Revista Facultad de Ingeniería, Universidad de Antioquia, No.110, pp. 48-55, Jan-Mar 2024
Estimation of the degree of internal
recirculation in Internal Combustion Engines
Evaluación del grado de recirculación interna en motores de combustión interna
Leonid Matiukhin 1*
1Department of Heat Engineering and Internal Combustion Engines Faculty of the Energy and Environmental, Moscow
Automobile and Road Construction University, Leningradsky Ave, 64. P. C. 125319. Moscow, Rusia.
CITE THIS ARTICLE AS:
L. Matiukhin. ”Estimation of
the degree of internal
recirculation in Internal
Combustion Engines”, Revista
Facultad de Ingeniería
Universidad de Antioquia, no.
110, pp. 48-55, Jan-Mar 2024.
[Online]. Available: https:
//www.doi.org/10.17533/
udea.redin.20230213
ARTICLE INFO:
Received: October 05, 2021
Accepted: February 20, 2023
Available online: February 20,
2023
KEYWORDS:
cylinder’s filling, fuel’s
molecular mass, volumetric
fractions, gaseous fuels,
hydrogen
Llenado del cilindro, masa
molecular del combustible,
fracciones volumétricas,
combustibles gaseosos,
hidrógeno
ABSTRACT: The concepts of residual gas and admission (or volumetric efficiency)
coefficients are used exclusively by specialists in the field of piston Internal Combustion
Engines. However, it is preferable to apply the concepts of volume fractions of
components of the working mixture consisting of air, fuel, residual, and recirculating
gases, for the evaluation of filling. This simplifies and makes it more easy-to-grasp the
influence of individual factors on the results of gas exchange processes. The proposed
approach makes it possible to take into account the impact on the engine indicators of
the molecular weight of the fuel used and the degree of external recirculation, as well
as to reduce the number of independent variables. At the same time, the displacement
coefficient A proposed by the author characterizes a decrease in filling when an engine
with external mixing is switched to a gaseous fuel with a lower molecular weight. A
change in the valve timing made it possible to produce an effect on the composition
of the working mixture and, thereby, the environmental characteristics of the engine.
In the case of external recirculation, it becomes necessary to estimate the summary
fraction of neutral combustion products in the working mixture, on which all engine
operation depended. This ”overall degree of recirculation” can also be determined using
the proposed approach.
RESUMEN: Las nociones de coeficientes de llenado y de gases residuales son utilizadas
exclusivamente por especialistas en el campo de los motores de combustión interna de
pistón. Sin embargo, se pueden utilizar las nociones técnicas generales y desde hace
mucho tiempo conocidas de la termodinámica – es decir las fracciones de volumen de
los componentes de la mezcla. Usándolos, es posible evaluar el llenado y la composición
de la mezcla de trabajo que consiste en aire, combustible, gases residuales y de
recirculación. En este caso, la fracción de gases residuales en el cilindro determina de
forma única el grado de recirculación interna. Metodológicamente, el uso de fracciones
no solo simplifica, sino que también hace que sea más fácil de interpretar y comprensible
de analizar la influencia de factores individuales en los resultados de los procesos
de intercambio de gases. Tal enfoque permite tener en cuenta la influencia del peso
molecular del combustible utilizado, del grado de recirculación externa y la de la fracción
total de productos de combustión neutros en la mezcla de trabajo en los índices de
llenado y los de desempeño, así como reducir el número de variables independientes. Al
mismo tiempo, el coeficiente de desplazamiento A propuesto por el autor caracteriza la
disminución del llenado cuando el motor con formación de mezcla externa se transfiere
a un combustible gaseoso con un peso molecular más bajo.
1. Introduction The systems of external recirculation are now widely used
in Internal Combustion Engines. The main alternative
to these systems can be the organization of internal
recirculation – a change in the amount of residual gases
in the working mixture (VM), that is, the air-fuel-residual
gas mixture. To analyze its effect on the engine’s
characteristics, it is necessary to have a criterion that
48
* Corresponding author: Leonid Matiukhin
E-mail: panam1@mail.ru
ISSN 0120-6230
e-ISSN 2422-2844
DOI: 10.17533/udea.redin.20230213
48
Estimation of the degree of internal
recirculation in Internal Combustion Engines
Evaluación del grado de recirculación interna en motores de combustión interna
Leonid Matiukhin 1*
1Department of Heat Engineering and Internal Combustion Engines Faculty of the Energy and Environmental, Moscow
Automobile and Road Construction University, Leningradsky Ave, 64. P. C. 125319. Moscow, Rusia.
CITE THIS ARTICLE AS:
L. Matiukhin. ”Estimation of
the degree of internal
recirculation in Internal
Combustion Engines”, Revista
Facultad de Ingeniería
Universidad de Antioquia, no.
110, pp. 48-55, Jan-Mar 2024.
[Online]. Available: https:
//www.doi.org/10.17533/
udea.redin.20230213
ARTICLE INFO:
Received: October 05, 2021
Accepted: February 20, 2023
Available online: February 20,
2023
KEYWORDS:
cylinder’s filling, fuel’s
molecular mass, volumetric
fractions, gaseous fuels,
hydrogen
Llenado del cilindro, masa
molecular del combustible,
fracciones volumétricas,
combustibles gaseosos,
hidrógeno
ABSTRACT: The concepts of residual gas and admission (or volumetric efficiency)
coefficients are used exclusively by specialists in the field of piston Internal Combustion
Engines. However, it is preferable to apply the concepts of volume fractions of
components of the working mixture consisting of air, fuel, residual, and recirculating
gases, for the evaluation of filling. This simplifies and makes it more easy-to-grasp the
influence of individual factors on the results of gas exchange processes. The proposed
approach makes it possible to take into account the impact on the engine indicators of
the molecular weight of the fuel used and the degree of external recirculation, as well
as to reduce the number of independent variables. At the same time, the displacement
coefficient A proposed by the author characterizes a decrease in filling when an engine
with external mixing is switched to a gaseous fuel with a lower molecular weight. A
change in the valve timing made it possible to produce an effect on the composition
of the working mixture and, thereby, the environmental characteristics of the engine.
In the case of external recirculation, it becomes necessary to estimate the summary
fraction of neutral combustion products in the working mixture, on which all engine
operation depended. This ”overall degree of recirculation” can also be determined using
the proposed approach.
RESUMEN: Las nociones de coeficientes de llenado y de gases residuales son utilizadas
exclusivamente por especialistas en el campo de los motores de combustión interna de
pistón. Sin embargo, se pueden utilizar las nociones técnicas generales y desde hace
mucho tiempo conocidas de la termodinámica – es decir las fracciones de volumen de
los componentes de la mezcla. Usándolos, es posible evaluar el llenado y la composición
de la mezcla de trabajo que consiste en aire, combustible, gases residuales y de
recirculación. En este caso, la fracción de gases residuales en el cilindro determina de
forma única el grado de recirculación interna. Metodológicamente, el uso de fracciones
no solo simplifica, sino que también hace que sea más fácil de interpretar y comprensible
de analizar la influencia de factores individuales en los resultados de los procesos
de intercambio de gases. Tal enfoque permite tener en cuenta la influencia del peso
molecular del combustible utilizado, del grado de recirculación externa y la de la fracción
total de productos de combustión neutros en la mezcla de trabajo en los índices de
llenado y los de desempeño, así como reducir el número de variables independientes. Al
mismo tiempo, el coeficiente de desplazamiento A propuesto por el autor caracteriza la
disminución del llenado cuando el motor con formación de mezcla externa se transfiere
a un combustible gaseoso con un peso molecular más bajo.
1. Introduction The systems of external recirculation are now widely used
in Internal Combustion Engines. The main alternative
to these systems can be the organization of internal
recirculation – a change in the amount of residual gases
in the working mixture (VM), that is, the air-fuel-residual
gas mixture. To analyze its effect on the engine’s
characteristics, it is necessary to have a criterion that
48
* Corresponding author: Leonid Matiukhin
E-mail: panam1@mail.ru
ISSN 0120-6230
e-ISSN 2422-2844
DOI: 10.17533/udea.redin.20230213
48
L. Matiukhin, Revista Facultad de Ingeniería, Universidad de Antioquia, No. 110, pp. 48-55, 2024
estimates the degree of internal recirculation.
