12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022

THE FORWARD-FACING FIN – AN UNUSUAL HYDRODYNAMIC DESIGN
M. G. Mungal
Mechanical Engineering Department
Santa Clara University
Santa Clara, CA USA
mgmungal@scu.edu

Tioga Benner
Mechanical Engineering Department
Santa Clara University
Santa Clara, CA USA
tbenner@alumni.scu.edu

ABSTRACT
Motivated by the surprising existence of forward-facing
fins in some tropical fish, we investigate their hydrodynamic
behaviour at low aspect ratio and moderate Reynolds
numbers from low to high angles of attack. Computations
using STAR-CCM+ and related wind tunnel experiments
reveal a complex flow field with positive and negative shedvortices, and an important trapped stall bubble. The forwardfacing fin, either in single or tandem configurations, shows asmooth lift curve vs. angle of attack (“rolling stall”), while
the backward-facing fin exhibits sudden lift decrease(“classical stall”), while the straight fin shows a “two-timestall” behaviour previously reported by others. Experimental
surface flow visualizations in such highly separated flows arerich in detail and were crucial in the choice of the k-omega
turbulence model used in the simulations, while thecorresponding surface pressure distribution lacks such detailand is seen to be smooth and relatively benign.

Related past works are those of Van Dam (1987), Van
Dam et al. (1991) and Ardonceau (1994) who suggest modest
aerodynamic improvements for backward-pointing wings,
termed “crescent wings,” when compared to unswept
elliptical wings. These crescent wings resemble thebackward-pointing fin studied here and are more commonly
seen on some (“lunate”) fish tails. The term crescent wing
had been used earlier by Lee (1955) for sweptback wings ofa segmented design with differing sweep angles. Forward
swept wings were used in the Grumman X-29 aircraft toimprove aerobatic performance, but with the drawback ofnegative aeroelastic stability. In the original crescent wing
concept of Lee (1955) and the X-29, both applications use
wings of higher aspect ratio, and tend to have straight edges.
The present study is oriented more towards low aspect ratios
and uses upstream and downstream curved wing edges.
Model fins, Fig. 2, with root cord length of 7 in, a span of
1.3 chords (9.1 in) and a thickness of 1/10 of a chord (.7 in),
for an aspect ratio of ~2 were designed in SolidWorks andinvestigated using the STAR-CCM+ code, with a segmented
flow model and k-omega turbulence model at a Re of 2 x
10^5 based on root chord for both rounded tips and pointed
tips. The fin was set in a large box of size 50 inch width by
50 inch length in the streamwise direction with a height of 25
inch in the fin direction with a uniform water flow inlet of 1
m/s and solid wall boundary conditions. To circumvent adifficulty in SolidWorks the leading edge was an ellipse witha major axis of 5 in and a minor axis of 0.7 in (the thicknessof the fin). The trailing edge was a spline curve set to be
horizontal when it meets the ellipse. Furthermore, we
adopted 0.35 inch radius fillets on the leading edge of bothfins resulting in a somewhat more blunt airfoil body, which
does impact the findings. We also tested, to a lesser extent, a
fin which is more aerodynamic in shape with those results
described below and compared to the original fin.
Rigid models of the pointed fin case were 3-D printed
using PLA plastic with each fin made of two parts whichwere epoxied together at roughly the half span location.
Experiments were performed in a wind tunnel of 24 in x 24
in x 48 in test section size and maximum speed of 50 m/s
with less than 1% free stream velocity variation andturbulence level less than 0.25%. Three nominal speeds of
15.7, 21.0 and 26.2 m/s were used for testing and little
Reynolds effect was observed, as would be expected forhighly separated flows. Note that in the lift/drag experiments
the 9 inch tall fin resides in a portion of the wind tunnel thatis 24 in by 12 in inlet size, owing to use of a false wall, sosome confinement effects might be felt at the higher angles
of attack. In the surface oil flow visualizations the full tunnel
size was used, so little confinement effect is expected. The
experimental results will be presented after the initial
numerical findings are discussed.

INTRODUCTION AND BACKGROUND
Bioinspired flows have received increasing attention in
the last several years (Fish & Launder, 2006), with the
Humpback whale flipper showing surface vortices shed fromleading edge tubercles which extend the lift and dragperformance of the flipper (Fish et al., 2011). The present
study is motivated by the surgeonfish family Acanthuridae
which have spines, either single or multiple, Fig. 1, that arequite sharp and extend outwards pointing towards the fish’s
head (Winterbottom, 1971), which are used for aggressive
and defensive behaviors (Schober & Ditrich, 1992). Given
the unusual forward orientation of the fins, we conjecturethat shed vorticity, both positive and negative, from thevarious fin orientations – i.e. upstream or downstream facing- will lead to differing hydrodynamic behaviors. A straight
fin is included in the present study for comparison. While theReynolds number for the fish are estimated to be relatively
low, we investigate the flow behavior at moderate Reynolds
numbers that might occur in practical applications (e.g.
surfboards).

