Approximate Analytical Models of Shock-Wave Structure at Steady Mach Reflection

In this study, we obtain the comparative analysis of methods of quick approximate analytical prediction of Mach shock height in planar steady supersonic flows (for example, in supersonic jet flow and in narrowing channel between two wedges), that are developed since the 1980s and being actively modernized now. A new analytical model based on flow averaging downstream curved Mach shock is proposed, which seems more accurate than preceding models, comparing with numerical and experimental data.

Investigation of the stability of transverse hydrogen injection combustion caused by plate vibration using the dynamic mode decomposition method

This article investigated the stability of transverse hydrogen injection combustion caused by the plate vibration. The finite-rate method is used to simulate the combustion. The unsteady flow field in the unstable phase of combustion is extracted. The unstable mode of the shock wave structure and the flame structure during the stage of combustion instability, the spatial and temporal characteristics of the dominant modes, as well as their stability are analyzed based on the dynamic mode decomposition (DMD) method. The results indicate that, according to the sequence of energy, the extracted first six orders modes of the shock wave structure and the flame structure have relatively low frequency with a negative growth rate and small numerical value, which presents a trend of weak convergence. The characteristics of the dominant structure of DMD modes show that the plate vibration has great effects on the reflected shock wave structure near the plate and on the upper wall surface, as well as the flame structure near the plate. According to the sequence of the mode energy and the growth rate, respectively, the extracted first six orders modes have relatively high frequency. Simultaneously, the structures of the modes extracted by the sequence of mode energy are more regular, while those extracted by the sequence of growth rate are more disorderly. The unstable shock wave structure is mainly manifested by the reflected shock wave in the vibration region and the shock wave structure reflected by the upper wall surface. The unstable flame structure is mainly concentrated near the vibration region and downstream areas.

Nematic Dispersive Shock Waves from Nonlocal to Local

The structure of optical dispersive shock waves in nematic liquid crystals is investigated as the power of the optical beam is varied, with six regimes identified, which complements previous work pertinent to low power beams only. It is found that the dispersive shock wave structure depends critically on the input beam power. In addition, it is known that nematic dispersive shock waves are resonant and the structure of this resonance is also critically dependent on the beam power. Whitham modulation theory is used to find solutions for the six regimes with the existence intervals for each identified. These dispersive shock wave solutions are compared with full numerical solutions of the nematic equations, and excellent agreement is found.

Operation Rule of Steam Ejector and Influence Analysis of Ejection Position

In order to analyze the operation rule of steam ejector used in sewage treatment field, this paper established the mathematical model of steam ejector, simulated the internal flow state, analyzed the influence rule of external parameters on the performance of steam ejector, and analyzed the influence rule of ejector position on the water production ratio of steam ejector multi-effect evaporation desalination system. The research results show that under the same steam ejector structure, as the pressure of the working steam increases, the mixing and disturbance of the working steam and the ejected steam become more intense, and the diamond shock wave structure increases. As the pressure of the ejected steam increases, the momentum exchange effect of the shear blending of working steam and ejected steam is accelerated, and the speed increase rate becomes larger, and the diamond shock wave structure gradually gathers toward the nozzle. As the pressure rise of the ejected steam inlet and outlet increases, the backflow phenomenon near the wall in the mixing chamber becomes more serious, and the diamond shock wave structure is reduced. With the forward movement of the ejector position of the thermal steam compressor, the pressure of the ejected steam increases, and the water production ratio of the steam ejector multi-effect evaporation seawater desalination system shows a downward trend. Therefore, choosing appropriate working condition parameters can effectively improve the working performance of steam ejector and improve its operating efficiency in the field of sewage treatment.

Exact solutions of (2 + 1)-Ablowitz-Kaup-Newell-Segur equation

The aim of the present study is to obtain different types of hyperbolic type solutions of the (2+1)-Ablowitz-Kaup-Newell-Segur (AKNS) equation. In order to construction exact solutions of AKNS equation, (1/G′)-expansion method is successfully applied. At the end of this application, singular soliton wave with considerable importance for the shock wave structure and asymptotic behavior employees have emerged. By giving arbitrary values to the constants in the solutions obtained, 3D, 2D and contour graphics are presented. The method used in this article can be used in other nonlinear differential equations (NPDEs) as it is reliable, easy and effective. Ready package programs are used to solve complex and difficult processes in this study.