Investigation of ignition dynamics in a H2/air mixing ... · Investigation of ignition dynamics in a H2/air mixing layer with an embedded vortex ... and fuel/air temperatures on ignition

Paper # 070LT-0211 Topic: Laminar Flames

The 8th US National Meeting of the Combustion Institute, Park City, UT, May 19-22, 2013

Investigation of ignition dynamics in a H2/air mixing layer with anembedded vortex

S.K. Menon1 and G. Blanquart1

1Department of Mechanical EngineeringCalifornia Institute of Technology, Pasadena, CA, USA

Numerical simulations are carried out to study the effect of a vortex on the ignition dynamics of hydro-gen/air in a quiescent mixing layer. The problem has direct implications on the auto-ignition behaviorand stabilization mechanism in turbulent non-premixed flames, recirculating burners and supersoniccombustion. Similar problems have been studied in the past using different approximations like in-finitely fast and single-step chemistry and large activation energy asymptotics. While useful insightis obtained, the role of multi-step reaction chemistry is neglected. More recent work utilizing detailedchemical kinetics has been limited in its scope due to computational requirements. These difficulties areovercome in the present study by utilizing a tabulated approach. Chemistry tabulations are generatedutilizing steady-state solutions of the non-premixed flamelet equations. The fluid dynamic simulationsare carried out using a lookup table approach. Similar calculations are also performed with detailedchemistry to demonstrate the accuracy of the tabulated approach. The reduction in computational timeobtained using the tabulated approach is utilized to conduct a parametric study investigating the effectsof vortex strength, characteristic size, center location, and fuel/air temperatures on ignition delay timeand location. The effect of these parameters are correlated to the scalar dissipation rate to explain thephysical processes leading to ignition.

1 Introduction

The interaction of chemistry with turbulence plays a crucial role in the operation of many practicalcombustion devices and forms a wide body of research. One related area is the ignition dynamicsassociated with a non-premixed configuration in a turbulent flow field. It has direct implications onthe auto-ignition and stabilization mechanisms in turbulent lifted jet flames, recirculating burnersand supersonic combustion.

Experiments conducted by Blouch et al [1, 2] investigated the effects of turbulence on non-premixedignition of hydrogen in a heated counterflow. The results showed enhancement of the ignition pro-cess by turbulent eddies whose size was comparable to that of the ignition kernel and also revealedconsiderable effect of the mixing process on chemical reaction pathways. An experimental studyconducted by Mastorakos et al [3] investigated the effect of air velocities and temperatures on theturbulent auto-ignition process in a co-flow with hydrogen. The experiments suggested a delayingeffect of turbulence on the auto-ignition process. The flowfields involved in these configurationstend to be complicated and efforts have been made to study more basic problems using theoreticaland numerical methods.

One of the earliest studies by Linan and Crespo [4] investigated the structure of a diffusion flamein the unsteady mixing layer between fuel and oxidizer using large activation energy asymptotics.A similar problem was later studied by Marble [5] who developed a model to describe the dyamics

1

USSCI 2013 Meeting– Paper # 070LT-0211 Topic: Laminar Flames

and heat release of a flame wrapped in a small scale eddy assuming infinitely fast chemistry. Thesestudies however did not address the ignition process directly. More recent work by Macareg etal. [6] attempted to study the structure of the ignition process in the presence of a vortex for acase with equal fuel and oxidizer temperatures in a quiescent flowfield using asymptotic theory.This study was later extended to include the effect of shear flow motion between the fuel and airstreams [7]. Thevenin and Candel [8] performed a similar calculation in a quiescent flow field withvarying air and fuel (H2) temperatures assuming constant density, unity Lewis number and one-step reaction chemistry. Zheng et al [9] conducted a similar calculation with the oxidizer at 2000Kand fuel (H2) at 300K incorporating detailed reaction kinetics. The increasingly sophisticatedtreatment of reaction chemistry has shown finite-rate chemistry to be an important factor governingthe ignition process. This has also led to the use of direct numerical simulations(DNS) to studythe auto-ignition mechanism in several studies by Mastorakos [10], Im [11], Thevenin [12] andChen [13]. However, the added computational requirements and complexity in studies using DNSor detailed reaction kinetics has limited the range of parameters that can be studied as experiencedby Zheng et al [9].

