MCS 4 Lisbon, October 6-10 2005 MEASUREMENTS AND SIMULATIONS OF MIXING AND AUTOIGNITION OF AN N-HEPTANE PLUME IN A TURBULENT FLOW OF HEATED AIR C.N. Markides*, G. De Paola* and E. Mastorakos* [email protected]*Hopkinson Laboratory, Department of Engineering University of Cambridge, U.K. Abstract Autoignition of a gaseous n-heptane plume in heated turbulent air has been investigated experimentally and numerically with the Conditional Moment Closure and a CFD code. It has been demonstrated that, consistent with previous experimental results for hydrogen and acetylene, the increased scalar dissipation rate created by faster co-flow air delays autoignition, as revealed by a disproportionate increase of ignition length with air velocity. The predicted mean and variance of the mixture fraction, the mixture fraction PDF and the conditional scalar dissipation rate are in good agreement with experimental results obtained with acetone-tracer PLIF. The first-order, spatially-averaged CMC model reproduces the experimental trends quite well, despite the neglect of conditional fluctuations and spatial dependence of the conditional averages. This is attributed to the fact that for a significant period of time before autoignition the conditional scalar dissipation rate at the most reactive mixture fraction is much smaller than the critical value above which autoignition is precluded.
Transcript
MCS 4 Lisbon, October 6-10 2005
MEASUREMENTS AND SIMULATIONS OF MIXING AND AUTOIGNITION OF AN N-HEPTANE PLUME IN A TURBULENT FLOW OF HEATED AIR
Abstract Autoignition of a gaseous n-heptane plume in heated turbulent air has been investigated
experimentally and numerically with the Conditional Moment Closure and a CFD code. It has been demonstrated that, consistent with previous experimental results for hydrogen and acetylene, the increased scalar dissipation rate created by faster co-flow air delays autoignition, as revealed by a disproportionate increase of ignition length with air velocity. The predicted mean and variance of the mixture fraction, the mixture fraction PDF and the conditional scalar dissipation rate are in good agreement with experimental results obtained with acetone-tracer PLIF. The first-order, spatially-averaged CMC model reproduces the experimental trends quite well, despite the neglect of conditional fluctuations and spatial dependence of the conditional averages. This is attributed to the fact that for a significant period of time before autoignition the conditional scalar dissipation rate at the most reactive mixture fraction is much smaller than the critical value above which autoignition is precluded.
MCS 4 Lisbon, October 6-10 2005
MEASUREMENTS AND SIMULATIONS OF MIXING AND AUTOIGNITION OF AN N-HEPTANE PLUME IN A TURBULENT FLOW OF HEATED AIR
Abstract Autoignition of a gaseous n-heptane plume in heated turbulent air has been investigated
experimentally and numerically with the Conditional Moment Closure and a CFD code. It has been demonstrated that, consistent with previous experimental results for hydrogen and acetylene, the increased scalar dissipation rate created by faster co-flow air delays autoignition, as revealed by a disproportionate increase of ignition length with air velocity. The predicted mean and variance of the mixture fraction, the mixture fraction PDF and the conditional scalar dissipation rate are in good agreement with experimental results obtained with acetone-tracer PLIF. The first-order, spatially-averaged CMC model reproduces the experimental trends quite well, despite the neglect of conditional fluctuations and spatial dependence of the conditional averages. This is attributed to the fact that for a significant period of time before autoignition the conditional scalar dissipation rate at the most reactive mixture fraction is much smaller than the critical value above which autoignition is precluded. Introduction
Autoignition in a turbulent mixing flow is a problem of great fundamental importance and practical interest. The development of combustors for Homogeneous Charge Compression Ignition (HCCI) engines and Lean Premixed Pre-vaporized (LPP) gas turbines, in terms of improved efficiency and reduced emissions, can be significantly aided by an improved understanding and ability to predict the phenomenon of autoignition. In such applications, autoignition occurs in the presence of considerable fluctuations of velocity, composition and temperature, which cannot be neglected and whose effect must be understood. This problem becomes theoretically difficult, especially when the chemical and fluid-mechanical timescales are of the same order so that mixing has a direct effect on the pre-ignition reactions.