Figure 1. Picture of Orangespine Unicorn Fish spines
with two forward-facing pointed fins.
https://www.projectnoah.org/spottings/5391098/fullscreen.

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022
RESULTS AND DISCUSSION
Figure 3 for the rounded tip case (left plot) shows typicalnumerical findings and reveal the three types of behavior
seen in this study. The conventional backward-facing fin(blue diamond symbol) shows the sudden stall associatedwith separation originating off the curved leading edge. The
straight fin (green triangle symbol) shows an initial stall,recovery, and then a second stall at much higher angles ofattack. This type of behavior has been reported
experimentally by Guo et al. (2019) for rigid and flexible
finite wings at comparable Reynolds numbers and withsimilar stall angles for their rigid case. They describe this asa “two-time stall” given the two peaks in the lift coefficientas angle of attack increases. The forward-facing fin (redsquare symbol), on the other hand, shows a smooth stall
behavior (i.e. no sudden drops) over all angles of attack, abehavior we deem “rolling stall,” since the lift curve rolls
over smoothly from a rising to a falling behavior.
The drag, Fig. 4 (left plot), generally shows two
behaviors: a low drag behavior for angles of attack less than
5 degrees, transitioning around 10 degrees, followed by alinearly increasing trend beyond this, most likely associatedwith the increasing induced drag from the shed vorticity.
Simulation results for the pointed-tip case are also shownin Figs. 3, 4 (right plots). The trends seen for the rounded-tip
case are all seen in the pointed-tip case, except at lower
levels of lift and drag coefficients. The experimental results
will be shown later (Fig. 10) for the pointed-tip case and will
be seen to be in reasonably good agreement with thenumerical predictions. Hence, the computational results will
now be used to infer the flow physics in greater detail. All
subsequent discussions will not include the rounded-tip casefor brevity, and those results are generally consistent with thepointed-tip case to be shown.
Figures 5, 6 shows computational results for the axial
velocity and vorticity for the pointed-fin case at various
downstream (“Trefftz”) planes (1/10, 1 and 2 chord lengths)
normal to the main flow direction. The velocity deficit,
positive tip vorticity and negative inboard vorticity are seen
with the expected eventual dominance of positive vorticity
with downstream distance, as expected for a lifting surface.
Results for the rounded-tip are not shown but the trends are
similar, with the exception that the tip vortex is stronger fromthe outset when compared to the pointed-tip case. This is to
be expected as the rounded-tip case has more lifting surface
area near the tip region.
Perhaps the easiest way to understand the flow field isseen in Figs. 7, 8. These show streaklines released from thepressure and suction surfaces of the model i.e. throughout theboundary layer regions of the fin, which are allowed topropagate into the freestream, thus marking vortical fluid
behaviour. The 10-degree angle of attack, Fig. 7, shows
essentially attached flow for the backward-facing fin, but the
beginnings of an inboard separation bubble for the forwardfacing fin (and also implying less lift when compared to thebackward-pointing case). This is to be contrasted with the
30-degree angle of attack images, Fig. 8, which show that afull separation bubble has appeared for the backward-facingcase while the forward-facing separation bubble has grown,
both normal to and spanwise towards the tip. We believe it is
the appearance of this nearly 2-D separation bubble for the
backward-facing fin which first forms at high angles ofattack that leads to the sudden stall behaviour. This iscontrasted with the 3-D separation bubble for the forward-

