Extension of Single-Pipe Methods to Networks

Methods to solve the single pipe equations are available in the literature (Anderson, 1982Anderson, J.D., Jr., Modern Compressible Flow: With Historical Perspective, McGraw-Hill, New York, NY, 1982., Saad, 1993Saad, M.A., Compressible Fluid Flow, 2nd Edition, Prentice-Hall, Englewood Cliffs, NJ, 1993, and Shapiro, 1953Shapiro, A.H., The Dynamics and Thermodynamics of Compressible Fluid Flow, 2 vols., Ronald, New York, NY, 1953.), but their extension to pipe networks involves significant difficulties. In a network system, the flow and energy must balance at each branch point. Traditional solution methods in incompressible flow systems break down because the relationships between pressure and flow cannot be expressed in a single convenient equation. Thus the calculation speed and reliable convergence benefits of incompressible flow matrix methods are much more difficult to obtain in compressible flow calculations. Heat transfer and the resulting temperature effects further complicate the analysis.

To address these issues, AFT xStream's primary steady solver incorporates unique methods of relating the various thermodynamic and fluid dynamic parameters to each other resulting in a solution methodology that is fast and offers good convergence characteristics. AFT xStream’s primary steady methods maintain the integrity of single pipe methods while preserving the required mass and energy balances at all branch points.

The specific techniques used by AFT xStream's primary steady solver to obtain solutions to the equations of compressible flow are proprietary and probably of little interest to the user. What the user will be most interested in is what equations are solved (so that results can be cross-checked) and what balances are calculated at branch points. Therefore, sufficient information is provided to enable users to verify results, while the proprietary aspects of AFT xStream’s solution methods are not described.