Numerical Investigation of Combustion Characteristics of a...

Research ArticleNumerical Investigation of CombustionCharacteristics of a Wave Rotor Combustor Based on aReduced Reaction Mechanism of Ethylene

Jianzhong Li ,1 Li Yuan,2 Wei Li,1 and Kaichen Zhang1

1Key Laboratory of Aero-engine Thermal Environment and Structure, Ministry of Industry and Information Technology,Nanjing University of Aeronautics and Astronautics, 29 Yudao St., Nanjing 210016, China2School of National Defense Engineering, The Army Engineering University of PLA, 88 Biaoying Rd., Nanjing 210007, China

Correspondence should be addressed to Jianzhong Li; [email protected]

Received 14 May 2018; Accepted 29 August 2018; Published 1 November 2018

Academic Editor: Dan Zhao

Copyright © 2018 Jianzhong Li et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

To improve simulations of the flame and pressure wave propagation process and investigate the combustion characteristics of awave rotor combustor (WRC), direct relation graphs with error propagation (DRGEP), quasi-steady-state assumption (QSSA),and sensitivity analysis were used to establish a reduced reaction mechanism comprised of 23 species and 55 elementaryreactions, based on the LLNL N-Butane mechanism. The reduced reaction mechanism of ethylene was combined with an eddydissipation concept (EDC) model to simulate the flame propagation characteristics in a simplified WRC channel. The effects ofspoilers with different blockage ratios and hot-jets of different species on combustion characteristics of flame propagation andpressure rise in the WRC channel were investigated. When the heated inert air was used as hot-jet, the ignition delay time ofWRC would increase, which indicated that the activity of the burned gas from the hot-jet igniter would affect the ignition delaytime. The spoiler facilitates the coupling of flame and shock waves to reduce the coupling time and distance. With the blockageratio of the spoiler increasing, the coupling time and distance would be reduced.

1. Introduction

An aeroengine is comprised of three main components, suchas compressor, combustor, and turbine. The chemical energyin the fuel is transformed into thermal energy in the combus-tion chamber. The thermal energy is used to heat high-pressure air after boosting the pressure in the compressorto the allowable turbine inlet temperature. The heat capacityof the working medium can be improved by enhancingenthalpy, which directly affects the overall performance ofan aeroengine [1–3]. To further enhance the aeroengineand achieve more favorable performance, improvements tothe combustor can be made with respect to two aspects.One is increasing the turbine inlet temperature (i.e., the tra-ditional method for enhancing performance), the other isexploring novel technologies (i.e., replacing conventional iso-baric combustion modes with constant-volume combustionmodes of higher cycle efficiency) [4–6]. Compared to results

based on a traditional isobaric combustion mode, the thermalefficiency in the thermodynamic cycle of a gas turbine enginewith a wave rotor combustor (WRC) using constant-volumecombustion can be enhanced by 30%~50%, thereby realizinga huge leap forward in terms of power performance.

A WRC is mainly comprised of an inlet duct, wave rotorchannel, outlet duct, and ignitor and adopts a high-efficiencyconstant-volume combustion mode. As shown in Figure 1,the wave rotor channel forms a direct passage structurearound the axis to form a rotary barrel, which is in slidingcontact with the inlet and outlet ducts via a slide sealing tech-nique. Corresponding ports are set on both the inlet and out-let ducts and bearings fix the wave rotor onto the axis. WhentheWRC operates, rotation of the axis is driven by the motor,which further drives the wave rotor channel to rotate at highspeed. Moreover, both the inlet and outlet ducts remain sta-tionary. Accordingly, flow in both inlet and outlet ducts isperiodically exposed to the channel, which could produce

HindawiInternational Journal of Aerospace EngineeringVolume 2018, Article ID 8672760, 21 pageshttps://doi.org/10.1155/2018/8672760

http://orcid.org/0000-0001-6797-5740https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1155/2018/8672760

complex waves and facilitate energy exchange. While thechannel is filled with fuel/air mixture, the hot-jets enter thechannel of WRC and the combustible fuel/air mixture isignited to realize the high-efficiency constant-volume com-bustion. Afterwards, the outlet duct is opened to finish theexhaust of burned gas.

As shown in Figure 2, the entire WRC operating processcan be divided into six procedures. First, the inlet duct of thewave rotor channel opens and the outlet duct closes. At thisstage, the end of the channel is mostly filled with combustiblemixture, and the front region is partly filled with air. In thesecond step, both the inlet and outlet ducts close, the hot-jet enters the wave rotor channel, and the combustiblefuel/air mixture is ignited; i.e., the constant-volume combus-tion process begins. In the third step, after the combustion iscompleted, the channel is filled with high-temperature andhigh-pressure burned gas, and the outlet duct opens to dis-charge the burned gas from the wave rotor channel. This isaccompanied by the production of an expansion wave,which propagates upstream in the channel. In the fourthstep, the inlet duct opens to fill the chamber with combusti-ble fuel/air mixture so that the high-temperature burned gasproduced in the previous cycle could be isolated from the airflow. In the fifth step, both the inlet and outlet ducts openand the inlet duct is filled with the premixed combustiblefuel/air mixture. Finally, the outlet duct closes, the inlet ductremains open, and shock waves are produced at the outletduct. This process is also referred to the precompressionprocess of the WRC [7, 8].

Currently, a large emphasis is placed on research of WRCin which micromolecule gaseous hydrocarbon fuels such asmethane, ethylene, and propane are used. However, directlyusing macromolecule liquid kerosene under a special operat-ing environment in a WRC is difficult and a series of mea-sures should be taken, such as dissociation and gasification[9]. Ethylene is a type of micromolecule hydrocarbon fuelthat possesses much higher ignition, combustion velocity,and explosibility than other micromolecule hydrocarbonfuels making it suitable for use in WRCs [10]. Combustionof ethylene in the wave rotor channel is nonpremixed turbu-lent combustion, and previous numerical simulations oncombustion in WRC generally adopt a single-step reaction

mechanism [7]. The single-step reactionmechanism of ethyl-ene can be used to provide flow distribution and temperaturedistribution information in the WRC channel; however, itfails to effectively analyze detailed ignition processes andflame front propagation. Therefore, it is necessary to estab-lish a reduced mechanism for simulating the combustionprocess of ethylene in a WRC.

Detailed chemical reaction mechanisms of ethylene aregenerally quite complex. Wide variation of certain parame-ters including temperature, pressure, equivalence ratio, mix-ing time, and dwelling time should be taken into account.Therefore, detailed reaction mechanisms generally includehundreds or even thousands of elementary reactions. Thecombustion of hydrogen is the simplest hydrocarbon com-bustion. Nonetheless, the detailed chemical reaction mecha-nism includes hundreds of steps. The relevant mechanismsunder low temperatures are particularly complex. At present,a number of common detailed chemical reaction mecha-nisms are used, such as 111 species and 784 elementary reac-tions proposed by Wang et al. [11], another reactionmechanism including 127 species and 1207 elementary reac-tions proposed by Konnov [13], and the LLNL N-Butanemechanism. Unfortunately, these detailed mechanisms aretoo complex to be directly applied in practical situations.

In recent years, reduced mechanisms of ethylene havebeen investigated. Liu et al. applied reaction path analysisand the approximate trajectory optimization algorithm(ATOA) to simplify the oxidation mechanism of ethyleneand constructed a reduced mechanism including 32 speciesand 194 elementary reactions [14]. By analyzing reactionpaths, Yu et al. constructed a reduced mechanism of ethylenewith 56 species [15]. Based on the detailed reaction mecha-nisms of ethylene chemical reactions, Zhang et al. performedsystematic simulations on the production of black smoke andprecursors of the intermediates during the oxidation processof ethylene [16]. Previous investigations of reduced mecha-nisms of ethylene mainly focus on the oxidation mechanism,but do not effectively capture the development of waves andflames in WRCs. In addition, some reduced mechanisms donot satisfy the requirements of CFD software.

