The approximate analytical solution for the propagation of gas ionizing cylindrical blast (shock) wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field is investigated. The axial and azimuthal components of fluid velocity are taken into consideration and these flow variables, magnetic field in the ambient medium are assumed to be varying according to the power laws with distance from the axis of symmetry. The shock is supposed to be strong one for the ratio C0Vs2${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ to be a negligible small quantity, where C 0 is the sound velocity in undisturbed fluid and V S is the shock velocity. In the undisturbed medium the density is assumed to be constant to obtain the similarity solution. The flow variables in power series of C0Vs2${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ are expanded to obtain the approximate analytical solutions. The first order and second order approximations to the solutions are discussed with the help of power series expansion. For the first order approximation the analytical solutions are derived. In the flow-field region behind the blast wave the distribution of the flow variables in the case of first order approximation is shown in graphs. It is observed that in the flow field region the quantity J 0 increases with an increase in the value of gas non-idealness parameter or Alfven-Mach number or rotational parameter. Hence, the non-idealness of the gas and the presence of rotation or magnetic field have decaying effect on shock wave.

中文翻译：

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旋转轴对称非理想气体中具有方位角或轴向磁场的电离冲击波背后的非定常流动的解析解

研究了旋转的轴对称非理想气体中具有方位角或轴向磁场的气体电离圆柱形爆炸（激波）波的近似解析解。考虑到流体速度的轴向分量和方位角分量，并假定这些流量变量，环境介质中的磁场根据幂律随距对称轴的距离而变化。比率C0Vs2 $ {\ left（\ frac {{C} _ {0}} {{V} _ {s}} \ right）} ^ {2} $可以忽略不计C 0是未受扰动的流体中的声速，而VS是冲击速度。在未受干扰的介质中，假定密度为常数以获得相似度解。展开幂函数为C0Vs2 $ {\ left（\ frac {{C} _ {0}} {{V} _ {s}} \ right）} ^ {2} $的流量变量以获得近似解析解。在幂级数展开的帮助下讨论了解的一阶和二阶近似。对于一阶近似，导出了解析解。在爆炸波后的流场区域中，一阶近似情况下的流量变量分布如图所示。可以看出，在流场区域中，量J 0随着气体非理想参数或Alfven-Mach数或旋转参数的值的增加而增加。因此，气体的非理想性以及旋转或磁场的存在会对冲击波产生衰减作用。在幂级数展开的帮助下讨论了解的一阶和二阶近似。对于一阶近似，导出了解析解。在爆炸波后面的流场区域中，一阶近似情况下的流量变量分布如图所示。可以看出，在流场区域中，量J 0随着气体非理想参数或Alfven-Mach数或旋转参数的值的增加而增加。因此，气体的非理想性以及旋转或磁场的存在会对冲击波产生衰减作用。在幂级数展开的帮助下讨论了解的一阶和二阶近似。对于一阶近似，导出了解析解。在爆炸波后的流场区域中，一阶近似情况下的流量变量分布如图所示。可以看出，在流场区域中，量J 0随着气体非理想参数或Alfven-Mach数或旋转参数的值的增加而增加。因此，气体的非理想性以及旋转或磁场的存在会对冲击波产生衰减作用。在爆炸波后面的流场区域中，一阶近似情况下的流量变量分布如图所示。可以看出，在流场区域中，量J 0随着气体非理想参数或Alfven-Mach数或旋转参数的值的增加而增加。因此，气体的非理想性以及旋转或磁场的存在会对冲击波产生衰减作用。在爆炸波后的流场区域中，一阶近似情况下的流量变量分布如图所示。可以看出，在流场区域中，量J 0随着气体非理想参数或Alfven-Mach数或旋转参数的值的增加而增加。因此，气体的非理想性以及旋转或磁场的存在会对冲击波产生衰减作用。