Study of Blade/Vortex interaction using Computational Fluid
Dynamics and Computational Aeroacoustics
R.Morvant,K.J.Badcock,G.N.Barakos,and B.E.Richards
Computational Fluid Dynamics Lab,
Department of Aerospace Engineering,
University of Glasgow,
Scotland G12 8QQ,United Kingdom.
Abstract
A parametric study of the aerodynamics and the acoustics of parallel BVI has been carried out for dierent aerofoil
shapes and vortex properties.Computing BVI using Computational Fluid Dynamics is challenging since the solution
scheme tends to alter the characteristics of the vortex which must be preserved until the interaction.The present
work uses the Compressible Vorticity Connement Method (CVCM) for capturing the vortex characteristics,which is
easier to implement and has minimal overhead in the performance of existing CFD solvers either in terms of CPU
time or robustness during convergence.Apart from applying the CVCM method with an upwind solver,something not
encountered in the literature,the present work couples CFD with Computational Aeroacoustics (CAA) and uses the
strengths of both techniques in order to predict the neareld and fareld noise.Results illustrate the importance of the
aerofoil shape at transonic ow and show that the magnitude of the BVI noise depends strongly on the vortex strength
and the missdistance.The eect of the vortex core radius was also found to be important.
Notation
ε Connement parameter
ˆ
Γ Normalised circulation
µ Numerical viscosity,advance ratio
ω Vorticity
ρ Density
Σ Surface
S Source term
ϑ Volume
~
f
b
Body force term
~n Normalised vorticity gradient vector to the
surface S
~
V Velocity vector
M
tip
Tip Mach number
R Rotor radius
r Distance from the vortex core,radial co
ordinates
R
c
Nondimensionalised core radius
U
∞
Freestream velocity
v
θ
Tangential velocity
y
0
Missdistance
a Speed of the sound
BVI Blade Vortex Interaction
c Chord length
CAA Computational Aeroacoustics
CFD Computational Fluid Dynamics
Cp Surface pressure coecient
CVCM Compressible Vorticity Connement Method
M Freestream Mach number
NS NavierStokes
OASPL Overall Sound Pressure Level
SPL Sound Pressure Level
Presented at the AHS 4
th
Decennial Specialist's Conference
on Aeromechanics,San Francisco,California,January 2123,
2004.Copyright c 2004 by the American Helicopter Society
International,Inc.All rights reserved.
Introduction
Blade/vortex interaction (BVI) is one of the most chal
lenging problems encountered in modern rotorcraft since
it aects both the aerodynamic performance of rotors,as
well as,the acoustic signature of the aircraft.Despite
its importance,the phenomenon is not fully understood
and it is still the subject of numerous experimental and
theoretical investigations [1,2,3].The diculty in suc
cessfully simulating BVI stems from the fact that Compu
tational Fluid Dynamics solvers tends to dissipate small
disturbances in the ow eld.Upwind and dissipative
schemes work fairly well in problems where acoustic dis
turbances are not of interest since in most of the cases the
ow physics of the problem is not altered by the inherent
numerical dissipation.
In aeroacoustics problems,however,this situation is
not acceptable.Not only acoustic disturbances but ow
structures may be aected by the properties of numeri
cal schemes.A wellknown example is the convection of
vortices where the core properties are altered during cal
culation.High order schemes are currently available,with
better properties both in terms of acoustics and dissipation
of vortices oering substantial improvements over conven
tional second/third order schemes.Their implementation
in CFD solvers is,however,dicult and most of the times
is associated with a long period of validation and in prac
tice it may result in loss of eciency and stability during
calculation.
The present work attempts to present a method for
modelling BVI using CFD and Computational Aeroacous
tics (CAA).CFD is used to generate the unsteady pressure
eld around a blade during BVI and this is used as a source
in a CAA method.Central to this eort is the Compress
ible Vorticity Connement Method (CVCM) which allows
traditional CFD methods to preserve vortices.CVCM is
used for preserving vortices up to and beyond their inter
action with the blade.Once the acoustics waves are gen
erated very close to the surface of the blade,the Ffowes
WilliamsHawkings method is used for assessing their ef
fect on the fareld acoustics of the aircraft.The method
has been validated in a sequence of simple cases start
ing from vortex convection and getting into inviscid and
viscous calculations for a set of welldocumented headon
BVI cases.
It has to be mentioned that the CVCM technique is
able to help with one aspect of the problem i.e.the dissi
pation of vortices.It is of little help with the preservation
of acoustic waves in the ow and this is something that
only a highorder scheme combined with a ne discretisa
tion grid could achieve.Near a blade,however,the com
putational grid is suciently ne to capture the acoustic
waves provided the vortex in the ow is wellpreserved.
Using the pressure eld near the blade to source,a CAA
method is therefore a way of tackling the BVI problem.
It is the objective of this paper to present the validation
of the method as well as the results of a parametric study
revealing the characteristics of both the neareld and far
eld acoustics of the phenomenon.Inviscid and viscous
calculations have been carried out and the obtained re
sults highlight the dierences in the acoustic behaviour
of various aerofoil sections and of vortices with dierent
properties.
Numerical Method
CFD Solver
The PMB code of the University of Glasgow [4] is used
in the present work.This is a parallel,structured,multi
block code with implicit time stepping.It uses the Osher's
and Roe's schemes combined with a preconditioned Krylov
solver for eciency.
To extend the capability of the code for predicting ows
with strong vortical structures the Compressible Vorticity
Connement Method (CVCM) [5] has been implemented.
This method is particularly attractive since it is economic
in terms of memory and CPU time and relatively simple to
implement in existing solvers.This method has been suc
cessfully used for tracking vortices [6,7] and more specif
ically for rotorcraft simulations [8].Application of the
method is also reported for several other ow cases includ
ing ows over complex bodies,massively separated ows
and even ow visualization.Recently,it was applied to
allow the simulation of bladevortex interaction [9] which
is the main focus of this paper.
The Compressible Vorticity Connement
Method
The Vorticity Connement Method (VCM) developed
by Steinho [10] is aimed at countering the dissipation
of the numerical scheme employed in CFD.The VCM is
based on the observation that the numerical scheme tends
to dissipate the vortices in the ow.The basic modica
tion is to add a body force term
~
f
b
to the momentum
transport equations which for incompressible ow reads:
ρ
∂
~
V
∂t
+ρ(
~
V:∇)
~
V+∇p =µ∇
2
~
V
~
f
b
:(1)
The body force term
~
f
b
is given by ρε
jΔ
~
ωj
jΔj~ωjj
~
ω where
ε,µ and ~ω are respectively the connement parameter,
an articial viscosity term and the vorticity.
The extension of the VCM to the compressible Navier
Stokes (NS) equations has been realised by including the
work of the body source term in the energy equation [11].
The integral form of the NS equations can be rewritten
for a twodimensional problem as
d
dt
Z
ϑ
Wdϑ+
Z
Σ
F:~ndΣ+
Z
Σ
G:~ndΣ =
Z
ϑ
Sdϑ:(2)
where W is the vector of the conservative variables,F and
G are the inviscid uxes in two spatial dimensions and the
source term S can be expressed as
2
S =
8
>
>
<
>
>
:
0
ερ(~n~ω):
~
i
ερ(~n~ω):
~
j
ερ(~n
~
ω):
~
V
9
>
>
=
>
>
;
with
8
<
:
~n =
∇j~ωj
j∇j~ωjj
~ω=
~
∂
∂M
~
V
:(3)
The term ρε
jΔωj
jΔjωjj
ω is added to the transport equa
tions of the momentum components,while ε,ρ and ω
represent the connement parameter,the density and the
vorticity,respectively.In order to include the work done
by the body source term in the energy conservation law,
the term ερ(~n~ω) also contributes as a part of the
residual.A complete review of the Compressible Vorticity
Connement Method is given in the thesis by Hu [12].
The implementation of the method in the PMB solver
as well as the selection of the optimum scheme for scaling
the connement parameter ε are presented in [9].
Computational Aeroacoustics
Method
Two dierent approaches are common for determin
ing the fareld noise:the Kirchho method [13] and the
Ffowes WilliamsHawkings (FWH) [14].
The use of the Kirchho method requires that all the
nonlinearities of the ow are inside a control surface which
is supposed to be representative of the ow phenomena
occurring during the BVI.In this case,using Green's the
orem,it is possible to calculate exactly the pressure dis
tribution outside the surface.The method also requires
knowledge of the time history of the ow quantities.Al
though the method is easy to adopt in potentiallike ows,
cases with strong vortices traveling in the ow domain or
cases with higher Mach number require a larger surface
since the nonlinearities prevail longer in all spatial direc
tions [15].This is a hard requirement to be met since
CFD methods loose resolution of the ow eld in coarse
grids far away of the main area of interest in the ow.
This implies that a judicious choice of the Kirchho sur
face [16] is necessary.As reported by Brentner [17],the
Kirchho approach for moving surfaces can lead to er
roneous results for two reasons.First,the integrations
over the control surface do not represent the physics of
the BVI when the vortex passes through the surface and
predictions can be misleading unless the integration sur
face is large enough to include the vortex before or during
the interaction.Furthermore,the Kirchho method re
quires the use of a neareld which is usually distant by
at least one chord from the aerofoil to include the non
linear eects of the ow on the acoustics.This makes the
Kirchho method unreliable for most CFD solvers which
tend to dissipate the pressure waves unless adaptive grid
renement or/and highorder spatial schemes are used to
preserve the acoustical waves for longer.Nevertheless,the
determination of the fareld noise remains possible with
the use of the FWH method [18] which can be formulated
to include surface properties only.
