Numerical investigations of the nozzle performance for a rocket-based rotating detonation engine with film cooling

https://doi.org/10.1016/j.ast.2023.108221Get rights and content

Abstract

This study numerically investigates the nozzle performance of a rotating detonation engine with film cooling. The premixed stoichiometric hydrogen/air mixture serves as the reactant, and the pure air is pumped into the film cooling holes. The diverging section of the nozzle is designed based on the characteristic method and the maximum thrust theory. The spike truncation ratio is optimized to ΔLspike = 40% Lcowl, reducing the weight and maintaining a high axial thrust coefficient of 0.9456. In contrast with the steady condition, the flow loss of the practically transient condition mainly comes from three parts. The first is the pressure loss of the continuously sweeping shock waves, the second is the viscous effect of the flow passage, and the third is the energy dissipation of the recirculation zone in the base region. When the film cooling strategies are introduced on the inner and outer walls, the hole type a/b < 1.0/1.0 is preferred thanks to a more considerable coolant coverage induced by more violent interactions between the radial jet and the mainstream. The cooling effects and the aerodynamic performance can be further balanced within a moderate injection velocity. The final optimized nozzle configuration with ΔLspike = 40% Lcowl, a/b = 1.0/2.0, and Vsec = 100 m/s corresponds to an axial thrust coefficient of 0.9552, a discharge coefficient of 0.9344, a pressure gain of -16.48%, and a root mean square deviation of the flow deflection angle of 14.42°.

Introduction

The increasing demand for the fast-reach capability and prolonged endurance of aircraft has driven people to seek a sustainable and efficient propulsion system for many decades. In contrast with the conventional deflagration-based engine, the detonation-based engine provides a faster heat release and less entropy production, drawing people's great attention. In the early stage, the researchers spent much time on the pulse detonation engine (PDE), of which the configuration is a straight tube. In the PDEs, the detonation waves propagate in the axial direction, followed by a series of rarefaction waves (see Fig. 1(a)). The negative thrust usually occupies a relatively big cycle time interval, leading to a severe total impulse penalty. Meanwhile, the operating frequencies of PDEs are limited by the mechanical valves [1], [2], [3], [4], causing structural vibrations.

Concerning this problem, some researchers proposed the concept of the standing detonation engine (see Fig. 1(b)), which fastens the detonation wave at a specific location and can generate a considerably steady flow. However, the robustness of the SDE is usually realized at Mach 6∼14, considering the coupling effects between the shock wave and the chemical reaction [5], [6], [7], [8]. Another promising detonation-based engine is called a rotating detonation engine (RDE), of which the detonation wave propagates in the circumferential direction, and the mainstream runs in the axial direction (see Fig. 1(c)). A dynamically stable triangle of the fresh reactants is bounded by the contact discontinuity, the detonation wave, and the injection plane, enabling the self-adaptive resistance to the flameout. Meanwhile, the shear layer and the shock wave originate from the apex of the reactant triangle and extend through the combustion chamber exit, distorting the exit flowfield of the combustion chamber in temporal and spatial scales. In contrast with PDEs and SDEs, RDEs have two advantages. One is that the dynamically stable detonation wave at the injection plane provides a linear impulse gain, and the other is that the inclined shear layer constrains the diverging flow passage and the injection plane to accelerate the flow [9], [10], [11], [12].

