No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Three-dimensional Numerical Simulations of a Liquid RP-2/O 2 based Rotating Detonation Engine
... It can be inferred that for the kerosene two-phase RDC used in experiments, the location of the peak value of wall heat flux does not exhibit a significant correlation with the propagation region of detonation waves, which differs from the results of some existing researches, where the wall heat flux shows a trend of initially increasing and then decreasing along the RDC axial direction, and the location of peak value of wall heat flux along axial direction of RDC essentially coincides with the axial location of detonation wave triple point [21,31]. Considering the current RDC configuration, we believe that the wall heat flux in the head of combustor is higher than that in the detonation wave propagation region mainly for the following three reasons: 1: A portion of the high-temperature burned gas will recirculate to the head of combustor near the inner and outer walls, and in addition, the fuel/oxidizer jet along the combustor axis behind the detonation wave will enhance the recirculation of burned products [32], with some fuel droplets undergoing deflagration and heat release in the recirculation zone [33]. Therefore, there is a long-term residence of high-temperature burned gas in the recirculation zone near the inner and outer walls in the head of combustor. ...
... Existing researches indicate that in two-phase RDCs, there is a certain amount of fuel droplets evaporating after the detonation wave and being consumed in deflagration in downstream region of RDC [32,36,37]. For the kerosene two phase RDC used in this study, the mixing effect of kerosene and oxidizer is reduced by non-premixed injection, and there is amount of kerosene not participating in detonation combustion and being consumed in secondary combustion such as parasitic combustion and commensal combustion [38,34]. ...
... α represents the mass fraction of kerosene spray which burn at detonation waves. Some numerical simulation results indicate that in two-phase RDCs, there is amount of liquid fuel not participating detonation combustion [32,33,36,37,44]. A portion of the fuel droplets will contact with the combustion products from the previous combustion cycle before the detonation wave, evaporating prematurely and being consumed in the form of deflagration [33]. ...
The parameter influence on the wall heat flux of the kerosene two-phase Rotating Detonation Combustor (RDC) are experimentally investigated, and the wall heat flux calculation model of RDC is established based on theoretical analysis and experimental results. Firstly, the characteristics of the wall heat flux distribution of the RDC are obtained by using the inverse heat conduction method based on the surface temperature of RDC, and the influence of mass flow rate, equivalence ratio, and combustor configuration on the distribution of heat flux are analyzed. The results indicate that the wall heat flux exhibits an L-shaped distribution along the axial direction of the investigated RDC, due to significant impingement cooling effects caused by kerosene spray. In the initial 10% of the RDC length, the specific wall heat load increases with the equivalence ratio, and is further heightened when transitioning from the single-wave mode to the counter two-wave mode, or when a contraction nozzle is added at the exit of the RDC. Furthermore, in the initial third of the RDC length, the ratio of wall heat load can reach up to approximately 50% of the overall wall heat load, and decreases with the rise in equivalence ratio. Based on the measured distribution of wall heat flux and the heat transfer properties in different combustor regions, the investigated RDC is divided into four axial regions: the head region, detonation wave propagation region, kerosene impingement region and the downstream region. Then the calculation model for average wall heat flux in each region is established. The comparison results show that the maximum deviation between the calculated results and experimental results in different regions does not exceed 30% relatively. The calculation model can offer accurate prediction on the effects of typical factors on the wall heat flux distribution, including the combustion modes, mass flow rate, equivalence ratio, and combustor configurations. It provides crucial guidance for the cooling and thermal protection design of two-phase RDCs.
... As a result, three-dimensional (3D) simulations on multiphase RDC have been increasingly utilized in recent years. [12][13][14][15] Prakash et al. 12 conducted high-fidelity simulations for a rocket-typed liquid RP-2/O 2 RDE with an injection temperature of 300 K for both liquid kerosene and gaseous oxygen. Their simulations revealed a wave speed of approximately 57% of the C-J detonation velocities. ...
... As a result, three-dimensional (3D) simulations on multiphase RDC have been increasingly utilized in recent years. [12][13][14][15] Prakash et al. 12 conducted high-fidelity simulations for a rocket-typed liquid RP-2/O 2 RDE with an injection temperature of 300 K for both liquid kerosene and gaseous oxygen. Their simulations revealed a wave speed of approximately 57% of the C-J detonation velocities. ...
... 42,43 In 2D simulations, pressure iso-contours 13,44 and numerical schlieren techniques 45 are commonly employed to visualize shock waves within the flowfield. For 3D simulations, approaches based on density isosurface, 46,47 pressure isosurface, 12,13,37,48 normal Mach number isosurface, 49,50 the pressure gradient magnitude isosurface, 40 and theory of characteristics 51 have been proposed. In contrast, detecting shock waves in multiphase RDCs poses significant challenges due to the unsteady, non-uniform, and heterogeneous nature of the flow ahead of shock fronts, making accurate detection difficult. ...
The wave dynamics play a crucial role in the operation characteristics of the rotating detonation engine. We conducted numerical simulations of a rotating detonation combustor (RDC) using multicomponent reactive Navier–Stokes equations coupled with a discrete phases model. The RDC in this research employs a configuration with multiple coaxial injectors supplying oxygen-enriched air and kerosene spray at room temperature. To accurately identify and analyze waves within the RDC, we proposed a three-dimensional transient detonation wave detection method based on the combined parameters of normal Mach number and heat release rate in the flow field. Two typical wave modes, referred to as single-wave mode and counter-waves mode, are identified and then selected to conduct a detailed wave dynamics analysis. The general wave behavior is discussed, and velocity deficit is compared for these two wave modes. For the single-wave mode, intermittent micro-explosions are observed generating retonation waves periodically in the unburnt pockets behind the rotating detonation shock front. For the counter-waves mode, we analyzed the collision process of the two waves and the coupling/decoupling of the shock front with the detonative heat release zone, revealing the reason for significant velocity deficits in this wave mode. This research demonstrates that micro-explosions intermittently occur in the multiphase RDC in both single-wave and counter-waves modes and generate micro explosion shock waves periodically, which influence the complicated wave dynamics behavior.
... Efficient mixing primarily occurs at three locations: (1) at the intersection between the C2H4 and O2 streams, (2) at a certain distance from the chamber bottom, and (3) near the outer wall, likely due to recirculation in this area. This trend is consistent with findings reported by others [40][41][42], highlighting similar mixing behaviors in detonation chambers. Additionally, the O2 stream impacts the outer wall at the BFS, creating a mode-locked lean layer near the outer wall. ...
... Efficient mixing primarily occurs at three locations: (1) at the intersection between the C 2 H 4 and O 2 streams, (2) at a certain distance from the chamber bottom, and (3) near the outer wall, likely due to recirculation in this area. This trend is consistent with findings reported by others [40][41][42], highlighting similar mixing behaviors in detonation chambers. Additionally, the O 2 stream impacts the outer wall at the BFS, creating a mode-locked lean layer near the outer wall. ...