At subsonic ow,the FWH method has the advan
tage of only requiring the accurate prediction of the loads
on a lifting surface and even though the surface has to
be carefully chosen when simulating transonic BVI,little
dierence in the region of maximum BVI noise intensity
was noticed by Singh and Baeder [19] when quadrupole
noise is neglected.The FHW method also decomposes
the noise into dierent sources making the analysis of the
obtained results easier.The BVI is then classied as an
impulsive loading noise.Due to the above reasons the
FWH method has gained popularity and it is possible to
predict the thickness and loading noises from the FWH
equations provided the surface loads are known [20].
Regardless of choice,both FWH and Kirchho meth
ods rely on the accuracy of the neareld acoustics which
in this work is obtained from CFD calculations.Therefore,
the ability of the CFD solver for preserving acoustic waves
needs to be investigated.As shown in Figure 1,acous
tic signals dissipate fast,which should not happen.So,
despite the fact that the CVCM is capable of conserving
vorticity,it does not help the preservation of the acoustical
waves.This implies that only the neareld close to the
aerofoil which is correctly captured by CFD can be used as
input data.Since the loads history can be wellpredicted
with the use of the CVCM,the FWH is preferred for the
study of the fareld noise.As in most acoustic codes
based on the FWH formulation [21],our approach con
siders the linear thickness and loading terms of the FWH
equation,neglecting the nonlinear quadrupole term.
Following Farassat's 1A formulation [22,23] which is
suitable for moving bodies such as helicopter blades and
assuming the blades are rigid,the FWH equation can be
reformulated as follows:
4πP
0
(~x;t) =
1
a
∂
∂t
Z
f =0
ρ
0
cv
n
+L
r
r (1M
r
)
ret
dΣ
+
Z
f =0
L
r
r
2
(1M
r
)
ret
dΣ
(4)
In the Farassat formulation 1A,it is possible to use the
retarded time as a reference:
∂
∂t
x
=
1
1M
r
∂
∂τ
x
ret
(5)
Then the loading and thickness acoustic pressure P
0
L
and
P
0
T
are deduced from Equations 4 and 5.Their respective
expression is
4πP
0
L
(~x;t) =
1
a
Z
f =0
"
˙
L
i
ˆr
i
r (1M
r
)
2
#
ret
dΣ
I
+
Z
f =0
"
L
r
L
i
M
i
r
2
(1M
r
)
2
#
ret
dΣ
II
(6)
3
+
1
a
Z
f =0
"
L
r
r
˙
M
i
ˆr
i
+cM
r
cM
2
r
2
(1M
r
)
3
#
ret
dΣ
III
4πP
0
T
(~x;t) =
1
a
Z
f =0
"
ρ
o
v
n
r
˙
M
i
ˆr
i
+cM
r
cM
2
r
2
(1M
r
)
3
#
ret
dΣ
(7)
The acoustic pressure is expressed as the sum of the load
ing and thickness noise sources:
P
0
(~x;t) =P
0
L
(~x;t) +P
0
T
(~x;t) (8)
The thickness term [24] which considers the disturbance
of the uid medium caused by the airfoil is determined by
the blade characteristics and the forward velocities.The
loading terms which represents the noise caused by the
airfoil exerting a force on the uid [25] requires the calcu
lation of the forces acting on the blade.
It is interesting to note that"the loading noise depends
on the projection of the forces onto the direction from the
blade to the observer"[22].Term I is supposed to be
the dominant term of the loading noise.Therefore,only
term I of Equation 6 is estimated.Note that the dis
tance aircraftobserver was also approximated so that the
aircraft was seen as a source point.
According to [22],only subsonic motion of the blade
is allowed,i.e,for low forward speed (20m/s).Discrep
ancies appear in the prediction at high forward speeds
(V=67m/s) due to the large contribution of the quadrupo
lar noise [26] for higher tip Mach numbers,which is cre
ated by the velocity perturbation along the blade chord.
Furthermore,the presence of shocks,i.e.strong disconti
nuity in pressure,are also a possible source of noise.Both
quadrupole and shock noise are assumed to be at the ori
gin of the noise discrepancy.
For acoustic prediction,the integration of the lift force
(term I of Equation 4) over the chordwise direction is of
ten realised assuming that the blade can be seen as a point
source (r=c <<1).The force is then applied at the quar
ter chord and the BVI is said to be chordwise compact
[27].The compactness of the chordwise loading distribu
tion is justied as long as the aspect ratio of the blade
is high and the ow which is considered 2D locally make
the frequency range of BVI low enough for the observer
not to perceive any chordwise variations [26].Indeed,the
generation of an acoustic wave is associated with a partic
ular phase [28].Each section wave can be characterised
by a phase which corresponds to a xed section of the
blade.The radiated noise therefore depends on the phase
delay between all the acoustic pressures for a xed chord
wise section,which implies that the noise levels may be
overpredicted.
The modication of the phase delay is also an im
portant parameter of the BVI noise generation since BVI
acoustic phasing in uences the directionality of the radi
ated noise [29].A comparison between the noncompact
and the compact modeling has been undertaken by Sim
and Schmitz [27].They found that a lower peak value and
a larger acoustic pulse width is obtained for the compact
modeling.However,the dierence in terms of noise lev
els between the two methods appears especially near the
plane of the rotor and decreases underneath it.Although
noncompact chord assumptions does not overpredict the
noise levels as the compact does,the directivity patterns
or trends of the noise remains similar.
Parametric study
The complex oweld encountered during BVI is
known to produce a very intense impulsive noise [30].As
mentioned in [31],this noise has four main contributions:
(i) from the vortex at subsonic speed with its upwash or
downwash velocity component,(ii) fromthe stall and reat
tachment of the ow when the vortex approaches the aero
foil,(iii) from the oscillation of the stagnation point due
to the high pressure region generated at the leadingedge
(LE) of the aerofoil (compressibility waves) and (iv) from
the development of a supersonic area at the shoulder of
the aerofoil (transonic waves).It is known that the mag
nitude of the BVI noise and its directivity patterns are
related to the aerofoil shape,the freestream Mach num
ber,the vortex core radius,the vortex strength and the
missdistance between the vortex core and the surface of
the aerofoil.Using the combined CFD/CAA method de
scribed above,a study has been conducted in order to
investigate the in uence of each of the above mentioned
parameters on BVI.A list of the conditions along with the
nature of the calculations is given in Table 1.
Headon BVI has been simulated for six dierent
aerofoils at subsonic and transonic ow conditions:
NACA0006,NACA0012,NACA0018,NACA001234,
NACA16018 and SC1095 (see Figure 2).The three rst
sections are symmetric with increasing thickness while the
fourth and the fth ones are NACA 4digit proles with a
modied leading edge radius.The last one is a cambered
section and is representative of the sections currently used
in helicopter rotors.For the employed sections the lead
ing edge radius is respectively 0.397%,1.587%,3.57%,
0.397%,1.587% and 0.7% of the aerofoil chord.
The range of Mach numbers under consideration was
chosen to highlight the dierences between subsonic and
transonic ow,which explains why a high Mach number
of 0.8 was chosen for the latter.The Cp,lift and drag
histories of the vortexaerofoil interaction given by Euler
and NS calculations are presented for the dierent types of
BVI at dierent Mach numbers.Note that the Reynolds
number was xed to one million for viscous calculations
and the angle of attack was set to zero for all the calcu
lations.
4
Eects of aerofoil shape at sub
sonic and transonic conditions
Dierent NACA proles were used to highlight the role
of the thickness and the LE radius of the aerofoil.Cal
culations were also run with the SC1095 aerofoil to in
vestigate the in uence a cambered section may have.For
this prole (SC1095) the loaded aerofoil calculations were
performed by keeping the angle of attack to 0
0
.Further
runs were also carried out with the aerofoil set at its zero
lift angle.
For subsonic ow,the Cp history at x/c=0.02 on the
upper surface is similar for all aerofoils as shown in Fig
ure 3.It can be seen that the LE radius has a stronger
eect on the thinner aerofoils.It is expected that a
smaller leadingedge should actually be more sensitive to
the vortexinduced"downwash"[32],which is translated
into larger uctuations in the pressure distributions near
the LE [33].The dierences on the lower side seem to
be driven by the LE radius and the thickness,especially
for the chordwise location x/c=0.02.This is illustrated by
the Cp of the NACA0006 and NACA001234 aerofoils.As
depicted in Figure 4(ab),the secondary generated vortex
is weaker for the NACA001234,leading to lower Cp.Al
though this conrms the idea that the LE radius is more
important for thinner aerofoils at subsonic ow,the over
all in uence of the secondary vortex on the Cp is small
due to its short lifespan (see Figure 4(cd)).
Results are now discussed for transonic ow cases at a
freestreamMach number of 0.8.The history of the surface
pressure coecient is shown in Figure 5.Since the aero
foils have dierent shock locations,it remains dicult to
assess the importance of the thickness and the LE radius.
However,the BVI peaks seem to delay for thick aerofoils
with large LE radius and is remarkable that the peaks do
not occur at the same time due to compressibility.Note
that,although the peaks of the lift coecients are now
lower than the subsonic case,the lift forces exerted on the
body are in fact stronger due to the high dynamic head.
The presence of the vortex was found to aect the
shock.The vortex while moving over the surface of the
aerofoil encounters the shock,thickens the shock and re
gains some strength.This explains why the Cp curve has
wider peaks.It also explains the dierent loading of the
blades before the BVI.Indeed,the shock location on the
lower side was found to move upstream,which changes
the symmetry between the shocks on the lower and upper
surfaces and therefore modies the loads.For the SC1095
aerofoil,the dierence of loads before the interaction at
the transonic regime mainly comes from the cambered
shape of the aerofoil,the aerofoil osetting strong shock
formation.
