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Vortical Structures on Three-Dimensional Shock Control Bumps

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Abstract and Figures

Three-dimensional shock control bumps have long been investigated for their promising wave drag reduction capability. However, a recently emerging application has been their deployment as "smart" vortex generators, which offset the parasitic drag of their vortices against their wave drag reduction. It is known that three-dimensional shock control bumps produce streamwise vortices under most operating conditions; however, there have been very few investigations that have aimed to specifically examine the relevant flow structures. In particular, the strength of the vortices produced as well as the factors influencing their production are not well known. This paper uses a joint experimental and computational approach to test three different shock control bump shapes, categorizing their flow structures. Four common key vortical structures are observed, predominantly shear flows, although all bumps also produce a streamwise vortex pair. Both cases with and without flow separation on the bump tails are scrutinized. Finally, correlations between the strength of the main wake vortices and pressure gradients at various locations on the bumps are assessed to investigate which parts of the flow control the vortex formation. Spanwise flows on the bump ramp are seen to be the most influential factor in vortex strength. © Copyright 2015 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
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Vortical structures on three-dimensional shock control bumps
S.P. Collissand H. Babinsky
Cambridge University Engineering Department, Trumpington Street,
Cambridge, CB2 1PZ, UK
K. N¨ublerand T. Lutz§
IAG, Universit¨at Stuttgart, Pfaenwaldring 21, 70569, Germany
Abstract
Three-dimensional shock control bumps have long been investigated for their promising wave drag
reduction capability. However, a recently emerging application has been their deployment as ‘smart’
vortex generators, which oset the parasitic drag of their vortices against their wave drag reduction.
It is known that 3D SCBs produce streamwise vortices under most operating conditions; however,
there have been very few investigations which have aimed to specifically examine the relevant flow
structures. In particular, the strength of the vortices produced as well as the factors influencing their
production are not well known. This paper uses a joint experimental and computational approach
to test three dierent SCB shapes, categorising their flow structures. Four common key vortical
structures are observed, predominantly shear flows, although all bumps also produce a streamwise
vortex pair. Both cases with and without flow separation on the bump tails are scrutinised. Finally,
correlations between the strength of the main wake vortices and pressure gradients at various loca-
tions on the bumps are assessed to investigate which parts of the flow control the vortex formation.
Spanwise flows on the bump ramp are seen to be the most influential factor in vortex strength.
PhD student
Professor of Aerodynamics, AIAA Associate Fellow
Research engineer
§Senior researcher
1
Nomenclature
= Angle of attack of airfoil []
b= Width of computational domain [m]
= Shock angle relative to -direction []
Cf= Skin friction coecient
CDDrag
1
2U2
1S= Drag coecient
CLLift
1
2U2
1S= Lift coecient
c= Chord length [m]
0= Boundary layer thickness (measured to 99% freestream velocity) at in-flow [mm]
i= Incompressible boundary layer displacement thickness [mm]
e= Unit vector in -direction
Hi
i
i= Incompressible boundary layer shape factor
=RS!d2x= Circulation [m2/s]
h= Bump height [mm]
ci = Swirling strength vortex sensor
M1= Freestream Mach number
µ= Dynamic viscosity [kg/(ms)]
= Density [kg/m3]
ReU1
µ= Reynolds number based on length scale
S= Reference area [m2]
wx =µ@u
@y|y=0 = Streamwise wall shear stress [N/m2]
i= Incompressible boundary layer momentum thickness [mm]
x=[x, y, z] = Stream-wise, tunnel floor-normal, tunnel span-wise coordinates [mm]
u=[u, v] = Stream-wise and tunnel floor-normal velocity [m/s]
u1= Free-stream velocity [m/s]
uqwx
= Skin friction velocity [m/s]
xs= Stream-wise shock position relative to the bump tip [mm]
!x=ex·r⇥u= Streamwise vorticity [s1]
2
I. Introduction
Numerous previous investigations have attempted to mitigate the negative eects of weak normal
or near-normal shocks on transonic airfoils. Key phenomena of focus have been the drag increase due
to the presence of the shock, and unsteady shock-induced flow breakdown, [1]. The former is caused
by an additional component of drag, termed ‘wave drag’, which is related to the total pressure losses
through the shock. The latter, known as ‘buet’, is an oscillatory behaviour caused by the interactions
of the shock with a separated boundary layer; buet mechanisms are discussed in numerous sources, for
example [2–4].
Both of these eects can be influenced by the angle of attack of the airfoil as well as the flight
speed M1. With increasing or M1the shock tends to move downstream on the airfoil, strengthening
due to expansion waves emanating from the (typically) convex curvature of the surface. With increased
shock strength come both higher total pressure losses - and hence more wave drag - and an increased
tendency for the boundary layer to separate on interacting with the shock. Thus aircraft speed is limited
by the need to keep drag as low as possible and to stay away from the buet boundary. The problem is
that this is in conflict with airlines’ general desire to operate their aircraft at high cruise Mach numbers
to maximise eciency and utilisation; it is therefore increasingly important to control the flow in such a
way as to enable speed increases without straying too close to flow breakdown.
One device which has shown significant potential for the first of these problems is the shock control
bump (SCB). A large number of studies have been conducted in the past, including [1,5–10], investigating
both the potential performance gains for an airfoil using SCBs as well as the physics of how these gains
come about. The primary flow control mechanism of the SCB is the bifurcation of the shock into a
()-shock structure, sketched in figure 1(a). Since in decelerating a flow from one Mach number to
another the total pressure losses through multiple shocks are always less than those due to a single shock
(see [11]), the bifurcated ()-shock directly reduces the wave drag.
In general SCBs have been shown to give promising drag reduction at the design conditions, although
in general their CDM1polars tend to exhibit an unfavourable decline either side of the design M1
(see for example [12–14]). This is caused by the shock moving relative to the bump: if the shock is
too far forward, the bump serves only to reaccelerate the flow and thus a secondary shock is formed
(figure 1(b)); if the shock is too far downstream, the flow expands around the bump crest causing a
stronger shock and consequent boundary layer separation (figure 1(c)).
