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A numerical study of the autoignition of dimethyl ether with temperature inhomogeneities
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Proceedings of the
Proceedings of the Combustion Institute 34 (2013) 803–812
Combustion Institute www.elsevier.com/locate/proci
A numerical study of the autoignition of dimethyl ether with temperature inhomogeneities Haoyang Zhang a,⇑, Evatt R. Hawkes a,c, Jacqueline H. Chen b, Sanghoon Kook c a
School of Photovoltaic and Renewable Energy Engineering, The University of New South Wales, NSW 2052 Sydney, Australia b Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551, USA c School of Mechanical and Manufacturing Engineering, The University of New South Wales, NSW 2052 Sydney, Australia Available online 9 August 2012
Abstract The autoignition of dimethyl ether (DME) with temperature inhomogeneities is investigated by onedimensional numerical simulations with detailed chemistry at high pressure and a constant volume. The primary purpose of the study is to provide an understanding of the autoignition of DME in a simplified configuration that is relevant to homogeneous charge compression ignition (HCCI) engines. The ignition structure and the negative temperature coefficient (NTC) behaviour are characterised in a homogeneous domain and one-dimensional domains with thermal stratification, at different initial mean temperatures and length scales. The thermal stratification is shown to strongly affect the spatial structure and temporal progress of ignition. The importance of diffusion and conduction on the ignition progress is assessed. It is shown that the effects of molecular diffusion decay relative to those of chemical reaction as the length-scale increases. This is to be expected, however the present study shows that these characteristics also depend on the mean temperature due to NTC behaviour. For the range of conditions studied here, which encompass a range of stratification length scales expected in HCCI engines, the effects of molecular transport are found to be small compared with chemical reaction effects for mean temperatures within the NTC regime. This is in contrast to previous work with fuels with single-stage ignition behaviour where practically realisable temperature gradients can lead to molecular transport effects becoming important. In addition, thermal stratification is demonstrated to result in significant reductions of the pressure-rise rate (PRR), even for the present fuel with two-stage ignition and NTC behaviour. The reduction of PRR is however strongly dependent on the mean initial temperature. The stratification length-scale is also shown to have an important influence on the pressure oscillations, with large-amplitude oscillations possible for larger length scales typical of integral scales in HCCI engines. Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Autoignition; Dimethyl ether; Direct numerical simulation; Homogeneous charge compression ignition; Thermal stratification
⇑ Corresponding author. Fax: +61 02 9385 7762.
E-mail addresses: [email protected] (H. Zhang), [email protected] (H. Zhang). 1540-7489/$ - see front matter Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.proci.2012.07.026
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H. Zhang et al. / Proceedings of the Combustion Institute 34 (2013) 803–812
1. Introduction Homogeneous charge compression ignition (HCCI) engines have the potential to improve fuel-consumption economy relative to spark-ignition engines, to reduce particulate emissions relative to diesel engines and to reduce nitrogen oxides (NOx) relative to both spark-ignition and diesel engines [1]. However, difficulties of controlling the combustion timing and high integrated heat release rates, especially at high loads, pose serious challenges for practical applications [2]. Researchers have demonstrated that thermal and/or fuel mixture stratification can potentially reduce the heat release rate due to sequential rather than simultaneous combustion of the charge [3–7]. These characteristics are fuel-dependent. For example, Dec and Sjo¨berg [3] demonstrated that reduction of the pressure-rise rate (PRR) was possible by fuel stratification using primary reference fuels with two-stage ignition behaviour, but not with those having single-stage ignition. A key characteristic of all fuels in the HCCI context is their response to thermal stratification. Thermal stratification always occurs naturally in HCCI engines [8] due to wall-heat transfer and imperfect mixing with residuals. In previous studies [9–11], we investigated the response of hydrogen fuel ignition to thermal stratification. Hydrogen has single-stage ignition behaviour and no “negative temperature coefficient” (NTC) characteristics (i.e. there is a single, clearly defined ignition event with a timing that monotonically decreases with increasing temperature). It was found that thermal stratification had the potential to introduce a range of ignition delay times into the mixture, thus preventing the undesirable high PRR that would results from the simultaneous autoignition of the whole fuel charge. Furthermore, at large stratification length scales, the ignition behaved as a spontaneous ignition front which propagates into the unburned reactants without significant assistance from heat conduction or molecular diffusion. In contrast, at small stratification length scales, it was found that transport terms became important, and the combustion process came to resemble a conventional propagating premixed deflagration. This distinction between sequential ignition and deflagration, first discussed by Zel’dovich [12], is important because it has a strong bearing on the approach to modelling. In the former case, a simple well-mixed [13] or multi-zone [14] model should be sufficient while in the latter, modelling of the coupled behaviour of mixing and chemistry must be considered [15– 16]. Identification of different ignition regimes was further discussed by Gu et al. [17] and Bansal and Im [18]. Yoo et al. [19] investigated the effect of thermal stratification on the ignition of a lean n-heptane/air mixture using two-dimensional
direct numerical simulation (DNS). It was found that turbulent mixing can have important effects on controlling the ignition delay by reducing scalar fluctuations and dissipating heat and radicals from developing ignition kernels. However, the overall effects of turbulence during ignitions were comparatively less significant than those of thermal stratification, which is produced by turbulence prior to ignition. The qualitative trends observed for hydrogen should be similar for other fuels that do not exhibit NTC behaviour, albeit possibly modulated by the fuel Lewis number. However, there is a large class of practical fuels that exhibit NTC behaviour, that is, the ignition delay time is a nonmonotonic function of temperature. Such fuels have a range of temperatures in which the ignition delay time increases with increasing temperature. In this situation, it is not clear to what extent initial temperature gradients can lead to molecular transport and conduction becoming an important influence. Furthermore, it is not clear to what extent thermal stratification can be employed as a means to reduce problematic high PRR that is accompanied by ringing and knock [6]. This study aims to explore these questions. In the present study, numerical experiments of the autoignition of DME in a one-dimensional constant volume domain at high pressure with temperature nonuniformities were performed. Numerical simulations were used to investigate, in a simplified setting, the combustion process in an environment analogous to the core fluid of a HCCI engine cylinder at top dead centre. Dimethyl ether (DME) was chosen for study because it is perhaps the simplest molecule of potential future importance as a fuel that exhibits two-stage ignition and NTC behaviour, and a computationally tractable chemical kinetic mechanism exists. In this article, homogeneous simulations (0-D) are first presented to characterize the autoignition behaviour of DME. One-dimensional simulations (1-D) are then examined to investigate the effects of thermal stratification and molecular diffusion on the ignition and the propensity for development of large-amplitude pressure waves (ringing). The present work highlights the importance of both the stratification length-scale and the mean temperature on the results. 2. Configuration The DNS code S3D was employed [20]. The code solves the compressible equations for continuity, momentum, total internal energy, and species partial densities. In order to deal with chemical stiffness that inevitably arises in large chemical kinetic schemes, an implicitly additive Runge–Kutta time integration method [21] was used in which the chemical reaction rates are
H. Zhang et al. / Proceedings of the Combustion Institute 34 (2013) 803–812
3. 0-D homogeneous cases For basic orientation that will inform the discussion of the stratified cases, spatially homogeneous cases are first considered. Figure 1 shows the ignition delay time as a function of the initial temperature for the 0-D cases. It can be observed that between 840 and 1000 K the ignition mechanism leads to increased ignition delay time with increasing initial temperature. This is the so-called NTC regime. Five initial mean temperatures were selected for the 1-D studies. Three temperatures are within the NTC regime, i.e. T0 = 840, 925, and 1000 K; two temperatures are outside NTC regime, i.e. T0 = 788.5 and 1050.4 K, but with a homogeneous ignition delay time identical to T0 = 925 K. Figure 2 shows the temporal evolutions of the temperature for homogeneous autoignition at various initial temperatures. DME demonstrates expected two-stage ignition characteristics for T0 < 1000 K: after an initial induction the temperature rapidly increases (low-temperature heat release), which is then followed by another induction period in which temperature only gradually increases, until eventually the mixture goes into thermal runaway corresponding to the high-temperature kinetic pathways. It may be also seen that the first-stage ignition is advanced with initial temperature, indicating the low temperature combustion occurs earlier. From T0 = 788.5 to 840 K the main ignition
1.2
Ignition delay time (ms)
implicitly integrated via a Newton method and the other terms are advanced explicitly. The time-step size was controlled adaptively according to the estimated solution error [21]. Spatial derivatives were approximated with an eighth order accurate spatial finite differencing scheme [22]. Thermodynamic properties were considered in NASA polynomial format [23]. A detailed DME chemical mechanism with 55 species and 290 reversible reactions was employed [24]with a mixture-averaged molecular transport model [25]. Turbulence was not explicitly considered: it was assumed that its role is simply to establish stratification with a characteristic gradient, which is a parameter varied in the study. Previous studies including turbulence [9–10,19] have demonstrated the usefulness of studying one-dimensional ignitions as a tool to understand the more complex turbulent situation. The 1-D cases considered an initially sinusoidal temperature profile upon which periodic boundary conditions were imposed. The periodicity enforced a fixed volume which allowed compression heating and pressure-rise of the reactants due to the ignition [9].The length-scale (size of domain) of the constant volume represented the wavelength of the temperature fluctuation. The amplitude of the temperature fluctuation (T0 ) was fixed to give a root-mean-square (RMS) value of 50 K for all cases. This corresponds to an upper limit of what might be expected in a typical HCCI engine without the deliberate introduction of stratification [26–27]. The equivalence ratio of 0.45 was uniform throughout the domain and a mean pressure of 40 atm was considered. Parametric studies were conducted by varying the mean temperature (T0) to traverse the NTC regime, and by varying the length-scale (L) of the stratification (at fixed mean temperature). In order to resolve some very thin reaction layers the resolution requirements were generally high. Different resolutions were ultimately required depending on the temperature and length-scale considered. The final resolutions were determined by increasing the grid number until the solution did not appreciably change. There was a minimum of 20 grid points across the main reaction layers in all cases. The parameters studied and the resolutions used to cover one complete wavelength in each case are noted in Table 1.
