# Comprehensive Performance Analysis for the Rotating Detonation-Based Turboshaft Engine

Authors: Zifei Ji; Ruize Duan; Renshuai Zhang; Huiqiang Zhang; Bing Wang
Journal: International Journal of Aerospace Engineering
 (2020)

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## Abstract

The potential advantages of rotating detonation combustion are gradually approved, and it is becoming a stable and controllable energy conversion way adopted to the propulsion devices or ground-engines. This study focuses on the rotating detonation-based turboshaft engine, and the architecture is presented for this form of engine with compatibility between the turbomachinery and rotating detonation combustor being realized. The parametric performance simulation model for the rotating detonation-based turboshaft engine are developed. Further, the potential performance benefits as well as their generation mechanism are revealed, based on the comprehensive performance analysis of the rotating detonation-based turboshaft engine. Comparisons between the rotating detonation turboshaft engine and the conventional one reveal that the former holds significant improvements in specific power, thermal efficiency, and specific fuel consumption at lower compressor pressure ratios, and these improvements decrease with the increase of compressor pressure ratio and increase as turbine inlet temperature increases. The critical compressor pressure ratio corresponding to the disappearance of specific power improvement is higher than that corresponding to the disappearance of thermal efficiency and specific fuel consumption. These critical compressor pressure ratios are positively correlated with flight altitude and negatively correlated with flight velocity. The conductive research conclusion is guidable for the design and engineering application of rotating detonation-based engines.


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## Body

## 1. Introduction

The helicopters have promising development and application foreground in both military and civil fields, owing to their superior performance operating at low altitude, low velocity, and maneuvering flight conditions. The turboshaft engine is the unique powerplant for the helicopter; therefore, advanced technologies for turboshaft engines have attracted significant interest in both academia and industry. The regenerative cycle and variable capacity technologies have the potential for improving the overall performance of the turboshaft engine, but the low technical maturity and poor technical versatility currently may be unacceptable. The turboshaft engine with simple cycle is still the first choice of advanced technology programs at present [1, 2].For the conventional turboshaft with simple cycle, the key to enhancing the overall performance is to improve the total pressure ratio and temperature ratio [3]. After several decades of developments, the performance improvement of conventional turboshaft engine has entered a bottleneck period, as shown in Figure 1 [2]. Pressure-gain combustion is a prospective technology for the further performance improvement of the turboshaft with simple cycle [4]. Rotating detonation is a form of pressure-gain combustion, and it holds many potential advantages, such as high intensity of reaction, high thermal efficiency, and low entropy increase [5–7], which are helpful to improve the thrust and fuel consumption performance and reduce the structural weight. In the past decades, numerous studies relating to the ignition and detonation initiation performance, the operating diagram, and the unstable modes and their generation mechanism of the rotating detonation combustor (RDC) are experimentally performed, and the detailed flowfield structure and cellular structure information are revealed by multidimensional numerical methods [8–12]. The above studies have made the rotating detonation technology being regarded as a stable and controllable energy conversion way. Naples et al. [13, 14] studied the interaction between the RDC and conventional turbine elements by the integration system of the T63 turboshaft engine embedded with an RDC. With the main combustor of GTD-350 engine being replace by an RDC, the feasibility of the RDC being applied to turboshaft engine has been confirmed by Wolański [15]. George et al. [16, 17] experimentally investigated the axial turbine performance operating under pulsating flows, which hold the similar features with the detonation chamber exhaust, and approved that the pressure oscillations may lead to undesirable turbine performance degradation. With the performance of the supersonic turbine being characterized by the power extraction and total pressure loss parameters, Liu et al. [18, 19] numerically studied the effects of unsteady inlet conditions on the operating characteristics of the supersonic turbine and revealed that leading edge shock waves were the main factor for the unsteady loss mechanism. Sousa et al. [20] analyzed the thermodynamic performance of the gas turbine with an RDC with the T-MATS software coupled with the MOC solver of RDC model; the result showed that the thermal efficiency of the rotating detonation turbine engine could be 5% higher than that of the conventional one at low compressor pressure ratios, but the performance benefits decreased as the compressor pressure ratio increased. With the accumulation of the achievements on rotating detonation turbine engine, the feasibility and potential advantages of this new form of engine are gradually approved [20–23]. However, studies regarding the overall performance characteristics and the potential performance benefits as well as their generation mechanism of the turboshaft engine embedded with an RDC are quite scarce. Compared to the conventional turboshaft engine, the study of rotating detonation-based turboshaft engine is still in its infancy.Figure 1
Technical trend of representative conventional turboshaft engines [2].This study aims at revealing the potential performance benefits of the rotating detonation-based turboshaft engine and promoting further application of RDC in propulsion systems. Firstly, the parametric cycle analysis model of the rotating detonation-based turboshaft engine is developed based on the low-order analytical model of RDC and the compatibility relationship between the turbomachinery and RDC. Then, the overall performance characteristics of the new form of engine are achieved. Finally, a performance comparison between the rotating detonation-based turboshaft engine and the conventional one is performed, and the performance benefits as well as their generation mechanism are revealed.