However, the annular channel can not effectively convert the high enthalpy into kinetic energy. It is necessary to design an exhaust system to reorganize the flowfield and boost thrust. Many efforts have been made to give initial guidance on RDE nozzle design. Braun et al. [13] adopted the steady nozzle performance analysis method in a RDE cycle to obtain the tendency of the specific impulse to the area ratio. Stechmann et al. [14] established a fundamental thermodynamic model for RDEs to investigate the performance difference between the bell and aerospike nozzles. The finding revealed that the aerospike nozzle was preferred for RDEs in a wide range of operating pressures. A similar approach was proposed by Kaemming et al. [15], which can reproduce the circumferential distribution of the chamber pressure and estimate the expansion ratio of the RDE nozzle to some extent. Davidenko et al. [16] also tried to construct a 0D approach with a detailed combustion mechanism to reveal the relationship among the mixture ratio, injection pressure, ambient pressure, and area ratio. Shao et al. [17] made a parametric study to compare the propulsive features of different RDE nozzle types. The results showed that the Laval nozzle performed much better than others. Braun et al. [18] utilized the open-source software OpenFoam to quantify the effects of the outflow conditions on five nozzle geometries and concluded that the Bezier outer wall underperformed compared with the conical wall at low-pressure ratios. Schwer et al. [19] studied the RDE nozzles with a series of equivalence ratios, of which the pressure histories were recorded. They found that the flow dynamics of the aerospike nozzle were similar to the steady inflow results. Zhu et al. [20] conducted experiments to analyze the propulsive performance of a RDE with different aerospike nozzles. The researchers found that the total pressure gain varied with the nozzle configuration, and the nozzle profile designed by Angelino's method promoted the specific impulse. Fotia et al. [21] investigated the performance of different RDE nozzles experimentally and demonstrated that a stagnation pressure gain and specific thrust promotion benefited from the throat choking condition. The proof of this conclusion can also be found in the numerical simulation by Jourdaine et al. [22]. Sun et al. [23] simulated a RDE with a truncated spike nozzle and found that the thrust of the end faces fluctuates at high ambient pressure. Fievisohn et al. [24] introduced a lateral-expansion term into the method of characteristics to simulate the quasi-2D flowfields of RDEs with nozzles. However, it required dedicated handling of the interior points and ignored the influence of base recirculation. Huang et al. [25] studied the shock dynamics and expansion characteristics of an aerospike nozzle installed on a RDE numerically. The results revealed that the thrust and total pressure recovery were enhanced due to the detonation combustion. Their research also displayed a RDE nozzle design method, of which the feature was that the profile with a constant Mach number gradient merged with the profile calculated by MOC to generate a final configuration. Goto et al. [26] tested various throat geometries of spike nozzles for RDEs in the vacuum chamber. The experimental results showed that the combustor pressure was proportional to the throat mass flux, and RDEs can also reach the optimal specific impulse for a constant-pressure combustor.

In the beginning, most studies paid great attention to the heat-sink cooled models with a typically short duration of 1∼10 s and focused on improving the aerodynamic performance. With the technology maturation, researchers hope to elongate the working time of RDEs. However, the periodic heat flux spikes at the scale of 1∼9 MW/m2 always bring severe erosion and ablation. Though an external water cooling system can be utilized to absorb heat, its auxiliary pump system usually causes weight penalty. Therefore, the film cooling with gaseous coolant is more promising. Previous studies about the heat conduction and thermal management of RDEs give some initial guidance to thermal protection optimization. Lim et al. [27] conducted experiments on a RDE fed by gaseous oxygen and RP-2. The thermocouples recorded the heat fluxes on the inner wall, illustrating that the averaged maximum heat load of a RDE was situated between the frozen state and the chemical equilibrium state at the nozzle throat. Wu et al. [28] utilized the monotonicity preserving weighted essentially non-oscillatory scheme to simulate the RDE flowfields with different isothermal walls. The detonation flame quenched when the wall temperature was kept at 300 K; the topological structures of the detonation phenomena hardly changed when the wall temperature rose to 600 K; the flameout and re-ignition of the detonation wave occurred alternatively when the wall temperature reached 900 K. It can be deduced that the cooling strategy applied to RDEs is responsible for finite heat extraction from the wall, and the rest thermal load still needs to be overcome by the wall materials. Theuerkauf et al. [29] designed a closed annular cooling coat and analyzed the thermal management of a RDE. However, the closed cooling system carries additional liquid coolants, reducing the payload. Because the air serves as the coolant, film cooling shows advantages over closed cooling systems in the compact integration with the propulsion system. A related attempt was found in the experimental study conducted by Goto et al. [30]. They designed a hollow combustor with radial injection holes that simultaneously functioned as the reactant supplies and film cooling sources. Due to the heat exchange of the propellant injection, the heat fluxes through the combustor wall were reduced. Sada et al. [31] simulated the flow field of a configuration similar to Goto's and observed that reactants in the post-detonation region were concentrated into a spiral pattern near the axis. The numerical results also displayed that the downstream wall temperature of the radial injection strategy was much lower than the base injection strategy. Tian et al. [32] conducted a numerical study about a RDE with radial film cooling holes and an axial reactant inlet, demonstrating that the film cooling on a RDE reduced the wall temperatures in the middle and rear sections. In addition, the inherent oscillating effects of a RDE induced the coolant to behave more like a mixed jet.

Based on the present research status, this study targets the thrust boosting and film cooling strategies on RDEs. A maximum thrust nozzle profile is designed by the method of characteristics, and the transient simulations parametrically select the spike truncation. The radial cooling holes with different ellipticities are then drilled on the inner and outer walls of RDEs to analyze the coupling effects between the cooling film and the mainstream. The aerodynamic performance comparisons determine the configuration of the RDE with a nozzle and a thermal protection system.

