Point

0y

u

0w

Slit Suction

• L. Prandtl, in 1904, created a narrow slit in one side of a circular cylinder and applied suction. This slit with suction effectively acts as a sink.

• Slit suction is based on the change in velocity distribution, U(x), of the outer flow. The normal distribution of inviscid flow is superimposed on the velocity distribution of the sink flow. This causes the flow to accelerate in front of the slit (creating a favorable pressure gradient) and prevents separation. Behind the slit, the sink decelerates the outer flow, but since the boundary layer is again starting over from zero thickness, it can withstand some adverse pressure gradient before eventually separating.

Tangential Blowing and Suction• By supplying additional energy to fluid particles in the boundary-layer that are low in energy, flow can remain attached to the surface. Two ways of accomplishing this are blowing high velocity fluid from inside the body and sucking low energy fluid from the boundary-layer into the body.

Velocity Distribution Directly Behind Slit for Tangential Blowing

a – blowing

b - sucking

Continuous Suction and Blowing

• To be able to use continuous suction or blowing, the surface must be permeable.

• Continuous blowing reduces wall shear stress and friction drag. If a different fluid is injected into the boundary-layer, a binary boundary-layer occurs and can be used to produce transpiration cooling over the surface.

• Continuous suction prevents boundary-layer separation by removing the low energy fluid. Suction always stabilizes the boundary-layer.

• Surfaces must now be considered to be permeable to the fluid. The kinematic boundary condition, , is no longer valid. Fluid can now be sucked ( ) or blown ( ). The “no-slip” condition ( ) at the non-moving surface still remains valid.

• is still assumed to be of the order of magnitude

• The new wall boundary conditions are:

where:

Continuous Suction and Blowing

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0wv

0wv

Fundamentals

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xvv ww

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Continuous Suction and BlowingFundamentals

• The same boundary-layer equations as before apply with the addition of:

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2

2

y

u

Cy

Ta

y

Tv

x

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p

• The compatibility condition at the wall is now extended to:

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w

vdx

dp

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2

2

This implies that a pressure increase is a necessary condition for separation ( ).0w

Continuous Suction and BlowingFundamentals

• Integration of the continuity equation yields:

)()(

lim 1 xvdx

UdVv w

y

Remark:

This shows that, in principle, the displacement action of the boundary-layer can be prevented by suction.

Binary Boundary-Layers

• A binary boundary-layer is formed when a fluid other than that of the outer flow is being blown.

• Momentum and heat are still exchanged in the boundary-layer, but now mass is also exchanged through diffusion. This mass exchange introduces a concentration boundary-layer.

• These boundary-layers frequently occur in hypersonic flow.

Binary Boundary-LayersCooling

• Transpiration Cooling occurs when a light gas is blown over a surface. This results in a drastic reduction of heat transfer. Typically, transpiration cooling is used in heat protection applications.

• Evaporation Cooling occurs when a layer of liquid evaporates at the wall.

• Sublimation Cooling occurs if the wall material itself melts or sublimates.

There are three boundary-layer cooling scenarios, all of which result in the formation of binary boundary-layers.

Jet-Induced Boundary-Layer Vorticity• A series of jets spatially oriented at 45˚ in a plane transverse to the mean flow direction produces a series of counter-rotating vortices.

Experimental setup

Jet-Induced Boundary-Layer Vorticity

Velocity Flow Field in the (y,z) Plane at Two Different Times

Jet-Induced Boundary-Layer Vorticity

• The maximum wall normal velocity components are always lower than 3% of the external flow velocity.

• The transverse velocity components, w, are weak.

• The rotational nature of the flow in the direction transverse to the freestream direction creates an uneven transverse skin friction distribution.

• Jet-induced vorticity could be a means of creating long channels of turbulent attached flow due to the high rotational energy of the jet flow.

Effects of Wing Sweep on Natural Laminar Flow

Laminar Flow Control

Turbulent Boundary-Layer Control

• Laminar flow control causes a decrease in drag, but laminar flow is not always desirable.

• Turbulent flow is less prone to separation.• Turbulent flow control uses higher momentum to

advantage.

Benefits of Controlled Turbulence

• Maintain flow attachment.

• Eliminate counterproductive large scale vortices.

Riblets• Drag reduction device used to trip boundary- layer into

controlled turbulence.• Size on the order of tenths of a millimeter.• Prevents large scale vortex formation.• Naturally present on sharks.

