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SAE TECHNICALPAPER SERIES 2001-01-0154

Thermochemical Characteristics of DimethylEther — An Alternative Fuel for Compression-Ignition Engines

Ho Teng, James C. McCandless and Jeffrey B. SchneyerAVL Powertrain Technologies, Inc.

Reprinted From: New Developments in Alternative Fuels for CI Engines(SP–1608)

SAE 2001 World CongressDetroit, Michigan

March 5-8, 2001

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ISSN 0148-7191Copyright 2001 Society of Automotive Engineers, Inc.

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2001-01-0154

Ho Teng, James C. McCandless and Jeffrey B. SchneyerAVL Powertrain Technologies, Inc.

Copyright © 2001 Society of Automotive Engineers, Inc.

ABSTRACT

This paper analyzed chemical and thermophysicalproperties of dimethyl ether (DME) as an alternative fuelfor compression-ignition engines. On the basis of thechemical structure of DME and the molecularthermodynamics of fluids, equations have beendeveloped for most of the DME thermophysicalproperties that would influence the fuel-systemperformance. These equations are easy to use andaccurate in the pressure and temperature ranges for CIengine applications. The paper also pointed out that theDME spray in the engine cylinder would differsignificantly from that of diesel fuel due to thethermodynamic characteristics of DME. The DME spraypattern will affect the mixing and combustion processesin the engine cylinder, which, in turn, will influenceemissions from combustion.

INTRODUCTION

Many investigators have demonstrated that dimethylether (DME) has a high cetane number and lowemissions from combustion [1-5]. These good thermo-chemical characteristics make DME a promisingalternative fuel for compression-ignition engines.However, because the largest use of DME is as apropellant in aerosol engineering to date, the thermo-physical properties of DME are still not fully understood.The properties reported in the literature were vaporpressures and few properties at low pressures and roomtemperatures [6,7]. As a fuel for CI engines, thesubcooled-liquid properties, such as density, viscosity,compressibility/bulk-modulus, etc., are of greatimportance in design and modeling of the DME fuelsystem. Because DME has a poor lubricity and a highcompressibility in comparison to diesel fuel, none of theexisting fuel systems can be applied directly to the DMEapplication. The fuel system for DME must be speciallydesigned according to its characteristics. Therefore, agood understanding is necessary of the thermophysical

properties of DME, especially in the subcooled-liquidregion.

Although accurate thermophysical properties may beobtained only experimentally, because DME is a simplepure substance from the thermodynamic viewpoint, theexisting molecular thermodynamic theory [8,9] canpredict most of its properties with accuracy for theindustrial standard (errors ≤ 5%). This paper presents amolecular-thermodynamic study on those of DMEproperties related to the fuel-system design andmodeling.

CHEMICAL CHARACTERISTICS OF DME

CHEMICAL STRUCTURE OF DME

Most of the thermochemical properties of a pure fluidare closely related to its chemical structure. Therefore, itmay be helpful to review the chemical structure of DMEbefore the study of the structure-related properties. Thechemical formula of DME is CH3-O-CH3 and its chemicalstructure is shown in Fig.1. Although the oxygen atom inDME has only two C-O bonds, being a member of the VI-family elements, the oxygen atom has six outermost-layer electrons; and, plus the two shared electrons withthe carbon atoms, the outermost layer of the oxygenatom has a total of eight electrons. According to the octet

Fig.1 Chemical structure of dimethyl ether.

Orbitals of lone- electronpairs

H H

HH

HH

O

C C

Thermochemical Characteristics of Dimethyl Ether — AnAlternative Fuel for Compression-Ignition Engines

rule (the Lewis structure), these eight electrons form fourorbitals: two orbitals for the two pairs of shared electronsforming the C-O bonds and two orbitals for the two pairsof lone electrons. The electrostatic repulsion betweenany two pairs of electrons tends to make them as farapart as possible; and, as a net effect, all of the orbitalangles become the same. If each pair of the loneelectrons is imagined to be associated with a “pseudoatom”, then the four (two real plus two pseudo) atomsassociated with the oxygen atom through the orbitalsform a symmetrical shape of a regular tetrahedron a3-D figure with four equilateral-triangle faces: with theoxygen atom at the center and the other four at the fourcorners, and all the orbitals at 109.5° angles to eachother. In reality, the orbital angles cannot be exactly109.5° due to intra-molecular forces and they maydepart from the perfect tetrahedral angle a few degrees.For example, the angle between the two C-O bonds isactually 112° [10].

