Numerical Study on the Characteristics of Vaporization, Ignition, and

Oct 23, 2008 - of DME and diesel fuel sprays injected by a DI diesel injector. 1999, SAE ...... tail region of the fuel vapor jet, the scalar dissipat...
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Energy & Fuels 2008, 22, 3649–3660

3649

Numerical Study on the Characteristics of Vaporization, Ignition, and Turbulent Combustion Processes in Dimethyl Ether (DME)-Fueled Engine Conditions Yongwook Yu, Sungmo Kang, Yongmo Kim,* and Kwan-Soo Lee Department of Mechanical Engineering, Hanyang UniVersity, 17, Haengdang-Dong, Sungdong-Ku, Seoul 133-791, Korea ReceiVed March 24, 2008. ReVised Manuscript ReceiVed July 23, 2008

Among oxygenated fuels, the simplest ether fuel, dimethyl ether (DME), is often regarded as the next generation fuel because of its superior soot emission characteristics. However, DME has distinctly different spray combustion characteristics from the conventional hydrocarbon liquid diesel fuels in terms of evaporation, ignition, high vapor pressure, cetane number, oxygenate ingredient, heat release rate, liquid density, etc. In the present study, to understand the overall spray combustion characteristics of DME fuel as well as to identify the distinctive differences of DME combustion processes compared to conventional hydrocarbon liquid fuels, the sequence of the comparative analysis has been systematically made for DME and n-heptane liquid fuels. To realistically represent the physical processes involved in the spray combustion, this study employs the hybrid breakup model, the stochastic droplet tracking model, collision model, high-pressure evaporation model, and transient flamelet model with detailed chemistry. On the basis of numerical results, the detailed discussions are made in terms of the evaporation characteristics of a single droplet at high-pressure, combustion processes, ignition characteristics of homogeneous mixtures and spray jets, flame structure, and turbulence-chemistry interaction in the n-heptane and DME-fueled spray combustion processes.

1. Introduction Among oxygenated fuels, the simplest ether fuel, dimethyl ether (DME), has been attracting much attention as a clean alternative fuel for diesel engines. The cetane number of DME is high enough to operate conventional compression-ignition engines. The thermal efficiency of a DME-powered diesel engine is comparable to that of diesel fuel operation, and soot-free combustion can be achieved without any extra modifications. However, because DME has distinctly different spray combustion characteristics from conventional hydrocarbon liquid diesel fuels in terms of evaporation, ignition, vapor pressure, cetane number, oxygenate ingredient, heat release rate, and liquid density, the application of DME in diesel engines creates many problems associated with the fuel-air mixing processes. Although DME burns well in the combustion systems of direct-injection (DI) diesel engines at light and medium loads and all speeds, the combustion efficiency of DME-fueled diesel engines with insufficient mixing could be deteriorated at high loads and high speeds. In this respect, more research is needed for spray dynamics, vaporization, ignition, and turbulent combustion processes of DME fuel. There have been experimental1-5 and analytical6 studies to understand the characteristics of the DME spray combustions * To whom correspondence should be addressed: Department of Mechanical Engineering, Hanyang University, 17, Haengdang-Dong, SungdongKu, Seoul 133-791, Korea. Telephone: +82-2-2220-0428. Fax: +82-2-22973432. E-mail: [email protected]. (1) Arcoumanis, C. The second European auto-oil programme (AOLII). European Commission, 2000; Vol. 2, Alternative Fuels for Transportation. (2) Sorenson, S. C.; Glensvig, M.; Abata, D. Di-methyl ether in the diesel fuel injection systems. 1998; SAE Paper 981159. (3) Wakai, K.; Nishida, K.; Yoshizaki, T.; Hiroyasu, H. Spray and ignition characteristics of di-methyl ether injected by a DI diesel injector. Proceedings of the Fourth International Symposium COMODIA, 1998; pp 537-542.

as well as to optimally design the DME injection and combustion systems. The numerical modelings for the DME spray combustion processes are relatively rare because of the lack of reliable and fully informative experimental data as well as the shortcomings of the combustion model to realistically simulate the DME spray combustion processes. Golovitchev et al.7,8 performed numerical simulations of DME spray combustion. The predictive capability of their spray combustion model was validated against experimental data in terms of liquid and vapor penetration and ignition in a constant-volume chamber. Very recently, Kim et al.9 numerically and experimentally investigated the characteristics of the turbulent combustion processes of DME sprays. Numerical simulation of spray development and ignition process of DME sprays was performed using a transient flamelet model together with the low-pressure vaporization model and the reduced chemical kinetic mechanism. The numerical results agreed reasonably well with the experimental data. However, there is still a lot of room to improve the physical submodels (4) Kajitani, S.; Chen, Z.; Oguma, M.; Konno, M. A study of low compression-ratio di-methyl ether diesel engines. Int. J. Engine Res. 2002, 2, 1–11. (5) Wakai, K.; Nishida, K.; Yoshizaki, T.; Hiroyasu, H. Ignition delays of DME and diesel fuel sprays injected by a DI diesel injector. 1999, SAE Paper 1999-01-3600. (6) Teng, H.; McCandless, J. C.; Schneyer, J. B. Thermo-chemical characteristics of di-methyl ethersAn alternative fuel for compressionignition engines. 2001 SAE Paper 2001-01-0154. (7) Golovitchev, V. I.; Nordin, N.; Chomiak, J. Neat di-methyl ether: Is it really diesel fuel of promise? 1998, SAE Paper 982537. (8) Golovitchev, V. I.; Nordin, N.; Chomiak, J.; Nishida, N.; Wakai, K. Evaluation of ignition quality of DME at diesel engine conditions. Proceedings of the Fourth International Conference of Internal Combustion Engines 99 (ICE99): Experiments and Modeling, 1999; pp 299-306. (9) Kim, Y.; Lim, J.; Min, K. A study of the dimethyl ether spray characteristics and ignition delay. Int. J. Engine Res. 2007, 8, 337–346.