The lift history and the lift peaks are given in Figure 6
for dierent aerofoils at the transonic ow.The peak of
lift conrms that a small LE radius leads to higher BVI
loads for thicker aerofoils at transonic ow.The thick
ness of the aerofoils seems also to determine the timing
of occurrence of the peaks.As suggested by Hardin and
Lamkin [34],and Booth [23,35],the vortex decelerates
as it approaches the aerofoil,leading to the generation of
lift.It is interesting to establish a comparison between
the subsonic and transonic ows for the SC1095 aerofoil.
As shown in Figure 7,the initial loading of the aerofoil
has an eect on the unsteady loading both before and
after the encounter with the vortex.As mentioned in
[36],the lift coecient is observed to be positive when
the vortex induces a downwash at the LE of the aerofoil in
both subsonic and transonic ows.Afterwards,when the
vortex passes the LE,the lift coecient rapidly increases.
The drag peak increases with the strength of the shocks.
As expected,the SC1095 aerofoil has the lowest drag
coecient and,for the unloaded case,it appears to be
the less aected by the BVI at the Mach number of 0.8.
Note that only the integration of the lift over the time
domain could give a good estimation of the in uence of
the LE radius and of the thickness at subsonic ow due
to the small dierences between the lift of the aerofoils.
So far the aerodynamics of the interaction,as charac
terised by the surface pressures and the lift history,have
been considered.The dierences in acoustics are now dis
cussed for the dierent aerofoils.The high directivity of
BVI noise is usually illustrated by two distinct radiation
lobes.These two waves are called compressibility waves
and are typical for high subsonic ow.These waves are due
to the oscillation of the stagnation point induced by the
passage of the vortex.This generates an enlarged high
pressure region which propagates upstream like a steep
ening shock wave [37].The ow de ection at the LE of
the aerofoil is actually large enough for the acoustic waves
to detach from the aerofoil.The two waves are denoted
by A and B in Figure 8(a,c) and once they reach the
trailingedge,two new waves start to form which prop
agate upstream contributing to the trailingedge noise.
The trailingedge waves [34] are marked as C and D in
Figure 8(a,c).
The acoustic pressure was calculated at four probes
marked as P
1
;P
2
;P
3
;P
4
in Figure 8(a,c) to allow a com
parison of the magnitude and the phase of all acoustic
waves present in the ow.The calculation was repeated
for all aerofoils and at two freestreamMach numbers.Fig
ures 8(b) and 8(d) show the typical signature of the waves,
respectively at subsonic and transonic ow.The com
pressibility waves only pass through points P
1
and P
2
and
look very similar in terms of magnitude and are opposite
in phase.The same remark can be made for the transonic
waves at points P
3
and P
4
.It can be observed that the
TE waves also pass through points P
1
and P
2
.The time
history of the acoustic pressure for the probe at point P
1
indicates the passage of the acoustical wave A.The acous
tic behaviour of the dierent aerofoils in subsonic ow is
similar in terms of acoustic pressure peak.The acoustic
pressure of the main wave which propagates downstream
is of the same level (about 3% of the freestream pressure)
for the four symmetric aerofoils.However,the pressure
dierences encountered just after the vortex reaches the
aerofoil and again as it reaches the TE seem to increase
for the thinner aerofoils.
5
Figures 9(ab) and 9(ef) establish a comparison be
tween the compressibility waves propagating above and
below the aerofoil at the two ow regimes whereas Fig
ures 9(cd) and 9(gh) depict the TE waves propagating
upstream.It has to be noticed that there are signicant
dierences in the strength and direction of the acoustical
waves between the two Mach numbers.Despite the fact
that at low Mach the passage of the vortex does not per
turb the loads on the aerofoil as much as in transonic ow,
the level of acoustic pressure at transonic Mach is higher
than the subsonic case.The time history of the acoustic
pressure through the point P
1
at high Mach diers from
the subsonic one in three aspects.First,the dierence
of SPL for the transonic ow from the subsonic ow is
about 10dB.Secondly,the acoustic waves are generated
earlier after the interaction for the transonic case than for
the subsonic one.Finally,the acoustic response of the
aerofoils after the interaction varies with the location and
strength of the shocks which are likely to make the BVI
less impulsive as the vortex passes through them.The re
sulting directivity patterns of the radiated acoustic waves
which is a result of the complex interaction between the
vortex,the boundary layer and the shocks are all dierent.
The acoustic waves seemto propagate more upstreamand
to be wider for thicker sections.
An additional acoustic wave is present for transonic
ow.This wave,called the transonic wave emerges when
a supersonic ow region is present on the shoulder of the
aerofoil [37].As explained in [31,38],a shock wave ap
pears after the vortex reaches the maximum thickness of
the aerofoil beyond which the supersonic area collapses.
Then the shock wave moves upstream leaving the LE in a
downward direction while the stagnation point moves up
wards.This results in the generation of a sound wave
propagating upstream [39] which is marked by E.The
compressibility wave propagates upstreamat zero angle to
the chord of the section while the transonic wave moves
in a vertical downward direction [15].As expected,the
compressibility and trailingedge wave are also present for
the transonic ow case.
It is also interesting to note that the BVI magnitude
seems to be related to the loading of the aerofoil,as
shown by the dierent peaks obtained on the loaded and
unloaded SC1095 cases.The acoustical signal at point
P is similar at the subsonic ow (see Figure 10(a,b)).
However,the unloaded aerofoil seems to be less critical
in terms of BVI noise magnitude at the transonic ow.
As illustrated by Figure 10(c,d),the transonic wave E
merges with the compressibility waves for the loaded aero
foil whereas both waves are more separated for the un
loaded aerofoil,explaining the dierence of acoustic pres
sure levels.
Eects of vortex properties
Vortex core radius
Calculations were run inviscid for headon and miss
distance (y
0
= 0:15) BVI,and the employed grids
were of 240k and 170k points,respectively.The non
dimensionalised vortex strength was set to 0.283 at a
Mach number of 0.5 for the rst case and to 0.42 for a
Mach number of 0.73 for the last case.The radii were set
to 0.018,0.04,0.06 and 0.10 for the headon BVI and to
0.4,0.06,0.10 and 0.15 for the missdistance BVI.
The surface pressure coecients are given in Figure 11.
A stronger BVI is obtained for a smaller vortex core size.
For the headon BVI,the loads seem to be more sensitive
to the vortex core size,the loads magnitude being much
larger for the smaller vortex.Since the vortex strength was
kept the same for the dierent vortices,it appears that the
headon BVI strongly depends on the core radius.For the
missdistance BVI,the size of the vortex core is not as
important as the headon BVI.Although the interaction
becomes stronger when the vortex core size decreases,a
vortex of smaller core radius is found to have a lesser ef
fect on the loads.This is a important dierence between
headon and missdistance BVI for nonlifting aerofoils as
far as the in uence of the vortex core size is regarded.
The time histories of the lift and pressure drag are
shown in Figures 12 and 13.It is noticeable that the
overall shape of the lift is the same for the four dierent
core radii.The lift tends to increase for vortices of smaller
radius but the overall shape of the lift curve remains the
same except for the part where the interaction occurs.
The apparent angle of attack induced by the vortex is
larger for the vortex with the highest tangential velocity
and this suggests that the induced angle is primarily a
function of the vortex strength of the initial vortex.The
same remarks can be made for the drag coecient:the
drag reduces more for the clockwiserotating vortex of the
smaller core radius.
The neareld acoustics is now discussed.The non
dimensionalised pressure is given in Figure 14.For the
headon BVI,the acoustic waves are weaker and wider for
vortices of initially larger core radius.Although the acous
tic waves are not as wide for a given missdistance,the
vortex core size also in uences the magnitude of the pres
sure wave with the stronger BVI obtained for the smaller
radius.This is expected since the magnitude of the max
imum tangential velocity is a function of the core radius
to missdistance ratio and the times of emission of the
acoustical waves are dierent for the two freestream con
ditions.
Regarding the acoustic signal passing through point
P,the rst BVI peak due to the compressibility wave is
observed for both ow cases.This is illustrated by Fig
ure 15.However,the time history of the acoustic pressure
diers afterwards.Indeed,for the rst BVI,the acoustic
pressure decreases towards zero after the highpressure re
gion near the LE is stabilised whereas a positive peak of
pressure uctuations which stems from the passage of the
transonic wave occurs for the second type of BVI.
6
Vortex strength
The ow Mach number and the nondimensionalised
core radius were respectively xed at 0.57 and 0.1.It is
interesting that the apparent angle of attack induced by
the incoming vortex is negative before the interaction and
becomes positive after reaching the trailingedge of the
aerofoil.The clockwiserotating vortex creates a down
wash distribution of vertical velocity before the LE [33]
and induces a upwash eect after the TE.It is possible to
assimilate the pressure dierence across the airfoil as the
response of the ow to a decrease in angle of attack,this
means that the vertical velocity eld induced by the vor
tex is negative when approaching the aerofoil and becomes
positive after it passes behind the aerofoil as explained by
McCroskey and Goorjian [32].After the vortex passes past
the TE,another pulse of opposite sign is observed for the
pressure at the TE [18] as shown in Figure 16.
Regarding the Cp history obtained for dierent vortex
strengths,the amplitude of the Cp uctuations increases
with the vortex strength for all chordwise sections.It is
also observed that the lift is driven by the vortex strength
as depicted by Figure 17.This is also valid for the drag
whose magnitude is larger for an initial stronger vortex.
