computational optimization of internal combustion engines || scaling laws for diesel combustion...

Chapter 5Scaling Laws for Diesel CombustionSystems

Scaling laws are developed to guide the transfer of combustion system designsbetween diesel engines of different sizes using simple formulations. In this chapter,the concepts and formulation of scaling laws are presented. A practical example isprovided to study a light-duty and a heavy-duty production diesel engines usingthe established scaling laws.

5.1 Introduction

Engine design is a time consuming and expensive process in which many costlyexperimental tests are usually conducted. Even with efficient and reliable CFDtools, engine optimization could take a very long time to complete. Engine designwork is often repeated for different engines that share similar features. Thismotivates a study of scaling laws, which describe scaling relationships betweenengines with different sizes, such as large off-road heavy-duty diesel engines andsmall high-speed auto engines. CFD simulation again offers an efficient andinformative option for this task. The intent of the scaling laws is to maintaingeometric similarity of key parameters influencing diesel combustion, such as in-cylinder spray tip penetration and flame lift-off length. Based on relatively simpleformulations, one well-established engine can be down-scaled or up-scaled toanother engine, which has similar features as the original engine. In this way, theamount of engine design work is significantly reduced in both time and cost.

Initial work was proposed by Bergin and Reitz (2005) who proved that similarcombustion behavior in two different size engines can be obtained by scaling a fewbasic engine geometry parameters, engine speed, and the injected fuel mass. Stagerand Reitz (2007) developed an extended model by adding a law to scale the flamelift-off length. The scaling laws were applied to two ideally-scaled engines wherethe small engine was obtained by halving the dimensions of the larger engine.Numerical results of multidimensional simulations showed that the scaling lawsworked well over a range of injection timings for engines with low temperature

Y. Shi et al., Computational Optimization of Internal Combustion Engines,DOI: 10.1007/978-0-85729-619-1_5, � Springer-Verlag London Limited 2011

147

combustion, and the results also suggested that three regions could be defined inthis range where turbulence and chemical kinetics timescales played different rolesin influencing combustion and emissions.

Shi and Reitz (2008c) conducted a CFD-based scaling study of two productiondiesel engines (one 0.5 L light-duty GM-Fiat engine and one 2.5 L heavy-dutyCaterpillar engine). It was found that the in-cylinder pressure trace and heat releaserate results could be well predicted based on the scaling laws. Emission results werewell captured in combustion regions controlled by turbulent time scales. Someprocesses (such as soot and NOx formation) are determined by chemical reactiontime scales and thus previous scaling laws had difficulty to reproduce them. Thesame two engines were also investigated experimentally (Staples et al. 2009), andthe scaling laws in Bergin and Reitz (2005) and Stager and Reitz (2007) werevalidated where the Caterpillar engine was modified before testing in order to beconsistent with the scaling laws. Experimental results showed that overall engineperformance including IMEP and ISFC were in good agreement for two scaledengines. Extended scaling laws accurately predicted the SOC, CA10, and CA90.NOx and PM emissions matched trend-wise and in approximate magnitude. NOxemissions showed dependence on chemical timescale differences that are caused byengine speed and temperature. Higher PM emissions in the small engine werethought to be due to reduced time and increased heat transfer. Lee et al. (2010)investigated the impact of design constraints/limitations on the applications ofscaling laws and identified key physical parameters that need to be respected withinengine design constraints. Ge et al. (2011) applied the scaling laws for downsizing alight-duty HSDI diesel engine from 450 to 400 cc. They found that the scaling lawswork well at least for engine downsizing with small size variations.

5.2 Scaling Laws

Scaling laws are desired to produce identical performance and emission levels inengines of different sizes. However, it is very difficult to achieve this aim in reality.Establishment of any scaling arguments for diesel engines should at least target thefollowing goals: (1) geometric similarity should be maximized, so that the twoscaled engines have similar boundary conditions. This includes scaling of the bore,stroke, squish height, and piston bowl shape, and the resulting compression ratioshould be the same in the two engines. By setting the same boost pressure andtemperature, the same wall temperatures, and the same initial flow conditions, suchas the swirl ratio, similar initial thermodynamic and fluid dynamic conditions priorto spray injection can be achieved in the combustion chamber; (2) similarity inspray dynamics should also be considered. Spray development has a primary effecton engine performance and pollutant emissions as it determines the mixing of thefuel and air. The aim is to have similar fuel distributions before the combustionevent. It is usually quantified in terms of spray tip penetration, which is the essentialparameter determining the fuel distribution; (3) similarity in the combustion

148 5 Scaling Laws for Diesel Combustion Systems

characteristics in the scaled engines should be maintained in order to providesimilar engine performance and emissions.

5.2.1 Combustion Chamber Geometry

Volume-related quantities are scaled by V, such as the displacement volume andthe volumes at TDC and BDC, while length is scaled by L, such as the bore, stroke,squish height and bowl diameter. The resulting compression ratios should be thesame. Valve opening and closing timings, swirl, wall temperatures, boost pressuresand temperatures are also kept the same. All of these scaling laws ensure that thethermodynamic and fluid dynamic conditions before spray injection are similarbetween two engines.

As an internal flow, the diesel combustion process is strongly influenced by thepiston bowl geometry. The in-cylinder flow after spray injection is dominated bythe spray-induced flow because the injected droplets have much higher speeds.The surrounding gas flow is dragged by droplets and interacts with the piston bowlmovement. This can form a tumble flow, which has a significant impact on theconsequent processes of mixing, combustion, and pollutant formation. Optimiza-tion of piston bowl shape is thus an important part of the whole process of enginedesign. In engine scaling, the piston bowl shape is also kept the same so that theresulting spray targeting, and the interaction of the spray induced tumble flow andgeometry are the same for the two engines.

