Rotating Detonation Combustor Research Articles

Stability investigation of two-phase n-decane rotating detonation waves

In this paper, three-dimensional rotating detonation combustor fuelled by n-decane sprays is numerically investigated with Eulerian-Lagrangian method. The flow field characteristics, the effects of injection total pressure and oxygen mass fraction on the stability of two-phase rotating detonation wave are analysed. The results show that the mixing-dominance and the reaction-dominance are two mechanisms affecting the stability of two-phase rotating detonation wave. Specifically, injection total pressure mainly affects the fuel mixing in non-premixed configuration. Increasing the total pressure improves the droplet evaporation, such as the reduce of the droplet evaporation distance, Sauter mean diameter and the rise of droplet evaporation rate. Besides, the stability of two-phase rotating detonation wave is nonlinear, the highest stability happens in 1.5MPa, which is due to the collision of shock wave and rotating detonation wave. On the other hand, oxygen mass fraction has a significant effect on the reactivity of reactant and leads to the wave propagation mode transition. The increasing of oxygen mass fraction broadens the high reaction rate zone, which provides a suitable environment for the generation of local explosions. The local explosions gradually develop into detonation waves and form multi-wave mode after a complex self-adjusted process. Moreover, the stability of two-phase rotating detonation wave is in proportion to the oxygen mass fraction. As the increase of oxygen mass fraction, the fluctuations of pressure and detonation speed tend to be smooth, which implied the higher stability in multi-wave mode. The analysis about stability of RDW may be beneficial to the design of two-phase rotating detonation engines.

Performance Characteristics of a Rotating Detonation Combustor Exiting Into a Pressurized Plenum to Simulate Gas Turbine Inlet

Abstract The present study aims to experimentally characterize the performance of a rotating detonation combustion (RDC) system integrated with a pressurized downstream plenum to simulate the high-pressure inlet conditions of power-generating gas turbines. A thorough understanding of the operational behavior including wave mode behavior, static pressure profile along the combustor length, and dynamic features of pressure fluctuations is crucial for successful integration of RDC with the turbine. In this study, two RDC configurations are investigated, RDC with a constant area annulus and RDC with a converging nozzle. In both cases, the RDC flow exited into a plenum chamber kept at pressures varying from 155 kPa to 330 kPa. RDC was operated on methane and oxygen-enriched air to represent reactants used in land-based power generation. Experiments were conducted for the two RDCs configurations operated at three reactant mass flow rates (0.23, 0.32, and 0.46 kg/s). The RDC performance is characterized by time-averaged static pressure measurements, and wave velocity determined by ionization probes. In addition, dynamic pressure measurements were recorded both inside and near the exit of RDC channel to investigate wave interactions between RDC and downstream plenum. Results show that the RDC with the converging nozzle achieved superior performance while minimizing detrimental interactions with the reflected shock and/or acoustic waves from the downstream plenum.

Validation of Rotating Detonation Combustor Computational Fluid Dynamics Simulations for Predicting Unsteady Supersonic–Subsonic Flow Field at the Exit

Abstract Rotating detonation combustors (RDCs) have gained increased interest for integration with power-generating gas turbines due to the potential to increase thermal efficiency. The unsteady flow field exiting the RDC is fundamentally different compared to traditional swirl-stabilized combustors. Successful integration of RDC with gas turbines will depend on the ability to properly condition the unsteady flow to achieve performance levels comparable to swirl-stabilized combustors. RDC simulations require significant computational resources due to the small spatial and temporal time scales required to resolve the detonation phenomenon. Furthermore, traditional steady-state computational fluid dynamics (CFD) analyses are not possible for RDC simulations. The present study develops and validates a computationally efficient approach for predicting unsteady flow fields exiting the combustor using 2D, transient reacting CFD with periodic boundary conditions in the combustor and a downstream plenum. Validation is performed by comparing the CFD results to various experimental measurements: (i) wave speed obtained from high-speed ion probe and dynamic pressure data, (ii) average wall static pressure measurements, and (iii) time-resolved particle image velocimetry (PIV) at 100 kHz at the RDC exit. Results indicate good agreement between CFD and experiments with respect to velocity field exiting the RDC, detonation wave speed, and static pressure distribution.