The freestreamMach number was xed to 0.57 and the
nondimensionalised core radius to 0.1.Contours of the
nondimensionalised pressure are given in Figures 18(a
d).The work of Hardin and Lambin [3] shows that the
acoustic pressure is a linear function of the strength of the
incoming vortex.This is veried for both compressibility
and transonic waves of which amplitude increases with the
vortex strength.However,the direction of propagation is
modied with the increase of the vortex strength,and
the compressibility waves almost propagate in directions
normal to the aerofoil chord.Furthermore,the directiv
ity patterns of the transonic waves remain similar,which
conrms the observations of Ballmann and Korber [38].
The time history of the acoustic pressure at point P
is shown in Figure 19.It is apparent that the magnitude
of the BVI noise is related to the vortex strength.The
transonic wave is clearly observable for
ˆ
Γ >0:283,this is
manifested as a positive pressure peak after the main in
teraction.The fact that the magnitude of the transonic
wave increases with the vortex strength suggests that the
supersonic pocket which is at the origin of the generation
of the transonic shock wave depends on the magnitude of
the velocity induced by the vortex,i.e.the vortex strength.
Missdistance
Inviscid calculations were run for two Mach numbers
of 0.57 and 0.73 at dierent missdistances of 0.00 c,0.10
c,0.15 c,0.31 c,0.45 c and 0.60 c.It was found that
the BVI loads decrease linearly with the miss distance by
about the same amount.
For the rst BVI case,it was observed that the peak in
terms of loads occurs earlier for the larger missdistance
BVI with the strength of the supersonic pocket directly
related to the proximity of the vortex to the aerofoil.How
ever,an increase of the missdistance does not necessarily
mean a proportional decrease of the main BVI [40].The
Cp history depicted by Figure 20 for the subsonic ow ac
tually shows the stronger interaction for a missdistance
of 0.15 c on the upper surface of the aerofoil whereas the
stronger BVI for the transonic ow is obtained for y
0
=0:0.
The lift and drag histories are given in Figure 21.It
is noticeable that the lift history is very similar for miss
distances of y
0
=0:0 and y
0
= 0:10.This veries that
the strongest interaction occurs for headon BVI and for a
missdistance equal to the radius core.The missdistance
may be an interesting way of alleviating BVI as long as the
distance vortexaerofoil is maintained to a distance supe
rior than twice the radius core size.The drag coecient
increases for both types of ow and becomes positive
for the transonic ow at missdistances y
0
>= 0:15.
This may be due to the vortexshock interaction since
the shock may distort due to the vortex or even gain
some strength.It is believed [41] that the drag forces in
uence the shock motion,more especially their directivity.
Both compressibility waves and transonic waves appear
for the two types of BVI (see Figure 22 and 23).The
acoustical waves noted A and B weaken with the miss
distance for both type of ows when the missdistance
is superior to the radius core.Indeed,the strongest BVI
is expected for a missdistance equal to the core radius.
The vortexinduced downwash also aects the aerofoil at
an early time for missdistance BVI.As a result,the acous
tical wave generated by missdistance BVI starts to propa
gate before the one of headon BVI.It is also interesting to
note that the directivity of the two compressibility waves
changes with the missdistance.They tend to propagate
more downstream and to merge with an increase of the
distance aerofoiltovortex.As observed by Booth [23],
the width of the acoustic waveform seems to be indepen
dent of the bladetovortex spacing.The compressibility
wave is also found to merge with the transonic wave for
small missdistances.Note that the transonic wave dis
appears for too large missdistances,i.e,when the gen
erated supersonic pocket is not strong enough to detach
and propagate into the fareld.
It is interesting to note that the transonic wave may be
as strong or even stronger than the compressibility wave
as shown in Figure 24.The strongest BVI appears to
be for a missdistance of 0.15 due to the transonic wave
for case 1 (M=0.57) and for the headon BVI due to the
compressibility wave for case 2 (M=0.73).
Fareld acoustics
The acoustics module was tested against data taken
from the experiments of Kitaplioglu [2].A schematic of
the experimental setup is shown in Figure 25(a) while a
schematic of the blade with its polar coordinates is given
in Figure 25(b).The angles Ψ and θ are respectively the
azimuth and the elevation angles.The azimuth angle is
equal to 0:0
o
behind the rotorcraft and to 180
o
in front
of.A point whose elevation is set to 90
o
is located just
7
beneath the rotorcraft.The ow conditions were the fol
lowing:µ=0:2;M
tip
=0:71;r=R=0:886 and the vortex
characteristics were
ˆ
Γ = 0:374;M = 0:63;R
c
= 0:162.
The loads calculated by CFD were used for the prediction
of the BVI noise at point 3 for the two missdistance BVI
(y
0
=0:0 and y
0
=0:25).
Due to the employed FWH formulation,it was nec
essary to generate 3D loads from the 2D CFD results.
First,the pressure signal had to be redistributed along the
spanwise direction.As mentioned by [27],the inboard
blade contributes very little to acoustics.Therefore,the
BVI should only in uence the loads for a spanwise ra
dius of r=R >0:65.Note that simple weighting functions
were used for generating the chordwise loading distribu
tion along the spanwise directions which correspond to
given blade sections of a rectangular blade.Calculations
were carried out so that the peak of BVI occurs at an az
imuth angle of 144
o
.It was observed that the time during
which BVI happens is essential for predicting the correct
BVI noise,which was expected since the lift force is inte
grated over the time domain.The number of steps for one
revolution was therefore set so that the azimuth angle Ψ
of the blade increases by an amount dΨ corresponding to
the time step of the CFD computations.The distribution
of the lift coecient over the spanwise direction and the
blade revolution is given in Figure 26 for the headon BVI.
The acoustic pressure was calculated at point 3 (see
Figure 25(a)) which is located ahead and below the air
craft.The results are shown in Figure 27 and are in good
agreement with the experiments,which indicates that the
BVI magnitude is correctly predicted by the aeroacoustical
module as long as the duration of the BVI is respected.
The computed acoustic pressure diers from the experi
mental one by its smoother shape.Indeed,the simulation
of the BVI was carried out in 2D,meaning that the vor
tex was introduced ahead of the aerofoil.The vortex was
aected by the presence of the aerofoil before the interac
tion,explaining why the computed signal is not as sharp
as the one provided by the experiments.Both loading
and thickness noises were calculated and as depicted by
Figure 27,the slap noise dominates.
Description of the rotor ight conditions
The ight conditions were chosen to be representative
of manoeuvres where BVI is likely to occur.It is known,
that the advancing side BVI dominates the overall radi
ation pattern [27] with most of the noise directed down
wards,beneath the helicopter in the direction of forward
ight.As reported by Preissier et al.[42],the blade un
dergoes multiple interactions on the advancing side due to
the tip vortices of the blade on the retreating side,espe
cially at lower speeds since there are more vortices present
in the rotor blade.Therefore,the advance ratio was set
to a relatively low value of 0.2 for a blade of 6.2 meters
of radius,the tip Mach number ranging from 0.5 to 0.8.
A nonlifting rotor based on the NACA0012 aerofoil
was chosen for most calculations.The tippathplane an
gle was also xed to zero for a rectangular blade with a
chord of around 40 cm length.Even though the local
pitch angle was set to zero,it was not expected to have
a large impact in terms of directivity [26] since the angle
on the advancing side of an helicopter is small.
The location of the BVI was set at azimuth Ψ=90
o
since it was demonstrated experimentally by Booth [35]
that the most intense BVI acoustic radiation is generated
between 65 and 90 degrees of azimuth angle.The Average
Overall Sound Pressure Level (OASPL) was calculated at
dierent observer positions to investigate the magnitude
and the directivity patterns of the BVI noise.The ob
servers have been positioned below and above the rotor
for both advancing and retreating blades.The directivity
of BVI has been highlighted using an (θ,Ψ) map which
represents the OASPL of BVI for dierent rotational and
azimuthal angles.
Although it has been shown previously that the tran
sonic waves may be as strong or even stronger than the
compressibility waves,it is assumed that they will not af
fect as much an observer below the rotorcraft than the
compressibility waves due to the fact that they propagate
upstream the aerofoil.Therefore,it is acceptable to say
that the present calculations are representative of the BVI
characteristics for the specied ight conditions.Note
that 1024 points were sampled per rotor revolution.
Eect of the aerofoil shape
The fareld noise levels are given for an observer lo
cated 50 meters below and 50 meters ahead of the air
craft which corresponds to point P.A comparison of the
acoustic pressure for the dierent aerofoils (see Figure 28)
shows that only slight dierences in terms of BVI noise
magnitude appear for Mach number of 0.5,the NACA
0018 remaining the less noisy,the three others giving sim
ilar acoustical response.It is interesting to note that the
unloaded SC1095 aerofoil is slightly less noisy than the
loaded SC1095 at point P,suggesting that the induced
loads aect the BVI noise directivity.The levels of thick
ness noise are negligible against the loading noise levels as
depicted by Figure 28.
The importance of the aerofoil shape [15] is veried for
transonic ow at which the behaviour of the BVI noise for
the nonsymmetric aerofoil SC1095 and the NACA0018
is dierent from the other NACA aerofoils as depicted by
Figure 29.It was found that the noise is radiated in some
preferred directions at transonic ow.The similar acousti
cal behaviour between the SC1095 and NACA0018 sug
gests that the camber and the movement of strong shocks
which induce loads around the aerofoil modify the direc
tivity of the BVI noise.
