In this study, we introduce a deep generative model, named Multi-Species Generative Adversarial Network (MS-GAN), which is developed to extract the low-dimensional manifold of three-dimensional multi-species surfaces. In the development of MS-GAN, we extend the free-form deformation by incorporating principal component analysis to increase the non-linear deformation ability while maintaining geometric smoothness. The implicit information of multiple baselines is embedded in the feature extraction layers, to enhance the diversity and parameterization of multi-species dataset. Furthermore, Wasserstein GAN with a gradient penalty is used to ensure the stability and convergence of the training networks. Two experiments, ruled surfaces and propeller blade surfaces, are performed to demonstrate the advantages and superiorities of MS-GAN.

Rectangular nozzles are increasingly valued in military aircraft design due to their excellent thrust vectoring control and stealth performance. However, twin jet coupling remains an attractive aero-acoustic problem as its noise characteristics and sound generation mechanism are still not well understood. In this paper, numerical simulations of supersonic under-expanded single/twin rectangular jets are conducted. High-precision numerical schemes and implicit large eddy simulation methods are used, and the predicted flow and acoustic characteristics of the single jet show good agreement with the experimental results. The findings indicate that when twin jet spacing is 3.5h, the interaction between twin jets has little impact on the internal structure and shear layer development of the jets. There are significant differences in the overall sound pressure level distribution and the noise directivity between single and twin jets. Compared with the single jet, twin jets exhibit a slightly reduced screech frequency, and a significantly increased intensity. Fourier mode decomposition and spectral proper orthogonal decomposition are employed to extract coherent structures in the flow field. A helical mode is revealed in the single jet, while in the twin jets, the mode switches to a flapping mode along the minor axis with the two jets oscillating in phase. Modal analysis further highlights the relationship between changes in screech frequency and intensity and the shift in the sound source location.

Implicit large-eddy simulation of an over-expanded screeching rectangular jet is performed with a seventh-order finite difference scheme. Good agreement is found between the predicted flow- and acoustic fields with the experimental observations. Fourier decomposition, phase-averaging analysis and Spectral Proper Orthogonal Decomposition (SPOD) are used to investigate the origin of the screech, the shock leakage during the shear-layer flapping, and the distinguishing fluctuating characteristics in the minor- and major-axis plane of the rectangular jet. It finds that the screech is radiated from the end of the forth shock cell, where the interaction of the shock waves with the shear layer causes periodic leakages of shock-wave tips in the minor-axis plane, resulting in the generation of intense acoustic waves in the surrounding air. An obvious flapping mode at the same frequency of the screech is captured in the minor-axis plane and dominates the dynamic motions of the rectangular jet. The SPOD modes of pressure and velocity fluctuations at the screech frequency help to reveal the relationship between the screech generation and the coherent structures.