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The influence of evaporation on the autoignition-delay of n-heptane air mixtures under gas turbine conditions
Twenty-Seventh Symposium (International) on Combustion/The Combustion Institute, 1998/pp. 2025–2031
THE INFLUENCE OF EVAPORATION ON THE AUTOIGNITION-DELAY OF n-HEPTANE AIR MIXTURES UNDER GAS TURBINE CONDITIONS M. CANO WOLFF, J. MEISL, R. KOCH and S. WITTIG Lehrstuhl und Institut fu¨r Thermische Stro¨mungsmaschinen Universita¨t Karlsruhe Kaiserstraße 12 76128 Karlsruhe, Germany
In this work, autoignition-delay times of liquid fuel sprays for flow situations similar to those in premixing ducts are calculated. An intensive parameter study was conducted to identify the influence of the evaporating spray on autoignition delay. The parameter variation covers duct conditions relevant to gas turbines. Three monodisperse sprays with droplet sizes of 10, 50, and 100 lm and two sprays with Rossin-Rammler droplet size distribution are investigated. A full 3-D Navier-Stokes code is used for the prediction of the turbulent flow. It is coupled to a code based on a Lagrangian formulation for the prediction of the motion and evaporation of the droplets. The evolution of the chemical kinetics is predicted with the CHEMKIN package for n-heptane, which is selected as fuel. A detailed n-heptane low-temperature mechanism including 168 species and 904 reactions describes the chemical kinetics. For initial temperatures inside the negative temperature coefficient region (NTC), the only spray parameter influencing autoignition delay is the spray evaporation time. If the initial temperature is on the lower boundary of the NTC region, the strong temperature dependence of autoignition in this region leads to a substantially longer autoignition delay due to the cooling of the gas phase caused by evaporation. A delaying effect of evaporation time is only present if the evaporation time is higher than the first induction time. Generally, the safety margin between autoignition and the end of evaporation is enhanced by utilization of a spray with small droplets and a narrow droplet size distribution. Also, a minimum autoignition delay for lean conditions at U 4 0.5 is identified.
Introduction Lean premixed prevaporized (LPP) combustion is the most promising concept for the reduction of NOx emissions from gas turbines. It also offers the possibility of an almost soot-free combustion of liquid fuels. Because thermal efficiency and specific power output are coupled to the compressor ratio, values of 40 are realized in modern gas turbines, and a further increase is to be expected for the future. At take-off conditions, pressures and temperatures at the compressor outlet of an aircraft gas turbine may reach 40 bar and 900 K. Because the autoignition delay (AID) of a fuel–air mixture decreases with growing pressure and temperature, the time available for liquid fuel evaporation and mixing with air in the premixing passage is limited. Especially with respect to aircraft gas turbines, safety reasons require that autoignition is avoided under all possible flight conditions. It is therefore necessary to predict and understand the interaction between turbulence, evaporating two-phase flow and chemical reactions in the combustor premixing section under a wide variety of conditions. Research in the field of internal combustion engines has led to an understanding of the gas-phase
chemical reactions leading to autoignition. Detailed kinetic mechanisms for alkanes such as n-heptane and n-decane [1,2] have been developed and validated under gas-turbine similar conditions by shock tube [3–5] and flow reactor [6] experiments. The interaction between autoignition gas-phase reactions and turbulence has been investigated numerically by Correa and Dean [7]. It was shown how inhomogeneities in the fuel–air concentration distribution could control the autoignition process. Slow mixing allowed separate autoignition of the stoichiometric fluid volumes, resulting in low ignition delays. The higher autoignition-delay time corresponding to the mean air–fuel ratio of the lean mixture was achieved only for fast mixing. Thibaut and Candel [8] have investigated the possible autoignition modes of a droplet cloud suspended in a hot stagnating atmosphere. Depending on initial conditions, autoignition could either take place inside the cloud or in the diffusion layer surrounding the cloud. This demonstrated how spatial nonuniformities and the cooling due to evaporation interact to influence the autoignition process. The objective of this study is to investigate the influence of the evaporation process on the gasphase chemical kinetics leading to autoignition of
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Fig. 1. Autoignition-delay times at p 4 20 bar; lines, initially premixed; n●, without evaporation enthalpy; ▫C, with evaporation enthalpy.
the air–fuel mixture in a typical LPP configuration. The model developed is designed to calculate autoignition-delay times allowing a wide parameter variation of the duct inlet conditions. In our study a verified detailed mechanism has been used to calculate the reaction progress of the gas phase. The range of LPP duct conditions examined included pressures of p 4 9 and 20 bar, inlet temperatures between T 4 673 and 973 K, and equivalence ratios from U 4 0.33 to 1. Because the evaporation process depends on droplet diameter, five different sprays have been investigated: three monodisperse sprays with droplet diameters of 10, 50, and 100 lm and two sprays with Rossin-Rammler distribution as representatives of real fuel sprays.
