A sparsity promoting dynamic mode decomposition (DMD) combined with a classical data-based statistical analysis is applied to the turbulent wake of a generic axisymmetric configuration of an Ariane 5-like launcher at Ma = 6.0 computed via a zonal Reynolds-averaged Navier-Stokes/large-eddy simulation (RANS/LES) method. The objective of this work is to gain a better understanding of the wake flow dynamics of the generic launcher by clarification and visualization of initially unknown pressure perturbation sources on its after-body in coherent flow patterns. The investigated wake topology is characterized by a subsonic cavity region around the cylindrical nozzle extension which is formed due to the displacement effect of the afterexpanding jet plume emanating from the rocket nozzle (Mae = 2.52, pe/p = 100) and the shear layer shedding from the main body. The cavity region contains two toroidal counter-rotating large-scale vortices which extensively interact with the turbulent shear layer, jet plume, and rocket walls, leading to the shear layer instability process to be amplified. The induced velocity fluctuations in the wake and the ultimately resulting pressure perturbations on the after-body feature three global characteristic frequency ranges, depending on the streamwise position inside the cavity. The most dominant peaks are detected at SrDr3 = 0.85 ± 0.075 near the nozzle exit, while the lower frequency peaks, in the range of SrDr2 = 0.55 ± 0.05 and SrDr1 = 0.25 ± 0.05, are found to be dominant closer to the rocket’s base. A sparse promoting DMD algorithm is applied to the time-resolved velocity field to clarify the origin of the detected peaks. This analysis extracts three low-frequency spatial modes at SrD = 0.27,  0.56,  and  0.85. From the three-dimensional shape of the DMD modes and the reconstructed modulation of the mean flow in time, it is deduced that the detected most dominant peaks of SrDr3 ≈ 0.85 are caused by the radial flapping motion of the shear layer, while the middle-frequency range of SrDr2 ≈ 0.55 is found to be associated with its swinging motion. The less intensive peaks of SrDr1 ≈ 0.25 pronounced on the base wall are caused by the low-frequency longitudinal pumping of the two toroidal large-scale vortices inside the cavity.

1.
D.
Deprés
,
P.
Reijasse
, and
J.
Dussauge
, “
Analysis of unsteadiness in afterbody transonic flows
,”
AIAA J.
42
,
2541
2550
(
2004
).
2.
P.
Meliga
and
P.
Reijasse
, “Unsteady transonic flow behind an axisymmetric afterbody equipped with two boosters,” AIAA Paper 2007-4564, 2007.
3.
S.
Deck
and
P.
Thorigny
, “
Unsteadiness of an axisymmetric separating-reattaching flow: Numerical investigation
,”
Phys. Fluids
19
,
065103
(
2007
).
4.
E.
Brewer
and
C.
Craven
, “Experimental investigation of base flow field at high altitude for a four-engine clustered nozzle configuration,” NASA TN D-5164, 1969.
5.
J.
Janssen
and
J.
Dutton
, “
Time-series analysis of supersonic base-pressure fluctuations
,” in
33rd AIAA Fluid Dynamics Conference and Exhibit
[
AIAA J.
42
,
605
613
(
2004
)].
6.
W.
Bannink
,
E.
Houtman
, and
P.
Bakker
, “Base flow/Underexpanded exhaust plume interaction in a supersonic external flow,” AIAA Paper 98-1598, 1998.
7.
F.
Scarano
,
B. W.
van Oudheusden
,
W. J.
Bannink
, and
M.
Bsibsi
, “
Experimental investigation of supersonic base flow plume interaction by means of particle image velocimetry
,” in
Proceedings of the Fifth European Symposium on Aerothermodynamics for Space Vehicles (ESA SP-563)
(
ESA Publications Division
,
2005
), pp.
601
607
.
8.
R.
Benay
and
P.
Servel
, “
Two-equation k-σ turbulence model: Application to a supersonic base flow
,”
AIAA J.
39
,
407
416
(
2001
).
9.
J.
Papp
and
K.
Ghia
, “Application of the RNG turbulence model to the simulation of axisymmetric supersonic separated base flows.” AIAA Paper 2001-027, 2001.
10.
J.
Forsythe
,
K.
Hoffmann
,
R.
Cummings
, and
K.
Squires
, “
Detached-eddy simulation with compressibility corrections applied to a supersonic axisymmetric base flow
,”
J. Fluid Eng.
124
,
911
923
(
2002
).
11.
S.
Kawai
and
K.
Fujii
, “Computational study of a supersonic base flow using LES/RANS hybrid methodology,” AIAA Paper 2004-68, 2004.
12.
C.
Fureby
, “Large eddy simulation of supersonic baseflow,” AIAA Paper 99-0426, 1999.
13.
R.
Sandberg
and
H.
Fasel
, “
High-accuracy DNS of supersonic base flows and control of the near wake
,” in
Proceedings of the Users Group Conference
(
IEEE Computer Society
,
2004
), pp.
96
104
.
14.
R.
Sandberg
and
H.
Fasel
, “
Numerical investigation of transitional supersonic axisymmetric wakes
,”
J. Fluid Mech.
563
,
1
41
(
2006
).
15.
R.
Sandberg
, “
Numerical investigation of turbulent supersonic axisymmetric wakes
,”
J. Fluid Mech.
702
,
488
520
(
2012
).
16.
V.
Statnikov
,
J.-H.
Meiß
,
M.
Meinke
, and
W.
Schröder
, “
Investigation of the turbulent wake flow of generic launcher configurations via a zonal RANS/LES method
,”
CEAS Space J.
5
,
75
86
(
2013
).
17.
D.
Saile
,
A.
Gülhan
, and
A.
