Association of Finite-Time Thermodynamics and a Bond-Graph Approach for Modeling an Endoreversible Heat Engine

Abstract

Abstract:In recent decades, the approach known as Finite-Time Thermodynamics has provided a fruitful theoretical framework for the optimization of heat engines operating between a heat source (at temperature hs T ) and a heat sink (at temperature cs T ). The aim of this paper is to propose a more complete approach based on the association of Finite-Time Thermodynamics and the Bond-Graph approach for modeling endoreversible heat engines. This approach makes it possible for example to find in a simple way the characteristics of the optimal operating point at which the maximum mechanical power of the endoreversible heat engine is obtained with entropy flow rate as control variable. Furthermore it provides the analytical expressions of the optimal operating point of an irreversible heat engine where the energy conversion is accompanied by irreversibilities related to internal heat transfer and heat dissipation phenomena. This original approach, applied to an analysis of the performance of a thermoelectric generator, will be the object of a future publication.

Association of Finite-Dimension Thermodynamics and a Bond-Graph Approach for Modeling an Irreversible Heat Engine

“…Figure 8). By deriving the expression (21) regarding the entropy flow rate S , we obtain an expression similar to that obtained in the case of an endoreversible heat engine [1] where the temperatures of the heat source and the heat sink have been replaced by their apparent values [cf. Equation (22) (24) we immediately deduce the expression of the optimal entropy flow rate: (21), we obtain the expression of the maximum output mechanical power by using the apparent temperatures (27) By studying the direction of the variation of the function ( ) Moreover, the derivative of the output mechanical power (24) at the origin point is equal to the difference of temperatures of thermostats.…”

“…For example, the entropy flow rate from the heat source to the exo-reversible heat engine is the term hs S while the entropy flow rate from the exo-reversible heat engine to the heat sink is the term cs S ( Figure 2). To remain consistent with the case of the endoreversible heat engine that we detailed in another article [1], we call S the entropy flow rate involved in reversible energy conversion and we use it as control variable of the exo-reversible heat engine. Similarly, we keep the same notation for the energy flow rates at the border of the machine: To simplify the problem in order to obtain analytical solutions, we make the following assumptions:…”

“…Finally the operating curve of the heat engine in the presence of internal dissipation in the [W , 1 η ] diagram deforms according to the diagram on the right of Figure 8.…”

“…Relation (7) forms the parametric equations of the operating curve of the exo-reversible heat engine that we are going to study in the [W , 1 η ] diagram (cf. Figure 4).…”

“…By neglecting the heat loss within the thermoelectric generators, they showed that the optimum condition for maximum power is not unique but depends on the combination of the electrical load resistances of each generator. In this paper, we will firstly recall the notion of an Exo-reversible Heat Engine where only the internal irreversibilities are taken into account [36,37], and then by applying a new approach [1] based on the association of Finite-Dimension Thermodynamics and the Bond-Graph approach [38,39], we give the analytical expressions of the optimal operating point of an Irreversible Heat Engine where the energy conversion is accompanied by irreversibilities related to internal heat leakage and internal dissipation. An application of this approach to a thermoelectric generator [40,41] allows one to optimize the design of the machine and express the energy recovery potential based on the physical parameters of the system.…”