10.1021/ef8002119 CCC: $40.75  2008 American Chemical Society Published on Web 10/23/2008

3650 Energy & Fuels, Vol. 22, No. 6, 2008

Yu et al.

to realistically predict the physically complex DME spray combustion processes. In general, the comprehensive modeling of the spray combustion in DME-fueled combustion engines requires physical submodels for the complex physical processes, such as the atomization of the liquid fuel, the evaporation of the fuel droplets, the mixing of fuel and air, auto-ignition of fuel vapor, and turbulence-chemistry interaction. Among these physical processes, vaporization is one of the dominant mechanisms in DME spray combustion. Because the pressure level during the combustion process of the compression ignition engines is usually higher than the critical pressure of the liquid hydrocarbon fuels, the reliable droplet vaporization model is an essential element to realistically predict the high-pressure spray combustion processes. The modeling of the droplet vaporization process under high-pressure conditions requires to take into account the additionally complex effects such as the real gas behavior, the variation of thermophysical properties, the non-ideality of the latent heat of evaporation, and the non-ideal phase equilibrium including the solubility of the ambient gas inside the droplet. So far, most spray combustion models are based on the low-pressure model similar to the vaporization routine of the KIVA code.10 However, the low-pressure vaporization model unrealistically predicts the vaporization process in the high-pressure environment. In this respect, it is quite desirable to develop an improved vaporization model that can be applicable to a wide range of operating pressures. Recently, Yang11 made a comprehensive review of high-pressure vaporization, mixing, and combustion processes encountered in liquid-fueled propulsion systems. The fuel vapor auto-ignition also considerably influences the characteristics of the spray combustion. The spray ignition process is often simulated by the Shell ignition model,12-14 which is unable to include the turbulent effects on the ignition process. Moreover, this Shell ignition model has the basic shortcoming that the parameters must be tuned according to the combustion conditions. To overcome these defects, Pitsch et al.15 suggested the representative interactive flamelet (RIF) model, which does not require the tuning of parameters and can account for the turbulence-chemistry interaction based on the detailed chemistry. Hence, auto-ignition, partially premixed burning, diffusive combustion, and pollutant formation need not be modeled individually. These RIF calculations are made interactively with the changes of flow and mixing fields, which are obtained by a CFD solver. Therefore, the time-dependent effects of flow and mixing fields are accounted for in RIF through appropriate modeling of the scalar dissipation rate. To account for the spatial inhomogeneity of the scalar dissipation rate in the nonstationary spray flame field of direct-injection diesel engines, Barths et al.16 devised the multiple flamelets procedure. On the other hand, most of the previous works for

the simulation of turbulent spray combustion have neglected the vaporization effects on turbulent spray combustion, except the interphase vaporization source term in the mean mixture fraction. However, the DNS results by Reveillon and Vervisch17 revealed that the impact of vaporization sources on the small scales of the turbulent fuel distribution significantly modifies the fluctuations of mixture fraction and subsequently the scalar dissipation rate. Recently, Demoulin and Borghi18 proposed the new model to include these major effects of spray vaporization on the mixture fraction fluctuations and the PDF model. To realistically represent the spray combustion processes involved in the high-pressure environment, the present study employs the KH-RT breakup model,19 the stochastic droplet tracking model,10 the collision model,20 the high-pressure evaporation model,21 and the transient flamelet model with detailed chemistry. Moreover, to include the spray vaporization effects on the mixture fraction fluctuations and the PDF model, the present study employs the model proposed by Demoulin and Borghi.18 The present high-pressure evaporation model can account for transient liquid heating, circulation effect inside the droplet, forced convection, Stefan flow effect, real gas effect, and ambient gas solubility in the liquid droplets in high-pressure conditions. The coupling between complex chemistry and turbulence is treated by employing the representative interactive flamelet (RIF) model. The spatial inhomogeneity of the scalar dissipation rate is treated by the multiple RIF procedure.16,22 The chemistries used in this study are based on the detailed chemical mechanisms, which include low- and high-temperature auto-ignition, fuel decomposition, and fuel oxidation. This improved spray combustion model has been applied to simulate the spray dynamics, vaporization, auto-ignition, and combustion process in n-heptane- and DME-fueled engine conditions. In the present study, to understand the overall spray combustion characteristics of DME fuel as well as to identify the distinctive differences of DME combustion processes compared to conventional hydrocarbon liquid fuels, the sequence of the comparative analysis has been systematically made for n-heptane and DME liquid fuels. On the basis of numerical results, the detailed discussions are also made in terms of the evaporation characteristics of single droplet under high-pressure conditions, combustion processes, ignition characteristics of homogeneous mixtures and spray jets, flame structure, and turbulence-chemistry interaction in n-heptane- and DME-fueled diesel-like combustion conditions.

(10) Amsden, A. A.; O’Rourke, P. J.; Butler, T. D. KIVA II: A computer program for chemically reactive flows with sprays. Los Alamos National Laboratory Report, 1989, LA-11560-MS. (11) Yang, V. Modeling of supercritical vaporization, mixing, and combustion processes in liquid-fueled propulsion systems. Proceedings of the 28th International Symposium on Combustion, The Combustion Institute, Pittsburgh, PA, 2000. (12) Halstead, M. P.; Kirsch, L. J.; Prothero, A.; Quinn, C. P. A mathematical model for hydrocarbon auto-ignition at high pressures. Proc. R. Soc. London, Ser. A 1975, 346, 515–538. (13) Kong, S. C.; Han, Z.; Reitz, R. D. The development and application of a diesel ignition and combustion model for multidimensional engine simulations. 1995, SAE Paper 950278. (14) Sazhina, E. M.; Sazhin, S. S.; Heikal, M. R.; Marooney, C. J. The shell autoignition model: Applications to gasoline and diesel fuels. Fuel 1999, 78, 389–401. (15) Pitsch, H.; Barths, H.; Peters, N. Three-dimensional modeling of NOx and soot formation in DI-diesel engines using detailed chemistry based on the interactive flamelet approach. 1996, SAE Paper 962057.

