International journal of automotive technology, tập 12, số 4, 2011

Catalyst response to sinusoidal modulations in A/F for different exhaust gas temperatures under lean operating conditions mean A/F = 17.5, frequency = 1 Hz, amplitude = 5%.. Catalyst res

(Received 2 April 2010; Revised 8 September 2010)

ABSTRACT−In an HLA (hydraulic lash adjuster) piston engine, “pump up” can occur when a valve is opened by the HLAwhen it should be closed HLA pump up is more frequently encountered with exhaust valves than with intake valves WhenHLA pump up in occurs in the exhaust valve, exhaust gas from the exhaust manifold enters the cylinder on the intake stroke,and fresh air-fuel mixture exits through the exhaust manifold on the compression stroke and is burned in the catalyst, causingpartial burning, misfire, catalyst melting and power drop HLA pump up occurs when the force on the valve from the HLA

is higher than the force on the HLA from the valve HLA pump up is related to design parameters, such as oil pressure, rockerratio, spring load, spring surge, and both intake and exhaust valve timing In this study, valve lift and load on a roller fingerfollower were measured at varying engine firing conditions to evaluate HLA pump up The results indicated that effectivemeasures to reduce HLA pump up include a higher rocker ratio, a lower oil supply pressure to the HLA, a higher springinstallation load and a lower spring surge

KEY WORDS : Engine, Combustion, Emission, Valve, HLA, Spring

1 INTRODUCTION

The types of valve trains used in internal combustion

engines are classified according to the method of valve

operation: by cam, such as a direct acting type, by roller

rocker arm type and by roller finger follower (RFF) It is

very important to select the correct valve type in an engine

because the valving greatly determines basic engine

characteristics, such as cost, volume, and friction

Depend-ing on the type of valve train, the amount of friction of may

differ by up to 30% (Heywood, 1988) Every engine

manufacturer has a preference for one type of valve train

Nissan uses a direct acting type, Honda a rocker arm,

BMW a roller finger follower, and Toyota a direct acting

type However, in recent years, Toyota has been changing

from direct acting valves to roller finger followers to

reduce friction The roles of valves in engine are air

aspiration and sealing The hydraulic lash adjuster (HLA)

is an effective device for adjusting valve gap If the HLA

becomes “pumped up” on the exhaust valve, exhaust gas

can enter the cylinder on the intake stroke and fuel mixture

is lost through the exhaust manifold on the compression

stroke, resulting in partial burning, misfire and possible

catalyst melting HLA pump up is not only caused by the

HLA itself but due to overall engine conditions such as

rocker ratio, oil pressure, valve spring surge (Eaton, 1946),

intake valve timing and back pressure

Therefore, the main concern in addressing HLA pump

up is to minimize power loss and negative effects on otherfunctional devices This study of HLA pump up was donewith a Hyundai Tau V8 4.6L engine (see Figure 1) The cam and general specifications of the Tau engine aredescribed in Tables 1 and 2, respectively

2 MECHANISM OF HLA PUMP UPValve opening with HLA pump up is illustrated in Figure 2.The HLA is pumped up, and the valve is opened in the cambase circle To keep the valves closed in the cam basecircle, the forces on the valves in the closing direction must

be higher than the forces in the opening direction (Choi,Han, 2006) The forces on the exhaust valve in the closingdirection in the cam base circle are valve spring force and

*Corresponding author e-mail: ms_choi@hyundai.com Figure 1 Hyundai 4.6L V8 Tau engine

pressure in the combustion chamber in the induction,

compression, and expansion strokes Conversely, the forces

on the exhaust valve in the opening direction are the

pressure of the exhaust manifold, acting on back of the

exhaust valve, the cylinder pressure on the induction

stroke, spring force reduced by spring surge and the HLA

lifting force due to oil pressure If the force on the HLA is

less than the force from the HLA, then the HLA pumps up

The forces acting on the valve are shown in Figure 3 Theforce balance for the HLA is described by Equation (1):Force balance on HLA

Fon_HLA= (FS– FSS–FBP–FV-Fbounce)×(RR –1) (2)Condition for HLA pump up

Fin_HLA : Internal force from HLA

Fps : Force of plunger spring

Fop : Force due to oil pressure

Fon_HLA: Force on HLA

FS : Spring force

FSS : Force from spring surge

FBP : Force from back-pressure acting on valve

Fcyl : Force from cylinder pressure acting on valve

RR : Rocker ratio2.1 HLA Pump Up and Valve Lift Signal and Load on RFFSignal

To better understand HLA pump up, valve lift was measuredwith a gap sensor, as shown in Figure 4, and the load on theRFF was measured with a strain gauge, as shown in Figure 5

Table 2 General specifications of the Tau engine

Emission regulation ULEV-II, USA

Figure 3 Force components on a valve

Figure 2 HLA pump up and valve lift Figure 4 Gap sensor installation above valve retainer

the strain gauge was installed on the RFF to measure cam

load (see Figure 5) (Schwarz et al., 2009).

In normal engine conditions, without HLA pump up, the

compression pressure and combustion pressure are high In

contrast, in abnormal engine conditions with HLA pump

up, the exhaust valve is not closed during the compression

stroke and the compression pressure is thus lower than in

normal conditions, as shown in Figure 6 The low peak

pressure in abnormal conditions seems to be the result of

partial burning or misfire (see Figure 6)

Without HLA pump up, as shown in Figure 7, the

exhaust valve lift signal on the intake stroke is unchanged

However, the exhaust valve lift signal reached a minimum

on the compression and expansion strokes, as the gapbetween the valve and the gap sensor was reduced due tothe reduced pressure in the combustion chamber acting onthe valve With HLA pump up conditions (Figure 7), theexhaust valve lift on the intake stroke was approximately

200 µm; due to HLA, the exhaust valve was open when itshould have been closed

The load signal on the RFF, shown at the top of Figure 8,showed a normal pattern without HLA pump up As HLApump up increased, the load signal between EVC (exhaustvalve closed) and EVO (exhaust valve open) was increas-

ed When the valve was closed, the pressure variance in thecombustion chamber was shown as the load signal on theRFF The amount of load on the RFF from the valve duringthe expansion stroke is proportional to the amount of HLApump up, as shown in Figure 8

Figure 5 Strain gauge on RFF

Figure 6 PV diagram with or without HLA pump up

Figure 7 Valve lift signal with or without HLA pump up Figure 8 Load signals on RFF and HLA pump up

3 TEST RESULTS

3.1 HLA Pump Up on the Exhaust Valve

The load on the RFF is closely related to the pressure in the

combustion chamber HLA pump up on the exhaust valve

occurs ahead of that on the intake valve (Choi et al., 2007).

As the intake valve was closed on the compression stroke,

pressure in the combustion chamber acted on the intake

valve in the valve closing direction Conversely, as the

exhaust valve was closed during the induction stroke, the

pressure in the combustion chamber was lower than the

atmospheric pressure, and the back pressure acted on the

exhaust valve in the valve opening direction The forces on

the intake valve in the closing direction were higher than

those on the exhaust valve The forces on the intake and

exhaust valves were calculated at 6,000 rpm in a wide-open

test condition, as shown in Figure 9 The force difference

between Fcyl_IVC and Fcyl_EVC was 214.9 [N]

Fcyl_IVC = (2.5-1)/10×362×3.14/4 = 152.6 [N] (Intake)

Fcyl_EVC={(0.9-1)/10×322-(1.7-1)/10×(322-62)}×π/4

= -62.3 [N] (Exhaust)

Diameter of intake / exhaust valve: 36 mm /32 mm

Dia of valve stem = 6 mm

At the same engine conditions, the load signal on the

RFF during exhaust and intake differed, as shown in Figure

10 The load at EVO was much higher than at IVO HLApump up occurred on the exhaust side but did not occur onthe intake side

3.2 Rocker Ratio and HLA Pump UpThe rocker ratio (RR) of the RFF is related to HLA pump

up by Equation (2) The force on the HLA with an RR of2.17 is 1.46 times higher than with an RR of 1.8 Althoughthere was no HLA pump up with an RR of 2.17 RFF at

6,500 rpm (Otsubo et al., 2004), there was HLA pump up

with an RR of 1.8 RFF at 6,000 rpm as Figure 11 Thus, ahigher rocker ratio created a higher load acting on thebearing in the RFF Therefore, the use of a higher RR is aneffective way to reduce HLA pump up, but the durability ofthe bearing in the RFF must also be considered

3.3 Oil Pressure in HLA and HLA Pump Up Oil pressure in the HLA is the origin of HLA pump up The

upward force on the HLA (Koshimizu et al., 2004) can be

calculated from Equation (4)

F = Oil pressure × Cross-sectional area of HLA (4)Ex.) F = (3.5-1) [bar]×105[N/m2] × π × (10/2/1,000)2

= 19.6[N]

HLA pump up occurred at an oil pressure of 4.3 [bar]

To reduce the oil pressure, a relief valve was installed at theentrance of the oil gallery in the engine head Oil pressurewas reduced from 4.3 [bar] to 3.0 [bar] by the relief valve.The upward force was correspondingly decreased by 13[N] as calculated by Equation (4), and HLA pump updisappeared, as shown in Figure 12

3.4 Spring Surge and HLA Pump Up

To better understand the correlation between spring loadand HLA pump up, spring load was measured with a strain

Figure 9 Pressure in the combustion chamber (WOT 6,000

RPM)

Figure 10 Load signals on the RFF during intake and exhaust

Figure 11 Load signal on exhaust valve with and withoutHLA pump up at rocker ratios of 1.8 and 2.17

Figure 12 HLA pump up with oil pressure

gauge installed on the upper part of the spring, as shown in

Figure 13, with a 100 µm wire-to-wire gap when the spring

was compressed with maximum valve lift

Table 3 lists the specifications of the test springs and the

test results When spring sample #1 was in the engine, there

was no HLA pump up (bottom of Figure 14), but there was

HLA pump up with spring samples #2, and #3, even with

similar maximum spring load

Spring load signals from the strain gauge showed a sine

wave during the valve closing period When the valve was

closed, the amplitude of the sine wave was at the maximum

and then gradually reduced, as shown in Figure 15 For this

test, springs with unequal pitches at either end were used

Rate of spring load change = (MAXdynamic-MINdynamic) ÷

Springs with unequal pitches on either end, i.e., smallerwire diameters, show less spring surge There was verysmall spring surge with a diameter of Φ3.3, as shown inFigures 15 and 16

The result of the analysis for the design factor of springsurge show that the spring active coil mass was linearlycorrelated with spring surge, as shown in Figures 15, 16,and 17 Among the springs with unequal pitches at eachend (NE2), only #1 (Φ3.3) showed no HLA pump up, and

it had the lowest rate of spring load change With a similar

Figure 13 Strain gauge on spring

Table 3 Specifications of test springs and test results

Spring shape Cylinder Cylinder Cylinder

Spring mass (+ retainer)[g] 33 (43) 34 (44) 37 (47)

Engine speed of HLA

*NE2 = Unequal pitches at each end

Figure 14 HLA pump up with different springs

Figure 15 Spring surge @ 6000 RPM

Figure 16 Amplitude of spring surge and ratio of springload change

Figure 17 Correlation between mass of spring active coiland rate of spring maximum load change

spring load, sample #2 and sample #3 experienced HLA

pump up whereas sample #1 did not

4 CONCLUSIONS

HLA pump up is one of the most undesirable phenomena

in engine operation When HLA pumps up an exhaust

valve, fresh air fuel mixture is lost and is burned in the

catalyst As a result of HLA pump up, the catalyst can be

melted and engine power is reduced The main results are

summarized as follows:

(1) HLA pump up in an exhaust valve occurs ahead of that

in an intake valve because the forces on the intake

valve in the closing direction are higher than those for

the exhaust valve

(2) HLA pump up occurs at a low rocker ratio, but a higher

rocker ratio places a higher load on the swing arm,

which is related to bearing axle pitting Therefore, in

selecting a rocker ratio not only HLA pump up but also

engine durability must be considered

(3) Oil pressure to the HLA is one of the main sources of

HLA pump up Without sufficient oil pressure for

HLA, there could be no HLA pump up Therefore, oil

pressure for the HLA should be managed to within a

certain range

(4) The amplitude of spring surge and rate of spring load

change are linearly correlated with the mass of the

spring active coil Lower mass in the active coil results

in less spring surge In cylindrical springs with unequal

pitches at each end, the spring with the lowest surge

amplitude showed no HLA pump up

ACKNOWLEDGEMENT−Test data for this paper was from

Tau engine development in HMC Till the Tau engine was mass

produced, lots of problems in valve train were occurred I wasvery appreciated with Mr Kyu Bong Han who had been workedfor valve train of Tau engine and poured his all energies to curethe troubles And I was very appreciated with Douglas Nielsen inEaton who cooperated with us and tried to do his best to find rootcauses for troubles and solutions Finally I appreciated with all theengineers who worked for Tau engine in HMC and in Eaton

REFERENCESBota, J., Kumagai, T., Fujimura, T., Takayama, S andHatamura, K (2009) Comparison of MBD simulationwith measurements for roller-finger-follower with HLAvalve train system behavior in higher engine speed

Conf JSAE, JSAE 20095248

Choi, M S., Han, K B., Kim, H I., Oh, D Y and W T.Kim (2007) Mechanical parameters for durability and

HLA pump up in Tau engine Conf Hyundai-Kia Motors

EN 01-07, 2007EN0108.