At present, methods commonly used for simplifyingdetailed chemical reaction models include sensitivity analy-sis, principal component analysis (PRA), computational sin-gular perturbation (CSP), direct relation diagram (DRG),reaction path analysis, and quasi-stationary approximationanalysis (QSSA) [17]. More specifically, during the simplifi-cation process, a skeletal mechanism is first constructed,then stiffness problems in the system are eliminated toacquire a reduced mechanism with fewer species and fewerelementary reactions.

In this study, a DRGwas first used to construct a model ofethylene combustion, then stiffness problems were addressedby means of QSSA and sensitivity analysis, and finally, areduced mechanism of ethylene including 23 species and 55elementary reactions was established. Using the detailedand reduced mechanisms, combustion processes of ethylenein the shock tube were calculated, and calculated ignitiondelay time data as well as overall variation of reactants andproducts were compared to validate the effectiveness of the

Channel (rotation)

Inlet duct

Outlet duct

Inflow (air + fuel)from compressor

Outflowto turbine

End-wall seal plate

Igniter

Channel (rotation)

Inlet duct

Outlet duct

Outflowto turbine

End-wall seal plate

Igniter

Figure 1: The typical WRC model.

2 International Journal of Aerospace Engineering

reduced mechanism. Furthermore, a simplified physicalmodel of the WRC was established. Combining the reducedmechanism and EDC combustion model, the combustionprocess in the wave rotor channel was simulated to determinethe effects of the activity of the burned gas from the hot-jetigniter and spoilers with various blockage ratios on the prop-agation characteristics of shock wave and flames in the waverotor channel.

2. Simplification and Validation of EthyleneReaction Mechanisms

Detailed chemical reaction mechanisms are generally com-plex. Wide variation in temperature, pressure, and equiva-lence ratio, as well as mixing and dwelling times, shouldbe considered when establishing new mechanisms. There-fore, hundreds or even thousands of elementary reactionsmust be included. Common mechanisms, species, numbersof elementary reactions, and application ranges are listedin Table 1.

Each detailed chemical reaction mechanism has its ownapplication conditions. The production and emission ofNOx were taken into account in the Konnov mechanismbut neglected in the mechanism proposed by H. Wang. Sim-ulation precision for combustion processes decreases whenthe established model is outside the application range. Insome cases, established mechanisms may not be applicableat all. During simulations of medium- and high-temperatureoperating processes of a WRC, production of NOx shouldbe neglected.

Two important parameters are generally used for evaluat-ing chemical reaction mechanisms, ignition delay time andflame propagation velocity. In combustion, ignition delay isa ubiquitous phenomenon and refers to the fuel/air mixturenot immediately igniting and burning when the mixture tem-perature is higher than the ignition temperature. In general,ignition delay time has several definitions, and among these,the most common are OH maximum moment and CH max-imum moment. In this study, CH maximum moment wasselected for measuring the ignition delay time. Flame isalways measured by the propagation speed of flames in lam-inar premixed combustion. Numerous studies have been per-formed on the ignition of ethylene. The ignition delay time ofethylene and propagation speed of laminar premixed flameshave been acquired. Related ignition delay times of ethylenein the shock tubes and propagation velocities of flames inpremixed flame furnaces are listed in Table 2.

Rota

tion

Fuel + air

Air

AirExhau

st gas

Compressor Turbine

InletExpansion wave

Hammer shock

Combustion

Combustion

Igniter

OutletIII

II

I

V

IV

Figure 2: Illustration of the operating process for WRC.

Table 1: Summary of common detailed chemical reactionmechanisms of ethylene.

Name ofmechanisms

Number ofspecies

Number ofelementaryreactions

References

GRI-Mech 3.0 53 325 [17]

UC San Diego 46 235 [18]

Konnov 127 1207 [13]

H. Wang 75 529 [11]

LLNL N-Butane 155 689 [12]

3International Journal of Aerospace Engineering

In this study, some common detailed chemical reactionmodels of ethylene were selected and used to create a closing-phase homogenousmodel and laminar premixedflamemodelin Chemkin-Pro combustion simulation software. The par-tially stirred reactor (PaSR) model was used for calculatingthe ignition delay time. Moreover, both the ignition processof ethylene in a shock tube and the laminar combustion pro-cess in a premixed furnace were simulated. Conditions usedin calculations were identical to experimental conditions. Acomparison of the results is presented in Figure 3.

From Figure 3(a), it can be observed that the UC SanDiego, GRI-3.0, H. Wang, and LLNL, N-Butane mechanismsall predict the ignition delay time of ethylene relatively closelyand are consistent with experimental data. Overall, the pre-dicted ignition delay time using the GRI-3.0 mechanism islower than values predicted using other detailed chemicalmechanisms; however, using LLNL N-Butane, the predictedvalue is slightly higher. Two sets of experimental data agreewell with each other in the high-temperature region butexhibit a certain amount of deviation in the low-temperatureregion. The reason for this is that two different methods wereused for measuring the ignition delay time. More specifically,Kalitan et al. used ignition traces on the side wall as the mea-suring point of ignition delay time, whereas Baker and Skin-ner conducted measurements using ignition traces on theend wall. The results of Kalitan et al. showed that ignitiontraces on the side wall output have a quicker ignition delaytime than those on the end wall, particularly in the low-temperature reaction zone which is highly sensitive to tem-perature. As shown in Figure 3(b), the additional threedetailed chemical reaction mechanisms, except GRI-3.0, canreasonably predict the laminar premixed flame propagationspeed of ethylene. According to the ignition delay time andflame speed in Figure 3, the UC San Diego mechanism, LLNLN-Butane mechanism, and H. Wang mechanism wereselected as the comprehensive detailed kinetic mechanismsand three reduced reaction mechanisms were gained. Thethree reduced reaction mechanisms were applied in thenumerical simulation for the WRC, but the reduced reactionmechanisms from UC San Diego mechanism and H. Wangmechanism would make a floating point error and causethe calculation to stop. The reduced reaction mechanismfrom the LLNL N-Butane mechanism could be applied inthe numerical simulation for WRC. Output of the LLNL N-Butane mechanism results in slightly smaller predictedvalues. Then, the optimizing and perfecting of the reducedreaction mechanism from the LLNL N-Butane mechanismwere focused on and the other reduced reaction mechanismswere given up. Considering construction conditions, the

LLNL N-Butane mechanism was selected as the detailedchemical reaction mechanism of ethylene in this study.

The LLNL N-Butane model included 155 species and 689elementary reactions in total. Although the LLNL N-Butanemechanism can adequately describe the combustion charac-teristics of ethylene, it cannot be directly applied in combus-tion simulations. Fluid simulation software always presentscertain limitations in coupled elementary reaction models.Further, large differences in the concentration and time scaleof various chemical species involved in the chemical reactionas well as stiffness problems in calculations lead to numerousissues in applying simple combustion simulations. Perform-ing simulations on unsteady and turbulent WRC combus-tions are particularly difficult. Therefore, before couplingthe elementary reaction model for the combustion simula-tion, the detailed chemical reaction model should be reducedto one that used fewer species and elementary reactions, toaccurately replace the detailed chemical reaction model.

The skeletal mechanism of ethylene was first constructedusing DRG. Stiffness problems in the skeletal mechanismwere eliminated by using QSSA and sensitivity analysisresults to establish the reduced chemical reaction model.Correlation coefficients were first determined among the var-ious chemical species and the importance of each componentwas assessed. Figure 4 displays a typical DRG that reflects therelationships among species.

If removing component B can lead to the production andconsumption of component A, as well as great error, the linediagram from A to B, the skeletal mechanism in the left partof Figure 4, should include components A, B, and D. Further,components E and F are coupled but irrelevant to componentsA, B, and D. Therefore, components E and F should both beeither removed or retained. Setting appropriate thresholds inthe skeletal mechanism using DRG is particularly importantfor establishing an accurate reduced mechanism.

The QSSA method judges whether species are in quasi-steady state based on the quasi-steady-state hypothesis. Themechanism is simplified by removing quasi-steady materialsin the chemical reactions. According to the quasi-steady-state hypothesis, the production rate of material in the reac-tion is approximately equal to the consumption rate, andthe following expression can be derived:

dykdt = 〠

l

i=1vi, k wi = 0, 1

where yk denotes the concentration of the k − th component,t denotes time, l denotes the total number of reactions, vi, k

Table 2: Experimental data of ignition delay time and flame propagation speed under certain conditions.

