Energy and Power En gi neering, 2011, 3, 625-629
doi:10.4236/epe.2011.35078 Published Online November 2011 (
Copyright © 2011 SciRes. EPE
Optimal Mixture Ratios of Biodiesel Ethanol Diesel for
Diesel Engines*
Jun Li, Chao Guo, Wenbin Wang, Zhuojian Wu
Chongqing Jiaotong University, Chongqing, China
Recieved September 27, 2011; revised October 28, 2011; accepted November 9, 2011
In this paper, we study the best-mixture ratio of biodiesel-ethanol-diesel for diesel engines. The simulation
results show that the integrated indexes including engine power, cost-effectiveness and emission properties
are rather better with different optimizing index when the ratio of bio-diesel, ethanol and diesel are 71.58:
2.72:25.70 and 50:2.4127:47.5873.
Keywords: Diesel Engine, Biodiesel, Ethanol, Best-Mixture Ratio, Integrated Indexes
1. Introduction
Developing new energy car is the top research issue in
the automobile industry, for the energy crisis and air
pollution had become severe global problems [1]. In Chi-
na, the project of exploring biodiesel as an automobile
substitutable fuel has been formulated to achieve the
nation energy developing plan in biology liquid fuel. In
this paper the ethanol is ejected into the biodiesel-diesel
with high mixture ratio, the mixture ratio of biodiesel is
over 50%, as an assistant burning material. The power,
cost-effectiveness performance and SOOT, NOx emis-
sions property of diesel engine is analyzed and resear-
ched. And the torque fuel consumption rate, NOx and
SOOT emissions are chosen as the integrated indexes for
the best mixture ratio of biodiesel-ethanoldiesel.
2. Simulation Test and Uniformity Design
The diesel engine with biodiesel-ethanol-diesel fuel in dif-
ferent mixture ratio is simulated by using GT-Power [2]
to research the best mixture ratio of biodiesel-ethanol-die-
sel for optimizing the power, cost-effectiveness permance
and SOOT, NOx emissions property of diesel engine.
2.1. Introduction of Uniformity Design Principle
Uniformity design principle is an experiment design
method, put forward by Professor Fang Kai Tai and
Wang Yuan in China Academy of Scientist, Application
mathematics department in 1970s. The process of uni-
formity design principle method includes steps as fol-
lowing, 1) ensuring the experiment aims and evaluation
indexes, 2) choosing experiment factors, 3) ensuring the
level of each factor, 4) choosing uniformity design table
and assign relative factors, 5) making experiment schemes
and operations, 6) analyzing the experimental results.
2.2. Choosing of Factors, Level and Optimization
1) Choosing experiment factors, the mass fractions of
ethanol and biodiesel are chosen to be experimental fac-
tor 1 and 2 respectively. For the diesel ratio in mixture is
fixed as soon as the ratios of biodiesel and ethanol are
defined, it is needn’t to take the mass fraction of diesel as
experimental factor as well. Because the engine runs
under variable modes practically, it is unreliable to en-
sure the best-mixture ratio under a single mode [3,4].
Besides, the revolution and load alteration are taken con-
sideration in building math model to ensure the best
mixture ratio. The revolution and load are chosen to be
factor 3 and 4.
2) Determining the factor level, in this paper that the
assistant fuel, ethanol, is ejected in the mixture fuel with
high mixture ratio is researched. So the biodiesel factor
levels are chosen at 50%, 60%, 70%, 80%, 90%. The
ethanol factor levels are at 2.5%, 5%, 7.5%, and 10%.
Considering the various practical modes the revolution
*Supported by: Foundation Project of the Key Laboratory of Chongqing
Communication Engineering (2008CQJY002); Education and Teaching
Reform Project of Chongqing CSTC, China (No. 0903070).
levels are chosen at 800, 1000, 1400, 1800, 2200 r/m. the
load levels are at 25%, 50%, 75% and full load.
