Fig. 10. Bond graph model of pipe control volume
Repeating this model N times and adding inflow and outflow boundary conditions results in a compact finite volume model for the pipe segment.
The junction structure (the zeros and ones) of the model represents conservation of total mass, mass of burnt fuel, total energy including kinetic energy and momentum. The R-field to the right of the figure represents the flux of mass, mass of component two, total energy and momentum flowing through the right boundary of the control volume. The IC-field represents the relations between the state variables mass, mass of burnt fuel, total energy and momentum and the average pressure, fuel factor, temperature and velocity in the control volume. The state equations for the control volume can be derived directly from the bond graph and the constitutive laws for the IC-field are generally given as functions of the state variables.
The relations for the R-field are derived based on the upstream biased Mach modulated approach as in [18], and inflow and outflow relations are introduced that handles both the subsonic and sonic flow case. The pipe model requires that pressure, fuel factor and temperature is known on both ends, and as so is a fixed causality sub-model.
The required input data for the one dimensional gas dynamics pipe model are the pipe diameter, the pipe length, the number of control volumes, the friction factor, the heat loss coefficient and entry and exit loss coefficients.
5. CONCLUSIONS
Utilizing the strengths of the bond graph method for modeling dynamic systems, a consistent set of submodels for simulation of diesel engine transient performance has been developed. Introducing the extended pseudo bond graph concept the conservation of mass and energy, and the thermodynamics are treated consistently.
Adding the models developed to a flexible modeling environment and model library, opens up for reuse of models in different simulation environments and in different problem solving situations.
A large number of advanced models for diesel engine system simulation is developed for flexible use "as is", or as skeletons for further refinements.
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