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Show 2011 AFRC Combustion Symposium September 18-21, 2011 Houston, Texas Turbulent Flame Speeds of High H2 Mixtures Prabhakar Venkateswarana, Andrew Marshallb, Edouard Bahousb, Jerry Seitzmana, Tim Lieuwena a Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, 30332 b Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 30332 This paper describes turbulent global consumption speed, ST,GC, measurements of H2/CO mixtures at atmospheric conditions. The turbulent flame properties of these mixtures are of strong practical interest due to the rising interest in expanding the role of coal-derived syngas fuels in the current energy portfolio. Furthermore, these mixtures are also of fundamental interest because of their strong stretch sensitivity. Data are obtained in a Bunsen burner configuration at mean flow velocities and turbulence intensities of 4 < U0 < 65 m/s and 1 < u'rms /SL,0 < 100, respectively, for H2/CO mixtures ranging from 30-90% H2 by volume. Data from two sets of experiments are reported. In the first, for a range of fuel blends from 30-90% H2, mixture equivalence ratio, , was adjusted at each fuel composition to have nominally the same un-stretched laminar flame speed, SL,0. In the second set, equivalence ratios were varied at constant H2 levels. The data clearly corroborate results from other studies that show significant sensitivity of ST,GC to fuel composition. We have also developed a scaling law to correlate the consumption speed data of these negative Markstein length mixtures using the leading points framework. The derived scaling law closely resembles Damkohler‟s classical turbulent flame speed model except the maximum stretched laminar flame speed, SL,max, and not SL,0, arises as the normalizing parameter. 1. Introduction There is significant interest in developing dry low NOx combustion technologies that can operate with synthetic gas (syngas) fuels derived from gasified coal or biomass [1]. Syngas fuels are typically composed primarily of H2 and CO, and may also contain smaller amounts of CH4, N2, CO2, H2O, and other higher order hydrocarbons [1]. However, the specific composition depends upon the fuel source and processing technique, leading to substantial variability in composition. A variety of operability, emissions, and structural life issues must be addressed in evaluating the impact of fuel composition on a gas turbine combustor; e.g., NOx and CO emissions, liner and fuel nozzle thermal loading, blow-off and flashback limits, and combustion instabilities. The turbulent flame speed, ST, which can be defined analogously to the laminar flame speed as the average rate of propagation of a turbulent flame, is an important parameter through which the fuel composition exert an influence on many of these issues [2]. For example, the turbulent flame speed has a direct impact on the flame length and its spatial distribution in the combustor. This, in turn, affects the thermal loading distribution on the combustor liners, fuel nozzles and other hardware. Furthermore, the flames proclivity to flashback is directly a function of how rapidly the flame propagates into the reactants, which is dependent on the turbulent flame speed. In addition, the turbulent flame speed has an important influence on combustion instability limits through its influence on the flame shape and length [3]. For example, measurements from Santavicca [4] have clearly shown how combustion instability boundaries are influenced by changes in flame location due to changes in H2 content of the fuel or mixture stoichiometry. This paper is particularly motivated by studies showing substantial sensitivities of ST to fuel composition [5, 6]. In other words, two different fuel mixtures can have appreciably different turbulent flame speeds, despite having the same un-stretched laminar flame speed, SL,0, turbulence intensity and burner configuration. These fuels effects are believed to be associated with the stretch sensitivity of the reactant mixture which leads to significant variation in the flame speed along the turbulent flame front. In particular, the high mass diffusivity of H2 makes the flame front particularly susceptible to stretch. The effect of stretch manifest themselves in two ways; non-unity Lewis number effects and preferential diffusion effects [7]. Non-unity Lewis number effects produce local energy imbalances due to relative diffusion rates of heat (by thermal diffusion) and chemical energy (by mass diffusion). Preferential diffusion effects produce local variations in the equivalence ratio because of the differences in mass diffusivities of the various constituents of the reactant mixture. This paper extends several prior studies by the authors on turbulent consumption