CROSS-VALIDATION OF A NEW GRAZING FLOW LINER TEST RIG USING MULTIPLE IMPEDANCE EDUCTION TECHNIQUES

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CROSS-VALIDATION OF A NEW GRAZING FLOW LINER TEST RIG USING MULTIPLE IMPEDANCE EDUCTION TECHNIQUES André M. N. Spillere, Augusto A. Medeiros, Pablo G. Serrano and Júlio A.

1 CROSS-VALIDATION OF A NEW GRAZING FLOW LINER TEST RIG USING MULTIPLE IMPEDANCE EDUCTION TECHNIQUES André M. N. Spillere, Augusto A. Medeiros, Pablo G. Serrano and Júlio A. Cordioli Vibration and Acoustics Laboratory, Federal University of Santa Catarina, Campus Trindade, Florianópolis, Brazil andre.mateus@grad.ufsc.br A new grazing flow liner impedance eduction test rig (FLIR) was built at the Vibration and Acoustics Laboratory of Federal University of Santa Catarina, Brazil. Measurements can be made at up to Mach 0.25 in the lined section, where and acoustic field of up to 130 db SPL can be generated by compression drivers upstream or downstream of the test section. In this paper, the new test rig will be described, highlighting its modular design and signal acquisition/processing characteristics, including a flow speed measurement technique based on acoustic measurements. New microphone mountings designed to reduce flow noise by recessing the microphones and covering the cavities will also be described, and their flow noise levels compared to flush-mounting the microphones. Typical honeycomb core, perforated face-sheet liner samples were tested at different flow speeds at FLIR. Results were fed to multiple, previously validated impedance eduction codes implemented in the laboratory. Results show good agreement between different methods at all test flow speeds. 1. Introduction The aircraft transportation sector growth in the last decades, as well the urbanization of airport surrounding areas, has lead to stricter regulations in regard to noise generated by aircraft. Government organizations are responsible for certifying airplanes based on measurements in specific points near the runway. During the phases of take-off and landing the engines are a major source of noise due to jet noise and tonal components generated by the blade passage frequency in turbofan engines. The latter is aggravated by the fact that discrete frequencies are more perceptive by the human ear and have higher penalties in aircraft certification [1]. In order to reduce this tonal component, a lot of effort has been applied to develop acoustic liners, whose structure is usually based on a honeycomb core between a rigid and a perforated plate. These engine treatment materials are placed in the inlet, bypass and exhaust ducts and can be seen as an array of Helmholtz resonators, in such a way that good sound attenuation is achievable over a narrow frequency band. By changes in its geometric parameters, such as percent open area, sheet thickness and cavity depth, it is possible to tune the liner to the frequencies of interest [2]. The liner performance can be characterized by its acoustic impedance, a parameter also used to predict engine far-field noise. However, this parameter is highly dependent on the speed of the grazing flow over its surface [3]. The task of measuring acoustic impedance in the presence of grazing flow ICSV22, Florence, Italy, July

is not trivial, and multiple methods have been proposed in the last decades. They usually consist in measuring the acoustic field in a test rig where a liner sample is subject to grazing flow.

