Experimental Study of the Polytropic Coefficient for an Air-Cooled

Dec 24, 2017 - (5) High compression ratios in spark-ignition (SI) engines can be .... In the first experimental phase, the engine was fueled with natu...
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Experimental study of polytropic coefficient for an air cooled high compression ratio-spark ignition engine fueled with natural gas, biogas, and propane-syngas blend Sebastián Heredia Quintana, Edisson S. Castaño-Mesa, and Iván D. Bedoya Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b03063 • Publication Date (Web): 24 Dec 2017 Downloaded from http://pubs.acs.org on December 29, 2017

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Energy & Fuels

Experimental study of polytropic coecient for an air cooled high compression ratio-spark ignition engine fueled with natural gas, biogas, and propane-syngas blend ∗

Sebastián H. Quintana, Edisson S. Castaño-Mesa, and Iván D. Bedoya

Grupo de Ciencia y Tecnología del Gas y Uso Racional de la Energía, University of Antioquia, Medellín E-mail: [email protected] Phone: +57 (4) 2198548

Abstract The polytropic coecient is an important variable for determining errors in pressure and volume measurements and for apparent heat release calculation in engine combustion analysis. For commercial gasoline-fueled spark ignition engines and diesel-fueled compression ignition engines exist a wide understanding about the thermodynamic models and values of polytropic coecient, however, in other technologies, in which gaseous fuels are used, the pressure treatment strategies and heat transfer models should be adjusted to allow a better calculation of polytropic coecient. This paper presents a research on the eects of fuel composition, spark timing, and engine load on polytropic coecient in an air cooled spark ignition engine with high compression ratio (15.5 : 1). The fuels tested were natural gas, biogas, and a propane-syngas blend. The experimental results suggests that during compression the appropriate crank angle interval for 1

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polytropic coecient estimation is between 50 and 30 crank angle degree (CAD) before top dead center (TDC), and during expansion the appropriate crank angle interval is between 40 and 60 CAD aTDC. It was found that the polytropic coecient is lowered during compression and increased during expansion with advanced spark timings. Cycle-to-cycle variations tend to increase the polytropic coecient during compression and to reduce it during expansion.

Introduction The continuous increase in the energy demand worldwide and the consequent increase in pollution have led many researchers to focus their research on fuel eciency and emission reduction strategies in power generation systems.

In the internal combustion engines re-

search eld, the downsizing is a strategy to attend these challenges;

1,2

however, it must

be complemented with other actions, such as turbo-charging and direct injection, to meet these objectives without decreasing power output. The use of high compression ratios is an interesting alternative to combine along with downsizing, especially in countries with large sources of natural gas and renewable fuels, such as biogas, and syngas, which can be used in transportation and electricity generation.

3,4

Higher compression ratios combined with high

methane number fuels allow high thermal eciency and fewer propensities to knock compared to liquid fuels at high load; however, this strategy leads to retarded spark timing under rich mixture conditions to avoid knocking.

5

High compression ratios in spark ignition engines can

be achieved using retrotted diesel engines or modifying the combustion chamber.

6

Several

previous studies have been focused on showing the eectiveness of using high compression ratio in SI engines and its eects on combustion, emissions and engine performance. example, in India, Porpatham et al. pression ratios between

9.3 : 1

and

7,8

reported eciency between

15 : 1,

21%

and

25%

For

for com-

respectively, operating at fully open throttle valve

and fueled by biogas. In China, Hu and Huang

9

evaluated the eect of compression ratio

on the performance and combustion of a natural gas direct-injection engine.

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They found

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Energy & Fuels

that the most recommended compression ratio to obtain a better thermal eciency without a large penalty on emissions under the tested conditions is close to that a compression ratio of

12 : 1

12 : 1;

Ma et al.,

10

found

is also the limit to ensure low coecient of variation in

the indicated mean eective pressure and low NOx emissions. On the other hand, previous study of Ma et al.

11

showed that complemented turbo-charging and direct injection in SI

engine fueled with blends of H2 /natural gas (under ratios of

0−50 vol%) improvements in the

indicated thermal eciency and reductions in NOx, CO and HC emissions can be reached, however, under the same ignition timing, NOx and CO emissions rises with the increase of hydrogen blend ratio; hydrogen addition is a promising strategy to extend the lean limit operation

12

and, combined with ignition timing retardation, an eective way to reduce idle

emissions and cycle-to-cycle variations.

