In this theoretical study, we use linear stability analysis to investigate the cause of parietal vortex shedding in Taylor–Culick flow, which is representative of the flow in solid rocket motors. We focus on the effects of the lateral-injection Reynolds number and the length-to-radius ratio of the combustion chamber. Through a comparison with pipe flow, we find that flow turning is a major contributor to parietal vortex shedding. We explore the role of amphidromic points and find that they can divide the flow field into two distinct regions, an outer region with strong perturbations and an inner region with weak perturbations. In the outer region, we find that the velocity perturbations develop advection patterns with axial (streamwise) periodicity, while the pressure perturbations induce flow gradients that enhance shear stresses. Collectively, these effects are thought to combine to induce parietal vortex shedding in solid rocket motors.
REFERENCES
1.
G. A.
Flandro
, “Vortex driving mechanism in oscillatory rocket flows
,” J. Propul. Power
2
, 206
–214
(1986
).2.
K. W.
Dotson
, S.
Koshigoe
, and K. K.
Pace
, “Vortex shedding in a large solid rocket motor without inhibitors at the segment interfaces
,” J. Propul. Power
13
, 197
–206
(1997
).3.
F.
Blomshield
, “Historical perspective of combustion instability in motors—Case studies
,” in 37th Joint Propulsion Conference and Exhibit
(American Institute of Aeronautics and Astronautics
, 2001
).4.
Y.
Fabignon
, J.
Dupays
, G.
Avalon
, F.
Vuillot
, N.
Lupoglazoff
, G.
Casalis
et al., “Instabilities and pressure oscillations in solid rocket motors
,” Aerosp. Sci. Technol.
7
, 191
–200
(2003
).5.
N.
Lupoglazoff
and F.
Vuillot
, “Numerical simulations of parietal vortex-shedding phenomenon in a cold flow set-up
,” in 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit
(American Institute of Aeronautics and Astronautics
, 1998
).6.
G.
Avalon
, B.
Ugurtas
, F.
Grisch
, and A.
Bresson
, “Numerical computations and visualization tests of the flow inside a cold gas simulation with characterization of a parietal vortex shedding
,” in AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit
(American Institute of Aeronautics and Astronautics
, 2013
).7.
G.
Avalon
and D.
Lambert
, “Cold gas experiments applied to the understanding of aeroacoustic phenomena inside solid propellant boosters
,” in 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit
(American Institute of Aeronautics and Astronautics
, 2006
).8.
G.
Casalis
, G.
Avalon
, and J.-P.
Pineau
, “Spatial instability of planar channel flow with fluid injection through porous walls
,” Phys. Fluids
10
, 2558
–2568
(1998
).9.
J.
Griffond
and G.
Casalis
, “On the dependence on the formulation of some nonparallel stability approaches applied to the Taylor flow
,” Phys. Fluids
12
, 466
–468
(2000
).10.
F.
Chedevergne
, G.
Casalis
, and T.
Féraille
, “Biglobal linear stability analysis of the flow induced by wall injection
,” Phys. Fluids
18
, 014103
(2006
).11.
N.
Lupoglazoff
and F.
Vuillot
, “Parietal vortex shedding as a cause of instability for long solid propellant motors—Numerial simulations and comparisons with firing tests
,” in Aerospace Sciences Meeting and Exhibit
(American Institute of Aeronautics and Astronautics
, 1996
).12.
S.
Apte
and V.
Yang
, “Unsteady flow evolution in porous chamber with surface mass injection, Part 1: Free oscillation
,” AIAA J.
39
, 1577
–1586
(2001
).13.
T.-Y.
Qi
, C.
Liu
, M.-J.
Ni
, and J.-C.
Yang
, “The linear stability of Hunt-Rayleigh-Bénard flow
,” Phys. Fluids
29
, 064103
(2017
).14.
A.
Kourta
, “Instability of channel flow with fluid injection and parietal vortex shedding
,” Comput. Fluids
33
, 155
–178
(2004
).15.
G.
Boyer
, G.
Casalis
, and J.-L.
Estivalèzes
, “Stability analysis and numerical simulation of simplified solid rocket motors
,” Phys. Fluids
25
, 084109
(2013
).16.
G.
Boyer
, G.
Casalis
, and J.
Estivalèzes
, “Theoretical investigation of the parietal vortex shedding in solid rocket motors
,” in 8th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit
(American Institute of Aeronautics and Astronautics
, 2012
).17.
Y.
Guan
, P.
Liu
, B.
Jin
, V.
Gupta
, and L. K. B.
Li
, “Nonlinear time-series analysis of thermoacoustic oscillations in a solid rocket motor
,” Exp. Therm. Fluid Sci.
98
, 217
–226
(2018
).18.
W.
Ao
, Z.
Fan
, L.
Liu
, Y.
An
, J.
Ren
, M.
Zhao
, P.
Liu
, and L. K. B.
Li
, “Agglomeration and combustion characteristics of solid composite propellants containing aluminum-based alloys
,” Combust. Flame
220
, 288
–297
(2020
).19.
W.
Ao
, P.
Liu
, H.
Liu
, S.
Wu
, B.
Tao
, X.
Huang
, and L. K. B.
Li
, “Tuning the agglomeration and combustion characteristics of aluminized propellants via a new functionalized fluoropolymer
,” Chem. Eng. J.
382
, 122987
(2020
).20.
P.
Liu
, M.
Wang
, W.
Yang
, V.
Gupta
, Y.
Guan
, and L. K. B.
Li
, “Modified computation of the nozzle damping coefficient in solid rocket motors
,” Acta Astronaut.
143
, 391
–397
(2018
).21.
Y.
Li
, Z.
Wang
, and P.
Liu
, “On the grid dependence of hydrodynamic stability analysis in solid rocket motors
,” Phys. Fluids
32
, 034103
(2020
).22.
V.
Theofilis
, “Global linear instability
,” Annu. Rev. Fluid Mech.
43
, 319
–352
(2011
).23.
D.
Couton
, F.
Plourde
, and S.
Doan-Kim
, “Cold gas simulation of a solid propellant rocket motor
,” AIAA J.
34
, 2514
–2522
(1996
).© 2020 Author(s).
2020
Author(s)
You do not currently have access to this content.
