Pure Bond Graph Libraries with Thermal Effects

Pure Bond Graph Libraries with Thermal Effects

All the resistive, capacitive and inertial powers for the bond graph libraries are described in the Pure Bond Graph Libraries section. Therefore, only the specific case of the Thermal library (TH_lib) will be dealt with here.

Although the TH library is not a pure bond graph, the classic framework to define the elements still applies. In the TH library, the flux variable is the heat transfer in [W] and is usually called dh and the effort variable is the temperature T in [degC]. As opposed to classic Bond Graph libraries, the power flow between two ports is given directly by the flux variable, instead of the product of flux with effort. That is why it is called a Pseudo Bond Graph library.

Why is there no I power in TH?

An inertial element is then defined by an algebraic equation between the derivative of the flux and the effort variable:

There is simply no inertial element with this type of state equation.

Why is there no R power in TH?

For resistive elements, it is quite different. The bond graph theory gives us:

All the heat transfer elements (convection, radiation, conduction) are a direct calculation of the heat transfer as a function of the temperature difference. That is why we usually call these elements resistive elements or, more precisely, they are said to have a resistive causality.

However, this heat transfer, this power, is applied to both ports with the same value. This means that the components neither absorb nor give energy to the system; it just calculates a power and returns it at both ports.

In terms of physics, it is quite normal. Indeed, resistive powers can be considered as the power that is converted into heat from another physical domain (mechanical, electrical, hydraulic). In the TH library, we already are in the thermal domain. As a consequence there is no conversion and so no R power. Its actually assimilated to a Resistive-Source RS element.

C powers

Capacitive elements are thermal masses that can store heat:

With:

• dh heat flux [W].

This heat is stored

and restored

.

The corresponding energy is calculated as the integral value of this power.