This work attempts to use tabulated chemistry to conduct studies similar to those by Zheng [9] andCandel [8], so as to incorporate multi-step reaction chemistry into the fluid dynamic simulation ina computationally efficient manner. It extends on the previous studies by investigating the effect ofoxidizer temperature and scalar dissipation rate on the ignition process. As part of this effort, it isalso desired to obtain a better understanding of tabulated approaches for ignition in a non-premixedenvironment especially at lower oxidizer temperatures.

The first section of the paper presents a brief discussion of the physical problem being modeledin this work. The next sections describe the governing equations, chemistry modeling and tabula-tion and the initial and boundary conditions used to solve the coupled fluid-dynamic combustionproblem. The next section describes simulation results showing the effect of variation of vortexparameters on ignition dynamics followed by a discussion of the underlying physical mechanisms.Finally, conclusions are presented and discussed.

2 Physical Problem

Figure 1: Schematic of the configuration investigated computationally in this work.

Figure 1 illustrates the physical problem studied in this work. The ignition dynamics taking placein a non-premixed, quiescent layer of hot air and cold hydrogen is investigated with and without

2


the presence of a single vortex. Initially, a one dimensional problem without a vortex is solved toget insight into the purely diffusion driven ignition process. Next the 2-D problem is solved witha vortex present. The fuel is purely hydrogen whose temperature is maintained at 300K in all thetest cases. The hot air consisting of oxygen and nitrogen is subject to different temperatures in therange between 800–2000K.

3 Simulation details

3.1 Governing equations

The governing equations of fluid motion for the simulations performed here are the variable den-sity low-Mach number Navier-Stokes equations. The governing equations for laminar flow arepresented as follows:

Mass conservation∂ρ

∂t+∇ · (ρu) = 0 (1)

Momentum conservation

∂(ρu)

∂t+∇ · (ρuu) = −∇p+∇ · τ + ρg (2)

3.2 Chemistry modeling

A reaction mechanism for H2-air combustion consisting of 13 species and 76 reactions is utilizedin this work [14]. Two different approaches are used to model the reaction kinetics for the con-figuration illustrated in Fig. 1, the main difference being the method used to capture finite-ratechemical kinetics. The first approach solves the full set of transport equations for each of the re-acting species as well as an energy equation in addition to the mass and momentum conservationequations. In the second approach, the chemistry is tabulated a priori using solutions to 1D un-steady diffusion flames. The main reason for pursuing these two different approaches is to validatethe tabulated approach for ignition calculations. The two approaches are now described in furtherdetail.

3.2.1 Detailed chemistry

In this case, simulations are conducted by solving species transport equations for all the species inthe reaction mechanism and an energy equation in addition to the mass and momentum conserva-tion equations. The species transport equations take the form,

∂(ρYi)

∂t+∇ · (ρuYi) = ∇ · (ρD∇Yi) + ω̇i (3)

where the Soret effect (mass diffusion due to temperature gradients) has been neglected and Fick’slaw is assumed with constant, unity Lewis numbers for all species. The energy equation written in

3


the temperature form is given by,

∂(ρCpT )

∂t+∇ · (ρuCpT ) =

Dp

Dt+∇ · (λ∇T )−

∑i

ρCp,iji · ∇T −∑i

ρhiω̇i (4)

where the Dufour effect (heat diffusion due to species concentration gradients) and radiation heatlosses have been neglected and ji is the species mass flux.

3.2.2 Tabulated approach

In this approach, reaction chemistry is modeled using the flame progress variable (FPV) approachas formulated by Knudsen and Pitsch [15]. The FPV approach requires the solution of transportequations for additional scalar variables given by,

Transport of progress variable

∂(ρC)

∂t+∇ · (ρuC) = ∇ · (ρD∇C) + ω̇C (5)

and transport of mixture fraction

∂(ρZ)

∂t+∇ · (ρuZ) = ∇ · (ρD∇Z). (6)

The progress variable represents the extent of reaction and is estimated as the mass fraction of themajor product species, i.e. H2O. The mixture fraction is calculated from the mass fractions of fueland oxygen using,

Z =νYF − YO2 + YO2,2

νYF,1 + YO2,2

(7)

where YF and YO2 represent fuel and oxygen mass fractions in the mixture, YF,1 represents thefuel mass fraction in the fuel stream(1), YO2,2 represents the oxygen mass fraction in the airstream(0.232) and ν represents the stoichiometric mass ratio(8). The stoichiometric mixture frac-tion is given by,

Zst =

[1 +

νYF,1YO2,2

]−1

(8)

and works out to 0.0284. The diffusivity, D used in Eq. 5 and 6 is the thermal diffusivity using aconstant, unity Lewis number assumption for all species.