If the bump profile is applied uniformly across the span of a wing - referred to as a “two-dimensional”
3
Main shock
Curved front shock leg
separation
expansion waves



 


Main shock
Overlapping shock structures
main shock
M > 1
secondary shock
Figure 1: Operating priniple of SCB: (a) 2D bump at design-conditions; (b) shock ahead of design
location; (c) shock downstream of design location; (d) 3D bump ( [15]); (e) array of 3D bumps ( [15])
bump - these o-design eects will be highly detrimental to the wing aerodynamic performance. However,
the more recent research into SCBs has attempted to localise these eects and therefore reduce the o-
design penalty. This results in “three-dimensional bumps”, and it has been found that in spite of the
()-shock decaying in the spanwise direction (figure 1(d)) an array of 3D SCBs can still produce a benefit
across the span (figure 1(e)), [7]. A full account of drag reduction capabilities of SCBs is given by Bruce
and Colliss, [15].
A secondary flow feature of the 3D SCBs is a streamwise vortex pair, [7,9, 16]. These usually appear
to emanate from the bump tail, [7, 9], and occur principally in two dierent manners: firstly, under
design conditions a (typically) common-flow-down pair is observed (shown in figure 2); secondly, under
o-design conditions the flow separation itself sheds a streamwise vortex pair into the flow, [7, 17], an
example of which is shown in figure 3.
It has been suggested that these vortices could give the SCB potential to exert direct boundary
layer control, acting as a ‘smart’ vortex generator (VG) which osets the parasitic drag of its vortices
with the alleviation of wave drag through its ()-shock, [7, 10, 18]. This, it is claimed, would give it
potential for controlling buet on wings, [10, 19], as well as having the potential for use in supersonic
engine inlets, [19]. Although a number of studies have observed the formation of vortices, very few have
4
v0
-5
5
approximate vortex path




Figure 2: Measurements of vortices on SCBs, adapted from Bruce et al. [17]: (a) vertical velocities; (b)
surface oil flow
shock position
smaller wake
streamwise vortex
streamwise vortex
S1
S2
Fvortex core
S1
S2
F
F
(a)
(b)
Figure 3: Generation of streamwise vortices under o-design conditions: (a) separation topology (adapted
from [7]); (b) resulting external flow field (adapted from [29])
attempted to characterise them, with the one exception being Eastwood and Jarrett’s computational
investigation, [10]. Their study focussed on ‘wedge’-type bumps generated by flat ramps, crests and tails
with linear lofting methods generating the (angular) side flanks. These bumps were found to produce
vortices of total circulation of around 0.15m2/s. It is currently unclear to what extent their results
extend to other bump shapes; in particular, more typical SCBs tested tend to have more progressive
5
curves and the significance of edges in vortex generation is not known, [7–9,16].
Whilst all the studies cited thus far agree that SCBs produce measurable vortices, they do not agree
on the generation mechanism. Earlier studies of the flow physics such as Ogawa et al., [7], tended to
concentrate on the vortices produced by flow separation on the tail (such as that shown in figure 3);
more recent work such as [9, 10, 16, 17] has made observations of the vortices in ‘on-design’ conditions
(i.e. in the absence of flow separation). However, there is no consensus on the mechanism of generating
the vortices, with some authors proposing that opposing spanwise pressure gradients cause the flow to
wrap up, [10], whilst others favour local small-scale separations, [9]. Nevertheless, all the vortices are
first observed on the bump tail, leading to the overwhelming majority of SCB studies concluding that
pressure gradients on the rear part of the bumps are responsible for the vortex generation, although there
has thus far been no direct evidence to confirm this. A parametric study by Bruce et al. [17] found small
dierences in the vortices produced by increasing the width of the bump tail, although these were small
variations and it was not possible to calculate the change in vortex strength with their data. In addition,
it is likely that the bumps will produce a number of other vortical structures - indeed the results of
Colliss et al. [16] strongly suggest this - which may vary between bump geometries and play a part in
the changing the potential for boundary layer control.
The potential benefits of the SCB in boundary layer control are largely unknown, although there
is some indication that they would be beneficial on transonic wings. Eastwood [20] examined an array
of SCBs placed on a DLR-F4 swept wing/fuselage combination, set up such that the uncontrolled flow
exhibited a large-scale separation over the rear part of the wing at mid-span (figure 4(a)); he took this to
be indicative of a wing at the onset of buet. The 3D SCBs were seen to significantly reduce the extent
of the separation (figure 4(b)), judged by the level of reversed flow at the wall (wx <0), suggesting that
they would have a tangible control benefit, at least locally modifying the buet characteristics. Although
these conclusions were drawn from steady RANS calculations, with a somewhat questionable separation
criterion for separated flow, they are nonetheless promising for the SCB concept.
This paper aims to examine and characterise the vortical structures produced by SCBs. Use is made
of the joint experimental and computational approach to SCB investigations developed in [16]. This
methodology uses numerical simulations to compute the flow field around an airfoil, with simplistic
experiments tuned to mimic only the flow in the vicinity of the shock. This has the advantage that
detailed experimental measurements can be made of smaller scale flow structures, whilst retaining a
whilst this would give an indication of the presence of separation, it would not give an accurate representation of its
extent since there can exist regions of wx >0 within a separation topology
6
Figure 4: Separation extent on a DLR-F4 wing/half-body combination visualised by contours of stream-
wise surface shear stress, adapted from [20]: (a) uncontrolled flow; (b) 3D SCBs
direct link to the application. The computed flow fields for three dierent SCB geometries are compared
with experimental results to ensure that the simulated flow physics are believable, before these are then
used to give an overview of the vortical structures generated by the bumps. Both situations with and
without flow separation on the tail of the bumps will be examined, denoted on- and o-design respectively.
Finally, the strength of the main vortex structure in the wake (corresponding to that described in previous
research papers including [7,9,16]) is examined against pressure gradients at various points on the bumps,
in an attempt to understand the influential factors.
II. Methodology
A. Experiments
Experiments were performed in the No. 1 Supersonic Wind Tunnel at Cambridge University Engineering
Department. This is a blow-down tunnel, capable of operating at Mach numbers between 0.7 and
3.5 depending on the chosen nozzle geometry. For the present work, the Mach number was fixed at
M1=1.3, which was shown in [16] to give a representative shock strength for the airfoil model employed
in the computations (described in section B.). The stagnation pressure of the flow was 172kPa, and the
stagnation temperature was 300K; the Reynolds number was approximately 25 million m1. Although,
7
as described in [16], boundary layer suction could be employed to either manipulate the boundary layer
ahead of the bump (at “in-flow”) or reduce the influence of corner flows, it was not used in this work. A
schematic of the wind tunnel working section is shown in figure 5.