Carbon belongs to the IV family and it has fourelectrons in its outermost layer. In alkanes and radicalsof alkanes, the carbon atom forms four bonds throughassociation with four other atoms; thus, it also has eightelectrons in its outermost layer. Each of the carbonatoms in alkanes and radicals of alkanes is associatedwith a tetrahedron with the carbon atom at the center andthe four associated atoms at the four corners. This leadsto a reasonable prediction that angles between C-Hbonds in the methyl radicals in DME are 109.5° thisprediction is accurate enough: the actual angles are108° [10]. The similar features of the oxygen andcarbon atoms suggest that the chemical structure ofpropane (its chemical formula is CH3-CH2-CH3) shouldbe very similar to that of DME. The chemical structure ofpropane is shown in Fig.2. Indeed, if the oxygen atom isreplaced with a carbon atom and the two pseudo atomsassociated with the oxygen atom are replaced with twohydrogen atoms, then the chemical structure of DMEturns into that of propane. In propane, the anglebetween the two C-C bonds remains 112° [10].However, because of changes in intra-molecular forces,angles between C-H bonds become 107° [10]. It is seenin Figs. 1 and 2 that, although both propane and DMEare often mentioned as straight-chain molecules in theliterature, actually, their chains are zigzag due to thetetrahedral bonding nature of the carbon and oxygen

Fig.2 Chemical structure of propane.

atoms in them. The C-O bond length in DME (1.42 Å) isshorter than the C-C bond length in propane (1.53 Å) [10]and the C-O bond energy (351 kJ/mol) is larger than thatof the C-C bond (341 kJ/mol) [11]; thus, intra-molecularforces in a DME molecule may be larger than those in apropane molecule. However, because two of the fourcorners of the oxygen-atom-centered tetrahedron are notactually associated with atoms, the angle between thetwo C-O bonds is flexible; and, the two C-O bonds areoften under the distortion from the two methyl radicals,which significantly weakens the stability of the chemicalstructure of DME. Because the function group thatcharacterizes DME (Fig.3) is not chemically active, DMEis often considered to be inert chemically.

Fig.3 The function group of DME.

Due to the polarity induced by the two pairs of loneelectrons of the oxygen atom in the DME molecule, theinter-molecular forces in DME are greater than inpropane (noting that propane is a non-polar fluid). Theintra-molecular forces influence the chemicalcharacteristics while the inter-molecular forces affectthermodynamic properties. It is difficult to predict thecombustion characteristics solely on the basis of thechemical structure and intra-molecular forces becausecombustion of an organic fuel undergoes a complicatedchain reaction. However, it is possible to predict some ofthermophysical properties on the ground of the molecularstructure and inter-molecular forces. Large inter-molecular forces lead to strong attractions amonginteracting molecules in a liquid fluid. Thus, it takesmore energy for a DME molecule than a propanemolecule to overcome attractive forces from neighboringmolecules to travel from the liquid phase to the vaporphase. As a result of the stronger molecular attraction,DME has a higher critical temperature, a higher normalboiling point, and larger latent heat and saturated-liquiddensity at a normal temperature (e.g., at 20 ° C) thanpropane does. And, due to the same reason, propanehas a higher vapor pressure than DME does at the sametemperature [4].

HEAT OF COMBUSTION OF DME

Because DME is a pure substance, the heat ofcombustion of DME can be calculated accurately on thebasis of the following chemical reaction:

C2H6O (l,g) + 3O2 (g) → 2CO2 (g) + 3H2O (g), (1)

O

C C

HH

H H

HH

HH

C

C C

where l = liquid and g = gas, indicating the states ofreactants and products. The heat release from DMEcombustion described by Eq.(1) is

,iP iiR iC HnHnQ ∑−∑= (2)

where R and P indicate reactants and products, and niand Hi are, respectively, the mole number and formationenthalpy of the ith substance. Following the tradition, theheat of DME combustion is considered at the standardstate (1 atm and 25 ° C). At this state, formationenthalpies of CO2 (g), H2O (g), DME (g) (DME is a gas atthe standard state), and O2 (g) are, respectively, HCO2 = –393.51 kJ/mol, HH2O = – 241.87 kJ/mol, HDME = – 184.10kJ/mol, and HO2 = 0 kJ/mol (by convention, formationenthalpy of a stable element is zero) [10]. Substitutingthese values into Eq.(2) the heat of combustion of DMEis obtained as

QC = HDME + 3HO2 – 2HCO2 – 3HH2O

= 1328.53 kJ/mol = 28.88 MJ/kg (3)

Considering that, in reality, oxygen is from air and thatevery 4.76 moles of air contains 1 mole oxygen, Eq.(1)may be rewritten as

C2H6O (l,g) + 3× [O2 (g) + 3.76 N2 (g)]

→ 2CO2 (g) + 3H2O (g) + 3×3.76 N2 (g). (4)

