Nonlinear flow analysis in pipe networks

✍ Scribed by O. Ohtmer

• Publisher: John Wiley and Sons
• Year: 1983
• Tongue: English
• Weight: 875 KB
• Volume: 19
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620190306

✦ Synopsis

Abstract

Pipe networks are computed in an analogous mannner to frameworks in structural mechanics loaded only by moments. The mesh method (force method) is applied. Due to the boundary layer effects in special pipe members, the flow problem is in general nonlinear. Therefore, the Newton‐Raphson iteration procedure is used to solve the nonlinear system of equations. Using the computed flow rates in the TREE structure (determined by graph theory) as initial values, the iteration procedure converges rapidly to a user specified tolerance value. The loss coefficients of pressure for different pipe members (TUBE, VALVE, BOW, TEE, PUMP, KNEE, ±CONTR, ±DIFSR) need only be given in diagrams. These diagrams are used in digitalized form. In the back‐substitution phase with known flow rates in all members, the pressure at the joints is computed.

The main advantages of the analysis as outlined are that no initial values for the member flow rates need be known, the iteration procedure converges rapidly, and within each iteration step only small systems of linear equations need to be solved. Due to the fact that the loss coefficients of pressure need only be given in diagrams, arbitrary nonlinear networks can be analysed by the unchanged program system. A flow rate assumption may be specified in the input for a member of a mesh.

The pressures at the joints are defined as unknowns (displacement method) in References 7, 8 and 10. The flow rates in the members are defined as unknowns (force method) in Reference 9. The nonlinear system of equations is always solved by the Newton‐Raphson procedure. In Reference 10 a strategy is presented to take into account different pipe members, but in a different way from that outlined in this paper. The members BOW, TEE, KNEE, CONTR, DIFSR are not examined in Reference 10.