805
1
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0.8
925 K 0.6
1000 K 840 K
0.4
0.2
1050.4 K
T0= 788.5 K
700
800
900
1000
1100
Temperature (K)
Fig. 1. Homogeneous ignition delay time as a function of the initial temperatures.
Table 1 Simulation parameters in the present study. Number of grid points in the 1-D domain Lengthscale Initial mean temperature
788.5 K 840 K 925 K 1000 K 1050.4 K
0.5 mm
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Temperature (K)
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Fig. 2. Temperature as a function of time at various initial temperatures for 0-D cases.
advances, however, fromT0 = 840 to 1000 K the main ignition is retarded, indicating NTC behaviour. At T0 = 1000 K, the first-stage ignition disappears indicating the return to conventional high-temperature pathways and single-stage ignition occurs, and T0 = 1050.4 K again ignites earlier than T0 = 1000 K. These observations are consistent with previous discussions of DME kinetics [24,28]. According to Ref. [28], the DME consumption pathway in the low-temperature regime primarily involves decomposition of hydro-peroxy-methyl-formate, leading to chain branching with the formation of two hydroxyl radicals. However, as the temperature increases, the reaction pathway trends towards the b-scission of the hydroperoxy-methoxymethyl radical, resulting in the reduction of overall reactivity due to the formation of stable formaldehyde and only one hydroxyl radical, leading to NTC behaviour [28]. At high initial temperatures, above 1000 K, high-temperature kinetic routes become active, undergoing the unimolecular decomposition of the DME and the b-scission of the methoxymethyl radical [24]. Further discussion of the chemical kinetics can be found in Refs. [24,28]. 4. 1-D thermally stratified cases
Figure 3 shows temperature versus distance for several instants at T0 = 788.5 K and L = 4 mm (the times are given in the caption). The initial temperature distribution at L = 4 mm was imposed with colder outer boundary at x = 0 mm and x = 4 mm with 50 K RMS. Two-stage ignition can be observed: ignition occurs initially at the hottest region, at the centre of the domain, and then an ignition front propagates towards the left and right boundaries to consume the remaining fuel. Within the NTC region (T0 = 840 to 1000 K) the combustion behaviour is qualitatively different. Figure 4 shows the temperature as a function of distance for sequential times at T0 = 925 K and L = 4 mm. The combustion event still occurs in two stages, and NTC behaviour is observed. The fuel ignites firstly at the colder regions at the boundaries (compare times 1 and 2 in Fig. 4), not at the central region where the local temperature is higher, due to the NTC behaviour. Subsequently ignition begins to occur throughout the domain, with the final point to ignite being the initially hottest region. Accordingly, it may be summarised that the initial temperatures which would have the identical homogeneous ignition delay time showed totally different spatial dependence of the ignition structures in stratified conditions due to the temperature inhomogeneities and the NTC behaviour. For T0 at transition points (the start and end of the NTC region, T0 = 840 K and T0 = 1000 K, respectively) ignition events could be even more complex, since different types of ignition behaviour would occur in the same domain. For example, at T0 = 1000 K, a half portion of the 2450
2100
9
Temperature (K)
806
9 8
8
1750
7
7 6
1400
5 4 3 2 1
1050
4.1. Structure of the ignitions In the 1-D cases where the initial temperature distribution was spatially inhomogeneous, a range of ignition delay times were introduced into the domain, leading to different ignition behaviours. To highlight these differences, the spatial and temporal structures of ignition at three initial mean temperatures with the same homogeneous ignition delay are compared.
6
700
0
1
2
3
4
x (mm)
Fig. 3. Temporal evolution of the temperature at T0 = 788.5 K and L = 4 mm for the 1-D case. Time sequence: No.1 = 0.100 ms, No.2 = 0.200 ms, No.3 = 0.450 ms, No.4 = 0.550 ms, No.5 = 0.575 ms, No.6 = 0.600 ms, No.7 = 0.625 ms, No.8 = 0.800 ms, and No.9 = 1.000 ms, respectively.
H. Zhang et al. / Proceedings of the Combustion Institute 34 (2013) 803–812
To conclude, the spatial and temporal structure of DME ignition strongly depends on the initial mean temperature, especially whether it falls inside or outside the NTC regime. These different structures should have a bearing on the importance of molecular diffusion on the overall ignition development, as well as on the propensity towards development of high-amplitude pressure waves and ringing.
2400
9 8
Temperature (K)
2000
7
7
1600
6
6
5
807
5
4.2. Importance of molecular diffusion
1200
4
4
3
3 2
800
2
1
0
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2
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4
x (mm)
Fig. 4. Temporal evolution of the temperature at T0 = 925 K and L = 4 mm for the 1-D case. Time sequence: No.1 = 0.100 ms, No.2 = 0.200 ms, No.3 = 0.500 ms, No.4 = 0.575 ms, No.5 = 0.600 ms, No.6 = 0.610 ms, No.7 = 0.620 ms, No.8 = 0.625 ms, and No.9 = 1.000 ms, respectively.
domain in the central area has a local temperature higher than the mean, leading to only single-stage ignition; while the boundary areas have local temperatures less than the mean (with the NTC regime), resulting in the two-stage ignition and NTC behaviour. This is indeed observed in Fig. 5, showing the development of the spatial structure of the ignition for T0 = 1000 K. The spatial temperature histories at T0 = 840 and 1050.4 K (both at L = 4 mm) are given in Supplementary Data [29].
10 2400
7 6 5
10
Temperature (K)
9
10 9
2100
8
8
1800
7
7 4
1500
6
6 3 2 1
1200
900
0
1
2
3
4
x (mm)
Fig. 5. Temporal evolution of the temperature at T0 = 1000 K and L = 4 mm for the 1-D case. Time sequence: No.1 = 0.100 ms, No.2 = 0.400 ms, No.3 = 0.500 ms, No.4 = 0.550 ms, No.5 = 0.570 ms, No.6 = 0.610 ms, No.7 = 0.620 ms, No.8 = 0.625 ms, No.9 = 0.628 ms, and No.10 = 0.700 ms, respectively.