2.3. Diesel Engine Simulation Model and
Supercharging & middle cooling diesel engine is resear-
ched in this paper, and its technical parameters are shown
in Table 1.
Table 1. The main technical parameters of diesel engine.
Engine Form
Six-cylinder, Four-stroke,
Supercharging & middle cooling
diesel engine
Cylinder diameter × Stroke
length 114 mm × 135 mm
Compression ratio 18
Total cylinders cubage/L 8.27 L
torque/Revolution 1000 N·m/1400 r/min
Rating power/Revolution 184 kw/2200 r/min
The diesel engine is predigested different models such
intake system, exhaust system, cylinder, crankcase, eject-
ing device, middle cooler, circumstance and the relative
pipe among them based on the parameters above all. The
diesel model seems as Figure 1.
In this paper the biodiesel composes of saturated and
unsaturated fatty acid methyl ester such as, palmitic acid
methyl ester, stearic acid methyl ester, oleic acid methyl
ester, linoleic acid methyl ester, linolenic acid methyl
ester [5-8]. And their structure forms are following as:
Their chemical forms and ratios are shown in Table 2.
3. Analyzing Simulation Results
Simulation experiment is carried out with GT-Power
according the experiment scheme, and experimental re-
Figure 1. Diesel engine simulation model diagram.
Copyright © 2011 SciRes. EPE
J. LI ET AL.627
sults (torque, BSFC, NOx, SOOT) are shown in Table 3.
3.1. Ensuring Integrated Index
The experiment results shown in Table 3 dedicate that
the optimization aim is a multi-index, which needs to be
quantitated firstly, and then optimized comprehensively.
Integrated evaluation method based on weighting factor
is adopted to acquire the integrated index value yi [3,4],
whose computing formula is as following.
y b1y1b2y2byiii iiiji   (1)
Therein, bij are the coefficient. Yij are the experiment
indexes. i expresses the ith experimental level. j ex-
presses the jth experiment index.
The total weighting factor is supposed as 100. And
then the weighting factor of every index would be evalu-
ated as bij, determined by the index’s weight compared
with total weighting factor 100. After analyzing the
comparative weight of different index comprehensively
based on professional knowledge, there are two series of
the integrated weighting evaluation are set in this paper.
In the first set the weights of torque, fuel consumption
rate, NOx and SOOT all are 25. In the second set the
weight of torque is 15, that of fuel consume rate is 35,
that of NOx is 15, and that of SOOT is 35. The values of
integrated index Y1 and Y2 are contra posed to the first
and second set respectively.
The difference between the maximum and the mini-
mum of every experiment is its variation spectrum k. The
k of torque is 670.544, that of fuel consumption rate is
126.504, and that of NOx is 209.3779, while that of
SOOT is 2.101513.
The coefficient is computed by following formula.
Weight kij
Computing the integrated evaluation of the weighting
factor is corresponded to evaluate every experiment re-
sult. The values of different indexes should be supposed
as lesser numbers at the same class before calculating the
integrated index value in case of wrong in calculating.
Besides, the value of torque index should be as larger as
possible, and the values of fuel consume rate, NOx and
SOOT are as small as possible. The value of torque is
supposed as a minus to acquire the minimums of all in-
dexes unifiedly. The acquired integrated evaluations
based on weighting factor are Y1 and Y2, as shown in
Table 3.
Table 2. Basic information of the biodiesel [6,7].
Name Chemical Form Molecular Weight Ratio (%)
palmitic acid methyl ester C17H34O2 270.45 10.74
stearic acid methyl ester C19H38O2 298.50 4.28
oleic acid methyl ester C19H36O2 296.49 24.03
linoleic acid methyl ester C19H34O2 294.48 54.23
linolenic acid methyl ester C19H32O2 292.46 6.72
Table 3. Results of experiment and integrate d inde xes.