## 2. Mathematical and Physical Model

### 2.1. System Formulation

With the compatibility between RDC and turbomachinery under consideration, the isolator and mixer chamber are arranged upstream and downstream from RDC, respectively, in the dual-duct rotating detonation aeroturbine engine (DRDATE) [22]. With the power turbine and power shaft arranged downstream from the turbine of the DRDATE (which is used as the gas generator), a configuration for the rotating detonation-based turboshaft engine is proposed, as shown in Figure 2(a). Figure 2(b) further displays the ideal thermodynamic cycle process comparison between the rotating detonation-based turboshaft engine and the conventional one. For the rotating detonation-based turboshaft engine, air flows into the engine at state 0; the process 0-3 is the integrated compression process proceeding in the intake, isolator, and compressor; the processes 3′-3.5′ and 3.5′-4′ represent the shock compression and heat release due to combustion, respectively; the process 4′-9′ represents the integrated expansion process proceeding in the turbine, power turbine, and nozzle; and the thermodynamic cycle is closed via the imaginary exothermic process 9′-0. The thermodynamic cycle processes of the conventional turboshaft engine can be analyzed in exactly the same manner.Figure 2
(a) Configuration and (b) ideal thermodynamic cycle processes of the rotating detonation-based turboshaft engine.
(a)(b)The final temperature of the heating process in rotating detonation-based turboshaft engine is higher than that in the conventional turboshaft engine with the same heat addition, as the specific heat capacity of detonation process is lower than that of the deflagration process. Therefore, the former corresponds less entropy production, which implies the heat loss owing to exhaust (which can be estimated with the projected area of the exothermic process tos-axis, as shown in Figure 2(b)) of the rotating detonation-based turboshaft engine is higher than that of the conventional one. The above has revealed the thermal efficiency benefit of the rotating detonation turbine engine conceptually.


### 2.2. Parametric Cycle Analysis Model

The thermodynamic processes proceeding in the rotating detonation-based turboshaft engine can be simplified as “polytropic compression-rotating detonation-adiabatic mixing-polytropic expansion,” and the reduced order model which was developed based on the matching relationship between the injection process and pressure decay after the detonation front [22] is adopted in this study for the estimation of the rotating detonation process. The RDC is fueled by kerosene, and the reaction mechanism is taken from [24]. The models of the remaining processes are consistent with the conventional turboshaft engine. The thermodynamic process in the conventional compressor can be regarded as nonisentropic polytropic compression, and the mathematical model can be expressed as follows:
(1)p3∗=πcp1∗,(2)∫T1∗T3∗cpdTT=R0Inπc,(3)h3∗=h1∗+∫T1∗T3∗cpdT,(4)ηc=h3i∗−h1∗h3∗−h1∗.where h3i∗ is the total enthalpy corresponding to the isentropic compression with a compression pressure ratio πc. The thermodynamic process in the turbine can be modeled in exactly the same way.The gas properties are a function of the gas temperature. In this study, the parametric performance simulation model of the engine is developed based on the “variable-γ” strategy. Firstly, the gas properties of the single component can be calculated by polynomial fitting of temperature (the polynomial coefficients are referred to NASA [25]); then, the gas properties of working medium can be obtained by mass flow average.
(5)cpi=Ria0i+a1iT+a2iT2+a3iT3+a4iT4,(6)cp=∑i=1NcpiYi,(7)γ=∑i=1NcpiYi∑i=1NYicpi/γi.Similar to the conventional turboshaft engine, specific powerPs, thermal efficiency ηth, and specific fuel consumption sfc are used as metrics to characterize the overall performance of the rotating detonation-based turboshaft engine. According to the parametric cycle analysis model and component matching equations, the performance metrics can be calculated by Equations (4)–(6). And α represents the air split parameter, which is the ratio of the mass flow rate of the inner duct to that of the outer duct in DRDATE. κ is the power split parameter, which is adopted to characterized the power split between the power turbine and the nozzle. According to the representative turboshaft engines, the value of κ is taken as 0.96. The subscripts 6 and 9 represent the parameters of power turbine inlet and exhaust nozzle outlet sections, respectively.
(8)Ps=1+f1+ακh6∗1−p9p6∗γ−1/γ,(9)ηth=Ps/f⋅Hf/1+α,(10)sfc=3600f/Ps1+α.The utilization of reduced order model of RDC can introduce calculation errors, owing to the assumptions. Compared to the 2D CFD solver, the calculation error of the reduced order model is below 10% [22, 23]. The overall uncertainty of the performance metrics of the rotating detonation-based turboshaft engine can be estimated by the sensitivity analysis of the calculation errors of RDC outlet parameters on overall performance of the engine. Assuming that Ψ is the performance metric; then, the overall uncertainty of Ψ can be calculated by
(11)u1=Ψp4∗+εp4∗−Ψp4∗/Ψp4∗,(12)u2=ΨT4∗+εT4∗−ΨT4∗/ΨT4∗,(13)u=∑ui2=u12+u22,where ε is the model error of RDC, ui represents the uncertainty component, and u represents the overall uncertainty. Table 1 summarizes the uncertainty components and overall uncertainty of the Ps, ηth, and sfc, which are generated by the calculation errors of the RDC model. It shows that the overall uncertainties of performance metrics remain at a relatively low level (<10%). In addition, the uncertainty of Ps is lower than that of ηth and sfc.Table 1
Uncertainty analysis of the performance metrics of the rotating detonation-based turboshaft engine.
Performance metricsPsηthsfcCycle parametersp4∗T4∗p4∗T4∗p4∗T4∗ε10%10%10%10%10%10%ui (i=1,2)0.96%3.31%2.14%9.39%2.09%9.37%u4.19%9.63%9.60%


## 2.1. System Formulation

With the compatibility between RDC and turbomachinery under consideration, the isolator and mixer chamber are arranged upstream and downstream from RDC, respectively, in the dual-duct rotating detonation aeroturbine engine (DRDATE) [22]. With the power turbine and power shaft arranged downstream from the turbine of the DRDATE (which is used as the gas generator), a configuration for the rotating detonation-based turboshaft engine is proposed, as shown in Figure 2(a). Figure 2(b) further displays the ideal thermodynamic cycle process comparison between the rotating detonation-based turboshaft engine and the conventional one. For the rotating detonation-based turboshaft engine, air flows into the engine at state 0; the process 0-3 is the integrated compression process proceeding in the intake, isolator, and compressor; the processes 3′-3.5′ and 3.5′-4′ represent the shock compression and heat release due to combustion, respectively; the process 4′-9′ represents the integrated expansion process proceeding in the turbine, power turbine, and nozzle; and the thermodynamic cycle is closed via the imaginary exothermic process 9′-0. The thermodynamic cycle processes of the conventional turboshaft engine can be analyzed in exactly the same manner.Figure 2
(a) Configuration and (b) ideal thermodynamic cycle processes of the rotating detonation-based turboshaft engine.
(a)(b)The final temperature of the heating process in rotating detonation-based turboshaft engine is higher than that in the conventional turboshaft engine with the same heat addition, as the specific heat capacity of detonation process is lower than that of the deflagration process. Therefore, the former corresponds less entropy production, which implies the heat loss owing to exhaust (which can be estimated with the projected area of the exothermic process tos-axis, as shown in Figure 2(b)) of the rotating detonation-based turboshaft engine is higher than that of the conventional one. The above has revealed the thermal efficiency benefit of the rotating detonation turbine engine conceptually.