Equivalence ratio Percentage of diluent gas (%) Pressure (atm) Temperature (K) Definition/method References

1,1.5,3 98,97,96 1–5 1400–2100 CH∗ onset/sidewall [19]

1 96.75 1–3 1000–1800 CH∗ onset/endwall [20]

0.5–1.4 21 1 298 Counter-flow/nonlinear extrapolation [21]

0.5–1.4 21 1,2,5 298Outwardly propagating sphericalflame/nonlinear extrapolation

[22]


represents the coefficient of the k − th component of the i −th reaction, and wi is the net production rate of the i − threaction. The quasi-steady-state species can be added to theunsteady-state species via the change of matrix to removequasi-steady species and acquire the reduced mechanism inthe total reaction format.

Using sensitivity analysis, the degree of sensitivity of cal-culation results to the reaction parameters was calculated bychanging the parameters in the chemical reaction system.Through sensitivity analysis, important steps in the elemen-tary reactions can be assessed. Reactions with less sensitivitywere eliminated to simplify the mechanisms and addressstiffness problems in the chemical reaction system.

With respect to the detailed LLNL N-Butane mechanism,the laminar premixed flame model was calculated under apressure of 1 atm, unburned temperature of 298K, equiva-lence ratio of 0.6~1.2, and mass flow at the inlet equal to0.02 g/(cm2/sec). Flame speed was used as the target errorfor control, defined as

Error tolerance = Va −VsR × Va + A , 2

where R denotes the relative error and A is the absolute error.

The relationship between number of species and error isshown in Figure 5. Using the mechanism with a great num-ber of species results in less error, and greater errors are pro-duced as more species are removed. As the number of speciesin the mechanism decreases, great errors are produced whenfewer species are removed. With a small number of species inthe mechanism, species are tightly coupled and error doesnot always increase and is even significantly reduced afterremoving certain species.

To acquire an accurate skeletal mechanism with fewerspecies, a skeletal mechanism including 33 species and 180elementary reactions was first selected. Then, QSSA was car-ried out on the skeletal mechanism. Results demonstratedthat ten chemical compounds, C3H6, C3H5, HCOH, C2H6,CH2OH, C4H10, C2H, CH3O, CH2(s), and CH2CHCHO,were approximately in steady state and thus removed. Usingthis method, a skeletal model comprised of 23 species and116 elementary reactions was acquired. Finally, based on sen-sitivity analysis results, a reduced mechanism model of 23species and 55 elementary reactions was established.

3. Validation of Reduced Chemical ReactionMechanism for Ethylene Combustion

Simplification of the model aims to adequately use fewerspecies and elementary reactions to replace the detailedmechanisms. However, there seems to be a contradictoryrelationship. The reduced mechanism can be considered rea-sonable within a certain error range.

Simulation results for ignition delay time and flame prop-agation speed using reduced mechanism, skeletal mecha-nism, and detailed mechanism are shown in Figure 6.According to the ignition delay time curves based on differ-ent calculation conditions, the present reduced mechanismprovides accurate predictions within the largest range of

0.01

P = 3.0 atm

AR = 96%Ignition criteria CH⁎ max

�휙 = 1.01E − 3

1E − 4

Igni

tion

delay

tim

e (s)

1E − 5

1E − 60.55 0.60 0.65 0.70

(1000T)/K0.75

Kalitan et al. (2005)Baker et al. (1972)UC San Diego model

Gri-mesh 3.0 modelH.wang modelLLNL N-Butane model

0.80 0.85

(a)

100

90

80

70

60

50

40

30

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0

Lam

inar

flam

e spe

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m/s

)

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7Equivalence ratio

T = 298 KP = 1.0 atm

Hirasawa et al. (2002)Jomaas et al. (2005)UC San Diego modle

Gri-Mech 3.0 modleH.wang modleLLNL N-Butane modle

(b)

Figure 3: Comparison of calculated values versus experimental results, in which (a) ignition delay time and (b) flame propagation speed.

A A

B B

C CD D

E E

F F

Figure 4: Typical DRG among various species.


thermodynamic parameters. Moreover, the skeletal mecha-nism achieved fairly accurate predictions. Overall, ignitiondelay time decreases with increasing initial temperature.Ignition is difficult at low temperatures and ignition delaytime increases as the gradient of the initial temperature vari-ation curve increases. This is due to the fact that a lot of chainreactions are removed in the reduced mechanism and igni-tion is more difficult than for the detailed mechanism.Accordingly, the curve obtained using the reduced mecha-nism has a more obvious change in gradient than the detailedmechanism at low temperatures, thereby leading to largerdifferences in the ignition delay time. The variation of igni-tion delay time with pressure of the reduced mechanism isconsistent with results using the detailed mechanism. Usingthe reduced mechanism, variation of ignition delay time withequivalence ratio is almost consistent with the more detailedmechanism. The ignition delay time error may be as great as22%. The reduced mechanism also provides an accurate pre-diction of propagation speed of laminar premixed flames,and the predicted flame propagation prediction speed at thestoichiometric ratio are even more accurate than with thedetailed mechanism. The flame speed error may be as greatas 8%. To obtain more in-depth knowledge of flame structureand concentration changes of various species in the chemicalreaction zone, flame structure was also analyzed using thecombustion furnace model, as shown in Figure 7. The curvesrepresenting the concentration of various chemicals and by-products over time generated using the three mechanismsare similar, except that the concentration of HO2 in certainregions with low flame heights differs. This can be attributedto deleting certain important reactions related to the con-sumption of HO2. Overall, the reduced mechanism generatesaccurate predictions of chemical component concentrationsat different flame heights. The OH concentration error maybe as great as 7%. Using the reduced mechanism, the pre-dicted results for temperature on the flame front are lowerthan values predicted using the detailed mechanism byapproximately 100K. The temperature error may be as greatas 6%. Predicted results of temperature distribution using the

two mechanisms correspond well with each other for engi-neering applications. The errors of the results in Figures 6and 7 are similar to the results of reference [23], and the var-iation tendency matches the data of the detailed mechanism.

Based on a comprehensive comparison, it can be con-cluded that the reduced mechanism with 23 species can accu-rately describe the ignition delay time, flame propagationspeed, and flame structure and produces values relevant tocertain engineering applications, shown in Table 3.

To further identify differences between the reducedmechanism and detailed mechanism and to visually displaythe oxidation paths involved in the reaction, reaction pathsat an initial temperature of 1350K were analyzed, as shownin Figure 8. The thickness of the line indicates the importanceof elementary chemical reactions. It can be observed that oxi-dation occurs along the path C2H4-C2H3-C2H2-HCCO-HCO-CO in the reduced mechanism. In contrast, oxidationin the detailed mechanism occurs along many paths, includ-ing some initial chain reactions such as C2H5-C2H4. Based onthe initial chain reactions, the detailed mechanism results inmore accurate prediction of ignition delay time in the low-temperature region.

For sensitivity analysis, calculation conditions were iden-tical to those used in the reaction path analysis. The impor-tant parameters of each reaction can be assessed usingresults of the sensitivity analysis. A comparison of the sensi-tivities of several important chemical species is presented inFigure 9 and identifies important reactions used in thereduced mechanism.

4. Computational Approach and Modeling

4.1. Mathematical Descriptions and Numerical Models.Navier-Stokes equations [24–26] were used in the numericalsimulation and have been extensively applied to 2D non-steady flows for simulating dynamic processes of fluids. Theequations were solved by Fluent CFD software. Since flowand combustion in the WRC exhibit distinct unsteady char-acteristics, Pressure-Implicit with the Splitting of Operators(PISO) algorithm was selected for iteration of the flow field.Similar to the SIMPLE algorithm and SIMPLEC algorithm,a modified step was added to the PISO algorithm to satisfythe momentum equation and continuity equation simulta-neously. Accordingly, PISO can accelerate the convergenceof a single iterative step and is therefore more applicable totransient problems [27]. Near-wall regions were describedby standard wall functions, and the shear stress transport(SST) k − ω turbulence model was used. In general, k − εmodels are suitable for cases where the boundary layer main-tains a stable pressure. Although the SST k − ω double-equation turbulence model obeys assumptions of isotropicturbulence similar to the standard k − ε model, renormaliza-tion group (RNG) k − ε model, and realizable k − ε model,after appropriate modifications, the SST k − ω model can beused for calculating viscous internal layers in near-wallregions. Thus, the SST k − ω model is preferable for simulat-ing flow fields with varying pressure gradients.