Although Eq.(4) is equivalent to Eq.(1) in the sense ofchemical reaction, it offers information on the air/fuelratio. It is seen from Eq.(4) that complete combustion of1-mol DME requires 3× (1 + 3.76) = 14.28-mol air. Thus,the air/fuel ratio at the stoichiometric condition is

(A/F)ST = 14.28 mol-air/mol-DME. (5)

Noting that the molar mass of air = 28.97 g/mol = 28.97kg/kmol and the molar mass of DME = 46 g/mol = 46kg/kmol, (A/F)ST can be given alternatively as

(A/F)ST = 8.99 kg-air/kg-DME. (6)

Equation (6) indicates that complete combustion of 1-kgDME requires much less air than that of 1-kg gasoline ordiesel fuel at the stoichiometric condition.

CETANE NUMBER OF DME

The cetane number of a fuel measures itscompression-ignition quality. For a given fuel, the higherits cetane number, the better its compression-ignitionquality. The compression-ignition quality of a fuel maybe characterized by the time lag between the start of fuelinjection and the commence of ignition. This ignitiondelay is due to that it takes a certain period of time forthe fuel injected into the compressed air in the enginecylinder to reach a temperature that is high enough to

Fig.4 A typical cylinder-temperature history showing thecompression-ignition delay [12].

ignite the air-fuel mixture. The ignition delay, as shown inFig.4 for a case reported in the literature [12], has twostages. The first stage is the physical delay, which isdue to the fuel evaporation, mixing, and establishment ofthe critical concentration of radicals for initiation of thechain reaction; because the heat release of the early-stage, unsteady reactions are just enough to balance theheat dissipation, physical processes are predominantand there is no apparent temperature rise. The secondstage is the chemical delay, which is associated with thesubsequent steady chain reaction and is the time for theair-fuel mixture to reach the chain explosive condition.

Because the critical temperature of DME is only 127° C, which is lower than the compressed-air temperatureat the later stage of the compression stroke, the DMEinjected into the cylinder may vaporize immediately dueto the fact that a liquid phase is thermodynamicallyunstable above the critical temperature. When thetemperature of DME is greater than 127 ° C, DMEbecomes a superheated gas and, therefore, noevaporation is associated during mixing. The chainreaction of the DME combustion may be initiated byeither (or both) of the two competing pathways [12,13]:

C-O bond fission (pyrolysis mechanism):

CH3OCH3 → CH3O + CH3; (7)

Hydrogen abstraction (oxidation mechanism):

CH3OCH3 + O2 → CH3OCH2 + HO2, (8)

CH3OCH2 → CH2O + CH3. (9)

The C-O bond energy is smaller than that of the C-Hbond (414 kJ/mol [11]) and the distortion of the C-Obonds in the DME molecule weakens the bondingstrength; thus, the C-O bond breaks easier than the C-Hbond. Therefore, the pyrolysis mechanism may be more

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delayPhysical delay

Total ignition delay

Tem

pera

ture

(o C

)

Time (ms)

possible to start the chain reaction of the DMEcombustion at relatively low temperatures.

Because DME has a low critical temperature and theC-O bond in DME breaks easily, the physical delay ofDME is much shorter than many conventional fuels,resulting in a short total ignition delay. The short ignitiondelay of DME leads to a high cetane number: the cetanenumber of DME is greater than 55 [3,14]. In comparison,the cetane number of diesel fuel falls in a range between40 and 54 [15].

EMISSIONS FROM DME COMBUSTION

Carbon monoxide (CO), unburned hydrocarbons(HC), oxides of nitrogen (NOx, comprised of NO andNO2) and particulate matter (PM) are emissions that areregulated for compression-ignition engines. Manyinvestigators have demonstrated that emissions of thesepollutants from DME combustion are significantly lowerthan those from diesel combustion [1-3,5,14]. Emissionsfrom DME combustion are analyzed in the following.

CO is an intermediate product from incompletecombustion and HC emissions consist of partially orcompletely unburned fuel. Therefore, both CO and HCare resulted from fuel-rich combustion and they can bereduced significantly under stoichiometric or lean-fuelcombustion. Although a CI engine operates with anoverall lean mixture, its combustion is non-homogeneousand, thus, both CO and HC are produced in locationswhere the combustion takes place under a fuel-richcondition due to incomplete air-fuel mixing. Becauseonly mixtures within combustible limits (for DME, leanlimit = 3.4 vol% and rich limit = 27 vol% [16]) will burn,the over-rich and over-lean mixture formed during thefuel injection (ignition delay period) may escape the maincombustion [15], resulting in the unburned fuel. DMEhas a short ignition-delay period; thus, it significantlyreduces the HC emissions from the above mechanism.DME is an oxygenated fuel containing 35-wt% oxygenand has a good mixing characteristic due to that itbasically is a superheated gas after entering the enginecylinder. Thus, the levels of the CO and HC emissionsfrom DME combustion should be much lower than thatfrom combustion of diesel fuel. The similarity inchemical structures of DME and propane suggests thatthe CO and HC emissions from DME combustion maybe close to those from propane combustion [17].

