A SPECTRAL APPROACH FOR SOLVING TWO-FLUID FLOW STABILITY PROBLEM

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A SPECTRAL APPROACH FOR SOLVING TWO-FLUID FLOW STABILITY PROBLEM [Mehmet Emin Çelikkıran] [2022] [MSc].pdf

Date

2022-2

Author

Çelikkıran, Mehmet Emin

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Turbulence and transition to turbulence are still one of the unresolved topics in physics. Multiphase applications of the transitional flows are more complex than their single-phase counterparts due to having many options for the source of instability. From oceanography to rocket engines, from oil industry to astrophysical phenomena, multiphase instabilities have many examples in both nature and industry. Acquiring the knowledge of the starting point of transition is crucial in all these applications. In this study focus is the instability of multiphase flows, especially the instabilities at interfaces. Linear hydrodynamic stability approach is used, and the Orr-Sommerfeld equation is solved in order to capture the behavior of perturbations. For multiphase flow, Orr-Sommerfeld equations for each phase are built, and interface conditions are applied to connect individual phases. The Reynolds number is not the only dimensionless parameter for multiphase flows to affect the perturbations and instability. Stratifications of density and viscosity, the effect of surface tension, gravity, and derivatives of mean velocity profiles will all have characteristic effects on the instabilities at the interface. A spectral method, Chebyshev Collocation method, is used for discretization. Matlab, Octave, and C++ programming languages are used for validation cases. Validation of codes for both single-phase and multiphase flow is acquired by the comparison of numerical results and results from the literature.

Subject Keywords

hydrodynamic instability, multifluid flow, spectral methods, eigenvalue problem

URI

https://hdl.handle.net/11511/96344

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

M. E. Çelikkıran, “A SPECTRAL APPROACH FOR SOLVING TWO-FLUID FLOW STABILITY PROBLEM,” M.S. - Master of Science, Middle East Technical University, 2022.