Experiments of inhomogeneous autoignition of nitrogen-diluted hydrogen in a turbulent co-flow of heated air in a pipe [1,2], performed in the same apparatus as the one used here, have shown that an increase in the mean air velocity leads to an increase in the mean residence time until autoignition, revealed by a non-linear increase of autoignition length from the injector with velocity. Together with the counterflow results of [3] for the same fuel, these findings suggest that increased turbulence levels (u') inflict a delaying effect on autoignition. These findings are in subtle contrast with Direct Numerical Simulations (DNS) [4] that have demonstrated, for simple chemistry, slightly earlier autoignition as u' increases. This was explained in terms of an acceleration of mixing leading to a greater probability of having low values of scalar dissipation rate (χ) at the most-reactive mixture fraction (ξMR). Whether this also occurs in the experiment is not clear.
In an attempt to extend our understanding of these phenomena, we have performed experiments of the autoignition of pre-vaporized n-heptane, but away from conditions for
which this fuel is known to exhibit complex chemical kinetic behaviour, i.e. a negative temperature coefficient. In addition, to assist interpretation of the data concerning ignition locations and the effect of turbulence on these, measurements of the mixture fraction and the scalar dissipation rate with acetone tracer Planar Laser Induced Fluorescence (PLIF) have also been performed. We also attempt to model this flow with a k-ε CFD code and the Conditional Moment Closure (CMC). First-order CMC has already been successfully applied to autoignition of a turbulent methane jet [5] and a liquid spray injection in a diesel-like chamber [6], showing good agreement in terms of autoignition delay time compared with experiments. Second-order closure was also investigated [7] with one step chemistry and a good comparison with DNS data was found. The important conclusions achieved in that work were that the fluctuations around the conditional temperature and around the scalar dissipation rate accelerate autoignition, especially in flows with high χ where a first-order closure may even fail to predict autoignition. However, the range of validity of a first-order closure is still not clear and in practical problems a full second-order closure can become computationally expensive. In the present paper, first-order CMC will be used to assess further its range of validity and in particular to give a better insight to the experimental results.
Experimental Methods
The experiment involves continuous, axi-symmetric injection of a gaseous fuel into a stream of pre-heated, turbulent co-flowing air, confined by a well-insulated, vertically positioned outer quartz tube (Figure 1). This arrangement has been used previously for similar measurements of autoignition location with hydrogen and acetylene [1,2]. The advantage of this experimental configuration is that it involves a relatively simple mixing pattern, a well-characterized, uniform turbulent air stream, which allows an estimate of a mean residence until autoignition, equivalent to an autoignition “delay time”, from the measurement of autoignition location.
Specifically, air was electrically pre-heated to Tair of 1100 to 1140K and flowed vertically upwards, through a grid with 3.0mm holes and 44% solidity and into a vacuum-insulated (‘jacketed’) fully transparent quartz tube (referred to as ‘tube’), with bulk velocities ranging between 10 and 20m/s. The ‘jacketed’ tube consisted of two concentric quartz pipes, sealed with a vacuum in the annular region between the two during the manufacture process. The inside tube had an inner diameter (DIN) of 24.8mm. The assembly was designed specifically to reduce heat losses and measurements of the mean temperature decay along the centreline with a fine (0.076mm) thermocouple showed that this quantity did not fall by more than 1.0 – 1.3K per 10mm at the Tair and Uair used in the experiments. The bulk air velocity (Uair) is defined as the averaged volumetric-flux, integrated over the annular clearance between the outer diameter of the injector tube and the tube inner wall. The tube exit was open to atmosphere.
A fuel injector tube (referred to as ‘injector’) with inner (d) and outer diameters 2.27 and 2.96mm respectively, was placed inside the tube, aligned along its centreline. The distance from the grid to the injector nozzle and hence the location of injection was 63 mm. For all experiments, nitrogen-diluted pre-vaporized n-heptane (C7H16) was used, with the mass fraction of C7H16 in the C7H16/N2 mixture (YC7H16) kept constant at 0.95. Averaged bulk velocities (Ufuel) based on the injector nozzle area ranged from 10 to 30m/s, with values for the non-dimensional velocity ratio υfuel=Ufuel/Uair of 1.05 to 1.20. Note that the υfuel≈1 conditions do not exhibit the strong mean shear associated with jet flows and are referred to as ‘equal velocity’. The nitrogen-diluted fuel was injected at temperatures (Tfuel) that were measured to be in the range 1020 to 1050K, with the difference between Tfuel and Tair within 70 to 100K.