Comprehensive analysis method of acquiring wall heat fluxes in rotating detonation combustors

Accurate perception of the combustor thermal environment is crucial for thermal protection design of a rotating detonation combustor (RDC). In this study, a comprehensive analysis method is established to calculate the non-uniform heat flux distribution of the RDC by utilizing the measured temperature distribution of the combustor outer wall obtained by the high-speed infrared thermal imager. Firstly, a physical model based on the geometric characteristics of the RDC is constructed and its thermal conductive process is simulated, given by different heat flux boundary conditions. The analysis results indicate that the method used in current research for computing the heat flux of RDC leads to significant discrepancies, particularly in regions of obvious axial heat flux gradients near the top of the combustor. Then the Levenberg-Marquardt (L-M) method for inversely solving non-uniform heat flux is developed based on the two-dimensional heat conduction equation, and the wall heat fluxes are inversely calculated by the L-M method based on the above numerical data. Results show that the L-M method can obtain more accurate heat flux distribution even in the zones with large heat flux gradients, considering the axial heat conduction within the combustor outer wall caused by the non-uniform heat flux. Finally, the wall heat flux distribution is analyzed coupling the L-M method together with the experimental measurements in kerosene two-phase RDC. The analyses show that the wall heat flux exhibits non-uniform distributions both circumferentially and axially, with axial non-uniformity being particularly pronounced. The highest temperature of combustor outer surface and the highest wall heat flux occurs within the region of 20 mm from the combustor head, which corresponds to nearly 14 % of the combustor length. The heat flux peak and thermal heat rate are positively correlated with the combustor equivalence ratio in the range between 0.44 and 0.64. In this study, the distribution of wall temperature field in the two-phase RDC is obtained for the first time and the wall heat flux is calculated inversely by L-M method. This work provides a more accurate method for calculating heat flux in RDC and offers references for thermal protection designs in RDCs.

Experimental Study on Combustion Efficiency and Pressure Gain Characteristic of RDC with Guide Vanes

ABSTRACT The influence of guide vanes on the combustion efficiency and pressure gain characteristic of rotating detonation combustor was studied. In this experiment, aviation kerosene (RP-3) was used as fuel and hot air was used as oxidant under the condition of maintaining a certain air flow of 1.5 kg/s. The Temperature rise method was used and the combustion products were analyzed by the flue gas analyzer to calculate the combustion efficiency. Pressure gain characteristic of the rotating detonation combustor was calculated by the mass flow function method (MFFM). The detonation was successfully initiated and operated stably in two rotating detonation combustor configurations without guide vanes and with guide vanes installed. Without the guide vanes, the equivalent ratios for reliable operation of the rotating detonation combustor were relatively small, and the mode of detonation wave propagation is mainly two-counter rotating wave mode. Behind the guide vanes were installed, the range of equivalent ratios for reliable operation of the rotating detonation combustor moved to the appropriate chemical equivalent ratio, and the main mode of detonation wave propagation is two-co rotating wave mode. When the guide vanes were installed, the combustion efficiency of the rotating detonation combustor reached the maximum value of 60.29% when the equivalence ratio is 0.78. In both combustor structures, the pressure gain characteristic increased with the increase of equivalence ratio.

Parametric Influence on Rotating Detonation Combustion: Insights from Fast Reactive Euler Simulations

A two-dimensional unsteady reactive Euler solver is employed to model rotating detonation combustion (RDC). A baseline case is chosen, and several combustor geometric and design parameters are varied individually in order to assess their effect on flowfield structure, exhaust flow properties, and performance. The parameters of interest are the perimeter and axial lengths of the combustor annulus, mass flux, outlet throat area, air injector throat area, and equivalence ratio. Quantification of the isentropically available work (IAW) in the exhaust flow is employed as a performance criterion. IAW is primarily affected by mass flux and outlet throat area through the effects of one-dimensional flow and, to a lesser degree, by perimeter and axial length through changes in the fraction of the flow that experiences irreversible shock processing. For all cases in the present study, this fraction appears to be solely determined by the ratio of detonation height to axial length. This ratio is also highly correlated to the angle of the oblique shock and the strength of the flow fluctuations. The predicted wave speed is between 90 and 95% of the Chapman–Jouguet velocity for a range of equivalence ratios between 0.6 and 1.4.