Heywood, J B (1988) Internal Combustion Engine

Koshimizu, T., Kikuoka, S., Hibino, Y., Otsubo, M andIshikawa, S (2004) Development of high response

hydraulic lash adjuster Conf JSAE, JSAE 20045667.

Lee, S and Kim, W (2008?) Development of a new high

performance 4.6 liter V-8 HMC Tau engine FISITA

2008, F2008-06-085.

Otsubo, M., Saito, T and Hibino, Y (2004) Analysismethod for high-speed performance of valve train with

HLA Conf JSAE, JSAE 20045615.

Schwarz, D., Bach, M and Fuoss, K (2009) Valvetrain

investigation on fired engines Porsche Engineering

EFFECT OF ENGINE EXHAUST GAS MODULATION

ON THE COLD START EMISSIONS

T SHAMIM*Department of Mechanical Engineering, The University of Michigan – Dearborn, Dearborn, MI 48128-2406, USA

(Received 7 June 2010: Revised 20 January 2011)

ABSTRACT−This paper presents a computational investigation of the effect of engine exhaust gas modulations on theperformance of an automotive catalytic converter during cold starts The objective is to assess if the modulations can result

in faster catalyst light-off conditions and thus reduce cold-start emissions The study employs a single-channel based, dimensional, non-adiabatic model The modulations are generated by forcing the variations in exhaust gases air-fuel ratio andgas compositions The results show that the imposed modulations cause a significant departure in the catalyst behavior fromits steady behavior, and modulations have both favorable and harmful effects on pollutant conversion during the cold-starts.The operating conditions and the modulating parameters have substantial influence on catalyst behavior

one-KEY WORDS : Engine emissions, Engine exhaust after-treatment, Dynamic behavior, Numerical simulations

NOMENCLATURE

C g j : gas phase concentration of species j, mol/m3

C s j : surface concentration of species j, mol/m3

c pg : specific heat of gas, J/(kg·K)

c ps : specific heat of substrate, J/(kg·K)

D h : hydraulic diameter, m

D j : diffusion coefficient of species j, m2/s

G a : geometric surface area, m2/m3

DH k : heat of reaction of species k, J/mol

h g : heat transfer coefficient between flow and substrate,

Nu : Nusselt number, dimensionless

Pr : Prandtl number, dimensionless

R k : reaction rate of kth reaction, mol/(m2·s)

Re : Reynolds number, dimensionless

Sc : Schmidt number, dimensionless

S ext : external surface to volume area ratio, m2/m3

t : time, s

T∞ :ambient temperature, K

T g : gas temperature, K

T s : substrate temperature, K

v g gas flow velocity, m/s

z : coordinate along catalyst axis, m

ε : void volume fraction, dimensionless

λg : thermal conductivity of gas, J/m·s·K

λs : thermal conductivity of substrate, J/(m·s·K)

ρg : gas density, kg/m3

ρs : substrate density, kg/m3

1 INTRODUCTIONThe progress in catalyst technology has resulted in highlyefficient catalytic converters, which can easily meet theemission regulations However, since a catalytic converterremains essentially ineffective until it reaches the light-offtemperature, the main challenge in meeting the progressivelystringent emission regulations is the control of cold-startemissions This may require either lowering the light-offtemperature or shortening the time taken by the catalyticconverter in reaching the light-off temperature during acold start This objective has led to the development ofseveral fast light-off techniques (FLTs) These techniquesmay be classified as passive and active depending on theneed of additional energy sources Passive techniques arefocused on achieving fast light-off by optimization of theexhaust system design that includes the modification ofcatalytic converter design to improve heat transfer and/orchange in the converter position relative to the engine, and

the use of close-coupled catalyst (Lee et al., 2002; Persoons et al., 2004) and hydrocarbon traps (Noda et al., 1997; Yamamoto et al., 2002) These methods generally

have less fuel penalty Active techniques, on the otherhand, are based on providing the additional energy to raiseexhaust system temperature during cold starts Theygenerally require preheating of the catalytic converters

*Corresponding author e-mail: shamim@umich.edu

The external energy may be provided by using various

means, such as electrically and chemically preheating the

catalyst (Socha and Thompson, 1992; Pulkrabek and

Shaver, 1993; Akcayol and Cinar, 2005), use of burner

(Oeser et al., 1994) or exhaust gas ignition with secondary

air injection (Ma et al., 1992; Cho and Kim, 2005) These

methods usually need auxiliary devices and are relatively

expensive

Many past studies have shown that the catalyst

conversion performance can be significantly influenced by

the transient nature of the engine exhaust gases entering the

catalyst (Herz, 1981, 1987; Silveston, 1995 and 1996;

Shamim and Medisetty, 2003; Shamim, 2005) The effects

of variations in exhaust gas air-fuel ratio and composition

have been shown to alter the catalyst pollutant conversion

performance (Silveston, 1996; Shamim and Medisetty,

2003; Shamim, 2005) Particularly, at temperatures below

light-off values, the exhaust gas composition modulation

has been found to result in a significant rate enhancement

for CO oxidation over catalyst (Cutlip, 1979;

Abdul-Kareem et al., 1980; Schlatter and Mitchell, 1980; Taylor

and Sinkevitch, 1983; Cho and West, 1986; Zhou et al.,

1986) Cho (1988) found higher conversions for all three

pollutants by feed composition modulation around a

time-average stoichiometric point below the reaction light-off

temperature This trend reverses above the reaction light-off

temperatures Ko í et al (2004) reported the reduction in

the light-off temperature and the increase in the HC and NO

conversions by the forced modulation of oxygen concentration

The difference in the catalyst behavior at temperature

below and above the light-off value was explained by Lie

et al (1993) on the basis of the coverage of catalyst site

with CO for a catalyst with only CO oxidation They

postulated that an increase in the time average conversion

is possible only if the surface is almost completely covered

with CO at steady state Therefore, a positive effect of

cycling is to be expected only below the light-off

temperature since such a situation only occurs at low

temperatures Silveston (1996) also found modulations to

be beneficial for cold start conditions but not for warm-up

conditions

In summary, the findings of the past studies indicate a

positive effect of modulations on the catalyst pollutant

conversion performance during cold start conditions Most

of the past studies were laboratory-based and employed

catalyst bed reactors However, there are differences

between laboratory-based catalyst and the automotive

three-way catalytic converter For example, many

laboratory-based catalysts have smaller volume and are

single channel and adiabatic reactors Whereas, the

automotive three-way catalytic converters have larger

volume, hundreds of channels and different heat transfer

environment Furthermore, the composition of the sample

gas passing through the laboratory-based reactor may be

different from the engine exhaust gas passing through the

automotive three-way catalytic converter under realisticdriving conditions Owing to these differences, the results

of past studies may not be accurately extrapolated topredict the influence of modulations on the cold-startperformance of an actual automotive three-way catalyticconverter during driving conditions The present study ismotivated by realizing such an existing gap in theliterature This study employs a mathematical model toinvestigate the influence of exhaust gas modulations on thecatalyst performance during cold-start The catalystconsidered is multi-channel and non-adiabatic, similar tothose used in automotive applications However, thetransient conditions considered in the study are not realdriving conditions, which involve coupling effects ofvariations in exhaust flow, composition and temperature Inthis study, the transients are simulated by considering thecatalyst subjected to temporal modulation in air-fuel ratio(A/F) and exhaust gas composition To isolate the effect ofindividual modulating parameters, the current simulationswere performed by isolating and decoupling the effects ofmodulations in A/F and individual exhaust gas species TheA/F was modulated through variations in oxygenconcentrations while keeping the exhaust gas composition

of CO, HC, and NO constant The exhaust gas compositionwas modulated by individually varying the concentrations

of CO, HC and NO, while keeping the A/F constantthrough appropriate variations in the oxygen concentration

2 MATHEMATICAL FORMULATIONThe governing equations were developed by considering theconservation of mass, energy and chemical species Using

the assumptions listed elsewhere (Shamim et al., 2002), the

governing conservation equations for a typical singlechannel may be written as follows:

Gas phase energy equation:

(1)

Gas phase species equations (for 7 species: CO, NO,

NH 3 , O 2 , C 3 H 6 , H 2 and C 3 H 8 ):

(2)Surface energy equation:

∂T g

∂z

+

g G a(T g–T s)–

=

ε∂C g j

∂t - v g ∂C g

j

∂z

+

G a C g j

C s j

∂t - km j G a(C g j–C s j ) G a R j T s C s1… C s

The conservation equation for the surface oxygen

storage mechanism is represented by Equation (4)

excluding the convective mass transport term The heat and

mass transfer coefficients (h g and ) in the above

equations are calculated from

(5)(6)

Values of Nu and Sh numbers are obtained from the

following forms of correlations with Re, Pr and Sc

numbers:

(7)and (8)

The values of constants c and n used in this study were

based on proprietary information (Shamim, 2003) The

chemical reactions and the corresponding kinetic data used

in the present study were similar to those used in our past

study (Shamim et al., 2002) The governing equations were

discretized by using a non-uniform grid and employing the

control volume approach with the central implicit difference

scheme in the spatial direction A standard tridiagonal

matrix algorithm with an iterative successive line under

relaxation method was used to solve the finite difference

equations The spatial node size ranging from 0.1693 mm to

19.32 mm and the time step of 0.001 second were

employed The grid insensitivity of results was ensured by

performing a sensitivity study Details of the solution

procedure are described elsewhere (Shamim et al., 2002).

3 RESULTS AND DISCUSSION

The numerical model was validated by comparing with the

experimental measurements as reported elsewhere (Shamim

et al., 2002) The validation results showed the suitability of

the model in simulating the transient performance of

catalyst The catalyst used for the present study was

palladium-based and had a length of 3 cm, cross-sectional

area of 86.0254 cm2, cell density of 62 cells/cm2, and wall

thickness of 0.1905 mm The gas mass flow rate was

1.417×10-2 kg/s with 4.7184×10-5 kg/s CO, 8.0727×10-6 kg/s

total HC, and 2.0363×10-6 kg/s NO, and the stoichiometric

value of A/F was 14.51 Five feed gas temperatures were

investigated: 100oC, 150oC, 200oC, 250oC, and 300oC The

low feed gas temperature were selected to investigate the

effect of exhaust gas modulations on the catalyst conversion

performance during cold starts The exhaust gas

modula-tions were simulated by sinusoidal and independent

variations of A/F and exhaust gas composition The A/F was

varied by changing the oxygen concentration and keeping

the exhaust composition of CO, HC and NO concentrationsunchanged The exhaust composition was modulated byindividually varying the concentrations of CO, HC and NO,while keeping the A/F constant During these oscillations,other inlet conditions remained unchanged

3.1 Effect of Modulation in Air-Fuel RatioThe effect of A/F modulation on the catalyst performanceduring cold starts was investigated by considering a steadystate catalyst subjected to sinusoidal modulation in A/F atdifferent exhaust temperatures Figure 1 shows the results

of the imposed modulation near stoichiometric conditions.During the simulations, the A/F, initially set at 14.7, isvaried sinusoidally with a frequency of 1 Hz and amplitude

of 5% During the cold-start, the near stoichiometricconditions (A/F = 14.7) in the catalyst can be achieved byinjecting additional air in the exhaust prior to the catalystinlet since the exhaust has low A/F value under theseconditions The modulating A/F ranges between 13.97 and15.43, and the catalyst undergoes a transition between richand lean operating conditions during each modulation timeperiod The catalyst responds to A/F modulation withdifferent amplitudes at different exhaust temperatures.The results show that the catalyst conversion performance

of all three species responds to the imposed A/F tion The response amplitude increases with an increase ofexhaust temperature, which is expected since the catalyst isoperating in the kinetically controlled regime The response

modula-is generally smooth and periodic The CO conversion exhibits

a stronger influence of the imposed modulation and the

Figure 1 Catalyst response to sinusoidal modulations in A/

F for different exhaust gas temperatures near stoichiometricoperating conditions (mean A/F = 14.7, frequency = 1 Hz,amplitude = 5%)

response is more sinusoidal The modulation improves the CO

conversion up to 250oC The time-average conversion

efficiency, which is obtained by considering the cumulative

pollutant species in and out of the catalyst during the first

10 cycles, is increased from its steady state values for all

temperatures up to 250oC (see Table 1) At 300oC, however,

the modulation results in a significant drop in the CO

conversion and the time-average conversion efficiency

drops to 52.6% from its steady state value of 68.6% While

the trend of negative effect of modulation on the catalyst

conversion performance at higher temperatures has been

reported in literature (Cho 1988), the significant drop in

CO conversion at 300oC requires further investigation

Under these operating conditions and low exhaust

temperatures, HC conversion is low However, it is improved

by the imposed modulation As shown in Table 1, the HC

time-average conversion efficiency is increased from itssteady state value for the whole temperature range studied

in the present work The imposed modulation has anegative influence on NO conversion The NO time-average conversion efficiency drops from its steady statevalue The reason for this drop is that the imposed A/Fmodulation causes the catalyst operating condition tofluctuate between lean and rich zones This fluctuationaffects the catalyst’s NO conversion performance, which ishigh in the rich zone and low in the lean zone For thepresent case, the NO conversion is very high at the initialsteady state condition and there is not much additional gain

