AN EXACT SOLUTION FOR AXIAL-FLOW IN CYLINDRICALLY SYMMETRICAL, STEADY-STATE DETONATION IN POLYTROPIC EXPLOSIVE WITH AN ARBITRARY RATE OF DECOMPOSITION

Methods of differential geometry and Bernoulli's equation, written as B=O, are used to develop a new approach for constructing an exact solu tion for axial flow in a classical, two-dimensional, ZND detonation wa ve in a polytropic explosive with an arbitrary rate of decomposition. This geometric approach is fundamentally different from the traditiona l approaches to this axial flow problem formulated by Wood and Kirkwoo d (WK) and Fickett and Davis (FD), and gives equations for the axial p article velocity (u), the sound speed (c), the pressure (p), and the d ensity (p), that are expressed in terms of the detonation velocity (D) , the extent of decomposition (lambda), the polytropic index (K), and two nonideal parameters epsilon(3) and epsilon(1), and reduce to the e quations for steady-state, one-dimensional detonation as epsilon(3) an d epsilon(1) approach zero. In contrast to the FD approach, the equati ons for u and c are obtained from first integrals of a tangent vector (A) over tilde on (u,c,lambda) space, and the invariant condition, (A) over tilde B=aB=O, bypasses the FD eigenvalue problem by defining eps ilon(3) in terms of the detonation velocity deficit D/D-infinity and K . In contrast to the WK approach, the equations for p and p are obtain ed from equations expressing the conservation of axial momentum and en ergy. Because the equations for these flow variables are derived witho ut using the conservation of mass, the axial radial particle velocity gradient (w(r)(a)) associated with the flow can be obtained from the c ontinuity equation without making approximations. The relationship bet ween epsilon(1) and epsilon(3) that closes the solution is obtained fr om equations expressing constraints imposed on the axial flow at the s hock front by the axial and radial momentum equations, the curved shoc k and the decomposition rate law, and a particular solution is constru cted from the epsilon(1)-epsilon(3) relationship determined by a presc ribed rate law and value of K. Properties of particular solutions are presented to provide a better understanding of two-dimensional detonat ion, and a new axial condition for detonation failure is used to show that detonation failure can occur before the curve relating D/D-infini ty to the axial radius of curvature of the shock (S-a) becomes infinit e.