International journal of automotive technology, tập 11, số 3, 2010

During the dyno-mometer tests, the following cycle-averaged quantities were acquired: engine speed; torque; engine-out emissions downstream from the catalyst; temperatures at the exhaust

M BARATTA 1) , E SPESSA 1)* and P MAIRONE 2)

1)IC Engines Advanced Laboratory, Politecnico di Torino, Torino 10129, Italy

2)Centro Ricerche Fiat, Orbassano 10043, Italy

(Received 17 October 2008; Revised 3 August 2009)

ABSTRACT− Turbocharging port-injected Natural Gas (NG) engines allows them to recover gaseous-fuel related power gap with respect to gasoline engines However, turbolag reduction is necessary to achieve high performance during engine transient operations and to improve vehicle fun-to-drive characteristics Significant support for the study of turbocharged Compressed Natural Gas (CNG) engines and guidelines for the turbo-matching process can be provided by 1-D numerical simulation tools However, 1-D models are predictive only when a careful tuning procedure is set-up and carried out on the basis of the experimental data In this paper, a 1-D model of a Heavy-Duty (HD) turbocharged CNG engine was set up in the GT-POWER (Gamma Technologies Inc., Westmont, IL, US) environment to simulate transient operations and to evaluate the turbolag An extensive experimental activity was carried out to provide experimental data for model tuning The model buildup and tuning processes are described in detail with specific reference to the turbocharger model, whose correct calibration is a key factor in accounting for the effects of turbine flow pulsations The second part of the paper focuses on the evaluation of different strategies for turbolag reduction, namely, exhaust valve variable actuation and spark timing control Such strategies were aimed at increasing the engine exhaust-gas power transferred to the turbine, thus reducing the time required to accelerate the turbocharger group The effects of these strategies were examined for tip-in maneuvers at a fixed engine speed Depending on the engine speed and the applied turbolag reduction strategy, turbolag reductions from 70% to 10% were achieved.

KEY WORDS : Turbocharging, Turbolag, 1-D simulation

NOMENCLATURE

A : advance of EVO

bmep : brake mean effective pressure

BSR : blade speed ratio

cp : air specific heat at constant pressure

C : engine brake torque

CA : crank angle

CNG : compressed natural gas

Cs : isentropic gas velocity

E : Wiebe exponent

E-EVO : early exhaust valve opening

EVO : exhaust valve opening

HRR : heat release rate

IC : inter-cooler

L : lift (of the exhaust valve)

: mass flow rate

MAP : manifold absolute pressure

N : engine speed

n : turbocharger shaft speed

NG : natural gas

p : in-cylinder pressure at EVO

P : prelift (of the exhaust valve)PFP : peak firing pressure

PR : pressure ratio/turbine pressure ratioSOC : start of combustion

WC : Wiebe constant

WG : waste gateWOT : wide open throttle

xb : burned mass fraction

γ : ratio of specific heats (of air)

NG-fuelled engines have recently emerged as a promising

solution for the transportation sector in industrialized

countries, thanks to the intrinsic environmental features of

NG and to the favorable geopolitical distribution of

reservoirs (d’Ambrosio et al., 2006) The application of

NG engines is most advantageous for public urban

trans-portation Any limitations to the vehicle’s operating range,

due to the storage of fuel in a gaseous state, can be

over-come by scheduling refueling stops at stations that are

directly operated by the transportation providers The

gaseous state of the fuel also reduces the engine power

output (Kato et al., 1999; Zhang et al., 1998) However,

that gap can be recovered by turbocharging (d’Ambrosio et

al., 2006), as in the new-generation high-performance NG

buses which exploit the high knock resistance of methane

In contrast, the turbolag phenomenon is one of the major

concerns regarding these engines due to driver perception

of the vehicle’s performance Turbolag introduces a delay

in the torque response under severe tip-in maneuvers The

delay is due to the time required to increase the pressure in

the intake manifold, which is influenced by the acceleration

time of the turbocharger shaft Hence, particular attention

should be paid to the optimization of engine behavior undersevere transient operations

The introduction of a turbocharger strongly increases thecomplexity of the engine system and of the design process

In particular, the problem of matching the engine with theturbocharger arises Although the final setup has to bedefined through experimental analysis, a great deal ofinformation about turbo-matching can be derived fromnumerical simulation based on 1-D fluid-dynamics codes.These simulations allow engines to be studied under a widerange of operating conditions with limited cost penaltiesand are extremely useful for addressing the engine optimi-zation process (Bush et al., 2000; Sammut and Alkidas,2007) 1-D simulations are also widely used for valve liftselection and timing, intake and exhaust manifold layoutoptimization, and valve dimensioning (Westin and ngström,2003; Galindo et al., 2004, 2006) For turbocharged engines,

it has been found that if simulation models are not properlytuned, calculation outcomes are likely to be quite differentfrom the experimental results Such discrepancies are theresult of turbine and compressor map quality as well as oferrors in accounting for pulsating-flow effects on the tur-bine performance Turbine maps are typically measuredunder steady-state operations

In order to overcome such discrepancies, a reliable cedure for correcting turbine steady-state maps is required(Westin and ngström, 2003; Westin et al., 2004; Winkler

pro-Å'

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Figure 1 Test engine: (a) Intake manifold and ports; (b) Manifold inlet, injectors and rail

Table 1 Test engine characteristics

Number of cylinders 6 (in line)Number of valves 4 (per cylinder)

and ngström, 2007).

This paper can be divided into two parts In the first part,

the engine exhaust-gas power transferred to the turbine,thus reducing the time required to accelerate the turbo-charger group

2 TEST ENGINE AND EXPERIMENTAL SETUPThe test engine was developed at Fiat Research Centre forapplication to urban buses The major engine characteristicsare reported in Table 1, and an engine schematic is provid-

ed in Figure 1 Figure 2 shows the nominal performance ofthe engine at Wide Open Throttle (WOT) The engine head

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Figure 2 Engine performance at WOT Each quantity is

normalized to its maximum value

Figure 3 GT-Power engine model

Figure 4 Raw turbine performance maps Each quantity is normalized to a specific reference value

features a spherical bowl-in-piston combustion chamber

with a compression ratio (CR) of 11:1, four valves per

cylinder, and one centrally-located spark plug

The engine is boosted by a turbocharger with a

twin-entry turbine A closed-loop controller for the air

temper-ature at the intercooler (IC) outlet is used During the

dyno-mometer tests, the following cycle-averaged quantities

were acquired: engine speed; torque; engine-out emissions

downstream from the catalyst; temperatures at the exhaust

ports; temperature and pressure values at compressor inlet,

compressor outlet, IC outlet, intake manifold, intake ducts,

turbine entries, locations upstream and downstream from

the catalytic converter The in-chamber pressure

time-history was also acquired by means of a piezoelectric

trans-ducer installed in the first cylinder In-cylinder pressuretraces were referenced based on the intake absolute pre-ssure measured by a piezoresistive transducer in the inletmanifold Finally, the engine was equipped with two air-fuel ratio ‘NGK’ UEGO sensors (one for rich mixtures andthe other for lean mixtures) in the exhaust system and with

a pressure sensor in the injection rail

3 ENGINE MODEL IN GT-POWERThe engine was modeled with GT-POWER v6.2 build #3, a1-D simulation tool licensed by Gamma Technologies, Inc.(Westmont, IL, US) The GT-POWER model map is shown

in Figure 3 Figure 3(a) shows the cylinders, intake and

Figure 5 Turbine performance maps: (a), (b) Mass flow and efficiency fit versus data as functions of BSR; (c), (d) Massflow and efficiency fit versus data as functions of PR; (e), (f) Final turbine maps, including the extrapolated range ofreduced speed and PR

3.1 Pipe and Flowsplit Submodels

GT-POWER solves the inviscid form of the conservation

laws of mass, momentum and energy With reference to

pipes, these equations are discretized using a 1-D approach

and a finite volume technique Pressure losses due to

friction are computed automatically by the code, taking the

Reynolds number and the surface roughness of the walls

into account The modeled global heat exchange

coeffi-cient was proportional to friction using the Colburn analogy

In some cases, it may be necessary to tune friction and heat

transfer coefficients on the basis of experimental data

regard-ing gas pressure and temperatures at relevant points

Flow-splits were specifically designed (Gamma

Techno-logies, 2006) to account for the conservation of momentum

in three dimensions, even though the code is otherwise

one-dimensional It is important to correctly specify the

flow-split parameters (expansion diameter, characteristic length

and orientation) to correctly reproduce wave phenomena

and friction without using friction multipliers that are too

far from unity

3.2 Turbocharger Submodel

The turbocharger sub-model is a critical part of the overall

engine model The approach followed in GT-POWER is to

include turbocharger performance data in the form of

look-up tables, which are processed by the software to obtain

interpolated maps The quality of the final maps is highly

dependent on the amount and type of experimental data,

which are usually measured in a flow rig under steady-state

conditions

As an example, Figure 4 shows the raw turbine map

data, in terms of the reduced mass flow rate (left graph) and

efficiency (right graph) versus pressure ratio (PR) for

diff-erent speed lines (each colored line represents a diffdiff-erent

reduced speed nred) Each quantity has been normalized to

its maximum value In GT-POWER, the performance tables

are preprocessed to create internal maps that define the

performance of the turbine and compressor in a wide range

of operating conditions In particular, the turbine data, the

quality of which is critical for turbocharged engine

simu-lation (Westin and ngström, 2003; Westin et al., 2004;

Winkler ngström, 2007), are preprocessed by the

soft-ware (Gamma Technologies, 2006) based on well-known

characteristics of turbines regarding efficiency, reduced mass

flow rates and blade speed ratio (BSR) For a

fixed-geometry turbine, efficiency and reduced mass flow rate

should lie on specific trend lines when plotted against BSR,

provided that each quantity is normalized to its value at the

correspondent preprocessed values (lines) obtained fromthe fit in Figures 5(a), (b) This highlights the capability ofaccurately reproducing the whole set of experimentalturbine data with the exception of a couple of efficiencyvalues at low PR and at high nred (Figure 5(d))

Figures 5(e), (f) show the complete extent of the massflow (Figure 5(e)) and efficiency (Figure 5(f)) maps, whichare obtained based on the fit curves, including the extra-polated ranges of nred and PR These plots are a graphicalrepresentation of the maps internally used by GT-POWERfor the present application

3.3 Combustion SubmodelThe instantaneous value of the burned mass fraction x b wasmodeled by means of a Wiebe function:

(1)where is the combustion efficiency, WC is the Wiebeconstant, SOC is the crank angle at the start of combustion,

θ is the instantaneous crank angle and E is the Wiebeexponent The combustion model was applied using thetwo-zone thermodynamic approach of GT-POWER (GammaTechnologies, 2006)

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x b ( )=η θ c [ 1 exp – ( ( WC ) θ SOC ( – ) E 1 + ) ]