The combustion process in a WRC involves turbulentflow and chemical reaction. The reduced mechanism of

0.700.650.600.550.500.450.400.350.30

Erro

r tol

eran

ce

0.250.200.150.100.05

−0.050.00

0 10 20 30 40 50 60 70 80Species

90 100110120130140

P = 1 atmT = 298 Kma = 0.02g/(cm2/s)

150160

Figure 5: Relationship between number of species and calculatederror.


ethylene included 23 species and 55 elementary reactions. Inturbulent combustion, the turbulent flow and chemical reac-tion are highly correlated and have mutual effects. Specifi-cally, turbulent flow affects the time-average chemicalreaction rate by increasing mixing while the heat releasedduring the chemical reaction affects turbulent flow. A reason-able and economic turbulent combustion model is the key toour numerical simulation. The eddy dissipation concept(EDC) model was selected, which is an extended applicationof the eddy dissipation (ED) model in terms of fine chemicalreaction mechanisms, including turbulent flow, and includesdetailed chemical reaction mechanisms. With EDC, chemicalreactions are assumed to occur in a small turbulent structureat the microscale, and chemical reactions at the microscaleoccur after a particular time scale. The reduced reaction

mechanism of ethylene was combined with an eddy dissipa-tion concept (EDC) model to simulate the flame propagationcharacteristics in a simplified WRC channel. The second-order upwind discrete scheme and PISO algorithm were alsoused and exhibit remarkable advantages for solving transientproblems. To improve calculation precision, the time stepwas set as 3× 10−7 s.

4.2. Computational Configuration and Boundary Conditions.Establishing a numerical simulation model is a comprehen-sive process in which numerous factors, including the partic-ular research objectives and simulation precision, should beconsidered. The WRC was investigated in this study, asshown in Figure 10, with the aim of determining the propa-gation characteristics of waves and flames in the WRC. The

0.01

P = 1 atm, T = 1800 kIgnition criteria OH max

1E − 3

1E − 4

Igni

tion

delay

tim

e (s)

1E − 5

1E − 60.5 0.6 0.7 0.8 0.9

Equivalence ratio1.0 1.1 1.2 1.3

SkeletalDetailed

Reduced

(a)

P = 1 atm, �휙 = 1Ignition criteria OH max

0.01

1E − 3

1E − 4

Igni

tion

delay

tim

e (s)

1E − 5

1E − 60.475 0.500 0.525 0.550 0.575

(1000/T0)/K−10.600 0.625 0.650 0.675

SkeletalDetailed

Reduced(b)

T = 1800 K, �휙 = 1Ignition criteria OH max

0.01

1E − 3

1E − 4

Igni

tion

delay

tim

e (s)

1E − 5

1E − 60 1 2 3 4

Pressure (atm)5 6 7 8 9 10

SkeletalDetailed

Reduced

(c)

0.5 0.6 0.7 0.8 0.9Equivalence ratio

1.0 1.1 1.2 1.3

80

70

60

50

40

30

20

10

0

Flam

e spe

ed/(

cm/s

ec)

SkeletalDetailed

Reduced

(d)

Figure 6: Simulation results for ignition delay time and flame propagation speed using reduced mechanism, skeletal mechanism, and detailedmechanism.


ignition and combustion processes should first be extractedand a simulation model of the single-channel WRC con-structed. A number of factors such as interactions among dif-ferent channels and filling of the chamber with combustiblefuel/air mixture were neglected in this model. Therefore,2D simulation models of the WRC were established to simu-late its complete operating process.

With regard to a WRC, the operating process is quitecomplex involving a number of processes including fillingthe chamber with combustible fuel/air mixture, ignition,flame formation and propagation, wave formation and prop-agation, and exhaust of burned gas. A simulation of the igni-tion process in the WRC was first conducted. In general, theignition process includes some unusual phenomena such asthe triggering and propagation of detonation waves.

Denotation waves always have a small characteristic scale,4~6 orders of magnitude lower than in experimental systemsand 10 orders of magnitude lower than practical results.Thus, certain requirements for the numerical simulation pro-cess can be defined: (1) small mesh size, (2) relatively smalltime step, (3) huge computation requirements due to thedetailed chemical reaction mechanism, and (4) unsteady sim-ulation. Even simple 2D simulations can last several days.Considering practical conditions, the channel length in theWRC was set to approximately 200mm, which is a relativelyshort distance, and therefore makes it difficult to experimen-tally determine the detonation combustion conditions fromdeflagration to detonation. Based on unknown detonationcombustion conditions in the WRC, it is difficult to directlycarry out numerical simulations of the WRC operating

0.05

0.04

0.03

Mol

e fra

ctio

n

0.02

0.01

0.00

−0.05 0.00 0.05 0.10

C2H4

P = 1 atm�휙 = 1.0

0.15Distance (cm)

0.20 0.25 0.30 0.35

SkeletalDetailed

Reduced

C2H4

P = 1 atmm�휙 = 1.0

(a)

0.0045

0.0040

0.0035

0.0030

0.0025

0.0020

0.0015

0.0010

0.0005

−0.0005

0.0000

Mol

e fra

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OH

P = 1 atm�휙 = 1.0

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SkeletalDetailed

Reduced

OH

P = 1 atm=�휙 = 1.0

(b)

0.00040

0.00035

0.00030

0.00025

0.00020

0.00015

0.00010

0.00005

−0.00005

0.00000

Mol

e fra

ctio

n

HO2 P = 1 atm�휙 = 1.0

−0.05 0.00 0.05 0.10 0.15Distance (cm)

0.20 0.25 0.30 0.35

SkeletalDetailed

Reduced

HOO2 PPP = 1 atm1 atmm�휙 = 1.0

(c)

2000

1800

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1400

1200

1000

800

600

400

200

Tem

pera

ture

(K)

T

P = 1 atm�휙 = 1.0

−0.05 0.00 0.05 0.10 0.15Distance (cm)

0.20 0.25 0.30 0.35

SkeletalDetailed

Reduced

TT

P = 1 atm1�휙�휙 = 1.01.1

(d)

Figure 7: Changes in concentration of various chemical reagents and by-products calculated based on reduced mechanism, skeletalmechanism, and detailed mechanism.


process and a more in-depth analysis of the detonation con-ditions and determining the rules of a single-channel WRCare first required.

To simplify the model and reduce simulation times, thefollowing assumptions were made:

(a) Since 3D numerical simulations are time-consuming,3D effects were neglected in this study and a 2Dnumerical simulation was adopted.

(b) A uniform premixed combustible mixture filled theWRC channel, and the relationship between pressureand density satisfied the state equations of an ideal gas.

(c) Heat exchange between the walls was ignored, andwalls were assumed to be adiabatic.

(d) During the actual operating process, the channelmoves whereas the hot-jet igniter remains stationary.To reduce the calculation burden, the channel was setas stationary, the hot-jet igniter was allowed to move,and movement of the channel was neglected.

The WRC model and related 2D simplified model areshown in Figure 11, in which the hot-jet is perpendicular tothe channel, moving upwards, and ignites the premixed com-bustible mixture. The established simulation model wasmainly focused on the combustion process in channel 2,whereas channels 1 and 3 were mainly used for simulatingthe environment in the WRC and not taken into account insubsequent analyses. Two sets of spoilers were set in thechannel. The entire computational domain was meshed witha size of 0.4mm, and the wall surface was set as a boundary

layer mesh. Laval nozzles were used to replace the heat flowignition, and the hot-jet was simulated by assigning reason-able boundary conditions to the nozzles. An enlarged draw-ing of the nozzle structure and dimensions are presented inFigure 11.

