On the Propagation and Structure of the Blast Wave, I

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Concerning blast waves with front surfaces of plane, cylindrical and spherical shape, the propagation velocity $U$ and the distribution of hydrodynamical quantities are discussed. The solutions are constructed in the form of power series in $(C/U)^{2}$, where $C$ is the sound velocity of undisturbed fluid. Especially $R$, the distance of shock front from the charge, is represented as, $\left(\frac{C}{U}\right)^{2}\left(\frac{R_{0}}{R}\right)^{\alpha+1}{=}J_{0}\left[1+\lambda_{1}\left(\frac{C}{U}\right)^{2}+\frac{1}{2}\lambda_{2}\left(\frac{C}{U}\right)^{4}+\cdot\cdot\cdot\cdot\cdot\cdot\right]$, where $R_{0}$ is the characteristic length related to the energy of explosion, $J_{0}$ and $\lambda_{i}$ are constants, and $\alpha{=}0$,1,2 correspond to plane, cylindrical and spherical case, respectively. In this paper the first approximations for $\alpha{=}0$,1 are discussed (The case $\alpha{=}2$ has been discussed by G. I. Taylor). The solution is obtained numerically for the case of the adiabatic index $\lambda{=}1.4$. The approximate solution is also considered. Using these solutions, $J_{0}$ is found to be: \includegraphics{dummy.eps} The second approximation will appear in part II to be published subsequently.
社団法人日本物理学会の論文
1953-09-25