5.2.2 Power Output

The power outputs of the two engines should scale with their displacement volumes.Assuming that the down-scaled engine has the same combustion and thermal effi-ciencies, its power output should be scaled by the injected fuel mass m. Thus, theinjected fuel mass m scales with V. The injected fuel mass is related to the fuel injectornozzle hole diameter d0, injection velocity Uinj, and injection duration Dt by:

m ¼ p4qld

20UinjDt: ð5:1Þ

5.2.3 Spray Tip Penetration

In direct injection engines spray tip penetration, which is defined as the distancebetween the spray plume tip and nozzle tip, is a primary parameter that characterizesthe following fuel distribution and mixing. Additionally, if the spray tip penetrationis too long, spray wall impingement may occur, which will lead to poor emission

5.2 Scaling Laws 149

results. To maintain similarity in the fuel distributions, the spray tip penetrationsshould be scaled by the length scale of the cylinder, which is L. Parameters that affectspray tip penetration include the injector orifice diameter, ambient gas conditions,and fuel characteristics (Siebers 1999). Hiroyasu et al. (1978) experimentallyinvestigated the effects of nozzle orifice size, injection pressure, fuel density, andambient density on transient spray tip penetration. They found that spray tip pene-tration is directly proportional to time in the early stages of injection, but becomesproportional to the square root of time as the injection progresses according Eq. 5.2.The time duration of the first stage is defined as breakup time tbreak. Modest changesin ambient temperature had little to no effect on spray tip penetration. Even inexperiments where the temperature varied from room temperature to 320�C, thechange in spray tip penetration was minimal. The jet disintegration theory of Levich(1962) gives consistent results and the spray tip penetration s were described usingthe following empirical explicit equations:

s ¼0:39t 2Dp

ql

� �12; t\tbreak

2:95 Dpq

� �14ðd0tÞ

12; t� tbreak

8>><>>:

;

ð5:2Þ

with the breakup time scale tbreak ¼ 28:65qld0ðqDpÞ1=2. ql and q are density of theliquid fuel and air, respectively. Dp is the pressure drop across the injector, whichis related to the injection velocity Uinj, through Bernoulli’s principle:

Dp ¼ 12

qlU2inj: ð5:3Þ

Generally, only the second stage (t� tbreak) is considered except for very shortinjections. Substituting Eq. 5.1 into Eq. 5.2 gives

s2 / Uinjd0t: ð5:4Þ

5.2.4 Flame Lift-Off Length

The combustion process of diesel combustion can be well characterized by theflame lift-off length, which is defined as the length away from the injector tip thatthe combusting flame stabilizes once the initial auto-ignition phase is over.

Dec (1997) developed a conceptual model of DI diesel combustion based onlaser sheet imaging. His study indicated that a rich reaction zone exists justdownstream of the lift-off length in the central region of the fuel jet. Significantlocal heat release and fuel-rich product gases are generated in this region. Fur-thermore, it has also been hypothesized that soot formation begins in the productgas in this region under typical diesel conditions, and then the soot concentrationand particle size grow as the product gas is transported further downstream.


Siebers et al. (2002) investigated the effects of oxygen concentration on flamelift-off on DI diesel fuel jets, and concluded that lift-off length is inversely pro-portional to the ambient gas oxygen concentration. They also confirmed previouslyobserved trends in lift-off length with respect to other parameters, such as theinjector hole size, ambient gas temperature, and injection pressure. Pickett et al.(2005) extended Siebers’ study on lift-off length and studied the relationshipsbetween ignition processes and the lift-off length. A power-law relationship of thelift-off length to various parameters was summarized in their paper (Pickett et al.2005) based on an extensive database obtained using #2 diesel fuel. The expres-sion is:

H / T�3:74q�0:85d0:340 UinjZ

�1st : ð5:5Þ

T is the ambient temperature. Zst is the stoichiometric mixture fraction. Thiscorrelation was also compared with a scaling law for lift-off length proposed byPeters (2000), which is based on a flame stabilization concept and given as

H / UinjZstaT S�2L ðZstÞ; ð5:6Þ

where aT is thermal diffusivity, and SL as a function of Zst is laminar flame speed.Equation 5.6 was found to be in reasonable agreement with Eq. 5.5 regarding tothe scaling of ambient temperature and density, and injection velocity. However, itwas shown that the experimental lift-off length trends for orifice diameter andambient oxygen concentration were not in agreement with Eq. 5.6. Both injectorgeometry and injection conditions are of much interest to the present scaling study.Therefore, Eq. 5.5 was selected as one of the scaling arguments (Stager and Reitz2007; Shi and Reitz 2008c; Staples et al. 2009).

5.2.5 Swirl Ratio

Swirl is usually defined as organized rotation of the charge about the cylinder axis(Heywood 1988) and is generated by the confined, annular jet flow through thevalve, which gives rise to strong recirculation regions and high turbulence levels(Arcoumanis et al. 1984). Due to friction swirl decays during the engine cycle butit persists through the compression, combustion and expansion processes. Whenswirl is discussed in an operating engine, a mathematical term swirl ratio is nor-mally used to define the swirl, which is (Arcoumanis et al. 1984):

Rs ¼xs

2pN; ð5:7Þ

where xs is the angular velocity of a rigid-body rotating flow, and N represents theengine speed. In diesel engines swirl is used to improve mixing of the injected fueland surrounding air charge. Ogawa et al. (1996) numerically investigated the


effects of swirl ratio on NOx and soot emissions of DI diesel engines. Kook et al.(2006) focused their research on the effects of swirl motion on CO emissions andfuel consumption of low-temperature combustion engines by means of numericalstudies and experiments. Optimization studies (Genzale et al. 2007; Shi and Reitz2008a; Ge et al. 2009a, b) also found significant influence of swirl on engine-outemissions and fuel economy on heavy-duty and light-duty diesel engines. Theseprevious studies indicated that swirl motion is influential during the post-combustion process besides its direct influence on the fuel mixing process prior tocombustion.

