International journal of automotive technology, tập 10, số 6, 2009

663 − 668 20092School of Mechanical and Automotive Engineering, Keimyung University, Daegu 704-701, Korea 3The Center for Automotive Parts Technology, Keimyung University, Daegu 704-701,

International Journal of Automotive Technology , Vol 10, No 6, pp 645 − 652 (2009)

645

HCCI COMBUSTION CHARACTERISTICS DURING OPERATION

ON DME AND METHANE FUELS

Y TSUTSUMI 1)* , A IIJIMA 1) , K YOSHIDA 1) , H SHOJI 1) and J T LEE 2) 1)Department of Mechanical Engineering, College of Science and Technology, Nihon University,

1-8-14 Kanda-Surugadai, Chiyoda-gu, Tokyo 101-8308, Japan

2)School of Mechanical Engineering, Sungkyunkwan University, Gyeonggi 440-746, Korea

(Received 28 July 2008; Revised 19 December 2008) ABSTRACT− The Homogeneous Charge Compression Ignition (HCCI) engine has attracted much interest because it can simultaneously achieve high efficiency and low emissions However, the ignition timing is difficult to control because this engine has no physical ignition mechanism In addition, combustion proceeds very rapidly because the premixed mixture ignites simultaneously at multiple locations in the cylinder, making it difficult to increase the operating load In this study, an HCCI engine was operated using blended test fuels comprised of dimethyl ether (DME) and methane, each of which have different ignition characteristics The effects of mixing ratios and absolute quantities of the two types of fuel on the ignition timing and rapidity of combustion were investigated Cool flame reaction behavior, which significantly influences the ignition, was also analyzed in detail on the basis of in-cylinder spectroscopic measurements The experimental results revealed that within the range of the experimental conditions used in this study, the quantity of DME supplied substantially influenced the ignition timing, whereas there was little observed effect from the quantity of methane supplied Spectroscopic measurements

of the behavior of a substance corresponding to HCHO also indicated that the quantity of DME supplied significantly influenced the cool flame behavior However, the rapidity of combustion could not be controlled even by varying the mixing ratios of DME and methane It was made clear that changes in the ignition timing substantially influence the rapidity of combustion.

KEY WORDS : Internal combustion engine, Combustion, HCCI, DME, Methane, Spectroscopic measurement

1 INTRODUCTION

The Homogeneous Charge Compression Ignition (HCCI)

engine (Thring, 1989) can simultaneously reduce nitrogen

oxide (NOx) and particulate matter (PM) emissions (Aoyama

et al., 1996) because, among other factors, the air and fuel

are premixed homogeneously and operation is possible in

the lean mixture region Another reason for the increased

interest the HCCI combustion process is that it achieves

thermal efficiency on par with that of diesel engines

How-ever, it is difficult to control the ignition timing of HCCI

combustion because the fuel is ignited by the temperature

rise resulting from compression Furthermore, the fact that

combustion occurs simultaneously throughout the combustion

chamber causes the pressure to rise too quickly

Various methods of controlling HCCI combustion have

been proposed, including varying the compression ratio

(Hyvonen, 2005), varying the intake air temperature (Yoshida

et al., 2005), applying exhaust gas recirculation (EGR)

(Urushihara et al., 2003; Urata et al., 2004; Persson et al.,

2004; Iijima et al., 2007), and using two types of fuel

having significantly different ignition characteristics (Ozaki

et al., 2006; Sato et al., 2006) This study examined themethod of using a blend of two types of fuel The test fuelsused were dimethyl ether (DME), which tends to autoigniteeasily because of its active low-temperature oxidation reac-tions, and methane, which does not autoignite readily, as ithas no low-temperature oxidation reaction mechanism Theheat release rate was analyzed to investigate the influence

of each type of test fuel on combustion behavior when thefuel mixing ratios were varied Spectroscopic techniques(Shoji et al., 1994, 1996) were used to measure the lightemission intensity and absorbance of HCHO, which israpidly produced in cool flame reactions

2 TEST FUELS

2.1 Characteristics of DME and MethaneThe properties of DME and methane are shown in Table 1(Glassman, 1996) DME has drawn interest as an alternativefuel for compression ignition engines because its highcetane number allows for compression ignition It also has

a negative temperature coefficient region in which theignition delay is not shortened even though the mixturereaches a higher temperature due to compression For thatreason, it displays a multi-stage heat release pattern attribut-

*Corresponding author. e-mail: shoji@mech.cst.nihon-u.ac.jp

ed to low-temperature and high-temperature oxidation

reac-tions

Methane has vastly different ignition characteristics from

DME It does not autoignite easily because it has a cetane

number of zero and displays only a single-stage heat release

pattern ascribable to high-temperature oxidation reactions

2.2 DME and Methane Reaction Mechanisms

Figure 1 shows the oxidation reaction process of a blended

DME and methane fuel (Pilling et al., 1997; Konno, 2003)

DME reactions (denoted as A in the figure) are divided into

two processes One reaction process (1) begins from the

first O2 addition and, depending on the temperature region,

follows a path to a second O2 addition; the other reaction

process (2) proceeds without any addition of O2 At low

temperatures below 800 K, reaction (1) takes place and is

accelerated by a chain-branching reaction (cool flame region)

As the temperature rises further, the process switches to

reaction (2), which is a chain propagation reaction, such

that acceleration of the reaction ceases (negative

temper-ature coefficient (NTC) region (Leppard, 1998; Shoji et al.,

1992)) in spite of the temperature rise A subsequent increase

in temperature induces reaction (3), resulting in excessive

production of OH radicals and causing an acceleration of

the reaction, leading to autoignition In relation to the

temperature rise, two-stage ignition (Koyama et al., 2001)

occurs owing to the progression from a cool flame through

the NTC region to autoignition as the reactions proceed

from (1) to (3)

In the case of a blended DME and methane fuel, the OH

radicals produced by the reaction of DME are consumed by

the initial H-atom abstraction reaction (5) of methane This

is said to influence the progress of the oxidation reaction ofDME In the cool flame region of DME, rapid production

of HCHO occurs, and therefore attention was focused onHCHO in this study in order to investigate cool flamebehavior

3 EXPERIMENTAL PROCEDURE

3.1 Experimental EquipmentSpecifications for the test engine are given in Table 2, andthe configuration of the test equipment is shown schemati-cally in Figure 2 A 4-cycle air-cooled single-cylinder dieselengine was used as the test engine The engine inducted apremixed mixture that was ignited by compression to accom-plish HCCI combustion Mass flow controllers (denoted as(C) in the figure) were used to control the respective supply

of DME and methane The cylinder pressure was measuredwith a crystal pressure transducer (P) In order to investi-gate the engine operating condition, K-type sheath thermo-couples were used to measure the combustion chamberwall temperature and the intake air temperature

The equipment shown in Figure 3 was attached betweenthe cylinder head and the cylinder as well as to the pistoncrown for measurement of light emission and absorption.Flame light was extracted through a quartz window andintroduced into a spectroscope via an optical fiber cable.Light was separated at a wavelength of 395.2 nm, corre-sponding to the light emission wavelength of HCHO Theinside of the combustion chamber was also irradiated withlight from a xenon lamp and the transmitted light was intro-duced through an optical fiber cable into the spectroscope.Light was separated at a wavelength of 293.1 nm corre-

Table 1 Properties of test fuels

Fuel DME Methane

Molecular Formula CH3OCH3 CH4

Cetane Number >55 0

Auto Ignition Temperature [K] 623 905

Figure 1 Oxidation reaction process of blended DME and

methane fuels Figure 2 Configuration of test equipment

Table 2 Specifications of test engine

Number of cylinders 1Bore×Stroke 76×66 mmDisplacement 299 cm3

Compression ratio 12:1Intake valve close 54 deg ABDCExhaust valve open 56 deg BBDC

HCCI COMBUSTION CHARACTERISTICS DURING OPERATION ON DME AND METHANE FUELS 647

sponding tothe absorption wavelength of HCHO (Gaydon,

1974) The wavelength resolution of the spectroscope used

in the light emission and absorption measurements was 4.0

nm in terms of the half-bandwidth value The separated light

in each case was input into a photomultiplier for

conver-sionto an electric signal The output voltage of the

photo-multiplier was regarded as the emission intensity of the

flame light For the transmitted light from the xenon lamp,

absorbance A HCHO was calculated using Equation (1) below,

where E 0 denotes the baseline output voltage of the

photo-multiplier at bottom dead center and E denotes the output

voltage at each crank angle

(1)

In the experiments, the test engine was operated at 1400

rpm, and the intake air temperature and the combustion

chamber wall temperature were controlled to 313 K and

353 K, respectively The quantity of fuel supplied was kept

within the range where misfiring and knocking did not

occur

3.2 Method of Calculating Heat Release Rate

In a combustion process with a fast burning velocity, the

rate of change in the specific heat ratio influences the

calculated heat release rate Accordingly, it is important to

take into account that rate of change when calculating the

heat release rate (HRR) for HCCI combustion, which

pro-ceeds extremely rapidly Therefore, in this study, the change

in the in-cylinder gas composition and the

temperature-related change in the specific heat ratio were factored into

the HRR calculation (Shudo et al., 2000; Muto et al.,

2006) The specific heat ratio κ (n i, T) was calculated based

on the in-cylinder gas composition n i and average gas

temperature T at crank angle θ Taking into account the rate

of change in the specific heat ratio dκ/dθ, the HRR was

calculated with Equation (2) below

(2)

In calculating the HRR, the composition and number ofmoles of the gaseous body filling the cylinder were deter-mined from the intake air mass and quantity of DME andmethane consumed The change in the number of moles ofthe fuel was calculated, under the assumption of completecombustion, by finding the cumulative heat release fromthe measured cylinder pressure data Using the change inthe number of moles of the fuel, the respective change inthe number of moles of O2, CO2, and H2O was found In thecase of a blended DME and methane fuel, the autoignitiontemperature of methane is higher than that of DME, asindicated by the fuel properties in Table 1 Therefore, thechange in the in-cylinder gas composition was calculated

on the assumption that methane burned after the DME hadburned The average temperature of the in-cylinder gas wascalculated using the equation of state for an ideal gas Thespecific heat of each component was calculated at thattemperature (Prothero, 1969; Fujimoto et al., 2006) andthen the average specific heat ratio of the working gas wasfound

3.3 Experimental ConditionsFigure 4 shows the range of the injected heat value of thefuel per cycle Experiments were conducted under theconditions defined in the four cases below in order toinvestigate in detail how changes in the injected heat value

of DME and methane influenced combustion

Case 1: Only DME was supplied and the injected heat

value of DME Q DME was varied This conditionwas used to investigate the basic combustioncharacteristics when DME was supplied as asingle component fuel

Case 2: Both DME and methane were supplied The

injected heat value of methane Q CH4 was variedwhile keeping that of DME Q DME constant Thiscondition was designed for investigating the com-bustion characteristics of methane as a singlecomponent fuel However, the test engine couldnot be operated under this experimental condition

-Figure 3 Schematic of spectroscopy system

Figure 4 Operating map

because the high autoignition temperature of

methane gave rise to misfiring Therefore, a

con-stant amount of DME was injected

Case 3: Both DME and methane were supplied The

methane share of the injected heat value γ CH4

(=Q CH4/Q in) was varied while keeping the total

injected heat value Q in (=Q DME+Q CH4) constant

Because the injected heat value of the fuel has a

large influence on ignition characteristics, the

influence of the mixing ratio of DME and methane

was investigated while keeping the quantity of

fuel injected constant

Case 4: Under the conditions of Case 3, the intake air

temperature was adjusted so that the ignition

tim-ing for each level of the methane share of the

injected heat value γ CH4 was 10 degrees or 2 degrees

before top dead center (BTDC) The influence of

the ignition timing was excluded in this case

because of its large influence on combustion

characteristics

4 RESULTS AND DISCUSSION

4.1 Investigation of Separate Control of Ignition Timing

and Operating Load

Figure 5 shows the HRR results for Case 1 With only

DME as the test fuel, heat release of the high-temperature

oxidation reactions increased as the injected heat value was

increased Simultaneously, the ignition timing was advanced

considerably to an earlier crank angle (X in the figure)

These results indicate that the load and ignition timingcannot be varied independently with a single-componentfuel of DME Additionally, increasing the injected heatvalue of DME results in extremely rapid combustion.The indicated mean effective pressure (IMEP) relative tothe injected heat value is compared in Figure 6 for Cases 1and 2 For Case 1, the IMEP increased due to the increase

in heat release until the injected heat value reached point A.However, it was observed that IMEP stopped increasingafter point A because the ignition timing advanced too far.Even though the injected heat value was increased, it didnot increase the load owing to the advance of the ignitiontiming

The HRR results for Case 2 are shown in Figure 7 Theignition timing (Y in the figure) did not change appreciablyeven though the injected heat value of methane wasincreased It was also seen that the heat release of the high-temperature oxidation reactions increased These resultsindicate that varying the injected heat value of methanealone can change the load, without changing the ignitiontiming As is also clear from the IMEP graph in Figure 6,the IMEP continued to increase because the ignition timingdid not change even though the injected heat value wasincreased Furthermore, the knock limit was higher com-pared with Case 1 (i in Fig 6) because combustion did notbecome extremely rapid owing to the fact that the ignitiontiming did not change

An investigation was made of the ignition timing θ ign andthe interval τ from the occurrence of a cool flame untilignition, under a condition where the quantities of fuel sup-plied were varied The definitions of θ ign and τ are shown inFigure 8 The fuel supply conditions were those of Case 1with only DME as the fuel, Case 2 in which the injected

Figure 5 Influence of Q DME on HRR in Case 1

Figure 6 Injected heat value (Q in) vs IMEP in Case 1 and

Case 2

Figure 7 Influence of Q CH4 on HRR in Case 2

Figure 8 Definitions of cool flame used for analysis

HCCI COMBUSTION CHARACTERISTICS DURING OPERATION ON DME AND METHANE FUELS 649

heat value of methane was varied (while keeping that of

DME constant at values of Q DME=240, 260, 278, and 297 J/

cycle), and Case 3 in which the mixing ratios of DME and

methane were varied while keeping the total injected heat

value Q in constant at 357, 387 and 417 J/cycle, respectively

Figure 9 shows θ ign and τ in relation to the injected heat

value of DME as the parameter The results in this figure

show that the plots of θ ign and τ continued along the same

line even though the injected heat value of methane

differ-ed, indicating that θ ign and τ were dependent on the injected

heat value of DME This result suggests that, under the

condition used in this study (γ CH4<50%), the cool flame

reaction was not influenced by the H-atom abstraction

reaction of methane, which consumes the OH radicals

produced by the reaction of DME in cool flame (reaction

(5) in Figure 1) This indicates that the ignition timing can

be varied independently by changing the injected heat

value of DME The results show that t became shorter and

θ ign was advanced as the injected heat value of DME was

increased

Figure 10 shows the maximum HRR of the cool flame

HRRcool as a function of the injected heat value of DME Itcan be seen that the plots of HRRcool are arranged along thesame line in relation to the increase in the injected heatvalue of DME under all of the conditions examined.Accordingly, the following reason can be inferred for thedependence of τ and θ ign on the injected heat value ofDME, as shown in Figure 10 This is attributed to the factthat the level of cool flame activity is strongly dependent

on the injected heat value of DME and is little influenced

10 degrees BTDC and 2 degress BTDC, respectively Themaximum HRR values decreased and the combustionduration became longer as the ignition timing was retarded,indicating that the rate of combustion was moderated This

is probably attributable to a drop in the in-cylinder ature commensurate with the increase in the cylindervolume due to the faster descent speed of the piston during

temper-Figure 9 Influence of Q DME on ignition timing (θ ign) and

ignition delay after occurrence of a cool flame (τ)

Figure 10 Influence of Q DME on maximum HRR of cool

flame

Figure 11 Influence of γ CH4 on HRR in Case 3

Figure 12 Influence of γ CH4 on HRR in Case 4

the combustion period, when ignition timing is retarded.

