Velocity effects in transverse mode liquid propellant rocket combustion instability

Crocco, L.; Harrje, D. T.; Reardon, Frederick H.

doi:10.2514/3.2631

Cited by 31 publications

(9 citation statements)

References 4 publications

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“…The pressure variation in the x 3 direction may be assumed to be minor for many transverse oscillations, especially if the mean-flow Mach number M ≪ 1. The major variation of pressure will be in the transverse direction, as indicated by experimental findings [1] and theory [5,9]. For a pure transverse wave behavior, there is no acoustical oscillation in the x 3 direction; so, only advection can be expected to produce variations in that flow direction.…”

Section: B Reduction To Two-dimensional Wave Equationmentioning

confidence: 99%

“…For a pure transverse wave behavior, there is no acoustical oscillation in the x 3 direction; so, only advection can be expected to produce variations in that flow direction. These variations tend to be slow exponential variations according to the theory [5,9].…”

Section: B Reduction To Two-dimensional Wave Equationmentioning

confidence: 99%

“…Additionally, isentropic relations are used to describe the thermodynamic relations during the oscillation. For transverse oscillations in a cylindrical chamber, shock waves do not form [1,2,5,9]. Also, the acoustic wavelengths are sufficiently long that viscous and diffusive effects are small, except for a combustion zone near an injector.…”

Section: B Reduction To Two-dimensional Wave Equationmentioning

confidence: 99%

“…Each resonant mode oscillation is a characteristic of the particular combustion chamber and convergent portion of the nozzle. These resonant mode oscillations and their well-approximated frequencies are predictable by linear theory [1,[4][5][6]. The lowest frequency mode is identified as the fundamental mode, while the other modes are overtones.…”

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confidence: 97%

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Two-Time-Variable Perturbation Theory for Liquid-Rocket Combustion Instability

Sirignano

Krieg

2016

Journal of Propulsion and Power

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Nonlinear, transverse-mode, liquid-propellant-rocket-motor combustion instability is examined for the first time via a two-time-variable perturbation expansion in an amplitude parameter. Both triggered and spontaneous instability domains are studied. A specific coaxial multi-injector example demonstrates the matching process between wave dynamics and injection/combustion mechanisms. The combustion has a characteristic time for mixing, producing a time lag in the energy release rate relative to pressure. The coupled combustion process and wave dynamics are calculated for the first tangential mode. Two first-order ordinary differential equations are developed and solved for the amplitude and phase angle in the slow time. Limit cycles and transient behaviors are resolved. Nonlinear triggering is predicted in certain operational domains; above a critical initial amplitude, the amplitude grows; otherwise, it decays with time. A linear representation of the combustion process suffices to balance nonlinear nozzle damping. This perturbation approach provides better physical understanding than a computational fluid dynamics approach and allows lower-cost computation to determine trends over the key parameter domains. Moving a higher fraction of the propellant flow away from the chamber center has a destabilizing effect on the tangential mode. A most stable Mach-number value is deduced. The reduction to two governing ordinary differential equations benefits future optimization and control analyses.

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Section: B Reduction To Two-dimensional Wave Equationmentioning

confidence: 99%

Section: B Reduction To Two-dimensional Wave Equationmentioning

confidence: 99%

Section: B Reduction To Two-dimensional Wave Equationmentioning

confidence: 99%

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confidence: 97%

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Two-Time-Variable Perturbation Theory for Liquid-Rocket Combustion Instability

Sirignano

Krieg

2016

Journal of Propulsion and Power

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“…These early studies have paved the way to the establishment of stability models associated with the emergence of Helmholtz-type acoustic modes in simple geometric configurations. Corresponding analyses have been occasionally accompanied by experiments, such as those conducted by Brownlee and Marble, 9 Temkin 10 , and Chester, 11 who investigated the structure of longitudinal waves, and those by Crocco, 12 Reardon, Crocco, and Harrje, 13 Krieg,14 and Heidmann, 15 who shifted their attention to the behavior of transverse waves. Nearly two decades later, attention would turn to isolating the effect of vorticity production at resonant frequencies, which proved to be a potentially strong driving factor for instability.…”

Section: Introductionmentioning

confidence: 97%

Transverse Vortico-Acoustic Waves in the Presence of Strong Mean Flow Shear Layers

Kovacic¹,

Batterson²,

Majdalani³

2015

51st AIAA/SAE/ASEE Joint Propulsion Conference

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Several analytical models describing the formation of resonant waves in simple geometric configurations are available in the open literature. Their solutions are predicated on several limiting assumptions, namely, that the mean flow velocity is uniform and that the wall injection Mach number is sufficiently small to justify asymptotic reductions to the governing equations. When considering acoustic waves in a convecting medium where 1 M  , the effect of mean flow motion appears at 2 ( ) M which, from an asymptotic standpoint, represents a higher-order correction that is traditionally dismissed with no afterthought. Naturally, the ensuing truncation leads to a simple Helmholtz-type wave equation. In practice though, the influence of the mean flow appears at leading order when accounting for acoustic boundary layers. Acoustic boundary layers, when strongly coupled with the mean flow, give rise to the so-called vorticity (or vortical) waves. When combined with the acoustic wave motion, the resulting pair constitutes what is typically referred to as a vortico-acoustic wave. By strictly enforcing the 1 M  condition, analytical solutions can be recovered for vortico-acoustic waves in simple planar and axisymmetric chambers. The present study focuses on a numerical approach that resolves the unsteady field equations computationally for the threefold purpose of verifying existing analytical solutions, providing practical bounds for their applicability, and extending their predictive capabilities to more complex configurations. In particular, the interaction between acoustic waves and a strong mean flow shear layer is investigated by computationally resolving the vortico-acoustic field developing behind a backward facing step. In this context, deviations from the analytical solutions are reported both at high injection Mach numbers and when considering the emergence of acoustically-synchronized vortex cells around a shear layer. These vortex cells exhibit a spatial instability that continues to grow as the flow is further accelerated. Lastly, the temporal stability of the flow is quantified by computing the rate of energy transfer into the unsteady field. Similarly to the spatial instability, the increased vorticity at higher injection velocities tends to drive temporal instability as well. Nomenclature a = chamber radius or half-height [m] s a = speed of sound [m/s] j = mode number M = injection Mach number, / inj s U a p = pressure [Pa] R = specific gas constant [J/kg-K] j R = pressure amplitude for mode j [Pa] r = spatial coordinate, , , r z  T = temperature [K] inj U = injection velocity [m/s] u = velocity vector [m/s] j u = velocity associated with mode j [m/s] Symbols  = acoustic velocity potential [m 2 /s]  = dynamic viscosity [N-m/s]  = density [kg/m 3 ] Ω = steady vorticity [1/s] ω = unsteady vorticity [1/s] j  = circular frequency of mode j [rad/s] Superscripts and Subscripts 0 = denotes a mean flow variable 1= denotes an unsteady flow variable , , m n l = denotes the tangential, radial, and axial acoust...

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