A three-dimensional numerical investigation using ethylene–oxygen was conducted to examine the characteristics of detonation waves in a non-premixed rotating detonation engine (RDE) across three equivalence ratio conditions: fuel-lean, stoichiometric, and fuel-rich. The study aims to identify the distinct timescales associated with detonation wave propagation within the combustor and to analyze their impact on detonation wave behavior, emphasizing the influence of equivalence ratio and injector behavior on detonation wave characteristics. The results indicate that the wave behavior varies with mixture concentration, with the ethylene injector demonstrating greater stiffness compared to the oxygen injector. In lean mixtures, characterized by excess oxidizer, waves exhibit less intensity and slower progression toward equilibrium, resulting in prolonged reaction times. Rich mixtures, with excess fuel, also show a delayed approach to equilibrium and an extended chemical reaction timescale. In contrast, the near-stoichiometric mixture achieves efficient combustion with the highest thermicity, rapidly reaching equilibrium and exhibiting the shortest chemical reaction timescale. Overall, the induction timescale is generally 2–3 times longer than its respective chemical reaction timescale, while the equilibrium timescale spans a broad range, reflecting the complex, rapid dynamics inherent in these chemical processes. This study identifies the role of the characteristic chemical timescale in influencing the progression of pre-detonation deflagration in practical RDEs. Prolonged induction times in non-ideal conditions, such as those arising from equivalence ratio variations, promote incomplete reactions, thereby contributing to pre-detonation phenomena and advancing our understanding of the underlying flow physics.
... We employ a three-dimensional cubic domain with a side of = 600 m spanning 128 3 cells (fetching a resolution of Δ = Δ = Δ = 0.47 m ensuring we are well above the continuum limit which is in the O ( )) shown in Fig. 4. The evaporation of a stationary spherical n-dodecane droplet of initial diameter 0 = 30 m placed at the center of the domain is studied at a range of thermodynamic conditions. The droplet diameter is chosen based on the typical droplet size encountered in RDEs [25] and diesel-engines [26]. The thermodynamic conditions are chosen based on the most probable states a droplet experiences when it encounters a typical 2D detonation. ...
... The ambient temperatures are chosen based on Fig. 2(a) where the lower limit of the ambient temperature is = 1500K. At higher temperatures we note that the the probability of auto-ignition of the droplet [25] is higher due to which evaporation timescales are expected to be smaller than reaction timescales. Consequently we study two lower temperatures = 800&1000K. ...
This paper numerically investigates the evaporation characteristics of a single n-dodecane fuel droplet in high-pressure nitrogen environment relevant to rotating detonation engines. A validated computational fluid dynamics solver coupled with real-fluid thermophysical models is utilized. The effects of pressure, droplet temperature, and ambient gas temperature on the evaporation rate are analyzed by tracking the droplet diameter evolution. Two interface tracking techniques, namely a mean density-based method and a novel vapor-liquid equilibrium-based method, are implemented and compared. The results show appreciable deviations from the classical d2-law for droplet evaporation. Increasing the ambient temperature and droplet temperature (toward critical point) substantially accelerate the evaporation process. Meanwhile, higher pressures decrease the evaporation rate owing to slower species/thermal diffusions. At certain conditions, discernible differences are observed between the two interface tracking methods indicating deficiencies in the simple mean density approach. The paper demonstrates an effective computational framework for transcritical droplet evaporation simulations. And the generated high-pressure droplet evaporation datasets can inform sub-model development for spray combustion modeling.
... Considerable explorations on direct initiation 15,16 or selfsustained detonations with neglection of the initiation stage, 17,18 have been performed, while limited work concentrates on the heterogeneous hydrocarbon mixtures. The inherent complications in spray detonations, such as fragmentation, vaporization, and shock-droplet interactions, make it challenging to understand the initiation, detonation characterization, and droplet behavior through direct initiation. ...
In this paper, direct initiated detonation with various initial energy depositions and droplet diameters in a one-dimensional n-heptane/oxygen/nitrogen heterogeneous system is simulated. Detonation evolution, frontal structure, and fuel droplet behavior are investigated. For a stoichiometric mixture with d0 = 5 μm, the critical initiation energy is around 1.6 × 10⁵ J/m² with no evidence of non-uniqueness. Initiation energy is crucial to activate the reaction O2 + H = OH + O, significantly contributing to OH production and sustaining the detonation. For a self-sustained detonation, initiation energy has a marginal influence on the variations of induction zone length, which is primarily determined by the initial droplet diameter. As droplet size increases, extended induction zone lengths with pronounced fluctuations are seen because of the increased breakup and evaporation time. Elevated Weber number is found both in the vicinity of the leading shock and reaction front, caused by large gas–droplet velocity differences and the low surface tension at the boiling point, respectively. Critical droplet in post-detonation region is found, which leads to the flash vaporization despite the droplet size is still large and yields localized high equivalence ratio and elevated heat release rate, accompanied by amplified shock.
... It is also noteworthy to distinguish our gas-phase droplet detonation scenario from liquid droplet detonation, an area of intensive contemporary research. Liquid droplet detonation involves additional complexities, including droplet evaporation (Wen et al., 2023), shock-liquid interactions (Prakash et al., 2024;Xu et al., 2024), droplet deformation, breakup, and sec-ondary atomization (Srinivasan et al., 2024;Xu et al., 2024;Dammati et al., 2025). Such phenomena necessitate computationally demanding multiphase simulations. ...
Rotating detonation engines (RDEs) are a critical technology for advancing combustion engines, particularly in applications requiring high efficiency and performance. Understanding the supersonic detonation structure and how various parameters influence these phenomena is essential for optimizing RDE design. In this study, we perform detailed simulations of detonations in an RDE and analyze how the flow patterns are affected by key parameters associated with the droplet arrangement within the engine. To further explore the system's sensitivity, we apply polynomial chaos expansion to investigate the propagation of uncertainties from input parameters to quantities of interest (QoIs). Additionally, we develop a framework to accurately characterize the joint distributions of QoIs with a limited number of simulations. Our findings indicate that the strategic arrangement of droplets is crucial for sustaining continuous detonation waves in the engine, and high-order chaos expansion is essential to accurately capture the dependence between QoIs and input uncertainties. These insights provide a strong foundation for further optimization of RDE designs.
... The first is Lagrangian particle tracking (LPT), wherein discrete liquid particles in a Lagrangian reference frame interact with the surrounding gaseous flow, which is simulated in the Eulerian reference frame. This approach is commonly used to study spray combustion and full-scale propulsion devices [36][37][38], but its predictive capabilities are often limited by its need for heat transfer, evaporation, and breakup models [39,40]. The second type of numerical approach encompasses interface-tracking techniques, such as level set or ghost-fluid methods, where liquid-gas interfaces are represented as discontinuities within the flow [41][42][43]. ...
Canonical jet in supersonic crossflow studies have been widely used to study fundamental physics relevant to a variety of applications. While most JISC works have considered gaseous injection, liquid injection is also of practical interest and introduces additional multiscale physics, such as atomization and evaporation, that complicate the flow dynamics. To facilitate further understanding of these complex phenomena, this work presents multiphase simulations of reacting and non-reacting JISC configurations with freestream Mach numbers of roughly 4.5. Adaptive mesh refinement is used with a volume of fluid scheme to capture liquid breakup and turbulent mixing at high resolution. The results compare the effects of the jet momentum ratio and freestream temperature on jet penetration, mixing, and combustion dynamics. For similar jet momentum ratios, the jet penetration and mixing characteristics are similar for the reacting and non-reacting cases. Mixing analyses reveal that vorticity and turbulent kinetic energy intensities peak in the jet shear layers, where vortex stretching is the dominant turbulence generation mechanism for all cases. Cases with lower freestream temperatures yield negligible heat release, while cases with elevated freestream temperatures exhibit chemical reactions primarily along the leading bow shock and within the boundary layer in the jet wake. The evaporative cooling quenches the chemical reactions in the primary atomization zone at the injection height, such that the flow rates of several product species plateau after x/d=20. Substantial concentrations of final product species are only observed along the bow shock-due to locally elevated temperature and pressure-and in the boundary layer far downstream-where lower flow velocities counteract the effects of prolonged ignition delays. This combination of factors leads to low combustion efficiency at the domain exit.
