Combined Cycle Engine Research Articles

Finite-time control for polynomial parameter-varying systems and its application in mode transition of turbine-based combined cycle engines

This article investigates the problem of finite-time control for the mode transition of turbine-based combined cycle (TBCC) engines described in the polynomial parameter-varying (PPV) framework. In order to realize small-deviation mode transition, a PPV model that can be applied to different opening rates of an inlet splitter is established for a TBCC project put forward by Xiamen University named Xiamen Turbine-based Ejector Ramjet (XTER). The concepts of [Formula: see text] uniformly finite-time stability and [Formula: see text] uniformly finite-time output tracking performance are proposed, together with the corresponding state-and-parameter-dependent controller design conditions which can be efficiently solved by using sum-of-squares programming. Meanwhile, based on the PPV system of XTER, the controllers are designed in the designed flight conditions and the non-designed flight conditions, respectively. Finally, simulation results on the mode transition of the XTER are given to verify the feasibility and effectiveness of the proposed control scheme.

Flight trajectory optimization study of a variable-cycle turbine-based combined cycle engine hypersonic vehicle based on airframe/engine integration

Abstract To investigate the optimal flight trajectory for hypersonic vehicle and Turbine-Based Combined Cycle (TBCC) engine to enhance mission efficacy, a performance calculation model of a variable-cycle TBCC engine is developed utilizing the method of airframe/engine integrated performance analysis. Employing the Radau pseudospectral method for trajectory optimization, the study of the hypersonic vehicle involves the angle of attack, the scramjet engine equivalence ratio, and the core driven fan stage (CDFS) stator vane angle as control variables. Two optimization scenarios were considered: minimizing climb time and maximizing range. The findings indicate that by optimally adjusting the angle of attack and the scramjet engine’s equivalence ratio, the vehicle’s climb time can be reduced by up to 33.68 %, and the total flight duration by 8.07 %. Moreover, optimizing these variables, along with CDFS stator vane angle, can decrease fuel consumption during climb and potentially extend cruising distance by 8.56 %, increasing overall range by 3.63 %.

Combustion performance of an evaporative flameholder under subsonic-supersonic mixing inflow

The combustion process in rocket-assisted subsonic ramjet engines represents a key advancement in integrated aerospace propulsion, particularly for embedded rocket-based systems. These engines offer the potential to improve combustion performance at altitudes of 25–35 km. However, the significant temperature and velocity differentials between the rocket jet and the subsonic ramjet flow restrict heat and mass transfer. Investigating the relationship between combustion performance and inlet parameters under subsonic-supersonic mixing conditions offers a promising approach to enhancing thrust performance. This study introduces subsonic and supersonic airflow mixing via a flat-plate shear layer in a rectangular channel, with an evaporative flameholder placed centrally to assess combustion. Results reveal that combustion efficiency decreases as the equivalence ratio exceeds 0.2, while the static temperature ratio has minimal impact on efficiency but strongly influences the maximum flame stabilization limit. As the temperature ratio increases from 1.30 to 1.80, the flame limit narrows from 1.656 to 0.237. Higher pressure ratios initially enhance combustion efficiency and flame coverage but eventually cause a decrease. The flame limit broadens from 0.900 to 1.626 as the pressure ratio increases from 1.12 to 1.50. While Mach number changes have little effect on efficiency, the flame limit exhibits an initial rise followed by a drop. Novel findings include an asymmetrical flame pattern and a “Z” shaped outlet temperature distribution, contributing to optimized combustion strategies for combined-cycle engines.

Energy and exergy analyses on the high-pressure bleeding-air variable cycle designed for a wide-speed-range airbreathing propulsion system

The performance of the traditional turbojet decreases sharply with the increase of the Mach number in the supersonic flight, especially for the turbine-based combined cycle (TBCC) engine in the transition region of the turbojet and scramjet engine. This paper proposes a new high-pressure bleeding-air variable cycle engine (HB-VCE) concept that aims to ease the sharp contradiction between thrust output and fuel consumption of TBCC in the transition region. Through the energy and exergy analyses, the HB-VCE shows greater potential in energy utilization under high Mach flight conditions. The performance of HB-VCE significantly improves as the bleed ratio increases, with a more pronounced effect at higher Mach numbers. At Mach 1.5, the HB-VCE increases the specific thrust (ST) by 2.84 % and reduces the specific fuel consumption (SFC) by 2.73 %. At Mach 2.4, it increases the ST by 6.60 % and reduces the SFC by 6.52 %. Additionally, the controlling law of the critical bleeding ratio constrained by the turbine outlet temperature is proposed. Finally, the effect of the turbine inlet temperature, overall pressure ratio, and Mach number on the critical bleeding ratio is analyzed. This paper provides a promising HB-VCE concept with greater energy utilization for the TBCC design in the transition region.

