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Stability of Stratified Two-Phase Flow by Chebyshev Collocation Method

Sajadian, Ahmad | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45002 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Nouri, Ali
  7. Abstract:
  8. In this thesis fluid flow stability will be studied using Chebychev collocation spectral method. In general instability occurs between layers of a single fluid or at the interface of two different fluids. In case of an unstable flow small imposed perturbations on the flow will grow with time and their amplitudes will grow larger. Instability in most cases is an unfavorable phenomenon and therefore should be avoided.Two-phase flow processes in horizontal or vertical pipes under various conditions like natural or forced convection are of considerable importance in industrial applications. Two-phase flow can be found in many devices and industries like boilers, nuclear reactors, cooling and refrigeration systems, heat pumps and petrochemical and oil industries. Two-phase flow with annular regime is one of the most frequent flows in the industry. In annular flow small waves and perturbations may be present at the interface. In fact these waves and perturbations are always present at the interface, and according to the flow conditions these perturbations may grow with time and cause the interface to be unstable. Waviness of the interface results in entrainment of particles of the fluid flowing along the pipe wall in the central fluid. Entrainment significantly influences heat transfer and pressure drop in two-phase flows and therefore an understanding of conditions under which annular two-phase flow will become unstable is of considerable practical importance.In this study first equations of stability will be derived using linear theory of hydrodynamics for annular two-phase flow. Stability problem is an eigenvalue problem. The governing equations will be transformed into a system of linear equations and then solved using QZ algorithm hence giving eigenvalues that determine stability of the flow.The problem will be solved for the case of oil-water and air-water and in each case the effect of different parameters will be investigated. For example it will be seen that surface tension has a stabilizing effect for short wavelengths and with neglecting its effect the flow will be always unstable. Also the effect the thickness of the fluid flowing in the annulus, density ratio, viscosity ration, etc. will be studied
  9. Keywords:
  10. Instability ; Annular Two Phase Flow ; Linear Hydrodynamic Stability THeory ; Chebyshev Collocation Spectral Method

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