摘要：In this paper a Bond Graph methodology is used to model incompressible fluid
flows with viscosity and heat transfer. The distinctive characteristic of
these flows is the role of pressure, which doesn’t behave as a state variable
but as a function that must act in such a way that the resulting velocity
field has divergence zero. Velocity and entropy per unit volume are used
as independent variables for a single-phase, single-component flow.
Time-dependent nodal values and interpolation functions are introduced to
represent the flow field, from which nodal vectors of velocity and entropy
are defined as Bond Graph state variables. The system of equations for the
momentum equation and for the incompressibility constraint is coincident with
the one obtained by using the Galerkin formulation of the problem in the
Finite Element Method, in which general boundary conditions are possible
through superficial forces. The integral incompressibility constraint is
derived based on the integral conservation of mechanical energy. All kind of
boundary conditions are handled consistently and can be represented as
generalized effort or flow sources for the velocity and entropy balance
equations. A procedure for causality assignment is derived for the resulting
graph, satisfying the Second principle of Thermodynamics.