2 is not trivial, and multiple methods have been proposed in the last decades. They usually consist in measuring the acoustic field in a test rig where a liner sample is subject to grazing flow. A numerical or analytical approach is then used to calculate the acoustic field inside the duct for a given impedance, which is then varied until the calculated field converges to the measured one. The main difference between the methods are the assumptions regarding the acoustic field model. In the Vibration and Acoustics Laboratory at Federal University of Santa Catarina, a new grazing Flow Liner Impedance Test Rig (FLIR) was designed and built by the authors. One of the main characteristics expected for the new test rig is a modular design, so that it can accommodate the requirements of different impedance eduction methods. This paper describes, in Section 2, the FLIR, highlighting some of its features, like its modular design, the flow velocity measurement technique based on acoustic measurements, and microphone mountings designed to minimize flow-induced noise. Then, the theoretical background pertaining some impedance measurement techniques will be described in Section 3, and their main equations and requirements outlined, as well the results for different liner samples. Lastly, some conclusions will be drawn based on the obtained results. 2. Grazing Flow Impedance Eduction Test Rig (FLIR) This section will be used to describe the FLIR. Figure 1 gives an overview of the rig layout. The main ducts of the test rig are currently assembled inside a reverberant room to minimize the noise impact of the rig on nearby facilities. A series of ducts with larger cross-sections to reduce energy losses lead the flow from the test section to the suctioning fan sitting below the reverberant room. Figure 1: Overview of the test rig, including the suctioning fan (top, center) and the acrylic test section (left). Figure 2 shows in more detail the test section, composed by modular sections with a cross-section of dimensions 100 mm by 40 mm, which gives a cut-off frequency of 1700 Hz for no-flow condition. By default, the sections containing the microphones and the liner sample are kept in same position, whereas the loudspeark section can be placed downstream or upstream to the liner section, a requirement for the two-source technique [4]. Up to eight microphones can be mounted (four on each side of the liner section), which allows an overdetermination of the solution for the wave decomposition, necessary for the mean flow velocity calculation and impedance eduction techniques. An alternative liner sample section with ten microphone positions in the liner opposite wall was also built in order to evaluate other impedance eduction techniques, but it will not be covered in this paper. 2 ICSV22, Florence, Italy, July 2015

3 Flow Loudspeakers section Liner sample section Figure 2: Test section detail. Interchangeable section 2.1 Measuring Flow Velocity from Acoustic Measurements This technique is largely inspired by the one described in Holmberg et al.[5], but here an optimization approach based on a multiple-microphone wave decomposition scheme was used. As seen the microphone positions in Fig. 2, and assuming that all high order modes have decayed in the hard wall sections (below the cut-off frequency), the acoustic pressure at the n-th microphone, before and after the lined section, can be calculated from ( ) (1) p n = a (1) e jk(1) zi zn 1i + a (1) 1r e jk(1) zr z n e jωt, (2) p n = ( a (1) 2i e jk(1) zi zn + a (1) 2r e jk(1) zr z n ) e jωt. where the indexes i and r represent the incident and reflected waves which propagate respectively in the z+ and z directions, z n = z 1, z 2,..., z 2n are the positions of the microphones, a (1) 1 and a (1) 2 are the amplitudes of plane wave mode respectively before and after the lined section, and k z (1) is given by the dispersion relation [6], (3) k (1) z = k 0 1 ± M, where k 0 is the wavenumber ω/c 0, c 0 being the speed of sound in the fluid and M the uniform mean flow Mach number in the z direction. The plus sign is used for the incident wave (k (1) zi ) and the minus, for the reflected wave (k zr (1) ). For a given Mach number M and plane wave amplitudes a 1i, a 1r, a 2i and a 2r, Eqs. 1 and 2 can be used to calculate the acoustic field at the n-th position. Compared to the measured pressure, p n,meas, the error function e n is defined as (4) e n = p n p n,meas, which is minimized for all microphone positions, by means of a system of 2n equations and 5 unknowns. It can be solved using a standard non-linear solver, for instance, the fsolve minimizer with the Levenberg-Marquardt [7] algorithm in MATLAB [8]. A comparison with results obtained by averaging Pitot-tube velocity profiles (25 points) measured in the test rig is shown in Table 1. Table 1: Comparison between mean flow velocity using acoustic measurements and Pitot tube. Pitot-tube velocity (Mach) Acoustic measurements (Mach) Relative error (%) 0,10 0,0998 0,20 0,15 0,1524 1,60 0,20 0,2026 1,30 0,25 0,2506 0,24 ICSV22, Florence, Italy, July

measurements. New mounts were designed in which the microphones are recessed 2 mm from the wall, and a wire-mesh is mounted flush to the duct walls, as seen in Fig. 3.