in the NO conversion performance when the catalyst moves

to the rich zone However, there is a considerable loss inthe NO conversion performance when the catalyst is in thelean zone, which results in the net loss of the NOTable 1 Comparison of time-average conversion efficiencies for exhaust gas A/F and composition modulations (Modulationamplitude = 5% for A/F modulations and 50% for composition modulations, Frequency = 1 Hz)

conversion performance At low temperatures (100oC –

200oC), HC and NO conversion responses also exhibit a

significant phase shift The phase shift decreases with an

increase of temperature as the catalyst becomes less

kinetically-controlled and the response becomes gradually

in-phase with the imposed modulations

The catalyst’s conversion performance depends greatly

on the mean A/F Hence, the catalyst’s response to A/F

modulation in rich and lean zones was also investigated

The lean zone results were obtained by initially setting the

A/F at 17.5 (see Figure 2) The catalyst is subjected to

sinusoidal modulations in the A/F with a 1 Hz frequency

and 5% amplitude The resulting A/F ranges between 16.63

and 18.38, which keeps the A/F in the lean zone during the

imposed modulation Under these conditions, the CO

conversion is very high for all exhaust temperatures At

300oC, the imposed A/F modulation has no substantial

influence on the CO conversion, which remains very high

At low temperatures, the catalyst is more responsive to the

imposed modulation and exhibits a slight decrease in the

conversion performance

Under lean conditions and at low temperatures (100oC –

200oC), the HC conversion remains low (~ 1%) and is not

influenced by the imposed A/F modulation With an

increase of temperature, the catalyst’s HC conversion

performance is improved and starts responding to the

imposed modulation, which results in a slight decrease of

HC conversion performance at 300oC (see Table 1) The

NO conversion response to imposed A/F modulation under

lean condition is significantly affected by the exhaust

temperature At low temperatures, the NO conversion andits response amplitude to the modulation are higher At

300oC, the NO conversion is very low (< 6%) and theresponse amplitude is very small Overall, the imposedmodulation has a positive effect on the NO conversionperformance for 200oC and higher temperatures

The rich zone results, as shown in Figure 3, wereobtained by initially setting the A/F at 12.5 The catalyst issubjected to sinusoidal modulations in the A/F with a 1 Hzfrequency and 5% amplitude The resulting A/F rangesbetween 11.88 and 13.13 Under rich conditions, thecatalyst conversion performance is relatively less sensitive

to the imposed A/F modulation Particularly, the COconversion is completely insensitive since the chemicalreactions for converting CO do not take place for thetemperature and A/F ranges simulated under rich operatingconditions The HC conversion is also small under theseoperating conditions and the imposed modulations havelittle effect on the HC conversion performance As expect-

ed, the NO conversion is high under rich conditions but thecatalyst responses to the imposed A/F modulation are smallsince the modulations keep the A/F value in the richregime, under which the NO conversion is high

3.1.1 Effect of modulation frequencyThe effect of modulation frequency was investigated byconsidering the imposed modulations with differentfrequencies Figure 4 presents the results for a catalyst,operating at A/F of 14.7, and subjected to sinusoidal A/Fmodulation of 5% amplitude, and of different frequencies

Figure 2 Catalyst response to sinusoidal modulations in A/F

for different exhaust gas temperatures under lean operating

conditions (mean A/F = 17.5, frequency = 1 Hz, amplitude

= 5%)

Figure 3 Catalyst response to sinusoidal modulations in A/Ffor different exhaust gas temperatures under rich operatingconditions (mean A/F = 12.5, frequency = 1 Hz, amplitude =5%)

ranging from 0.1 Hz to 50 Hz The exhaust gas temperature

at the catalyst inlet was maintained at 200oC The figure

depicts, as expected, that the catalyst response to imposed

modulation is maximum at low frequencies and its

amplitude decreases and the initial phase lag increases with

an increase of the imposed modulation frequency Beyond

certain frequency (cut-off value), the catalyst becomes

insensitive to imposed fluctuations at high frequencies The

catalyst’s “insensitivity” is due to effective neutralization

of high frequency fluctuations by diffusion processes over

the time period required to convect them to the reaction

sites The cut-off frequency corresponding to the catalyst’s

insensitivity is different for CO, HC, and NO since the

effect of A/F on different species conversion is different

For the conditions studied, the cutoff frequency for CO and

HC conversions is beyond 50 Hz As mentioned earlier, the

NO conversion is relatively less influenced by the imposed

A/F modulations for the present conditions and its cutoff

frequency is only 5 Hz

3.1.2 Effect of modulation amplitude

The effect of modulation amplitude was investigated by

considering the imposed modulations with different

amplitudes Figure 5 shows the results for a catalyst, which

is initially operating at A/F of 14.7 and is subjected to

sinusoidal modulations in A/F of 1 Hz frequency, and of

different amplitudes ranging from 5% to 50% The exhaust

gas temperature at the catalyst inlet was maintained at

200oC As expected, the results show that an increase of

modulation amplitude increases the catalyst response The

catalyst response is very sensitive to imposed modulation

amplitude since a high modulation amplitude causes thecatalyst to be operating in a wide range of A/F ratio andoscillating between very lean to very rich conditions Therelative effect of amplitude on NO conversion is higherthan that on other pollutant conversion The relative effect

of increasing the modulation amplitude from 5% to 10% ishigher than that from 40% to 50% For some highamplitudes, the catalyst HC conversion response exhibitssome discontinuous behavior, which is mainly caused bynumerical convergence problem

An increase of modulation amplitude has substantialeffects on the time-average conversion efficiencies Asmentioned earlier, the A/F modulation has positive effects

on CO and HC conversions and a negative effect on NOconversion An increase of modulation amplitude increasesthese effects, resulting in significant increase of COconversion, slight increase of HC conversion and significantdecrease of NO conversion

3.2 Effect of Modulation in Exhaust CompositionThe catalyst’s response to composition modulation duringcold starts was investigated by considering a steady statecatalyst subjected to sinusoidal modulation in exhaustcomposition

3.2.1 Modulation in CO concentrationFigures 6-8 show the results of the imposed modulation

in CO concentration at the catalyst inlet The COconcentration is varied sinusoidally with a frequency of 1

Hz and amplitude of 50% with the inlet CO mass flow rateranging between 2.3592×10-5 kg/s and 7.0776×10-5 kg/s

Figure 4 Effect of modulation frequency on the catalyst

response to sinusoidal modulations in A/F (mean A/F =

14.7, amplitude = 5%, exhaust gas temperature = 200oC)

Figure 5 Effect of modulation amplitude on the catalystresponse to sinusoidal modulations in A/F (mean A/F =14.7, frequency = 1 Hz, exhaust gas temperature = 200oC)

The results of near stoichiometric conditions (A/F set at

14.7) show that the CO and HC conversion efficiencies

respond to the imposed modulation sinusoidally (see Figure

6) The response amplitudes decrease with an increase of

exhaust temperature The effect of imposed CO modulation

is relatively higher on the CO conversion The NO

conversion is high for this operating condition and remains

insensitive to the range of imposed CO modulation

Figure 7 shows that, under lean conditions (A/F set at

17.5), NO conversion is relatively more sensitive to the

imposed CO concentration modulation for the temperature

range of 200oC – 300oC The response is higher at 200oC

and decreases with an increase of temperature At low

temperatures (100oC and 150oC), the NO conversion is

very high and is not influenced by variation in inlet CO

concentration The CO conversion also responds to the

imposed CO modulation It is more sensitive to the

modulation at low temperatures At higher temperatures

(250oC and 300oC), the CO conversion is high and remains

high for the range of modulating CO concentrations

Consequently, the catalyst CO conversion performance is

insensitive to the imposed modulations At low

temperatures (100oC – 300oC), the HC conversion is

negligibly small and is not affected by the modulating CO

concentrations At higher temperature, the HC conversion

increases and exhibits a small influence of CO concentration

modulations Under rich conditions (A/F set at 12.5), the

CO and HC conversions are very small and, hence, they are

not much influenced by the modulating CO concentration

Whereas, the NO conversion is high and is relatively moreinfluenced by the modulating CO concentrations (see

Figure 6 Catalyst response to sinusoidal modulations in inlet

CO concentrations for different exhaust gas temperatures

near stoichiometric operating conditions (mean A/F = 14.7,

frequency = 1 Hz, amplitude = 50%)

Figure 7 Catalyst response to sinusoidal modulations in inlet

CO concentrations for different exhaust gas temperaturesunder lean operating conditions (mean A/F = 17.5, frequency

= 1 Hz, amplitude = 50%)

Figure 8 Catalyst response to sinusoidal modulations in inlet

CO concentrations for different exhaust gas temperaturesunder rich operating conditions (mean A/F = 12.5, frequency

= 1 Hz, amplitude = 50%)

Figure 8) The exhaust temperature has relatively less

influence on the catalyst response amplitude under these

conditions Overall, the imposed CO modulation does not

have any significant influence on the catalyst’s

time-average conversion efficiencies during rich and lean

conditions since A/F value is more dominating parameter

3.2.2 Modulation in HC concentration

Figures 9−11 present the results for the catalyst subjected

to modulations of HC concentration at the catalyst inlet

The HC concentration is varied sinusoidally with a

frequency of 1 Hz and amplitude of 50% with the inlet HC

mass flow rate ranging between 4.0364×10-6 kg/s and

1.2109×10-5 kg/s

Figure 9 shows that, near stoichiometric conditions (A/F

set at 14.7), the CO conversion efficiency responds to the

imposed HC modulation sinusoidally With an increase of

exhaust temperature, the CO conversion and its sensitivity

to the imposed modulation increase The increase is due to

faster kinetic rates at higher temperature The CO

conversion is affected by the modulating HC concentration

since there is competition for the available oxygen between

CO and HC oxidation reactions As expected, the HC

conversion also responds to the imposed HC modulation

The response is non-sinusodial, however, this behavior is

mainly caused by the effect of imposed inlet HC

modulation on the calculation of HC conversion efficiency,

whereas the HC outlet concentration shows a sinusoidal

response For the temperature range investigated, the HC

concentration response is not influenced by exhausttemperature For these conditions, the NO conversion ishigh and remains insensitive to the range of imposed HCmodulation

The catalyst is more sensitive to HC modulation underlean conditions (see Figure 10) The CO conversionresponds to the imposed modulation for the temperaturerange of 100oC – 200oC For higher temperature, the COconversion is at the maximum level and is not influenced

by the imposed modulation The HC outlet concentrationresponse is sinusoidal for all temperatures except at 300oC,which shows some discontinuity owing to numericalproblem Its response amplitudes are similar for lowtemperatures but are different for higher temperatures.Under these conditions, NO conversion is high at lowtemperatures (100oC and 150oC) and is not influenced bythe imposed modulation As the exhaust temperature isincreased and the CO and HC conversions improve (owing

to the reduced availability of CO and HC for NOreduction), the NO conversion drops and becomes sensitive

to the imposed modulation At 300oC, the NO conversiondrops to a very low level and is not influenced by theimposed modulation any more Under rich conditions, the

HC modulation results in relatively modest responses from

HC and NO conversions Under these operating conditions,the CO conversion is negligibly small and is not influenced

by the imposed HC modulations (see Figure 11) The HCconversion response does not exhibit any temperaturedependence, whereas the NO conversion response shows

Figure 9 Catalyst response to sinusoidal modulations in inlet

HC concentrations for different exhaust gas temperatures

near stoichiometric operating conditions (mean A/F = 14.7,

frequency = 1 Hz, amplitude = 50%)

Figure 10 Catalyst response to sinusoidal modulations ininlet HC concentrations for different exhaust gas temperaturesunder lean operating conditions (mean A/F = 17.5,frequency = 1 Hz, amplitude = 50%)

small temperature dependence.