η c

Figure 6 Time histories of cylinder pressure, normalized to

a specific value, at the indicated operating conditions

The parameters in Equation (1) can be extracted by the

heat-release analysis of experimental in-cylinder pressure

time-histories To that end, a large number of experiments

were carried out on the engine test rig under steady-state

operating conditions at different values of engine speed (N)

and brake mean effective pressure (bmep) for nominal spark

timing (ST) operation Heat-release analysis was carried

out with the specific tools embedded in GT-POWER so that

the same thermodynamic and chemistry routines were

ap-plied for both diagnostic and prediction purposes For

nominal ST operations, the obtained Wiebe parameters

were organized in look-up tables as functions of N and

bmep Such look-up tables were then used as inputs for the

predictive model

Figure 6 provides an example of the experimental

(dia-monds) and simulated (solid line) pressure traces, both

normalized to a specific reference value

4 MODEL CALIBRATION

It is generally accepted that 1-D models need to be

care-fully calibrated in order to provide accurate results (Westin

and ngström, 2003), especially in turbocharged engine

applications Such a calibration is usually carried out by

tuning the model so that it accurately reproduces

experi-mental measurements taken under selected steady-state

operating conditions

In order to achieve the correct values of compressor and

turbine operating points, it is necessary to adjust the turbine

efficiency so as to match turbine and compressor

cycle-averaged powers (Iwasaki et al., 1994, Westin and ngström,

2002):

(2)

where is the mass flow rate through the compressor,

is the mass flow rate of the exhaust gases through the

turbine, c p is the specific heat at constant pressure of air, γ is

the ratio of specific heats of air, γ' is the ratio of specific

heats of exhaust gases, T 0

in,cmp is the total gas temperature atthe compressor inlet, PR cmp is the pressure ratio across the

compressor, and η cmp and η trb are the efficiencies of

com-pressor and turbine, respectively All of the above

quan-tities are instantaneous and the power balance is made with

reference to a complete engine cycle The motivation for

adjusting steady-state turbine efficiency is mainly related to

the pulsating flow to which the turbine is exposed in the

engine installation (Westin et al., 2004, Winkler and ngström,

2007, Westin, 2005, Rakopoulos and Giakoumis, 2006)

More specifically, under engine operations, the fraction of

exhaust-gas energy that is available at the turbine inlet can

be different from that under steady-state conditions (Baines,

2005) In addition, the extent of the pulsating flow-field

requires that turbine maps cover a wide operating rangewith respect to both N and PR Flow pulsations are alsopresent on the compressor side but they are much lesssignificant

4.1 Model Calibration Results – Steady-StateFigure 7 provides the results of the model calibration pro-cedure at three different loads (WOT, 25% and 4.2% of themaximum torque) and four engine speeds The followingengine quantities are reported: Manifold Absolute Pressure(MAP; Figure 7(a)), boost pressure (Figure 7(b)), pressure(p in,trb) and temperature (T in,trb) at the first turbine inlet(Figures 7(c), (d)), pressure (p out,trb) at the turbine outlet(Figure 7(e)), compressor mass-flow rate (Figure 7(f)),peak firing pressure (PFP; Figure 7(g)), and engine braketorque (Figure 7(h)) Each quantity has been normalizedwith respect to a specific value

The model is generally well calibrated in all the testedcases (Figure 7)

With reference to the whole intake system and the tion of the exhaust ports within the cylinder head, the walltemperatures at the fluid side were set to specific values,which were selected based on the outcomes of the experi-mental tests For the pipes downstream from the exhaustports, the GT-POWER Wall Temperature Solver wasactivated and the external temperature was set equal to thevalue in the cell cabinet Intake and exhaust ports weremodeled as straight pipes, and therefore heat-transfer multi-pliers were introduced to account for bends, roughness,additional surface area and turbulence caused by the valvesand stems (Gamma Technologies, 2006) There was noneed to set heat-transfer multipliers elsewhere in the intakesystem or to add friction multipliers to the model becausepressures and temperatures in the engine manifolds andports were well reproduced (Figures 7(a), (b), (d)) Theagreement between simulated and experimental values ofPFP (Figure 7(g)) and engine brake torque (Figure 7(h))demonstrate the accuracy of the combustion and enginefriction sub-models, respectively

por-As suggested by Westin and ngström (2003) and byGamma Technologies (2006), the above calibration was madewith reference to a simplified model, which was obtained

by removing both the turbocharger group and the IC, and

by setting pressure, temperature and fluid composition atthe domain boundariesto their experimentally measuredvalues

The first variable tuned during the calibration of thecomplete model, including the turbocharger and IC, wasthe turbine outlet pressure because it directly influenced theturbine power (Equation (2)) The pressure drop across thecatalyst was simulated through a Multiple-Pipe object inwhich the diameter and the length of each pipe were based

on the geometric characteristics of the catalyst The frictionmultiplier of the Multiple-Pipe object was set for eachoperating point in order to match the experimental valuesfor pressure at the turbine outlet (Figure 7(e))

For the calibration of the turbine efficiency, it is

worth-while making reference to the WOT conditions in Figure 7

The first three experimental points on each WOT curve

(engine speeds between 0.35 and 0.5 on the normalized

scale) were characterized by closed waste-gate (WG)

valve, whereas the WG valve was partially open for the

remaining two points on each curve For closed WG

operations, the turbine efficiency multiplier was selected to

match the measured turbocharger-shaft speed In the gated cases, both shaft speed and mass-flow rate across thewaste-gate valve should be matched However, the latterquantity was not measured in the experimental tests There-fore, as suggested by Westin and ngström (2003), themultiplier for turbine efficiency was chosen so as to matchthe turbo speed and the pressure at turbine inlet (Figure7(c)) Differences between simulated (solid line) and experi-

waste-Å'

Figure 7 Model results under steady-state working conditions, as functions of engine speed: (a) Manifold AbsolutePressure; (b) Boost pressure; (c) Pressure at turbine inlet (cylinder 1 side); (d) Temperature at turbine inlet; (e) Pressure atturbine outlet; (f) Air mass-flow rate; (g) Peak Firing Pressure (cylinder 1); (h) Engine brake torque – Each quantity isnormalized to a specific value

mental (circles) data are consistent with the uncertainty of

the pressure measurements The results of this tuning

pro-cedure are reported in Figure 8, where the ratio between the

resultant apparent turbine efficiency under pulse-flow

conditions (η trb,apparent) and the correspondent steady-state

efficiency from turbine maps (η trb,steady) are plotted as

func-tions of cycle-averaged turbine PR η trb,apparentcorresponds to

η trb in Equation (2) Figure 8 was organized in a look-up

table as a function of PR and included in the model

4.2 Model Calibration Results – Transients

Two load steps at different constant engine speeds (N/N max

=0.55 and 0.75) were considered For both load steps, the

throttle was opened abruptly and the torque varied from

about 4.2% load to the steady-state values at WOT Before

applying the model to the transient simulations, the

follow-ing changes were made:

• the Wall Temperature Solver was activated in the pipes

between the compressor and the intercooler in order to

accurately simulate the temperature time-history at the

compressor outlet;

• the catalyst friction multiplier was organized in a look-up

table as a function of the mass flow and was included in

the model

The calibration results for transient operations are shown

in Figure 9 for N/N max=0.55 The model was well

calibrat-ed Not only are the asymptotic values well reproduced but

also the simulated slopes occurring during the transient are

comparable to the experimental ones However, some

di-screpancies are observed in the time-histories of the

temperature at the turbine inlet (Figure 9(d)) and the brake

torque (Figure 9(f))

The main differences between simulated and

experi-mental T in, trb time-histories are that:

• the simulated asymptotic value at the end of the transient

is higher than the experimental one This can be ascribed

to an underestimation of the measured gas temperature,

which is due to the heat transferred from the

thermo-couple to the pipe walls by both radiation and conduction

through thermocouple stem (Westin and ngström, 2003;

Westin, 2005)

To reduce the heat transfer by conduction, the

thermo-couple should be immersed as far as possible into thepipe To reduce the measurement error due to radiation,proper radiation shields should be used (Doebelin, 1990)

In the considered experimental setup, no shielded couples were used, and the engine test-bench layoutlimited the insertion length of the probe to about 10~15times the probe diameter, which is generally reported to

thermo-be insufficient (Ehrlich, 1998; Westin, 2005) Hence, anunderestimation of the gas temperature had to be takeninto account

• Due to thermocouple thermal inertia, the slopes of lated and measured temperature rise are different Fasttemperature oscillations, such as those calculated duringthe first transient phase, cannot be measured by thethermocouple (Westin and ngström, 2003)

simu-• The computed gas temperature before the tip-in event islower than that measured during the experiment Undersuch a partial load, the turbocharger group produces vir-tually no boost, which in turn has no practical influence

on the transient simulation Therefore, the calibration ofexhaust-pipe heat-transfer multiplier and wall temper-ature were not performed at this operating condition,likely contributing to the observed difference in gas temper-atures

Experimental temperature measures can also be affected

by both uncertainty in the thermocouple position and hightemperature gradients in the exhaust manifold (Westin andngström, 2003)

The slight difference between the calculated and themeasured brake torque at the transient end (Figure 9(f)) can

be primarily ascribed to an underestimation of the gaspressure contribution to the friction mean effective pressureunder full-load operations

5 TECHNIQUES FOR TURBOLAG REDUCTIONThe described GT-POWER engine model was applied tothe analysis of turbolag during tip-in events at constantengine speeds Two strategies were investigated:

• Early-Exhaust Valve Opening-Variable Valve Actuation(E-EVO-VVA): immediately after the tip-in event, ExhaustValve Opening (EVO) was advanced for fixed exhaustvalve closing and a different profile for exhaust valve liftwas actuated After a selected number of engine cycleshad elapsed, EVO and valve lift were switched back totheir baseline values and profiles

• Combustion Retard (ComR): immediately after the tip-inevent a retard in ST was set Then, after a selected number

of engine cycles, ST was switched back to its baselinevalue

Both strategies determined a higher enthalpy drop acrossthe turbine and a consequent increase in the turbine power.This in turn caused faster turbo-shaft accelerations How-ever, such approaches might reduce piston work during theexpansion stroke As such, the trade-off between turboshaft acceleration and reduced piston work has to be analy-

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Figure 8 Ratio of apparent turbine efficiency under

pulsat-ing flow conditions to steady-state flow efficiency

Cycle-averaged PR is normalized to a specific value

zed as a function of EVO advances, valve lift profiles,EVO and valve lift switch-back timings, ST retards and STswitch-back timings.