... To address this gap, high-fidelity simulations can be leveraged to probe the underlying microscale phenomena in greater detail. One common approach for simulating shock-and detonation-droplet interactions [23][24][25], as well as full-scale detonation engines [26][27][28], is to use Euler-Lagrangian formulations with empirical breakup and evaporation models. However, in order to examine breakup processes themselves, numerical approaches that capture or track phasic interfaces are needed. ...
Detonation-based propulsion devices, such as rotating detonation engines (RDEs), must be able to leverage the higher energy densities of liquid fuels in order for them to be utilized in practical contexts. This necessitates a comprehensive understanding of the physical processes and timescales that dictate the shock-induced breakup of liquid droplets. These processes are difficult to probe and quantify experimentally, often limiting measurements to macroscopic properties. Here, fundamental mechanisms in such interactions are elucidated through detailed numerical simulation of Mach 2 and 3 shock waves interacting with 100 m water droplets. Using a thermodynamically consistent two-phase formulation with adaptive mesh refinement, the simulations capture droplet surface instabilities and atomization into secondary droplets in great detail. The results show that droplet breakup occurs through a coupled multi-stage process, including droplet flattening, formation of surface instabilities and piercing, and the shedding of secondary droplets from the ligaments of the deformed primary droplet. When considering the dimensionless timescale of Ranger and Nicholls (), these processes occur at similar rates for the different shock strengths. The PDFs for the Sauter mean diameters of secondary droplets are bimodal log-normal distributions at . Modest differences in the degree and rate of liquid mass transfer into droplets less than 5 m in diameter are hypothesized to partially derive from differences in droplet surface piercing modes. These results are illustrative of the complex multi-scale processes driving droplet breakup and have implications for the ability of shocks to effectively process liquid fuels.
... Meanwhile, to overcome the challenges posed by liquid fuel detonation initiation and sustainment, there have also been studies on exploring the physics of multi-phase rotating detonations. [22][23][24][25][26][27][28][29][30] Advanced diagnostic techniques like chemiluminescence imaging, 31 planar laser-induced fluorescence (PLIF), 32 and high-speed schlieren 33 and optical imaging 34 have also been used for visualization of the supersonic rotating detonation flow field. ...
In this study, we conduct a numerical investigation of an annular rotating detonation combustor (RDC) with regional full-coverage film cooling designed for thermal protection. The effects of three different film cooling hole configurations—sequential, interlaced, and front-region circumferential coverage—are examined. We focus on the propagation behavior of the rotating detonation wave (RDW) through the film-cooled regions and evaluate the impact of film cooling jets on detonation wave stability and the overall flow field structure. The results indicate that the RDW can propagate stably across all configurations, though the interaction with film holes generates reflected waves, which propagate and couple with the oblique shock wave (OSW), increasing the OSW pressure and influencing the RDW's propagation velocity and pressure. Sequential and interlaced hole arrangements both demonstrate effective thermal protection: sequential configurations offer superior cooling upstream, while interlaced arrangements enhance cooling downstream. Furthermore, the numerical observations of cooling jet patterns are compared to experimental results from an RDC with full-coverage film cooling using the same interlaced, shaped film holes, and the results demonstrate good consistency. The numerical results demonstrate that film cooling effectiveness improves with increasing injection pressure, as this raises the outflow rate through the film holes and reduces reverse flow in regions affected by the RDW. Additionally, the introduction of a circumferential ring arrangement of film cooling holes at the detonation front forms distinct multi-layered cooling films, offering effective thermal protection to the outer wall of the RDC.
... Numerical simulation is utilized to reveal the two-phase RDW structure and the underlying dynamics. Prakash et al. 28 conducted the high-fidelity three-dimensional numerical simulations with the heterogeneous reactants of RP-2 and oxygen. It is found that the stiff injectors rapidly recovered following RDW passage and the penetration of the injected droplets is crucial in their ability to evaporate. ...
The Eulerian–Lagrangian method is used to conduct the numerical simulation of the non-premixed two-phase rotating detonation wave (RDW) fueled by n-decane/air. The stratified spray detonation transient phenomena, as well as the effects of total temperature (850, 900, 1000 K) and equivalence ratio (0.5, 0.7, 1.0) on the RDW dynamics and propagation characteristics are discussed in detail. The results indicate that the velocity difference caused by separate injection of fuel and air generates the low-temperature zone behind the oblique shock wave, which hinders the direct contact between the droplets and the detonation products. Droplets in the refilled zone are broken by the shear effect and evaporate in high total temperature air, forming the stratified distribution structure of droplets and vapor. In addition, the coupling–decoupling–recoupling dynamic mechanism is observed between the leading shock front and the heat release zone, which leads to the local decoupling of RDW during the propagation. Moreover, the spatial variation of high-pressure zones at the leading shock front leads to multiple leading shock fronts and transverse pressure waves. It is revealed that the increase in total temperature broadens the lower boundary of equivalence ratio to obtain two-phase RDW. RDW velocity and velocity deficit are insensitive to the total temperature in the considered parameter range. However, the increase in the total equivalence ratio not only improves the mean velocity significantly but also enlarges the velocity deficit. With the increasing total temperature and equivalence ratio, the stability of pressure becomes worse. Furthermore, the stability of velocity declines with the increasing equivalence ratio at the total temperature of 1000 K.
... For example, Salvadori et al. 28 investigated the mode-switching process of the kerosene-fueled RDW with hydrogen addition and showed that the transition from a dualwave mode to a stable single-wave mode occurred upon injecting kerosene spray into the lean hydrogen gas. High-fidelity simulations of a liquid rocket propellant-fueled RDE were conducted by Prakash et al. 29 in a practical three-dimensional setup using two injector geometries. The study highlighted the significance of droplet dynamics and injector behavior in determining detonation wave structures. ...
We present a numerical simulation of a two-phase rotating detonation fueled by liquid ethanol and pre-heated air in a two-dimensional rotating detonation combustor. The study aims to understand the structure and shock interactions of the two-phase rotating detonation wave (RDW) using a two-way coupled Eulerian–Lagrangian framework. Initially, the flow field is ignited with a gaseous rotating detonation, followed by the injection of liquid ethanol and pre-heated air at near-stoichiometric and fuel-lean conditions. Observations reveal incomplete evaporation of the newly injected liquid droplets, which affects the propagation of the initial gaseous RDW and leads to its decoupling. Subsequently, a two-phase RDW is re-initiated. Different types of shock waves are identified in the unsteady flow field, and their interactions and contribution to the re-initiation of the rotating detonation are discussed. An analysis of the established two-phase rotating detonation elucidates mechanisms underlying droplet evaporation and RDW propagation, highlighting the roles of incident shocks, transverse waves, and Mach stems. Additionally, we investigate the two-phase RDW under the fuel-lean condition, where the excessive presence of air mixing with unburned ethanol vapor can cause pre-ignition, leading to a chaotic rotating detonation field. The existence of reversed shock waves and ongoing collisions with the RDW can gradually reduce its intensity, induce fluctuations in the propagation velocity of the two-phase RDW, and ultimately lead to quenching.
... Parkash conducted high-precision simulations on liquid kerosene, primarily discussing fuel injection and droplet interactions. 36 Han conducted experiments and simulations on liquid kerosene, pointing out that the single-wave mode has an efficiency advantage over the dual-wave collision mode. 37 Zhong achieved the initiation of rotating detonation under kerosene cracking conditions and studied the effects of oxidizer annular gap width and combustion chamber width on the propagation characteristics of detonation waves. ...