Numerical Model The entire model was developed to determine AID of flows typical for LPP ducts. Thus, two verified submodels were used for the calculations. In a first step, the evaporating two-phase flow was simulated by the two in-house codes Epos and Ladrop. Epos [9] is a fully 3-D Navier-Stokes code for the prediction of turbulent flows, based on a finite-volume method and the k-e turbulence model. It is coupled with Ladrop, a program for the simulation of the liquid-phase flow, which is based on a Lagrangian formulation and computes the motion of evaporating droplets. The computational domain consists of a rectangular mesh containing 120 cells in the flow direction and 4 2 4 cells in the directions perpendicular to the flow. The length of the duct was set to 0.2 m in the flow direction. Since an ideal LPP duct would have a plug-flow characteristic, the problem
was made quasi one dimensional by assuming symmetric boundary conditions in the directions lateral to the main flow direction. Therefore, effects resulting from droplet-wall interactions or a boundary layer are not accounted for. Air and droplet velocity at the inlet were set to 20 m/s and 40 m/s, respectively. The location of the droplet injection point was randomly distributed. The liquid fuel temperature at the inlet was set to 350 K, a temperature typical for gas turbines. Droplet vaporization was calculated with the assumption of a uniform temperature inside the droplet. The liquid-phase calculations give the mass and enthalpy source terms resulting from the evaporating spray as a function of the distance downstream of the fuel injection point. The resulting source terms were passed to a second routine that predicts the progress of the chemical reactions. The chemical kinetics code consists of the SENKIN subroutine from the CHEMKIN II [10,11] package. SENKIN predicts the time-dependent chemical kinetics of a homogeneous gas mixture under the assumption of infinitely fast mixing and, hence, describes the chemical reactions in a plug-flow reactor. Therefore, the flow structure in both submodels is similar. Effects resulting from turbulent mixing are not considered within this kinetic model. As basis for the kinetic calculations, a detailed low-temperature mechanism for n-heptane [2] consisting of 168 species and 904 reactions was used. The event of autoignition is defined as the time when the temperature gradient ]T/]t reaches a maximum and additionally the temperature exceeds 1200 K. The most remarkable characteristic of n-heptane autoignition is the negative temperature coefficient region (NTC) at T . 800 K (Fig. 1). In this region the AID is independent of or increases slightly with temperature, a characteristic shown by all higherorder alkanes. Experiments [5,12] show that n-heptane is also well suited for the modeling of kerosene AID. Another property influencing AID is the evaporation time sE of the fuel droplets. Kerosene has a high content of volatile compounds that are well represented by n-heptane. Still, due to the presence of components with lower volatility, evaporation times of real fuels will generally be underestimated when considering n-heptane. As a consequence, the predicted AID has to be regarded as a lower limit for kerosene fuels.
Discussion of Results Under the assumption of fast mixing, autoignition of liquid fuel sprays can be characterised by two global timescales, one being the AID for an initially homogeneous, premixed fuel–air mixture (Fig. 1), the other the evaporation time sE of the spray (Fig. 2). Spray evaporation does affect autoignition by (a)
EVAPORATION INFLUENCE ON n-HEPTANE SPRAY AUTOIGNITION
Fig. 2. Time for evaporation of 95% of different liquid fuel sprays. Rossin-Rammler spread parameter set to m 4 1.8 for all polydisperse sprays.
Fig. 3. Autoignition delay as a function of pressure and initial temperature (comparison between initially premixed case and a 50-lm monodisperse spray); solid lines, 20 bar; dashed lines, 9 bar; nm, 50-lm droplets.
delaying the fuel supply to the hot air and (b) lowering the temperature of the mixture due to the release of evaporation enthalpy. With the assumption of infinitely fast evaporation, Fig. 1 illustrates how the autoignition time is affected by the “cooling” effect of the evaporating droplets. Solid symbols show the cases of initially premixed conditions, open symbols represent the cases where the exchange of evaporation enthalpy is taken into account. Because of the weak temperature dependence of AID inside the NTC region, almost no influence of cooling exists for T . 800 K, independent of U. The expected additional delay due to cooling is present only at
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Fig. 4. Autoignition delay for p 4 20 bar and U 4 0.5 (comparison between initially premixed case and monodisperse sprays); C, 10 lm; n, 50 lm; ▫, 100 lm.
lower initial temperatures. A linear dependence exists between the temperature drop due to liquid fuel evaporation and U. This dependence results in a minimum AID at f 4 0.5 for T 4 773 K initial temperature. Figure 3 shows AID for a monodisperse spray with 50-lm droplets. As expected, AID for the spray is higher than for the initially premixed gas. AID is reasonably increased at T , 750 K, which is due to cooling in the region of strong temperature dependence. Inside the NTC region, the increase in AID ranges between 2 and 4 ms, which is roughly the evaporation time of the spray (Fig. 2). In the further discussion, only cases at p 4 20 bar will be discussed, because AID longer than 10 ms is not critical to LPP combustion. A clearer picture of the relative importance between sE and cooling is given in Fig. 4. The time history of evaporation itself is mainly governed by the droplet size distribution of the spray (Fig. 2). As shown, AID increases with droplet size. Inside the NTC region, the increase of AID depends mainly on sE. At lower initial temperatures, the cooling effect gradually becomes more important. It is remarkable that although the 50-lm spray evaporates about 10 times slower than the 10-lm spray, at T 4 773 K the same ignition delay is found for both. An explanation is given in Figs. 5 to 8, which show the time histories of temperature and of the mass fractions of n-heptane, OH, and HO2. The two-stage ignition typical for n-heptane [3] is most evident in the temperature histories of the 10-lm spray. The time until the appearance of the first coolflame reactions is characterized by an induction time s1. The heat release of these reactions results in a temperature rise up to T ' 850 K. At this temperature the change from the degenerate chain-branching mode to a nonbranching mode takes place, thus inhibiting reactions [1,2].