Species mass fractions, production rates, mixture transport properties etc., are assumed to dependonly on mixture fraction and the reaction progress variable. These properties are tabulated a prioriusing a chemical kinetic solver - FlameMaster[16]. The tabulation process is described in detailin the next section. The numerical solver utilizes a lookup table procedure to acquire species andmixture properties during the course of the simulation.

4


3.2.3 Chemistry tabulation

The chemistry tabulation forms a vital part of the simulations conducted in this work. The tabula-tions are generated using solutions for counterflow diffusion flames obtained using FlameMaster.The solutions are generated in the mixture fraction space by solving the steady state version of theflamelet equations given by [17],

ρχ

2

∂2ψi∂Z2

+ ωi = 0 (9)

where ψi and ωi are the mass fractions and source terms for each reactive scalar. The scalardissipation rate, χ, for non-premixed combustion is given by,

χ = 2D|∇Z|2. (10)

The Lewis numbers for all species are assumed to be equal to unity and the diffusivityD, in Eq. 10

(a) (b)

Figure 2: Temperature and progress variable as a function of mixture fraction for oxidizer tempera-ture of 2000K, fuel temperature of 300K and different values of χ.

is taken to be the thermal diffusivity. For a fixed oxidizer and fuel temperature, a set of solutionsare obtained by varying the scalar dissipation rate, χ, so as to go from a non-burning, pure mixingregion (large χ) to a burning region (small χ) and points in between. Figure 2(a) and Fig. 2(b)show the results of a solution obtained for an oxidizer temperature of 2000K, a fuel temperature of300K and three different initial values of χ. Temperature is plotted in Fig. 2(a) while the progressvariable is plotted in Fig. 2(b). As seen in the figures, for a high value of χ, no ignition occurs andthe temperature varies smoothly going from hot air (Z=0) to fuel (Z=1). On the other hand, themixture ignites for smaller values of χ and a corresponding increase is observed in temperatureand progress variable.

Figure 3(a) and Fig. 3(b) show the entire set of solutions obtained for different oxidizer tempera-tures ranging from 800–2000K and fuel temperature of 300K. Maximum temperature is plotted asa function of χ in Fig. 3(a) while the progress variable, C, is plotted as a function of χ in Fig. 3(b).Both figures present results for the stoichiometric value of the mixture fraction, Zst = 0.0284. Asseen in Fig. 3(a), for a high oxidizer temperature (eg. 2000K), no unstable solutions between the

5


(a) (b)

Figure 3: Maximum temperature and progress variable as a function of χ for different oxidizer tem-peratures between 800–2000K and fuel temperature of 300K at the stoichiometric mixture fraction.

Figure 4: Contour plot showing source term of the progress variable (ω̇C)as a function of the tableparameters (C and Z).

burning and non-burning branches are found. However, at lower oxidizer temperatures (eg. 800K),an S-shaped curve with unstable points between the burning and non-burning solutions is obtained.

The next step is to generate a unique chemistry tabulation utilizing the steady flamelet solutionsshown in Fig. 3(a) and 3(b). Since a tabulation generated using χ would be non-unique on accountof the S-shaped curves, the progress variable in addition to the mixture fraction are chosen as theindependent co-ordinates for the chemistry tabulation. Figure 4 shows a result from the chemistrytabulation for an oxidizer temperature of 1200K where contours of the source term are plottedwith the x-coordinate representing the progress variable and y-coordinate representing the mixturefraction. As seen in the figure, the source term is considerably larger in the vicinity of the stoichio-metric mixture fraction (Zst =0.0284). To capture this region adequately, a considerable numberof points in the table are clustered around Zst.

