Two-dimensional large eddy simulation of a flow experiment intended for studying and understanding transition and parietal vortex shedding has brought to light some interesting features that have never been seen in previous similar simulations and have implications for future computational work on combustion instabilities in rocket motors. The frequency spectrum of pressure at head end shows a peak at the expected value associated with parietal vortex shedding but an additional peak at half this frequency emerges at downstream location. Using vorticity spectra at various distances away from the wall, it is shown that the frequency halving is due to vortex pairing as hypothesized by Dunlap et al. [“Internal flow field studies in a simulated cylindrical port rocket chamber,” J. Propul. Power 6(6), 690–704 (1990)] for a similar experiment. As the flow transitions to turbulence towards the nozzle end, inertial range with Kolmogorov scaling becomes evident in the velocity spectrum. Given that the simulation is two-dimensional, such a scaling could be associated with a reverse energy cascade as per Kraichnan-Leith-Bachelor theory. By filtering the simulated flow field and identifying where the energy backscatters into the filtered scales, the regions with a reverse cascade are identified. The implications of this finding on combustion modeling are discussed.
REFERENCES
1.
R.
Dunlap
, A. M.
Blackner
, R. C.
Waugh
, J. R. S.
Brown
, and P. G.
Willoughby
, “Internal flow field studies in a simulated cylindrical port rocket chamber
,” J. Propul. Power
6
(6
), 690
–704
(1990
).2.
B.
Gazanion
, F.
Chedevergne
, X.
de Saint-Victor
, J.-L.
Estivalezes
, and G.
Casalis
, “Laminar-turbulent transition investigation in a solid rocket motor representative cold flow setup
,” AIAA Paper 2013-3918, 2013
.3.
K. O.
Sabdenov
, “On the threshold nature of erosive burning
,” Combust. Explosion Shock Waves
44
(3
), 300
–309
(2008
).4.
F.
Blomshield
, H.
Mathes
, J.
Crump
, C.
Beiter
, and M.
Beckstead
, “Nonlinear stability testing of full-scale tactical motors
,” J. Propul. Power
13
(3
), 356
–366
(1997
).5.
R.
Glick
, M.
Micci
, and L.
Caveny
, “Transition to nonlinear instability in solid propellant rocket motors
,” AIAA Paper No. 81-1520, 1981
.6.
W.
Brownlee
, “Nonlinear axial combustion instability in solid propellant motors
,” AIAA J.
2
(2
), 275
–284
(1964
).7.
R. H.
Kraichnan
, “Inertial ranges in two-dimensional turbulence
,” Phys. Fluids
10
, 1417
–1423
(1967
).8.
N.
Lupoglazoff
and F.
Vuillot
, “Parietal vortex shedding as a cause of instability for long solid propellant motors–Numerical simulations and comparison with firing tests
,” AIAA Paper No. 96-0761, 1996
.9.
Y.
Fabignon
, J.
Dupays
, G.
Avalon
, F.
Vuillot
, N.
Lupoglazoff
, G.
Casalis
, and M.
Prevost
, “Instabilities and pressure oscillations in solid rocket motors
,” Aerosp. Sci. Technol.
7
(3
), 191
–200
(2003
).10.
F.
Chedevergne
, G.
Casalis
, and J.
Majdalani
, “Direct numerical simulation and biglobal stability investigations of the gaseous motion in solid rocket motors
,” J. Fluid Mech.
706
, 190
–218
(2012
).11.
G.
Boyer
, G.
Casalis
, and J. L.
Estivalezes
, “Stability analysis and numerical simulation of simplified solid rocket motors
,” Phys. Fluids
25
, 084109
(2013
).12.
A.
Kourta
, “Instability of channel flow with fluid injection and parietal vortex shedding
,” Comput. Fluids
33
, 155
–178
(2004
).13.
P.
Hughes
and A.
Saber
, “Nonlinear combustion instability in a solid propellant two-dimensional window motor
,” AIAA Paper No. 78-1008, 1978
.14.
E.
Shima
and K.
Kitamura
, “On new simple low-dissipation scheme of AUSM-family for all speeds
,” AIAA Paper 2009-136, 2009
.15.
K.
Kitamura
and E.
Shima
, “Improvements of simple low-dissipation AUSM against shock instabilities in consideration of interfacial speed of sound
,” in 5th European Conference on Computational Fluid Dynamics, ECCOMAS CFD
, Lisbon, Portugal
, 2010
.16.
V. K.
Chakravarthy
and D.
Chakraborty
, “Modified SLAU2 scheme with enhanced shock stability
,” Comput. Fluids
100
, 176
–184
(2014
).17.
V. K.
Chakravarthy
, K.
Arora
, and D.
Chakraborty
, “A simple hybrid finite volume solver for compressible turbulence
,” Int. J. Numer. Methods Fluids
77
(12
), 707
–731
(2015
).18.
J.
