摘要
本文在W-K模型的基础上,采用自然坐标系,导出了二维定常爆轰波的声速面条件,即二维C-J条件。经典的一维C-J条件和准一维C-J条件是它的两个特例。声速面条件又可作为判定流线形状正确与否的必要条件。通过分析讨论,认为在二维定常爆轰波的有效反应区中,流线应呈先向内,后向外偏转的波纹型形。在确定声速面形状的同时,有效反应区的流场分布也随之确定。
In this paper, we extend W-K model to the whole flow field of two-dimen- sional ( 2 -D) steady-state detonation wave (SSDW). Let a natural coordinate system be attached to the shock front which travels with steady velocity D as shown in Fig. 1. we can get the following relationship on the sonic surfaceU=C (5)Eqs. (5) and (6) define the sonic surface condition which must be satisfied for a 2-D SSDW.For 1-D plane SSDW. we have θ=0 and θ/ n= 0, so λ/ 1 must be zero. Thus the sonic surface condition turns out to be the classical C-J condition. Dealing with the flow field close to the axis. Wood and Kirkwood and others pointed out that besides U=c, the condition σ λ/ t= 2 ω/ r must be satisfied at the sonic point, which is called quasi-1-D C-J condition.It can be easily shown that σ λ/ 1=( 2/U) ω/ r=2 θ/ r, sinθ-θ, θ/r- θ/ r and d θ/ n- θ/ r in the neighbourhood of the symmetry axis. Thus we can get the same relation from Eq. (6). However Eq. (6) is a more general one and not limited to the near axis flow. For this reason. we call the sonic surface condition the 2-D C-J condition.At the same time, the sonic surface condition is a necessary one to judge whether the shape of a streamline is right or not. Through analysis and discussion. we hold that the streamline in the effective reaction zone of 2-D SSDW must take a corrugated shape which is deflected toward symmetry axis at first and toward outside near the sonic surface range. When the sonic surface is determined, the distribution of the flow field ineffective reaction zone of 2-D SSDW can also be determined.
出处
《爆炸与冲击》
EI
CAS
CSCD
北大核心
1989年第1期11-16,共6页
Explosion and Shock Waves
关键词
爆轰波
C-J条件
流线
二维波
2-D detonation, detonation theory, diameter effect, streamline.
