## 1 Introduction  
Due to obvious advantages in size, weight, and maneuverability, gas turbines play a crucial role in fields such as industry, marine, and aerospace. Nowadays, faced the rising demands for energy conservation and emissions reduction, the development of high-performance gas turbines with low fuel consumption and low pollutant emission is attracting growing attention [1]. Therefore, how to improve the overall thermal cycle performance of gas turbines is a very important challenge for both academia and industry. Simple cycle-based gas turbines usually follow the classic Brayton cycle theory and their thermal cycle performance directly depends on the thermodynamic processes of components, such as compressors, combustors, and turbines. In general, Brayton cycle-based gas turbines burn fuel in a limited space and steady state combustor at an approximate constant pressure (commonly called an approximate constant pressure combustion process) [2]. Due to complex chemistry reactions, heat transfer, and turbulent flow, this kind of combustion process can generate a large amount of entropy that is usually higher than that of the compressor and turbine. Additionally, because the pressure gain in Brayton cycle-based gas turbines is mainly or only obtained by compressors, which are driven by turbines, the enhancement degree of gas turbine cycle efficiency can be further restrained by the thermodynamic performance of the combustor. In order to break through the bottleneck of constant pressure combustors on the thermal cycle performance of gas turbines, many advanced pressure gain and low entropy generation combustion technologies have been developed in recent decades, including resonant pulse [3], wave rotor [4; 5; 6; 7], shockless explosion [8], and detonation [9]. As a kind of advanced detonation and combustion mode strong coupling of shock waves and chemical reactions, continuously rotating detonation (CRD) combustion has many potential advantages (such as self-pressure gain, fast heat release, low entropy generation, easy operation, and control) in comparison with conventional approximate constant pressure combustion and many other pressure gain combustion types [10]. In recent years, many studies have been published into the potential application values of CRD combustion across various fields. Most of the available results indicate that the rapid development of CRD combustors could provide an effective way to improve the thermal cycle performance of gas turbines. For example, researchers from a U.S. naval research laboratory reported that CRD-based engines had the potential to meet 10% increased power requirements, as well as reduce future fuel use by 25%, which could save approximately 300 to 400 million dollars a year [11]. [PERSON] et al. [12] and [PERSON] et al. [13] quantitatively evaluated the thermodynamic benefits of gas turbines equipped with CRD combustors versus conventional technology using constant pressure combustion, under different operating conditions. Their analyses consistently demonstrated the significant promise of CRD combustors at relatively low compressor pressure ratios. In past research [14], the present authors investigated the effects of different factors on the performance enhancement of marine gas turbines using CRD combustors. The results also indicated that CRD combustors could significantly improve the thermodynamic performance of marine gas turbines under various conditions. When the compression ratio ranged from 13 to 30, both thermal cycle efficiency and specific power enhancements were about 20-27%. Over the past decades, various studies have also been carried out to analyze how and why CRD combustors could affect engine performance. [PERSON] et al. [15] developed a reduced-order model to study the characteristics of streamline and thermodynamic paths in CRD combustors, which provided a good zero-dimensional tool to analyze the T-S diagram of the CRD cycle. [PERSON] et al. [16] modified a one-dimensional detonation thermodynamic cycle by using velocity triangles.