As no specic trends could be deduced fromthese aero
foils for the thickness and the LE radius which are linked
together for the NACA 4digit proles,the NACA001234
and the NACA16018 aerofoils were used.It appears from
Figure 30 that both LE radius and thickness do not make
much of a dierence in terms of noise.However,it can
be observed at subsonic ow that the leadingedge radius
plays a more important role for thinner aerofoils whereas
8
the thickness in uences more the BVI magnitude for aero
foils of larger LE radius.For the transonic ow,it re
mained dicult to assess the role of the thickness and of
the LE radius due to the dierence of directivity of the
aerofoils and to the necessity of using a very small time
step for the CFD calculations for this headon BVI.Never
theless,it is suspected that the LE radius is of importance
for thicker aerofoils whereas the thickness matters more
for small LE radius at transonic ow.
It is observed for the two dierent types of ow that
the AOSPL becomes a linear function of the inverse of the
square distance observeraircraft after a certain distance
for dierent elevation angles as illustrated by Figure 31.
For the transonic case,an increase of the tip Mach num
ber also increases the amplitudes of the BVI radiation [27]
through the Doppler factor [24].
Eects of vortex properties
Vortex core radius
The acoustic pressure at an observer located at point
P is given in Figure 32 for dierent radii.Two calcula
tions were run.The rst type of BVI was headon,the
freestream Mach number and the vortex strength being
respectively 0.5 and 0.283.The second BVI was set for a
missdistance of 0.15 at a Mach number of 0.73,the vor
tex strength was xed to 0.42.As expected,the stronger
BVI remains for the vortex of smaller radius core which is
characterised by the higher tangential velocity magnitude.
It is noticeable that the decrease of the core radius
aects dramatically the headon BVI in terms of peak
magnitude whereas its in uence seems to decrease for the
missdistance BVI after a certain cuto value.It is ob
served that the noise decreases linearly with increasing
vortex core for headon BVI as long as the radius is not
too small.Regarding the missdistance BVI,the peak of
BVI noise was found to be a linear function of the vortex
core size for the largest core radii (see Figure 33).The
noise is less and less aected by the radius core size for
small enough vortices,which is expected since the expres
sion of the tangential velocity can then be approximated
by
v
θ
V
∞
=
ˆ
Γ
2πr
f or R
c
<<r
This is in agreement with the observations of Malovrh,
Gandhi and Tauszig [43] who reported that the changes
in the vortex structure aect the BVI noise when the miss
distance is less than half the blade chord.
As depicted by Figures 34,the BVI directivity patterns
are more likely to enlarge for an initial vortex of larger vis
cous radius.Note that the BVI noise is radiated forward
and downwards 60
0
beneath the rotor plane for the four
aerofoils.The lobes of the headon BVI noise get larger
and the overall magnitude tends to decrease with the vor
tex core size.It may suggest that an increase of the radius
core leads to a more spreadout radiated noise for headon
BVI.Since BVI is more likely to happen for a descending
ight,i.e,when the the tippathplane of the rotor is tilted
rearward [44],the BVI noise more often results from the
interaction of the blade with an older vortex.It implies
that a headon BVI with the tip vortices may lead to a
enlarged lobes of radiated noise,the core size increasing
in wake age [29].
Vortex strength
The noise levels perceived by an observer located at
point P for the four dierent types of BVI are shown in
Figure 35(a).As mentioned by Lyrintzis and George [15],
the disturbances increase more than linearly with the vor
tex strength.Indeed,a"slightly superlinear"dependence
is found for the BVI peaks [16].However,Figure 35(b)
suggests that the dependence of the BVI peak on the
vortex strength decreases for very strong vortices.This
means that the vortex strength has to be signicantly re
duced [43] to alleviate the peaks in the loads.
The directivity of the BVI noise is related to compress
ibility eects.Headon BVI propagates more uniformly for
a stronger initial vortex as shown by the size of the lobes
of the radiated noise of Figure 36.
Missdistance
Results are discussed for two types of BVI.The rst
BVI was simulated at a Mach number of 0.73 for an ini
tial vortex of nondimensionalised strength 0.42.The
second case was for a Mach number of 0.57 with a vor
tex strength 1.8.The nondimensionalised radius R
c
of
the initial vortex was xed to 0.1.BVI amplitude shows
a linear dependence on the missdistance [16] as long as
the missdistance is superiour to R
c
(see Figure 37).It
is observed that the BVI noise is inversely proportional to
the missdistance [29].Note that the maximum BVI noise
occurs when the missdistance is equal to the vortex core
size.
However,the SPL fallorate with core radius gets
smaller when the core radius is less than the miss dis
tance [24].In addition,the linear dependence of the BVI
noise with the missdistance is not valid any more for miss
distances superiour to the vortex core size for the second
BVI as shown in Figure 38.The interaction between the
vortex and the generated supersonic pocket may be at the
origin of this behaviour.
The insensitivity to small missdistance increases for
larger vortex core radii [43].It means that the reduction
of the noise levels passes by the decrease of the velocities
induced on the rotor blade [24].Then it is more eective
for reducing the BVI noise to increase the miss distance
than the core radius since the vortex core size has only a
strong in uence on the BVI noise for headon BVI.
Figure 39 shows the BVI trends for headon and miss
distance BVI.It appears that the size of lobes of radiated
noise increases with the missdistances,the OASPL de
creasing.It just means that the BVI noise energy is more
spreadout in the case of increasing missdistances.
9
Unsteady case
Parameter
M
y
0
ˆ
Γ
R
c
Aerof oil
NACA0006
NACA0012
Viscous
Aerofoil
0.5
0.0
0.283
0.018
NACA0018
Shape
0.8
0.177
SC1095
NACA01234
NACA16018
0.018
0.5
0.0
0.283
0.04
NACA0012
0.06
Inviscid
Vortex
0.10
core
0.04
radius
0.73
0.15
0.42
0.06
NACA0012
0.10
0.15
0.248
Vortex
0.538
Inviscid
strength
0.57
0.0
1.16
0.1
NACA0012
1.8
0.0
0.10
Inviscid
Miss
0.57
0.15
1.80
0.1
NACA0012
distance
0.73
0.31
0.42
0.45
0.60
Table 1:List of the parameters examined.M,R
c
,
ˆ
Γ,(x
0
;y
0
) represent respectively the freestreamMach number,
the vortex core radius nondimensionalised against the chord,the vortex strength nondimensionalised against
the product freestream velocitychord and the missdistance nondimensionalised against the chord.A number
of 0.8 was chosen to highlight the dierences of behaviour for the dierent aerofoils.Note that a negative
strength
ˆ
Γ corresponds to a clockwiserotating vortex.
(a)
(b)
Figure 1:(a) Acoustic pressure history at points 1,2,3 above the aerofoil  (b) Acoustic pressure history at
points 4,5,6 below the aerofoil.Headon BVI problem,NACA0012 aerofoil,viscous calculations,M=0.5.
ˆ
Γ =0:283;R
c
=0:018.
10
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0
0.2
0.4
0.6
0.8
1
Y
X
NACA0006
NACA0012
NACA0018
SC1095
NACA001234
NACA16018
Figure 2:Geometry of the dierent aerofoils.The aerofoils NACA0012,NACA0018,SC1095,NACA001234
and NACA16018 are respectively oset by 0.2,0.4,0.6,0.8 and 1.0 for clarity.
4
3.5
3
2.5
2
1.5
1
0.5
0
0.5
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
CP,L
Time
NACA0006
NACA001234
NACA0012
NACA16018
NACA0018
SC1095
SC1095, unl.
(a) Lower surface  x/c=0.02
1
0.5
0
0.5
1
1.5
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
CP,U
Time
NACA0006
NACA001234
NACA0012
NACA16018
NACA0018
SC1095
SC1095, unl.
(b) Upper surface  x/c=0.02
Figure 3:Time history of the surface pressure coecient at dierent chordwise locations.Headon BVI
problem,six dierent aerofoils,viscous calculations,M=0.5,
ˆ
Γ =0:283;R
c
=0:018.
(a) NACA0006
(b) NACA001234
11
5
4
3
2
1
0
1
2
0
0.2
0.4
0.6
0.8
1
CP
x/c
Lower surface
Upper surface
Clean case
(c) NACA0006
5
4
3
2
1
0
1
2
0
0.2
0.4
0.6
0.8
1
CP
x/c
Lower surface
Upper surface
Clean case
(d) NACA001234
Figure 4:(ab) Isobars (p/q
∞
) along with the velocity streamlines for the NACA0006 and NACA001234
aerofoils.(cd) Surface pressure coecient at time t (U
∞
=c)=4.51.Headon BVI,viscous calculations,M=0.5.
ˆ
Γ =0:283;R
c
=0:018.
2
1.5
1
0.5
0
0.5
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5
5.1
CP,L
Time
NACA0006
NACA001234
NACA0012
NACA16018
NACA0018
SC1095
SC1095, unl.
(a) Lower surface  x/c=0.02
1
0.5
0
0.5
1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5
CP,U
Time
NACA0006
NACA001234
NACA0012
NACA16018
NACA0018
SC1095
SC1095, unl.
(b) Upper surface  x/c=0.02
Figure 5:Time history of the surface pressure coecient at dierent chordwise locations.Headon BVI
problem,six dierent aerofoils,viscous calculations,M=0.8,
ˆ
Γ =0:177;R
c
=0:018.
0.12
0.1
0.08
0.06
0.04
0.02
0
0.02
0.04
3
3.5
4
4.5
5
5.5
6
CL
Time
NACA0006
NACA001234
NACA0012
NACA16018
(a) Same LE radius
0.12
0.1
0.08
0.06
0.04
0.02
0
0.02
0.04
0.06
3
3.5
4
4.5
5
5.5
6
CL
Time
NACA0012
NACA001234
NACA0018
NACA16018
(b) Same thickness
Figure 6:Time history of the lift for dierent aerofoils of the same thickness or the same LE radius at freestream
Mach number 0.8.
