Exp Fluids (2009) 47:897–911

DOI 10.1007/s00348-009-0686-6

RESEARCH ARTICLE

Skin friction fields on delta wings

S. A. Woodiga Æ Tianshu Liu

Received: 15 December 2008 / Revised: 1 May 2009 / Accepted: 11 May 2009 / Published online: 29 May 2009
Ó Springer-Verlag 2009

Abstract The normalized skin friction fields on a 65° observe the topology of skin friction fields, surface visu-
delta wing and a 76°/40° double-delta wing are measured alization by using oil such as the silicone oil with titanium
by using a global luminescent oil-film skin friction meter. dioxide mixture has been traditionally applied to wind
The detailed topological structures of skin friction fields on tunnel tests. Typically, by visually inspecting the streaky
the wings are revealed for different angles of attack and patterns of oil on a surface, the skin friction lines and
the important features are detected such as reattachment conjectured topological structures are manually depicted
lines, secondary separation lines, vortex bursting and vor- by following the basic topological rules if they are appli-
tex interaction. The comparisons with the existing flow cable (Verhaagen et al. 1995; Huang et al. 1996; Verha-
visualization results are discussed. agen 2002; Verhaagen and Jobe 2003; Van Bossuyt 2005).
However, this approach is qualitative and somewhat sub-
jective, although it has been used as a major experimental
tool to obtain a large amount of valuable knowledge on the
1 Introduction topological structures of skin friction fields on delta wings.
Directly from oil images, it is very difficult to identify
Delta wings have been widely used in various flight some detailed topological structures on more complicated
vehicles including high performance combat aircraft, wings like a double-delta wing. Shear-sensitive liquid
supersonic civil aircraft, hypersonic aircraft and the space crystal visualization on delta wings suffers the same
shuttle orbiter. The flow past a delta wing is dominated by problem in non-quantitative skin friction diagnostics due to
the vortical structures that originate from its leading edges. the complexity of calibration for wind tunnel testing
The structure of these vortices has been the focus of (Zhong 2002). Near-surface particle image velocimetry
extensive experimental and numerical studies (Narayan (PIV) has been used to obtain near-surface topology on a
and Seshadri 1997; Gursul 2004; Huang and Verhaagen delta wing (Yavuz et al. 2004; Taylor and Gursul 2004).
2008). In order to study the underlying mechanisms of Although the measurement of near-surface flow closely
such complex separated flows, one useful method is an related to skin friction sheds a useful insight into the sur-
analysis of topological structures of skin friction fields face topology, the near-surface streamlines obtained by
(Tobak and Peake 1982; Délery 1992). The combined PIV cannot be interpreted exactly as skin friction lines.
topological analysis of skin friction and velocity fields on Numerical simulations have been conducted to understand
delta wings is particularly powerful (Rockwell 1993). To the flow structures over delta wings (Fuji and Schiff 1989;
Rizzi and Miillerf 1989; Kern 1992, 1993; Ekaterinaris
et al. 1995; Gordnier 1997). However, somewhat surpris-
ingly, high-fidelity skin friction fields generated by CFD
S. A. Woodiga
T. Liu (&) codes are rare for a systematical comparison with experi-
Department of Mechanical and Aeronautical Engineering,
mental observations. This reflects, to a certain sense, the
Western Michigan University, G-220, Parkview Campus,
Kalamazoo, MI 49008, USA difficulty in accurate calculation of skin friction fields in
e-mail: tianshu.liu@wmich.edu complex separated flows.

