Shock Waves (2002) 12: 177 180
Digital Object Identifier (DOI) 10.1007/s00193-002-0159-9
Cavity effects on transonic convex-corner flows
K. Chung
Aerospace Science and Technology Research Center, National Cheng Kung University, Kueijen, Tainan, Taiwan, 711, R.O.C
Received 14 January 2002 / Accepted 7 June 2002 /
Published online 1 October 2002  © Springer-Verlag 2002
Abstract. An experimental study was conducted to investigate the transonic convex-corner flows, with and
without the presence of an upstream cavity. Measurements were made for the effect of cavity type, including
transitional and closed-type cavities, on the mild and extensively separated turbulent boundary layer. The
effect of spacing distance between the trailing edge of the cavity and the corner was also studied. It is found
that the downstream convex-corner flow is affected by the presence of an upstream cavity, particularly near
the corner. The closed-type cavity with smaller spacing distance results in upstream movement of the shock
wave and higher level of surface pressure fluctuations.
Key words: Transonic flow, Cavity, Convex corner
PACS: 47.40.Hg, 47.40.Nm, 47.27.Nz
List of symbols
Cp wall pressure coefficient (pw - p")/q"
CÃp pressure fluctuation coefficient (Ãp - Ãp")/q"
D, L, W cavity depth, length and width
M Mach number
X lengthwise distance
X" x/´
Fig. 1. Test configuration
Z distance between the cavity trailing edge and
the corner
allowable deflection of control surfaces. In the work of
Z" z/´
Chung (2000), a simplified model of a deflected control
´ upstream undisturbed boundary layer thickness
surface was studied. When a turbulent boundary layer
· convex-corner angle
flows over a convex corner, the typical subsonic type ex-
Ãp surface pressure fluctuation
pansion flows are in the form of upstream expansion and
2
downstream recompression. When M"· is greater than
6.14, the flow expands to supersonic downstream of the
corner and switches to the transonic type expansion flow.
1 Introduction
Stronger upstream expansion and mild initial recompres-
2
sion are observed. When M"· (e" 8.95) further increases,
Aircraft design has employed flaps for takeoff and landing
the boundary layer is separated downstream of the corner.
performance and ailerons for routine turning maneuver.
A slower recovery process is associated with the separated
With developing technology in transonic aerodynamics,
boundary layer (Chung, 2001b).
previous studies indicated that active modification of the
Cutouts, steps, gaps or grooves upstream of a deflected
control surfaces could potentially play a role in perfor-
control surface have an important effect on the unsteadi-
mance optimization for an aircraft (Bolonki and Gilyard,
ness of the flow field and its aerodynamic characteristics.
1999). Deflected control surfaces can be used in combi-
The study of Chung (1999) indicated that the presence of
nation to provide variable camber control during cruise
a cavity in transonic flow results in a stronger expansion
flight. However, the study of Szodruch and Hilbig (1988)
near the cavity trailing edge, which induces a large vor-
indi cated that the critical Mach number, onset of bound-
tical structure propagating downstream (Zhang, 1995). It
ary layer separation, and drag are strongly related to the
is considered that the cavity can be used for the passive
control of separated convex-corner flow, which includes
An abridged version of this paper was presented at the 23rd
the cavity effect on the upstream expansion, the down-
Int. Symposium on Shock Waves at Fort Worth, Texas, from
July 22 to 27, 2001. stream recompression, and the recovery process. The test
178 K. Chung: Cavity effects on transonic convex-corner flows
configuration used in the present study is shown in Fig. 1.
The cavity is located at about one to three boundary layer
thicknesses (Z") upstream of the convex corner. The ef-
fects of geometric parameters and spacing on the mean
and fluctuating pressures downstream of the corner are
investigated.
2 Experiment
2.1 Facility and instrumentation
The ASTRC/NCKU transonic wind tunnel is a blowdown
type. It operates at Mach 0.2 to 1.4, and at Reynolds num-
bers up to 20 million per meter. The test section is assem-
bled with solid sidewalls and perforated top/bottom walls
to reduce the amplitude of background acoustic waves.
For the surface pressure measurements, Kulite pressure
transducers (Model XCS-093-25A, B screen) are used. The
natural frequency is 200 kHz as quoted by the manufac-
turer. The typical sampling period in the present study is
5 µs (200 kHz). Each data record possesses 131 072 data
points for statistical analysis. The uncertainty of experi-
mental data is estimated to be 0.43 and 0.13 percent for
the static pressure coefficient and surface pressure fluctu-
ation coefficient, respectively.
2.2 Test models and test conditions
The test model consists of a flat plate, an interchange-
able plate with cavity and an instrumentation plate. The
boundary layer is developed naturally along the flat plate,
and the trailing edge of the cavity is located at about one
to three boundary layer thicknesses upstream of the con-
vex corner. The length-to-depth ratio (L/D) of the cav-
ities is 7.0, 14.0, and 21.0, and the length-to-width ra-
tio (L/W ) is 0.35. This corresponds to the transitional
Fig. 2. Surface pressure distributions, · =13ć%
(L/D = 7.0) and closed-type cavities (L/D = 14.0 and
21.0) (Chung, 2001a). Three instrumentation plates, with
13ć%, 15ć%, and 17ć% convex-corner angle, were fabricated.
to the initial separation of the convex-corner flow (Chung,
One row of 10 holes was installed along the centerline of
2001b). When a transitional-type cavity (L/D = 7.0) is
each instrumentation plate. All the pressure transducers
located upstream of the corner, the wall pressure distribu-
within the holes were flush-mounted to the test surface
tions show stronger expansion downstream of the corner.
and potted using silicone rubber sealant.
