Numerical application of additive Runge-Kutta methods on detonation interaction with pipe bends

A detailed reaction model comprised of 9 species and 48 reactions is employed in simulating two-dimensional cellular detonations propagating through smooth pipe bends in a stoichiometric H₂/O₂ mixture diluted by Argon. Additive Runge-Kutta (ARK) methods are applied to solve the stiff reactive Euler equations, in which the stiff and non-stiff terms are solved implicitly and explicitly. The numerical results indicate that, as the regular cellular detonation wave propagating through the bend section, the diffraction near the inner wall causes an increase in detonation cell size while the detonation reflection occurring on the bottom wall leads to a decrease in cell size. In addition, an expansion wave is generated continuously. The expansion wave causes the failure as well as the partial failure of the detonations near the inner and outer walls, respectively. On the contrary, the transverse re-initiation waves evolve into a detonation in the decoupling zone just downstream of the bend outlet owing to continuous compression imposed by other transverse waves propagating right behind. Meanwhile, there exists a transition length after the detonation propagating out of the bend and entering the sloped tube section.