Impact of Absorber Ring Position and Cavity Length on Acoustic Damping

Abstract

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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