Abstract
The internal meanflow with nonuniform distributions of velocity and temperature is a major challenge for acoustic analysis of a muffler in the frequency domain. On the other hand, the three-dimensional time-domain numerical method is well suited for solving the influence of meanflow on the muffler, but it is time-consuming, especially for calculating the transfer matrix that requires two sets of boundary conditions. We proposed a more efficient time-domain method to calculate the scattering matrix (SM) of an actual engine muffler using a numerical model with only one set of boundary conditions. The reciprocity, as a basic property of waves, was for the first time demonstrated in such a complex muffler with hot nonuniform flow exhausted from the engine and used to reduce the procedures for calculating the SM. The reciprocal relationship was not only expressed in the modules of the transmission coefficients in the SM but also corrected in the phases using the time delay between the incident and transmitted waves observed with the time-domain method. At last, the SM was adopted to obtain the performance of the muffler, which was validated with the measurement. The proposed method shall make the time-domain method more efficient for calculating the characterizing matrix of a muffler without or with meanflow.
Similar content being viewed by others
Data Availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
Munjal, M.L.: Acoustics of Ducts and Mufflers with Application to Exhaust and Ventilation System design, 2nd edn. Wiley, New York (2014)
Dokumac, E.: Duct Acoustics: Fundamentals and Applications to Mufflers and Silencers. Cambridge University Press, Cambridge (2021)
Mimani, A.: Acoustic Analysis and Design of Short Elliptical End-Chamber Mufflers. Springer, New York (2021)
Kim, Y.H., Choi, J.W., Lim, B.D.: Acoustic characteristics of an expansion chamber with constant mass flow and steady temperature gradient (theory and numerical simulation). J. Vib. Acoust. 112, 460 (1990)
Sujith, R.I., Waldherr, G.A., Zinn, B.T.: An exact solution for one-dimensional acoustic fields in ducts with an axial temperature gradient. J. Sound Vib. 184, 97 (1995)
Dokumaci, E.: Transmission of sound in uniform pipes carrying hot gas flows. J. Sound Vib. 195, 257 (1996)
Li, J., Morgans, A.S.: The one-dimensional acoustic field in a duct with arbitrary mean axial temperature gradient and mean flow. J. Sound Vib. 400, 248 (2017)
Wang, C.N., Chen, Y.N., Tsai, J.Y.: The application of boundary element evaluation on a silencer in the presence of a linear temperature gradient. Appl. Acoust. 62, 707 (2001)
Denia, F.D., Sánchez-Orgaz, E.M., Martínez-Casas, J., Kirby, R.: Finite element based acoustic analysis of dissipative silencers with high temperature and thermal-induced heterogeneity. Finite Elem. Anal. Des. 101, 46 (2015)
Chu, Z., Kuang, F., Kang, R., Gao, X.: Effects of airflow on the acoustic attenuation performance of reactive muffler. J. Vibroeng. 18, 637 (2016)
Desjouy, C., Ollivier, S., Marsden, O., Karzova, M., Blanc-Benon, P.: Irregular reflection of weak acoustic shock pulses on rigid boundaries: Schlieren experiments and direct numerical simulation based on a Navier–Stokes solver. Phys. Fluids 28, 027102 (2016)
Chakravarthy, R.V.K., Nair, V., Muruganandam, T.M., Ghosh, S.: Analytical and numerical study of normal shock response in a uniform duct. Phys. Fluids 30, 086101 (2018)
Liu, L., Qiu, Y., Hao, Z., Zheng, X.: A modified time domain approach for calculation of noise reduction and acoustic impedance of intake duct system. Appl. Acoust. 168, 107420 (2020)
Zhu, D.D., Ji, Z.L.: Transmission loss prediction of reactive silencers using 3-D time-domain CFD approach and plane wave decomposition technique. Appl. Acoust. 112, 25–31 (2016)
Liu, L.Y., Zheng, X., Hao, Z.Y., Qiu, Y.: A computational fluid dynamics approach for full characterization of muffler without and with exhaust flow. Phys. Fluids 32, 066101 (2020)
Liu, L., Hao, Z., Zheng, X., Qiu, Y.: A hybrid time-frequency domain method to predict insertion loss of intake system. J. Acoust. Soc. Am. 148, 2945 (2020)
Liu, L., Zheng, X., Hao, Z., Qiu, Y.: A time-domain simulation method to predict insertion loss of a dissipative muffler with exhaust flow. Phys. Fluids 33, 067114 (2020)
Liu, L.Y., Hao, Z.Y., Liu, C.: CFD analysis of a transfer matrix of exhaust muffler with mean flow and prediction of exhaust noise. J. Zhejiang Univ. Sci. A 13, 709 (2012)
Liu, L., Zheng, X., Hao, Z., Qiu, Y.: A modified reciprocal equation to predict the complex transmission coefficient of a flow duct. AIP Adv. 11, 095001 (2021)
Föller, S., Polifke, W.: Identification of aero-acoustic scattering matrices from large eddy simulation. Application to a sudden area expansion of a duct. J. Sound Vib. 331, 3096 (2012)
Lacombe, R., Föller, S., Jasor, G., Polifke, W.: Identification of aeroacoustic scattering matrices from large eddy simulation: Application to whistling orifices in duct. J. Sound Vib. 332, 5059 (2013)
Mohring, W.: Energy conservation, time-reversal invariance and reciprocity in ducts with flow. J. Fluid Mech. 431, 223–237 (2001)
Pagneux, V., Maurel, A.: Scattering matrix properties with evanescent modes for waveguides in fluids and solids. J. Acoust. Soc. Am. 116, 1913–1920 (2004)
Torregrosa, A.J., Piqueras, P., Sanchis, E.J., Guilain, S., Dubarry, M.: Assessment of acoustic reciprocity and conservativeness in exhaust aftertreatment systems. J. Sound Vib. 436, 46 (2018)
Wang, P., Wu, T.W., Ruan, K., Zhou, H.: Impedance-to-scattering matrix method for large silencers part II: integral formulation, acoustic reciprocity and practical issues. Eng. Anal. Bound. Elem. 119, 235–245 (2020)
Jang, S., Ih, J.: Refined multiload method for measuring acoustical source characteristics of an intake or exhaust system. J. Acoust. Soc. Am. 107, 3217 (2000)
Fluent, A.: 19.2 Theory Guide. ANSYS Inc., Canonsburg (2018)
Acknowledgements
The authors would like to acknowledge the support from the National Natural Science Foundation of China (No. 51905474 and No. 51975515).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Liu, L., Zheng, X., Hao, Z. et al. Application of Reciprocity to Calculating the Scattering Matrix of a Complex Muffler Without and With Nonuniform Meanflow. Acoust Aust 50, 331–342 (2022). https://doi.org/10.1007/s40857-022-00269-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40857-022-00269-2