Mechanical Engineering
Department
Instituto Superior Técnico, UTL, Lisbon, Portugal
BOUNDARY LAYER CONTROL IN HIGH SPEED TRAINS
Alexandre Miguel Calhau Martins
1987.martins@gmail.com
October 2010
ABSTRACT
The control of flow around a vehicle plays a very
important role in safety, in comfort, possibility of
increasing the speed or energy savings. Plasma actuators
seem promising devices for the control of three dimensional
boundary layers due to their small dimensions, low weight,
easy construction and adaptation to the aerodynamic
surfaces.
In this work we built a plasma actuator DBD
(Dielectric Barrier Discharge) and its electronic circuit.
We tested several configurations to optimize the results.
Over the “nose of the train”, due to crosswise pressure
gradients, the boundary layer became three dimensional,
giving rises to longitudinal vortices. The purpose of this
research was to inhibit this torsion of the boundary layer
with a plasma driven wind near the skin of the train.
A transverse pressure gradient was created in a test rig
and the crosswise momentum was increased near the wall
by a plasma actuator, to counteract the torsion of the
boundary layer. It was found that the plasma actuator has
improved significantly the flow and prevented the
development of longitudinal vorticity.
Plasma actuators can perhaps be an alternative to reduce
aerodynamic forces, increase the energetic efficiency and
reduce the noise.
The purpose of this study is to build a plasma actuator
and evaluate its performance in the wind tunnel. Three
objectives were established:
• Build a plasma actuator.
• Test various configurations of electrodes and
electric pulses to optimize the output.
• Test the actuator in a wind tunnel, in boundary
layers subjected to crosswise pressure
gradients.
2. FLOW CONTROL
2.1. Traditional methods of active control of
boundary layers
Delaying the transition of a boundary layer, increasing
or reducing the turbulence to promote the separation of the
boundary layer is examples of the control of flows. Increase
the lift force, reduce aerodynamic drag or noise, are some
of the results achieved in some studies [2].
The traditional control of boundary layers makes use
of the injection [3] or removal of fluid [4] or the movement
of fluid from the surface in the direction of flow [5].
KEYWORDS - Flow Control, Plasma Actuator, Trains,
Boundary Layer, Longitudinal Vortices.
1. INTRODUCTION
The aerodynamic resistance is the most important
contribution for the total resistance in land transportation
[1]. The high aerodynamic loads to which trains are
subjected may cause overturning. This danger limits the
maximum velocity at which they can travel. The flow
turbulence, particularly intense in some areas of separated
flow, is the primary source of high-speed railway noise
generates. These phenomena are aerodynamic effects that
can be addressed by an improved control of the flow.
Some control systems such as vortex generators or
synthetic wall jets, have found success in controlling
boundary layer separation or mixing of jets. But they have
some drawbacks, such as heavy or complicated structures.
2.2. Other methods of flow control
Other methods of flow control are the control by
periodic excitation flow which may be by external acoustic
excitation [6] or excitation of the surface mechanically or
externally [7]. Magneto-hydrodynamic actuators also
showed good results when applied to bodies submerged in
water currents [8].
2.3. Plasma actuators
The use of plasma actuators is a technique that is
booming for the control of flows. Mechanical actuators
have satisfactory results however have some weaknesses
particularly the requirement of moving parts, relatively
large dimension and sometimes complex assembly. Instead,
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plasma actuators have no moving parts, their assembly is
simpler and the response times are relatively short. The
currents are relatively low in these actuators and a no
external magnetic fields are applied. They are divided into
two groups: those in which the electrodes are separated by a
dielectric barrier, DBD (Dielectric Barrier Discharge)
actuators and those in which both electrodes are facing each
other, BED (Bare Electrode Devices).
the flow direction (co-flow) and an increase in resistance
when the discharge has the opposite direction (counter
flow), Figura.3.
2.4. DBD Actuators
In this work a DBD actuator was built. Description of
the coupling mechanism that underlies this type of
discharge is an issue that is not yet fully understood. Roth
tried to explain this mechanism [9], saying that the force
acting on the fluid comes from the Coulomb force on
charged particles (1) and considering the equation of Gauss
(2), Roth was derived for the one-dimensional case, an
expression for the electric force that he called paraelectric
force (3).
→
→
f e = ρ f .E
→
ε 0 .∇ ⋅ E = ρ f
→
f e = ε0.