Moreover, since the plots are arranged nearly along the

same line under all of the conditions, this indicates that the

rapidity of combustion is strongly dependent on the ignition

timing

4.3 Light Emission Intensity and Light Absorbance of

HCHO

Figure 14 shows a typical example of the experimental

light emission and absorption results for HCHO From the

top, the figure shows the cylinder pressure P, HRR, light

emission intensity E HCHO at a wavelength of 395.2 nm, and

absorbance A HCHO at a wavelength of 293.1 nm In the

absorbance waveform, point “a” is where the absorbance

began to rise, point “b” is where the increase subsequently

started to become more moderate, and point “c” is where it

began to decline sharply At the onset of heat release fromthe cool flame (denoted as “Occurrence of Cool Flame” inthe figure), absorbance at the wavelength corresponding toHCHO began to rise (point a) In the interval betweenpoints “a” and “b”, where the absorbance waveform has asteep slope, the light emission intensity at the wavelengthcorresponding to HCHO shows a peak (denoted as “LightEmission” in the figure) This behavior is assumed to indi-cate rapid production of HCHO by the cool flame reactions

in the a-b interval Subsequently, HCHO was not produced

in the b-c interval because it was in the NTC region andabsorbance remained relatively flat It is also clear thatpoint “c” occurred near the time of ignition (denoted as

“Ignition” in the figure) These results are thought to reflectthe rapid production of HCHO by the cool flame and thenits decomposition owing to the temperature rise induced byignition The large increase seen in the light emission inten-sity after point “b” is attributed to the light emission of acontinuous spectrum resulting from the recombinationreaction of CO and O, and not to light emission fromHCHO This suggests that the recombination reaction of

Figure 13 Ignition timing vs maximum HRR and

com-bustion duration

Figure 14 Typical experimental results

Figure 15 Experimental results for Case 1 (Q CH4=0 J/cycleconstant)

Figure 16 Experimental results for Case 2 (Q DME=297 J/cycle constant)

HCCI COMBUSTION CHARACTERISTICS DURING OPERATION ON DME AND METHANE FUELS 651

CO and O produces a strong light emission at wavelengths

between 250 nm and 500 nm (Iijima and Shoji, 2007)

These features were observed for all of the fuel supply and

injected heat value conditions used in this study

Figures 15, 16, and 17 present the measured light emission

and absorption waveforms for the conditions of Cases 1

through 3, respectively The results in Figure 15 for Case 1

show that the ignition timing advanced and absorbance

increased (i in the figure) as the injected heat value of DME

was increased The results in Figure 16 for Case 2 indicate

that absorbance did not change appreciably in the interval

to ignition even though the injected heat value of methane

was varied The results in Figure 17 for Case 3 reveal that

the ignition timing was retarded and absorbance decreased

(d in the figure) as the methane share of the injected heat

value was increased These results suggest that the ignition

timing was advanced in proportion to the quantity of HCHO

produced

Absorbance A b at point “b”, as defined in Figure 18, was

examined in order to investigate the influence of HCHO

produced by the cool flame Figure 19 shows A b as a

function of the injected heat value of DME in Case 1 with

only DME as the test fuel, in Case 2 where the injected heat

value of methane was varied while keeping that of DME

constant at Q DME=240, 260, 278, and 297 J/cycle, and in

Case 3 in which the mixing ratios of DME and methane

were varied while keeping the total injected heat value Q in

constant at 357, 387, and 417 J/cycle, respectively The

figure shows that A b increased linearly as the injected heat

value of DME was increased This makes it clear that thequantity of HCHO produced by the cool flame was largelydependent on the injected heat value of DME and was notinfluenced by the injected heat value of methane Withinthe scope of the conditions used in this study, the quantity

of HCHO produced increased in proportion to the increase

in the injected heat value of DME Accordingly, the HCHObehavior as measured with absorption spectroscopy revea-led that cool flame behavior was substantially influenced

by the change in the injected heat value of DME

5 CONCLUSIONS

The experimental results measured under the conditionsused in this study for HCCI engine operation with blendedDME and methane fuels made the following points clear:(1) The interval from the appearance of the cool flame untilignition as well as the ignition timing were stronglydependent on the injected heat value of DME and werelittle influenced by that of methane Accordingly, theignition timing can be varied independently by thequantity of DME supplied, while adjusting the quantity

of methane supplied makes it possible to vary the loadindependently

(2) Under a condition where the total injected heat valuewas kept constant, varying the mixing ratios of DMEand methane did not suppress the rapidity of combus-tion This suggests that the rapidity of combustion isstrongly influenced by the ignition timing As the igni-tion timing was retarded, the maximum HRR decreas-

ed and the combustion duration became longer.(3) The results of in-cylinder spectroscopic measurementsshowed that the quantity of substance corresponding toHCHO produced during cool flame reactions was strong-

ly dependent on the amount of DME supplied and littleinfluenced by the amount of methane supplied

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Figure 17 Experimental results for Case 3 (Q in=417 J/cycle

constant)

Figure 18 Definition of light absorbance

Figure 19 Influence of Q DME on A b

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International Journal of Automotive Technology , Vol 10, No 6, pp 653 − 662 (2009)

653

MODEL-BASED CONTROL SYSTEM DESIGN IN A UREA-SCR

M DEVARAKONDA 1)* , G PARKER 1) , J H JOHNSON 1) and V STROTS 2) 1)ME-EM Department, Michigan Technological University, Houghton, MI 49931, USA

2)Advanced Aftertreatment Technologies, Navistar Inc, Melrose Park, IL 60160, USA

(Received 25 November 2008; Revised 1 February 2009) ABSTRACT− This paper presents preliminary control system simulation results in a urea-selective catalytic reduction (SCR) aftertreatment system based on NH 3 sensor feedback A four-state control-oriented lumped parameter model is used to analyze the controllability and observability properties of the urea-SCR plant A model-based estimator is designed via simulation and

a control system is developed with design based on a sliding mode control framework The control system based on NH 3

sensor feedback is analyzed via simulation by comparing it to a control system developed based on NO x sensor feedback Simulation results show that the NH 3 sensor-based strategy performs very similarly in comparison to a NO x sensor-based strategy The control system performance metrics for NO x index, urea index, urea usage, and NH 3 slip suggest that the NO x

sensor can be a potential alternative to a NO x sensor for urea-SCR control applications

KEY WORDS : Urea-SCR catalyst, Model-based estimation, Observer, Control system design, NH 3 sensor, Sliding mode control

1 INTRODUCTION

Urea-SCR catalysts are regarded as the leading NOx

after-treatment technology for compliance with the 2010 NOx

emission standards set by the US EPA (Environmental

Protection Agency) for heavy duty diesel engines SCR

catalysts have long been used for NOx reduction in

stationary applications such as power plants and industrial

reactors (Tronconi et al., 1996) In such applications, NH3

is introduced directly into the catalyst, which reduces the

NOx in the flue gases With regards to mobile sources,

urea-SCR catalysts are a proven technology in Europe for

meeting Euro III and Euro IV diesel engine NOx standards

(Schar et al., 2006) A urea solution spray is injected into

the exhaust gas upstream of the SCR catalyst At

suffici-ently high exhaust gas temperature, the urea droplets

evaporate and mix with the exhaust gas NH3 is formed as a

result of urea decomposition and HNCO hydrolysis

reac-tions in the exhaust pipe and in the SCR catalyst NOx is

reduced to N2 via several SCR reactions aided by the

catalyst

The urea-SCR catalyst must be actively controlled to

ensure high NOx reduction, low NH3 slip, and low urea

consumption NOx sensors are placed downstream of the

SCR catalyst to provide NOx feedback to the closed loop

control system in order to determine the urea injection rate

necessary to minimize NH3 slip and maximize NOx

conver-sion efficiency The state-of-the-art NOx sensors have

cross-sensitivity to NH3, which is a limitation for accurate NOx

feedback This limitation can be overcome to certain extentthrough a NOx sensor model with the objective of deter-mining the components of the NOx sensor signal Toimplement this strategy on a vehicle, for example, using anFTP (Federal Transient Procedure) cycle, an accurate NOx

sensor model is needed to reduce NOx and NH3, a topicwhich is not addressed in the literature

Another approach used to overcome this limitation is touse an NH3 sensor, developed by Delphi (Wang et al.,2007) and in the process of testing for SCR control appli-cations NH3 sensors, which are relatively new to auto-motive applications, have been researched from a materialsstandpoint in Europe in order to meet the NOx emissionregulations (Moos et al., 2002) Additionally, Wingbrant et

al. developed a MISiC-FET (Metal Insulated Silicon CarbideField Effect Transistor) for detection of NH3 in SCRsystems (Wingbrandt et al., 2005) The authors concludedthat the presence of water vapor was shown to have thelargest effect on the sensors at low levels Because the NOx

sensors are limited for closed loop SCR control applicationsbecause of the sensor’s cross-sensitivity towards NH3, NH3

sensors are being explored as an alternative (Wang, 2007).This gives the motivation for the study and analysis of the

NH3 sensor in simulation for possible SCR control cations This paper focuses on the development of a model-based estimator and control strategy based on NH3 sensorfeedback and compares its control system performance insimulation to a control strategy based on NOx sensor feed-back

appli-*Corresponding author. e-mail: mndevara@mtu.edu

The paper is organized as starting with a brief

descrip-tion of the four-state model with parameter identificadescrip-tion,

and validation is then presented followed by a linear systems

analysis of the model based on NH3 sensor feedback The

estimator design is discussed next, followed by the control

system design Sample simulation results analyzing the

control system performance based on NOx and NH3 sensor

models are discussed, and then a summary of conclusions

is presented

2 FOUR-STATE MODEL

Upadhyay et al proposed a three-state control-oriented

lumped parameter model that contains the gas phase

con-centrations of NOx and NH3 and ammonia storage as the

states (Upadhyay and van Nieuwstadt, 2006, 2002)

Incorpo-rating NO and NO2 individually into the model enables the

tracking of NO2 slip from the tailpipe, which is a major

concern for many environmental agencies, such as CARB

and MSHA, and a recent reference shows concern about

the increase of NO2 levels in the atmosphere while NO

levels decrease (Czerwinski, 2007) A higher order model

with detailed modeling methodology and assumptions is

discussed by Devarakonda et al. (Devarakonda et al.,

2008a) and is not discussed here for compactness Also, the

four-state model is selected for this work because it has

been shown that a strategy based on individual NO-NO2

concentrations performs better than the NOx based strategy

(Devarakonda et al., 2008b) The chemical reactions relevant

to the four-state model are shown here

The three main SCR reactions used in the model are the

‘fast’ SCR, the ‘standard’ SCR, and NO2 based SCR (‘slow’

SCR), respectively shown in Equations (1) to (3):

4NH3+2NO+2NO2 → 4N2+6H2O (1)

4NH3+4NO+O2 → 4N2+6H2O (2)

8NH3+6NO2 → 7N2+12H2O (3)

The authors in references (Krocher et al., 2006) and

(Devadas et al., 2006) report that the rate of reaction shown

in Equation (3) is comparable to the fast SCR reaction rate

and is greater than the standard SCR reaction rate on

Fe-zeolite catalysts at high temperatures Only oxidation of

NH3 to N2 is used in the model given by Equation (4)

4NH3+3O2 → 2N2+6H2O (4)

The authors in references (Tronconi et al., 2007) and

(Devadas et al., 2005) report 100% selectivity of NH3

oxidation towards N2 up to T=600oC, which is an

advant-age in Fe-zeolite catalysts The NO formed from NH3

oxidation can be considered as an intermediate species that

participates in the SCR reaction, and therefore, NH3

oxid-ation to NO can be neglected Fe-zeolites also exhibit

dis-tinct NO oxidation to NO2 capability as reported in (Devadas

et al., 2006) and (Devadas et al., 2005) This reaction is

also neglected in the model because NO2 is reduced by NH3

through the SCR reactions, even when produced by the NO

oxidation reaction NH3 adsorption and desorption reactionsare included in the models as shown in Equation (5) andEquation (6)

NH3+S → NH3 (5)

NH3 → NH3+S (6)For detailed information on the reaction rates included inthe four-state model, the reader is referred to (Devarakonda,2008a)

2.1 Assumptions and Equations

A high level illustration of a urea-SCR aftertreatmentsystem is shown in Figure 1 As the exhaust gas movesthrough the SCR catalyst, molecules of NO, NO2, and NH3

are transported to the stagnant thin layer at the surface ofthe monolith wall and then take part in the catalytic reactions.Reaction products are desorbed back into the thin layer,then are transported into the bulk flow, and to the monolithexit The major assumptions in the four-state model (inaddition to the assumptions listed in Devarakonda et al.(2008a)) are:

(1) Mass transfer is neglected in the model, meaning thatthe chemical kinetics in the catalyst are reaction-con-trolled

(2) Surface phase concentrations of the species are neglected.(3) Reaction rates are defined as a function of ammoniastorage and gas phase concentrations of NO and NO2.The four-state model contains the gas phase concent-rations of NO, NO2, and NH3 and ammonia storage as thestates, shown in Equation (7) All of the six reactions consi-dered in the higher order model discussed in Devarakonda(2008b) are considered in the four-state model

(7)The reaction rate constants k i are defined using theArrhenius expression shown in Equation (8)

(i=1 6) (8)Here, A i are the pre-exponential factors, E i are theactivation energies of the reactions, and R is the universalgas constant A total of 13 parameters need to be identified

in this reduced order model, which includes the

Figure 1 High level illustration of the urea-SCR ment system

aftertreat-MODEL-BASED CONTROL SYSTEM DESIGN IN A UREA-SCR AFTERTREATMENT SYSTEM 655

ential factors and activation energies of the six reactions

considered in the model and the total NH3 adsorption capacity

2.2 Parameter Identification and Model Validation

Experiments were conducted on a Navistar I6 7.6-L engine

The experimental setup with a Horiba emission bench and

an MKS FTIR analyzer at locations denoted as a and b is

shown in Figure 2

Tests were designed to facilitate parameter identification

and validate the model The urea flow rate was manually

set to cover a wide range of NH3/NOx ratios in the test The

experiments were conducted at various steady-state engine

operating points The step changes from point to point were

used to capture the transient effects of temperature and

mass flow rates on catalyst dynamics The parameter

iden-tification exercise was formulated as an optimization

pro-blem and Matlab’s simplex method-based optimization

function fminsearch is used to identify the parameters

while minimizing the cost function in the species

concent-rations The optimization problem is defined as:

Find the model parameters (x i) where x i are the

pre-exponential factors and activation energies of the reactions

which minimize the cost function in Equation (9)

i=NO, NO2, NH3 (9)

C i,s and C i,t in Equation (9) refer to the simulated and test

concentrations of the species The reaction rate parameters

identified (calibrated) for the four-state model are tabulated

in Table 1

The total NH3 adsorption capacity, Ω, is identified as 157

moles of NH3 per m3 of exhaust gas volume Figure 3

shows the validation of the four-state model based on the

test data in NO, NO2, and NH3 concentrations

A detailed analysis demonstrating the adequacy of

re-duced order models is shown in Devarakonda, 2008a The

adequacy is demonstrated based on the RMS error in the

concentrations of species and NOx and NH3 conversion

efficiencies

3 SIMULATION-BASED ANALYSIS OF NH 3

SENSORS

A high level illustration of the control strategy based on the

four-state model is shown in Figure 4 The estimator is

based on the NH3 concentration from a NH3 sensor

down-stream of SCR and estimates the concentrations of the four

states required to design the control strategy

A detailed observability analysis is done based on NH3

feedback from the NH3 sensor To design a model-basedestimator based on the NH3 sensor, the linear system must

Figure 2 Schematic of aftertreatment setup used to conduct

tests for parameter identification exercise

Table 1 Reaction rate parameters identified for the state model

four-Reaction A E (kJ/mol)Fast SCR 4.50E14 100Standard SCR 3.50E5 75

m 3

mol sec – -

m 3

mol sec – - 1 sec -

m 3

mol sec – - 1 sec -

Figure 3 Four-state model validation using data from thetests on the engine-aftertreatment set-up shown in Figure 2

Figure 4 Model-based control system with a state mator and a control law based on the four-state model

Here, u is the input vector, x represents the dynamic state

vector, and c represents the output matrix The elements of

the A matrix remain the same as shown in Appendix A

The observability matrix O is then formulated using the

expression shown in Equation (11)

(11)resulting in

(12)

The details of the observability matrix are shown in

Appendix A The rank of the observability matrix is then

determined and is found to be equal to the rank of the

linearized plant, thus indicating that the system is

observ-able The observability matrix might lose rank (full rank=

4) at certain conditions, and the system can become

unobservable There is one such instance when this can

happen theoretically, but it is not true physically When A 43

=0, the observability matrix loses its rank (rank=2)

Physi-cally, this is not possible, as the imposed condition results

in a relation that should satisfy

(13)which ends up in a relation shown in Equation (14)

(14)which can never happen as θ 0 cannot be greater than 1 The

controllability matrix is shown in Appendix A and the

matrix remains at its full rank at all conditions Thus, the

linear system formulated based on NH3 sensor feedback isobservable and controllable This indicates that, based on

NH3 measurement downstream of the SCR catalyst, amodel-based estimator can be designed to estimate theunmeasurable state θ in the catalyst

3.2 Model Based Estimator Design

A linear estimator of the form shown in Equation (15) isproposed

(15)where

denotes the estimated states,

f indicates the nonlinear reduced order model given inEquation (7), L is the estimated gain vector, and CNH3 is themeasured NH3 sensor reading

In this work, the NH3 sensor reading is assumed to be the

NH3 concentration measured by FTIR analyzer The value

of L must be chosen such that the estimator is stable Sincethe linear portion of the nonlinear model is stable, this ispossible The estimator gains are tuned in the simulationand are obtained as L=[−5; −5; −1; −5]T With these gains,the error in the true and estimated states are found Thepercentage absolute error between the true and estimatedstates falls to 0.03% within 1.2 seconds of simulation time.This indicates that the estimator gains yield a fasterconvergence to the true states

3.3 Model-Based Control System DesignThe control objective is to minimize the NO, NO2, and NH3

slip from the SCR catalyst A modified conversion ency (based on the definition in Upadhyay and vanNieuwstadt (2006) in reference to NO, NO2, and NH3) isdefined in Equation (16)

effici-(16)This definition is used in defining the response goal,which can be expressed as where and

is a linear combination of the four-state model states

C NO, C NO2, and C NH3 shown in Equation (17)

(17)

is the sum of the desired NO, NO2, and NH3 rations coming out of the catalyst, which is set to zero inthis work Substituting the model equations into the responsegoal, the dynamic portion of the control law is obtained asshown in Equation (18)

-x· est = f x ( est , u, t )+L C ( NH 3 – C NH 3 ,est )

x est = C [ NO,est C NO 2 ,est θ est C NH 3 ,est ] T

η T =CNO,in+CNO2 ,in – C NO,out – C NO 2 ,out – λC NH 3 ,out

p=C NO +C NO2+λCH 3

P des

C NH 3 ,in,dyn =C NH 3 ,est +1λ - C ( NO,est + C NH 3 ,est – C NO,in – C NO 2 ,in )

+ 1Q k ( 5 Ω 1 θ ( – est )C NH 3 ,est − k 6 Ωθ est ) + 1λQ - p· des +2Ωθ est k 1 C NO,est C NO2,est

+Ωθ est k 2 C NO,est C O 2 +Ωθ est k 3 C NO 2 ,est

MODEL-BASED CONTROL SYSTEM DESIGN IN A UREA-SCR AFTERTREATMENT SYSTEM 657

The NO and NO2 concentrations (CNO,in, C NO2,in) can be

obtained using a NOx sensor or an engine NOx emissions

model in conjunction with models for aftertreatment

com-ponents upstream of the SCR catalyst, such as DOC and/or

CPF The models should incorporate reversible NO-NO2

oxidation in both DOC and CPF as well as the NO2

reduc-tion by PM

The complete control law is created by appending a

correction term that penalizes deviations from the objective

of , as shown in Equation (19)

(19)Here, Γ is a control variable that can be tuned in the

simulation to meet the control objective Based on the sign

of , the sign of the sgn function changes The sgn

function is defined as:

(20)Ensuring stability in the presence of the model, mea-

surement and disturbance uncertainties place constraints on

the design parameter These constraints are developed

using Lyapunovs’ direct method illustrated below A

candidate Lyapunov function, as shown in Equation (21), is

created

(21)

If <0 for the four-state model dynamics, then the

closed loop system is asymptotically stable

(22)Thus, Γ>0 guarantees closed loop stability

4 MODEL REDUCTION FOR REAL TIME

IMPLEMENTATION

The time constants associated with the concentrations in

the four-state model are on the order of micro-seconds, and

hence the four-state model cannot be used for control

strategy implementation on a vehicle Therefore, the

four-state model is reduced to a one-four-state model with θ as the

only state in the model, with the concentrations of NO,

NO2, and NH3 species calculated as steady-state expressions

Setting the time derivatives of and shown in

Equation (7) to zero, a quadratic equation in CNO2 is

(25)For control system performance analysis and sensorrelated studies, the experimental setup shown in Figure 5 isused In accordance with the setup, two catalyst models areused in series

NH3 storage is the only state estimated in both models,and the concentrations of the species are calculated assteady-state expressions shown in Equations (23)~(25).Based on the corresponding sensor signals (NOx sensor or

NH3 sensor), model-based estimators are designed based

on the plant and their respective sensor models, which areexplained in the next section

5 SENSOR MODELS AND EXPERIMENTAL VALIDATION

The NOx sensor model is developed based on the NOx

sensor data and the species concentrations from the FTIRdownstream of the second SCR catalyst (SCR2 in Figure5) The NOx sensor signal with cross-sensitivity towards

NH3 can be represented as a function of NO, NO2, and NH3

concentrations, as shown in Equation (26)

(26)where S is the NOx sensor signal in ppm, and A 1, A 2, and

A 3(α) are the coefficients to be obtained from the NOx

sensor model The variable α is known as the NormalizedStoichiometric Ratio (NSR) and is defined as the concent-ration of NH3 in ppm to the concentration of NOx in ppm inthe exhaust gas, as given by Equation (27)

(27)

NH3 concentration at the inlet of the catalyst is notmeasured and is calculated from the urea injection flowrate as shown in Equation (28) It is based on the assump-tion that one mole of urea forms two moles of NH3 and isavailable for NOx conversion in the catalyst

(28)Here, CNH3 is the concentration of NH3 in ppm is the

mass flow rate of urea in kg/sec, and MW urea is the

mole-cular weight of urea in gm/gm-mole (MW urea=60

gm/gm-mole) MW exh is the molecular weight of exhaust gas in gm/

gm-mole (MW exh=28.8 gm/gm-mole)

For experimental validation, C NO, CNO2, and CNH3 are the

concentrations obtained from the FTIR analyzer at the SCR

2 outlet (Γ) A 1 and A 2 are obtained when no urea was

injected in the aftertreatment system The coefficients are

determined as A 1=1.0 and A 2=0.95 with a mean of 1 ppm

and a standard deviation of 2 ppm The coefficient A3 is

determined as a function of a for various test cases and is

shown in Figure 6 The functional relationship between A 3

and α is used in the NOx sensor model The sensor model is

validated using two different sets of test data Exhaust gas

temperature and α are also shown on the figures to illustrate

the effect of these variables on the NOx sensor signal

Figure 7 shows the validation of the NOx sensor model

using the data from Test 2 as input The details of the test

are shown in Appendix B

The NH3 sensor is assumed not to have a

cross-sensi-tivity towards NO and NO2 species Here, the NH3

concent-ration from the FTIR analyzer is assumed to be the NH3

sensor signal The NOx sensor model given in Equation

(26) is slightly modified to obtain the NH3 sensor model

and is shown in Equation (29)

(29)For further details about the NH3 sensor, the reader is referred

to (Devarakonda, 2008c) and (Devarakonda et al., 2008d)

6 CONTROL SYSTEM PERFORMANCE BASED

ON NO x SENSOR AND NH 3 SENSOR MODELS

An estimator is designed based on the two catalyst model

to compare the downstream NOx concentrations from the

model-based estimator and the test data As the designed

estimator is intended for real time implementation, the state model is used A linear NH3 storage estimator based

one-on NOx sensor feedback is shown in Equation (30)

A linear NH3 storage estimator based on NH3 sensorfeedback is shown in Equation (31)

Figure 6 Coefficient of NH3 component in the NOx sensor

signal as a function of α using Test 2 data as input Figure 7 Experimental validation of NOusing Test 2 data as input. x sensor model

Figure 8 Test and estimated NOx sensor signal comparisonusing Test 2 data as input

MODEL-BASED CONTROL SYSTEM DESIGN IN A UREA-SCR AFTERTREATMENT SYSTEM 659

CNH3,meas is the measured NH3 from the NH3 sensor (FTIR

concentration) and CNH3,est is the estimated NH3

concent-ration calculated from the estimator with the NH3 sensor

model shown in Equation (29) is the scalar estimator

gain tuned in simulation The estimator with the NH3

sensor model is tested in simulation and the concentrations

are compared using the test data discussed in Appendix B

as shown in Figure 9 The tuned estimator gain is 1E-3

The closed loop control strategies with their respective

model-based estimators and sensor models are compared

The control system based on the NOx sensor model is

hereby denoted as ‘NOx sensor’ and the control system

based on the NH3 sensor model is hereby termed as ‘NH3

sensor’ The closed loop control strategies are compared

based on the NOx index, urea index, NH3 index, and urea

usage All indices are calculated based on a lumped

quan-tity NOx rather than individual NO and NO2 concentrations

The NOx index is defined as an NO2 equivalent, as shown

in Equation (32)

(32)

Here, is defined based on the US EPA’s approach

of defining NOx regulation (x=2) where the total NOx at theinlet and outlet of the catalyst is calculated as an equivalent

of NO2 Also, such an approach has been suggested inCzerwinski, 2007 Hence, is calculated from thetotal concentration of NOx in ppm as a function of themolecular weight of NO2 and is defined in Equation (33)

(33)

is calculated in the same manner and is defined inEquation (34)

(34)For this analysis, the urea index is defined as a function

of the overall NOx quantity reacted and is shown inEquation (35) As the urea index is defined in NOx, 1:1stoichiometry between NOx and NH3 is assumed

(35) The total slip from the catalysts is calculated from bothstrategies using the equation shown in Equation (36)

(36)Here, MWNH3 is the molecular weight of NH3 (MWNH3=

17 grams/gm-mole) For both the strategies, λ is set to 0.1,

Γ is set to 0.06, and is set to 0.0 The performancecomparison of both the strategies in the performancemetrics mentioned is shown in Table 2 From Table 2, itcan be observed that the control strategy based on the NOxsensor model shows a better performance than the control

Figure 9 Test and estimated NH3 sensor signal comparison

using Test 2 as input

Table 1 Performance comparison in various metrics using NOx sensor- and NH3 sensor-based control strategies

Strategy NOx Index Urea Index Urea Total NH3 Slip

gm of urea injected -

Table 2 Performance comparison in various metrics using the control strategies and the test data

Strategy NOx Index Urea Index Urea Total NH3 Slip

NOx sensor based 0.42 0.27 0.99 0.0289

NH3 sensor based 0.40 0.26 1.04 0.0315Test data 0.43 0.28 1.01 0.0162

gm of NO x reacted

gm of urea injected gm of urea injectedgm of urea reacted

strategy based on the NH3 sensor model in all of the

performance metrics Though the percent improvement is

approximately 5% in NOx index, urea index, and urea

usage, the control strategy based on the NOx sensor model

controls the NH3 slip out of the SCR2 better than the NH3

sensor

Table 3 shows the comparison in NOx index, urea index,

urea usage, and NH3 slip between the control strategies and

the test data The NOx sensor-based control strategy uses

less urea while obtaining an approximately similar NOx

index and urea index, which makes it a better candidate

than the NH3 sensor-based control strategy whose indices

are slightly less Both of the sensor-based control strategies

exhibit higher NH3 slip than the test data This might be

due to linear approximation of the dependency of α on the

NH3 concentration in the NOx sensor signal An interesting

task for the future will be to study whether the NH3

concentration in the NOx sensor signal is dependent on á in

a polynomial formulation

The concentrations of NO, NO2, and NH3 species from

both sensor-based control strategies are compared to the

concentrations recorded by FTIR at the SCR2 in Figure 10

Both strategies show similar trends in NO, NO2, and

NH3 concentrations except at high temperatures,

approxi-mately between 200 min<time<250 min, when an increase

in exhaust gas temperatures results in slight NH3 slip and

thus a discrepancy in NO output Figure 11 shows a

com-parison in urea injection rate from the closed loop

cont-rollers and from the test data The estimated NH3 storage

curves from both control strategies are also shown in the

figure

From Figures 10 and 11, it is observed that though the

state-of-the-art NOx sensor has cross-sensitivity towards

NH3, the control strategy based on a NOx sensor model

shows better catalyst performance than the strategy based

on an assumed NH3 sensor model One important

obser-vation from this simulation-based analysis of the NH3 sensor

is that the sensor can be used for model-based control bymeasuring NH3 at SCR out Linear systems theory showedthat the system is observable and controllable at all prac-tical operating conditions and can used for model-basedSCR control applications as a potential alternative to NOx

sensors

7 RESULTS AND DISCUSSION

State-of-the-art NOx sensors are cross-sensitive to NH3 andare a drawback for real time NOx control if the cross-sensitivity is not compensated A NOx sensor model isdeveloped based on the test data and is tested in simulationusing a two catalyst model A single state is used in the twocatalyst model and an estimator is developed in conjunc-tion with the NOx sensor model NH3 sensors (which do notexhibit cross-sensitivity according to the literature) areanalyzed in simulation and an estimator is developed based

on the sensor model Though the two catalyst model is notperfectly validated in simulation, it is used to study thecontrol strategy performance based on the sensor models.The control strategies based on the two sensor models arecompared using the performance metrics in NOx index,urea index, NH3 slip, and urea usage The control perfor-mance analysis showed that the strategy based on a NOx

sensor model performed slightly better than the NH3 based strategy and is close to the performance metricscalculated based on experimental data One important out-come of the simulation-based analysis of the NH3 sensor isthat, in the absence of an NOx sensor model, model-basedSCR control systems can be developed in conjunction with

sensor-an NH3 sensor and can be implemented in real time

8 CONCLUSION

An NOx sensor model based on experimental data isdeveloped and validated using various sets of test data Thesensor model is then tested in simulation using a one-state

Figure 10 Comparison of NO, NO2, and NH3 species

concentrations from the control strategies based on sensor

models and the test data

Figure 11 Comparison of urea injection rates and

estimat-ed NH3 storage curves from the control strategies based onsensor models

MODEL-BASED CONTROL SYSTEM DESIGN IN A UREA-SCR AFTERTREATMENT SYSTEM 661

model by considering the two catalysts in series An NH3

sensor assuming no cross-sensitivity towards any other

species is analyzed using linear systems theory for

observ-ability and controllobserv-ability Sensor models and model-based

estimators based on the two catalyst models are developed

and tuned in simulation The control strategies based on the

sensor models are then compared based on the

mance metrics The outcome of the control systems

perfor-mance analysis is that the control strategy in conjunction

with the NOx sensor model performs slightly better than the

NH3 sensor model One important conclusion from the

analysis is that the NH3 sensor model, from its

simulation-based performance, can be regarded as a potential

candi-date for SCR control applications in the absence of an

accurate NOx sensor model An interesting observation

from the analysis is that the estimated NH3 storage and urea

injection flow rate from the strategy based on the NH3

sensor match within 2~5% of those obtained from a strategy

based on the NOx sensor

ACKNOWLEDGEMENT−The authors would like to thank

Navistar Inc for their financial support throughout the project.