As is known, the external recirculation is estimated by the
degree of recirculation R′
c, which is the ratio of the number
of kilomoles NR or mass MR of recirculation gases to the
number of kilomoles NN Ch / mass MN Ch of new charge
(NCh) [1–3]:
R′
c = NR
NN Ch
= NR
Nf−a + NR
(1)
Or Rc = MR
MN Ch = MR
Mf −a+MR
A new charge is a mixture of air, recirculation gases
and (in engines with spark ignition) fuel coming into
engine cylinders.
A reciprocal recalculation of the values of R′
c and Rc is
possible using expressions [1, 4, 5]:
Rc = μr R′
c
μN Ch and R′
c = Rc
μr μN Ch
where the μr and the μN Ch are the molecular masses of
combustion products and a new charge.
In fact, the degree of recirculation is a volumetric / mass
fraction [1, 4] of the recirculation gases in the new charge.
In this regard, as shown in [6], thermal calculation of the
piston engines solely on the basis of volumetric fractions is
very convenient. In this case, there is no need to use such
traditionally used observables as the volumetric efficiency
ηv and the residual gases coefficient γr .
Key points
It can be stated that volumetric efficiency assesses not
the filling per se, but its deterioration in comparison
with some virtual filling in the absence of residual gases,
heating of new charge, and hydraulic resistance [5, 7]. At
the same time, unrelated coefficients ηv and γr , as well
as the excess-air coefficient, only indirectly characterize
the composition of the working mixture (WM), which
determines all engine properties and performances. A
big drawback of volumetric efficiency is the lack of its
permanent ultimate magnitude, which should be sought
to achieve maximum power. In addition, it is impossible
on the basis of ηv to judge the reserves of filling or loss of
new charge as a result of scavenging [7–9]. The volumetric
fraction of air σair or new charge σNCh in the working
mixture, and the estimation the degree of air filling of the
cylinder’s total volume, are devoid of these deficiencies
[6, 10–12].
Because the total volume of the cylinder is equal to the
amount of the partial volumes of the components of the
working mixture (Figure 1), one can write [10–13]:
VW M = Va = Vr + Vair + Vf + VR
Here Va is the total volume of the cylinder, VW M
– the volume of the working mixture, Vi – partial
Figure 1 Total cylinder volume as the sum of partial volumes of
components of the working mixture
volumes, respectively, of residual gases (RG), air, fuel, and
recirculation gases.
After dividing the given equality by the volume of Va we get:
1 = σr + σair + σf + σR = σr + σN Ch (2)
that allows estimating the content of RG in the working
mixture by the difference σr = 1 − σN Ch, since the sum
of the fractions is equal to one.
At the same time, it is obvious that in the absence of RG
(σr = 0) the volume of the cylinder is completely filled with
a new charge. Therefore, the best to achieve maximum
power should be considered a filling corresponding to
the σNCh = 1. The lower values of the σN Ch indicate
the availability of filling reserves, and the exceeding unit
shows the loss of a part of the new charge as a result of the
scavenging during overlapping of valves[13].
In general, the volumetric fraction of new charge is
the sum of air, fuel and recycling gases fractions. In turn,
the fraction of the NCh is represented by the sum of
σ′
air + σ′
f + ′σR = σ′
f−a + σ′
R = σ′
f−a + R′
c = 1
Therefore, the fraction of fuel-air mixture in NCh is equal
to the difference
σ′
f−a = 1 − R′
c
In these equations, one stroke in the designation of the
fraction corresponds to the composition of the new charge.
49
estimates the degree of internal recirculation.
As is known, the external recirculation is estimated by the
degree of recirculation R′
c, which is the ratio of the number
of kilomoles NR or mass MR of recirculation gases to the
number of kilomoles NN Ch / mass MN Ch of new charge
(NCh) [1–3]:
R′
c = NR
NN Ch
= NR
Nf−a + NR
(1)
Or Rc = MR
MN Ch = MR
Mf −a+MR
A new charge is a mixture of air, recirculation gases
and (in engines with spark ignition) fuel coming into
engine cylinders.
A reciprocal recalculation of the values of R′
c and Rc is
possible using expressions [1, 4, 5]:
Rc = μr R′
c
μN Ch and R′
c = Rc
μr μN Ch
where the μr and the μN Ch are the molecular masses of
combustion products and a new charge.
In fact, the degree of recirculation is a volumetric / mass
fraction [1, 4] of the recirculation gases in the new charge.
In this regard, as shown in [6], thermal calculation of the
piston engines solely on the basis of volumetric fractions is
very convenient. In this case, there is no need to use such
traditionally used observables as the volumetric efficiency
ηv and the residual gases coefficient γr .
Key points
It can be stated that volumetric efficiency assesses not
the filling per se, but its deterioration in comparison
with some virtual filling in the absence of residual gases,
heating of new charge, and hydraulic resistance [5, 7]. At
the same time, unrelated coefficients ηv and γr , as well
as the excess-air coefficient, only indirectly characterize
the composition of the working mixture (WM), which
determines all engine properties and performances. A
big drawback of volumetric efficiency is the lack of its
permanent ultimate magnitude, which should be sought
to achieve maximum power. In addition, it is impossible
on the basis of ηv to judge the reserves of filling or loss of
new charge as a result of scavenging [7–9]. The volumetric
fraction of air σair or new charge σNCh in the working
mixture, and the estimation the degree of air filling of the
cylinder’s total volume, are devoid of these deficiencies
[6, 10–12].
Because the total volume of the cylinder is equal to the
amount of the partial volumes of the components of the
working mixture (Figure 1), one can write [10–13]:
VW M = Va = Vr + Vair + Vf + VR
Here Va is the total volume of the cylinder, VW M
– the volume of the working mixture, Vi – partial
Figure 1 Total cylinder volume as the sum of partial volumes of
components of the working mixture
volumes, respectively, of residual gases (RG), air, fuel, and
recirculation gases.
After dividing the given equality by the volume of Va we get:
1 = σr + σair + σf + σR = σr + σN Ch (2)
that allows estimating the content of RG in the working
mixture by the difference σr = 1 − σN Ch, since the sum
of the fractions is equal to one.
At the same time, it is obvious that in the absence of RG
(σr = 0) the volume of the cylinder is completely filled with
a new charge. Therefore, the best to achieve maximum
power should be considered a filling corresponding to
the σNCh = 1. The lower values of the σN Ch indicate
the availability of filling reserves, and the exceeding unit
shows the loss of a part of the new charge as a result of the
scavenging during overlapping of valves[13].
In general, the volumetric fraction of new charge is
the sum of air, fuel and recycling gases fractions. In turn,
the fraction of the NCh is represented by the sum of
σ′
air + σ′
f + ′σR = σ′
f−a + σ′
R = σ′
f−a + R′
c = 1
Therefore, the fraction of fuel-air mixture in NCh is equal
to the difference
σ′
f−a = 1 − R′
c
In these equations, one stroke in the designation of the
fraction corresponds to the composition of the new charge.
49
L. Matiukhin, Revista Facultad de Ingeniería, Universidad de Antioquia, No. 110, pp. 48-55, 2024
Consequently, according to the expression (1), R′
c = σ′
R.
An approach based on the proportion of volumetric
fractions reveals under external mixture formation the
effect of the molecular mass of the fuel used on the filling
of cylinders with air. Indeed, the excess-air coefficient
α (the relationship of the quantity of air involved in the
combustion reaction to that theoretically required for the
complete combustion of fuel) is the ratio:
α = Gair
Gf l0 = Nair μair
Nf μf l0 = Nair
Nf μf L0 .
Here Nair and Nf – are quantities of kilomoles of air and
fuel; μair and μf – their molecular mass; l0 and L0 =
l0
μair – are the stoichiometric ratios, that are respectively
the mass and the number of kilomoles of air needed for
complete combustion of 1 kg of fuel. Therefore, one can
record the following:
Nair
Nf = α μf
μair l0.