M < 1
M > 1
M = 1.3
nozzle diffuser
shock holding plateshock position
Figure 5: Wind tunnel working section
Bumps were manufactured from VeroWhite resin, a non soluble opaque plastic, using a Polyjet rapid
prototyping technique. These were glued to the wind tunnel floor using superglue, with the position
accurate to within 0.5mm. A small amount of epoxy filler was used to give a smooth transition between
the floor and the bump, although this was kept to a minimum to avoid interfering with the temperature-
sensitive measurement techniques.
An array of methods were employed to measure the flow field. A two-mirror schlieren system with
horizontal knife-edge was used to visualise the shock waves; this enabled the main normal shock position
to be set to within ±1mm, as well as giving an indication of the ()-shock structure generated by the
bumps tested. Skin friction lines were examined by surface oil flow visualisation, using a mixture of
paran, titanium dioxide and oleic acid.
Surface pressures were measured using single channel pressure sensitive paint (PSP), calibrated in-
situ by a number of static pressure tappings. Dierent calibrations were performed for the (aluminium)
wind tunnel floor and (plastic) bump surface, since the dierent thermal properties of the materials
aected the behaviour of the paint; the pressure field was then stitched together from the results of each
calibration.
Velocity measurements were taken using two-component laser Doppler velocimetry (LDV), giving the
streamwise and vertical velocities (uand vrespectively). The flow was seeded with paran; the mean
particle diameter was found to be approximately 0.5µm using measurements of particle lag through
a normal shock, [21]. Boundary layer traverses were performed with variable measurement resolution
between 0.2y0.5mm. The kinematic integral boundary layer parameters, equations 1, were
calculated from this data using trapezoidal numerical integration with a correction factor applied to
8
account for the error introduced by the discretisation of the profile, following [22]. Full details of the
experimental methods may be found in [16, 21].
i=Z1
01u
u1dy,
i=Z1
0
u
u11u
u1dy, H
i=
i
i
(1)
Errors in each of the parameters determined from experimental measurements are presented in table 1.
Table 1: Experimental errors
Quantity Source Error
Shock position image resolution, tunnel set-up ±0.20
Surface pressures PSP sensitivity, thermal eects ±3%
Streamwise velocity (u) LDA calibration, head angle ±1%
Vertical velocity (v) LDA calibration, head angle ±10%
B-L parameters (
i,i,Hi) LDA calibration, discretisation ±2.5%
B. Computations
Numerical simulations were performed at IAG, University of Stuttgart, for a streamwise cross section
of the Pathfinder wing, a low-camber transonic design developed by a consortium of European research
institutions as part of the TELFONA project for research on natural laminar flow wings and flow control,
[23]. Computations were performed using FLOWer, a well-established density-based structured RANS
flow solver developed by the German Aerospace Center (DLR), [24]. The two equation SST turbulence
model due to Menter, [25], was chosen. No unsteady computations were required for the present work,
except for the highest resolution used in the grid convergence study, where weak numerical damping
required the addition of 100 inner unsteady iterations within the principal iteration loop.
A multi-block structured C-grid, illustrated in figure 6, was used to enable parallelisation of the
numerical solution. This was divided into twenty-seven zones, solved to second order accuracy within
the zone and first order accuracy across zone boundaries. Twelve of these zones were distributed within
30mm of the wing surface (labelled group I on figure 6(a)); twelve were in the outer field (group II),
which extended to a distance of 50cfrom the wing surface; and the wake region (group III) was divided
into three equal sections across the span. The near-wing region carried mesh refinement in the boundary
layer region, with the first grid point from the surface located at y+1. Periodic boundary conditions
were specified on the spanwise limits of the domain, such that the set-up represents an infinite unswept
wing.
In order to find an appropriate balance between computational cost and solution accuracy, a grid
9
50c
c
Group (II)
Group (III)
Group (I)
12
4
3
56
longitudinal zone
boundary
spanwise zone
boundary
periodic boundary
conditions applied
712
zones to
on lower surface
(a) (b)
(c)
~0.03c
mesh refinement
Figure 6: Details of the mesh used for computations
convergence study was performed, as first described in [16, 26]. This examined a dense reference (“level
0”) mesh consisting of 46 million cells, as well as three levels of coarsening: level 1 with 5.8 million cells;
level 2 with 0.75 million; and level 3 with 0.1 million. The geometry tested was a HSCB as described in [16]
positioned beneath the shock such that the flow is on the point of incipient shock-induced separation.
This was chosen as separated flows are typically poorly modelled by RANS simulations and this therefore
represents a ‘dicult’ test case for the CFD. Results of this study, in the form of profiles of cpand Cf,
are shown in figure 7, adapted from [16,26]. Level 3 fails to resolve the shock signature and completely
misses the separation, whilst level 2 broadly captures the shock structure but Cfdoes not get suciently
low to suggest incipient separation. By contrast, level 1 is seen to capture both the shock structure’s
pressure signature and the incipient separation observed in the dense level 0 mesh, although the shocks
were slightly weaker as a result of a relatively coarse streamwise resolution. It was thus concluded that a
mesh of 5.8 million cells would be the optimal trade between computational cost and solution accuracy,
and this was duly applied for the remainder of the study.
Bumps are ‘mounted’ on the airfoil by displacing the relevant nodes in the mesh by an amount
prescribed by a set of mathematical functions describing the SCB shape. They are placed symmetrically
on the centreline of the domain, so that the eective geometry is an infinite array of uniformly spaced
bumps on the unswept wing.
10
Level 0 (unsteady) Level 1 Level 2 Level 3
0
-0.5
-1
0.5
1
0 0.2 10.4 0.6 0.8
x / c
-cp
(a)
SCB
main shock

-5
0
5
10
15
0 0.2 10.4 0.6 0.8
x / c
Cf (×10-3)
(b)
SCB

Figure 7: Results of the grid convergence study, adapted from [16, 26]
The flight conditions used are shown in table 2, which were chosen by [16] alongside the wind tunnel
set-up to give good agreement between the computational and experimental uncontrolled flow fields. The
agreement between the important features of the uncontrolled flow - the surface pressure distribution
and boundary layer profile ahead of the SCB - are shown in figure 8, reproduced from [16]. The integral
boundary layer parameters are compared in table 3. All length scales in the remainder of this paper are
normalised by the in-flow boundary layer thickness, 0.
