11-08-2012, 12:10 PM
Thermodynamic analysis of spark-ignition engine using a gas mixture model for the working fluid
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SUMMARY
This paper presents thermodynamic analysis of spark-ignition engine. A theoretical model of Otto cycle,
with a working fluid consisting of various gas mixtures, has been implemented. It is compared to those
which use air as the working fluid with variable temperature specific heats. A wide range of engine
parameters were studied, such as equivalence ratio, engine speed, maximum and outlet temperatures, brake
mean effective pressure, gas pressure, and cycle thermal efficiency. For example, for the air model, the
maximum temperature, brake mean effective pressure (BMEP), and efficiency were about 3000 K, 15 bar,
and 32%, respectively, at 5000 rpm and 1.2 equivalence ratio. On the other hand, by using the gas mixture
model under the same conditions, the maximum temperature, BMEP, and efficiency were about 2500 K,
13.7 bar, and 29%. However, for the air model, at lower engine speeds of 2000 rpm and equivalence ratio of
0.8, the maximum temperature, BMEP, and efficiency were about 2000 K, 8.7 bar, and 28%, respectively.
Also, by using the gas mixture model under these conditions, the maximum temperature, BMEP, and
efficiency were about 1900 K, 8.4 bar, and 27%, i.e. with insignificant differences. Therefore, it is more
realistic to use gas mixture in cycle analysis instead of merely assuming air to be the working fluid,
especially at high engine speeds. Copyright # 2007 John Wiley & Sons, Ltd.
INTRODUCTION
In most models of air-standard power cycles, the air–fuel mixture and combustion products are
approximated as ideal gases. In such cases air is assumed to be the working fluid with constant
specific heats without taking into consideration the temperature dependence of the specific heats
of the working fluid (Akash, 2001; Al-Sarkhi et al., 2002; Ge et al., 2005a; Chen et al., 1998;
Hou, 2004; Jafari and Hannani, 2006; Ozsoysal, 2006; Parlak, 2005a, b). However, due to
the high rise in combustion temperature this assumption becomes less realistic.
SOLUTION METHODOLOGY
Equation (38) is solved for each crank angle for the range of 1804y41808 using a step size
Dy ¼ 18: The values of y ¼ 1808 correspond to bottom dead centre (BDC), whereas the value
of y ¼ 0 corresponds to top dead centre (TDC). The heat addition in Equation (38) is only valid
for ys5y5 ðys þ DyÞ; i.e. during the period of combustion. In solving Equation (38), note that
k;P; T; and hcg are coupled, i.e. solution of one of these variables depends on the solution of
others. Therefore, the solution methodology depends on using an iterative solution procedure.
The solution procedure is as follows: by knowing the initial pressure of the gases at the BDC, the
initial temperature of the gases is first calculated using Equation (43). Once the value of the
initial temperature is obtained, then the temperature-dependent property Cp is calculated. For
crank angle less than ys; the specific heat of the air is calculated using Equation (1). Also, the
specific heat for the fuel is calculated by using Equation (3). Then, the specific heat for the
air–fuel mixture before combustion is calculated by using Equation (11). During combustion,
i.e. ys5y5 ðys þ DyÞ; Equation (15) is used to calculate the specific heat. However, for y > ys
the number of moles for the product species for lean and rich mixture are calculated by using
Equations (18) and (19), respectively. Then the specific heats for the combustion products are
calculated by using Equation (12). After that, the gas constant for the mixture is determined by
applying Equations (4)–(7).
RESULTS AND DISCUSSION
Figure 2 represents cylinder pressure in order to examine the validity and sensitivity of the
presented model. It shows the variation of cylinder pressure versus volume for SI engine running
at 3000 rpm. Air with variable specific heats is compared to gas mixture running at a
stoichiometric air–fuel mixture. The deviation between the two models is obvious. Higher values
of pressure are obtained when air is assumed as the working fluid. However, when air–fuel
mixture model is used the same trend is reported but the values are lower. For example, a
maximum pressure of 53 bar is reported when the working fluid used is assumed as air, and a
maximum pressure of about 46 bar is reported when the gas mixture model is implemented. The
reason for such a difference can be explained as follows: during combustion process species with
high values of specific heats are generated. These species include CO2 and H2O besides the
existence of heated unburned fuel. These components absorb some of the heat generated during
combustion. This absorbed heat will be reflected as a temperature and pressure increase in the
combustion chamber. This difference is very important from engineering point of view absorbed
because the absorbed heat is not transformed into useful work. Such physics is not evident when
air is used as the working fluid because the temperature-dependent specific heat of the air is
much lower than that of the mentioned combustion species. Therefore, the use of air as the
working fluid leads to an over-estimation of the power produced by the engine.
CONCLUSION
The effect of using a gas mixture model instead of air as the working fluid for the analysis of SI
engines was investigated. The investigation covered in-cylinder pressure and temperature,
BMEP and efficiency under a wide range of engine speeds (ranging from 2000 to 6000 rpm) and
equivalence ratios (ranging from 0.6 to 1.6).
It was found that the use of air as the working fluid results in significant overestimation of the
maximum pressure and temperature at high engine speeds and rich mixtures. This variation in
temperature and pressure calculations has a direct effect on power and efficiency calculations.
Moreover, it can influence the estimation of heat losses, exhaust emissions and detonation
properties. However, the variation between the two models becomes less significant at low
engine speeds and lean mixtures. An overestimation in the calculated values of BMEP and
efficiency was also evident when air is used as the working fluid in comparison to the values
obtained from the gas mixture model. Although this variation is almost negligible at low engine
speeds and lean mixtures, it becomes increasingly significant as the engine speed increases and
when rich mixtures are used. For example, at 5000 rpm and 1.2 equivalence ratio the efficiency
value drops from 32 to 29% when using the gas mixture model instead of air.