Equations of Shock Dynamics for a Nonuniform Quiescent Gas Ahead of a Shock Wave

Author(s):  
Zhaoyuan Han ◽  
Xiezhen Yin
Keyword(s):  

In this paper, a new numerical method for calculating the motion of shock waves in two and three dimensions is presented. The numerical method is based on Whitham’s theory of geometrical shock dynamics, which is an approximate theory that determines the motion of the leading shockfront explicitly. The numerical method uses a conservative finite difference discretization of the equations of geometrical shock dynamics. These equations are similar to those for steady supersonic potential flow, and thus the numerical method developed here is similar to ones developed for that context. Numerical results are presented for shock propagation in channels and for converging cylindrical and spherical shocks. The channel problem is used in part to compare this new numerical method with ones developed earlier. Converging cylindrical and spherical shocks are calculated to analyse their stability.


1997 ◽  
Vol 9 (10) ◽  
pp. 3058-3068 ◽  
Author(s):  
J. E. Cates ◽  
B. Sturtevant

Shock Waves ◽  
2022 ◽  
Author(s):  
M. Rezay Haghdoost ◽  
B. S. Thethy ◽  
M. Nadolski ◽  
B. Seo ◽  
C. O. Paschereit ◽  
...  

AbstractMitigation of pressure pulsations in the exhaust of a pulse detonation combustor is crucial for operation with a downstream turbine. For this purpose, a device termed the shock divider is designed and investigated. The intention of the divider is to split the leading shock wave into two weaker waves that propagate along separated ducts with different cross sections, allowing the shock waves to travel with different velocities along different paths. The separated shock waves redistribute the energy of the incident shock wave. The shock dynamics inside the divider are investigated using numerical simulations. A second-order dimensional split finite volume MUSCL-scheme is used to solve the compressible Euler equations. Furthermore, low-cost simulations are performed using geometrical shock dynamics to predict the shock wave propagation inside the divider. The numerical simulations are compared to high-speed schlieren images and time-resolved total pressure recording. For the latter, a high-frequency pressure probe is placed at the divider outlet, which is shown to resolve the transient total pressure during the shock passage. Moreover, the separation of the shock waves is investigated and found to grow as the divider duct width ratio increases. The numerical and experimental results allow for a better understanding of the dynamic evolution of the flow inside the divider and inform its capability to reduce the pressure pulsations at the exhaust of the pulse detonation combustor.


2020 ◽  
Vol 172 ◽  
pp. 134-139 ◽  
Author(s):  
N. Brahmi ◽  
A. Hadjadj ◽  
V. Soni ◽  
A. Chaudhuri

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