4 2.2 Microphone Mountings The original couplers were designed to mount the B&K 1/4 microphones flush to the duct walls. This was found to leave the microphone diaphagram exposed to the turbulence near the wall, which results in high flow-induced noise levels, deteriorating the signal-to-noise ratios (SNR) of the measurements. New mounts were designed in which the microphones are recessed 2 mm from the wall, and a wire-mesh is mounted flush to the duct walls, as seen in Fig. 3. Figure 3: Original and new couplers on the left. Mounting detail on the right. The flow noise at Mach 0.28 was reduced up to 5 db for some microphones, e.g. position 7, whereas the difference is not noticeable in others, e.g. position 3, as seen in Fig. 4. It was decided to keep the new configuration for future measurements, but further investigations regarding the type of wire-mesh could lead to further improvements in the flow noise level [9] Old design New design Old design New design Flow Noise [db] Flow Noise [db] Figure 4: Flow noise in microphone positions 3 (left) and 7 (right). 3. Impedance Eduction Techniques The impedance eduction methods here described are based on measuring the acoustic field in a duct where a liner sample is subject to grazing flow. Propagation models for the acoustic field in the duct are compared to the measured data, and the liner impedance can be found using an optimization approach. Since all methods used in this paper have been described in great detail elsewhere, only sufficient detail pertinent to the current analysis will be given in the following description of the methods. 4 ICSV22, Florence, Italy, July 2015

5 x h x The 22 nd International Congress of Sound and Vibration x z l All methods assume a straight, rectangular duct, with a liner sample in one wall covering a section of length l of the duct, as shown in Fig. 5. z b y b y h x l z Figure 5: Rectangular duct with height h and width b, whose wall at x = b has an impedance Z wx along a section of length l. This duct can be seen as consisting of three sections: a hard-wall inlet section (1), followed by a lined section (2), and by a hard-wall outlet section (3). The acoustic field in the n-th section can be seen as a summation of all Q modes that propagate inside it as given by (5) p n = a (q) e jk(q) ni Φ(q) zni z ni + a (q) nr Φ (q) nr e jk(q) znrz, where q is the index of the mode, in a crescent order of its cut-off frequency and k (q) zn is the wavenumber in the z direction for the q-th mode, that satisfies the dispersion relation [6] (6) k 2 x + k 2 y + k 2 z = (k 0 ± Mk z ) 2. Using the hard-wall boundary conditions, the wavenumbers and mode-shapes can be calculated in sections 1 and 3[10]. In section 2, calculation of the wavenumbers in directions x and z depend on the unknown impedance Z wx. Below plane-wave cut-off frequency in direction y, however, k y2i = k y2r, and from the dispersion relation, Eq. (6), the wavenumbers in directions x and z are related by (7) k (q) x2i = (k 0 Mk (q) z2i )2 (k (q) z2i )2, and k (q) x2r = (8) Z wx = jz 0 k 0 k (q) x2i 1 M k(q) z2i k 0 (k 0 + Mk (q) z2r) 2 (k (q) z2r) 2. Application of the Myers [11] boundary condition for the acoustic impedance in the presence of flow to the wall at x = b where the unknown impedance Z wx is set results in [12] ( ) 2 cot(k (q) x2i b), where Z 0 is the characteristic impedance of the fluid, given by the product of its density and speed of sound. 3.1 Two-Port Matrix Method (TPM) If only one dominating mode is considered to propagate in the duct, then Eq. (5) for the lined section, i.e., section 2, is reduced to (9) p 2 = a 2i Φ 2i e jk z2iz + a 2r Φ 2r e jk z2rz. ICSV22, Florence, Italy, July

