Experimental and theoretical determination of the admittances of a family of nozzles subjected to axial instabilities

Bell, W.; Daniel, B.R.; Zinn, B. T.

doi:10.1016/s0022-460x(73)80112-9

Cited by 23 publications

(10 citation statements)

References 6 publications

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“…A more realistic nozzle is also considered to evaluate the influence of the exact Mach number profile on the transfer functions. The analytical model is then compared with the experimental data of Bell et al (1973) in section § 6.2. In § 6.3 the invariant method is compared with the phase correction of the reflection coefficient through an effective nozzle length proposed by Stow et al (2002) and to the extension proposed by Goh & Morgans (2011a) when considering a choked flow through the nozzle.…”

Section: Resultsmentioning

confidence: 99%

“…These simplifications, such as considering a steady, inviscid main flow, neglecting boundary layers or considering a 1D flow inside the nozzle can only be verified when compared either with fully turbulent 3D high-fidelity numerical simulations in which every lengthscale of the flow is considered, or with experimental data in real configurations. Zinn (1973) and Bell et al (1973) developed an experiment to measure the admittance of several rocket engine nozzle geometries, showing the influence of the nozzle geometry on the admittance at non-zero frequencies. This experiment is used in this section to validate the invariants method.…”

Section: Comparison With Experimental Measurementsmentioning

confidence: 99%

“…The axisymmetric nozzles considered by Bell et al (1973) are shown in figure 13, where the contour of the nozzle, r(x), is plotted. They are made up of three sections: first a circular arc of radius r cc starting at the inlet and turned an angle θ 1 ; this arc joins a conical section with the same half-angle, connecting with the third part, a circular arc of the same radius turned an angle of θ 1 .…”

Section: Comparison With Experimental Measurementsmentioning

confidence: 99%

“…The reflected wave w − 0 is obtained in this way and, using (2.7), the admittance can be calculated as (6.4) where R 0 = w − 0 /w + 0 is the reflection coefficient. Results will be plotted as a function of the non-dimensional frequency S = 2πf r c /c 0 as done by Bell et al (1973), where the angular frequency (2πf ), the nozzle inlet radius (r c ) and sound speed (c 0 ) are used. This reduced frequency can be easily related to the one used previously in this paper (S = 2πΩr c /L n ) but S will be used in this section as done by Bell et al (1973) to compare with their results.…”

Section: Comparison With Experimental Measurementsmentioning

confidence: 99%

“…Out of all the cases studied by Bell et al (1973) three will be considered here, corresponding to an inlet Mach number of 0.08, a radius ratio r cc /r c = 0.44 and three half-angles, θ 1 = 15, 30 and 45. Figure 14 shows the admittance of the three nozzles computed with the analytical method of § 4 compared to the experimental values.…”

Section: Comparison With Experimental Measurementsmentioning

confidence: 99%

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Solution of the quasi-one-dimensional linearized Euler equations using flow invariants and the Magnus expansion

2013

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The acoustic and entropy transfer functions of quasi-one-dimensional nozzles are studied analytically for both subsonic and choked flows with and without shock waves. The present analytical study extends both the compact nozzle solution obtained by Marble & Candel (1977) and the effective nozzle length proposed by Stow et al. (2002) and by Goh & Morgans (2011a) to non-zero frequencies for both modulus and phase through an asymptotic expansion of the linearized Euler equations. It also extends the piecewiselinear approximation of the velocity profile in the nozzle proposed by Moase et al. (2007) to any arbitrary profile or equivalently any nozzle geometry. The equations are written as a function of three variables, namely the dimensionless mass, total temperature and entropy fluctuations, yielding a first order linear system of differential equations with varying coefficients, which is solved using the Magnus expansion. The solution shows that both the modulus and the phase of the transfer functions of the nozzle have a strong dependence on the frequency. This holds for both choked flows and subsonic converging diverging nozzles. The method is used to compare two different nozzle geometries with the same inlet and outlet Mach numbers showing that, even if the compact solution predicts no differences between the transfer functions of the two nozzles, significant differences are found at non-zero frequencies. A parametric study is finally performed to calculate the indirect to direct noise ratio for a model combustor, showing that this ratio decreases at higher frequencies.

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Section: Resultsmentioning

confidence: 99%

Section: Comparison With Experimental Measurementsmentioning

confidence: 99%

Section: Comparison With Experimental Measurementsmentioning

confidence: 99%

Section: Comparison With Experimental Measurementsmentioning

confidence: 99%

Section: Comparison With Experimental Measurementsmentioning

confidence: 99%

See 3 more Smart Citations