## 2.2. Parametric Cycle Analysis Model

The thermodynamic processes proceeding in the rotating detonation-based turboshaft engine can be simplified as “polytropic compression-rotating detonation-adiabatic mixing-polytropic expansion,” and the reduced order model which was developed based on the matching relationship between the injection process and pressure decay after the detonation front [22] is adopted in this study for the estimation of the rotating detonation process. The RDC is fueled by kerosene, and the reaction mechanism is taken from [24]. The models of the remaining processes are consistent with the conventional turboshaft engine. The thermodynamic process in the conventional compressor can be regarded as nonisentropic polytropic compression, and the mathematical model can be expressed as follows:
(1)p3∗=πcp1∗,(2)∫T1∗T3∗cpdTT=R0Inπc,(3)h3∗=h1∗+∫T1∗T3∗cpdT,(4)ηc=h3i∗−h1∗h3∗−h1∗.where h3i∗ is the total enthalpy corresponding to the isentropic compression with a compression pressure ratio πc. The thermodynamic process in the turbine can be modeled in exactly the same way.The gas properties are a function of the gas temperature. In this study, the parametric performance simulation model of the engine is developed based on the “variable-γ” strategy. Firstly, the gas properties of the single component can be calculated by polynomial fitting of temperature (the polynomial coefficients are referred to NASA [25]); then, the gas properties of working medium can be obtained by mass flow average.
(5)cpi=Ria0i+a1iT+a2iT2+a3iT3+a4iT4,(6)cp=∑i=1NcpiYi,(7)γ=∑i=1NcpiYi∑i=1NYicpi/γi.Similar to the conventional turboshaft engine, specific powerPs, thermal efficiency ηth, and specific fuel consumption sfc are used as metrics to characterize the overall performance of the rotating detonation-based turboshaft engine. According to the parametric cycle analysis model and component matching equations, the performance metrics can be calculated by Equations (4)–(6). And α represents the air split parameter, which is the ratio of the mass flow rate of the inner duct to that of the outer duct in DRDATE. κ is the power split parameter, which is adopted to characterized the power split between the power turbine and the nozzle. According to the representative turboshaft engines, the value of κ is taken as 0.96. The subscripts 6 and 9 represent the parameters of power turbine inlet and exhaust nozzle outlet sections, respectively.
(8)Ps=1+f1+ακh6∗1−p9p6∗γ−1/γ,(9)ηth=Ps/f⋅Hf/1+α,(10)sfc=3600f/Ps1+α.The utilization of reduced order model of RDC can introduce calculation errors, owing to the assumptions. Compared to the 2D CFD solver, the calculation error of the reduced order model is below 10% [22, 23]. The overall uncertainty of the performance metrics of the rotating detonation-based turboshaft engine can be estimated by the sensitivity analysis of the calculation errors of RDC outlet parameters on overall performance of the engine. Assuming that Ψ is the performance metric; then, the overall uncertainty of Ψ can be calculated by
(11)u1=Ψp4∗+εp4∗−Ψp4∗/Ψp4∗,(12)u2=ΨT4∗+εT4∗−ΨT4∗/ΨT4∗,(13)u=∑ui2=u12+u22,where ε is the model error of RDC, ui represents the uncertainty component, and u represents the overall uncertainty. Table 1 summarizes the uncertainty components and overall uncertainty of the Ps, ηth, and sfc, which are generated by the calculation errors of the RDC model. It shows that the overall uncertainties of performance metrics remain at a relatively low level (<10%). In addition, the uncertainty of Ps is lower than that of ηth and sfc.Table 1
Uncertainty analysis of the performance metrics of the rotating detonation-based turboshaft engine.
Performance metricsPsηthsfcCycle parametersp4∗T4∗p4∗T4∗p4∗T4∗ε10%10%10%10%10%10%ui (i=1,2)0.96%3.31%2.14%9.39%2.09%9.37%u4.19%9.63%9.60%