13

In Colombia, Gomez et al.

14

investigated the eect

of adding methane to biogas in a spark ignition engine with a compression of found that for blends of of

12

50%

biogas and

50%

15 : 1.

They

CH4 (volumetric basis) using a spark timing

CAD bTDC, the best thermal eciency was achieved (close to

28%)

and the specic

emissions (g/kWh) of CO, CH4 and NOx were kept in the lowest values. Combustion analysis using the in-cylinder pressure provides important information on how the changes in fuel-air mixture composition and changes in compression ratio aect combustion stability and operating range. These changes aect sub-models utilized for heat transfer calculations, residual gases estimation, absolute cylinder pressure correction and apparent heat release. The polytropic coecient is an important variable to detect errors in cylinder pressure treatment. It contains information of gas-surroundings heat exchange, allowing the tuning of apparen heat release calculation and it is typically used to model the in-cylinder pressure history due to the fact that the compression and combustion processes tends to behave close to an isentropic process for most conventional fuels. Brunt et al.

16

15

studied the eect of several techniques for absolute pressure correction and

their sources of errors on polytropic coecient.

They reported that errors on referencing

pressure estimation aect the compression polytropic coecient, being these errors indepen-

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Page 4 of 26

dent on load. Moreover, during the compression stroke, the polytropic coecient is slightly lowered because specic-heats ratio diminishes and heat transfer increases, showing typical values

1.28 to 1.35 for gasoline engines at a crank angle interval between 100◦

to

65◦

BTDC.

However, these values can be dierent for engines admitting lean mixtures or for technologies operating on advanced combustion concepts. Lapuerta et al.

18

17

analyzed the eect of TDC correction and pressure referencing on the com-

pression polytropic coecient in a direct injection Diesel engine. They found that there are two points, one in compression stroke and other in expansion stroke, in which the polytropic coecient is aected only for heat transfer.

On the other hand, the adiabatic and poly-

tropic coecient are associated with the gas surroundings heat exchange by the following expression:

δQ = where

δQ

is the gas-surrounding heat exchange,

specic heats ratio,

Equation 1

n−γ pδV 1−γ

p

n

is the in-cylinder pressure and

(1)

is the polytropic coecient,

δV

γ

is the

is the cylinder volume variation.

allows the tuning of heat transfer model with the heat transfer calculated,

however, this equation is only valid when no leakages are supposed.

Armas et al.

19

used

the methodology of Lapuerta et al. to study the eect of errors on estimation of blow-by, trapped mass and its composition on the heat transfer during motored and ring conditions in a direct injection Diesel engine. They found that calculations of these eects are possible when some corrections are introduced in

equation 1.

Although the evolution and average values of polytropic coecient during compression and expansion in CI engines and SI engines fueled with Diesel and Gasoline respectively are well understood, there is a need for research of this parameter for emerging technologies and gaseous fuel-air mixtures.

17

The right compression polytropic coecient allows tuning

the heat transfer model when there is no combustion and it is an adequate parameter for in-cylinder pressure-volume synchronization and zero level correction in real-time engine

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Energy & Fuels

analysis. This paper presents an analysis of characteristics of the compression and expansion polytropic coecients of a high compression ratio spark ignition engine fueled with natural gas, biogas, and a propane-syngas blend. The energy transfer ratio, previously dened by Christians,

20

is used as criterion for determining the proper crank angle interval where the polytropic coecient is valid. Additionally, the eects of spark timing, engine load, and cyclic variability on polytropic coecients are determined for the gaseous fuels tested.

Experimental setup A two cylinders, four strokes, air cooled, naturally aspired, direct injection diesel engine was converted to operate as a spark ignition engine in Medellin city (1500 m above sea level). A generator was selected to run at maximum torque speed (1800 rpm).

Table 1

shows

technical engine characteristics. Engine loads were established with a variable electrical resistance bank from

3

to

10

kW

connected to the generator and power output was dissipated as heat. The engine speed was measured with an crank angle encoder (Kistler

2614C11).

