Fig. 2.3.3. Primary thermodynamic flow paths in a rotating
detonation engine [65].

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Since the radial size is much smaller than the azimuthal and axial dimensions, the flow in the RDC
can be approximated as two-dimensional in space. Fig. 2.3.2 depicts the typical two-dimensional
numerical solution of the flow field in the RDC [64]. It can be seen that, the primary thermodynamic
flow paths of the flow particles in the different region of the RDE contains four forms [65]: deflagrated
flow, detonated flow, a mixed flow comprising both detonated and deflagrated flows, and detonated flow
plus secondary shock, as shown in Fig. 2.3.3. The thermal efficiency of the different flow paths are quite
different, and the equivalent thermal efficiency of the RDE can be estimated by mass-flow average
method.
2.3.2. system configuration and component matching
The operational stability of the RDC can only be achieved with a specific air mass flow rate.
When the mass flow rate is high, the single-wave mode can be replaced by the multi-wave mode in
the RDC [66-67]. However, the stable detonation wave cannot be formed when the mass flow rate is
quite low [68-69]. In contrast to the single-wave mode, the total pressure improvement is reduced [70].
In addition, the flow capacity of the typical single-annular RDC, which is a narrow annular chamber, is
limited, and the annulus width should be broadened for improving the flow capacity. However, as the
annulus width increases, the curvature effect of the inner wall becomes more significant [71], and an
oblique shock system establishes between the inner and outer walls [72]. Considering the abovementioned problems, the concept of multi-annular RDC is proposed [73-74]. As shown in Fig. 2.3.4,
the single large annular chamber is replaced by several isometric small ones, and then the “staged
combustion” can be achieved. The geometrical dimensions of single small-size chamber is defined by
the lower boundary of the engine mass flow rate, and the chamber number is defined by the upper
boundary of the engine mass flow rate. The number of annular chambers in the “on” mode varies with
the engine operating condition. Compared with the conventional single-annular RDC, the multi-annular
one shows the potential advantages of wider stable operation range and more uniform outlet parameter
distribution [74-75].

(a) Circular chamber
(b) Track shaped chamber
Fig. 2.3.4 Schematic of circumferential multi-annular RDC [74-75].

The feedback pressure perturbation of the RDC has been confirmed in previous studies [76-78], and
it has certain unfavorable effects on turbomachinery operability and engine stability. Schwer et al. [77]
attempted to weaken the pressure perturbation by different injectors, but the effect was not significant.
ji et al. [73-74] proposed a form of isolator configuration to reduce the effects of feedback pressure, as
shown in Fig. 2.3.5, according to the propagation of feedback pressure perturbation. Based on numerical
simulation, the feasibility and practicability of the isolator has been verified, and the results also show that,

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q. XIE, z. jI, H. WEN, z. REN, P. WOlANSkI AND B. WANg

the geometric parameters of the obstacles play a critical role in reducing the feedback pressure of
the RDC. zhou et al. [79-80] verified the feasibility of the integrated system of the compressor and
the RDC, and studied the impact of the turbine guide vane on the propagation characteristics of
the detonation wave. liu et al [81-82] studied the effects of supersonic high-frequency pulsating exhaust
of the RDC on the operating characteristics of axial turbine based on three-dimensional numerical
simulation, and revealed that the leading-edge shock waves play a critical role in the overall unsteady loss
mechanism.

Fig. 2.3.5. Schematic structure of the isolator [73].

(a) Diagrammatic representation of the DRDATE

(b) Sectional view of
the multi-annular RDC

Fig. 2.3.6. Schematic structure of DRDATE with the multi-annular RDC [73].

The studies regarding the compatibility between the turbomachinery and RDC have led a deeper
understanding of the operating principle and matching mechanism of the rotating detonation turbine
engine. For the potential configuration of the rotating detonation turbine engine, the previous solutions
mainly focused on the main combustor being replaced by the RDC directly [79-80, 83-84], without
considering the interaction between the turbomachinery and RDC. Sousa et al. [85] proposed to cure
the turbine-RDC matching by replacing the conventional turbine with a supersonic one, however,
the technical maturity is quite low. ji et al. [73-74] presented a configuration of dual-duct rotating
detonation aero-turbine engine (DRDATE), as shown in Fig. 2.3.6. With the isolator and mixer arranged
upstream and downstream from the RDC, the turbomachinery-RDC matching was realized. With
the DRDATE being used as the gas generator, the rotating detonation-based turboprop, turboshaft,
turbofan, and industrial gas turbine can also be derived. just thank to the shock trains formed in

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the isolator of the ramjet engine, the interactions between the combustor and intake are weakened [8687]. As the shock trains can also reduce the effects of feedback pressure, there is no need to introduce any
new components for the configuration of rotating detonation ramjet engine. The rotating detonation
ramjet engine exhibits competitive improvements in overall performance at low flight Mach numbers,
compared to the conventional ramjet [74].
2.3.3. evaluation model for overall performance
With the improvement of the technical maturity of rotating detonation technology, the application
of rotating detonation in propulsion systems has attracted significant interest in both academia and
industry. Reduced-order method is effective for the evaluation and optimization of the overall
performance of the rotating detonation engine. However, the research related to the low-order model of
the RDE is quite scarce. As the detonation wave propagation characteristics were partially ignored, some
low-order models might overestimate the potential benefits of the RDC [68, 88]. Some low-order models
were developed based on the empirical and semi-empirical equations derived by numerical simulation or
experimental results [65, 89-90]. With the method of characteristics method and shock-expansion theory
combined with the C-j detonation solver, a quasi-2D analytical model of the RDC can be built, but this
model requires spatial discretization [91-92]. Based on the matching relationship between the injection
process and pressure decay after the detonation front, a low-order model of the RDC can be developed.
This model avoids spatial discretization and solving differential equations, and shows satisfactory accuracy
over a wide range of injection parameters [73-74].
Based on the reduced-order models, the technical feasibility and potential benefits of the RDE have
been preliminarily verified. The method of characteristics method coupled with T-MATS software is
developed to estimate the overall performance of the turboshaft engine with a rotating detonation
combustor, and the results show that the thermal efficiency of the gas turbine with an RDC is 5% higher
than the similar engine with a deflagration combustor, but the performance improvement decreases with
the increase of compressor pressure ratio [85]. ji et al. [73-74, 88] demonstrated that, the rotating
detonation turbine engine exhibits competitive improvements in overall performance at low compressor
pressure ratios, compared to the conventional turbojet. With the increase of compressor pressure ratio,
the performance improvements in thermal efficiency and specific fuel consumption tend to disappear.
Furthermore, as the flow path of the bypass duct is ideal for the rotating detonation combustor,
the concept of rotating detonation duct burner is proposed, and it is regarded as an alternative to
the afterburner for mixed exhaust turbofan engine [74-75].
3. research proGress oF continUoUsLY rotatinG Detonation enGine