NOx is not a direct fuel-combustion product but aside effect of combustion. Because nitrogen is basicallychemically inert at temperatures lower than 1370 ° C [18],NOx formation requires a high temperature (T > 1370° C) and plentiful oxygen. Thus, the most favorablecondition for NOx formation should be in the combustionstage from the start of combustion to the time when thepeak temperature is reached. Any factors that influencethe early-stage heat release will affect the NOx formation.

Shortening the ignition delay is one of such factorsbecause it can reduce the amount of fuel burned in thepre-mixed burning stage and, therefore, it can reduce thepeak temperature [15,18]. Because DME has a shortignition-delay period, this feature of DME tends to reducethe NOx formation. Note that although DME is anoxygenated fuel, the chance to release free oxygen isvery limited as revealed by the DME chemical kinetics[12]; thus, the effect of the oxygen content in DME onNOx formation is negligibly small.

PM consists of carbon particles, commonly known assoot, coated with absorbed and condensed organiccompounds such as unburned hydrocarbon andoxygenated hydrocarbon. Soot forms by thermalpyrolysis during combustion and formation of sootrequires a fuel-rich condition and a high temperature. Afast mixing before reaching the pyrolysis temperature willreduce the soot formation. The precursors of soot arethe unsaturated carbons [16,19]. Acetylene (C2H2),ethylene (C2H4), and proparagyl (C3H3) are commonunsaturated carbons in diesel-fuel combustion [19]. Thepercentage of fuel carbons that form soot precursorsdecreases with increase in the oxygen content in the fuel[19] and with decrease in the number of C-C bonds (thesource of the unsaturated carbons) in the fuel [16]. Theexperimental evidence has shown that as the oxygencontent in the fuel reaches approximately 25 ∼ 30 wt%,virtually no soot is produced from the fuel combustion[19]. Because the oxygen content of DME is 35 wt% andthere is no C-C bond in DME, the percentage of fuelcarbons that form soot precursors in DME combustion isalmost zero [19].

Overall, due to its thermochemical characteristics,DME is a clean alternative fuel for CI engines. Withemploying conventional emission-control techniques(e.g., injection rate shaping, EGR, etc.), DME canachieve ultra-low emissions [14].

THERMOPHYSICAL PROPERTIES OF LIQUID DME

Since only liquid properties of DME are involved inthe fuel system design and modeling, the present studyfocuses on the liquid properties of DME. However,because DME is a low-boiling-point fluid, its vaporproperties can be easily predicted using a general-purpose equation of state (e.g., Peng-Robinson equationor Benedict-Webb-Rubin equation).

A liquid fluid has a local structure although it is highlydisordered globally. This local structure makes thethermophysical properties of a liquid fluid be dependenton the weight, shape, size, and polarity of the moleculeof the fluid and on the inter-molecular forces in the fluid.The thermodynamic behavior of a liquid fluid is closelyrelated to its properties at the critical point. On the basisof the critical properties and the molecular structure ofthe fluid, many of the liquid properties can be predicted.

The critical properties of DME and some parameters thathelp to characterize the behavior of DME are given in thefollowing:

Critical temperature Tc : 127 ° CCritical pressure pc : 53.7 barCritical density ρc : 259 kg/m3

Boiling point at 1 atm Tb : - 24.9 ° CAcentric factor ω : 0.192Dipole moment µD : 1.3 debyes

On the basis of the above properties and the molecularthermodynamic theory, equations for basic properties ofliquid DME were developed. These equations are givenin the following.

SATURATED LIQUID

Vapor pressure

An Antoine-type vapor-pressure equation wasdeveloped for DME:

,24412749.273.1

+−×+=

TTpLog (10)

where Log is the common logarithm function, p is thevapor pressure in bar and T is the temperature in ° C.Equation (10) gives a very good prediction of the DMEvapor pressure in the temperature range T = − 40 ∼ 127° C in comparison with the data reported in the literature[6]. For example, the boiling point at 1 atm (= 1.013 bar)reported in the literature is – 24.9 ° C [6,8,10] and theprediction by Eq.(10) is – 24.8 ° C; at 127 ° C, Eq.(10)gives p = 53.7 bar, which is precisely the critical pressureof DME. Figure 5 shows the predicted DME vaporpressures.