Super-resolution flow-field reconstruction in rotating detonation combustors

The high-resolution flow field information is crucial for understanding the operational mechanisms of rotating detonation combustors (RDCs). However, due to limitations in sensor technology and observation techniques, the present experimental methods face great challenges in obtaining high-resolution data of RDCs. In the study, a novel physics-informed deep generative model is proposed for super-resolution flow-field reconstruction with low-resolution inputs. Compare to other methods, the application of physics-based constraints in this method enables accurate reconstruction of critical phenomena in RDCs while maintaining physics consistency. Additionally, the proposed super-resolution reconstruction method can be further employed for low sampling depth even binary input data, thereby evidently reducing the sampling depth per measurement point, which helps to overcome the challenges associated with high-frequency data acquisition and facility the implementation of larger-scale measurement arrays. As an extension to the measurement capabilities in reactive flow systems, the presented model possesses notable engineering significance.

Evaluation of Uncertainties of Pressure Gain Measurements in Rotating Detonation Combustor

Experimentally measuring the pressure gain of a rotating detonation combustor through the method of equivalent available pressure is prone to many experimental uncertainties. A detailed analysis of sources of random and systematic uncertainties in the thrust and pressure gain is performed using data from a hydrogen/air-operated rotating detonation combustor. The combustor had an axial air inlet and a 50% exit constriction. The measured (negative) pressure gain values agree with the results in the literature for similar inlet-to-exit area ratios. The base drag correction on the centerbody was found to be the greatest source of uncertainty for the thrust. While thrust is the predominant source of random uncertainty in the pressure gain calculation, significant systematic errors can be committed due to the assumed exit Mach number. The impact of this assumption becomes more detrimental the closer to positive the measured pressure gain is. By experimentally evaluating the exit Mach number, the random and systematic uncertainty in pressure gain both decreased, indicating that this should be an essential step. A definitive demonstration of gain is challenging, given the assessed uncertainties, and recommendations are provided to increase the precision of the equivalent available pressure methodology.

Combined Joule-Humphrey-Recuperator Cycle: Performance and Parametric Analysis Evaluation Toward More Efficient Air Transportation

Abstract A three-stream combined Joule-Humphrey cycle that employs a heat recovery stream to function as a recuperator is presented. Based on an in-house developed thermodynamic performance tool, the operation of a modified dual-shaft turbofan engine is proposed. The engine core is modified by adding an intercooler and a reheating chamber to approach isothermal compression and expansion processes. A fraction of the primary flow is introduced into a reheat chamber that uses rotating detonation combustion (RDC) technology. The outflow of the RDC is then merged with the rest of the nucleus current before being discharged to the next turbine stage. The overall system behavior is captured by means of a nonlinear mathematical model featuring eight decision variables, including mass flow rates and compression ratios. A parametric analysis identifies the operational and performance envelope of the proposed engine concept. Ultimately, the model is endowed with an objective function, which includes global efficiency and thrust looking for an operation regime that boosts the thermodynamic performance. A generalized reduced gradient based algorithm is used to solve the nonlinear model, where each iteration solves a linearly constrained subproblem to generate a search direction. The performance and operational envelope presented here could be used as guidance for others considering the implementation of any of the discussed Joule cycle modifications or assessing the cost-effective balance of their use.

Numerical study on the interaction between rotating detonation wave and turbine stator blades with multicomponent mixtures

Aiming at the coupling problem between rotating detonation combustor and turbine components, this paper uses methane recuperation gas as fuel and adopts two-dimensional numerical simulation to study the working process after coupling between rotating detonation combustor and turbine stator blades. The results show that with the increase of methane conversion, the propagation mode changes from single wave mode to unstable single wave mode. Under the two modes, after the oblique shock wave sweep, the turbine stator blade outlet Mach number suddenly rises to 2.5. In addition, the flow field structure of a single turbine blade is also analyzed, and it is found that after oblique shock wave sweep, the flow field structure changes, and boundary layer separation occurs at the trailing edge of turbine stator blades. Turbine stator blades have a certain inhibition effect on the pressure oscillation at the combustion chamber outlet, and the disturbance generated by detonation wave extinguishing in unstable single-wave mode will be transmitted through turbine stator blades to the outlet. With the increase of fuel activity, turbine stator blade pressure loss gradually increases. The total pressure loss coefficient of single-wave mode is 9%, and the total pressure loss coefficient of unstable single-wave mode is 4%–6% higher than that of single-wave mode.