## 3. Results and Discussions

### 3.1. Sensitivity Analysis of Component Parameters on Overall Performance of the Engine

A sensitivity analysis is conducted below to reveal the variation in overall performance of the rotating detonation-based turboshaft engine versus the component parameters. The compressor pressure ratioπc and turbine inlet temperature T4∗ play a major role in the overall performance of the engine. The variations in Ps, ηth, and sfc with respect to πc and T4∗ under standard sea-level and high altitude cruise conditions are, respectively, illustrated in Figures 3 and 4. In the figures, the coordinate values of each points are determined by the Ps and sfc of the cases with the corresponding values of πc and T4∗, and the values of ηth are presented by the color scales. The sensitivity of performance metrics to the πc and T4∗ can be presented intuitively by the trends of curves and color scales. It can be seen that, with an increase in πc, Ps and ηth first increase but then decrease, and sfc first decreases but then increases. As πc increases, on the one hand, the power turbine pressure ratio πt increases, and the sensitivity of πt to changes in πc decreases, as the pressure-gain of the RDC is negatively correlated with πc [22]. On the other hand, the cycle heat addition decreases owing to the increase of combustor inlet temperature T3∗ and air split parameter α. In addition, the increase of α can weaken the potential benefits relating to the pressure gain of the RDC. At low values of πc, the increase of πt is the main factor influencing Ps, and Ps increases with the increase of πc. As πc increases, the increase of T3∗ and α becomes the dominant factor influencing Ps, and Ps decreases as πc increases. The thermal efficiency ηth is positively correlated with Ps, so the variation of ηth is consistent with that of Ps. In addition, ηth is positively correlated with α according to Equation (9), so the unfavorable impact of T3∗ can be weakened. Therefore, the downward trend of ηth at high values of πc is less obvious than that of Ps. On the basis of Equation (10), sfc is actually determined by Ps, α, and fuel-air ratio f. When T4∗ remains constant, α is positively correlated with πc, and f is negatively correlated with πc. At low values of πc, the increase of Ps and α and the decrease of f are all favorable factors for reducing sfc. When the value of πc is relatively high, the favorable effects due to the increase of α and decrease of f are not sufficient to overcome the effect unfavorable effect from the decrease in Ps, and the variation of sfc shows opposing trend. As shown in Figures 3 and 4, the isopleths of ηth run nearly parallel to the horizontal ordinate, which implies that there is a strong correction between the variation of ηth and that of sfc.Figure 3
Variations in performance metrics with cycle parameters under standard sea-level condition.Figure 4
Variations in performance metrics with cycle parameters under high altitude cruise condition.When the compressor pressure ratioπc remains constant, Ps and ηth exhibit positive correlation with T4∗, and sfc exhibits negative correlation with T4∗. Furthermore, the performance metrics are less sensitive to changes in T4∗ than them to changes in πc. As T4∗ increases, the cycle heat addition increases, resulting in the proportion of heat loss owing to exhaust decreases, which is favorable for the improvement of ηth. In addition, ηth is positively correlated with α, and α decreases with the increase of T4∗. Therefore, the improvement of ηth due to the increase of cycle heat addition is weakened by the effect of α. In summary, ηth increases with an increase in T4∗, and the sensitivity of ηth to changes in T4∗ decreases with an increase in T4∗. The variation sfc can be explained in exactly the same manner. For a constant value of πc, Ps is actually determined by the cycle heat addition. Therefore, Ps increases monotonically with the increase of T4∗. Generally, the application of rotating detonation technology does not change the variation trends of performance metrics of the turboshaft engine versus cycle parameters.There is strong agreement between the variation trends of performance metrics under high-altitude cruise condition and those under standard sea-level condition versus cycle parameters. Under cruise condition, the total pressure ratio improves owing to the ram compression, and so do the performance metrics. AsH increases, the freestream temperature T0 as well as the combustor inlet temperature T3∗ decreases, which is favorable for the total pressure gain in the RDC. Therefore, the high-altitude cruise condition corresponds to higher Ps and ηth and lower sfc.The cycle parameter comparison between the rotating detonation-based turboshaft engine and the conventional one with the same performance metrics is displayed in Figure5. It can be seen that the former corresponds to a lower πc and T4∗. The reduction in πc is conducive to improving the structural compactness and power weight ratio, and the reduction in T4∗ is a benefit for increasing the service life of the turbine. Furthermore, the benefits of reducing πc and T4∗ exhibit a positive correlation with T4∗ and a negative correlation with πc, and the internal mechanism is consistent with the variations in performance benefits versus πc and T4∗, which have been expressed above.Figure 5
Cycle parameters mapping between the rotating detonation turboshaft engine and the conventional one with the same performance metrics.The feedback pressure perturbation generated by the RDC can be reduced effectively by the isolator, but it cannot be eliminated thoroughly [22]. The weakened pressure perturbation may result in reduction in compressor efficiency. Similarly, the turbine inlet parameter distribution can be improved owing to the mixing process in the mixer, but the turbine inlet parameter distribution of the rotating detonation-based turboshaft engine, which has a direct relationship with the turbine efficiency, is still less uniform than that of the conventional one. Therefore, the sensitivity analysis of turbomachinery efficiency and the total pressure recovery of the isolator on overall performance of the rotating detonation-based turboshaft engine is of significance. As the turbomachinery polytropic efficiency ec and et is hardly dependent on the pressure ratios πc and πt [3], ec and et are utilized to characterize the turbomachinery efficiency in this study. Figure 6 displays the effects of compressor polytropic efficiency ec, turbine polytropic efficiency et and total pressure recovery coefficient of isolator σis on the overall performance of the engine. As πc remains constant, the increase of ec and et could improve the overall performance of the engine. And the performance metrics are more sensitive to changes in ec and et at higher values of πc. Furthermore, Ps and sfc are more sensitive to changes in ec than to changes in et, as the compressor pressure ratio is normally higher than the turbine pressure ratio. Unlike the influence mechanism of ec and et, the increase of σis has the same impact as improving the total pressure ratio of the engine. According to the sensitivity analysis of cycle parameters on overall performance of the engine, as πc increases, Ps first increases but then decreases, and sfc first decreases but then increases. At low values of πc, the higher the value of σis, the higher the value of Ps. When the value of πc is relatively high, the situation is the opposite. As the optimum compressor pressure ratios corresponding to the maximum ηth and minimum sfc are higher than that corresponding to the maximum Ps, when the values of πc are not quite high, the higher the value of σis, the higher the value of ηth and the lower the value of sfc.Figure 6
Variations in performance metrics with (a) compressor polytropic efficiencyec, (b) turbine polytropic efficiency et, and (c) total pressure recovery coefficient of isolator σis.
(a)(b)(c)