But, for ideal gases Nair
Nf = Vair
Vf and Vair
Vf = α μf
μair l0 =
αμf L0 On the other hand, after dividing the numerator and
the denominator by the total number of kilomoles of the
fuel-air mixture N we get Nair
Nf = Nair N
Nf N = σair
σf and then:
Vair
Vf = σair
σf = αμf L0.
Thus, in the case of the stoichiometric mixture, this
ratio for gasoline vapors is equal to Vair
Vf = αμf L0 =
1 · 113, 3 14.9
28.9 = 58, 4 and for hydrogen – only
Vair
Vf = 1 · 2 34.8
28.9 = 2.4 (Here μ = 113.3 is the value of
the apparent molecular weight of gasoline, corresponding
to a mixture of 95% isooctane C8H18 and 5% n-heptane
C7H16). In other words, in the latter case, under external
mixture formation and the excess-air coefficient α = 1 about
a quarter of the cylinder’s volume is occupied by hydrogen.
At α = 0.8„ the partial volume of air, exceeds the volume
of hydrogen by less than 2 times, which, with the constant
cylinder’s volume means a reduction in the volume of
air due to a corresponding increase in the fraction of
hydrogen. This means that the impact of the type of fuel
used on the results of gas exchange must be taken into
account [13–20].
As we know from experience, the converting transfer
of engines to power gas fuel is accompanied by a
change in its performances [21–26], including volumetric
efficiency.
In the case of spark ignition engines with external mixture
formation, the link between the fractions of the new charge
and the air is easily found with the so-called “displacement
factor” A [13].
A = αL0μf
αL0μf + 1 (3)
In the given relation, L0 is a stechiometric ratio in
kilomoles of air per kilogram of fuel, α− excess-air
coefficient and μf − fuel’s molecular mass. The
dimensionless complex A inevitably appears, including
when the volumetric efficiency is deduced on the basis of
the partial volumes of working mixture’s components [13].
If the displacement factor is presented as a
A = αL0( 1
μf +αL0
) , then its physical meaning becomes
clear, it is equal to the volumetric fraction of air in the
fuel-air mixture. The volumetric fraction of fuel in the
fuel-air– , as well as in the working mixture, under the
constant value of excess-air coefficient α, increases as the
molecular mass of the fuel used decreases.
Similarly, the fraction of air in the fuel-air mixture (i.e.,
factor A) decreases in the case of enrichment of the
fuel mixture (fig. 2). Therefore, it can be concluded
that the volumetric (molar) fractions of air and fuel in
the fuel-air– and in the working mixture are linked by
the excess-air coefficient and the (seeming) molecular
fuel mass. Consequently, any change in the excess-air
coefficient or switching to fuel with a significantly different
(seeming) molecular mass in engines with external
mixture formation should affect the fraction of air σa in the
WM, i.e., the filling. In turn, the average indicated mean
pressure is a function of the σair , which is illustrated by
equations [6, 13]:
pi = ε
ε−1
Hu
l0
ηi
α σair ρa
air and pi =
1
ε−1
Hu
l0 ηi εpaTr −pr Taφs
287Tr Ta
A
α (1 − R′c) .
Here, E is the compression ratio, Hu is the lower working
combustion heat, ηi is the indicator efficiency, ρa
air is the
air density at point ”a” parameter of the indicator diagram
and φs is the coefficient of purging, which is the ratio of
the actual quantity of kilomoles of the RG to the calculated
one. The product σair ρa
air is the density of air at its partial
pressure in the working mixture.
Figure 2 Effect of the excess-air coefficient on the value of
displacement factor A [13]
From the last expression, it can be concluded that the
efficiency of qualitative regulation of engines with external
mixture formation depends on the magnitude of the ratio
A/α. The smaller the molecular mass of the fuel, the
50
Consequently, according to the expression (1), R′
c = σ′
R.
An approach based on the proportion of volumetric
fractions reveals under external mixture formation the
effect of the molecular mass of the fuel used on the filling
of cylinders with air. Indeed, the excess-air coefficient
α (the relationship of the quantity of air involved in the
combustion reaction to that theoretically required for the
complete combustion of fuel) is the ratio:
α = Gair
Gf l0 = Nair μair
Nf μf l0 = Nair
Nf μf L0 .
Here Nair and Nf – are quantities of kilomoles of air and
fuel; μair and μf – their molecular mass; l0 and L0 =
l0
μair – are the stoichiometric ratios, that are respectively
the mass and the number of kilomoles of air needed for
complete combustion of 1 kg of fuel. Therefore, one can
record the following:
Nair
Nf = α μf
μair l0.
But, for ideal gases Nair
Nf = Vair
Vf and Vair
Vf = α μf
μair l0 =
αμf L0 On the other hand, after dividing the numerator and
the denominator by the total number of kilomoles of the
fuel-air mixture N we get Nair
Nf = Nair N
Nf N = σair
σf and then:
Vair
Vf = σair
σf = αμf L0.
Thus, in the case of the stoichiometric mixture, this
ratio for gasoline vapors is equal to Vair
Vf = αμf L0 =
1 · 113, 3 14.9
28.9 = 58, 4 and for hydrogen – only
Vair
Vf = 1 · 2 34.8
28.9 = 2.4 (Here μ = 113.3 is the value of
the apparent molecular weight of gasoline, corresponding
to a mixture of 95% isooctane C8H18 and 5% n-heptane
C7H16). In other words, in the latter case, under external
mixture formation and the excess-air coefficient α = 1 about
a quarter of the cylinder’s volume is occupied by hydrogen.
At α = 0.8„ the partial volume of air, exceeds the volume
of hydrogen by less than 2 times, which, with the constant
cylinder’s volume means a reduction in the volume of
air due to a corresponding increase in the fraction of
hydrogen. This means that the impact of the type of fuel
used on the results of gas exchange must be taken into
account [13–20].
As we know from experience, the converting transfer
of engines to power gas fuel is accompanied by a
change in its performances [21–26], including volumetric
efficiency.
In the case of spark ignition engines with external mixture
formation, the link between the fractions of the new charge
and the air is easily found with the so-called “displacement
factor” A [13].
A = αL0μf
αL0μf + 1 (3)
In the given relation, L0 is a stechiometric ratio in
kilomoles of air per kilogram of fuel, α− excess-air
coefficient and μf − fuel’s molecular mass. The
dimensionless complex A inevitably appears, including
when the volumetric efficiency is deduced on the basis of
the partial volumes of working mixture’s components [13].
If the displacement factor is presented as a
A = αL0( 1
μf +αL0
) , then its physical meaning becomes
clear, it is equal to the volumetric fraction of air in the
fuel-air mixture. The volumetric fraction of fuel in the
fuel-air– , as well as in the working mixture, under the
constant value of excess-air coefficient α, increases as the
molecular mass of the fuel used decreases.
Similarly, the fraction of air in the fuel-air mixture (i.e.,
factor A) decreases in the case of enrichment of the
fuel mixture (fig. 2). Therefore, it can be concluded
that the volumetric (molar) fractions of air and fuel in
the fuel-air– and in the working mixture are linked by
the excess-air coefficient and the (seeming) molecular
fuel mass. Consequently, any change in the excess-air
coefficient or switching to fuel with a significantly different
(seeming) molecular mass in engines with external
mixture formation should affect the fraction of air σa in the
WM, i.e., the filling. In turn, the average indicated mean
pressure is a function of the σair , which is illustrated by
equations [6, 13]:
pi = ε
ε−1
Hu
l0
ηi
α σair ρa
air and pi =
1
ε−1
Hu
l0 ηi εpaTr −pr Taφs
287Tr Ta
A
α (1 − R′c) .
Here, E is the compression ratio, Hu is the lower working
combustion heat, ηi is the indicator efficiency, ρa
air is the
air density at point ”a” parameter of the indicator diagram
and φs is the coefficient of purging, which is the ratio of
the actual quantity of kilomoles of the RG to the calculated
one. The product σair ρa
air is the density of air at its partial
pressure in the working mixture.