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Recently, a global luminescent oil-film skin friction 2 Global luminescent oil-film skin friction meter
meter has been developed and applied to diagnostics of
skin friction fields in complex separated flows by Liu et al. The basic theory of a global luminescent oil-film skin
(2008, 2009). This is a more rigorous method for quanti- friction meter is briefly described here, and the detailed
tative global high-spatial-resolution diagnostics of skin development of this technique is given by Liu et al. (2008).
friction fields from luminescent oil images. The imaging For an optically thin luminescent oil film on a surface,
system for this method is essentially the same as that for the luminescent emission intensity I under excitation is
the conventional surface oil visualization, and therefore it proportional to the oil-film thickness, i.e., IðX1 ; X2 Þ ¼
is easy to apply it to various facilities from subsonic to a Iex ðX1 ; X2 Þ hðX1 ; X2 Þ; where h is the oil-film thickness,
hypersonic wind tunnels. Without calibration, normalized Iex is the intensity of the excitation light on the surface,
skin friction fields can be obtained, and further absolute a is a coefficient proportional to the quantum efficiency of
skin friction fields can be determined through in situ cali- seeded luminescent molecules and dye concentration, and
bration that utilizes some accurate values of skin friction at (X1, X2) are the surface coordinates. Typically, in appli-
a few reference locations (at least one) provided by reliable cation of the global luminescent oil-film skin friction
point-based techniques and CFD. meter, the pre-coated luminescent oil-film thickness is
This paper focuses on application of the global lumi- about 20 lm and then the oil thickness is decreased to a
nescent oil-film skin friction meter to diagnostics of skin few microns during a run depending on the magnitude of
friction fields on a 65° delta wing and a 76°/40° double- local skin friction. Although a luminescent oil film in this
delta wing with different fillets. The topology of the flows study is physically much thicker than that in an interfero-
on a 65° delta wing has been experimentally studied by metric oil-film skin friction meter, the luminescent silicone
Huang et al. (1996), Verhaagen (2002) and Verhaagen and oil film used here can be considered to be optically thin.
Jobe (2003) based on qualitative surface oil visualizations. Thus, the thin-oil-film equation is transformed to a differ-
The flow structures on a 65° delta wing have been ential equation relating the relative luminescent intensity
numerically simulated by Rizzi and Miillerf (1989) and I=Iex to the skin friction vector s. The surface coordinates
Gordnier (1997). The 76°/40° double-delta wing has been (X1, X2) in the object space can be mapped onto the image
extensively studied, and the junction diamond and para- plane (x1, x2). In particular, when the image plane of a
bolic fillets have been used for vortical flow control. It is camera is parallel to the flat surface area to be measured,
shown that the juncture fillets can delay vortex bursting and the perspective projection transformation is simple, and in
thus contribute toward lift augmentation at higher angles of this case, o=oXi ¼ k o=o xi holds, where the scaling factor
attack (AoAs). Extensive flow visualization and surface k is considered as a constant. Introducing the normalized
pressure measurements on the double-delta wing have been luminescent intensity g ¼ I=Iex and the equivalent skin
conducted by Verhaagen et al. (1995) and Erickson and friction s ¼ sg ðk =2l aÞ; we have the projected thin-oil-
Gonzalez (2006). Flow visualizations have been also car- film equation for a luminescent oil
ried out for vortical flow control using junction fillets in a
water tunnel facility (Hebbar et al. 1994, 1995, 1996,
2000). Numerical simulations have been conducted by
Kern (1992, 1993), in which vortex visualization and force
data have been presented.
In this study, the mapping capability of the global
luminescent oil-film skin friction meter allows revealing
the detailed topological structures on the delta wings that
cannot be quantitatively obtained by using conventional
techniques. The dominant features like reattachment and
separation lines are identified, and other subtle features
associated with vortex bursting and vortex interactions are
quantitatively mapped. The changes of the topological
structures of skin friction fields are studied as the AoA
increases. The local topological structures, such as spirals
associated with tornado-like vortices in 3D separation and
the merged and bifurcated reattachment line near the apex,
are revealed on the double-delta wings. The effects of the
fillets on the topological structures on the double-delta Fig. 1 Illustration of luminescent oil-film skin friction measurement
wing are investigated. setup

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  3 
o g=ot þ r
ðg sÞ ¼ f ðx1 ; x2 ; gÞ; ð1Þ o op g
f ðx1 ; x2 ; gÞ ¼ k k  qgi ði ¼ 1; 2Þ
where r ¼ o=o xi is the gradient operator in the image oxi oxi 3l a2
plane, l is the dynamical viscosity of the oil, and the ð2Þ
effects of the pressure gradient op=oxi and gravity vector gi Equation 1 has the same mathematical form as the
are given by physics-based optical flow equation given by Liu and Shen

Fig. 2 Skin friction measurement on the 65° delta wing for AoA of 10°, a typical luminescent oil-film image, b skin friction vectors, and c skin
friction lines, and d normalized skin friction magnitude

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Fig. 3 Skin friction lines on the 65° delta wing for AoAs of a 5°, b 13°, c 15°, and d 20°

(2008). Therefore, to determine the equivalent skin friction Shen 2008), where the Neumann condition os =on ¼ 0 is
field s ¼ ðs1 ; s2 Þ; the same variational formulation for imposed on the domain boundary in images. A discussion
optical flow computation can be used, which is constrained on the relevant error sources in the determination of skin
by a smoothness regularization term of a skin friction field. friction is given by Liu et al. (2008), and an error analysis
The corresponding Euler–Lagrange equations are obtained of optical flow computation is given by Liu and Shen
and then solved numerically for s; (Liu et al. 2008; Liu and (2008).