Hiroyasu et al. (1978) proposed two factors to supplement the empiricalequations of spray tip penetration and angle in quiescent air in order to considerthe fact that the spray is bent by air swirl. These two dimensionless correlationfactors are defined as:

Cs ¼ 1þ pRsNs

30Uinj

� ��1

; ð5:8Þ

Ch ¼ C�2s ¼ 1þ pRsNs

30Uinj

� �2

; ð5:9Þ

where Cs and Ch are proportional to the reduction in axial penetration and theazimuthal deflection of the spray axis, respectively; s is the spray tip penetration.

5.2.6 Summary of Scaling Laws

All of the time scales (Dt and t) are scaled by the same factor. When Eq. 5.1 isdivided by Eq. 5.4, we get:

d0 /m

s2/ L3

L2¼ L: ð5:10Þ

Thus, the nozzle diameter d0 should be scaled by the factor L.The flame lift-off length H should be scaled by the geometry length L, and since

the scaled engines should have the same ambient conditions and fuel properties, itcan be directly deduced from Eq. 5.5 and Eq. 5.10 that

Uinj / Hd�0:340 / L � L�0:34 � L2=3: ð5:11Þ

Therefore, the injection velocity Uinj should be scaled by L2=3. Consequently, theinjection pressure should be scaled by L4=3 with the help of Eq. 5.3. And scalingrelation for time scales can be deduced from Eq. 5.4:

t / s2U�1inj d�1

0 / L2 � L�2=3 � L�1 ¼ L1=3: ð5:12Þ


In order to achieve the same injection duration on a crank angle basis such that thein-cylinder pressure as a function of a crank angle and the specific indicated workare independent of scales,

N / t�1 / L�1=3: ð5:13Þ

Thus, the engine speed is scaled with L�1=3.To keep similarity in the swirl flow, the non-dimensional parameters Cs and Ch

should be kept the same, which implies

Rs / UinjN�1s�1 / L2=3 � L1=3 � L�1 ¼ 1: ð5:14Þ

Thus, swirl ratio should be kept the same for scaled engines.The final scaling relations are listed in Table 5.1.

5.3 Validation of Scaling Laws on a Light-Dutyand a Heavy-Duty Diesel Engine

5.3.1 Engine Specifications

The scaling laws described in the previous section were validated in a light-dutyGM-Fiat engine and a heavy-duty Caterpillar engine, which are single-cylinderexperimental engines corresponding to respective production models. The speci-fications of these two engines are described in Table 5.2.

As indicated in Table 5.2 and examined by the scaling relations in Table 5.1,the two engines differ in many geometrical parameters and injection relatedvariables. Figure 5.1 shows a comparison of the piston profiles of the two engines,which shows that the engines also feature different bowl curves. The GM-Fiatengine has a deep bowl design with vertical side wall, but the bowl shape of theCaterpillar engine is shallow and the curved chamber wall is relatively closer tothe cylinder wall.

Table 5.1 Scaling relations Parameter Scaling factor: length Scaling factor: volume

m L3 Vs L V1/3

H L V1/3

d0 L V1/3

Uinj L2/3 V2/9

Dp L4/3 V4/9

Dt, t L1/3 V1/9

N L-1/3 V-1/9

Rs = =


To eliminate the differences in bowl geometrical similarity the baseline pistonbowl profile of the GM-Fiat engine was up-scaled to produce the bowl profile for amodified Caterpillar engine. Correspondingly, other parameters, such as theinjection related parameters and operating conditions were scaled based onthe scaling arguments listed in Table 5.1. More detailed discussion is given in thefollowing sections.

5.3.2 Numerical Models

An improved version of the KIVA3v2 code was used to simulate the closed-valveportion of the engine cycle. The ignition and combustion processes were solved bya direct chemistry solver (Chemkin II) coupled in the KIVA code and a reducedn-heptane reaction mechanism (Patel et al. 2004) was used to simulate diesel fuelchemistry. A reduced NO mechanism (Kong et al. 2007) that contains only fourspecies (N, NO, NO2, N2O) and nine reactions extracted from the GRI NOmechanism was used to calculate the sum of NO and NO2 to give the engine-outNOx emissions. Soot emissions were predicted with a two-step model acetylene(C2H2) as the soot precursor (Kong et al. 2007).

The simulated results of the present KIVA-Chemkin code were compared withthe experimental study conducted on the GM-Fiat engine by Lee and Reitz (2006).Figure 5.2 represents one of the comparisons. The engine was operated at low-loadwith IMEP around 5 bar, and SOI equal to 10 BTDC. The EGR rate was 51% inorder to suppress the ignition and realize low-temperature combustion. As can beseen in Fig. 5.2, the numerical pressure trace matches the experimental result well,although it gives slightly higher peak pressure and earlier ignition. The predictedengine-out NOx is in very good agreement with the experimental value. However,

Table 5.2 Engine specifications

Engine type GM-fiat Caterpillar

Bore (cm) 8.2 13.716Stroke (cm) 9.04 16.51Bowl diameter (cm) 4.99 9.8Connecting rod length (cm) 14.5 26.16Squish height (cm) 0.067 0.157Displacement (L) 0.477 2.439Compression ratio 16.53 16.1Swirl ratio 2.2 * 5.6 0.5IVC 142 BTDC 143 BTDCEVO 142 ATDC 130 ATDCInjector type High-pressure solid-cone High-pressure solid-coneManufacturer Bosch HEUIInjection pressure (bar) 1,600 1,500Number of holes 8 6Nozzle holes diameter (lm) 133 158


higher soot emissions are produced. Possible reasons include discrepancies of theinitial mixture composition at the intake valve closing time between the simulationand experiment (which were found to have a significant influence on soot). Basedon the present and many previous validation studies (Patel et al. 2004; Sun andReitz 2006; Opat et al. 2007), the model was deemed adequate.