speed, ST,GC, characteristics of H2/CO blends [8, 9]. The key new contribution of this work is the correlation of these data using a physics-based model incorporating the leading points concept. Leading points are defined as the positively curved points on the flame that propagate out farthest into the reactants [10-12]. The leading point is established where the local flame speed is greater than the local flow velocity. Due to this kinematic imbalance, the flame propagates out into this point. For negative Markstein length mixtures, the burning rate of this positively curved leading point increases [7]. Because the turbulent burning velocity is controlled by the leading point characteristics [12], the ensemble averaged laminar burning rate of this leading point turns out to be a very significant turbulent flame property. From this analysis, a scaling law is derived, which very closely resembles Damkohler‟s classical turbulent flame speed scaling, except the maximum stretched laminar flame speed, SL,max, arises as the natural normalizing parameter. 2. Experimental Facility This study focuses on the quantification of the turbulent global consumption speed, ST,GC, defined in Eq. (1), using a Bunsen burner, which is a turbulent flame speed measurement approach recommended by Gouldin and Cheng [13]. This approach was selected because of the Bunsen burner data sets available in the literature for bench-making purposes. S T ,G C mR (1) u A c The details of the experimental facility are documented in Venkateswaran et al. [8], but are very briefly overviewed here. The facility consists of a contoured nozzle Bunsen burner with a 20mm nozzle exit diameter, as shown in Figure 1. Figure 1: Schematic of experimental facility In this study, a novel turbulence generator is used where the turbulence intensity is varied independently of the mean flow velocity. The assembly consists of thin plates with milled slots that induce flow separation and vorticity generation as the flow passes through them. These vortical structures then impinge on the wall of the converging nozzle and break down into fine-scale turbulence [14-16]. The complete details on the features of the variable turbulence generator as well as the velocity characterization studies using both LDV and PIV can be found in Ref. [17]. 3. Results a) Experimental Conditions In the study two sets of experiments were conducted. In the first set, the H2/CO ratio and mixture equivalence ratio were varied simultaneously to obtain mixtures with the same SL,0. Data were collected for volumetric H2/CO ratios of 30/70, 50/50, 70/30 and 90/10. The equivalence ratio required at each H2/CO ratio to obtain an SL,0 of 34cm/s was estimated using the PREMIX module in CHEMKIN with the Davis H2/CO mechanism [18]. A pure CH4/air case was also run, and the GRI 3.0 mechanism [19] was used to estimate the equivalence ratio required for the same SL,0 In the second set of experiments the H2/CO ratio was held fixed while the equivalence ratio was varied. This was done for H2/CO ratios of 30/70 and 60/40. The measurements shown in this paper were taken using a 20mm burner diameter at 1atm and 300K reactant temperature. Table 1 below provides a summary of the experimental conditions, along with the color and symbol scheme used to plot the data. Table 1: Parameter space explored and color and symbol scheme used to plot the data b) Stretch Sensitivity Calculations Stretch sensitivity calculations were performed for the mixtures investigated in Table 1. The stretch sensitivities were calculated using an opposed flow calculation of two premixed flames with a nozzle separation distance of 20mm using the OPPDIF module in CHEMKIN. From these calculations, various stretch properties of the mixture were extracted. In this paper, both displacement and consumption laminar flame speeds have been calculated [20]. The displacement speed, SL,D is defined the speed at which the flame front propagates normal itself with respect to the flow, and this has been determined from the minimum velocity just upstream of the reaction zone as suggested by Wu and Law [21]. The consumption speed, SL,C, is based on the spatially integrated chemical production rates. The consumption speed is basically the mass or sensible heat production rate integrated along a streamline through the flame, normalized by the unburned density or sensible enthalpy, respectively [20, 22]. Equation (2) and (3) provides the expressions for the mass and thermal consumption speeds, which can be derived from a one-dimensional form of the species and energy equation neglecting body forces and viscosity respectively [20]. S L ,C w i dx u Yi , Yi , (2) S L ,C qdx u h sens , h sens , (3) In a one-dimensional adiabatic scenario, the displacement and consumption speeds are all