A combination of the strategies introduced above wasalso investigated by advancing EVO and by setting a retard

in ST at the same time The resultant strategy will bereferred to as Combined in the following sections.5.1 E-EVO-VVA Strategy

Figure 10 shows the investigated lift profiles of the exhaustvalve A suitable advance (A) in EVO along with the newlift profiles (solid lines in Figure 10) were set immediatelyafter throttle-valve step-opening, whereas the lift profilewas switched back to its baseline value (dashed lines) after

a specific number of engine cycles Preliminary analysesindicated that the effects of the Prelift (Figure 10(b)) profilewith P/Lmax ≥0.3 on turbolag were equivalent to those of aFull Lift (Figure 10(a)) profile with the same EVOadvance In addition, a Prelift profile can be realized by

Figure 9 Model results under transient working conditions (load step at constant engine speed – N = 0.55 Nmax): (a)Manifold absolute pressure; (b) Boost pressure; (c) Pressure at turbine inlet (cylinder 1 side); (d) Temperature at turbineinlet (cylinder 1 side); (e) Exhaust mass-flow rate; (f) Engine brake torque Each quantity is normalized to a specific value

Figure 10 E-EVO-VVA lift profiles: (a) Full Lift; (b)

Prelift Dashed lines indicate the baseline lift profile

means of proper modifications of engine-brake devices,

which are commonly used in HD engines Therefore, our

investigation focused on the Prelift profile

In order to minimize turbolag during tip-in events at

con-stant N, the optimal values for prelift (P) and EVO advance

(A) in Figure 10(b) had to be determined In addition, it

was necessary to determine the timing, during the transient,

at which the advanced EVO profile would be switched

back to baseline In the engine model, switch-back occurred

when the boost pressure reached a specific level Therefore,

identifying the optimal timing involved the identification

of the optimal boost level at which the profile had to be

switched back (switch-boost) To perform this optimization,

parameter A was varied from 55 CA deg to 85 CA deg(steps of 5 deg), parameter P/Lmax was variedfrom 0.05 to0.3 (steps of 0.05), and the switch-boost level was variedfrom 0.55 to 0.80 (steps of 0.05) The levels of the switch-boost were normalized to a specific boost pressure value,which was kept constant for all tests

In order to rank the investigated strategies, two indiceswere defined to measure the turbolag (Figure 11) The firstindex was the Torque Rising Time (tr); the time intervalrequired for engine torque to rise from 10% to 90% of thetotal torque step The second index was the Average Torque during the transient:

(3)

In Equation (3), τ is the transient duration, which wasdefined with reference to the brake torque time-history(Figure 11) More specifically, the end of the transient wasidentified by the first point in which both the first andsecond time-derivatives of torque were under a fixed thre-shold The torque evolution always showed an overshoot,and therefore the second-derivative zero after the torquemaximum was selected

Figure 12 reports the effects of different EVO advances(A) on the time histories of MAP (Figure 12(a)), boostpressure (Figure 12(b)), temperature at turbine inlet (Figure12(c)) and brake torque (Figure 12(d)) for a tip-in mane-uver at N/Nmax= 0.55 In each plot, circles indicate thebaseline case (reference) and lines refer to different A

C C=1τ -

0

τ

∫C t()dt

Figure 11 Parameters for turbolag evaluation

Figure 12 E-EVO-VVA strategies vs baseline condition: time histories of (a) Manifold absolute pressure; (b) Boostpressure; (c) Temperature at turbine inlet (cylinder 1 side); (d) Engine brake torque Switch-boost set at a fixed level, loadstep at N=0.55 Nmax Each quantity is normalized to a specific value

the brake torque obtained in the reference condition due to

penalties in indicated-cycle work that increased as EVO

timing advanced Nevertheless, when the lift profile was

switched back to baseline, a prompt increase in engine

torque occurred, as a consequence of the higher boost level

5.2 Combustion Retard (ComR) Strategy

Increasing burned gas temperatures during late combustion

and expansion phases is another way to increase the

enthalpy drop across the turbine Diagnostic analyses of

several ST sweeps at fixed throttle positions, A/F ratios and

engine speeds were carried out to ensure that the previously

described Wiebe combustion model could be used for

simulating the effects of ST variations on combustion As

an example, the results obtained for a ST sweep are

reported in Figure 13 for N=0.5 Nmax and WOT (ST was

normalized by means of the MBT timing value and the

vertical axis was normalized to a specific value) The

anchor angle (black squares) increased of an amount that is

virtually equal to the retard in ST, whereas the combustion

duration (empty red diamonds) remained almost constant

The Wiebe exponent (blue circles) initially increased

slight-ly and then tended toward an asymptotic value Thebehavior described above, for the working conditions ofFigure 13, was also diagnosed for different engine speedsand loads Hence, for the ST ranges covered in this paper, agiven retard of ST could be simulated by means of acorresponding retard of the anchor angle, i.e., by means of

a shift in the baseline xb profile

The impact of the ComR strategy on the engine's dynamicresponse during the tip-in maneuver at N/Nmax= 0.55 isshown in Figure 14, which reports the time histories of thesame quantity previously shown in Figure 12 for E-EVO-VVA strategies ST retards of 5 CA deg (blue dashed line),

10 CA deg (red dotted line) and 15 CA deg (black solid

Figure 13 Wiebe parameters: anchor angle, duration from10% to 90% xb,exponent, as functions of ST

Figure 14 ComR strategies vs baseline condition: time histories of (a) Manifold absolute pressure; (b) Boost pressure; (c)Temperature at turbine inlet (cylinder 1 side); (d) Engine brake torque Switch-boost set at a fixed level, load step atN=0.55 Nmax Each quantity is normalized to a specific value

line) at a fixed switch-boost level (0.75) were considered.

The circles in Figure 14 refer to the baseline case The

effects of ST retard on MAP (Figure 14(a)) and boost

pres-sure (Figure 14(b)) traces were similar to those for the

E-EVO-VVA strategy, though their increase with respect to

the baseline case was less pronounced It is worthwhile to

point out that brake torque (Figure 14(d)) penalization

during the portion of the transient with retarded ST was

almost negligible because torque vs ST curves of the

engine were quite flat

6 RESULTS AND DISCUSSION

The developed GT-POWER engine model was applied to

the simulation of tip-in maneuvers at a constant N so as to

evaluate the effects of E-EVO-VVA, ComR and Combined

techniques on turbolag reduction

E-EVO-VVA and ComR techniques were investigated

for a tip-in maneuver at N/Nmax= 0.55 (Figures 15, 16, 17)

Figures 15 and 16 show the values of Torque Rising Time

(tr) versus Average Torque ( ) for E-EVO-VVA strategies

with Prelift (Figure 15) and Full Lift (Figure 16) profiles

The effects of different EVO advances (A = 65, 75, 85 CA

deg), switch-boost levels (0.60, 0.65, 0.70, 0.80) and prelift

values (P/Lmax= 0.2 in Figure 15(a); P/Lmax= 0.3 in Figure

15(b)) were examined Figure 17 reports tr vs for ComR

strategies featuring different ST retards (5, 10, 15 CA deg)

and switch-boost levels (0.60, 0.65, 0.70, 0.80) Values of tr

and are expressed as percentages with respect to the

corresponding values obtained in the baseline condition

(standard exhaust valve lift profile, no EVO advance and

no combustion retard)

For E-EVO-VVA strategies, increases of either A or

switch-boost level caused a reduction of tr and an increase

of , thus indicating a turbolag reduction With specific

reference to Prelift profile (Figure 15), turbolag can be

reduced by increasing P/Lmax However, it was found out

that the higher is P/Lmax, the less is the turbolag reduction

produced by a further increase of P/Lmax It can also be

observed that the tr vs plot obtained with Prelift profileand P/Lmax= 0.3 (Figure 15(b)) is virtually equivalent tothat attained with the Full Lift profile (Figure 16) Hence,

in this paper, the investigation of E-EVO-VVA techniqueswill be focused on Prelift profiles with P/Lmax ≤0.3.With reference to ComR strategies (Figure 17), eitherretarding combustion or increasing the switch-boost level

C

C C

Figure 17 ComR strategies: effects of anchor delay andswitch-boost on turbolag Load step at N = 0.55 Nmax

produces both a reduction of tr and an increase of These

effects were more pronounced for the E-EVO-VVA strategy

The simulations of tip-in maneuvers at fixed engine

speeds were then extended to different N/Nmax values

E-EVO-VVA techniques with Prelift profiles and ComR

strate-gies were taken into account, along with several

combi-nations of these two approaches Figure 18 shows tr vs

for N/Nmax= 0.375 (Figure 18(a)), 0.55 (Figure 18(b)),

0.75 (Figure 18(c)) and 1 (Figure 18(d)) Each symbol inthe figures refer to the outcomes of a different strategy.Empty black diamonds indicate E-EVO-VVA techniqueswith Prelift profiles, solid blue squares refer to ComRtechniques, and solid red triangles represent Combinedstrategies The parameters that characterize the mostsignificant test cases are detailed in Table 2, and thecorrespondent points on tr vs plots are identified with an

Table 2 Summary of the most significant test cases

(*) For N/Nmax= 0.375 the normalized boost-switch is 0.575 for all cases, due to the limited achievable boost level.Test case Strategy P/Lmax

[−] [CA deg advance]A [CA deg retard]ST retard switch-boost level [Normalized −] (*)

arrow and a test-case number In addition, values of tr and

are reported in Table 3 for each test case in Table 2 at all

considered values of N/Nmax

Figure 18 suggests that Combined strategies usually duce turbolag improvements that are slightly lower thanthose estimated by linearly accounting for the separatebenefits of the correspondent E-EVO-VVA and ComRstrategies For instance, for N/Nmax= 0.55 (Figure 18(b)),

pro-by linearly combining the benefits of test case #2 VVA with P/Lmax= 0.2, A = 85 CA deg and switch-boostlevel = 0.75) and test case #4 (ComR with ST retard = 10and switch-boost level = 0.75), ≈110% and tr ≈35% areexpected, whereas the correspondent Combined strategy(test case #6) shows and tr equal to 108% and 37%,respectively In addition, in Combined strategies a limitarises for maximum ST retard, since the opening of theexhaust-valve before the end of combustion should beavoided (for instance, at A=85 CA deg, ST cannot beusually retarded further than 10 CA deg)

(E-EVO-From Figure 18, one can infer that test case #5 bined strategy with P/Lmax= 0.3, A = 85 CA deg, ST retard

(Com-= 10 and switch-boost level (Com-= 0.75) represents the best case

in terms of tr at all N/Nmax More specifically, Table 3 andFigure 18 show that tr can be reduced to ≈30~65% of thebaseline condition, depending on the engine speed increased by ≈2~8% with respect to baseline for N/Nmax

≤0.75 and reduced ≈2% for N/Nmax= 1 Similar derations hold for the best E-EVO-VVA (test case #1) andthe best ComR (test case #3) strategies, though the attained

consi-tr and values are different

Figure 19 shows the Torque Rising Time (Figure 19(a))and the Average Torque (Figure 19(b)) as a function of N/

Nmax for the best cases #1, #3, #5 previously examined Itcan be observed that:

• Combined techniques allowed the highest tr reductionover the whole speed range;

• at all N/Nmax, the E-EVO-VVA technique enables a morepronounced tr reduction than the ComR strategy;

• for all strategies, tr reduction tended to be less relevant asN/Nmax increased beyond N/Nmax= 0.55;

• at the lowest N/Nmax, for ComR technique tr reductionwas less pronounced than that obtained at N/Nmax= 0.55.For E-EVO-VVA and Combined strategies, a decrease ofN/Nmax from 0.55 to 0.375 had only a slight effect on tr;

C

C C

N / Nmax= 0.55Average

torque

[%]

Torque rising time [%]

Average torque [%]

Torque rising time [%]

N / Nmax= 1Average

torque

[%]

Torque rising time [%]

Average torque [%]

Torque rising time [%]

Figure 20 Time-histories of (a), (c) torque, (b), (d) boost pressure during tip-in maneuvers at different N/Nmax

• the increase in peaked at N/Nmax= 0.55;

• at N/Nmax= 1, was usually lower than baseline;

• the relationships between and N/Nmax were similar for

all E-EVO-VVA and Combined strategies, whereas for

ComR strategies was less affected by N/Nmax

The relationships between N/Nmax and tr or can be

explained by Figure 20, which shows torque (Figures

20(a), (c) and boost pressure (Figures 20(b), (d))

time-histories during tip-in maneuvers at different N/Nmax for

E-EVO-VVA (Figures 20(a), (b)) and ComR (Figures 20(c),

(d)) strategies Basically, it can be seen that:

• the engine torque at WOT (i.e., the torque value at the end

of the transient in Figures 20(a), (c)) significantly

decreased as N/Nmax departed from 0.55;

