Wave propagation due to pneumatic surge in diabatic circuits and systems

This study describes the behaviour of circuits with a pneumatic or otherwise gaseous working or control fluid during fast transients. The fluid energy evolution mode is defined taking into account friction and thermal exchange through the walls. Given the short times involved and the large thermal capacity of the walls by comparison with fluid mass, wall temperature is assumed to be constant. Wave propagation is supposed to occur only in continuous parameters (ducts), while vessels, actuators, restrictors, branchings and so on are considered lumped. Wave propagation equations are hyperbolic and can be reduced to ordinary differential equations along characteristic lines. Dependent variables are pressure, volumetric flow per unit time and density (or temperature). Boundary conditions of the characteristic equations are expressed by the relations amongst dependent variables at duct input and output, which are given by analysis of the joined components. A practical procedure for numerical analysis of pneumatic or gaseous circuits with any number of components and branches has been developed from this theoretical basis, and has been shown to provide very good agreement with experimental results. Furthermore, it appears that the method developed herein is the only one capable of simulating the behaviour of fast circuit transient closely.