identical. However, in the presence of tangential flow, as is the case in the opposed jet configuration, different definitions yield different values and exhibit different definitions have different stretch sensitivities, as shown in Figure 2 below. Note that as 0 all the curves converge towards the same value on the yaxis which corresponds to SL,0. In this paper, the thermal consumption speed has been used instead of the species consumption speed because the multicomponent nature of the fuel makes it ambiguous as to which species to base the calculation on. Figure 2: Differences in stretch dependencies of the displacement speed, the species consumption speed, and the thermal consumption speed for a 90% H2 mixture at 0.46 The Markstein length, lM, was determined from the slope of the linear fit to the low strain regime of the κ vs SL,D or SL,C curve. From Figure 2 it can be clearly seen that the Markstein length based on the displacement and consumption speeds can be quite different. The extinction strain rate, κext, was calculated using an arc length continuation method. An example set of calculations are shown in Figure 3 for the mixtures investigated in the equivalence ratio sweeps for the 30% H2 mixture. These stretch sensitivities are used in the subsequent sections to model the consumption speed data. Figure 3: Displacement speed stretch sensitivity calculations of mixtures investigated in the equivalence ratio sweep studies for the 30% H2 mixture (see Table 1 for conditions) c) Experimental Results Figure 4 plots ST,GC/SL,0 as a function of u'rms/SL,0 for H2/CO mixtures of 30/70, 50/50, 70/30, and 90/10 at mean flow velocities of 4, 10, 30, and 50 m/s. As expected, ST,GC increases monotonically with turbulence intensity, for a given fuel composition. The main observation from this data is the monotonically increasing value of ST,GC with H2 levels. For example, at U0 = 30 m/s and u'rms/SL,0 = 25, ST,GC/SL,0 has a value of 8 for CH4, of 14 for the 30/70 H2/CO mix and 22 for the 90/10 H2/CO mix. Moreover, the data indicate that these "fuel effects" persist even at very high turbulence intensities. Note also the significant similarities between each fixed mean flow velocity, U0, group as fuel composition is varied. It appears that the same curve is shifted vertically to higher ST,GC values as H2 fraction is increased. Figure 4: Dependence of ST,GC upon u'rms normalized by SL,0 at various mean flow velocities and H2/CO ratios ( See Table 1 for legend of mixture conditions and flow velocities) Equivalence ratio sweeps were also performed at fixed H2 contents of 30% and 60% for three equivalence ratios. Figure 5(a) shows the results for a 60% H2 mixture at = 0.40, 0.60, 0.80 while Figure 5(b) shows the results for a 30% H2 mixture at = 0.61, 0.70, 0.80 for mean flow velocities of 4, 10, 30, and 50 m/s. Note that SL,0 is not held nominally constant for these data, as it was in the prior section. Similar conclusions can be reached from this data as discussed above. (a) (b) Figure 5: Dependence of ST,GC upon u'rms normalized by SL,0 at various mean flow velocities and equivalence ratios at a fixed H2 content of (a) 30% and (b) 60% ( See Table 1 for legend of mixture conditions and flow velocities) 4. Analysis and Discussion These data are consistent with prior studies showing that stretch sensitivity of the reactants has an important impact on the turbulent flame speed [23, 24]. A common approach for scaling turbulent flame speeds is to use the consumption based definition [24]: ST S L AT A c (4) Equation (4) has been derived by equating the average reactant mass flow consumed at a specified <c> surface of area A<c> to the ensemble averaged reactant mass flow consumed by the instantaneous flame front of area AT, which is propagating locally at the laminar flame speed, SL. By introducing the stretch factor, I0 = SL/SL,0 [20, 25], Eq. (4) can be re-written as: ST S L ,0 I 0 AT A c (5) For stretch insensitive flames, the I0 factor equals unity, leading to the classical ST scaling described by Damköhler [26]. For stretch sensitive flames, one is left with the function <I0A>, which requires understanding the correlation between local flame speed and flame area. Assuming that these functions are uncorrelated, i.e., that <I0A> = <I0><A> leads to the erroneous prediction that the mixture‟s stretch sensitivity should not influence ST [27]. This prediction follows from measurements and computations which show that the flame curvature PDF is roughly symmetric about κ = 0 [28-31], implying that regions of enhanced and diminished local consumption rate should roughly cancel and, thus, that <I0> 1. Hydrodynamic strain, which is not symmetric about κ = 0 [30-32] does introduce a non-unity <I0> value, but it seems unlikely that this effect is significant