Colombian commercial natural gas (87.67%CH4 , and

0.93%N2

80%CH4 of

and

50%C3 H8

The fuels used in this research were

6.54%C2 H6 , 1.3%C3 H8 , 2.28%C4+ , 1.28%CO2 ,

in a volumetric basis), simulated biogas with a volumetric composition of

20%CO2 , and a propane - simulated syngas blend, with a volumetric composition

and

50%

syngas (40%H2 ,

40%CO ,

and

20%CO2 ).

was controlled by ow- meters calibrated for each gas.

The composition of the blends

Table 2

summarizes important

properties of fuels utilized in the experimental procedure. The mass ow rates of fuels were measured with a coriolis sensor (SIEMENS SITRANS FC MASS

2100

DI), whereas ow rate of air was measured with a calibrated orice meter. In-

cylinder pressure was recorded with a piezoelectric transducer (Kistler charge amplier (Kistler

5064B)

6125C)

coupled to a

and the intake pressure was measured with a piezoresistive

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pressure sensor (Kistler

4005B)

conditioning a Kistler SCP

coupled to a Kistler

2853A120

4665B

amplier.

For pressure signal

system was used. Crank angle position was measured

using an incremental encoder with resolution of

Table 3

Page 6 of 26

3600 pulses per revolution (Kistler 2614C11).

shows the more important data on accuracy and uncertainty of the instruments

used during the experiments. All signals were recorded on a personal computer. The acquisition card could collect data at a rate of

250

kHz, with a resolution of

16

bits. In

Figure 1,

the experimental setup is

shown. Table 1: Technical engine specications Lister Petter TR2 DI, four stroke,

Designation

two cylinders, air cooled, Diesel engine After conversion

Spark ignition

Charge aspiration

Naturally aspired

Displacement

1550 cm 15.1 : 1 98.42 x 101.6 mm 69 CAD BTDC 32 CAD ABDC 76 CAD BBDC 36 CAD ATDC 17.3 kW at 2500 rpm 76.4 Nm at 1800 rpm

3

Compression ratio Bore x stroke Intake valve open (IVO) Intake valve close (IVC) Exhaust valve close (EVO) Exhaust valve close (EVC) Rated power Maximum torque

Table 2: Fuel properties Property

Natural gas

Biogas

Propane-Syngas blend

Low heating value (MJ/kg)

47.16

29.69

34.72

Simplied chemical composition

C1.15 H4.23 O0.03 N0.02

C1 H3.2 O0.4

C1.8 H4.4 O0.4

Stoichiometric air fuel ratio (AFR) 3 Lower Woobe index (kWh/Nm )

16.01 13.66

10.16 9.22

11.43 13.54

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Energy & Fuels

Table 3: Associate accuracy and uncertainty of measurements Measurement

Accuracy

Uncertainty

In-cylinder pressure

±0.0008 bar ±0.1 CAD ±10 rpm ±0.1 mg/s

0.5% 8% 6% 5%

Crank angle position Engine speed Fuel ow Calculated variables

0.4%

IMEPn

Figure 1: Schematic diagram of the experimental engine.

Experimental procedure In the rst experimental phase, the engine was fueled with natural gas at several part loads (4 kW,

5

kW, and

6

kW, which correspond to electric outputs at

50%, 63%,

and

75%

of full

load, respectively) varying the spark timing within the stable operation ranges (low cycle dispersion and non-knocking conditions) to determine the eect of load and spark advance

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Page 8 of 26

on polytropic coecients. The throttle valve openings had to be restricted to values between

18% and 30% to avoid knocking combustion.

Although power output and thermal eciency

showed similar values compared with the original Diesel engine, volumetric eciency was considerable lowered.

Figure 2

shows volumetric eciency and equivalence ratio related

with the spark timings and loads tested.

A factorial experimental design was conducted

using the methodology described by Montgomery.

21

Table 4

shows the levels and factors

evaluated in this experimental design, which was replicated twice.

Figure 2: Variation of volumetric eciency and equivalence ratio with the load and spark timing for natural gas.

