Thermal Efficiency and Exergy Analysis Methods for Engineering Thermodynamic Cycles
In engineering thermodynamics, the quantitative evaluation and diagnosis of the performance of energy conversion devices is a core link in optimizing system design and improving energy utilization efficiency. Facing complex power plants and thermodynamic systems, engineers need to transcend mere intuitive perception and adopt scientifically rigorous calculation methods to measure the merits of energy conversion. This article focuses on the calculation methods for energy conversion efficiency in engineering thermodynamic cycles, systematically introduces traditional thermal efficiency definitions, and deeply explores the energy quality evaluation system based on exergy balance.
Classic Definitions and Calculations of Thermal Efficiency in Thermodynamic Cycles
Thermal efficiency is the most fundamental and intuitive macroscopic index for evaluating the energy conversion performance of power cycles. According to the first law of thermodynamics, the purpose of a power cycle is to enable the working fluid to absorb heat from a high-temperature heat source, output useful work to the outside during the expansion process, and simultaneously discharge unavoidable cold-source heat losses to a low-temperature heat source. Therefore, thermal efficiency is strictly defined as the ratio of the net useful work output of the cycle (or the converted mechanical/electrical energy) to the heat absorbed by the working fluid from the high-temperature heat source.
In specific calculations, for a theoretical cycle composed of a series of ideal thermodynamic processes (such as isothermal, adiabatic, isobaric, and isochoric processes), the heat absorption and heat rejection can be calculated item by item through thermodynamic parameters such as temperature, pressure, specific volume, and specific enthalpy of the working fluid at each state point. For example, in a Rankine cycle or Brayton cycle, the net work of the system equals the work output by the turbine expansion machine minus the work consumed by the pump or compressor. By listing the energy conservation equations for each major component in the cycle (boiler, turbine, condenser, pump), the thermal efficiency of the cycle can be accurately solved. Thermal efficiency intuitively reflects what proportion of the input heat is successfully converted into macroscopic mechanical work, serving as a universal scale for horizontally comparing the merits of different cycle schemes.
Limitations of Traditional Thermal Efficiency and the Necessity of Energy Quality Evaluation
Although thermal efficiency is widely applied in engineering calculations, it suffers from a fundamental blind spot: it completely follows the conservation of energy quantity according to the first law of thermodynamics while ignoring the differences in energy "quality." In thermodynamics, high-temperature thermal energy and low-grade thermal energy in a low-temperature heat source may be completely identical in quantity (joules), but their potential to convert into useful work (i.e., work-producing capability) differs vastly.
Taking a condensing power plant as an example, the circulating cooling water discharged into the ambient atmosphere carries away a massive amount of heat. Viewed solely from the energy quantity balance of the first law of thermodynamics, this portion of heat does not disappear out of thin air. However, because this heat exists at a tiny temperature difference state relative to the environment, its work-producing capability has approached zero. Traditional thermal efficiency lumps these low-grade energy losses together with the unavailable losses of high-temperature and high-pressure steam, failing to reveal the root cause of the true degradation of energy during the conversion process. To make up for this deficiency, an energy quality evaluation method based on the second law of thermodynamics—the exergy analysis method—must be introduced.
Energy Quality Evaluation Method Based on Exergy Balance
"Exergy" (also known as availability) refers to the maximum theoretical useful work that a system or substance can perform under a given environmental state. Unlike energy, which obeys the conservation law, exergy is not only non-conservative during energy conversion processes, but is always consumed and destroyed due to the existence of actual process irreversibilities (such as friction, heat transfer temperature differences, throttling, etc.). The exergy balance equation is essentially a combination of the first and second laws of thermodynamics, quantitatively describing the quantitative relationship among input exergy, output exergy, accumulated exergy, and exergy destruction.
In the evaluation system based on exergy balance, energy conversion efficiency is usually characterized by "exergy efficiency" (also known as second-law efficiency). Exergy efficiency is defined as the ratio of the effective exergy output in a cycle or device (such as output mechanical work or product exergy) to the exergy input (such as chemical exergy of consumed fuel or physical exergy of a high-temperature heat source). When calculating, it is first necessary to determine the environmental reference state (usually taking the ambient temperature $T_0$ and ambient pressure $p_0$), and then calculate the specific exergy values of each state point. By performing exergy balance calculations for each thermodynamic process in the cycle, one can not only comprehensively evaluate the thermodynamic perfection of the system, but also precisely locate the "weak links" with the greatest exergy destruction in the system.
Application of Exergy Destruction Analysis in the Optimization of Engineering Thermodynamic Cycles
Applying the exergy balance calculation method to practical engineering thermodynamic cycles can provide clear guidance for system improvement. In complex energy systems, irreversible losses are always present. For example, during the boiler combustion and heat transfer processes, huge combustion and heat transfer temperature differences lead to extremely high exergy destruction, which is the fundamental reason why the thermal efficiency of the entire power generation system is difficult to substantially improve; inside turbines and compressors, airflow boundary layer friction and shock waves cause internal exergy destruction.
By calculating the exergy destruction rates of various sub-components, engineers can draw the exergy flow diagram (Grassmann diagram) of the system, intuitively exposing the regions with the most severe energy degradation. This energy quality-based evaluation method changes the blind design mode of the past—treating the head when the head aches and the foot when the foot hurts—and shifts the optimization of energy systems from a single pursuit of "heat recovery" to the deep-seated connotation of "reducing temperature difference losses and lowering exergy destruction," thereby guiding the entire engineering thermodynamic cycle to continuously evolve toward high efficiency, energy saving, and low carbon.