Figure 2 Effect of the excess-air coefficient on the value of
displacement factor A [13]
From the last expression, it can be concluded that the
efficiency of qualitative regulation of engines with external
mixture formation depends on the magnitude of the ratio
A/α. The smaller the molecular mass of the fuel, the
50
L. Matiukhin, Revista Facultad de Ingeniería, Universidad de Antioquia, No. 110, pp. 48-55, 2024
lower the displacement factor A (3) and the greater the
effect of the enrichment of the fuel-air mixture on the
reduction of the air fraction in the working mixture (figure
3). As a result, the qualitative power governing in gas
engines with spark ignition is less efficient than in gasoline
engines [6, 13].
Figure 3 The plot of the effectiveness of quality regulation,
which is determined by the ratio of displacement– and excess air
factor A/α in the function of the coefficient α[6]
The partial volume of air and its fraction in the
air-fuel-residual gases WM are determined by expressions
[6, 13]:
Vair = Vc
( εpaTr − φspr Ta
paTr
)
A (1 − R′
c) and
σair =
( εpaTr − φspr Ta
εpaTr
)
A (1 − R′
c)
(4)
Unlike the expression of the volumetric efficiency
ηv traditionally used in calculations (e.g., ηv =
φ1 ε
ε−1
pa
po
To
(Tr +∆T +φγr Tr )) [5, 27], the formula deduced to
determine the air fraction σair contains fewer variables.
In addition, the value of σair = 1 indicates the maximum
possible filling in the absence of loss of fresh charge. The
corresponding value of the ηv at which maximum power
is reached cannot be called due to its dependence on
constantly changing atmospheric conditions ( from p0 and
T0).
In (4) ε is the compression ratio, Vc is the volume of the
combustion chamber, the pa and Ta are the parameters of
the working mixture at the beginning of the compression,
pr and Tr – parameters of residual gases at the end of the
exhaust.
Since all characteristics of piston ICE are determined
by the composition of the ignition working mixture, it is
important to know the proportion of individual components
obtained during the gas exchange process.
Knowing the value of the air fraction σair , it is easy to find
the volumetric fractions of the remaining components of
the working mixture (table 1).
At a known frequency of rotation of the crankshaft
and hourly air consumption, its volume in the WM can be
determined by the expression
σactual
air = (ε−1)
ε
Vair ·103
30·niVh
pk
pa′′
Tan
Tk .
The required pressure values (see Fig. 1) are determined
by the results of the indication of processes. Volume-based
calculations make it easier to obtain equations to
determine the number of kilomoles of new charge and
recirculation gases [6, 10, 13]. The expression below
shows the link between the recirculation degree and the
composition of the fuel-air mixture (with the displacement
factor A)
R′C = ANR
NB+ANR .
From this expression, it follows [6, 13] that, all other things
being equal, the convert an engine to another fuel, as well
as the variation in excess-air coefficient, are accompanied
by a change in the recirculation degree (see fig. 4).
Figure 4 Effect of excess-air coefficient and fuel type (its
molecular mass) on the value of recirculation degree R′
c under
constant amounts of air and recirculation gases (the values of
”Naire” and ”N R” remain unchanged)
2. Estimation of internal recirculation
Currently, engines with variable phases of gas distribution
have been widely distributed. By variable valve timing,
neutral combustion products can be thrown into the intake
tract and therefore increase their fraction in the working
mixture. In other words, modern technologies allow for
internal recirculation.
The volume of residual gases is determined by the
assumption that the working mixture at the beginning of
the compression stroke contains the amount of RG equal
to their content in the combustion chamber at the time of
the piston was found in the top dead center (TDC).
Thus, the partial volume Vr of residual gases can be found
by its reduction to the conditions at the point ”a” indicator
diagram: Vcpr
Tr = Vr pa
Ta . Hence, the volume of RG at
parameters of the point ”a” is Vr = Vc pr
pa
Ta
Tr or, given the
coefficient of purging φS , is equal to
Vr = Vc pr
pa
Ta
Tr φs
After dividing the partial volume Vr by the volume of the
WM, equal to the total volume of the cylinder Va, we get an
51
lower the displacement factor A (3) and the greater the
effect of the enrichment of the fuel-air mixture on the
reduction of the air fraction in the working mixture (figure
3). As a result, the qualitative power governing in gas
engines with spark ignition is less efficient than in gasoline
engines [6, 13].
Figure 3 The plot of the effectiveness of quality regulation,
which is determined by the ratio of displacement– and excess air
factor A/α in the function of the coefficient α[6]
The partial volume of air and its fraction in the
air-fuel-residual gases WM are determined by expressions
[6, 13]:
Vair = Vc
( εpaTr − φspr Ta
paTr
)
A (1 − R′
c) and
σair =
( εpaTr − φspr Ta
εpaTr
)
A (1 − R′
c)
(4)
Unlike the expression of the volumetric efficiency
ηv traditionally used in calculations (e.g., ηv =
φ1 ε
ε−1
pa
po
To
(Tr +∆T +φγr Tr )) [5, 27], the formula deduced to
determine the air fraction σair contains fewer variables.
In addition, the value of σair = 1 indicates the maximum
possible filling in the absence of loss of fresh charge. The
corresponding value of the ηv at which maximum power
is reached cannot be called due to its dependence on
constantly changing atmospheric conditions ( from p0 and
T0).
In (4) ε is the compression ratio, Vc is the volume of the
combustion chamber, the pa and Ta are the parameters of
the working mixture at the beginning of the compression,
pr and Tr – parameters of residual gases at the end of the
exhaust.
Since all characteristics of piston ICE are determined
by the composition of the ignition working mixture, it is
important to know the proportion of individual components
obtained during the gas exchange process.
Knowing the value of the air fraction σair , it is easy to find
the volumetric fractions of the remaining components of
the working mixture (table 1).
At a known frequency of rotation of the crankshaft
and hourly air consumption, its volume in the WM can be
determined by the expression
σactual
air = (ε−1)
ε
Vair ·103
30·niVh
pk
pa′′
Tan
Tk .
The required pressure values (see Fig. 1) are determined
by the results of the indication of processes. Volume-based
calculations make it easier to obtain equations to
determine the number of kilomoles of new charge and
recirculation gases [6, 10, 13]. The expression below
shows the link between the recirculation degree and the
composition of the fuel-air mixture (with the displacement
factor A)
R′C = ANR
NB+ANR .
From this expression, it follows [6, 13] that, all other things
being equal, the convert an engine to another fuel, as well
as the variation in excess-air coefficient, are accompanied
by a change in the recirculation degree (see fig. 4).
Figure 4 Effect of excess-air coefficient and fuel type (its
molecular mass) on the value of recirculation degree R′
c under
constant amounts of air and recirculation gases (the values of
”Naire” and ”N R” remain unchanged)
2. Estimation of internal recirculation
Currently, engines with variable phases of gas distribution
have been widely distributed. By variable valve timing,
neutral combustion products can be thrown into the intake
tract and therefore increase their fraction in the working
mixture. In other words, modern technologies allow for
internal recirculation.
The volume of residual gases is determined by the
assumption that the working mixture at the beginning of
the compression stroke contains the amount of RG equal
to their content in the combustion chamber at the time of
the piston was found in the top dead center (TDC).