5.3.3 Results and Discussion

Before exploring the scaling relationships between the investigated engines, theissue of the mesh size dependency needed to be addressed for the CFD scaling

Fig. 5.1 Original pistonbowl profiles

Fig. 5.2 Comparisons ofexperimental and numericalresults (SOI = 10 BTDC)

5.3 Validation of Scaling Laws on a Light-Duty and a Heavy-Duty Diesel Engine 155

study. In addition to the numerical issues, other practical concerns are alsohighlighted and discussed in this section, such as the effect of injection rate shape,engine heat transfer, and initial flow motion at IVC. Next, a numerical study wasconducted on the two engines based on the displacement scaling factor ofTable 5.1. The investigation was done for the two engines operated at low-andmid-load. Inspired by the results obtained from the displacement scaling, a newscaling factor based on the TDC volume was suggested, and improved matchingresults were obtained for the engines at low-load. This work was also extended toengines at low and high speed with TDC scaling.

5.3.3.1 Mesh Size Dependency

It is known that current CFD engine simulation tools show grid dependency to acertain degree due to their spray, turbulence, and combustion models. However,the models are usually calibrated for a certain mesh size. For diesel applications,the grid dependency of the spray model is important and it is necessary to mini-mize the interference of grid-dependent models from the present CFD enginescaling study in order to obtain comparable results on both the small and largeengines. For the same resolution, the same computational mesh size in the smalland large engine is required. However, this would increase the computationalburden of simulating the large engine, since the computational time increasesproportionally with L3, where L is the ratio of bore sizes of the large and smallengines, 1.672 for the present study.

Note that the spray targeting in the present study targets the piston bowl, andthus the grid size in the axial direction in the squish region is less important thanthat of the radial and azimuthal directions in the bowl region. So focus was placedon a study of mesh sizes in the bowl region. A sector of the large Caterpillarengine was created with the same mesh size as in the small GM-Fiat engine in thebowl, and the simulation results were compared with a coarse mesh sector of theCaterpillar engine, which are shown in Fig. 5.3. As can be seen in Fig. 5.3b, thethermal characteristics predicted with the two meshes are almost identical.Although there is some discrepancy in the soot emissions using the different meshsizes as shown in Fig. 5.3c, considering the similar in-cylinder details shown inFig. 5.3d, the coarse mesh of the Caterpillar engine was used in this scaling workto make the computational time affordable.

5.3.3.2 Injection Rate Shape

According to the scaling relations listed in Table 5.1, the smaller engine has a lowerinjection pressure, thus smaller injection velocity, which is proportional to the 4/3power of the scaling factor. This suggests that care must be taken in the large engineif the maximum injection pressure is limited. The current investigated Caterpillarengine has a maximum injection pressure 1500 bar, as listed in Table 5.2, and


based on the scaling relations and the ratio of the sizes of the two engines, themaximum injection pressure of the GM-Fiat engine would be around 750 bar.

The injection rate shape defines how much fuel is injected into the cylinder ineach crank angle during the injection event, and this influences the combustionphasing. In order to match the combustion phasing of the small engine and thescaled large engine, the injection rate shape has to be scaled to supply a propor-tionally injected fuel amount. In this study, the experimental injection rate shape

Fig. 5.3 Comparison of results using coarse and fine meshes. a Mesh density at TDC. b Pressuretrace and heat release. c Emissions. d In-cylinder details-soot distribution (side view)


obtained with injection pressure of 700 bar from the GM-Fiat engine was selectedand scaled for use in the large engine, which is described in Fig. 5.4.

5.3.3.3 Engine Heat Transfer

Based on the specifications given in Table 5.2, the ratios of the surface area to thedisplacement volume are 0.71 and 0.41 for the GM-Fiat and the Caterpillarengines, respectively. The convection heat loss component through the cylinderwalls of the small engine is larger than that of the large engine. If it is assumed thatthe heat release of the two engines is proportional to the injected fuel amount(which is required in the current study), the thermal efficiency of the small enginewill be lower than that of large engine. Therefore a treatment is needed to considerthe effect of heat transfer for an engine scaling study.

To compensate for the relatively greater heat loss of the small engine, the intaketemperature was increased. The increment of the intake temperature of the smallengine was determined such that the motoring pressure trace of the small enginematched that of the scaled large engine under the same compression ratio. Anincrease of 10 K intake temperature was found to be required from this procedure.Although it might be argued that for a fired engine more heat loss is produced thanthat of the motoring case, the important consideration is that the combustionprocess starts at the same thermal conditions in the two engines. It was also foundthat a large difference of intake temperature between the engines affects the initialthermal condition significantly, and therefore can influence the controlling roles ofchemistry and turbulence scales between the scaled engines. For example, theignition timing would be advanced in the small engine due to an increase ofthe intake temperature. However, the increase of 10 K will be further justified inthe subsequent discussion, and was found to be an appropriate value in this study.

Fig. 5.4 Comparison ofscaled injection rate shapes ofthe small and large engines


5.3.3.4 Intake Flow and Initial Flow Field at IVC

As described above, the swirl ratios of the investigated engines have to be equal toproduce similar initial flow fields at IVC with comparable influences on the spraytip penetration. However, the intake systems of the two real engines have differentcapabilities of generating initial swirl. Referring to Table 5.2, it is seen that thesmall GM-Fiat engine generates variable swirl ratios from 2.2 to 5.6 (steadybenchmarking results) using butterfly valves, but the Caterpillar engine has a fixedswirl ratio of about 0.5. It is of interest to numerically investigate how to producethe same swirl level for the two engines, and thus to provide guidelines forpractical engine design. As a preliminary work, the mesh of the Caterpillar enginewith the intake system was scaled down to the GM-Fiat engine based on the ratioof the bore sizes. Other parameters, such as the valve-lifts and engine speeds werealso scaled based on the scaling relations in Table 5.1. A motoring simulation wasconducted to compare the intake flow and initial flow fields at IVC of the twoengines.