6 The acoustic velocity distribution can also be derived: ( 1 (10) u z2 = Φ 2i e jkz2iz 1 ) Φ 2r e jk z2rz, Z i Z r where Z i e Z r are defined as (11) Z i = Z 0 ( k0 Mk z2i k z2i ) ( ) k0 + Mk z2r, and Z r = Z 0. k z2r Using Eq. (9) and Eq. (10), expressions for the relations between pressure and velocity before (index 2in) and after (index 2out) the test section can be written, resulting in a transfer matrix, [T ], of the form (12) { p2out u 2out } = Z i e jk z2i l +Z re jk z2r l Z i Z r(e jkz2il e ikz2rl ) Z i +Z r ZZ i +Z r e jk z2i l e jk z2r l Z i +Z r Z re jk z2i l +Z + e jk z2r l Z i +Z r { p2in A new matrix, called scattering matrix, [T tr ], and its inverse matrix, respectively can also be added before and after the transfer matrix given in Eq. (12) [13]. These new scattering matrices represent the effect of the hard-soft wall transitions on the acoustic field, given that higher-order modes generated by scattering would be present in the vicinities and are not taken into account by the current approach. The final system of equations is thus given 2 equations and 6 unknowns (the 4 terms in the scattering matrices and the 2 wavenumbers in the z direction). In order to build a determined system, it is necessary to measure the acoustic field at least three times guaranteeing linearly independent measurements. This can be done by means of the two-source or two-load techniques[4]. 3.2 Mode-Matching Method (MMM) The main difference between the MMM and the TPM, presented previously, is that the MMM takes into account as many modes as necessary in each duct section. It still assumes that the only mode propagating towards both sides of the lined section is a plane wave mode [14], such that the acoustic fields in sections 1 to 3 can be written as: (13) p 1 = a (1) 1i Φ(1) 1 e jk(1) z1i z + a (q) 1r Φ (q) 1 e jk(q) z1r z, u 2in }. (14) p 2 = a (q) e jk(q) 2i Φ(q) z2i z 2i + a (q) 2r Φ (q) 2r e jk(q) z2r (z l), (15) p 3 = a (q) 3i Φ(q) 3 e jk(q) z3i (z l) + a (1) 3r Φ (1) 3 e jk(1) z3r (z l). In Eq. (13) the summation only occurs for the reflected modes, since the only incident mode is the plane-wave mode (q = 1). Analogously, in Eq. (15) the summation only occurs for the incident modes, since the only reflected mode (which propagates in z, i.e., towards duct 2) is the plane-wave mode. Mode-Matching is the name of the technique used to determine how acoustic energy is transferred from one duct to the other through the propagating modes at the discontinuities. First, continuity of pressure and velocity is assumed at the interfaces of section 1 to section 2, and from section 2 to 6 ICSV22, Florence, Italy, July 2015

7 section 3. The cited boundary conditions are then applied to end up with a system of 4Q equations and 4Q unknowns, the model amplitudes a (q) 1r, a (q) 2i, a(q) 2r and a (q) 3i, for the first mode to the Q-th mode. The required inputs to the system of equations are the incident plane-wave amplitude in section 1,, and the exit reflection coefficient R(q) e = a (q), which is zero for all q > 1 since the only a (1) 1i 3r /a (q) 3i reflected mode is the plane-wave mode, as per Eq. (15). From solving the forementioned system of equations for an expected impedance value, the modal amplitudes are found, and the acoustic field can be computed at any position in the sections. The microphone positions already used to compute the required inputs are then used to compare the measured acoustic field to the calculated one. From that, a cost function is built, and by minimizing it the unknown impedance can be found [15]. 3.3 Results Some preliminary test results using the TPM and the MMM are shown below for no-flow condition and Mach Figure 6 refers to liner samples with different geometric parameters. Overall, a good agreement can be seen between methods. As it can be seen, the TPM implemented code still requires optimization for no-flow condition. For Mach 0.25 the imaginary part of both methods only converge only at high frequencies Normalized Impedance 0 1 Normalized Impedance MMM Real MMM Img TPM Real TPM Img MMM Real MMM Img TPM Real TPM Img Normalized Impedance 0 1 Normalized Impedance MMM Real MMM Img TPM Real TPM Img MMM Real MMM Img TPM Real TPM Img Figure 6: Impedance eduction for liner sample A (top) and B (bottom). Vertical blue line represents the plane-wave cut-off frequency. (Left no-flow condition and right Mach 0.25) 4. Conclusion A grazing flow impedance eduction test rig was built at the Federal University of Santa Catarina with a modular design so that different impedance eduction techniques may be applied. The acoustic ICSV22, Florence, Italy, July