Overall, the imposed HC modulation does not have any

significant influence on the catalyst’s time-average conversion

efficiencies, which remain close to their steady state values

Furthermore, the catalyst response to the HC modulation is

relatively less influenced by the exhaust temperature

3.2.3 Modulation in NO concentration

Figures 12−14 present the results for the catalyst subjected

to modulations of NO concentration at the catalyst inlet

The NO concentration is varied sinusoidally with a

frequency of 1 Hz and amplitude of 50% with the inlet NO

mass flow rate ranging between 1.0182×10-6 kg/s and

3.0545×10-6 kg/s Compared to the CO and HC

modula-tions, the NO modulation has a relatively less influence on

the catalyst conversion performance at various exhaust

temperatures

The results show that the catalyst responds to the

imposed NO modulation However, the response

amplitudes for CO, HC and NO conversions are very

small, particularly, near the stoichiometric conditions The

imposed modulation affects the NO outlet concentration,

which responds sinusoidally but the effect is so small that

the NO conversion remains practically insensitive

Under lean conditions, the effect of the imposed NO

modulation is relatively higher than that at stoichiometric

conditions The major effect is on the NO outlet

concentra-tion and its conversion The effect on the CO and HC

Figure 11 Catalyst response to sinusoidal modulations in inlet

HC concentrations for different exhaust gas temperatures

under rich operating conditions (mean A/F = 12.5, frequency

= 1 Hz, amplitude = 50%)

Figure 12 Catalyst response to sinusoidal modulations in inlet

NO concentrations for different exhaust gas temperatures nearstoichiometric operating conditions (mean A/F = 14.7,frequency = 1 Hz, amplitude = 50%)

Figure 13 Catalyst response to sinusoidal modulations in inlet

NO concentrations for different exhaust gas temperaturesunder lean operating conditions (mean A/F = 17.5, frequency

= 1 Hz, amplitude = 50%)

conversions is relatively small since NO conversion does

not have any significant influence on the CO and HC

oxidation reactions The exhaust temperature influences

the catalyst response to the imposed NO modulations

The catalyst response to NO modulation under rich

conditions is similar to its response to HC modulation

Under these conditions, the NO modulation results in small

responses from HC and NO conversions (with the

conversion efficiency values fluctuating within 6%) but the

CO conversion remains insensitive (see Figure 14) The

exhaust temperature does not have any significant influence

on the catalyst response amplitudes

Overall, the imposed NO modulation also does not have

any significant influence on the catalyst’s time-average

conversion efficiencies, which remain close to their steady

state values

3.2.4 Effect of modulation frequency

The effects of modulation frequency on the catalyst’s

response to modulating exhaust gas concentration are

shown in Figures 15−17 These results are obtained by

considering a catalyst, operating at A/F of 14.7, and

subjected to sinusoidal exhaust gas modulation (CO, HC or

NO) of 50% amplitude, and of different frequencies

ranging from 0.1 Hz to 50 Hz The exhaust gas temperature

at the catalyst inlet was maintained at 200oC Similar to the

modulating A/F case, the catalyst response amplitude

decreases with an increase of modulating frequency Thecatalyst becomes insensitive at high frequencies (the cutoff

Figure 14 Catalyst response to sinusoidal modulations in

inlet NO concentrations for different exhaust gas

temperatures under rich operating conditions (mean A/F =

12.5, frequency = 1 Hz, amplitude = 50%)

Figure 15 Effect of modulation frequency on the catalystresponse to sinusoidal modulations in inlet CO concentra-tions (mean A/F = 14.7, amplitude = 50%, exhaust gastemperature = 200oC)

Figure 16 Effect of modulation frequency on the catalystresponse to sinusoidal modulations in inlet HC concentra-tions (mean A/F = 14.7, amplitude = 50%, exhaust gastemperature = 200oC)

frequency is beyond 50 Hz for CO and HC conversions).

The increase of frequency also increases the catalyst

response phase lag However, the modulating exhaust gas

case also exhibits an apparent different behavior for the

conversion of a species which is subjected to modulation

For example, for the modulating CO case, an increase of

modulating frequency increases the CO conversion

response up to 10 Hz followed by a decreasing pattern for

further increase of frequency However, a look at the CO

outlet concentration depicts that this apparent different

behavior is only caused by the effect of modulating inlet

CO concentration, which is used in the calculation of CO

conversion response The effect of frequency on the CO

outlet concentration response decreases with an increase of

modulating frequency and becomes insensitive at higher

frequencies similar to the modulating A/F case Similar

behavior is shown by HC conversion for the modulating

HC case As mentioned earlier, the NO conversion is not

influenced by exhaust gas concentration modulation for the

present conditions and remains insensitive at all frequencies

invesgated in the study

3.2.5 Effect of modulation amplitude

The effects of modulation amplitude on the catalyst’s

response to modulating exhaust gas concentration are

shown in Figures 18−20 These results are obtained by

considering a catalyst, operating at A/F of 14.7, and

subjected to sinusoidal exhaust gas modulation (CO, HC orNO) of 1 Hz, and of different amplitudes ranging from

Figure 17 Effect of modulation frequency on the catalyst

response to sinusoidal modulations in inlet NO

concentra-tions (mean A/F = 14.7, amplitude = 50%, exhaust gas

temperature = 200oC)

Figure 18 Effect of modulation amplitude on the catalystresponse to sinusoidal modulations in inlet CO concentra-tions (mean A/F = 14.7, frequency = 1Hz, exhaust gastemperature = 200oC)

Figure 19 Effect of modulation amplitude on the catalystresponse to sinusoidal modulations in inlet HC concentra-tions (mean A/F = 14.7, frequency = 1Hz, exhaust gastemperature = 200oC)

10% to 50% During the simulations, the exhaust gas

temperature at the catalyst inlet was maintained at 200oC

Similar to the modulating A/F case, the catalyst response

amplitude increases with an increase of modulating

amplitude However, the effect of modulation amplitude is

relatively smaller than that for the A/F modulation case

since the catalyst for the present case remains near

stoichiometric operating conditions for all modulation

amplitudes The increase of modulation amplitude has no

appreciable effect on the time-average conversion efficiencies

4 CONCLUSIONS

This study investigated the influence of temporal variations

in air-fuel ratio and exhaust gas composition on the

performance of an automotive catalytic converter during

cold-start The catalyst operations under stoichiometric,

lean and rich conditions were considered The results led to

the following conclusions:

The conversion performance of a catalytic converter

during cold start conditions can be improved by subjecting

the catalyst to temporal variations in exhaust gas air-fuel

ratio The study finds that the imposed A/F modulations

near stoichiometric conditions have positive effect on

catalyst CO and HC conversion performance at low

temperatures (below light off values) During the

cold-start, the engine runs rich and the engine exhaust has rich

environment However, the stoichiometric conditions in the

catalyst can be achieved by injecting additional air in theexhaust prior to the catalyst inlet The modulations haveslight negative effect on NO conversion However, owing

to low temperatures and rich operating conditions in engineduring cold-start, NO emission is relatively of less concern.Near stoichiometric conditions, the performance of acatalytic converter and its response to imposed modula-tions are strongly dependent on the exhaust gas temperature.The difference between catalyst conversion efficiency atsteady state and under imposed transient conditions growswith temperature The imposed modulations cause significantreductions in CO and NO conversions at high temperatures(above light off values) The imposed modulations havepositive effect on HC conversion for the temperature rangeinvestigated in this work

Away from stoichiometric conditions (lean or richconditions), the imposed A/F modulations do not have anysignificant influence on the catalyst cold start conversionperformance

The exhaust gas composition modulations, while ing A/F constant, do not result in any significant influence

keep-on the catalytic ckeep-onverter performance during cold startconditions With the exception of NO and CO conversionresponse under lean conditions, the catalyst responseamplitudes to imposed modulations are generally lower atlower temperatures

The catalyst response to imposed modulation is high atlow frequencies and its amplitude decreases and initialphase lag increases with an increase of the imposedfrequency At higher frequencies, the catalyst becomes

“insensitive” to imposed modulations The cut-offfrequency corresponding to the catalyst’s insensitivity isdifferent for CO, HC, and NO

The modulation amplitude is also an importantparameter, but of less significance than the modulationfrequency In general, the increase of oscillation amplitudeincreases the catalyst response Compared to the exhaustgas concentration modulation case, the modulationamplitude has greater influence on the catalyst response forthe A/F modulation case For this case, an increase ofmodulation amplitude results in a significant increase of

CO conversion, slight increase of HC conversion and asignificant decrease of NO conversion

ACKNOWLEDGMENTS−The financial support from the FordScientific Research Laboratory, Oak Ridge National Laboratoryand the HP Center for Engineering Education and Practice (HP-CEEP) of the University of Michigan-Dearborn is greatlyappreciated An earlier version of this work (SAE2006-01-0627)was presented at the SAE 2006 World Congress in Detroit, MI.REFERENCES

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BREAKUP MODELING OF A LIQUID JET IN CROSS FLOW

K.-S IM1), K.-C LIN2), M.-C LAI3) and M S CHON4)*

1)Livermore Software Technology Company, Livermore, CA 94551, USA

2)Taitec, Inc, Beavercreek, OH 45230, USA

3)Department of Mechanical Engineering, Wayne State University, Detroit, MI 48202, USA

4)Department of Energy System Engineering, Chungju National University, Chungbuk 380-702, Korea

(Received 12 August 2010 ; Revised 26 January 2011)

ABSTRACT−We propose a novel breakup model to simulate the catastrophic breakup regime in a supersonic cross flow Adeveloped model has been extended from an existing Kelvin-Helmholtz/Rayleigh-Taylor (K-H/R-T) hybrid model A newmass reduction rate equation, which has critical effects on overall spray structure, is successfully adopted, and the breakuplength, which is an important parameter in existing model, is replaced by the breakup initiation time Measured data from thesupersonic wind tunnel with a dimension of 762×152×127 mm was employed to validate the newly developed breakup model

A nonaerated injector with an orifice diameter of 0.5 mm is used to inject water into a supersonic flow prescribed by the

momentum flux ratio of the liquid jet to free stream air, q 0 The conservation-element and solution-element (CE/SE) method,

a novel numerical framework for the general conservation law, is applied to simulate the supersonic compressible flow Thespray penetration height and average droplet size along with a spray penetration axis are quantitatively compared with data.The shock train flow structures induced by the presence of a liquid jet are further discussed

KEY WORDS : Cross flow, Breakup, K-H/R-T hybrid model, CE/SE method

NOMENCLATURE

B0 : drop size - constant

B1 : breakup time - constant

C D : drag coefficient

D : drag function or drop diameter

d0 : nozzle diameter

e : specific internal energy

E : specific total energy

h0 : penetration height

M s : free stream Mach number

m0 : initial mass

p : pressure

Q s : energy exchange term

r : jet radius or drop radius

σ : surface tension coefficient

τ : liquid breakup time

T : transpose matrix

1 INTRODUCTIONThe injection of liquid jets into the high-speed flow stream

is an important process in modern propulsions and powerapplications such as gas turbine, ramjet, and scramjetengines In such applications, the combustion performancedepends heavily on liquid atomization, spray penetration,and the mixing process between the free stream air and theliquid fuel As a result, the study of the liquid spray in high-speed cross flow has become an important research area.The overall breakup process including deformation, liquid

*Corresponding author e-mail: mschon@cjnu.ac.kr

fragmentation, and completing disintegration is mostly

dictated by two independent nondimensional numbers: the

Weber number and the Ohnesorge number, in conjunction

with the characteristic breakup time (Pilch and Erdman,

1987; Hsiang and Faeth, 1992; Chen et al., 1993; Wu et al.,

1997)

The first attempt to describe transitions between breakup

regimes using control variables was made by Hinze (1955)

He found that increasingly larger disturbances were

requir-ed for the breakup initiation with increasing Ohnesorge

number Plich and Erdman (1987) categorized in detail the

breakup mechanism according to the initial Weber number

with breakup mechanism categories, such as vibration, bag,

bag and stamen, sheet stripping, and wave crest stripping

followed by catastrophic breakup Hsiang and Faeth (1992)

presented the deformation and breakup regime map for the

drop breakup, showing transitions as functions of Weber

and Ohnesorge numbers They categorized the breakup

regime into different transitions considering more detailed

deformation, i.e., nonoscillatory and oscillatory deformations,

bag breakup, multimode breakup, shear breakup, and

catastrophic breakup Chen et al (1993) and Wu et al (1997)

characterized the near-field jet breakup process as three

different regimes: liquid column, ligament, and droplet

regimes

Ranger and Nicholls (1969) may have been the first to

use the characteristic breakup time to demonstrate the

effects of the high free-stream velocity (M s=1.5~3.5) on

drop deformation, displacement, and breakup time, i.e., the

time for the complete breakup process By sending a shock

wave across water droplets with diameters in the range of

750~4,400 µm, they provided the parametric data on

disintegration rate, displacement, and breakup time of the

droplet using a dimensionless form near the catastrophic

breakup regime They also provided a theoretical relation

for the rate of mass reduction, which is the mass stripped

away from the drop surface, by utilizing the equations from

Taylor’s analysis (1963) To date, the study by Reinecke

and Waldman (1970) is probably the only investigation

providing detailed mass reduction data based on the x-ray

radiograph technology They derived a correlation for

breakup time at the catastrophic breakup regime, i.e.,

approximately We > 1000.