To identify the roles of molecular diffusion, the contributions of mass diffusion and reaction to the net rate of change of the species mass fractions were compared at various length scales. The hydroxyl radical was selected for comparison, since it is an important radical both in high-temperature chain-branching and also plays a role in low-temperature kinetics. The evolution of the hydroxyl radical mass fraction YOH is given by [9] DY OH 1 @J OH ¼ ð1Þ þ x_ OH ; q @xi Dt where the first and second term in the bracket on the right-hand side represents the rate of change of species partial density due to molecular diffusion, and that due to chemical reaction, respectively. The flux due to molecular diffusion [19], is denoted as JOH, x_ is the reaction rate, and q is the density. Figure 6a and b shows the spatial dependence of the chemical reaction rate for the OH radical partial density and also its diffusion rate for different times at T0 = 788.5 K on the two length scales L = 0.5 mm and L = 4 mm, respectively. It can be seen that diffusion does not play a significant role at L = 4 mm, but becomes significant at L = 0.5 mm. This result is similar to previous findings with hydrogen fuel [10]. In addition, L = 4 mm tends to ignite earlier due to having lower scalar dissipation, compared to L = 0.5 mm; but ignition at L = 0.5 mm tends to complete quicker due to diffusive gains. Figure 7 shows the same data, except now with T0 = 925 K, which is within the NTC region. As may be observed, diffusion is always negligible relative to reaction, indicating a pure spontaneously propagating ignition front [9–10,12]. Figure 8 shows the result for T0 = 1050.4 K, once more outside the NTC regime. Diffusion once again can play a significant role, comparable to that of reaction at L = 0.5 mm. To further condense the information regarding the importance of molecular diffusion, we calculated the maximum within the computational domain of the absolute values of the source term for the species partial density due to molecular diffusion and that due to chemical reaction. The ratio of these two quantities was formed and named henceforth as the “diffusion-to-reaction
H. Zhang et al. / Proceedings of the Combustion Institute 34 (2013) 803–812
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(b). L = 4 mm Rate of OH partial density (kg/s-m )
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x (mm)
(b). L = 4 mm 2500
4
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x (mm)
3
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(a). L = 0.5 mm 25000
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3
Rate of OH partial density (kg/s-m )
(a). L = 0.5 mm 3600
Rate of OH partial density (kg/s-m )
808
6
6
5
10000
5000 5
5 2
0
2
5
5 6
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0
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x (mm)
Fig. 6. Comparison of the chemical reaction rate and diffusion rate at T0 = 788.5 K on length-scale (a). L = 0.5 mm and (b). L = 4 mm. Time sequence: No.1 = 0.600 ms, No.2 = 0.606 ms, No.3 = 0.625 ms, No.4 = 0.650 ms, No.5 = 0.680 ms, and No.6 = 0.800 ms, respectively.
Fig. 7. Comparison of the chemical reaction rate and diffusion rate at T0 = 925 K on length-scale (a). L = 0.5 mm and (b). L = 4 mm. Time sequence: No.1 = 0.613 ms, No.2 = 0.614 ms, No.3 = 0.615 ms, No.4 = 0.617 ms, No.5 = 0.619 ms, and No.6 = 0.624 ms, respectively.
ratio”. Subsequently, the maximum value of this ratio over the main ignition event was calculated so that effects of mean temperature and lengthscale could be easily compared. The results are shown in Fig. 9. It can be observed that the effects of molecular diffusion uniformly tend to decay with an increase of the length-scale, as expected. Moreover, the cases with two-stage ignition behaviour and inside the NTC regime (i.e. T0 = 840 K and T0 = 925 K) exhibit much less diffusion and lower sensitivity to length-scale than the other cases. At T0 = 925 K, the local temperature gradient became rather small and homogeneity was actually increased relative to the initial condition after the first-stage ignition due to NTC behaviour, as may be observed in Fig. 4 comparing time 1–3. As a result, a more homogeneous second-stage ignition (high-temperature ignition) occurred rapidly, leading to considerably lower diffusion. At T0 = 1000 K, although this initial temperature was located partly inside the
NTC region (at the boundaries), rapid single-stage ignition in the central area outside of the NTC region still caused relatively high diffusion. Hence, diffusive effects became significant at smaller length scales. Diffusion was most significant for the two cases that were entirely outside of the NTC regime (i.e. T0 = 788.5 K and T0 = 1050.4 K). Similar results were also found considering a number of other different chemical species. Note that the temperature fluctuation T0 = 50 K used in the present study is higher than expected in practical HCCI engines, where thermal stratifications prior to igntionare approximately 15–20 K [7]. The measured integral length scales in practical HCCI engines are typically larger than 2 mm [30–31]. Hence, the smaller length scales in the present study (0.5 and 1 mm) where molecular diffusion appears significant might not exist in practical HCCI environments. Furthermore, additional 1-D cases, with identical conditions at corresponding T0 and length-scale
H. Zhang et al. / Proceedings of the Combustion Institute 34 (2013) 803–812 Reaction Diffusion 6 7
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7
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5
(b). L = 4 mm
45
6
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2
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Length Scale (mm)
Fig. 9. Comparison of maximum diffusion-to-reaction ratio of OH radical at various initial temperatures and length scales for the 1-D cases.
1
12000 9000 6000 3000 0 -3000
0
1
2
3
4
x (mm)
Fig. 8. Comparison of the chemical reaction rate and diffusion rate at T0 = 1050.4 K on length-scale (a). L = 0.5 mm and (b). L = 4 mm. Time sequence: No.1 = 0.365 ms, No.2 = 0.400 ms, No.3 = 0.420 ms, No.4 = 0.430 ms, No.5 = 0.450 ms, No.6 = 0.480 ms, and No.7 = 0.490 ms, respectively.
but the transport coefficients (i.e. thermal conductivity, diffusivity and viscosity) being intentionally reduced by a factor of 10, were examined to determine the effect of diffusion under thermal stratification. It was found that the temperature evolutions of original cases appeared similar to those of the cases with 10 times less diffusion, indicating that diffusion indeed played a minor role. The results are given in Supplementary Data [29].Thus, overall, at the studied conditions, the effect of diffusion induced by thermal stratification is not expected to be significant relative to chemical reaction during the combustion event for ignitions occurring within the NTC regime, but could be significant for ignitions outside of it if temperature gradients are in the range of 25–100 K/mm. 4.3. Effects on the pressure-rise rate The spatial structure of the ignition can have a strong bearing on the overall pressure-rise rate
(PRR), which if too great can lead to ringing and knock, e.g. [26–27]. Previous studies [3–5,13,18–19] demonstrated that thermal stratification can greatly reduce PRR for single-stage ignition fuels but there has been little discussion for two-stage ignition fuels. The maximum PRR of the mean pressure over the time-span of the ignition event at various T0 and length scales are compared in Fig. 10, where the values have been normalised by the maximum PRR in the corresponding homogeneous cases. It is evident that thermal stratification significantly reduces the maximum PRR relative to the homogeneous ignition for DME ignition, even within
1
Normalised pressur−rise rate
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Rate of OH partial density (kg/s-m )
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Rate of OH partial density (kg/s-m )
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Fig. 10. Comparison of maximum pressure-rise rate at various initial temperatures and length scales for the 1-D cases, normalised by the maximum pressure-rise rate in the corresponding homogeneous cases. Inner plot shows the comparison of temporal evolutions of normalised pressure-rise at T0 = 1000 K for 0-D homogeneous case, L = 0.5 mm, and L = 4 mm, respectively.
