The shock-cell structures and screech tone frequencies of rectangular and non-axisymmetric supersonic jets

• Published in: Journal of sound and vibration Vol. 121; no. 1; pp. 135 - 147
• Main Author: Tam, C.K.W.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 22.02.1988; Elsevier
• Subjects: Compressible flows; shock and detonation phenomena; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Physics; Acustical wave; Convergent divergent nozzle; Frequency; Supersonic jet; Shock wave; Rectangular nozzle
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/S0022-460X(88)80066-X

The screech tone frequencies and shock cell structures of non-axisymmetric supersonic jets from convergent-divergent nozzles operating at off-design conditions are investigated. For the purpose of providing a simple yet fairly accurate first order estimate of the gross features of these shock structures and screech tone frequencies, a linear shock cell model is developed. In the model the mixing layer of the jet is approximated by a vortex sheet. It is shown that the model problem for a jet with arbitrary cross-sectional geometry can be solved by eigenfunction expansion. In this paper the associated eigenvalue problems for rectangular and elliptical jets are solved and explicit shock cell structure solutions for these jets are found. To test the validity of the model the theoretical shock cell spacings are compared with the experimental measurements of Powell [1] and Hammitt [2]. Good agreements are obtained over a wide range of Mach number. The shock cell spacing formula is then used to compute the screech tone frequencies of rectangular jets by incorporating it into the weakest link theory of Tam, Seiner and Yu [3]. The calculated tone frequencies are found to agree favorably with the measurements of Powell [4] and Krothapalli et al. [5] over the Mach number range of 1·15 to 1·80. The present theory is simple but admittedly crude. If a more accurate description of the shock cell structures of non-axisymmetric supersonic jets is desired a multiple-scales model following the recent work of Tam, Jackson and Seiner [24] may be constructed. In this case the present vortex sheet model solution could be used as the starting solution (at the nozzle exit) of such a multiple-scales expansion. At the nozzle exit region the mixing layers of the jet is usually fairly thin.