So far, only limited numerical results have been reported

regarding the high-speed cross flow due to the difficulty in

the complex breakup processes In addition, numerous

definitions and interpretations concerning the degree of

deformation and breakup time make it more difficult to

precisely understand the experimental observations, which

were conducted by using various techniques, such as Mie

scattering, shadowgraph, and the Schlieren technique

A detailed modeling of the breakup process in the cross

flow was conducted by Rachner et al (2002) Since there

are several different breakup regimes as described earlier,

they divided the breakup processes into several sub models

to deal separately with column breakup, jet breakup

process, total breakup criterion, and liquid stripping Byreferencing the breakup parameters from the experimentaldata, they modeled the breakup process as a one-timeprocess in the secondary breakup regime and no furtherbreakup was allowed for the stripped-off droplets on theliquid surface Madabhushi (2003) also reported anumerical simulation model for a liquid jet in the crossflow His proposed model consisted of two sub models:column breakup and secondary breakup During thecolumn breakup, the spray breakup was modeled by theKelvin-Helmholtz wave model, suggested by Reitz (1987)

In the secondary breakup regime which includes thedroplet deformation period, the total breakup time wasmodeled by increasing the Weber number Additionally,most of the spray variables, such as deformation diameters,drag coefficients, droplet diameters, droplet velocities, anddroplet distributions after breakup, were prescribed based

on the experimental data (Pilch and Erdman, 1987; Hsiangand Faeth, 1992)

These previous simulation models have focused on thesubsonic flow regime only; therefore, there is nocatastrophic breakup model Furthermore, previous modelswere controlled by many artificial parameters, such as thenumber of child droplets after breakup There is also a lack

of consistency in referring to the experimental parameterswith one parameter from one experiment and the otherparameter from another experiment

In the present investigation, we propose a consistentbreakup model to simulate the catastrophic breakup regime

in supersonic cross flow The basic structure of the presentbreakup model is inherited from the most recent version ofthe K-H/R-T hybrid model (Bealeand Reitz, 1999), butmost importantly, the mass reduction rate and the breakuplength based on experimental data are modified to simulatethe column and secondary breakup process in supersoniccross flow

2 NUMERICAL APPROACHE2.1 Gas Phase Equations

The governing systems of the supersonic flow with ing spray particles are the 3-D unsteady Euler equations andcan be given by the vector form as,

+

coordinates, respectively The variables ρ, u, v, w, p, and E

defined in the flow and the flux vectors represent density,

x-, y-, and z-velocity, pressure, and specific total energy of

the gas phase, respectively The specific total energy E is

defined as,

(2)

where e = p/(γ - 1) is the internal energy of the gas phase,

and γ = C p /C v is the ratio of specific heats The source

terms that appear on the right-hand side of Equation (1)

account for effects of the particle interaction In the present

study, because we assumed the nonevaporating spray, there

is no source term in the continuity equation The terms M x,

M y , and M z in the momentum equations are the terms

defining the x, y, and z momentum exchanges, respectively,

induced by spray particles at the differential control

volume The term Q s in the energy equation represents the

work done by the particles to the gas

(3)(4)

In Equations (3) and (4), the summation represents the

total number of particles in the calculation cell, δ(x) is the

Dirac delta function, and D k (u i) is the drag function, which

will be described in the following section

The space-time conservation element solution element

(CESE) method has been applied to solve the shock-spray

interacting flow (Zhang et al., 2002) The space-time CESE

method is a high-resolution and genuinely multidimensional

method for solving conservation laws It has a solid

foundation in physics, and yet is mathematically simple Its

nontraditional features are: (i) a unified treatment of space

and time, (ii) the introduction of a conservation element

(CE) a and solution element (SE) as the vehicles for

enforc-ing space-time flux conservation, and (iii) a time marchenforc-ing

strategy that has a space-time staggered stencil at its core

and, as such, can capture shocks without using Riemann

solvers Note that conservation elements are

nonoverlapp-ing space-time subdomains introduced such that (i) the

computational domains can be filled by these subdomains;

and (ii) flux conservation can be enforced over each of

them and also over the union of any combination of them

On the other hand, solution elements are nonoverlapping

space-time subdomains introduced such that (i) the

boundary of any CE is covered by a combination of SEs; and

(ii) within a SE, any physical flux vector is approximated

using a simple smooth function

2.2 Spray Equations

For the spray flow in a Lagrangian reference frame, each

computational particle represents a finite number of

particles having the same diameter, velocity, and

temperature (Dukowics, 1980) Then, the particle position

is given by,

(5)The rate of particle momentum change is given byenforcing the conservation law of an individual particle andcan be expressed as,

(6)

where g k, i (i = x, y, z), is the particle gravity exerted in the x-, y-, and z-direction D k is the drag function and is given by,

(7)where is the drag coefficient, typically determined by aempirical relation and is given for the supersonic flow as(Crowe, 1998),

where g(Re k ) and h(M) are given by,

(9)(10)

In Equation (8), C D,0 is the standard drag coefficient and

is given by,

(11)

where Rek is the particle Reynolds number evaluated by arelative velocity between the surrounding gas and particle,that is,

(12)

In the present study, Equations (5) - (12) are the systemequations for simulating the spray flow in conjunction withthe supersonic cross flow Note that in the present study theparticle temperature is assumed to be constant without anymass change, so that the particle energy equation is notconsidered

2.3 Breakup ModelThere have been proposed several K-H/R-T hybridbreakup models in the literature, which were mostly appli-

ed to internal combustion engine applications (Reitz, 1987;

exp

⋅+

=

h M( )

-⋅exp(–Rek⁄2M)+

Beale and Reitz, 1999; Patterson and Reitz, 1998; Ricart et

al., 1997) In general, such models can be categorized into

two different types depending on the interacting order

between the K-H and R-T breakup modes The first one

proposed by Patterson and Reitz (1998) postulated that the

breakup process is the simultaneous phenomenon both in

the K-H and R-T modes As a result, such a model allows

unstable waves to grow simultaneously The other is the

K-H/R-T model proposed by Ricart et al (1997), in which

two breakup modes arose in a priority order such that the

R-T mode does not start until the K-H mode is completed

For example, the breakup process in the intact liquid core

region, defined as the breakup length, is governed by the

K-H mode only while the R-T mode is the dominant mode

beyond that region Later on, Beale and Reitz (1999)

extended their model to two models such that the R-T

mode was allowed not only beyond the breakup length, but

also the region within the breakup length for the drops

generated by the K-H mode

In the present study, the previously proposed K-H/R-T

models are further extended to simulate spray breakup in

the high-speed cross flow, where the dominant modes are

the surface and column breakup in the “catastrophic

regime” (Pilch and Erdman, 1987; Hsiang and Faeth, 1992;

Chen et al., 1993; Reinecke and Waldman, 1970) With

increasing cross flow velocity, the injected liquid jet first

undergoes the surface breakup, with small droplets stripped

from the leeward side of the liquid surface, as shown in the

first circled area in Figure 1

In the meantime, strong aerodynamics forces crossing

the liquid jet generates deformation, into ligaments and

eventually droplets from the windward side of the liquid

column to the downstream, as shown in location 2 in

Figure 1 In general, the K-H instability is generated by the

shearing force between two fluids, and thus it is a typical

surface phenomenon when the liquid is injected into the

quiescent environment By contrast, the normal force

(aerodynamic force) induced by confronting two fluids

generates the R-T instability

Therefore, upon implementing our model, the surface

breakup is simulated by the K-H mode and the R-T mode is

used to simulate the column breakup both on the primaryand secondary process

The detail descriptions of the K-H/R-T breakup theorycan be easily found because several variants now exist inthe literature However, they are also included here forcompleteness, to highlight the differences in the cross flowapplication, and to emphasize our implementation in thepresent model

In the K-H mode, the model assumed that an injected

parent discrete particle with radius r0, breaks up to form

several new child droplets of radius r with suitable

condi-tion, such as,

(13)

where B0 is a constant equal to 0.61 and ΛKH is thewavelength corresponding to the most unstable K-H wavegiven by the dispersion relationship derived from thelinearized hydrodynamics equations for the liquid and gas:

(14)

parameter We l is the liquid Weber number, and Re l is theliquid Reynolds number, respectively The parameter

is the Taylor number, and We g is the Webernumber of the gas During the breakup, the parent particlesreduce in radius due to the mass stripped from the surface.Thus, the rate of change of their droplet radius is given by(Beale and Reitz, 1999; Patterson and Reitz, 1998),

(15)where τ is the breakup time defined as,

(16)

with B1 as an arbitrary constant and ΩKH is the mostunstable wave Its growth rate is given by,

(17)During the computation, the liquid mass reduction or themass shed from the parent parcel is precisely evaluated sothat a new particle is produced from the liquid surfacewhen the shed mass reaches or exceeds 3% of the averageinjected parent droplet mass (Patterson and Reitz, 1998) Inthe present study, however, we adopted a different massreduction relation originally developed by Reinecke andWaldman (1970) based on the X-ray radiography measure-ment when the parent drop was exposed in supersonic crossflow Therefore, the flow conditions are precisely coincidentwith the present study so that the breakup process should

be well governed by the “catastrophic mode.”

- ∆rτ -

⎛ ⎞0.5 (0.34 0.38We+ g1.5)

1 Z+( ) 1 1.4T0.6

+

-=

Figure 1 Conceptual schematic of the liquid breakup

model in supersonic cross flow

In Equation (18), t is the breakup time calculated by the

K-H mode from Equation (16), and m0 is the initial drop

mass at time t0

As illustrated in Figure 2, Equation (18) implies that

initially the rate of the mass reduction with dimensionless

time is fairly slow, and it subsequently becomes more

effective With sufficient time near the end of the breakup,

the rate becomes slow again Most importantly, the rate of

mass reduction in the present study is the key mechanism

used to simulate the catastrophic breakup, where most of

the breakup could be completed in a certain period with a

short delay time after the start of injection (Reinecke and

Waldman, 1970)

During the breakup process, when the mass shed at each

time step reaches a certain value as a fraction of the

average injected parent particle mass, the equivalent

discrete particle radius is determined first, and the liquid

mass conservation and Sauter mean diameter (SMD)

conservation model are applied to determine the size

distribution of child droplets (Patterson and Reitz, 1998)

Then, the secondary breakup by the R-T mode is applied

regardless of the breakup time criterion, which simulates

the shearing breakup in the leeward side of the liquid

column

Unlike most existing models, where the break up length

is used as the active boundary for the R-T mode, the

present model adopted a breakup time that is empirically

validated by experimental data in the liquid column

breakup process (Pilch and Erdman, 1987) The equation

for the initiation of the breakup, which is the first signal for

the creation of new drops in the liquid column or ligaments

is given by,

(19)

As a result, if the dimensionless time after

start-of-injection is greater than the breakup time, the R-T mode is

activated for each particle After this time, the two breakupmodes compete for the droplet breakup, which is similar tothe model proposed by Patterson and Reitz (1998)

3 RESULTS AND DISCUSSIONDetails about the description of the injector and its

controlling issues can be found in the study by Lin et al.

(2001) Water was used as a liquid injectant, which has adensity of 998 kg/m3, a viscosity of 2.67×10-3 kg/m⋅s, and asurface tension of 0.072 N/m The test section for thenumerical simulation of the breakup model has a height of

127 mm, a width of 152 mm, and a length of 762 mm Theinjection orifice diameter, do, of 0.5 mm was tested andlocated 139 mm downstream from the leading edge of thetest section (see Figure 3)

The jet-to-free-stream air momentum flux ratio, q0

defin-ed as a ratio of ρi v j2 /ρ∞v∞ 2 was used to calculate theinjection velocity of the liquid jet Initially, the totalpressure and temperature inside the test section weremaintained at 206 kPa and 533 K, respectively

Then, the corresponding static pressure and temperatureunder the isentropic assumption are converted to give 29kPa and 304.1 K with a flow velocity of 678.13 m/s, which

is based on the free-stream Mach number of 1.94.

Figure 3 shows a spray flow illustrating the detailedbreakup process in 3-dimensional plan with the air stream

velocity that results in a Mach number of 1.94 and the to-air momentum of q0 = 7 The snapshot was taken whenthe spray flow reached the steady-state condition Althoughinitial spray started with large droplets that were of thesame diameter as the nozzle, many small drops on theleeward side were clearly observed, indicating that the K-Hbreakup mode was performing well On the other hand,large droplets deformed like ligaments still existed up tothe spray height of 20 mm, and thereafter, only smalldroplets generated by column breakup were clearlyobserved More dispersion to the normal direction and less

jet-dense sprays are obvious after x = 40 cm, suggesting the

spray undergoes further breakup processes downstream.The spray behaviors described in the present study agree

Figure 2 Mass reduction histories for the breakup model

calculated from Equation (18)

Figure 3 Spray flow with breakup process in high speed

cross flow an M = 1.94 cross flow with q0 = 7

well qualitatively with the experimental results for high

speed cross flow

To validate the model, we compared simulation results

with experimental data for the spray penetration height in

Figure 4 The experimental correlation function in the

supersonic cross flow was developed by Lin et al (2004)

and is given by,

(20)

where h0 is the penetration height defined as the location

where the measured liquid volume flux is equal to 0.01 cc/

s/cm2 at the center position of the z-axis, and x is the flow

direction coordinate For illustration purposes, results from

two earlier popular cases, the TAP breakup model

(O’Rourke and Amsden, 1987) and a “no-breakup” case, in

which a prescribed droplet size is used for injection, are

also shown for comparison Without any breakup model,

the trajectory of the spray penetration clearly overshoots

the experimental data, especially the position after x = 20

cm Although the injected particles interact with the cross

flow by exchanging their momentum and kinetic energy,

their momentums are still high enough to compete with the

crossing air flow without losing mass

By contrast, the spray particles do not seem to penetrate

into the flow in the case of the TAB breakup model,

indicating that too much breakup happens immediately

after the droplets are injected into the stream As a result,

earlier broken particles are too small to passively follow

the strong air flow The penetration trajectory in the present

model shows a better match with experimental data,

although the result from the simulation is slightly different

from the experimental data The initial discrepancy between

the experimental data and the prediction is probably due to the

boundary layer effect, which the simulation does take into

consideration for lack of information If the momentum

layer is considered, a better agreement is expected

Further validation with data can be seen in Figure 5

where the measured SMD distribution was compared with

simulation results at x = 100 mm, along with y-direction,

under the same operating condition In the pre-broken-upcase, where the initial stochastic distribution was employ-

ed, the size distributions monotonously increase until themaximum penetration point is reached, meaning that theinjected droplets simply penetrate to the position wheretheir momentums are allowed

When the TAB breakup model is applied, the size

Figure 4 Comparisons of spray penetration heights between

simulation and data along the y-axis at z = center The

experimental curve is calculated from Equation (20)

Figure 5 Average droplet size comparisons between

simulation and experiment along with y-axis at z = center and x =100 mm from the nozzle center.

