Numerical simulation of the growth and interaction of vapour bubbles in superheated liquid jets

Abstract

Operating fluids for steering and propulsion of orbital manoeuvring systems are to be changed from toxic substances to environmentally less harmful alternatives. Liquid oxygen (LOX) can be used as oxidizer but the near vacuum conditions of outer space lead to a fast expansion into a superheated state when LOX is injected into the combustion chamber. The disintegration of the liquid jet is driven by bubble nucleation and growth, which is called flash boiling. These processes typically occur at small length and time scales and need to be modelled in macroscopic simulations of the entire combustion chamber. The goal of the present work is a quantification of bubble growth rates and bubble-bubble interactions that can be used to improve the existing submodels needed for full-scale simulations of the entire thruster. We use direct numerical simulations (DNS) of bubble clusters and compare the resulting growth rates to standard models for single bubble growth. The DNS solver is based on a discontinuous Galerkin approach and combined to a level-set equation to transport the interface between liquid and vapour. A modified HLLC Riemann solver accounts for the phase transfer. The computations show that vapour bubbles grow more slowly in the center of a jet than at its surface. The bubble radii exponentially decrease with distance from the liquid jet interface and growth rates are reduced by more than 70% in the center of the jet such that their volumetric expansion can be neglected for the computation of the jet expansion. The reduced growth can be associated with the interactions of the pressure fields surrounding the bubbles as the liquid pressure increases due to bubble growth and evaporation. The degree of superheat is locally reduced and bubbles grow at a smaller rate. The growth rates of individual bubbles can be parameterised with the local degree superheat, which may serve as a potential sub-scale model. These findings hold for various operating conditions that are characteristic for LOX flash evaporation under vacuum conditions.