Ethanol mass
Biodiesel mass
index value
index value
N1 5 70 1000 75 598.959235.123 105.0022.02225 60.7289 92.8554
N2 5 50 1000 25 188.958235.577 4.934081.09812 53.1629 79.5927
N3 2.5 90 800 50 418.092259.641 30.46080.636468 46.9316 75.2649
N4 2.5 80 1800 75 544.014259.641 93.49121.24741 57.0307 87.1386
N5 10 60 800 100 829.374239.685 214.3120.529577 48.3345 71.9343
N6 5 90 2200 100 731.667282.368 130.9810.775017 53.3824 84.047
N7 2.5 70 2200 25 179.289361.627 57.35552.63109 102.9293 143.97
N8 5 60 1400 50 478.244240.247 119.8962.06413 68.5187 98.738
N9 10 90 1400 25 199.145265.033 17.03141.31078 62.5785 91.9229
N10 7.5 60 1800 75 561.163253.786 87.13411.37306 55.9699 86.7723
Copyright © 2011 SciRes. EPE
Copyright © 2011 SciRes. EPE
3.2. Quadratic Multinomial Regression Model
The quadratic multinomial regression models of inte-
grated indexes in Table 3 are acquired by statistics soft-
ware and their formula are as following.
Y1=7045.01+2656.13*X1 197.90*X2
Y2= 649.08+97.06*X1+5.09*X2
3.3. Obtaining the Best Mixture Ratio
The regression formula shows that the integrated index is
related to mixture ratio, revolution and load. It means the
integrated index is only related to revolution and load
when the mixture ratio is fixed. The function relationship
among the integrated index, revolution and load vary
from each mixture ratio. In 3D coordinate series, the
revolution, load and integrated index are respectively
supposed as X axis, Y axis and Z axis. The bend roof
cylinder could be computed by z = f (x, y) (x1 x x2,
y1 y y2). Therein, x1 and x2 are the maximum and
minimum of revolution respectively. And y1 and y2 are
the maximum and minimum of load. The cubage of the
bend roof cylinder (Vintegrated index) can be used to evaluate
the value of the integrated index under the prefixed mix-
ture ratio. The smaller the cubage is, the smaller the in-
tegrated index value is at the same mixture ratio.
Taking consideration of the various mode of engine,
practically, the final integrated index value judged by the
above way is comprehensive and comparative reasonable.
The Vintegrated index with different mixture ratio could be
obtained by double integral [9,10]. The relationship
among Vintegrated index, ethanol and biodiesel are shown in
Figures 2 and 3 corresponding to the first and second
scheme respectively. The minimum of Vintegrated index is X1
= 2.72 and X2 = 71.58 when the first scheme is adopted.
And when the second scheme is adopted the minimum of
Vintegrated index is X1 = 2.4127, X2 = 50. This dedicates the
best mixture ratio of bio-diesel, ethanol and diesel are
71.58:2.72:25.70 and 50:2.4127:47.5873 when the torque,
fuel consumption rate, NOx and SOOT emissions
Figure 2. Relation between Integrated optimization index
(option one) on all kinds of conditions and the proportion of
ethanol and biodiesel.
Figure 3. Relation between Integrated optimization index
(option two) on all kinds of conditions and the proportion of
ethanol and biodiesel.
are considered under all modes comprehensively.
4. Conclusions
1) The diesel engine power, cost-effectiveness and emis-
sion vary between good and bad as the biodiesel-ethanol-
diesel mixture with different mixture ratio is burning in it
under different revolution and load.
2) After analyzing the torque, fuel consumption rate,
NOx and SOOT emissions with two weighting factor
schemes, the results show that the integrated index in-
cluding engine power, cost-effectiveness and emission
properties is rather better with different optimizing index
when the ratio of bio-diesel, ethanol and diesel are
71.58:2.72:25.70 and 50:2.4127:47.5873.
5. Acknowledgements
The work was supported by Foundation Project of the
Key Laboratory of Chongqing Communication Engi-
neering (2008CQJY002) and by Education and Teaching
Reform Project of Chongqing CSTC, China (No.0903070).
J. LI ET AL.629
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