Density: saturated liquid

Following a technique developed by Rackett [8], anequation was developed, for prediction of the saturated-liquid density of DME, as follows:

ρs = ρref α−CZ (11)

where ρs is the saturated-liquid density in kg/m3, ρref =280.68 kg/m3 is a reference density for DME; 287.0=cZis the critical compressibility factor of DME; and

7/2α = [(127 − T) / 400] is a temperature-dependentparameter, and T is the temperature in ° C. Equation(11) should be used in the temperature range between –40 and 100 ° C. It is well known that the saturated-liquiddensity of DME at 20 ° C is about 660 kg/m (= 0.663

g/cc). The prediction given by Eq.(11) is ρs = 661 kg/m3

(= 0.661 g/cc) at 20 ° C. Dependence of the DME

density on temperature predicted by Eq.(11) is shown inFig.6.

Fig.5 Vapor pressures of DME at T = – 40 ∼ 120 ° C.

Fig.6 Saturated liquid density of DME.

Fig.7 Latent heat of DME.

Latent heat

The latent heat of DME can be predicted using thePitzer-acentric-factor correlation [8]. When applied toDME, this correlation can be written as

-40 -20 0 20 40 60 80 100 120

0

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Vapo

r pre

ssur

e (b

ar)

Temperature (oC)

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rate

d liq

uid

dens

ity (k

g/m

3 )

Temperature (oC)

-40 -20 0 20 40 60 80 100200

250

300

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450

500

550

Late

nt h

eat (

kJ/k

g)

Temperature (oC)

,)1(79.151)1(18.511 456.0354.0rrV TTH −×+−×=∆ (12)

where ∆HV is the latent heat in kJ/kg, Tr = (T + 273)/400is the corresponding temperature, and T is in ° C. Thesuggested temperature range for application of Eq.(12) isT = – 40 ∼ 100 ° C. Values of the latent heat of DME attwo temperatures reported in the literature are 468 kJ/kgat – 24.9 ° C and 402 kJ/kg at 25 ° C [10]. At thesetemperatures Eq.(12) predicts ∆HV = 460 kJ/kg (at – 24.9° C) and ∆HV = 397 kJ/kg (at 25 ° C). They are closeenough for an industrial standard. The predicted ∆HV =∆HV(T) relationship is given in Fig.7.

Ethanol is isomeric with DME and both ethanol andDME can be expressed by the chemical formula C2H6O.The chemical structure of ethanol is shown in Fig.8. The

Fig.8 Chemical structure of ethanol.

oxygen atom in ethanol can possibly induce threehydrogen bonds (two lone-electron pairs as receiversand the proton of the hydrogen atom associated with itas a donor) [20]. Because the molecules in liquidethanol are strongly associated with each other viahydrogen bonding, which is much stronger than themolecular interaction in DME, the thermodynamicbehavior of ethanol differs significantly from that of DME.Due to the very strong inter-molecular forces in ethanol,the normal boiling point of ethanol is 78 ° C (103 ° Chigher than that of DME!); thus, at the atmosphericpressure and normal temperatures, ethanol is a liquidwhile DME is a gas. Due also to the hydrogen bonding,the latent heat of ethanol is 942 kJ/kg at 25 ° C, which is2.34 times of the latent heat of DME at the sametemperature. This explains why ethanol has a cold-startproblem when used as a fuel for IC engines. Incomparison, the latent heat of DME at 25 ° C is close tothat of gasoline [21]. And, because the C-C bond isweaker than the C-OH bond in ethanol, ethanol does notlose its OH group at the initial step of the chain reaction;thus, chemical characteristics of ethanol also differsignificantly from those of DME. As an overall effect, theautoignition temperature of ethanol is much higher thanthat of DME [16].

Surface tension

The surface tension of DME may be predicted usingthe Macleod-Sugden equation [8]:

σ = [P × (ρL − ρV )/M]4, (13)

where σ is the surface tension in dyn/cm (= 10-3 N/m), Pis the parachor of DME, M is the molar mass of DME ing/mol, and ρL and ρV are, respectively, the densities ofsaturated liquid and vapor of DME in g/cc. On the basisof the chemical structure of DME, (CH3)2O, the parachorof DME is obtained as P = [CH3-] + [-O-] + [-CH3] =131.0, where [CH3-], [-O-], and [-CH3] representcontributions of the chemical groups forming DME. ρL

can be given by Eq.(11). ρV may be calculated using thefollowing 2nd-order virial equation of state:

),/(ZRTp=ρ (14)

),/(1 RTBpZ += (15)

),( 10 ffp

RTBc

c ω+= (16)

20 /1385.0/330.01445.0 rr TTf −−= (17) ,/000607.0/0121.0 83

rr TT −−

,/008.0/423.0/331.00637.0 8321rrr TTTf −−+= (18)

where R is the gas constant, Z is the compressibilityfactor, B is the second virial coefficient, and cr TTT /= isthe corresponding temperature. Note that in using anequation of state and calculating correspondingtemperatures, the temperature must be in the absolutescale; thus, in Eqs. (14)-(18), T and cT are in K. Therecommended temperature range for application of Eqs.(14)-(18) is T < 373 K (= 100 ° C).

