TO-98-16-1 — A Numerical Procedure for Simulation of Fanno Flows of Refrigerants or Refrigerant Mixtures in Capillary Tubes

An ordinary differential equation (ODE), particularly suitable for numerical simulations of fanno flows in capillary tubes, is derived by combining the conservation equations. Taking pressure as the independent variable, better control over design variables is achieved and the singularities involved in the choked flows can be avoided. For refrigerants without temperature glide, such as pure refrigerants or azeotropic refrigerant mixtures, the single ODE can be easily integrated if the saturation thermodynamic properties are given. For nonazeotropic refrigerant mixtures (NARMs), iteration in the temperature glide zone is required. As an alternative procedure for the iteration, a system of two ODEs is derived by taking thermodynamic relations into account. The system of ODE is not only in a numerically efficient form but also reveals important physics regarding choking. Sample numerical results for ternary NARM R-407C are presented to show the performance of the proposed procedures.