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Fig. 5. Temperature time history of different sprays ( p 4 20 bar, T 4 773 K, and U 4 0.5); C, 10 lm; n, 50 lm; ▫, 100 lm.
Fig. 6. Time history of species mass fraction of different sprays ( p 4 20 bar, T 4 773 K, and U 4 0.5); solid, nheptane; dotted, HO2; dashed, OH.
At 773 K initial temperature, the 10-lm spray is completely evaporated before s1 (Figs. 5 and 6), whereas the 50-lm spray has almost finished evaporation before the onset of cool-flame reactions. The time history of the radicals is nearly the same for both sprays. Obviously, only reactions after s1, where the first significant fuel consumption and buildup of the radical pool takes place, are of importance. Because sE # s1 is valid for both sprays, almost the same conditions are present in the gaseous phase at s1, leading to similar AID. Since s1 falls with temperature, whereas sE is only a weak function of temperature (Fig. 2), at 873 K initial temperature only the 10-lm spray is evaporated before s1. At the onset of first reactions, only
Fig. 7. Temperature time history of different sprays ( p 4 20 bar, T 4 873 K, and U 4 0.5); C, 10 lm; n, 50 lm; ▫, 100 lm.
Fig. 8. Time history of species mass fraction of different sprays ( p 4 20 bar, T 4 873 K, and U 4 0.5); solid, nheptane; dotted, HO2; dashed, OH.
a part of the 50-lm spray is evaporated (Fig. 8), thus leading to fuel lean conditions at this stage resulting in a lower radical concentration. This clarifies that a delaying effect resulting from sE can only be expected when first reactions start during the course of evaporation. The dependence on U is shown in Figs. 9 and 10. At 873 K, where only an influence of sE is to be expected, the interpretation of the results is straightforward. AID for the sprays can be obtained roughly by adding sE to the AID of the initially premixed case. The delaying influence of evaporation is present for all droplet sizes, because s1 is always smaller than sE, except for the 10-lm spray. Both s1 [3] and
EVAPORATION INFLUENCE ON n-HEPTANE SPRAY AUTOIGNITION
Fig. 9. Autoignition delay of monodisperse and polydisperse sprays (T 4 773 K, p 4 20 bar); L, initially premixed; C, 10 lm; n, 50 lm; ▫, 100 lm; b, D63 4 20 lm, m 4 1.8; c, D63 4 40 lm, m 4 1.8.
almost finished before s1, leading to a negligible influence of sE. For those cases where sE has no influence, AID is almost constant for U 4 0.5 to 1. For the 10-lm spray, even a minimum exists at U 4 0.5 (Fig. 1). Hence, not only stoichiometric conditions may lead to minimum autoignition delays. With respect to LPP combustion, it is very important that a fine spray is generated allowing fast fuel evaporation and mixing with air. In view of this study, two regimes have to be discriminated. A significant increase in AID is achieved only for conditions similar to those at 773 K, almost independent of spray characteristics. If the duct parameters are such that the governing fuel chemistry shows a NTC dependence of AID, as for n-heptane at p 4 20 bar and T 4 873 and 973 K, the cooling effect of evaporation will have no influence. At these temperatures, small droplets with low sE will result in shorter AID. This may be misleading with respect to LPP combustion, because the time difference between the end of evaporation and the onset of autoignition, which can be regarded as being a safety margin, is more important than the absolute value of AID. Hence, the effect of the different droplet size distributions on this safety margin will be discussed. Subsequently, the assumption is made that the AID for a spray sign,S can be expressed as the sum of the evaporation time sE and the AID for the initially premixed case sign,P. Here sE is defined as the time needed for the evaporation of 95% of the fuel (Fig. 2). This relation may be written in a nondimensional form as sign,S /sign,P 4 1 ` sE /sign,P
Fig. 10. Autoignition delay of monodisperse and polydisperse sprays (T 4 873 K, p 4 20 bar); L, initially premixed; C, 10 lm; n, 50 lm; ▫, 100 lm; b, D63 4 20 lm, m 4 1.8; c, D63 4 40 lm, m 4 1.8.