REFERENCES

Czerwsinki, J., Peterman, J., Comte, P., Lemaire, J and

Mayer, A (2007) Diesel NO/NO2/NOx emissions – New

experiences and challenges SAE Paper No

2007-01-0321

Devadas, M., Krocher, O and Wokaun, A (2005)

Cata-lytic investigation of Fe-ZSM5 in the selective cataCata-lytic

reduction of NOx with NH3 Reaction Kinetics and

Catalysis Letters, 86, 347−354

Devadas, M., Krocher, O., Elsener, M., Wokaun, A., Soger,

N., Pfeifer, M., Demel, Y and Mussmann, L (2006)

Influence of NO2 on the selective catalytic reduction of

NO with NH3 over Fe-ZSM5 Applied Catalysis B:

Environmental, 67, 187−196

Devarakonda, M N., (2008c) Dynamic Modeling,

Simu-lation and Development of Model Based Control

Strate-gies in a Urea-SCR Aftertreatment System for Heavy

Duty Diesel Engines Ph.D Dissertation Michigan Tech

University

Devarakonda, M., Parker, G., Johnson, J H and Strots, V

(2008d) Simulation based control system analysis of a

urea SCR aftertreatment system based on NH3 sensor

feedback Cross-cut Lean Exhaust Emissions Reduction

Simullation (CLEERS) Workshop www.cleers.org.

Devarakonda, M., Parker, G., Johnson, J H., Strots, V and

Santhanam, S (2008a) Adequacy of reduced order

models for model based control in a urea-SCR

after-treatment system SAE Paper No 2008-01-0617 (Also

accepted as a special publication in SP-2155)

Devarakonda, M., Parker, G., Johnson, J H., Strots, V and

Santhanam, S (2008b) Model based estimation and

control strategy development for urea-SCR aftertreatment

system Int J Fuels and Lubricants 1, 1, 646−661.Krocher, O., Devadas, M., Elsener, M., Wokaun, A., Soger,N., Pfeifer, M., Demel, Y and Mussmann, L (2006).Investigation of the selective catalytic reduction of NO

by NH3 on Fe-ZSM5 monolith catalysts Applied Catalysis B: Environmental, 66, 208−216

Moss, R., Muller, R., Plog, C., Knezevic, A., Leye, H.,Irion, E., Braun, T., Marquardt, K and Binder, K (2002).Selective ammonia exhaust gas sensor for automotiveapplications Sensors and Actuators B, 83, 181−189.Schar, C., Onder, C and Geering, H (2006) Control of anSCR catalytic converter system for heavy duty dieselapplication IEEE Trans Control Systems Technology,

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Appendix A: Linear Systems Analysis for NH3

Here, Sensor Feedback

The elements of the A matrix linearized about the brium point (C NO,0, C NO2,0, θ 0, C NH3,0) are shown in Equation(37)

The observability matrix based on NH3 sensor feedback is

shown here in Equation (38) to explain the elements of the

matrix

(38)Here,

(39)

A Controllability Matrix

The controllability matrix is shown here in Equation (40) to

explain the elements of the matrix

(40)

(41)

Appendix B: Input Data for Test 2

The steady state conditions used in test 2 are shown inTable 4 The exhaust temperature, urea injection flow rate,engine variables such as speed and load, mass flow rate atvarious conditions are shown in Figure 12 Theconcentrations of species NO, NO2 and NH3 at the inlet ofthe catalyst are shown in Figure 13

sec -

Figure 12 Input profiles of exhaust gas temperature, ureainjection flow rate, speed, load, and mass flow rate duringTest 2

Figure 13 Concentrations of NO, NO2, and NH3 species atthe inlet of the SCR catalyst during Test 2

International Journal of Automotive Technology , Vol 10, No 6, pp 663 − 668 (2009)

2)School of Mechanical and Automotive Engineering, Keimyung University, Daegu 704-701, Korea

3)The Center for Automotive Parts Technology, Keimyung University, Daegu 704-701, Korea

(Received 16 September 2008; Revised 1 June 2009) ABSTRACT− In an earlier study, the current authors showed that an unsteady-state lifted flame generated by an equivalence ratio conversion system for a given fuel, was similar to a steady-state lifted flame in terms of the change characteristics from

a premixed flame to a critical flame and then to a triple flame with a diffusion flame positioned in the middle according to the concentration difference Therefore, this study used an OH-PLIF method to investigate the characteristics of a steady-state lifted flame and an unsteady-state lifted flame created under conditions identical to the flames in the preceding study PLIF (Planar laser induced fluorescence) is practically effective for visualizing the concentration fields within a flame The resulting OH-radical measurements showed that an unsteady-state lifted flame created under the specific conditions used in this study showed similar tendencies in terms of OH-radical distribution, fluorescence intensity, and liftoff height, to a steady-state lifted flame, thereby confirming that the behavior of an unsteady-state lifted flame can be effectively predicted based on the behavior

of a steady-state lifted flame.

KEY WORDS : Lifted flame, Premixed flame, Triple flame, Unsteady flame, OH-PLIF

1 INTRODUCTION

A lifted flame provides important information for a

turbulent nonpremixed flame model The characteristics of

a lifted flame, such as the liftoff height and flame shape,

change depending on the flow velocity of the fuel and the

equivalence ratio Thus, various studies have been carried

out to understand the stabilization mechanism of a lifted

flame The most representative stabilization model is a

premixed combustion model Because the fuel and air are

well mixed upstream of the leading edge of a flame and the

region of the leading edge of a flame becomes a premixed

flame, the premixed combustion model predicts that the

leading edge is stabilized in the region where the burning

velocity at that edge coincides with the velocity of the flow

supply Recently, a triple flame (Lee and Seo, 2005) model

has also been studied as an important feature of lifted flame

stabilization (Kioni et al., 1993, 1999, Azzoni et al., 1999)

In addition, Dold (1989) suggested that the mixture

frac-tion is an important clue when determining the structure

and propagation speed of a triple flame

A combustion diagnostic and measurement method

using a laser (Park et al., 2002) is primarily utilized to

obtain information about the velocity field and

concent-ration field in a combustion field and also the lifted flame

and triple flame characteristics Schefer et al. (1994)

studied the concentration of chemical species and theirtemperature distribution, and noted that flame stability isgoverned by the local stoichiometry and turbulence charac-teristics through the PLIF method Mu iz and Mungal(1997) studied flame propagation speed using the liftoffheight and particle image velocimetry (PIV) as the jet exitvelocity and coflow velocity varied, while supplyingmethane and ethylene as fuel to the nozzle and air with acoflow They showed that the mean liftoff height of theflame increases when the jet exit velocity and coflowvelocity increase, and that the flame stabilizes itself whenthe local gas velocity is close to the premixed laminarflame speed and does not exceed 3S L Schefer and Goix(1998) extended Muñiz and Mungal (1997)’s experimentand carried out PIV and OH-PLIF measurements for aturbulent lifted flame over a range of Reynolds numbersfrom 7,000 to 19,500 Consequently, they found that themean axial velocity at the stabilization point was about fivetimes below the laminar burning velocity at the lowestReynolds number; however it was nearly 20% higher thanthe laminar burning velocity when the Reynolds numberincreased Pressing et al. (1998) studied the characteristics

of the liftoff of a triple flame experimentally and tically, while adjusting the flow velocity and the dilutedfuel and lean fuel concentration based on supplying dilutedfuel, lean fuel, and air using a three-stream coflow nozzle.Kioni et al. (1999) studied the velocity field inside a flamebased on the PIV and OH radical distribution in a laminar

analy-n

ó

*Corresponding author. e-mail: suhjun@knu.ac.kr

triple flame using PLIF From simultaneous measurements

of the PIV, CH-PLIF, and OH-PLIF of lifted flames (Kim

et al., 2006), Watson et al. (1999) discovered that a triple

flame stabilizes in the region where the incoming gas speed

is low and close to the laminar burning velocity Jang et al.

(2005) and Kim and Jang (2005) studied the behavioral

characteristics of a premixed flame, critical flame, and

triple flame as function of the concentration difference

using a lifted flame stabilization model Moreover, they

installed a direct sampling probe inside the combustion

field, measured the local concentration, and compared the

characteristics of each flame However, they did not

measure the radical generated in the combustion process

using an optical method Thus, in a previous study (Jun et

al., 2008), the current authors investigated the behavioral

characteristics of an unsteady-state lifted flame that was

varied from a premixed flame to a triple flame based on

instantaneous change of the equivalence ratio using an

equivalence ratio conversion system, and compared the

results with those for a steady-state lifted flame While

direct photographs showed similarity between the

behavi-oral characteristics of an unsteady-state lifted flame and a

steady-state lifted flame, an analysis of the major reactions

inside the flame was not conducted Therefore, to confirm

the concentration characteristics of the major reactions

inside the flames, this study used an OH-PLIF method to

investigate the characteristics of the concentration fields of

a steady-state lifted flame and an unsteady-state lifted

flame

2 EXPERIMENTAL SETUP AND PROCEDURE

2.1 Experimental Setup

The experimental equipment was the same as that used in

our preceding study (Jun et al., 2008) except for the

addi-tion of an Nd:YAG laser, a Dye laser, sheet beam optics, a

reflector, and a narrowband pass filter Commercial LPG

was used as the fuel, and high purity air (99.99% purity)

comprised of 79% nitrogen and 21% oxygen was used as

the oxidant To ensure the gases were supplied at a constant

pressure, each gas was passed through a regulator, and the

flow rate was controlled by flow meters (Matheson 602,

604) that were adjusted to a precise flow rate using a

bubble meter After the flow meter, the gases were passed

through a mixing chamber before being supplied to the slot

burner The mixing chamber was cylindrical in shape, 160

mm in length, 314 ml in volume, and had an inside

diameter of 50 mm Thus, the fuel and oxidant, set at a

certain equivalence ratio, flowed into the mixing chamber

and became homogeneous as a result of the swirl flow

inside

The slot burner, designed to alter the gas concentration,

included 4-four slots with a 10 mm width inside, 40 mm

width, and 700 mm length, which were made of a 10

mm-thick acrylic plate and 0.5 mm-mm-thick stainless steel plate

combined with bolts Inside the slot burner, a vinyl pipe (5

mm diameter and 200 mm length) and ceramic honeycomb(1.5 mm width, 1.5 mm length, and 250 mm height) wereinstalled to ensure uniform velocity for the flow field Thepremixture was supplied to the two slots in the center,while ambient nitrogen was supplied at an ambient flow tothe other two slots at the edge The nitrogen increased theexit velocity of the mixture to prevent any inflow of anexternal oxidant as well as disruption from an outside flow.After passing through the ceramic honeycomb, the pre-mixture entered a contraction nozzle, and a flame wasgenerated due to the concentration difference The exit ofthe contraction nozzle was 21 mm wide, 30 mm long, andmade using a plaster mold based on a 3rd order polynomialfitting of the inside shape used in the previous study con-ducted by Morel (1975); its rectangular shape minimizesthe three dimensional influence on a flame as pictures aretaken

The equivalence ratio conversion system consisted of asolenoid valve to change the equivalence ratio of each slot

of the slot burner from the condition for the generation of apremixed flame to that of a triple flame, hardware (com-puter and PCI-MIO-16EI board) and software (LabVIEW)

In the slot burner, the premixture was supplied to the 2 slots

in the center, while ambient nitrogen was supplied to theother two slots at the edges In this study, the focus was tomeasure the OH radicals in a steady-state lifted flame andunsteady-state lifted flame, as in our preceding study (Jun

et al., 2008)

Figure 1 shows the experimental setup of the OH-PLIF Alaser beam with a 532 nm wavelength was generated by anNd:YAG laser (Lee and Nishido, 2008), then passedthrough a dye laser to form a beam with a 566 nm wave-length, and finally passed through a UVT (UV Tracker)containing a double crystal The result was a beam with a

283 nm wavelength that is appropriate for measuring OHradicals Rodamine 590 was used as the dye for the dyelaser to create the excitation wavelength The laser beamchanged into a sheet beam after passing through the optics;the sheet beam then passed through the upper part of thecontraction nozzle of the slot burner The laser beam wasemitted at the moment the flame was changed by the