Riblets

• Thickening of viscous sublayer.

• Reduction in turbulence intensities and Reynolds stress at the riblet wall.

• Work as a constraint to the production of the Reyonlds stresses associated with the growth and eruption of the eddies in the the low-speed regions of the boundary-layers.

Numerical Analysis

Drag Savings• Estimates of between 5% to 10-11% reduction in

parasite drag.

• Average parasite drag reduction of 8%.

• Parasite drag makes up 45% of total drag on jet transports. With half of the skin covered with riblets producing 8% reduction, total drag reduction would be approximately 4%, which is significant in commercial circles.

• Data reported for a 1/11 scale model of the Airbus A320 at cruise Mach number M = 0.7 was a viscous drag saving of 4.85 %, with about 66 % of the aircraft wetted area covered by V-riblets.

• Further benefits possibly gained with suction or blowing along riblet surface.

Off-design Performance

• Several concerns– Flow alignment.– Surface quality.– Pressure gradients.– Three-dimensional flows.– Increased wetted area effects.

Flow Misalignment

• Beyond 15 degree misalignment with riblet axis, no significant benefits observed.

• Extremely high angles of attack (>40 degrees) can cause riblet effects to become detrimental.

• Flow misalignment side-effects can be alleviated with compound riblets which are three dimensional and locally optimized to flow direction.

Surface Contamination

• Material trapped in crevices or riblets can disrupt carefully engineered beneficial riblet surface creating detrimental effects.

• Results in increasing necessary maintenance.

Miscellaneous Effects

• Pressure gradient effects have approximately 1-2% effect, thus these effects with relation to drag savings are negligible.

• Wetted area increase is a factor with any riblet, but this is negated by skin friction savings.

• Avoiding the use of L riblets alleviates this problem.

Large Eddy Break-up Devices (LEBU)

• Similar to riblets in design.• Designed to disrupt large scale eddy formation.• Drag reductions similar to riblets (7-8%).• At higher Reynolds numbers, performance is

diminished.• Theoretically, coupling with riblets could provide

optimum control of turbulence. This requires extensive experimentation, as numerical methods are insufficient to provide effective analysis.

Compliant Walls

• Flexible Skins absorb momentum which would otherwise be detrimental.

• Passive walls absorb momentum without actuation, which is then damped internally.

• Active walls determine optimum absorption and actuate wall deflections accordingly, creating optimum boundary layer interactions.

Microelectromechanical Systems (MEMS)

• Smaller scale of similar principle to compliant walls.

• Sensors detect condition of flow and manipulate or introduce vortices through microelectromechanical actuators.

MEMS• Through creation of controlled small

scale turbulence, drag benefits can be achieved which cause lower drag than laminar flow.

MEMS

• To gain significant advantage, high percentage of vehicle would need to be covered with MEMS.

• Result of significant MEMS coverage would be large cost increase for resulting drag savings.

• Independent processing for each MEMS which would be necessary to gain significant benefit would cause significant weight increase.

• Problems can be alleviated with continued reduction of micromechanics and microprocessors size, weight, and cost.

Uses in the Real World• Riblets were used on the Stars and Stripes in the

1987 America’s Cup helping that boat to win. Riblet advantage was considered so significant, their use was subsequently banned.

• 3M has developed a tape which can be applied to aircraft or watercraft that has riblets, but it is not in mass production yet as production cost is still significant, and not yet low enough so the reduction in operating cost offsets the increased cost for riblet production and application.

• Riblets and vortex generators used for speed skaters, skiers and swimmers to reduce pressure drag.

• Exploratory tests of MEMS. Development is still in very early stages.

Advanced Methods

(it can be “easily shown” that)

Magneto-Fluid-dynamic Control

• Lorentz Force: The force induced by motion of charge (current) through a magnetic field.

• This principle affords flow control when an electrically conducting fluid flows through an electromagnetic field.

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• By embedding electrodes and magnets in a flat surface over which flow passes, the Lorenz force can be produced.


• It can be shown that for an electrically conducting, magnetically permeable, incompressible Newtonian fluid:

– is the wall Reynolds number based on wall-sheer velocity and channel half-width

– is the ratio of Lorentz force to fluidic inertia

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u

2

Re

1

Re

200

u

BJSt


The key to drag reduction is to disturb the semiequilibrium state between the near-wall streamwise vorticies and the wall. This can effectively be done by introducing Lorentz force perturbations perpendicular to the vorticies.



