Lagrangian modeling of turbulent spray combustion: application to rocket engines cryogenic conditions

Abstract

The present work is concerned with the application of a turbulent two-phase flow combustion model to a spray flame of Liquid Oxygen (LOx) and Gaseous Hydrogen (GH2 ). The proposed strategy relies on a joint Eulerian-Lagrangian framework. The Probability Density Function (PDF) that characterizes the liquid phase is evaluated by simulating the Williams spray equation [1] thanks to the semifluid approach introduced in [2]. The Lagrangian approach provides the classical exchange terms with the gaseous phase and, especially, several vaporization source terms. They are required to describe turbulent combustion but difficult to evaluate from the Eulerian point of view. The turbulent combustion model retained here relies on the consideration of the mixture fraction to evaluate the local fuel-to-oxidizer ratio, and the oxygen mass fraction to follow the deviations from chemical equilibrium. The difficulty associated with the estimation of a joint scalar PDF is circumvented by invoking the sudden chemistry hypothesis [3]. In this manner, the problem reduces to the estimation of the mixture fraction PDF, but with the influence of the terms related to vaporization that are the source of additional fluctuations of composition. Following the early proposal of [4], these terms are easily obtained from the Lagrangian framework adopted to describe the two-phase flows. The resulting computational model is applied to the numerical simulation of LOx-GH2 spray flames. The test case (Mascotte) is representative of combustion in rocket engine conditions. The results of numerical simulations display a satisfactory agreement with available experimental data.