Effect of equivalence ratio on rotating detonation combustion with n-heptane sprays

Three-dimensional simulations are conducted for rotating detonative combustion fueled by n-heptane sprays without any fuel pre-vaporization. Parametric studies are performed to study the influences of equivalence ratio on the rotating detonation wave. The decoupled process of the detonation wave with lean equivalence ratio is also been analyzed. It is found that when the global equivalence ratio is lower than 0.6, a stable propagating detonation wave cannot be observed in the combustion chamber. With the gradual increase of the global equivalence ratio, the detonation wave can stably propagate in the combustion chamber after ignition. When the global equivalence ratio is 0.8–1.5, the propagation mode of the detonation wave in the combustion chamber is one-way propagation mode. When the global equivalence ratio gradually increase from 0.8 to 1.5, the formation time of the detonation wave first decreases and then increases with the increase of the equivalence ratio. Besides, the stability of the detonation wave first increases and then decreases with the increase of the equivalence ratio. Moreover, the thrust of the rotating detonation chamber fueled by n-heptane increases gradually with the increase of the equivalence ratio. The specific impulse of the combustion chamber first increases and then decreases with the increase of the equivalence ratio.

Experimental study of mode control in rotating detonation combustor using Tesla valve mode control configuration fueled by kerosene

The detonation mode has a significant impact on the operational characteristics and propulsion performance of the rotating detonation combustor (RDC). Controlling the combustion mode effectively is advantageous for improving the propulsion performance of the pressure gain combustor. A Tesla valve mode control combustion chamber (TVMC) was used for experimental research in this study. An equal-width annular combustion chamber (EWA) was used as a control test, with room temperature kerosene as the fuel, and oxygen-enriched air as an oxidizer. The experiment successfully validated the feasibility of mode control in TVMC along with its operational characteristics. Monitoring the pressure pulsation of detonation and guide channels in TVMC led to the unfolding of possible mode control mechanism. The results indicated that the rotating detonation wave (RDW) propagates clockwise in TVMC. After RDW propagating counterclockwise enters the guide channel, the width limitation of guide channel causes RDW decoupling. It changes the propagation direction of the leading shock wave, resulting in mode control. Because of the presence of a guide channel, the RDW is unstable at low equivalence ratios, and the operation range is also narrower.

Consideration of Nonideal Detonation Regimes Influenced by Wave Modes in a Water-Cooled Rotating Detonation Engine Using OH* Chemiluminescence

Abstract Although inherently unstable, existing research in rotating detonation combustion supports its application in notionally steady processes resulting in greater availability compared to conventional, constant pressure combustion. Further improvements rely on a more in-depth understanding of system losses and identifying conditions which optimize device performance. Within this study, the presence and proportion of ideal and nonideal combustion regimes are compared across a variety of process conditions and wave modes. Large-scale data analysis seeks to summarize proportional heat release associated with commensal, parasitic, and detonative combustion averaged across individual traces of OH* chemiluminescent data acquired at the detonation plane. Means of regime partitioning based on the anatomy of the time-resolved OH* signal are proposed to ensure consistent analysis throughout the current and future studies concerning combustion regimes. Of particular interest is the possible influence of wave on the nonideal combustion in relative proportion to the desired detonation. Results showed improved percent detonation with increasing significance for the following trends: decreasing equivalence ratio, increasing wave count, decreasing wave velocity, and increasing detonation time. Increased wave number, brought on by decreased equivalence ratios and wave velocities, is thought to decrease fill region surface area, and therefore, decrease nonideal contact burning. Additional analysis is performed to consider possible trend variation due to the presence of stable galloping waves, which were found to have minimal influence on relative percent detonation values. The outcome of this study suggests operational states, which correspond to increased wave quantities for increased proportions of reactants consumed by the targeted detonative combustion regime.

Characterization of refill region and mixing state immediately ahead of a hydrogen-air rotating detonation using LES