Figure 1 Schematic diagram of experimental setup

OH-RADICAL BEHAVIOR OF UNSTEADY LIFTED FLAME BASED ON INSTANTANEOUS CHANGE 665

equivalence ratio conversion system; moreover, to take a

picture, the laser and operation signal of the ICCD camera

were synchronized and triggered by a signal emitted from

the conversion system The resolution of the ICCD camera

was 1,024×1,024 pixels, and the exposure time and gain

were set to 50 ns and 250, respectively A narrow band pass

filter (WG-305) and UG-11 filter were also included for the

OH-radical measurement

2.2 Experimental Procedure

The mixture and ambient flow supplied at a flow velocity

of 1.1m/s generated a lifted flame without blowing out or

flashing back to the exit of the burner For the steady-state

lifted flame, the fluorescence intensity of the OH radicals

was measured under the conditions created by the

equi-valence ratio (φ R) in the center right slot in the slot burner,

which was fixed at 1.2, and the equivalence ratio (φ L)

created using the center left side slot, changed stepwise

from 1.2 to 0.4 Meanwhile, for the unsteady-state lifted

flame, the fluorescence intensity of the OH radicals was

measured under the φ R conditions fixed at 1.2, and φ L

instantly changed from 1.2 to 0.4 As previously reported

(Jun et al., 2008), the unsteady-state lifted flame stayed for

1.6 seconds, which was 1.2 to 2.8 seconds after activating

the solenoid valves, and then turned into a steady-state

lifted flame Therefore, because the concentration changed

with the passage of time, the suggested data are expressed

according to time

3 RESULTS AND DISCUSSION

During the combustion reaction, the OH radicals are

generated by the reaction of hydrogen and oxygen and then

destroyed by the combustion reaction with CO Thus, a

thick distribution of OH radicals appeared in the region of

the lean premixed flame that contain a significant amount

of hydrogen and the diffusion flame Furthermore, in the

region of the diffusion flame, the distribution of OH

radicals increased when they approached the slightly lean

premixed flame, yet almost disappeared when approaching

the rich premixed flame

Figure 2 shows the shape of the OH-radical distribution

in the steady-state lifted flames, where φ L was 1.2, 1.0, 0.8,

0.7, 0.5, and 0.4, while φ R was 1.2 The black arrow at the

bottom of the photos identifies the slot burner nozzle exit

As previously reported (Jun et al., 2008), when changing

the concentration difference, the steady-state lifted flame

was altered from a premixed flame to a critical flame, and

then to a triple flame with a diffusion trailing flame in the

middle Thus, the steady-state lifted flames created under

the specific conditions in this study were classified into

three groups according to the distribution shape and

fluore-scence intensity of the OH radicals: φ L=1.2-1.0, φ L

=1.0-0.8, and φ L=0.7-0.4, where φ L=1.2-1.0 represents the

pre-mixed flame region, φ L=0.7-0.4 represents the triple flame

region, and φ L=1.0-0.8 represents the critical flame region

For the steady-state lifted flame at φ R=1.2 and φ L=1.2, therewas a thick distribution of OH radicals around the leadingedge of the flame, while the distribution downstream in theflame was thin As previously reported (Jun et al., 2008),the flame at φ R=1.2 and φ L=1.2 was a premixed flame withthe same equivalence ratio and was very round and showed

a semi-spherical shape The shape formed by the OHradicals was similar to the flame shape taken by the directphotograph As φ L decreased, the OH-radical distributionfor the flames at φ L=0.8, 0.7, 0.5, and 0.4 was quite differ-ent from that at φ L=1.2 A decrease in φ L generated a tripleflame due to the concentration difference of the mixturesupplied to the center slots in the slot burner A triple flame

is generated because of a concentration difference when thecomposition of the fuel and oxidant from the two slots aredifferent from each other When a laminar flame is formed

by a partial premixed mixture, a rich mixture with morefuel than the stoichiometric equivalence ratio is formed inthe region near the leading edge; meanwhile, a lean mix-ture with less fuel than the stoichiometric equivalence ratio

is formed in the other region As the residual fuel spreadsfrom the rich premixed flame and the oxidant spreads fromthe lean premixed flame, a diffusion flame with a stoichi-ometric equivalence ratio is then generated at the center,the key feature of a triple flame These three branches werepreviously confirmed based on a direct photograph of atriple flame (Jun et al., 2008)

From the OH-radical distribution in the triple flame at

φ L=0.7, 0.5, and 0.4, shown in Figure 2, the fluorescenceintensity was high around the leading edge, at the left side

of the slot burner, and around the middle As such, a lean

Figure 2 OH radical of steady state lifted flame (φ R=1.2)

premixed flame was formed around the left side of the slot

burner by the lean mixture, while a diffusion flame was

formed in the middle due to the concentration difference

between the rich mixture and the lean mixture The

fluorescence intensity was high in the middle of the flames

because the diffusion flame had a stoichiometric

equi-valence ratio (Kim et al., 2006)

Based on the OH-PLIF of a triple flame, Kioni et al.

(1999) reported that the concentration of hydroxyl radicals

was high around the leading edge and the diffusion flame

with a stoichiometric equivalence ratio They also found

that the OH-radical concentration decreased rapidly when

moving away from the leading edge and approaching the

rich premixed flame rather than the lean premixed flame

The presented results also showed a very high OH-radical

concentration in the middle of the flame at the location of

the diffusion trailing flame

With the use of a gas chromatograph and sampling

probes, Kim and Jang (2005) compared the concentration

of the reactant and product inside a flame to analyze the

concentration fields of a premixed flame and triple flame

They measured the concentrations of hydrogen and oxygen

as the reactant and carbon monoxide as the product In the

premixed flame region, the concentrations of hydrogen and

oxygen maintained a constant value in the flame-center, yet

the triple flame region displayed a distinctive difference

that decreased rapidly, as the excess oxidant from a lean

region and hydrogen from a rich region diffused toward the

centerline downstream, resulting in a very active diffusion

combustion reaction Similarly, in Figure 2 the premixed

flame showed an almost even OH-radical distribution

throughout the flame, whereas the fluorescence intensity of

the OH radicals in the triple flame was high due to the

active diffusion combustion reaction of hydrogen and

oxygen around the flame center

In contrast, Kioni et al (1999) measured a thin

bution of CO in the diffusion flame, while the CO

distri-bution was thicker in the rich premixed flame than in the

lean premixed flame Kim and Jang (2005) also found that

the density of CO was thin in the region of the lean

premixed flame with abundant oxidants, yet increased

rapidly when approaching the region of the rich premixed

flame Thus, because this increase of CO is a major

reac-tion source of OH-radical extincreac-tion, the hydroxyl radical

distribution is expected to be thin in the region of the rich

premixed flame

Figure 3 shows the shape of the OH-radical distribution

for the state lifted flame Because the

unsteady-state lifted flames remained for only 1.6 seconds, the

OH-radical distribution in the unsteady-state lifted flame

appeared slightly thinner than that in the steady-state lifted

flame However, the change trend was similar in both

flames The unsteady-state lifted flame was created through

an instant change of the equivalence ratio from φ R=1.2 and

φ L=1.2 to φ R=1.2 and φ L=0.4 using the equivalence ratio

conversion system As previously reported (Jun et al.,

2008), after activating the solenoid valve of the valence ratio conversion system, the unsteady-state flamebegan to be created after t=1.2 sec and ended after t=2.8sec The unsteady-state lifted flame changed from a semi-spherical shape similar to the steady-state lifted flame to astreamline shape that became sharper with the passage oftime At t=1.2 sec, the flame shape was the same as that ofthe steady state flame at φ R=1.2 and φ L=1.2; then, fromt=1.8-2.8 sec, the flame exhibited a diffusion trailing flame

equi-in the middle that was similar to the steady-state flame at

φ R=1.2 and φ L=0.8-0.4 After t=2.8, the flame became thesame as the steady-state lifted flame at φ R=1.2 and φ L=0.4.With respect to the distribution of hydroxyl radicals, theunsteady-state lifted flame at t=1.2 sec exhibited a verysimilar distribution to that of the steady-state flame at

φ L=1.2 in Figure 2 The density of hydroxyl (OH) radicalsappeared to be thick around the leading edge, and thengradually thinned farther from the leading edge

Over time, the fluorescence intensity of the OH radicalsbecame high around the leading edge of flame, at the leftFigure 3 OH radical of unsteady state lifted flame

OH-RADICAL BEHAVIOR OF UNSTEADY LIFTED FLAME BASED ON INSTANTANEOUS CHANGE 667

side of the slot burner, and around the middle of the flame

After t=2.8 seconds, the flame showed a high fluorescence

intensity around the center due to the diffusion flame

Thus, when comparing the distribution of OH radicals in

the unsteady-state lifted flame and steady-state lifted flame,

the two flames showed a similar change progression and

similar results, as previously reported based on the

flame-shape changes (Jun et al., 2008)

Figure 4 shows a comparison of the fluorescence

intensity of the OH radicals along the horizontal direction

of a 28-mm position from the leading edge of the lifted

flames in Figures 2 and 3 In our previous study (Jun et al.,

2008), the luminescence intensity was obtained at a height

of 28.9 mm from the leading edge of the lifted flames using

a direct photograph Based on the central area of the picture

(x=0, flame center), the right area (x>0) was the region

where the flame of φ R appeared, while the left area (x<0)

was the region where the flame of φ L appeared In addition,

the intensity at the center was greatly increased because of

the diffusion flame Similarly, the steady-state lifted flame

and unsteady-state lifted flame in Figure 4 exhibited the

same trend for the fluorescent intensity, i.e., the gradient of

the intensity increased greatly because of the influence of

the diffusion flame in the central area; the left side of the

flames was relatively stronger in intensity than the right

side

Figure 5 shows the liftoff height of the steady-state liftedflame and unsteady-state lifted flame determined on thebasis of the lifted flame shape as well as the distribution of

OH radicals The equivalence ratio, φ L is indicated on thehorizontal axis of the steady-state lifted flame, while thetime (sec) is indicated on the horizontal axis of the un-steady-state lifted flame As previously reported (Jun et al.,2008), the liftoff height changed depending on the concent-ration difference of the mixture, and the liftoff height of theunsteady-state lifted flame exhibited a similar change tothat seen with the steady-state lifted flame The liftoffheight according to the distribution of hydroxyl radicalsalso showed a similar result to that of the flame shape Thelower sections in Figure 5 show the three regions of thesteady-state and unsteady-state lifted flame, which areclassified according to the OH-radical distribution, gradient

of the liftoff height and fluorescence intensity

The results in Figures 2-5 and our preceding study showthat the characteristics of an unsteady-state lifted flame,such as the liftoff height, fluorescence intensity, and OH-radical distribution, are similar to those of a steady statelifted flame Moreover, the behavior of an unsteady-statelifted flame involves the same phenomena as a steady-statelifted flame, i.e., it changes from a premixed flame, to aFigure 4 Intensity of OH radicals Figure 5 Lift-off height.

critical flame region, and then to a triple flame with a

diffusion trailing flame, depending on the concentration

difference

Therefore, it is concluded that the behavior of an

un-steady-state lifted flame created under the specific

condi-tions in this study, can effectively forecast the behavior of a

steady-state lifted flame

4 CONCLUSIONS

In a previous study, the current authors investigated the

similarity of the behavioral characteristics of an

unsteady-state lifted flame and steady-unsteady-state lifted flame, yet there

was no analysis of the major reactions occurring inside the

two flames Thus, using OH-PLIF to analyze the

concent-ration fields, experiments were performed to understand

the concentration fields of an unsteady-state lifted flame

and steady-state lifted flame with the following results:

(1) For a steady-state lifted flame, the hydroxyl radicals in

the premixed flame are mainly distributed around the

leading edge and thin out farther from the leading edge

In addition, when increasing the concentration

differ-ence, high fluorescence intensity occurs around the

leading edge, the region of the lean premixed flame

and the central region It appears that the central region

is the diffusion trailing flame region of a triple flame,

and the high intensity of OH radicals is due to an active

diffusion combustion reaction of hydrogen and oxygen

(2) For an unsteady-state lifted flame, the OH radicals are

thickly distributed around the leading edge during the

initial stage of t=1.2 sec Over time, the fluorescence

intensity increases around the leading edge, the left

side of the slot burner and around the center Thus, the

characteristics of the unsteady-state lifted flame,

includ-ing the distribution of hydroxyl (OH) radicals, liftoff

height, fluorescence intensity, and three classified

regions, showed a similar tendency to the

characteri-stics of the steady-state lifted flame

In conclusion, the behavior of an unsteady-lifted flame

created under the specific conditions used in this study, can

be effectively predicted based on the behavior of a

steady-lifted flame, as reported in our previous study

ACKNOWLEDGEMENT− The present research has been

partially conducted by the Bisa Research Grant of Keimyung

University in 2005.

REFERENCES

Azzoni, R., Ratti, S., Aggarwal, S K and Puri, I K (1999)

The structure of triple flame stabilized on a slot burner

Combustion and Flame, 119, 23−40

Dold, J W (1989) Flame propagation in a nonuniform

mixture: Analysis of a slowly varying triple flame bustion and Flame, 76, 71−88

Com-Jang, J Y., Kim, T K and Park, J (2005) A transitionalbehavior of a premixed flame and a triple flame in alifted flame (I) Trans Korean Society Mechanical Engi- neer (B) 29, 3, 368−375

Jun, S H., Kidoguchi, Y., Kim, T K and Miwa, K (2008).Characteristics of lifted flame resulting from impulsivechange of equivalence ratio J Combustion Society of Japan 50, 152, 145−151

Kim, N I., Seo, J I., Guahk, Y T and Shin, H D (2006).The propagation of tribrachial flames in a confinedchannel Combustion and Flame, 144, 168−179.Kim, T K and Jang, J Y (2005) A transitional behavior

of a premixed flame and a triple flame in a lifted flame(II) Trans Korean Society Mechanical Engineer (B) 29,

3, 376−383

Kioni, P N., Bray, K N C., Greenhalgh, D A and Rogg,

B (1999) Experimental and numerical studies of a tripleflame Combustion and Flame, 116, 192−206

Kioni, P N., Rogg, B., Bray, K N C and Liñán, A (1993).Flame spread in laminar mixing Layers: The triple flame

Combustion and Flame, 95, 276−290

Lee, J K and Nishido, K (2008) Development of an LIFprocessing technique for measuring drop sizes in a pre-swirl spray Int J Automotive Technology 9, 4, 381−390.Lee, W N and Seo, D G (2005) A study on the stability

of rich/lean methane premixed flame Trans Korean Society of Automotive Engineers 13, 2, 225−233.Morel, T (1975) Comprehensive design of axisymmetricwind tunnel contractions ASME J Fluids Eng., 225−

233

Mu iz, L and Mungal, M G (1997) Instantaneous stabilization velocities in lifted-jet diffusion flames Com- bustion and Flame, 111, 16−31

flame-Park, J K., Lee, S Y and Santoro, R (2002) induced soot vaporization characteristics in the laminardiffusion flames Trans Korean Society of Automotive Engineers 3, 3, 95−99

Laser-Plessing, T., Terhoeven, P., Peter, N and Mansour, M S.(1998) Experimental and numerical study of a laminartriple flame Combustion and Flame, 115, 335−353 Schefer, R W and Goix, P J (1998) Mechanism of flamestabilization in turbulent lifted-jet flames Combustion and Flame, 112, 559−574

Schefer, R W., Namazian, M and Kelly, J (1994) zation of lifted turbulent-jet flames Combustion and Flame, 99, 75−86

Stabili-Watson, K A., Lyons, K M., Donbar, J M and Carter, C

D (1999) Scalar and velocity field measurements in alifted CH4-Air diffusion flame Combustion and Flame,

117, 257−271

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International Journal of Automotive Technology , Vol 10, No 6, pp 669 − 674 (2009)

669

DEVELOPMENT OF A FLOW NETWORK SIMULATION PROGRAM

PART I – FLOW ANALYSIS

J LIM * and Y HWANG

Hyundai Motor Company, 772-1 Jangduk-dong, Hwaseong-si, Gyeonggi 445-706, Korea

(Received 21 March 2008; Revised 25 May 2009)

ABSTRACT− An in-house simulation program was developed that can be utilized to predict flow characteristics such as pressure and velocities in any flow network system comprising multiple flow components, i.e., pipe, pump, heat exchanger, valves, etc Although the code is intended for applications to network flow systems in a vehicle, it is written in a generalized manner to handle any possible network configuration of flow components Therefore, it can easily function in various industrial applications The network system where the flow is assumed to be one-dimensional is mathematically formulated

by applying two conservation rules, mass and energy, to each flow component These rules produce a set of non-linear equations These non-linear equations are solved iteratively by adopting the Newton-Raphson scheme This program has been tested in many different cases to demonstrate its validity and applicability In this paper, two examples are introduced to show how the program can be used to find solutions in real engineering problems Throughout the study, it was found that the code can most efficiently be used to verify a proposed design concept in an early design stage of the vehicle development cycle The thermal analysis portion of the program will be dealt with in Part II of the paper.