### 3.2. Comparison Between the Rotating Detonation-Based Turboshaft Engine and the Conventional One

Figure7 shows the variations in performance difference between the rotating detonation-based turboshaft engine and the conventional one with the same component parameters versus cycle parameters under the standard sea-level condition at takeoff. It can be seen that, at low values of πc, the rotating detonation-based turboshaft engine exhibits significant potential benefits in Ps, ηth, and sfc. As πc increases, the potential benefits decrease and tend to disappear. Furthermore, the compressor pressure ratio range corresponding to the rotating detonation-based turboshaft engine exhibiting benefit in Ps is wider than that corresponding to the engine exhibiting benefit in ηth and sfc. The fuel-air ratio f of the rotating detonation-based turboshaft engine is higher than that of the conventional one with the same cycle parameters. Then, the total pressure gain of the RDC is significant at low values of πc, resulting in a higher power turbine pressure ratio πpt of the rotating detonation-based turboshaft engine compared to the conventional one. As the total pressure gain of the RDC decreases with an increase in πc, so does the benefit of πpt. For the ηth and sfc of turboshaft engines, the higher value of f is an unfavorable factor, and the higher value of πpt is a favorable factor. The potential benefits of ηth and sfc can be achieved by the rotating detonation-based turboshaft engine under the premise that the favorable effects generated by πpt are sufficient to overcome the unfavorable effects of a higher value of f. Therefore, there is a strong agreement between the variations of the potential benefits in ηth and sfc and the variation of the benefit of πpt. The higher value of f and the higher value of πpt are all favorable factors for the improvement of Ps. Therefore, the rotating detonation-based turboshaft engine exhibits significant benefit in Ps at low values of πc. In addition, the power turbine inlet total enthalpy h6∗ of the rotating detonation-based turboshaft engine is lower than that of the conventional one, owing to the rear stage of compressor. Therefore, the benefit in Ps tends to disappear at high values of πc. It is not difficult to draw the conclusion that the critical compressor pressure ratio πcrit1 corresponding to the disappearance of Ps improvement is higher than that corresponding to the disappearance of ηth and sfc, according to the above explanation.Figure 7
Performance comparison of turboshaft engine based on rotating detonation and the conventional one for different cycle parameters. (a)Ps, (b) sfc, and (c) ηth.
(a)(b)(c)When the value ofπc remains constant, as T4∗ increases, the potential performance benefits of the rotating detonation-based turboshaft engine increase continuously. And the potential benefits in ηth and sfc are more sensitive to changes in T4∗ compared to the potential benefit in Ps. Although the total pressure gain of the RDC is independent of T4∗, the effect of the total pressure gain of the RDC can be enlarged owing to the decrease of α. Therefore, the performance differences between the rotating detonation-based turboshaft engine and the conventional one increase with an increase in T4∗. In addition, the fuel-air ratio difference increases as T4∗ increases owing to the decrease of α. As ηth is positively correlated with Ps and negatively correlated with f, the potential benefits in ηth is more sensitive to changes in T4∗. According to the explanation in Section 3.1, there is a strong correction between the variation of ηth and that of sfc, so do the variations of performance benefits in ηth and sfc. The variations in critical compressor pressure ratio πcrit1 corresponding to the disappearance of Ps improvement and the critical compressor pressure ratio πcrit2 corresponding to the disappearance of sfc improvement of the rotating detonation-based turboshaft engine versus T4∗ are displayed in Table 2. It can be seen that πcrit1 and πcrit2 exhibit positive correlation with T4∗, and πcrit1 is normally larger than πcrit2.Table 2
Variations in critical compressor pressure ratiosπcrit1 and πcrit2 with T4∗.
T4∗, Kπcrit1πcrit2140014.2012.37150018.2313.87160023.5215.26170030.6916.5180040.8717.71As the value ofπc remains constant at 12 and the value of T4∗ remains constant at 1600 K, the variations in performance differences between the rotating detonation-based turboshaft engine and the conventional one versus flight parameters are shown in Figure 8. As V0 increases, Ps and ηth of the two forms of engines increase, and sfc decreases monotonically. And the performance differences between the two forms of engines decreases with an increase in V0. And the performance differences of ηth and sfc are more sensitive to changes in V0 compared to the performance difference of Ps. As V0 increases, the total pressure ratio of the engine increases owing to the ram compression, which is favorable for improving the overall performance. The performance benefits of the rotating detonation-based turboshaft engine compared to the conventional one are mainly contributed by the total pressure gain of the RDC. As V0 increases, the combustor inlet temperature T3∗ increases, which is detrimental to the total pressure gain of the RDC [22, 23]. In addition, α increases with an increase in V0, owing to the decrease of cooling capacity of the compressed air. Then, the effect of the total pressure gain of the RDC can be weakened. In summary, the potential performance benefits of the rotating detonation-based turboshaft decrease with an increase in V0. Ps and ηth of the two forms of engines exhibit a positive correlation with H, and sfc exhibits a negative correlation with H. And the performance differences between the two forms of engines exhibit a positive correction with H. With the increase of H, the freestream temperature T0 decreases monotonically, which is favorable for the improvement of the overall performance. T3∗ decreases with an increase in H, resulting in the improvement of the total pressure gain of the RDC. In addition, α decreases with an increase in H, and the effect of the total pressure gain of the RDC can be enlarged. With the combined effects of these two factors, the potential performance benefits of the rotating detonation-based turboshaft increase with an increase in H. The effects of flight parameters on πcrit1 and πcrit2 are displayed in Tables 3 and 4. According to the calculation results, πcrit1 and πcrit2 are positively correlated with H and negatively correlated with V0.Figure 8
Performance comparison of turboshaft engine based on rotating detonation and the conventional one for different cycle parameters. (a)Ps, (b) sfc, and (c) ηth.
(a)(b)(c)Table 3
Variations in critical compressor pressure ratiosπcrit1 and πcrit2 with V0.
V0, km h-1πcrit1πcrit2023.5215.2615023.3215.130022.7214.6345021.7713.89Table 4
Variations in critical compressor pressure ratiosπcrit1 and πcrit2 with H.
H, kmπcrit1πcrit2021.7713.89223.7215.4425.9417.17628.4519.27831.3521.77