Details concerning the operation of the burner, qualitative observations of autoignition phenomena that been achieved and the method of measurement taking can be found in [1,2]
for hydrogen and acetylene. For a certain range of Tair, Uair and Ufuel, individual autoignition events manifested in the form of localised ‘flashes’ accompanied by a ‘popping’ sound. Each event was associated with an ignition kernel that ignited successfully somewhere inside the tube downstream of the injector, propagated and quenched. Autoignition behaviour was statistically steady (both temporally and spatially) for a wide range of Tair, Uair and Ufuel. Random, consecutive autoignition events occurred continuously at a well defined mean frequency and location, each with its own history of local explosion, flame propagation and quenching. We refer to this regime as ‘Random Spots’ and such operation was attained with n-heptane in the experiments that are the subject of this paper.
The air and nitrogen flow rates were set with Bronkhorst Hi-Tec Mass Flow Controllers (MFC). A pre-calibrated peristaltic pump was used to supply n-heptane from a tank to a small electric liquid vaporizer with an integral K-Type thermocouple. The nitrogen supply was connected to the vaporizer in order to entrain and dilute the gaseous n-heptane. Both air and C7H16/N2 mixture temperatures were measured with thermocouples, 0.20mm R-Type and 0.25mm K-Type in diameter respectively, in the immediate vicinity of the injector and corrected for radiation and conduction losses. Figure 1 shows the approximate placement of the thermocouples. The indeterminate (random) error in Tair and Tfuel is ±4K, while that associated with the volumetric flow rates is ±1–2% for the MCFs. The mass flow error of the liquid pump was measured and found to be ±5%.
A Dantec constant temperature anemometer system and 5µm hot wire were calibrated, fine-tuned with square wave tests and used to inspect turbulence spectra by sampling at twice the Shannon-Nyquist frequency, mostly in the absence of, but in a few cases with flow from the injector. The power spectra showed that the air flow was turbulent, in the manner expected from the current geometry, i.e. downstream of a grid but also confined in the tube. No evidence of organized shear flow such as vortex shedding or separated regions was found. The Kolmogorov lengthscale was measured from the turbulent dissipation, i.e. from the variance of the spatial gradients of the velocity, assuming isotropic turbulence and found to be 0.1–0.2mm. An estimate of the integral lengthscale, Lurb, was obtained from Taylor’s hypothesis of frozen turbulence and the measured timescale. Finally, independent measurements for the local mean (U) and fluctuations (u') of the velocity field, were also obtained by setting a sampling interval of two measured integral timescales. Lturb, was found to be 3–4mm at the injector, i.e. of the order of the grid hole size, increasing by approximately 1mm in the first 40mm downstream. Some measurements were also made at high temperatures with a special Pitot tube and hot wire.
Planar Laser Induced Fluorescence (PLIF) measurements were undertaken to help clarify the effect of the turbulent flow field on the plume mixing downstream of the injector and to validate the CFD predictions. These experiments were performed at low temperatures, by passing the fuel stream through a ‘bubbler’-type seeder filled with a fluorescent tracer (acetone). Measurements of the local volumetric (or molar) concentration of the injected fluorescent-laden ‘fuel’ were suitably normalized to obtain the mixture fraction (ξ) field, from relatively close lengths to the injector nozzle to a downstream distance of about 30d. The two-dimensional scalar dissipation rate χ2D was calculated from the sum of the axial and radial gradients of the measured two-dimensional, planar ξ. The effects on the global mixing and dissipation fields, obtained by changes to the inlet dynamic conditions, described by a co-flow turbulent Reynolds number (Returb=u'Lturb/ν), with the inlet kinematic condition, or non-dimensional injection to co-flow velocity ratio, υfuel, kept constant and approximately equal to unity, were investigated. Because of the choice of υfuel≈1, the resulting mixing patterns were similar to diffusion downstream of a low-momentum release from a point source. Together with the 0.050–0.055mm pixel resolution, extensive tests for the determination of the laser sheet thickness (found to have a waist thickness of 0.17±0.03) and Modulation Transfer
Function (measured as 4 to 6 pixels for an 80–90% resolution of spatial detail) revealed that the measurement was able to resolve the smallest lengthscales in the flow, already measured with a hot wire and found to be ~0.2mm.