• when N/Nmax increased between 0.55 and 1, the transient

duration was reduced

With reference to E-EVO-VVA techniques (dotted lines

in Figures 20(a), (b)), the first effect supported the

reduction of in the low speed range, whereas the second

effect explained the trend of for N/Nmax> 0.55 (Figure

19(b)) As a matter of fact, Figure 20(a) shows that the

duration of the transient portion in which brake torque is

lower than baseline (which approximately corresponds to

the part of the transient between throttle opening and

switch-boost occurrence) is almost independent on N/Nmax

As N/Nmax increased from 0.55 to 1, the timelength of the

transient portion, in which the brake torque was higher thanbaseline, was reduced due to the reduction of the transientduration Consequently, decreased and for N/Nmax= 1 values lower than baseline were obtained

In addition, Figure 20(a) shows that:

• 90% of the total torque step was always attained shortlyafter the switch-boost;

• 10% of the total torque was always reached during theintake manifold filling process, triggered by the throttlestep, and was thus unaffected by N/Nmax

These effects support the conclusion that for VVA strategies, tr is lower than the baseline over the entirespeed range

E-EVO-For ComR (Figures 20(c), (d)) techniques, it can beobserved that:

• the part of the transient before the switch-boost producednegligible torque penalties, due to the reduced sensitivity

of brake torque versus ST in this engine;

• the remaining part of the transient showed less significanttorque increases with respect to E-EVO-VVA This can

be ascribed to a lower increase in the turbine inlet ature (compare Figure 12(c) to Figure 14(c)) with ComRand, consequently, to a reduced rate of boost pressureincrease with respect to E-EVO-VVA (compare Figure20(d) to Figure 20(b))

temper-This can explain why tr and are less affected by N/

C C

C C

C

C

C

C C

C

Nmax in ComR strategies than in E-EVO-VVA techniques

(Figures 19(a), (b)) Finally, the red trace in Figure 20(c)

shows that for N/Nmax= 0.375 the baseline and ComR

torques reach 90% of the total torque step (about 0.5 on the

normalized scale) at almost the same time This can be

ascribed to lower brake torque at WOT for N/Nmax= 0.375

and can support the less pronounced tr reduction at the

lowest N/Nmax (as was already observed in Figure 19(a))

In general, for a given strategy, a decrease in tr vs

base-line (i.e., a shorter transient duration) is usually

accompani-ed by an increase in (i.e., a higher average brake torque

during the transient) Both effects indicated a decrease in

turbolag However, in the test cases at N/Nmax= 1,

values were usually lower than baseline even though the

transient duration was shorter Therefore, the most suitable

parameter for turbolag evaluation appears to be the Torque

Rising Time tr

Further investigations into the durability of exhaust valves

in relation to higher burned gas temperatures and pressures

were also carried out

Figure 21 shows the maximum value of the in-cylinder

pressure at EVO (pmax) versus tr for several E-EVO-VVA

and Combined strategies during tip-in maneuvers at the

four examined N/Nmax

For a considered test-case, when N/Nmax> 0.375 (Figures

21(b), (c), (d)) pmax was almost independent of N/Nmax,

whereas at N/Nmax= 0.375 pmax was significantly reduced

due to lower achievable boost pressure

The best strategy for turbolag reduction is dependent onthe pmax that is considered acceptable for valve train dur-ability If the requirement is pmax ≤20 bar, the best strategy

is represented by test case #10 (Combined strategy with P/

Lmax= 0.3, A = 65 CA deg, ST retard = 15 and boost level = 0.75), which leads to tr equal to ≈50%~80%

switch-of baseline condition depending on N/Nmax For VVA techniques, the best case with pmax ≤20 bar was case

E-EVO-#7 (P/Lmax= 0.3, A = 65 CA deg, and a switch-boost level

of 0.75), which features tr equal to ≈60%~90% of baselinecondition depending on N/Nmax By adding a combustionretard to a specific E-EVO-VVA strategy or to the refer-ence case, no significant increase in pmax were observed(compare test case #7 to test case #10)

Finally, fuel penalties were evaluated as the ratio ween the fuel consumption calculated during the transientsfor the considered strategy and the reference case Figure

bet-22 shows the fuel penalty values vs tr for several VVA, ComR and Combined strategies during tip-in mane-uvers at the four examined values of N/Nmax

E-EVO-For each test-case, fuel penalties varied significantly withengine speed More specifically, fuel penalties were mostsignificant at N/Nmax= 0.55, whereas they reach minimumvalues at the highest speeds Such a trend is very similar tothat shown in Figure 19(b) for and may be explained byrecalling that for roughly fixed engine efficiencies, average

fuel consumption deteriorates as average brake torque

increases

Finally, by adding a combustion retard to a specific

E-EVO-VVA strategy or to the baseline case a significant

increase in fuel consumption was usually obtained This

can be inferred from Figure 22 by comparing either test

case #7 (E-EVO-VVA) to test case #10 (same parameters

as case #7 plus a combustion retard of 15 CA deg) or test

case #8 (E-EVO-VVA) to test case #9 (same parameters as

case #8 plus a combustion retard of 15 CA deg)

7 CONCLUSION

In this paper, different strategies for turbolag reduction,

Early-Exhaust Valve Opening-Variable Valve Actuation

(E-EVO-VVA), combustion retard (ComR) and Combined

techni-ques were assessed by numerical simulation Such strategies

were aimed at increasing the engine exhaust-gas power

transferred to the turbine, thus reducing the time required to

accelerate the turbocharger group The effects of these

strategies were examined for tip-in maneuvers at fixed

engine speeds To this end, the 1-D model of an HD

turbo-charged CNG engine was set up and calibrated in the

GT-POWER environment for the simulation of transient

opera-tions

The different techniques for turbolag reduction were

ranked in terms of the Average Torque, ,during the

transi-ent and Torque Rising Time, tr, (i.e., the time interval

requir-ed by engine torque to rise from 10% to 90% of the totaltorque step) Constraints due to the maximum pressure ofthe in-cylinder gases (pmax) on the valve plate at EVO andfuel penalties were also taken into account The main resultwere:

• Torque Rising Time was the most suitable parameter fordefining turbolag;

• if no limits on pmax were introduced, then the Combinedstrategies allowed us to reduce tr by 35%~70% withrespect to baseline, depending on the engine speed;

• if pmax was required to be ≤20 bar, then, with VVA techniques, tr could be reduced by 10%~40% (testcase #7), whereas with Combined strategies, 20%~50%reductions could be achieved (test case #10);

E-EVO-• E-EVO-VVA strategies always had lower fuel tion than the corresponding Combined techniques When

consump-pmax ≤20 bar was required, the best E-EVO-VVA strategy(test case #7) had a fuel penalty of 0~6% with respect tobaseline, whereas the best Combined technique (test case

#10) had a fuel penalty of 0.5~8%, depending on theengine speed

The extent to which a specific strategy can be effective

in reducing turbolag varied according to engine speed.More specifically:

• for N/Nmax ≥0.55, tr reduction tended to be less relevant

as N/Nmax increased, for all strategies;

C

Figure 22 Trade-off between Torque Rising Time and fuel consumption penalties - Load steps at the indicated N/Nmax

• for all N/Nmax values, Combined and E-EVO-VVA

techni-ques permitted a more pronounced turbolag reduction than

the ComR strategy

Reasons for these behaviours were thoroughly discussed

in the ‘Result and Discussion’ section

ACKNOWLEDGEMENT− The present research work was

carried out within the GREEN Integrated Project of the European

Community, VI Framework Program The invaluable support of

S Golini, G Migliaccio and F Pidello from Fiat Research Center

is also acknowledged.

REFERENCES

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and Design 4th Edn McGraw Hill New York

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Guilain, S (2004) Design of an exhaust manifold to

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turbo-charged diesel engine Experimental Thermal and Fluid

Science 28, 8, 863−875

Galindo, J., Luján, J M., Serrano, J R., Dolz, V and

Guilain, S (2006) Description of a heat transfer model

suitable to calculate transient processes of turbocharged

diesel engines with one-dimensional gas-dynamic codes

Applied Thermal Engineering 26, 1, 66−76

Gamma Technologies (2006) GT-POWER® V6.2 User’s

Manual

Iwasaki, M., Ikeya, N., Marutani, Y and Kitazawa, T.(1994.) Comparison of turbocharger performance bet-ween steady flow and pulsating flow on engines SAE Paper No. 940839

Kato, K., Igarashi, K., Masuda, M., Otsubo, K., Yasuda, A.,Takeda, K and Sato, T (1999) Development of enginefor natural gas vehicle SAE SP-1436 ‘Combustion in SI Engines’, 52−60

Rakopoulos, C D and Giakoumis, E G (2006) Review ofthermodynamic diesel engine simulations under transientoperating conditions SAE Paper No. 2006-01-0884.Sammut, G and Alkidas, A C (2007) Relative contribu-tions of intake and exhaust tuning on SI engine breathing– A computational study SAE Paper No. 2007-01-0492.Westin, F and ngström, H E (2002) A method ofinvestigating the on-engine turbine efficiency combiningexperiments and modeling IMechE Paper C602/029/2002

Westin, F and ngström, H E (2003) Simulation of aturbocharged SI-engine with two software and compari-son with measured data SAE Paper No. 2003-01-3124.Westin, F., Rosenqvist, J and ngström, H E (2004).Heat losses from the turbine of a turbocharged SIengine – Measurements and simulation SAE Paper No.2004-01-0996

Westin, F (2005) Simulation of Turbocharged SI Engines – With Focus on the Turbine. Ph.D Dissertation TheRoyal Institute of Technology Sweden

Winkler, N and ngström, H E (2007) Study of measuredand model based generated turbine performance mapswithin a 1D model of a heavy-duty diesel engine operat-

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2007-01-Zhang, F R., Okamoto, K., Morimoto, S and Shoji, F (1998).Methods of increasing the BMEP (Power Output) fornatural gas spark ignition engines SAE SP-1371 ‘Com- bustion Processes in Engines Utilizing Gaseous Fuels’,

J M LEE , N W SUNG , G B CHO and K O OH

1)Alantum Corporation, StarWood Building, Sangdaewon 2-dong, Seongnam-si, Gyeonggi 462-819, Korea

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

3)Engine R&D Group, Korea Institute of Machinery & Metals, 171 Jang-dong, Yuseong-gu, Deajeon 305-343, Korea

(Received 22 December 2008; Revised 12 October 2009)

ABSTRACT− An analytical study of the performance of a radial-type, metal foam diesel particulate filter is reported A mathematical model for the filtration and regeneration of soot in a metal foam filter was developed Nickel foam was selected for the filter medium due to its large specific area, high porosity, and high thermal resistance For various metal foams, the filtration efficiency and the pressure drop through the filter were calculated, as was the deposition of soot The results from the analytical model were compared with experimental data In comparison with a conventional wall flow filter, the metal foam diesel particulate filter (DPF) is effective in utilizing the volume of material, due to the porous structures As the size

of the metal foam pores in the DPF increases from 580 µ m to 800 µ m, the filtration efficiency decreases from 90% to 50%, and the pressure drop decreases from 380 mbar to 20 mbar The metal foam DPF with a large pore size is effective in utilizing the volume of material with a small pressure drop The regeneration is completed within four minutes by the flow of hot exhaust gases under full load conditions

KEY WORDS : Diesel particulate filter (DPF), Metal foam, Radial-type DPF, Soot, Filtration, Regeneration

NOMENCLATURE

A p : area of the computational cell

A t : total cross-section area of the metal foam specimen

A v : void cross-section area of the metal foam specimen

C pf : specific heat of gas [1038 J/kgK]

C s : specific heat of metal [410 J/kgK]

k f : reaction rate constant for CO

d c : diameter of the collector [m]

k the : reaction rate constant of soot oxidation

d cell : diameter of the cell [m]

d pore : pore diameter [m]

