Linear models for the shock cell structure of supersonic jets with noncircular exit geometries

Broadband shock associated noise is generated by the interaction of the large-scale structures in the jet mixing layer and the quasi-periodic shock cell structure of the jet. This dissertation concerns the development of models to predict the shock structure of imperfectly expanded supersonic jets with noncircular exit geometry. Numerical methods to obtain solutions for these models are also developed.; Two different models to predict the shock cell structure are developed using a linearized analysis. The Vortex-Sheet Shock Cell Model assumes that the jet mixing layer can be represented by a vortex-sheet. The boundary element method is used to predict the shock spacing and the frequency of the screech tones. The results are compared with analysis and experiment and it is shown that the agreement is good.; The second model, the Finite Thickness Shear Layer Model, takes into account the finite thickness of the jet shear layer and the effects of the turbulence. Two different numerical schemes are developed to obtain predictions using this model. In the first method, a body-fitted coordinate system is used to set up the governing equations. The numerical method involves the integration of the linearized equations through the shear layer. The variation of the pressure fluctuation with downstream distance is obtained for circular jets and an elliptic jet of aspect ratio two.; The second numerical method uses a series of conformal mappings to transform the physical space to a rectangular computational domain. In the computational space, the flow variables are represented in a series form using a hybrid pseudo-spectral approximation. This method is used to obtain predictions of the shock cell structure for an elliptic jet of aspect ratio two.; The results obtained are in reasonable agreement with the experimental data. This is especially true for the gross features of the shock cells, i.e. the shock cell spacings and the amplitudes. The fine structure seen in the experimental data is also reproduced by the model. It is shown that beyond the first few shock cells, the shock structure can be approximated by a single mode.