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Table 4: Experimental factorial design to tests with natural gas Factor

Level description

Level designation

1

50

2

65

3

75

Spark

1

3

timing

2

6

advancing

3

9

(CAD

4

12

bTDC)

5

15

6

18

7

21

8

24

1

1800

Load (%)

Engine speed (rpm)

In the second experimental phase, the engine was fueled with biogas and a propanesyngas blend. Prior to test, the engine was fueled with natural gas to pre-heat it, to ensure a stable operation when it was running with these fuels. In this phase, the engine was operated at

63%

load with a throttle valve opening of

22%. Table 5

shows the levels and factors

evaluated in this experimental design, which was replicated twice. Table 5: Experimental factorial design to second experimental phase Factor

Level description

Level designation

Load (%)

1

63

1

Biogas

Fuel

2

Propane-Syngas blend

Spark

1

3

(CAD

2

6

bTDC)

3

9

4

12

5

15

6

18

7

21

8

24

1

1800

Engine speed (rpm)

Similar trends for volumetric ecinecy and equivalence ratio, as observed in was achieved in the second experimental phase.

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Figure 2,

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Page 10 of 26

In this research, the polytropic coecient was expressed as:

n=− In the

Equation 2

ln∆p V δp = pδV ln∆V

(2)

the working uid is supposed to be an ideal gas and leakages are

neglected. Residual gas fraction was calculated using expression proposed by Ortiz-Soto et al.

22

Heat

released to cylinder walls was estimated by means of the universally applicable correlation proposed by Woschni.

23

Six hundred cycles were recorded for each operating point.

Results and discussion CAD interval selection for coecients calculation In this research the polytropic coecients was calculated from a thermodynamic approach which uses in-cylinder pressure analysis.

The thermodynamic approach assumes that the

compression process can be modeled as a constant polytropic process between a crank angle interval, this assumption implies that mass leakages in the cylinder are neglected and the charge is the same during each cycle. The polytropic coecients determined using this methodology are frequently used to evaluate the quality of pressure signal treatment process, which involves recording, ltering, amplifying, and averaging among others. For CI engines and SI engines using Diesel and Gasoline as fuels respectively, the value of polytropic coefcients should be close to

1.37

and

1.33

during compression. The crank angle interval for

determining compression polytropic coecient is usually located between

100

and

65

CAD

bTDC to avoid noise or spikes in the in-cylinder pressure trace. These disturbances in the pressure trace of the charge compressed can appear during intake valve motion as result of motion structure-borne vibrations, but it is unlikely that aects the pressure traces in the mentioned crank angle interval.

17

When the fuels used in SI engines are substantially dier-

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Energy & Fuels

ent to Gasoline or compression ratios are increased to typical values of CI engines, the right crank angle interval for determining the polytropic coecients could be signicantly varied because of the eect of residual gases, fuel composition, and equivalence ratio on pressure evolution during compression process, whereby it is required an estimation of appropriate crank angle interval for polytropic coecients determination.

Figure 3 shows the progress of polytropic coecient, measured as ln∆p/ln∆V , during compression process using natural gas at

6

kW power output and several spark timings. High

values and high change rate of compression polytropic coecient between the typical crank angle interval (100 to

65 CAD bTDC) were found, therefore this interval is inappropriate for

the estimation of this coecient at tested conditions. At the beginning of interval, the high values of the slope suggest that the compression process signicantly diers from a constant polytropic coecient process.

Figure 3: Variation of compression polytropic coecient for spark timings of CAD bTDC. Engine fueled with natural gas, power

According to

Equation 1,

6

6, 15,

and

21

kW.

the high values of polytropic coecient in

Figure 3

can

be associated with higher heat transfer rate, lower work transfer to the charge, and lower

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Page 12 of 26

specic heats ratio than expected for SI engines running with Gasoline. The upper rigth side window located in

Figure 3

shows that a proper crank angle interval for a quasi-constant

polytropic coecient compression at tested conditions is between

Figure 4

50

and

30

CAD bTDC.

shows the temporal evolution of polytropic coecient during compression for a

spark timing of

15

CAD bTDC and several power outputs using natural gas.

