Research on the Influence of the Unit Reynold’s Number on the Characteristics of N-Waves at M = 2.5

This paper presents the results of studying the features of the development of weak shock waves generated by a twodimensional roughness on the wall of the working part of a supersonic wind tunnel in a free flow at a Mach number of 2.5. The measurements were performed with a constant resistance thermoanemometer. It is shown that a twodimensional sticker induces weak shock waves into the free flow. They cause distortion of the average flow, the shape of which corresponds to the N-wave. High-intensity pulsations were recorded in the region of passage of a pair of weak shock waves. With an increase in the unit Reynolds number, the level of distortions of the average flow remains practically constant, but an increase in nonstationary disturbances is observed. It was found that the greatest increase in pulsations caused by Mach waves is observed in the area of the maximum gradient of the average flow. It is found that an increase in the number ReLleads to an expansion of the frequency range of unstable disturbances generated by a pair of weak shock waves.

Steepened Mach waves near supersonic jets: study of azimuthal structure and generation process using conditional averages

The azimuthal structure and the generation process of steepened acoustic waves are investigated in the near field of temporal round jets at Mach numbers of 2 and 3. Initially, the shear layers of the jets are in a laminar state and display instability waves whose main properties are close to those predicted from linear temporal analysis. Then, they transition to a turbulent state and generate high-intensity Mach waves displaying sharp compressions typical of those recorded for jets producing crackle noise. These waves are first shown to be poorly reproduced when only the axisymmetric mode is considered, but to be well captured with the first five azimuthal modes. Their generation process is investigated by performing conditional averages of the flow and acoustic fields triggered by the detection of intense positive pressure peak close to the jets. No steepened waves are visible in the conditionally averaged pressure profiles when the procedure involves only one azimuthal mode at a time. However, sharp compressions are obtained based on the first five modes taken together. In that case, the steep compressions are correlated over a limited portion of the jet circumference and are steeper as more azimuthal modes are considered. Moreover, a direct link is established between the steepened waves and the supersonic convection of large-scale coherent flow structures located in the supersonic core of the jets. This indicates that these waves constitute an extreme, nonlinear case of Mach wave radiation by these structures. In addition, the capacity of flow structures to generate sharp, steepened waves is related to their shapes. More particularly, flow structures with a large extent in the radial direction are shown to produce stronger and steeper Mach waves than those that are elongated in the flow direction.

Size and shape of shock waves and slipline for Mach reflection in steady flow

For Mach reflection in steady supersonic flow, the slipline and reflected shock wave from the triple point are disturbed by secondary Mach waves generated over the slipline and by the expansion fan from the rear wedge corner. Analytical expressions for the shape of the curved slipline and reflected shock wave are derived in this paper. It is found that, due to transmitted expansion waves from the expansion fan, the slipline has a slope discontinuity at the turning point, i.e., the intersection point of the slipline and the leading characteristics of the transmitted expansion wave. The hypothetical shock wave calculated by considering this slope discontinuity as flow deflection angle matches a similar wave observed in numerical results by computational fluid dynamics, suggesting the existence of a weak shock wave from this turning point. The effects of the secondary Mach waves upstream of the turning point and of the turning point weak shock wave mutually cancel out approximately so that the transmitted Mach waves can be approximated as straight characteristic lines. This simplification leads to a fast analytical model which can predict the Mach stem height and shape of the slipline and reflected shock wave with increasing accuracy for the decreasing deflection angle of the slipline at the triple point. The slipline slope discontinuity at the turning point and the hypothetical turning point weak shock wave are new phenomena found in this work.