Figure 6 Projected droplet distributions on the y-z plane at

x =100 mm from the nozzle center; (a) Tap model; (b)Present model; and (c) No-breakup

distributions only reach the maximum position of y = 7

mm, because breakup process begins too early and too fast

so that only small sizes are present close to the wall Even

though there are still minor differences, the size

distribu-tions of the present model agree much better both

qualitatively and quantitatively with the phase Doppler

measurements, compared with the other two cases

One of most important and difficult measurement in the

cross flow is the cross-sectional particle distribution along

the flow direction, because it is directly related to the mixing

process, and eventually the combustion performance Figure

6 shows comparisons of the cross-sectional particle

distribu-tions at x = 100 mm among simulation results As expected,

the distribution area from the TAB model is too small for

small particles because of earlier breakup, and the prescribed

drop size case shows monotonously increasing particle

distributions along the y-direction In comparison, the

prediction from the present model shows a more reasonably

wide distribution of well atomized droplets

Figure 7 shows the 3-dimensional shock wave structure

in the flow channel induced by the liquid jet with

2-dimensional contours cut by the x-y plane and y-z plane, and x-z plane.

When a normal shock wave propagates into the flowdirection, the conical shock wave is first developed fromthe position where the liquid jet is injected The bifurcatedshock wave is then reflected from the wall surfaces, and aseries of shocks follow downstream of the flow Thedeveloping conical shock, its reflection, and interactionsamong the reflected shocks can be seen by cutting along 2-

dimensional planes, clearly showing the oblique shock at z

= center plane and the bow shaped shocks standing near thecenter planes However, it is not clear whether the reflectedshock waves affect the mixing process of the liquid jet andthus combustion processes More details about internalshock structures and their influences should be the focus offuture study

4 CONCLUSION

A new spray atomization model has been developed tosimulate spray interaction in supersonic cross flow Theimplantation of a consistent breakup time and the rate ofthe mass reduction based on the sinusoidal function areconducted within the K-H/R-T hybrid model By compar-ing with experimental data in terms of the spray penetrationheight and droplet size, the present results demonstrated anexcellent performance of the developed model Thisperformance was much better than the TAB and no-breakupmodels In addition, we have provided the complex shock-wave structures developed in the supersonic internal flowfield Therefore, the present study paves the way to furtherinvestigate the interactions between the spray and shockwaves generated in the supersonic environment of the flowand can directly extended to the spray interaction with

more diverse supersonic flows in terms of different Mach

numbers

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high-speed flow AIAA Paper 93-0453.

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and reflected shock waves; (b) selected 2- dimensional

contours on x-y planes; (c) selected 2- dimensional contours

on y-z planes.

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TORQUE CHARACTERISTICS ANALYSIS FOR OPTIMAL DESIGN

OF A COPPER-LAYERED EDDY CURRENT BRAKE SYSTEM

S ANWAR1)* and R C STEVENSON2)

1)Department of Mechanical Engineering, Purdue University Indianapolis, Indiana 46202, USA

2)Automotive Component Holdings, LLC, Ypsilanti, MI 48198, USA

(Received 19 June 2008; Revised 23 April 2011)

ABSTRACT−An enhanced parametric model for a copper-layered eddy current electric machine (retarder) is introduced inthis paper The modeled torque characteristics of the copper-layered electromagnetic retarders are based on the results from

a detailed electromagnetic finite element analysis (FEA) of these eddy current machines The model uses a parameterizeddouble-exponential function to model the steady state speed-torque characteristics of the retarder The parameters are adjustedfor optimal braking performance in conjunction with predicted speed-torque characteristics of a copper–layered retarder A fullvehicle model, along with the proposed retarder speed-torque model has been used to simulate a series braking events Thesimulation results show that the peaks of the retarder speed-torque curves must be designed to occur within a specific range

of speeds for optimal braking performance

KEY WORDS : Eddy current brake (ECB), Finite element analysis, Copper layered ECB, Vehicle model

1 INTRODUCTION

Electromagnetic retarders, or eddy current brakes (ECBs),

have been used to aid vehicle braking for many years,

particularly in commercial trucks, and particularly in trucks

that frequent mountain road routes ECBs act as assists to

conventional brakes, because the conventional brakes can

fail on long downhill mountain passages due to

overheat-ing This braking assistance highlights the most apparent

advantage of ECBs over conventional brakes, that of

contact braking For more conventional vehicles,

non-contact braking translates to extended brake life However,

ECBs have not found their place in passenger vehicles

primarily due to their lower torque density (torque per unit

volume) when compared with the traditional contact

friction brakes To increase the torque available from the

retarder within the operating vehicle speeds, the former

Visteon Chassis Advanced Technology group developed a

patented copper-layered eddy current machine (Stevenson

and Li, 2004) with substantial increase in the torque

density compared to that of currently available eddy

current machines

There are additional, less apparent, advantages to using

ECBs: One advantage is that ECBs may be directly

electronically controlled (brake-by-wire) more readily than

conventional hydraulic friction brakes This electronic

control then leads to faster response times, typically 40-50

milliseconds for retarders, compared with 300-400milliseconds for hydraulically actuated friction brakes

To predict the performance of an ECB-based brakingsystem one needs a model of the retarder speed-torquecharacteristics The modeling of ECBs has been the subject

of several publications over the past two decades Simeuand Georges (1996) reported a control scheme for ECBsbased on a model for the torque that varied linearly withspeed They employed a polynomial-n-control and state-affine model for the ECB system Their model was based

on Wouterse’s (1991) experimental results Lee and Park(1999, 2001, 2002) presented a number of papers on theoptimal robust control of an ECB system The principalfocus of these papers was an enhanced parametric modelfor the eddy current brake system to facilitate the design oftorque-based automotive control systems (e.g anti-lock

brake system, etc.) Ryoo et al (2000) presented a design

and analysis of an eddy current brake for a high-speedrailway train with constant torque control Anwar (2004)proposed a parametric model for an eddy current retarderfor automotive braking applications A double quadraticfunction (a quadratic function in speed as well as aquadratic function excitation current) was used here tomodel the steady state torque of the ECBs

An enhanced parametric (double-exponential function)model for the speed-torque characteristics for a copperlayered ECB is proposed here The accuracy of theexponential-based parametric model is particularly importantfor an automotive ECB system, since it directly impacts theaccuracy of the torque control, which then determines the

*Corresponding author e-mail: soanwar@iupui.edu

braking performance in a brake-by-wire setting The

propos-ed model is baspropos-ed on the results a detailpropos-ed electromagnetic

FEA analysis As a result of the excellent fit of the FEA

generated data (Figure 2) to a set of double exponential

curves (Figure 3), one can observe that a double exponential

type steady state torque model is more accurate than those

proposed by Simeu and Georges (1996) and Anwar (2004)

Braking simulation results are presented, based on a number

of model parameter variations These simulation results show

that the ECB peak torque points must be designed to occur

within a specific speed range for optimal braking performance

2 TORQUE MODEL OF THE EDDY CURRENT

MACHINE

Electromagnetic retarders follow the basic principles of

electromagnetic induction For one type of retarder

topology, (Figure 1), an eddy current machine has an iron

core, which is a field-wound stator The stator windings

induce currents in a rotor element, which is typically a

featureless metal ring A torque is generated according to

the Lorentz equation (Fitzgerald et al., 1992) That the

torque is retarding, and does not average to zero, which one

might expect due to the periodic nature of the excitation

winding, is due to the fact that the induced eddy currents

generate power loss through Joule heating

The shape of the speed-torque curve for a retarder will

display the general peaked behavior as indicated in Figure

2; these steady state speed-torque curves were generated

from a detailed electromagnetic FEA analysis (Stevenson,

2002) As one can see from Figure 2, without the copper

layer (0.00 mm layer thickness), the peak torque may fall

outside normal vehicle speeds e.g 0 to 100 kph), and with

the copper layer, the speed-torque curves displays a

quasi-linear behavior within the operating speed range of the

vehicle How does one explain the general shape of these

curves? It is noted from (Anwar, 2004) that, for low

angular speeds, the magnetic flux (generated by the

induced eddy currents) opposes the excitation flux from the

stator, and it is smaller than the excitation flux As a result,

the braking torque increases approximately linearly withangular speed However, as the angular speed increases, themagnetic flux generated by the eddy currents increases,which causes the net magnetic flux to decrease with speed

As a result, the rate of braking torque increase does notkeep pace with the rate of increase in the angular speed

As noted above, without the copper layer added to therotor, the peak torque of the ECB can occur outside normalvehicle speeds A thin copper layer adds design flexibility

in the placement of the peak torque, as well as enhancingthe peak torque Indeed, one may obtain a maximum 40%enhancement of peak torque within the normal operatingspeed range (approximate range, 0-1000 RPM whichcorresponds to 0 to 128 kph in vehicle linear speed) of thevehicle For the proposed design, the torque peak reaches amaximum value for a copper layer thickness of 0.5 mm.The copper layer concentrates current because of the higherconductivity of copper relative to steel One can then gain

in braking torque with a copper layer, over a retarder with

no copper layer, because the concentrated current increaseslinearly with layer thickness, while the Joule heating goes asthe square of the current One cannot continue in this mannerindefinitely; as the layer thickness increases the, machinegap effectively increases (copper has a permeability ofessentially the vacuum), thereby leading to a generaldecrease in the coupling of stator to rotor, and thus adecrease in induced current Hence, there exists a layerthickness that leads to a maximum peak torque

Given the characteristics of the speed-torque curvesfrom the copper-layered retarders, a control algorithm must

be designed around these curves That meant finding afaithful, yet simple, parameterization of these curves Adouble-exponential function is chosen for the torque Tb as afunction of the angular velocity ω

(1)There are three parameters, α, β, and γ, which are

T b( )ω =γ(e–βω e– –αω)Figure 1 Schematic (not drawn to scale) of an eddy current

brake, with an added copper layer on the rotor

Figure 2 Torque vs rotor speed curve for a copper-layered EC

at various layer thicknesses based on transient electromagneFEA analysis

dependent on the design variables, e.g copper layer

thickness, and excitation current It is observed that one

may view the double-exponential curve as the sum of two

competing processes with different rate constants α and β,

which reflects the discussion of the physical origins for the

shape of the speed-torque curves

Since the retarder torque peaks at a particular rotational

speed wp, the specification of wp for control should be

based on the optimization of a performance objective For

the present analysis, minimization of the stopping distance

is the selected objective

Figure 3 shows the braking torque vs speed characteristics

of the eddy current machine using equation (1) representing

various thickness levels of the copper layer

T b (ω) captures the torque saturation characteristics of the

retarder reasonably well for a wide speed ranges At very

low speeds, the accuracy of torque estimation for the

retarder is somewhat less than that at higher speeds T b (ω)

represents the steady state relationship between retarder

torque and rotor speed at a particular excitation current It

is assumed here that the torque response with respect to the

feedback current is instantaneous

It is very important to ensure the fastest possible torque

response from the eddy current machines, particularly in a

safety critical application such as automobile braking A

simple example of the controller that will ensure fast torque

response for such a brake system is an open loop control

strategy that derives the current command from equation

(1), where g is a function of input current The equation

captures the retarder torque characteristics as a function of

current and rotor speed, through the adjustment of the

constants α, β, and γ to fit simulated, or measured data

Assuming that the current embedded in γ is same as the

commanded current (this assumption is good for the

relatively short time constants of the present design), one

may solve the exponential equation for the commanded

current, given a desired torque command This scheme

represents an open loop control strategy for the eddy

current retarders to produce the desired wheel brakingtorque for an automobile

Thus, in order to investigate whether, by selecting one ofthe ostensibly realizable speed-torque curves of Figure 2,one could reduce breaking distance with an ECB systemover a hydraulic/friction brake system However, in thepresent analysis, the physically realizable set of speed-torque curves of Figure 2 was not initially used, but analternative set of curves, generated from equation (1) wasused, as illustrated in Figure 3 The curves of figure 3 wereused to explore first whether a device with “double-exponential” like speed-toque characteristics could reducebraking distance over a hydraulic/friction system, andaround what angular velocity ωp that peak torque shouldreside

The performance objective in designing a retarder is tominimize the stopping distance Given speed torque curves(Figure 3) having the same peak torque, this objective thenbecomes equivalent to choosing the peak torque speed wp

3 WHEEL MODEL

In order to analyze the performance of the ECB withvarying torque characteristics, a vehicle model is needed Afull description of the 14 DOF (degree of freedom) vehiclemodel is outside the scope of this paper However, asimplified vehicle model for vehicle motion in thelongitudinal direction on the road plane is described inKiencke and Nielsen (2005)