Again the

crank angle interval in which the polytropic coecient could be considered constant without an appreciable error is between

50

and

30

CAD bTDC.

Figure 4: Variation of compression polytropic coecient for several loads. with natural gas, spark timing

Christians

20

15

CAD bTDC.

developed an approach for studying the polytropic processes. For reversible

processes in closed systems, an expression similar to

n = (γ − 1) Where

Engine fueled

δW = pδV

and

K

Equation 1 is:

δQ + γ = (γ − 1)K + γ pdV

is known as

Energy Transfer Ratio.

(3)

Based on

Equation 3

the compression and expansion processes can be characterized according to the value of

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Energy & Fuels

ergy Transfer Ratio.

Compression and expansion processes are considered as quasi-constant

polytropic coecient process if the ing specic heats ratio variations.

Energy Transfer Ratio

Figure 5

shows the

compression process at tested conditions showed in

Transfer Ratio

is constant throughout, neglect-

Energy Transfer Ratio

Figure 4.

could be considered almost constant between

variation for

It is observed that the

50

and

30

Energy

CAD bTDC, there-

fore both gures allow to conclude that this crank angle interval is most recommended than the typical interval used for SI engines (100 to

60

CAD bTDC) to calculate de compression

polytropic coecient, therefore this is the crank angle interval used in further analysis for compression process.

Figure 5: Energy transfer ratio for dierent loads during compression process. Engine fueled with natural gas, spark timing

Figure 6

15

CAD bTDC.

shows the slope variation of

ral gas, for electric power of

6

ln∆p/ln∆V

traces for engine fueled with natu-

kW, during expansion process.

combustion generates a distortion in the slope of curve

For delayed spark timings,

ln∆p/ln∆V ,

which leads to lower

expansion coecient values at the start of the expansion stroke. For advanced spark timings, the slope of

ln∆p/ln∆V

traces shows a more stable trend, but the crank angle interval for

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Page 14 of 26

a quasi-constant polytropic coecient process is not clearly.

Figure 6: Variation of compression polytropic coecient for dierent spark timings. Engine fueled with natural gas, power

6

kW.

Due to the lack of criteria that can be obtained from the slope of

ln∆p/ln∆V

traces

to dene a crank angle interval for expansion polytropic coecient calculation, the concept of

Energy Transfer Ratio

high

is used and the results results are shown in the

Energy Transfer Ratio

Figure 7.

The

values near to TDC are associated with the singularity in the

piston work, generated by the change of piston movement direction where piston work is lower compared to heat released during combustion.

When the combustion develops, the

in-cylinder temperature increases, therefore the heat transfer to combustion chamber walls and the

Energy Transfer Ratio

tend to be higher.

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Energy & Fuels

Figure 7: Energy transfer ratio for dierent loads during expansion process. Engine fueled with natural gas, power

From

6

kW.

Energy Transfer Ratio

trends in

a constant polytropic process between

40

Figure 7 is possible to assume that expansion is and

60

CAD aTDC. Similar trends were found for

the dierent loads and fuels tested during this research. The approximate symmetry between the crank angle interval for compression and expansion polytropic coecients calculation suggests a similarity with the two G points highlighted by Lapuerta et al.

18

Compression and expansion coecients for natural gas Spark timing is a phasing combustion control parameter in SI engines. The variation in this parameter aects the engine performance and combustion development, and it is expected that spark timing also aects the polytropic coecients too.

Figure 8

shows the eect of

load and spark timing on polytropic coecients when the engine is fueled with natural gas. Polytropic coecient is higher during compression and lower during expansion when spark

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timing is advanced. The observed trend in polytropic coecients with the spark timing is associated to combustion phasing and heat released. In the case of compression coecient, the advancing in the spark timing increases heat released and wall temperature, leading to lower heat transfer from the charge to the cylinder walls during compression and lower polytropic coecients.

Figure 8: Variation of polytropic coecient with the load and spark timing for natural gas.

Figure 9 shows the polytropic coecient related with the coecient of variation of mean

imep ) for several loads and spark timings tested.

eective pressure COV(

The higher values

imep ) are explained by higher amount of cycles with partial or total misre, which

of COV(

generates colder walls during compression and therefore higher heat transfer to the cylinder walls and higher polytropic coecients.