enough to explain the appreciable fuel effects reported here and in the literature. However, it can easily be seen that assuming uncorrelated A and I0 passes over key physics: in particular, there are implicit I0 effects in the <A> term because the local flame speed and area are highly correlated. To illustrate, let‟s consider Figure 6, which depicts the instantaneous flame front at two time instants. Clearly, for lM < 0 flames, the local flame speed at the positively curved leading point of the flame will be enhanced causing it to propagate at a faster speed into the unburned reactants, increasing the flame area accordingly. In the same way, the slower, negatively curved trailing point of the flame will lag backwards, also increasing flame area. Figure 6: Instantaneous turbulent flame fronts at two different time instants Given the implicit presence of the I0 term in the <A> term, modeling approaches based upon leading points concepts [10, 12, 23] may be more useful for explicitly bringing out stretch sensitivity effects. The leading points are roughly defined as the necessarily positively curved points on the turbulent flame front that propagate farthest into the reactants. It has been argued that the propagation speed of these points with respect to the average flow velocity control the overall turbulent flame speed [12]. As a result, fuel/air mixtures with negative Markstein numbers will have enhanced laminar flame speeds at the positively curved leading points, resulting in larger displacement speeds. The basic leading points argument can be readily understood from the simple model problem of a flat flame propagating into a spatially varying velocity field with zero mean flow velocity, as depicted in Figure 7. Figure 7: Model problem of a flat flame propagating into a spatially varying flow field. If we assume that SL remains constant, then it is seen that the portion of the flame at the lowest velocity point propagates out the fastest. In the lab-fixed coordinate system, the flame at Point B moves at a speed of SL + (u)LP, where the subscript "LP" denotes the leading point. Moreover, it can easily be shown by a front tracking computation that, after an initial transient, the entire front reaches a stationary shape and propagation speed which has the same value; i.e., SD = SL + (u)LP. As such, the overall displacement speed is controlled by the leading points of the flame that propagate into the lowest velocity regions ahead of the flame. Note also that the flame area would increase as well, but this is an effect of the higher displacement speed, not the cause. In reality, the positively curved leading point of the flame will have an altered flame speed, (SL)LP = SL,0 + S L L P , where S L L P is the modification of the un-stretched laminar flame speed at the leading point, because of the mixtures nonzero Markstein length. If the mixture has a negative Markstein number, then the flame speed at this point will further increase, causing an increase in curvature, further increasing the local flame speed. This is analogous to the processes causing the thermo-diffusive instability in premixed flames [7]. As a result, the above expression can be modified to take into account the flame speed augmentation: S D S L LP u LP (6) The key difference to note from this scaling approach relative to Eq. (1) is that this focuses on a local flame characteristic - namely the positively curved leading point - as opposed to some global average, <I0A>, which obscures the stretch effect. The key problem lies in scaling S L L P . The value of (SL)LP is bounded by some SL,max value; e.g., for an opposed flow flame, SL,max can be directly extracted from the simulations shown in Figure 3. Thus, note that SL,max > (SL)LP > SL,0. For example, this leads to the following inequality for the 30% H2 blend: 95 cm/s > (SL)LP > 34 cm/s. Substituting this SL,max value in for (SL)LP and writing (u)LP as u L P , leads to the following: SD S L , m ax 1 u L P (7) S L , m ax Note that this is nearly identical to Damköhler‟s classical result [26] where SL has been replaced by SL,max and u' by u L P . This inequality can be replaced by an equality in certain situations. Since the mixtures investigated are thermo-diffusively unstable, SL,0 is a „repelling‟ point since a positively curved perturbation on a flat flame will grow with increasing curvature and correspondingly increasing flame speeds as shown in Figure 8. In fact, it can be rigorously shown that SL,max is a steady-state „attracting‟ point for positively curved wrinkles. Figure 8: Example plot showing the attracting nature of SL,max As such, if the turbulent eddies evolve over a time scale that is slow relative to that required for the leading points to be attracted to the SL,max point, then Eq. (7) can be