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H. Zhang et al. / Proceedings of the Combustion Institute 34 (2013) 803–812
the NTC regime. Importantly, however, the reduction of PRR is observed to be dependent on T0. The greatest potential for reduction occurs for the cases completely outside the NTC regime, i.e. T0 = 788.5 K and T0 = 1050.4 K due to a relatively inhomogeneous ignition event as discussed in Section 4.1, and the potential for reduction is least at T0 = 925 K due to a relatively homogeneous ignition event. For T0 = 788.5 K, T0 = 840 K and T0 = 1050.5 K, PRR may be observed to increase as the lengthscale is increased. At T0 = 1000 K, PRR increases as L increases from 0.5 to 1 mm, and thereafter decreases with L. At T0 = 925 K, a non-monotonic trend with length-scale may be also noted. Decreasing PRR with increasing L may be noted from L = 0.5 mm to L = 4 mm, with increasing PRR from L = 4 mm to L = 8 mm. As discussed by Zel’dovich [12] the speed of a spontaneous ignition front sig is given by sig ¼
1 1 ¼ ; jrsj ds jrT j 0 dT 0
ð2Þ
where s is the ignition delay time. If sig is sufficiently large and comparable to the speed of sound, the combustion wave can become coupled to the acoustic wave, leading to rapid pressure-rise and in some circumstances a detonation [12,20]. In the present situation, s is approximately a function of initial temperature, as such, sig can become large if either ds/dT0 or the temperature gradient becomes small. The latter may contribute to the trend of significantly larger pressure oscillation for the increasing length-scale for T0 = 788.5 K, T0 = 840 K and T0 = 1050.4 K. The former may contribute to the trend of larger PRR for the mean temperatures inside the NTC regime (i.e. the cases of T0 = 840, 925 and 1000 K compared with the cases of T0 = 788.5 and 1050.4 K).
Maximum amplitude of pressure fluctuations (atm)
14
788.5 K 840 K 925 K
12 10 8 6 4 2 0 0.5
1
2
4
8
Length scale (mm)
Fig. 11. Maximum amplitude of pressure fluctuations at various length scales for two-stage ignition events.
Figure 11 shows the amplitude of pressure fluctuations, defined as half the difference of the maximum and minimum pressures in the domain, after the ignition event is completed (focusing on two-stage ignition only). The fluctuations are plotted versus length-scale for different T0. Two main points may be noted. First, the pressure fluctuation increases with length-scale. This was consistent with the arguments above considering the coalescence of acoustic and combustion waves due to large ignition front speeds arising from lower temperature gradients. Second, the amplitude of the pressure fluctuations are also dependent on T0. The largest fluctuations are observed at T0 = 925 K, in the middle of the NTC regime. In comparison, at T0 = 840 K, the fluctuations are lower, and at T0 = 788.5 K lower still. This is consistent with the PRR trends and may be readily explained considering the lower ds/dT0 at T0 = 840 K compared with T0 = 788.5 K. 5. Conclusions One-dimensional numerical simulations of DME autoignition were performed to understand the influence of thermal stratification on ignition inside and outside of the negative-temperature coefficient regime. Stratified ignitions were observed to proceed differently from the corresponding homogeneous ignition. Importantly, the spatial and temporal structure of the ignition was found to strongly depend on whether the mean initial temperature was inside or outside the NTC region, a behaviour which is qualitatively different from fuels with a single-stage ignition and no NTC behaviour. Thermal stratification was found to affect both the reaction–diffusion balance in the ignition, as well as the maximum rates of pressure-rise and the amplitude of pressure fluctuations. The relative importance of molecular diffusion and chemical reaction was found to change significantly with the mean temperature, behaviour not observed for fuels without NTC behaviour. Diffusion became relatively less significant for the cases with two-stage ignition and fully inside the NTC regime compared to the other cases outside the regime. As the length-scale was increased, diffusion eventually became negligible in all cases. Based on the present study and previous measurements of in-cylinder temperature fluctuations [7,30], we expect that in practical HCCI engines, diffusion due to initial thermal stratification is not an important influence on the ignition evolution for initial mean temperatures in the NTC regime (for the fuel mixture considered). Diffusion could still be important outside of this regime if pre-ignition temperature gradients are in the range of 25– 100 K/mm. The observed effects are expected to
H. Zhang et al. / Proceedings of the Combustion Institute 34 (2013) 803–812
be modulated somewhat by the kinetics of the specific fuel, but qualitatively it is possible to project that a greater ds/dT0 will lead to a greater importance of diffusion effects of the ignition. In the modelling strategy, the reduced importance of molecular diffusion within the NTC regime suggests that simple multi-zone modelling, which neglects the effects of molecular diffusion [4,10,14] may be sufficient to capture effects of thermal stratification on ignition within that regime, and more detailed modelling is not necessary [15,16]. Note that mixture stratification is another matter entirely but out of the scope of the present study. Turbulence is another effect that can potentially have an influence. The main effect of turbulence in HCCI is to set up the thermal field prior to ignition, but persistent straining during ignition could also lead to an increased importance of molecular diffusion effects. Further work is needed to assess effects of turbulence. It was also demonstrated that thermal stratification can significantly reduce PRR, even for the present fuel with a two-stage ignition and NTC behaviour. However, the reduction of PRR was very dependent on T0. The greatest potential for reduction was found for the cases completely outside the NTC regime due to a more inhomogeneous ignition event. It was found across all of the considered mean temperatures that an increased stratification length-scale led to increased amplitude of pressure fluctuations, which in practical engines would be observed as undesirable ringing. The amplitude of these fluctuations was found to depend on mean temperature, with the largest amplitude again observed for the conditions fully inside the NTC regime. Thus qualitatively, it is anticipated that larger PRR and pressure fluctuations can result from either lower ds/dT0 or large stratification length scales. The latter effect, however, can implicate coupled physics of compressible flow and combustion which can lead to counter-intuitive trends as mean temperature is varied. Acknowledgments This work was supported by the Australian Research Council under Grant numbers DP110104763 and FT100100536. In addition, this research benefited from the resources of the National Computational Infrastructure, Australia.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http:// dx.doi.org/10.1016/j.proci.2012.07.026.
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References [1] F. Zhao, T.W. Asmus, D.N. Assanis, J.E. Dec, J.A. Eng, P.M. Najt (Eds.), Homogeneous charge compression ignition (HCCI) engines: Key Research and Development Issues, Society of Automotive Engineers, Warrendale, PA, 2003. [2] A. Hultqvist, M. Christensen, B. Johansson, A. Franke, M. Richter, M. Alde´n, SAE Technical Paper 1999-01-3680, 1999. [3] M. Sjo¨berg, J.E. Dec, SAE Technical Paper 200501-2125, 2005. [4] M. Sjo¨berg, J.E. Dec, A. Babajimopoulos, D. Assanis, SAE Technical Paper 2004-01-2994, 2004. [5] M. Sjo¨berg, J.E. Dec, N.P. Cernansky, SAE Technical Paper 2005-01-0113, 2005. [6] J.E. Dec, W. Hwang, M. Sjo¨berg, SAE Technical Paper 2006-01-1518, 2006. [7] W. Hwang, J.E. Dec, M. Sjo¨berg, SAE Technical Paper 2007-01-4130, 2007. [8] J.E. Dec, Proc. Combust. Inst. 32 (2) (2009) 2727– 2742. [9] J.H. Chen, E.R. Hawkes, R. Sankaran, S.D. Mason, H.G. Im, Combust. Flame 145 (1–2) (2006) 128–144. [10] E.R. Hawkes, R. Sankaran, P.P. Pe´bay, J.H. Chen, Combust. Flame 145 (1–2) (2006) 145–159. [11] R. Sankaran, H.G. Im, E.R. Hawkes, J.H. Chen, Proc. Combust. Inst. 30 (1) (2005) 875–882. [12] Ya.B. Zel’dovich, Combust. Flame 39 (1980) 211– 214. [13] T. Joelsson, X.S. Bai, A. Vressner, B. Johansson, SAE Technical Paper 2008-01-1668, 2008. [14] S.M. Aceves, D.L. Flowers, C.K. Westbrook, et al., SAE Technical Paper 2000-01-0327, 2000. [15] D.J. Cook, H. Pitsch, J.H. Chen, E.R. Hawkes, Proc. Combust. Inst. 31 (2007) 2903–2911. [16] F. Bisetti, J.Y. Chen, J.H. Chen, E.R. Hawkes, Proc. Combust. Inst. 32 (2009) 1465–1472. [17] X.J. Gu, D.R. Emerson, D. Bradley, Combust. Flame 133 (2003) 63–74. [18] G. Bansal, H.G. Im, Combust. Flame 158 (2011) 2105–2112. [19] C.S. Yoo, T. Lu, J.H. Chen, C.K. Law, Combust. Flame 158 (2011) 1727–1741. [20] J.H. Chen, A. Choudhary, B. de Supinski, et al., Comput. Sci. & Disc. 2 (2009) 015001. [21] C.A. Kennedy, M.H. Carpenter, R.M. Lewis, Appl. Numer. Math. 35 (3) (2000) 177–219. [22] C.A. Kennedy, M.H. Carpenter, Appl. Numer. Math. 14 (4) (1994) 397–433. [23] R. Kee, F. Rupley, E. Meeks, J. Miller, CHEMKIN-III: A FORTRAN chemical kinetics package for the analysis of gas-phase chemical and plasma kinetics, Report No. SAND96-8216, Sandia National Laboratories, 1996. [24] Z. Zhao, M. Chaos, A. Kazakov, F. Dryer, Int. J. Chem. Kinet. 40 (1) (2007) 1–18. [25] R.J. Kee, G. Dixon-Lewis, J. Warnatz, M.E. Coltrin, J.A. Miller, A Fortran computer code package for the evaluation of gas-phase multicomponent transport properties, Report No. SAND868246, Sandia National Laboratories, 1986. [26] M. Sjo¨berg, J.E. Dec, SAE Technical Paper 200801-0054, 2008. [27] M. Sjo¨berg, J.E. Dec, SAE Technical Paper 200901-0666, 2009.