Figure 5 shows the source term as a function of the progress variable for different oxidizer temper-

6


Figure 5: Source term as a function of the progress variable for different oxidizer temperaturesplotted on a log-log scale. Symbols are points from detailed chemistry calculations and lines arevalues extracted from the tabulation.

atures at the stoichiometric mixture fraction. The points represent the flamelet solutions obtainedfrom FlameMaster and the lines represent the solutions as represented in the tabulation. Goodagreement is obtained between the two which is necessary for accurate representation of finite-ratechemistry. The chemistry tabulation utilizes 200 points in each direction (C and Z). Of the 200points in the C direction, 175 are estimated on a log-scale to accurately capture the evolution ofthe progress variable from a very small value of about 1e-16 to about 0.1. This ensures a smoothand continuous representation of the ignition process.

3.3 Initial conditions

The initial conditions consist of a uniform profile for mixture fraction on either side of the mixinglayer with a hyperbolic tangent function used to smooth the jumps across the layer. The transitionin Z going from pure fuel to pure oxidizer is represented by 10 grid points. The progress variable isset to a very small initial value(1e-10). As seen from Fig. 5, this is necessary because the minimumvalue of C in the table is about 1e-16. Varying the initial value of the progress variable for valuesless than 1e-8 was found to produce no significant effect on the ignition delay time or location.Specifying the initial mixture fraction profile and progress variable simultaneously determines thetemperature and species mass fractions in the tabulated approach. The data file generated by thisstep is used to initialize the simulations in both the approaches (tabulated and detailed chemistry)described previously. This ensures consistency between the two approaches.

A quiescent mean velocity field is assumed at the initial time. At the same time, for the caseswhere the effect of a vortex is investigated, a velocity field for the vortex is prescribed using thestream function for an incompressible, inviscid vortex given by [18],

ψ = Cexp

(−x

2 + y2

2R2c

)(11)

where Rc is the characteristic vortex radius and C is the vortex strength. The velocity field pre-

7


scribed by the stream function ψ can be written as [9],{uv

}=

{ ∂ψ∂y

−∂ψ∂x

}=

C

R2c

exp

(−x

2 + y2

2R2c

){−yx

}(12)

The vortex strength, radius and center location are three key parameters that are varied in this studyto study their influence on ignition location and timing. Varying the vortex strength essentiallyvaries the vortex Reynolds number which can be expressed as,

Re =Γ

2πν(13)

where Γ represents the vortex circulation.

3.4 Grid and boundary conditions

The 1D simulations are done on a domain 4 cm in length while the 2D simulations are conductedon a domain 4cm x 4cm in size. In both cases, a non-uniform grid is used with about half the meshpoints concentrated close to the center of the domain. The total number of points in all simulationsare 256 in each direction. The size of the domain and distribution of mesh points imposes an initialvalue for the scalar dissipation rate (χ). χ forms an additional parameter whose effect on ignitiondynamics is explored in this work. Finally, non-reflecting boundary conditions are imposed on allfour boundaries.

4 Results

A set of test cases in a 1D configuration were first investigated to understand the purely diffusiondriven ignition process. Additionally the ignition delay times obtained from the 1D calculationsserve as baseline values to compare with those obtained in the presence of a vortex. Next, 2Dsimulations are run with a vortex present, for different initial values of χ and oxidizer temperature,and the effect of vortex size, strength, and center location on ignition delay time are investigated.

4.1 1D simulations without a vortex

Figure 6 shows a series of plots illustrating the ignition process from a 1D simulation. The oxidizertemperature is 2000K, fuel temperature is 300K, mixture fraction is initialized as described in Sec-tion 3.3 and the initial velocity is zero in the domain. The results are obtained using the tabulatedapproach described in Section 3.2.2. Figure 6(a) shows the maximum value of the source termin the domain plotted over time. The ignition delay time is identified as 9.3 µ seconds. Ignitiondelay in all the test cases presented in this work is determined as the time taken to reach a valuefor the progress variable equal to 0.05, which roughly estimates to a 20% increase in the progressvariable. Diffusion of heat and species decreases the gradient in mixture fraction resulting in acorresponding decrease in the value of χ. This can be seen in Fig. 6(b) where the maximum valueof χ in the domain is plotted as a function of time. A better understanding of the local ignitionprocess can be obtained by identifying the most reactive mixture fraction (ZMR). ZMR is defined

8


(a) (b)

(c) (d)

Figure 6: Illustration of the 1-D diffusion driven ignition process for an air temperature of 2000K andfuel temperature of 300K.