∂ 1 2
 E 
∂x  2

Figure 2 – Electrode configurations [11]
(1)
(2)
(3)
The numerical simulation of this set of equations is
the only tool to assess the values of the volumetric charge
density and the electric field (1), and thus the paraelectric
force. A discharge in pure oxygen was simulated and the
author distinguishes two phases in the discharge. First the
"forward discharge", during which the exposed electrode
(top) has a negative potential relatively to the covered
electrode (bottom), so the electrons are expelled from the
electrode exposed. The second phase "back discharge",
during which the exposed electrode has a positive potential
relatively to the covered electrode, so the electrons are
attracted to the exposed electrode. The study showed that
the average force during the "forward discharge" is about
one order of magnitude higher than during the previous
cycle and therefore the mean flow induced by the discharge
always takes the same direction, Figure 1 [10].
Figure 3 – Tests in a flat plate [11]
Tests on cylinders with flow Re <7400 reduced the
level of turbulence in the wake of the cylinder by 66%,
Figure 4 [12].
Then he applied the DBD actuators in wing profiles, to
control the separation of two dimensional boundary layers.
Roth [9] studied the effect of applying a DBD actuator
composed of eight pairs of electrodes. Even with a
relatively low velocity Figure 5 shows a notorious
reattachment of the fluid at the wall.
Figure 4 – (b)- actuator off. (c) – actuator on [12]
Figure 1 – a – Back discharge. b – Forward discharge [10]
Roth developed in 90's, a surface DBD actuator and
called it "One Atmosphere Uniform Glow Discharge
Plasma" (OAUGDP) [11]. He tested various geometries of
the electrodes, Figure.2. His studies were focused on the
control of two dimensional boundary layers on a flat plate
and found a reduction in resistance when the discharge has
Figure 5 – (a) - actuator off. (b) – actuator on [9]
NACA0015. Angle of attack 12º. U=2.85m/s
2
There was a characterization of the electronic system in
order to know the magnitude of the voltage that is obtained
in the terminals of the load circuit, maximum voltage was
close to 18 kV.
3. CONSTRUCTION AND OPTIMIZATION OF THE
PLASMA ACTUATOR
The DBD plasma actuator consists in one or more pairs
of electrodes separated by a dielectric, Figure.6. In this
work the dielectric used was FR-4 (common in printed
circuit boards, PCBs), which has a dielectric strength of
20kV/mm.
3.1. Optimization
We tested several geometries of the electrodes to
maximize the wind velocity of the plasma actuator. The
tests consisted in measuring the velocity and the voltage of
the secondary that each electrode could produce under
different electrical signal, the frequency and voltage of the
primary.
It was found that the ionic velocity produced by the
actuators increases with the voltage applied of the terminals
of the actuator (Figure 9) and that each model of actuator
produces a maximum velocity for a given frequency
(Figure 10). It was also noted that different actuators can
produce the same wind velocity, but consume different
powers.
The electrode configuration was chosen that produces
a higher velocity and that, compared with the others,
consumes less power.
Figure 6 – Schematic of a DBD plasma actuator
When a high voltage (on the order of kV) is applied in
the electrodes, a disruption of the air molecules occurs, the
air is separated in ions and electrons. In the presence of a
strong electric field, the ionized air is accelerated. These
ions collide with the inert molecules of the air, imparting
them momentum. An asymmetric geometry of the
electrodes allows accelerating the air in one direction, thus
forming a thin layer of ionically generated wind along the
wall. It’s possible to observe a plasma discharge with an
electrode constructed in this work, Figure 7.
Figure 9 – Velocity as a function of voltage
Figure 7 – Plasma discharge
We built an electronic circuit, to generate a square
wave and create spikes of voltage in the secondary circuit.
To increase the voltage and produces the spikes, a coil was
mounted between the electronics and the plasma actuator. A
scheme with all these components is presented in Figure 8.
Figure 10 – Optimum frequency for each actuator
It was also found that increasing the number of pairs
of electrodes, produced an increase in the velocity induced,
Figure 11.