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[28] H. Curran, S. Fischer, F. Dryer, Int. J. Chem. Kinet. 32 (12) (2000) 741–759. [29] H. Zhang, E.R. Hawkes, J.H. Chen, S. Kook, Proc. Combust. Inst. 34 (2012).
[30] P. Miles, M. Megerle, Z. Nagel, R.D. Reitz, M.D. Lai, V. Sick, SAE Technical Paper 2003-01-1072, 2003. [31] D. Heim, J. Ghandhi, SAE Technical Paper 201101-1287, 2011.
Proceedings of the
Proceedings of the Combustion Institute 34 (2013) 803–812
Combustion Institute www.elsevier.com/locate/proci
A numerical study of the autoignition of dimethyl ether with temperature inhomogeneities Haoyang Zhang a,⇑, Evatt R. Hawkes a,c, Jacqueline H. Chen b, Sanghoon Kook c a
School of Photovoltaic and Renewable Energy Engineering, The University of New South Wales, NSW 2052 Sydney, Australia b Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551, USA c School of Mechanical and Manufacturing Engineering, The University of New South Wales, NSW 2052 Sydney, Australia Available online 9 August 2012
Abstract The autoignition of dimethyl ether (DME) with temperature inhomogeneities is investigated by onedimensional numerical simulations with detailed chemistry at high pressure and a constant volume. The primary purpose of the study is to provide an understanding of the autoignition of DME in a simplified configuration that is relevant to homogeneous charge compression ignition (HCCI) engines. The ignition structure and the negative temperature coefficient (NTC) behaviour are characterised in a homogeneous domain and one-dimensional domains with thermal stratification, at different initial mean temperatures and length scales. The thermal stratification is shown to strongly affect the spatial structure and temporal progress of ignition. The importance of diffusion and conduction on the ignition progress is assessed. It is shown that the effects of molecular diffusion decay relative to those of chemical reaction as the length-scale increases. This is to be expected, however the present study shows that these characteristics also depend on the mean temperature due to NTC behaviour. For the range of conditions studied here, which encompass a range of stratification length scales expected in HCCI engines, the effects of molecular transport are found to be small compared with chemical reaction effects for mean temperatures within the NTC regime. This is in contrast to previous work with fuels with single-stage ignition behaviour where practically realisable temperature gradients can lead to molecular transport effects becoming important. In addition, thermal stratification is demonstrated to result in significant reductions of the pressure-rise rate (PRR), even for the present fuel with two-stage ignition and NTC behaviour. The reduction of PRR is however strongly dependent on the mean initial temperature. The stratification length-scale is also shown to have an important influence on the pressure oscillations, with large-amplitude oscillations possible for larger length scales typical of integral scales in HCCI engines. Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Autoignition; Dimethyl ether; Direct numerical simulation; Homogeneous charge compression ignition; Thermal stratification
⇑ Corresponding author. Fax: +61 02 9385 7762.
E-mail addresses: [email protected] (H. Zhang), [email protected] (H. Zhang). 1540-7489/$ - see front matter Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.proci.2012.07.026
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H. Zhang et al. / Proceedings of the Combustion Institute 34 (2013) 803–812
1. Introduction Homogeneous charge compression ignition (HCCI) engines have the potential to improve fuel-consumption economy relative to spark-ignition engines, to reduce particulate emissions relative to diesel engines and to reduce nitrogen oxides (NOx) relative to both spark-ignition and diesel engines [1]. However, difficulties of controlling the combustion timing and high integrated heat release rates, especially at high loads, pose serious challenges for practical applications [2]. Researchers have demonstrated that thermal and/or fuel mixture stratification can potentially reduce the heat release rate due to sequential rather than simultaneous combustion of the charge [3–7]. These characteristics are fuel-dependent. For example, Dec and Sjo¨berg [3] demonstrated that reduction of the pressure-rise rate (PRR) was possible by fuel stratification using primary reference fuels with two-stage ignition behaviour, but not with those having single-stage ignition. A key characteristic of all fuels in the HCCI context is their response to thermal stratification. Thermal stratification always occurs naturally in HCCI engines [8] due to wall-heat transfer and imperfect mixing with residuals. In previous studies [9–11], we investigated the response of hydrogen fuel ignition to thermal stratification. Hydrogen has single-stage ignition behaviour and no “negative temperature coefficient” (NTC) characteristics (i.e. there is a single, clearly defined ignition event with a timing that monotonically decreases with increasing temperature). It was found that thermal stratification had the potential to introduce a range of ignition delay times into the mixture, thus preventing the undesirable high PRR that would results from the simultaneous autoignition of the whole fuel charge. Furthermore, at large stratification length scales, the ignition behaved as a spontaneous ignition front which propagates into the unburned reactants without significant assistance from heat conduction or molecular diffusion. In contrast, at small stratification length scales, it was found that transport terms became important, and the combustion process came to resemble a conventional propagating premixed deflagration. This distinction between sequential ignition and deflagration, first discussed by Zel’dovich [12], is important because it has a strong bearing on the approach to modelling. In the former case, a simple well-mixed [13] or multi-zone [14] model should be sufficient while in the latter, modelling of the coupled behaviour of mixing and chemistry must be considered [15– 16]. Identification of different ignition regimes was further discussed by Gu et al. [17] and Bansal and Im [18]. Yoo et al. [19] investigated the effect of thermal stratification on the ignition of a lean n-heptane/air mixture using two-dimensional
direct numerical simulation (DNS). It was found that turbulent mixing can have important effects on controlling the ignition delay by reducing scalar fluctuations and dissipating heat and radicals from developing ignition kernels. However, the overall effects of turbulence during ignitions were comparatively less significant than those of thermal stratification, which is produced by turbulence prior to ignition. The qualitative trends observed for hydrogen should be similar for other fuels that do not exhibit NTC behaviour, albeit possibly modulated by the fuel Lewis number. However, there is a large class of practical fuels that exhibit NTC behaviour, that is, the ignition delay time is a nonmonotonic function of temperature. Such fuels have a range of temperatures in which the ignition delay time increases with increasing temperature. In this situation, it is not clear to what extent initial temperature gradients can lead to molecular transport and conduction becoming an important influence. Furthermore, it is not clear to what extent thermal stratification can be employed as a means to reduce problematic high PRR that is accompanied by ringing and knock [6]. This study aims to explore these questions. In the present study, numerical experiments of the autoignition of DME in a one-dimensional constant volume domain at high pressure with temperature nonuniformities were performed. Numerical simulations were used to investigate, in a simplified setting, the combustion process in an environment analogous to the core fluid of a HCCI engine cylinder at top dead centre. Dimethyl ether (DME) was chosen for study because it is perhaps the simplest molecule of potential future importance as a fuel that exhibits two-stage ignition and NTC behaviour, and a computationally tractable chemical kinetic mechanism exists. In this article, homogeneous simulations (0-D) are first presented to characterize the autoignition behaviour of DME. One-dimensional simulations (1-D) are then examined to investigate the effects of thermal stratification and molecular diffusion on the ignition and the propensity for development of large-amplitude pressure waves (ringing). The present work highlights the importance of both the stratification length-scale and the mean temperature on the results. 2. Configuration The DNS code S3D was employed [20]. The code solves the compressible equations for continuity, momentum, total internal energy, and species partial densities. In order to deal with chemical stiffness that inevitably arises in large chemical kinetic schemes, an implicitly additive Runge–Kutta time integration method [21] was used in which the chemical reaction rates are