Since the measured surface tension of DME is notcurrently available, verification of Eq.(13) is conductedusing diethyl ether (DEE) whose chemical formula is

Fig.9 Surface tension of DME.

HH

HH

H

H

C

C O

-40 -20 0 20 40 60 80 1000.000

0.005

0.010

0.015

0.020

0.025

Surfa

ce te

nsio

n (N

/m)

Temperature (oC)

(C2H5)2O. DME and DEE are the most similar ethers inthe ether family except for that both the parachor andliquid density of DEE are larger than those of DME,which results in a larger surface tension for DEE at thesame temperature. At 25 ° C, Eq.(13) predicts σ = 16.40dyn/cm for DEE, which is basically the same as thesurface tension for DEE given in the literature: σ = 16.47dyn/cm [10]. Because DME and DEE have very similarchemical and thermodynamic behavior, Eq.(13) shouldpredict reasonably accurate values for the surfacetension of DME. Figure 9 shows the variation of thesurface tension of DME with temperature.

SUBCOOLED LIQUID

Density: subcooled liquid

Equation (14) also applies to subcooled liquid. In thisstudy, the Lee-Kesler equation [8], which may beexpressed in a generalized form as Z = Z(T, p, Tc, pc, ω ,Zc), was used to calculate the compressibility factor Z forsubcooled-liquid DME. The results can be representedby the following correlation:

,1037.7146.0)( 25 ppTT−×−+ρ=ρ (19)

,72.1690)( TTT −=ρ (20)

where ρ is the subcooled-liquid density in ,m/kg 3 T is in° C, and p is in bar. For T ≤ 100 ° C, the above equationgives reasonably good predictions for pressures up to550 bar. Selected values of predictions are presented inFig.10.

Bulk modulus

The compressibility of a liquid, β, is defined as

,1)(1Ep T =

∂ρ∂

ρ≡β (21)

where E is the bulk modulus of the liquid. ApplyingEq.(14) into Eq.(21) yields

,)/(

ZppZpZ T∂∂−

=β (22)

or

.)/( TpZpZ

ZpE∂∂−

= (23)

For any given temperature, the compressibility or bulkmodulus of liquid DME can be solved by applying theLee-Kesler equation into Eq.(22) or (23). The bulk-modulus calculations are represented by the followingcorrelation:

(24)

Fig.10 Subcooled liquid density of DME: ■ , -20 ° C; ● , 0 ° C;▲, 20 ° C; ▼, 40 ° C; ◆ , 60 ° C; + , 80 ° C.

Fig.11 Bulk modulus of liquid DME: ■ , -20 ° C; ● , 0 ° C;▲, 20 ° C; ▼, 40 ° C; ◆ , 60 ° C; + , 80 ° C.

Fig.12 Speed of sound in liquid DME: ■ , -20 ° C; ● , 0 ° C;▲, 20 ° C; ▼, 40 ° C; ◆ , 60 ° C; + , 80 ° C.

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quid

den

sity

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k m

odul

us o

f DM

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f sou

nd in

liqu

id D

ME

(m

/s)

Pressure (bar)

,10 pEEE ×+=

,253.023.724984 20 TTE +−= (25)

,65.91 =E (26)

where E and p are in bar, and T is in ° C. Equations (24)-(26) can give reasonably good predictions for

temperatures between – 50 and 100 ° C and pressuresup to 550 bar. Predictions by Eqs. (24)-(26) agreereasonably well with the literature data [22]. Selectedpredictions of the bulk modulus are presented in Fig.11.

Speed of sound

The speed of sound in liquid DME is given by thefollowing equation

,])/(/[)273(/ TpZpZTRZEa ∂∂−+=ρ= (27)

where a is in m/s, E and p are in N/m2, ρ in kg/m3, T in° C, and R = 180.74 J/kg.° C is the gas constant of DME.The speed of sound in liquid DME can be solved bycombining Eqs. (19) and (20) and Eqs. (24)-(26) intoEq.(27). Because TpZpZ )/( ∂∂> and in the subcooled-liquid region Z is more sensitive to changes in T than inp, the influence of temperature on the speed of sound isstronger than that of pressure. Figure 12 shows selectedpredictions of the speed of sound. Figure 13 comparespredictions by Eq.(27) and the authors’ measurements ofthe speed of sound in liquid DME at 28.3 ° C (= 83 ° F)and five different pressures (12, 40, 69, 98, and 135 bar).It is seen in Fig.13 that the predictions agree well withthe measurements.