E : filtration efficiency

h : heat transfer coefficient of metal [W/m2oC]

M c : molecular weight of soot [kg/kmole]

M o2 : molecular weight of O2 [kg/kmole]

N p : particle number density [#/m3]

Pe : peclet number

Pr : prandtl number

R : interception parameter

Re : Reynolds number

R t : O2 rate of consumption per unit area [kg/m2s]

S p : specific area of a collected soot particleSCF : stokes Cunningham factor

Stk : stokes number

u p : velocity of flow in the pore [m/s]

u w, v : velocity of flow in the inlet channel [m/s]

w : soot layer thickness [m]

β : forchheimer coefficient [1/m]

ε : porosity

λ : mean free path of gas molecules

λ eff : effective thermal conductivity of foam

0 : clean metal foam

*Corresponding author. e-mail: nwsung@skku.edu

p : particle, pore

d p : particle diameter

1 INTRODUCTION

The soot and NOx emissions from diesel engines are not

simultaneously controlled by a simple optimization of the

combustion process due to their trade-off relationships

Generally, NOx emission is reduced by exhaust gas

re-circulation or selective catalytic reactors, and soot is

con-trolled by a diesel particulate filter for meeting emission

regulations The soot is produced mainly by the incomplete

combustion of fuel in the fuel-rich region during the

combustion process The DPF has two major functions of

filtration and regeneration During the filtration process,

the soot particles in the exhaust are filtered by the porous

material, which results in a drop in pressure With the

increased pressure drop in the DPF, the power output of the

engine decreases, and an excessive pressure drop is critical

to stable engine operation The DPF is generally

regene-rated by burning the deposited soot

The conventional cordierite monolith filter is efficient in

the filtration of soot in a wall flow DPF The soot is

deposited on the surface of the wall Nickel-based metal

foam is considered as a good material for DPFs because of

its good thermal resistance and large specific surface area

for filtration Due to the high porosity and large pore size, a

metal foam DPF results in a substantially lower pressure

drop as compared with a wall flow DPF A uniform and

smooth temperature distribution is expected during

regene-ration in DPFs due to the high thermal conductivity and

uniform soot loading

Bissett (1984) introduced a mathematical model for the

filtration and regeneration processes of a wall flow-type

ceramic DPF Konstandopoulos and Johnson (1989) used

Bissett’s model to predict the pressure drop through DPFs

They calculated the pressure drop inside the filter substrate

and the inlet and outlet channels They showed that the

pressure drop inside the filter substrate was relatively

independent of the flow rate Later, they extended their

filtration model to include regeneration for 3D application

With the 3D model, for a non-uniform inlet flow, they

found an increased pressure drop through the DPF and

uniform soot loading During regeneration, the

non-uniform soot loading resulted in an excessive rise in the

local temperature (Konstandopoulos et al., 2001a) Huynh

et al (2003) developed a 1D filtration and regeneration

model for wall flow DPF Through experimental data, they

showed changes in the local properties of DPFs during

filtration and regeneration

The most critical variables in the analytical model are:

the packed soot density, ρ p; the permeability, k; and the

Forchheimer coefficient, β Konstandopoulos et al (2001b)

attempted to correlate ρ p with the flow They used the

Peclet number to calculate ρ p and the permeability Masoudi

et al (2000) studied the effects of DPF geometry and

showed good filtration with a minimum pressure drop bychanging the aspect ratio of the DPF Koltsakis et al.(2006) developed a filtration model for metal foam DPFs.They showed that the metal foam DPF had a greaterfiltration efficiency with a smaller pressure drop, whencompared with the wall flow-type DPF Additionally, throughexperiments, they showed that under low temperatures,catalysis-coated metal foam had fast regeneration as com-pared with ceramic material

The performance of the DPF is determined by thefiltration efficiency, the pressure drop during filtration, andthe rise in temperature during regeneration The purpose ofthis study is to evaluate the performance of a radial-typemetal foam DPF For this evaluation, a mathematical model

of filtration and regeneration processes in DPFs is

develop-ed Based on this model, the effects of important meters on filtration and regeneration are studied

para-2 STRUCTURE OF METAL FOAMMetal foam is made up of many irregular metal struts Thepores of metal foam are the spaces that are enclosed by thestruts The typical parameters in metal foam are: the strutdiameter, ds; the pore diameter, dpore; the porosity, ε; and thespecific area, S Figure 1 shows the structure of metal foam

as observed from a 3D X-ray scope From the image, ds and

dpore are measured as average values The specific area isdefined as the surface area of struts in a unit volume Theporosity is determined as the ratio of the pore area to thetotal area,

3 MODELING

A radial-type DPF has the advantages of a large filtration

area and flexibility of design, compared with an axial-type

DPF For a large power diesel engine, the radial-type DPF

is more effective for handling the large exhaust flow

exhaust flow Figure 2 shows the radial-type metal foam

DPF that was selected in this study The exhaust gas enters

the inlet tube at the center of the can, passes through the

metal foam substrate, and collects in the outer tube in the

periphery of the can for exiting The flow in the inlet and

outlet tubes is axisymmetric The flow in the filter substrate

is mainly in the radial direction

The governing equations of flow in the inlet tube are:

3 In a unit cell, the pore is replaced by a cell and the strut

is replaced by a cylindrical collector in the center Then, themetal foam is composed of many slabs of cells (Hinds,1999) The size of the collector is found from the hydraulicstrut diameter,

-∂rP

∂r

-= µ f

k -u f +βρ f u f2

µ=1.457 10 × 6 T 2/3 / T 10 ( + )

1 ε – ( )ρ s C s ∂T s

∂t

-=λeff ∂2Ts

∂z 2

- 1 r - + ∂∂r - r∂T s

∂r -

1 ε – ( )ρ C -=λTijn+∆t1–Tijn eff T i + 1 j – 2T ij + T i −1 j

∆z ( ) 2

-+λ eff T ij −1 – T ij

∆r ( ) 2

-+TTij+1 – T ij

∆r ( ) 2

- rj

∆r 2 - +

r j ∆r 2 - –

∆r -=H f ( ( ) T s i j n , − T ( ) f i j n , )

In Equation (19), ε 0 is the initial porosity.

From the filtration theory of particles, the soot particles

are captured by a cylindrical collector by the mechanisms

of diffusion, interception, and impaction Kirsch and Stechina

(1978) expressed the collection efficiency of cylindrical

collectors for soot particles by Brownian diffusion as:

In Equation (20), the Knudsen number, Kn, is 2λ/d p, where

λ is the mean free path of gas molecules and d p is the

diameter of the particles K is the hydrodynamic factor of a

cylindrical cell and is given by:

The Peclet number is defined by:

In Equation (22), u p is the flow velocity inside the metal

foam, which is found from:

D p is the diffusion coefficient of the particles,

(24)

In Equation (24), k b is the Boltzmann constant, T is the gas

temperature, and SCF is the Stokes Cunningham factor,

(25)When the small particles move along the stream lines

around the cylindrical collector, some particles that

ap-proach the collector within a distance of d p/2 from the

surface of the collector are captured by interception The

filtration efficiency of a single collector from intercepton

For large particles of micron size, the inertial impaction

is the dominant mechanism of filtration, while the bution of Brownian diffusion is negligible The large parti-cles can cross the stream lines, due to their considerableinertia, and collide with the surface of the collector(Konstandopoulos et al., 2000; Oh et al., 1981; Song andPark, 2006) For flows of Re > 100, the single-collectorfiltration efficiency of inertial impaction is:

1 N + R

+1.24K – 1/2 Pe – 1/2 N R2/3

-Figure 3 Schematic of the structure of metal foam by a unit

cell/collector

Figure 4 Schematic representation of a filter through slabs

of a unit cell/collector

pass the surface of the metal foam flow into the first slab

and are captured by the collector in the slab In the same

way, the particles are collected in the following slab

The soot mass that is collected at each slab can be

calculated by:

The diameter of the unit collector is increased by the

captured soot to:

In Equation (34), m p,s is the mass of soot collected per unit

length of the unit collector in the slab The porosity and the

pore size also change to:

In Equation (36), the tortuosity, χ, is calculated by:

The new values of the permeability and the Forchheimer

coefficient are calculated from correlations that were

derived by Du Plessis et al., (1994):

The rate of growth of the soot layer on the surface of the

metal foam is given by:

After the filtration process, regeneration commences The

reaction of soot oxidation is:

In Equation (40), f is the selectivity of CO

The continuity equation for O 2 through the metal foam inthe radial direction is:

4 EXPERIMENTS AND CALCULATION

To check the validity of the analytical model for filtrationand regeneration, engine tests were conducted for differentradial-type DPFs Table 2 summarizes the specifications ofthe radial-type DPF and the engine The filtration testswere conducted in an engine dynamometer at a constantspeed of 40 km/h for 2.5 hours The weight of the metalfoam DPF was measured before and after the tests Duringthe test, the pressures and temperatures at the inlet andoutlet of the DPF and inside the metal foam were measuredalong with the rate of flow The size and number of parti-cles were measured both upstream and downstream of the

- r ρ o2u = – k the 1 f

2 - –

∆ H the = f co ∆ H co + 1 ( – f co )∆ H co2

DPF by SMPS (Grimm Aerosol Technik) A thermodenuder

(Dekaki Ltd.) was used to prevent condensation of the

exhaust gas The error of SMPS is reported as ±2.5%

Following the filtration test, a regeneration test was

con-ducted for 15 minutes under full load conditions A

sche-matic of the test setup is shown in Figure 5

5 RESULTS AND DISCUSSION

Calculations were carried out for the 2.5-hour-long

fil-tration process For the calculations, the number of node in

the axial direction for the inlet and outlet channels was 41,

and the size of grids in the radial direction in the metal

foam substrates was determined by the diameter of a unit

The running time for one calculation was about 4 hours on

a 3.2-GHz Pentium 4 PC The experimental data of the

temperature and the flow rate of the exhaust gases and the

soot number density were used as the initial conditions for

the calculations Figure 6 shows the variation of the ssure drop and the mass of soot collected in the DPF duringfiltration Compared with the experimental pressure dropdata, the calculation results show a linear increase in thepressure drop This increase is mainly due to the idealdeposition of soot in the calculation, which does not accountfor the actual blow-off mechanism that arises during filtra-tion From this result, it is concluded that the model issatisfactory for analyzing the filtration process For ex-amining the effect of different pore sizes on filtration, metalfoams of 580, 800, and 1200µm were tested by the model.The gradient DPF shown in Figure 7 was also consideredfor this study Figure 8 shows the calculated and measuredresults of filtration for a 580-µm DPF The dominant size

pre-of particles in the exhaust is around 60 nm For particles pre-ofsize 40~80 nm, filtration is rather limited but improvesover time because the soot that collects in the metal foamdecreases the pore size

Figure 9 shows the filtration efficiency for various particlesizes, following a time lapse of 30 minutes The filtrationefficiency is almost 100% for the nano- particles and de-creases for the larger particles The filtration efficiency ofDPFs of large pore sizes is very low for micron particles.The DPFs with large pore sizes show poor filtration whencompared to those with small pore sizes The gradient DPFand the 800-µm DPF show similar results The filtration

Exhaust gas flow rate (kg/hr) 160

Soot emission rate (g/hr) 5.24

Inner diameter of foam (mm) 57.2

Metal foam thickness (mm) 34

Pore size (ìm) 450, 580, 800, 1200

Figure 5 Experimental setup for the engine tests

Figure 6 Measured and calculated mass of soot collectedand pressure drop in the radial-type DPF