Autoignition was detected by chemiluminescence radiated from the reacting regions. A characteristic emission spectrum for n-heptane can be seen in Figure 1(ii). This measurement shows that chemiluminescence of the hydroxyl radical (OH*) is an excellent marker for the detection of autoignition in the conditions investigated here, because of the strong radiation attributed to the presence of this radical (c. 310nm) in regions of autoigniting gases. Motivated by this finding, direct OH* images were taken at 10 Hz with a LaVision NanoStar ICCD camera equipped with a UV-Lens and 307+/-10nm optical filter. In the resulting instantaneous images, the intensity signal at each pixel can be considered roughly proportional to the volume-averaged presence of OH* along the line-of-sight corresponding to the location of that pixel. The exposure time was set so as to ensure that (on average) the instantaneous images captured as much of the complete history of individual autoignition events, while keeping the number of autoignition spots per image to a minimum. A value of 5ms was chosen based on separate high speed observations [1,2].
The autoignition length (LIGN), specified as the axial distance from the injector to the autoigniting region, was determined by a variety of methods. Up to 200 non-zero images were generated per run (set of constant Tair, Tfuel, Uair and υfuel conditions) and a single average image was compiled. Two measures of LIGN are presented in this paper: (a) the minimum autoignition length, LMIN, based on a 3% rise in signal from the background relative to the peak intensity, and, (b) the ‘most likely’ autoignition location, LMODE, determined as the location of peak intensity. Due to flame propagation following autoignition, the instantaneous images also include contributions from post-ignition flamelets. However, an investigation with the high speed imaging system (Figure 2) revealed that the true mean location of autoignition lies between LMIN and LMODE and hence both lengths are used to provide lower and upper limits to the true autoignition length.
The υfuel≈1 (to within 20%) condition and the quick decay of the jet velocity to the co-flow value allowed for the mean residence time until autoignition, or autoignition delay time, τIGN, to be estimated from LIGN/Uair with little error. A more accurate estimation [2] introduces very small differences.
Modelling Approach
The Conditional Moment Closure is a conserved scalar based approach. It is motivated by the experimental evidence that fluctuations of the reactive scalars can be correlated with the fluctuations of a conserved scalar. Because the conditional fluctuations are often small, it is possible to close the chemical source term in the conditional average transport equation at the first conditional moment. This assumption has been relaxed in second-order CMC [7], but here we consider only first-order closure for simplicity. Decomposing the instantaneous species mass fraction in terms of conditional mean and its fluctuation [8], Yα(x,y)=Qα(ξ(x,t),x,t)+Y”(x,t) and Qα(η,x,t)=⟨Yα(x,t)|ξ(x,t)=η⟩, the following transport equations for conditional averages can be derived:
( ) ηη
ηηρηηρ
η αα
ααα w
QNPYu
xPxQ
ut
Qi
iii +
∂∂
+′′′′∂∂
−=∂∂
+∂∂
2
2
)(~)(~
1 (1)
where the first and the second term in the l.h.s. are the accumulation and the convection term respectively. In the r.h.s., the first term represents diffusion in physical space, the second diffusion in conserved scalar space, and the chemical source term is last. Further simplifications are also possible depending on the flow in question. For thin boundary-layer
flows, it is assumed that the conditional statistics vary little over the width of the flow and under the hypothesis of steady and parabolic flow the CMC equation can be simplified as:
ηη
ηη ααα w
QN
zQ
uz +∂
∂=
∂∂
2
2** (2)
where *ηzu and *ηN are values obtained with a cross-stream averaging operation [8]:
∫∫
∞
∞∗=
0
0
2)(
2)(
rdrP
rdrP
πη
πηηφηφ (3)
ηφ and P(η) are evaluated locally in the CFD cells and the integral is calculated across the flow. The P(η) is assumed to be a β-function. According to [8], the range of η at very small probability P(η), should not affect the solution of eq. (2) in high probability regions. A threshold at P(η)=10-10 has been defined, so that transport in physical and in η-space can be allowed only for larger values. A linear model is used for the conditional velocity while the Amplitude Mapping Closure (AMC) is employed to model the conditional scalar dissipation rate [8]. Its validation, for the present flow field, is discussed in the Results section.
