Linearized Euler Equations for the Determination of Scattering Matrices for Orifice and Perforated Plate Configurations in the High Mach Number Regime

Schulze, Moritz; Wagner, Michael; Sattelmayer, Thomas

doi:10.3390/aerospace3040033

Cited by 12 publications

(2 citation statements)

References 43 publications

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“…Essentially, interaction mechanisms between the acoustics and the shear layers downstream of the perforated plate lead to a production of vortical structures, which are convectively transported throughout the system. The energy of formation is gained from the acoustics leading to a reduction of amplitudes [16,17].…”

Section: Reference Configurationmentioning

confidence: 99%

Impact of Absorber Ring Position and Cavity Length on Acoustic Damping

Schulze

Kathan

Sattelmayer

2015

Journal of Spacecraft and Rockets

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The influence of axial position and cavity length of an absorber ring with grazing flow on damping of acoustic amplitudes in a rocket combustion chamber is experimentally investigated under nonreactive ambient temperature conditions. At the perforated inlet, high-bias flow velocities are present, providing strong damping. On the basis of power spectral densities gained from flow noise excitation, damping rates for the first transverse mode are derived using a Lorentzian profile fitting procedure. Results show that an absorber ring located in close proximity to the nozzle leads to enhanced damping, whereas in the case of a ring placed closely to the inlet, damping rates are reduced. Absorption coefficients show that an isolated absorber ring is not capable of acoustic amplification. It is concluded that reduced damping originates from weaker impact of the perforated inlet on the acoustics, resulting from a shielding effect by the absorber ring. The highest damping rate is found for a cavity length below the theoretically predicted optimum length for an absorber ring located close to the nozzle. Nomenclature c = speed of sound, m∕s D = diameter, m F,Ĝ = characteristic wave amplitude, m∕s f = frequency, Hz hIi = acoustic intensity averaged over one acoustic period, W∕m 2 J 1 = Bessel function of first kind and order 1 k = wave number, 1∕m L = length, m Ma = Mach number _ m = mass flow, kg∕s p = pressure, Pâ p = complex amplitude of pressure, Pa R = radius, m s 10 = zeroth root of first-order Bessel function derivative x, r, ϕ = axial, radial, and circumferential position; m, m, rad α = damping rate, rad∕s δ = offset angle with respect to frame of reference, rad λ = wavelength, m ξ = absorption coefficient ρ = density, kg∕m 3 ρ = mean density, kg∕m 3 φ = phase, rad 1T = first transverse mode for a system with absorber ring 1T − = additional transverse mode for a configuration with absorber ring 1T∕2T = first/second transverse mode 1T1L = first transverse and first longitudinal coupled mode 1T2L = first transverse and second longitudinal coupled mode Subscripts A = absorber ring cavity length C = chamber co = cut-on e = effective i = ith measurement location num = numerical Optimal = optimal (highest) damping t = nozzle throat u, d = upstream/downstream λ∕4 = property of λ∕4 absorber I = case I, absorber ring located closely to the face plate II = case II, absorber ring located closely to the nozzle * = complex conjugation Superscripts A, B = excitation states u, d = upstream/downstream x = in positive/negative axial direction * = complex conjugation

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Section: Reference Configurationmentioning

confidence: 99%

Impact of Absorber Ring Position and Cavity Length on Acoustic Damping

Schulze

Kathan

Sattelmayer

2015

Journal of Spacecraft and Rockets

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“…Additionally, some authors have considered the energy equation for laminar flows, e.g. Schulze et al [52] to characterise perforations and Ullrich et al [53] to investigate the acoustic-entropic coupling in a Laval nozzle. In this work, we consider both the effect of turbulence and the energy equation in the governing equations.…”

Section: Introductionmentioning

confidence: 99%

On the scattering of entropy waves at sudden area expansions

Guzmán-Iñigo,

Yang,

Gaudron

et al. 2021

Preprint

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In this work, we investigate both numerically and theoretically the sound generated by entropy waves passing through sudden area expansions. This is a canonical configuration representing internal flows with flow separation and stagnation pressure losses. The numerical approach is based on a triple decomposition of the flow variables into a steady mean, a small-amplitude coherent part, and a stochastic turbulent part. The coherent part contains acoustic, vortical, and entropy waves. The mean flow is obtained as the solution of the Reynolds-Averaged Navier-Stokes (RANS) equations. The equations governing the coherent perturbations are linearised and solved in the frequency domain. To account for the effect of turbulence on the coherent perturbations, a frozen eddy viscosity model is employed. When entropy fluctuations pass through the area expansion, the generated entropy noise behaves as a low-pass filter. The numerical predictions of the noise at low frequencies are compared to the predictions of compact, quasi-one-dimensional, and isentropic theory and large discrepancies are observed. An alternative model for the generated entropy noise tailored for area expansions is then proposed. Such model is based on the conservation of mass, momentum, and energy written in integral form. The model assumes zero frequency and the one-dimensionality of the flow variables far upstream and downstream of the expansion. The predictions of this model agree well with the numerical simulations across a range of finite subsonic Mach numbers including low, intermediate, and high Mach numbers. The contributions of this work are both numerical and theoretical. Numerically, a triple decomposition adapted to high-Mach-number, compressible flows is introduced for the first time in the context of acoustic simulations. From a theoretical point of view, the model proposed here represents the first quasi-steady model that captures correctly the low-frequency entropy noise generated at sudden area expansions, including at high subsonic Mach numbers.

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Noise optimization of multi-stage orifice plates based on RBF neural network response surface and adaptive NSGA-II

Gan

Tang

et al. 2022

Annals of Nuclear Energy

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Linearized Euler Equations for the Determination of Scattering Matrices for Orifice and Perforated Plate Configurations in the High Mach Number Regime

Cited by 12 publications

References 43 publications

Impact of Absorber Ring Position and Cavity Length on Acoustic Damping

Impact of Absorber Ring Position and Cavity Length on Acoustic Damping

On the scattering of entropy waves at sudden area expansions

Noise optimization of multi-stage orifice plates based on RBF neural network response surface and adaptive NSGA-II

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