Figures 5.5 and 5.6 show swirl ratio and tumble flow profiles during thecompression stroke. It can be seen that the swirl and tumble ratios in the radial andazimulthal directions (averaged momentum values) are almost identical in bothengines. Further examination of Fig. 5.7 reveals that the velocity distribution inthe small engine also resembles that of the large engine at BDC. The large enginehas higher values of velocity, which was also found to roughly scale with the meanpiston speed with the scaling factor L2/3. These findings confirm that the geometryof the intake system and the lift profiles of the valves determine the intake flow andflow field in the cylinder. As long as they are geometrically scaled and the enginespeed is also scaled, similar flow fields result. Furthermore, the results of Figs. 5.5and 5.6 verify the current scaling factor with respect to the engine speed, since theswirl ratio and tumble flow are the normalized results with respect to the enginespeed, and they show matching trends. Note that the self-consistency of the results

Fig. 5.5 Comparison ofswirl ratio duringcompression stroke


Fig. 5.6 Comparison of tumble flow during compression stroke. Left: tumble in radial direction;right: Tumble in azimuthal direction

Fig. 5.7 Velocity distribution at the BDC. Top: side view; bottom: top view


also confirms that numerical grid size effects are unimportant for modeling theintake process. For the next study to simplify the problem, sector meshes wereused, but the flow field at IVC was initialized using a swirl ratio, which was set tobe equal for the two engines.

5.3.3.5 Displacement Volume Scaling

It is well known that the thermal efficiency of a diesel engine is correlated with itscompression ratio. In order to match the thermal efficiency of the scaled engines, itis necessary to keep the same compression ratio. This presents two options, whichare either to use the relation of the displacement volume to scale the TDC volume,or to use the TDC volume to scale the IVC volume. The use of displacementvolume scaling is discussed in this section, and inspired by the results, an inves-tigation based on TDC volume scaling was further explored.

Following the scaling relations listed in Table 5.1, the scaled parameters of theCaterpillar engine based on the displacement scaling factor V = 2.439/0.477 arecompared with the corresponding parameters of the GM-Fiat engine in Table 5.3.

As indicated in the fourth column of Table 5.3, it is not possible to simultaneouslyscale some primary geometrical parameters of the Caterpillar engine, such as boresize, stroke, and connecting rod length. The bowl profile of the Caterpillar engine wasscaled from the bowl profile of the GM-Fiat engine, which gives the scaled bowlvolume. However, the squish height at TDC was not scaled due to the presence ofvalve cut-out volumes at TDC of the practical engine. The geometrical compressionratio for the two engines was adjusted to be 15.5, and since they have similar IVCtimings, their effective compression ratios are also close. The simulation was

Table 5.3 Scaled parameters of the displacement volume scaling engines

Engine type GM-fiat Caterpillar(Scaled)

Scaled?

Bore (cm) 8.2 13.716 N/AStroke (cm) 9.04 16.51 N/ABowl diameter (cm) 4.99 8.59 YesConnecting rod length (cm) 14.5 26.16 N/ASquish height (cm) 0.163 0.223 NoDisplacement (L) 0.477 2.439 YesTDC volume (L) 0.0329 0.1682 YesCompression ratio 15.5 15.5 YesSwirl ratio 1.8 1.8 YesIVC 142 BTDC 143 BTDC NoEVO 142 ATDC 130 ATDC NoInjection pressure (bar) 726 1,500 YesNumber of holes 8 8 YesNozzle holes diameter (lm) 133 229 YesSpray angle 130 130 Yes


conducted under low-load (for HCCI, Case A) and mid-load (for SOI sweep, Case B)operating conditions, which are shown in Table 5.4.

Stager and Reitz (2007) found that for early injection timings the scaling ofengine combustion and emissions were dependent on mixing and charge prepa-ration processes that are controlled by turbulent timescales. For late injectiontimings, however the scaling was found to be controlled by kinetic (chemistry)timescales and hot gas residence times. Scaling of mid-range injection timingswere controlled by a combination of both the turbulence and kinetic timescales. Itis of interest to further investigate the scaling relations between the engines ofdifferent sizes over a broad range of injection timings. Therefore, Start of Injection(SOI) sweeps from 35 BTDC to 5 BTDC were conducted on the two engines. Inaddition, the two engines were also explored under a Homogeneous ChargeCompression Ignition (HCCI) condition in order to remove the influence of spraymixing and charge preparation from the scaling study and to gain a more directsense of the influences of chemistry timescales in engine scaling.

5.3.3.6 HCCI Engines

The HCCI simulation was run at low-load (Case A in Table 5.4), which makes itrelevant to practical engines. The research was also extended to low and highspeed cases in order to study the influence of residence times on engine scaling.

Table 5.4 Operating conditions for the displacement volume scaled engines. A: low-load;B: mid-load

Engine type GM-fiat Caterpillar(Scaled)

Scaled?

Speed (rpm) A 1,000 834 Yes2,000 1,668 Yes3,000 2,502 Yes

B 2,000 1,668 YesGross IMEP (bar) A 5.0 5.0 Yes

B 7.5 7.5 YesEquivalence ratio A 0.25 0.25 Yes

B 0.75 0.75 YesEGR rate (%) A 0 0 Yes

B 55 55 YesOxygen (volume%) A 20.91 20.91 Yes

B 11.97 11.97 YesIVC Temperature(K) A 380 370 Yes

B 380 370 YesIVC Pressure (bar) A 1.791 1.736 Yes

B 1.791 1.736 YesInjected fuel (mg/cyc.) A 12.8 65.5 Yes

B 22.2 114 YesInjection duration

(�CA)A N/A N/A N/AB 13.2 13.2 Yes


In Fig. 5.8, the pressure trace and heat release rates of the scaled engines arecompared. Two stage heat release is seen in the HCCI engines. The cool flamestage occurs slightly later in the large engine than in the small engine, which is dueto the higher intake temperature of the small engine in order to compensate for itsgreater heat loss, as discussed previously. But the main heat release (scaled) of thelarge engine matches that of the small engine, and they have matched pressuretraces. This indicates that the simple strategy of treating the unscaled heat loss isvalid in the present study.