Enhancing Ignition Reliability with Tail-Groove Strut Designs in Cavity-Based Combustors

As the flight envelopes of turbine-based combined cycle (TBCC) engines expand, ensuring reliable ignition and flame stability under varying conditions becomes increasingly critical. Previous work has shown a significantly changed ignition performance and flow pattern in cavity-based combustors when strut structure parameters were altered, indicating a strong correlation between the ignition process, flame structure, and the strut configuration. This suggests that further investigation is required to determine the optimal strut design. Therefore, this study examines the impact of various strut configurations through numerical simulations, validated by high-speed imaging. Findings show that the tail-groove strut designs improve the flame propagation performance compared to the normal struts, with a critical depth beyond which further increases do not enhance performance. Changes in strut length have a lesser impact than depth. Flow analysis indicates that tail-groove struts create additional recirculation zones that enhance fuel atomization and flame stability. These results suggest that optimizing strut configurations is vital for achieving reliable ignition and flame stability, advancing the development of efficient engines across a wide range of operational conditions.

Mixing enhancement assisted by dual plate cavity in supersonic flow

Fast and efficient mixing of high-speed shear flow formed by fuel and oxidizer is of great importance for the improvement of rocket-based combined cycle engine performance. Nevertheless, the existence of compressibility effects of high-speed flow significantly inhibits the growth process of a mixing layer. Moreover, a finite-length combustor of the engine calls for more effective enhanced-mixing strategies to complete mixing in a shorter streamwise distance. To this end, in present paper, the strategy called dual plate cavity (DPC) is proposed to promote mixing. Three cases including the benchmark, front-DPC and back-DPC cases are selected to perform the comparative study. By means of high-order direct numerical simulations, the structure evolution characteristics and turbulence intensity distributions are researched. The index of velocity thickness is utilized to assess the mixing layer growth. The results indicate that with the introduction of DPC, the mixing process is dramatically promoted. The penetration behavior of newly found T-shaped structures into the upper main stream can engulf more fluid into the mixing region. Specifically, in the back-DPC case, the coexistence of both large-scale and small-scale structures in the far flow field can improve the turbulence intensity. The spatial correlation analysis results show that with the influence of DPC, the structure sizes are much larger than that of the benchmark case in the same streamwise position. Meanwhile, the contour line equal to 0.5 possesses property of distortion for the back-DPC case. The drastic pulsation of a mixing layer edge can obviously promote the mixing process. Through exploration of the enhanced-mixing mechanisms, this work indicates that the proposed DPC strategy is a good candidate for efficient mixing, and in the future, more detailed work including three-dimensional simulations concerning the strategy optimization is suggested to be performed.

Numerical investigation of the distributed combustion in the thermal choked solid fuel combined cycle engine

In this study, a solid fuel combined cycle engine concept based on the distributed combustion and the self-adaptive thermal choking is proposed, which can operate effectively within a wide Mach number range. By regulating the heat release through the distributed fuel injection, the thermal choking can be formed in the fixed geometry combustor. The air intake controls the flow capture and circulation area through the movement of its head cone, ensuring stable air breathing over a wide range. Numerical simulations conducted under Ma = 3.0 and 6.0 conditions using the validated Eulerian-Lagrangian method coupled with gaseous and particle reaction models demonstrate the concept's capability to operate within the Mach number range of 3.0–6.0, delivering improved mixing, combustion, and specific impulse performance.

