Figure1: Schematic representation of 2-D separation
(top)
showing
that
the
vorticity
vector
is
perpendicular to the free stream velocity. In the
bottom frame we show the same case in Frame (a)
and the more general case of three-dimensional flow
in Frame (b)
Figure 2:Vortex shedding patterns over long
cylinders at different angles of incidence
(Ramberg [4])
Figure 3: Schematic of the separation over a delta
Figure 4a: Schematic of vortex sheets feeding in
wing. The line of separation is inclined with respect
from 2-D separation
to the delta wing.
Figure 4b: Schematic of vortex sheets feeding in
from 3-D separation
19
Figure 5: Frozen wake patterns along a cut of the
wake of a slender body at incidence (Lamont [11[)
Figure 6: Hot-wire traces in the wake of a yawed
cylinder (Poll [14])
Figure 7: Vortex shedding frequencies of a finite
Figure 8: Frequencies detected along the span of
length cylinder at different axial stations from the
finite cylinders with different end-shapes
free end., (Ayoub and Karamcheti [17])
(Hoang & Telionis [19])
20
Figure 9: Vortex Shedding over an inclined long cylinder (Ramberg [4])
21
Figure 10: Normalized Strouhal numbers for a
variety of free-ended inclined cylinders
(Ramberg [4]).
Figure 12: Stationary separating vortices and
shedding vortices over forebodies with different
aspect ratios. (Montividas er al. [28])
Figure 11: Schematic of the three wake regimes
identified by Tobak et al. [[24])
Parallel shedding (2)Oblique shedding
(3) Stationary vortices
22
Figure 13: Topology of streamline patterns of steady
wakes over an inclined forebody shape (Lowson &
Ponton [12])
Figure 15:Time averaged yaw forces as a function of
model roll angle [34].
Figure 14:Side force history with and without a nose
disturbance (Degani [31])
23
Figure
16:
Yaw
force
coefficient
with
the
introduction of a small disturbance using a wire of
finite length (Zilliac et al. [34])
24
Figure 17:Pressure Spectra obtained along the length of the body for four angles of attack (Degani and Zilliac
[27])
Figure 19: Approximate locations of separation of
Figure 18. Side force coefficient from Hall [41].
vortices at different angles of attack. Data obtained
from results of Fig. 18.
25
Figure 21: Surface-pressure power spectra (a) with
splitter (b) without splitter plate. Re=26,00 a=60 o .
(Degani [31])
Figure 20: Pressure Spectra showing peaks caused
by shear layer instabilities (Degani and Zilliac [27])
Figure 22:
splitter-plate
Helicity density contour planes for a
configuration
Re=26,000
a=40o.
(Degani [31])
Figure 23: Schematic of vortex interaction at a=5060 degrees (Degani and Zilliac[31])
26
Figure 24a: Time = 1 sec
Figure 24b: Time = 2 sec
27
Figure 24c: Time = 4 sec
Figure 24d: Time = 6 sec
Figure 24: Velocity vectors in the wake of an ogive cylinder (Zeiger et al. [43]). The interrogation plane is
normal to the free stream. AOA=39.6 o. Axial position x/D=4.5. Re=4000. Four different times demonstrating
the vortex interaction of vortices 1 and 2(further from the body).
28
Figure 25:Frequncy response of separating vortices
providing evidence of vortex heaving
(Hoang and Telionis [19])
Figure 27:Transient pressure difference for a=50 o
(Lamont and Hunt [11])
Figure 28:Evidence of vortex flipping as detected by
Lamont and Hunt [11])
Figure 26: Power spectra M=0.6, a=45o φ=0o
x/D=7.38, y/D=0.2 (Calarese [44])
29
Figure 31: Coordinate axes on a forebody model
(Montevidas et al. [28])
Figure 29: Variations of pressure fludctuations as a
function of the macimum pressure coefficient.
(Wardlaw and Yanta [46])
Figure 30:Cp (open symbols) and σCp (solid symbols) as a function of Cy (Wardlaw and Yanta [46])
30
Figure 32a:Variation of wake pattern with angle of
Figure 32b: Variation of wake pattern with angle of
attack for fixed negative sweep rate [28].
attack for fixed positive sweep rate [28].
31
Figure 33b
Figure 33a
Figure 33: Cross-section of the vortices cut by a plane normal to the stream of a pitching ogive cylinder at
Re=4x103 Figure (a) upstroke. Figure (b) downstroke. (Gad-el-Hak and Ho [54])
32
Figure 34:Evolution of streamwise vorticity contours on an ogive body at the cross plane x/D=8.51 for a sharp
pitch up. Solid and dashed lines represent positive and negative vorticity respectively. (Stanek and Visbal
[13]).
33
Figure 35:Coordinate system and Measurement
Figure
Plane Orientation for Pitch axis location L=4D
36:
Asymmetry
arrival
times
Figure 37: Evolution of 3-D velocity field over an ogive cylinder undergoing a pitching motion [55].
34
[55].
Figure 38:Variation of side force coefficient w/roll-angle for a round cross-section, Re=102,800
(Iwanski and Nelson [58])
Figure 39:Round foreboby dynamic data: Pitch rate=0.5Hz,0-90 deg AOA, Re=76,300 (Iwanski and
Nelson [58])
Figure 40:Normal force coefficients for various pitch rates (Iwanski and Nelson [58])
35
Figure 41: Coning characteristics of a cone cylinder with pointed nose (top) and truncated nose
(bottom) (Smith and Nunn [59])
Figure 42: Comparison of steady and unsteady separation lines at =20.2°. P indicates primary
separation and S indicates secondary separation. Dashed lines are equivalent steady separation lines
and solid lines are separation lines from ensemble-average unsteady data (Wetzel and Simpson [64]).
36