The extraordinary complexity of real Rotating Detonation Combustors (RDC) demands a deep knowledge of each phenomenon involved in the wave development and propagation. Since the reactants are typically injected separately, a key element for the combustor design optimization is understanding the refilling process and the reactants mixing. However, due to the harsh environment and high working frequencies of RDCs, the experimental diagnostics is usually limited, so high-fidelity simulations represent an essential tool to complement the measurements with detailed insights into the flow. In the present work, the non-premixed RDC installed at TU Berlin is simulated with the AVBP code by solving the fully-compressible, spatially-filtered reactive Navier-Stokes equations. The complete hydrogen and air injection system is included in the numerical model to accurately describe both the reactants mixing and the complex turbulent flow field in the resulting refill region. This study shows how both the injection system configuration and its transient interaction with the wave are fundamental for the reactants mixing, as they directly influence the refilled gas properties. Limiting the imbalances between the blockage dynamics of the fuel and oxidizer ducts and optimizing the fuel injectors can improve considerably the homogeneity of the fresh mixture, and consequently the leading shock strength and reasonably the pressure gain. In fact, the detailed analysis of the detonation front speed shown a higher instability near the chamber base for the periodic presence of unmixed reactants. Nevertheless, the unstable root of the front does not affect the whole wave speed, and remaining part propagates steadily thanks to the tangential mixture uniformity. Moreover, the local speed distribution does not appear directly related to the small-scale mixture properties, indicating a higher sensibility to the annulus curvature rather than to the local gas state.

Numerical study on rotating detonation combustion with the discrete distribution of partially pre-vaporized n-heptane sprays

The rotating detonation engine (RDE) is a novel aerospace propulsion device, with liquid fuel playing a pivotal role in enabling the practical implementation of the RDE. The Eulerian-Lagrangian simulation is used to analyze a two-dimensional rotating detonation combustion with partially pre-vaporized n-heptane sprays. The investigation aims to examine the influence of various inlet area ratios (ψ) on both the droplet evaporation and rotating detonation combustion within the combustion chamber. The findings indicate that a smaller ψ is advantageous for droplet evaporation within the fuel filling area, and the droplet traverses sequentially through the acceleration layer, the deceleration layer, and the re-acceleration layer within this region. With a relatively large ψ, a burned gas bump becomes evident on the deflagration surface, augmenting the evaporation rate of droplets within its proximity. The droplet continues to accelerate within the fuel filling area, while its velocity remains low at the burned gas bump. Furthermore, spot-like diffused flames emerge subsequent to the RDW, with their area expanding to the increase in ψ. Meanwhile, the average heat release rate (HRR) and thrust within the combustor of the rotating detonation engine (RDE) demonstrates diverse oscillation patterns in response to changes in ψ. In this study, when the inlet area ratio is around 0.6, the RDE obtains the most stable average HRR and thrust.

On the Potentials of the Integration of Pressure Gain Combustion with a Hybrid Electric Propulsion System

As the issue of pollutant emissions from aviation propulsion escalates, research into alternative powertrains is gaining momentum. Two promising technologies are the Hybrid Electric Propulsion System (HEPS) and Pressure Gain Combustion (PGC). HEPS is expected to reduce pollutant emissions by decreasing fuel consumption, whereas PGC uses detonation in the combustor to increase the thermal efficiency of engines by elevating the total pressure during combustion. This study extensively explores the integration of these two emerging technologies, thoroughly assessing the advantages that arise from their combination. First, the renowned turboprop engine PW127 is benchmarked and modeled using Gasturb software. The model is integrated into Simulink using the T-MATS tool, with HEPS and pressure gain components added to analyze the thermodynamics of various configurations under different pressure gain values and HEPS parameters. The analysis, conducted up to the cruise phase of the baseline aircraft, reveals that applying pressure gain combustion through Rotating Detonation Combustion (RDC) results in a more significant increase in efficiency and decrease in fuel consumption compared to HEPS with conventional gas turbines. However, HEPS helps maintain a more uniform combustor inlet condition and reduces the Turbine Inlet Temperature (TIT) at the takeoff phase, where the highest TIT otherwise occurs. The results suggest that integrating HEPS with PGC can be beneficial in maintaining optimal combustor conditions and mitigating turbine efficiency degradation.

Experimental investigation on pulse operation characteristics of rotating detonation rocket engine

The pressure-gain rotating detonation rocket engine is expected to develop as an attitude/orbit control power device for high-performance spacecraft. In this paper, the short-time pulse operation characteristics of a rotating detonation rocket engine were investigated experimentally. A rotating detonation combustor with a diameter of 60 mm was employed, and the H2 and oxygen-rich air were separately injected into the combustor to initiate the detonation wave. The results showed that the rotating detonation rocket engine can obtain continuous rotating detonation modes with the pulse operating frequency of 1–5 Hz, and the pulse frequency could not affect the propagation mode and velocity of the detonation wave. During the multi-pulse operation of the rotating detonation rocket engine, the detonation wave could realize continuous propagation at each pulse stage. With the increase of the pulse number, the propagation velocity of the rotating detonation wave tended to increase slightly, and the establishment time gradually decreased. A suitable multi-pulse operation timing of the rotating detonation rocket engine was set in this experiment, and the feasibility of long-duration multi-pulse operation with rotating detonation mode was successfully verified.

