Swaminathan N., Bray K.N.C. (eds.) Turbulent Premixed Flames

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4.1 Application of Lean Flames in Internal Combustion Engines 253

The legislation applies generally to SI gasoline-fuelled vehicles (‘positively ig-

nited’, in the wording of the legislation – a distinction that is of signiﬁcance as CI

engines based on gasoline fuel are subsequently considered), so LBDI engines must

also meet the same regulations for the emissions of CO, HC, and NO

. For sto-

ichiometrically fuelled engines, so-called three-way catalytic converters – for CO,

HC and NO

– are a well-developed, long-established, and effective technology. In

contrast, for lean-burn engines, the three potential NO

after-treatment technolo-

gies are regrettably not (yet, at least) comparable to the three-way catalyst in terms

of cost beneﬁt. The conversion efﬁciency of catalysts is currently inadequate; and

lean NO

traps and selective catalytic reduction with on-board urea are also not as

well developed as three-way catalytic converters. The development of an economic,

reliable, durable, and efﬁcient lean NO

after-treatment is an enabling technology

for the LBDI engine, and the current generation of these technologies is at present

available on only a few so-called premium vehicles. The science and technology un-

derpinning the removal of NO

upstream of emission to the atmosphere are critically

important to the successful development and commercialisation of lean-burn com-

bustion in SI engines. These subjects are, however, beyond the scope of this section,

but an excellent introduction to the technology is given in [13]. Nevertheless it is

worth noting that some stakeholders have commented, at the time the legislation

was open for comment [31], that reducing the permitted emission levels for NO

could be problematic for DI vehicles.

Diesel – CI. The main intention of the current Euro 5 regulation (which came into

force in 2005) was to reduce the emission of PM from diesel cars by 80%, relative to

Euro 4, to 5 mg/km. This large reduction was selected because more lenient emission

limits were found to be insufﬁciently stringent to ensure a signiﬁcant improvement

in ambient air quality [47]. It has become possible to set such low limits in view of

the relatively recent development of ‘internal’ and ‘external’ engine measures: The

former include advanced fuel injection systems and advanced combustion control

of the type described later in this section. The latter include diesel particulate ﬁlters

(DPFs), although these imply, because of the associated pressure drop, a lowering

of the efﬁciency of the diesel engine. It is worth noting that the emission limit is

comparable with emissions from current engines ﬁtted with DPFs and with emissions

legislation in the United States and Japan. However, the new regulations are s o

stringent that it is difﬁcult to measure such low levels of emission with current

particulate measurement techniques and, as a consequence, an even stricter limit

would have given rise to difﬁculties for both manufacturers and for monitoring

[47, 48]. For example, under some typical test conditions, the mass change on a ﬁlter

paper can be as low as 10 or 20 μg: This is comparable t o the weight of a human

ﬁngerprint.

The subsequent regulation, Euro 6 (scheduled to enter into force in 2014), also

takes account of the rapid developments in diesel-engine-related technologies (such

as turbochargers and combustion control through advanced fuel injection equipment,

to mention only two). The legislator’s intent is mainly to reduce the emissions of NO

from diesel cars by more than 50% for some categories of vehicle, to 80 mg/km, with

the result that the regulation level will be similar to that for a gasoline engine. This

development thus sees an end, for these categories, to the historically less stringent

254 Lean Flames in Practice

Table 4.1. Changes in health impacts associated with Euro 5 and 6 in 2020 [49]

Reduction due Reduction due Increase in

Parameter to Euro 5 to Euro 5 and 6 % beneﬁt Unit Pollutant

Acute mortality (all ages) 72 112 57 Premature O

deaths

Chronic mortality (30 yr+) 2 000 3 800 90 Premature PM

deaths

Chronic mortality (all ages) 20 600 35 900 74 Life years lost PM

Restricted-activity days

(RADs, 15–64 yr)

1 850 000 3 180 000 71 Days PM

limit for diesel engines. However, it has been more difﬁcult to control NO

emissions from diesel than from (stoichiometrically fuelled) gasoline engines: This

can be gauged from the fact that ‘type-approval’ values of NO

and PM emissions

for diesel vehicles have – for Euro 4 and 3 and in contrast to gasoline vehicles –

been clustered towards the legislative limits, signifying that the emission limits are