facing fin which grows continuously from the root region
towards the tip region, with increasing angle of attack. Since
the bubble growth increases smoothly with angle, this resultsin the smooth rolling stall behaviour.
It was noted above that some fish species have double
forward-facing fins, while some species have single fins. We
investigated this effect by simulating fins at spacings of ¼,½, 1 and 2 chord lengths to determine the interference effect.
Figure 9 shows the lift-drag polars for pairs of fins. For
backward-facing fins, the interference effect is seen to besignificant, depending upon the spacing of the fins, while forforward-facing fins, the interference effect is negligible withessentially a universal curve for all spacings, and in close
agreement with the single-fin case. In this sense the forwardfacing fin configuration is robust in behaviour whencompared to the backward-facing and straight fin cases.
Experiments were performed for only the pointed fin
case. For brevity, images of surface tufts consisting of shortthreads taped to the fin are not shown. Movies of the tufts
reveal the highly recirculating, unsteady flow over various
parts of the suction surface at high angles of attack, while thetufts are perfectly still, as expected, on the pressure surface.
Figure 10 shows comparisons of the experimental results
at 0, 10, 20 and 30 degrees angle of attack with the previous
numerical simulations for the backward-facing and forwardfacing pointed fin cases. The blue diamond simulations are to
be compared with the green diamond measurements and thered square simulations to the purple square measurements.
The lift forces were measured using a strain gauge balanceover a range of 0 to 70 microstrain, with typical values of 30
microstrain and uncertainties of +/- ½ microstrain. Results
were averaged over several seconds given the overall flow
unsteadiness at high angles of attack. The agreement inmagnitude and trends appears satisfactory lending credence
to the computations.
No pressure measurements were made directly on themodels, hence we sought additional measures for comparison
with the simulations. To this end, Fig. 11 shows the surface
separation lines (Lu, 2010) obtained from use of a mixture of
rubbing alcohol and chalk dust to simulate traditional surface
oil flow visualization. For safety reasons, we were unable touse kerosine as a carrier fluid, and several commonly
available liquids (as found in a typical pharmacy) were tried,
and this alcohol/chalk mixture proved best and safest in an
open circuit wind tunnel environment. For thesevisualizations, the same forward-facing fin was mounted
horizontally on the centerline of the vertical sidewall of thetunnel, and the entire tunnel cross section area was used,
hence the blockage effects are minimal.
As the alcohol evaporates three chalk appearances are
revealed: smooth, quick-drying regions (indicative of fastflow), rough slow-drying regions (indicative of slow flow),
and lines of accumulation indicative of flow separation. The
latter are extracted and compared to surface flow
visualization using the four turbulence models available inSTAR-CCM+: k-omega, k-epsilon, Reynolds Stress Model,
and Spalart-Allmaras. The k-omega model showed very good
agreement, Fig. 11, while the other three models showedpoor agreement as seen in Fig. 12. These computational
images are all obtained by releasing surface streaklines for ashort elapsed time and then comparing to the surface chalk
images. In this sense, the short streaklines shown here are thebeginnings, or footprint, of the long streaklines shown earlier
in Fig. 8, the only difference being that in Fig. 8 the2

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022
turbulence model for this flow application, and not the otherturbulence models available in the STAR-CCM+ code.
Finally, we conjecture that since some birds (e.g. owls) holdtheir wings in a forward fin configuration at high angles ofattack during hunting and landing, they likely benefit fromrolling stall i.e. no sudden stall, as seen here. For future work
it would be beneficial to perform simulations at higher
numerical accuracy given the limitations of the current code.

streaklines are allowed to develop for a much longer time,
evolving into the main flow, thus marking the downstream
vortical fluid. To the extent that the k-omega model captured
the surface flow patterns, it was used as the model of choicein all the reported results described above. It is also implicit
in our thinking that since the complex flow features close thesurface are captured via the k-omega model, then the flow
features away from the fin, which are less demanding
computationally, are then representative of the time-averaged
flow features. Additionally, the surface pressure distributions
are also shown in Fig. 13 and, as expected, show none of thedetails and richness of the suction surface flow behaviour
seen in the separation lines of Fig. 11.
Finally, to investigate a more aerodynamic fin, we
performed computations for the fin shown (inset) in Fig. 14.
Here elliptical surfaces were applied to the leading edge for a
fin that more closely represents a practical fin shape. Figure
14 shows results for this more aerodynamic fin whencompared to the earlier (less aerodynamic) pointed fin. As
can be seen, the more aerodynamic fin shows a more marked
catastrophic stall behaviour for the backward-facing fin, as
might be expected, while it continues to show the smoothrolling stall behaviour of the forward-facing fin. Interestingly
the backward fin case shows a maximum lift coefficient of
0.85, comparable to the maximum value of 0.90 foundexperimentally by Ardonceau (1994) for a crescent wing
aspect ratio of 5, i.e. equivalent to a backward-facing pointed
fin of aspect ratio 2.5.