Section snippets

Governing equations

Because only aerodynamic performances, such as the axial thrust and specific impulse, instead of the details of detonation structures, are considered in a combustion chamber, a one-step Arrhenius kinetics is adopted for this study. The governing equations are 3D unsteady Reynolds-averaged Navier-Stokes (RANS) equations with source terms of chemical reactions, which can be defined as follows:

Continuity equation:ρt+(ρui)xi=0 Momentum equation:(ρui)t+(ρuiuj)xj=pxi+τijxj Energy

Method of characteristics

The design of a RDE nozzle has two essential factors: 1) Similar to a conventional rocket nozzle, a RDE nozzle requires a geometrical throat to generate a chocked flow, thereby maintaining a high chamber pressure. The throat area can be estimated by the 1D steady flow theory; 2) it is empirically recognized that time-averaged stagnation parameters at the combustor exits of RDEs can be utilized as the aerodynamic constraints on the RDE nozzle design [20], [25], [41], [42]. Because the flow

Definitions of performance parameters

In order to quantify the aerodynamic performance of RDE nozzles and the cooling effects of the secondary injection, the related parameters are introduced. The axial thrust coefficient of the nozzle is defined byCfx=Factual/Fideal where Factual and Fideal correspond to the actual and ideal thrust, respectively.

The discharge coefficient is calculated as follows,ψ=m˙m˙ideal=m˙T0,cKp0,cAth where T0,c, p0,c, and Ath are the stagnation temperature, stagnation pressure, and throat area, respectively.

Results and discussion

In this study, the inner and outer radii of the RDE combustor are 40 mm and 50 mm. The lengths of the combustor, nozzle converging section, and nozzle diverging section are 50 mm, 5 mm, and 80 mm. In addition, the contraction and expansion ratios of the nozzle are 1.1 and 6.2 to achieve efficient flow acceleration. As plotted in Fig. 11, the velocity-inlet boundary condition is imposed on the combustor entrance. The injection law of the fresh reactant (stoichiometric hydrogen/air mixture) is

Conclusion

This study investigates the design method of RDE nozzles and related film cooling strategies on the combustor and nozzle walls. The diverging nozzle section is designed by the characteristic method, and the spike truncation is optimized according to the thrust penalty and the effects on the stagnation parameters. With a determined nozzle profile, the parametric study of the cooling hole type and related inlet parameters is conducted. The conclusions are summarized as follows:

(1) The

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

We would like to acknowledge the support of the National Science and Technology Major Project on contract number J2019-II-0007-027 and the “Fundamental Research Fund for the Central Universities” under contract numbers 1002-XQA22020 and 1002- XBC22044. We are also grateful to the editors and reviewers.

References (47)

  • J. Sun et al.

    Effects of air injection throat width on a non-premixed rotating detonation engine

    Acta Astronaut.

    (2019)
  • X. Liu et al.

    Design and optimization of aerospike nozzle for rotating detonation engine

    Aerosp. Sci. Technol.

    (2022)
  • L. Deng et al.

    Secondary shock wave in rotating detonation combustor

    Aerosp. Sci. Technol.

    (2019)
  • J. Sun et al.

    Effects of injection nozzle exit width on rotating detonation engine

    Acta Astronaut.

    (2017)
  • S. Yao et al.

    Multiple ignitions and the stability of rotating detonation waves

    Appl. Therm. Eng.

    (2016)
  • E. Wintenbenberger et al.

    Model for the performance of airbreathing pulse-detonation engines

    J. Propuls. Power

    (2006)
  • K. Wang et al.

    Efforts on high-frequency pulse detonation engines

    J. Propuls. Power

    (2017)
  • F. Ma et al.

    Propulsive performance of airbreathing pulse detonation engines

    J. Propuls. Power

    (2006)
  • R. Gross et al.

    A study of supersonic combustion

    J. Aerosp. Sci.

    (1960)
  • P. Rubins et al.

    Review of shock-induced supersonic combustion research and hypersonic applications

    J. Propuls. Power

    (1994)
  • P. Wolanski

    RDE research and development in Poland

    Shock Waves

    (2021)
  • B.A. Rankin et al.

    Overview of performance, application, and analysis of rotating detonation engine technologies

    J. Propuls. Power

    (2017)
  • F.K. Lu et al.

    Rotating detonation wave propulsion: experimental challenges, modeling, and engine concepts

    J. Propuls. Power

    (2014)
  • Cited by (0)

    View full text