H. Zhang et al. / Proceedings of the Combustion Institute 34 (2013) 803–812
3. 0-D homogeneous cases For basic orientation that will inform the discussion of the stratified cases, spatially homogeneous cases are first considered. Figure 1 shows the ignition delay time as a function of the initial temperature for the 0-D cases. It can be observed that between 840 and 1000 K the ignition mechanism leads to increased ignition delay time with increasing initial temperature. This is the so-called NTC regime. Five initial mean temperatures were selected for the 1-D studies. Three temperatures are within the NTC regime, i.e. T0 = 840, 925, and 1000 K; two temperatures are outside NTC regime, i.e. T0 = 788.5 and 1050.4 K, but with a homogeneous ignition delay time identical to T0 = 925 K. Figure 2 shows the temporal evolutions of the temperature for homogeneous autoignition at various initial temperatures. DME demonstrates expected two-stage ignition characteristics for T0 < 1000 K: after an initial induction the temperature rapidly increases (low-temperature heat release), which is then followed by another induction period in which temperature only gradually increases, until eventually the mixture goes into thermal runaway corresponding to the high-temperature kinetic pathways. It may be also seen that the first-stage ignition is advanced with initial temperature, indicating the low temperature combustion occurs earlier. From T0 = 788.5 to 840 K the main ignition
1.2
Ignition delay time (ms)
implicitly integrated via a Newton method and the other terms are advanced explicitly. The time-step size was controlled adaptively according to the estimated solution error [21]. Spatial derivatives were approximated with an eighth order accurate spatial finite differencing scheme [22]. Thermodynamic properties were considered in NASA polynomial format [23]. A detailed DME chemical mechanism with 55 species and 290 reversible reactions was employed [24]with a mixture-averaged molecular transport model [25]. Turbulence was not explicitly considered: it was assumed that its role is simply to establish stratification with a characteristic gradient, which is a parameter varied in the study. Previous studies including turbulence [9–10,19] have demonstrated the usefulness of studying one-dimensional ignitions as a tool to understand the more complex turbulent situation. The 1-D cases considered an initially sinusoidal temperature profile upon which periodic boundary conditions were imposed. The periodicity enforced a fixed volume which allowed compression heating and pressure-rise of the reactants due to the ignition [9].The length-scale (size of domain) of the constant volume represented the wavelength of the temperature fluctuation. The amplitude of the temperature fluctuation (T0 ) was fixed to give a root-mean-square (RMS) value of 50 K for all cases. This corresponds to an upper limit of what might be expected in a typical HCCI engine without the deliberate introduction of stratification [26–27]. The equivalence ratio of 0.45 was uniform throughout the domain and a mean pressure of 40 atm was considered. Parametric studies were conducted by varying the mean temperature (T0) to traverse the NTC regime, and by varying the length-scale (L) of the stratification (at fixed mean temperature). In order to resolve some very thin reaction layers the resolution requirements were generally high. Different resolutions were ultimately required depending on the temperature and length-scale considered. The final resolutions were determined by increasing the grid number until the solution did not appreciably change. There was a minimum of 20 grid points across the main reaction layers in all cases. The parameters studied and the resolutions used to cover one complete wavelength in each case are noted in Table 1.
805
1
NTC
0.8
925 K 0.6
1000 K 840 K
0.4
0.2
1050.4 K
T0= 788.5 K
700
800
900
1000
1100
Temperature (K)
Fig. 1. Homogeneous ignition delay time as a function of the initial temperatures.
Table 1 Simulation parameters in the present study. Number of grid points in the 1-D domain Lengthscale Initial mean temperature
788.5 K 840 K 925 K 1000 K 1050.4 K
0.5 mm
1 mm
2 mm
4 mm
8 mm
480 480 480 480 1440
480 480 480 960 2880
960 480 480 2880 2880
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H. Zhang et al. / Proceedings of the Combustion Institute 34 (2013) 803–812 2450
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Temperature (K)
2100
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0
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Fig. 2. Temperature as a function of time at various initial temperatures for 0-D cases.
advances, however, fromT0 = 840 to 1000 K the main ignition is retarded, indicating NTC behaviour. At T0 = 1000 K, the first-stage ignition disappears indicating the return to conventional high-temperature pathways and single-stage ignition occurs, and T0 = 1050.4 K again ignites earlier than T0 = 1000 K. These observations are consistent with previous discussions of DME kinetics [24,28]. According to Ref. [28], the DME consumption pathway in the low-temperature regime primarily involves decomposition of hydro-peroxy-methyl-formate, leading to chain branching with the formation of two hydroxyl radicals. However, as the temperature increases, the reaction pathway trends towards the b-scission of the hydroperoxy-methoxymethyl radical, resulting in the reduction of overall reactivity due to the formation of stable formaldehyde and only one hydroxyl radical, leading to NTC behaviour [28]. At high initial temperatures, above 1000 K, high-temperature kinetic routes become active, undergoing the unimolecular decomposition of the DME and the b-scission of the methoxymethyl radical [24]. Further discussion of the chemical kinetics can be found in Refs. [24,28]. 4. 1-D thermally stratified cases
Figure 3 shows temperature versus distance for several instants at T0 = 788.5 K and L = 4 mm (the times are given in the caption). The initial temperature distribution at L = 4 mm was imposed with colder outer boundary at x = 0 mm and x = 4 mm with 50 K RMS. Two-stage ignition can be observed: ignition occurs initially at the hottest region, at the centre of the domain, and then an ignition front propagates towards the left and right boundaries to consume the remaining fuel. Within the NTC region (T0 = 840 to 1000 K) the combustion behaviour is qualitatively different. Figure 4 shows the temperature as a function of distance for sequential times at T0 = 925 K and L = 4 mm. The combustion event still occurs in two stages, and NTC behaviour is observed. The fuel ignites firstly at the colder regions at the boundaries (compare times 1 and 2 in Fig. 4), not at the central region where the local temperature is higher, due to the NTC behaviour. Subsequently ignition begins to occur throughout the domain, with the final point to ignite being the initially hottest region. Accordingly, it may be summarised that the initial temperatures which would have the identical homogeneous ignition delay time showed totally different spatial dependence of the ignition structures in stratified conditions due to the temperature inhomogeneities and the NTC behaviour. For T0 at transition points (the start and end of the NTC region, T0 = 840 K and T0 = 1000 K, respectively) ignition events could be even more complex, since different types of ignition behaviour would occur in the same domain. For example, at T0 = 1000 K, a half portion of the 2450
2100
9
Temperature (K)
806
9 8
8
1750
7
7 6
1400
5 4 3 2 1
1050
4.1. Structure of the ignitions In the 1-D cases where the initial temperature distribution was spatially inhomogeneous, a range of ignition delay times were introduced into the domain, leading to different ignition behaviours. To highlight these differences, the spatial and temporal structures of ignition at three initial mean temperatures with the same homogeneous ignition delay are compared.
