Applicability of the Lattice Boltzmann Method to Simulate Fluid Flows in Rocket Engines

Abstract

Space Transportation is only feasible when structure weight is reduced down to the minimum and energy density brought to the maximum limit. These requirements are to a certain extent contra-dicting and lead to solutions at the technical limit. Great effort in the design phase is necessary to ensure an unproblematic opera-tion. For this reason, high fidelity simulations of unsteady phe-nomena are used extensively in the design and operation of a rocket engine. This research focuses on the specific challenges associated with cryogenic liquids in rocket engines, where signifi-cant temperature gradients and evaporation phenomena occur during the chilldown phase prior to engine start-up. The chilldown process often results in high-pressure surges and high-velocity gas flows, complicating the safe start-up of the engine. The Lattice Boltzmann Method promises to yield high quality re-sults in a fast time. The LBM, known for its effectiveness in han-dling two-phase flows, was selected for its potential to manage the steep temperature gradients, evaporation, and compressible flows characteristic of these systems. A thermal two-phase model incor-porating a multi-speed finite difference approach and an additional force term was chosen from the literature. Validation of the model was conducted through simulations of various scenarios, each representing different phenomena of inter-est in rocket engines. The first validation case is the driven cavity flow to show that the chosen LBM is capable to correctly repro-duce incompressible steady single-phase flow. The evaporation of a single bubble on a heated surface was chosen because the code should be able to handle instantaneous evaporation as is the case during chilldown. A Riemann shock tube simulation shows the capability of the model to handle shocks and supersonic flows and finally the model is used to simulate pressure surges with liquid nitrogen. The results demonstrated that the LBM accurately reproduced the main flow features and dynamic behaviours in these cases. Specifi-cally, it showed good agreement in the driven cavity flow, effective simulation of evaporation processes, and low error rates in repli-cating the characteristics of a Riemann shock tube. However, minor shortcomings were noted in the pressure attenuation and peak pressure prediction during pressure surge simulations. The work concludes with a simulation of a duct filled with bubbles to study the attenuation of pressure waves due to multiple wave scattering in the bubble cloud. The LBM effectively captured the strong pressure wave attenuation observed in this scenario. How-ever, limitations were identified, including the need for an im-proved real gas model, as the current model's adherence to the van-der-Waals equation of state was found to be restrictive. Fur-thermore, the stability of the model and the accuracy of pressure wave attenuation require enhancement. Overall, the LBM simulations demonstrated the method's potential for addressing the physical challenges associated with fluid flows in rocket engines. The study emphasizes the importance of careful simulation setup, as LBM equations inherently describe their own fluid properties, necessitating the mapping of physical fluid prop-erties via similarity laws and non-dimensional numbers, such as the Reynolds number and the corresponding states principle. While the latter is accurate for single atomic gases, it becomes less precise with more asymmetrical fluid molecules.