Determination of the Real Loss of Power for a Condensing and a Backpressure Turbine by Means of Second Law Analysis

Abstract

All real processes generate entropy and the power/exergy loss is usually determined by means of the Gouy-Stodola law. If the system only exchanges heat at the environmental temperature, the Gouy-Stodola law gives the correct loss of power. However, most industrial processes exchange heat at higher or lower temperatures than the actual environmental temperature. When calculating the real loss of power in these cases, the Gouy-Stodola law does not give the correct loss if the actual environmental temperature is used. The first aim of this paper is to show through simple steam turbine examples that the previous statement is true. The second aim of the paper is to define the effective temperature to calculate the real power loss of the system with the Gouy-Stodola law, and to apply it to turbine examples. Example calculations also show that the correct power loss can be defined if the effective temperature is used instead of the real environmental temperature.

The thermal analysis of a combined heat and power plant undergoing Clausius–Rankine cycle based on the theory of effective heat-absorbing and heat-emitting temperatures

“…The effective temperature in Ref. [9] is quite similar to the thermodynamic equivalent temperature of heat transfer that Woudstra et al have used for the thermodynamic evaluation of GTCC process in Ref. [10].…”

“…In an earlier study, Holmberg et al [9] have shown through a simple steam turbine and condenser system (see Appendix A) that the power loss of the system becomes too small if the entropy generation rate is multiplied with the real environmental temperature when vapor after the turbine condenses in a heat exchanger at the higher temperature than the real environmental temperature. The same example also shows that the law of GouyeStodola gives exactly the correct power loss if the condensing temperature of vapor is the same as the real environmental temperature and there is no temperature difference between vapor and cooling water in a condenser.…”

“…In the previous mentioned example, the entropy generation rate has been multiplied with the so called effective temperature which has been defined in Ref. [9] for an open flow system. The effective temperature in Ref.…”

A review on the thermodynamic optimisation and modelling of the solar thermal Brayton cycle

“…They explained that according to Holmberg et al [46], if the system only exchanges heat at the environmental temperature, the Gouy-Stodola theorem gives the correct loss of power. Most industrial processes, however, exchange heat at higher or lower temperatures than the environmental temperature [46]. If the environmental temperature is then used to calculate the loss of power in these cases, the Gouy-Stodola theorem does not…”

NLP model based thermoeconomic optimization of vapor compression–absorption cascaded refrigeration system

“…However, most of the thermodynamic processes emit or absorb heat at a temperature level other than the environmental temperature. In such cases, concept of the environmental temperature in GouyStodola equation does not provide actual loss [10]. Researchers [10][11][12][13][14][15][16][17] have used the concept of effective temperature instead of environmental temperature in Gouy-Stodola equation for the computation of irreversible loss.…”