The stability of expanding reactive shocks in a van der Waals fluid
Abstract
Despite the extensive literature accumulated since the pioneering works of D'yakov and Kontorovich in the 1950s, the stability of steady shocks is still an open question when realistic boundary conditions are accounted. The consideration of a supporting mechanism, which is indeed a necessary condition for shock steadiness, modifies the perturbation shock dynamics in the unstable range. The Noh problem is a suitable example to form steady expanding shocks. This configuration is of great interest to the high-energy-density-physics community because of its direct application to inertial confinement fusion and astrophysics, for which the stagnation of a supersonically converging material via an accretion shock front is ubiquitous. In this work, we extend the generalized Noh problem, both base-flow solution and linear stability analysis, to conditions where endothermic or exothermic transformations undergo across the shock. Within the spontaneous acoustic emission conditions found for a van der Waals gas [J. W. Bates and D. C. Montgomery, “The D'yakov-Kontorovich instability of shock waves in real gases,” Phys. Rev. Lett. 84, 1180 (2000)], we find that cylindrical and spherical expanding shocks become literally unstable for sufficiently high mode numbers. Counterintuitively, the effect of exothermicity or endothermicity across the shock is found to be stabilizing or destabilizing, respectively.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Apr 01, 2022
- Source ID
- 10.1063/5.0087073
Entities
People
- A. L. Velikovich
- Andrés Calvo-Rivera
- Cesar Huete
Organizations
- Ministry of Science, Innovation and Universities
- United States Naval Research Laboratory
- Universidad Carlos III de Madrid