Bond Graphs for 1-Dimensional Duct Flows Using Nonlinear Finite Lumps

摘要

Duct flows are characterized by fluid filled tubes where information and/or energy are propagated from one end to the other. Engine exhaust and intake systems, pneumatic power systems, and HVAC systems are examples of nearly 1-dimensional compressible gas flows. If the pressure amplitudes are sufficiently small, then the wave propagation is considered "acoustic", and linear modeling methods are fine. In a bond graph this implies a ladder structure composed of 0-junctions with attached compliances and 1-junctions with attached inertias. For large amplitude pressures the acoustic assumption is a poor one and alternative representations are necessary. To "exactly" represent 1-D, nonlinear compressible flows, the Navier-Stokes equations, energy equation, and mass conservation equations must be solved. This is typically done in the field of Computational Fluid Dynamics(CFD) using finite difference techniques. But if the duct flow is just part of an overall system, the computational procedures for CFD may be too tedious for the intended modeling goals of the overall system, or it may not even be possible to integrate system dynamics and controls up- and downstream of the duct flow section. In this paper, finite lumped bond graphs are used to represent 1-D compressible gas dynamics including momentum transport. The modeling approach is compared to more "exact" approaches and shown to produce reasonable results. The virtue of this approach is that external dynamics and controls can be straightforwardly integrated with the gas dynamic model using conventional bond graph representations. This is demonstrated through example.