Flame evolution characteristics during ignition of a combined flameholder fueled by RP-3 liquid kerosene

This paper proposes a combined flameholder comprising a pilot flameholder and a bluff body flameholder, interconnected by a radial V-gutter. The configuration of this combined flameholder is widely utilized in current afterburners and ram combustors, and its outstanding performance in future advanced combined cycle engines has been proved. To avoid the issue of uniform airflow at the inlet observed in most previous studies, this research installed a diffuser to simulate relatively realistic inlet airflow conditions of combustor. Particle Image Velocimetry (PIV) and high-speed camera are employed to measure the flow field structure of the combined flameholder, as well as the ignition flame evolution process under inlet Mach number of 0.3 – 0.5, temperature of 500 – 700 K, and pressure of 0.05 – 0.1 MPa. This paper reveals the combustion organization method of the combined flameholder through combining flow field characteristics and the ignition flame evolution process. Furthermore, the research findings indicate that flame evolution processes, flame projection area, and ignition delay time are significantly influenced by the inlet conditions. The variations in these flame evolution characteristics with different inlet conditions are summarized and the contributing factors are analyzed. The results of the paper are expected to serve as a reference for the optimization and design of flame stabilization systems in current and future afterburners and ram combustors.

Simple model of turbine-based combined cycle propulsion system and smooth mode transition

Abstract Turbine-based combined cycle (TBCC) propulsion system is becoming one of the most promising propulsion systems for two-stage-to-orbit reusable launch vehicle. Mathematic model of this combined cycle engine is helpful for the basic understanding of performance analysis of this propulsion system. We developed mathematic model of TBCC propulsion system based on C++ platform in this paper. Firstly, turbojet engine was built on component level and ramjet engine was calculated through stream thrust function. Then, performance of turbine-based combined cycle propulsion system along a specific flight trajectory was investigated. According to the thrust of this combined cycle engine, mode transition point was suggested at Ma 2.5, which may achieve smooth mode transition from turbine mode to ramjet mode. Finally, mode transition based on smooth mass flow and smooth thrust criteria were studied. The thrust gap arises during smooth mass flow mode transition, particularly when the turbojet engine afterburner is powered off at the start of the mode transition, and it meets 34 % of the total thrust. Smooth thrust mode transition may be achieved by delaying the turbojet engine afterburner power off and injecting additional fuel into ramjet burner.

Influence of a double-mixer configuration on the mixing and combustion characteristics of a multibypass combustor for a turbine-based combined cycle engine

The changes in the flow field and combustion characteristics induced by the mode transition process of a turbine-based combined cycle (TBCC) engine may lead to failure of the mode transition. In this paper, the cold mixing characteristics, combustion efficiency, and cold and thermal flow losses of a TBCC multibypass combustor with a double-mixer configuration are investigated through numerical simulations, and the correlations between the thermal mixing efficiency and combustion efficiency is established. The results show that the thermal mixing efficiency of double-lobed mixer combustors is better at low ram inlet Mach numbers, but the ring-plus-lobed mixer combustor has better mixing and combustor characteristics at relatively high Mach numbers. However, the effect of the turbo core inlet Mach number on the combustion efficiency is not regular. The spacing between the double mixers that maximizes the mixing and combustion characteristics of the combustor is 75 mm. With increasing of expansion angle of the lobed mixer, the thermal mixing efficiency and combustion efficiency increase by 31.9 % and 23.3 %, respectively. In addition, the positive correlation coefficient between combustion efficiency and thermal mixing efficiency caused by changes in the inlet Mach number is greater than that caused by changes in structural parameters.

Effect of strut schemes on combustion characteristics in innovative combined ramjet engine

The Mach 6-capable turbine based combined cycle engine is a potential first-stage propulsion for TSTO mission. In order to improve thrust-to-weight ratio, an innovative tandem combined ramjet engine-FABRE (Fan Augmented Air-Breathing Ramjet Engine) is designed utilizing a versatile multi-mode combustor working at both high-speed ramjet mode and low-speed turbocharged mode. Employing the strut as mixer and flame holder in multi-mode combustor presents theoretical advantages. Nonetheless, a thorough investigation into its practical feasibility and combustion characteristics is essential. This paper experimentally verifies the feasibility of strut approach in multi-mode combustor at various speeds and evaluates the effects of different strut schemes on flow field structure, thermodynamic characteristics, and combustion performance via simulation. The experimental results affirm that employing the strut scheme as a combustion organization method enables the multi-mode combustor to operate effectively under diverse inflow conditions at both high and low speeds. Simulation results further validate that these strut solutions consistently demonstrate superior combustion performance. Additionally, the influences of the strut geometry on heat release and high-temperature area are highly consistent with its effects on combustion efficiency. At low speed, wider struts lead to increased combustion efficiency, while at high speed, they initially rise before declining with further widening. Regardless of speed, increasing strut slant angle consistently reduces efficiency. At low speed, widening the strut lowers the total pressure recovery coefficient, peaking at 45° with varying strut slant angle. Conversely, at high speed, changes in strut width minimally impact, while increasing strut slant angle reduces the coefficient. These conclusions provide valuable insights for the optimization of combustion organization in the design of combined ramjet engine with a wide range of operating conditions.