Thus, the partial volume Vr of residual gases can be found
by its reduction to the conditions at the point ”a” indicator
diagram: Vcpr
Tr = Vr pa
Ta . Hence, the volume of RG at
parameters of the point ”a” is Vr = Vc pr
pa
Ta
Tr or, given the
coefficient of purging φS , is equal to
Vr = Vc pr
pa
Ta
Tr φs
After dividing the partial volume Vr by the volume of the
WM, equal to the total volume of the cylinder Va, we get an
51
L. Matiukhin, Revista Facultad de Ingeniería, Universidad de Antioquia, No. 110, pp. 48-55, 2024
Table 1 Proportions of the components of the working mixture [13]
σi σR σC3 σΓC σT σB σi
σB σR = R′cσB
A(1−R′
c) σC3 = σB
A(1−R′c) σΓC = σB
A σT = σB
αμTL0 1 σB
σT σR = R′
cαL0μTσT
A(1−R′c) σC3 = σT(1+αL0μT)
(1−R′
c) σTC = σT (1 + αL0μT ) 1 σB = αL0μTσT σT
σΓC σR = R′cσΓC
(1−R′
c) σC3 = σΓC
(1−R′c) 1 σT = σΓC
(1+αμTL0) σB = AσΓC σΓC
σC3 σR = R′
cσC3 1 σΓC = σC3 (1 − R′
c) σT = σC3(1−R′
c)
(1+αL0μT) σz = σC3A (1 − R′
c) σC3
σR 1 σC3 = σR
R′c σΓC = σR (1−R′
c)
R′
c
σT = σR (1−R′
c)
R′
c(1+αL0μT) σB = AσR (1−R′
c)
R′
c
σR
expression to determine the volumetric fraction of residual
gases [13, 28]
σr = φ1
pr Ta
εpaTr
(5)
The coefficient of additional charging φ1 is the ratio of the
number of moles of fresh charge actually received in the
cylinder to the calculated one. It takes into account the
increase in filling as a result of better cleaning during the
period of overlapping of valves, as well as due to inertial
phenomena during the delay in closing the intake valves.
It follows from the last equation that the fraction σr
increases when covering the throttle (when the pa is
lowered) and the pressure of residual gases goes up.
As shown in the [24, 25], the additional charging- and
purging coefficients [28] are interlinked in the result
that the sum of all partial volumes of working mixture
components is equal to the total volume of the cylinder Va,
and the sum of their volumetric fractions is equal to unit.
The relationship between these coefficients is determined
by expressions.
φS = 1−φ1σC3
1−σC3 and φ1 = 1−φsσr
1−σr
It is an expression (5) that can describe the influence of
various factors on the quantity of combustion products
remaining in the cylinder, i.e., the volume of residual gases
σr is the sole estimated criterion for the degree of internal
recirculation. As the temperature Tr increases, RG reduce
their density and mass. As a result of cooling by the
subsequent mixing with a new charge, there is a decrease
in the volume of RG, which results in a slight decrease
in the fraction of RG and a corresponding increase in the
fraction of the new charge in the working mixture.
According to expression (5), the volumetric fraction of RG
in the working mix is proportional to their pressure. In this
regard, the increase in pr means an increase in the density
and mass of RG, and therefore (as the example suggests
in fig. 5), after mixing with a new charge, their fraction in
the working mix increases by 0.011, while the fraction of
new charge, defined by the expression σNCh = 1 − σr , it
decreases by the same value.
As will be recalled, the worsening of clearing is the main
way of organizing internal recirculation. By increasing the
pressure and organizing the ingress of RG into the inlet
Figure 5 The effect of residual gases pressure pr [bar] on the
fraction σr
manifold during the valves overlap period, it is possible to
increase the proportion of neutral combustion products
in the working mixture in order to reduce the toxicity of
exhaust gases.
By influencing the RG parameters at the end of the exhaust
process, which appear in the expression (5), and therefore
on the parameters of the working mixture at the beginning
of the compression stroke, it is possible to change the
composition of the working mixture and influence the
properties of the engine - environmental, economic, as
well as its power [6, 13, 19].
Thus, the thermal calculation of the cycle based on
the composition of the working mixture allows evaluating
the degree of internal recirculation quantitatively and,
because of that, controlling the composition of the working
mixture.
As it follows from figure 5, due to the high degrees
of compression and the small volumes of the combustion
chamber of modern engines, it is impossible to achieve any
significant values of the fraction of σr only by increasing
the pressure of the combustion products in the combustion
chamber. In order to implement internal recirculation,
it is necessary to organize the backstreaming of residual
gas from the exhaust to the intake manifold during the
valve overlap period. Re-entering the cylinder and mixing
with a fresh charge, these combustion products increase
the fraction of RG in the working mixture.
The actual value of the fraction σr , at a known value
of the new charge fraction σactual
N Ch , will be determined by
the expression σactual
r = 1 − σactual
N Ch .
52
Table 1 Proportions of the components of the working mixture [13]
σi σR σC3 σΓC σT σB σi
σB σR = R′cσB
A(1−R′
c) σC3 = σB
A(1−R′c) σΓC = σB
A σT = σB
αμTL0 1 σB
σT σR = R′
cαL0μTσT
A(1−R′c) σC3 = σT(1+αL0μT)
(1−R′
c) σTC = σT (1 + αL0μT ) 1 σB = αL0μTσT σT
σΓC σR = R′cσΓC
(1−R′
c) σC3 = σΓC
(1−R′c) 1 σT = σΓC
(1+αμTL0) σB = AσΓC σΓC
σC3 σR = R′
cσC3 1 σΓC = σC3 (1 − R′
c) σT = σC3(1−R′
c)
(1+αL0μT) σz = σC3A (1 − R′
c) σC3
σR 1 σC3 = σR
R′c σΓC = σR (1−R′
c)
R′
c
σT = σR (1−R′
c)
R′
c(1+αL0μT) σB = AσR (1−R′
c)
R′
c
σR
expression to determine the volumetric fraction of residual
gases [13, 28]
σr = φ1
pr Ta
εpaTr
(5)
The coefficient of additional charging φ1 is the ratio of the
number of moles of fresh charge actually received in the
cylinder to the calculated one. It takes into account the
increase in filling as a result of better cleaning during the
period of overlapping of valves, as well as due to inertial
phenomena during the delay in closing the intake valves.
It follows from the last equation that the fraction σr
increases when covering the throttle (when the pa is
lowered) and the pressure of residual gases goes up.
As shown in the [24, 25], the additional charging- and
purging coefficients [28] are interlinked in the result
that the sum of all partial volumes of working mixture
components is equal to the total volume of the cylinder Va,
and the sum of their volumetric fractions is equal to unit.
The relationship between these coefficients is determined
by expressions.
φS = 1−φ1σC3
1−σC3 and φ1 = 1−φsσr
1−σr
It is an expression (5) that can describe the influence of
various factors on the quantity of combustion products
remaining in the cylinder, i.e., the volume of residual gases
σr is the sole estimated criterion for the degree of internal
recirculation. As the temperature Tr increases, RG reduce
their density and mass. As a result of cooling by the
subsequent mixing with a new charge, there is a decrease
in the volume of RG, which results in a slight decrease
in the fraction of RG and a corresponding increase in the
fraction of the new charge in the working mixture.
According to expression (5), the volumetric fraction of RG
in the working mix is proportional to their pressure. In this
regard, the increase in pr means an increase in the density
and mass of RG, and therefore (as the example suggests
in fig. 5), after mixing with a new charge, their fraction in
the working mix increases by 0.011, while the fraction of
new charge, defined by the expression σNCh = 1 − σr , it
decreases by the same value.
As will be recalled, the worsening of clearing is the main
way of organizing internal recirculation. By increasing the
pressure and organizing the ingress of RG into the inlet
Figure 5 The effect of residual gases pressure pr [bar] on the
fraction σr
manifold during the valves overlap period, it is possible to
increase the proportion of neutral combustion products
in the working mixture in order to reduce the toxicity of
exhaust gases.
By influencing the RG parameters at the end of the exhaust
process, which appear in the expression (5), and therefore
on the parameters of the working mixture at the beginning
of the compression stroke, it is possible to change the
composition of the working mixture and influence the
properties of the engine - environmental, economic, as
well as its power [6, 13, 19].
Thus, the thermal calculation of the cycle based on
the composition of the working mixture allows evaluating
the degree of internal recirculation quantitatively and,
because of that, controlling the composition of the working
mixture.
As it follows from figure 5, due to the high degrees
of compression and the small volumes of the combustion
chamber of modern engines, it is impossible to achieve any
significant values of the fraction of σr only by increasing
the pressure of the combustion products in the combustion
chamber. In order to implement internal recirculation,
it is necessary to organize the backstreaming of residual
gas from the exhaust to the intake manifold during the
valve overlap period. Re-entering the cylinder and mixing
with a fresh charge, these combustion products increase
the fraction of RG in the working mixture.
The actual value of the fraction σr , at a known value
of the new charge fraction σactual
N Ch , will be determined by
the expression σactual
r = 1 − σactual
N Ch .