ˆ
Γ =0:177;R
c
=0:018.
12
1
0.8
0.6
0.4
0.2
0
0.2
0
1
2
3
4
5
6
7
CL
Time
Loaded, M=0.5
Loaded, M=0.8
Unloaded, M=0.5
Unloaded, M=0.8
(a)
0.1
0.05
0
0.05
0.1
0
1
2
3
4
5
6
7
CD
Time
Loaded, M=0.5
Loaded, M=0.8
Unloaded, M=0.5
Unloaded, M=0.8
(b)
Figure 7:Time histories of the lift and drag coecients at Mach numbers of 0.5 (a) and 0.8 (b) for the loaded
and unloaded SC1095 aerofoil.
ˆ
Γ =0:283 (M=0.5),R
c
=0:018.Note that the drag is nondimensionalised
against ρ
∞
U
2
∞
c.
(a) M=0.5,t (U
∞
=c) =5:1
(b) M=0.5
(c) M=0.8,t (U
∞
=c) =5:4
(d) M=0.8
Figure 8:(a,c) Contours of the acoustic pressure along with the location of the four probes and (b,d) time
history of the acoustic pressure at the probes.The absolute value of the acoustic pressure is represented for
the NACA0012 at a freestream Mach number of 0.5 (a,b) and 0.8 (c,d).The scale is exponential.
13
7000
6000
5000
4000
3000
2000
1000
0
1000
2000
3000
4.4
4.45
4.5
4.55
4.6
4.65
4.7
4.75
4.8
4.85
4.9
Pacous [Pa]
Time
NACA0006
NACA001234
NACA0012
NACA16018
NACA0018
SC1095
SC1095, unloaded
(a) M=0.5,point P
1
2000
1000
0
1000
2000
3000
4000
5000
6000
4.4
4.45
4.5
4.55
4.6
4.65
4.7
4.75
4.8
4.85
4.9
Pacous [Pa]
Time
NACA0006
NACA001234
NACA0012
NACA16018
NACA0018
SC1095
SC1095, unloaded
(b) M=0.5,point P
2
3000
2000
1000
0
1000
2000
3000
4.4
4.6
4.8
5
5.2
5.4
Pacous [Pa]
Time
NACA0006
NACA001234
NACA0012
NACA16018
NACA0018
SC1095
SC1095, unl.
(c) M=0.5,point P
3
3000
2000
1000
0
1000
2000
3000
4.4
4.6
4.8
5
5.2
5.4
Pacous [Pa]
Time
NACA0006
NACA001234
NACA0012
NACA16018
NACA0018
SC1095
SC1095, unl.
(d) M=0.5,point P
4
15000
10000
5000
0
5000
4.6
4.65
4.7
4.75
4.8
4.85
4.9
4.95
5
5.05
5.1
Pacous [Pa]
Time
NACA0006
NACA001234
NACA0012
NACA16018
NACA0018
SC1095
SC1095, unl.
(e) M=0.8,point P
1
2000
0
2000
4000
6000
8000
10000
4.6
4.65
4.7
4.75
4.8
4.85
4.9
4.95
5
5.05
5.1
Pacous [Pa]
Time
NACA0006
NACA001234
NACA0012
NACA16018
NACA0018
SC1095
SC1095, unl.
(f) M=0.8,point P
2
6000
5000
4000
3000
2000
1000
0
1000
2000
3000
4000
5000
4.4
4.6
4.8
5
5.2
5.4
Pacous [Pa]
Time
NACA0006
NACA001234
NACA0012
NACA16018
NACA0018
SC1095
SC1095, unl.
(g) M=0.8,point P
3
4000
3000
2000
1000
0
1000
2000
3000
4000
5000
4.4
4.6
4.8
5
5.2
5.4
Pacous [Pa]
Time
NACA0006
NACA001234
NACA0012
NACA16018
NACA0018
SC1095
SC1095, unl.
(h) M=0.8,point P
4
Figure 9:Acoustic pressure history for the aerofoils at points P
1
(a,e),P
2
(b,f),P
3
(c,g) and P
4
(d,h).
Headon BVI,R
c
=0:018,(ad) Mach=0.5,
ˆ
Γ =0:283,(eh) Mach=0.8,
ˆ
Γ =0:177.
14
6000
4000
2000
0
2000
4.6
4.8
5
5.2
5.4
Pacous [Pa]
Time
Loaded
Unloaded
(a) M=0.5
6000
4000
2000
0
2000
5
5.2
5.4
5.6
5.8
6
6.2
6.4
Pacous [Pa]
Time
Loaded
Unloaded
(b) M=0.8
0.95
1.07
1.16
0.98
1.1
1
x/c
y/c
0.3
0.2
0.7
1.2
1.4
0.9
0.4
0.1
0.6
1.1
1.63
1.52
1.41
1.30
1.19
1.14
1.08
1.02
0.91
0.80
0.69
P
E
B
C
D
A
(c) Loaded
0.95
1.08
1.21
1.01
1.10
x/c
y/c
0.3
0.2
0.7
1.2
1.4
0.9
0.4
0.1
0.6
1.1
1.64
1.51
1.38
1.25
1.15
1.07
0.97
0.86
0.73
0.60
P
A
B
C
D
E
(d) Unloaded
Figure 10:(ab) Acoustic pressure history at point P at two freestream Mach numbers.(cd) Isobars (p=q
∞
)
at t (U
∞
=c)=5.40 the loaded (c) and unloaded (d) SC1095 aerofoil.Viscous calculations,headon BVI case,
M=0.8,
ˆ
Γ =0:177,R
c
=0:018.
15
5
4
3
2
1
0
1
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
CP,L
Time
R
c
=0.018
R
c
=0.040
R
c
=0.060
R
c
=0.100
(a) Lower surface,x/c=0.02,M=0.5
0.4
0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
CP,U
Time
R
c
=0.018
R
c
=0.040
R
c
=0.060
R
c
=0.100
(b) Upper surface,x/c=0.02,M=0.5
1.2
1
0.8
0.6
0.4
0.2
0
0.2
2
2.5
3
3.5
4
4.5
5
5.5
6
CP,L
Time
R
c
=0.04
R
c
=0.06
R
c
=0.10
R
c
=0.15
(c) Lower surface,x/c=0.02,M=0.73
0.4
0.2
0
0.2
0.4
0.6
0.8
1
2
2.5
3
3.5
4
4.5
5
5.5
6
CP,U
Time
R
c
=0.04
R
c
=0.06
R
c
=0.10
R
c
=0.15
(d) Upper surface,x/c=0.02,M=0.73
Figure 11:Time history of the surface pressure coecient at the chordwise location x/c=0.02.Headon BVI
problem,NACA0012 aerofoil,inviscid calculations,(a,b) M=0.5,
ˆ
Γ =0:283;y
0
=0:00.(c,d) M=0.73,
ˆ
Γ =0:42;y
0
=0:15.
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.1
0.2
0.3
0
1
2
3
4
5
6
7
CL
Time
R
c
=0.018
R
c
=0.040
R
c
=0.060
R
c
=0.100
(a)
0.1
0.08
0.06
0.04
0.02
0
0.02
0
1
2
3
4
5
6
7
CD
Time
R
c
=0.018
R
c
=0.040
R
c
=0.060
R
c
=0.100
(b)
Figure 12:Time histories of the lift and drag for four vortices of dierent initial core radius.Headon BVI,
NACA0012,inviscid calculations,M=0.5,
ˆ
Γ =0:283;(a) y
0
=0:0;(b) y
0
=0:15.
16
0.6
0.4
0.2
0
0.2
0
1
2
3
4
5
6
7
CL
Time
R
c
=0.04
R
c
=0.06
R
c
=0.10
R
c
=0.15
(a)
0.01
0.005
0
0.005
0.01
0.015
0.02
0
1
2
3
4
5
6
7
C
D
Time
R
c
=0.04
R
c
=0.06
R
c
=0.10
R
c
=0.15
(b)
Figure 13:Time histories of the lift and drag for four vortices of dierent initial core radius.Headon BVI,
NACA0012,inviscid calculations,M=0.73,
ˆ
Γ =0:42;y0 =0:15.
2.74
2.68
2.79
2.96
2.89
2.91
2.83
x/c
y/c
0.3
0.2
0.7
1.2
1.4
0.9
0.4
0.1
0.6
1.1
3.36
3.26
3.16
3.06
2.96
2.86
2.76
2.66
2.56
A
B
C
D
P
(a) y
0
=0:00,R
c
=0:018
2.80
2.69
2
.78
2.95
2.90
2.88
2.85
x/c
y/c
0.3
0.2
0.7
1.2
1.4
0.9
0.4
0.1
0.6
1.1
3.36
3.26
3.16
3.06
2.96
2.87
2.77
2.67
2.57
A
B
C
D
(b) y
0
=0:00,R
c
=0:10
1.17
1.06
1.1
2
1.3
6
1.42
1.36
1.36
x/c
y/c
0.3
0.2
0.7
1.2
1.4
0.9
0.4
0.1
0.6
1.1
1.89
1.76
1.64
1.51
1.38
1.25
1.12
1.00
0.87
A
B
C
D
P
(c) y
0
=0:15,R
c
=0:04
1.21
1.08
1.10
1.43
1.37
1.34
1.37
x/c
y/c
0.3
0.2
0.7
1.2
1.4
0.9
0.4
0.1
0.6
1.1
1.89
1.76
1.63
1.50
1.37
1.24
1.10
0.97
0.84
A
B
C
D
P
(d) y
0
=0:15,R
c
=0:10
Figure 14:Isobars (p=q
∞
) at t (U
∞
=c)=5.10 for dierent core radii.(a,b) M=0.5,
ˆ
Γ =0:283;y
0
=0:0.(c,
d) M=0.73,
ˆ
Γ =0:42;y
0
=0:15.