as the value of Z corresponding to the maximum heat release when ignition occurs. For this caseZMR is identified as 0.04 which is slightly higher than Zst which is 0.0284. Figure 6(c) shows thelocal χ as a function of Z over time. As seen in the figure, at the point when ignition occurs, thevalue of χ corresponding to ZMR is about 400. This gives the value for the most reactive χ or χMR.Thus, in the 1D case, ignition can be predicted to occur at the value of Z = ZMR when the localvalue of χ ≤ χMR. This result can be further visualized in Fig. 6(d), where the progress variableis plotted as a function of χ for the set of solutions corresponding to an oxidizer temperature of2000K from Fig. 3(b). As diffusion drives the value of χ below χMR, it is possible to move froma non-burning condition to a burning condition leading to ignition of the mixture. The values ofZMR and χMR vary with oxidizer temperature. Table 1 summarizes ZMR and χMR for differentoxidizer temperatures investigated in this study.

Table 1: ZMR and χMR for different oxidizer temperatures investigated in this study.

Oxidizer temperature [K] ZMR χMR [1/s]1000 0.010 0.51200 0.016 101400 0.022 361600 0.027 1021800 0.027 1482000 0.040 400

9


4.1.1 Effect of air temperature

Figure 7: 1D calculations showing ignition delay as a function of air temperature. Note that they-axis is on a log scale.

Figure 7 shows a plot of ignition delay time calculated for a 1D configuration in a quiescent velocityfield as a function of air temperature. The grid spacing is maintained the same for all cases. Ineach case, the χ distribution in the domain decreases due to diffusion till at the point correspondingto ZMR, the value of χ goes below χMR resulting in ignition. The effect of air temperature canbe clearly seen in the figure. There is a rapid increase in ignition delay time with decrease in airtemperature. No ignition is seen to occur for an air temperature of 900K and below. Figure 7 alsoshows similar results obtained from a detailed chemistry calculation as described in Section 3.2.1.The two data sets show good agreement at high temperatures but deviate at lower temperaturesbelow 1200K. Although the validation is not perfect, the trends are correctly predicted, enablingthe tabulated approach to be used to investigate ignition dynamics in the 2D test cases.

4.1.2 Heat release rate

Some interesting aspects of the ignition process leading to the development of a flame can beinvestigated by observing the heat release rate in the 1D domain. The heat release rate is analogousto the progress variable source term(ω̇C) which is plotted in Fig. 8. Figure 8(a) shows a plot ofsource term plotted as a function of the length of the domain at different time intervals during thecourse of the simulation where the air temperature is set at 2000K. Figure 8(b) shows a similarplot for an air temperature of 1000K. As seen in Fig. 8(a), a single peak in the source term appearsat the point of ignition(9.3µs) at the location in the domain corresponding to ZMR and χMR asdescribed in the analysis in the previous section. This peak grows to a considerably larger valuecorresponding to the peak heat release rate(10µs). Further on in time, twin peaks appear in thesource term of which one propagates to the right(fuel rich side) and establishes a diffusion flamefront. The peak to the left which corresponds to a premixed-type ignition travels some distance andthen extinguishes. This behavior is more prominent in Fig. 8(b), where the lower air temperature

10


(a) Tair=2000K (b) Tair=1000K

Figure 8: Source term along the domain at different time instances for two different air temperatures.The first two datasets in each case are plotted with respect to the left hand y-axis and the otherswith respect to the right hand y-axis.

which requires more time to ignite allows for a greater amount of premixing. Similar results areseen in the theoretical analysis by Linan [4] and numerical simulations by Candel [8] and Law [9].

4.2 2D simulations with an imposed vortex

The effect of a vortex on ignition dynamics is now studied using 2D simulations conducted us-ing tabulated chemistry. The sections below report the effects of vortex strength, size and centerlocation on ignition delay.

4.2.1 Effect of vortex strength

The effect of vortex strength is studied by varying the parameter C in Eq. 12 over a range 0.005–0.5. This corresponds to a vortex Reynolds number ranging from 55–5538. Figure 9(a) andFig. 9(b) show the effect of vortex strength on ignition delay time for two different air temper-atures(1000K and 1200K) and two different scalar dissipation rates. The ignition delay in eachcase is normalized by the value obtained from the 1D analysis presented previously. In both fig-ures, the ignition delay time is seen to drop slightly with increasing vortex strength before attainingan almost constant value. The case with χ=4900 and an air temperature of 1200K however seemsto be an exception where increasing vortex strength does not appear to affect ignition delay. Thevortex radius is held constant while increasing the vortex strength resulting in an increasinglystronger velocity field.