Table 2: Flight conditions used for numerical simulations
M1[]xtrans/c Rec
0.76 1.8 0.1 20106
Table 3: In-flow boundary layer properties

iiHiRe
i
(mm) (mm) (mm)
Exp. 6.0 0.67 0.53 1.28 27,650
CFD 6.0 0.67 0.51 1.31 25,670
C. Bump geometries
Three bump geometries were tested: the hill SCB (HSCB), wedge bump and extended SCB (exSCB), all
shown in figure 9. The HSCB is a smooth contour bump originally defined by K¨onig et al., [8], the profiles
of which are given by formulae for the bending of an elastic beam under a point load with dierent end
conditions: the longitudinal profile has a ‘simply supported’ end at the bump nose and a clamped end at
11
0 20 40 60
0.4
0.5
0.6
0.7
p
p0
x / 0u (m/s)
0100 200 300 4000
6
8
10
2
4
y (mm)
(b)
(a)
experiment (wind tunnel)
computation (airfoil)
no optical access for PSP
(a) (b)
experiment
computation
Figure 8: Comparison of uncontrolled flows in experiment and CFD: (a) surface pressure distribution;
(b) in-flow boundary layer. Measurement locations shown inset.
the bump trailing edge; the lateral profile is simply supported on both sides. The wedge bump is similar
to that used by various studies by Bruce et al., [9, 17]; all profiles are flat, except the side flanks which
are cubic splines. The exSCB geometry is based on the wedge bump, except that the length and width
of the tail have been increased. This was designed to make the flow locally more two-dimensional on the
tail, thereby reducing pressure gradients and attenuating vortex production by the bump.
D. Vortex detection
A method of detecting vortices is required for analysis of the CFD data. It is well accepted that the
existence of a maximum in streamwise vorticity !x=ex·r⇥uis a necessary but not sucient condition
for a vortex, with some pure shear flows also providing a maximum in !x- Jeong and Hussain, [27],
in particular provide a number of examples. In the present work, the swirling strength criterion first
proposed by Zhou et al. [28] is employed. This analyses the eigenvalues of the velocity gradient tensor,
given by solutions to the characteristic equation:
3(r·u)2+1
2((r·u)2trace(ru2))det(ru) = 0 (2)
Let the solutions be {1,
2,
3}, with corresponding eigenvectors {r1,r2,r3}. Then, if the solutions
contain a complex conjugate pair (2and 3, say) it can be shown that the flow field contains a spiral
node in the r2r3plane about which the flow swirls at rate =(2)ci. Any point for which |ci|>0
may therefore be taken as belonging to a vortex core. Following [28], the vortices are visualised using
plots of 2
ci, in order to be dimensionally consistent with other popular vortex detection methods such
12
33.330
16.67 0
20
8.330
11.67
0
4.170
(c)
(a) (b)
8.33 0
15 0
C
C
A
A
250
12.50
15.830
8.330
15.83 0
12.5 0
diffuser entrance
shock positions
25
0
4.170
8.330
8.330
11.67
0
diffuser entrance
shock positions
8.33 0
11.67 0
diffuser entrance
0
Section A-A
Section B-B
Section C-C
B
B
0.830
2.080
40º
4.170
40º
crest geometry
0.830
Figure 9: Bump geometries tested: (a) HSCB; (b) wedge bump; (c) exSCB
as the Q-criterion and the enstrophy E.
III. Comparison of CFD with experiments
Figure 10 shows a comparison of the experimental and computational shock structures generated by
the three bumps at o-design conditions (i.e. the shock in the downstream position). The experimental
data was obtained by schlieren photography; the computational results show contours of the density
gradients in the streamwise direction (i.e. ex·r), mimicking schlieren with a vertical knife-edge.The
relatively low streamwise resolution used in the computations is apparent in the numerical schlieren
images through the width of the shocks, although the results of the grid convergence study showed that
although the experiments were performed with a horizontal knife-edge, matching this in the computations did not
produce as clear a shock structure as that shown in figure 10 due to the streamwise mesh resolution
13
this does not present an issue for the surface pressure field or the impact on the boundary layer. There
is a slight discrepancy which becomes apparent towards the top of the domain, caused by the underlying
curvature of the airfoil surface in the CFD generating a small wall-normal pressure gradient that is not
modelled in the wind tunnel. Nonetheless, the region of interest for this study (local to the boundary
layer) is comparable: the angles of the front shock legs (indicated in figure 10) are given in table 4, from
which a good level of agreement between the experiment and CFD is observed.
(a)
(b)
(c)
y
Figure 10: Comparison of experimental and computational shock structures for three bumps at o-design
condition: (a) HSCB; (b) wedge bump; (c) exSCB
Table 4: Front shock leg angles, y[], from experiment and CFD
Experiment Computations
HSCB 57 59
wedge bump 59 59
exSCB 53 54
Surface flow topologies of the three bumps at o-design conditions are presented in figure 11. As has
been remarked in previous studies, [9, 16, 17], the separation topology may be classified as an ‘owl-face
of the first kind’ (see Perry and Hornung, [29]) comprising a pair of saddle points (marked S1 and S2 on
figure 11) between which a region of reversed flow branches laterally to feed a pair of spiral nodes (F).
14
S1 F S2
S1
FS2
S1 F S2
S1
F S2
S1
FS2
S1 F S2
xS1 LS1-S2
zFWF
Figure 11: Surface flow visualisation from experiment and computations: (a) HSCB; (b) wedge bump;
(c) exSCB
Whilst this is very clear for the HSCB and wedge bumps, on the exSCB the separation is divided into
two separate parts with a channel of attached flow between them. Each of these separated regions has
the owl-face topology. Because the separation entrains flow from the bump ramp, it must be open - i.e.
the foci Ffeed a common-flow-up counter-rotating vortex pair into the flow.
For comparison purposes, the size of the separation may be categorized by the distance between the
critical points: in particular the length is the streamwise distance between the saddle points, LS1S2,
whilst the width is the spanwise distance between the foci, WF(see figure 11). The position of the
separation is categorized by the streamwise location of S1, xS1, and the spanwise location of the spiral
node zF. For the exSCB, the latter of these is measured for the closest spiral node to the centreline.
These are compared for the computations and experimental results in table 5. In general, the CFD
over-predicts the size of the separations, with first saddle point slightly further upstream than observed
in the experiments.
