Irreversible Power Cycle Research Articles

Analogy to help learn and understand the second law of thermodynamics, entropy, entropy generation, irreversibility, and power cycles

Teaching and learning Thermodynamics have challenges. Energy and the First Law as the Energy Conservation Principle are usually well accepted. This is not the case with the Second Law, entropy, entropy generation, and the consequences of the Second Law. Analogies can be used to help learn and understand the Second Law of Thermodynamics, entropy, entropy generation, irreversibility, and power cycles. The present work proposes a Thermodynamics-Economics analogy. The analog of heat transfer (flowing in the decreasing temperature direction, driven by a temperature difference) is the traded merchandise transfer (flowing in the increasing unit price direction) in normal trading operations. Developments start with the economic analog of Clausius inequality. The analog of entropy is the merchandise financial value, and the analog of the entropy generation is the financial value generation. Irreversibility is associated with entropy generation, and economic irreversibility is related to economic entropy (financial value) generation. The reversible and irreversible power cycles also have their economic analogs. The irreversibility associated with heat transfer through a finite temperature difference also has its economic analog. The economic Second Law developments are more familiar to students and more easily understandable, which can help them learn the Second Law of Thermodynamics and its implications.

Specific Entropy Generation in a Gas Turbine Power Cycle

Numerous studies have shown that the minimization of entropy generation does not always lead to an optimum performance in energy conversion systems. The equivalence between minimum entropy generation and maximum power output or maximum thermal efficiency in an irreversible power cycle occurs subject to certain design constraints. This article introduces specific entropy generation defined as the rate of total entropy generated due to the operation of a power cycle per unit flowrate of fuel. Through a detailed thermodynamic modeling of a gas turbine cycle, it is shown that the specific entropy generation correlates unconditionally with the thermal efficiency of the cycle. A design at maximum thermal efficiency is found to be identical to that at minimum specific entropy generation. The results are presented for five different fuels including methane, hydrogen, propane, methanol, and ethanol. Under identical operating conditions, the thermal efficiency is approximately the same for all five fuels. However, a power cycle that burns a fuel with a higher heating value produces a higher specific entropy generation. An emphasis is placed to distinguish between the specific entropy generation (with the unit of J/K mol fuel) and the entropy generation rate (W/K). A reduction in entropy generation rate does not necessarily lead to an increase in thermal efficiency.

Irreversible Carnot cycle under per-unit-time efficiency optimization

A Carnot-like irreversible power cycle is analyzed under maximum per-unit-time efficiency conditions. The model includes finite-rate heat transfers between the working fluid and the external heat reservoirs, heat leak between heat reservoirs, and internal dissipations of the working fluid. We present the results for the optimum distribution of the external and internal thermal heat conductances and the optimum area allocation ratio in terms of a dimensionless price parameter, the engine temperature ratio, and the internal irreversibility factor. The calculated optimized efficiencies agree with observed values for real power plants.

Maximum power and thermal efficiency of an irreversible power cycle

A simple Carnot-like irreversible power cycle is modeled with two isothermal and two adiabatic, irreversible processes. The generic source of internal irreversibility, deduced from the Clausius inequality, produces entropy at a rate proportional to the external heat conductance and the engine temperature ratio. This cycle is optimized for maximum power and maximum efficiency, and its performances compared to those of the endoreversible cycle, based on typical heat source and heat sink temperatures. Both cycles produce maximum power at the same engine temperature ratio, but the irreversible cycle prediction of maximum efficiency and heat conductance allocation between steam boiler and condenser, appear to be not only more realistic, but also more relevant to actual design considerations of power plants.

Thermodynamic Optimization of Irreversible Power Cycles With Constant External Reservoir Temperatures

An extended version of the Bejan model of irreversible power plants is proposed using a log-mean temperature difference (LMTD) representation for both the high and low-temperature heat exchangers. The analysis focuses on minimizing the irreversibilities associated with the hot and cold heat exchangers. The results indicate that the maximum power output, external conductance allocation ratio, and second law efficiency are functions of the number total heat exchanger transfer units (N), and are asymptotic to Bejan’s original results as N → O. This asymptote represents a global power output maximum and occurs for either extremely high cycle flow rates or cycle phase change processes in both heat exchangers. The LMTD representation also shows that under optimal conditions, more conductance should be allocated to the low-temperature heat exchanger as N increases.