Abstract
AbstractThis chapter gives an example of application which concerns a bubbly flow in a vertical pipe. First of all we summarize the balance equations and a set of closure relations for them. The choice of the closure relations does not really matter and other choices could be done. The flow is assumed to be upwardly directed in a vertical pipe having a circular cross section. Due to this particular geometry, we choose to project the equations in a cylindrical coordinates system and assume the flow to be axisymmetric. The cylindrical coordinates are a special kind of more general curvilinear coordinates. After summarizing some elements of the theory of curvilinear orthogonal coordinate systems, we come back to the particular case of cylindrical coordinates and project our equations in this coordinates system. Then, we discretize all the equations by using a method proposed par Patankar (1980) and indicate how to solve them.KeywordsBubble FlowVertical PipeSemi-implicit Method For Pressure-linked Equations (SIMPLE)General Orthogonal Curvilinear Coordinate SystemAxisymmetric Cylindrical CoordinatesThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
