Mathematical and numerical modelling of high-speed rarefied flow of binary gas mixtures

Todorova, Blaga Nenkova (2020) Mathematical and numerical modelling of high-speed rarefied flow of binary gas mixtures. PhD thesis, University of Glasgow.

Abstract

Engineering applications that include flows with thermodynamic non-equilibrium and rarefaction effects require modelling with an increased level of physical detail. Practical problems often involve more than one constituent in the flow and therefore the capability to analyse gas mixtures is important. Extending kinetic model equations of the Bhatnagar-Gross-Krook (BGK)-type from a single-species gas to a gas mixture presents a number of difficulties. These are further pronounced when diatomic gas mixtures are considered, due to the addition of internal energy. This is a challenging research area and available models present a number of shortcomings. This thesis presents new mathematical models for high-speed flow applications with moderate levels of rarefaction. The novel kinetic models are derived for mixtures of binary gases: two new models for mixtures of monoatomic gases and a model for mixtures of diatomic gases are introduced. The novel kinetic models are shown to have good mathematical properties and demonstrate significant advances over models in the literature. Transport properties in the continuum limit are obtained through the Chapman-Enskog (CE) type expansion and shown for each model. The models account for separate species-mean velocity such that the species diffusion and velocity drift are accurately represented. For mixtures of monoatomic gases a Shakhov-based model and an Ellipsoidal-Statistical (ES)-based model are derived. The main advantage of the newly introduced models is the recovery of three correct transport coefficients in the hydrodynamic limit and as a result having a correct Prandtl number for the mixture. For the diatomic mixture model, the key improvement is the inclusion of separate species velocities, species- translational, -rotational and -vibrational temperatures and three-step relaxation process. Furthermore, the new models are numerically evaluated for a range of high-speed flows with strong thermodynamic non-equilibrium. Validation and good agreement with results from the Boltzmann model and the direct simulation Monte Carlo (DSMC) demonstrates the models’ capabilities and limitations. A parametric study shows the variation of flow properties under varied free-stream conditions. A numerically efficient gas-kinetic scheme (GKS) based on the monoatomic Shakhov-based mixture model is also presented and the results show good accuracy, while reducing the required computational time. Overall, the newly-introduced gas mixture models demonstrate promising computational results for relevant applications. The current work can form the basis for further work on improved kinetic modelling of high-speed nonequilibrium flows.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: nonquilibrium flow, high-speed flow, rarefied gas, mixture models, kinetic models, numerical evaluation, shockwave.
• Subjects: Q Science > QA Mathematics; Q Science > QC Physics
• Colleges/Schools: College of Science and Engineering > School of Engineering > Autonomous Systems and Connectivity
• Funder's Name: University of Glasgow, EPSRC
• Supervisor's Name: Steijl, Dr. Rene and Barakos, Prof. George
• Date of Award: 2020
• Depositing User: Miss Blaga Todorova
• Unique ID: glathesis:2020-81878
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 17 Dec 2020 16:54
• Last Modified: 08 Apr 2022 17:04
• Thesis DOI: 10.5525/gla.thesis.81878
• URI: https://theses.gla.ac.uk/id/eprint/81878

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