15
Table 5: Comparison of separation sizes in computations and experiments
LS1S2/0WF±xS1zF
Exp. CFD Exp. CFD Exp. CFD Exp. CFD
HSCB 9.5 13.7 4.0 4.3 17.0 16.0 2.3 2.2
wedge 7.3 17.7 5.0 4.9 12.3 10.4 2.7 2.4
exSCB 3.3 3.8 0.8 1.7 15.8 15.9 2.3 1.7
The surface pressure fields for the on-design cases of all the bumps are shown in figure 12. In general
the agreement between the experiments and computations is good, particularly with respect to the
shape of the flow (seen in the surface fields) and the pressure gradients away from the shocks (seen in the
centreline distributions). However, there are some minor discrepancies: The shock is more smeared in
the numerical results, doubtless a consequence of the streamwise mesh resolution. Notably, the pressure
is over-predicted by the CFD on the bump tail - this is thought to be caused by a combination of slight
dierences in shock position between the experiment and computation, as well as some minor influence
of the wind tunnel side-walls in the experimental results.
A final comparison between the wind tunnel and numerical data is in the state of the boundary
layer downstream of the bumps; measurements of this at x/0= 28.33 are presented in figure 13. The
horizontal dashed lines in figure 13 indicate the mean boundary layer parameters for the uncontrolled
flow from both computational and experimental results. The computations are seen to over-predict the
boundary layer parameters, and this is thought to be due to two eects. Firstly, the curvature of the
airfoil surface induces a wall-normal pressure gradient which will distort the boundary layer and thus
increase both its displacement thickness (
i) and shape factor (Hi); the wind tunnel walls are flat, so
this eect is not present in the experiment. Secondly, there appears to be a tendency of the RANS
computations used in the present work to over-predict the increase in the integral parameters through
the shock/boundary layer interaction, [21]; this can be seen here by the dierence in the uncontrolled
values of
iand Hi. However, if the change in the integral parameters relative to the uncontrolled flow
is considered (i.e. the direct impact of the SCB), then the agreement between CFD and experiment is
seen to be better.
For the purpose of the present study, the shock smearing due to the streamwise resolution of the CFD
is likely to be the most severe limitation. Consequently all analysis of pressure gradients - particularly
in section V. - will be restricted to regions away from the shock footprints as well as on the surface. The
above comparisons with PSP data shows that if such precautions are taken, the CFD and the experiments
generally agree quite well in the shape of the flow, whilst the grid convergence study analysis also suggests
16
0.3
0.4
0.5
0.6
0.7
p
p0
0 10 20 30
x / 0
0 10 20 30
x / 0
0 10 20 30
x / 0
(a) (b) (c)
0.3 0.4 0.5 0.6 0.7
p / p0
CFD
exp
CFD
exp
CFD
exp
SCB extent SCB extent SCB extent
Figure 12: Surface pressure fields from experiment (top row), CFD (middle row) and centreline distri-
butions (bottom row): (a) HSCB; (b) wedge bump; (c) exSCB
4
6
8
10
1.6
2.4
2
2.8
0 2 4-2-4
z / 0z / 0
i
*
*
i,0
i
0 2 4-2-4
z / 0
0 2 4-2-4
Figure 13: Integral boundary layer parameters across the span at x/0= 28.33, symbols show experimen-
tal data; lines show computations: (a) HSCB; (b) wedge bump; (c) exSCB. Horizontal dashed lines show
the state of the boundary layer in the uncontrolled flow from experiments (light grey) and computations
(dark grey).
a similar conclusion. Finally, the resolution is the same relative to the bump length scales for all cases
tested, which ensures a safer comparison between geometries. It is therefore not expected that the shock
17
resolution will present a significant problem to the analysis of the present work.
IV. Vortical flow structures
A. Design behaviour
Attention is now turned to the vortical flow structures generated by the bumps. Since it would be
prohibitively expensive to gather sucient data to build a complete picture of the flow structures, the
computational data is used to provide an overview of the flow field. Contours of both the streamwise
component of vorticity, !x=ex·r⇥u, are presented in figure 14, as well as contours of the swirling
strength vortex sensor, 2
ci. No contour levels are shown for the latter as it is intended as a qualitative
guide to the flow features.
(a) (b) (c)
10.50-0.5-1
x (×103)
(I)
(II)
(II)
(IV) (IV)
(III)
(III)
(I)
(IV)
(IV)
(II*)
(IV)(IV)
Figure 14: Vortical structures on SCBs under design conditions visualized by contours of !x(top row)
and 2
ci (bottom row): (a) HSCB; (b) wedge bump; (c) exSCB
A number of flow structures common to all the bumps are visible:
(I) shear flow caused by the curved front ()-shock leg
(II) secondary vorticity structure generated on the tail; this is predominantly shear flow although there
18
are weak secondary vortices detected for the HSCB and a more noticeable vortex for the exSCB
(labelled (II*) in figure 14(c))
(III) centreline shear flow, associated with having a flat section between the bump flanks - this only
appears on the wedge and exSCB, but not the HSCB which has continuous surface curvature over
the bump width
(IV) primary vortex - the dominant vortical structure in the wake for all SCBs tested
The contours of 2
ci show that only the primary vortices are of importance for potential boundary
layer control, since this is the only structure relating to streamwise vortices that persists into the wake.
Some key characteristics of these vortices, extracted from the data in figure 14, are shown in table 6.
The maximum streamwise vorticity is the peak observed in the primary vortex structure 5hdownstream
of the bump trailing edge. The circulation shown is evaluated for a circuit enclosing half the domain -
from the centreline to the domain edge - and extending to a height of 50to capture all of the vortical
structures. The results are non-dimensionalised using the bump height hand the skin friction velocity
of the uncontrolled flow at the same point on the airfoil u.
Table 6: Characteristics of primary vortices under design conditions, measured 5hSCB downstream of
the bump trailing edge
!x,max /(uh)
HSCB 1200 3.61
wedge 1998 3.76
exSCB 1500 1.79
These results suggest that the vortices are remarkably strong, considering that the bumps have
not been designed to optimise vortex production. To put the magnitudes into context, a typical sub-
boundary layer VG might have a non-dimensional circulation of around 20. The integration also includes
contributions from flow structures of the opposite sense (that this will happen is clear from figure 14)
which will detract from the overall calculated circulation at this point; hence the values given above are
likely to be underestimates of the true primary vortex strengths.