In this study, the effects of three injection parameters on the propagation and instabilities of rotating detonation waves (RDWs) in a kerosene/air rotating detonation engine (RDE) with an S-shaped isolator are experimentally evaluated. The dimensionless parameter momentum flux ratio is considered a pivotal factor, and the influence of the injection geometry factors is analyzed. An empirical formula concerning the characteristic factor of oxidizer-fuel blending is derived to facilitate the RDE injection configuration design. The research reveals a significant correlation among the injection parameters, kerosene-air momentum flux ratios, and instability of RDWs. High dimensionless injection parameters do not necessarily result in a stable RDW phenomenon. Stable RDWs and unstable detonations are discussed under various injection parameters and momentum flux ratios. Additionally, a statistical analysis of the detonation instability is conducted, revealing two distinct cyclic categories: ignition-extinguishment-ignition and attenuation-recovery-attenuation. Two pathways of RDW instability propagation are identified to summarize the evolutionary processes of these variations and elucidate their mechanisms. Changes in the injection parameters cause the RDW to develop in two unstable orientations, resulting in the extinguishing and re-generating phenomenon of the RDW.
... Numerical simulation of detonation waves in both canonical [1,2,3] and complex configurations [4,5] is becoming increasingly important due to emerging interest in detonation-based propulsion devices [6,7]. Such simulations are also crucial in other related applications, including condensed-phase explosives [8,9] and hazard prediction [10]. ...
Numerical simulations of detonation-containing flows have emerged as crucial tools for designing next-generation power and propulsion devices. As these tools mature, it is important for the combustion community to properly understand and isolate grid resolution effects when simulating detonations. To this end, this work provides a comprehensive analysis of the numerical convergence of unsteady detonation simulations, with focus on isolating the impacts of chemical timescale modifications on convergence characteristics in the context of operator splitting. With the aid of an adaptive mesh refinement based flow solver, the convergence analysis is conducted using two kinetics configurations: (1) a simplified three-step model mechanism, in which chemical timescales in the detonation are modified by adjusting activation energies, and (2) a detailed hydrogen mechanism, in which chemical timescales are adjusted through ambient pressure modifications. The convergence of unsteady self-sustained detonations in one-dimensional channels is then analyzed with reference to steady-state theoretical baseline solutions using these mechanisms. The goal of the analysis is to provide a detailed comparison of the effects of grid resolution on both macroscopic (peak pressures and detonation wave speeds) and microscopic (detonation wave structure) quantities of interest, drawing connections between the deviations from steady-state baselines and minimum chemical timescales. This work uncovers resolution-dependent unsteady detonation regimes, and highlights the important role played by not only the chemical timescales, but also the ratio between chemical and induction timescales in the detonation wave structure on simulation convergence properties.
... The few experimental studies available in the literature [17][18][19] have shown that within a RDE, a detonation can self-propagate using liquid droplets only if a small amount of reactive gas such as hydrogen, oxygen-enriched oxidizer [20], or increased injection temperature [21] are used. Computational studies by Prakash et al. [22] of a non-premixed rocket-based RDE were the first to have shown that stable detonation propagation can be achieved using liquid RP-2 fuel and gaseous oxygen. We recently studied such two-phase Kerosene-hydrogen-air detonation computationally in both a full-scale engine [14] and reduced configurations [15] and the results show that kerosene vaporization and burning helps sustain the detonation propagation in lean hydrogen. ...
Three-dimensional simulations of a realistic two-phase rotating detonation engine are conducted to understand the effects of gaseous and liquid fuel on mechanisms of wave mode switching. A fully compressible solver coupled with an Eulerian-Lagrangian approach is used for this numerical study.
Hydrogen and kerosene are used as gaseous and liquid fuels, respectively, with air as an oxidizer. Starting from an established dual-wave mode solution with gaseous hydrogen as fuel, when the hydrogen mass flow rate is reduced to half, a weak/unstable wave propagation is obtained. On the other hand, while injecting kerosene spray in addition to the lean hydrogen gas, the original two-wave system transitions into a single stable self-sustained detonation wave.
Analyses of these results show that during the wave mode switching from dual-wave to single wave mode, the velocity of one wave increases first but then drops substantially leading to an uncoupled front, whereas, the other wave first slows down and then catches up transitioning into a stable detonation wave. Even though kerosene helps sustain a detonation wave in a lean hydrogen-air mixture which otherwise is unstable, the detonation wave that decays has insufficient available hydrogen and highly rich kerosene vapor ahead of it and this causes weakening the shock front. Upon stabilization, the resultant single propagating front remains as a hydrogen-driven and kerosene-supported detonation wave.
The rotating detonation turbine engine (RDTE) offers significant advantages, including higher thermal efficiency,
compactness, and energy savings. While hydrogen/air RDTEs have been extensively studied through experiments,
numerical simulations, and theoretical analysis, practical implementation requires the use of liquid fuels,
such as those in current gas turbine engines. The breakup and evaporation of fuel droplets can significantly
impact detonation dynamics, affecting RDTE performance. To investigate the effects of liquid fuel introduction
on RDTE systems, this study employs the unsteady RANS simulations to analyze the flow field characteristics and
working performance of an n-decane/air two-phase rotating detonation combustor (RDC) integrated with supersonic
turbine guide vanes (TGVs). The study focuses on the influence of detonation wave propagation direction
(aligned and misaligned) and cascade solidity (ranging from 1.08 to 3.02) on system integration
characteristics. The results show that dynamic shock envelopes form both upstream and downstream of the
TGVs, significantly affecting droplet distribution in the fuel refilling zone and weakening the rotating detonation
wave strength. The detonation inflow generates a distinct flow field structure within the cascade channel,
including channel shock waves, slip lines, and low temperature zones, which notably increase local entropy
production rates. The supersonic guide vanes exhibit substantial flow regulation capabilities. When the vane
solidity ranges from 1.51 to 3.02, the aligned mode results in smaller flow deviation angles at the vane outlet but
leads to higher total pressure loss. In contrast, the misaligned mode promotes stronger expansion and acceleration
of the working fluid, accompanied by lower total pressure loss. This study provides valuable insights into
the internal flow field structure of two-phase RDTE systems, investigates the combustor’s operational performance,
the flow regulation capabilities of guide vanes, and the mechanisms of total pressure loss, offering
meaningful guidance for the practical application of two-phase RDTE technology.
Recent research towards using liquid fuel in rotating detonation engines (RDE) has been assessed here using numerical simulations of a representative three-dimensional (3D) configuration. Eulerian-Lagrangian simulations of a 3D non-premixed RDE configuration are conducted and it is demonstrated that kerosene injection through the air plenum helps stabilize the RDE operation at the conditions where a pure gaseous H2 RDE is unable to sustain the propagation of a detonation. The H2-fueled RDE is first simulated at a global equivalence ratio of 0.5, which shows unstable burning with localized extinction and re-ignition followed by system failure, and then compared against another simulation where kerosene droplets are injected in the air plenum keeping the same H2 fueling condition. The results show that the existence of the detonation aids in the evaporation of the injected droplets behind it, allowing the vaporized mixture to properly mix before the next detonation cycle such that continuous (cyclic and stable) propagation can be achieved. It is further shown that whereas hydrogen mainly reacts near the bottom of the chamber, the injected droplets vaporize slow and react at larger heights. As a result, for the latter case the heat release is more distributed and provides an additional mechanism to stabilize the detonation cycle.