A closure at first order has been used to evaluate the reaction rate. The non-linear source term was obtained using a reduced n-heptane mechanism developed by Bikas [9], also validated in [6]. Equation (4) has been discretized in mixture fraction space using central finite differences. A grid of 101 nodes clustered around the most reactive value (see later) has been used. The Method of Lines has been employed to build a set of Ordinary Differential Equations (ODEs) therefore integrating simultaneously diffusion and reaction in mixture fraction space without any decoupling [6,10]. The system of ODEs has then been implicitly integrated by the package VODPK [11]. The fluid mechanical quantities appearing in the CMC equations are updated at every timestep corresponding to a resolution equal to the CFD cell size in the axial direction (d/10) in order to have smooth changes in the calculated PDF.
As the reactions are slow before autoignition, the density changes in the flow field can be neglected allowing the assumption of frozen mixing and a decoupling between the CFD and the CMC solver. The flow and mixing field were predicted by the solution of a two dimensional axi-symmetric problem using the STAR-CD package. A standard high Reynolds number k-ε turbulence model has been used, with no modification in the values of the constants. Two extra transport equations for the mean and variance of mixture fraction have also been solved in order to reconstruct the presumed PDF. The inlet conditions for the air and the fuel stream were defined as polynomial fits from the measured values. Hence the mean velocity, turbulent intensity and integral length scale were prescribed. A turbulent Schmidt number of Sc=0.4 was used to establish a reasonable decay for the conserved scalar plume, as found from comparison with the experimental data. Despite the small difference in velocities between the fuel and the background air, a dense CFD grid with spacing d/20 was clustered around the axis to resolve the initial mixing adequately. The domain extends for 0.4m downstream (16DIN) so as to limit the influence of the outlet boundary in the case of autoignition at long lengths.
Results and Discussion
In this section, we first present results from the CFD for the flow and mixing fields at cold conditions and a comparison with experiments from the hot wire and acetone PLIF. Based on the reasonable agreement between the two, the mixing field during hot conditions was estimated numerically in a similar fashion. Following this, both experimental and numerical
results of autoignition are shown, in terms of the effects of the most important parameters such as Tair and Uair. The importance of the conditional scalar dissipation rate is highlighted.
Figure 3 shows measurements and predictions from the CFD for the velocity field. In Figure 3(i) we can see that the boundary layers were confined to regions close to the injector and the tube walls. Overall the predictions are reasonable, given the fact that close to the walls and downstream of the injector the accuracy of the hot wire measurements is reduced due to the higher local turbulence levels. Figure 3(ii) shows that the downstream axial decay of u' is captured accurately. The slight over-prediction near the wall of the tube is not expected to significantly influence the mixing patterns that are close to the injector (see Figure 4).
The computed mean mixture fraction contours under cold conditions (in which the acetone PLIF measurements were performed) are compared with the computed ones in Figure 4. Reasonable agreement in terms of plume length and thickness can be noticed. In more detail, a comparison between prediction and experiment along the centreline for mixture fraction, mixture fraction variance and mean scalar dissipation rate are shown in Figure 5(i-iii). The computed axial profiles match well with the experiment. Concerning the mixture fraction variance and dissipation, the maximum value close to the injector is accurately captured, although the computation tends to decay slightly slower than the experiment. A constant value of Cd=2 for the dissipation term in the variance equation in the CFD has been used. This value is in accordance with the one calculated from the experiments [12], where it was reasonably constant along the axial direction on the centreline and close to 2 for z>10d.
Finally, Figure 5(iv) shows a comparison between the conditional scalar dissipation rate compiled over different radial locations from the experiments at an axial location of 22mm with the conditional scalar dissipation calculated by PDF averaging using the AMC model. Apart from the scatter plots at relatively rich mixture fractions, where the number of the points compiled was not enough to reach statistical convergence, the hypothesis of radial independence for conditional statistics is well suited and the calculated scalar dissipation with the AMC agrees very well with the measurement.
Figure 6 contains the main results concerning the location of autoignition in the tube. Figure 6(i), on the left, presents measured and computed autoignition lengths as a function of inlet air temperature, Tair. Data groups belonging to the same conditions are connected by lines, with each line representing a different set of constant Uair, Yfuel and υfuel. Figure 6(ii), on the right, presents the same data, but in terms of the natural logarithm of the mean residence time until autoignition, ln(τIGN). Furthermore, the independent axis is now 1000/Tair, such that this figure can be considered an Arrhenius plot and its gradient an activation temperature, Tact. For a situation in which the mixing is not playing an active role in determining the delay time until autoignition, one would expect straight lines in this plot.