(16) Barths, H.; Antoni, C.; Peters, N. Three-dimensional simulation of pollutant formation in a DI-diesel engines using multiple interactive flamelets. 1998, SAE Paper 982456. (17) Reveillon, J.; Vervish, L. Spray vaporization in nonpremixed turbulent combustion modeling: A single droplet model. Combust. Flame 2000, 121, 75–90. (18) Demoulin, F. X.; Borghi, R. Assumed PDF modeling of turbulent spray combustion. Combust. Sci. Technol. 2000, 158, 249–271. (19) Patterson, M. A.; Reitz, R. D. Modeling of the effects of fuel spray characteristics on diesel engine combustion and emission. 1998, SAE Paper 980131. (20) O’Rourke, P. J. Collective drop effects on vaporing liquid sprays. Los Alamos National Laboratory Report 1981, LA-9069T. (21) Yu, Y. W.; Kim, S. K.; Kim, Y. M. Numerical modeling for autoignition and combustion processes of fuel spays in high-pressure environment. Combust. Sci. Technol. 2001, 168, 85–112. (22) Kim, S. K.; Yu, Y. W.; Ahn, J. H.; Kim, Y. M. Numerical investigation of the autoignition of turbulent gaseous jets in a high-pressure environment using the multiple-RIF model. Fuel 2004, 83, 375–386.

2. Physical and Numerical Models The spray combustion involves complex physical processes, such as the atomization of the liquid fuel, droplet breakup, droplet

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Energy & Fuels, Vol. 22, No. 6, 2008 3651

dispersion by turbulence, droplet collision, evaporation, turbulent mixing, auto-ignition, and turbulence-chemistry interaction. In this study, all submodels for these important physical processes are implemented in the multidimensional Eulerian-Lagrangian formulation. The gas-phase equation is written in an Eulerian coordinate, whereas the liquid-phase is presented in Lagrangian coordinates. The two-way coupling between the two phases is described by the interphase source terms that represent the rate of momentum and mass and heat transfer. The physical models used in the present study include the hybrid droplet breakup model,19 stochastic droplet tracking technique,10 O’Rourke’s droplet collision model,20 high-pressure vaporization model, standard k-ε turbulent model, and transient flamelet model.15,21 All of these physical models for the spray dynamics are implemented in the KIVA II code.10 The atomization process occurs on time and length scales too short to be resolved with practical computational grid sizes and time steps. Thus, atomization should be modeled as a subgrid-scale process. To account for the liquid atomization and droplet breakup, the hybrid droplet breakup model19 has been employed. This breakup model is based on the assumption that atomization and drop breakup are indistinguishable processes within a dense spray near the nozzle exit. Accordingly, atomization is prescribed by injecting drops that have a characteristic size equal to the nozzle exit diameter. In the stochastic droplet tracking approach,10 to account for the droplet dispersion by turbulence, the instantaneous velocity components are obtained by adding stochastically generated turbulent fluctuating velocity components to the mean gas-phase velocity field. If the gas-phase turbulence is assumed to be isotropic, the random turbulent fluctuating velocity components are assumed to have a Gaussian probability distribution with the standard deviation based on the turbulent kinetic energy. The droplet-eddy interaction time is assumed to be the minimum of either the eddy lifetime or the droplet transit time to cross the eddy. In the drop collision model,20 the probability distributions governing the number and outcomes of the collisions between two drops are sampled randomly in consistency with the stochastic particle tracking method. Among the physical submodels adopted in this study, the highpressure vaporization model and the transient flamelet model are precisely described below. 2.1. High-Pressure Vaporization Model. To account for the high-pressure vaporization processes in context with the comprehensive spray combustion modeling, the present high-pressure vaporization model is based on the following assumptions: (1) The fuel droplet is assumed to be a continuum of perfect sphere. (2) The gas phase is assumed to be spherically symmetric using a modified relation based on the film theory to account for the effect of convection. (3) The liquid phase is also assumed to be spherically symmetric. (4) The interface between the liquid and gas phases is calculated by the condition of phase equilibrium. (5) The gas phase is assumed by the quasi-equilibrium state. (6) The 1/3 law is adopted to calculate the average properties of the gas phase, and properties of the liquid phase are accounted for by the spatial and time variance. (7) The ambient pressure is constant. (8) There is no radiation effect. (9) Dufour effect and viscous dissipation are neglected. To calculate the heat and mass flux between the droplet and gas field, a film correction presented by Abramzon and Sirignano23 is chosen. The convective effects on heat and mass transfer of the droplet evaporation are determined by

(Nu0 - 2) F(BT) (Sh0 - 2) Sh* ) 2 + F(BM)

Nu* ) 2 +

(1) (2)

(23) Abramzon, B.; Sirignano, W. A. Approximate theory of a single droplet vaporization in a convective field: Effects of variable properties, Stefan flow and transient liquid heating. Proceedings of Second ASMEJSME Thermal Engineering Joint Conference, 1987; Vol. 1, pp 11-18.

where Nu is the Nusselt number and Sh is the Sherwood number. BM and BT are the Spalding numbers of mass and heat transfer. The subscript “0” and the superscript “/” denote nonvaporizing and vaporizing spheres, respectively. The Stefan flow resulting from mass transfer increases the film thickness. Abramzon and Sirignano23 suggest that the variation of film thickness has the following relationship with Spalding transfer number, B

F(B) ) (1 + B)0.7

ln(1 + B) B

(3)

The convective heat or mass transfer between a solid nonvaporizing spherical particle and a fluid flow are calculated from the correlation of Ranz and Marshall.

Nu0 ) 2.0 + 0.6Re1/2Pr1/3 Sh0 ) 2.0 + 0.6Re1/2Sc1/3

(4)

Here, Re, Pr, and Sc denote the Reynolds number, Prandtl number, and Schmidt number, respectively. The thermophysical properties used in the above equations are obtained in the film by the 1/3 rule, but the gas density of the Reynolds number is calculated from the free stream conditions. Using film theory, the mass transfer rates m ˙ F are calculated from

m ˙ F ) 2πrsFgDgSh* ln(1 + BM)

(5)

Kg Nu* ln(1 + BT) Cpg

(6)

m ˙ F ) 2πrs

Here, rs, Fg, Dg, Kg, and Cpg denote droplet radius, gas density, diffusion coefficient, thermal conductivity, and specific heat of the gas phase, respectively. Subscripts “s” and “g” represent the values of the droplet surface and gas film, respectively. BM and BT are the Spalding number of mass and heat transfer, defined as below

YFs - YF∞ 1 - YFs

(7)

Cpg(T∞ - Ts) L(p, Ts) + QL/m ˙F

(8)

BM ) BT )

Here, YFs and YF∞ represent the mass fraction of fuel vapor at the droplet surface and ambient, respectively, and L(p,Ts) denotes the latent heat of vaporization. QL, the heat transferred into the droplet, is defined as below

