Numerical Modelling of LOX Droplet Combustion in Hydrogen under Micro-gravity Conditions

Abstract

One of the most frequent liquid rocket propellant configurations is LOX/LH2. Specifically,since this fuel/oxidizer mixture produces an extremely high specific impulse (Isp) with only water vapor as an exhaust. This makes LOX combustion research critical for improving combustion efficiency and avoiding flame instabilities in the rocket engine’s combustion chamber. The spray dispersion method is used to inject liquid oxygen into the combustion chamber, whereas hydrogen enters the combustion chamber in a gas phase, as it is most likely to be pre-vaporized due to the regenerative cooling in the rocket nozzle. When the LOX droplets ignite, combustion happens between them and the surrounding hydrogen fuel environment. The essential building block of this process is considered for this study, which is a single LOX droplet with a surrounding hydrogen environment, in order to analyze this physical process in an optimum fashion. This study assumes a micro-gravity environment as it slows down the process and allows for large droplets to be considered which facilitates better analysis of the phenomenon. It enables radially symmetrical domains. As a result, this problem is modeled in spherically symmetric co-ordinates using OpenFOAM. To model counter-flow combustion with 6-step oxygen/hydrogen reactions, the reactingFoam solver from the OpenFOAM library is employed. A modified version of this reactingFoam solver names ’EBI-DNS’, developed by a team at KIT, Germany, is also considered in this study which includes variable binary diffusion coefficients. The new solver considers the non-unity Lewis number constraint for each species required for this laminar combustion involving 100% hydrogen concentration. The new solution predicts flame temperatures more accurately than the traditional reactingFoam solver, which produces incorrect flame temperatures when using 100% pure hydrogen as the fuel. A droplet vaporization model developed by the team at ZARM is considered in this study to match the gaseous phase flame modelling in OpenFOAM with liquid droplet evaporation. The rate of heat transfer at the droplet is studied in both cases to couple them as a single numerical solution of droplet combustion. Radiation heat transfer is also considered, as an addition to the flame model to match the rate of heat transfer for droplet evaporation obtained in experimentation. The new EBI-DNS solver predicts flame temperatures close to 3100 K, which is quite similar to theoretical models’ predictions of adiabatic flame temperatures. The outcomes provide a reasonable flame solution that can be tested using the experimental rate of heat transfer to the LOX droplet. The droplet model has been observed to not work for practical conditions of a surrounding temperature of about 3000K. Modelling conditions possible for radiation heat transfer such as black-body radiation, optically thin/thick assumption, and emissivities of the flame are proposed in this study. With a seemingly successful flame solution, and proposed additions to the model, this study contributes immensely to the ways in which a complete numerical solution to the LOX droplet combustion can be developed.