After the optimization analysis, the best combination
of electrodes, produced 1.1 m / s, when the signal frequency
Figure 8 – Electronic components and plasma actuator
3
was around 600 Hz and voltage in the primary 30 V,
consuming close 40 W under these conditions. This
actuator consists in 4 pairs of electrodes at 10mm distance
from each other, with 1 mm distance between each
electrode. The electrodes are 10 mm wide, 90 mm long and
0.1 mm thick.
and considering the infinite relative pressure equal to zero,
the pressure field is given by (7).
q
x

u = 2π ⋅ x 2 + y 2 + V∞ .co s (θ )

→
q
y

V (u , v, w ) = v =
⋅ 2
2π x + y 2

 w = V∞ ⋅ sen(θ )


1
p rel ( x, y, z ) = ρ (V∞2 − (u 2 + v 2 + w 2 ))
2
(
)
(4)
(
)
(5)
(6)
(7)
Using a coordinate system that follows the fluid, Figure
12, the velocity field is given by expressions (8), (9) and
(10).
Figure 11 – Power required for the different pairs of
electrodes
4. AERODYNAMICS OF TRAINS
The aerodynamic drag is the largest contribution to the
resistance of trains. The corresponding power is
proportional to the square of the relative air velocity. At
constant speed, the aerodynamic resistance is clearly
dominant in vehicles moving at high speed, including on
trains, due to their low rolling resistance.
The shape of the "nose of the train" influences forces
and moments to which the train is subject. If the nose of the
train is shorter, the boundary layer is strongly threedimensional and generates longitudinal vorticity due to the
transverse pressure gradients. The variations of the
curvature of the cross section of the trains affect the surface
distribution of vorticity also creating longitudinal vortices.
With crosswind this phenomenon becomes more intense. A
small angular deviation in the incident flow can cause a
significant increase in aerodynamic drag.
The longitudinal vortices are stretched into multiple
turbulent filaments that modify the turbulent pressure field
with high frequency, producing noise.
Figure 12 - Coordinate system
u' =
(u
2
+ v 2 + w2
v' = 0
w' = 0
)
(8)
(9)
(10)
Because the ramp has a certain inclination, a transverse
pressure gradient is produced, that deflects the streamlines
near the wall, more than the streamlines away from the
wall.
Boundary Layer
5. ANALYTICAL AND EXPERIMENTAL ANALYSIS
OF THE FLOW
An inclined steep ramp has been used to model the
three dimensional character of the boundary layer on the
surface of a train.
A coordinate system aligned with the external flow
was applied to the transport equation of momentum in the
transverse direction inside the boundary layer.
Making an analysis of orders of magnitude and
neglecting the diffusive terms compared with the
convective terms (except close to the wall), we arrive at the
expression 11.
5.1. Description of the flow
External flow
∂w'
1 ∂p rel
=−
∂x '
ρ u´ ∂z '
Modelling each section of the ramp, with a Rankine
half body (Figure.12), the expressions (4), (5) and (6)
define the velocity field. Applying the Bernoulli equation
4
(11)
5.3. Summary of the results observed
The main flow velocity longitudinal at the beginning of
the ramp was approximately 11 m/s.
The first verification was the presence a strong
transverse pressure gradient that deflects the streamlines
near the wall of the ramp, Figure 15.
This expression shows why the spatial variation of the
transversal component of the velocity is inversely
proportional to the longitudinal velocity and explains why
the variations of w' are higher close to the wall, Figure 13.
As the ratio of the components u' and w' varies in the y'
direction, the streamlines are deflected differently,
according to their distance to the wall. Close to the wall, the
streamlines deviate more from the longitudinal direction.
Thus torsion of the boundary layer occurs that gives rise to
longitudinal vortices in the nose of the train.
In tests of the optimization of the plasma actuator, the
maximum speed occurred close to the wall (1 to 3mm) and
decreased in y' direction. Several measurements were
carried out by Roth [13] that shows that the velocity profile
created by the plasma actuator had also a top speed close to
the wall and decreases in the vertical direction.
.
Figure 13 - Profiles on the three-dimensional boundary
layer
5.2. Experimental assembly
The experiments were conducted in an open wind
tunnel in the laboratory of IST. It has a Pitot tube inside the
contraction, which together with the static pressure probes
along the duct and a movable Pitot tube allows the
calculation of the static pressure distribution and the flow
velocity. In Figure 14 is shown the overall arrangement of
the test rig.
The purpose of this experiment is to observe the
changes of the flow field with and without the plasma
actuator.