52
L. Matiukhin, Revista Facultad de Ingeniería, Universidad de Antioquia, No. 110, pp. 48-55, 2024
With the known value of air hourly consumption Gair ,
the consumption per minute is Gair /60[ kg/min] and the
cycle consumption in grams is Gcycle
air = Gair
0,03 in [g/cycle
]. Here «i» is the number of cylinders, and «n» - the
frequency of rotation of the crankshaft.
In view of the fact that Gcycle
air = V k
air ρk = V a
air ρa,
the volume that air takes up in the cylinder upon the
parameters of the working mixture at the point ”a” of the
indicator chart, is determined by the expression.
V a
air = Gcycle
air
ρa
In this equality ρa = ρk pa
pk
Tk
Ta and, therefore,
V a
air = Gair
0,03 in ρk
pk Ta
paTk or V a
air = Vair
0,03in
pk Ta
paTk
Here Vair is a hour’s volume air consumption.
And, after dividing by the volume of the working mixture
equal to the total volume of the cylinder Va, we get the
actual value of the air fraction in the working mixture
σαctual
air = Gair
0,03ρk niVa
pk Ta
paTk
or, more conveniently,
σαctual
air = Vair
0,03niVa
pk Ta
paTk .
We use the displacement factor A to determine the fraction
of the new charge.
σαctual
N Ch = Vair
0,03AniVa
pk Ta
paTk .
Consequently, the total fraction of RG in the cylinder by the
beginning of the compression stroke will
be determined by the difference σαctual
r = 1 − σαctual
N Ch =
1 − Vair
0,03 AniV a
pk Ta
paTk or, finally,
σαctual
r = 0,03AniVapaTk −VBpk Ta
0,03AniVapaTk
But the total volume of the cylinder Va can be represented
by displacement volume Vh as Va = Vc + Vh = εVh
(ε−1) ,
because Vc = Vh
(ε−1) . In this case
σαctual
r = (ε−1)
ε
0,03AniVapaTk −VBpk Ta
0,03AniVhpaTk
where iVh is the total displacement volume of an engine.
The difference in the values of σαctual
r and σr , that is,∆σ =
σαctual
r − σr , equals the increase in the fraction of residual
gases as a result of their backstreaming from the exhaust
to the intake manifold. This value, in fact, characterizes a
change in the degree of internal recirculation.
The degree of internal recirculation is the volume / molar
fraction of RG in the working mixture
R′
ci = V αctual
r
VW M = V αctual
r
Va = N αctual
r
N = σαctual
r
and (under the absence of external recirculation) is
equivalent to the total fraction of neutral combustion
products in the working mixture.
In the case of external recirculation, the total fraction of
combustion products in the working mixture is determined
by the expression.
R′
cΣ = V αctual
r +VR
VW M = σαctual
r + σR = R′
ci + R′
c =
1 − (σair + σf )
Thus, from (2) follows:
R′
cΣ = 1 − (σair + σf ) .
Because the combustion process of the working mixture is
affected by the value of R′
cΣ , it seems preferable to analyze
the environmental, economic, and power performance
data of the engine in the function of this quantity.
The author’s approach to estimation filling by volume
fractions (in contrast to the traditionally based on the
concepts of the volumetric efficiency and coefficient of
residual gases) equally applies to the calculation of
supercharged engines, two-stroke ICE [28], and engines
operating on the Miller-Atkinson cycle [29]. It allows
deriving equations for calculating the composition of the
working mixture, taking into account the actual, rather
than geometric, compression ratio.
3. Conclusions
The totality of all WM components determines its
composition. All engine performance data are a function
of the WM composition. At the same time, the fraction of
new charge / air unequivocally characterizes the state of
fullness of total cylinder volume Va, that is, its filling.
To determine the optimal magnitudes of the degree
of internal recirculation, a certain quantitative value is
needed to estimate this degree. This is the fraction of
residual gases in the working mixture. If the volumetric
composition of the air-fuel-residual gases mixture is
known, the fraction of residual gases is defined as the
difference σr = 1 − σN Ch·
The displacement factor A, based on the ratio of the
partial volumes of the components in the new charge,
allows analyzing and considering the effect on the filling
of each particular fuel (its molecular mass), which is
important in the case of gaseous fuels and, above all,
hydrogen. Is it clear from the expression σr = 1 − σN Ch,
that in order to achieve maximum capacity without
loss of the new charge as a result of the scavenging,
it is necessary to tend to σN Ch = 1. At the same
time, the magnitude of the fraction of σr unequivocally
characterizes the reserves for filling, and its negative
value indicates that there are losses of part of the new
53
With the known value of air hourly consumption Gair ,
the consumption per minute is Gair /60[ kg/min] and the
cycle consumption in grams is Gcycle
air = Gair
0,03 in [g/cycle
]. Here «i» is the number of cylinders, and «n» - the
frequency of rotation of the crankshaft.
In view of the fact that Gcycle
air = V k
air ρk = V a
air ρa,
the volume that air takes up in the cylinder upon the
parameters of the working mixture at the point ”a” of the
indicator chart, is determined by the expression.
V a
air = Gcycle
air
ρa
In this equality ρa = ρk pa
pk
Tk
Ta and, therefore,
V a
air = Gair
0,03 in ρk
pk Ta
paTk or V a
air = Vair
0,03in
pk Ta
paTk
Here Vair is a hour’s volume air consumption.
And, after dividing by the volume of the working mixture
equal to the total volume of the cylinder Va, we get the
actual value of the air fraction in the working mixture
σαctual
air = Gair
0,03ρk niVa
pk Ta
paTk
or, more conveniently,
σαctual
air = Vair
0,03niVa
pk Ta
paTk .
We use the displacement factor A to determine the fraction
of the new charge.
σαctual
N Ch = Vair
0,03AniVa
pk Ta
paTk .
Consequently, the total fraction of RG in the cylinder by the
beginning of the compression stroke will
be determined by the difference σαctual
r = 1 − σαctual
N Ch =
1 − Vair
0,03 AniV a
pk Ta
paTk or, finally,
σαctual
r = 0,03AniVapaTk −VBpk Ta
0,03AniVapaTk
But the total volume of the cylinder Va can be represented
by displacement volume Vh as Va = Vc + Vh = εVh
(ε−1) ,
because Vc = Vh
(ε−1) . In this case
σαctual
r = (ε−1)
ε
0,03AniVapaTk −VBpk Ta
0,03AniVhpaTk
where iVh is the total displacement volume of an engine.
The difference in the values of σαctual
r and σr , that is,∆σ =
σαctual
r − σr , equals the increase in the fraction of residual
gases as a result of their backstreaming from the exhaust
to the intake manifold. This value, in fact, characterizes a
change in the degree of internal recirculation.
The degree of internal recirculation is the volume / molar
fraction of RG in the working mixture
R′
ci = V αctual
r
VW M = V αctual
r
Va = N αctual
r
N = σαctual
r
and (under the absence of external recirculation) is
equivalent to the total fraction of neutral combustion
products in the working mixture.
In the case of external recirculation, the total fraction of
combustion products in the working mixture is determined
by the expression.
R′
cΣ = V αctual
r +VR
VW M = σαctual
r + σR = R′
ci + R′
c =
1 − (σair + σf )
Thus, from (2) follows:
R′
cΣ = 1 − (σair + σf ) .
Because the combustion process of the working mixture is
affected by the value of R′
cΣ , it seems preferable to analyze
the environmental, economic, and power performance
data of the engine in the function of this quantity.
The author’s approach to estimation filling by volume
fractions (in contrast to the traditionally based on the
concepts of the volumetric efficiency and coefficient of
residual gases) equally applies to the calculation of
supercharged engines, two-stroke ICE [28], and engines
operating on the Miller-Atkinson cycle [29]. It allows
deriving equations for calculating the composition of the
working mixture, taking into account the actual, rather
than geometric, compression ratio.
3. Conclusions
The totality of all WM components determines its
composition. All engine performance data are a function
of the WM composition. At the same time, the fraction of
new charge / air unequivocally characterizes the state of
fullness of total cylinder volume Va, that is, its filling.
