About the complexity of propagation and radiation of ducted modes

Montetagaud, Fabienne; Batard, Hervé

doi:10.2514/6.2000-1955

Cited by 4 publications

(4 citation statements)

References 9 publications

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“…Indeed it is difficult to distinguish mode orders. 17 This becomes more difficult as the optimum impedance is approached. This phenomenon has been noted and identified as ''surface acoustic waves'' 21 and the ''double-eigenvalue'' 16 in earlier papers.…”

Section: Simulated Modal Datamentioning

confidence: 99%

“…Equation (17) shows that the determination of the soft-wall mode shapes is a function of Mach number. Eversman cases were run with a uniform duct Mach number (Table 7: cases A-C, M ¼ -0.115; cases D-F, M ¼ 0.5).…”

Section: Simulated Modal Datamentioning

confidence: 99%

“…The data were acquired using the standard rotating rake acquisition procedure 2 and decomposed into circumferential modes. The circumferential modes were decomposed into radial modes using the eigenvalues and eigen-functions determined based on impedance from equation (17). Two linear single-degree-of-freedom liners with a screen mesh on a 34% open area perforate were used in these experiments.…”

Section: Measured Datamentioning

confidence: 99%

“…However in this case, as the eigenvalues change rapidly with small changes in admittance, the shapes of the radial basis functions converted from one radial order to another as the trajectories passed near the double-eigenvalue point. 17 In this example, the (2,0) radial basis functions shown in black convert to (2,1) radial basis functions as the black trajectory passes on the right side, larger < k x f g values, of the double-eigenvalue. Conversely, on the left side, lower < k x f g values, the radial basis functions convert from a (2,1) to a (2,0) type of radial basis function.…”

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Techniques for analyzing rotating rake mode measurements over passive treatment

Sutliff

Dahl

2016

International Journal of Aeroacoustics

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The NASA Glenn Research Center’s rotating rake mode measurement system has been successful in measuring the modal content propagating in hard-wall ducts. This paper proposes an extension of the rotating rake measurement and analysis technique to treated sections by developing basis functions based on wall impedance boundary conditions for flow conditions (i.e. constant duct area and Mach number), where the closed-form analytical solution exists. Analytical equations developed to estimate mode power are incorporated. Using the impedance boundary conditions results in better mode measurement solutions. This method is verified by decomposing and analyzing radial pressure profiles generated numerically by the Eversman propagation code. Several modes, frequencies, and impedances are evaluated. For ducts with soft-walls and mean flow, the radial basis functions must be numerically computed. The linear companion matrix method is used to obtain both the eigenvalues of interest, without the need for an initial guess, and the radial basis functions. The governing equations allow for the mean flow to have a boundary layer at the wall. In addition, a nonlinear least-squares method is used to adjust the wall impedance to best fit the data in an attempt to use the rotating system as an in-duct wall impedance measurement tool. Simulated and measured data are used to show the effects of wall impedance and mean flow on the computed results. Data from an inlet of a low-speed ducted fan with several different impedance conditions on the outer wall were acquired and reduced to determine the best fit to the data. The methodology and analysis documented in this paper were directly inspired by the groundbreaking work of Dr. Edward J Rice.

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Section: Simulated Modal Datamentioning

confidence: 99%

Section: Simulated Modal Datamentioning

confidence: 99%

Section: Measured Datamentioning

confidence: 99%

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confidence: 95%

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