Figure 7 Gradient metal foam filter

efficiency for large soot particles of micron size is very

low, especially for the DPF with a 1200-µm pore size

Figure 10 shows the variation of the total filtration

effici-ency for a 30-minute filtration process The total Figure 10

Variations of total filtration efficiency during the filtration

process with a 40-km/hr vehicle speed for various metal

foam DPFs

The total filtration efficiency is 90% for the 580-µm DPF

and 50% for the 1200-µm DPF

Figure 11 shows the variation of the mass of soot that is

collected in the DPF with the total filtration efficiency

during the 30-minute filtration The collected soot will

accrete layers on the surface of the metal foam and reduce

the pore size inside, which will result in an increase in the

filtration efficiency The total filtration efficiency of the1200-µm DPF is lower than that of the 800-µm DPF afterthe 30-minute filtration Figure 12 shows the pressure drop

in the DPFs during filtration The 580-µm DPF shows arapid pressure drop when compared with the 800-µm and1200-µm DPFs The pressure drop in the gradient DPF islower than that in the 800-µm and 1200-µm DPFs Withthe same mass of soot that is collected in the 800-µm DPF,shown in Figure 11, it is thought that the soot collectsevenly inside the foam in the gradient DPF Figure 13shows the radial flow velocities at the surface of the metalfoam in the inlet tube When the flow moves into the inlettube, a high pressure is built up near the closed end, whichresults in high radial velocities The variation in radial flowvelocities in the inlet tube is greater for DPFs with large

E =1 m soot,out

m soot,in

-–

Figure 8 Development of filtration for a 580-µm DPF

Figure 9 Filtration efficiencies for various metal foam

DPFs at the beginning and end of the filtration process with

a 40-km/hr vehicle speed

Figure 10 Variations of total filtration efficiency during thefiltration process with a 40-km/hr vehicle speed for variousmetal foam DPFs

Figure 11 Variation of the total filtration efficiency as afunction of the mass of soot collected at a 40-km/hr vehiclespeed for various metal foam DPFs

pore sizes After the 30-minute filtration, the magnitude of

the radial velocities becomes uniform because the surface

area of the metal foam is reduced by the deposited soot

layer Figure 14 shows the thickness of the soot layer on thesurface of the metal foam, following the 30-minutefiltration Given the high flow rate near the closed end, thesoot layer becomes thicker in that region The 580-µm DPFshows a thicker layer of soot on the surface of the metalfoam, when compared with the 1200-µm DPF The sootlayer in the gradient DPF has a thickness similar to that inthe 1200-µm DPF Figure 15 shows the mass of soot that iscollected in the metal foam in the radial direction The 580-

µm DPF shows a heavy deposit of soot in the entranceregion, when compared with the 800- or 1200-µm DPFs.For small pores, under larger filtration efficiencies, the poresize decreases quickly For large pores, under lower filtra-tion efficiencies, the change in pore size is slow, and thesoot collects gradually inside the foam The heavy deposit

of soot in the entrance region will result in a large pressuredrop there The 1200-µm DPF shows an evenly distributed

Figure 12 Variation of the pressure drop during the

filtra-tion process at a 40-km/hr vehicle speed for various metal

deposit of soot inside the foam The soot deposit under the

gradient DPF is even more uniform than under the

1200-µm DPF From these results, it is concluded that the

gradi-ent foam can work as well as: an 800-µm foam in terms of

the filtration efficiency; a 580-µm foam in terms of the

mass of soot that is collected; and a 1200-µm foam in terms

of the pressure drop Following a 2.5-hour filtration

pro-cess at a vehicle speed of 40 km/hr, the regeneration starts

at the full load condition Regeneration continues for four

minutes under full load conditions for the different DPFs

When the temperature of the metal foam rises to 800 K at

the full load condition, regeneration commences Figure 16

shows the variation of the pressure drop during the

regene-ration The pressure drop abruptly increases in the early

part of the regeneration due to an increased rate of flow at

the full load condition Figure 17 shows the variation of the

mass of soot in the DPF during regeneration Because the

soot is heavily loaded at the entrance region of the DPF,

From the results of the analytical model of the filtration andregeneration processes for the radial-type metal foam DPF,the following conclusions are reached

(1) As the filtration process continues, the collected sootmass and pressure drop through the DPF increaselinearly with time

(2) As the size of the metal foam pores in the DPFincreases from 580 µm to 800 µm, the filtration dropdecreases from 380 mbar to 20 mbar

(3) The regeneration starts with a flow of hot exhaust gasesand completes within four minutes under full loadconditions

ACKNOWLEDGEMENT− This study was supported by the CEFV (Center for Environmentally Friendly Vehicle) of the Eco- STAR Project of the Ministry of Environment of Republic of Korea in 2008.

REFERENCESBissett, E J (1984) Mathematical model of the thermalregeneration of a wall flow monolith diesel particulatefilter Chem Eng Sci., 39,1233−1244

Davis, N (1973) Air Filtration Academic Press NewYork

Du Plessis, P., Montillet, A., Comti, J and Legrand, M.(1994) Pressure drop for flow through high porositymetallic foam Chem Eng Sci.,49,3545−3553.Hinds, W (1999) Aerosol Technology A Wiley-IntersciencePub New York

Huynh, T., Johnson, J H., Yang, S L., Bagley, S T andWarner, J R (2003) A one-dimensional computationmodel for studying the filtration and regeneration charac-teristics of a catalyzed wall flow diesel particulate filter.SAE Paper No 2003-01-0841

Kirsch, M and Stechkina, I B (1978) Fundamentals of Aerosol Science: The Theory of Aerosol Filtration with Fibrous Filters John Wiley & Sons New York.Konstandopoulos, G A and Johnson, J H (1989) Wall-flow diesel particulate filters - Their pressure drop andcollection efficiency SAE Paper No 890405

Konstandopoulos, G A., Kostoglou, M., Skaperdas, E.,Papaiounnou, E., Zarvalis, D and Kladopoulou, E A.(2000) Fundamental studies of diesel particulate filters:Transient loading, regeneration and aging SAE Paper

trap regeneration SAE Paper No 2001-01-0908.

Konstandopoulos, G A., Skaperdas, E and Masoudi, M

(2001b) Inertial contributions to the pressure drop of

diesel particulate filters SAE Paper No 2001-01-0909

Koltsakis, G C., Katsaounis, D., Samaras, Z., Naumann,

D., Saberi, S and Boem, A (2006) Filtration and

regeneration performance of a catalyzed metal foam

particulate filter SAE Paper No 2006-01-1524

Masoudi, M., Heibel, A and Then, P M (2000) Predicting

pressure drop of wall flow diesel particulate filters Theory and experiment SAE Paper No 2000-01-0184

-Oh, S H., MacDonald, J S., Vaneman, G L and Hegedus,

L L (1981) Mathematical modeling of fibrous filtersfor diesel particulates - Theory and experiment SAE Paper No 810113

Song, A and Park, H S (2006) Analytic solutions forfiltration of polydisperse aerosol in fibrous filter Power Technology, 170,64−70

J VENKATESAN 1)* , G NAGARAJAN 2) , R V SEENIRAJ 2) and R MURUGAN 1)

1)Department of Mechanical Engineering, Sri Venkateswara College of Engineering, Chennai 602 105, India

2)Department of Mechanical Engineering, College of Engineering, Anna University, Chennai 600 025, India

(Received 25 November 2008; Revised 28 October 2009)

ABSTRACT− Mathematical simulation is the process of designing a model of a real system and then conducting experiments with the simulation to understand the system’s behavior Mathematical simulation is widely used for investigating and designing compressors, and with a minimal number of simplifying assumptions, mathematical models can be used in conjunction with modern computing tools to solve complicated problems A considerable amount of previous research has focused on the mathematical modeling of reciprocating air compressors used in automotive braking The aim of the present work was to experimentally validate the mathematical model for such compressors We present a simplified and effective mathematical model for estimating compressor performance, and this model can easily be executed using personal computers Parameters such as compressor speed, discharge pressure and clearance volume were evaluated in terms of their effect on the thermodynamic behavior of compressors The model can predict cylinder pressure, cylinder volume, cylinder temperature, valve lift and resultant torque at different crank angles; it can also predict the free air delivered and the indicated power of the compressor Therefore, the model has been validated using experimental results.

KEY WORDS : Resultant torque, Indicated power, Peak pressure, Free air delivered (FAD), Volumetric efficiency

NOMENCLATURE

Ac : dross sectional area of cylinder, m2

D : diameter of cylinder, m

L : stroke length, m

T : temperature of air at particular crank angle, K

Tr : torque on the crankshaft, Nm

lc : length of connecting rod, m

r : crank radius (L/2), m

θ : crank angle, deg

ω : angular velocity of the crank, rad/s

N : compressor speed, rpm

p : pressure of air an instant, Pa

V : volume of air inside the cylinder, m3

Z : number of ports (openings in the compressor head

on suction and delivery sides)

E : young’s modulus of valve material, N/m2

ks : stiffness of the suction valve, m/N

I : area moment of inertia of valve, m4

xd : distance of point of application of force from fixed

end, m

Cv : specific heat at constant volume, J/kg-K

m : mass of air in the cylinder, kg

ms : mass of air flowing through the suction valve, kg

md : mass of air discharged out through the delivery

valve, kg

S : valve lift (distance between valve plate and valve), m

n : ratio of connecting rod length to cylinder diameter

Fc : force acting on the crank, N

Fd : net force acting on the delivery valve, N

Fp : net force acting on the piston, N

Fsi : force due to initial compression of valve, N

ω n : natural frequency of valve, rad/s

B : factor accounting the instantaneous change of

specific volume, m3/kg

ρ : density of air, kg/m3

ζ : damping factor

m : instantaneous mass, kg

Q : heat transfer to actuating medium, J

α(θ) : heat transfer coefficient, W/m-KExp : experimental

Pre : predictedSUBSCRIPTS

1 INTRODUCTION

A reciprocating compressor consists of a crankshaft (driven

by a gas engine, electric motor, or turbine) attached to a

connecting rod, which transfers the rotary motion of the

crankshaft to the piston The piston travels back and forth

in a cylinder Air enters the cylinder through a suction

valve at suction pressure, and the piston compresses the air

to reach the desired discharge pressure When the air

reaches the desired pressure, it is then discharged through a

discharge valve The desired discharge pressure can be

reached through utilization of either a single or

double-acting cylinder In a double-double-acting cylinder, compression

takes place at both the head-end and the crank-end of the

cylinder The cylinder can be designed to accommodate

any pressure or capacity, thus making the reciprocating

compressor the most popular type used in the automobile

and gas industries Therefore, it is important to construct an

accurate mathematical model that can predict the behavior

of these compressor systems

Building a mathematical model (Venkatesan et al., 2007;

Lawson and McLaren, 1984; Tian et al., 2005) for any

project may be a challenging, yet interesting, task To build

such models, a thorough understanding of the relevant

underlying scientific concepts is necessary, and a mentor

with expertise in the project is invaluable It is also best to

work as part of a team that can provide more brainstorming

power In industry and engineering, it is common practice

for a team of people to work together toward building a

model, and the individual team members bring different

areas of expertise to the project Once the model has been

developed and applied to the problem, the resulting model

solution must be analyzed and checked for accuracy This

process may require modifying the model to obtain a

reasonable outcome This refining process should continueuntil a model that agrees as closely as possible with real-world observation is obtained