KEY WORDS : Flow network, Pipe system, Simulation code, Newton-Raphson method, Flow components

1 INTRODUCTION

The flow network systems found in a vehicle may include a

diverse group of systems such as an engine coolant path,

cabin heating/air-conditioning system, brake line, air/gas/

fuel feeding system, etc In addition, an air duct can be

considered a flow network system, provided that its

cross-sectional size is sufficiently small compared to its

stream-wise characteristic length The flow in network systems

can be considered 1D (one-dimensional) since the flow is

predominantly unidirectional, and any 3D effect can be

handled in terms of empirical parameters This study is

based on the 1D nature of flow network systems and how

1D flow behavior greatly simplifies the mathematical model

(Chang et al., 2003; Lim et al., 2005; Myung et al., 2007;

Shallhorn and Popok, 1999)

In flow network systems, pressure decreases as the flow

moves along a path due to major loss, caused by viscous

friction between the flow and a path wall, and minor loss,

caused by path configuration Major loss depends on the

friction factor, length and equivalent diameter of the path

The friction factor is given as a function of Reynolds

Number, which represents the viscous effect of flow, and

relative roughness of a path wall The friction factor is

determined from a Moody chart or computed through the

Colebrook formula In laminar flow, the friction factor is

solely determined by Reynolds Number In turbulent flow,

the friction factor is provided as a function of relativeroughness only

Along with major loss, there is minor loss occurring due

to geometric changes in a path−bended pipe, connectors,valves, sectional area change, etc The minor loss is repre-sented by a loss coefficient, which is mainly determinedexperimentally This loss coefficient is normally influenced

by Reynolds Number However, it can be consideredconstant in a flow range of high Reynolds Number (Young

et al., 1997)

For flow to be present in a flow network system, thereshould be energy source components, i.e., pumps or fans.Power generated by these flow components can be usedeither to boost pressure or to increase flow rate Thecharacteristics of the energy components can be represent-

ed in terms of a relationship between the pressure boost andthe flow rate increase at various revolution speeds, which isnormally provided by the component manufacturers Theoperating point of the network system is determined bybalancing the overall pressure drop in the system and thepressure increase from energy sources Thus, with thegiven energy to pumps or fans, more energy can be used toincrease a flow rate by reducing the pressure drop in thenetwork to optimize the network design

To cope with diverse configurations of flow networksystems, branched and merged components are introduced.These components allow the network program to handlecomplex configurations analyses In this work, the flownetwork system application is limited to a steady incompre-

*Corresponding author. e-mail: limjung@hyundai.com

ssible flow.

2 MATHEMATICAL FORMULATION

The mathematical algorithm to approach flow network

systems is as follows:

First, identify each flow element that comprises the

system, and then apply appropriate governing equations to

each element depending on element type Also, assign

necessary boundary conditions to corresponding node points

of the elements In this way, a set of non-linear equations

can be established, and finally, these equations can be

solved with any appropriate method

2.1 Governing Equations-Conservation Rules

Assuming that the flow passing through a flow element, as

shown in Figure 1, is steady, incompressible, viscous, and

one-dimensional, an energy equation can be stated as

(Young et al., 1997),

(1)where p is pressure (Pa), v is velocity (m/s), z is height (m),

g is gravity (9.8 m/s2), γ=ρg, ρ is density (kg/m3), h p is

head provided by an energy source such as a pump or a fan

(m), and hl is energy loss from major and minor loss (m)

For the major loss, the energy (head) loss can be

represent-ed in terms of the square of velocity,

The minor loss can also be described in a similar form,

(3)where f is friction factor in a pipe, l is pipe length (m), d is

pipe diameter (m), and K is the loss coefficient Generally,

only one of the loss terms is used for a flow element, but in

some cases an element requires both loss terms

The other conservation rule that is applied to a flow

element is for mass The following simple equation is

established for mass conservation in the flow element in

Figure 1,

Here, A is a cross-sectional area of an element (m2)

2.2 Energy Equations in Different Element Types

In the previous section, governing equations are discussed

that are applied to arbitrary flow elements In this section,

the way that these equations are implemented to each

specific element type is discussed Here five differentelement types are introduced These elements are believed

to encompass most of the flow elements encountered inreal-life engineering applications

(5)where f, a friction factor in a turbulent flow, can be found

by the Colebrook formula (Young et al., 1997),

(6)where ε is roughness of the pipe inner surface (m).2.2.2 Minor loss element

In the flow network system, there are many flow elementsover which energy loss occurs due to minor loss, i.e.,orifice, regulators, connectors, etc The loss coefficient, K

in Equation (3), is practically constant over the flow range

of interest in the above elements However, in cases wherethe K value changes strongly depending on velocity, thiselement can be treated as a characteristic element, which isdiscussed in Section 2.2.5 The energy equation for minorloss is,

(7)where K can be found in various literature (ASHRAE, 1981;Hydraulic Institute, 1979; Streeter, 1961; White, 1979).Here attention should be paid to ascertain on whichvelocity, v 1 or v 2, the value of K in the minor loss term isbased In Equation (7), K is given in terms of v 1 as in themajority of cases

2.2.3 Branched elementThis is an element where a flow divides into two differentpaths, as shown in Figure 2a A proper combination of thebranched elements is capable of representing multiplebranches, i.e., greater than two Two energy equations arerequired to fully describe the energy balance over theelement,

(8a) (8b)

-DEVELOPMENT OF A FLOW NETWORK SIMULATION PROGRAM PART I – FLOW ANALYSIS 671

where K 12 is a loss coefficient corresponding to a flow from

node ① to node ②, and so on Each equation is valid along

a respective streamline In addition, a slight different version

of the mass conservation equation from Equation (4) is

required,

(9)2.2.4 Merged element

Contrary to the branched element, a merged element

represents a flow element where two flow paths merge into

one, as in Figure 2b Similar to the branched element, two

energy equations and one mass equation are introduced,

(10a) (10b) (11)

Also, any number of multiple merged elements can be

described by a combination of the merged elements

2.2.5 Characteristic element

As discussed in Section 2.2.2., the loss coefficient, K, can

be assumed to be constant over a flow range of interest

However, in flow components, such as heat exchangers and

flow filters, values of K vary with velocity In this case, the

characteristic data for these components are usually

provid-ed by their suppliers in the form of a pressure drop ∆p

versus a volume flow rate Here the pressure drop ∆p is

proportional to the flow rate

Other elements which characteristic data are given with

‘a relationship between ∆p and V’ are energy sources, such

as pumps and fans, where ∆p is an increased pressure and

inversely varies with the flow rate In other words, an energy

supplied to the flow by source is used both to increase the

pressure and to increase the flow rate Normally,

charac-teristic data is provided at various rpms in a tabulated form

or graphically as curves Thus, an energy equation for the

characteristic elements can be represented as,

(12)and a mass conservation equation is identical to Equation

(4)

3 NUMERICAL IMPLEMENTATION

3.1 Discretization The first step of numerical implementation is to discretizethe whole flow network system; that is to say, divide thesystem into many appropriately sized elements Each ofthese elements may correspond to one of the element typesintroduced in Section 2.2 With the application of energyequations and a mass conservation equation to each element,

a set of non-linear equations can be achieved There aretwo unknowns, velocity and pressure, at each node Inorder for these equations to be solvable, proper boundaryconditions should be provided by specifying pressure orvelocity at certain nodes that are not necessarily end nodes

In principle, these could be any node However, the choice

of boundary condition nodes should be performed in a waythat the number of equations is equal to the number ofunknowns, and physically it is valid

3.2 Numerical ComputationOnce a set of non-linear equations with appropriate bound-ary conditions is established, Newton-Raphson method isadopted to compute this group of equations This method is

to at first assume the unknowns, and to at each iterativestep renew the unknowns in a proper manner until theyconverge Mathematically, it can be explained as follows(Press et al., 1986):

The governing equations from the conservation rulesintroduced in the section 2.1 are represented as,

The new solutions at each iterative step can be found as,

(14) (15)where Equation (14) is a matrix equation for δx j, F i/ x j

are obtained by differentiating the governing equations with

respect to the unknowns, and both the matrix coefficients

F i/ x j and the right hand side vector −F i are computed

from the solutions defined at a previous iterative step, x iold

Once the matrix equation is solved to obtain δx i, the new

solutions, x inew, are determined by Equation (15)

A logic flow chart showing the simulation program is

shown in Figure 3

4 VALIDATION OF PROGRAM

In this section, two examples are discussed to illustrate the

validity of the developed program The results obtained

from the program are compared to experimental results, as

well as 3D CFD analyses

4.1 Heater Line Analysis of Small Size Bus

The heating system of a small-sized bus is the first

ex-ample A schematic of the heating system is shown in

Figure 4, where a part of an engine coolant is divided into

two different loops, a front defrosting loop and a rear cabin

heating loop The objective of this analysis is to predict

flow rate in the individual loops

For a numerical application, the above system is

di-scretized into 19 elements and 21 nodes as shown in Figure

5 The types of elements used in the system are in Table 1

Here, loss coefficients for the heat exchangers are

com-puted from one-point measurements of the pressure drop

and flow rate in each component Characteristic elements

should be used for the heat exchangers for a more accurate

calculation if the data is available

As boundary conditions, pressure and velocity measured

from tests are assigned to node 1 Then, all values of

pressure and velocity at the rest of the nodes are calculated

by the program The input data and results are summarized

in Table 2

Also, in Table 2, the test results are introduced for

comparison with the computed ones It is shown that both

results are remarkably well matched, which demonstrates asalient feature of the program Another interesting analysisfrom the results can be made as shown in Table 3.Both in a front and a rear circuit, a majority of thepressure drop occurs in the heat exchangers rather than inthe pipe line Therefore, the flow characteristic data of theheat exchangers are critical to the accuracy of the com-puted results Minor loss in the pipes may be trivial to anoverall pressure drop In addition, the established model forthe bus heater system can be utilized for a parametric study

to obtain more balanced flow distribution between the frontand the rear circuit

4.2 Heater Duct Analysis of Coach BusAnother study to demonstrate applicability of the program

Figure 4 Heating system layout of a small size bus

Table 1 Element types of bus heater system

Type of element No of element

−Heat Exchanger

−Expansion/Contraction −−34Branched/Merged 2

Figure 5 Discretized elements of the heating system.Table 2 Results of bus heater system analysis

Inputdata Inlet pr. 0.45 (kgf/cm

2)Total flow 16.3 (l/min)Results

Computed TestedOutlet pr 0.325 0.33

Pr drop 0.125 0.12

Fr flow 10.00 10.2

Rr flow 6.18 6.1Table 3 Pressure drop distribution in bus heater system.Circuit Pressure drop (kgf/cm2)

Pipe line Heat ExchangerFront 0.0309 (24.7%) 0.0942 (75.3%)Rear 0.0220 (17.6%) 0.1031 (82.4%)

DEVELOPMENT OF A FLOW NETWORK SIMULATION PROGRAM PART I – FLOW ANALYSIS 673

shows flow distribution in louvers of the heater duct of a

coach bus Flow distribution is calculated using the program,

as well as the 3D flow distribution as determined by a

commercial CFD tool The configuration of the heater duct

system is shown in Figure 6 The heater duct is installed

longitudinally at the corner where the passenger cabin floor

meets a vertical side wall A flow induced by two blowers

is divided by passing through an air guide to both a front

and a rear duct

To discretize the system, 54 nodes and 42 elements are

used In the heater duct system, the flow through the

louvers are simulated as a combination of a branched

element and a pipe element, where an identical loss

coeffi-cient is used for all branched flow into the louvers with the

exception of the two louvers located at the ends of the duct

A flow rate is given as a boundary condition at an inlet, and

atmospheric pressures are assigned to all exit locations

Besides a 1D analysis, a 3D flow behavior is also

com-puted using a commercially available code Figure 7 shows

a comparison of the flow rate distributions along the duct

both from 1D and 3D analysis

In the heater pipe application in Section 4.1 where an

average pipe length, 151 cm, is much greater than an

aver-age pipe diameter, 1.7 cm, the flow can be expected to be

unidirectional However, this example has a cross sectional

area of approximately 12 cm, and the average distance

between louvers is 67 cm Therefore, it is hard to expectthat the flow in the duct is mainly unidirectional Even so,overall flow rate distribution patterns are relatively thesame in the 1D and 3D analyses with the exceptions at thelouvers near the inlet such as louver No 3 and 4 where 3Dflow behaviors are predominant

Even if the 1D analysis loses its accuracy as compared tothe 3D analysis in certain applications, the 1D analysisproduces results much faster than the 3D Also, the 1D ana-lysis requires limited design information for the simulation

In contrast, the 3D analysis requires detailed 3D CAD data.Usually in a conceptual design stage, many design optionsare suggested and tested in comparative evaluations with-out the details of CAD data In this application, the 1Danalysis is the more feasible choice, or sometimes the onlyviable option

In this regard, the 1D model of the heater duct can beconveniently used in an early design stage to find out anoptimal louver array for even distribution of heated air

5 CONCLUSIONS

A 1D in-house simulation program has been developed topredict flow characteristics, pressure and velocity distribu-tion in any flow network system The program has beentested in many engineering applications, especially in vehicledesign, to prove its validity The salient features of theprogram may include the following:

(1) The program can handle a variety of flow networksystems with the merged and branched elements adopt-

ed in addition to the wide collection of flow elements.(2) Although a current version of the program includes fivedifferent flow elements, if necessary, additional elementscan easily be added to enhance the scope of the pro-gram The program is written in a manner to handlevarious types of element characteristic expressions,which can be either mathematical equations, non-linear

as well as linear, or discrete tabular data

(3) The program establishes a matrix equation to find thevelocity and pressure distribution in the network Theknown velocity or pressure can be assigned to anypoint in the network as the boundary condition, but notnecessarily to a starting or an ending point of thenetwork

(4) The input data for the program is limited, i.e., pathdimension and flow physical properties, which arereadily available in the conceptual design stage How-ever, 3D analysis requires a full text of the CAD data.(5) Normally, the 1D model is applied to the piping net-work flow where a unidirectional flow is predominant.However, in this study, the heat duct system showing alocally strong 3D nature of flow can successfully behandled by the program using a proper combination ofthe flow components

(6) Hence, the program can readily be utilized to evaluatemany design concepts proposed at an early designFigure 6 Heater duct system of a coach bus

Figure 7 Flow rates from 1D and 3D analysis

stage It is able to provide opportunities to save time

and cost in a vehicle design cycle by quickly selecting

an optimal design solution

This paper deals with flow calculation in a flow network

system The thermal analysis part of the program will be

introduced in Part II of the paper

REFERENCES

ASHRAE (1981) ASHRAE Handbook of Fundamentals.