It is assumed that vehicle lateral, vertical, roll, pitch, andyaw dynamics are negligible for the braking applicationunder consideration and hence the related equations areomitted Similarly the wheel rotational dynamics is given

by the following equation (Figure 4),

(2)where

Tbi = Brake torque at i-th wheel (e.g rear left, rear right)

ωi = Angular speed of i-th wheel

Fxi = Longitudinal friction force at i-th tire contact patch

R = Effective tire rolling radius

M yi=T bi–F xi R F+ rri R T– di=–I wiω·i

∑

Figure 3 Theoretical torque curves for a copper layered

ECB with varying copper layer thicknesses

Figure 4 Wheel dynamics in a braking event

Frri = Rolling Resistance at i-th tire contact patch

Tdi = Drive torque at i-th wheel

Iwi = i-th wheel rotational inertia

= Angular acceleration of i-th wheel

In the above wheel dynamics model, a braking torque is

applied according to equation (1) to stop the vehicle during

a braking simulation event Thus,

4 SIMULATION RESULTS: TORQUE CURVE

ANALYSIS FOR STOPPING DISTANCE

The proposed brake model was implemented in a MATLAB/

SIMULINK environment This model was then integrated

with a full vehicle model (also in matlab/simulink) for

simulation purposes The block diagram of Figure 5

represents the simulation model The simulation vehicle is

rear-wheel-drive vehicle with eddy current brakes applied

only to the rear wheel for simulation evaluation purposes

The electromagnetic braking function was accomplished

via a basic control algorithm that applied full available

torque from the ECBs on the wheels according to equation

(1) In all of the simulation results presented here, it is

assumed that there has been no engine intervention during

the straight-line braking event It is also noted that “panic

braking” scenario has not been considered in this paper

The vehicle model has 14 degrees of freedom (DOF) and

was validated for vehicle dynamics against Volkswagen

Golf The vehicle is assumed to have speed sensors on all

four wheels A vehicle speed estimator, which is not the

subject of this paper, is utilized to obtain the vehicle speed

Wheel speed information is directly obtained for the vehicle

model In reality, the wheel speed will be obtained from the

sensors The tire-rolling radius is the vehicle is 0.34 meter It

is further assumed that none of the ECB wheels locks up

during the braking event which is reasonable given the

speed dependent torque characteristics of the eddy currentmachines

The optimization of the stopping distance has beenperformed through the simulation of a number of torquecurves with peak torque RPM ranging from 100 RPM to

1000 RPM By varying the shape parameters, the peak ofthe torque curve is shifted over the RPM range The peaktorque is kept at the same value of 900 N-m Table 1illustrates the shape parameters with respect to the torquecurve

As indicated, Figure 3 shows the pictorial depiction ofthe torque curves based on Table 1 The above torquecurves were introduced in the full vehicle model for aneddy current brake actuation system No friction brakeswere applied to the wheel The full vehicle model wasmodified based on the proposed eddy current actuatormodel A stopping distance calculator was also introduced

in the full vehicle model The simulation of the full vehiclemodel was performed as follows:

(1) The vehicle was accelerated to a speed of 100 kph inabout 9 seconds (0.32 g acceleration)

(2) The brake pedal was applied from zero to maximumpedal displacement in 0.2 second

(3) The vehicle was on a high friction coefficient surfaceand was preconditioned not to be in wheel lock-upmode

(4) The following outputs from the full car model wererecorded: stopping distance, vehicle speed, vehicleacceleration/deceleration, wheel speed, braking torque.The information in steps 1 and 2 are based on real dataobtain from a test vehicle It was assumed that maximumcurrent was applied to the retarders during whole brakingevent Simulation results presented some interestingfeatures, which are illustrated in the following section.Table 2 shows the stopping distance corresponding toeach curve in table 1 A plot of the stopping distance versus

ωp is shown in Figure 6 It is clear from Figure 6 that theoptimum peak torque rpm for the retarder lies in the range

of 300~500 rpm Thus, given the results on Table 2, where

the minimum stopping distance occurs for a peak torque

range of approximately, 300-500 rpm, it is seen from the

results of Figure 2, that it should be possible to achieve a

retarder design of a peak torque of 900 nm at about 500

rpm with a copper layer of thickness 0.5, approximately

Other vehicle parameters for the target vehicle are as

follows:

Vehicle Parameters (Volkswagen Golf):

Wheel Inertia = 0.5 (kg-m2); Vehicle Inertia = 3136

(kg-m2); Vehicle Mass = 1250 kg; Distance from C.G to front

axle = 1.05 (m); Distance from C.G to rear axle = 1.71 (m)

The optimum range of rotor speed at which the peak

torque occurs can be explained as follows: The vehicle

speed at the start of braking event is 100 KPH, which

translates into about 700 RPM at the road wheel, and 700

RPM is also the retarder rotor speed The total braking

power for the vehicle can be obtained by computing the

area under the torque curves in Figure 3 from rotor speed of

700 RPM to 0 RPM The torque curves that provide higher

total braking power for an ECB will yield a shorter

stopping distance on a given road-tire interface (assuming

no wheel lock-up) The braking power is then obtained byintegrating Tb(w) over the wheel speed range as follows:

(4)

It is noted that the total braking power is proportional tothe average torque It is noted from the plots of velocityversus time (Figure 6) that over a large part of the brakingevent the velocity decreases linearly with time Thus, onehas essentially constant deceleration Thus, there is anapproximately constant effective braking torque Thatconstant braking torque is the average torque

A plot of the total braking power P vs peak-torque-RPM

(rotor speed at which the eddy current machine providesmaximum torque) for each torque curve in Figure 3 isshown in Figure 7 According to Figure 7, the total braking

αωmax–

1

α

- e

βωmax–

1

β

–

Table 2 Simulated stopping distances corresponding to the

double exponential torque curves in Figure 4

Curve # Rotor RPM at peak torque (RPM) Stopping distance (m)

Figure 6 Simulated stopping distances for a test vehicle

with the proposed ECB model

Figure 7 Braking power for different torque curves inFigure 3

Figure 8 (a) Rear left retarder torques corresponding to thetorque curves in Figure 3 (b) Rear right retarder torquescorresponding to the torque curves in Figure 3

power reaches a maximum over a peak torque RPM range

of 200~400 RPM This observation supports the results

obtained in Table 2 The minor discrepancy in the optimal

peak torque RPM range for the eddy current brakes may be

attributed to vehicle dynamics effects on the braking

performance and the fact that the present study was limited

to only rear wheel braking

Figures 8 and 9 show the plots of braking torque at the

rear wheels and vehicle deceleration & vehicle speed for

each torque curve in Figure 3 No wheel lock-up occurred

at the rear wheels which is evident from the rear wheel

torque profiles having smooth transitions While the brake

torque fluctuated over a wide range for different

torque-speed curves, these torque variations over the torque-speed range

had little effect on the vehicle velocity and acceleration

profiles This is due to the fact the front wheel brakes

performed majority of the braking while the rear wheel

eddy current brakes provided remainder of the braking

torque to stop the vehicle

5 CONCLUSION

An enhanced exponential-based parametric model of a

copper-layered eddy current electric machine for

automotive braking applications has been introduced in this

paper The modeled torque characteristics of the

copper-layered electromagnetic retarder is based on the results

from a detailed electromagnetic finite element analysis of

such an eddy current machine The model parameters are

adjusted for optimal braking performance A full vehicle

model along with the proposed eddy current machine

model with the adjusted parameters has been used to

simulate a series of torque curves with peaks shifting over a

range of rotor speeds The simulation results show that thepeaks of the torques curve should be designed to occurbetween a specific range of speeds for optimal brakingperformance Further studies are needed in order todetermine the design sensitivities with respect to road-timeinterface parameters

ACKNOWLEDGEMENT−This work was supported in part bythe Chassis Advanced Technology Department of VisteonCorporation, Van Buren Twp, MI 48111, USA

REFERENCESAnwar, S (2004) A parametric model of an eddy currentelectric machine for automotive braking application

Fitzgerald, A E., Kingsley, Jr., C and Umans, S D

(1992) Electric Machinery 5th Edn McGraw Hill

Electrical Engineering Series

Kiencke, U and Nielsen, L (2005) Automotive Control

System for Engine, Driveline, and Vehicle

Springer-Verlag Germany

Lee, Jr., K and Park, K (2001) Modeling of the eddy currents

with the consideration of the induced magnetic flux Proc.

Int Conf Electrical and Electronic Technology, Singapore,

Ryoo, H.-J., Kim, J.-S., Kang, D.-H., Rim, G.-H., Kim,

Y.-J and Won, C.-Y (2000) Design and analysis of aneddy current brake for a high-speed railway train with

constant torque control Conf Record of the IEEE

Simeu, E and Georges, D (1996) Modeling and control of

an eddy current brake Control Engineering Practice 4,

1, 19−26

Stevenson, R C and Li, Z (2004) Increased Torque in

Retarder Brake System through Use of Conductive Layer United States Patent Application Number

20040051414 A1

Stevenson, R C (2002) Torque Analysis of a Copper

Layered Electromagnetic Retarder Internal Memo,

Chassis Advanced Technology Department, VisteonCorporation

Wouterse, J H (1991) Critical torque of eddy current

brake with widely separated soft iron poles IEE Proc.,

138, B, 4.

Figure 9 Vehicle deceleration and speed corresponding to

the torque curves in Figure 3

PERFORMANCE MEASUREMENTS OF A TRACKED VEHICLE SYSTEM

A RAHMAN*, A K M MOHIUDDIN and A HOSSAINDepartment of Mechanical Engineering, Faculty of Engineering, International Islamic

University Malaysia (IIUM), Kuala Lumpur 50728, Malaysia

(Received 13 October 2009; Revised 21 January 2011)

ABSTRACT−To improve crossing ability, the most important performance factor for tracked vehicle systems operating onlow-bearing capacity peats, and to minimize income losses that result from downtime and maintenance costs, a vehicle wasdesigned in order to adapt to operating condition changes This article describes the mobile performance of a novel vehiclewith segmented rubber tracks on a low-bearing capacity peat At an equivalent travelling speed, the novel vehicle’s tractiveperformance in a variable operating environment caused by changes in terrain cohesiveness and hydrodynamic responses wassuperior to that of the previous model The new vehicle, which could be operated on the Sepang peat, showed a tractive effort

of 42.2% of the gross vehicle weight in field experiments; the recommended minimum tractive effort is between 30 and 36%

of the gross vehicle weight

KEY WORDS : Mobility, Operating environment, Cohesiveness, Hydrodynamics response

NOMENCLATURE

A : contact area of the track

B : width of the track

B stc : vehicle tracked tread

c : terrain cohesiveness

C x : longitudinal distance between the CG and the lateral

centerline of the vehicle's hull

D : instantaneous center point shifting distance

e 1 : exponential

F b : tractive effort at the bottom of the track

F s : tractive effort at the side of the track

F it : tractive effort of the inner track

F ot : tractive effort of the outer track

F Lit : longitudinal tractive effort of the inner track

F Lot : longitudinal tractive effort of the outer track

F sit : tractive effort at the side of the inner track

F sot : tractive effort at the side of the outer track

g : acceleration due to gravity

H : height of the grouser

i : slippage of the vehicle

K w : terrain shear deformation modulus

L : length of the track in contact with the ground

M r : turning moment of the vehicle

Q : torque of the sprocket

R lnit : longitudinal motion resistance for the inner track

R lnot : longitudinal motion resistance for the outer track

W : weight of the vehicle

W it : weight transfer to the inner track

W ot : weight transfer to the outer track

x : abscissa

α : angle of the track system between the grouser and

the width of the track

a ground contact pressure of 21.5 kN/m2, discussed by

Yahya et al (1997) have been proposed for use on peat

terrains to collect and transport FFBs None of the tracked

or wheeled vehicle systems designed and developed inMalaysia can traverse low bearing capacity peats becausethese vehicles were not designed and developed to meetpeat-terrain requirements This article introduces a newtracked vehicle, with a ground contact pressure of 12.69 kN/

m2, that was mainly designed for the low bearing capacitypeats of Sepang The vehicle proposed in this articlefacilitates mobility on low bearing peats and can collect

*Corresponding author e-mail: arat@iiu.edu.my

and transport FFBs under any working conditions.

Furthermore, the ability to replace damaged track segments

rather than replacing the entire track reduces maintenance

costs The major objective of this study was to measure the

performance of the proposed vehicle on the Sepang peat

terrain in Malaysia

2 MATERIALS AND METHODS

2.1 Mathematical Models

The mathematical models for the power of the vehicle's

engine and the tractive performance were developed for

straight and turning motions and a non-uniform pressure

distribution Non-uniform ground pressure distribution was

achieved by locating the vehicle's center of gravity (CG) to

the rear of the mid-point of the ground contact length of the

track The ground pressure distribution was assumed to

increase from the front idler to the rear sprocket The

mathematical model was developed by simplifying the

general tractive equations and motion resistance equations

of Wong et al (1982), Wong (2001), Muro (1989) and

Okello et al (1998) for peat terrain To develop the

mathematical model for straight and turning motions, the

track was assumed to be a medium pitch rigid link track

The tractive effort of the vehicle, with a non-uniform

ground pressure distribution, during straight motion was

based on the forces shown in Figure 1 The model of

tractive effort considers the portion of the track that is in

contact with the ground and the side portions of the track

grouser Furthermore, it includes parts of the front idler and

rear sprocket The general equations for computing the

tractive effort of the vehicle during straight and turning

motions are described in the following sections

2.1.1 Straight motion

The tractive effort of the vehicle is computed with the

equation of Rahman et al (2005a).