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Energy & Fuels

Figure 9: Relation between coecient of variation of

imep

and compression polytropic coef-

cient.

The above results show a strong dependency of compression polytropic coecient with the combustion phasing and stable engine operation, because of their eects on heat transfer and in-cylinder pressure uctuations.

On the other hand, in the case of expansion poly-

tropic coecient, the trend respect to the spark timing and load is clear.

Figure 8

shows

that all expansion polytropic coecients converge to a same value when the spark timing is advanced.

Figure 10

and CA50 (angle for

50%

shows the relation between the expansion polytropic coecient of fuel burned). Delayed combustion presents smaller values for

polytropic coecient because in these cases a higher portion of fuel energy is released during the polytropic coecient calculation interval, hence the expansion process in this interval cannot be approximated to polytropic process, invalidating the

2.

Equation 1 and Equation

As the spark timing advanced, the combustion is developed near to TDC, making that

the expansion proceed closer to a polytropic process.

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Page 18 of 26

Figure 10: Relation between CA50 and expansion polytropic coecient.

Compression and expansion coecients for biogas and propane-syngas Fuel composition aects ignition delay and combustion time, leading to changes in polytropic coecient.

Figure 11 shows the polytropic coecients at compression and expansion and COV(imep ) related with spark timings for the engine fueled with biogas and propane-syngas blend at power output indicated in

Table 5.

Similar trends for polytropic coecients related with

the spark timing were found for both fuels. The presence of CO2 in the biogas and generates lower polytropic coecient values, even for spark timing with low cycle-to-cycle variation, because the charge specic heats ratio tends to be higher, reducing the temperature during compression strokes and reducing the heat transfer to cylinder walls.

Figure 12 shows the

in-cylinder pressure in the interval where compression polytropic coecient was calculated for the three fuels at same load and equivalence ratio. It is observed how in-cylinder pressure is lower in the cases of propane-syngas blend and biogas compared with gas natural case, reecting the reduction in the in-cylinder temperature.

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Figure 11: Variation of polytropic coecient and coecient of variation

imep

with the load

and spark timing for propane-syngas blend and biogas.

Figure 12: In-cylinder pressure traces for the three fuels. Power of

0.71.

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5

kW and equivalence ratio

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Page 20 of 26

The low range of spark timing in the propane-syngas blend case do not allow to make an adequate analysis about the real trend in the polytropic coecient, however, as in natural gas cases, the values obtained are slightly higher than the typical values reported for SI engines fueled with gasoline and similar to the value reported by Rogers

17

for spark ignition engines

with homo-heterogeneous charge. Therefore, the use of typical polytropic coecient values for zero-level correction can be a source of error during pressure treatment process in air cooled high compression ratio-spark ignition engine fueled with gaseous fuels. The dierence between the polytropic coecients found in this research and the typical values reported for SI engine makes revising the level of tuning of current engine heat transfer models in this technology necessary and this is done in the following section of results.

Heat transfer analysis through engine heat transfer model and polytropic model A rst approximation to the heat transfer in an air cooled high compression ratio-spark ignition engine fueled with gaseous fuels was made by direct comparison between the heat ux obtained with the

Equation 1 and the obtained with Woschni, Hohenberg, and Eichelberg

heat transfer models.

24

Although the heat ux obtained with the

Equation 1 neglects the

eect of the leakages on the heat transfer process, this mass is about

IVC ,

15

1.5%

of the mass at

therefore the equation can be used to obtain an acceptable approximation.

Figure 13

shows the heat ux between the charge and cylinder walls during compression

stroke using the most common heat transfer models for natural gas. The condition tested was chosen taking into account low cycle-to-cycle variation, which allows to have a better appreciation of heat transfer process using the mentioned models.