sE depend only slightly on U (Fig. 2), which explains the similar behavior over the whole range of U considered. At 773 K initial temperature, AID is nearly the same for all sprays, the 100-lm spray being the only exception. In the case of 10-lm droplets, the increase in AID compared with the initially premixed case must be attributed to the cooling effect of evaporation (Fig. 1), because here sE is negligibly small. Hence, those sprays having the same AID as the 10lm spray must also be influenced by the cooling effect. For all these cases, evaporation is finished or
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(1)
In Figs. 11 and 12, sign,S /sign,P is plotted versus sE /sign,P. Variations of U are not explicitly marked. Equation 1 is denoted by the solid black line. Vertical displacements above this line are caused by the additional delay due to cooling. The dashed line indicates the equalities of sE and sign,S. Large vertical displacements above the dashed line correspond to large safety margins, whereas the region below the dashed line denotes cases where autoignition takes place before the end of evaporation. For T 4 873 K and 973 K, no case is found above the black line (Fig. 11), which again indicates that no cooling influence exists in this temperature region. The influence of the chemical reactions that take place during the course of evaporation is most evident for sprays with larger droplets. Also, different tendencies between the sprays with monodisperse and Rossin-Rammler droplet size distributions are present. Although all the 50-lm sprays show autoignition after the end of evaporation, this is not the case for the Rossin-Rammler spray with D63 4 40 lm. An explanation can be given by considering the Rossin-Rammler droplet size distribution. The
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of autoignition. The 10-lm and D63 4 20 lm sprays have the biggest safety margin for the temperatures considered. It follows that a narrow droplet size distribution with small droplets is favorable with respect to a high safety margin between the end of evaporation and autoignition. At 773 K initial temperature, the effect of cooling is evident (Fig. 12). Except for one 100-lm spray, all cases have a significant safety margin to autoignition. The additional delay is most pronounced for U 4 1, being highest for the smallest droplets. Also, in this temperature regime, a narrow droplet size distribution with small sprays is beneficial to the safety margin to autoignition. Conclusions Fig. 11. Effect of spray characteristics on the prolongation of the autoignition time (p 4 20 bar, T 4 873 and 973 K, and U 4 0.33 to 1); s, 10 lm; n, 50 lm; j, 100 lm; b, D63 4 20 lm, m 4 1.8; c, D63 4 40 lm, m 4 1.8.
Fig. 12. Effect of spray characteristics on the prolongation of the autoignition time (p 4 20 bar, T 4 773 K, and U 4 0.33 to 1); s, 10 lm; n, 50 lm; j, 100 lm; b, D63 4 20 lm, m 4 1.8; c, D63 4 40 lm, m 4 1.8.
Autoignition-delay times of liquid fuel spray/air mixtures have been investigated for a range of pressure, temperature, and equivalence ratio that is relevant to gas turbines. The effects of evaporation resulting from the existence of two temperature regions were shown. For cases where the initial air temperature is inside the NTC region, autoignition can be prolonged only by the delayed fuel supply to the airflow during the process of droplet evaporation. Cooling of the mixture due to evaporation has a negligible effect in this temperature region, since a weak dependence of AID on temperature exists here. For lower temperatures outside the NTC region, a strong temperature dependence exists, and cooling of the gas phase due to liquid fuel evaporation leads to a significant increase of AID, almost independent of spray characteristics. Only if the evaporation phase takes longer than the induction phase, defined by the onset of cool-flame reactions, is autoignition also increased by the delayed fuel supply to the airflow. The time gap between the end of evaporation and the event of autoignition is greatest for a spray with narrow droplet size distribution and small droplets. The assumption that the autoignition process is governed by those parts of the gas phase that are at stoichiometric conditions is not generally valid. In some cases, the shortest AID is found for lean cases at U 4 0.5. Acknowledgments
D63 4 40 lm spray contains 63% of its mass in droplets smaller than 40 lm. In the early stage of evaporation, the D63 4 40 lm spray will release more fuel vapor than the Ddr 4 50 lm monodisperse spray and will promote chemical reactions earlier. However, the D63 4 40 lm spray also contains mass in droplets bigger than, for example, 75 lm and, therefore, has a higher sE than the 50-lm spray. Hence, the wide droplet distribution decreases the time between the end of evaporation and the onset
This work has been supported by the European Community BRITE/EURAM Low-NOx III research program, contract number BRPR-CT95-0122.
REFERENCES 1. Chevalier, C., Louessard, P., Mueller, U. C., and Warnatz, J., in International Symposium COMODIA 90, 1990, pp. 93–97.
EVAPORATION INFLUENCE ON n-HEPTANE SPRAY AUTOIGNITION 2. Nehse, M., Warnatz, J., and Chevalier, C., in TwentySixth Symposium (International) on Combustion, 1996, pp. 773–780. 3. Ciezki, H. K. and Adomeit, G., Combust. Flame 93:421–433 (1993). 4. Fieweger, K., Blumental, R., and Adomeit, G., in Twenty-Fifth Symposium (International) on Combustion, 1994, pp. 1579–1585. 5. Pfahl, U., Fieweger, K., and Adomeit, G., in TwentySixth Symposium (International) on Combustion, 1996, pp. 781–789. 6. Shaddix, C. R., Brezinsky, K., and Glassman, I., in Twenty-Fourth Symposium (International) on Combustion, 1992, pp. 683–690.
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7. Correa, S. M. and Dean, A. J., in Twenty-Fifth Symposium (International) on Combustion, 1994, pp. 1293–1299. 8. Thibaut, D. and Candel, S., in Twenty-Sixth Symposium (International) on Combustion, 1996, pp. 2565– 2572. 9. Kurreck, M. and Wittig, S., ASME paper 94-GT-404 (1994). 10. Kee, R. J., Rupley, F. M., and Miller, J. A., SANDIA report SAND89-8009B. 11. Lutz, A. E., Kee, R. J., and Miller, J. A., SANDIA report SAND87-8248. 12. Dagaut, P., Reuillon, M., Boettner, J. C., and Chatonnet, M., in Twenty-Fifth Symposium (International) on Combustion, 1994, pp. 919–926.