Viscosity

The Morris equation [23] was selected to predict theviscosity of liquid DME because it includes themolecular-structure information. The Morris equation isgiven in the following:

Log (µ /µref) = J × [400/(T + 273) – 1], (28)

where µref is a reference viscosity in cP (= 10-3 Pa.s), J =(0.0577 + Σbini)1/2, bi and ni are the contributions and therepeat numbers of the ith radical in the chemicalstructure, and T is in ° C. On the basis of the chemicalformula for DME, (CH3)2O, the repeat numbers for theradical CH3 is 2 and for the radical O is 1; and, it can bedetermined that b = 0.0825 for the radical CH3, and b =0.1090 for the radical O in ethers, and that the referenceviscosity for ethers is µ ref = 0.096 cP. Substituting thesevalues into Eq.(28) yields a viscosity equation for liquidDME:

]1)273/(400[5759.010096.0 −+××=µ T . (29)

At 25 ° C, the viscosity given by Eq.(29) is 0.151 cP. Thisprediction agrees with the value reported in the literature[5], µ = 0.150 cP. The dependence of the liquid-DMEviscosity on temperature is given in Fig.14.

Fig.13. Speed of sound in liquid DME at 28.3 ° C:▲, measurement; , prediction by Eq.(27).

Fig.14. Viscosity of liquid DME.

Fig.15 Thermal conductivity of liquid DME.

Thermal conductivity

-40 -20 0 20 40 60 80 1000.05

0.10

0.15

0.20

0.25

0.30

Visc

osity

of l

iqui

d D

ME

(cP)

Temperature (oC)

-40 -20 0 20 40 60 80 1000.05

0.10

0.15

0.20

0.25

Ther

mal

con

duct

ivity

of l

iqui

d D

ME

(W/m

.o C)

Temperature (oC)

10 20 30 40 50 60 70 80 90 100 110 120 130 140600

650

700

750

800

850

900

Prediction by Eq.(27)

Spe

ed o

f sou

nd in

liqu

id D

ME

(m

/s)

Pressure (bar)

The thermal conductivity of liquid DME may bepredicted using the Robbns-Kingrea equation [23]. TheR-K equation is as follows:

,)273

220(10)94.40.88( 3/4*

3

ρ+

×−=−

pN C

TSHk

∆ (30)

with )],273/(273[)273/(* +++= TRLnTHS bV∆∆

where k is the thermal conductivity in cal/(cm.s.° C), T isin ° C, the heat capacity Cp and gas constant R are incal/(mol.° C), the latent heat ∆HV is in cal/mol, and theliquid density ρ is in g/mol; N and H are chemicalstructure related constants. Substituting the relatedparameters for DME into Eq.(30), with converting all theproperties into SI units, yields,

,273

10774.63/4

3

+ρ××= −

Tk (31)

where the thermal conductivity k is in W/m.° C and theliquid density ρ is given by Eqs. (19) and (20).Predictions of the thermal conductivity of liquid DMEagree excellently with the literature data [30] for T ≤ 80

53 bar because Eq.(24) contains information on thelatent heat of DME. The dependence of the thermalconductivity of liquid-DME on temperature is given inFig.15.

HYDRODYNAMICS OF DME SPRAY IN ENGINECYLINDER

Being a low-boiling-point fluid, DME has a low criticaltemperature and a low critical pressure. Thus, thebehavior of liquid DME injected into the engine cylinder isvery sensitive to the cylinder temperature and pressure.Due to the surface tension (Rayleigh instability) and/or jetvelocity (Weber instability), liquid DME injected into thecompressed air in the cylinder breaks up into droplets. Ifthe liquid injected breaks up completely into droplets, it istermed as a spray; otherwise, it is termed as a liquid jet[25]. From the hydrodynamic viewpoint, the differencebetween a spray and a miscible turbulent jet is theexistence of the droplets in the spray because thedroplets carry a large percent of the initial momentum ofthe spray. Due also to the droplets, a spray is a two-phase phenomenon while a miscible turbulent jet fallsinto the category of the single-phase flow. The behaviorof the spray is governed by sizes of the droplets and theirdistribution; thus, the spray characteristics, such as thespray developing time, spray angle, and penetrationlength, all are affected considerably by sizes of thedroplets and droplet distribution.

