Numerical and analytical modelling of entropy noise in a supersonic nozzle with a shock

Analytical and numerical assessments of the indirect noise generated through a nozzle are presented. The configuration corresponds to an experiment achieved at DLR by Bake et al. [F. Bake, C. Richter, B. Mühlbauer, N. Kings, I. Röhle, F. Thiele, B. Noll, The Entropy Wave Generator (EWG): A reference case on entropy noise, Journal of Sound and Vibration 326 (2009) 574-598] where an entropy wave is generated upstream of a nozzle by an electrical heating device. Both 3-D and 2-D axisymmetric simulations are performed to demonstrate that the experiment is mostly driven by linear acoustic phenomena, including pressure wave reflection at the outlet and entropy-to-acoustic conversion in the accelerated regions. Moreover, the spatial inhomogeneity of the upstream entropy fluctuation has no visible effect for the investigated frequency range (0-100 Hz). Similar results are obtained with a purely analytical method based on the compact nozzle approximation of Marble and Candel [F. Marble, S. Candel, Acoustic disturbances from gas nonuniformities convected through a nozzle, Journal of Sound and Vibration 55 (1977) 225-243] demonstrating that the DLR results can be reproduced simply on the basis of a low-frequency compact-elements approximation. Like in the present simulations, the analytical method shows Corresponding author. Email addresses: [email protected] (M. Leyko), [email protected] (S. Moreau), [email protected] (F. Nicoud), [email protected] (T. Poinsot) Preprint submitted to Elsevier March 12, 2010 ha l-0 08 02 47 8, v er si on 1 17 O ct 2 01 3 Author manuscript, published in "Journal of Sound and Vibration 330, 16 (2011) 3944-3958" DOI : 10.1016/j.jsv.2011.01.025