THE INFLUENCE OF EVAPORATION ON THE AUTOIGNITION-DELAY OF n-HEPTANE AIR MIXTURES UNDER GAS TURBINE CONDITIONS M. CANO WOLFF, J. MEISL, R. KOCH and S. WITTIG Lehrstuhl und Institut fu¨r Thermische Stro¨mungsmaschinen Universita¨t Karlsruhe Kaiserstraße 12 76128 Karlsruhe, Germany
In this work, autoignition-delay times of liquid fuel sprays for flow situations similar to those in premixing ducts are calculated. An intensive parameter study was conducted to identify the influence of the evaporating spray on autoignition delay. The parameter variation covers duct conditions relevant to gas turbines. Three monodisperse sprays with droplet sizes of 10, 50, and 100 lm and two sprays with Rossin-Rammler droplet size distribution are investigated. A full 3-D Navier-Stokes code is used for the prediction of the turbulent flow. It is coupled to a code based on a Lagrangian formulation for the prediction of the motion and evaporation of the droplets. The evolution of the chemical kinetics is predicted with the CHEMKIN package for n-heptane, which is selected as fuel. A detailed n-heptane low-temperature mechanism including 168 species and 904 reactions describes the chemical kinetics. For initial temperatures inside the negative temperature coefficient region (NTC), the only spray parameter influencing autoignition delay is the spray evaporation time. If the initial temperature is on the lower boundary of the NTC region, the strong temperature dependence of autoignition in this region leads to a substantially longer autoignition delay due to the cooling of the gas phase caused by evaporation. A delaying effect of evaporation time is only present if the evaporation time is higher than the first induction time. Generally, the safety margin between autoignition and the end of evaporation is enhanced by utilization of a spray with small droplets and a narrow droplet size distribution. Also, a minimum autoignition delay for lean conditions at U 4 0.5 is identified.
Introduction Lean premixed prevaporized (LPP) combustion is the most promising concept for the reduction of NOx emissions from gas turbines. It also offers the possibility of an almost soot-free combustion of liquid fuels. Because thermal efficiency and specific power output are coupled to the compressor ratio, values of 40 are realized in modern gas turbines, and a further increase is to be expected for the future. At take-off conditions, pressures and temperatures at the compressor outlet of an aircraft gas turbine may reach 40 bar and 900 K. Because the autoignition delay (AID) of a fuel–air mixture decreases with growing pressure and temperature, the time available for liquid fuel evaporation and mixing with air in the premixing passage is limited. Especially with respect to aircraft gas turbines, safety reasons require that autoignition is avoided under all possible flight conditions. It is therefore necessary to predict and understand the interaction between turbulence, evaporating two-phase flow and chemical reactions in the combustor premixing section under a wide variety of conditions. Research in the field of internal combustion engines has led to an understanding of the gas-phase
chemical reactions leading to autoignition. Detailed kinetic mechanisms for alkanes such as n-heptane and n-decane [1,2] have been developed and validated under gas-turbine similar conditions by shock tube [3–5] and flow reactor [6] experiments. The interaction between autoignition gas-phase reactions and turbulence has been investigated numerically by Correa and Dean [7]. It was shown how inhomogeneities in the fuel–air concentration distribution could control the autoignition process. Slow mixing allowed separate autoignition of the stoichiometric fluid volumes, resulting in low ignition delays. The higher autoignition-delay time corresponding to the mean air–fuel ratio of the lean mixture was achieved only for fast mixing. Thibaut and Candel [8] have investigated the possible autoignition modes of a droplet cloud suspended in a hot stagnating atmosphere. Depending on initial conditions, autoignition could either take place inside the cloud or in the diffusion layer surrounding the cloud. This demonstrated how spatial nonuniformities and the cooling due to evaporation interact to influence the autoignition process. The objective of this study is to investigate the influence of the evaporation process on the gasphase chemical kinetics leading to autoignition of
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Fig. 1. Autoignition-delay times at p 4 20 bar; lines, initially premixed; n●, without evaporation enthalpy; ▫C, with evaporation enthalpy.
the air–fuel mixture in a typical LPP configuration. The model developed is designed to calculate autoignition-delay times allowing a wide parameter variation of the duct inlet conditions. In our study a verified detailed mechanism has been used to calculate the reaction progress of the gas phase. The range of LPP duct conditions examined included pressures of p 4 9 and 20 bar, inlet temperatures between T 4 673 and 973 K, and equivalence ratios from U 4 0.33 to 1. Because the evaporation process depends on droplet diameter, five different sprays have been investigated: three monodisperse sprays with droplet diameters of 10, 50, and 100 lm and two sprays with Rossin-Rammler distribution as representatives of real fuel sprays.