The 2D calculationmodel of the single-channelWRCwasmainly focusedon ignition andflamepropagationprocesses intheWRC.Using a premixed combustible fuel/air mixture, i.e.,ignoring the filling process for the combustible fuel/air mix-ture in the WRC, means the exhaust of high-temperatureburned gas can be neglected. Simplifying the 3D channelrotation as a 2D translation, as shown in Figure 11, the hot-jet ignition is parallel to the channel and simultaneouslymoves in a direction perpendicular to the channel at a veloc-ity of 85.032m/s (corresponding to the WRC of 4000 rpm).Channels 1 and 3 were mainly used for coordinating thehot-jet generator and producing continuous stable hot-jetflow. Channel 2 is where combustion mainly occurs andwas filled with premixed fuel/air mixture under ambient tem-perature conditions. In channel 2, the mass fractions of C2H4,O2, and N2 were 0.169, 0.579, and 0.252, respectively. Thehot-jet generator was set as the “pressure inlet” at a pressureof 1.5 atmospheres and temperature of 2000K, and thechemical species were included the combustion products.

The combustion products of the hot-jet were determinedusing an adiabatic combustion phase equilibriummodel. Theinitial temperature and pressure of ethylene were set as 298Kand 0.1MPa, respectively. At the stoichiometric ratio, thecombustion phase included combustion species in the equi-librium state. Concentrations of various combustion speciesare listed in Table 4.

Next, the effect of simplifying the chemical species of thehot-jet on the single-channel WRC was examined. Jets of

Table 3: Elementary reactions in reduced mechanism.

No. Reaction steps No. Reaction steps No. Reaction steps

1 oh + h2 = h + h2o 20 ch3 + o= ch2o + h 39 c2h3 + h= c2h2 + h2

2 o + oh= o2 + h 21 ch3 + oh= ch2o + h2 40 c2h3 + o2 = ch2o + hco

3 o + h2 = oh + h 22 ch3 + h = ch2 + h2 41 c2h3 + o2 = ch2hco + o

4 h + o2(+M) = ho2(+M) 23 ch2 + o2 = co + h2o 42 c2h3 + o2= c2h2 + ho2

5 h + o2(+n2) = ho2(+n2) 24 2ch2 = c2h2+ 2 h 43 c2h3 + oh= c2h2 + h2o

6 oh + ho2 = h2o + o2 25 ch2 + hcco = c2h3 + co 44 c2h3 + ch3 = c2h2 + ch4

7 h + ho2 = 2oh 26 ch2o + h = hco + h2 45 c2h2 + oh= ch2co + h

8 h + ho2 = h2 + o2 27 hco + o2 = ho2 + co 46 c2h2 + o= ch2 + co

9 h + ho2 = o+ h2o 28 hco +M=h+ co +M 47 c2h2 + o = hcco+h

10 o + ho2 = o2 + oh 29 hco + oh = h2o + co 48 c2h2 + o2 = hcco+oh

11 2ho2 = h2o2 + o2 30 hco + h = co + h2 49 c2h2 + h(+M) = c2h3(+M)

12 2oh(+M)= h2o2(+M) 31 co + oh = co2 + h 50 ch2co + h = ch3 + co

13 h2o2 + oh= h2o + ho2 32 c2h4 + h = c2h3 + h2 51 ch2co + oh = hcco+h2o

14 h2o2 + h = ho2 + h2 33 c2h4 + oh= c2h3 + h2o 52 hcco+o = h+ 2co

15 h2o2 + h= oh + h2o 34 c2h4 + o= ch3 + hco 53 hcco+o2 = hco + co + o

16 h2o2 + o = oh + ho2 35 c2h4 + o = ch2hco + h 54 hcco+o2 = co2 + hco

17 ch4 + h = ch3 + h2 36 c2h4 + ch3 = c2h3 + ch4 55 2hcco = c2h2+ 2co

18 ch4 + oh= ch3 + h2o 37 c2h4(+M) = c2h2 + h2(+M)

19 ch3 + ho2 = ch4 + o2 38 c2h4(+M) = c2h3 + h(+M)


different chemical species were examined while simulationconditions remained unchanged. Operating conditions usedin the simulations are listed in Table. 5.

Spoilers were also set in theWRC channel for strengthen-ing turbulivity and increasing mixing in the channel, to pro-mote the folding and deformation of flames, intensify heatrelease on the frontal flame surfaces, and accelerate propaga-tion of flames [28]. However, adding spoilers could increaselosses during flow, and the effects of characteristic parame-ters, such as the blockage ratio (BR) of the spoiler and com-bustion properties in the WRC and their variation, shouldbe clarified. Simulations were conducted for different block-age ratios of spoilers while other conditions remainedunchanged. Operating conditions used in the simulationare listed in Table 6.

4.3. Code Validation. Two methods are generally used forvalidating simulations. The first directly compares experi-mental data with simulation results under the same condi-tions, and the other uses a similar model to verify thereliability of the algorithm when experimental conditionscannot satisfy simulation requirements. It is difficult todirectly use experiments for validating numerical simulationresults of a WRC; therefore, reliability of the proposedmethod was indirectly validated. In theory, a WRC exhibitsdenotation combustion or near-denotation combustion. Arelevant simulation method should be able to satisfy the sim-ulation of denotation combustion. In addition, WRC chan-nels always have short distances, and thus, realization of thetransition from deflagration to denotation combustion is

crucial. A 2D single-channel spark plug ignition model forsimulating the denotation combustion process is most oftenused to validate the algorithm model, as shown inFigure 12. The red line denotes the outlet of the denotationtube, which was set as the “pressure outlet” and includes sixgroups of spoilers for shortening the DDT process. Theremaining parts represent the wall surface. Before the simula-tion, the Patch assignment method was used to set the massfractions of C2H4, O2, and N2 as 0.169, 0.579, and 0.252,respectively. An excessive amount of oxidant was requireddue to the fact that denotation waves are hard to generatewhen the reaction between air and ethylene is directly used.The red star in Figure 12 represents the position where thespark plug was ignited instantaneously at high temperature.

Simulation results for pressure distributions in the cen-tral axis of the detonation tube at three different momentsafter stable denotation waves had already formed are dis-played in Figure 13. The denotation wave velocities, denotedVdetonation, were calculated as 2291.6m/s and 2291.3m/s. Fur-thermore, using Cantera, an open-source chemical reactionkinetics software, it was found that VCJ = 2326m/s [29].The detonation wave velocity error may be as great as 1.5%,which indicates that the error of ignition delay time duringvalidation of reduced chemical reaction mechanism for eth-ylene combustion is acceptable. The simulation value ofdetonation wave velocity is quite close to the theoreticalvalue, which suggests that the numerical simulation canaccurately capture the denotation combustion process.Moreover, the reduced reaction mechanism of ethylenecan sufficiently describe the characteristics of denotation

ch4

ch3

0.0621

ch2o

0.106

hco

0.113

ch2

0.0196

c2h3

0.0153

co

0.0474

c2h4

0.0927 1

0.0927

c2h2

0.094

ch2hco

0.0603 0.927

0.0891

0.459

co2

0.0418

0.0984

0.127

hcco

0.621

ch2co

0.0218

0.248

0.188

0.0963

(a)

ch3

ch3o

0.0191

ch2o

0.0169

0.0103

ch2(s)

0.0109

hcoh

0.0358

ac3h5

0.0192

hco

0.106

co

0.0584

co2

0.0351

c2h4

0.104

0.0205

0.041 0.0164

0.0201

c2h3

1

c2h2

0.0777

ch2hco

0.0744

ch2chcho

0.0944

ch2co

ch2ch2oh

0.028

0.046

hcco

0.165

0.112

0.0345

0.0279

0.385

0.0194

0.885 0.0864

0.0379

0.0476

0.145

0.156

0.0564

0.0502

0.0522

0.0102

0.293

c2h

0.0692

0.0174

0.0338

0.162

c3h6

(b)

Figure 8: Analysis of reaction paths based on reaction mechanisms, (a) reduced mechanism and (b) detailed mechanism.


waves. The combustion properties in the WRC, such asinteraction between shock wave and flame, were similar tothe proposed simulation method, and the reaction mecha-nism can be adequately employed to simulate the combus-tion process in a WRC.