The effect of air temperature is directly evident from these plots. The experimental results show a decreasing trend for both LMIN and LMODE with increasing Tair. Because for each line of points Uair (and hence υfuel) is constant, as the temperature is increased (and 1000/Tair is decreased), τMIN and τMODE decrease monotonically, following the decrease in length. From the delay time plots of Figure 7, where it is apparent that the gradient is not constant, it is possible to conclude that the turbulent mixing is actively affecting the pre-ignition chemistry. At higher temperatures, autoignition occurs closer to the injector, where the local scalar dissipation rate is higher. At these locations, the effective activation temperature increases, reflecting a decelerating effect of the enhanced mixing on the chemistry. The computational predictions fall between LMIN and LMODE in terms of length and τMIN and τMODE in terms of delay time and reproduce the above salient points with respect to the air temperature. It is concluded that the present CMC model can make very reasonable predictions of the autoignition of the plume.
A closer look at Tair=1113K reveals that for the same Tair and an increase in Uair from 13.8m/s to 17.8m/s, autoignition is shifted non-linearly downstream, such that the autoignition delay time is increased. This is captured by both experiment and simulation and can be explained in terms of an increase in the scalar dissipation caused by the increase in u’ (that increases with Uair). For this particular case the influence of Tfuel has also been assessed: at high flow rate Tfuel decreases slightly due to the reduced heat transfer from the hot air, but the calculations show that the effect of fuel temperature is minor compared to the increase in velocity. Further discussion on the effect of χ on autoignition time is given next.
In mixture fraction space, autoignition occurs at the most reactive mixture fraction ξMR, which is by definition the location at which the reaction rate is a maximum and can be estimated as the value of η at which the conditional temperature has its maximum during the rise before autoignition. The location of ξMR depends on the chemistry, on the initial conditions in temperature, and the scalar dissipation rate, and it varies slightly with time. Figure 7 shows the evolution of the conditional temperature for the long and short ignition lengths and it is clear that the mixture fraction that eventually ignites is about ξMR=0.1 for both.
All other conditions being the same, as the conditional scalar dissipation rate at ξMR increases, the autoignition delay increases. Figure 8(i) shows this increase of the autoignition delay time versus the conditional scalar dissipation rate (parametrised by the maximum value at η=0.5) calculated with a stand-alone homogeneous CMC (i.e. equivalent to a flamelet model with unity Lewis number). A critical value, above which autoignition does not occur, is evident. Figure 8(ii) shows the evolution, along the axial direction, of the conditional scalar dissipation rate evaluated at ξMR for the same initial temperatures but different velocities. It is evident that the high velocity flow experiences a higher conditional scalar dissipation rate, which is higher than the critical value for a longer distance, than the low velocity flow. This explains fully why the high velocity plume autoignites later than the low velocity plume (Fig. 7ii). The fact that ⟨N|η=ξMR⟩ becomes lower than the critical value for a significant time before autoignition explains why first-order CMC, which is expected to be less accurate than second-order for autoignition [7], is adequate for this problem. The same comparison led to the same conclusion with an n-heptane spray in Ref. [6]. We expect that first-order CMC predictions for situations with low LIGN are less accurate than in situations where ignition happens farther downstream due to the high scalar dissipation rates relative to the critical value at low z. Second-order will offer an improvement in these situations.
A reference value for the autoignition delay, τref, can be defined as the autoignition delay for a homogeneous stagnant adiabatic mixture with initial composition and temperature corresponding to the frozen values of a mixture with ξMR and represents the minimum possible ignition time [4]. Values for τref at different conditions can be found in Table 1, where the data of Figure 6 are compared with additional calculations for the homogeneous autoignition delay time, τpremix, of the fully-premixed mixture asymptotically reached far from injection with the flow rates used in the experiments, which corresponds to a mixture fraction ξpremix about 0.01. The autoignition time from experiment and CMC is longer than τref, consistent with [4], which shows that mixing delays autoignition. τpremix is much longer, which shows that in autoignition of a bounded non-premixed flow the well-mixed equivalence ratio is an irrelevant quantity.