( dTdr )

QL ) 4πrs K

s

(9)

Combining eqs 5 and 6, the following relationship between the Spalding number of mass and heat transfer is obtained:

BT ) (1 + BM)φ - 1 where φ )

(10)

CpFFgDg Sh* Kg Nu*

In the liquid vaporization model,24 it is important to calculate the physical properties accurately at both the vapor and liquid phase of each species. Internal circulation arising from shear force must be considered when the relative velocity exists between the droplet surface and the nearby gas. To include the internal circulation effect, the effective conductivity model is introduced by Abramzon and Sirignano.23 In the present study, the properties of each species at both the vapor and liquid phase are calculated as a function of the temperature and pressure. The appropriate mixing rules are also used for calculations of mixture properties.25 Thermodynamic equilibrium at the droplet surface requires that the fugacities of each species in the gas phase be equal to its fugacities in the liquid phase. Thermodynamic equilibrium conditions at the droplet interface are given by

3652 Energy & Fuels, Vol. 22, No. 6, 2008

Tv ) Tl ;

pv ) pl ;

Yu et al.

f vi ) f li

where subscript v represents the vapor phase and subscript l represents the liquid phase. The fugacities of each species in the gaseous and liquid phases are calculated from

( ) ∫ {( )

fi RuT ln ) XiP

∞

∂p ∂ni

V

}

RuT dV - RuT ln Z (12) V T,V,ni

Here, Ru, fi, Xi, V, and Z represent the universal gas constant, the fugacity of the ith species, the mole fraction of species i, the total volume of the system, and the compressibility factor of the mixture, respectively. Deviation between the latent heat of vaporization for the pure component and the enthalpy of vaporization of a gas mixture is determined by employing the Peng-Robinson EOS. The energy required for the phase change is given by

∆h )

∑Y

∑Y

lj v iHi(T, p, Y i ) -

i

l iHi,l(T, p)

(13)

j i - H0i ) ) -RuT2 (H

∼

〈χ/Z〉i ) 〈χst 〉if(Z)

∂ ln fi ∂T

(14)

2.2. Turbulent Combustion Model. In the present study, the RIF model15 has been employed to realistically simulate the turbulence-chemistry interaction in the spray combustion processes. For convenience of presentation, brief descriptions are given below. The governing equation of species and energy in laminar flamelet can be written by mixture fraction Z.

-

∫ I˜ F〈χ 〉 〈χ 〉 (t) ) ∫ I˜ F〈χ 〉 ∼

st i

∂Yi Fχ ∂ Yi ) +m ˙i ∂t 2 ∂Z2

∑

(

(15)

N

+ ∇q ∑ h ω - ∂p ∂t ·

k

k

k)1

)

rad

(16)

( )

∂Z χ ≡ 2D ∂xj

Z2ln Z = χstf(Z) ) χst 2 Zstln Zst

∑ I˜ (xb, t)∫

1

i

i)1

V i

st

〈χst 〉(x b, t) )

0

3/2 ˜

P(Zst) dV

(21)

1/2 ˜

P(Zst) dV

ε˜ cχ Z˜′′2 k˜

∫

1

(22)

f(Z*)P˜(Z*) dZ*

To account for the vaporization effects on the turbulent spray combustion, the present study adopts the model proposed by Demoulin and Borghi.18 The transport equation of the mixture fraction variance is derived by using the PDF transport equation for the mixture fraction. The equations for the mean mixture fraction Z˜ and its variance Z˜′′2 coupled with the vaporization effects can be written as follows:

( ) ( )

-∼ ∂ -˜ ∂ ∂ µt ∂Z˜ (FZ) + (Fu˜jZ˜) ) + F ωv ∂t ∂xj ∂xj σZ ∂xj

(23)

2µt ∂2Z˜ ∂ -˜ 2 ∂ ∂ µt ∂Z˜′′2 (FZ′′ ) + (Fu˜jZ˜′′2) ) + ∂t ∂xj ∂xj σZ′′2 ∂xj σZ′′2 ∂x 2 -∼

-

-

∼

-

(17)

Yik(Z, 〈χ/Z〉i ;t)P˜(Z; b x , t)dZ

(18)

where I˜i(x b,t) is the probability that the ith flamelet is found in the cell at location x at time t. An Eulerian transport equation for this probability I˜i(x b,t) can be derived. (24) Kneer, R.; Schneider, M.; Noll, B.; Witting, S. Diffusion controlled evaporation of a multicomponent droplet: Theoretical studies on the importance of variable liquid properties. Int. J. Heat Mass Transfer 1993, 36 (9), 2403–2415. (25) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987.

˜2

j

∼

-

The last four additional source terms appearing in eq 24 account for the vaporization effects on the mixture fraction variance. These new correlations, to take into account the fluctuation of equivalence ratio because of vaporization, are in an unclosed form. By assuming that the spray vaporization takes places only at the liquid surface, Demoulin and Borghi18 have proposed the model for these correlations: -

-

˜ ≈ FZ ˜ FZω v sωv )

∑Z

p s

p

2

The Eulerian particle flamelet model (EPRM)16 using the multiple RIFs model is to handle the spatial inhomogeneity of the scalar dissipation rate N

st

where

As spatial coordinates transform mixture fraction coordinates, the scalar dissipation rate, χ, appeared in the above equations, can be expressed as the molecular diffusion to a reciprocal of characteristic time in the laminar flamelet.

b, t) ) Y˜k(x

V i -

2 ˜ - FZ˜ω ) + FZ ω - FZ ˜ ωv (24) Fχ + 2(FZω V v v

2

N ∂2Yk ∂T χ 1 ∂2h χ 1 1 ) h ∂t 2 cp ∂Z2 2 cp k)1 k ∂Z2 Fcp

(20)

Here, the average conditional scalar dissipation rate for the ith RIF in a given time is calculated as follows

0

( )

(19)

Yki in eq 18 is an unsteady solution for the ith RIF, and to obtain the solution, the conditional scalar dissipation rate, 〈χ/Z〉i, is expressed by

i

Here, Hi,l represents the enthalpy of the ith component at the liquid j i and its ideal gas phase. The partial enthalpy of ith component H enthalpy H0i are related through the following thermodynamic relation:

F

( )

∂ -˜ ∂ ∂ µeff ∂I˜i (FIi) + (Fu˜jI˜i) ) ∂t ∂xj ∂xj σI ∂xj

(11)

-

2 2 ˜ ˜ FZ ωv ≈ FZ s ωv )

m ˙p V

∑ (Z )

p 2 s

p

(25)

mp V

(26)

where the subscript “s” denotes the value at the liquid surface. These additional source terms are mainly contributed to the production of mixture fraction fluctuations. In spray combustion processes, these terms are contributed to increase the scalar dissipation rate and the ignition delay time as well as to modify the small-scale mixing processes and the spray structure. Another important effect arising from vaporization is related to the fact that the upper limit of the mixture fraction is not in unity in spray combustion processes. Therefore, the upper limit (Zini) of the mixture has to be determined. Using the conditional PDF of Zini and mixture fraction equation, Demoulin and Borghi18 derived the following balance equation:

(

)

j ini ∂ -˜ j ∂ - j ∂ µt ∂Z˜Z (FZZini) + (Fu˜jZ˜Z + ini) ) ∂t ∂xj ∂xj σZ ∂xj -

F

∫

1

0

∼

Ziniωv|Zini dZini (27)

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Energy & Fuels, Vol. 22, No. 6, 2008 3653

Figure 1. Temporal evolutions of the evaporation rate and droplet surface temperature of n-heptane and DME at different temperatures.

For a given position, therefore, the allowable space for mixture fraction Z has to be automatically adjusted from 0 to Zj ini. In the present study, the β-pdf P˜(Z;x b,t) is employed and its shape has been renormalized from the three constraints:

1)

∫

j ini Z P˜(Z)dZ, 0

Z˜ )

∫

j ini Z ZP˜(Z) 0

dZ,

Z˜′′2 )

∫

j ini Z (Z - Z˜)2P˜(Z) 0

dZ (28)

This modified upper limit of the mixture fraction also influences the ignition delay and the spray combustion processes. A decrease in the upper limit mixture fraction is contributed to increase in the probability of combustion in a given mixture fraction interval and to possibly decrease in the ignition delay time. The mean species mass fractions are calculated by integrating the flamelet solution weighted with a presumed probability density function:

Y˜i(x b, t) )

∫

j ini Z P˜(Z; b x , t)Yi(Z;t) 0

dZ

(29)

The calculation procedure of the RIF model is performed interactively with the CFD solver. During one time step of the main CFD code, the flamelet equations are solved by the stiff ODE solver, in which the time step is subdivided adaptively into subcycles to resolve the much smaller chemical time scales. The detailed numerical procedure for the RIF approach15,16,22 and comprehensive spray combustion model10,21 including the RIF approach can be found elsewhere.

3. Results and Discussion 3.1. Evaporation Characteristics of DME and n-Heptane Droplet. Previously, the present high-pressure vaporization model21 was validated against experimental data26,27 for the evaporation process of a freely falling n-heptane droplet at three ambient pressures (20, 30, and 40 bar) and two gas temperatures (550 and 650 K). Our previous numerical results21 indicate that, compared to the high-pressure evaporation model, the low-pressure evaporation model based on the infinite conductivity model and Clausius-Clapeyron equation for phase equilibrium was unable to account for the high-pressure effects including solubility and real gas effects. For all pressure levels (26) Stengele, J.; Willmann, M.; Wittig, S. Experimental and theoretical study of droplet vaporization in a high pressure environment. 1997, ASME97-GT-151. (27) Stengele, J.; Prommersberger, K.; Willmann, M.; Wittig, S. Experimental and theoretical study of one- and two-component droplet vaporization in a high pressure environment. Int. J. Heat Mass Transfer 1999, 42, 2683–2694.

investigated, in terms of droplet size and droplet velocity, numerical results21 obtained by the high-pressure evaporation model favorably agreed with experimental data, while the lowpressure model considerably overpredicted the droplet lifetime. To understand the vaporization process of DME fuel as well as to identify the distinctive differences of the DME vaporization process compared to conventional hydrocarbon liquid fuels, the high-pressure vaporization model has been applied to simulate the vaporization characteristics of DME and n-heptane liquid fuels at a wide range of operating conditions. To simulate the vaporization process of a single droplet, 51 grids are used to resolve the computational domain within the droplet. All numerical calculations are stopped when the droplet radius becomes 30% of the initial droplet radius. Figure 1 shows the effects of temperature on the evaporation rate and droplet surface temperature for n-heptane and DME liquid droplet at three ambient temperatures (T∞ ) 723, 823, and 923 K), the ambient pressure, P∞ ) 41 bar, the initial interphase relative velocity, Ud ) 10 m/s, the initial droplet diameter, Dd ) 50 µm, and the initial droplet temperature, Td ) 293 K. Numerical results displayed in Figure 1 indicate that the web-bulb temperatures for n-heptane and DME droplet at the given ambient condition (41 bar and 723 K) are 470 and 330 K, respectively. When temperature is increased, the wet-bulb temperature and the vaporization rate increase and the droplet lifetime decreases for both fuels. In comparison to n-heptane, DME has a much higher vaporization rate and a much lower wet-bulb temperature. As shown in Figure 1, n-heptane has a much slower heat-up process and takes a much longer time to reach the wet-bulb temperature. On the other hand, DME shows explosively high evaporation characteristics during the initial stage. The peak evaporation rate of DME is nearly 2.5 times higher than that of n-heptane. Numerical results also indicate that the higher ambient temperature results in a higher droplet surface temperature and wetbulb temperature, higher vaporization rate, and shorter droplet lifetime. In the case of DME, the droplet quickly reaches the thermal equilibrium and heat transfer into the droplet is fully used to evaporate the droplet after the short heat-up period. On the other hand, the n-heptane droplet slowly reaches the thermal equilibrium and the heat transfer into the droplet is partially used to evaporate the droplet during the relatively long heat-up period. Figure 2 shows the effect of pressure on the droplet evaporation for n-heptane and DME liquid droplets at three ambient pressures (31, 41, and 51 bar), the ambient temperature,

3654 Energy & Fuels, Vol. 22, No. 6, 2008

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Figure 2. Temporal evolutions of the evaporation rate and droplet surface temperature of n-heptane and DME at different pressures.

