The increase in the share of NG in the dual-fuel D-NG engine results in a decrease in , particularly when the engine is running at partial load from 0.55 to 0.29–0.33. The corresponding increase in 40–47% of fuel consumption has a negative effect on the engine’s toxic components and on the emissions of CO2, which is a GHG. It should be noted that the specific CO2 emissions decreased from 123 to 72 g/kWh (depending on φinj) when the engine was running in HLM, and when operating at partial load, GHG increased from 298 to 497 g/kWh. The conversion of DE to dual-fuel provides a CO2 reduction effect owing to the lower carbon content of the fuel compared to diesel. Thus, when engines are converted to gas, the task of improving fuel economy is linked to the complex improvement of key performance indicators.
3.1. Calibration of the Mathematical Model for the Research Engine
The initial stage of the research was the calibration of the engine mathematical model parameters with the engine running on diesel and dual fuel (diesel—natural gas): D60-NG40; D40-NG60; D20-NG80.
The subsection presents the verification fragments of the mathematical model with the engine running D and D20-NG80, taking into account the maximum experimental changes of the parameters (compared to D) at the highest part of NG in the dual fuel. The comparison also includes the cut-off values for the range of the fuel injection advance angle 2 (1)° CA BTDC and 13° CA BTDC.
The calibration of MM with the engine running on D, was performed in load mode BEMP = 6 bar with further comparison of calculation and experimental data BEMP = 8 bar, BEMP = 4 ÷ 2 bar (i.e., at higher and lower up to 25% nominal load).
During the modeling of the uncountable modes, only the cyclic portion of the fuel injection was changed, and while evaluating the influence of the fuel injection advance angle—φinj. Engine mathematical model (MM) running on D20-NG80, the calibration involves two stages. During the first stage, when changing the D-calibration MM settings, only the elemental chemical composition of the fuel was changed.
However, due to the discrepancy between the parameters of the heat release characteristic (m and φz) according to the experimental data, the modeling errors of the engine energy indicators reach 30–35%, and in individual cases, 50%. Therefore, in the second stage for MM were used the experimentally determined heat release characteristic parameters.
During this step, a positive result was obtained, in parallel the heat release parameters m and φ
z were determined according to the [
55] method. The realization of fuel in the operation of the engine does not cause any difficulties and is based on the use of integrated energy indicators of the engine.
An error of 1–2% between the calculation and the experimentally determined basic parameters testifies to the accurate calibration of the MM for the tested engine according to all aspects determining the modeling accuracy (especially calculation of heat release characteristics, heat exchanger, etc.). The good agreement between the modeled and experimental indicator diagrams (see
Figure 2) also testifies to the correct determination and calculation of the heat release characteristics in MM. Charge air pressure parameters deviation is observed in the experiment low load mode BEMP = 2
bar. The deviations are mainly determined by the modeling of the boost air pressure according to the generalized characteristics of the compressor used in the mathematical algorithm. The second reason is the possible deviation of the heat exchange in the engine cylinder simulation results from the actual data during the combustion cycle. The decision is based on an overall research strategy—the evaluation of pre-controlled engines to convert to dual-fuel operation in the absence of detailed engine technology data including turbocharger characteristics. However, in order to determine the parameters of the heat release with G. Woschni’s model testing with the engine running on dual fuel, the necessary corrections of the compressor characteristics were done in further studies (see
Table 3 and
Table 4). Results of the engine parameters that are based on the actual characteristics of the turbocharger and adjusting the heat exchange in the cylinder according to experimental data of the engine heat balance are presented in
Table 3 for verification. As the increase in the excess air ratio shows, it ensures better pressure adequacy in the indicator diagrams (see
Figure 2 and
Figure 3) by increasing the values of the excess air ratio and the corresponding COP. The increase of the parameter
η can be explained in turn by a decrease in the duration of fuel combustion (MM heat release) with an increase in α [
41,
53,
57] and a shift in the combustion cycle towards TDC. On the other hand, the adjustment of the heat exchange analytical dependences of empirical coefficients based on of the engine heat balance experiment data also has an influence. The error of
ηi is ~4% and considered to be an acceptable result of the practical tasks.
Validation of a mathematical model for practical tasks has been approved in studies at constant engine speed. However, the mathematical model used for a wide range of different types of engine operation also confirms its validity [
47,
48,
49]. In order to ensure the main adequacy of the simulation modeling results, it is necessary to match the parameters of the charging air unit, combustion cycle heat exchange, and the mechanical COP (friction loss) of the engine with the experimental data. Accurate calibration of heat release and heat exchange dependences of the mathematical model ensures sufficiently accurate modeling results of engine energy indicators (3–4% error). However, it obviously requires approbation and approval of converting the engine to dual-fuel (D-NG).