Smagorinsky
, “General circulation experiments with the primitive equations
,” Mon. Weather Rev.
91
, 99
–110
(1963
).19.
J. C.
Traineau
, P.
Hervat
, and P.
Kuentzmann
, “Cold-flow simulation of a two-dimensional nozzleless solid-rocket motor
,” AIAA Paper No. 86-1447, 1986
.20.
S.
Apte
and V.
Yang
, “Unsteady flow evolution is porous chamber with surface mass injection. Part I: Free oscillations
,” AIAA J.
39
(8
), 1577
–1586
(2001
).21.
S. V.
Apte
and V.
Yang
, “A large-eddy simulation study of transition and flow instability in a porous-walled chamber with mass injection
,” J. Fluid Mech.
477
, 215
–225
(2003
).22.
B.
Wasistho
, S.
Balachandar
, and R.
Moser
, “Compressible wall-injection flows in laminar, transitional, and turbulent regimes: Numerical prediction
,” J. Spacecr. Rockets
41
(6
), 915
–924
(2004
).23.
B.
Wasistho
and R.
Moser
, “Simulation strategy of turbulent internal flow in solid rocket motor
,” J. Propul. Power
21
(2
), 251
–263
(2005
).24.
M.
Germano
, U.
Piomelli
, P.
Moin
, and W. H.
Cabot
, “A dynamic subgrid-scale eddy viscosity model
,” Phys. Fluids A
3
(7
), 1760
–1765
(1991
).25.
C. E.
Leith
, “Diffusion approximation for two-dimensional turbulence
,” Phys. Fluids
11
, 671
–673
(1968
).26.
G. K.
Batchelor
, “Computation of the energy spectrum in homogeneous two-dimensional turbulence
,” Phys. Fluids
12
, 233
–239
(1969
).27.
E.
Gkioulekas
and K.
Tung
, “Recent developments in understanding two-dimensional turbulence and the Nastrom-Gage spectrum
,” J. Low Temp. Phys.
145
, 25
–57
(2006
).28.
M. M.
Farazmand
, N. K. R.
Kevlahan
, and B.
Protas
, “Controlling the dual cascade of two-dimensional turbulence
,” J. Fluid Mech.
668
, 202
–222
(2011
).29.
M.
Baum
, T. J.
Poinsot
, D. C.
Haworth
, and N.
Darabiha
, “Direct numerical simulation of H2/O2/N2 flames with complex chemistry in two-dimensional turbulent flows
,” J. Fluid Mech.
281
, 1
–32
(1994
).30.
N.
Peters
, P.
Terhoeven
, J. H.
Chen
, and T.
Echekki
, “Statistics of flame displacement speeds from computations of 2-D unsteady methane-air flames
,” Proc. Combust. Inst.
27
, 833
–839
(1998
).31.
N.
Chakraborty
, M.
Klein
, and R. S.
Cant
, “Effects of turbulent Reynolds number on the displacement speed statistics in the thin reaction zones regime of turbulent premixed combustion
,” J. Combust.
2011
(473679
), 1
–19
.32.
I.
Shepherd
and W.
Ashurst
, “Flame front geometry in premixed turbulent flames
,” Proc. Combust. Inst.
24
(1
), 485
–503
(1992
).33.
V. K.
Chakravarthy
and S.
Menon
, “Subgrid modeling of turbulent premixed flames in the flamelet regime
,” Flow, Turbul. Combust.
65
, 131
–161
(2001
).34.
S. S.
Ibrahim
, A. M. S.
Ali
, and A. R.
Masri
, “Two-versus three-dimensional LES of premixed turbulent propagating flames
,” in Third Symposium on Turbulence and Shear Flow Phenomena
, Sendai, Japan
, 2003
.35.
B.
Ugurtas
, G.
Avalon
, N.
Lupoglazoff
, and G.
Casalis
, “Stability and acoustic resonance of internal flows generated by side injection
,” in Solid Propellant Chemistry, Combustion and Motor Internal Ballistics
, Progress in Astronautics and Aeronautics (AIAA, New York
, 2000
), Vol. 185.36.
T.-M.
Liou
, W.-Y.
Lien
, and P.-W.
Hwang
, “Transition characteristics of flowfield in a simulated solid-rocket motor
,” J. Propul. Power
14
(3
), 282
–289
(1988
).37.
R.
Beddini
and T.
Roberts
, “Turbularization of an acoustic boundary layer on a transpiring surface
,” AIAA Paper No. 86-1448, 1986
.38.
Y.
Lee
and R. A.
Beddini
, “Effect of solid rocket chamber pressure on acoustically-induced turbulent transition
,” AIAA Paper 2000-3802, 2000
.39.
S.
Apte
and V.
Yang
, “Unsteady flow evolution is porous chamber with surface mass injection. Part II: Forced oscillations
,” AIAA J.
40
(22
), 244
–253
(2001
).© 2017 Author(s).
2017
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