4.2.2 Effect of vortex radius

The effect of vortex size is studied by varying the parameter Rc in Eq. 12 over a range 0.1–4mm.This range is within typical integral length scales of 2–3mm observed in turbulent ignition exper-iments by Blouch and Law [1]. Effects similar to those for vortex strength are seen in Fig. 9(c)

11


and 9(d). An initial slight decrease in ignition delay is seen with increasing vortex size which thenattains a nearly constant value. The vortex strength is held constant while increasing the size of thevortex resulting in an progressively weaker velocity field.

(a) Tair=1000K (b) Tair=1200K

(c) Tair=1000K (d) Tair=1200K

(e) Tair=1000K (f) Tair=1200K

Figure 9: Effect of varying vortex parameters on ignition delay time.

4.2.3 Effect of vortex center location

The effect of vortex center location with respect to the center of the domain is studied by movingthe x co-ordinate of the center of the vortex progressively to the left and right of the domain.Figure 9(e) and Fig. 9(f) show the effect on ignition delay with the x axis showing the displacementdistance(δx = xvortex,center − xdomain,center) normalized by the vortex radius. As the vortex ismoved to the left or the right of the domain center, a ‘W’-shaped behavior is observed in the

12


normalized ignition delay time. The ignition delay decreases on either side to a minimum valuebefore increasing back to the 1D ignition delay time. The center of this ‘W’-shaped profile is notaligned with zero displacement of the vortex as can be seen in Fig. 9(e) and Fig. 9(f).

5 Discussion

(a) Mixture fraction (b) χ

(c) Progress variable (d) Velocity(m/s)

Figure 10: Contour plots of various quantities at the point of ignition for an air temperature of 2000K,fuel temperature of 300K, vortex strength of 0.2, Re = 703 and vortex radius of 0.5 mm.

The effect of a vortex on the mixing layer is visualized using contour plots of various parametersshown in Fig. 10. The plots shown at the point of ignition in the domain correspond to a casewith an air temperature of 2000K, fuel temperature of 300K, vortex strength of 0.2 and radiusof 0.5mm. In Fig. 10(c) and Fig. 10(d), iso-contours of the mixture fraction are overlaid on thecontour plots. The orange line in all four plots corresponds to an iso-contour of the most reactivemixture fraction(ZMR) which for this case corresponds to a value of 0.04. The red dots in eachplot correspond to the point of ignition while the yellow dots represent the location with the lowestχ on the iso-contour of ZMR.

As seen in Fig. 10(a), the presence of the vortex has led to considerable mixing of fuel and air inthe core of the vortex. The distortion of the mixture fraction field which in the 1D case was purelyby diffusion, is now aided by convection resulting in a more rapid decrease in the scalar dissipationrate shown in Fig. 10(b). The presence of the vortex results in the stretching and compression ofthe iso-contours of Z leading to a corresponding decrease or increase in χ as seen in previousstudies.

13


Ignition is seen to take place at the location corresponding to the red dot on the iso-contour ofZMR. This can be seen more clearly in Fig. 10(c) where contours of the progress variable areplotted. Accumulation of the progress variable is seen around the iso-contour of ZMR just outsidethe mixing region while almost no progress variable is seen in the region immediately affected bythe vortex. The reason for this can be attributed to the velocity field shown in Fig. 10(d). Theconvection dominated field prevents the accumulation of reactive species delaying ignition at thepoints closest to the vortex center. However, just outside the convection dominated field, a lowvalue of χ coupled with low velocity allows sufficient accumulation of reactive species leading toignition.

(a) C = 0.05, Re = 554 (b) C = 0.1, Re = 1108

(c) C = 0.2, Re = 2217 (d) C = 0.5, Re = 5538

Figure 11: Contour plots of velocity(m/s) along with iso-contours of mixture fraction for differentvortex strengths at the point of ignition whose location is indicated by the red dot. Air temperatureis 1000K and fuel temperature is 300K. Vortex radius(Rc) is 0.5mm.