### 3.3. Optimum Pressure Ratios

On the basis of the variations inPs and sfc of the rotating detonation-based turboshaft engine versus πc, there exist an optimum compressor pressure ratio πopt1 that maximizes the specific power and an optimum compressor pressure ratio πopt2 that minimizes the specific fuel consumption. Table 5 shows the variations in πopt1 and πopt2 versus T4∗. It can be seen that πopt1 and πopt2 increase with an increase in T4∗, as Ps exhibits a positive correlation with T4∗ and sfc exhibits a negative correlation with T4∗. The variations in πopt1 and πopt2 versus flight parameters V0 and H are listed in Tables 6 and 7. With the increase of V0, the optimum compressor pressure ratios decrease continuously owing to the ram compression. As H increases, the RDC inlet temperature decreases, and the pressure gain of the RDC increases monotonically. In addition, α decreases as the freestream temperature decreases with an increase in H. For the effects of the above factors, sfc performance improves with H as does πopt2.Table 5
Variations in optimum compressor pressure ratiosπopt1 and πopt2 with T4∗.
T4∗, Kπopt1πopt214004.1811.0415004.9514.0716005.7917.6717006.6821.9318007.7126.52Table 6
Variations in optimum compressor pressure ratiosπopt1 and πopt2 with V0.
V0, km h-1πopt1πopt205.7917.671505.7317.563005.5517.284505.3116.81Table 7
Variations in optimum compressor pressure ratiosπopt1 and πopt2 with H.
H, kmπopt1πopt205.4016.9825.6618.7345.9420.7666.2523.1386.6025.92


## 3.1. Sensitivity Analysis of Component Parameters on Overall Performance of the Engine

A sensitivity analysis is conducted below to reveal the variation in overall performance of the rotating detonation-based turboshaft engine versus the component parameters. The compressor pressure ratioπc and turbine inlet temperature T4∗ play a major role in the overall performance of the engine. The variations in Ps, ηth, and sfc with respect to πc and T4∗ under standard sea-level and high altitude cruise conditions are, respectively, illustrated in Figures 3 and 4. In the figures, the coordinate values of each points are determined by the Ps and sfc of the cases with the corresponding values of πc and T4∗, and the values of ηth are presented by the color scales. The sensitivity of performance metrics to the πc and T4∗ can be presented intuitively by the trends of curves and color scales. It can be seen that, with an increase in πc, Ps and ηth first increase but then decrease, and sfc first decreases but then increases. As πc increases, on the one hand, the power turbine pressure ratio πt increases, and the sensitivity of πt to changes in πc decreases, as the pressure-gain of the RDC is negatively correlated with πc [22]. On the other hand, the cycle heat addition decreases owing to the increase of combustor inlet temperature T3∗ and air split parameter α. In addition, the increase of α can weaken the potential benefits relating to the pressure gain of the RDC. At low values of πc, the increase of πt is the main factor influencing Ps, and Ps increases with the increase of πc. As πc increases, the increase of T3∗ and α becomes the dominant factor influencing Ps, and Ps decreases as πc increases. The thermal efficiency ηth is positively correlated with Ps, so the variation of ηth is consistent with that of Ps. In addition, ηth is positively correlated with α according to Equation (9), so the unfavorable impact of T3∗ can be weakened. Therefore, the downward trend of ηth at high values of πc is less obvious than that of Ps. On the basis of Equation (10), sfc is actually determined by Ps, α, and fuel-air ratio f. When T4∗ remains constant, α is positively correlated with πc, and f is negatively correlated with πc. At low values of πc, the increase of Ps and α and the decrease of f are all favorable factors for reducing sfc. When the value of πc is relatively high, the favorable effects due to the increase of α and decrease of f are not sufficient to overcome the effect unfavorable effect from the decrease in Ps, and the variation of sfc shows opposing trend. As shown in Figures 3 and 4, the isopleths of ηth run nearly parallel to the horizontal ordinate, which implies that there is a strong correction between the variation of ηth and that of sfc.Figure 3
Variations in performance metrics with cycle parameters under standard sea-level condition.Figure 4
Variations in performance metrics with cycle parameters under high altitude cruise condition.When the compressor pressure ratioπc remains constant, Ps and ηth exhibit positive correlation with T4∗, and sfc exhibits negative correlation with T4∗. Furthermore, the performance metrics are less sensitive to changes in T4∗ than them to changes in πc. As T4∗ increases, the cycle heat addition increases, resulting in the proportion of heat loss owing to exhaust decreases, which is favorable for the improvement of ηth. In addition, ηth is positively correlated with α, and α decreases with the increase of T4∗. Therefore, the improvement of ηth due to the increase of cycle heat addition is weakened by the effect of α. In summary, ηth increases with an increase in T4∗, and the sensitivity of ηth to changes in T4∗ decreases with an increase in T4∗. The variation sfc can be explained in exactly the same manner. For a constant value of πc, Ps is actually determined by the cycle heat addition. Therefore, Ps increases monotonically with the increase of T4∗. Generally, the application of rotating detonation technology does not change the variation trends of performance metrics of the turboshaft engine versus cycle parameters.There is strong agreement between the variation trends of performance metrics under high-altitude cruise condition and those under standard sea-level condition versus cycle parameters. Under cruise condition, the total pressure ratio improves owing to the ram compression, and so do the performance metrics. AsH increases, the freestream temperature T0 as well as the combustor inlet temperature T3∗ decreases, which is favorable for the total pressure gain in the RDC. Therefore, the high-altitude cruise condition corresponds to higher Ps and ηth and lower sfc.The cycle parameter comparison between the rotating detonation-based turboshaft engine and the conventional one with the same performance metrics is displayed in Figure5. It can be seen that the former corresponds to a lower πc and T4∗. The reduction in πc is conducive to improving the structural compactness and power weight ratio, and the reduction in T4∗ is a benefit for increasing the service life of the turbine. Furthermore, the benefits of reducing πc and T4∗ exhibit a positive correlation with T4∗ and a negative correlation with πc, and the internal mechanism is consistent with the variations in performance benefits versus πc and T4∗, which have been expressed above.Figure 5
Cycle parameters mapping between the rotating detonation turboshaft engine and the conventional one with the same performance metrics.The feedback pressure perturbation generated by the RDC can be reduced effectively by the isolator, but it cannot be eliminated thoroughly [22]. The weakened pressure perturbation may result in reduction in compressor efficiency. Similarly, the turbine inlet parameter distribution can be improved owing to the mixing process in the mixer, but the turbine inlet parameter distribution of the rotating detonation-based turboshaft engine, which has a direct relationship with the turbine efficiency, is still less uniform than that of the conventional one. Therefore, the sensitivity analysis of turbomachinery efficiency and the total pressure recovery of the isolator on overall performance of the rotating detonation-based turboshaft engine is of significance. As the turbomachinery polytropic efficiency ec and et is hardly dependent on the pressure ratios πc and πt [3], ec and et are utilized to characterize the turbomachinery efficiency in this study. Figure 6 displays the effects of compressor polytropic efficiency ec, turbine polytropic efficiency et and total pressure recovery coefficient of isolator σis on the overall performance of the engine. As πc remains constant, the increase of ec and et could improve the overall performance of the engine. And the performance metrics are more sensitive to changes in ec and et at higher values of πc. Furthermore, Ps and sfc are more sensitive to changes in ec than to changes in et, as the compressor pressure ratio is normally higher than the turbine pressure ratio. Unlike the influence mechanism of ec and et, the increase of σis has the same impact as improving the total pressure ratio of the engine. According to the sensitivity analysis of cycle parameters on overall performance of the engine, as πc increases, Ps first increases but then decreases, and sfc first decreases but then increases. At low values of πc, the higher the value of σis, the higher the value of Ps. When the value of πc is relatively high, the situation is the opposite. As the optimum compressor pressure ratios corresponding to the maximum ηth and minimum sfc are higher than that corresponding to the maximum Ps, when the values of πc are not quite high, the higher the value of σis, the higher the value of ηth and the lower the value of sfc.Figure 6
Variations in performance metrics with (a) compressor polytropic efficiencyec, (b) turbine polytropic efficiency et, and (c) total pressure recovery coefficient of isolator σis.
(a)(b)(c)