High-fidelity simulations of turbulent flames are computationally expensive when using detailed chemical kinetics. For practical fuels and flow configurations, chemical kinetics can account for the vast majority of the computational time due to the highly non-linear nature of multi-step chemistry mechanisms and the inherent stiffness of combustion chemistry. While reducing this cost has been a key focus area in combustion modeling, the recent growth in graphics processing units (GPUs) that offer very fast arithmetic processing, combined with the development of highly optimized libraries for artificial neural networks used in machine learning, provides a unique pathway for acceleration. The goal of this paper is to recast Arrhenius kinetics as a neural network using matrix-based formulations. Unlike ANNs that rely on data, this formulation does not require training and exactly represents the chemistry mechanism. More specifically, connections between the exact matrix equations for kinetics and traditional artificial neural network layers are used to enable the usage of GPU-optimized linear algebra libraries without the need for modeling. Regarding GPU performance, speedup and saturation behaviors are assessed for several chemical mechanisms of varying complexity. The performance analysis is based on trends for absolute compute times and throughput for the various arithmetic operations encountered during the source term computation. The goals are ultimately to provide insights into how the source term calculations scale with the reaction mechanism complexity, which types of reactions benefit the GPU formulations most, and how to exploit the matrix-based formulations to provide optimal speedup for large mechanisms by using sparsity properties. Overall, the GPU performance for the species source term evaluations reveals many informative trends with regards to the effect of cell number on device saturation and speedup. Most importantly, it is shown that the matrix-based method enables highly efficient GPU performance across the board, achieving near-peak performance in saturated regimes.
In the present work, a novel computational fluid dynamics (CFD) methodology was developed to simulate full-scale non-premixed rotating detonation engines (RDEs). A unique feature of the modeling approach was incorporation of adaptive mesh refinement (AMR) to achieve good trade-off between model accuracy and computational expense. Unsteady Reynolds-Averaged Navier-Stokes (RANS) simulations were performed for an Air Force Research Laboratory (AFRL) non-premixed RDE configuration with hydrogen as fuel and air as the oxidizer. The finite-rate chemistry model along with a 10-species detailed kinetic mechanism were employed to describe the H2-Air combustion chemistry. Three distinct operating conditions were simulated, corresponding to the same global equivalence ratio of unity but different fuel/air mass flow rates. For all conditions, the capability of the model to capture essential detonation wave dynamics was assessed. An exhaustive verification and validation study was performed against experimental data in terms of number of waves, wave frequency, wave height, reactant fill height, oblique shock angle, axial pressure distribution in the channel, and fuel/air plenum pressure. The CFD model was demonstrated to accurately predict the sensitivity of these wave characteristics to the operating conditions, both qualitatively and quantitatively. A comprehensive heat release analysis was also conducted to quantify detonative versus deflagrative burning for the three simulated cases. The present CFD model offers a potential capability to perform rapid design space exploration and/or performance optimization studies for realistic full-scale RDE configurations.
Rotating detonation rocket engines (RDRE) exhibit various unsteady phenomena that significantly affect their operation, performance, and stability. These unsteady phenomena are in the form of detonation wave interactions and modal transitions particularly in multi-wave systems. In this study, a descending modal transition is studied where four co-rotating detonation waves decrease to three. An updated methodology is used to extract and analyze 3D detonation wave dynamics and upstream data within the combustion chamber of the RDRE. A Mach less than one criterion behind each wave is applied to capture, visualize, and analyze unsteady, 3D detonation wave dynamics. The post-processing tool is capable of delineating between the detonation and non-detonation regions in the RDRE 3D annulus, and determining detonation wave failure. Comparisons are performed of each wave and their respective upstream regions of pressure, heat release, temperature, and mixture. Additionally, pressure disturbances are captured upstream of each detonation. The results herein, show high upstream pressure, heat release, temperature, and pressure disturbances, coupled with insufficient propellant, lead to detonation wave failure and non-recovery of the trailing wave during a descending modal transition.
Hydrogen is the most common molecule in the universe. It is an excellent fuel for thermal engines: piston, turbojet, rocket, and, going forward, in thermonuclear power plants. Hydrogen is currently used across a range of industrial applications including propulsion systems, e.g., cars and rockets. One obstacle to expanding hydrogen use, especially in the transportation sector, is its low density. This paper explores hydrogen as an addition to liquid fuel in the detonation chamber to generate thermal energy for potential use in transportation and generation of electrical energy. Experiments with liquid kerosene, hexane, and ethanol with the addition of gaseous hydrogen were conducted in a modern rotating detonation chamber. Detonation combustion delivers greater thermal efficiency and reduced NOx emission. Since detonation propagates about three orders of magnitude faster than deflagration, the injection, evaporation, and mixing with air must be almost instantaneous. Hydrogen addition helps initiate the detonation process and sustain continuous work of the chamber. The presented work proves that the addition of gaseous hydrogen to a liquid fuel–air mixture is well suited to the rotating detonation process, making combustion more effective and environmentally friendly.
The influence of complex chemical kinetics on the induction length in Chapman-Jouguet detonation was studied, with emphases on hydrogen chemistry and applications in pulse detonation engines (PDEs). Problems studied include the role of branching-termination reactions on the overall reaction rate, the reduction of the detailed hydrogen oxidation mechanism to simpler ones without compromising comprehensiveness of description, the coupled influence of chemical reactivity and the upstream speed of sound on ignition, and the use of hydrogen as a potential ignition enhancer. Results show that the presence of the pressure-sensitive and temperature-insensitive three-body termination reactions can significantly prolong the ignition delay, that an operation map for PDE operation can be constructed based on the crossover temperature so that operation regimes with excessively long ignition delays can be avoided, and that while the extent of chemistry reduction for the hydrogen/air PDE system depends on the degree of parametric comprehensiveness required, a two-step reduced mechanism appears to be adequate for near-stoichiometric descriptions. Furthermore, it is demonstrated that the benefit of the fast hydrogen chemistry is moderated by hydrogen's high speed of sound, which reduces the detonation Mach number and thereby the postshock temperature.
We introduce new Godunov-type semidiscrete central schemes for hyperbolic systems of conservation laws and Hamilton–Jacobi equations. The schemes are based on the use of more precise information about the local speeds of propagation and can be viewed as a generalization of the schemes from [A. A. Kurganov and G. Petrova, A third-order semidiscrete genuinely multidimensional central scheme for hyperbolic conservation laws and related problems, Numer. Math., to appear] and [A. Kurganov and E. Tadmor, J. Comput. Phys., 160 (2000), pp. 720–742]. The main advantages of the proposed central schemes are the high resolution, due to the smaller amount of the numerical dissipation, and the simplicity. There are no Riemann solvers and character-istic decomposition involved, and this makes them a universal tool for a wide variety of applications. At the same time, the developed schemes have an upwind nature, since they respect the directions of wave propagation by measuring the one-sided local speeds. This is why we call them central-upwind schemes. The constructed schemes are applied to various problems, such as the Euler equations of gas dynamics, the Hamilton–Jacobi equations with convex and nonconvex Hamiltonians, and the incom-pressible Euler and Navier–Stokes equations. The incompressibility condition in the latter equations allows us to treat them both in their conservative and transport form. We apply to these problems the central-upwind schemes, developed separately for each of them, and compute the corresponding numerical solutions.
Detonation-based engines such as Rotating Detonating Engines (RDEs) have been of significant interest for aerospace propulsion. However, most detonation-related studies have focused on gaseous reactants with the majority of investigations focusing on liquid water interactions with gaseous detonations and shocks. This study explores the dynamics of detonation waves driven by aerosolized liquid fuel sprays. An unlike-doublet impinging-jet injector is used to atomize RP-2 and water into aerosolized liquid droplet cloud of measured droplet size distribution where the detonation wave interacts with the cloud mixture. Evidence of RP-2 driving the detonation phenomenon is quantified using dynamic pressure measurements and four simultaneous optical diagnostic measurements: high-speed schlieren, CH* chemiluminescence, formaldehyde planar laser-induced fluorescence (PLIF), and particle Mie scatter. The results show formaldehyde and CH* generation along with a substantial increase in pressure and wave speed when the detonation wave interacts with the RP2 mixture cloud. On the contrary, the detonation pressure and wave speed decrease are observed when the detonation wave interacts with the water droplet cloud. The investigation provides supporting information on liquid fuel droplet burning and heat release driving the detonation wave.