The droplet sizes in a DME spray are affected highlyby the cylinder temperature and pressure. The DMEspray may encounter two possible phenomena. The first

is a temperature effect. If the droplets are small enough,their temperature may surpass the DME criticaltemperature very rapidly because both the values of thelatent heat and surface tension decrease with increase intemperature and become zero at the critical temperature.In this case, the DME droplets will undergo a very rapidvaporization process, as if they vaporize immediately.The second phenomenon is related to the cylinderpressure. The DME droplets in the spray may be in asubcooled liquid state initially because the pressure ofthe droplets is always higher than that of the ambient dueto the surface tension pressure [16]. Due to combustiondelay, the fuel is injected in an advance crankshaft anglebefore TDC. The heat release from the early-stagecombustion makes the cylinder pressure increase.During this period, the pressure of the droplets increaseswith the cylinder pressure. When the pressure of thedroplets reaches the DME critical pressure (53.7 bar),the droplets are in a supercritical state. In this case, theliquid-vapor interface disappears and the droplets mayspread to the neighborhood “explosively”. In either of thetwo cases, the spray turns into a miscible turbulent jet.

Glensvig et al. [26,27] and Sorenson et al. [28,29]have studied the characteristics of the DME spray. Intheir studies, the high-pressure liquid DME was injectedinto a nitrogen environment with T < 40 ° C and p = 15,25, 40, and 55 bar. Thus, their tests were conducted atsubcritical temperature and both subcritical andsupercritical pressures. Both single-hole-nozzle andpintle-nozzle injectors were used and comparisonbetween diesel-fuel and DME sprays under the sameconditions also was conducted. Following were noticedin their investigations: (1) Vaporization of DME dropswas immediately. (2) Although the penetration of theDME spray was similar to that of diesel fuel, the DME-spray developing time was much shorter than that ofdiesel fuel. (3) The spray angle of DME was greater thanthat of diesel fuel in all cases. (4) Unlike a diesel spray,the boundary of a DME spray was irregular and theirregularity increased with the cylinder pressure. Atcylinder pressures near the DME critical pressure,breakup of the DME spray was noticed (which neveroccurs for diesel fuel). (5) Above four phenomena weresimilar in both cases of hole- and pintle-nozzle injectors.(6) The spray penetration and the spray angle for bothdiesel fuel and DME were calculated using empiricalcorrelations. These correlations well described dieselsprays but poorly predicted patterns of DME sprays. Bekand Sorenson [30] studied the DME combustion by usinga turbulent-jet model and obtained a good prediction forheat release it seems that the usual combustion delaydue to the time required for vaporization of droplets indiesel-fuel sprays did not exist in the DME-spraycombustion.

The above experimental findings indicate that spraysof diesel fuel and DME differ significantly. Thephenomena of the enlarged angle, irregular boundary,and breakup of the DME spray suggest that the DME

°C. The pressure range of application of Eq.(31) is p ≤

spray behave more like injection of a gaseous fluid intoanother gas, which is supported by Bek and Sorenson’sturbulent-jet combustion model [30]. As was mentionedpreviously, the hydrodynamic behavior of a DME spray inthe engine cylinder is influenced highly by thethermodynamic state of the droplets in the spray. Whenthe temperature and pressure fall in the subcritical regionof DME, the DME spray should not show any unusualbehavior in comparison to that of diesel fuel. However,when the temperature and/or pressure of the dropletsenter the supercritical region of DME, the spray maybehave more like a miscible turbulent jet because thereis no difference between liquid and vapor in thesupercritical region. In this case, a turbulent-jet modelmay well characterize the “spray”. The transition from aspray (a two-phase phenomenon) to a miscible turbulentjet (a single-phase phenomenon) may also beencountered during the spray development: if the sizesof the droplets are small enough, the droplets maycompletely vaporize before reaching the spray tip due tothe temperature distribution in the spray. In this case,during the spray development, the dispersing dropletsmay dominate the spray hydrodynamics in the earlystage while the air entrainment may affect considerablythe later stage of the spray hydrodynamics.

SUMMARY

In this paper, the thermochemical characteristics ofDME were studied. From the viewpoint of the chemicalstructure, the reasons that DME has a high cetanenumber and low emissions from combustion wereanalyzed. On the basis of the molecular thermodynamicsof fluids, equations for commonly-used thermophysicalproperties of liquid DME were developed. Theseequations are easy to use and with engineeringaccuracy. Hydrodynamic characteristics of the DMEspray in the engine cylinder also were analyzed. It wasfound that the spray behavior is influenced significantlyby the thermodynamic state of the droplets in the spray.This study explained characteristics of the DMEcombustion reported by previous investigators.

ACKNOWLEDGMENTS

The authors wish to express their gratitude to theUSCAR 4SDI team, the National Renewable EnergyLaboratory and the U.S. Department of Energy for theirfinancial support of this project.

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