Conceptual design methodology and performance evaluation of turbine-based combined cycle inward-turning inlet with twin-design points

Turbine-based combined cycle (TBCC) engines attract intensive attention due to adequate high working efficiency within the full speed range of air-breathing vehicles. Challenges of TBCC engines lie mostly in common-used components in particular the inlet system, which needs to satisfy the mass flow distribution of different sub-engines and to reconcile the performance requirement in the full speed range. In the present work, a new conceptual design methodology of the three-dimensional inward-turning TBCC inlet with twin-design points is proposed according to the basic flow field with double incident shock waves. The shock structures and flow field parameters at the high-speed design point Ma=4 and mass flow distribution at the low-speed design point Ma=3 both can be designed by the basic flow field. On that basis, a typical inlet model is designed and the corresponding aerodynamic performance is evaluated at two design points. Simulation results prove that the shock structure, the mass flow distribution, and the averaged throat parameters of the TBCC inlet are all consistent with the basic flow field with sufficient accuracy at twin-design points, where the maximum relative error is only 6.3%. Meanwhile, the aerodynamic performance of the inlet shows that the inlet has stable and efficient operation characteristics, which fully affirms the feasibility of the design method.

Cyclic coupling and working characteristics analysis of a novel combined cycle engine concept for aviation applications

The imperative for small aviation engines lies in the pursuit of heightened power-to-weight ratios and thermal efficiencies. Relying solely on piston engines and gas turbines is insufficient to concurrently meet these evolving performance demands. This paper introduces the concept of a combined cycle aviation engine (CCAE), amalgamating the cycle modes of piston engines and gas turbines. The CCAE achieves flexible control over turbine operating states and engine performance through the adjustment of the energy distribution between these two cycles. The air diversion strategy (α) and the burner's fuel supply strategy (λb) are identified as the key determinants of system performance. To comprehensively investigate the impact of α and λb on CCAE's performance, this paper constructs a theoretical model, a simulation model, and a test bench. The simulation model's accuracy is validated through test data, and the air-fuel ratio range for burner stable combustion is explored. The simulation results indicate a reduction of 50 % in the fluctuation of turbine speed within a single cycle. Under high-altitude conditions, CCAE's intake mass flow rate, power, and efficiency are notably enhanced when compared to conventional turbocharged piston engines. These findings contribute valuable insights that can inform the application of CCAE within the aviation domain.

Experimental and numerical study on flow mixing and combustion characteristics of a novel multibypass integrated combustor

The integrated design of multibypass augmented/ramjet combustors can reduce the weight of turbine-based combined cycle (TBCC) engines and improve the thrust-to-weight ratio, but low-resistance mixing and efficient stable combustion of multiple airflows over short distances are necessary prerequisites. In this study, a novel structure for a TBCC multibypass integrated augmented/ramjet combustor is proposed. The influence of the inlet aerodynamic parameters on the flow field, mixing efficiency, flow loss, and combustion performance of the combustor under different working modes was obtained via experimental and numerical methods. The experimental results show that the outlet mixing efficiency is greater than 86% in the double-bypass mode (DB-mode). While the triple-bypass mode (TB-mode) has a larger decrease, the total pressure loss is slightly reduced (by approximately 0.5%). The opening of the ram duct has a significant impact on the flow field, resulting in different rules for the influence of the inlet temperature on the outlet mixing efficiency: in the DB-mode, the mixing efficiency decreases with increasing inlet temperature, while the rule is completely opposite after entering the TB-mode. Because the dominant role of the two mixing zones in the flow field changes with the velocity, the inlet velocity has a significant impact on the mixing efficiency in the flow direction. The combustion simulation results show that the combustion efficiency in the DB-mode is almost always above 90% and the high-temperature zone is mainly concentrated downstream of the integrated strut. The radial temperature gradient increases and the combustion efficiency decreases in the TB-mode.