A rotating detonation engine (RDE) is a realization of pressure-gain combustion, wherein a traveling detonation wave confined in a chamber provides shock-based compression along with chemical heat release. Due to the high wave speeds, such devices can process high mass flow rates in small volumes, leading to compact and unconventional designs. RDEs involve unsteady and multiscale physics, and their operational characteristics are determined by an equilibrium between large- and small-scale processes. While RDEs can provide a significant theoretical gain in efficiency, achieving this improvement requires an understanding of the multiscale coupling. Specifically, unavoidable nonidealities, such as unsteady mixing, secondary combustion, and multiple competing waves associated with practical designs, need to be understood and managed. The secondary combustion processes arise from fuel/air injection and unsteady and incomplete mixing, and can create spurious losses. In addition, a combination of multiple detonation and secondary waves compete and define the dynamical behavior of mixing, heat release distribution, and the overall mode of operation of the device. This review discusses the current understanding of such nonidealities and describes the tools and techniques used to gain insight into the extreme unsteady environment in such combustors.
Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 55 is January 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
Eulerian-Lagrangian simulations are conducted for two-dimensional Rotating Detonative Combustion fueled by bi-disperse n-heptane sprays without any fuel pre-vaporization. Parametric studies are performed to study the influences of droplet diameter and droplet distribution on the rotating detonation wave. The extinction process of the detonation wave is also been analyzed. It is found that small n-heptane droplets (e.g., 2 µm) are completely vaporized in the fuel refilling area. Increasing the droplet diameter causes the droplet to fail to evaporate completely within the fuel refilling area and exist after the detonation wave. A reflected shock can be observed after the detonation wave. When the droplet diameter is larger than 10 μm, the higher pressure after the detonation wave leads to the reactants cannot be sprayed into the combustor, eventually leading to extinction of the detonation wave. In bi-disperse n-heptane sprays, presence of droplets with small diameter stabilizes the detonation wave. The average equivalence ratio (up to 0.66 only) in the fuel refilling area is lower than total equivalence ratio (1.0 in this work), and the average equivalence ratio decreases with increased droplet diameter in the bi-disperse n-heptane sprays. The increase in droplet diameter decreases the detonated fuel fraction and detonation wave speed. The detonation speeds in bi-disperse n-heptane sprays are 3–9% lower than the respective gaseous cases. Moreover, the results also show that propulsion performance of rotating detonation combustor, such as thrust and specific impulse, decreases with the droplet diameter.
Eulerian-Lagrangian simulations are conducted for two-dimensional Rotating Detonative Combustion (RDC) fueled by partially prevaporized n-heptane dilute sprays by using coarse mesh resolution. The air is used as the oxidizer in the present simulations. The influences of droplet diameter and total equivalence ratio on detonation combustion and droplet dynamics are studied. It is found that small n-heptane droplets (e.g. 5 µm) are completely vaporized around the detonation wave, while intermediate n-heptane droplets (e.g. 20 µm) are consumed in or behind the detonation wave, with the escaped ones being continuously evaporated and deflagrated. The droplet distributions in the rotating detonation combustor are significantly affected by the droplet evaporation behaviors. Both premixed and non-premixed combustion modes are seen in two-phase RDC. The detonated fuel fraction is high when the droplet diameters are small or large, reaching its minimal value with diameter being 20 µm. The detonation propagation speed decreases with increased droplet diameter and is almost constant when the diameter is larger (>30 µm). The velocity deficits are 2-18% compared to the respective gaseous cases. Moreover, the propagation speed increases as the total equivalence ratio increases for the same droplet diameter. It is also found that the detonation propagation speed and detonated fuel fraction are considerably affected by the pre-vaporized gas equivalence ratio. The specific impulse first decreases for cases with initial diameter<5 μm, then increases with droplet diameter between 5 μm and 20 μm, and finally decreases with droplet diameter>20 μm.
Rotating detonation combustion fueled with partially prevaporized n-heptane sprays is studied with the Eulerian–Lagrangian method. A flattened two-dimensional domain with periodic boundaries is considered to mimic the annular rotating detonation combustor. This work focuses on the effects of prevaporized gas temperature and equivalence ratio on two-phase rotating detonation wave propagation and n-heptane droplet vaporization characteristics in the refill zone. The results show that gas temperature has a great impact on n-heptane sprays vaporization in the refill zone. The droplet evaporation rate increases with the gas temperature, especially when they are close to the deflagration surface. High evaporation rate can be observed for those droplets that are freshly injected into the chamber because they closely interact with the hot product gas from the previous cycle of the rotating detonation. A vapor layer between the droplet-laden area and deflagration surface exists and high concentrations of n-heptane can be found along the deflagration surface. A conceptual model for the droplet and vapor distribution in the refill zone is proposed. The results also show that the blast waves can encroach the refill zone and therefore influence the droplet thermodynamic properties inside the refill zone. The blast waves influence the droplet evaporation rate but have limited effects on droplet temperature, diameter, and spatial distributions. Also, the detonation propagation speed increases with increased prevaporized gas temperature and/or equivalence ratio. The detonation cell size decreases and becomes more uniform as the reactant temperature increases. Moreover, the size and irregularity of rotating detonation cells increase when the prevaporized gas equivalence ratio decreases.
Rotating detonation combustion (RDC) fuelled with partially pre-vaporized n-heptane sprays and gaseous hydrogen is studied with an Eulerian-Lagrangian method and a simplified two-dimensional model. Our focus is the effects of various pre-vaporized n-heptane equivalence ratios and droplet diameters on detonation wave propagation and droplet dynamics in two-phase RDC. The results show that when the droplets are small, they are fully vaporized by the detonation wave. However, when the droplet diameter is relatively large and/or the detonation wave number is bifurcated, liquid droplets are observable beyond the refill zone. Moreover, the detonation speed is considerably influenced by the droplet pre-vaporization and diameter. The velocity deficits from our simulated two-phase RDC vary between 5% and 30%. Over 70% n-heptane is detonated in the simulated cases, and it is found that there exists a critical droplet diameter (about 20 µm), around which the detonated fuel fraction is minimal. Four droplet trajectories in RDC are identified, which are differentiated by various evaporation times, residence times and interactions between droplets and the basic RDC flow structures. Inside the refill zone, three droplet categories are qualitatively identified. Droplets injected at the right end of the refill zone directly interact with the deflagration surface and meanwhile have relatively long residence time. However, droplets injected closer to the travelling detonation front have insufficient time to be heated and vaporized. Novel technologies and implementations may be needed to enhance the in-situ droplet evaporation during the refill period in practical liquid fuelled RDE’s. Our results also demonstrate that when pre-vaporization level is low and initial droplet diameter is large, the liquid fuel droplets may disperse towards the combustor exit. Furthermore, the droplet dispersion height decreases with liquid fuel pre-vaporization, while increases with droplet diameter.