It is also worth to underline the effect that P(η) has on the autoignition location. Proceeding downstream from the injector, the P(η) passes from a bimodal shape to unimodal, to a δ-delta function if the flow mixes perfectly. According to the threshold defined in the previous paragraph on its lower limit, the region in η with finite probability will change moving along the axial direction. Solving the CMC equations in the interval defined by P(η), two conditions can be encountered depending whether ξMR has a finite probability or not in the domain of interest. In the first case, the autoignition is located at ξMR and the scalar
dissipation rate will determine the delay from τref. In the second case, the farther the η interval is from the nominal ξMR, the slower the reaction rate is and ignition will be further delayed. This argument supports the experimental observation that autoignition time may increase very quickly at operating conditions that shift autoignition downstream, to the point that suddenly no ignition spots are observed in the tube [2,12]. This is clearly the condition that LPP gas turbine designers should aim for to avoid autoignition.
Finally, the experimentally-determined LMIN/LMODE is about 50–60% and from Figure 2 it may be deduced that there is considerable spread of the true autoignition location. This can only be due to a real effect of the turbulent, mixing flow on the random nature of the emergence of autoignition. The CMC model reproduces only the average ignition location, but this is probably sufficient for most engineering purposes.
1138 1043 63.74 3.61 25.43 2.42 Table 1. CMC autoignition length, corresponding estimated autoignition delay time, autoignition delay time of a homogeneous premixed mixture, and autoignition delay time of a homogeneous mixture at ξMR. Conclusions
Autoignition of a gaseous n-heptane plume in heated turbulent air has been investigated experimentally and numerically with CMC. It has been demonstrated that, consistent with previous results for hydrogen and acetylene, the increased scalar dissipation rate created by faster background turbulence delays autoignition, as revealed by a disproportionate increase of ignition length with air velocity. The first-order, spatially-averaged CMC model reproduces the experimental trends quite well despite the neglect of conditional fluctuations and spatial dependence of the conditional averages.
References [1] Markides, C.N., and Mastorakos, E., Proc. European Combustion Meeting, Orléans,
France, October 2003, pp. 195-200. [2] Markides, C.N., and Mastorakos, E., Proc. Combust. Inst., 30(1):883-891 (2005). [3] Blouch, D., and Law, C.K., Combust. and Flame, 123(3):512-522 (2003). [4] Mastorakos, E., Baritaud, T.B., Poinsot, T.J., Combust. Flame, 109(1-2):198-223 (1997). [5] Kim, S.H., Huh, K.Y., Fraser, R.A., Proc. Combust. Inst., 28:185-191 (2000). [6] Wright, Y.M., De Paola, G., Boulouchos, K., Mastorakos, E., Combust. Flame
(submitted). [7] Mastorakos, E., and Bilger, R.W., Phys. Fluids, 10(6):1246-1248 (1998). [8] Klimenko, A.Y., and Bilger, R.W., Prog. Energy and Combust. Sci., 25:595-687,1999. [9] Bikas, G., Ph.D. Thesis, University of Aachen, 2001. [10] Kim, I.S. and Mastorakos, E., Proc. Combust. Inst., 30(1):911-918 (2005). [11] Brown, P.N., and Hindmarsh, A.C., J. Appl. Math. Comp., 31:40-91,1989. [12] Markides, C.N., Ph.D. Thesis, University of Cambridge, In preparation.
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rect
ed A
bsol
ute
Inte
nsity
(a.u
.) Low LIGNIntermediate LIGNHigh LIGN
OH*
CH* C2
*
NO*
Background
Decreasing ⟨ fIGN⟩ Increasing ⟨LIGN⟩
(i) (ii)
Figure 1. (i) Apparatus Schematic. Not to Scale. Mixing patterns are for illustration only. Geometry and measured variables are shown in bold font. (ii) Averaged emission
chemiluminescence spectra recorded during ‘Random Spots’ autoignition with n-Heptane.
-4 -2 0 2 4 60
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/σIGN
pdf(
L IGN)/p
df(L
IGN=L
MO
DE)
LTRUE
AutoignitionRegion
Reacting Region (Autoignition + Flame Propagation)
LMIN
⟨LTRUE⟩
LMODE
LIGN
Axial Direction
(Away fromthe Injector)
Figure 2. Normalized Probability Density Functions (PDFs) of true autoignition locations and
effect of flame propagation on measurement of LIGN.
Figure 3. Radial profiles of: (i) the mean and (ii) RMS axial velocity at z=2, 22 and 42mm from the injector from the experiment and the CFD at cold conditions.
