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 §ow combustion model to a spray §ame of Liquid Oxygen (LOx) and Gaseous Hydrogen (GH 2 ). 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 semi §uid 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 di©cult 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 di©culty 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 in §uence of the terms related to vaporization that are the source of additional §uctuations of composition. Following the early proposal of [4], these terms are easily obtained from the Lagrangian framework adopted to describe the two-phase §ows. The resulting computational model is applied to the numerical simulation of LOx GH 2 spray §ames. 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.

Unsteady High-Order Simulation of a Liquid Oxygen/Gaseous Hydrogen Rocket Combustor

“…For a given geometry, it is mainly defined by the incoming mass fluxes, degree of combustion, and wall heat losses. In previous compressible simulations [11,18,21], the reported combustor pressures are close to the measured 10 bar [32]. This is surprising because the employed adiabatic walls (recommended by the IWRCM-2 [32]) should result in higher pressures.…”

“…All simulations confirmed an anchoring of the flame at the injector tip (except for a slight liftoff in [18]). The characteristic shape of the flame close to the injector could also be reproduced in many simulations in a qualitative manner.…”

“…Although the numerical approaches and physical models in the cited papers differ significantly, reasonable agreement with experimental data could be obtained in most simulations irrespective of whether a continuous Euler [11][12][13][14] or a discontinuous Euler-Lagrange approach [11,[15][16][17][18][19][20][21] were used. All simulations confirmed an anchoring of the flame at the injector tip (except for a slight liftoff in [18]).…”

“…The fluid may be treated either in a single Eulerian [11][12][13] or an Eulerian-Eulerian framework [14] applying a statistical averaging in space. The second approach is a discontinuous one and requires two different codes, which have to be coupled [11,[15][16][17][18][19][20][21]. One code solves the governing equations for a turbulent, reactive gas mixture in an Eulerian framework.…”

“…Therefore, it is chosen for the investigations in this paper. This test case has also been a validation test case at the Second International Workshop on Rocket Combustion Modeling (IWRCM-2) [32] and for many research groups afterward [11][12][13][14][15][16][17][18][19][20][21]. Common features of all previous simulations are the use of steady-state RANS in combination with a rather coarse grid and a second-order spatial discretization of inviscid fluxes at most.…”