The early ignition of the small engine is also reflected in the start of combustiontimings (defined as the crank angle when 10% of accumulated heat is reached)with different engine speeds shown in Fig. 5.9. It can be seen that the start ofcombustion timing is linearly retarded with the linearly increasing engine speeds.This confirms that the ignition delay on a real time basis is the same for bothengines operating under different speeds, which is understandable since the HCCIcombustion is chemistry-controlled. In addition, the chemistry ignition delaybetween the two engines can be estimated from the linear relation in Fig. 5.9 to beabout 0.375 ms in all cases.

The later combustion phasing of the large engine is the reason that it producesslightly less NOx than the small engine, which is shown in Fig. 5.10 (left). Thematched soot emissions in Fig. 5.10 (right) further confirm the chemistry pro-cesses in the two engines are equally scaled. To summarize, the scaling laws ofTable 5.1 work very well for scaling engines at HCCI conditions, which meansthat the influence of the chemistry timescales on the combustion and emissionsare considered and scaled. The discrepancy of ignition timing that leads todifferent NOx emissions is essentially caused by the unscaled heat loss due tothe different surface-to-volume characteristics of the two engines. However, theproposed method of treating this problem by increasing the intake temperature iseffective.

Fig. 5.8 Pressure trace andheat release rate for HCCIconditions (Case A,Table 5.4)


5.3.3.7 SOI Sweep

Simulations were conducted over a SOI sweep to investigate the scaling relationsdue to turbulence and chemistry timescales, and their interactions. Figures 5.11,5.12, 5.13 illustrate the comparison for the engines at mid-load (Case B inTable 5.4).

As indicated in Fig. 5.11, the pressure traces of the scaled Caterpillar engine areclose to those of the GM-Fiat engine over the broad range of injection timings, aswell as its heat release rates (scaled by the displacement volume). This indicatesthat the current scaling argument regarding the engine power output works fairlywell. The small inset plots in Fig. 5.11 are included to show that the scaled liquidspray tip penetrations in the Caterpillar engine also agree with those in the GM-Fiat engine, which further supports the scaling argument for spray tip penetration.However, the combustion phasing of the large engine is earlier than that of thesmall engine, which is also represented by the shorter ignition delay (the time frominjection timing to the crank angle when 10% of accumulated total heat release isreached) as shown in Fig. 5.12.

Based on the scaling relations the large engine has lower speed, and thusthe mixture preparation during the spray development is longer in real time for the

Fig. 5.9 Comparison of startof combustion timing (10%burn) of the HCCI engineunder different speeds

Fig. 5.10 Comparison of NOx (left) and soot (right) emissions of the HCCI engine underdifferent speeds


large engine. Therefore, a more flammable mixture is formed compared to thesmall engine, which results in the earlier ignition timing on a crank angle basis.This result differs from the HCCI engine comparison, since the ignition is pri-marily determined by how much flammable fuel-air mixture has been prepared.The timescale of spray mixing and interaction with turbulence is much larger thanthe chemistry timescale. More support for this conclusion is also revealed inFig. 5.12 that illustrates the difference in the ignition delay increases with retardedSOI timing where less time is available for mixing.

The NOx and soot emissions show opposite trends over the SOI sweep inFig. 5.13. With retarded injection timing, the difference in NOx emissions betweenthe two engines decreases, and in the traditional diesel combustion region(SOI [ -15), the results are close. Inversely, the soot emissions are close at earlyinjection timings, and then the difference increases with retarded injection timing.

The comparison of the temperature distributions shown in Fig. 5.14 explainswhy the large engine produces more NOx emissions at early injection timings. Ithas a larger high temperature area where the NOx formation is active. Thedifference is caused by the different injection pressures since for the large engine,the higher injection pressure benefits the mixing process and produces a moreflammable mixture close to the piston symmetry axis, which is later ignited.Although the spray tip penetration is found to be scaled with the current scaling

Fig. 5.11 Comparison of the displacement volume scaled engines at mid-load: pressure traceand heat release rate with different SOI.a SOI = -35, b SOI = -20, c SOI = -5


law, the spray mixing process appears to be weakly scaled due to the differentinjection pressures. The soot formation region is located at the bottom of the bowl,as shown in Fig. 5.15, due to the similar temperature distribution in that regionseen in Fig. 5.14. Examination of the turbulence quantities and local equivalenceratios also revealed local similarity (not shown). Considering that the ignitiondelay for this early injection case is about twice the injection duration, it can beconcluded that the effects of local turbulence levels and bulk flow on the mixingprocess after the end of injection are scaled or are not important.

For the late injection case, a difference in the temperatures is also seen inFig. 5.16 for the same reasons as discussed before. However, it is noticed that thehigh temperature area around the piston axis in the large engine is around 1,900 K,at which temperature NOx formation is not prominent. This explains why with theretarded SOI timing, the difference in NOx emissions reduces. Compared to the

Fig. 5.12 Comparison of thedisplacement volume scaledengines at mid-load: ignitiondelay

Fig. 5.13 Comparison of the displacement volume scaled engines at mid-load: NOx (left) andsoot (right) emissions


early injection case, the combustion temperature of the late injection case is lower,and thus the chemistry timescales of reactions relevant to NOx formation are alsolarger. Therefore, the difference of NOx formation in the two scaled engines isrelatively insensitive to the difference of real time (due to the difference of speed).

As can be seen in Fig. 5.17, more soot is formed in the squish region of thelarge engine. In addition, the concentration of soot is also larger in the largeengine. For the late injection case the ignition delay is comparable to (or less than)the injection duration, which results in more interaction between the spraydevelopment and the turbulent flow. Furthermore, the preparation of the flammablemixture is faster for the late injection case due to higher ambient temperature(consequently faster vaporization) and stronger squish flow, and the chemistrytimescale also becomes smaller under more thermally active ambient conditions.This leads to stronger interaction between the mixing process and the chemistry.

