Zeldovich–Taylor flow (also known as Zeldovich–Taylor expansion wave) is the fluid motion of gaseous detonation products behind Chapman–Jouguet detonation wave. The flow was described independently by Yakov Zeldovich in 1942 and G. I. Taylor in 1950, although G. I. Taylor carried out the work in 1941 that being circulated in the British Ministry of Home Security. Since naturally occurring detonation waves are in general a Chapman–Jouguet detonation wave, the solution becomes very useful in describing real-life detonation waves.
Mathematical description Consider a spherically outgoing Chapman–Jouguet detonation wave propagating with a constant velocity D {\displaystyle D} . By definition, immediately behind the detonation wave, the gas velocity is equal to the local sound speed c {\displaystyle c} with respect to the wave. Let v ( r , t ) {\displaystyle v(r,t)} be the radial velocity of the gas behind the wave, in a fixed frame. The detonation is ignited at t = 0 {\displaystyle t=0} at r = 0 {\displaystyle r=0} . For t > 0 {\displaystyle t>0} , the gas velocity must be zero at the center r = 0 {\displaystyle r=0} and should take the value v = D − c {\displaystyle v=D-c} at the detonation location r = D t {\displaystyle r=Dt} . The fluid motion is governed by the inviscid Euler equations
∂ ρ ∂ t + v ∂ ρ ∂ r = − ρ ( ∂ v ∂ r + 2 v r ) , ∂ v ∂ t + v ∂ v ∂ r = − 1 ρ ∂ p ∂ r , ∂ s ∂ t + v ∂ s ∂ r = 0 {\displaystyle {\begin{aligned}{\frac {\partial \rho }{\partial t}}+v{\frac {\partial \rho }{\partial r}}&=-\rho \left({\frac {\partial v}{\partial r}}+{\frac {2v}{r}}\right),\\{\frac {\partial v}{\partial t}}+v{\frac {\partial v}{\partial r}}&=-{\frac {1}{\rho }}{\frac {\partial p}{\partial r}},\\{\frac {\partial s}{\partial t}}+v{\frac {\partial s}{\partial r}}&=0\end{aligned}}}
… excerpt ends here. Continue reading the full article.