‘technology forcing’. The associated technology for such control downstream of the

engine [e.g., selective catalytic reduction (SCR), using ammonia as the reducing

agent; lean NO

catalysis (LNC), using either HCs from the engine or exhaust fuel

injection as the reducing agent; and storage catalysts, lean NO

traps (LNT), with

periodic regeneration] remains under development and is relatively costly. Note also

that all three technologies imply a direct or indirect lowering of the efﬁciency of

the engine by a few percentage points. The legislators concluded that there was a

need for a balance to be struck relating to the cost-effectiveness of the emission

limits corresponding to a cost estimate [49] for complying with Euro 5 and 6 relative

to Euro 4, of the order of e590 (sales-weighted average cost per diesel vehicle).

It is, however, acknowledged that this estimate may be too large by a factor of 2.

Per tonne of NO

, these measures are about 15% more costly than abatement from

other, non-transport sectors. The balance in terms of cost-effectiveness needs to take

into account, on the one hand, the affordability of Euro 6 generation vehicles both

for continued renewal of the diesel ﬂeet, so that Euro 6 standards gain market share

as rapidly as possible, and to maintain the market share of diesel vehicles, which

make a s igniﬁcant contribution to reduced CO

emissions. On the other hand, the

argument for abating NO

emissions from road vehicles is also strong, given that

high transport NO

emission places at particular risk the relatively large population

who live close to roads. The net result of Euro 5 and 6 measures is predicted to

be a 26% reduction in NO

emissions and a 5% reduction in HC emissions of

those required in 2020 and an 11% overall reduction of PM

2.5

relative to Euro 4

alone. It is estimated that the reduction in emission limits this is due to Euro 6

relative to Euro 5 increases the health beneﬁts by between 60 and 90%, as shown in

Table 4.1.

European Emission Standards – Heavy-Duty Vehicles (Diesel CI)

The standards have undergone major revisions ﬁve times since the original directive

in 1988 (88/77/EEC), the most recent being the so-called ‘Euro V’, which entered

4.1 Application of Lean Flames in Internal Combustion Engines 255

into force in late 2008. Even so, [33] identiﬁed that a review of the emission limits

for heavy-duty vehicles beyond Euro V is needed to meet the air-quality targets for

2020. Thus there is a proposal for a new regulation, Euro VI, in 2014 [50], the main

aspects of which are a 66% reduction in the mass of particulate emissions and a

reduction of 80% in NO

emissions. The new emission limits are comparable to the

U.S. 2010 standards and ‘...reduce the risk of vehicles producing unnecessary levels

of pollution . . . without imposing excessive costs . . . ’ [34]. In other words, a balance

is once again struck between higher environmental standards and the continued

affordability of heavy-duty vehicles for the operators. However, it should be noted

that, in the future, legislators may have to take into account the fact that there is

strong evidence that heavy-duty diesel vehicles make a major contribution to NO

emissions and to primary NO

emissions [51].

Emissions – Perspectives for Lean-Burn Combustion

The legislation for vehicle emissions sits within the broader context of the quality of

the ambient air. As noted in [25] in the context of the United States,

. . . Certainly, conventional air pollution is not the national priority today that it was at

the time of the passage of the 1970 CAA [Clean Air Act] Amendments. . . . Yet, we still

have a signiﬁcant number of areas that do not meet the O

and PM

2.5

standards, . . . and

acid and nutrient deposition is still a concern for some ecosystems. We are well on the

way to signiﬁcant new improvements in all of these areas, but the end is not fully in sight.

Moreover, whereas risks from air pollution are, on average, modest, it is still reasonable

to expect that the cumulative effect may number in tens of thousands of early deaths

nation-wide. . . . mainstream experts believe the risks remain signiﬁcant.

The situation is broadly similar in Europe, and, on both continents, it is likely

that legislators will continue to review ambient air quality and the contribution of

transport to it. Even the currently known evidence could justify further reduction in

the emission levels, and it is likely that new epidemiological or controlled evidence

will appear, particularly for particulates, that will strengthen this tendency. In addi-

tion, the impending change in regulation of emission of PM

2.5

from a mass-number

to a particle-number basis may be accompanied by more information about research

into the importance of particle size. It will be interesting to know the health effects,

if any, of ultra-ﬁne particles.