Fig. 5.14 Comparison ofSOI = 35 BTDC cases:Temperature distribution(side view, in the plane ofthe spray)

Fig. 5.15 Comparison ofSOI = 35 BTDC cases:Distribution of soot massfraction (side view, in theplane of the spray)

Fig. 5.16 Comparison ofSOI = 5 BTDC cases:Temperature distribution(side view, in the plane ofthe spray)


5.3.3.8 TDC Volume Scaling

The results from the displacement volume scaling above imply that the flow andthermal conditions at TDC are very important to combustion and emissions. Thismotivated consideration of an alternative scaling strategy referred as TDC volumescaling. The idea is that instead of matching the displacement volume, the ratio ofthe bore sizes of the two engines is used to scale the piston bowl geometry, squishheight, and crevice volume at TDC. This gives the same in-cylinder geometry atTDC based on the scaling arguments. In this section, the piston geometry of theCaterpillar engine used in the previous section of the displacement volume scalingwas maintained and the GM-Fiat piston geometry was scaled from the Caterpillarpiston with the scaling factor L = 8.2/13.716. Table 5.5 lists the scaled parametersfor the TDC volume scaling study.

Note that the strokes of the two engines are not scaled linearly with the boresize, with the result that the displacement volume cannot be scaled with the currentscaling factor. Therefore the geometrical compression ratio defined with the

Fig. 5.17 Comparison ofSOI = 5 BTDC cases:Distribution of soot massfraction (side view, in theplane of the spray)

Table 5.5 Scaled parameters for the TDC volume scaled engines

Engine type GM-Fiat (Scaled) Caterpillar (Scaled) Scaled?

Bore (cm) 8.2 13.716 N/AStroke (cm) 9.04 16.51 N/ABowl diameter (cm) 5.13 8.59 YesConnecting rod length (cm) 14.5 26.16 N/ASquish height (cm) 0.133 0.223 YesDisplacement (L) 0.477 2.439 NoTDC volume (L) 0.0359 0.1682 YesGeometrical compression ratio 14.3 15.5 NoEffective compression ratio 13.3 13.3 YesSwirl ratio 1.8 1.8 YesIVC 142 BTDC 126 BTDC YesEVO 142 ATDC 130 ATDC NoInjection pressure (bar) 755 1,500 YesNumber of holes 8 8 YesNozzle holes diameter (lm) 137 229 YesSpray angle 130 130 Yes


displacement volume is no longer the same for the two engines. In order to obtainthe same effective compression ratio, the IVC timing of the Caterpillar engine hasto be retarded to 126 BTDC. The simulation was extended to consider moreoperating conditions from low-load to high-load, which are given in Table 5.6.Cases A, B, and C represent low-, mid-, and high-load respectively.

Similar to the study of displacement volume scaling, simulations were con-ducted with SOI sweeps on the engines operated at low- and mid-load.

With the TDC volume scaling, the pressure, heat release rate, and the scaledspray tip penetration for both engines at low-load match very well over the SOIsweep, which are shown in Fig. 5.18. However, because the IVC timing of thelarge engine needs to be altered to match the effective compression ratio, itscompression processes differ slightly from those of the small engine, but nonoticeable influence of this discrepancy was seen on the combustion andemissions.

Compared to Fig. 5.13, more similarities of the emission trends are seen inFig. 5.19 using the TDC volume scaling. This indicates that TDC conditions are

Table 5.6 Operating conditions of the TDC volume scaled engines: A, B, and C are low-, mid-,and high-load, respectively

Engine type GM-Fiat(Scaled)

Caterpillar(Scaled)

Scaled?

Speed (rpm) 2,000 1,685 YesGross IMEP (bar) A 4.5 4.5 Yes

B 7.0 7.0 YesC 1.0 1.0 Yes

Equivalence ratio A 0.25 0.25 YesB 0.75 0.75 YesC 0.75 0.75 Yes

EGR rate (%) A 55 55 YesB 55 55 YesC 25 25 Yes

Oxygen (volume%) A 17.93 17.93 YesB 11.97 11.97 YesC 17.65 17.65 Yes

IVC Temperature(K) A 380 370 YesB 380 370 YesC 380 370 Yes

IVC Pressure (bar) A 1.790 1.736 YesB 1.791 1.732 YesC 1.791 1.732 Yes

Injected fuel (mg/cyc.) A 11 51.5 YesB 22.2 104 YesC 32.5 151 Yes

Injection duration(�CA)

A 6.2 6.2 YesB 12.4 12.4 YesC 18 18 Yes


significant to diesel combustion and emissions due to the interactions between thesquish flows and the fuel mixing and post-combustion processes.

The injection duration of the low-load case (6.2�CA) is about half that of themid-load case (see Tables 5.4 and 5.6). The short injection duration reduces the

Fig. 5.18 Comparison of the TDC volume scaled engines at low-load: pressure trace and heatrelease rate with different SOI. a SOI = -35, b SOI = -20, c SOI = -5

Fig. 5.19 Comparison of the TDC volume scaled engines at low-load: NOx (left) and soot(right) emissions


time of spray jet flow interaction with the ambient turbulent flow. This leaves moretime for the transport of evaporated fuel by turbulence and bulk flow. Figure 5.20reveals that the ignition delay is larger than the injection duration for all SOItimings, which allows time for mixing before combustion. As in the HCCI enginestudy with similar fuel distribution, the combustion should be expected to scale ifthe chemistry timescale is more influential. Therefore, the explanation of bettermatching of the combustion characteristics and emission trends in the two enginesat low-load can be understood.

Simulation of the two engines at low-load was repeated at 1,000 and 843 rev/minfor the small and large engine, respectively. The balance of bulk flow andchemistry timescales is changed due to the longer injection duration in real time.

