Bond Graph Modeling Of Incompressible Thermofluid Flows.

Abstract

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.