Pressure gain combustion in the form of continuous detonations can provide a significant increase in the efficiency of a variety of propulsion and energy conversion devices. In this regard, rotating detonation engines (RDEs) that utilize an azimuthally-moving detonation wave in annular systems are increasingly seen as a viable approach to realizing pressure gain combustion. However, practical RDEs that employ non-premixed fuel and oxidizer injection need to minimize losses through a number of mechanisms, including turbulence-induced shock-front variations, incomplete fuel-air mixing, and premature deflagration. In this study, a canonical stratified detonation configuration is used to understand the impact of preburning on detonation efficiency. It was found that heat release ahead of the detonation wave leads to weaker shock fronts, delayed combustion of partially-oxidized fuel-air mixture, and non-compact heat release. Furthermore, large variations in wave speeds were observed, which is consistent with wave behavior in full-scale RDEs. Peak pressures in the compression region or near triple points were considerably lower than the theoretically-predicted values for ideal detonations. Analysis of the detonation structure indicates that this deflagration process is parasitic in nature, reducing the detonation efficiency but also leading to heat release far behind the wave that cannot directly strengthen the shock wave. This parasitic combustion leads to commensal combustion (heat release far downstream of the wave), indicating that it is the root cause of combustion efficiency losses.
The rotating detonation engine (RDE) is an important realization of pressure gain combustion for rocket applications. The RDE system is characterized by a highly unsteady flow field, with multiple reflected pressure waves following detonation and an entrainment of partially-burnt gases in the post-detonation region. While experimental efforts have provided macroscopic properties of RDE operation, limited accessibility for optical and flow-field diagnostic equipment constrain the understanding of mechanisms that lend to wave stability, controllability, and sustainability. To this end, high-fidelity numerical simulations of a methane-oxygen rotating detonation rocket engine (RDRE) with an impinging discrete injection scheme are performed to provide detailed insight into the detonation and mixing physics and anomalous behavior within the system. Two primary detonation waves reside at a standoff distance from the base of the channel, with peak detonation heat release at approximately 10 mm from the injection plane. The high plenum pressures and micro-nozzle injector geometry contribute to fairly stiff injectors that are minimally affected by the passing detonation wave. There is no large scale circulation observed in the reactant mixing region, and the fuel distribution is asymmetric with a rich mixture attached to the inner wall of the annulus. The detonation waves’ strengths spatially fluctuate, with large variations in local wave speed and flow compression. The flow field is characterized by parasitic combustion of the fresh reactant mixture as well as post-detonation deflagration of residual gases. By the exit plane of the RDRE, approximately 95.7% of the fuel has been consumed. In this work, a detailed statistical analysis of the interaction between mixing and detonation is presented. The results highlight the merit of high-fidelity numerical studies in investigating an RDRE system and the outcomes may be used to improve its performance.
High-fidelity simulations of an experimental rotating detonation engine with an axial air inlet were conducted. The system operated with hydrogen as fuel at globally stoichiometric conditions. Instantaneous data showed that the detonation front is highly corrugated, and is considerably weaker than an ideal Chapman–Jouguet wave. Regions of deflagration are present ahead of the wave, caused by mixing with product gases from the previous cycle, as well as the injector recovery process. It is found that as the post-detonation high pressure flow expands, the injectors recover unsteadily, leading to a transient mixing process ahead of the next cycle. The resulting flow structure not only promotes mixing between product and reactant gases, but also increases likelihood of autoignition. These results show that the detonation process is very sensitive to injector design and the transient behavior during the detonation cycle. Phase-averaged statistics and conditionally averaged data are used to understand the overall reaction structure. Comparisons with available experimental data on this configuration show remarkable good agreement of the predicted reacting flow structure.
JP-10/air two-phase detonation and rotating detonation engine (RDE) are numerically studied to find out their limits of physical values as a function of equivalence ratio, prevaporization, fuel concentration, droplet diameter, and initial pressure and temperature. To find such limits, the JP-10/air two-step chemical reaction mechanism is used and the Eulerian–Eulerian two-phase governing system is developed to simulate those limits. Especially the JP-10/air two-phase detonation velocity and cell size are investigated in detail and the generation of nonreacted region and quenching mechanism of JP-10/air two-phase RDE are simulated. The findings from those studies are that 1) the JP-10/air two-phase detonation and RDE codes are developed and validated to calculate detonation and RDE; 2) the JP-10/air detonation cell size is calculated by the developed code to show a good agreement with the experimental data; and 3) the JP-10/air RDE simulation shows a detonation quenching at the condition when the droplet diameter is larger than 4 μm and the prevaporization factor is smaller than 20%.
The rotating detonation engine is increasingly favored as a viable pressure gain combustion technology for both propulsion and power generation applications. Practical designs involve the discrete injection of fuel and air, which then partially mix to produce the reactive mixture that is processed by a continuously moving detonation wave within the detonation chamber. One of the fundamental challenges in the successful operation of rotating detonation engines is the design of a robust fuel-oxidizer injection system. To minimize pressure losses while ensuring efficient mixing that promotes stable detonation, the injection has to satisfy many different constraints. In this work, the impact of discrete injection on wave propagation is studied in an effort to understand the impact of fuel stratification on detonation stability. To this end, the structure of the detonation wave within a linearized rotating detonation engine with fully premixed hydrogen-air and hydrogen-oxygen injection at various equivalence ratios is analyzed. The direct numerical simulation of the linearized model detonation engine is compared with experimental results, and wave behavior is correlated to the wave structure and flow turbulence. The flow properties and chemical composition of the gases across the detonation wave are studied to examine the characteristics of the reaction zone.
Rotating detonation combustors (RDC) are at the forefront of pressure gain combustion (PGC) research, utilizing one or more azimuthally spinning detonation waves, an intrinsically unsteady process, to effect a stagnation pressure rise across the device. The prospective step-increase in efficiency, simplicity of design without the requirement for mechanical actuations and the ease of assembly make it an especially promising technology that could be integrated into existing propulsion and power generation architectures. This is coupled with the significant complexity of the detonation-based multi-axis flow field and the associated combustion modes and coupling mechanisms. The current paper is an overview of the research done worldwide to address some of the challenges and questions pertaining to the physics of RDC operation. When appropriate, notable parallels are drawn to the phenomena of low and high frequency instabilities in solid and liquid rockets that have been recognized as the most severe hindrance to their operation.
Real distillate fuels usually contain thousands of hydrocarbon components. Over a wide range of combustion conditions, large hydrocarbon molecules undergo thermal decomposition to form a small set of low molecular weight fragments. In the case of conventional petroleum-derived fuels, the composition variation of the decomposition products is washed out due to the principle of large component number in real, multicomponent fuels. From a joint consideration of elemental conservation, thermodynamics and chemical kinetics, it is shown that the composition of the thermal decomposition products is a weak function of the thermodynamic condition, the fuel-oxidizer ratio and the fuel composition within the range of temperatures of relevance to flames and high temperature ignition. Based on these findings, we explore a hybrid chemistry (HyChem) approach to modeling the high-temperature oxidation of real, distillate fuels. In this approach, the kinetics of thermal and oxidative pyrolysis of the fuel is modeled using lumped kinetic parameters derived from experiments, while the oxidation of the pyrolysis fragments is described by a detailed reaction model. Sample model results are provided to support the HyChem approach.
We propose and test an alternative approach to modeling high-temperature combustion chemistry of multicomponent real fuels. The hybrid chemistry (HyChem) approach decouples fuel pyrolysis from the oxidation of fuel pyrolysis products. The pyrolysis (or oxidative pyrolysis) process is modeled by seven lumped reaction steps in which the stoichiometric and reaction rate coefficients are derived from experiments. The oxidation process is described by detailed chemistry of foundational hydrocarbon fuels. We present results obtained for three conventional jet fuels and two rocket fuels as examples. Modeling results demonstrate that HyChem models are capable of predicting a wide range of combustion properties, including ignition delay times, laminar flame speeds, and non-premixed flame extinction strain rates of all five fuels. Sensitivity analysis shows that for conventional, petroleum-derived real fuels, the uncertainties in the experimental measurements of C2H4 and CH4 impact model predictions to an extent, but the largest influence of the model predictability stems from the uncertainties of the foundational fuel chemistry model used (USC Mech II). In addition, we introduce an approach in the realm of the HyChem approach to address the need to predict the negative-temperature coefficient (NTC) behaviors of jet fuels, in which the CH2O speciation history is proposed to be a viable NTC-activity marker for model development. Finally, the paper shows that the HyChem model can be reduced to about 30 species in size to enable turbulent combustion modeling of real fuels with a testable chemistry model.
