The impact of viscous dissipation on the flow parameters during round tube filling

• Published in: Acta mechanica 2016-09, Vol.227 (9), p.2609-2623
• Main Authors: Borzenko, E. I., Shrager, G. R., Frolov, O. Y.
• Format: Article
• Language: English
• Subjects: Analysis; Boundary conditions; Classical and Continuum Physics; Continuity (mathematics); Control; Dissipation; Dynamical Systems; Engineering; Engineering Thermodynamics; Flow (Dynamics); Fluid dynamics; Free boundaries; Heat and Mass Transfer; Mathematical analysis; Mathematical models; Mathematics; Mechanical properties; Original Paper; Parameters; Solid Mechanics; Theoretical and Applied Mechanics; Vibration; Viscosity
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-016-1655-9

The fountain non-isothermal flow of a viscous fluid realized during circular pipe filling is investigated. The mathematical basis of the process is formed by the equations of motion, continuity and energy with respective initial and boundary conditions with due account of the temperature dependence of viscosity, the presence of a free boundary, and dissipation of mechanical energy. To solve the problem numerically, a finite difference method is used. Depending on the values defining the dimensionless parameters, the results of parametric studies in temperature, viscosity, dynamic and kinematic characteristics of the flow are shown. Flow patterns for the formulation of problems with different initial and boundary conditions are given. The distributions of velocity and temperature in different cross sections of the pipe and the shape characteristics of the free surface are presented. The separation of flow into the zone of spatial flow in the vicinity of the free surface and one-dimensional flow away from it, and changing the shape of the free boundary, depending on the level of dissipative heating, are demonstrated.