6
700
0
1
2
3
4
x (mm)
Fig. 3. Temporal evolution of the temperature at T0 = 788.5 K and L = 4 mm for the 1-D case. Time sequence: No.1 = 0.100 ms, No.2 = 0.200 ms, No.3 = 0.450 ms, No.4 = 0.550 ms, No.5 = 0.575 ms, No.6 = 0.600 ms, No.7 = 0.625 ms, No.8 = 0.800 ms, and No.9 = 1.000 ms, respectively.
H. Zhang et al. / Proceedings of the Combustion Institute 34 (2013) 803–812
To conclude, the spatial and temporal structure of DME ignition strongly depends on the initial mean temperature, especially whether it falls inside or outside the NTC regime. These different structures should have a bearing on the importance of molecular diffusion on the overall ignition development, as well as on the propensity towards development of high-amplitude pressure waves and ringing.
2400
9 8
Temperature (K)
2000
7
7
1600
6
6
5
807
5
4.2. Importance of molecular diffusion
1200
4
4
3
3 2
800
2
1
0
1
2
3
4
x (mm)
Fig. 4. Temporal evolution of the temperature at T0 = 925 K and L = 4 mm for the 1-D case. Time sequence: No.1 = 0.100 ms, No.2 = 0.200 ms, No.3 = 0.500 ms, No.4 = 0.575 ms, No.5 = 0.600 ms, No.6 = 0.610 ms, No.7 = 0.620 ms, No.8 = 0.625 ms, and No.9 = 1.000 ms, respectively.
domain in the central area has a local temperature higher than the mean, leading to only single-stage ignition; while the boundary areas have local temperatures less than the mean (with the NTC regime), resulting in the two-stage ignition and NTC behaviour. This is indeed observed in Fig. 5, showing the development of the spatial structure of the ignition for T0 = 1000 K. The spatial temperature histories at T0 = 840 and 1050.4 K (both at L = 4 mm) are given in Supplementary Data [29].
10 2400
7 6 5
10
Temperature (K)
9
10 9
2100
8
8
1800
7
7 4
1500
6
6 3 2 1
1200
900
0
1
2
3
4
x (mm)
Fig. 5. Temporal evolution of the temperature at T0 = 1000 K and L = 4 mm for the 1-D case. Time sequence: No.1 = 0.100 ms, No.2 = 0.400 ms, No.3 = 0.500 ms, No.4 = 0.550 ms, No.5 = 0.570 ms, No.6 = 0.610 ms, No.7 = 0.620 ms, No.8 = 0.625 ms, No.9 = 0.628 ms, and No.10 = 0.700 ms, respectively.
To identify the roles of molecular diffusion, the contributions of mass diffusion and reaction to the net rate of change of the species mass fractions were compared at various length scales. The hydroxyl radical was selected for comparison, since it is an important radical both in high-temperature chain-branching and also plays a role in low-temperature kinetics. The evolution of the hydroxyl radical mass fraction YOH is given by [9] DY OH 1 @J OH ¼ ð1Þ þ x_ OH ; q @xi Dt where the first and second term in the bracket on the right-hand side represents the rate of change of species partial density due to molecular diffusion, and that due to chemical reaction, respectively. The flux due to molecular diffusion [19], is denoted as JOH, x_ is the reaction rate, and q is the density. Figure 6a and b shows the spatial dependence of the chemical reaction rate for the OH radical partial density and also its diffusion rate for different times at T0 = 788.5 K on the two length scales L = 0.5 mm and L = 4 mm, respectively. It can be seen that diffusion does not play a significant role at L = 4 mm, but becomes significant at L = 0.5 mm. This result is similar to previous findings with hydrogen fuel [10]. In addition, L = 4 mm tends to ignite earlier due to having lower scalar dissipation, compared to L = 0.5 mm; but ignition at L = 0.5 mm tends to complete quicker due to diffusive gains. Figure 7 shows the same data, except now with T0 = 925 K, which is within the NTC region. As may be observed, diffusion is always negligible relative to reaction, indicating a pure spontaneously propagating ignition front [9–10,12]. Figure 8 shows the result for T0 = 1050.4 K, once more outside the NTC regime. Diffusion once again can play a significant role, comparable to that of reaction at L = 0.5 mm. To further condense the information regarding the importance of molecular diffusion, we calculated the maximum within the computational domain of the absolute values of the source term for the species partial density due to molecular diffusion and that due to chemical reaction. The ratio of these two quantities was formed and named henceforth as the “diffusion-to-reaction
H. Zhang et al. / Proceedings of the Combustion Institute 34 (2013) 803–812
5
4
4 3
Reaction Diffusion 5
3
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(b). L = 4 mm Rate of OH partial density (kg/s-m )
3
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x (mm)
(b). L = 4 mm 2500
4
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x (mm)
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Reaction Diffusion
(a). L = 0.5 mm 25000
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Rate of OH partial density (kg/s-m )
(a). L = 0.5 mm 3600
Rate of OH partial density (kg/s-m )
808
6
6
5
10000
5000 5
5 2
0
2
5
5 6
-5000
0
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6
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Fig. 6. Comparison of the chemical reaction rate and diffusion rate at T0 = 788.5 K on length-scale (a). L = 0.5 mm and (b). L = 4 mm. Time sequence: No.1 = 0.600 ms, No.2 = 0.606 ms, No.3 = 0.625 ms, No.4 = 0.650 ms, No.5 = 0.680 ms, and No.6 = 0.800 ms, respectively.
Fig. 7. Comparison of the chemical reaction rate and diffusion rate at T0 = 925 K on length-scale (a). L = 0.5 mm and (b). L = 4 mm. Time sequence: No.1 = 0.613 ms, No.2 = 0.614 ms, No.3 = 0.615 ms, No.4 = 0.617 ms, No.5 = 0.619 ms, and No.6 = 0.624 ms, respectively.
ratio”. Subsequently, the maximum value of this ratio over the main ignition event was calculated so that effects of mean temperature and lengthscale could be easily compared. The results are shown in Fig. 9. It can be observed that the effects of molecular diffusion uniformly tend to decay with an increase of the length-scale, as expected. Moreover, the cases with two-stage ignition behaviour and inside the NTC regime (i.e. T0 = 840 K and T0 = 925 K) exhibit much less diffusion and lower sensitivity to length-scale than the other cases. At T0 = 925 K, the local temperature gradient became rather small and homogeneity was actually increased relative to the initial condition after the first-stage ignition due to NTC behaviour, as may be observed in Fig. 4 comparing time 1–3. As a result, a more homogeneous second-stage ignition (high-temperature ignition) occurred rapidly, leading to considerably lower diffusion. At T0 = 1000 K, although this initial temperature was located partly inside the
NTC region (at the boundaries), rapid single-stage ignition in the central area outside of the NTC region still caused relatively high diffusion. Hence, diffusive effects became significant at smaller length scales. Diffusion was most significant for the two cases that were entirely outside of the NTC regime (i.e. T0 = 788.5 K and T0 = 1050.4 K). Similar results were also found considering a number of other different chemical species. Note that the temperature fluctuation T0 = 50 K used in the present study is higher than expected in practical HCCI engines, where thermal stratifications prior to igntionare approximately 15–20 K [7]. The measured integral length scales in practical HCCI engines are typically larger than 2 mm [30–31]. Hence, the smaller length scales in the present study (0.5 and 1 mm) where molecular diffusion appears significant might not exist in practical HCCI environments. Furthermore, additional 1-D cases, with identical conditions at corresponding T0 and length-scale
H. Zhang et al. / Proceedings of the Combustion Institute 34 (2013) 803–812 Reaction Diffusion 6 7
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5 4
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7
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Maximum diffusion−to−reaction ratio
5
(b). L = 4 mm
45
6
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2
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Length Scale (mm)
Fig. 9. Comparison of maximum diffusion-to-reaction ratio of OH radical at various initial temperatures and length scales for the 1-D cases.
