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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 coe cient 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 coe cient 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 coe cient, 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 coe cient. This paper presents a research on the eects of fuel composition, spark timing, and engine load on polytropic coe cient 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 coe cient 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 coe cient is lowered during compression and increased during expansion with advanced spark timings. Cycle-to-cycle variations tend to increase the polytropic coe cient 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 e ciency 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 e ciency 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 retro tted 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 e ciency 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 e ciency 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 coe cient 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 e ciency 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 e ciency was achieved (close to
28%)
and the speci c
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 coe cient 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 coe cient.
They reported that errors on referencing
pressure estimation aect the compression polytropic coe cient, being these errors indepen-
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dent on load. Moreover, during the compression stroke, the polytropic coe cient is slightly lowered because speci c-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 coe cient 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 coe cient is aected only for heat transfer.
On the other hand, the adiabatic and poly-
tropic coe cient are associated with the gas surroundings heat exchange by the following expression:
δQ = where
δQ
is the gas-surrounding heat exchange,
speci c heats ratio,
Equation 1
n−γ pδV 1−γ
p
n
is the in-cylinder pressure and
(1)
is the polytropic coe cient,
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 coe cient 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 coe cient 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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analysis. This paper presents an analysis of characteristics of the compression and expansion polytropic coe cients of a high compression ratio spark ignition engine fueled with natural gas, biogas, and a propane-syngas blend. The energy transfer ratio, previously de ned by Christians,
20
is used as criterion for determining the proper crank angle interval where the polytropic coe cient is valid. Additionally, the eects of spark timing, engine load, and cyclic variability on polytropic coe cients 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 ori ce meter. In-
cylinder pressure was recorded with a piezoelectric transducer (Kistler charge ampli er (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
ampli er.
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 speci cations 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
Simpli ed 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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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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on polytropic coe cients. The throttle valve openings had to be restricted to values between
18% and 30% to avoid knocking combustion.
Although power output and thermal e ciency
showed similar values compared with the original Diesel engine, volumetric e ciency was considerable lowered.
Figure 2
shows volumetric e ciency 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 e ciency 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 e cinecy and equivalence ratio, as observed in was achieved in the second experimental phase.
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Figure 2,
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In this research, the polytropic coe cient 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 coe cients calculation In this research the polytropic coe cients 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 coe cients 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 coef cients should be close to
1.37
and
1.33
during compression. The crank angle interval for
determining compression polytropic coe cient 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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ent to Gasoline or compression ratios are increased to typical values of CI engines, the right crank angle interval for determining the polytropic coe cients could be signi cantly 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 coe cients determination.
Figure 3 shows the progress of polytropic coe cient, 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 coe cient between the typical crank angle interval (100 to
65 CAD bTDC) were found, therefore this interval is inappropriate for
the estimation of this coe cient at tested conditions. At the beginning of interval, the high values of the slope suggest that the compression process signi cantly diers from a constant polytropic coe cient process.
Figure 3: Variation of compression polytropic coe cient 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 coe cient 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
speci c 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 coe cient compression at tested conditions is between
Figure 4
50
and
30
CAD bTDC.
shows the temporal evolution of polytropic coe cient 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 coe cient could be considered constant without an appreciable error is between
50
and
30
CAD bTDC.
Figure 4: Variation of compression polytropic coe cient 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 coe cient process if the ing speci c 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 coe cient, 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 coe cient 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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a quasi-constant polytropic coe cient process is not clearly.
Figure 6: Variation of compression polytropic coe cient 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 de ne a crank angle interval for expansion polytropic coe cient 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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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 coe cients calculation suggests a similarity with the two G points highlighted by Lapuerta et al.
18
Compression and expansion coe cients 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 coe cients too.
Figure 8
shows the eect of
load and spark timing on polytropic coe cients when the engine is fueled with natural gas. Polytropic coe cient is higher during compression and lower during expansion when spark
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timing is advanced. The observed trend in polytropic coe cients with the spark timing is associated to combustion phasing and heat released. In the case of compression coe cient, 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 coe cients.
Figure 8: Variation of polytropic coe cient with the load and spark timing for natural gas.
Figure 9 shows the polytropic coe cient related with the coe cient 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 mis re, which
of COV(
generates colder walls during compression and therefore higher heat transfer to the cylinder walls and higher polytropic coe cients.
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Figure 9: Relation between coe cient of variation of
imep
and compression polytropic coef-
cient.
The above results show a strong dependency of compression polytropic coe cient 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 coe cient, the trend respect to the spark timing and load is clear.
Figure 8
shows
that all expansion polytropic coe cients 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 coe cient of fuel burned). Delayed combustion presents smaller values for
polytropic coe cient because in these cases a higher portion of fuel energy is released during the polytropic coe cient 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 coe cient.
Compression and expansion coe cients for biogas and propane-syngas Fuel composition aects ignition delay and combustion time, leading to changes in polytropic coe cient.
Figure 11 shows the polytropic coe cients 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 coe cients related with
the spark timing were found for both fuels. The presence of CO2 in the biogas and generates lower polytropic coe cient values, even for spark timing with low cycle-to-cycle variation, because the charge speci c 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 coe cient 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, re ecting the reduction in the in-cylinder temperature.
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Figure 11: Variation of polytropic coe cient and coe cient 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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kW and equivalence ratio
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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 coe cient, 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 coe cient 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 coe cients 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 insu cient (with their default coe cients) 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 di culty 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 coe cients 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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Conclusion In this paper the polytropic coe cients 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 coe cients 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 coe cient, 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 coe cient and cycle-to-cycle variations, making of this coe cient very useful for quality data analysis.
4. Combustion phasing has a great in uence on expansion polytropic coe cient.
It was
found for a CA50 near to TDC, polytropic coe cient tends to have values close to
1.4
for dierent loads and fuels. The above suggests that the expansion polytropic coe cient has good potential as combustion phasing criteria (low cost computational parameter in online analysis methodologies) in technologies where the CA50 is important variable that de nes 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 coe cients 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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