One- and Three-Dimensional Wall Heat Flux Calculations in a O2/H2 System

Abstract

OVER the past several decades, considerable effort has been dedicated to model combustion in rocket chambers to understand and predict the conjugate heat transfer to the chamberwalls [1]. Validation of computational fluid dynamics (CFD) design tools requires, in turn, reliable experimental data assessment. This involves the need to acquire a comprehensive set of data in the same facility, including wall heat fluxes along with inflow measurements over a broad range of pressures [2]. The experimental data for CFD validation acquired to date were obtained from a range of facilities of different sizes, various internal geometry or fuel composition, and injection configurations [3–9]; therefore, wall heat fluxes were considerably different among these studies. The strength, the life cycle, and the cooling system effectiveness are highly dependent on heat transfer into and out of the system [10], and the number of studies addressing the heat transfer into the chamber walls are still inadequate. In a previous study, which was the first of its kind, Marshall et al. [11] obtained the heat flux measurements using Gordon heat flux gauges from coaxial temperature measurements that were placed along the chamber wall. The heat fluxes were, then, calculated by solving the transient axisymmetric heat flux equation. Conley et al. [12] calculated the heat fluxes from the temperature measurements at several longitudinal locations. In these studies, the heatfluxeswere calculated by solving the steady-state one-dimensional (1-D) heat conduction equation and adding a correction term to compensate the heat absorption by the chamberwalls. Thevery nature of heat transfer in the combustion chamber is, in fact, three-dimensional (3-D). Thus, calculation of heat fluxes based on a 1-D assumption may lead to errors. Vaidyanathan et al. [13] calculated wall heat fluxes by numerically solving the two-dimensional (2-D) unsteady heat conduction equation. Although more accurate when compared with 1-D assumption, the 2-D heat conduction assumption still does not take into account the longitudinal heat transfer. The current study is aimed at calculating the heat fluxes in the combustion chamber by numerically solving the 3-D heat conduction equation to assess the validity of 1-D unsteady heat conduction assumption in wall heat flux calculation. Hence, the data presented next include wall heat fluxes calculated from 3-D heat transfer assumption for a GO2=GH2 single-element shear coaxial injector at 37 bar.