Modeling and simulation of flash evaporation of cryogenic liquid jets

Abstract

In recent years, advancements in orbital maneuvering systems and upper-stage rocket propulsion technologies, exemplified by the cryogenic Ariane 6 Vinci engine, have been directed towards the substitution of conventional toxic and hypergolic propellants by environmentally benign and operationally safer alternatives, such as hydrogen, methane or kerosene. However, the injection of the typically cryogenic liquids into the near vacuum conditions of space prior to ignition causes a depressurization below saturation conditions, leading to rapid bubble nucleation, growth, and subsequent spray breakup, called flash evaporation. Understanding the spray breakup and mixing of the flashing cryogenic liquids is imperative for ensuring the success of engine ignition, particularly when employing advanced ignition techniques such as laser ignition. However, the extreme environmental conditions render experimental investigations extremely challenging and allow only limited optical access. Therefore, numerical tools can provide additional information to gain a complete picture of the flashing process. In this work, a novel compressible, one-fluid, two-phase computational fluid dynamic solver is developed for flashing cryogenic liquids in OpenFOAM. Emphasis is placed on the comprehensive representation of the entire flashing phenomenon, from the nearly incompressible liquid state to the highly compressible vapor-droplet mixture following spray breakup. After validating the solver's capability to capture the transonic effects in 2D and 3D faithfully, it is applied to three different cryogenic liquid nitrogen cases, experimentally investigated at the German Aerospace Center (DLR) Lampoldshausen. This investigation revealed a pronounced recirculation zone in the 2D simulations where motionless or even slightly upstream floating regions have been observed in the shadowgraph images, providing an explanation for the observed phenomenon. However, further 3D investigation with highly resolved large eddy simulations could not reproduce the recirculation zone, yet regions of comparable low axial velocity have been identified at the same location. Therefore, the simpler 2D simulations can predict the overall characteristics of mass flow rate and spray angle yet overpredict the recirculation downstream of the shock front due to missing 3D effects. Further, the dynamics of larger droplets, which do not adhere to the no-slip assumption of the one-fluid model, are studied with the 3D LES by including a cloud of one-way coupled particles. This investigation revealed an excellent agreement with measured particle velocities, indicating that the dynamics of the larger droplets are governed by their inertia and the vapor velocity field captured by the one-fluid model. Finally, a novel model for the development of the surface density of flashing flows called the flashing liquid atomization model (FLAM) is presented. With this model, the lost information of surface density and the mean droplet diameter can be recovered. A comparison of the droplet size measurements of the cryogenic liquid nitrogen cases showed that the model can predict the droplet size on the central axis and capture the trend of decreasing droplet size with increasing superheat ratio. Thus, this work introduces, for the first time, a solver designed for simulating flashing cryogenic flows, including surface density modeling to capture droplet sizes.