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Fig. 4 Zoomed-in view of skin friction lines showing the appearance

of the vortex bursting on the left side of the 65° delta wing for AoA of
15°

From two successive images, the solution of Eq. 1 gives

a ‘snapshot’ solution for a skin friction field in a short
interval during a relatively long evolution of oil film driven
by a steady-state skin friction force. A sequence of snap-
shot solutions can be obtained at successive moments. A
snapshot solution captures the salient skin friction signa-
ture in the regions where the oil-film evolution is the most
sensitive to flow at that moment. A time sequence of
snapshot solutions is required to capture the major skin
friction signatures in different regions at different moments
during the oil-film evolution. In order to reconstruct a
Fig. 5 Locations of the reattachment lines on the 65° delta wing for a
complete steady-state skin friction field, the snapshot AoAs of 5°, 10° and 13° and b AoAs of 15°, 17° and 20°
solutions should be appropriately fused by either a direct
superposition method or a wavelet-based method (Liu et al.
2008). It is found that the two methods are basically Corning silicone oil (200 cs). The resulting luminescent oil
equivalent in reconstruction of a complete relative skin emits the radiation at a longer wavelength due to the Stokes
friction field. In general, a relative or normalized skin shift when illuminated by an appropriate light source like
friction field can be obtained by using this method without UV lamp. In the present experiments, the temperature
calibration. To determine the unknown proportional coef- sensitivity of the luminescent material is not a concern for
ficient in the relative skin friction field, in situ calibration low-speed flows with a constant temperature. All skin
utilizes some accurate values of skin friction at several friction measurements were conducted in a low-speed wind
locations (at least one) given by an interferometric oil-film tunnel with a test section of 0.406 9 0.406 m at the
skin friction meter (or other reliable experimental, com- Applied Aerodynamics Laboratory of Western Michigan
putational and theoretical methods). Therefore, a global, University. The freestream turbulent intensity was about
absolute skin friction field can be obtained using this in situ 0.2%. A glass window at the top of the test section allowed
approach. In this paper, the normalized skin friction fields optical access. Figure 1 shows a typical setup for lumi-
are presented without a priori or in situ calibration. nescent oil-film measurements. The luminescent oil was
To make a luminescent oil, a small amount of high brushed onto the test surface and excited to luminescence
visibility UV powders (UVHiVisOR) produced by LDP by the UV lamps. The UV lamps were arranged to ensure
LLC (http://www.MaxMax.com) was mixed with Dow a uniform illumination field in the test area. A 550 nm

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Fig. 6 The 76°/40° double-

delta wing models: a baseline
configuration, b diamond-fillet
configuration, and c parabolic
fillet configuration

long-pass filter was used to filter the light captured by the after which the wind tunnel was run and images acquired at
camera allowing only detection of the luminescent oil a frame rate of 25 fps. Figure 2a shows a typical lumi-
emission centered at approximately 590 nm. The wind nescent oil image on the leeside of the delta wing at AoA
tunnel was run in a dark environment, and images were of 10°. Figure 2b–d show the normalized skin friction
captured by an ISG Lightwise CMOS camera by using vectors, lines and magnitude on the delta wing at AoA of
Streampix 4.0 image acquisition software (NorPix) at 25 10°, where the x and y coordinates are normalized by the
frames per second. The acquired images were then pro- root chord c. A total of 150 snapshot solutions were used
cessed by using a specialized Matlab code to extract skin for superposition from successive image pairs with a 0.4-s
friction fields. interval for reconstruction of the skin friction field. Image
recording typically took about 2 min at 25 fps in a run that
was shorter than that in application of an interferometric
3 65° Delta wing oil-film skin friction meter in a similar case, and only a
subset of the acquired images was used for reconstruction
This study performs global quantitative skin friction mea- of a skin friction field since the evolution of the oil film
surements on a 65° delta wing model with a flat upper was relatively slow. The skin friction fields are normalized
surface and a 45° leading-edge angle. The root chord and by the skin friction magnitude at a reference location that is
span of the delta wing are 13 and 12 in. (330.2 and 10% of the root chord on the centerline of the delta wing.
304.8 mm), respectively. Tests were conducted at a free- The reattachment lines associated with the primary leading
stream velocity of 20 m/s corresponding to a Reynolds edge vortices and the secondary separation lines between
number based on the root chord of Rec = 4.4 9 105 for the primary and secondary vortices can be clearly identified
AoAs of 5°, 10°, 13°, 15°, 17° and 20°. The upper surface in Fig. 2c.
of the delta wing was covered with a white Mylar sheet to Figure 3 shows the skin friction lines for the delta wing
enhance the luminescent emission of the luminescent oil. at AoAs of 5°, 13°, 15°, and 20°, respectively. The skin
The luminescent oil was brushed on the Mylar surface, friction topological structures for AoAs of 5°, 10° and 13°