Atlanta

Chang, F C., Malipeddi, S., Uppuluri, S and Shapiro, S

(2003) Underhood thermal management of off-highway

machines using 1D-network simulations SAE Paper No.

2003-01-3405

Hydraulic Institute (1979) Engineering Data Book 1st

Edn Cleveland Hydraulic Institute

Lim, J., Yang, K Y and Kim, M H (2005) Comparative

evaluation of engine room cooling performance with 1D

network flow and 3D CFD model SAE Paper No.

2005-03-0209

Myung, C L., Kwak, H., Hwang, I G and Park, S (2007).Theoretical flow analysis and experimental study ontime resolved THC formation with residual gas in a dualCVVT engine Int J Automotive Technology 8, 4, 697−

704

Press, W H., Flannery, B P., Teukolsky, S A and Vetterling,

W T (1986) Numerical Recipes: The Art of Scientific Computing Cambridge University Press 269−272.Shallhorn, P and Popok, D (1999) Interfacing a generalpurpose fluid network flow program with the SINDA/Gthermal analysis program SAE Paper No 1999-01-2162.Streeter, V L (1961) Handbook of Fluid Dynamics Mc-Graw-Hill New York

White, F M (1979) Viscous Fluid Flow McGraw-Hill.New York

Young, D F., Munson, B D and Okiishi, T H (1997) A Brief Introduction to Fluid Mechanics John Wiley &Sons New York 323−368

International Journal of Automotive Technology , Vol 10, No 6, pp 675 − 685 (2009)

675

VEHICLE VELOCITY ESTIMATION FOR REAL-TIME DYNAMIC

STABILITY CONTROL

L LI * , J SONG, L KONG and Q HUANG

State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China

(Received June 7 2007; Revised 24 February 2009)

ABSTRACT− A new approach is proposed for nonlinear asymptotic observers based on the cascade observer system with a fusion of sensor signals In the observers, the characteristic of the vehicle dynamic system, the nonlinear tire force estimation, load transfer estimation, and road ramp angle compensation are considered The errors in the observation of vehicle velocity were diminished, and the computation cost was decreased for a real-time microcontroller Simulation and real vehicle test results validate the higher accuracy of the velocity estimation by the proposed observers under complicated handling maneuver conditions

KEY WORDS : Vehicle dynamic control, Longitudinal velocity, Lateral velocity, Observer, Tire force, Road ramp

1 INTRODUCTION

A vehicle dynamic control system, e.g., ABS/TCS/ESP and

active steering system, can improve handling performance

in extreme driving conditions, such as emergency steering,

braking, driving, and even combined handling conditions

The performance of the vehicle dynamic control is based

on precise vehicle dynamic state observation (Van Zanten,

2002) As the slip angle is the primary indicator of vehicle

handling maneuver capability, developing an effective method

to estimate the vehicle longitudinal and lateral velocity is

very significant; however, it is the most challenging aspect

of the real-time control system (Shibahata et al., 1993;

Tseng et al., 1999)

The dynamic states are seldom measured directly in

vehicle dynamic control system due to the cost of the

sensors Therefore, the states could be computed from

other low-cost measurements, such as wheel speed, yaw

rate, acceleration, and pressure (Van Zanten, 1996) Senger

developed an observer of lateral velocity with the

assump-tion that the tires were operating in the linear region

(Senger and Kortum, 1989) However, in a real-time

con-trol process, tires may work on the nonlinear region,

especially in a low friction ground Cao (1994) used a

physical model of the vehicle and tire to estimate the lateral

velocity; however, he did not consider the dynamic

distur-bances induced by the actuators of the dynamics control

system, the oscillation of the handling input, and the

uneven road condition Tseng et al (1999) developed an

asymptotic observer to estimate the lateral velocity;

how-ever, he considered that the lateral tire force was only a

linear function of the vertical load

These earlier approaches used in kinematic models out vehicle dynamics considerations were mainly based onlinear or quasi-linear techniques (Kiencke and Daiss, 1997;Boada and Boada, 2006; Li et al., 2006).In order toimprove the estimation precision, Ray (1995) developed anonlinear Extended Kalman Filter to estimate vehicle velo-city based on a nonlinear tire-friction model Lee (2006)developed a reliability-indexed sensor fusing method toestimate vehicle velocity Imsland (2006) proposed a non-linear adaptive observer to estimate the velocity and, simul-taneously, the tire parameters (Liu and Peng, 1998).The linear and nonlinear approaches mentioned aboveprovided different approaches to estimate the vehicle velo-city; however, they have shortcomings The assumptionthat vehicle motion is dynamically stable, especially thatthe tire dynamic characteristics are equal on the same axle,may induce inevitable errors, especially on low tire-roadfriction conditions

with-One challenge is that there are two kinds of errors pering the application of an observer One is induced by thelinearization of the vehicle dynamics functions because thetransient effects during active braking force modulation arenot accurately considered by the bicycle model in thementioned observers (Imsland et al., 2006) The other one

ham-is induced by a mham-ismatch between the dynamic functionand the physical motion of the vehicle under steering-braking or steering-driving handling conditions The loadtransfer, that is, the vertical load transfer from inner toouter wheels when the vehicle is steering, will quicken thevehicle sideslip that occurs when cornering(Li and Song,2007a) The other challenge is that the observers need largeamounts of computation resources and convergence time

*Corresponding author. e-mail: daeliliang@gmail.com

Therefore, the observers can hardly be used in a real-time

system

In this paper, a method is designed of a cascade observer,

and the observer system is subdivided into sequentially and

independently solved elementary sub-problems Based on

this method, we proposed a new approach for nonlinear

asymptotic observers; thus, the output errors are used as

feedback loops for the observer system The nonlinear

characteristics of the vehicle under a complicated handling

maneuver, such as a road ramp or load transfer, and the

dynamic state difference among the four wheels from the

active brake, were considered Meanwhile, the cascade

observer system has a lower computation cost Thus, the

proposed observers may effectively reduce estimation errors

and decrease computation cost The quality of the observers

is proven by simulation, and a vehicle test

The paper is organized as follows The vehicle model is

explained in Sec 2 A 7-DOF-4-Wheel vehicle dynamic

model is more appropriate than others are because of the

better balance between the observing errors and the

com-putation cost The construction of cascade observers for the

longitudinal velocity and lateral velocity is detailed in Sec

3 The difficult problems, such as the tire forces estimation

and road ramp angle compensation, were considered

Vali-dation of the observers by simulation and the real vehicle

ground test are discussed in Sec 4 and Sec 5

2 VEHICLE MODEL AND TIRE MODLE

A 7-DOF-4-Wheel vehicle dynamic model (Figure 1),

involving longitudinal, lateral, and yaw movements and the

rotations of four wheels, may reflect the load transfer

effects and the dynamic characteristics of individual wheels

under active brake control; therefore, the model can be

used to describe the planar dynamic motion of the vehicle

with the vehicle stability control system The equations may

be expressed as follows

Equation of longitudinal motion:

(1)Equation of lateral motion:

(2)Equation of yaw motion:

(3)

Equation of the motion of four wheels:

(4)where the subscript ij represents the number of the wheel, i,

j= 1, 2 F x and F y are the tire longitudinal force and tire

lateral force, respectively m is the mass of the vehicle V x

and V y are longitudinal velocity and lateral velocity,

respec-tively is the yaw rate of the vehicle δ w is the steer angle

of the wheel J v is the inertia moment about the verticalaxis a and c are the distance from the gravity center tofront and rear axles, respectively b is half the distancebetween the two front wheels or two rear wheels T w isbrake torque of the wheel R is the wheel radius M cahalf isdriven torque, which is available within the vehicle archi-tecture from Electronic Throttle Control engine controllers,for the free wheel, M cahalf =0 J w is the inertia moment of thewheel R is the radius of the wheel w whl is the wheel angularvelocity

The HSRI (Dugoff) tire model can be used to describethe nonlinear friction model for its simple relationship ofthe tire dynamic states for real-time control (Li and Song2007; Dugoff et al., 1970), which may be expressed asfollows:

(5) (6) (7) (8)

3 OBSERVERS

We propose an observer system for the vehicle dynamicscontrol system, as illustrated in Figure 2 The observersystem includes the tire force dynamic state observer and

m V· ( x – V y ϕ· )= F ( x11 + F x12 )cosδ 2 − F ( y11 + F y12 )sinδ w +F x21 + F x22

m V· ( y – V x ϕ· )= F ( x11 + F x12 )sinδ w − F ( y11 + F y12 )cosδ w +F y21 + F y22

J v ϕ··= F ( y11 + F y12 )acosδ w − F ( y11 – F y12 )bsinδ w

− F ( y21 + F y22 )c− F ( y11 + F y12 )asinδ w

− F ( x11 – F x12 )bcosδ w − F ( x21 – F x22 )b

F x ij ( ) =T w ij ( ) /R−M calhalf /R+ J ( w ij ( ) /R ) dw ⋅ whl ij ( ) /dt

ϕ·

µ =µ peak ⋅ ( 1 A – S ⋅ ⋅ ⋅ R ω λ 2 + tan 2 α ) H= 1 λ -λ– Cλ

1 λ – - C λ 1

H

- 1 4H 2

–

1 λ – - C α 1

H

- 1 4H 2

–

VEHICLE VELOCITY ESTIMATION FOR REAL-TIME DYNAMIC STABILITY CONTROL 677

the velocity observer based on actuator characteristics of

the vehicle dynamic control system and the vehicle dynamic

characteristics in a steering maneuver The observer system

consists of substrate level, a middle level, and an upper

level The substrate level is to directly observe the basic

states from the filtered measured signals using the low-pass

filter method The middle level is to observe the dynamic

states with the basic states The upper level is to observe

the states for the system control The wheel speed filter, tire

force estimation, and road ramp angle compensation

sub-systems comprise the observer system for vehicle

longitu-dinal velocity and lateral velocity

3.1 Tire Force Estimation

When the vehicle dynamic control system is active, the

active brake time is short, typically less than 2 seconds, and

the pressure of the brake cylinder is less than 15 MPa

Thus, the thermal fade of the brake torque can be ignored,

and the brake works in the linear region The friction

coefficient between the disk and the pad is assumed

constant, and the tire brake force is proportional to the

brake pressure The dynamic brake torque produced by

brake may be expressed as:

(10)where µ' is the friction coefficient of the brake pad and the

disk Re is the effective radium of the brake pad A we is the

cross-section area of the wheel cylinder P is the pressure in

the wheel cylinder, and η is brake efficiency

If λ ij> 0.95, T w reaches its maximum value, which can

be substituted by 2µR e A we ηP|λ ij=0.95; P|λ ij=0.95 represents the

brake pressure value when λ ij=0.95

Based on the definition of the slip rate, the slip rate in a

real-time controller may be expressed as:

(11)thus,

(12)

Considering the differential of dw whl/dt may introduce largeoscillations, we substitute dw whl/dt in Equation (4) byEquation (12) The brake force can be expressed as:

(13)Van Zanten (1996) proposed the concept of the hydraulicmodel to estimate the brake pressure P when ESP is active.Based on the dominant characteristics of the active brakesubsystems, the author developed the math model toestimate the active brake pressure in active brake pressurecontrol processes(Li and Song, 2007b):

(14)where is the brake pressure of wheel cylinder i atinstant t 0; is the brake pressure of main cylinder atinstant t 0; is the brake pressure of wheel cylinder i atinstant t 0+nT; τ 0 is the time lag between the pressureincrease and the valve modulating order; T and n are cycletime and number, respectively x 1 and x 2 are characteristicparameters of the hydraulic model and can be calibrated forthe given hydraulic brake system

If the wheel works under the large combined slip tions, such as a strong brake or driven handling with asteering maneuver, the lateral force may be expressed as:

(15)Otherwise, at small combined slip conditions, the lateralforce may be expressed as follows:

(16)where λ th and α th are the thresholds of the linear region ofthe tire lateral force related to the combined slip In real-time control of a discrete time control system, F xmay becalculated using Equation (13); λ may be deduced from thewheel speed and the estimated longitudinal velocity of thelast cycle loop; and α may be deduced from estimatedlateral velocity of the last cycle loop and steering angleinput These parameters may be obtained from the controlloop (Van Zanten, 1996; Li and Song, 2007b) However,when the vehicle is steering at high velocity ,the lateral tire force is affected by the load transfer effects.Thus, the compensation equations may be expressed as:

(17)where σ x and σ y are load transfer coefficients in thelongitudinal and lateral direction, respectively If σ x and σ y

are larger than 0, + is selected; otherwise, − is selected F z0

is the static vertical load

3.2 Longitudinal Velocity ObserverWhen steering, the vehicle undergoes circular motion and

T w t()=T S ( t τ – )=2µ′ R ⋅ ⋅ e A we ⋅ ⋅ t τ η P ( – )

λ t()=

V x − w whl ( ) dw t 0 whl

dt - + ⋅ ∆t

spin motion, as illustrated in Figure 3.