In terms of emissions, the stoichiometrically fuelled SI gasoline engine with a

three-way catalytic converter has set, and continues to set, a high standard for IC

engines with other combustion modes to meet. Legislation in Europe governing the

CI diesel engine has allowed in the past either larger emission levels or extended

periods of ‘grace’ for the emission levels to be lowered (a situation that currently

includes the SI LBDI engine). This has been, in part at least, because of the lower

emissions from diesel engines. As technological solutions to produce lower

diesel emissions have started to appear, however, recent legislation suggests that the

compromise is struck in favour of a modest sacriﬁce of some of the fuel efﬁciency

to improve the ambient air quality. There is thus little question that, whatever other

merits the application of lean-burn combustion to IC engines may have in terms

of fuel economy, these must be accompanied by low emissions, particularly of ﬁne

particulates, at an acceptable ﬁnancial and fuel economy cost.

256 Lean Flames in Practice

Log v

Stoichiometric

Lower

negative

pressure

Higher

negative

pressure

wider open Throttle

narrower open Throttle

Lean burn

Log p

Log v

Lean burn

Ambient

pressure

Log p

Effective work :A>a

Pumping loss :B<b

Figure 4.1. Comparison of schematic indica-

tor diagrams for stoichiometric and lean-burn

operation for a throttled four-stroke SI engine

showing the reduced pumping losses and larger

work output for the latter.

4.1.2 Lean-Burn Combustion Concepts for IC Engines

The technical applications of lean-burn combustion can be categorised according to

the mode of combustion, either spark ignition or compression ignition, and these are

subsequently considerd in turn.

Lean-Burn SI Combustion

CONCEPTS. One method of introducing the fuel, usually but not necessarily gaso-

line, into an SI engine is upstream of the inlet valves, through either (in the past)

a carburettor or (currently) a ‘port fuel injector’ (PFI). The fuel mixes with the in-

ducted air so that, at t he time of ignition, a premixed gas surrounds the spark plug:

The control of the fuel ﬂow rate leads to control of the engine’s output (load, speed).

The physical distance between the point of introduction of the fuel and the spark

plug, combined with the need to ensure a combustible mixture in the vicinity of the

spark plug at ignition, has generally led to the fuel and air ﬂow rates being metered

to remain in approximately stoichiometric proportions. This thus implies the need

to ‘throttle’ the mass ﬂow rate of air through the engine at part load and leads to the

p–V diagram for throttled operation shown in Fig. 4.1, with the well-known associ-

ated loss of pumping work. However, as brieﬂy described later, it has been possible

to produce designs that stratify the charge, and burn a portion of the fuel through

lean combustion, and so extend the engine’s lean stable operating limit by several

air–fuel ratios (AFRs) from stoichiometric, say up to about 25:1. The ﬁrst beneﬁt of

doing so is that the loss to pumping work is smaller for a given power output, which is

of great technical importance because of the large amount of throttling needed by a

conventional, unstratiﬁed lean-burn SI engine during urban drive cycles. The second

beneﬁt is thermodynamic and is shown in Fig. 4.2: The fuel-conversion efﬁciency as

a function of the equivalence ratio, based on isochoric combustion and a fuel–air

cycle analysis, increases with increased leaning of the mixture. This is because the

effective value of the ratio of the speciﬁc heat increases over the expansion stroke

4.1 Application of Lean Flames in Internal Combustion Engines 257

Fuel–air equivalence ratio φ

0.4

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.6 0.8 1.0 1.2 1.4 1.6

f, i

= 1.0 atm

= 388 K

= 0.05

Figure 4.2. Fuel–air cycle results for in-

dicated fuel-conversion efﬁciency as a

function of equivalence ratio and com-

pression ratio, r

, (octene fule, inlet pres-

sure p

is 1 atm, temperature T

is 388

K, and the residual gas fraction x

is 5%).