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Fig. 7 The aerodynamic characteristics of the double-delta wing with the baseline, diamond fillet, and parabolic fillet configurations, a lift
coefficient as a function of AoA, b drag polar, and c lift-to-drag ratio

are similar and remain largely symmetrical. These results, move inboard as AoA increases. In contrast, when AoA is
which are basically consistent with previous observations larger than 15°, the reattachment lines start to move out-
in flow visualizations, provide more quantitative details of board, which may be related to the vortex bursting
topology. For AoAs of 15° and 20°, a sudden expansion of observed in Fig. 3c and d. The effects of the blockage and
the well-defined reattachment line at about 0.6c is a foot- wall interference are not investigated here. The ratio
print of the leading-edge vortex bursting in the skin friction between the front-projected wing area and the cross-section
field. A zoomed-in view of skin friction lines is shown in area of the test section varies from 0.004 to 0.1 for AoAs of
Fig. 4, indicating the appearance of the skin friction lines 5°–20°. At high AoAs, the velocity at the leading edge
where the vortex bursting occurs on the left half of the 65° would be increased due to the blockage effect. However, at
delta wing for AoA of 15°. The vortex bursting locations this stage, it is premature to speculate how the blockage
correspond to the lower bound of data collected from many effect changes the flow structure and surface topology, and
experiments (Jobe 1998). Figure 5 shows the locations of in fact the large differences in the vortex bursting locations
the reattachment lines on the 65° delta wing for different between different measurements on 65° delta wings may
AoAs. In a range of 5–13° in AoA where no massive vortex reflect the sensitivity of the flow to various factors
bursting is observed, the locations of the reattachment lines including the blockage and wall interference (Jobe 1998).

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Fig. 8 Skin friction lines on the baseline 76°/40° double-delta wing for AoAs of a 10°, b 12°, c 16° and d 20°

4 76°/40° Double-delta wings root chord and wing span of all the three delta wings was
203 and 207 mm, respectively. Figure 6 shows images of
4.1 Aerodynamic characteristics the 76°/40° double-delta wing models with the baseline,
diamond fillet and parabolic fillet configurations. The
This study focuses on three 76°/40° double-delta wing aerodynamic forces of the 76°/40° double-delta wing
configurations: the baseline, diamond fillet and parabolic models with the baseline, diamond fillet and parabolic fillet
fillet configurations. The models are half-scale models to configurations were measured using an external balance in
the double-delta wing model tested extensively in pressure the same wind tunnel at WMU. Figure 7a–c show the lift
sensitive paint (PSP) measurements by Erickson and coefficient, drag polar, and lift-to-drag ratio, respectively.
Gonzalez (2006) at NASA Langley Research Center. The The lift increase is clearly observed for the double-delta

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double-delta wings with the fillets show an improvement in

the lift-to-drag ratio, as indicated in Fig. 7c. The lift-to-
drag ratio is improved by 3.95 and 4.97% for the wings
with the diamond fillet and parabolic fillet for AoA of 20°,
respectively. These observations are consistent with the
numerical results presented by Kern (1992, 1993), indi-
cating that the fillets provided a lift enhancement at a small
drag penalty which resulted in the overall improvement of
the lift-to-drag ratio.

