Direct numerical simulation of a PMMA–GO₂ slab burner: Experimental validation and extension to Marxman theory

In this study, Polymethyl methacrylate slabs are burned in a pure oxygen environment and also modeled using direct numerical simulation (DNS) of the reacting Navier–Stokes equations. The DNS is validated against experiments using novel simultaneous non-intrusive temperature and velocity measurements. The experimental temperature profiles and 3D flame hulls are measured and reconstructed using two color pyrometry (TCP) from multiple high speed camera videos of different views. The stream-wise velocity fields above the slab burner are processed from the experimental images using a methodology similar to particle image velocimetry. The DNS data is processed in a similar manner using a novel virtual-TCP (VTCP) method for temperature and velocities condition on soot volume fraction. Comparison of time averaged DNS fuel regression rates, temperatures, and velocities agree reasonably well to the experiments indicating the DNS provides a faithful representation of the physics. The DNS data is then used to examine the assumptions made in Marxman's 1960’s analysis of an ablating reacting boundary layer. The analysis reveals that Marxman's assumed momentum profiles are not good approximations, due to the neglection of volumetric expansion from the reacting flame. Further investigation of the DNS also reveals the existence of self-similar solutions using a new set of conservative variables. A new similarity formulation is then derived by assuming that vertical and stream-wise mass flux, total enthalpy and mass fractions are functions of the normalized boundary layer height only. The chemical state solutions of the similarity problem are shown to agree reasonably to the DNS. Novelty and significance statement This study presents the DNS of a fuel slab burner experiment that, for the first time, allow for detailed examination of theories used in hybrid rocket propulsion. These theories originate from Marxman's early work in the 1960s and are still widely used today. The DNS shows the limitations of Marxman's theories and presents a new DNS guided similarity theory. In addition, this work presents a novel virtual two-color pyrometry (TCP) technique used in the DNS so direct comparisons to data may be conducted for model validation purposes. This approach avoids many of the pitfalls comparing DNS to non-intrusive TCP measurement techniques through temperature interpretation comparisons.