(i) Under the bottom of the track,

(1)with

where F b is the tractive effort that develops along the

bottom of the track in kN; A is the contact area of the track

in m2; c is the terrain cohesiveness in kN/m2; σ is the

vehicle normal stress in kN/m2; σfi is the normal stress on

the bottom of the front idler in kN/m2; σms is the stress onthe main straight portions in kN/m2; σrs is the stress on thebottom of the rear sprocket in kN/m2; j is the terrain internal friction angle in degrees; K w is the shear deforma-

tion modulus in m; L is the length of the track that is in contact with the ground in m; L fi is the length of contact of

the front idler in m; L ms is the length of contact of the main

straight part in m; L rs is the length of contact of the rear

sprocket in m; i is the slippage of the track in percentage; i fi

is the slippage of the front idler in percentage; and i ms is the

slippage of the main straight part in percentage and i ms is

the slippage of the rear sprocket

The slippage of the front idler track that is in contactwith the ground can be represented by the followingderived equations:

(2)

By integrating equation (2), the slippage of the frontidler can be computed as

where Similarly, the slippage of the rear sprocket can becomputed as

in degrees; θrs is the exit angle of the rear sprocket in

degrees; z fi is the sinkage of the front idler in m; z rs is the

sinkage of the rear sprocket in m; R fi is the front idler radius

in m and R rs is the rear sprocket radius in m

The slippage of the straight part of the main track can becomputed with the following equation:

K w

–

exp–

=

A 4 B L= ( × ) σ W, = -A

σ σ= fi+σms+σrs, L L= fi+L ms+L rs and i i= fi+i ms+i rs

-+sin

=

i mp i fi+i rs

2 -

=

Figure 1 Forces acting on the driven track belt (Rahman et

al., 2005b).

(5)with

where F s is the thrust developed to the side of the front idler

grouser in kN; H is the height of the grouser in m and α is

the angle between the grouser and wide portion of the track

system in degrees

The vehicle's resistance to motion due to terrain

compac-tion can be represented by the following equacompac-tion, derived

from Rahman et al.(2005a):

(6)

where

R c is the vehicle's resistance to motion due to terrain

compaction in kN; B is the track width in m; z fi ,, z mp and z rs

are the sinkages of the vehicle in m D hfi ,, D hmp , and D hrs are

the hydraulic diameters of the front idler track, the straight

part of the track, and the rear sprocket track, respectively,

in m; k p is the internal peat stiffness in kN/m3 and m m is the

surface mat stiffness in kN/m3

The sinkages of the front idler, the main straight part and

the rear sprocket can be represented by the equations of

Rahman et al (2005a):

and

where P fi is the pressure under the front idler in kN/m2 and

P rs is the pressure under the rear sprocket in kN/m2

The ground pressure distribution between the tracked

vehicle and the terrain during loading and unloading can be

represented with Muro's (1989) equation:

(7)

(8)

where P0 is the normal exit pressure of the vehicle in kN/

m2; Pu is the unloading pressure in kN/m2 and e i is the load

eccentricity

2.1.2 Turning motion

Figure 2 shows that the effective driving tractive effort F′ot

acting on the outer track and the effective braking or

driving tractive effort F′it acting on the inner track can be

represented by balancing the forces acting on each of the

tracks while the vehicle is making a turn of radius R with a

where F tt is the effective tractive effort of the vehicle in kN;

F ot and F it are the tractive efforts of the outer and inner

tracks, respectively, in kN; F lot and F lit are the longitudinal

tractive efforts kN; F sot and F sit are the tractive efforts of the

side of the track; R lnit and R lnot are the longitudinal motionresistances for the inner and outer tracks, respectively and

effort of the vehicle during longitudinal movements can be

represented by the following equation from Rahman et al.

(2005a):

(11)where ;

F Lo(i)t is the tractive effort that develops along the bottom

of the outer and inner tracks in kN; L is the length of the

track in contact with the ground in m; σo(i)t is the vehicle

normal stress either for the outer and inner tracks in kN/m2;

friction angle of the terrain in degrees; K w is the shear

deformation modulus in m and i is the slippage of the

F s 4HL c( +σtanϕ) α K w

iL

-e 1 K–⎝⎛ +iL⎠⎞ 1 iL K w

–

expcos

= ,

-±

2 -

-⎝ ⎠

⎛ ⎞ 1 i o i ( )t L

K w

–

-⎝ ⎠

⎛ ⎞ exp –

=

σo i ( )t W o i ( )t LB

-=

Figure 2 Forces acting on the track during turning at 16

km/h (Rahman et al., 2005a).

vehicle in percentage.

Because the CG shifts during turning, the equivalent

moment of turning resistance M r has two components: the

moment of lateral resistance exerted on the tracks by the

terrain about O′ and the moment of centrifugal force about

O′ Thus, the moment of turning resistance M r about O′ can

be computed with the following equation from Rahman et

al (2005a):

(12)with ; ;

Here, M r is the turning moment resistance of the vehicle

in N-m; W it and W ot are the distributed loads of the inner

and outer tracks, in kN respectively; R is the turning radius

in m; i it and i ot are the slippages of the inner and outer

tracks, respectively; D is the longitudinal shifting distance

of the CG from the original point O in m; R lot and R lit are the

lateral resistances of the outer and inner tracks, respectively, in

kN; W is the total weight of the vehicle in kN; B stc is the

center-to-center distance of the track in m; L is the length of

the track in contact with the ground in m; µl is the

coefficient of lateral resistance in kN; h cg is the height of

the CG; Cx is the longitudinal distance between the CG and

the lateral centerline of the vehicle's hull in m; Ω is the yaw

motion in rad./s; and β is the slip angle in dagree

The vehicle turning moment resistance must be less than

the total amount of developed torque (i.e, M r ≤ Q) to

maintain steady-state turning Therefore, to maintain

steer-ing ability, a necessary condition for maintainsteer-ing

steady-state turning, the turning radius is increased while the

travelling speed remains unchanged Kitano and Kuma

(1997) and Shiller et al (1993) stated that the slip angle β

appears to be zero during straight-line motion and has some

sine value when the vehicle turns left or right, as shown in

Figure 2

The vehicle, as shown in Figure 2, turns at a speed of 10

km/h on peat terrain, and the instantaneous center point

shifts to O at a distance D in front of the vehicle’s CG The

vehicle’s outer and inner tracks demonstrate different

longitudinal resistances to motion as a result of the dynamic

loads on the tracks The total motion resistance due to

terrain compaction can be represented by the following

equation:

(13)

where R co(i)t is the total motion resistance of the vehicle due

to soil compaction for either the outer or inner track

The lateral motion resistance force exerted on the track

by the displacement of the terrain surface can be computed

by the following derived equation:

(14)

(15)

where R lot and R lit are the lateral resistances of the outer andinner tracks, respectively, in kN; W is the total weight of

the vehicle in kN; B stc is the center-to-center distance of the

track in m; L is the length of the track in contact with the

ground in m; µL is the lateral motion resistance coefficient;

the longitudinal distance between the CG and the lateralcenterline of the vehicle's hull in m

The vehicle's lateral resistance must be higher than orequal to the vehicle's centrifugal force to maintain stability

during turning In equation form, (i.e., R lot + R lit ≥ (F cent =

(Wv t2 cos β/gR))) where vt is the theoretical velocity in m/sand g is the acceleration due to gravity in m/s2

The vehicle shown in Figure 3 was developed based on

the parameters in Table 1 The road wheels, supportingrollers and sprockets are rigidly attached to the vehicletrack frame by deep-groove ball bearings, and the frontidler is mounted to the track frame with a tension device.The vehicle is based on a custom-built, hydrostatic skid-steertransmission system, and both sides of the unit are poweredindependently This design results in a much smoother rideand increases maneuverability and responsiveness Thegeometrical arrangement of the vehicle’s engine, hydraulicpumps, hydraulic tank, fuel tank, hydraulic motor andundercarriage components results in an equal and balanced

-B stc g

-C ssinβ

– cos

3D hmp -m m z mpo i ( )t3

loading that reduces balance problems during straight and

turning maneuvers on unprepared peat terrains The overall

length and width of the vehicle are 2,820 mm and 1,900

mm, respectively The CG is located at (–860 mm, 590

mm) in relation to the center of the rear sprocket, which

was taken as the origin (0,0) in the vehicle coordinate

system The total estimated dry weight of the vehicle is 2.0

metric ton Each of the undercarriage components is made

from high-speed stainless steel The vehicle is powered by

a 4-cylinder NISSAN TD27 44.5 kW@2500 rpm single

turbo water-cooled diesel engine, which is directly coupled

with two SAMHYDRAULIK H1C50M axial piston

pumps The piston pumps operate the high-torque and

low-speed SAI series 800 cc/rev radial piston hydraulic motors

The vehicle was outfitted with instrumentation to measure

tractive effort and slippage Strain gauge transducers were

installed on the left and right track drive shafts to measure

the torque transmitted to the sprockets Slip rings were

used to transmit signals to the on-board DEWE-2010 data

acquisition system Proximity sensors were used to monitor

the rotations of the left and right sprockets The groundspeed of the vehicle was measured by a Doppler DICKEY-John Radar II Velocity Sensor From the measurements ofthe left and right sprockets, angular speeds, the groundspeed, and the slip of the left and right tracks were derived

A proximity switch and an OMRON K3GN-NDC-FLKDC24 digital panel meter were used to monitor therevolutions per minute (RPM) of the engine flywheel to fixthe vehicle's travelling speed

3 DESCRIPTION OF TEST AREASThe vehicle was designed and developed based on theSepang peat terrain located across from the Kuala LumpurInternational Airport (KLIA), 56 km south of KualaLumpur, Malaysia The mechanical properties of theterrain were reported previously by Rahman (2004) Three

different types of peat terrain, Terrain I, Terrain II, and

Terrain III, as shown in Figures 4, 5 and 6, respectively,were considered for testing Located near the mainroadside, portions of Terrain I between rows of oil palmtrees were dry and clean Long grass and ferns were found

in the rows of oil palm trees The water table was located

350 mm below the surface Terrain II, located near the side

Table 1 Basic vehicle design parameters

Vehicle parameters

Total weight including an 8.0-kN payload, kN W 20.0

Vehicle traveling speed, km/hr v t 10

Center of gravity, x coordinate, m x cg -0.86

Center of gravity, y coordinate, m y cg 0.45

Sprocket pitch diameter, m D rs 0.40

Idler center, x coordinate, m x cfi -2.0

Idler center, y coordinate, m y cfi 0

Number of road-wheels (each side) n 7

Number of supporting rollers (each side) n s 3

Diameter of supporting rollers, m D s 0.10

Track parameters

Total track length (each side), m L c 5.40

Length of track in contact with the ground, m L 2.25

Road-wheel spacing to track pitch S r /T p 2.25

Vehicle speed fluctuation, percentage δ 3.17

Coordinate origin is at the center of the sprocket Positive

x-and y-coordinates are to the rear x-and top, respectively

(Rah-man et al., 2005b)

Figure 4 Terrain type I

Figure 5 Terrain type II

of a dam, was wet, soft, and covered with long grass The

water table was 10-300 mm below the surface Terrain III

was considered to be waste peat terrain It was heavily

infested with palm roots, low shrubs, grasses, and sedges

The field conditions were wet, and the water table was

0-100 mm below the surface The surface mat and the peat

deposit thickness could not be visually distinguished The

surface mat thickness was approximately 50-250 mm in the

center of adjacent palm rows and 100-350 mm around the

palms The underlying peat deposit thickness for the entire

area was approximately 500-1000 mm The field was

nearly saturated, and walking in such terrain conditions

was only possible with the use of specially made wooden

clogs, as shown in Figure 6(a) The dominant features of

this site include a high water content and a weak

underly-ing peat that could easily be disturbed by vehicles Testunderly-ing

the vehicle on Terrain III was difficult, as shown in Figure

6(a) Therefore, the vehicle was tested on Terrain III after

draining, as shown in Figure 6(b) The mechanical

properties of the terrain are listed in Table 2

4 VEHICLE FIELD TESTING

The straight motion tests of the vehicle were performed at

two travelling speeds, 6 km/h and 10 km/h, and at twoloading conditions, 12.0 kN and 20.0 kN The turningmotion tests were performed at a single speed of 16 km/hand at two loading conditions, 12.0 kN and 20.0 kN Foreach of the loading conditions and travelling speeds, thevehicle was twice driven over a series of travelling paths oneach terrain The sprocket-driven motor is capable ofproducing sufficient torque only in the range from 2000 to

2500 rpm Because of engine overheating problems, theengine was only operated at 2000 rpm during the turningtests; the vehicle was maintained at a speed of 16 km/h

Figure 6 Terrain type III

Table 2 Mechanical properties of the peat terrain (Rahmanet

al (2004))

Mean value SD Mean value SD