2 MODEL FORMATIONThe physical dimensions of the reciprocating compressorare shown in Figure 1

The model was based on the following thermodynamicequations (Venkatesan et al., 2007; Lawson and McLaren,1984)

Suction

(1)Compression and reexpansion

(2)Discharge

(3)The governing equation for determining the instantaneouscylinder pressure was expressed as the following:

(4)The second term in equation (4) accounts for the com-pressibility of air Because single-stage compressors aredesigned for limited pressure ratios, the second term can beneglected for analysis purposes

The governing equation for determining the mass flowwas expressed as the following:

(5)The third term in equation (5) indicates losses by variousprocesses (e.g., leakage loss, etc)

The governing equation for determining the workingvolume (Venkatesan et al., 2007; Francis et al., 1965) wasexpressed as the following:

(6)The resultant torque (Tr) was calculated using the followingexpression

(7)

2.1 Indicated Power (IP)Because all of the processes do not follow a particularthermodynamic law, it was not advisable to use readily

mCv = dT dt

-+ mRT V

- dV dt

-− dQ dt

-=0

mCvdT -+dt mRT

V

- dV dt

d θ -− dm o

d θ -− ∑dmop

d θ -

dV

d θ -=± A c L

2

- sinθ + n sinθ cosθ

1 – n 2 sin 2 θ -

T r = F p r sinθ + sin2θ

2 ( l c / r ) 2 −sin 2 θ -

Figure 1 Schematic diagram showing the physical

dimen-sions of the reciprocating compressor

available equations for determining the indicated power

during a suction or discharge process Figure 2 illustrates

the integration method used to estimate the indicated

power The following general and effective model was

used for estimating IP during any incremental change in

crank angle (Venkatesan et al., 2007)

(8)

2.2 Discharge Process

The deflection of the delivery reed was calculated from the

following expression (Werner, 2007; Arne, 1974)

(9)2.3 Suction Process

Using effective valve dynamics (Kazutaka and Susuma,

1980; Stif Helmer Joergensen, 1980) the following

expre-ssion can be written:

a speed pot in the control panel, and it was cooled by afan The compressor was connected to a 50 liter re-servoir, and the pressure was maintained by using agovernor valve

IP θ =IP θ-1 + V ( θ-1 – V θ ) p θ-1 + p θ

2 -

60 -

Figure 3 Delivery reed in the closed position

Figure 4 Delivery reed in the full-open position

Figure 5 Suction reed in the closed position

Figure 6 Suction reed in the full open position

Figure 7 Experimental setup

Compressor details:

4 RESULTS AND DISCUSSION

In an ideal compressor, the suction pressure and the

discharge pressure are constant because the cylinder

dia-meter is assumed to be equal to the suction/discharge port

diameter In an actual compressor, the port diameter is less

than the cylinder diameter Therefore, during the suction

process, the volume displaced by the piston is greater than

the volume of air entering the cylinder during a particular

time interval The net effect is a decrease in the suction

pressure to a level below that of an ideal compressor

Similarly, during the discharge process, the volume

dis-placed by the piston is greater than the volume of air

discharged through the discharge port The net effect is an

increase in the cylinder pressure to a level above the

discharge pressure Due to excess peak pressure during the

discharge process, the indicated power of the compressor is

always greater than the ideal indicated power for aparticular amount of free air delivered (FAD) Compressorcapacity is generally expressed in terms of FAD, which isdefined as the volume of air delivered by the compressorwhen the condition (the temperature and the pressure) ofair is reduced to the intake condition The compressor’s

Bore diameter (D) 66.67 mm

Connecting rod length (lc) 70 mm

Suction reed lift (hs) 2.2 mm

Delivery reed lift (hd) 1.8 mm

Mass of reciprocating parts (mrec) 0.245 kg

Discharge pressure (pd) 5 to 9 bar (abs)

Diameter of suction port (dos) 11 mm

Diameter of delivery port (dod) 11 mm

Effective length of suction reed (ls) 71 mm

Effective length of delivery reed (ld) 45.5 mm

Mass of delivery valve (mdv) 2 g

Number of suction ports (Zs) 4

Number of delivery ports (Zd) 2

Table 1 Performance of the compressor at different discharge pressures (N=3000 rpm)

Results

Pre 6 barExp 7 barPre 7 barExp 8 barPre 8 barExp 9 barPre 9 barExp

Figure 8 Pressure-volume diagram (speed=3000 rpm)

Figure 9 Pressure-crank angle diagram (speed=3000 rpm)

Figure 10 Valve lift-crank angle diagram (speed=3000rpm)

volumetric efficiency is mainly dependent on the suction

pressure The effect of reduced suction pressure is to

significantly reduce the volumetric efficiency Here, the

aforementioned model was tested using different discharge

pressures and compressor speeds The simulated results

were very close to the experimental results, which

indicat-ed the accuracy of the model

4.1 Sensitivity Analysis

The clearance volume was increased to 8.31 cc in an

existing 160 cc air-cooled compressor, and the system’s

performance was tested at different speeds and delivery

pressures The sensitivity of the developed model was

tested using the experimental results from the modified

compressor Table 2 summarizes the results obtained from

experiments and from simulations using the developed

model

The increase in clearance volume caused a decrease in

the volumetric efficiency and the FAD Both the

experi-mental and the predicted results indicate that the metric efficiency and the FAD were each reduced when theclearance volume was increased from 6.67 cc to 8.31 cc Inthe modified compressor, the deviation of the predictedvalue from the actual value was about 6% for peakpressure, 8% for both FAD and volumetric efficiency, and5% for shaft power The predicted values are slightlyhigher than the values from the actual compressor, but theyare still acceptably close to the expected level Based onprevious work on compressor design, it has been shownthat clearance volumes ranging from 2.5 to 4.5% of thestroke volume give better performance (Venkatesan et al.,2007; Werner, 1980; Lawson and McLaren, 1984) In ourmodified compressor, the clearance volume was 5.2%,which was the primary cause of the large observed devia-tions

volu-Figure 11 Torque-crank angle diagram (speed=3000 rpm)

Figure 12 Free air delivered-discharge pressure diagram

Pre 6 barExp 7 barPre 7 barExp 8 barPre 8 barExp 9 barPre 9 barExp

5 CONCLUSION

The model presented here predicts fluctuations in pressure

during the suction and discharge processes of a

reciprocat-ing compressor It also predicts valve flutterreciprocat-ing durreciprocat-ing

suction and discharge at all delivery pressures The

simu-lated results from the model are comparable with the

experimental results Using this model, it is possible to

compute volumetric efficiency, free air delivered, indicated

power, cylinder air pressure, cylinder air temperature,

resultant torque and mass of air imported or discharged per

cycle It is also possible to determine these values after

varying either the operating parameters (e.g., speed,

dis-charge pressure, etc.) or the physical parameters (e.g.,

clearance volume, crank radius, connecting rod length and

cylinder diameter) The model can be used for theoretical

analysis of single-stage, single-cylinder reciprocating air

compressors with a disc valve The development of this

model was based on the previous research and technical

resources available from the compressor-design field The

constants used in the development of the model were based

on the available experimental results and on information

from previous research in the compressor-design field

Simple assumptions were made in the development of the

model, and these assumptions could be varied or omitted

depending on the operating parameters and physical

condi-tions of the compressor Finally, the effectiveness of the

developed model was very much dependent on the “usage

of suitable constants” in the model (e.g., coefficient of

discharge, index of compression, etc)

REFERENCES

Arne, M B (1974) Computer simulation of valve dynamics

as an aid to design Norwegian Institute of Technology Proc Int Conf Compressor Technology, Purdue Univer-sity, West Lafayette, Indiana, USA

-Francis, L S., LaiSing, T and -Francis, T (1965) anical Vibrations CBS Distributors Delhi India.Kazutaka, S and Susuma, N (1980) Practical method foranalysis and estimation of reciprocating hermetic com-pressor performance Hitachi Ltd, Japan -Proc Int Conf Compressor Technology, Purdue University, WestLafayette, Indiana, USA

Mech-Lawson, S and McLaren, R J L (1984) An approach tocomputer modeling of reciprocating compressors pre-stoold limited U.K, Proc 1984 Purdue Compressor Technology Conf., Purdue University, West Lafayette,Indiana, USA

Stif Helmer, J and Danfoss, N (1980) Transient valveplate vibrations Proc Int Conf Compressor Technology,Purdue University, West Lafayette, Indiana, USA.Tian, C., Liao, Y and Li, X (2005).A Mathematical model

of variable displacement swash plate compressor forautomotive air conditioning system Int J Refrigeration

29, 2, 270−280

Venkatesan, J., Nagarajan, G., Seeniraj, R V and Sampath,

S (2007) Mathematical model for theoretical gation of a disc valve reciprocating air compressor ofautomotive braking system Int J Applied Mathematical Analysis and Applications 2, 1-2, 209−227, Serial Publi-cations, New Delhi, India

investi-Werner, S (1980) Design and Mechanics of Compressor Valves. Ray W Herrick Laboratories School of Mech-anical Engineering Purdue University West Lafayette.Indiana USA

D DANARDONO , K S Kim , E ROZIBOYEV and C U KIM

1)Department of Mechanical Design Engineering, Chonnam National University, Jeonnam 550-749, Korea

2)Korean Institute of Machinery and Materials, 171 Jang-dong, Yuseong-gu, Daejeon 305-343, Korea

(Received 8 April 2009; Revised 21 July 2009)

ABSTRACT− A roller vane type liquefied petroleum gas (LPG) pump was developed for a liquid phase LPG injection (LPLi) engine Most of the LPG pumps used in the current LPLi engines are installed inside of the LPG tank, but this pump is intended to be installed outside of the LPG tank to overcome the difficulty of fixing an in-tank pump Because LPG has a low boiling point and high vapor pressure, it usually causes cavitation in the pump and consequently deteriorates the flow rate of the pump The purpose of this work is to optimize the design of the roller vane pump in order to suppress cavitation and increase the fuel flow rate by using a computational fluid dynamics (CFD) analysis In order to achieve these goals, the intake port configuration and the rotor of the roller vane pump were redesigned and simulated using STAR-CD code Computation was performed for six different models to obtain the optimized design of the roller vane pump at a constant speed of 2600 rpm and a constant pressure difference between the inlet and outlet of 5 bar The computation results show that an increased intake port cross-section area can suppress cavitation, and the pump can achieve a higher flow rate when the rotor configuration is changed to increase its chamber volume When the inlet pressure difference is 0.1 bar higher than the fluid saturation pressure, the pump reaches its maximum flow rate

KEY WORDS : LPG (liquefied petroleum gas), Roller vane pump, Cavitation, Intake port, Rotor, Flow rate

1 INTRODUCTION

Cavitation can occur in a positive displacement pump such

as a roller vane pump, especially when it works at high

operating speeds (Choi and Kang, 2003) As fluid enters

the suction side of the pump, its pressure is reduced If the

absolute pressure drops below the vapor pressure of the

fluid, vapor bubbles begin to form These bubbles implode

or collapse when transferred to the high pressure side of the

pump These implosions acting on pump parts result in

tremendous surface fatigue and, hence, cavitation damage

in the form of pitting (Lee et al., 2002) Additionally, the

bubble formation causes the pump chamber to fill with

vapor and as a result the pump flow rate will decrease

Cavitation also produces a shrill noise created by the

implosion of the bubbles It is obvious that to avoid

cavitation, the pressure on the suction side must remain

above the fluid vapor pressure under all operating

condi-tions of the pump

This pump design has established the need to understand

the flow through the suction port of the pump The

illustra-tion in Figure 1 can be used to understand the sucillustra-tion

process in a roller vane pump In a roller vane pump a set

of roller vanes are mounted on a rotor that rotates inside a

cavity The centers of the rotor and the stator are offset,

causing an eccentricity (Manco et al., 2004) The rollervanes can slide into and out of the rotor and are sealed onthe edge, creating chambers (Zhurba and Cleghorn, 2000).The chambers are mechanically coupled to a rotatingshaft, and periodically, their volumes are changed while theshaft rotates When the roller vane chamber is brought intocontact with the intake port, the volume of the chamberincreases and the pressure in the chamber drops slightly.This results in a pressure gradient, which induces a flow offluid that fills the chamber After the chamber is filled withfluid, then it is brought into contact with the pressure sidethrough another opening The volume of the chamber isdecreased, and the contained fluid is displaced into thepressure channel