ACKNOWLEDGEMENTS
This work was supported by a Kuehler grant from Santa
Clara University. We thank Jason Chong from theEngineering Computing Center and Anne Mahacek of theMaker Lab for assistance.
REFERENCES
Ardonceau, P. L. “Aerodynamic Properties of Crescent
Wing Planforms,” J. Aircraft, 31(2), 462-465, 1994.
Fish, F. E., and Lauder, G. V. “Passive and active flow
control by swimming fishes and mammals.” Ann. Rev. Fluid
Mech., 38, 193–224, 2006.
Fish, F. E., Weber, P. W., Murray, M. M., and Howle, L.
E. “The Tubercles on Humpback Whales' Flippers:
Application of Bio-Inspired Technology,” Integrative andComparative Biology, 51 (1), 203-213, 2011.
Guo, Q., Wang, Z., and Wang, J., “Effects of Flexible
Wing on the Aerodynamic Performance of Aircraft”, 13th
International Symposium on Particle Image Velocimetry –ISPIV 2019, Munich, Germany, July 22-24, 2019.
Lee, G. H., “The Aerodynamic and Aeroelastic
Characteristics of the Crescent Wing,” The Aeronautical
Journal , Volume 59 , Issue 529 , pp. 37 – 44, January 1955.
Lu, F. K., “Surface Oil Flow Visualization – Still Useful
After All These Years,” Eur. Phys. J. Special Topics 182,
51–63, 2010.
NASA Armstrong Fact Sheet: X-29 Advanced
Technology Demonstrator Aircraft https://www.nasa.gov/
centers/armstrong/news/FactSheets/FS-008-DFRC.html
Schober, U.M., and Ditrich, H., “Anatomy and Use of
the Caudal Spine in the Aggressive Behavior of a
Surgeonfish (Osteichthyes: Acanthuridae),” Marine andFreshwater Behavior and Psychology, 21 (4), 277-284, 1992.
Van Dam, C. P. “Induced-Drag Characteristics ofCrescent-Moon-Shaped Wings,” J. Aircraft, 24 (2), 115-119,
1987.
Van Dam, C. P,, Vijgen, P. M. H. W., and Holmes, B. J.
“Experimental Investigation on the Effect of Crescent
Planform on Lift and Drag,” J. Aircraft, 28 (11), 713-720,
1991.
Winterbottom, R., “Movement of the Caudal Spine ofSome Surgeonfishes (Acanthuridae, Perciformes).” Copeia,
Vol. 1971, No. 3, pp. 562-566, 1971.

CONCLUSIONSIn this study numerical simulations, supported by windtunnel experiments show that backward facing fins show aclassical stall behaviour that is sudden and occurs at a highangle of attack. This behaviour is consistent withexperimental results for earlier crescent shaped wings.
Straight fins reveal a two-time stall behaviour previously
reported by others. The new forward-facing fins reveal agentle rolling stall behaviour, to higher angles of attack, withno sudden drops. The numerical simulations suggest thatthese behaviours are a result of a trapped spanwise stall
bubble which forms on the suction side of the fin: suddenlyin the backward-facing fin case, but growing slowly outward
in the forward-facing fin case. Simulation of a more
aerodynamic fin accentuated these differences in behaviour.
In addition, simulations of two inline fins of various
separations suggest that forward-facing fins are quite
insensitive to separation distances and are thus robust in
behaviour, suggesting no performance penalty, while
backward-facing fins show a strong dependence on
separation distance. Finally, experimental surface flow
visualization (alcohol/chalk), and not the pressure field, wasseen to be instrumental in the choice of the k-omega

Figure 2. Left: Planform sections of pointed and rounded fins and sketch of the airfoil shape from the side for forward and backward
swept fins. Right: Pointed and rounded straight fin showing planform and side airfoil shape3

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022

Figure 3. Lift coefficients of fins at different angles of attack. Left – rounded fins, Right - pointed fins. Symbols: blue diamond –backward fin, red square – forward fin, green triangle – straight fin.

Figure 4. Drag coefficients of fins at different angles of attack. Left – rounded fins, Right - pointed fins. Symbols: blue diamond –backward fin, red square – forward fin, green triangle – straight fin.

Figure 5. Axial velocity (left) and streamwise vorticity (right) of backward-facing pointed fin at 30 degrees angle of attack.

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022

Figure 6. Axial velocity (left) and streamwise vorticity (right) of forward-facing pointed fin at 30 degrees angle of attack.

Figure 7. Long streaklines from surfaces of backward-facing pointed fin (left) and forward-facing pointed fin (right) at 10 degrees
angle of attack. Flow is right to left.

Figure 8. Long streaklines from surfaces of backward-facing pointed fin (left) and forward-facing pointed fin (right) at 30 degrees
angle of attack. Flow is right to left.

Figure 9. Lift-drag polars for inline pointed fins at various separations. Left: backward-facing. Right: forward-facing.

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022

Figure 10. Lift and Drag Coefficients of forward-facing pointed fin with experimental measurements (green, purple points).

Figure 11. Comparison of suction surface flow patterns, forward-facing pointed fin at 30 degree angle of attack. Flow is right to left.
Left pair: Experimental surface flow measurements. Right pair: k-omega surface flow predictions. Orange separation lines aretransferred from experiments to flow predictions.

Figure 12. Comparison of short surface streaklines for four turbulence models at 30 degree angle of attack. Left to right: k-omega, kepsilon, Reynolds Stress Model, Spalart-Allmaras.

Figure 13. Surface pressure for pointed fins at 30 degree angle of attack. Left pair: backward-facing fin, suction (left) and pressure(right) surfaces shown. Right pair: forward facing fin, suction (left) and pressure (right) surfaces shown.

Figure 14. Comparison of more aerodynamic fin (red squares, red inset image) with previous less aerodynamic fin (blue diamonds,
blue inset image). Left: Backward-facing pointed fin. Right: Forward-facing pointed fin

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