Numerical Model The entire model was developed to determine AID of flows typical for LPP ducts. Thus, two verified submodels were used for the calculations. In a first step, the evaporating two-phase flow was simulated by the two in-house codes Epos and Ladrop. Epos [9] is a fully 3-D Navier-Stokes code for the prediction of turbulent flows, based on a finite-volume method and the k-e turbulence model. It is coupled with Ladrop, a program for the simulation of the liquid-phase flow, which is based on a Lagrangian formulation and computes the motion of evaporating droplets. The computational domain consists of a rectangular mesh containing 120 cells in the flow direction and 4 2 4 cells in the directions perpendicular to the flow. The length of the duct was set to 0.2 m in the flow direction. Since an ideal LPP duct would have a plug-flow characteristic, the problem
was made quasi one dimensional by assuming symmetric boundary conditions in the directions lateral to the main flow direction. Therefore, effects resulting from droplet-wall interactions or a boundary layer are not accounted for. Air and droplet velocity at the inlet were set to 20 m/s and 40 m/s, respectively. The location of the droplet injection point was randomly distributed. The liquid fuel temperature at the inlet was set to 350 K, a temperature typical for gas turbines. Droplet vaporization was calculated with the assumption of a uniform temperature inside the droplet. The liquid-phase calculations give the mass and enthalpy source terms resulting from the evaporating spray as a function of the distance downstream of the fuel injection point. The resulting source terms were passed to a second routine that predicts the progress of the chemical reactions. The chemical kinetics code consists of the SENKIN subroutine from the CHEMKIN II [10,11] package. SENKIN predicts the time-dependent chemical kinetics of a homogeneous gas mixture under the assumption of infinitely fast mixing and, hence, describes the chemical reactions in a plug-flow reactor. Therefore, the flow structure in both submodels is similar. Effects resulting from turbulent mixing are not considered within this kinetic model. As basis for the kinetic calculations, a detailed low-temperature mechanism for n-heptane [2] consisting of 168 species and 904 reactions was used. The event of autoignition is defined as the time when the temperature gradient ]T/]t reaches a maximum and additionally the temperature exceeds 1200 K. The most remarkable characteristic of n-heptane autoignition is the negative temperature coefficient region (NTC) at T . 800 K (Fig. 1). In this region the AID is independent of or increases slightly with temperature, a characteristic shown by all higherorder alkanes. Experiments [5,12] show that n-heptane is also well suited for the modeling of kerosene AID. Another property influencing AID is the evaporation time sE of the fuel droplets. Kerosene has a high content of volatile compounds that are well represented by n-heptane. Still, due to the presence of components with lower volatility, evaporation times of real fuels will generally be underestimated when considering n-heptane. As a consequence, the predicted AID has to be regarded as a lower limit for kerosene fuels.
Discussion of Results Under the assumption of fast mixing, autoignition of liquid fuel sprays can be characterised by two global timescales, one being the AID for an initially homogeneous, premixed fuel–air mixture (Fig. 1), the other the evaporation time sE of the spray (Fig. 2). Spray evaporation does affect autoignition by (a)
EVAPORATION INFLUENCE ON n-HEPTANE SPRAY AUTOIGNITION
Fig. 2. Time for evaporation of 95% of different liquid fuel sprays. Rossin-Rammler spread parameter set to m 4 1.8 for all polydisperse sprays.
Fig. 3. Autoignition delay as a function of pressure and initial temperature (comparison between initially premixed case and a 50-lm monodisperse spray); solid lines, 20 bar; dashed lines, 9 bar; nm, 50-lm droplets.
delaying the fuel supply to the hot air and (b) lowering the temperature of the mixture due to the release of evaporation enthalpy. With the assumption of infinitely fast evaporation, Fig. 1 illustrates how the autoignition time is affected by the “cooling” effect of the evaporating droplets. Solid symbols show the cases of initially premixed conditions, open symbols represent the cases where the exchange of evaporation enthalpy is taken into account. Because of the weak temperature dependence of AID inside the NTC region, almost no influence of cooling exists for T . 800 K, independent of U. The expected additional delay due to cooling is present only at
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Fig. 4. Autoignition delay for p 4 20 bar and U 4 0.5 (comparison between initially premixed case and monodisperse sprays); C, 10 lm; n, 50 lm; ▫, 100 lm.
lower initial temperatures. A linear dependence exists between the temperature drop due to liquid fuel evaporation and U. This dependence results in a minimum AID at f 4 0.5 for T 4 773 K initial temperature. Figure 3 shows AID for a monodisperse spray with 50-lm droplets. As expected, AID for the spray is higher than for the initially premixed gas. AID is reasonably increased at T , 750 K, which is due to cooling in the region of strong temperature dependence. Inside the NTC region, the increase in AID ranges between 2 and 4 ms, which is roughly the evaporation time of the spray (Fig. 2). In the further discussion, only cases at p 4 20 bar will be discussed, because AID longer than 10 ms is not critical to LPP combustion. A clearer picture of the relative importance between sE and cooling is given in Fig. 4. The time history of evaporation itself is mainly governed by the droplet size distribution of the spray (Fig. 2). As shown, AID increases with droplet size. Inside the NTC region, the increase of AID depends mainly on sE. At lower initial temperatures, the cooling effect gradually becomes more important. It is remarkable that although the 50-lm spray evaporates about 10 times slower than the 10-lm spray, at T 4 773 K the same ignition delay is found for both. An explanation is given in Figs. 5 to 8, which show the time histories of temperature and of the mass fractions of n-heptane, OH, and HO2. The two-stage ignition typical for n-heptane [3] is most evident in the temperature histories of the 10-lm spray. The time until the appearance of the first coolflame reactions is characterized by an induction time s1. The heat release of these reactions results in a temperature rise up to T ' 850 K. At this temperature the change from the degenerate chain-branching mode to a nonbranching mode takes place, thus inhibiting reactions [1,2].
