Example of application: Bubbly flow in a vertical pipe

Abstract

This 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.