Henckels
, “Investigations on the near-wake region of a generic space launcher geometry,” AIAA Paper 2011-2352, 2011.
18.
M.
Bitter
,
T.
Hara
,
R.
Hain
,
D.
Yorita
,
K.
Asai
, and
C. J.
Kähler
, “
Characterization of pressure dynamics in an axisymmetric separating/reattaching flow using fast-responding pressure-sensitive paint
,”
Exp. Fluids
53
,
1737
1749
(
2012
).
19.
D.
Saile
and
A.
Gülhan
, “Plume-induced effects on the near-wake region of a generic space launcher geometry,” AIAA Paper 2014-3137, 2014.
20.
S.
Marié
,
Ph.
Druault
,
H.
Lambaré
, and
F.
Schrijer
, “
Experimental analysis of the pressure–velocity correlations of external unsteady flow over rocket launchers
,”
Aerosp. Sci. Technol.
30
,
83
93
(
2013
).
21.
P. J.
Schmid
, “
Dynamic mode decomposition of numerical and experimental data
,”
J. Fluid Mech.
656
,
5
28
(
2010
).
22.
Y.
Mizuno
,
D.
Duke
,
C.
Atkinson
, and
J.
Soria
, “
Investigation of wall-bounded turbulent flow using dynamic mode decomposition
,”
J. Phys.: Conf. Ser.
318
,
042040
(
2011
).
23.
M. R.
Jovanović
,
P. J.
Schmid
, and
J. W.
Nichols
, “
Sparsity-promoting dynamic mode decomposition
,”
Phys. Fluids
26
,
024103
024125
(
2014
).
24.
M.
Sippel
and
A.
Herbertz
, “
System requirements on investigation of base flow/plume interaction
,” in
NNFM: RESPACE-Key Technologies for Reusable Space Systems
(
Springer
,
2003-2007
), Vol.
98
, pp.
3
19
.
25.
B.
Roidl
,
M.
Meinke
, and
W.
Schröder
, “
Reformulated synthetic turbulence generation method for a zonal RANS-LES method and its application to zero-pressure gradient boundary layers
,”
Int. J. Heat Fluid Flow
44
,
28
40
(
2013
).
26.
B.
Roidl
,
M.
Meinke
, and
W.
Schröder
, “
Boundary layers affected by different pressure gradients investigated computationally by a zonal RANS-LES method
,”
Int. J. Heat Fluid Flow
45
,
1
13
(
2014
).
27.
M.-S.
Liou
and
C. J.
Steffen
, “
A new flux splitting scheme
,”
J. Comput. Phys.
107
,
23
39
(
1993
).
28.
J.
Boris
,
F.
Grinstein
,
E.
Oran
, and
R.
Kolbe
, “
New insights into large eddy simulation
,”
Fluid Dyn. Res.
10
,
199
228
(
1992
).
29.
M.
Meinke
,
W.
Schröder
,
E.
Krause
, and
T.
Rister
, “
A comparison of second- and sixth-order methods for large-eddy simulations
,”
Comput. Fluids
31
,
695
718
(
2002
).
30.
N.
Alkishriwi
,
M.
Meinke
, and
W.
Schröder
, “
A large-eddy simulation method for low Mach number flows using preconditioning and multigrid
,”
Comput. Fluids
35
,
1126
1136
(
2006
).
31.
W.
El-Askary
,
W.
Schröder
, and
M.
Meinke
, “LES of compressible wall-bounded flows,” AIAA Paper 2003-3554, 2003.
32.
E.
Fares
and
W.
Schröder
, “
A general one-equation turbulence model for free shear and wall-bounded flows
,”
Flow, Turbul. Combust.
73
,
187
215
(
2004
).
33.
N.
Jarrin
,
N.
Benhamadouche
,
S.
Laurence
, and
D.
Prosser
, “
A synthetic-eddy-method for generating inflow conditions for large-eddy simulations
,”
Int. J. Heat Fluid Flow
27
,
585
593
(
2006
).
34.
M.
Pamiès
,
P.
Weiss
,
E.
Garnier
,
S.
Deck
, and
P.
Sagaut
, “
Generation of synthetic turbulent inflow data for large eddy simulation of spatially evolving wall-bounded flows
,”
Phys. Fluids
21
,
045103
(
2009
).
35.
C. W.
Rowley
,
T.
Colonius
, and
A. J.
Basu
, “
On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities
,”
J. Fluid Mech.
455
,
315
346
(
2002
).
36.
L.
Larchevêque
,
P.
Sagaut
,
T.-H.
, and
P.
Comte
, “
Large-eddy simulation of a compressible flow in a three-dimensional open cavity at high Reynolds number
,”
J. Fluid Mech.
516
,
265
301
(
2004
).
37.
G. L.
Brown
and
A.
Roshko
, “
On density effects and large structure in turbulent mixing layers
,”
J. Fluid Mech.
64
,
775
816
(
1974
).
38.
D.
Papamoschou
and
A.
Roshko
, “
The compressible turbulent shear layer: An experimental study
,”
J. Fluid Mech.
197
,
453
477
(
1988
).
39.
D.
Saile
,
A.
Gülhan
,
A.
Henckels
,
C.
Glatzer
,
V.
Statnikov
, and
M.
Meinke
, “
Investigations on the turbulent wake of a generic space launcher geometry in the hypersonic flow regime
,”
EUCASS Prog. Flight Phys.
5
,
209
234
(
2013
).
40.
A.
Sevilla
and
C.
Martínez-Bazán
, “
Vortex shedding in high Reynolds number axisymmetric bluff-body wakes: Local linear instability and global bleed control
,”
Phys. Fluids
16
,
3460
3469
(
2004
).
You do not currently have access to this content.