replaced by: SD 1 S L , m ax u L P S L , m ax (8) On the basis of the scaling derived above, all the ST,GC data presented above are replotted using the SL,max normalization, where SL,max is based on the displacement speed definition of the laminar flame speed, SL,D,max. Figure 9 plots the entire data set, which contains both the constant SL,0 studies and the equivalence ratio sweep studies. Figure 9: SL,D,max normalized ST,GC data including constant SL,0 and equivalence ratio sweep studies (see Table 1 for legend) The data collapses generally well across all the mean flow velocities although there is some scatter in the 4 m/s data that largely disappears at the higher flow velocities. Also, note that the 30 m/s CH 4/air data does not collapse with the H2/CO data set while it collapses at 10 m/s and 4 m/s. In fact, the variation in the normalized turbulent flame speed values for the 30/70 to 90/10 reduced from 50% to about 10% (for the 50 m/s case) between Figure 4 and Figure 9. Larger disparities (about 50% at u'rms/SL,max = 12.5) are seen between the H2/CO data and CH4 data. This scatter and some caveats are discussed further in the following paragraphs. First, some scatter is inevitable as the ext and SL,D,max value are not constants for a given mixture but depends upon the strain profile the flame is subjected to [33]. For example, repeating these calculations using nozzle separation distances ranging from 10 to 40 mm causes variations in SL,D,max of 5% for the 30/70 H2/CO mixture. Moreover, this SL,D,max value is a function of the experimental configuration - in particular, the sensitivity of strained and curved flames to high levels of stretch are different. Presumably, the SL,max at the leading point of the turbulent flame brush would be related to the strain rate associated with the highly curved leading edge, whose radius of curvature is bounded by the flame thickness. Second, the local burning velocity at the leading point, (SL)LP is not identically equal to SL,max; rather, SL,max is simply an upper bound of an inequality as discussed earlier. Only in the quasi-steady turbulence limit can this inequality be replaced by equality. Third, from the derivation of the scaling, it is evident that this scaling may be more suitable for a local displacement turbulent flame speed definition. Finally, note that the ST,GC data reported here by virtue of Eq. (1) necessarily average over potentially significant variations in local flame speeds whereas the scaling shown in Eq. (8) is essentially valid at a single point on the instantaneous flame front. As a result, adjustments to suitably average over a spatially developing flow field and flame brush are required. Nonetheless, the very good collapse of the large data set obtained here provides strong evidence for the basic validity of the scaling argument shown in Eq.(8). Note that this argument will need revisiting for lM > 0 flames, where the attracting point argument discussed above requires modification. The next goal is to extend this scaling law to correlate other data in the literature. The largest database of ST,GC measurements of H2/CO mixtures known to this author is that obtained by Daniele et al. [34], making it a natural place to start testing this scaling law. The Daniele dataset [34] was obtained at highly preheated conditions, and the stretch sensitivity calculations for these mixtures revealed that at high stretch rates, the twin flames merged together making it impossible to detect a velocity minimum upstream of the reaction zone, and consequently extract a displacement speed. This is what motivated the calculation of consumption speeds. As a check, we renormalized our dataset using the SL,max based on the thermal consumption speed definition of the laminar flame speed, SL,C,max, and the results are shown in Figure 10. Figure 10: SL,C,max normalized ST,GC data including constant SL,0 and equivalence ratio sweep studies (see Table 1 for legend) Note that data collapses almost identically, except that range has been essentially doubled. The reason for this can be seen from Figure 2, where the displacement speed is roughly twice the thermal consumption speed. In fact, to investigate this relationship further, the SL,max obtained from the two different definitions for all the mixtures investigated in this study have been plotted against each other in Figure 11. Figure 11: Comparison of SL,D,max and SL,C,max Figure 11 shows that across the mixtures investigated that SL,C,max is half of SL,D,max, which explains the differences seen between Figure 9 and Figure 10. This suggests that if the data collapses with one definition of SL,max then it should also collapse with the other definition. However, more light needs to be shed on which definition of the laminar flame speed needs to be utilized in the leading points framework, and this is currently under consideration. 