John H. Doty

Benefits of Exergy-Based Analysis for Aerospace Engineering Applications—Part I

This paper compares the analysis of systems from two different perspectives: an energy-based focus and an exergy-based focus. A complex system was simply modeled as interacting thermodynamic systems to illustrate the differences in analysis methodologies and results. The energy-based analysis had combinations of calculated states that are infeasible. On the other hand, the exergy-based analyses only allow feasible states. More importantly, the exergy-based analyses provide clearer insight to the combination of operating conditions for optimum system-level performance. The results strongly suggest changing the analysis/design paradigm used in aerospace engineering from energy-based to exergy-based. This methodology shift is even more critical in exploratory research and development where previous experience may not be available to provide guidance. Although the models used herein may appear simplistic, the message is very powerful and extensible to higher-fidelity models: the 1st Law is only a necessary condition for design, whereas the 1st and 2nd Laws provide the sufficiency condition.

Designed Experiments: Statistical Approach to Energy- and Exergy-Based Optimization

We extend the energy and exergy-based methodology presented in previous work 1,2 from analysis to preliminary design. Therein, a three-component system was modeled in which heat transfer from the energy source was allowed, while the other devices were considered to be reversible. Those single-parameter studies yielded many results which were physically impossible, clearly suggesting that the analysis/design paradigm be changed from energybased to exergy-based. Here, we extend the analysis to preliminary design applications. A steam turbine with fixed inlet conditions was modeled thermodynamically and simulated in MATLAB using three design variables: turbine exit quality, turbine exit pressure, and turbine heat transfer. A statistically generated test matrix was developed using Design of Experiments (DOE) for three test cases. For the first test case, only the quality was varied while exit pressure and heat transfer remained constant. For the second test case, both quality and exit pressure were varied while heat transfer remained constant. The last case allowed all three design variables to vary simultaneously. The test matrix was analyzed using a 1 st Law as well as combined 1 st and 2 nd Law methodology to determine turbine specific work and exergy destruction for the system. Results from the test cases were analyzed to generate surrogate models used for turbine optimization.

Statistical, Modular Systems Integration Using Combined Energy & Exergy Concepts

This paper details statistical concepts to systems-level applications with relevance to integration, operation, and optimization of engineering components and systems. A physicsbased exergy analysis is combined with system performance goals. Designed experiments are used to pre-determine relevant simulation points for the analysis in order to develop the statistical models most effectively and efficiently. The results of the simulation are then processed via advanced statistics to create a surrogate model that identifies the component and/or system within desired or anticipated operational ranges. These statistical surrogate models represent the system in a modular fashion. In this manner, a statistical module may be interfaced independently from its origination and a “system of systems” may be built from the surrogate modules that may be used to efficiently investigate engineering trades and perform preliminary design studies. Quantitative examples from aerospace components and systems are used to demonstrate the overall process.

Approximate Approach for Direct Calculation of Unsteady Entropy Generation Rate for Engineering Applications

A new formulation is presented for calculation of unsteady entropy generation rate for thermophysical systems. This formulation has far-reaching implications for analysis and design of all systems. It has long been considered that direct calculation of entropy generation rate was impossible due to the insufficiency of independent information for simultaneous determination of both unsteady entropy change and entropy generation rate. The formulation presented herein is consistent with numerical implementations and presents a unique approach to solving this dilemma. Entropy is re-cast is terms of other, independent, state properties via the state postulate of thermodynamics and then the rate of change of entropy is represented in terms of other known state derivatives. The concept is generally applicable to physical systems as long as the state postulate is valid and the state derivatives are known. The application of this formulation allows for the path-dependent entropy generation rate to be directly calculated.

Metastable Equilibrium of a Dynamic Electrical System in Terms of Entropy Generation Rate

Transient dynamic DC electrical systems are often characterized by response time, amount of damping, and dynamic behavior of outputs in terms of input functions. This investigation correlates some of these standard responses in terms of nonequilibrium entropy generation rates to illustrate the concept of thermodynamic equivalence of metastable DC electrical systems. A resistor, inductor, capacitor (R, L, Ca, respectively) series circuit is subjected to a direct current (DC) step load change in voltage and the response is characterized using standard methodologies and compared/contrasted to the thermodynamic approach in which the metric is entropy generation rate. It is determined that metastable equilibrium is equivalent to the rate of change of entropy generation rate with respect to temporal rate of change in voltage of the dissipative resistor component. Using combined 1 st and 2 nd Laws of Thermodynamics, the total entropy generated is directly related to the thermal waste energy of the circuit.

Statistical Exergy-Based Analysis of a Steam Power Plant for Concept Verification and Plant Optimization

In this statistical exergy study of a conventional power plant, the concept of statistical exergy analysis as an alternative to common engineering approaches is examined. The statistical aspect is drawn from conducting Analysis of Variance (ANOVA) factorial design on the components of a proposed system. The exergy aspect comes in the extension of the typical energy analysis on engineering systems to include the limitations on the system imposed by the second law of thermodynamics.To test this approach, a steam power plant discussed in an example exercise in Cengel and Boles’ 5th Edition Thermodynamics textbook was used as the subject of analysis. Effects of three input parameters on 13 responses were closely examined.While using only 8 data points, the analysis still showed highly reliable and predictable results with square of residuals (R2) values of almost 100%. Predicted R2 values ranged between 88% and 99% with one outlier of 14.36%, depending on the input parameters.Derived from the results, a new plant design concept was proposed and analyzed. This design eliminated all theoretically unnecessary drivers of exergy destruction in the plant. It also utilized the force of gravity to achieve the desired power output. The design showed an increase of 3.85% to 18% in kilowatts of work output and 5% to 7% in first and second law efficiencies. In this case, the derived design was shown to be impractical due to difficult maintenance as well as the difficulty in reaching the required pressures without a pump. However, this method of statistical exergy analysis is still valuable, as practicality of application will vary from one proposed system to another.Copyright