Figure 14 – (a) - Away from the wall. (b) - Near the wall
The second observation was the effect of the plasma
actuator, close to the wall (~5 mm), showing that the
comparatively small amount of momentum imparted to the
boundary layer by the actuator was sufficient to re-orient
the streamlines close to the wall, in the main flow direction,
Figure 14, suppressing, as far as could be observed, the
generation of longitudinal vorticity and the three
dimensional boundary layer separation.
6. CONCLUSIONS
In this work a DBD plasma actuator and its electronic
system were built and optimized. The actuator was tested in
a specific application in a wind tunnel. To meet these
objectives, it was necessary to develop some knowledge in
the areas of electronics, plasma physics and aerodynamics.
Among all the steps and discussions, the following
conclusions are worthwhile noting: the actuator selected
can deliver 1.1 m / s, at a voltage of 30V on the primary
and a frequency close to 600Hz. The power required to
create these conditions is about 40W. The maximum speed
is at a distance close to the wall (between 1 to 3 mm). With
an inclined ramp mounted on the wind tunnel, it was
possible to observe the deflection of streamlines close to the
wall. When the actuator was turned on, there was a
Figure 15 – Test rig
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[3] Attinello, J., “Boundary layer and flow control. Its
principles and application”, Vol.1, pp 122-143. New York:
Pergamon Press, 1961.
[4] Betz, A. “Boundary layer and flow control. Its
principles and application”, Vol.1, pp 1-20. New York:
Pergamon Press, 1961.
[5] Modi, V., Hill, S., Yokomizo, T.,“Drag reduction
of trucks throught boundary layer control”, Vol.54, pp 583594. 1995.
[6] Zaman, K., Mangalam, S., "Effect of acoustic
excitation on the flow over low-Re airfoil", J. Fluid Mech.,
Vol.182, pp 127-148. 1987.
[7] Hsiao, F., Wang, T., Zohar, Y., "Flow separation
comtrol of a 2-D airfoil by leading edge oscillating flap",
Pacific International Conference on Aerospace Science an
Technology, Vol.1, pp 250-256. Taiwan, 1993.
[8] Nosenchuck, D., Brown, G., "The direct control od
wall shear stress in a turbulent boundary layer", MAE
Report T1954. New Jersey, 1992.
[9] Roth, J.Phys. Plasmas 10 2117-26. 2003
[10] Font, G. “Boundary layer control with
atmospheric plasma discharges”, AIAA J. 44, pp. 1572–8.
2006.
[11] Roth, J. “Electrohydrodynamically induced
airflow in a one atmosphere uniform glow discharge
plasma", 25th IEEE int. Conf. Plasma Science. Raleigh,
1998.
[12] Thomas, F., Kozlov, A., Corke, T., “Plasma
actuators for bluff body flow control” AIAA Meeting, paper
- 2845. San Francisco, 2006.
[13] Roth, J., Sherman, D., Wilkinson, S., "Boundary
layer flow control with a one atmosphere uniform glow
discharge surface plasma" AIAA Meeting, paper - 328.
Reno, 1998.
notorious alignment of the streamlines close to the wall
with the longitudinal direction of the flow. This result
shows that the actuator can operate close to the wall. It was
also observed along the curvature of the cross section, when
the radius of curvature increases, the
Figure 16 – (a) – actuator off. (b) – actuator on
transitions of flow are smoother, thus eliminating the
formation of vortices.
The number of tasks opened to future studies is
relatively large, since the plasma actuators are an area in
full expansion, for example:
• New types of waves in the electronic circuit may
change the pulses in the secondary circuit and have
some impact on the speed produced by the
actuator.
• In this study we were limited by the dielectric
rigidity of the dielectric barrier, which limited the
maximum tension difference and hence the wind
speed generated by the actuator. Using a greater
dielectric rigidity, for instance with kapton or
Mylar, it may be possible to increase the wind
velocity.
• The PIV (Particle Image Velocimetry) technique
provides good images of the flow. In this type of
work it is widely used to acess the velocity field of
the flow.
REFERENCES
[1] André, José Maria., Transporte Interurbano em
Portugal: Concepção técnica de uma alternativa
ferroviária para o transporte de passageiros (Volume 2),
Lisboa: IST Press, 2008.
[2] Gad-El-Hak, M., Flow Control, Cambridge:
Cambridge University Press, 2000.
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