The presence of the primary vortices is well-documented for the HSCB and wedge type bumps (see,
for example, Bruce and Babinsky [9], Colliss et al. [16]); however, for the exSCB its presence is somewhat
troubling within the framework of current bump physics understanding. As seen in the introduction to
this paper, the consensus in the literature is that spanwise pressure gradients over the tail section of
the bumps are responsible for generating and controlling the streamwise vortices. In increasing the
19
length and width of the bump tail - as for the exSCB - these pressure gradients should be reduced, thus
attenuating the production of streamwise vortices. Structure (IV) should not therefore be observed, yet
there is clear evidence of it in figure 14 and moreover it is seen to be quite strong in table 6. This
suggests that the current understanding of vortex production may be incomplete or incorrect, and this
is something that will be investigated further (see section V.).
B. O-design behaviour
The streamwise vorticity and swirling strength contour maps for o-design conditions are shown in
figure 15.
(a) (b) (c)
10.50-0.5-1
x (×103)
(I)
(III)
(I)
(V)
(V)
(II*)
(IV)(IV)
(V) (V)
(IV)
(V)
(III+V)
(IV)
(II)
(II)
Figure 15: Vortical structures on SCBs under o-design conditions visualized by contours of !x(top
row) and 2
ci (bottom row): (a) HSCB; (b) wedge bump; (c) exSCB
As labelled in the figure, most of the flow structures observed for the on-design case are once again
visible here. In particular, for all bumps the vorticity within the ()-shock (structure (I)) is unchanged
from design conditions (as should be the case), whilst the secondary vorticity (II) can also be identified.
The key dierence from design conditions is around the flow separation on the bump tails. The details of
this were shown in figure 11, and it was stated that the separation topology should produce a common-
20
flow-down vortex pair: this can be observed in the figure 15, labelled (V).
For the HSCB and wedge bump, structure (V) is seen to dissipate relatively rapidly downstream in
the 2
ci data. In both cases the vortex is seen to have decayed by around 0.25LSCB downstream of the
tail, although on the wedge bump there is still a high peak in !xat, and downstream of, this location.
This is caused by the presence of shear, observed in the on-design case as structure (III).
On the exSCB, structure (V) persists far downstream - indeed it is the primary constituent of the
wake. Examining the rotation of the vortices (using !x), it can be inferred that the inner vortices
emanating from the two separations (i.e. those closest to the centreline) are dominant, with the others
(the ones closest to the bump flanks) being indistinguishable in both the !xand 2
ci data, and therefore
very weak. The result is that the net wake structure is a common-flow-down vortex pair, similar to the
on-design case, but generated in a very dierent way.
Because of the decay of the separation vortices on the HSCB and wedge bump, the wake structure is
dominated by flow features which are not caused by the separation. This comprises a common-flow-down
pair of vortices which appear similar in character to those generated in the on-design case. In fact, these
can be identified with those of the on-design case, due to their similarity in character and position, hence
are labelled (IV) in figure 15.
This is a particularly interesting observation because it shows that even if the flow on the bump
tail separates, thus radically changing the eective aerodynamic shape of the tail, the primary vortex
structure is still generated. As with the generation of vortices on the exSCB under design conditions,
this seemingly contradicts the understanding that the SCB tail is responsible for generating the vortices.
V. Factors influencing vorticity
In order to investigate the apparent anomalies of vortex production noted in the previous section, a
number of parametric variations of the bumps tested in this paper have been examined, looking at the
relationship between pressure gradients at various locations and the strength of the vortices generated.
Figure 16 shows the SCB geometries and the key geometry dimensions varied; table 7 shows the values
of the dimensions tested; the domain width (which is eectively the lateral bump spacing due to the
periodic boundary conditions) is denoted band not shown on the figure. The data is collected from
numerical simulations, since the relatively inexpensive nature of the CFD enabled a larger number of
bumps to be examined.
A number of locations for measuring the pressure gradients were tested, of which three were found
21
(a) (b) (c)
h
w
L
Lramp
Lramp
wtail
w
h
wtail
Figure 16: SCB geometries and key dimensions
Table 7: Dimensions of bumps tested and symbols used in figure ??
Symbol SCB type L/0w/0h/0b/0Lramp /0wtail/0
HSCB 25 8.33 0.5 16.67 12.5 8.33
25 8.33 0.67 16.67 12.5 8.33
25 8.33 1 16.67 12.5 8.33
25 8.33 1.33 16.67 12.5 8.33
25 8.33 1.5 16.67 12.5 8.33
25 8.33 0.67 25 12.5 8.33
25 8.33 1 25 12.5 8.33
25 8.33 1.33 25 12.5 8.33
50 16.67 3 25 25 16.67
wedge 25 8.33 0.83 16.67 8.33 4.17
25 8.33 0.83 25 8.33 4.17
exSCB 33.33 4.17 0.83 16.67 8.33 16.67
to be particularly representative: these are shown in figure 17. The streamwise pressure gradient on the
tail was measured half way between the shock location and the bump trailing edge, on the centreline
of the bump (figure 17(a)). The tail spanwise pressure gradient was measured at the same streamwise
location, but taken at the spanwise location directly beneath the peak vorticity within the primary
vortex core (figure 17(b)). . Spanwise pressure gradients on the bump ramp are characterised by the
highest pressure gradient observed half way between the bump nose and the shock, i.e. x=xs/2
(figure 17(c)). Any pressure gradients taken through the front ()-shock leg are discarded, such that the
pressure gradient recorded is always on the bump surface (and usually on the bump flanks). Although
the streamwise location of xs/2 is quite arbitrary, it was found that examining points ahead or behind
this (which avoided interference with the region with either forward or rearward shock leg) produced a
similar result.
The vortex strength was characterised using the peak streamwise vorticity. This was cross-checked
22
xs / 2
xs Lrear
Lrear / 2
(a) p/x
(c) p/z(b) p/z
primary vortex x
shock leg
max gradient
data excluded
p
z z
y
()-shock footprint
Figure 17: Pressure gradients and locations tested, as labelled: (a) streamwise pressure gradient on tail;
(b) spanwise pressure gradient on tail; (c) spanwise pressure gradient on ramp.
using 2
ci, both for identifying the appropriate peak in !xfor the primary vortex core (as in figures 14
and 15) and for ensuring that the vorticity recorded was representative of the swirl itself. The latter
was done using the fact that !x,swirl is twice the rotation rate of a fluid packet, i.e. 2ci . The vortex
strengths were then plotted against the various pressure gradients of figure 17, shown in figures 18 and 19.
