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This paper presents an impressive design of a convergent divergent (C-D) nozzle using the method of characteristics for a Mach number 2 test section. The nozzle’s geometry was meticulously crafted in SolidWorks, and its performance was evaluated through a CFD simulation in Ansys Fluent R22 software. Results showed excellent agreement between the simulation and analytical data, with the Mach number ranging from 1.78 to 2. The study also compared turbulence modeling techniques, concluding that the k-omega model produced superior results. The supersonic wind tunnel achieved remarkable efficiency, completing a run at 1.8 Mach number in just 6 seconds. Overall, the study showcased exceptional accuracy and meticulousness.

Abstract: We have done two-dimensional simulations of the Kelvin–Helmholtz instability (KHI) with super-sonic flow using the CIP method. The linear analyses of a simple uniform density case show that the KHI cannot grow vigorously when the velocity jump is more than twice the sound speed (when the flow speed relative to the vortex is super-sonic). In this study, by situating a high density contrast across the shear layer, we set the flow in only one of the sides to be super-sonic and then show that the KHI does grow and rolls up a vortex. The formation of a shock is essential for the KHI vigorous growth and the structure of the vortex is strongly influenced by the shock geometry. The results should have substantial implications to velocity shear layer dynamics involving large density jump, such as planetary magnetospheric boundary layers. [Copyright &y& Elsevier]

Part I [Int. J. Solids Struct., 39, 1165–1182] gives exact general solutions for steady dynamic extension by a semi-infinite crack along the interface of dissimilar orthotropic/transversely isotropic half-spaces under in-plane loading. Crack speed is any constant value, and results are valid for all six possible relations between the four body wave speeds. These results are applied here to sub-critical interface crack extension, and to debonding from a rigid half-space at any constant speed.The former case demonstrates well-known phenomena––the minimum Rayleigh speed is critical, and complex conjugate eigenvalues cause the crack edge oscillatory/square-root singular behavior that implies interpenetration. Calculations for representative materials show that eigenvalue and stress intensity factor amplitude variation with crack speed is small except near the critical value.Results for the latter case complement those of other recent studies: Singular behavior vanishes for super-critical/sub-sonic crack speeds, although oscillations remain. For trans-sonic crack speeds, eigenvalues are real, singular behavior is no longer square-root, and interpenetration can still occur below a critical speed. Lines of displacement gradient discontinuity radiate from the crack edge, but can vanish at a critical speed. Calculations show that eigenvalue variation with crack speed is more pronounced than in the first case. [Copyright &y& Elsevier]

A semi-infinite crack along the interface of two dissimilar half-spaces extends under in-plane loading. Each half-space belongs to a class of orthotropic or transversely isotropic elastic materials, the crack can extend at any constant speed, and all six possible relations between the four body wave speeds are considered. A steady dynamic situation is treated, and exact full displacement fields derived. A key step is a factorization that produces, despite anisotropy, simple solution forms and compact crack speed-dependent functions that exhibit the Rayleigh and Stoneley speeds as roots. These roots are calculated for various representative bimaterials.Closed-form crack opening displacement gradient and interface stress fields are also derived from a general set of coupled singular integral equations. The equation eigenvalues can, depending on crack speed, be complex/imaginary conjugates, purely real, or zero. This suggests possibilities observed in other studies: oscillations and square-root singular behavior at the crack edge, non-singular behavior, singular behavior not of square-root order, and the radiation of displacement gradient discontinuities at crack speeds beyond the purely sub-sonic range.These possibilities are explored further in terms of two important special cases in Part II of this study [Int. J. Solids Struct., 39, 1183–1198]. [Copyright &y& Elsevier]