4.2 Skin friction fields

Skin friction measurements were conducted at 20 m/s that

corresponds a Reynolds number of 2.75 9 105 based on
the root chord. For skin friction measurements, a white
Mylar sheet was applied to the upper flat surface to
enhance the luminescent oil emission. Skin friction fields
were obtained for the baseline double-delta wing for AoAs
of 5°–20°. Figure 8 shows the normalized skin friction
vectors and lines for the baseline wing at AoAs of 10°, 12°,
16° and 20°. The skin friction fields are normalized at a
reference location at 10% of the chord length from the
leading strake tip on the centerline of the wing. As shown
in Fig. 8a, for AoA of 10°, the primary reattachment lines
are highly curved at about x/c = 0.7, indicating the strake
and wing vortices are entangled there. The dye visualiza-
tion on a similar wing for AoA of 10° in a water tunnel
indicated the entanglement of the vortices at that location
(Hebbar et al. 1995). However, laser vapor flow visuali-
zation and PSP measurements of Erickson and Gonzalez
(2006) at the Mach number of 0.5 and Reynolds number of
2 million indicated the separated strake and wing vortices
for AoA of 10° for the baseline wing. The emergence of the
strake and wing vortices occurred as a dominant feature at
AoAs of 16° and 20° in their experiments. Obviously, the
effects of the Mach number and Reynolds number on the
interactions of the vortices are significant.
In Fig. 8a and b, the secondary separation lines are
observed near the wing tips for AoAs of 10° and 12°. The
vortex bursting occurs at about x/c = 0.95 for AoA of 10°.
Fig. 9 Skin friction lines near a the left spiral and b the apex on the The vortex bursting location moves upstream. The loca-
baseline 76°/40° double-delta wing for AoA of 16° tions for AoAs of 12°, 16° and 20° are x/c = 0.9, 0.82 and
0.75, respectively, which are consistent with the data
obtained from flow visualization at Rec of 0.5 million in the
wings with the diamond and parabolic fillets. A maximum Basic Aerodynamics Research Tunnel at NASA LaRC
lift increase of 7.98 and 9.41% is observed for the double- (Verhaagen et al. 1995). However, the vortex bursting
delta wings with the diamond and parabolic fillets at AoA locations in our experiments are 20–40% higher (farther
of 20°, respectively. A drag increase was also observed downstream) than those observed in a water tunnel at a
with the diamond and parabolic fillets, as shown in Fig. 7b. much lower Reynolds number (Rec = 18,000) (Hebbar
The drag increases were 3.87 and 4.23% for the double- et al. 1994, 1996). Note that a sudden expansion of the
delta wings with the diamond and parabolic fillets at AoA reattachment lines on the wing surface is a footprint of the
of 20°, respectively. Although there is a drag increase vortex bursting above the wall in the 3D space. The rela-
which corresponds to the lift increase with the fillets, the tionship between a skin friction field and the corresponding

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Fig. 10 Skin friction lines on the 76°/40° double-delta wing with a diamond fillet for AoAs of a 10°, b 12°, c 16° and d 20°

velocity field above the wall is worthwhile for further However, they were not able to give the detailed topo-
investigation. logical structure around it just from surface oil visualiza-
In addition, in Fig. 8c and d, spirals (or foci) are found tions. The topological structure around the spiral is
near the junction between the strake and wing for AoAs of depicted in Fig. 9a near the conjunction, and a saddle point
16°–20°. Figure 9 is a zoomed-in view of skin friction lines is also observed. As shown in Fig. 8, a single reattachment
near the left spiral on a baseline 76°/40° double-delta wing line initially appears near the apex at high AoAs and it
for AoA of 16°. The spiral is generally associated with the bifurcates downstream. Near the apex, the two counter-
tornado-like vortex in 3D separation (Délery 1992). Inter- rotating leading-edge vortices touch due to a small local
estingly, a spiral has been indicated by Verhaagen et al. span, forming a single reattachment line. As the local span
(1995) and Verhaagen (2002) for AoA of 22.5° in their increases downstream, the two vortices are separated and
conjectured topology based on oil visualization images. the single reattachment line is bifurcated. This scenario is

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Fig. 11 Skin friction lines on the 76°/40° double-delta wing with a parabolic fillet for AoAs of a 10°, b 12°, c 16° and d 20°

illustrated in Fig. 9b that shows the merged and bifurcated visualizations of the strake vortices on a diamond-fillet
reattachment line near the apex. This phenomenon has not wing for AoAs of 10° and 20° in a water tunnel (Hebbar
been revealed in previous surface oil visualizations since et al. 1995). Laser vapor visualizations and PSP measure-
the merged and bifurcated reattachment line near the apex ments in subsonic and transonic flows also showed this
cannot be extracted by visually inspecting surface oil feature for the diamond-fillet wing (Erickson and Gonzalez
images. 2006). The secondary separation lines are also observed
Figure 10 shows the normalized skin friction lines on near the wing tips. The vortex bursting locations for AoAs
the double-delta wing with a diamond fillet for AoAs of of 10°, 12°, 16° and 20° are x/c = 0.9, 0.85 and 0.8 and
10°, 12°, 16° and 20°. Compared with the baseline wing, 0.7, respectively. The locations for AoAs of 10° and 20°
the primary reattachment lines remain approximately are in agreement with the dye visualizations of Hebbar
straight, indicating the dominant strake vortices at high et al. (1995). In contrast to the baseline wing, spirals near
AoAs. This observation is consistent with the dye the junction between the strake and wing are not evident.