## 3.2. Comparison Between the Rotating Detonation-Based Turboshaft Engine and the Conventional One

Figure7 shows the variations in performance difference between the rotating detonation-based turboshaft engine and the conventional one with the same component parameters versus cycle parameters under the standard sea-level condition at takeoff. It can be seen that, at low values of πc, the rotating detonation-based turboshaft engine exhibits significant potential benefits in Ps, ηth, and sfc. As πc increases, the potential benefits decrease and tend to disappear. Furthermore, the compressor pressure ratio range corresponding to the rotating detonation-based turboshaft engine exhibiting benefit in Ps is wider than that corresponding to the engine exhibiting benefit in ηth and sfc. The fuel-air ratio f of the rotating detonation-based turboshaft engine is higher than that of the conventional one with the same cycle parameters. Then, the total pressure gain of the RDC is significant at low values of πc, resulting in a higher power turbine pressure ratio πpt of the rotating detonation-based turboshaft engine compared to the conventional one. As the total pressure gain of the RDC decreases with an increase in πc, so does the benefit of πpt. For the ηth and sfc of turboshaft engines, the higher value of f is an unfavorable factor, and the higher value of πpt is a favorable factor. The potential benefits of ηth and sfc can be achieved by the rotating detonation-based turboshaft engine under the premise that the favorable effects generated by πpt are sufficient to overcome the unfavorable effects of a higher value of f. Therefore, there is a strong agreement between the variations of the potential benefits in ηth and sfc and the variation of the benefit of πpt. The higher value of f and the higher value of πpt are all favorable factors for the improvement of Ps. Therefore, the rotating detonation-based turboshaft engine exhibits significant benefit in Ps at low values of πc. In addition, the power turbine inlet total enthalpy h6∗ of the rotating detonation-based turboshaft engine is lower than that of the conventional one, owing to the rear stage of compressor. Therefore, the benefit in Ps tends to disappear at high values of πc. It is not difficult to draw the conclusion that the critical compressor pressure ratio πcrit1 corresponding to the disappearance of Ps improvement is higher than that corresponding to the disappearance of ηth and sfc, according to the above explanation.Figure 7
Performance comparison of turboshaft engine based on rotating detonation and the conventional one for different cycle parameters. (a)Ps, (b) sfc, and (c) ηth.
(a)(b)(c)When the value ofπc remains constant, as T4∗ increases, the potential performance benefits of the rotating detonation-based turboshaft engine increase continuously. And the potential benefits in ηth and sfc are more sensitive to changes in T4∗ compared to the potential benefit in Ps. Although the total pressure gain of the RDC is independent of T4∗, the effect of the total pressure gain of the RDC can be enlarged owing to the decrease of α. Therefore, the performance differences between the rotating detonation-based turboshaft engine and the conventional one increase with an increase in T4∗. In addition, the fuel-air ratio difference increases as T4∗ increases owing to the decrease of α. As ηth is positively correlated with Ps and negatively correlated with f, the potential benefits in ηth is more sensitive to changes in T4∗. According to the explanation in Section 3.1, there is a strong correction between the variation of ηth and that of sfc, so do the variations of performance benefits in ηth and sfc. The variations in critical compressor pressure ratio πcrit1 corresponding to the disappearance of Ps improvement and the critical compressor pressure ratio πcrit2 corresponding to the disappearance of sfc improvement of the rotating detonation-based turboshaft engine versus T4∗ are displayed in Table 2. It can be seen that πcrit1 and πcrit2 exhibit positive correlation with T4∗, and πcrit1 is normally larger than πcrit2.Table 2
Variations in critical compressor pressure ratiosπcrit1 and πcrit2 with T4∗.
T4∗, Kπcrit1πcrit2140014.2012.37150018.2313.87160023.5215.26170030.6916.5180040.8717.71As the value ofπc remains constant at 12 and the value of T4∗ remains constant at 1600 K, the variations in performance differences between the rotating detonation-based turboshaft engine and the conventional one versus flight parameters are shown in Figure 8. As V0 increases, Ps and ηth of the two forms of engines increase, and sfc decreases monotonically. And the performance differences between the two forms of engines decreases with an increase in V0. And the performance differences of ηth and sfc are more sensitive to changes in V0 compared to the performance difference of Ps. As V0 increases, the total pressure ratio of the engine increases owing to the ram compression, which is favorable for improving the overall performance. The performance benefits of the rotating detonation-based turboshaft engine compared to the conventional one are mainly contributed by the total pressure gain of the RDC. As V0 increases, the combustor inlet temperature T3∗ increases, which is detrimental to the total pressure gain of the RDC [22, 23]. In addition, α increases with an increase in V0, owing to the decrease of cooling capacity of the compressed air. Then, the effect of the total pressure gain of the RDC can be weakened. In summary, the potential performance benefits of the rotating detonation-based turboshaft decrease with an increase in V0. Ps and ηth of the two forms of engines exhibit a positive correlation with H, and sfc exhibits a negative correlation with H. And the performance differences between the two forms of engines exhibit a positive correction with H. With the increase of H, the freestream temperature T0 decreases monotonically, which is favorable for the improvement of the overall performance. T3∗ decreases with an increase in H, resulting in the improvement of the total pressure gain of the RDC. In addition, α decreases with an increase in H, and the effect of the total pressure gain of the RDC can be enlarged. With the combined effects of these two factors, the potential performance benefits of the rotating detonation-based turboshaft increase with an increase in H. The effects of flight parameters on πcrit1 and πcrit2 are displayed in Tables 3 and 4. According to the calculation results, πcrit1 and πcrit2 are positively correlated with H and negatively correlated with V0.Figure 8
Performance comparison of turboshaft engine based on rotating detonation and the conventional one for different cycle parameters. (a)Ps, (b) sfc, and (c) ηth.
(a)(b)(c)Table 3
Variations in critical compressor pressure ratiosπcrit1 and πcrit2 with V0.
V0, km h-1πcrit1πcrit2023.5215.2615023.3215.130022.7214.6345021.7713.89Table 4
Variations in critical compressor pressure ratiosπcrit1 and πcrit2 with H.
H, kmπcrit1πcrit2021.7713.89223.7215.4425.9417.17628.4519.27831.3521.77