5. Results and Discussion

5.1. Ignition and Flame Propagation Process in WRC. Thesimplified propagation process for the wave and flames inthe channel of WRC are shown in Figure 14, in which theflame distribution is characterized by the cloud chart of OHmass distribution. It can be observed that when t = 3 12ms,the hot-jet ignition comes into contact with the wave rotorchannel and the fluid region is interconnected with the fluidregion in the channel. Therefore, at this moment, fluid canfreely pass through the channel and hot-jet enters the chan-nel. At the channel entrance, OH radicals quickly appear,generated by combustion of the combustible mixture in thewave rotor channel, which is ignited by and partially carriedby the hot-jet. Therefore, it can be confirmed that the pre-mixed combustible fuel/air mixture in the channel is ignitedby the hot-jet. The momentum carried by the hot-jet forms

a jet shock wave while entering the wave rotor channel, andthe region influenced by the jet shock waves is larger thanthe region affected by the jet energy. In other words, theshock wave is located in front of the flame surface and theleading edge of the OH mass fraction is referred to as theflame front surface. At t = 3 198ms, the flame profile showsthat the flame front propagates in the circumferential direc-tion. However, the axial propagation distance exceeds theradial propagation distance. Analyzing the motion state ofthe jet ignition, axial momentum of the hot-jet is greater thanin the radial direction. As a result, the axial propagation dis-tance of the flame is greater than in the radial direction, andthe jet shock wave exhibits local stagnation upon hitting theupper wall surface of the channel, thereby increasing pressureat this position. At the same moment, the position of thepressure wave is in front of the flame front surface. At t =3 234ms, flames are distributed in a rectangular patternand the axial propagation distance far exceeds the radialpropagation distance. Along the radial direction, flames arereflected as the compression wave approaches the wall,thereby affecting the flame front and hindering the propaga-tion of the flames. Furthermore, as the compression waveencounters obstacles, the jets are deflected and the propaga-tion of flames in the axial direction stops, thus creating astraight flame front. At this moment, the compression wavepasses over the obstacle and creates local stagnation behindthe obstacle, which increases pressure at these positions andfurther expands the distance between the compression waveand flame front. At t = 3 264ms, the flame crosses the firstobstacle and influence of the momentum of the hot-jet isweakened. Since the flame area is in the initial accelerationphase, propagation of the flame front is hindered and theflames expand after crossing the obstacle. Due to the exis-tence of obstacles, the flame front clearly exhibits a laceratedpattern which decreases the flow area and accelerates fluid inthe throat. The existence of obstacles causes the fluid to accel-erate and increases turbulence, which is conductive toadvancing the flame front, increasing the heat release area,

26

29

48

34

6

Reac

tion

num

ber

28

46

27

30

1

−0.03 −0.02 −0.01 0.00 0.01 0.02 0.03Flame speed sensitivity coefficients

0.04 0.05 0.06 0.07 0.08

(a)

Reac

tion

num

ber

10 # 10. h+ho2=2oh# 17.# 92.# 91.# 9.# 113.# 121.# 77.# 90.# 95.# 1.

17

92

91

9

113

121

77

90

95

1

−0.05 0.00 0.05 0.10 0.15Flame speed sensitivity coefficients

0.20 0.25 0.30 0.35

2h+h2o=h2+h2ohco+oh=h2o+cohco+M=h+co+Moh+ho2=h2o+o2c2h4+o=ch2o+hcoc2h3+o2=ch2o+hcoch2(s)+c2h6=ch3+c2h5hco+o2=ho2+cohco+o=co2+hoh+h2=h+h2o

(b)

Figure 9: Results of sensitivity analysis to identify important chemical species, (a) reduced mechanism and (b) detailed mechanism.

Electric motor

ExportImport

Hot jet

Jet holeChannel

Figure 10: The physical model of full-scale WRC.


and accelerating the propagation of flames [1]. As the radialflame approaches the wall, pressure between the flames andwall surface is further increased. At t = 3 234ms, the pressurewave crosses the obstacle and collides with the upper and

lower wall surfaces leading to the formation of two high-pressure regions (upper and lower). At t = 3 33ms, theflames are fully developed and both the flame front areaand the heat release rate rapidly increase, which acceleratesflame propagation and creates a positive feedback mecha-nism. At that time, the positions of the pressure wave andflame front drop, and pressure increases from 0.1MPa at t= 3 198ms to approximately 0.2MPa. At t = 3 36ms, thepressure wave first encounters the obstacle while the flameis still behind it. After acceleration of the flow due to theobstacle, the distance between the pressure wave and flamefront further increases. At that time, a local high-pressureregion appears both in front of and behind the obstacle.The rear pressure region is generated by stagnation effects,

69 mm 62 mm 69 mm

10 m

m

5 mm 11.5 mm

27 mm

13.6 mm

Channel 3 Channel 2 Channel 1 No-slip wall

Igniter movementspeed, v = 53.145 m/s

P,T,F

Pressureinlet

Obstacleheight, h = 3 mm

Channelheight, H = 27.5 mm

Obstaclewidth, w = 2 mm

Figure 11: The simplified model of WRC.

Table 4: Species and related mass fractions during adiabaticequilibrium phase of ethylene.

Component Mass fraction Component Mass fraction

H2 0.00334 O 0.0701

H 0.00343 OH 0.0629

CO2 0.197 H2O 0.069

CO 0.197 O2 0.127

Table 5: Parameters used to describe operating condition insimulation.

Operating condition Species of hot-jet

1 Combustion products

2 N23 Ar

Table 6: Operating conditions used in simulations.

Operating conditions Blockage ratio of the spoilers

1 BR = 0 (no obstacle)2 BR = 23 35%3 BR = 31 13%4 BR = 38 91%


whereas the front region is generated by collision and reflec-tion effects. At t = 3 39ms, the flame is rapidly accelerated bythe obstacle, which decreases the distance between the flamefront and the pressure wave. At that moment, the pressurereaches approximately 0.4MPa. At t = 3 414ms, the localhigh-temperature region, generally referred to as the high-temperature hot spot, can be regarded as an overdrive deno-tation combustion. At t = 3 42ms, an arch shock wave withpressure of approximately 0.56MPa appears at the flamefront; moreover, the shock wave and flame surface becomepartially coupled forming the denotation wave, but not fullydeveloped. At t = 3 426ms, the partly coupled detonationwave rapidly spreads and fills the entire channel and twolocal high-pressure regions are formed at the intersectionbetween the detonation wave and the wall surface. The tworegions are generated by collisions between the detonationwave and wall surfaces during the development process. Atthe same time, the arch rate of the detonation wave graduallydecreases and continues to decrease until t = 3 422ms. Att = 3 428ms, the arch detonation wave gradually transformsinto a plane wave, during which time the detonation wavegradually becomes fully developed and complete wave-flame coupling is realized. At t = 3 456ms, the detonationwave collides with the front wall and pressure is approxi-mately 0.55MPa.

In conclusion, the ignition and flame propagation pro-cess of the entire model can be described as detonationcombustion. However, this is unlike conditions in a tradi-tional detonation tube. One end of the traditional detonationtube is closed while the other end is open. In contrast, after

ignition, both two ends of the WRC channel are closed sug-gesting that the channel can be regarded as a constant-volume combustor. A detonation engine makes use of thereaction thrust of thedetonationwave,whereas aWRCmainlyuses detonation combustion to form high-temperature andhigh-pressure burned gas, which also validates the WRC asan improved pressurized combustion device.

