Numerical simulation of spark and flame driven detonation transition in a duct with obstacles

Accurately predicting detonations remains a stringent test for computational fluid dynamics because the governing processes—unsteady shock formation, stiff chemical kinetics, and turbulence–combustion coupling—span six to eight orders of magnitude in space and time. This study assesses the fidelity of CONVERGE v4 equipped with its SAGE detailed-chemistry module and block-structured adaptive mesh refinement (AMR) for modelling detonations. The fully compressible Navier–Stokes equations are solved using the MUSCL with double limited step limiter convective flux scheme, a variable time-step algorithm initially at 0.01 ns allowing a maximum time-step of 1 ns, and 7 levels of AMR that reduce the minimum cell size to 8 μm in reaction zones. The computational domain is constrained by 2D boundary conditions applied on Z-normal faces, while X- and Y-normal boundaries are adiabatic slip walls with no shear stress or heat flux.

Canonical two-dimensional configurations—including a smooth channel and an obstacle-laden duct—are examined over an initial-pressure range of 1–20 bar. Two deflagration-to-detonation transition (DDT) pathways are compared: (i) direct spark ignition yielding an over-driven detonation that relaxes to Chapman–Jouguet (CJ) conditions, and (ii) laminar-flame acceleration past obstacles that evolves into a detonation. Key performance metrics—induction length, CJ state pressure and temperature, and cumulative exothermic energy release—are extracted and benchmarked against NASA CEA and SDToolbox predictions. Results show that AMR captures the induction layer with 5 % CJ-state error when 2 cells are used to capture the local induction length; the required resolution tightens from ≈0.125 mm at 1 bar to ≈10 μm at 20 bar. Energy-release trends scale nearly linearly with initial pressure.