In addition, the maximum vorticity has been plotted against the shock location (relative to the bump
length) for the HSCBs with L/0= 25.
1
p0
p
x
xs
L
x (103 s-1)
(a)
0
1
2
3
4
5
x (103 s-1)
0
1
2
3
4
5
1.6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.4 0.8 1.2
(b)
Figure 18: Correlations of vortex strength with: (a) @p/@xon tail; (b) xs/L. Open symbols represent
unseparated flows; closed symbols represent flows where separation occurs on the bump tail.
23
No trend with the streamwise pressure gradient is seen to exist - the ‘best fit’ line drawn on figure 18(a)
has a very low correlation coecient (R2=0.096) and in fact similar correlation coecients could
obtained with a more horizontal line; this indicates that the data is more of a random point cloud.
Moreover, when the maximum streamwise vorticity is plotted against the shock location, there remains
no discernible trend. Given the significant variation in the local pressure gradients on the bump tail
that the shock location can generate, this suggests that the streamwise gradient may be of little or no
importance to the vortex generation. It therefore appears that the spanwise pressure gradients are the
most important for the generation of vortices by SCBs.
1
p0
p
z
1
p0
p
z
x (103 s-1)
(a) (b)
0
1
2
3
4
5
0 0 0.4 0.8 1.2 1.6 20.40.30.20.1
Figure 19: Correlations of vortex strength against pressure gradients: (a) @p/@xon tail; (b) @p/@zon
tail; (c) @p/@zon ramp. Open symbols represent unseparated flows; closed symbols represent flows
where separation occurs on the bump tail.
The spanwise pressure gradient on the tail shows more of a linear trend, although the correlation
coecient is still not particularly high in this case (R2=0.421). A much stronger correlation is observed
for the spanwise pressure gradients on the ramp (for which R2=0.885). This suggests that it is actually
the flow on the bump ramp which governs the formation of streamwise vortices in the wake, rather than
that on the tail as was previously thought.
The above analysis immediately explains the apparently anomalous observations made earlier in
this paper. The exSCB has a wider and longer tail, leading to lower local pressure gradients, but it
still produces vortices because the ramp section is of similar geometry to the wedge bump. Likewise,
the appearance of boundary layer separation on the bump tails under o-design conditions does not
significantly alter the vortex production, because this is governed by what is happening ahead of the
shock, which is of course unchanged.
24
This result is significant because it means that the flow control potential of a SCB is decoupled
from the bump’s eect on the boundary layer, which is controlled by the tail ( [7, 9, 17]). In particular,
the ramp geometry determines the inviscid control potential of the bump, governed by the ()-shock
characteristics, as well as the boundary layer control potential of the bump, governed by the vortices in
the wake.
VI. Conclusions
Computational results for a number of SCB geometries have been examined to understand the flow
structures generated by the bumps as well as investigate the factors governing the properties of their
wakes. A joint experimental and numerical approach developed and tested previously was used to validate
the computational data prior to investigating the details of the flow. Three bump geometries were tested:
hill (smooth contour), wedge and extended bumps. Two shock positions were considered, the ‘design’
condition where the shock sits at the crest; and the ‘o-design’ condition where the shock is suciently
far downstream of the crest to cause a localised flow separation.
It was found that under design conditions all bumps produce three principal flow structures: shear
flow within the ()-shock caused by the curvature of the front shock leg; shear emanating from the bump
tail around the crest region; and primary vortices, which are the main constituent of the wake. The
wedge and extended bumps also generated a region of weak shear on the flat section in between the side
flanks which was not present on the HSCB (due to the continuous surface curvature across the span).
That the exSCB produced a primary vortex pair at all was in conflict with the understanding that the
bump tail is responsible for generating the vortices.
Under o-design conditions, the presence of flow separation modified the wake flow structure, prin-
cipally through the addition of a common-flow-up counter-rotating vortex pair emanating from the
separation topology. This had the same form for the hill and wedge bumps, although the increased
width of the extended bump tail lead to the topology being localised to the bump flanks and duplicated
on either side such that the vortices closest to the centreline dominate, with a region of attached flow in
between. This directly resulted in the wake being dominated by a common-flow-down vortex pair on the
exSCB. The HSCB and wedge bump’s separation vortices were seen to decay quickly, however, with the
primary vortex pair like that generated under design conditions being the main component of the wake.
Thus all the bumps tested behave like vortex generators, creating a rotationally similar structure in all
cases even when the boundary layer separation on the tail modifies its eective aerodynamic shape. This
25
is also in conflict with previous explanations of vortex production by SCBs.
The strength of the primary vortices for all bumps at design conditions was found to be around 20%
of that of a typical vortex generator, surprisingly strong given that none of the bumps in this study were
designed or optimised for vortex production. A number of parametric modifications of the bumps were
made and the strengths of the vortices produced by each of the bumps in the resulting database were
correlated against pressure gradients at various locations on the bump. It was found that the vorticity is
most strongly related to spanwise pressure gradients on the bump ramp, suggesting that it is the front of
the bump which is responsible for generating the streamwise vortices and not the tail, as was previously
thought to be the case.
Acknowledgments
The research leading to these results has received funding from the European Union’s Seventh Frame-
work Programme (FP7/2007-2013) for the Clean Sky Joint Technology Initiative as part of the NextWing
program under grant agreement no. 271843.
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... In the US, the N+3 goal proposed by NASA is to reduce Nitrogen oxides (NOx) emission by up to 80% in the landing-take-off process and reduce fuel burn by 60% for an airliner entering service in 2030-2035 [3]. To achieve these objectives, a number of technologies, such as shock control [4][5][6][7], laminar flow control [8][9][10][11][12][13][14], turbulent drag reduction [15][16][17][18], as well as novel aircraft concepts, such as BWB or hybrid wing body (HWB) [19], 'double-bubble' [20], truss-braced wing (TBW) [21] and box-wing [22], have been proposed and investigated to explore a better aerodynamic performance. However, there are significant challenges in applying these technologies mentioned above on future aircraft, especially in terms of practical application. ...