Figure 3. Temporal evolutions of the evaporation rate and droplet surface temperature of n-heptane and DME at different initial relative velocities.

823 K, the initial interphase relative velocity, 10 m/s, the initial droplet diameter, 50 µm, and the initial droplet temperature, 293 K. When the pressure increases, the vaporization rate and the droplet surface temperature increase and the droplet lifetime decreases for both fuels. When the ambient pressure is increased, the n-heptane and DME droplets have a much larger subcooling effect, which increases evaporation, while they have a much higher wet-bulb temperature, which results in elevating the vaporization rate. Because of these two competing effects, the evaporation time of these liquid droplets is not quite sensitive to the variation of the ambient pressure. Figure 3 presents the effect of the initial relative velocity on the droplet evaporation characteristics as well as the Nusselt number and Sherwood number of DME and n-heptane droplets at the given ambient conditions (P∞ ) 41 bar, and T∞ ) 823 K) and the initial conditions (Td ) 293 K, and Dd ) 50 µm). A comparison is made for three initial droplet velocities: 1, 10, and 100 m/s. As shown in Figure 3, the increase of the relative velocity directly increases the convection between droplet and atmosphere as well as shear stress exerted on the droplet surface causing interior circulation in the droplet. When the initial relative velocity is increased, the vaporization rate remarkably increases and the droplet temperature quickly reaches the wetbulb temperature. In comparison to n-heptane, the vaporization characteristics of DME are more sensitive to the initial relative velocity, which has a much higher vaporization rate and a much

lower wet-bulb temperature. In the case of the highest relative velocity (100 m/s), the peak evaporation rate of DME is nearly 4.5 times higher than that of n-heptane. This drastically high evaporation rate of DME is mainly caused by the considerably short heat-up period and the substantially high heat and mass transfer at the high vapor-pressure state. Numerical results also indicate that the wet-bulb temperature is independent of the interphase relative velocity. In general, the elevated interphase velocity results in a much higher convective heat and mass transfer between the droplet and the gaseous flow field as well as enhanced internal circulation driven by Hill’s vortex inside the droplet. In comparison to the n-heptane droplet, these numerical results clearly indicate that the vaporization rate of the DME droplet is extremely sensitive to the interphase relative velocity. These numerical results suggest that these distinctly different evaporation characteristics of DME droplets could greatly influence the auto-ignition, mixing field, scalar dissipation rate, turbulence-chemistry interaction, and pollutant formation in the turbulent spray combustion of high-speed directinjection diesel engines. 3.2. Auto-ignition Characteristics of Homogeneous DME and n-Heptane Mixtures. The present n-heptane/air chemistry is based on the skeletal mechanism28 of 43 chemical species and 185 reactions, counting the forward and backward reactions individually. In Figure 4, the predicted auto-ignition

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Energy & Fuels, Vol. 22, No. 6, 2008 3655 Table 1. Ignition Characteristics of Homogeneous DME and n-Heptane Mixtures DME

Figure 4. Calculated and measured (Ciezki et al.29 and Minetti et al.30) ignition delay times of homogeneous n-heptane/air mixtures.

Figure 5. Predicted and measured32 ignition delay times of homogeneous DME/air mixtures.

delay times of homogeneous n-heptane/air mixtures are compared to measurements performed at the shock tube29 and the rapid compression machines.30 To check the accuracy of the detailed chemical kinetics used in this study, the ignition delay of homogeneous DME/air mixtures is calculated by the constantvolume homogeneous reactor model. In the auto-ignition calculation, the ignition is defined by the highest temperature gradient that nearly coincides with the maximum CH concentration. It can be clearly shown that the present chemistry model has the capability of correctly predicting the negative temperature coefficient (NTC) behavior arising from the nonlinearity of the chemistry. Numerical and experimental results also indicate that this (NTC) behavior is relatively strong at low chamber pressure. In terms of the auto-ignition delay time, the numerical results obtained in the present study agree well with experimental data. The detailed chemistry31 of 336 elementary reaction steps and 78 chemical species is adopted for the DME/ air reaction. In Figure 5, the predicted auto-ignition delay times of the homogeneous DME/air mixture are compared to measurements32 performed at the high-pressure shock tube. Measurements32 were performed at a range of temperatures from (28) Liu, S.; Hewson, J. C.; Chen, J. H.; Pitsch, H. Effects of strain rate on high-pressure non-premixed n-heptane autoignition in counterflow. Combust. Flame 2004, 137, 320–339. (29) Ciezki, H. K.; Adomeit, G. Shock-tube investigation of self-ignition of n-heptane-air mixtures under engine relevant conditions. Combust. Flame 1993, 93, 421–433.