Tair
Heptane Pump
AIR-MFC
N2-MFC
Electrical Heaters
Grid
Autoignition Length = Lign
Tfuel
Insulating Sheath
DIN/2
Autoignition
Injector d
Ufuel
Uair
Tube
Heptane Vaporizer
Figure 4. Mean mixture fraction field from the PLIF experiment and the CFD at cold
conditions.
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0.08
0.1
Axial Distance [mm]
Mix
ture
Fra
ctio
n V
aria
nce
[-]
CFDExperiment
(i) (ii)
0 10 20 30 40 50 60 70 80 900
5
10
15
20
25
Axial Distance [mm]
Scal
ar D
issi
patio
n R
ate
[s-1
]
CFDExperiment
0 0.2 0.4 0.6 0.8 1
0
2
4
6
8
10
12
14
16
Mixture Fraction [-]
Con
ditio
nal S
cala
r D
issi
patio
n R
ate
[s-1]
(iii) (iv)
Figure 5. Axial decay along the centreline of: (i) the mean and (ii) the variance of the mixture fraction and (iii) the mean (estimated) three-dimensional scalar dissipation rate.
(iv) Conditionally-averaged scalar dissipation at r=0.0 (circles), 0.7 (squares) and 1.5mm (diamonds) at z=22mm. The solid lines are the CFD predictions. Cold conditions.
-2 0 20
2
4
6
8
10
r/d (-)
z/d
(-)
1.0
0.8
0.6
0.4
0.2
0.0
CFDPLIF
1090 1100 1110 1120 1130 1140 11500
50
100
150
200
250
Aut
oign
ition
Len
gth
(mm
)
Tair (K)
OH LMODE: U=13.8,υ=1.05
OH LMIN: U=13.8,υ=1.05
LCMC : U=13.8,υ=1.05
OH LMODE: U=17.6,υ=1.20
OH LMIN: U=17.6,υ=1.05
LCMC : U=17.6,υ=1.20
0.875 0.88 0.885 0.89 0.895 0.9 0.905 0.91 0.915
0.5
1
1.5
2
2.5
3
3.5
4
ln(A
utoi
gniti
on T
ime)
(ms)
1000/Tair
(1/K)
OH τMODE: U=13.8,υ=1.05
OH τMIN: U=13.8,υ=1.05
τCMC: U=13.8,υ=1.05
OH τMODE: U=17.6,υ=1.05
OH τMIN: U=17.6,υ=1.05
τCMC: U=17.6,υ=1.05
(i) (ii)
Figure 6. (i) Minimum (LMIN) and Mode (LMODE) of autoignition length, as functions of Tair.
(ii) Natural logarithm of autoignition delay times, τMIN and τMODE, based on LMIN and LMODE, as functions of inverse Tair. Solid lines are the predictions from the CFD-CMC model.
0 0.2 0.4 0.6 0.8 11000
1100
1200
1300
1400
1500
1600
1700
1800
1900
Mixture Fraction [-]
Tem
pera
ture
[K]
0 0.2 0.4 0.6 0.8 11000
1100
1200
1300
1400
1500
1600
1700
1800
1900
Mixture Fraction [-]
Tem
pera
ture
[K]
(i) (ii)
Figure 7. Conditional temperature evolution at (i) Tair=1126K, Tfuel=1032K. (ii) Tair=1132K, Tfuel=1036K.
0 10 20 30 40 50 60 70 800
5
10
15
20
25
30
35
40
45
50
Max Conditional Scalar Dissipation Rate <N|η> [s-1]
Igni
tion
Del
ay T
ime
[ms]
0 20 40 60 80 1000
10
20
30
40
50
60
70
Axial Distance [m]
Con
ditio
nal S
cala
r D
issi
patio
n R
ate
at ξ
MR
17.64 m/s13.79 m/s
Autoignition limit <N|η=ξMR>
(i) (ii)
Figure 8. (i) τIGN from CMC as function of ⟨N|η=0.5⟩ with ⟨N|η⟩ calculated with the AMC model for Tair=1113K and Tfuel=1028K. (ii) ⟨N|η=ξMR⟩ axial evolution for low and high air
velocity. For both, Tair=1113K, while Tfuel=1028K and 1030K respectively. The scalar dissipation rate at the critical condition is also shown.