• System flaws– Although it is found that parasite drag can be

reduced by as much as 40% with a temporally oscillating spanwise Lorentz force (to low-speed flow), the power required to generate the Lorentz force is an order of magnitude larger than the power saved due to the drag reduction.

– Air is generally of a low electrical conductivity, so the Lorentz force is difficult to induce.

Electro-Aerodynamic Control

• Coulomb's Law: opposite charges attract with a force directly proportional to the charge magnitudes:

• This principle affords flow control when a layer of ionized gas and a longitudinal electric field are created in the boundary-layer region.

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• Practicality, from a technological standpoint, prevents local ionization of air along the airfoil.

Suction Pump

Air Ionizer


• The boundary-layer equations (including a “new” body force to account for electrical attractions.

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• Define non-dimensional quantities:

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• In general, it can be said that . For steady flow, by neglecting terms of order and , one obtains:

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• Assuming the electric field component normal to the airfoil is small, and the x-component equation, which can be expressed in terms of the fluid velocity as follows:

• To account for turbulence, incorporation of eddy shear stress ( ), with yields:

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• Defining the non-dimensional stream function and accompanying variables as follows:

one obtains:

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• The methods and equations described control the profile of the boundary-layer, specifically as applied to transition.

• Space-time electric-field modulation is equivalent to an effective viscous damping effect which delays the growth of the transition region instability.

• Because of the perturbations induced by injection (blowing ionized air), it is advisable to couple the system with suction at the rear of the airfoil.



Blowing/Sucking, a Systems Approach

• A controller designed upon linear theory has a strong stabilizing effect on two-dimensional finite-amplitude disturbances.

• Resulting secondary instabilities due to infinitesimal three-dimensional disturbances cease to exist.


• Wave destruction method– Boundary layer instabilities appear as a combination of

sinusoidally growing waves of certain frequencies, phases, and amplitudes.

– If these wave properties are measured, air can be added and removed (via blowing and sucking devices described earlier) from the boundary-layer in an opposing (destructive) waveform. In this way, flow may be stabilized.

• Instability Suppression Method– State Space and Galerikin’s method applied to systems

theory allow for the construction of a fluid-actuator-sensor-controller system that is inherently stable.

– Laminar flow linear instability suppression eliminates the need to explicitly measure phase and frequency of instabilities.


• It can laboriously be shown (Dr. Tso, UDI) that:

It’s justa Tso simple!

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• Coupling the previous equation with a state space model allows for the design of control systems as shown below:


• The previous feedback loop system allows for the stabilization of the velocity profile


• Wall sheer can be reduced as follows (with the system being initialized at t=50).

Conclusions

• We as engineers must realize that boundary-layer control methods usually suck or blow.

• By careful application of the above described methods, turbulence and parasite drag can be significantly reduced.

• No questions? Good. We’re done for today.

References• Abbott, I., Von Doenhoff, A., Theory of Wing Sections, Dover Publications, NY, New York, 1959.• Schlichting, H., Gersten, K., Boundary Layer Theory, 9th Ed., Springer-Verlag Berlin Heidelberg, New

York, 2000.• http://www2.icfd.co.jp.• http://www.aerospaceweb.org.• http://www.ae.utexas.edu/courses/ase463q/design_pages/summer02/activewing/page009.html.• Rasheed, A., “Passive Hypervelocity Boundary Layer Control Using an Ultrasonically Absorptive Surface,”

January 19, 2001.• Mendes, R., Dente, J., “Boundary-Layer Control by Electric Fields: A Feasibility Study,” December 29,

2001.• Berger, T., Kim, J., Lee, C., and Lim, J., “Turbulent Boundary-Layer Control utilizing the Lorentz Force,”

November 19, 1999.• Di Cicca, G., Onorato, M., Iuso, G., and Spazzini, P., “Turbulent Boundary-Layer Manipulation by

Longitudinal Embedded Vortices,” April 24, 1999.• Josh, S., Speyer, J., and Kim, J., "A Systems Theory Approach to the Feedback Stabilization of

Infinitesimal and Finite-Amplitude Disturbances in Plane Poiseuille Flow," July 15, 1996.

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Boundary Layer Control