The role of vortex strength in affecting the ignition delay time as shown in Fig. 9(a) and Fig. 9(b) isnow explained using contour plots shown in Fig. 11. The figure shows contour plots of velocity atthe point of ignition corresponding to four different vortex strengths overlaid with iso-contours ofmixture fraction. As seen in Fig. 11(a) and Fig. 11(b), increasing the strength of the vortex resultsin a larger and more rapid stretching of the iso-contours of mixture fraction resulting in a decreasein ignition delay time. However, once a critical vortex strength is reached as seen in Fig. 11(d),the velocity field loses all structure due to the large induced velocities. Any further increase invortex strength results in a rapid breakup of the mixture fraction distribution. This prevents anyfurther decrease in ignition delay which is the result of stretching the iso-contours of Z as seen inFig. 11(a), Fig. 11(b) and Fig. 11(c).

The role of vortex size in affecting ignition delay time shown in Fig. 9(c) and Fig. 9(d) is nowexplained using contour plots shown in Figure 12. The figure shows contour plots of velocityat the point of ignition corresponding to four different vortex sizes overlaid with iso-contours ofmixture fraction. When the vortex is very small(Fig. 12(a)), smaller than the thickness of the layer

14


(a) Rc = 0.1mm,Re = 89 (b) Rc = 0.5mm,Re = 221

(c) Rc = 3mm,Re = 238 (d) Rc = 4mm,Re = 238

Figure 12: Contour plots of velocity(m/s) along with iso-contours of mixture fraction for differentvortex sizes at the point of ignition whose location is indicated by the red dot. Air temperature is1000K and fuel temperature is 300K. Vortex strength(C) is 0.02.

indicated by the iso-contours of Z, it takes more time for the velocity field to adequately stretch theiso-contours of Z and cause ignition. As the size of the vortex increases(Fig. 12(b)), it stretches theiso-contours of Z faster leading to an initial decrease in ignition delay time. However, as the vortexsize is increased further(Fig. 12(c) and 12(d)), holding the vortex strength constant, the velocityfield decreases in magnitude resulting in a slower stretching of the iso-contours of Z leading to aprogressive increase in ignition delay time.

Figure 13 shows contour plots for velocity overlaid with iso-contours of mixture fraction corre-sponding to different cases presented in Fig. 9(e) earlier. The ‘W’-shaped behavior seen in igni-tion delay time can be explained using Fig. 13. The ‘W’-shaped behavior is centered around thecase shown in Fig. 13(a). As the vortex is moved progressively towards the left(Fig. 13(b) andFig.13(c)), ignition delay decreases due to the effect of the vortex in stretching the iso-contoursof Z. However, once this reaches a critical value, further displacement of the vortex towardsthe left(Fig. 13(d) and Fig. 13(e)) results in reduced effect of the vortex in enhancing ignitiondelay. Eventually, the vortex is far enough away that it has no influence on the ignition delaytime(Fig. 13(f)) and the 1D value is recovered.

6 Concluding Remarks

The ignition dynamics taking place in the quiescent mixing layer between hydrogen and air inthe presence of a vortex is investigated primarily using a tabulated chemistry method to capturefinite rate chemistry. The tabulation is generated using solutions to the steady flamelet equationfor counterflow diffusion flames with varying scalar dissipation rates. A comparison of ignitiondelay times predicted by the tabulated method with those given by detailed chemistry calculations

15


(a) δx = 2 ∗Rc (b) δx = 1 ∗Rc (c) δx = 0 ∗Rc

(d) δx = −2 ∗Rc (e) δx = −4 ∗Rc (f) δx = −6 ∗Rc

Figure 13: Contour plots of velocity along with iso-contours of mixture fraction for different vortexdisplacements from the domain center at the point of ignition whose location is indicated by the reddot. Air temperature is 1000K and fuel temperature is 300K. Vortex strength(C) is 0.02 and radius(Rc)is 0.5mm.

for a purely diffusion driven case in the absence of a vortex show good agreement with each other.Increasing the strength and size of the vortex produce similar behavior in ignition delay time whichdecreases slightly and then reaches a constant value. Displacing the center of the vortex from thecenter of the domain progressively, results in a ‘W’-shaped behavior in ignition delay which firstdecreases and then asymptotes to a constant value. The effects of variation in vortex parametersare seen to be qualitatively the same, irrespective of air temperature. However, the effects areamplified in magnitude at lower air temperatures. No ignition is obtained for air temperature atand below 900K with or without the presence of a vortex in the flow field. Inspection of the flowfield identifies the stretching and compression of the iso-contours of the mixture fraction resultingin corresponding changes in the scalar dissipation rate coupled with the effect of the velocity fieldinduced by the vortex affecting the accumulation of reactive species being the two main factorsdetermining the time and location of ignition.