8 flowmeter shows good agreement with Pitot-tube measurements and the new microphones mountings improved signal-to-noise ratios. Currently, two impedance eduction methods are implemented, the MMM and the TPM, and two more are being implemented. The main goal is to compare the results of different methods (with particular assumptions) in order to gain confidence on the impedance results already measured, identifying advantages and limitations of each method. Preliminary results using the TPM and MMM show good agreement at all flow speeds over the entire frequency range under analysis for the real part of the impedance. The results resemble typical liner impedance curves seen in the literature, except for no-flow condition. Interestingly, both methods, despite assuming plane-wave propagation on the hard-wall sections of the duct, converged to feasible results above the duct cut-off frequency for the flow condition, which suggests that the acoustic field is still dominated by the plane-wave mode. REFERENCES 1. Smith, M. J., Aircraft Noise. Cambridge University Press, (2004). 2. Richter, C., Liner impedance modeling in the time domain with flow. Univerlagtuberlin, (2010). 3. Bielak, G. W., Premo, J. W. and Hersh, A. S., Advanced turbofan duct liner concepts. National Aeronautics and Space Administration, Langley Research Center, (1999). 4. Åbom, M. Measurement of the scattering-matrix of acoustical two-ports, Mechanical Systems and Signal Processing, 5(2), , (1991). 5. Holmberg, A., Åbom, M. and Bodén, H. Accurate experimental two-port analysis of flow generated sound, Journal of Sound and Vibration, Vol. 110, n. 26, , (2011). 6. Munjal, M. L., Acoustics of ducts and mufflers with application to exhaust and ventilation system design, Wiley New York (NY) et al., (1987). 7. Levenberg, K., A method for the solution of certain problems in least squares, Quarterly of applied mathematics, 2, , (1944). 8. MATLAB Optimization Toolbox User s Guide. The MathWorks, Inc., Natick, Massachusetts, USA. (2013). 9. Fleury, V. et al., Optimization of microphone array wall-mountings in closed-section wind tunnels, AIAA Journal, 50(11), , (2012). 10. Medeiros, A. A., Masson, Z., Serrano, P. G., dos Reis, D. C. and Cordioli, J. A. Comparison of modematching and two-port formulations for acoustic impedance eduction of liners under grazing flow Forum Acusticum 2014, Krakow, Poland, 7 12 September, (2014). 11. Myers, M. On the acoustic boundary condition in the presence of flow, Journal of Sound and Vibration, Vol. 71, n. 3, , (1980). 12. De Roeck, W. and Desmet, W. Indirect acoustic impedance determination in flow ducts using a two-port formulation, AIAA Conference, Vol. 3302, (2009). 13. Santana, L. D., De Roeck, W., Desmet, W. and Ferrante, P. Two-Port indirect acoustic impedance eduction in presence of grazing flows, 17th AIAA/CEAS Aeroacoustics Conference 2011, Vol. 2868, (2011). 14. Elnady, T., Musharrof, M., Bodén, H. and Elhadidi, B. Validation of an inverse analytical technique to educe liner impedance with grazing flow, Proceedings of the 12th AIAA/CEAS Aeroacoustics Conference, Vol. 5, , (2006). 15. Elnady, T., Bodén, H. and Elhadidi, B. Validation of an inverse semi-analytical technique to educe liner impedance, AIAA journal, Vol. 47, n. 12, , (2009). 8 ICSV22, Florence, Italy, July 2015

Two-Port Indirect Acoustic Impedance eduction in presence of grazing flows

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