Machine Learning-Based Backpressure Unstart Prediction and Warning Method for Combined Cycle Engine Hypersonic Inlet-Oriented Wide Speed Range

Inlet unstart prediction and warning are strictly crucial to the operation of hypersonic engines, especially for combined cycle engines where implementation across a wide speed range poses significant challenges. This paper proposes a realization method that involves constructing the conditions of critical backpressure ratios for the inlet unstart and unstart warning states within a wide speed range and establishing the backpressure prediction models for each engine mode. The detection of the unstart and unstart warning states is achieved by predicting the backpressure ratio at the exit of the isolator and comparing it to the critical backpressure ratios. To achieve this, numerical simulations for a three-dimensional inward-turning multiducted hypersonic combined inlet at various Mach numbers and backpressure ratios are carried out to obtain the dataset of surface pressure. A 10-fold cross-validation support vector machine (10-CV SVM) is used to solve the unstart boundary of surface pressure, and an unstart margin is set to determine the unstart warning boundary. A back propagation (BP) neural network is constructed to estimate the critical backpressure ratios at each working point within a wide speed range. The data information of surface pressure on the boundaries is used as the input for the predictions. The overall average regression correlation coefficient approaches 0.99 on the test dataset at each working point. The backpressure prediction models are established by the one-dimensional convolutional neural network (1D-CNN). Only 2 to 4 measurement points of surface pressure are considered for cross-validation evaluation, and the mean absolute percentage error is between 4% and 8% with the average prediction time not exceeding 2 ms. Finally, the proposed method and prediction models are validated by wind tunnel experimental data.

Numerical Investigation on the Effect of Fuel-Rich Degree in the RBCC Engine under the Ejector Mode

The ejector mode of the Rocket-Based Combined-Cycle (RBCC) engine is characterized by high fuel consumption. This study is aimed at investigating the influence of the rocket fuel-rich degree on the RBCC engine’s performance under the ejector mode combined with simultaneous mixing and combustion (SMC). Numerical simulations were conducted for various rocket mixing ratios (Φ=1.6~3.2) under subsonic (Maf=0.9) and supersonic (Maf=1.8) flight conditions. It was observed that a high fuel-rich degree in the rocket plume negatively impacts the eject performance under all conditions. However, it improves the overall performance (Isp) at high flight Mach numbers (Maf). For supersonic conditions, increasing the fuel-rich degree promotes greater fuel participation in combustion, thereby enhancing RBCC engine performance. Nevertheless, the subsonic-supersonic mixing layer exhibits low evolution, resulting in a decrease in reaction efficiency from 29.2% to 12.0% as the Φ decreases from 3.2 to 1.6. Consequently, there is an inefficient utilization of fuel. To optimize RBCC engine performance, the rocket fuel-rich degree can be appropriately increased. However, this increase should be limited to prevent fuel wastage arising from low reaction efficiency. Under subsonic conditions (Maf=0.9), the low kinetic energy of captured air leads to the occurrence of “negative thrust surface” and “wall impact” phenomena, which hinder the efficient and stable operation of the RBCC engine. Consequently, adjusting the fuel-rich degree alone cannot promote specific impulse (Isp), and a low fuel-rich degree is considered an ideal strategy when combined with adjustable nozzle technology.

Thrust-matching and optimization design of turbine-based combined cycle engine with trajectory optimization

Abstract Based on the trajectory optimization method of the Gauss pseudospectral, an aircraft/engine matching method is established for the turbine-based combined cycle (TBCC) engine. For a horizontal-takeoff hypersonic aircraft designed at Mach 5, a thrust-matching analysis of the TBCC engine is performed, and a rocket is integrated for further optimization design. The results show that the aircraft for boost missions should adopt the TBCC thrust with a takeoff thrust-to-weight ratio of 99.8 % to reduce the acceleration time and fuel consumption. In contrast, due to the low thrust-to-weight ratio of the TBCC engine, a high-thrust TBCC increases the inert weight in the cruise phase. Therefore, the aircraft designed for cruise missions should adopt the takeoff thrust-to-weight ratio of 92.0 %. Introducing a rocket whose maximum thrust is 10 % of the takeoff weight could assist the aircraft in overcoming the problem of the “thrust pinch” during the transonic and mode transition. With the assistance of rockets, the optimal takeoff thrust-to-weight ratio is 65.3 % for cruise aircraft, and the cruise range is increased by 18 %. While for the boost aircraft, adopting an optimal TBCC of 86.8 % takeoff thrust-to-weight ratio, the introduced rocket could reduce the fuel consumption and the TBCC engine weight by 4 %.

