In this paper, the shear horizontal (SH) wave scattering by a circular pipeline in an inhomogeneous concrete with density variation is studied. A model of inhomogeneous concrete with density variation in the form of a polynomial-exponential coupling function is established. By using the complex function method and conformal transformation, the incident and scattering wave field of SH wave in concrete are obtained, and the analytic expression of dynamic stress concentration factor (DSCF) around the circular pipeline is given. The results show that the inhomogeneous density parameters, the wave number of the incident wave and the angle of the incident wave in concrete are important factors affecting the distribution of dynamic stress around the circular pipe in concrete with inhomogeneous density. The research results can provide a theoretical reference and a basis for analyzing the influence of circular pipeline on elastic wave propagation in an inhomogeneous concrete with density variation.

With the advancement of aerospace technology, full-scale wind tunnel testing has become a crucial approach to overcoming bottlenecks in hypersonic technology. The design of ultra-large, high-performance nozzles stands out as one of the core challenges. This paper focuses on a profiling design method for supersonic/hypersonic nozzles with interchangeable throats at the 6 m outlet scale, addressing issues such as significant boundary layer effects and difficulties in achieving variable Mach numbers due to the large dimensions. An empirical boundary layer correction method is proposed to efficiently compensate for viscous effects. By parameterizing and controlling the Mach number distribution along the nozzle axis using cubic B-spline curves and applying the method of characteristics for accurate inviscid supersonic flow field computation, the nozzle profile is optimized. To enable multi-Mach-number operation, a design strategy is adopted, where the high-Mach-number profile serves as the baseline, and the low-Mach-number throat section is inversely designed to ensure a smooth transition between multi-Mach nozzles and a shared expansion section. Using this approach, nozzle profiles for Mach numbers 4, 5, and 6 were successfully designed and validated through fully viscous CFD simulations. Results demonstrate that under all design conditions, a wide and uniform core flow region forms at the nozzle exit, with no strong shock waves present in the flow field. This study confirms the effectiveness and reliability of the integrated design method for large-scale interchangeable-throat nozzles, providing important theoretical foundation and technical support for the future development of advanced large-scale hypersonic wind tunnels.