Wave mode analysis of a turbine guide vane-integrated rotating detonation combustor based on instantaneous frequency identification

Owing to the pressure gain combustion characteristics, the gas turbine can enhance the system thermodynamic cycle efficiency by integrating a rotating detonation combustor (RDC). In this study, an experimental model of a hydrogen/air RDC with a variant installation of turbine guide vanes (TGVs) was developed. A mathematical model was proposed to identify the rotating detonation wave (RDW) propagation direction. The accuracy of the calculated RDW instantaneous velocity was improved, and the range of velocity fluctuations narrowed from 200 to 1700 m s−1 to 800–1600 m s−1. The impact of TGV installation on the rotating detonation characteristics was investigated. Both the RDW frequency and static pressure increased by installing the TGV at the combustor outlet. The propagation direction of the initial detonation wave induced the RDW to propagate along the same direction. TGV installation reduced the discrepancy in the RDW velocity between two opposite directions as well as the propagation direction changing frequency, while the inverse TGV installation achieved better optimization. The high-frequency pressure oscillations attenuated at the downstream of the TGV, and the amplitude varied depending on the TGV installation options. The static pressure decreased by 14%–16% in both TGV installation options when the combustion flow travelled through the TGV.

Experimental Study on the Propagation Characteristics of Rotating Detonation Wave with Liquid Hydrocarbon/High-Enthalpy Air Mixture

Rotating detonation engines (RDEs) are a promising propulsion technology featuring high thermal efficiency and a simple structure. To adapt the practical engineering applications of ramjet RDEs, rotating detonation combustion using a liquid hydrocarbon and pure air mixture will be required. This paper presents an experimental study on the propagation characteristics of rotating detonation waves with a liquid hydrocarbon and high-enthalpy air mixture in a hollow cylindrical chamber. The parameters, such as the equivalence ratio and inlet mass flux, are considered in this experiment. The frequency and the propagation velocity of rotating detonation combustion are analyzed under typical operations. The experimental results show that the peak pressure and propagation velocity of the rotating detonation wave are close to the C-J theoretical values under the inlet mass flux of 400 kg/(m2s). Both the propagation velocity and peak pressure of the rotating detonation wave decrease as the mass flux and equivalence ratio are reduced while the number of detonation wavefronts increases. Detonation wave instability tends to occur when the inlet mass flux decreases. There is a transition progress from thermo-acoustic combustion to rotating detonation combustion in the experiment under the condition of mass flux 350 kg/(m2s) and the equivalent ratio 0.8. The static pressure in the chamber is higher during detonation combustion than during thermo-acoustic combustion. These experimental results provide evidence that rotating detonation waves have the potential to significantly improve propulsion performance. The findings can serve as a valuable reference for the practical engineering application of rotating detonation engines.

Multi-wave effects on stability and performance in rotating detonation combustors

Recently, with the development of detonation-based propulsion systems, scholars have begun to study how to perform mode control on the rotating detonation combustor (RDC). It is important to figure out the influence of operation mode transition on the RDC. Actually, the essential of different modes is the different multi-wave structures. In this study, two-dimensional numerical simulations of the RDC are conducted to study the multi-wave effect on the stability and performance of the RDC. A uniform inlet condition is adopted in simulations to eliminate the impact of discrepancy mass flow rates, and a mode-locked ignition method is used to induce RDC flow fields with different detonation wave numbers. It is found that the flow field stability and outlet uniformity are improved with increasing detonation counts, and the energy proportion in the flow field is little affected by the multi-wave structure. However, the increase in detonation number will cause a reduction of the mass-averaged total pressure ratio at the exit. Underlying relationship between the unsteady flow field and the total pressure gain is discussed. The total pressure gain is directly linked with the non-uniformity of the circumferential flow field. Then, by utilizing particle trace, the envelope of the thermodynamic cycle is illustrated and the pseudo-thermal efficiency of each case is given. The result implies that the wave number has hardly effect on the thermal efficiency of the combustion chamber. By summarizing the perimeter, axial length, and wave number in the combustor, parameter ξ is carried out and its effects on the uniformity and total pressure ratio in the RDC are concluded.