Research on the flow and heat transfer characteristics of RP-3 and structural optimization in parallel bending cooling channels

The regenerative cooling channel is curved due to the unique structural form of the combined nozzle of the turbine-based combined cycle engine for hypersonic flight. Research on the flow and heat transfer characteristics of fuel in the parallel bending cooling channels is insufficient, which causes difficulties in properly designing the thermal protection structure of the combined nozzle. This paper numerically investigated of the flow and heat transfer characteristics of hydrocarbon fuel RP-3 under non-uniform heating conditions in parallel bending cooling channels. The basic heat flux is 0.50 MW/m2, and the heat flux ratio of the upper and lower channels is 1.2, 1.5, and 2.4 respectively. The heat transfer and flow distribution mechanisms of RP-3 in parallel bending channels are revealed. The bending structure is beneficial to reduce thermal stratification and prevent heat transfer deterioration caused by buoyancy. In the pseudo-critical region of the channel, a “thermal insulation zone” is formed due to the low thermal conductivity of RP-3, which hinders the transfer of heat to the mainstream and causes heat transfer deterioration. When the fluid temperature is below 455 K, viscosity is the primary factor affecting the flow resistance difference between parallel channels. As the temperature further increases, the density difference and velocity difference between the parallel channels dominate in the flow resistance differences. Additionally, a connected hole structure in the middle of the bending section has been applied to optimize the flow deviation of parallel bending channels, which promotes the secondary distribution of flow. Finally, the influence mechanism of the connected hole on flow distribution has been studied under different heat flux ratios and connected hole widths.

Heat transfer performance of RP-3 aviation kerosene at supercritical pressure within a rotating U-shaped channel

The combined cycle engine based on turbine is typical in the field of cycle engines. However, the problem of high temperature heat load of turbine blades is serious. In order to solve this kind of problem, the method of using hydrocarbon fuel as cooling medium to improve the cooling efficiency of turbine blades are proposed. In this paper, the flow and heat transfer characteristics of RP-3 aviation kerosene in a rotating U-shaped channel under supercritical pressure were studied by numerical simulation. The flow and heat transfer characteristics of RP-3 aviation kerosene under supercritical pressure at different rotational speeds were numerically simulated by SST k-ω model. The results show that the centrifugal section and the horizontal section show obvious fluid stratification, and the mainstream distribution in the centripetal section is relatively uniform due to the bending effect and rotational buoyancy. Compared with the heat transfer capacity in the static state of the centrifugal section, the heat transfer of the fluid in the rotating state deteriorates, recovers and strengthens with the increase in the rotational speed. Moreover, compared with the centripetal section, the rotational speed has a particularly significant effect on the heat transfer performance in the centrifugal section and the horizontal section. When the rotational speed exceeds 300 rpm, the deterioration trend of heat transfer is weakened and the overall heat transfer performance is greatly improved.

Effects of excess oxidizer coefficient on RBCC engine performance in ejector mode: A theoretical investigation

This study investigates the effects of the primary rocket’s excess oxidizer coefficient (EOC) on the performance of a kerosene-fueled rocket-based combined cycle (RBCC) engine operating in ejector mode using the diffuser and afterburning (DAB) cycle. Employing complete mixing and chemical equilibrium assumptions, a quasi-one-dimensional model is developed to simulate combustion processes in the primary rocket chamber, mixer, and afterburner. Experimental data and full three-dimensional simulation validate the model’s accuracy. Results indicate that increasing EOC mitigates thermal choking effects at the mixer exit, decreasing mixing and Rayleigh losses, enhancing the entrainment ratio, and providing more oxygen for secondary combustion. However, the gas mixture’s compression ratio and total temperature decrease, rendering secondary combustion more susceptible to thermal choking in a constant cross-sectional afterburner. As the flight Mach number increases from 0.8 to 2.5, the optimum EOC for maximum specific impulse shifts from 0.725 to 2.375. While the optimum EOC for maximum thrust remains consistently around 2.0. The findings underscore the necessity of a higher EOC to fully unlock the DAB cycle’s thrust augmentation potential.