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Fig. 5. Temperature time history of different sprays ( p 4 20 bar, T 4 773 K, and U 4 0.5); C, 10 lm; n, 50 lm; ▫, 100 lm.
Fig. 6. Time history of species mass fraction of different sprays ( p 4 20 bar, T 4 773 K, and U 4 0.5); solid, nheptane; dotted, HO2; dashed, OH.
At 773 K initial temperature, the 10-lm spray is completely evaporated before s1 (Figs. 5 and 6), whereas the 50-lm spray has almost finished evaporation before the onset of cool-flame reactions. The time history of the radicals is nearly the same for both sprays. Obviously, only reactions after s1, where the first significant fuel consumption and buildup of the radical pool takes place, are of importance. Because sE # s1 is valid for both sprays, almost the same conditions are present in the gaseous phase at s1, leading to similar AID. Since s1 falls with temperature, whereas sE is only a weak function of temperature (Fig. 2), at 873 K initial temperature only the 10-lm spray is evaporated before s1. At the onset of first reactions, only
Fig. 7. Temperature time history of different sprays ( p 4 20 bar, T 4 873 K, and U 4 0.5); C, 10 lm; n, 50 lm; ▫, 100 lm.
Fig. 8. Time history of species mass fraction of different sprays ( p 4 20 bar, T 4 873 K, and U 4 0.5); solid, nheptane; dotted, HO2; dashed, OH.
a part of the 50-lm spray is evaporated (Fig. 8), thus leading to fuel lean conditions at this stage resulting in a lower radical concentration. This clarifies that a delaying effect resulting from sE can only be expected when first reactions start during the course of evaporation. The dependence on U is shown in Figs. 9 and 10. At 873 K, where only an influence of sE is to be expected, the interpretation of the results is straightforward. AID for the sprays can be obtained roughly by adding sE to the AID of the initially premixed case. The delaying influence of evaporation is present for all droplet sizes, because s1 is always smaller than sE, except for the 10-lm spray. Both s1 [3] and
EVAPORATION INFLUENCE ON n-HEPTANE SPRAY AUTOIGNITION
Fig. 9. Autoignition delay of monodisperse and polydisperse sprays (T 4 773 K, p 4 20 bar); L, initially premixed; C, 10 lm; n, 50 lm; ▫, 100 lm; b, D63 4 20 lm, m 4 1.8; c, D63 4 40 lm, m 4 1.8.
almost finished before s1, leading to a negligible influence of sE. For those cases where sE has no influence, AID is almost constant for U 4 0.5 to 1. For the 10-lm spray, even a minimum exists at U 4 0.5 (Fig. 1). Hence, not only stoichiometric conditions may lead to minimum autoignition delays. With respect to LPP combustion, it is very important that a fine spray is generated allowing fast fuel evaporation and mixing with air. In view of this study, two regimes have to be discriminated. A significant increase in AID is achieved only for conditions similar to those at 773 K, almost independent of spray characteristics. If the duct parameters are such that the governing fuel chemistry shows a NTC dependence of AID, as for n-heptane at p 4 20 bar and T 4 873 and 973 K, the cooling effect of evaporation will have no influence. At these temperatures, small droplets with low sE will result in shorter AID. This may be misleading with respect to LPP combustion, because the time difference between the end of evaporation and the onset of autoignition, which can be regarded as being a safety margin, is more important than the absolute value of AID. Hence, the effect of the different droplet size distributions on this safety margin will be discussed. Subsequently, the assumption is made that the AID for a spray sign,S can be expressed as the sum of the evaporation time sE and the AID for the initially premixed case sign,P. Here sE is defined as the time needed for the evaporation of 95% of the fuel (Fig. 2). This relation may be written in a nondimensional form as sign,S /sign,P 4 1 ` sE /sign,P
Fig. 10. Autoignition delay of monodisperse and polydisperse sprays (T 4 873 K, p 4 20 bar); L, initially premixed; C, 10 lm; n, 50 lm; ▫, 100 lm; b, D63 4 20 lm, m 4 1.8; c, D63 4 40 lm, m 4 1.8.
