Simplified Theory And Application Of Steep Shock Wave

The problem of steep shock wave is a common problem of rapid open channel, it is also one of the key points of designing high-speed flow. Flood discharge building always has shock waves in the corners, steep shock wave will cause uneven distribution of unit discharge and negative flow, if it is not controlled well, there will be great harm to the building, it will cause bad impact on building design, what's more, it will cause cavitation erosion, or even damage to buildings. At present, some relatively good theories of shock wave are Von Karman's flat shock wave Integral theory,Arthur.T.Ippen's ideal shock wave theory, but these two theories are very complex, difficult to solve, and very inconvenient in practical applications, so many experts and scholars make a lot of study separately and found different simplified calculation methods. The purpose of this paper is to find out a relatively simple and convenient theory to resolve the steep shock wave problem.This paper analyzed the process of calculating steep shock wave using Ippen's ideal shock wave equation,typical simplified equation,Hager's simplified equation and Brete's simplified equation, Hager's improved approximate simplified equation, Ning Lizhong's approximate analytical equation, Tian Shihao's equation and Fang Yanjun's equation, Liu Hansheng's simplified equation and Ni Hangen's simplified equation, Wang Ruyun's iterative equation. Based on Ippen's experiment, this paper calculated deflection angleβand water depth ratio h 2under different the application of the various experts and scholars of the jet blast to simplify the style of the different Fr1 andαusing each equation. Then made tables and figures to compare the calculated results and experimental value, the results showed that each theory can be used to calculate the steep shock wave in symmetric linear contraction channel. While Liu Hansheng's simplified equation is simple,convenient,accurate and suitable for applications. For the flat shock wave theory equation, the author calculated the shock wave in different flow condition diffusion channel using Karman's integral equation,Liu Hansheng's simplified equation of flat shock wave . by calculating boundary angleθ1,θ2,water depth h2 after wave and Fr2 after wave which are effected by shock wave, we found that it is clear, targeted, relatively convenient to calculate flat shock wave in diffusion side wall using Liu Hansheng's simplified equation of flat shock wave. The calculated results are basically the same with the results calculated by Karman's integral equation, which is relatively accurate.According to the analysis and comparison of Chapter two, we found that Liu Hansheng's two simplified theory of shock wave have high precision,convenient to calculate and suitable for engineering applications. Therefore, the authors carried out further research on Liu Hansheng's shock wave theory, in the third chapter, the author discussed ways of solve shock wave problems of various channels. By induction and conclusion, the author found out solution process of symmetric linear contraction channel problems, symmetric linear diffusion channel problems, non-symmetric linear contraction channel problems, curve side wall transition section problems, steep shock bend transition section problems of open channel, pointed out design methods of various channels and using examples to illustrate the calculation, design process.