Theoretical analysis of sound propagation and entropy generation across a distributed steady heat source. (13th October 2022)

• Record Type: Journal Article
• Authors: Nan, Jiaqi; Li, Jingxuan; Morgans, Aimee S.; Qin, Lizi; Yang, Lijun
• Is Part Of: Journal of sound and vibration. Volume 536(2022)
• Publication Date: 2022-10-13
• Subjects: Asymptotic expansion -- Thermoacoustic instabilities -- Entropy generation -- Distributed mean temperature -- Invariant; Sound -- Periodicals; Vibration -- Periodicals; Son -- Périodiques; Vibration -- Périodiques; Sound; Vibration; Periodicals; Electronic journals; 620.205
• DOI: 10.1016/j.jsv.2022.117170
• Languages: English
• ISSNs: 0022-460X

Abstract

Abstract: Acoustic and entropy waves interacting in a duct with a steady heat source and mean flow are analysed using an asymptotic expansion (AE) for low frequencies. The analytical AE solutions are obtained by taking advantage of flow invariants and applying a multi-step strategy. The proposed solutions provide first-order corrections to the compact model in the form of integrals of mean flow variables. An eigenvalue system is then built to predict the thermoacoustic modes of a duct containing a distributed heat source or sink. Predictions from the AE solutions agree well with the numerical results of the linearised Euler equations for both frequencies and growth rates, as long as the low-frequency condition is satisfied. The AE solutions are able to accurately reconstruct the acoustic and entropy waves and correct the significant errors in the predicted entropy wave associated with the compact model. The analysis illustrates that the thermoacoustic system needs to account for the entropy wave generated by the interaction of acoustic wave and the distributed steady heat source, especially when density- or entropy-dependent boundary conditions are prescribed at the duct ends. Furthermore, a combination of the AE method and the modified WKB approximation method is discussed for a cooling case. The AE solutions remedy the disadvantage of the WKB solution in the low and very low-frequency domain and facilitate full-frequency theoretical analyses of sound propagation and entropy generation in inhomogeneous duct flow fields. Highlights: Analytical solution is obtained for sound in a one-dimensional non-uniform mean flow. Flow invariants are obtained for the ODE with varying coefficients. Asymptotic expansion is used to get the first-order correction to the compact model. Distributed length changes the resonant frequencies and their growth rates. An entropy-dependent boundary condition results in different thermoacoustic modes. Full-range predictions are achieved by combining a modified WKB method.