Closure relations effects on the prediction of the stratified two-phase flow stability via the two-fluid model |
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| Institution: | 1. Department of Physics, Indian Institute of Technology Kanpur, U.P. 208016, India;2. Niels Bohr International Academy, Niels Bohr Institute, 2100, Copenhagen Ø, Denmark;3. Mechanics & Applied Mathematics Group, Indian Institute of Technology Kanpur, U.P. 208016, India;1. Institute for Problems in Mechanics, Russian Academy of Sciences, 101 Vernadsky Avenue, bldg 1, 119526 Moscow, Russia;2. Bauman Moscow State Technical University, 5 Second Baumanskaya Street, 105005 Moscow, Russia;3. National Research Nuclear University MEPhI, 31 Kashirskoe Shosse, 115409 Moscow, Russia;4. Cardiff University, Heath Park, Cardiff CF14 4XY, UK;1. Universite de Lorraine, GeoRessources UMR 7359 CNRS-CREGU, 2 rue du Doyen Marcel Roubault TSA 70605, 54518 Vandoeuvre-les-Nancy Cedex, France;2. Perm State University, Department of Theoretical Physics, 15 Bukireva street, 614990 Perm, Russia;3. Institute of Continuous Media Mechanics UB RAS, Laboratory of Computational Fluid Dynamics, 1 Academica Koroleva street, 614013 Perm, Russia;1. Kielce University of Technology, Faculty of Mechatronics and Machine Building, Chair of Mechanics, al. 1000-lecia P.P.7, 25-314, Poland;2. Kielce University of Technology, Faculty of Management and Computer Modelling, Chair of Computer Science and Applied Mathematics, al. 1000-lecia P.P.7, 25-314, Poland;1. School of Science & Engineering, Teesside University, Middlesbrough TS1 3BA, UK;2. Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia |
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| Abstract: | The possibility of predicting the exact long wave linear stability boundary via the two-fluid (TF) model for horizontal and inclined stratified two-phase flow is examined. The application of the TF model requires the introduction of empirical closure relations for the velocity profile shape factors and for the wave induced wall and interfacial shear stresses. The latter are recognized as the problematic closure laws. In order to explore the closure relations effects and to suggest the necessary modifications that can improve the stability predictions of the TF model, the results are compared with the exact long wave solution of the Orr–Sommerfeld equations for the two-plate geometry. It is demonstrated that with the shape factors corrections and the inclusion of wave induced stresses effects, the TF model is able to fully reproduce the exact long wave neutral stability curves. The wave induced shear stresses in phase with the wave slope, which give rise to the so called “sheltering force”, were found to have a remarkable destabilizing effect in many cases of horizontal and inclined flows. In such cases, the sheltering effects must be included in the TF model, otherwise the region of smooth stratified flow would be significantly over predicted. Based on the results of the exact analysis, a simple closure relation for the sheltering term in the TF model is provided. |
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