To determine the optimal magnitudes of the degree
of internal recirculation, a certain quantitative value is
needed to estimate this degree. This is the fraction of
residual gases in the working mixture. If the volumetric
composition of the air-fuel-residual gases mixture is
known, the fraction of residual gases is defined as the
difference σr = 1 − σN Ch·
The displacement factor A, based on the ratio of the
partial volumes of the components in the new charge,
allows analyzing and considering the effect on the filling
of each particular fuel (its molecular mass), which is
important in the case of gaseous fuels and, above all,
hydrogen. Is it clear from the expression σr = 1 − σN Ch,
that in order to achieve maximum capacity without
loss of the new charge as a result of the scavenging,
it is necessary to tend to σN Ch = 1. At the same
time, the magnitude of the fraction of σr unequivocally
characterizes the reserves for filling, and its negative
value indicates that there are losses of part of the new
53
L. Matiukhin, Revista Facultad de Ingeniería, Universidad de Antioquia, No. 110, pp. 48-55, 2024
charge as a result of the scavenging.
Basing the thermal calculation of the engine on the
composition of the working mixture makes it easier to
analyze the impact of any characteristics of the mixture
on the main indicators of the cycle and on the degree
of internal recirculation estimated by the volumetric
fraction of residual gases. An additional advantage of
this approach is the opportunity to visualize the effects
of different factors on the composition of the working
mixture, which is very important for didactic purposes.
4. Declaration of competing interest
I declare that I have no significant competing interests,
including financial or non-financial, professional, or
personal interests interfering with the full and objective
presentation of the work described in this manuscript.
5. Funding
The author received no financial support for the research,
authorship, and/or publication of this article.
6. Author contributions
The material of the article belongs entirely to its author.
7. Data Availability Statement
The authors confirm that the data supporting the findings
of this study are available within the article [and/or] its
supplementary materials.
References
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2020. [Online]. Available: http://www.warse.org/IJETER/static/pdf/
file/ijeter94862020.pdf
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Verbrennungsmotor, ser. ATZ/MTZ-Fachbuch. Washington,
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[3] V. N. Lukanin, Internal Combustion Engines. Moscow: Mir, 2005.
[4] M. G. Shatrov, Automobile Engines. Moscow, RU: Akademia, 2010.
[5] V. N. Lukanin, Motores de combustión interna. Moscú: Mir, 1985.
[6] L. M. Matyukhin, “El método alternativo de la evaluación de
calidad de los resultados del intercámbio de gases en los
motores de combustión interna,” Revista Ingeniería, Universidad de
Carabobo, vol. 25, no. 1, Ene-Abr 2018. [Online]. Available: https:
//www.redalyc.org/journal/707/70757668005/70757668005.pdf
[7] B. A. Sharoglazov, M. F. Farafontov, and V. V. Klementiev, Internal
combustion engines: Theory, modeling and process calculation.
Russia: South Ural State University, 2005.
[8] Y. L. Kovylova and D. A. Uglanov, “The influence of various factors
on the filling ratio of a piston engine,” Bulletin of the Samara State
Aerospace University, vol. 2, pp. 114–117, 2007.
[9] B. A. Sharoglazov and V. A. Povalyaev, “Estimated quality
assessment of fresh charge filling of piston engine cylinders
at the design stage,” Bulletin of the National Research South Ural
State University, vol. 23, pp. 20–24, 2008.
[10] A. Jante, Leitfaden der technischen Thermodynamik. Germany, LE:
Teubner, 1950.
[11] A. P. Baskakov, Termotecnia. Moscú: Mir, 1985.
[12] W. Christian, Volume 1 of Technische Wärmelehre für Studierende des
Bergbaus, des Hüttenwesens und der Aufbereitung. Germany, LE:
VEB Dt. Verlag für Grundstoffindustrie, 1966.
[13] L. M. Matiukhin, “Analysis of filling and thermal calculation
of ice based on the composition of the working mix,” LAP
LAMBERT Academic Publishing GmbH & Co, 2011. [Online]. Available:
http://www.techweb.com/se/index.html
[14] P. Kovalenko, S. N. Devyanin, E. A. Ulyukina, and A. V. Todoriv,
“Prospects for the operation of agricultural machinery on
compressed natural gas,” Autogas filling complex+ Alternative
fuel, vol. 16, no. 7, pp. 313–315, 2017.
[15] V. V. Sinyavski, I. V. Alekseev, I. Y. Ivanov, S. N. Bogdanov, and
Y. V. Trofimenko, “Physical simulation of high-and medium-speed
engines powered by natural gas,” Pollution Research, vol. 36, no. 4,
pp. 798–804, 2017.
[16] G. G. Ter-Mkrtichyan, A. M. Saikin, K. E. Karpukhin, A. S.
Terenchenko, and Y. G. Ter-Mkrtichyan, “Diesel-to-natural
gas engine conversion with lower compression ratio,” Pollution
Research, vol. 36, no. 4, pp. 925–930, 2017.
[17] V. V. Sinyavski, M. G. Shatrov, V. V. Kremnev, and G. Pronchenko,
“Forecasting of a boosted locomotive gas diesel engine parameters
with one- and two-stage charging systems,” Reports in Mechanical
Engineering, vol. 1, no. 1, Dec. 30, 2020. [Online]. Available:
https://doi.org/10.31181/rme200101192s
[18] M. G. Shatrov, V. V. Sinyavski, A. Y. Dunina, I. G. Shishlov, and A. V.
Vakulenko, “Forecasting of a boosted locomotive gas diesel engine
parameters with one- and two-stage charging systemmethod of
conversion of high- and middle-speed diesel engines into gas
diesel enginess,” Facta Universitatis, vol. 15, no. 3, 2017. [Online].
Available: https://doi.org/10.22190/FUME171004023S
[19] V. I. Erokhov and A. L. Karunin, Gazodizel’nye avtomobili
(konstruktsiya, raschet, ekspluatatsiya) [Gas-diesel cars (design,
calculation, operation). Russia: Graf-press, 2005.
[20] K. Schmillen, “Nuzung von biogas in gaszundungstrahlmotoren,”
MTZ Motortechnische Zeitschrift, vol. 7, no. 9, pp. 351–357, 1989.
[21] V. A. Markov, S. N. Devyanin, L. I. Bykovskaya, I. G. Markova, and I. N.
Afteni, “Biogas is a promising for engines,” Gruzovik Press, vol. 5, pp.
29–39, 2018.
[22] V. L. Chumakov, S. N. Devyanin, F. N. Bizhaev, and A. V. Kapustin,
“Experimental studies to improve the toxic characteristics of gas
diesel,” in Readings of academician. Russia, MO: V. N. Boltinsky,
2021, pp. 104–112.
[23] V. A. Markov, S. Bowen, and S. N. Devyanin, “Emission performance
of a diesel engine running on petroleum diesel fuel with different
vegetable oil additives,” in 2020 International Multi-Conference on
Industrial Engineering and Modern Technologies, FarEastCon, A. Jante,
Ed. Germany, B.G: Teubner Verlagsgeselschaft, 1956.
[24] V. L. Chumakov and S. N. Devyanin, “Oxide emissions reduction
from combustion control in a diesel engine,” Selskohozâjstvennye
mašiny i tehnologii, vol. 15, no. 1, 2021. [Online]. Available:
https://doi.org/10.22314/2073-7599-2021-15-1-48-56
[25] V. L. Chumakov, S. N. Devyanin, F. N. Bizhaev, and A. V. Kapustin,
“Optimization of gas diesel regulation as a method of improving its
environmental characteristics,” Agroinzheneriya, vol. 4, no. 104, pp.
28–32, 2021.
[26] S. N. Devyanin, V. A. Markov, and A. A. Savastenko, “Use of biogas
as a motor fuel,” in Readings of academician V.N. Boltinsky (115 years
54
charge as a result of the scavenging.
Basing the thermal calculation of the engine on the
composition of the working mixture makes it easier to
analyze the impact of any characteristics of the mixture
on the main indicators of the cycle and on the degree
of internal recirculation estimated by the volumetric
fraction of residual gases. An additional advantage of
this approach is the opportunity to visualize the effects
of different factors on the composition of the working
mixture, which is very important for didactic purposes.