5.2. Effects of Hot-Jet with Different Species on Ignition andCombustion in WRC. The temperature cloud chart display-ing the flame propagation process is presented in Figure 15,from which the entire flame propagation process can beclearly observed from t = 0 132ms to t = 0 552ms, whenthe hot-jet enters the wave rotor channel 2 to when flamepropagation is accelerated in the channel. From the simula-tion results, it can also be observed that the hot-jet of differ-ent chemical species greatly affects the combustion process inthe WRC. Using the hot-jet of combustion products, detona-tion combustion is achieved in the WRC channel at t =0 552ms. However, detonation combustion does not occurwhen the hot-jets of N2 and Ar2 are used. Further, the flamepropagation distance in combustion using the heated N2 jetfar exceeds that in combustion using the heated Ar2 jet.The hot-jet of different species has significant effects on theignition process in the WRC.

The ignition process of a combustible fuel/air mixturecan be defined by its combustion products. Since the hot-jetof the combustion products includes OH radicals, HO2 radi-cals were used in this study to model radicals produced incombustion. Ignition processes in the WRC for hot-jets withdifferent species are illustrated in Figure 16. A hot-jet of com-bustion products can directly ignite the premixed combusti-ble fuel/air mixture in the channel, whereas hot-jets of N2and Ar2 result in ignition delays. According to the simula-tion, ignition delay times for the heated N2 and Ar2 jets wereapproximately 0.138ms and 0.246ms, respectively. Due todifferences in the ignition delay times, when the hot-jet con-sists of the combustion products, initial flames propagate inan arc pattern; however, hot-jets of N2 and Ar2 result inignition of the combustible fuel/air first around the vortexand flames, which then spread to the periphery. Since a lotof radicals directly participate in the combustion reaction,including H, OH, and O of the hot-jet of the combustionproducts, the reaction chain accelerates the initial reaction.Conversely, the hot-jets of N2 and Ar2 contain inertgases that are not involved in the reaction. Therefore,activation energy must be accumulated over a certainamount of time during the initial stage of the chemicalreaction chain. The smaller specific heat associated with

200 mm

27.5

mm

Figure 12: Algorithm validation model.

3.6

3.0 t = 84 �휇s t = 60 �휇s

53 mm55 mm

2291.6 m/s 2291.3 m/s

C-J velocity 2326 m/s (26)

t = 36 �휇s

C2H4+O2, �휙 = 1

2.4

1.8

Pres

sure

(Mpa

)

1.2

0.6

−0.6−100 −80 −60 −40 −20 0

Distance (mm)20 40 60 80 100

0.0

Figure 13: Pressure characteristic curves of denotation waves.


t = 3.126 ms

OH mass fraction

Pressure/atm

0.02

−0.06 −0.04 −0.02 −0.00 0.01 0.03 0.05 0.07 0.08 0.10 0.12 0.14

0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23

(a)

t = 3.198 ms

OH mass fraction

Pressure/atm−0.06 −0.03 −0.01 0.01 0.03 0.05 0.08 0.10 0.12 0.14 0.16 0.18

0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23

(b)

OH mass fraction

Pressure/atm

t = 3.234 ms

−0.04 −0.01 0.02 0.05 0.08 0.11 0.15 0.18 0.21 0.24 0.27 0.30

0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23

(c)

OH mass fraction

Pressure/atm

t = 3.264 ms

−0.04 −0.01 0.02 0.05 0.08 0.11 0.13 0.16 0.19 0.22 0.25 0.28

0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23

(d)

OH mass fraction

Pressure/atm

t = 3.330 ms

−0.03 0.00 0.03 0.06 0.10 0.13 0.16 0.19 0.23 0.26 0.29 0.32

0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23

(e)

OH mass fraction

Pressure/atm

t = 3.360 ms

0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23

0.02 0.10 0.17 0.25 0.33 0.40 0.43 0.55 0.63 0.71 0.78 0.86

(f)

OH mass fraction

Pressure/atm

t = 3.390 ms

0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23

0.01 0.08 0.15 0.21 0.28 0.34 0.41 0.48 0.54 0.61 0.67 0.74

(g)

OH mass fraction

Pressure/atm

t = 3.414 ms

0.13 0.31 0.49 0.67 0.85 1.08 1.21 1.39 1.57 1.75 1.93 2.11

0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23

(h)

OH mass fraction

Pressure/atm

t = 3.420 ms

0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23

0.43 0.91 1.39 1.86 2.34 2.82 3.29 3.77 4.25 4.72 5.20 5.67

(i)

OH mass fraction

Pressure/atm

t = 3.426 ms

0.43 1.00 1.57 2.14 2.70 3.27 3.84 4.41 4.97 5.54 6.11 6.67

0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23

(j)

Figure 14: Continued.


Ar2 compared to N2 results in a slower energy release andlonger ignition delay times.

Figure 17 shows flame propagation speed under theaction of hot-jets with different chemical species. At t = 0 13

ms, the hot-jet of combustion products enters the wave rotorchannel and immediately ignites the premixed combustiblefuel/air mixture. Afterwards, the flame propagation speedincreases steadily. At t = 0 375ms, the flame propagation

OH mass fraction

Pressure/atm

t = 3.432 ms

0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23

0.71 1.27 1.83 2.39 2.95 3.52 4.08 4.64 5.20 5.76 6.32 6.89

(k)

OH mass fraction

Pressure/atm

t = 3.438 ms

0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23

0.71 1.27 1.83 2.39 2.95 3.52 4.08 4.64 5.20 5.76 6.32 6.89

(l)

OH mass fraction

Pressure/atm

t = 3.456 ms

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22

0.47 0.97 1.48 1.98 2.49 3.00 3.50 4.01 4.51 5.02 5.52

(m)

Figure 14: Detailed ignition and flame propagation processes in WRC.

t = 0.132 ms

t = 0.168 ms

t = 0.204 ms

t = 0.228 ms

t = 0.288 ms

t = 0.312 ms

t = 0.360 ms

t = 0.372 ms

t = 0.384 ms

t = 0.396 ms

t = 0.426 ms

t = 0.510 ms

t = 0.552 ms

t = 0.132 ms

t = 0.168 ms

t = 0.204 ms

t = 0.228 ms

t = 0.288 ms

t = 0.312 ms

t = 0.360 ms

t = 0.372 ms

t = 0.384 ms

t = 0.396 ms

t = 0.426 ms

t = 0.510 ms

t = 0.552 ms

t = 0.132 ms

t = 0.168 ms

t = 0.204 ms

t = 0.228 ms

t = 0.288 ms

t = 0.312 ms

t = 0.360 ms

t = 0.372 ms

t = 0.384 ms

t = 0.396 ms

t = 0.426 ms

t = 0.510 ms

t = 0.552 ms

Temperature/K

(a) (b) (c)

t = 0.132 ms

t = 0.168 ms

t = 0.204 ms

t = 0.228 ms

t = 0.288 ms

t = 0.312 ms

t = 0.360 ms

t = 0.372 ms

t = 0.384 ms

t = 0.396 ms

400035253050200 675 1150 1625 2100 2575

Figure 15: Simulated temperature cloud charts in WRC channel 2 when hot-jets of different species are used: (a) combustion products, (b)N2, and (c) Ar2.


speed reaches the theoretical value (VCJ) and detonationcombustion is triggered. Using a hot-jet consisting of thecombustion products means the entire combustion processlasts only a short time. Hot-jets of N2 cause a delay of

approximately 0.245ms, then the flame propagation is accel-erated and flames spread during detonation combustion untilt = 0 7ms. Hot-jets of Ar2 exhibit longer ignition delay timesthan do jets of N2. The entire flame propagation acceleration

t = 0.312 ms t = 0.156 ms t = 0.192 ms

t = 0.240 ms t = 0.282 ms t = 0.306 ms

HO2 mass fraction

0.0007 0.0014 0.0021 0.0028 0.0007 0.0014 0.0021 0.0028 0.0007 0.0014 0.0021 0.0028

0.0007 0.0014 0.0021 0.0028 0.0007 0.0014 0.0021 0.0028 0.0007 0.0014 0.0021 0.0028

(a)

t = 0.132 ms t = 0.246 ms t = 0.270 ms

t = 0.300 ms t = 0.360 ms t = 0.408 ms

HO2 mass fraction

0.0003 0.0006 0.0009 0.0012 0.0003 0.0006 0.0009 0.0012 0.0003 0.0006 0.0009 0.0012

0.0003 0.0006 0.0009 0.0012 0.0003 0.0006 0.0009 0.0012 0.0003 0.0006 0.0009 0.0012

(b)

t = 0.132 ms t = 0.294 ms t = 0.372 ms

t = 0.378 ms t = 0.414 ms t = 0.462 ms

HO2 mass fraction

0.0003 0.0007 0.0010 0.0013 0.0003 0.0007 0.0010 0.0013 0.0003 0.0007 0.0010 0.0013

0.0003 0.0007 0.0010 0.0013 0.0003 0.0007 0.0010 0.0013 0.0003 0.0007 0.0010 0.0013

(c)

Figure 16: Cloud charts of HO2 concentration for hot-jets of different chemical species: (a) combustion products, (b) N2, and (c) Ar2.


process is similar to that of heated N2, jets and only a delay inthe process is observed.