A numerical model for liquid-fuelled detonation is developed. An Eulerian–Lagrangian formulation with two-way coupling between the gas and droplet phases is used to numerically simulate detonation of JP-10 fuel droplets in O 2 in a 1.5 m tube. The results of spatial and temporal resolution studies are presented. Then, the consequence of various choices of droplet drag and convective-enhancement sub-models is investigated. It is found that the detailed effects of such models are secondary to those of chemical energy release of the detonation. Detonation structure is shown to vary with initial droplet size and with the amount of initial fuel vapour present. For the range of small droplets considered, the self-propagating detonation velocity depends only minimally on such parameters. Small deficits in propagation velocity from the gaseous Chapman–Jouguet (C–J) value appear to be due to increasing inhomogeneity of the fuel–oxidant mixture as droplet size increases. Such results are in general agreement with the limited experimental data available. Also comparable to experimentally observed trends, results show that the existence of some initial fuel vapour increases the ease of detonability of liquid-fuelled mixtures. More generally, smaller droplet sizes and higher levels of heating and prevaporization are shown to enhance quick transition to a sustained self-propagating detonation.
A survey of propulsion based on detonation of chemical systems is provided in this paper. After a short historical review, basic schematics of engines utilizing detonation as the combustion mechanism are described. Possible improvement of propulsive efficiency due to detonative combustion which results in a significant pressure increase is presented, and a comparison of deflagrative and detonative combustion is discussed. Basic research on Pulsed Detonation Engines (PDE) and rotating detonations in cylindrical and disk-like chambers for different mixtures is presented. Basic principles of engines utilizing Standing Detonation Waves as well as Ram Accelerators are also provided. Detailed descriptions of PDE as well as Rotating Detonation Engines (RDE) are given. Different implementations of the PDE concept are presented and experimental and theoretical results to date are reviewed. Special attention is given to RDE, since rotating detonation can be applied to all kinds of propulsive engines including rocket, ramjet, turbine, and combined-cycle engines. A survey of detonative propulsion research carried out at different laboratories is presented, and possible future applications of such propulsion systems are discussed. A short note on detonative propulsion using non-chemical energy sources is also given.
This paper considers a class of approximate Riemann solver devised by Harten, Lax, and van Leer (denoted HLL) for the Euler equations of inviscid gas dynamics. In their 1983 paper, Harten, Lax, and van Leer showed how, with a priori knowledge of the signal velocities, a single-state approximate Riemann solver could be constructed so as to automatically satisfy the entropy condition and yield exact resolution of isolated shock waves. Harten, Lax, and van Leer further showed that a two-state approximation could be devised, such that both shock and contact waves would be resolved exactly. However, the full implementation of this two-state approximation was never given. We show that with an appropriate choice of acoustic and contact wave velocities, the two-state so-called HLLC construction of Toro, Spruce, and Speares will yield this exact resolution of isolated shock and contact waves. We further demonstrate that the resulting scheme is positively conservative. This property, which cannot be guaranteed by any linearized approximate Riemann solver, forces the numerical method to preserve initially positive pressures and densities. Numerical examples are given to demonstrate that the solutions generated are comparable to those produced with an exact Riemann solver, only with a stronger enforcement of the entropy condition across expansion waves.
The Bureau of Mines Helium Field Operations has developed a simple and accurate method for calculating the viscosity of gas mixtures. Only the composition of the mixture and the molecular weights and viscosities of the pure components in the mixture are required. The momentum fraction is calculated from the composition. The fluidity is calculated as a quadratic function of the momentum fractions. The efficiency factor for transfer of momentum in collisions between bodies of different masses is derived and used with one empirical constant. The viscosity is the reciprocal of the fluidity. Results of the method are compared with 752 reported viscosities for 40 dilute binary system at temperatures from [minus]78 to 276.9 C. Using this method the average absolute-deviation is 1.29%, the root-mean-square deviation is 1.99%, and the average deviation is [minus]0.84%.
The missing contact surface in the approximate Riemann solver of Harten, Lax, and van Leer is restored. This is achieved following the same principles as in the original solver. We also present new ways of obtaining wave-speed estimates. The resulting solver is as accurate and robust as the exact Riemann solver, but it is simpler and computationally more efficient than the latter, particulaly for non-ideal gases. The improved Riemann solver is implemented in the second-order WAF method and tested for one-dimensional problems with exact solutions and for a two-dimensional problem with experimental results.
A variety of liquid droplet evaporation models, including both classical equilibrium and non-equilibrium Langmuir–Knudsen formulations, are evaluated through comparisons with experiments with particular emphasis on computationally efficient procedures for gas–liquid flow simulations. The models considered are those used in droplet laden flow calculations such as direct numerical simulations for which large numbers of individual (isolated) droplet solutions are obtained. Diameter and temperature evolution predictions are made for single-component droplets of benzene, decane, heptane, hexane and water with relatively large initial sizes ∼1 mm vaporizing in convective air flows. All of the models perform nearly identically for low evaporation rates at gas temperatures significantly lower than the boiling temperature. For gas temperatures at and above the boiling point, large deviations are found between the various model predictions. The simulated results reveal that non-equilibrium effects become significant when the initial droplet diameter is <50 μm and that these effects are enhanced with increasing slip velocity. It is additionally observed that constant properties can be used throughout each simulation if both the gas and vapor values are calculated at either the wet-bulb or boiling temperature. The models based on the Langmuir–Knudsen law and a corrected (for evaporation effects) analytical heat transfer expression derived from the quasi-steady gas phase assumption are shown to agree most favorably with a wide variety of experimental results. Since the experimental droplet sizes are all much larger than the limit for non-equilibrium effects to be important, for these conditions the most crucial aspect of the current Langmuir–Knudsen models is the corrected analytical form for the heat transfer expression as compared to empirical relations used in the remaining models.
Libraries of thermodynamic data and transport properties are given for individual species in the form of least-squares coefficients. Values of C(sup 0)(sub p)(T), H(sup 0)(T), and S(sup 0)(T) are available for 1130 solid, liquid, and gaseous species. Viscosity and thermal conductivity data are given for 155 gases. The original C(sup 0)(sub p)(T) values were fit to a fourth-order polynomial with integration constants for H(sup 0)(T) and S(sup 0)(T). For each species the integration constant for H(sup 0)(T) includes the heat of formation. Transport properties have a different functional form. The temperature range for most of the data is 300 to 5000 K, although some of the newer thermodynamic data have a range of 200 to 6000 K. Because the species are mainly possible products of reaction, the data are useful for chemical equilibrium and kinetics computer codes. Much of the data has been distributed for several years with the NASA Lewis equilibrium program CET89. The thermodynamic properties of the reference elements were updated along with about 175 species that involve the elements carbon, hydrogen, oxygen, and nitrogen. These sets of data will be distributed with the NASA Lewis personal computer program for calculating chemical equilibria, CETPC.
Influence of unsteadiness on the analysis of pressure gain combustion devices
- Paxson
Liquid-fueled detonation modeling at the U.S. Naval Research Laboratory
- Schwer