4. Declaration of competing interest
I declare that I have no significant competing interests,
including financial or non-financial, professional, or
personal interests interfering with the full and objective
presentation of the work described in this manuscript.
5. Funding
The author received no financial support for the research,
authorship, and/or publication of this article.
6. Author contributions
The material of the article belongs entirely to its author.
7. Data Availability Statement
The authors confirm that the data supporting the findings
of this study are available within the article [and/or] its
supplementary materials.
References
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2020. [Online]. Available: http://www.warse.org/IJETER/static/pdf/
file/ijeter94862020.pdf
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[3] V. N. Lukanin, Internal Combustion Engines. Moscow: Mir, 2005.
[4] M. G. Shatrov, Automobile Engines. Moscow, RU: Akademia, 2010.
[5] V. N. Lukanin, Motores de combustión interna. Moscú: Mir, 1985.
[6] L. M. Matyukhin, “El método alternativo de la evaluación de
calidad de los resultados del intercámbio de gases en los
motores de combustión interna,” Revista Ingeniería, Universidad de
Carabobo, vol. 25, no. 1, Ene-Abr 2018. [Online]. Available: https:
//www.redalyc.org/journal/707/70757668005/70757668005.pdf
[7] B. A. Sharoglazov, M. F. Farafontov, and V. V. Klementiev, Internal
combustion engines: Theory, modeling and process calculation.
Russia: South Ural State University, 2005.
[8] Y. L. Kovylova and D. A. Uglanov, “The influence of various factors
on the filling ratio of a piston engine,” Bulletin of the Samara State
Aerospace University, vol. 2, pp. 114–117, 2007.
[9] B. A. Sharoglazov and V. A. Povalyaev, “Estimated quality
assessment of fresh charge filling of piston engine cylinders
at the design stage,” Bulletin of the National Research South Ural
State University, vol. 23, pp. 20–24, 2008.
[10] A. Jante, Leitfaden der technischen Thermodynamik. Germany, LE:
Teubner, 1950.
[11] A. P. Baskakov, Termotecnia. Moscú: Mir, 1985.
[12] W. Christian, Volume 1 of Technische Wärmelehre für Studierende des
Bergbaus, des Hüttenwesens und der Aufbereitung. Germany, LE:
VEB Dt. Verlag für Grundstoffindustrie, 1966.
[13] L. M. Matiukhin, “Analysis of filling and thermal calculation
of ice based on the composition of the working mix,” LAP
LAMBERT Academic Publishing GmbH & Co, 2011. [Online]. Available:
http://www.techweb.com/se/index.html
[14] P. Kovalenko, S. N. Devyanin, E. A. Ulyukina, and A. V. Todoriv,
“Prospects for the operation of agricultural machinery on
compressed natural gas,” Autogas filling complex+ Alternative
fuel, vol. 16, no. 7, pp. 313–315, 2017.
[15] V. V. Sinyavski, I. V. Alekseev, I. Y. Ivanov, S. N. Bogdanov, and
Y. V. Trofimenko, “Physical simulation of high-and medium-speed
engines powered by natural gas,” Pollution Research, vol. 36, no. 4,
pp. 798–804, 2017.
[16] G. G. Ter-Mkrtichyan, A. M. Saikin, K. E. Karpukhin, A. S.
Terenchenko, and Y. G. Ter-Mkrtichyan, “Diesel-to-natural
gas engine conversion with lower compression ratio,” Pollution
Research, vol. 36, no. 4, pp. 925–930, 2017.
[17] V. V. Sinyavski, M. G. Shatrov, V. V. Kremnev, and G. Pronchenko,
“Forecasting of a boosted locomotive gas diesel engine parameters
with one- and two-stage charging systems,” Reports in Mechanical
Engineering, vol. 1, no. 1, Dec. 30, 2020. [Online]. Available:
https://doi.org/10.31181/rme200101192s
[18] M. G. Shatrov, V. V. Sinyavski, A. Y. Dunina, I. G. Shishlov, and A. V.
Vakulenko, “Forecasting of a boosted locomotive gas diesel engine
parameters with one- and two-stage charging systemmethod of
conversion of high- and middle-speed diesel engines into gas
diesel enginess,” Facta Universitatis, vol. 15, no. 3, 2017. [Online].
Available: https://doi.org/10.22190/FUME171004023S
[19] V. I. Erokhov and A. L. Karunin, Gazodizel’nye avtomobili
(konstruktsiya, raschet, ekspluatatsiya) [Gas-diesel cars (design,
calculation, operation). Russia: Graf-press, 2005.
[20] K. Schmillen, “Nuzung von biogas in gaszundungstrahlmotoren,”
MTZ Motortechnische Zeitschrift, vol. 7, no. 9, pp. 351–357, 1989.
[21] V. A. Markov, S. N. Devyanin, L. I. Bykovskaya, I. G. Markova, and I. N.
Afteni, “Biogas is a promising for engines,” Gruzovik Press, vol. 5, pp.
29–39, 2018.
[22] V. L. Chumakov, S. N. Devyanin, F. N. Bizhaev, and A. V. Kapustin,
“Experimental studies to improve the toxic characteristics of gas
diesel,” in Readings of academician. Russia, MO: V. N. Boltinsky,
2021, pp. 104–112.
[23] V. A. Markov, S. Bowen, and S. N. Devyanin, “Emission performance
of a diesel engine running on petroleum diesel fuel with different
vegetable oil additives,” in 2020 International Multi-Conference on
Industrial Engineering and Modern Technologies, FarEastCon, A. Jante,
Ed. Germany, B.G: Teubner Verlagsgeselschaft, 1956.
[24] V. L. Chumakov and S. N. Devyanin, “Oxide emissions reduction
from combustion control in a diesel engine,” Selskohozâjstvennye
mašiny i tehnologii, vol. 15, no. 1, 2021. [Online]. Available:
https://doi.org/10.22314/2073-7599-2021-15-1-48-56
[25] V. L. Chumakov, S. N. Devyanin, F. N. Bizhaev, and A. V. Kapustin,
“Optimization of gas diesel regulation as a method of improving its
environmental characteristics,” Agroinzheneriya, vol. 4, no. 104, pp.
28–32, 2021.
[26] S. N. Devyanin, V. A. Markov, and A. A. Savastenko, “Use of biogas
as a motor fuel,” in Readings of academician V.N. Boltinsky (115 years
54
L. Matiukhin, Revista Facultad de Ingeniería, Universidad de Antioquia, No. 110, pp. 48-55, 2024
since birth). Collection of articles of the seminar, M. N. Erokhin, Ed.
Russia, MO: Megapolis, 2019.
[27] V. I. Erokhov and A. L. Karunin, Motores de automóvil. Russia, MO:
MIR, 1982.
[28] L. M. Matiukhin and G. G. Ter-Mkrtich’yan, “Thermodynamic
fundamentals for calculating the duty cycle of engines with a
shortened intake or shortened compression based on an analysis
of the composition of the working mixture,” Bulletins of NAMI, vol.
263, pp. 35–44, 2015.
[29] L. M. Matiukhin, “Evaluation of the results of gas exchange in the
4- and 2-stroke piston ice based on the analysis of the ratios of
individual components in the working mixture,” Bulletin of MADI,
vol. 6, pp. 36–41, 2006.
55
since birth). Collection of articles of the seminar, M. N. Erokhin, Ed.
Russia, MO: Megapolis, 2019.
[27] V. I. Erokhov and A. L. Karunin, Motores de automóvil. Russia, MO:
MIR, 1982.
[28] L. M. Matiukhin and G. G. Ter-Mkrtich’yan, “Thermodynamic
fundamentals for calculating the duty cycle of engines with a
shortened intake or shortened compression based on an analysis
of the composition of the working mixture,” Bulletins of NAMI, vol.
263, pp. 35–44, 2015.
[29] L. M. Matiukhin, “Evaluation of the results of gas exchange in the
4- and 2-stroke piston ice based on the analysis of the ratios of
individual components in the working mixture,” Bulletin of MADI,
vol. 6, pp. 36–41, 2006.
55