This effect is more significant when the cavity is closer
For the experiment, the test Mach number (M") is
to the corner (decreasing Z"). Further downstream, the
0.83Ä…0.01. The stagnation pressure (po) and temperature
flow is recompressed and returns to the subsonic condi-
(To) are 172Ä…0.5 kPa and room temperature, respectively.
tion. However, the kink of wall pressure distributions is
In addition, undisturbed boundary layer surveys are con-
not visible. This implies that the upstream cavity may
ducted at xle = 475 mm (or 25 mm upstream of the con-
delay the boundary layer separation. It is also observed
vex corner). Normalized velocity profiles appear to be full
that the presence of the cavity results in lower wall pres-
(n H" 11 for the velocity power law). This indicates tur-
sure toward the end of the measurement locations. The
bulent flow at the measurement locations. The boundary
closed-type cavities (L/D =14.0 and 21.0) show a similar
layer thickness is 6.9 Ä… 0.2 mm.
effect on the recompression process. Therefore, the effect
of cavity type appears to be not significant for the case of
initially separated convex-corner flow.
3 Results and discussions
Figure 2b shows the distributions of surface pressure
fluctuation. They follow a similar trend with and without
3.1 Surface pressure distributions
an upstream cavity. However, it appears that the values
The distributions of wall pressure coefficients Cp at · = of surface pressure fluctuation with an upstream cavity
2
13ć% (M"· =8.95) are shown in Fig. 2a, which corresponds are slightly lower near the corner. This is considered to be
K. Chung: Cavity effects on transonic convex-corner flows 179
Fig. 4. Cavity effect
induce higher levels of downstream surface pressure fluc-
tuations.
Fig. 3. Surface pressure distributions, · =17ć%
3.2 Cavity effect
due to the stronger expansion or the delay of boundary The minimum wall pressure downstream of the corner
layer separation as mentioned above. Further downstream is related to the boundary layer development near the
(X" > 3), higher levels of surface pressure fluctuations are corner. A lower Cp,min represents a higher peak Mach
observed. number, which is associated with the upstream expan-
2
At · = 17ć% (M"· = 11.71), this corresponds to the sion, downstream initial recompression, and the shock-
case of extensively separated boundary layer. The flow re- induced separation region. Without the upstream cavity,
mains supersonic within the measurement locations. Fig- the amplitude of Cp,min decrease with the convex-corner
ure 3a shows that the transitional-type cavity (Z" = 2 and angle, Fig. 4a. A higher peak Mach number is related
3) has a minor effect on the wall pressure distributions. For to stronger shock strength and longer separation length.
closed-type cavities, the cavity effect is not significant at With a transitional-type cavity, the variation of Cp,min val-
Z" = 2. When the cavity is closer to the corner (Z" = 1), ues follows a similar trend. However, stronger expansion
the wall pressures immediately downstream of the corner is observed at lower convex-corner angles (· = 13ć% and
increase up to 30 percent of the dynamic pressure. This 15ć%). A similar phenomenon is also observed for the cases
is thought to be due to the upstream movement of the with closed-type cavities. But at · =17ć%, it is found that
shock wave. For the cavity effect on the surface pressure presence of the upstream cavities increases the Cp,min val-
fluctuations (Fig. 3b), the amplification of the peak sur- ues, particularly for the closed-type cavity. This indicates
face pressure fluctuations near the corner can be seen for the upstream movement of the shock wave. For the effect
all the test cases. For transitional-type cavities, the down- of spacing, the Cp,min values with a transitional-type cav-
stream surface pressure fluctuations are roughly the same, ity are roughly the same at Z" = 2 and 3, and decrease
with and without the cavity. However, closed-type cavities when the cavity is closer to the corner (Z" = 1). It is also
180 K. Chung: Cavity effects on transonic convex-corner flows
seen that the closed-type cavities at Z" =1 and 2 have a References
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TM-1999-206586
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With an upstream cavity, Fig. 4b, the peak pressure fluc-
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mentioned above, this may correspond to the stronger ex-
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separation. At · = 15ć%, it appears that the presence of
33:1404 1411
a transitional-type cavity (L/D =7.0) has a minor influ-
ence on the level of peak pressure fluctuation. However,
the closed-type cavities (L/D = 14.0 and 21.0) enhance
the flow unsteadiness, or the shock wave excursion phe-
nomena. At · =17ć%, it can be seen that the cavities tend
to increase the values of peak pressure fluctuation for all
the test cases. Further, it is noted that the relative loca-
tion of a given cavity with respect to the corner has a
minor effect on the peak pressure fluctuation.
4 Conclusions
The results show that the transitional or closed-type cav-
ities induce stronger expansion and lower surface pres-
sure fluctuations near the convex corner at mild sepa-
rated boundary layer (· =13ć%). This suggests the delay of
boundary layer separation. Lower wall pressure and higher
surface pressure fluctuations at downstream locations are
also observed. In addition, the cavity type shows a minor
effect on the downstream flows. At · =17ć% (extensively
separated flows), the cavity effect is limited near the con-
vex corner. The presence of the closed-type cavities results
in upstream movement of the shock waves, and the excur-
sion of the shock wave increases the amplitude of surface
pressure fluctuations. This effect is more significant when
the cavity is closer to the corner. For other test cases, the
spacing effect on the distributions of mean and fluctuating
pressures is minimized.