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Effective control of aerodynamic loads, such as maneuvering load and gust load, allows for reduced structural weight and therefore greater aerodynamic efficiency. After a basic introduction in the types of gusts and the current gust load control strategies for aircraft, we outline the conventional gust load alleviation techniques using trailing-edge flaps and spoilers. As these devices also function as high-lift devices or inflight speed brakes, they are often too heavy for high-frequency activations such as control surfaces. Non-conventional active control devices via fluidic actuators have attracted some attention recently from researchers to explore more effective gust load alleviation techniques against traditional flaps for future aircraft design. Research progress of flow control using fluidic actuators, including surface jet blowing and circulation control (CC) for gust load alleviation, is reviewed in detail here. Their load control capabilities in terms of lift force modulations are outlined and compared. Also reviewed are the flow control performances of these fluidic actuators under gust conditions. Experiments and numerical efforts indicated that both CC and surface jet blowing demonstrate fast response characteristics, capable for timely adaptive gust load controls.
... Limitations to the optical access in this facility prevent a three-component system from being installed and so only the streamwise and vertical components of velocity, and , can be obtained. Previous measurements in this facility of particle lag through a normal shock have placed the seeding droplet diameter in the range 200 -500 nm [11]. The error in measured velocities due to the finite number density of seeding particles and due to the laser optics is 2% for and 19% for . ...
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Thesis
High fidelity numerical simulations are conducted to investigate wavy leading edges (WLEs) in transonic flows. In particular the focus is on the mitigation of shock buffet and its radiated noise. The main objective of this work is to give a comprehensive overview of the aerodynamic and aeroacoustic performance of this passive technique previously studied only in subsonic flows. Due to the novelty of this study, a preliminary analysis is conducted slowly varying the incidence angles. This gives information about the aerodynamic performance and the leading edge flow structures. After that, the shock buffet condition is analysed in details focusing first on the unsteady phenomena and then on the radiated noise. The aerodynamic and aeroacoustic performance analyses are conducted including the effect of the WLE amplitude. Finally, a sweep angle is introduced in order to investigate an aeronautical application of this passive technique. Two wavy swept configurations are studied. In the first one, the WLE direction has a sweep angle with respect to the upstream flow, while in the second one, the WLE direction is parallel to the upstream flow. The focus is on the mitigation of shock buffet and the additional unsteady phenomena introduced by the three dimensional configuration. Moreover, the leading edge flow structures are inspected and compared with the unswept case. The study shows that wavy leading edges over supercritical aerofoils represent a promising passive technique to mitigate the shock oscillations and it paves the ground for further studies.
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View Video Presentation: https://doi.org/10.2514/6.2021-2558.vid This experimental study investigates the use of shock control bumps (SCBs) for controlling transonic buffet. Three-dimensional SCBs have been applied on the suction side of an OAT15A supercritical airfoil with the experiments conducted in the transonic-supersonic wind tunnel of TU Delft for fully developed buffet conditions (Ma=0.7, α=3.5° and Re=2.6·10^6). The effectiveness of the SCBs for different spanwise spacings (ranging from 20%c to 30%c) was verified using two optical techniques: schlieren visualization and particle image velocimetry (PIV). Both techniques showed the possibility of controlling buffet using such devices, resulting in a reduction of the unsteadiness present in the flow, both in terms of shock oscillation and pulsation of the separated area. A dedicated PIV investigation in a spanwise-chordwise measurement plane was then conducted in order to understand the effect of the spatial distribution of the bumps, focusing on the interaction of the shockwave structures along the span. The configuration with a spacing of ΔxSCB=25%c demonstrated to be the most efficient in reducing the transonic buffet oscillations.
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Chapter
A method allowing a detailed investigation of the flow physics of shock control bumps (SCBs) on an unswept airfoil has been developed by comparison of the results of experiments and computations. A simple wind tunnel set-up is proposed which is shown to generate representative baseline conditions, allowing fine details of the flow to be measured using an array of techniques. Computational data for the same bump configuration is then validated against the experimental results, allowing a more intimate analysis of the flow physics as well as relating wind tunnel results to the performance of the SCB on an unswept wing.
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Results from wind tunnel experiments with three different geometry shock control bumps (SCBs) are presented and discussed. The primary aims of this study are to explore how 3-D SCBs generate stream-wise vorticity and to compare the flow features produced by different geometry 3-D SCBs. Results are presented in two parts: In part I, the flow development over a simple geometry baseline bump is described in detail with a focus on describing the evolution of vortical flow structures. In part II, results from tests with two different bumps (with subtle geometric variations from the baseline design) are presented and compared with those from the baseline bump. It is observed that the mechanism of vortex production for all 3-D SCBs tested is broadly in agreement with that reported in literature: Specifically, vortical flow structures are only observed downstream of the crest, on the SCB tail. Differences between the three SCB geometries tested are relatively subtle; increasing the width of the SCB tail reduces the extent of shock-induced separation at the crest, giving an anticipated reduction in viscous drag; steepening the SCB sides also reduces shock-induced separation at the crest (although to a lesser extent) and modifies the pressure profile on the off the bump such that the flow experiences lower span-wise pressure gradients. These findings suggest both geometric modifications considered may yield a benefit in performance for a 3-D SCB mounted on a transonic wing. © 2015, American Institute of Aeronautics and Astronautics Inc. All rights reserved.
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The aerospace industry increasingly relies on advanced numerical simulation tools in the early design phase. This volume provides the results of a German initiative which combines many of the CFD development activities from the German Aerospace Center (DLR), universities, and aircraft industry. Numerical algorithms for structured and hybrid Navier-Stokes solvers are presented in detail. The capabilities of the software for complex industrial applications are demonstrated.
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The desire to design more efficient transport aircraft has led to many different attempts to minimize drag. One approach is the use of three-dimensional shock control bumps, which have gained popularity in the research community as simple, efficient and robust devices capable of reducing the wave drag of transonic wings. This paper presents a computational study of the performance of three-dimensional bumps, relating key bump design variables to the overall wing aerodynamic performance. An efficient parameterization scheme allows three-dimensional bumps to be directly compared to two-dimensional designs, indicating that two-dimensional bumps are capable of greater design point aerodynamic performance in the transonic regime. An advantage of three-dimensional bumps lies in the production of streamwise vortices, such that, while two-dimensional bumps are capable of superior performance near the design point, three-dimensional bumps are capable of breaking up regions of separated flow at high Mach numbers, suggesting improvement in terms of buffet margin. A range of bump designs are developed that exhibit a tradeoff between design point aerodynamic efficiency and improvement in buffet margin, indicating the potential for bespoke designs to be generated for different sections of a wing based on its flow characteristics.