The reference longitudinal velocity may be expressed as:

(18)where w is the angular speed, and R' is the radius of the

vehicle in steering

Considering that the vehicle dynamics control system is

used to prevent the vehicle from spinning out, the wheel

speed may be expressed as (CEMACS, 2005):

(19)where u wh is the wheel speed, and b i is half the length of the

front axle or rear axle The + or − sign is dependent on

which side (front or rear) is selected for calculation Lateral

acceleration may be expressed as:

(20)The longitudinal velocity based on the selected wheel

speed may be then expressed as:

The following are defined: a w is the wheel deceleration,

which may be calculated from the wheel angular

accele-ration; a x is the measured longitudinal acceleration; is

the estimated longitudinal acceleration, which may be

estimated as:

(22)Considering that a x cannot be obtained directly from ESP

sensors, it may be substituted by

While the longitudinal acceleration is small, the vehicle

longitudinal velocity is dominated by u wh However, during

the full braking or active braking process, the difference

between the wheel speed and the vehicle velocity is very

large, which means that a w is larger than a x; thus, the

longitudinal acceleration is an important factor to estimate

the longitudinal velocity Therefore, V x may be calculated

based on the estimated extrapolation deceleration :

(23)

As illustrated in Figure 4, when a- is larger than a x, thefixed-slope extrapolation method can be used to estimatethe vehicle velocity; Equation (23) may be substituted forEquation (21) in the extrapolation area

The separation point and extrapolation slope may beselected according to the tire-road friction conditions Theabsolute values of the vehicle longitudinal acceleration,according to the separation point and the extrapolationslope, are proportional to The extrapolation decele-ration may be equal to ; however, in the real controlsystem, the conservative disposal method is applied toestimate the reference velocity Thus, the separation pointand extrapolation slope are conservatively selected Theabsolute value of a w and are larger than Thus, thereference longitudinal velocity calculated from Equation(23) is smaller than that from Equation (21); the slip rate ofthe vehicle is then larger than the real value, and the controlthreshold of the slip rate may be satisfied easily Based onthe calibration of the test vehicle, the relationship betweenthe separation point, the extrapolation slope, and thedeceleration of the vehicle is illustrated in Figure 5 The observer may then be expressed:

(24)The observer gain K adepends on the estimated longitu-dinal acceleration, and K ij(P ij) is dependent on the brakepressure P ij, which reflects when wheel speed measurement

is greater than the estimated velocity If the tire slips are

V x =w R′ ⋅

u wh ij ( ) = w R′ b( + i )cosδ w ij ( ) ±ϕ·b i for outer wheel speed

w R′ b ( – i )cosδ w ij ( ) ±ϕ·b i for inner wheel speed

Figure 3 Projecting vehicle position during steering Figure 4 Separation and extrapolation of the velocity

Figure 5 Relationship between the separation point, theextrapolation slope, and the deceleration

(21)

VEHICLE VELOCITY ESTIMATION FOR REAL-TIME DYNAMIC STABILITY CONTROL 679

low, which means the vehicle is working under normal

conditions, the controller may be triggered to adjust the

state of the vehicle The observer gains may be expressed

as follows: if , then K a=0 When the vehicle is

controlled by ABS, or the brake, the observer gains may be

expressed as: if , then K a=1 V x can be dominated by

u wh; meanwhile,

(25)The fixed-slope extrapolation method is integrated into

the observer as follows:

(26)where VL is very large, ML is middling large, MS is

middling small, VS is very small,and P max and P min are the

pressure thresholds of the wheel brake cylinders For the

test vehicle, P max is about 5 Mpa, and P min is about 0.2 MPa

Under some vibration conditions, a w is affected largely

by the noise, causing V xwh to be different from the real

vehicle velocity If is used in the real-time controller, V x

can be obtained by time integration of a x, defined as V xa,

which can be used to compensate for the difference

How-ever, in some conditions, such as in the intensive brake

control process, a x is large, and V xais separated from real

vehicle longitudinal velocity; thus, the longitudinal velocity

can be corrected by:

(27)where k w is the confidence index of V xwh; k a is the

confidence index of V xa; k w is inversely proportional to a w

k a is inversely proportional to

A two-layer longitudinal velocity observer integrating

the steering dynamics and the longitudinal acceleration

sensor is illustrated in Figure 6 The two-layer longitudinal

velocity observer can be used for all types of vehicle

hand-ling maneuvers, where the first layer is used to observe the

velocity and the second layer is used to compensate thedifference of full-wheel-brake conditions All signals can

be obtained from the sensors, and the computation plexity is low for the real-time control

com-3.3 Lateral Velocity Observer

In the proposed observers, the difference between the tireforces of the right side and the left side and the unstablecharacteristic of the tire dynamics are ignored, and thevehicle may be pushed into a sideslip by the oscillation ofthe feedback control mode Meanwhile, if the steer angle islarge, the Coriolis acceleration needs to be considered(Senger and Kortum, 1989; Cao, 1994; Kiencke and Daiss,1997; Boada and Boada, 2006) The derivative of thelateral velocity is then used (Van Zanten, 2002):

(28)

If the vehicle is stable and the slip angle β is less than 15deg on a high-friction road or less than 5 deg on icyground, then Equation (27) may be expanded using Taylorseries, and the lower order may be reserved:

(29)Based on the proposed observation system of the vehicledynamic states and the two-layer longitudinal velocityobserver, the longitudinal velocity and tire force are used asthe inputs of the observer The observer structure iscascaded because there are no feedback loops between thetwo velocity observers The other signals are obtained fromESP sensors The lateral velocity observer is illustrated inFigure 7

(30)where K ax and K ay are observer gains for the errors ofaccelerations If the vehicle runs on low-friction ground,longitudinal and lateral slip may occur, and the vehiclebecomes instable When longitudinal brake slip occurs,then and K ax< 0 When axle sideslip occurs,then , K ay> 0

3.4 Road Ramp Angle Compensation

The acceleration sensors cannot distinguish the effects

induced by a driver maneuver from those due to a road

ramp To minimize possible estimation errors, the road

ramp angles need to be estimated The major challenge is

to estimate the road disturbance component from the

vehicle lateral dynamics component because the vehicle

measurement is affected by both components, which can

change rapidly

(31) (32)The acceleration signals obtained from the sensors need

to be filtered to decrease the noise The applied the

low-pass filter may be expressed as:

(33)where is the acceleration value filtered at the instant i;

is the measured acceleration at the instant i; a/256 is

the filter coefficient, which can be quickly realized by

shifting 8 bits to the right direction in the microcontroller

If the vehicle velocity is constant but the acceleration

value measured does not equal 0, the longitudinal road

ramp angle may be included into the measured values In

the online controller, the method detailed below is applied

to estimate the longitudinal road ramp The following

assumptions may be satisfied due to the longitudinal vehicle

dynamic maneuver:

i)

ii)

Because the observed longitudinal acceleration may be

deduced from the reference longitudinal velocity and the

difference between the measured value and the observed

value of the longitudinal acceleration is caused by the

longitudinal road ramp angle, the longitudinal acceleration

deduced by the longitudinal road ramp may be estimated as

follows:

(34)where V x min and V x max are the supervising thresholds of the

longitudinal velocity; M is the threshold of longitudinal

acceleration; A is the threshold of wheel acceleration; ∆A is

the threshold of wheel acceleration increment in every

control loop; k x bank is the correction factor; and is the

longitudinal acceleration deduced by the longitudinal road

ramp

If the vehicle is running on a lateral ramp road, the

difference between the measured value and the observed

value of the lateral acceleration is mostly induced by the

lateral road ramp angle Considering the potential region of

the vehicle handling maneuver, the following assumptions

must be satisfied:

i) , ii) & , iii) the

steering angle is about 0 but the lateral acceleration is not0; that is, and

Thus, the road bank angle may not be ignored FromEquation (28) and Equation (31), the lateral accelerationdeduced by the lateral road ramp may be estimated fromthe difference between the measured value and the observedvalue of the lateral acceleration:

(35)where δ is the steering angle; δ0 is the supervising threshold

of the steering angle; ∆δ is the steering angle increment inevery control loop; ∆δ0 is the threshold of steering angleincrement; δ τ and δ τ+t are the steering angles at instant ôand τ+t; a y 0 is the threshold for the lateral road rampcomputation; a y is the lateral acceleration measured by theacceleration sensor; k y bank is the correction factor; and

is the lateral acceleration deduced by the lateral road ramp.3.5 Observer Robustness

Assuming that the estimation values of the longitudinalvelocity and the lateral velocity converge to their true values,the stability results hold in the overall system The stabilityanalysis of the observer shows that the longitudinal velocityobserver is globally ISS ((globally) input-to-state stable)problem (Sontag and Wang, 1995) The lateral velocityobserver can be proven to be Lyapunov stable The proof ofthis assumption is in the appendix

4 SIMULATIONS AND ANALYSIS

The proposed observers can be validated by simulation.The 15DOF nonlinear vehicle model is used in the vehicledynamic control system simulated by Matlab/Simulink/Stateflow, including 6DOF for the vehicle chassis (3DOFfor the linear motion, 3DOF for the rotary motion), 8DOFfor the four wheels (4DOF for the four wheels’ rotarymotion, 4DOF for the four wheels’ vertical motion), and1DOF for the steering The magic formula tire model isused to simulate the tire dynamic forces The enginedynamic characteristic was obtained with the interpolationmethod from the engine map The load transfer and thedynamic unbalance of the left and right wheels, even whenthe vehicle is maneuvered in the limited handling regions,are also taken into account

4.1 Validation of Road Ramp Angle Compensation

A 15DOF vehicle model is corrected based on the roadramp effects on the lateral motion, vertical motion, rollmotion, and the balance equation of the suspension force.The simulation conditions to validate the road ramp anglecompensation method are as follows: (1) Adding a whitenoise to a constant angle to simulate the lateral road rampangle The energy of the noise is 1×10− 5, the constant roadramp angle is 8 deg (the induced lateral acceleration is 1.4m/s2) (2) Initial velocity of the vehicle: 80 km/h (3) Steer-

a p =a˜ p −aˆ p_bank −a p_zero ( p=x or y )

V x ∈ [ V xmin V xmax ] &∆V x ∈ [ M – M]

a w ∈ [ – A A ] &∆a w ∈ [ – ∆A ∆A ]

aˆ x_bank =a x – k xbank ⋅ Vˆ· x

VEHICLE VELOCITY ESTIMATION FOR REAL-TIME DYNAMIC STABILITY CONTROL 681

ing input: double lane change according to ISO3888

The proposed method as expressed by Equation (35) was

applied to estimate the road ramp angle with the

assump-tion k ybank=0.95 The estimated lateral road ramp angle is

shown in Figure 8 The lateral acceleration deduced by the

road ramp angle is estimated

4.2 Simulation Test for the Velocity Observers

The simulation conditions are as follows: (1) On planar

ground; initial velocity of the vehicle: 80 km/h; vehicle

running in 4th gear ratio, and the throttle degree is 30% (3)

Maximum friction coefficient: 0.3; (4) Steering input: sine

wave measured from the vehicle handling test The observed

results of the vehicle dynamic states are illustrated in

Figure 9~11

The tire forces may be obtained based on the tire force

estimation method Simultaneously, the longitudinal

accele-ration and lateral acceleaccele-ration are accurately estimated withthe values measured by the sensors of ESP As shown inFigure 10, the estimated values of the longitudinal accele-ration and lateral acceleration are converged into the realvalue obtained from the simulation system

Using the values of the dynamic states from the basicobservers, the longitudinal velocity and the lateral velocitywere accurately observed, and the complicated steeringhandling maneuver and active brake slip controlling mane-uver in the real control loop of the individual active brakecontrol are considered As shown in Figure 11, theestimated velocities are slightly greater than the real valuefrom the simulation model, which is reasonable for theconservative estimation method to be applied in thedynamic control systems

5 TEST RESULTS AND ANALYSIS

The longitudinal road ramp angle was estimated based on

Figure 8 Validation of the road ramp angle estimation (1−

steer angle of front wheels [rad], 2−yaw rate of the vehicle

[rad/s], 3−given value of the lateral acceleration deduced

by road ramp [m/s2], 4−the lateral acceleration [m/s2], 5−

estimation value of the lateral acceleration deduced by road

ramp [m/s2])

Figure 9 Handling input, pressure and slip rate of wheel

Figure 10 Estimated and real values of acceleration

Figure 11 Longitudinal and lateral velocities (1−V xwh11,vehicle longitudinal velocity based on front left wheelspeed; 2−V xwh22, vehicle longitudinal velocity based on rearleft wheel speed; 3−V xwh12, vehicle longitudinal velocitybased on front right wheel speed; 4−V xwh21, vehicle longitu-dinal velocity based on rear right wheel speed; 5−V x, vehiclelongitudinal velocity from simulation; 6−V xp, estimatedvehicle longitudinal velocity; V y −vehicle lateral velocityfrom simulation, V y p−estimated vehicle lateral velocity)

filtered acceleration, which was obtained from different

operations The results of a x with eliminated road ramp

angle effect are illustrated in Figure 12

When the vehicle is braked on a µ-split road from a

high-friction road to a low-friction road, the ABS control

thresholds are adjusted in order to obtain the locking

up-trend of the four wheels The difference between V xwh and

V x is obvious; therefore, the confidence index k w is reduced

while k a is increased Thus, the accurate longitudinal value

can be estimated, as shown Figure 13 When the vehicle is

braked on an ascent road, the road ramp angle estimated

algorithm was disabled in order to obtain the low k a

condi-tion, following which, the longitudinal velocity observer

can increase k w and reduce k a, allowing V x to be accurately

observed, as shown in Figure 14

The test results indicate that this two-layer longitudinal

velocity observer integrating the steering dynamics and the

longitudinal acceleration signals can be used for real-time

control of ABS/TCS for a vehicle potentially running on

the locking uptrend or ramp road

The observers were tested by integrating them into thecontrol algorithm of a vehicle dynamic control system Thevehicle was maneuvered through a double lane change on ahigh-friction road (Choi et al., 2006) The real values of thedynamic states were measured by sensors of the dynamiccontrol system and by pressure sensors The vehicledynamic attitude was measured by DGPS (DifferentialGlobal Position System) The handling input, the vehicleheading angle, and the yaw angle of the C.G are shown inFigure 15 The vehicle was steered to follow a double lanechange and was then adjusted to achieve stability Theheading angle was measured by DGPS to denote the di-rection of the velocity vector The yaw angle was obtained

by integration from the measured yaw rate signals The active pressure control modulations are shown inFigure 16, where the over-steer is observed and the outerside wheels are actively braked At that time, the dynamiccharacteristics of each of the wheels are different during thecontrol process The yaw rate and the acceleration areshown in Figure 17 The wheel speed, the longitudinalvelocity measured by DGPS, and the longitudinal velocityobserved by the proposed observer are shown in Figure 18.Figure 12 Longitudinal road ramp anglecompensation

Figure 13 V x observed at low k w condition

Figure 14 V x observed at low k a condition

Figure 15 Steering input, heading, and yaw angles

Figure 16 Pressure of wheel cylinder adjusted by ESP

VEHICLE VELOCITY ESTIMATION FOR REAL-TIME DYNAMIC STABILITY CONTROL 683

The lateral velocity are shown in Figure 19 The measured

and observed values of the slip angle are shown in Figure

20 The measured slip angle is deduced from the heading

angle and yaw angle (Ryu, 2004)

As validated by test results, the observing system can

accurately observe the longitudinal and lateral velocity

The basic values can be measured by the sensors of ESP.Meanwhile, the observers are robust to the variables ofvehicle handling conditions and tire characteristics Addi-tionally, the computation complexity is reduced compared

to the EKF, or adaptive observer, and the entire time is lessthan 10 ms, as tested by x164 (16 bit microcontrollerproduced by Infineon) Thus, the proposed observers may

be used in an online controller of a vehicle dynamic stabilitycontrol system

6 CONCLUSION

In this paper, vehicle longitudinal velocity and lateral city observers have been proposed based on the cascadeobserver system of the vehicle dynamics control to reduceobservational errors of velocity, and to decrease the com-putation cost of the observer The proposed nonlinearobserver can estimate the vehicle velocity precisely with alower computation cost under complicated dynamic hand-ling maneuver conditions The load transfer and the roadramp angle compensation were considered according tohandling conditions Simulation and test results validatedthe observers

velo-ACKNOWLEDGEMENT− The research is supported by the National Natural Science Foundation of P.R China (No.

50575120 and No 50905092) The authors thank the Auto company for the experiment passenger cars and the test bench.

Brilliance-REFERENCES

Boada, B L and Boada, M J L (2006) Fuzzy-logicapplied to yaw moment control for vehicle stability

Vehicle System Dynamics 43, 10, 753−770

Cao (1994) Method of Obtaining the Yawing Velocity and/

or Transverse Velocity of a Vehicle US Patent No.5311431

CEMACS (2005) Vehicle State Observer Requirement fication Interim Report Work Package 4, Deliverable

Speci-Figure 17 Yaw rate and lateral acceleration

Figure 18 Wheel speeds; measured and observed values of

longitudinal velocity

Figure 19 Measured and observed values of lateral velocity

Figure 20 Measured and observed values of slip angle