n-heptane

temperature

13 bar

40 bar

13.2 bar

42 bar

700 K 800 K 900 K 1000 K

3.067 ms 1.518 ms 1.518 ms 1.003 ms

2.318 ms 0.343 ms 0.301 ms 0.208 ms

5.436 ms 2.093 ms 4.389 ms 1.863 ms

3.786 ms 0.433 ms 0.433 ms 0.456 ms

650 to 1300 K, the two pressures (13 and 40 bar), and the given equivalent ratio (1.0). In these calculations, the ignition is defined by the highest temperature. Numerical results agree well with experimental data for the wide range of temperatures (650 < T < 1300 K) at 40 bar. However, at 13 bar, there exist noticeable deviations in the lower temperature conditions. Table 1 presents the predicted ignition delay times of the n-heptane and DME homogeneous mixture in the low- and high-pressure conditions, four temperatures (700, 800, 900, and 1000 K), and the unitary equivalent ratio. In comparison to the n-heptane mixture, the DME mixture yields a much shorter ignition delay time. This trend is more apparent for the lower pressure case. These listed data indicate that the n-heptane mixture has a much stronger NTC behavior, especially at the lower pressure condition. 3.3. Comparison of Auto-ignition and Combustion Characteristics for n-Heptane and DME Sprays. Next, the present approach has been applied to simulate the auto-ignition and subsequent combustion processes of DME sprays. The validation case has been chosen as measurements of Kim et al.9 at chamber pressure, 2.1 MPa, and injection pressure, 40 MPa. In this case example, the high-pressure vaporization model and the vaporization coupled RIF turbulent combustion model are employed to predict the turbulent DME spray combustion processes. A computational domain of 40 mm in radius and 90 mm in length is resolved by 60 radial and 80 axial computational cells with a non-uniform mesh arrangement. The injection velocity (235 m/s) of the DME liquid fuel was assumed to be constant during the injection period. The nozzle diameter and total injected mass are 0.22 mm and 6.9 mg, respectively. The adiabatic condition is imposed at the wall. Figure 6 presents the measured9 and predicted ignition delay times for the chamber pressure, 2.1 MPa, and the injection pressure, 40 MPa. In this validation case, the predicted ignition delay times agreed well with experimental data of Kim et al.,9 which has relatively well-specified initial conditions. At the chamber pressure, 2.1 MPa, and temperature, 1132 K (1000/T ) 0.88), the predicted delay time (0.941 ms) is quite close to experimental data (0.898 ms). However, at the relatively low temperature conditions (T < 900 K), there exist certain deviations with measurements. To illustrate the auto-ignition process of the DME spray, the instantaneous DME spray jet flame fields for the initial chamber condition (2.1 MPa and 1132 K) and injection pressure, 40 MPa, are plotted in Figure 7. In this relatively short injection duration (0.64 ms) case, the autoignition occurs approximately at 0.94 ms after the completion of liquid fuel injection. The ignition is initiated around the (30) Minetti, R.; Carlier, M.; Ribaucour, M.; Therssen, E.; Soche, L. R. A rapid compression machine investigation of oxidation and auto-ignition of n-heptane: Measurement and modeling. Combust. Flame 1995, 102, 298– 309. (31) Lawrence Livermore National Laboratory (LLNL) site. https:// www.llnl.gov/. (32) Pfahl, U.; Fieweger, K.; Adomeit, G. Self-ignition of diesel-relevant hydrocarbon-air mixtures under engine conditions. Proceedings of the 26th International Symposium on Combustion, The Combustion Institute, Pittsburgh, PA, 1996; pp 781-789.

3656 Energy & Fuels, Vol. 22, No. 6, 2008

Figure 6. Predicted and measured9 ignition delay times of injected DME spray at constant volume chamber.

stoichiometric tail region of the DME fuel vapor jet. In terms of ignition site and delay time, these auto-ignition characteristics are distinctly different from the relatively long injection duration cases. During the injection period, ignition is almost impossible near the stoichiometric tail region of the fuel vapor jet, mainly because of the cooling effects of spray vaporization and the considerably high scalar dissipation rate. However, after the completion of liquid fuel injection, close to the stoichiometric tail region of the fuel vapor jet, the scalar dissipation rate is rapidly decreased and reaches a certain low level to allow for the auto-ignition. This trend is clearly displayed in Figure 7. On the other hand, it is quite possible that the relatively long injection duration cases create the auto-ignition site around the stoichiometric downstream region of the fuel vapor jet with a sufficiently low scalar dissipation rate. To compare the spray combustion characteristics of the n-heptane and DME fuels, numerical calculation is performed using the same injection mass flow rate (6 mg/1.4 ms), injection velocity (225 m/s), the diameter of nozzle (0.2 mm), initial chamber condition (P ) 4.1 MPa, and T ) 823 K), and the injection duration (1.4 ms). Figures 8-10 show the instantaneous distribution of temperature, OH radical, and scalar dissipation rate in the n-heptane and DME spray flame field. The predicted ignition delay time (1.303 ms) of DME sprays is much shorter than that of n-heptane sprays (1.602 ms). Thus, the DME spray jet is ignited during the injection period, while the n-heptane spray jet is ignited after the completion of fuel injection. These different ignition delay times relative to the injection duration result in the creation of the different ignition sites. For the DME spray jet ignited during the injection period, the auto-ignition occurs around the slightly rich downstream region of the DME fuel vapor jet with a sufficiently low scalar dissipation rate. On the other hand, for the n-heptane spray jet ignited after the completion of fuel injection, the auto-ignition is initiated around the stoichiometric tail region of the n-heptane fuel vapor jet with a certain low scalar dissipation rate to allow for the ignition. Because DME sprays have relatively short spray penetration length and higher evaporation rate than n-heptane sprays, the DME spray flame exists in the relatively upstream region. Because of the high evaporation rate of DME fuel at the initial injection stage, the scalar dissipation rate near the injector is much higher than that of n-heptane fuel. This trend is clearly shown in Figure 11. In the initial injection period,

Yu et al.

the maximum scalar dissipation rate for the DME spray jet is 7 times higher than that for the n-heptane spray jet. These distinctly different ignition characteristics of DME and n-heptane sprays are closely related to evaporation characteristics, spray behavior, and ignition delay time of the homogeneous mixture for DME and n-heptane fuel. It is necessary to note that the same injection condition of DME and n-heptane sprays cannot be arranged in an experiment or in real spray combustion systems. Therefore, future works must include systematic validations for the nonreacting, evaporating, and burning DME and n-heptane sprays with detailed and reliable injection information. Figures 12 and 13 present the time evolution of local flame structure in terms of temperature, mass fractions (fuel vapor, O2, H2, OH, CO, and CO2) of the major and minor species, and the consumption rates of the oxygen near auto-ignition of n-heptane and DME spray jets injected at initial chamber pressure and temperature of 4.1 MPa and 823 K, respectively. In comparison to the n-heptane spray jet, the predicted profiles of O2 and fuel vapor in the mixture fraction space indicate that the DME spray jet yields a much broader leakage zone, where the non-equilibrium chemical reaction mostly occurs. These results also suggest that the flame structure and pollutant formation of the DME-fueled engines could be more sensitive to the turbulence-chemistry interaction. At the early stage of auto-ignition, the magnitude of the reaction rate decreases and three peaks are formed. Thereafter, the center peak remains a certain value, which is supported mainly by the diffusion flame, while two peaks propagate toward the fuel-lean and fuel-rich side of the flame. These center peaks for the DME and n-heptane ignition processes lie on the slightly rich side. These complex chemical reaction processes occur within a very short time interval. In the overall flame structure, compared to the n-heptane spray jet, the DME spray jet has a much broader hottemperature flame zone in the fuel-rich side of the mixture fraction space. This distinctly different structure of the DME spray flame could be mainly related to the characteristics of the oxygenated fuels. The predicted profiles of oxygen mass fraction, fuel mass fraction, and oxygen consumption rate for both fuels clearly reflect this trend. In terms of the OH mass fraction, DME yields a much broader distribution at the fuelrich region. This distinctly broader OH distribution of the DME flame in the fuel-rich region possibly plays a crucial role to oxidate the soot particles in the actual spray flame field of the DI diesel engines. Moreover, in the fuel-rich region, DME generates a much broader and higher hydrogen distribution, which could greatly reduce the soot formation in the actual spray flames. These numerical results suggest that the distinctly broader and higher OH and H2 distribution in the fuel-rich region can remarkably reduce the soot formation in the DME-fueled diesel engines, compared to the conventional hydrocarbon-fueled diesel engines. 4. Conclusions On the basis of numerical results, the following conclusions are drawn in terms of the evaporation characteristics of single droplets, combustion processes, ignition characteristics of homogeneous mixtures and spray jets, flame structure, and turbulence-chemistry interaction in the n-heptane and DME spray combustion processes: (1) When temperature increases, the vaporization rate and the droplet surface temperature increase and the droplet lifetime decreases for n-heptane and DME liquid droplets. In comparison to n-heptane, DME has a much higher vaporization rate and a much lower wet-bulb temperature.

