Validation of the computation of rocket nozzle admittances with linearized euler equations

Kathan, R.; Morgenweck, Daniel; Kaess, R.; Sattelmayer, Thomas

doi:10.1051/eucass/201304135

Cited by 5 publications

(4 citation statements)

References 7 publications

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“…However, as it will be shown in the next section, these perturbed LNSEs are only valid for laminar flow regimes. The model has attracted growing attention for thermoacoustic problems in gas turbines [28,27] and rocket engines [29]. As already noted, in the absence of viscosity LEEs support the growth of Kelvin-Helmholtz instabilities in shear layers at certain frequencies.…”

Section: Acoustic Governing Equations For a Laminar Flow Fieldmentioning

confidence: 97%

Impact of turbulence on the prediction of linear aeroacoustic interactions: Acoustic response of a turbulent shear layer

Gikadi

Föller

Sattelmayer

2014

Journal of Sound and Vibration

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Section: Acoustic Governing Equations For a Laminar Flow Fieldmentioning

confidence: 97%

Impact of turbulence on the prediction of linear aeroacoustic interactions: Acoustic response of a turbulent shear layer

Gikadi

Föller

Sattelmayer

2014

Journal of Sound and Vibration

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“…In literature, such experimentally or numerically determined response functions can be found for laminar [5][6][7] and turbulent flames [8][9][10][11]. Other examples are found for pure acoustic systems, such as the frequency response behavior of boundaries (impedance measurements [12,13] or duct discontinuities [14][15][16][17]). In general, only the frequency response at real-valued frequencies is known but not at complex-valued frequencies.…”

Section: Scopementioning

confidence: 99%

Quantitative Stability Analysis Using Real-Valued Frequency Response Data

Schmid¹,

Blumenthal

Schulze

et al. 2013

Journal of Engineering for Gas Turbines and Power

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Quantitative Stahility Analysis Using Real-Valued Frequency Response DataModels for the analysis of thermoacoustic instabilities are conveniently formulated in the frequency domain. In this case one often faces the difficulty that the response behavior of some elements of the system is only known at real-valued frequencies, although the transfer behavior at complex-valued frequencies is required for the quantification of the growth rates of instabilities. The present paper discusses various methods for extrapolation of frequency response data at real-valued frequencies into the complex plane. Some methods have been used previously in thermoacoustic stability analysis; others are newly proposed. First the pertinent mathematical background is reviewed, then the sensitivity of predicted growth rates on the extrapolation scheme is explored. This is done by applying different methods to a simple thermoacoustic system, i.e., a ducted premixed flame, for which an analytical solution is known. A short analysis determining the region of confidence of the extrapolated transfer function is carried out to link the present study to practical applications. The present study can be seen as a practical guideline for using frequency response data collected for a set of real-valued frequencies in quantitative linear stability analysis.

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“…The geometry is described by the radii of curvature at the nozzle entrance r in and at the throat r out , as well as by the nozzle half-angle θ nozzle . For detailed discussion on the influence of the nozzle modeling refer, for example, to [17]. This model reflects the strong frequency-dependent damping of the nozzle accurately and is thus more sophisticated than the choked nozzle approach used in [5].…”

Section: Injector Plate Flame and Nozzlementioning

confidence: 99%

Mapping the Influence of Acoustic Resonators on Rocket Engine Combustion Stability

Miranda

Polifke

2015

Journal of Propulsion and Power

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A mode-based, acoustic low-order network model for rocket chambers with resonator ring is introduced. This model involves effects of dissipation as well as scattering and mode coupling associated with a resonator ring. Discontinuities at the interface between acoustic elements are treated with integral mode-matching conditions. Eigenfrequencies and accordingly the linear system stability can be determined with the generalized Nyquist plot method based on the network model. Because of low computational cost, parameter studies can be performed in a reasonable time. An additional chamber eigenmode is observed for well-tuned resonators. Both the original and the additional mode show favorable stability properties for a generic test chamber. The optimal length and number of cavities are identified for that chamber. The need for analyzing the coupled system of resonators and combustion chamber in the design process is made evident by the discrepancy between detected values and those of an a priori consideration. Derived stability maps demonstrate that the region of stable operation is increased considerably by inserting well-tuned resonators. The destabilizing influence of temperature deviations in the cavities is quantified. Such sensitivities to modifications of design conditions can be extenuated by a ring configuration with several nonidentical resonator types. Moreover, the strong impact of the nonlinear correlation factor in the resonator modeling on the overall system stability is worked out. Nomenclature A = system matrix of network model c = speed of sound d = diameter of quarter-wave tube F mn , G mn = amplitudes of up-and downstream traveling waves f mn , g mn = up-and downstream traveling waves i = imaginary unit equal to −1 p J m = mth Bessel function of first kind k mn = axial wave number L = length of the thrust chamber l, l e , l r = geometric, effective, and equivalent mass length of quarter-wave resonator M = Mach number N = number of modes considered in mode matching n = pressure interaction index, Eq. (16) n R = number of cavities placed in resonator ring p 0 = acoustic fluctuating pressure _ Q = heat release R = radius of thrust chamber; reference length scale r in , r out = radius of curvature at nozzle entrance and throat, respectively T = transfer matrix T = cycle t = time U = mean flow velocity x, r, θ = axial, radial, and tangential coordinates x F , x R = axial position of flame front and resonator ring center, respectively Z = Θ iΨ acoustic impedance α = radial wave numbers Γ = growth rate, Eq. (19) γ = isentropic exponent ΔT = deviation from design temperature ϵ nl = nonlinear resistance factor θ nozzle = nozzle half-angle κ = acoustic balancing parameter defined by Eq. (14) λ mn = nth roots of the derivative of the mth Bessel function of first kind μ = dynamic viscosity Ξ = excess temperature ξ = ratio of specific impedances ρ = density τ = combustion time lag, Eq. (16) Ω = ω iϑ complex valued angular frequency ω ref = angular frequency of the undamped 1T1L mode; used to normalize frequenc...

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Validation of the computation of rocket nozzle admittances with linearized euler equations

Cited by 5 publications

References 7 publications

Impact of turbulence on the prediction of linear aeroacoustic interactions: Acoustic response of a turbulent shear layer

Impact of turbulence on the prediction of linear aeroacoustic interactions: Acoustic response of a turbulent shear layer

Quantitative Stability Analysis Using Real-Valued Frequency Response Data

Mapping the Influence of Acoustic Resonators on Rocket Engine Combustion Stability

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