1
12000 9000 6000 3000 0 -3000
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1
2
3
4
x (mm)
Fig. 8. Comparison of the chemical reaction rate and diffusion rate at T0 = 1050.4 K on length-scale (a). L = 0.5 mm and (b). L = 4 mm. Time sequence: No.1 = 0.365 ms, No.2 = 0.400 ms, No.3 = 0.420 ms, No.4 = 0.430 ms, No.5 = 0.450 ms, No.6 = 0.480 ms, and No.7 = 0.490 ms, respectively.
but the transport coefficients (i.e. thermal conductivity, diffusivity and viscosity) being intentionally reduced by a factor of 10, were examined to determine the effect of diffusion under thermal stratification. It was found that the temperature evolutions of original cases appeared similar to those of the cases with 10 times less diffusion, indicating that diffusion indeed played a minor role. The results are given in Supplementary Data [29].Thus, overall, at the studied conditions, the effect of diffusion induced by thermal stratification is not expected to be significant relative to chemical reaction during the combustion event for ignitions occurring within the NTC regime, but could be significant for ignitions outside of it if temperature gradients are in the range of 25–100 K/mm. 4.3. Effects on the pressure-rise rate The spatial structure of the ignition can have a strong bearing on the overall pressure-rise rate
(PRR), which if too great can lead to ringing and knock, e.g. [26–27]. Previous studies [3–5,13,18–19] demonstrated that thermal stratification can greatly reduce PRR for single-stage ignition fuels but there has been little discussion for two-stage ignition fuels. The maximum PRR of the mean pressure over the time-span of the ignition event at various T0 and length scales are compared in Fig. 10, where the values have been normalised by the maximum PRR in the corresponding homogeneous cases. It is evident that thermal stratification significantly reduces the maximum PRR relative to the homogeneous ignition for DME ignition, even within
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Normalised pressur−rise rate
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Fig. 10. Comparison of maximum pressure-rise rate at various initial temperatures and length scales for the 1-D cases, normalised by the maximum pressure-rise rate in the corresponding homogeneous cases. Inner plot shows the comparison of temporal evolutions of normalised pressure-rise at T0 = 1000 K for 0-D homogeneous case, L = 0.5 mm, and L = 4 mm, respectively.
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the NTC regime. Importantly, however, the reduction of PRR is observed to be dependent on T0. The greatest potential for reduction occurs for the cases completely outside the NTC regime, i.e. T0 = 788.5 K and T0 = 1050.4 K due to a relatively inhomogeneous ignition event as discussed in Section 4.1, and the potential for reduction is least at T0 = 925 K due to a relatively homogeneous ignition event. For T0 = 788.5 K, T0 = 840 K and T0 = 1050.5 K, PRR may be observed to increase as the lengthscale is increased. At T0 = 1000 K, PRR increases as L increases from 0.5 to 1 mm, and thereafter decreases with L. At T0 = 925 K, a non-monotonic trend with length-scale may be also noted. Decreasing PRR with increasing L may be noted from L = 0.5 mm to L = 4 mm, with increasing PRR from L = 4 mm to L = 8 mm. As discussed by Zel’dovich [12] the speed of a spontaneous ignition front sig is given by sig ¼
1 1 ¼ ; jrsj ds jrT j 0 dT 0
ð2Þ
where s is the ignition delay time. If sig is sufficiently large and comparable to the speed of sound, the combustion wave can become coupled to the acoustic wave, leading to rapid pressure-rise and in some circumstances a detonation [12,20]. In the present situation, s is approximately a function of initial temperature, as such, sig can become large if either ds/dT0 or the temperature gradient becomes small. The latter may contribute to the trend of significantly larger pressure oscillation for the increasing length-scale for T0 = 788.5 K, T0 = 840 K and T0 = 1050.4 K. The former may contribute to the trend of larger PRR for the mean temperatures inside the NTC regime (i.e. the cases of T0 = 840, 925 and 1000 K compared with the cases of T0 = 788.5 and 1050.4 K).
Maximum amplitude of pressure fluctuations (atm)
14
788.5 K 840 K 925 K
12 10 8 6 4 2 0 0.5
1
2
4
8
Length scale (mm)
Fig. 11. Maximum amplitude of pressure fluctuations at various length scales for two-stage ignition events.
Figure 11 shows the amplitude of pressure fluctuations, defined as half the difference of the maximum and minimum pressures in the domain, after the ignition event is completed (focusing on two-stage ignition only). The fluctuations are plotted versus length-scale for different T0. Two main points may be noted. First, the pressure fluctuation increases with length-scale. This was consistent with the arguments above considering the coalescence of acoustic and combustion waves due to large ignition front speeds arising from lower temperature gradients. Second, the amplitude of the pressure fluctuations are also dependent on T0. The largest fluctuations are observed at T0 = 925 K, in the middle of the NTC regime. In comparison, at T0 = 840 K, the fluctuations are lower, and at T0 = 788.5 K lower still. This is consistent with the PRR trends and may be readily explained considering the lower ds/dT0 at T0 = 840 K compared with T0 = 788.5 K. 5. Conclusions One-dimensional numerical simulations of DME autoignition were performed to understand the influence of thermal stratification on ignition inside and outside of the negative-temperature coefficient regime. Stratified ignitions were observed to proceed differently from the corresponding homogeneous ignition. Importantly, the spatial and temporal structure of the ignition was found to strongly depend on whether the mean initial temperature was inside or outside the NTC region, a behaviour which is qualitatively different from fuels with a single-stage ignition and no NTC behaviour. Thermal stratification was found to affect both the reaction–diffusion balance in the ignition, as well as the maximum rates of pressure-rise and the amplitude of pressure fluctuations. The relative importance of molecular diffusion and chemical reaction was found to change significantly with the mean temperature, behaviour not observed for fuels without NTC behaviour. Diffusion became relatively less significant for the cases with two-stage ignition and fully inside the NTC regime compared to the other cases outside the regime. As the length-scale was increased, diffusion eventually became negligible in all cases. Based on the present study and previous measurements of in-cylinder temperature fluctuations [7,30], we expect that in practical HCCI engines, diffusion due to initial thermal stratification is not an important influence on the ignition evolution for initial mean temperatures in the NTC regime (for the fuel mixture considered). Diffusion could still be important outside of this regime if pre-ignition temperature gradients are in the range of 25– 100 K/mm. The observed effects are expected to
H. Zhang et al. / Proceedings of the Combustion Institute 34 (2013) 803–812
be modulated somewhat by the kinetics of the specific fuel, but qualitatively it is possible to project that a greater ds/dT0 will lead to a greater importance of diffusion effects of the ignition. In the modelling strategy, the reduced importance of molecular diffusion within the NTC regime suggests that simple multi-zone modelling, which neglects the effects of molecular diffusion [4,10,14] may be sufficient to capture effects of thermal stratification on ignition within that regime, and more detailed modelling is not necessary [15,16]. Note that mixture stratification is another matter entirely but out of the scope of the present study. Turbulence is another effect that can potentially have an influence. The main effect of turbulence in HCCI is to set up the thermal field prior to ignition, but persistent straining during ignition could also lead to an increased importance of molecular diffusion effects. Further work is needed to assess effects of turbulence. It was also demonstrated that thermal stratification can significantly reduce PRR, even for the present fuel with a two-stage ignition and NTC behaviour. However, the reduction of PRR was very dependent on T0. The greatest potential for reduction was found for the cases completely outside the NTC regime due to a more inhomogeneous ignition event. It was found across all of the considered mean temperatures that an increased stratification length-scale led to increased amplitude of pressure fluctuations, which in practical engines would be observed as undesirable ringing. The amplitude of these fluctuations was found to depend on mean temperature, with the largest amplitude again observed for the conditions fully inside the NTC regime. Thus qualitatively, it is anticipated that larger PRR and pressure fluctuations can result from either lower ds/dT0 or large stratification length scales. The latter effect, however, can implicate coupled physics of compressible flow and combustion which can lead to counter-intuitive trends as mean temperature is varied. Acknowledgments This work was supported by the Australian Research Council under Grant numbers DP110104763 and FT100100536. In addition, this research benefited from the resources of the National Computational Infrastructure, Australia.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http:// dx.doi.org/10.1016/j.proci.2012.07.026.
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