Acknowledgments

The authors gratefully acknowledge funding for this research by the Boeing Company through aStrategic Research and Development Relationship Agreement CT-BA-GTA-1.

References

[1] J. D. Blouch, C. J. Sung, C. G. Fotache, and C. K. Law, “Turbulent ignition of non-premixed hydrogen by heatedcounterflowing atmospheric air,” Symposium(International) on combustion, vol. 27, no. 1, 1998.

16


[2] J. D. Blouch and C. K. Law, “Effects of turbulence on nonpremixed ignition of hydrogen in heated counterflow,”Combustion and Flame, vol. 132, 2003.

[3] C. N. Markides and E. Mastorakos, “An experimental study of hydrogen autoignition in a turbulent co-flow ofheated air,” Proceedings of the combustion institute, vol. 30, no. 1, pp. 883–891, 2005.

[4] A. Linan and A.Crespo, “An asymptotic analysis of unsteady diffusion flames for large activation energies,”Combustion science and technology, vol. 14, pp. 95–117, 1976.

[5] F. E. Marble, “Growth of a diffusion flame in the field of a vortex,” Recent advances in aerospace sciences,pp. 395–413, 1985.

[6] M. G. Macareg, T. L. Jackson, and M. Y. Hussaini, “Ignition and structure of a laminar diffusion flame in thefield of a vortex,” Combustion science and technology, vol. 87, pp. 363–387, 1992.

[7] M. G. Macareg, T. L. Jackson, and M. Y. Hussaini, “Ignition dynamics of a laminar diffusion flame in the fieldof a vortex embedded in a shear flow,” Combustion science and technology, vol. 102, pp. 231–253, 1994.

[8] D. Thevenin and S. Candel, “Ignition dynamics of a diffusion flame rolled up in a vortex,” Physics of fluids,vol. 7, pp. 434–445, 1995.

[9] X. L. Zheng, J. Yuan, and C. K. Law, “Nonpremixed ignition of h2/air in a mixing layer with a vortex,” Proceed-ings of the combustion institute, vol. 30, pp. 415–421, 2004.

[10] E. Mastorakos, T. A. Baritaud, and T. J. Poinsot, “Numerical simulations of autoignition in turbulent mixingflows,” Combustion and flame, vol. 109, pp. 198–223, 1997.

[11] H. G. Im, J. H. Chen, and C. K. Law, “Ignition of hydrogen-air mixing layer in turbulent flows,” Sympo-sium(International) on combustion, 1998.

[12] R. Hilbert and D. Thevenin, “Autoignition of turbulent non-premixed flames investigated using direct numericalsimulations,” Combustion and flame, vol. 128, pp. 22–37, 2002.

[13] T. Echekki and J. H. Chen, “Direct numerical simulation of autoignition in nonhomogeneous hydrogen-air mix-tures,” Combustion and flame, vol. 134, pp. 169–191, 2003.

[14] H. Wang, X. You, A. Joshi, S. G. Davis, A. Laskin, F. Egolfopoulos, and C. K. Law, “High-temperature combus-tion reaction model of h2/co/c1-c4 compounds,” USC Mech Version II, 2007.

[15] E. Knudsen and H. Pitsch, “A general flamelet transformation useful for distinguishing between premixed andnon-premixed modes of combustion,” Combustion and Flame, vol. 156, pp. 678–696, 2009.

[16] H. Pitsch, “A C++ computer program for 0-D combustion and 1-D laminar flame calculations,” RWTH Aachen,1998.

[17] N. Peters, Turbulent Combustion, p. 219. Cambridge university press, 2000.

[18] T. Poinsot and S. Lele, “Boundary conditions for direct simulations of compressible reacting flows,” Journal ofComputational Physics, vol. 101, no. 1, pp. 104–129, 1992.

17

Documents

Investigation of ignition dynamics in a H2/air mixing ... · Investigation of ignition dynamics in a H2/air mixing layer with an embedded vortex ... and fuel/air temperatures on ignition