Cited by [52].

because of the dependence of the ratio of the speciﬁc heats of the burned gases both

on the temperature and on the AFRs as shown in Fig. 4.3 [52]. The third beneﬁt

relates to emissions and is shown in Fig. 4.4 [53], which shows that NO

(in fact,

mostly nitric oxide, NO) falls with increasingly lean operation. This is because the

temperature dependence of the reactions reduces the equilibrium concentration of

NO as the ﬂame temperature, which is consequent on increasingly leaner mixtures,

falls [54]. HC emissions, in this ﬁgure, are shown initially to reduce as the overall

equivalence ratio starts to become lean, but may rise again with increasingly lean op-

eration as the reduced ﬂammability of the mixture causes emissions from the ﬂame

quenching near cold walls, crevices, and, ultimately, misﬁres. As noted in [5], lean

operation is the reason that some engines, operating at a lean overall equivalence

ratio, could nearly meet early emission standards without the need for further emis-

sion control methods. In a stratiﬁed-charge engine, the equivalence ratio ranges from

near stoichiometric close to the spark-plug gap to leaner than stoichiometric with

increasing distance away from the gap. As a consequence, the emission characteris-

tics of a stratiﬁed-charge lean-burn engine are a composite between the undesirable

emissions that occur near stoichiometric mixtures and the more desirable character-

istics in the lean region. There is thus a compromise to be struck between having

reliable ignition (which requires a near-stoichiometric mixture to surround the gap)

and the beneﬁts of lean operation. Given the strong dependence of NO

emission

on temperature, there is an incentive to minimise the volume occupied by near-

stoichiometric mixtures. However, we anticipate the following discussion in stating

that, although the reduction in NO

consequent on burning lean is welcome, for SI

engines at least the reduction is insufﬁcient to meet the limits currently in force. As

258 Lean Flames in Practice

A/F = 29

A/F = 22

A/F = 14.7

1.22

1.42

1.4

1.38

1.36

1.34

1.32

1.3

1.28

1.26

1.24

500

Temperature (K)

1000 1500 2000

leaner combustion gas component

lower combustion gas temperature

Figure 4.3. Variation of the ratio of the spe-

ciﬁc heat, κ = c

, as a function of the

temperature of the gas with the compo-

nents of the gas as functions of the AFR as

parameters.

a consequence, some sort of NO

after-treatment is required. This requirement is

a signiﬁcant, although not insuperable, technological burden for lean-burn combus-

tion in SI engines, whether fuelled by port fuel injection or by DI, as described in

the following paragraphs.

The other method is to inject the fuel directly into the combustion chamber,

raising the possibility of dispensing with the throttle, thereby removing the pumping

loss altogether, controlling the load of the engine instead solely by controlling the

0.5

0.4

0.3

0.2

0.1

0.8 0.9

Lean

Rich

% vol.

Equivalence ratio, φ

1.0 1.1 1.2

Figure 4.4. SI engine emissions for differ-

ent fuel–air equivalence ratios. Reprinted

from [53]. (Also see Fig. 1.1.)

4.1 Application of Lean Flames in Internal Combustion Engines 259

fuel ﬂow rate. In this approach, the injection timing is usually an important variable

because this can determine whether an ignitable mixture is established in the vicinity

of the spark plug near the top dead center (TDC) of compression. The possibility of

achieving this goal over such a large implied variation of overall equivalence ratio

arises largely because the physical distance between the injector and the spark plug

is greatly reduced with DI, making it is possible to position a relatively small, yet

ignitable, cloud of fuel and air around the spark plug. The approach essentially relies

on retarding the timing of the s tart of injection: The leaner the required overall AFR,

the nearer the start of injection is to compression TDC. DI also raises the possibility

of increasing the cycle efﬁciency that is due to lean burn far beyond that attainable

by a PFI design, in principle, by operating at overall AFRs beyond 65:1, or an overall

equivalence ratio leaner than about 0.2 (see subsequent discussion). At low power,

this implies operation with relatively late injection to prevent the fuel cloud from

becoming too lean. Indeed, to have reliable ignition in this case, it is necessary to

have a spatially stratiﬁed mixture, close to stoichiometric at the spark-plug gap (at the

time of ignition) and leaner farther away, which is inﬂamed by the strongly growing

ﬂame kernel. As a consequence, the temperature rise in the gas is smaller than in

a s toichiometrically fuelled engine, and hence a further beneﬁt is that heat loss by

conduction to the cylinder walls can be smaller. (Note that spatially uniform mixtures

can also be used with DI: If the mixture is also stoichiometric this has the advantage

that a three-way catalytic converter can be used, but there is no thermodynamic

advantage. Alternatively, to gain some thermodynamic efﬁciency while retaining the

convenience of generating spatially uniform mixture, the equivalence ratios must

remain greater than about 0.7 to avoid misﬁres.)