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Energy & Fuels, Vol. 22, No. 6, 2008 3657

Figure 7. Instantaneous distribution patterns of temperature and droplets near auto-ignition in the transient spray field.

Figure 8. Instantaneous distribution patterns of the temperature distribution of n-heptane and DME spray flames.

n-Heptane has a much slower heat-up process and takes a much longer time to reach the wet-bulb temperature. On the other hand, DME shows quite high evaporation characteristics during

the initial stage. (2) When the pressure increases, the vaporization rate and the droplet surface temperature increase and the droplet lifetime decreases for both fuels. When the ambient

3658 Energy & Fuels, Vol. 22, No. 6, 2008

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Figure 9. Instantaneous contours of the OH radical mass fraction of n-heptane and DME spray flames.

Figure 10. Instantaneous distribution patterns of the scalar dissipation rate of n-heptane and DME spray flames.

pressure increased, the n-heptane and DME droplets have much larger subcooling effects, which increases evaporation time, while they have much higher wet-bulb temperature, which results in elevating the vaporization rate. Because of these two

competing effects, the evaporation time of these liquid droplets is not quite sensitive to the variation of the ambient pressure. (3) In comparison to the n-heptane droplet, the vaporization rate of the DME droplet is extremely sensitive to the interphase

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Energy & Fuels, Vol. 22, No. 6, 2008 3659

Figure 11. Temporal evolutions of the scalar dissipation rates and the maximum temperatures.

Figure 13. Time evolution of the temperature and mass fraction of various species in the interactive flamelet for DME spray.

Figure 12. Time evolutions of the temperature and mass fraction of various species in the interactive flamelet for n-heptane spray.

relative velocity. In the case of the highest relative velocity (100 m/s), the peak evaporation rate of DME is nearly 4.5 times higher than that of n-heptane. This drastically high evaporation rate of DME is mainly caused by the considerably short heatup period and the substantially high heat and mass transfer at the high vapor-pressure state. These numerical results suggest that these distinctly different evaporation characteristics of DME

droplets could greatly influence the auto-ignition, mixing field, scalar dissipation rate, turbulence-chemistry interaction, and pollutant formation in the turbulent spray combustion of highspeed direct-injection diesel engines. (4) Numerical results clearly indicate that the multiple RIF model together with the present high-pressure vaporization model reasonably well predict the ignition delay times for the DME spray jets in the diesellike environment. (5) For the DME spray jet-ignited during the injection period, the auto-ignition occurs around the slightly rich downstream region of the DME fuel vapor jet with a sufficiently low scalar dissipation rate. On the other hand, for the n-heptane spray jet-ignited after the completion of fuel injection, the autoignition is initiated around the stoichiometric tail region of the n-heptane fuel vapor jet, where a certain low scalar dissipation rate allows for the ignition. (6) In comparison to the n-heptane spray jet, the DME spray jet has a much broader hot-temperature flame zone in the fuel-rich side of the mixture fraction space. This distinctly different structure of the DME spray flame could be mainly related to the characteristics of the oxygenated fuels. (7) In terms of the OH mass fraction, DME yields a much broader distribution at the fuel-rich region. Moreover, in the fuel-rich region, DME generates a much broader and higher hydrogen distribution. This distinctly different OH and H2 distribution in the DME flame structure possibly plays a crucial role to oxidate the soot particles in the actual spray flame field of the DI diesel engines.

3660 Energy & Fuels, Vol. 22, No. 6, 2008 Acknowledgment. This work was supported by the Center for Environmentally Friendly Vehicle (CEFV) of the Eco-STAR project from the Ministry of Environment (MOE), Republic of Korea.

Nomenclature Roman Symbols cp ) specific heat of mixture at constant pressure Di ) diffusion coefficient of species i f ) fugacity h and hk ) enthalpy of mixture and species k Il ) probability to find lth particle at a certain location and time k ) turbulent kinetic energy K ) thermal conductivity L ) latent heat (enthalpy of vaporization) p ) pressure P ) probability density function Q ) heat flux t ) time T ) temperature uj ) Cartesian velocity component in xj direction xj ) Cartesian coordinates Yi ) mass fraction of species i Z ) mixture fraction Greek Symbols χ ) scalar dissipation rate

Yu et al. ε ) dissipation rate of turbulent kinetic energy φ ) fugacity coefficient µeff ) effective viscosity F ) density ω ˙ k ) chemical production rate of species k Subscripts d ) droplet condition l ) liquid phase s ) surface condition v ) vapor phase ∞ ) conditions at infinity of ambient Superscripts j ) Reynolds-averaged (density-unweighted) properties ψ ˜ ) Favre-averaged (density-weighted) properties ψ ψ′ ) turbulent fluctuating component Nondimensional Numbers Nu ) Nusselt number (hL/K) Pr ) Prandtl number (µcp/λ) Re ) Reynolds number (FuL/µ) Sc ) Schmidt number (µ/FD) Sh ) Sherwood number (hL/D) EF8002119