## 3.3. Optimum Pressure Ratios

On the basis of the variations inPs and sfc of the rotating detonation-based turboshaft engine versus πc, there exist an optimum compressor pressure ratio πopt1 that maximizes the specific power and an optimum compressor pressure ratio πopt2 that minimizes the specific fuel consumption. Table 5 shows the variations in πopt1 and πopt2 versus T4∗. It can be seen that πopt1 and πopt2 increase with an increase in T4∗, as Ps exhibits a positive correlation with T4∗ and sfc exhibits a negative correlation with T4∗. The variations in πopt1 and πopt2 versus flight parameters V0 and H are listed in Tables 6 and 7. With the increase of V0, the optimum compressor pressure ratios decrease continuously owing to the ram compression. As H increases, the RDC inlet temperature decreases, and the pressure gain of the RDC increases monotonically. In addition, α decreases as the freestream temperature decreases with an increase in H. For the effects of the above factors, sfc performance improves with H as does πopt2.Table 5
Variations in optimum compressor pressure ratiosπopt1 and πopt2 with T4∗.
T4∗, Kπopt1πopt214004.1811.0415004.9514.0716005.7917.6717006.6821.9318007.7126.52Table 6
Variations in optimum compressor pressure ratiosπopt1 and πopt2 with V0.
V0, km h-1πopt1πopt205.7917.671505.7317.563005.5517.284505.3116.81Table 7
Variations in optimum compressor pressure ratiosπopt1 and πopt2 with H.
H, kmπopt1πopt205.4016.9825.6618.7345.9420.7666.2523.1386.6025.92


## 4. Conclusion

In this study, a configuration of the rotating detonation-based turboshaft engine with the compatibility between the turbomachinery and RDC under consideration is presented. Then, the performance characteristics of this new form of engine are investigated based on the parametric thermodynamic cycle analysis model. In order to reveal the potential performance benefits and their generation mechanism, the performance comparison between the rotating detonation-based turboshaft engine and the conventional one is performed. The major conclusions are summarized as follows.(1)
When the flight parameters remain constant, as the compression ratioπc increases, the specific power Ps and thermal efficiency ηth of the rotating detonation-based turboshaft engine first increase but then decrease, and the specific fuel consumption sfc first decreases but then increases. As the turbine inlet temperature T4∗ increases, Ps and ηth increase, and sfc decreases continuously. When the component parameters remain constant, with the increase in flight velocity V0 and flight altitude H, Ps and ηth increase, and sfc decreases monotonically. There exist optimum compressor pressure ratios πopt1 and πopt2 which maximizes the specific power and minimizes the specific fuel consumption, respectively, and πopt1 is nominally larger than πopt2. Furthermore, πopt1 and πopt2 are positively correlated with T4∗ and H and are negatively correlated with V0.(2)
Compared to the conventional turboshaft engine, the thermal efficiency of the rotating detonation-based turboshaft engine can be improved above 7% at lower values ofπc, and the benefits decrease with an increase in πc. As πc remains constant, the performance improvements increase with the increase of T4∗. As T4∗ remains constant at 1600 K, the value of πcrit1 is about 23.5 corresponding to the disappearing of benefit in Ps, and value of πcrit2 is about 15.3 corresponding to the disappearing of benefit in ηth and sfc. The critical compressor pressure ratios are positively correlated with T4∗ corresponding to the disappearance of performance benefits.(3)
When the value ofπc is not quite high and the value of T4∗ is not relatively low, the rotating detonation-based turboshaft engine exhibits competitive potential benefits within the typical flight envelope of helicopters (i.e., V0<450km/h and H<8km). The potential benefits of the rotating detonation-based turboshaft engine exhibit a positive correlation with H and exhibit a negative correlation with V0. Furthermore, the values of πcrit1 and πcrit2 increase with the increase in H and decrease with an increase in V0.



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*Source: 9587813-2020-07-02.xml*