sE depend only slightly on U (Fig. 2), which explains the similar behavior over the whole range of U considered. At 773 K initial temperature, AID is nearly the same for all sprays, the 100-lm spray being the only exception. In the case of 10-lm droplets, the increase in AID compared with the initially premixed case must be attributed to the cooling effect of evaporation (Fig. 1), because here sE is negligibly small. Hence, those sprays having the same AID as the 10lm spray must also be influenced by the cooling effect. For all these cases, evaporation is finished or
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(1)
In Figs. 11 and 12, sign,S /sign,P is plotted versus sE /sign,P. Variations of U are not explicitly marked. Equation 1 is denoted by the solid black line. Vertical displacements above this line are caused by the additional delay due to cooling. The dashed line indicates the equalities of sE and sign,S. Large vertical displacements above the dashed line correspond to large safety margins, whereas the region below the dashed line denotes cases where autoignition takes place before the end of evaporation. For T 4 873 K and 973 K, no case is found above the black line (Fig. 11), which again indicates that no cooling influence exists in this temperature region. The influence of the chemical reactions that take place during the course of evaporation is most evident for sprays with larger droplets. Also, different tendencies between the sprays with monodisperse and Rossin-Rammler droplet size distributions are present. Although all the 50-lm sprays show autoignition after the end of evaporation, this is not the case for the Rossin-Rammler spray with D63 4 40 lm. An explanation can be given by considering the Rossin-Rammler droplet size distribution. The
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of autoignition. The 10-lm and D63 4 20 lm sprays have the biggest safety margin for the temperatures considered. It follows that a narrow droplet size distribution with small droplets is favorable with respect to a high safety margin between the end of evaporation and autoignition. At 773 K initial temperature, the effect of cooling is evident (Fig. 12). Except for one 100-lm spray, all cases have a significant safety margin to autoignition. The additional delay is most pronounced for U 4 1, being highest for the smallest droplets. Also, in this temperature regime, a narrow droplet size distribution with small sprays is beneficial to the safety margin to autoignition. Conclusions Fig. 11. Effect of spray characteristics on the prolongation of the autoignition time (p 4 20 bar, T 4 873 and 973 K, and U 4 0.33 to 1); s, 10 lm; n, 50 lm; j, 100 lm; b, D63 4 20 lm, m 4 1.8; c, D63 4 40 lm, m 4 1.8.
Fig. 12. Effect of spray characteristics on the prolongation of the autoignition time (p 4 20 bar, T 4 773 K, and U 4 0.33 to 1); s, 10 lm; n, 50 lm; j, 100 lm; b, D63 4 20 lm, m 4 1.8; c, D63 4 40 lm, m 4 1.8.
Autoignition-delay times of liquid fuel spray/air mixtures have been investigated for a range of pressure, temperature, and equivalence ratio that is relevant to gas turbines. The effects of evaporation resulting from the existence of two temperature regions were shown. For cases where the initial air temperature is inside the NTC region, autoignition can be prolonged only by the delayed fuel supply to the airflow during the process of droplet evaporation. Cooling of the mixture due to evaporation has a negligible effect in this temperature region, since a weak dependence of AID on temperature exists here. For lower temperatures outside the NTC region, a strong temperature dependence exists, and cooling of the gas phase due to liquid fuel evaporation leads to a significant increase of AID, almost independent of spray characteristics. Only if the evaporation phase takes longer than the induction phase, defined by the onset of cool-flame reactions, is autoignition also increased by the delayed fuel supply to the airflow. The time gap between the end of evaporation and the event of autoignition is greatest for a spray with narrow droplet size distribution and small droplets. The assumption that the autoignition process is governed by those parts of the gas phase that are at stoichiometric conditions is not generally valid. In some cases, the shortest AID is found for lean cases at U 4 0.5. Acknowledgments
D63 4 40 lm spray contains 63% of its mass in droplets smaller than 40 lm. In the early stage of evaporation, the D63 4 40 lm spray will release more fuel vapor than the Ddr 4 50 lm monodisperse spray and will promote chemical reactions earlier. However, the D63 4 40 lm spray also contains mass in droplets bigger than, for example, 75 lm and, therefore, has a higher sE than the 50-lm spray. Hence, the wide droplet distribution decreases the time between the end of evaporation and the onset
This work has been supported by the European Community BRITE/EURAM Low-NOx III research program, contract number BRPR-CT95-0122.
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EVAPORATION INFLUENCE ON n-HEPTANE SPRAY AUTOIGNITION 2. Nehse, M., Warnatz, J., and Chevalier, C., in TwentySixth Symposium (International) on Combustion, 1996, pp. 773–780. 3. Ciezki, H. K. and Adomeit, G., Combust. Flame 93:421–433 (1993). 4. Fieweger, K., Blumental, R., and Adomeit, G., in Twenty-Fifth Symposium (International) on Combustion, 1994, pp. 1579–1585. 5. Pfahl, U., Fieweger, K., and Adomeit, G., in TwentySixth Symposium (International) on Combustion, 1996, pp. 781–789. 6. Shaddix, C. R., Brezinsky, K., and Glassman, I., in Twenty-Fourth Symposium (International) on Combustion, 1992, pp. 683–690.
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7. Correa, S. M. and Dean, A. J., in Twenty-Fifth Symposium (International) on Combustion, 1994, pp. 1293–1299. 8. Thibaut, D. and Candel, S., in Twenty-Sixth Symposium (International) on Combustion, 1996, pp. 2565– 2572. 9. Kurreck, M. and Wittig, S., ASME paper 94-GT-404 (1994). 10. Kee, R. J., Rupley, F. M., and Miller, J. A., SANDIA report SAND89-8009B. 11. Lutz, A. E., Kee, R. J., and Miller, J. A., SANDIA report SAND87-8248. 12. Dagaut, P., Reuillon, M., Boettner, J. C., and Chatonnet, M., in Twenty-Fifth Symposium (International) on Combustion, 1994, pp. 919–926.