*Corresponding author. e-mail: sngkim@chonnam.ac.kr Figure 1 Illustration of a roller vane pump

Compared with the blade vane pump, the roller vane

pump has some advantages Rollers do not stick due to the

relative freedom and limited contact area between the roller

and carrier This allows the suction and discharge pressure

to become equal (Sluis, 2003) The velocity of the fluid at

any angular location in the suction port of the roller vane

pump is a function of the size and shape of the port, the

geometrical displacement of the pump and the pump speed

Additionally, the pressure drop through the suction port is

proportional to (1/Aport)2, where Aport is the average area of

the suction port (Singh, 1991) The pressure drop should be

as small as possible to obtain a suction pressure that is

higher than the vapor pressure, thus avoiding cavitation

(Singh, 1991, Wurtenberger, 2007) When cavitation occurs

within the pump, there will be a flow-limiting effect on the

pump The mass flow only increases slightly, although the

pump speed continues to increase (Wurtenberger, 2007)

The carrier geometry, the roller slot shape and the clearance

between the roller and the slot are also important factors in

the roller vane pump performance They influence the

pressure build-up and build-off in the pump (Sluis, 2003)

The flow type of the fluid within the pump can influence

the noise, vibration and harshness (NVH) performance

Reducing the degree of turbulence in the flow will reduce

the NVH of the pump (Wang et al., 2001)

The use of computational fluid dynamics (CFD) tools to

improve the design of the pump can be very useful A CFD

analysis of a vane pump can provide important information

about both the overall performance of the pump, and the

flow details within the pump, such as flow leakage patterns

for various head rises (Fluent, 2005) CFD analysis can

help to reduce redundant testing and the number of pump

prototypes, hence resulting in a reduction of product

development costs and cycle time (Wang et al., 2001;

Chandrasekhar, 2005; Wurtenberger, 2007) In this work,

by using CFD tools, the pump geometry was redesigned by

altering some design variables such as the intake port

cross-section area, the intake port angle against the rotor

and rotor configuration, in order to suppress cavitation

problems and to increase the flow rate of the pump

2 EXPERIMENTAL SETUP

For the purpose of measuring the base-line flow rate of the

prototype pump, experiments were conducted by using a

baseline liquefied petroleum gas (LPG) roller vane pump

Figure 2 shows the experimental system and the pump

breakdown parts used for testing the LPG roller vane

pump The experimental system consisted of the following:

The experiment of the inline pump is set at a constant

speed of 2600 rpm by using a BLDC (Brushless DC) driver

(Lim et al., 2007) The pressure difference between the inlet

and outlet is kept constant at 5 bar The pump flow rate of

the experiment result will be used as a base for the

computational model The composition of the LPG used in

the experiment is shown in Table 1

3 ANALYSIS FORMULATION3.1 CFD Analysis

Three-dimensional CFD models were created using WORKS and STAR-CD software The details of the pumpmodel are shown in Figure 3(a) In creating the mesh of thestationary part, a 3D model was drawn with SOLIDWORKS,and the surface mesh was generated with pro-STAR/surf.Finally, a solid mesh of the stationary part was automati-cally generated with pro-STAR/amm For the stator model,

SOLID-Figure 2 Experimental system and pump components.Table 1 LPG Composition

a hexahedral mesh with a trimmed-cell polyhedral was

chosen The rotor (the time-varying roller vane) motion

was simulated using a dynamic mesh model in STAR-CD

This model was used for simulating flows, where the shape

of the domain varied with time due to the motion of the

domain boundaries The model required only an initial mesh

volume and a description of the motion of the moving

zones The meshes of the two fluid volumes formed by the

pump components are shown in Figure 3(b) and Figure

3(c) Each of the CFD models has about 250,000 cells

To simulate the flow in the small gap of the rotary vane

pump a method called the sliding interfaces method is used

(Beilke, 1998) The sliding interfaces method enables the

interface cells to progressively change their connectivity

during the solution finding process The change in cell

connectivity is activated through the “cell attachment”

operation The cell pair to be attached and the time of

attachment are specified by the user EVENT command

module The cell attachment event is executed when the

current simulation time equals the time specified by the

event step within a given tolerance Using this method, the

space with a constantly changing rotary vane pump profile

is filled, according to the time and space events specified

by the user, with the cells between the vertices located at

the outer rotor and inner stator surfaces Since two

interfaces are constantly connected to each other out the full pump rotation cycle, the conditions in whichthe gap (0.05 mm in our model) between the rotor and thestator is very small can be simulated without deactivatingthe cells In the final stage of completion of the CFD pumpmodel, the rotor and the stationary part are assembled, asshown in Figure 4 and Figure 5

through-The CFD results were based on a transient analysis through-Thek-epsilon/high Reynolds number turbulence model wasused to account for the turbulent conditions A cavitationcalculation using the Rayleigh model was incorporated intothe simulation to analyze the cavitation flow in the pump.Constant pressure boundaries were applied for both theinlet and outlet in these CFD models Pressure and attachedboundaries were used in the CFD analysis of the roller vanepump (see, Figure 4 and Table 1) The roller vane pumpconsisted of six roller vanes rotating at 2600 rpm Thepressure rise across the pump was 5 bar At the inlet, thepressure was specified as the boundary condition based onthe pressure in the LPG experiment tank, and the outletpressure was 5 bar higher than the inlet pressure To sim-plify the computation model, n-C4H10 was used as the fluidtype, which is the most dominant component of the LPG.Although this would not give exactly the same result as theexperiment, with reference to the properties of the fluids, itwill still produce a very similar result

The AMG (algebraic multigrid) solution method was usedfor different analysis parameters, while the incompressibleflow and linear upwind differencing (UD) scheme was usedfor velocity and other variables Five cycles were simulatedusing 3600 time steps (iterations) per cycle; each time stepwas 0.1 degrees or 6.41e−06 s Simulations were performedusing a computer with specifications of Q9450 4 CPUs,

Figure 3 (a) Parts of the pump computation model, (b)

solid mesh of the stationary part, (c) solid mesh of the rotor

Figure 4 Boundary region of the CFD model

Figure 5 Close-up view of the mesh

2.66 GHz and 8 GB of RAM The simulations took 60

hours for each cycle Pump simulations were performed for

fuel temperatures of 273 K and 293 K with the inlet

pre-ssures set to 0.1 bar, 0.05 bar, 0.025 bar, and 0 bar higher

than the fluid saturation pressure The pressure difference

between the inlet and outlet of the pump was kept constant

at 5 bar (Gang and Sim, 2004)

3.2 Simulation Results of the Pump Baseline Model

For the CFD analysis, a baseline model was made The

specification and the rotor geometry of the actual pump

model are shown in Figure 6 and Table 2

The simulation results of the baseline model (Figure

7(a)) show the distribution of static pressure within the

chambers and gaps When the roller vane alignment is such

that the chambers are cut off from the inlet and outlet ports,

a pressure buildup is followed by a pressure dip The

pressure information is useful for determining if the flow

cavitates, as well as for assessing the pressure ripple effect

(a pressure change between roller vanes) The velocity

vectors in Figure 7(b), show the flow details, which can be

used as a guide for improving the pump design

The results also show that cavitation occurred in the

roller vane pump Figure 8 displays the cavitation contours

(the images were captured after two rotations of the rotor)

at the different inlet pressures and at inlet fluid

temper-atures of 293 K and 273 K According to Figure 8, when

the inlet pressure was equal to the saturation pressure ofbutane, significant cavitation in the roller vane chambersoccurred When the chambers were in contact with theintake port for a very short period of time, a complete pre-ssure build-up did not occur, so the pressure dropped belowthe saturation pressure, causing vapor bubble formation.Then, the chambers came closer to the outlet port, and theirvolumes decreased while the pressure increased, resulting

in the collapse of the bubbles and in turn, cavitation Infact, the LPG expands upon release, and 1 liter of liquidwill produce approximately 250 liters of vapor Thus, whenthe chambers carry the liquid mixed with vapor to theoutput port, the flow rate will drop significantly at the outlet.Figure 9 shows that the pressure affected the flow ratefor the actual (baseline) pump model (Model A) at thedifferent pressure differences and the two fluid temper-atures studied The flow rates changed to the same values

Table 2.Specification ofthe LPG roller vane pump

base-line model

Baseline model UnitInner ring radius, Rmin 12.5 mm

Outer ring radius, R max 13.47 mm

Distance between two eccentric

circles centers, d 0

Intake port cross section area 33.02 mm2

Angle between intake

Figure 6 Rotor configuration

Figure 7 Pressure contour (a) and velocity vector (b) in theroller vane pump

Figure 8.Cavitation distributions in the baseline LPG rollervane pump model at 273 K and 293 K

at the different temperatures and exhibited the same

ten-dencies When dP=0 bar, the flow rate was equal to 21.5 L/

hour, meaning that the pump worked at only 16.5% of the

pumping capacity due to the severe cavitation in the pump

With increasing dP values, the flow rate also increased

dramatically However, when dP=0.1 bar, the flow rate

reached its highest point in the graph (see Figure 10), also

known as the flooded inlet condition When the flooded

inlet condition was specified in the pump, the pumping

capacity reached its peak and did not exceed this point with

any further increase in the pressure unless the rotation

speed was increased The cavitation value in Figure 9 is

shown in arbitrary unit (AU)

If we compare the flow rate of the computation results

with the experimental data, it can be seen that with dP set

to 0.1bar, after 0.015 seconds, the average flow rate of the

computation is 130 L/hour, Figure 10, and the experimental

result is about 132 to 135 L/hour, Figure 11 Therefore the

CFD results are in good agreement with the experiment

3.3 Design Scenarios

3.3.1 Intake port cross-section area effect

In order to avoid back flow, the angle α must be higher

than the angle β If α<β, then the roller vane chamber will

connect with the intake and discharge ports Because the

LPG pressure is higher at the outlet than at the inlet, thefuel will flow back to the inlet port side As a result, theflow rate will drop significantly In this design scenario,Models B and C with different intake port cross-sectionareas were tested, as shown in Table 3

3.3.2 Angle (between intake port and rotor) and rotorconfiguration effect

In order to obtain a smooth flow from the intake to therotor, three different angles between the intake port and therotor of the model with the same intake port cross-section

Figure 9 Flow rate and cavitation characteristic of the

baseline pump model

Psat=Saturated Pressure of the fluid at 293 K

Figure 10 Flow rate of the baseline pump computation

results

Figure 11.Experimental flow rate

Figure 12 Intake port section area of the LPG roller vanepump

Table 3.Intake port cross-section area variation

Model Intake port cross section areaModel A (baseline) 33.02 mm2

Table 4.Intake port angle variation

Model Intake port cross-section area Angle between intake port and chambers, ϕ