Other advantages follow from DI that are not necessarily associated with lean

combustion but that are important insofar as these strengthen the case for the adop-

tion of equipment for DI – which is, as previously mentioned, the enabling technology

for lean, and particularly stratiﬁed lean, burn combustion. The compression ratio of

the engine can be increased because the likelihood of knock is decreased because of

evaporative charge cooling, and because the ‘end-gas’ residence time can be reduced.

Alternatively, the octane appetite of the engine is reduced at a given compression ra-

tio. If injection takes place early, during the induction stroke (which, however, tends

to result in homogeneous rather than stratiﬁed operation and hence tends to be lim-

ited to stoichiometric, high-load operation), the volumetric efﬁciency of the engine

improves. Other advantages include [55] improved response to transient changes

in load and speed, improved ignition and emissions during ‘cold start’ because of

the lack of the accumulation of fuel on walls, as occurs with PFI, and higher toler-

ance of exhaust-gas recirculation (EGR) for reduction in NO

and for dethrottling

strategies. The control of emissions during the cold-start phase is known to be of

importance in meeting emissions targets. If the fuel and air mixture is thought of as a

‘cloud’, isolated from the walls of the combustion chamber, then it may also be that

wall quenching of the ﬂame is reduced or eliminated altogether. Additionally, the

large heat losses that would otherwise occur in the expansion stroke can be reduced.

However, although the smaller heat transfer losses decrease the destruction of avail-

ability (exergy), this cannot all be realised as an increase in brake power [56]. Some

is transformed into an increase in the exhaust-gas availability, and turbocharging is a

favourable second-law process for recovery of this energy. As a consequence of the

260 Lean Flames in Practice

Combustion

Losses

Cylinder Heat

Losses

Exhaust

Losses

Fluid Flow

Friction

Brake Work

0.0

PFI

7% peak power

Fuel Consumption (g/s)

LBDI ULBDI

0.2

0.4

0.6

0.8

Combustion

Losses

Cylinder Heat

Losses

Exhaust

Losses

Fluid Flow

Friction

Brake Work

0.0

PFI

25% peak power

Fuel Consumption (g/s)

LBDI ULBDI

0.5

1.0

1.5

2.0

2.5

Figure 4.5. Comparison of fuel con-

sumption for the PFI, LBDI, and ULBDI

cases. 7% peak power for the top ﬁgure,

and 25% peak power for the bottom ﬁg-

ure [58].

preceding advantages, there are – in principle – substantial opportunities to reduce

fuel consumption, although the magnitude of the improvement varies greatly with

the location in the engine’s performance map [57] and on the details of the engine

technology.

To What Extent Do These Qualitative Arguments Result

in an Improvement in Efﬁciency?

[58] provides an extensive theoretical analysis based on availability: the authors

consider a 3.0-L stoichiometrically operated engine with port fuelled injection and

a compression ratio of 10.5:1 and compare it with a mildly downsized (2.9-L)

lean-burn (1/φ = λ = 1.7) DI engine and operated at a compression ratio of 12:1.

A third engine, a downsized (2.7-L), ultra-lean-burn (λ = 5.0), high-compression-

ratio (16:1), DI engine is also considered (ULBDI). The peak brake work of the

LBDI engine is about 40%, approximately 14 basis points higher than the PFI case;

that of the ULBDI is 43%. Figure 4.5 summarises the results at 7% and 25% of

full power on the basis that the brake work is the same. These values are repre-

sentative of loads in which a large fraction of engine operation occurs in typical

drive cycles. In both ﬁgures, the height of a bar gives the total fuel-consumption rate

(in grams per second). Under lower-power (7%) conditions, the greater frictional

losses and signiﬁcantly lower exhaust losses in the progression from PFI to LBDI to

ULBDI reﬂect the impact of increasing compression ratio from 10.5 to 12 to 16. The

4.1 Application of Lean Flames in Internal Combustion Engines 261

100

Fuel consumption (x)

Today’s gasoline engine

GDI

12%

Direct injection and lean stratified mixture

Reduction of therotteling loss

Increase of compression ratio

19%

23%

30%

40%

94%

100%

68%

GDI

Figure 4.6. Theoretical fuel savings with

gasolineDI.Citedby[57].

reduction in ﬂuid ﬂow losses (i.e., pumping losses) reﬂects the increasing degree of

lean-burn operation. The higher λ of the ULBDI case (λ = 5vs.1.7forLBDI)vir-

tually eliminates pumping losses. Lean-burn operation also leads to lower cylinder

heat losses by means of the reduced combustion temperatures. Whereas most of the

losses decrease going from PFI to ULBDI, the combustion irreversibilities do not.