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Fig. 13 Locations of the primary reattachment lines on the 76°/40°

double-delta wing with the baseline, diamond fillet and parabolic fillet
configurations for AoA of 10°

Similarly, a parabolic fillet is designed to generate a single

vortex system on each side of the wing. Figure 11 shows
the normalized skin friction lines for the double-delta wing
with a parabolic fillet for AoAs of 10°, 12°, 16° and 20°.
The topological structures of skin friction fields for the
wing with a parabolic fillet are very similar to those for the
wing with a diamond fillet. The primary reattachment lines
are just slightly curved, and the vortex bursting locations
are basically the same as those for the diamond fillet.
Figure 12 presents the zoomed-in views of skin friction
lines near the left diamond fillet and parabolic fillet of a
76°/40° double-delta wing for AoA of 16°. No spiral is
observed for these cases. The merged and bifurcated reat-
tachment line near the apex is observed on both the models
with a diamond fillet and a parabolic fillet, which is similar
to that on the baseline model.
Figure 13 shows the locations of the primary reattach-
ment lines for the baseline, diamond fillet and parabolic
fillet configurations for AoA of 10°. The reattachment lines
for the diamond fillet and parabolic fillet configurations are
less curved than that for the baseline wing. This observa-
tion is consistent with the water tunnel flow visualizations
of the strake vortex cores (Hebbar et al. 1996). Figure 14
Fig. 12 Zoomed-in views of skin friction lines near the left junction shows the locations of the primary reattachment lines in
of the 76°/40° double-delta wing for AoA of 16°: a diamond fillet and comparison with those of the strake vortex cores observed
b parabolic fillet by Hebbar et al. (1996). The strake vortex cores are located

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Fig. 14 Locations of the primary reattachment lines and strake vortex cores on the 76°/40° double-delta wing with a the baseline, b diamond
fillet and c parabolic fillet configurations for AoA of 10°

closer to the leading edge as expected. Note that the similar to the observed positions of the strake vortex cores
visualization experiments by Hebbar et al. (1996) were (Hebbar et al. 1996).
conducted at a much lower Reynolds number in a water
tunnel. Therefore, care should be taken when the compar-
isons in Fig. 14 are interpreted. Figures 15 and 16 show the 5 Conclusions
locations of the primary reattachment lines at different
AoAs for the baseline and diamond-fillet wings, respec- For the 65° delta wing, the reattachment lines and sec-
tively. These results are roughly collapsed, which are ondary separation lines are basically straight rays for AoAs

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Fig. 15 Locations of the primary reattachment lines on the baseline Fig. 16 Locations of the primary reattachment lines on the 76°/40°
76°/40° double-delta wing for a AoAs of 10°, 12° and 14° and b double-delta wing with the diamond fillet for a AoAs of 10°, 12° and
AoAs of 16°, 18° and 20° 14° and b AoAs of 16°, 18° and 20°

indicating the dominant strake vortices, and no obvious

of 5°–13° and the locations of the reattachment lines move spiral near the junction is observed at high AoAs. The
inboard as AoA increases. When AoA is larger than 15°, merged and bifurcated reattachment line near the apex is
the vortex bursting is observed which is evidenced by a revealed at high AoAs on all the 76°/40° double-delta wing
sudden expansion of the reattachment line, and the loca- configurations. The measured locations of the primary
tions of the reattachment lines start to move outboard. The reattachment lines and vortex bursting for all the double-
vortex bursting location as a function of AoA is consistent delta wing configurations are in agreement with the pub-
with the previous flow visualizations. For the baseline 76°/ lished flow visualization results.
40° double-delta wing, the primary reattachment lines are
highly curved due to the interactions between the strake
vortex and wing vortex. In addition, when AoA is larger
than 15°, the spirals near the junctions between the strake References
and wing are observed which may be associated with the
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delta wing, the reattachment lines are relatively straight delta wing. J Aircr 32(3):457–463

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