1. Introduction
Subject to the influence of flight speed and flight altitude, the ambient temperature and pressure change considerably throughout the entire flight envelope [
1,
2]. The environmental control system (ECS) performs the functions of pressurization, refrigeration and dehumidification simultaneously and provides the guarantee for the health and comfort of the pilot, crew, and passengers. The air cycle system (ACS) is the most commonly used ECS scheme.
Engine bleed air is the power source for ECS in the vast majority of civil and military aircraft. As the aircraft engine is considered as a highly optimized gas generator, there are penalties associated with the extraction of bleed air. Typically, the ratio of the engine power for driving ECS to the aircraft heat load is 10:1 [
3]. Vargas and Bejan [
4] reported that on a military transport plane such as the C17, the ECS accounts for 64.6% of the engine power at cruise conditions in addition to the irreversible loss of combustion and energy conversion in the engine. In this respect, ECS is one of the largest power consumers among all the nonpropulsive systems [
5]. Therefore, it is vital to explore the thermal power conversion mechanism of the ECS to reduce its penalty and improve the aircraft’s energetic response.
An ECS is composed of heat exchangers, the air cycle machine (ACM), and the water separation module. A variety of ECS architectures (such as two-wheel ACS, three-wheel ACS, and four-wheel ACS [
3]) have been developed to meet the environmental control requirements of different aircrafts under complex flight conditions. There are obvious differences in the thermodynamic performance among different architectures. Most of the existing research on ECS is focused on the two-wheel ACS. According to the different uses of turbine output power, the two-wheel ACS can be divided into simple and bootstrap types [
6]. Vargas and Bejan [
4,
7] optimized the heat exchanger in the bootstrap ACS. Ordonez and Bejan [
8] constructed four simplified ECS-cabin models to evaluate the minimum power requirement for the environmental control of the aircraft. Isabel and Leo [
9] optimized the main geometric characteristics of two finned cross-flow heat exchangers involved in a bootstrap ACS. The application of thermo-economics on ECS was also performed [
10]. These studies focused on achieving the best performance of a specific ECS. However, different architectures of ECS may change the thermal process and affect the layout of ECS on the aircraft.
There are few experimental studies on the ECS of the aircraft in the open literature, and fewer number of comparative studies on different ECSs because the development and testing of an ECS has a high financial cost. Santos et al. simulated the effects of flight and cabin parameters on the ECS performance [
11]. Herber et al. generated many different thermal management system architectures based on graph theory, and evaluated their performance [
12]. Conceição et al. developed the thermodynamic models of three-wheel ACS and four-wheel ACS with equation engineering solver [
13]. Compared with the existing research, this study significantly improves the analysis method of thermodynamic performance of ECS. The application of endoreversible thermodynamic analysis method (ETM) method to ECS can not only predict the performance of ECS under different working conditions rapidly, but also derive the general solutions of the thermodynamic performance of ECS. The ETM was first applied to a Carnot engine by Curzon and Ahlborn [
14]. Compared with the ideal Carnot cycle, the endoreversible cycle considers the temperature difference between the heat source and the working fluid, introduces a time scale and makes the actual thermal process different from the quasistatic process of the ideal cycle. Zhang et al. [
15] established a finite-time thermodynamic model for an air Brayton cycle for recovering waste heat from blast furnace slag. Wang et al. [
16] compared the performance of air-standard rectangular cycles using finite-time thermodynamics. Amir et al. [
17] evaluated and optimized endoreversible combined cycles that considered different heat exchangers. Studies have also been conducted on the Carnot refrigerator [
18], supercritical carbon dioxide brayton cycle [
19], Stirling engine [
20,
21,
22], diesel engines [
23], ocean thermal energy conversion [
24], and chemical engine [
25]. The relationships among the coefficient of performance (COP), the parameters of components and the environment of a two-wheel ACS [
26] and a four-wheel ACS [
27] were obtained based on the ETM. The analytical solutions of COP of five types of electrical-driven ECSs were also compared [
28]. The solutions derived from ETM are only related to the system architecture, have nothing to do with the operating conditions and the component performance, and have strong universality. However, the existing research mainly focuses on the temperature changes in thermal system especially ECS. As an open cycle, the pressure regulation of ECS is of great significance to ensure human safety in high altitude and low pressure environment.
Additionally, the ECS maintains an open system from disorder to order, and from a low-order degree to a high-order degree, conforming to the description of dissipative structure [
29,
30]. The theory of information entropy [
31] can quantitatively evaluate the order degree of a system [
32,
33], which have been applied to investigate the organizational structure of the electricity regulatory institution [
34], the developmental level and harmonious degree of urban ecosystems [
35], etc. The application of information entropy in thermal system will be interesting and worth developing.
In this study, four types of two-wheel ACSs with different architectures are investigated in terms of thermodynamic performance and network structure. The analytical solutions of the COP and pressure of the ECSs are derived based on ETM as algebraic equations, avoiding repeated modeling and calculation. The effects of different bleed conditions, flight conditions and component parameters are discussed. The network structure of the ECSs is constructed according to the graph theory [
36,
37] and compared based on the structure entropy method (SEM) [
38] from the perspective of timeliness and quality of information transmission. This study is conducive to the comparison of the performance of different ECSs, and can reduce the development period and cost considerably. The results provide a solid theoretical basis and a multi-dimensional perspective for ECS evaluation and design, which is conducive to aircraft optimization. With the development of more electric aircraft [
39], the ETM and SEM methods have the potential to be applied to the analysis and comparison of engine thermal management system [
40].
5. Conclusions
(1) The theoretical results based on ETM are consistent with the test results of ECS in the entire envelope. The average error of the temperature at each point of PB-ACS is within 1.8%. The average error of the pressure at each point is less than 2.61% after considering the pressure loss in HX1 and HX2.
(2) The analytical solutions of the outlet temperature, outlet pressure, and COP of four types of two-wheel ACSs with different architectures are derived based on the ETM. These successfully separate the external and internal factors on the thermal performance of the ECS. The forms of different systems are identical, but each system has unique coefficients.
(3) In the view of thermodynamic performance, the connection mode of the heat exchangers has minor effects on the performance of ECSs, but the influence of the ACM is obvious. In the aspect of network structure, the ACM scheme mainly affects the dispersion of timeliness and quality, and the connection mode of heat exchangers plays a role in the order degree of structure.
This study verifies the feasibility of ETM and SEM. Some useful conclusions have been obtained from the comparative analysis of the ECSs, which can provide suggestions for the design of aircraft engineers. However, the real physical system is a comprehensive network structure of material, energy, and information. We need to further explore the physical connection between the network structure and the actual system, realize the quantitative evaluation of different types of information transfer process, and analyze the relationship between information entropy and thermodynamic entropy.