This reﬂects the fact that lean-burn operation results in combustion at lower temper-

atures. Under the higher-power (25%) conditions, the qualitative beneﬁts of LBDI

as opposed to those of PFI are the same, reﬂecting the effects of lean operation and

higher compression ratio. The LBDI and ULBDI cases are quite similar. For both

cases, the AFR is slightly above λ ≈ 1.7 (the LBDI lean limit), and consequently

the major difference is the higher compression ratio. The slightly higher frictional

losses, cylinder heat losses, and slightly lower exhaust losses for the ULBDI engine

are all consistent with a higher compression ratio. Broadly similar conclusions are

reached in [57], shown in Fig. 4.6, in considering a slightly different comparison,

namely between a throttled stoichiometric PFI engine operating with a compression

ratio of 11:1 and a DI engine with a compression ratio of 12.5:1 operating up to a

λ ≈ 4. Although these analyses show that large reductions in fuel consumption are

possible, two points must be borne in mind. The ﬁrst is that the improvements over a

drive cycle will be more modest, because the drive cycle incorporates a wide range of

speeds and loads. Thus [59] quotes [60], showing that – compared with a PFI without

EGR – the advantage of a DI design is of the order of only a 15% fuel saving over the

U.S. federal test procedure. In addition, [59] states that thermal management and re-

generation of a lean NO

, catalyst, engine transients, cylinder-to-cylinder variation,

and injector aging can reduce the estimated cycle average beneﬁt to 8%–12%.

The second point is that suitably optimised stratiﬁed combustion is increasingly

difﬁcult to achieve as the load demanded from the engine increases, for reasons

that may include the excessive generation of NO

and particulates (from excessively

rich regions near the spark gap as well as from increased impingement of the fuel

on surfaces including the piston crown), unburnt HCs from insufﬁciently premixed

parts of the vapour cloud, and a degradation of fuel consumption [61]. Two of the

latest production engines are based on so-called ‘spray-guided’ stratiﬁed-charge, DI

262 Lean Flames in Practice

1.4

1.2

1.0

0.8

0.6

0.4

Specific effective work (km)

0.2

0.0

240

250

270

280

240

250

240

λ > 1

λ >> 1

240

270

250

280

290

300

310

325

350

375

400

450

500

600

1000

800

300

280

290

260

250

1000 3000

295

Engine speed (rpm)

5000 7000

Figure 4.7. Mode of fuelling and contours of speciﬁc fuel consumption (g/kWh) on an engine

map of a spray-guided DI combustion system. The excess air factor, λ, is the reciprocal of the

equivalence ratio, φ [62].

design (see the following discussion) and [62, 63] report the engine maps together

with the ‘road-load’ curve and the combustion mode superimposed on contours of

speciﬁc fuel consumption (grams per kilowatt hour). These are reproduced in Figs. 4.7

and 4.8 and show two features of interest in the context of lean-burn combustion.

The ﬁrst is that the fuel consumption at the key point of 2000 rpm and a mean

effective pressure of 2 bars, with stratiﬁed lean-burn operation, is reported as 295

and 290 g/kWh, respectively, which is claimed to be better than the best car diesel

engines. The second is that the engines operate in lean-burn mode over a low-load,

low-speed portion of the operation map only: The area, however, over which this lean

mode obtains is reported to be a signiﬁcant expansion over what was possible with

0 1000

Mean effective pressure (bar)

2000 3000

Engine revolutions (1/min)

4000 5000 6000

λ >> 1 Stratified operation

controlled NO

-strong catalyst

λ = 1 Homogeneous

operation controlled 3-way catalyst

215 KW

365 Nm

= 250 km/h

max

250 km/h

150 km/h

120 km/h

90 km/h

–10%

0...–2%

–15%

–20%

–25%

–30%

–40%

5. Gear

7. Gear

7000

Figure 4.8. Engine map showing region of stratiﬁed mode and potential fuel-consumption

improvement of a stratiﬁed DI engine compared with port injection. The excess air factor, λ,

is the reciprocal of the equivalence ratio, φ [63].