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To achieve high power density and thermodynamic cycle efficiency, the working pressures of liquid-propellant rocket engines, diesel engines, and gas turbines (based on deflagration or detonation) are continuously increasing, which could reach or go beyond the thermodynamic critical pressure of the liquid propellant. For this reason, the studies of trans- and super-critical injection are getting more and more attention. However, the simulation of transcritical phase change is still a challenging topic. The phase boundary, especially near the mixture critical point, needs to be accurately determined to investigate the multicomponent effects on transcritical injection and atomization. This work used our previously developed thermodynamic model based on the vapor-liquid equilibrium (VLE) theory, which can predict the phase separation near the mixture critical point. An \textit{in situ} adaptive tabulation (ISAT) method was developed to accelerate the computationally expensive multicomponent VLE computation such that it can be cheap enough for CFD. The new thermodynamic model was integrated into OpenFOAM to develop a VLE-based CFD solver. In this work, shock-droplet interaction and two-phase mixing simulations are conducted using our new VLE-based CFD solver. The shock-droplet interaction simulation results capture the thermodynamic condition of the surface entering the supercritical state after shock passes through. The atomization of droplets could be triggered by vorticity formed at the droplets' surface. 2D temporal mixing layer simulations show the evolution of the transcritical mixing layer and capture the phase split effect at the mixing layer.
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VLE-Based Phase Field Method to Simulate High-Pressure Diffuse Interface with Phase Change
Supercritical fluids, often present in modern high-performance propulsion systems, result from elevated operating pressures. When these systems utilize fluid mixtures as fuel or oxidizers, a transcritical effect often occurs. This effect can lead to misjudgments, as mixture critical points exceed those of individual components. Fluid mixing may induce phase separation, creating liquid and vapor phases due to the transcritical multi-component effect. Consequently, two-phase modeling is essential for transcritical and supercritical fluids. Traditional interface capturing methods, like Volume of Fluid (VOF) and Level Set (LS), present challenges such as computational expense and lack of conservatism. The Phase Field (PF) method, or the Diffuse Interface (DI) method which uses a phase fraction transport equation, emerges as a conservative alternative. Despite the absence of an initial interface in transcritical fluids, phase separation from mixing may form liquid droplets, necessitating multiphase modeling. To address these complexities, a Vapor-Liquid Equilibrium (VLE) model, coupled with the PR equation of state, is introduced. This model estimates phase fractions, liquid and vapor compositions, densities, and enthalpies through a flash problem solution. The conventional PF model is enhanced by replacing the phase fraction transport equation with VLE-derived values. The resulting VLE-based PF method is implemented into an OpenFOAM compressible solver, ensuring numerical stability with explicit phase field terms and a new CFL criterion. Test cases involve 1D interface convection and 2D droplet convection. In the 1D test, the VLE-based PF model adeptly captures interfaces, adjusting thickness as needed. The 2D droplet case, challenging due to a non-aligned Cartesian grid, exhibits uniform interface thickness and preserves droplet shape. The VLE-based PF model demonstrates versatility and reliability in capturing complex fluid behaviors, offering promising prospects for future research.
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- Award ID(s):
- 2023932
- PAR ID:
- 10562075
- Publisher / Repository:
- American Institute of Aeronautics and Astronautics
- Date Published:
- ISBN:
- 978-1-62410-711-5
- Page Range / eLocation ID:
- AIAA 2024-1635
- Format(s):
- Medium: X
- Location:
- Orlando, FL
- Sponsoring Org:
- National Science Foundation
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null (Ed.)The studies of transcritical and supercritical flow have attracted much interest in the past 30 years. However, most of them mainly focus on the single-component system, whose critical point is constant. We use the vapor-liquid equilibrium (VLE) theory to capture the thermodynamic properties of the mixture and investigate transcritical flows (i.e., supercritical CO2 oxy-combustion systems). In sCO2 oxy-combustion systems, due to the presence of water from the previous cycles, the mixture critical point increases significantly, such that the phase separation could occur in both the compressor and combustor. However, the VLE solver increases the computation cost of fluid simulation significantly, which limited the size of simulations we can conduct. Naturally, tabulation methods can be used to store the VLE solutions to avoids redundant computation. However, the size of the VLE table increases exponentially with respect to the number of components. When the number of species components is greater than three, the size of the VLE table far exceeds the RAM’s limit in today’s standard computers. In this research, an online tabulation method based on In Situ Adaptive Tabulation (ISAT) is developed to accelerate the computation of multicomponent fluids based on VLE theory. Accuracy and efficiency are analyzed and discussed. The CFD solver used in this research is based on the Pressure-Implicit with Splitting of Operators (PISO) method. Peng-Robinson equation of state (EOS) is used in the calculations of phase equilibrium.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.2514/6.2024-1635