5. Concluding Remarks This paper presents the development of a scaling law using the leading points concepts for the ST,GC measurements obtained in the authors‟ previous works. The application of the scaling law to normalize the consumption speed resulted in collapsing the data set quite effectively. The main features of the scaling law is the similarity it shares with Damköhler‟s scaling for the flame speed except that the maximum stretched laminar flame speed, SL,max, arises as the natural normalizing parameter. Acknowledgements This research was partially supported by University Turbine Systems Research program, Mark Freeman, contract monitor, under contract DE-FC21-92MC29061, by Siemens Energy through a subcontract with DOE prime contract DE-FC26-05NT42644, Dr. Scott Martin contract monitor, and by University of California-Irvine through a subcontract with the California Energy Commission. The authors gratefully acknowledge Reaction Design for making available the new release 15091 of CHEMKIN-PRO. References 1. G. A. Richards; K. H. Casleton, in: Synthesis Gas Combustion: Fundamentals and Applications, T. C. Lieuwen; V. Yang; R. A. Yetter, (Eds.) CRC Press: 2009; p 403. 2. T. Lieuwen, McDonell, V., Petersen, E., Santavicca, D., Journal of Engineering for Gas Turbines and Power 130 (2008) 011506 3. T. C. Lieuwen, Yang, V., Progress in Astronautics and Aeronautics (2005) 4. L. Figura; J. G. Lee; B. D. Quay; D. A. Santavicca, ASME Conference Proceedings 2007 (47918) (2007) 181-187 5. M. Nakahara; H. Kido, AIAA Journal 46 (7) (2008) 1569-1575 6. H. Kido; M. Nakahara; K. Nakashima; J. Hashimoto, Proceedings of the Combustion Institute 29 (2) (2002) 1855-1861 7. C. K. Law, Combustion Physics, Cambridge University Press, New York, 2006, p.^pp. 8. P. Venkateswaran; A. D. Marshall; D. R. Noble; J. Antezana; J. M. Seitzman; T. C. Lieuwen, ASME Conference Proceedings 2009 (48838) (2009) 559-570 9. A. Marshall; P. Venkateswaran; P. D'Souza; D. Noble; J. Antezana; J. Seitzman; T. Lieuwen, 6th US National Combustion Meeting (2009) 11 10. V. R. Kuznetsov; V. A. Sabel'nikov, in: Turbulence and Combustion, V. R. Kuznetsov; V. A. Sabel'nikov; P. A. Libby, (Eds.) Hemisphere Publishing Corporation: Moscow, 1986; p 362. 11. A. Lipatnikov; J. Chomiak, Progress in Energy and Combustion Science 31 (1) (2005) 1-73 12. V. P. Karpov; A. N. Lipatnikov; V. L. Zimont, in: Advances in Combustion Science: In honor of Ya. B. Zel'dovich, W. A. Sirignano; A. G. Merzhanov; L. De Luca, (Eds.) AIAA: Reston, VA, 1997; Vol. 173, pp 235-250. 13. F. Gouldin; R. K. Cheng International Workshop on Premixed Turbulent Flames. http://eetd.lbl.gov/aet/combustion/workshop/workshop.html 14. B. Bédat; R. K. Cheng, Combustion and Flame 100 (3) (1995) 485-494 15. B. Videto; D. Santavicca, Combustion Science and Technology 76 (1) (1991) 159-164 16. C. Kortschik; T. Plessing; N. Peters, Combustion and Flame 136 (1-2) (2004) 43-50 17. A. Marshall; P. Venkateswaran; D. Noble; J. Seitzman; T. Lieuwen, Experiments in Fluids (2011) 1-10 10.1007/s00348-011-1082-6. 18. S. G. Davis; A. V. Joshi; H. Wang; F. Egolfopoulos, Proceedings of the Combustion Institute 30 (1) (2005) 1283-1292 19. G. P. Smith; D. M. Golden; M. Frenklach; N. W. Moriarty; B. Eiteneer; M. Goldenberg; C. T. Bowman; R. K. Hanson; S. Song; W. C. Gardiner Jr; V. V. Lissianski; Z. Qin GRI-Mech 3.0. http://www.me.berkeley.edu/gri_mech/ 20. T. Poinsot; D. Veynante, Theoretical and numerical combustion, RT Edwards, Inc., 2005, p.^pp. 21. C. K. Wu; C. K. Law, Proceedings of the Combustion Institute 20 (1) (1985) 19411949 22. J. B. Chen; H. G. Im, Proceedings of the Combustion Institute 28 (1) (2000) 211-218 23. A. N. Lipatnikov; J. Chomiak, Progress in Energy and Combustion Science 31 (1) (2005) 1-73 24. J. F. Driscoll, Progress in Energy and Combustion Science 34 (1) (2008) 91-134 25. K. N. C. Bray; R. S. Cant, Proceedings: Mathematical and Physical Sciences (1991) 217-240 26. G. Damköhler, Zeitschrift Electrochem 46 (1940) 601-626 27. S. H. El Tahry; C. Rutland; J. Ferziger, Combustion and Flame 83 (1-2) (1991) 155173 28. A. Lipatnikov; J. Chomiak, Proceedings of the Combustion Institute 30 (1) (2005) 843-850 29. P. J. Goix; I. G. Shepherd, Combustion Science and Technology 91 (4) (1993) 191 206 30. C. Rutland; A. Trouvé, Combustion and Flame 94 (1) (1993) 41-57 31. D. Haworth; T. Poinsot, Journal of Fluid Mechanics 244 (1992) 405-436 32. M. Baum; T. Poinsot; D. Haworth; N. Darabiha, Journal of Fluid Mechanics 281 (1994) 1-32 33. F. N. Egolfopoulos, Proceedings of the Combustion Institute 25 (1) (1994) 13751381 34. S. Daniele; P. Jansohn; J. Mantzaras; K. Boulouchos, Proceedings of the Combustion Institute 33 (2) (2011) 2937-2944 |