17
(a)
(b)
Figure 15:Acoustic pressure history at point P at two Mach numbers.(b) M=0.57,(d) M=0.73
5
4
3
2
1
0
1
2
0
1
2
3
4
5
6
7
CP,L
Time
=0.283
=0.530
=1.160
=1.800
(a) Lower surface,x/c=0.02
2.5
2
1.5
1
0.5
0
0.5
1
1.5
2
2.5
0
1
2
3
4
5
6
7
CP,U
Time
=0.283
=0.530
=1.160
=1.800
(b) Upper surface,x/c=0.02
Figure 16:Time history of the surface pressure coecient at the chordwise location x/c=0.02 for vortices of
dierent strengths.Headon BVI problem,NACA0012 aerofoil,inviscid calculations,M=0.57.Note that the
vortex strengths are nondimensionalised against (U
∞
c).
2.5
2
1.5
1
0.5
0
0.5
1
1.5
0
1
2
3
4
5
6
7
CL
Time
=0.283
=0.530
=1.160
=1.800
(a)
0.2
0.15
0.1
0.05
0
0.05
0.1
0
1
2
3
4
5
6
7
CD
Time
=0.283
=0.530
=1.160
=1.800
(b)
Figure 17:Lift and drag histories for vortices of dierent strengths.NACA0012,headon BVI,M=0.57,
R
c
=0:018.Note that the vortex strengths are nondimensionalised against (U
∞
c).
18
2.13
2.02
2.10
2.30
2.23
2.22
2.20
x/c
y/c
0.3
0.2
0.7
1.2
1.4
0.9
0.4
0.1
0.6
1.1
2.72
2.62
2.52
2.42
2.32
2.22
2.12
2.02
1.92
A
B
C
D
P
(a)
ˆ
Γ =0:283
2.07
2.00
2.14
2.32
2.25
2.25
2.18
x/c
y/c
0.3
0.2
0.7
1.2
1.4
0.9
0.4
0.1
0.6
1.1
2.73
2.62
2.52
2.41
2.30
2.20
2.09
1.99
1.88
A
B
C
D
P
(b)
ˆ
Γ =0:530
2.01
1.92
2.25
2.35
2.19
2.32
2.10
x/c
y/c
0.3
0.2
0.7
1.2
1.4
0.9
0.4
0.1
0.6
1.1
2.74
2.56
2.38
2.19
2.01
1.83
1.64
1.46
1.28
A
B
C
D
P
(c)
ˆ
Γ =1:160
1.85
1.80
2.03
2.34
2.16
2.39
2.03
x/c
y/c
0.3
0.2
0.7
1.2
1.4
0.9
0.4
0.1
0.6
1.1
2.79
2.52
2.25
1.98
1.71
1.44
1.17
0.91
0.64
A
B
C
D
P
(d)
ˆ
Γ =1:800
Figure 18:Isobars (p=q
∞
) at t (U
∞
=c)=5.10 for vortices of dierent strengths.Headon BVI,NACA0012,
Mach number of 0.5.
Figure 19:Acoustic pressure history at point P for clockwiserotating vortices of dierent strengths.NACA
0012,M=0.57,R
c
=0:10.
19
5
4
3
2
1
0
1
2
1
2
3
4
5
6
7
CP,L
Time
y
0
= 0.00
y
0
=0.10
y
0
=0.15
y
0
=0.31
y
0
=0.45
y
0
=0.60
(a) Lower surface,x/c=0.02
3
2
1
0
1
2
3
1
2
3
4
5
6
7
CP,U
Time
y
0
= 0.00
y
0
=0.10
y
0
=0.15
y
0
=0.31
y
0
=0.45
y
0
=0.60
(b) Upper surface,x/c=0.02
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0.2
1
2
3
4
5
6
7
CP,L
Time
y
0
= 0.00
y
0
=0.10
y
0
=0.15
y
0
=0.31
y
0
=0.45
y
0
=0.60
(c) Lower surface,x/c=0.02
0.4
0.2
0
0.2
0.4
0.6
0.8
1
1
2
3
4
5
6
7
CP,U
Time
y
0
= 0.00
y
0
=0.10
y
0
=0.15
y
0
=0.31
y
0
=0.45
y
0
=0.60
(d) Upper surface,x/c=0.02
Figure 20:Time history of the surface pressure coecient at the chordwise location x/c=0.02 for dierent
missdistances.Headon BVI problem,NACA0012 aerofoil,inviscid calculations.(ab) Mach number of 0.57,
(cd) Mach number of 0.73.
20
3
2.5
2
1.5
1
0.5
0
0.5
1
1.5
0
1
2
3
4
5
6
7
CL
Time
y
0
= 0.00
y
0
=0.10
y
0
=0.15
y
0
=0.31
y
0
=0.45
y
0
=0.60
(a) M=0.57
0.2
0.15
0.1
0.05
0
0.05
0.1
0
1
2
3
4
5
6
7
C
D
Time
y
0
= 0.00
y
0
=0.10
y
0
=0.15
y
0
=0.31
y
0
=0.45
y
0
=0.60
(b) M=0.57
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.1
0.2
0.3
0
1
2
3
4
5
6
7
CL
Time
y
0
= 0.00
y
0
=0.10
y
0
=0.15
y
0
=0.31
y
0
=0.45
y
0
=0.60
(c) M=0.73
0.05
0.04
0.03
0.02
0.01
0
0.01
0.02
0
1
2
3
4
5
6
7
CD
Time
y
0
= 0.00
y
0
=0.10
y
0
=0.15
y
0
=0.31
y
0
=0.45
y
0
=0.60
(d) M=0.73
Figure 21:Lift and drag histories for vortex of various missdistances at two ow conditions.NACA0012.
(ab) Headon BVI,(cd) Missdistance BVI.
1.85
1.80
2.
12
2.34
2.16
2.39
2.03
x/c
y/c
0.3
0.2
0.7
1.2
1.4
0.9
0.4
0.1
0.6
1.1
2.79
2.52
2.25
1.98
1.71
1.44
1.17
0.91
0.64
A
B
C
D
P
(a) y
0
=0:00
1.87
1.87
2.39
2.47
2.13
2.39
2.00
x/c
y/c
0.3
0.2
0.7
1.2
1.4
0.9
0.4
0.1
0.6
1.1
2.82
2.56
2.30
2.04
1.78
1.52
1.26
1.01
0.75
A
B
C
D
P
E
(b) y
0
=0:15
21
1.98
1.88
1.79
2.40
2.36
2.31
2.17
x/c
y/c
0.3
0.2
0.7
1.2
1.4
0.9
0.4
0.1
0.6
1.1
2.83
2.55
2.26
1.98
1.69
1.41
1.12
0.84
0.55
A
D
P
C
(c) y
0
=0:45
2.07
1.92
1.67
2.41
2.32
2.27
2.22
x/c
y/c
0.3
0.2
0.7
1.2
1.4
0.9
0.4
0.1
0.6
1.1
2.86
2.56
2.27
1.97
1.67
1.38
1.08
0.78
0.49
D
P
C
(d) y
0
=0:60
Figure 22:Isobars (p=q
∞
) at t (U
∞
=c)=5.10.NACA0012,Mach number of 0.57.
1.12
1.10
1.26
1.44
1.38
1.42
1.36
x/c
y/c
0.3
0.2
0.7
1.2
1.4
0.9
0.4
0.1
0.6
1.1
1.87
1.75
1.63
1.52
1.40
1.28
1.16
1.05
0.93
A
B
C
D
P
(a) y
0
=0:00
1.17
1.09
1.30
1.48
1.39
1.48
1.37
x/c
y/c
0.3
0.2
0.7
1.2
1.4
0.9
0.4
0.1
0.6
1.1
1.89
1.76
1.63
1.50
1.37
1.24
1.11
0.98
0.85
A
B
C
D
P
(b) y
0
=0:15
1.27
1.10
0.91
1.
51
1.39
1.34
1.37
x/c
y/c
0.3
0.2
0.7
1.2
1.4
0.9
0.4
0.1
0.6
1.1
1.92
1.78
1.63
1.49
1.34
1.20
1.05
0.91
0.76
C
D
P
(c) y
0
=0:45
1.28
1.09
0.90
1.50
1.40
1.35
1.38
x/c
y/c
0.3
0.2
0.7
1.2
1.4
0.9
0.4
0.1
0.6
1.1
1.93
1.79
1.64
1.50
1.35
1.21
1.07
0.92
0.78
C
D
P
(d) y
0
=0:60
Figure 23:Isobars (p=q
∞
) at t (U
∞
=c)=5.10.NACA0012 and Mach number of 0.73..
22
20000
15000
10000
5000
0
5000
10000
15000
20000
4
4.5
5
5.5
6
6.5
7
Pacous [Pa]
Time
y
0
= 0.00
y
0
=0.10
y
0
=0.15
y
0
=0.31
y
0
=0.45
y
0
=0.60
(a) Case 1
8000
6000
4000
2000
0
2000
4000
6000
8000
4
4.5
5
5.5
6
6.5
7
Pacous [Pa]
Time
y
0
= 0.00
y
0
=0.10
y
0
=0.15
y
0
=0.31
y
0
=0.45
y
0
=0.60
(b) Case 2
Figure 24:Acoustic pressure history at point P at two freestream Mach numbers.(a) M=0.57,(b) M=0.73.