In the

Figure 13

is observed that the three models do not exhibit an appreciable dierence until

65

it

CAD

bTDC, the time from which the three curves begin to separate due to increments in the incylinder pressure gradients. The heat ux obtained with Eichelberg correlation has a smaller heat transfer rate increase due to a lower power for the in-cylinder pressure compared with

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the other two correlations (0.5 compared with

0.8),

while that the lower heat ux in the

Woschni correlation, respect to Hohenberg correlation, is associated to the average cylinder gas velocity term. It is observed that the trend in heat ux obtained with polytropic process equation is similar to obtained with the correlations in early stages of compression stroke, but from the crank angle where the in-cylinder pressure gradient begins to have higher increments, heat ux moves away of Woschni, Hohenberg and Eichelberg models predictions. Hohenberg model shows the best agreement in the heat ux compared with the polytropic process.

The

achieved results shows that engine design and operating parameters, such as ignition mode, kind of combustion, cooling method, and compression ratio considerably aect the heat transfer process, being the traditional heat transfer models insucient (with their default coecients) to describe the heat transfer process for all the current SI engine options.

Figure 13:

453.15

Heat ux between gas and cylinder walls for a constant wall temperature of

K. Engine fueled with natural gas. Power

equivalence ratio of

6

kW, spark timing

21

CAD bTDC, and

0.71.

An error source in the heat transfer rate estimation is to x with a constant value for

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Page 22 of 26

the in-cylinder wall temperature, but given the diculty to estimate the change of this temperature with the crank angle on heat release analysis, this assumption is widely accepted. Additionally, wall temperature values used in the experimental and numeric studies usually belong to water cooled engines, which is not the case of the technology studied in this research.

Figure 14 shows the comparison between the heat ux obtained with the polytropic

process equation and the Hohenberg correlation using constant wall temperatures values of

415 K, 435 K, and 475 K. It is observed that lower wall temperatures correspond with better agreements between heat ux, obtained with polytropic process equation and Hohenberg correlation. However, it is required an experimental methodology to estimate not only an adequate average wall temperature, but also the coecients that will improve the Hohenberg correlation prediction. This study will be addressed in a future research.

Figure 14: Comparison heat ux between gas and cylinder walls using polytropic process equation and Hohenberg correlation with dierence wall temperature values. Engine fueled with natural gas. Power

6

kW, spark timing

21

22

CAD bTDC, and equivalence ratio of

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Energy & Fuels

Conclusion In this paper the polytropic coecients for an air cooler high compression ratio-spark ignition engine, fueled with several gaseous fuels, and operating at several spark timings and loads were estimated. The main conclusions are the following:

1. Typical crank angle interval used for polytropic coecients calculation are inappropriate for their estimation in the technology studied. The appropriate intervals were found to be between

50

and

30

CAD bTDC for compression and between

40

and

60

CAD aTDC

for expansion. Both intervals are similar with the two G points highlighted by Lapuerta et al.

18

2. The use of

Energy Transfer Ratio

criteria is a useful tool to estimate an adequate crank

angle interval in new technologies.

3. Spark timing aects the compression polytropic coecient, due to its strong eect on heat release (and this in turn aects the wall temperatures and pressure uctuations in later cycles). It was found a strong correlation between compression polytropic coecient and cycle-to-cycle variations, making of this coecient very useful for quality data analysis.

4. Combustion phasing has a great inuence on expansion polytropic coecient.

It was

found for a CA50 near to TDC, polytropic coecient tends to have values close to

1.4

for dierent loads and fuels. The above suggests that the expansion polytropic coecient has good potential as combustion phasing criteria (low cost computational parameter in online analysis methodologies) in technologies where the CA50 is important variable that denes the engine stable operating range.

5. Woschni, Hohenberg and Eichelberg heat transfer correlations shows under-predictions of heat ux between charge and cylinder walls. Hohenberg correlation shows the lowest under-predictions.

Heat ux dierence between Hohenberg correlation and polytropic

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Page 24 of 26

process equation can be reduced assuming lower wall temperature respect to typical values. Experimental analyses are required to estimate adequate values for wall temperature and coecients of the heat transfer correlation for the tested technology.

Acknowledgement The authors express thanks to Vicerrectoría de Investigación of the University of Antioquia for giving nancial support to this research through the institutional program: Programa de Sostenibilidad de Grupos de Investigación 2016-2017", and through the research project: Estudio y optimización del desempeño de un motor diesel en modo encendido provocado con mezclas de gas natural y combustibles gaseosos de origen renovable".

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