Numerical analysis of the quasi-steady-state method for the unsteady modeling of the solid-fuel scramjet

The solid-fuel (SF) scramjet is a promising concept for the hypersonic industry, though its feasibility is challenged by the complexity of its continuously changing combustor geometry. To address this challenge, some researchers have adopted the quasi-steady-state (QSS) method, which approximates the unsteady evolution of the engine by generating a sequence of static geometries and steady-state solutions. In this method, each subsequent geometry is derived by applying the computed local regression rate and an advancing time step. Despite its utility, no comprehensive comparison of QSS-derived results with experimental data across the entire combustor has been presented. This paper fills that gap by analyzing the evolution of the combustor geometry, regression rates, flow fields, and efficiency metrics. The study models the flow using the compressible Navier-Stokes and species transport equations, coupled with the shear stress transport (SST) k - ω turbulence model. Polymethyl methacrylate (PMMA) is used as the fuel, with the local regression rate calculated via an energy balance. A two-dimensional axisymmetric formulation is employed. The results show that the numerical geometries effectively capture the overall evolution of the combustor geometry, however, with some missed local features. Flight efficiency metrics demonstrate excellent agreement, maintaining small errors of less than 6% throughout the engine's operation. These findings validate the QSS method as a reliable numerical tool for preliminary analyses of different SF scramjet configurations. • Comparison of the quasi-steady-state numerical method with experimental data. • Absence of formation of irregularities along the fuel grain during simulation. • Errors smaller than 6% for flight efficiency metrics during functioning. • Finding of a new flow structure during functioning of the SF Scramjet.