Fig. 5.20 Comparison of theTDC volume scaled enginesat low-load: ignition delay

Fig. 5.21 Comparison ofengines at low speed and low-load (1,000 and 843 rev/minfor the small and largeengine, respectively): ignitiondelay


This results in less scaled results in Fig. 5.21 and 5.22, especially for the NOxemissions. However, close soot trends were found, as seen in Fig. 5.22 (right),which is due to the increased time for soot oxidation during the expansion process,since both engines have the same low global equivalence ratio. In spite of the factthat the ignition delays are similar, the NOx is higher in the larger engine which

Fig. 5.22 Comparison of engines at low speed and low-load (1,000 and 843 rev/min for thesmall and large engine, respectively): NOx (left) and soot (right) emissions

Fig. 5.23 Comparison of the TDC volume scaling engines at mid-load: pressure trace and heatrelease rate with different SOI. a SOI = -35, b SOI = -20, c SOI = -5


has more time for NOx formation. This again demonstrates the significant role ofchemistry on emissions in engine scaling.

Compared to the results obtained with displacement volume scaling inFigs. 5.11, 5.12, 5.13, the results of the TDC volume scaling at mid-load do notshow noticeable improvement with respect to the differences of the emissionstrends, which are shown in Figs. 5.23, 5.24, 5.25. In general, the large engineproduces more NOx and soot emissions. The discrepancy of soot emissionsincreases as the SOI timing is retarded, but the difference in NOx emissionsdecreases. As discussed before, the longer injection duration at mid-load, and thusthe longer time of interaction of the jet flow with the bulk flow and weaker effectof the chemistry on the combustion is one of the reasons that the emissions are lessscaled. Together with the previous discussion on scaling engines at low speed and

Fig. 5.24 Comparison of theTDC volume scaling enginesat mid-load: ignition delay

Fig. 5.25 Comparison of the TDC volume scaling engines at mid-load: NOx (left) and soot(right) emissions


low-load, the scaling results of the engines at higher speed and mid-load suggeststhat scaled operation at low speed and mid- or high-load is more challenging.

In the current study, acetylene (C2H2) is taken as the precursor of sootformation, and higher concentration areas of C2H2 correspond to more soot pro-duction propensity. Before acetylene was formed, the distributions and quantitiesof the local temperature, evaporated fuel, as well as oxygen concentration werefound to be very similar in the two engines. However, a comparison betweenFig. 5.26 (top) and (middle) regarding the C2H2 mass fraction reveals that in thesame two �CA span, more C2H2 is generated in the large engine (note that the largeengine is shown at one �CA ahead of the small engine because of its earlierignition). This directly results in more soot emissions in the large engine shown inFig. 5.26 (bottom). The large engine has lower speed based on the current scalinglaws, and therefore longer real time in one �CA. The C2H2 formation reactions arefast under conditions of high temperature and low oxygen concentration, whichmeans that the chemistry timescale is much smaller than the time period of one

Fig. 5.26 Distributions ofC2H2 and soot mass fraction(SOI = 5 BTDC). Top andmiddle: C2H2. Bottom: soot


�CA. Therefore, a longer reaction time results in more C2H2 being formed. Forearly injection cases, the chemistry timescale of reactions of C2H2 is relative largedue to the higher local oxygen concentration (better mixing), which makes the sootformation less sensitive to the timing difference in one �CA span between twoengines. It should be pointed out that the better scaled soot emissions trend for thelow-load case was primarily due to the effect of the soot oxidation process, whosechemistry timescale is much larger than soot formation (or C2H2 formation). Basedon this discussion, it is expected that scaled engines operated at a higher speedwould produce smaller differences in soot emissions. This is proved in Fig. 5.27that shows less discrepancy of soot emissions between the two engines whenoperated at high speed. The small and large engines were run under the consid-eration of Case C listed in Table 5.6 with engine speeds of 3,000 and 2,502 rev/min, respectively.

5.4 Summary

Engine size-scaling arguments based on power output, spray tip penetration, andflame lift-off were explained. Several important issues for a study of engine size-scaling were addressed prior to investigation of the scaling relations between twoproduction engines. These include numerical mesh dependency and turbulence andheat transfer effects. Different scaling behaviors related to turbulence and chem-istry timescales and their effects on combustion and emissions in engines of diff-erent size were considered. The following conclusions can be drawn:

• The present scaling arguments are useful for analysis of engine size-scaling.Global performance results, such as the pressure trace and heat release rates arewell scaled based on the scaling laws.

Fig. 5.27 Comparison ofsoot emissions of engines athigh speed (engine speed3,000 and 2,502 rev/min forthe small and large engines,respectively)


• Soot emissions for the large engine operated at mid- or high-load conditions didnot scale as well as at light load. This is due to the fact that the soot formationprocess, which is controlled by chemistry timescales, at mid- or high-load ismore significant compared to that at light-load, in which the soot oxidation,which is controlled by turbulence mixing timescales, dominates. Therefore, atdifferent engine speeds (or different real time) the different timescales thatcontrol the net soot emissions contribute to the more poorly-scaled soot emis-sions for engines operated at mid- or high-load. For the low-load operatingcondition, better scaling of soot emissions was seen because sufficient time isavailable for oxidation.

• The large engine has longer time available for reactions compared to high speedsmall engines. Therefore, more NOx is produced, especially in cases with earlyinjection timings. Hence, higher EGR ratios may be needed to suppress the NOxformation.

• Unscaled heat losses and NOx can be compensated for by slightly increasing theintake temperature of the small size engine. Thermal management of the coolingsystem can be used to scale the heat losses for engines of different sizes.

• Engines operated under HCCI conditions that are chemistry-controlled exhibitwell-scaled thermal and emissions results since the power output is scaled withthe fuel amount and global equivalence ratio.

• In order to generate the same level of swirl, the geometry of the intake systemmust be scaled. The swirl ratio was found to affect the engine heat transfer.Therefore, for HCCI engines, the swirl level influences the ignition timing, andcan be used to control the ignition timing for different size engines operated atdifferent speeds.

• Conditions with reduced interaction time between the injection-generated jetflow and the bulk flow, or with increased time available for chemistry had betterscaled combustion characteristics and emissions. This is because the currentscaling laws consider lifted flames and lifted flames are more likely under theseconditions.


computational optimization of internal combustion engines || scaling laws for diesel combustion...

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