NACA0012,inviscid calculations,various missdistances.
(a)
(b)
Figure 25:(a) Schematic of the BVI rotor test.(b) Schematic of the blade with its polar coordinates.The
blade rotates anticlockwise at ω=(2π) revolutions per second.The spherical coordinates of the observer are
(r;θ;Ψ).
23
Figure 26:Distribution of the lift along the spanwise direction against the revolution of the blade.NACA0012,
headon BVI.
100
50
0
50
100
150
200
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
Pacous
[Pa]
Rev
Experiments
FWH
(a)
10
8
6
4
2
0
2
4
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pacous
[Pa]
Rev
Thickness noise
(b)
60
40
20
0
20
40
60
80
100
120
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
Pacous [Pa]
Rev
Experiments
FWH
(c)
10
8
6
4
2
0
2
4
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pacous [Pa]
Rev
Thickness noise
(d)
Figure 27:Acoustic pressure corresponding to the loading and thickness noises for the headon BVI (ab) and
the missdistance BVI (cd).Mach=0.63,
ˆ
Γ =0:374;R
c
=0:162.
24
100
50
0
50
100
150
0.252
0.254
0.256
0.258
Pacous [Pa]
Time
NACA0006
NACA0012
NACA0018
SC1095 unloaded
SC1095 loaded
(a) Slap noise
0.2
0.15
0.1
0.05
0
0.05
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Pacous [Pa]
Rev
NACA0006
NACA0012
NACA0018
SC1095
(b) Thickness noise
Figure 28:Acoustic pressure for dierent aerofoils at point P (50.0,0.0,50.0).(a) Slap noise,(b) thickness
noise.M=0.5,
ˆ
Γ =0:283;R
c
=0:018.
400
300
200
100
0
100
200
300
400
500
600
700
0.23
0.232
0.234
0.236
0.238
0.24
0.242
0.244
Pacous [Pa]
Time
NACA0006
NACA0012
NACA0018
SC1095 unloaded
SC1095 loaded
(a)
400
200
0
200
400
600
800
0.236
0.238
0.24
0.242
0.244
0.246
0.248
Pacous [Pa]
Time
NACA0006
NACA0012
NACA0018
SC1095 unloaded
SC1095 loaded
(b)
Figure 29:(a) Acoustic pressure for dierent aerofoils at point P (50.0,0.0,50).Results correspond to an
azimuth angle of 180
o
.(b) Acoustic pressure for dierent aerofoils at point P
0
(47.0,17.1,50.0).Results
correspond to an azimuth angle of 200
o
.The distance aircraftobserver is the same as point P.M=0.8,
ˆ
Γ =0:177;R
c
=0:018.
100
50
0
50
100
150
0.252
0.254
0.256
0.258
Pacous [Pa]
Time
NACA0006
NACA001234
NACA0012
NACA16018
(a)
100
50
0
50
100
150
0.252
0.254
0.256
0.258
Pacous [Pa]
Time
NACA0012
NACA001234
NACA0018
NACA16018
(b)
Figure 30:Acoustic pressure at point (50,0,50) for dierent thicknesses (ab) and LE radii (cd) of aerofoil.
M=0.5,
ˆ
Γ =0:283;R
c
=0:018.
25
r
2
OASPL
0
5000
10000
15000
20000
135
140
145
150
155
160
165
=30
0
=45
0
=60
0
137.52.5e4.r
2
(a) M=0.5
r
2
OASPL
0
5000
10000
15000
20000
145
150
155
160
165
170
175
=30
0
=45
0
=60
0
149.52.5e4.r
2
(b) M=0.8
Figure 31:Evolution of the AOSPL against the square of the distance observeraircraft at Ψ=180
o
for three
dierent elevation angles at two freestream Mach numbers.NACA0012,(a) M=0.5,(b) M=0.8.
50
0
50
100
0.25
0.252
0.254
0.256
0.258
0.26
0.262
Pacous [Pa]
Time
R
c
= 0.018
R
c
= 0.040
R
c
= 0.060
R
c
= 0.100
(a) M=0.5
200
100
0
100
200
300
400
500
600
0.236
0.238
0.24
0.242
0.244
Pacous [Pa]
Time
R
c
= 0.04
R
c
= 0.06
R
c
= 0.10
R
c
= 0.15
(b) M=0.73
Figure 32:Acoustic pressure for dierent vortex core radii at point P (50.0,0.0,50.0) for the headon and
missdistance BVI.(a)
ˆ
Γ =0:283,M=0.5 for the headon BVI,(b)
ˆ
Γ =0:42,y
0
=0:15,M=0.73 for the
missdistance BVI.
130
131
132
133
134
135
136
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.11
SPL [dB]
Nondimensionalised vortex core radius
SPL
(a) M=0.5
145
146
147
148
149
150
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
SPL [dB]
Nondimensionalised vortex core radius
SPL
(b) M=0.73
Figure 33:Maximum BVI noise amplitude in terms of Sound Pressure Level for dierent vortex core radii at
two ow conditions.
26
(a) R
c
=0.018
(b) R
c
=0.100
Figure 34:Contours of the OASPL for the range of azimuth angles Ψ where the BVI occurs.The elevation
angle θ indicates the directivity patterns of the BVI noise below (θ <0) and above (θ >0) the helicopter.
NACA0012,M=0.5,(a) R
c
=0.018,(b) R
c
=0.100.
200
100
0
100
200
300
400
500
600
0.24
0.245
0.25
0.255
0.26
Pacous [Pa]
Time
=0.283
=0.530
=1.160
=1.800
134
136
138
140
142
144
146
148
150
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
SPL [dB]
Nondimensionalised vortex strength
SPL
Figure 35:(a) Acoustic pressure for dierent aerofoils at point P (50.0,0.0,50.0).(b) Maximum BVI noise
amplitude in terms of Sound Pressure Level for dierent vortex strengths.
(a) OASPL in the (Ψ;θ) plane,
ˆ
Γ=0.283
(b) OASPL in the (Ψ;θ) plane,
ˆ
Γ=1.80
Figure 36:Contours of the OASPL for the range of azimuth angles Ψ where the BVI occurs.The elevation
angle θ indicates the directivity patterns of the BVI noise below (θ <0) and above (θ >0) the helicopter.
NACA0012,(a)
ˆ
Γ=0.283,M=0.57  (b)
ˆ
Γ=1.80,M=0.57.
27
200
100
0
100
200
300
400
500
600
0.236
0.238
0.24
0.242
0.244
Pacous [Pa]
Time
y
0
= 0.00
y
0
=0.10
y
0
=0.15
y
0
=0.31
y
0
=0.45
y
0
=0.60
(a)
132
134
136
138
140
142
144
146
148
150
0.6
0.5
0.4
0.3
0.2
0.1
0
SPL [dB]
Nondimensionalised missdistance
SPL
(b)
Figure 37:In uence of the missdistances on the fareld noise.NACA0012,
ˆ
Γ=0:42,M=0.73.(a) Acoustic
pressure for dierent aerofoils at point P (50.0,0.0,50.0) (b) Maximum BVI noise amplitude in terms of Sound
Pressure Level for dierent missdistances.
200
100
0
100
200
300
400
500
600
700
800
0.244
0.246
0.248
0.25
0.252
0.254
0.256
Pacous [Pa]
Time
y
0
= 0.00
y
0
=0.10
y
0
=0.15
y
0
=0.31
y
0
=0.45
y
0
=0.60
(a)
135
140
145
150
155
0.6
0.5
0.4
0.3
0.2
0.1
0
SPL [dB]
Nondimensionalised missdistance
SPL
(b)
Figure 38:In uence of the missdistances on the fareld noise.NACA0012,
ˆ
Γ =1:8,M=0.57.(a) Acoustic
pressure for dierent aerofoils at point P (50.0,0.0,50.0) (b) Maximum BVI noise amplitude in terms of Sound
Pressure Level for dierent missdistances.
(a) OASPL in the (Ψ;θ) plane,y
0
=0:00
(b) OASPL in the (Ψ;θ) plane,y
0
=0:60
Figure 39:Contours of the OASPL for the range of azimuth angles Ψ where the BVI occurs.The elevation
angle θ indicates the directivity patterns of the BVI noise below (θ <0) and above (θ >0) the helicopter.
NACA0012,(a) y
0
=0:00,
ˆ
Γ=0.42,M=0.73  (b) y
0
=0:60,
ˆ
Γ=0.42,M=0.73.
28
Conclusions and Future work
A combination of CFD and CAA methods has been
used for the study of the BVI problem.The potential of
the method has been demonstrated for several ow cases
suggesting that this technique is a valid,lowcost and easy
to implement alternative to higher order CFD methods.
The obtained results highlight the importance of the
aerofoil shape in the emitted sound during BVI and the
complex relationship between the vortex characteristics
and the resulting acoustic eld.Of signicant importance
is the relationship between the radius of the vortex core
and the intensity of BVI.The current set of results indicate
that alleviation or even total control of the sound is pos
sible provided the vortex core properties can be modied
in an ecient way.
Further work needs to be carried out in three
dimensions in order to validate the proposed technique
and clarify the role of vortex orientation in the emitted
sound.In parallel,research in low dissipation and dis
persion CFD algorithms is necessary which will allow the
direct computation of the acoustic eld without the need
to apply aeroacoustics methods in the very near eld of
the CFD solution.Regarding the current acoustics mod
ule,further developments include modications for ground
re ection and turbulence.
Acknowledgements
This work was supported by Westland Helicopters Lim
ited and the University of Glasgow.
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