Jack Ziegler

An adaptive high-order hybrid scheme for compressive, viscous flows with detailed chemistry

A hybrid weighted essentially non-oscillatory (WENO)/centered-difference numerical method, with low numerical dissipation, high-order shock-capturing, and structured adaptive mesh refinement (SAMR), has been developed for the direct numerical simulation of the multicomponent, compressible, reactive Navier–Stokes equations. The method enables accurate resolution of diffusive processes within reaction zones. The approach combines time-split reactive source terms with a high-order, shock-capturing scheme specifically designed for diffusive flows. A description of the order-optimized, symmetric, finite difference, flux-based, hybrid WENO/centered-difference scheme is given, along with its implementation in a high-order SAMR framework. The implementation of new techniques for discontinuity flagging, scheme-switching, and high-order prolongation and restriction is described. In particular, the refined methodology does not require upwinded WENO at grid refinement interfaces for stability, allowing high-order prolongation and thereby eliminating a significant source of numerical diffusion within the overall code performance. A series of one-and two-dimensional test problems is used to verify the implementation, specifically the high-order accuracy of the diffusion terms. One-dimensional benchmarks include a viscous shock wave and a laminar flame. In two-space dimensions, a Lamb–Oseen vortex and an unstable diffusive detonation are considered, for which quantitative convergence is demonstrated. Further, a two-dimensional high-resolution simulation of a reactive Mach reflection phenomenon with diffusive multi-species mixing is presented.

Shock Wave–Boundary Layer Interaction from Reflecting Detonations

The present work is concerned with the differences in how shock and detonation waves inside pipes or ducts reflect from closed ends. One of the motivations for the present study is that the large pressure rise associated with a detonation poses a hazard to pipes that contain flammable mixtures [1]. A detonation impinging normally on a planar wall creates a reflected shockwave to bring the flowat the wall to rest [2] and produces pressures 2.4 times that of an incident Chapman-Jouguet (CJ) detonation [3]. In examining the material deformation produced by reflected detonation loading [4] an inconsistency was discovered between the measured pressure jump across the reflected shock wave and the measured speed of the shock, with the measured pressure being as much as 25% below that predicted by the shock jump relations for the given shock speed. This was theorized to be due to bifurcation of the reflected shock wave associated with shock-wave boundary layer interaction.