5.3. Effects of the Spoilers with Blockage Ratio on CombustionCharacteristics of WRC. As shown in Figure 14, the prop-agation of the wave and flames shows similar trends underoperating conditions of BR = 23 35%, BR = 31 13%, and BR = 38 91%. However, using operating conditions of BR = 0,the wave and flames exhibit different propagation rules.The wave propagation process under operating conditionsof BR = 0 is displayed in Figure 18 from t = 3 09ms to t =3 912ms, from when the hot-jet enters the WRC channel towhen stable detonation waves are formed. In contrast to wavepropagation characteristics in the WRC with spoilers, wavesare propagated in a planar pattern. Moreover, at t = 3 492ms, the compression wave spreads to the end of the channeland the flame surface remains in the middle of the channel.At t = 3 528ms, the compression wave is reflected by the wallsurface and pressure increases from 0.2MPa to 0.8MPa.After reflection, the compression undergoes expansive backpropagation and pressure of the wave decreases. After, theflames are stagnated.

Flame propagation is further hindered by both thereflected compression wave and small concentrations ofcombustible fuel/air mixture in front of the flame. At t =3 708ms, the reflected compression wave encounters the wallon the inlet duct and is reflected, and pressure of the com-pression wave rises to 1.0MPa. At t = 3 906ms, the compres-sion wave encounters the flame surface and is partly coupled,and a strong arch shock wave is formed in front of the flame.At t = 3 912ms, the wave and flames are completely coupledforming a planar detonation wave.

Figure 19 displays the statistical variation of the wave andflame propagation when spoilers with different blockageratios were used. More specifically, variation of wave andflame propagation velocities over time, variations of the waveand flame velocities with position, and variation of the wave

and flame positions with time are presented. It can beobserved that under operating conditions of BR = 0, the wavepropagation speed is always greater. In general, during thepropagation process, flames are first accelerated, then decel-erated, and finally accelerated again. Combining the resultspresented in Figures 14 and 18, it can be concluded that flamepropagation speed is significantly affected by jets at thebeginning since in the initial stage, the flames are rapidlyaccelerated. Afterwards, action of the hot-jet is weakened,and the flame propagation speed decreases briefly and there-after increases. Furthermore, the compression wave in frontof the flames exhibits similar propagation rules, wherebypropagation speed first increases, then drops, and finallyincreases. Based on the relationship between the position ofthe wave and flames with time, it can be observed that thedistance between the wave and flames increases with time.Throughout the entire propagation period, the maximumflame propagation speed reaches up to 420m/s, suggestingthat rapid combustion occurs in the WRC channel. Theflame and wave propagation properties under operating con-ditions of BR = 23 35%, BR = 31 13%, and BR = 38 91% aresimilar. Under these operating conditions, flames catch upto the shock wave and complete coupling is achieved. Themaximum wave and flame propagation speeds under operat-ing condition of BR = 23 35% are greater than the valuesunder operating conditions of BR = 31 13% and BR = 38 91%. This is due to the fact that under operating conditions ofBR = 23 35%, the coupling position between the shock waveand flames occurs around spoiler 3, thereby acceleratingflame propagation. Under operating conditions of BR =31 13% and BR = 38 91%, coupling between the shock waveand flames occurs in front of spoiler 3, and flame propagationspeeds are close to theoretical values VCJ . Under operatingconditions of BR = 38 91%, the shock wave and flames arecoupled early and attenuation of the detonation wave isclearly observed; moreover, propagation of the detonationwave gradually becomes stable. Thus, a number of conclu-sions can be drawn. First, the existence of turbulent flowresults in coupling between the shock wave and flames in ashort time and distance. Since both ends of the wave rotorchannel are closed, the shock wave can be coupled to theflame surface during backward and forward propagationeven when no spoilers are used. However, the coupling posi-tion is always located at the end of the channel. Second, as theblockage ratio of the spoilers increases, the coupling positionbetween the shock wave and flames gradually advances.

6. Conclusions

In this study, the reduced chemical reaction mechanism ofethylene based on the LLNL N-Butane mechanism wasgained, which included 23 species and 55 elementary reac-tion steps. Then, ignition delay time, flame propagationspeed, and molar fractions of the reactants and main prod-ucts were simulated based on the reduced mechanism.Overall, numerical results using the reduced mechanismwere consistent with data derived from the detailed mecha-nism, thus verifying the effectiveness of the reduced mecha-nism. Furthermore, numerical simulations were performed

2500

Combustion productsN2Ar

2000

1500

1000

Flam

e spe

ed (m

/s)

500

0

0.1 0.2 0.3

t = 0.13 ms

Lag time

VCJ = 2183 m/s

0.4Time (ms)

0.5 0.6 0.7

Figure 17: Variation of flame propagation speed with time.


on the combustion process in the WRC using the reducedmechanism and EDC combustion model to investigate theeffects of hot-jets with different species and spoilers withdifferent blockage ratios on the ignition and propagationproperties in the channel of WRC. Simplifying hot-jets ofcombustion products as hot-jets of inert gases, ignition

delay time increases, whereas premixed combustible fuel/air mixture is directly ignited when the hot-jets of the com-bustion products are used. The existence of spoilers achievescoupling between wave and flames within a short time anddistance, and coupling position is also advanced with theblockage ratio of the spoiler increasing.

(a)

0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23

0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23

0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23

0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23

0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23

0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23

0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.02 0.04 0.06 0.08 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23

(b)

Figure 18: Propagation of wave and flame in the WRC channel under operating conditions of BR = 0: (a) propagation of wave and (b)propagation of flame.


3.1 3.2 3.3Time (ms)

FlameWave

L (mm)3.4

Br = 0

3.5 3.1 3.2 3.3Time (ms)

3.4 3.50 50 100 150 200

300

400

500

600

Flam

e spe

ed (m

/s)

300

400

500

600

Flam

e spe

ed (m

/s)

0

50

100

150

200

L (m

m)

(a)

Br = 23.35%

3.1 3.2 3.3Time (ms)

3.4 3.5 3.1 3.2 3.3Time (ms)

3.4 3.5L (mm)

0 50 100 150 200

FlameWave

0

750

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2250

3000

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e spe

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/s)

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750

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3000Fl

ame s

peed

(m/s

)

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L (m

m)

(b)

Br = 31.13%

3.1 3.2 3.3Time (ms)

3.4 3.5 3.1 3.2 3.3Time (ms)

3.4 3.5L (mm)

0 50 100 150 200

FlameWave

0

750

1500

2250

3000

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e spe

ed (m

/s)

0

750

1500

2250

3000

Flam

e spe

ed (m

/s)

0

50

100

150

200

L (m

m)

(c)

Br = 38.91%

3.1 3.2 3.3Time (ms)

3.4 3.5 0 50 100L (mm)

150 200 3.1 3.2 3.3Time (ms)

3.4 3.5

FlameWave

0

750

1500

2250

3000

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e spe

ed (m

/s)

0

750

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/s)

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L (m

m)

(d)

Figure 19: Propagation of shock wave and flames using spoilers with different blockage ratios.


Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work was supported by “the National Natural ScienceFoundation of China,” NO. 51476077.

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