MM calibration was performed at
φinj = 2° CA BTDC. During the verification, the modeling results were evaluated after changing
φinj to 13° CA BTDC. The value BEMP = 6 bar deviated the most from the calibration mode. A comparison of the low-load indicator diagrams (see
Figure 3) also depicts good coincidence results with the experiment.
It is stated that the MM used in the research adequately reveals the changes of the parameters of the engine running on diesel over a wide load range with the changes of the control parameters. In parallel, the deviation of the
pK and
pmax parameters from the experiment was observed. According to the algorithm of the mathematical model, one of the main factors influencing the simulated heat release characteristic in partial load modes is the coefficient of excess air. Its decrease compared to the experiment became the main reason for the increase of heat release characteristic in the duration
φz and the decrease in
pmax, respectively (see
Figure 3). In the modeling of dual-fuel engine parameters, this aspect was taken into account to ensure
pmax and
α consistency with the experimental data. Based on the research results, the necessary condition for the parametric analysis of the used [
46] mathematical model is the modeling of the parameters of the charge air unit, based on the MAP (MAPs of VNT/VGT) data of its characteristics. As mentioned, the calibration of the MM with the engine running on diesel showed negative results in the case of dual fuel use. To determine that the MM discrepancy is caused by a significant deviation of the heat release (HRR) characteristics from the actual experimentally determined data. The progress of the engine differential experimental values HRR
in transferring the engine to operation from D to D-NG fuel is well shown in
Figure 4a–c.
As the proportion of NG in the dual fuel increases, strong changes HRR take place: the first kinetic combustion phase of the fuel decreases and the diffuse combustion phase extends into the expansion cycle. Particularly significant changes are characterized by a decrease in engine load and an increase in the proportion of NG. In dual fuels, for example, (
Figure 4a) at BEMP = 6 bar, the maximum value of HRR in the kinetic phase decreases from 0.03
to 0.02
from D to D20-NG80; in low load mode
pme = 2 bar the corresponding changes are from 0.042
to 0.019
. Due to decrease in the kinematic component, the heat release in the second diffusion phase increased, especially in
φinj = 13° CA BTDC: correspondingly maximums values increased from 0.035
to 0.05
. The trends of HRR change do not change qualitatively in the studied
φinj range 1 ÷ 13° CA BTDC (see
Figure 4d–f). In terms of increasing energy efficiency, the increase in heat release intensity in the diffusion phase is positive, but is associated with a parallel reduction in total combustion time. The characteristic of the HRR change according to
φ °CA suggests that the heat release characteristic could be considered as single-phase, the kinetic and diffuse phase separation is more conditional.
HRR data confirmed by authors comparative studies of the heat balance with engine running on D and NG [
45]. When the engine is running on NG, the prolonged combustion process in the expansion stroke results in a significantly increased heat transfer to the cooling system, which contributes to deterioration of energy efficiency. In LLM modes, with the maximum tested NG fraction in dual fuel 80%, the heat loss to the engine cooling system increases up to 2.5–3.0 times. At that time, the indicative COP cycle decreases from 0.55 to 0.33. The experimental data of the heat balance confirm the determined parameters of the combustion process. The observed feature became an additional justification for the use of single—phase I.Vibe MM. In the investigated variant in the absence of the targeted engine design for D-NG fuel, the combustion period becomes very prolonged. If in high load modes (BEMP = 6 bar) the relative burning time according to I.Vibe model increases by ~5° CA, but in medium (BEMP = 4 bar) and low (BEMP = 2 bar) load modes φ
z compared to D variant lasts from 44° CA and 35° CA to 110° CA and 200° CA, respectively. At that time, the values of
φz calculated by G. Woschini [
53] decrease as it became the main reason for inaccurate modeling. It is obvious that in order to achieve the versatility of the parametric analysis method while engine working on a wide range of fuels (including D-NG fuels), it is necessary to refine the phenomenological model of heat release characteristics or to apply a more detailed model of physical processes in the engine cylinder.
In the performed research stage, in order to confirm the rationality of the application of the parametric analysis method, it is necessary to calibrate the MM separately for the D-NG variant, based on the real experimental data. The results of modeling of engine parameters when calibrating MM based on experimental data of D-NG variant are presented in
Table 4.
The decision to calibrate the engine MM with the engine running on D-NG fuel is confirmed by a sufficiently low error between the simulation and the experimental results, error is between 3–4%, it is important to note that error is low—in the whole range of known φinj changes.
A good agreement between the results of the experiment and the modeling is substantiated by the comparison of the indicator diagrams of the relative form of the heat release characteristics, the fragments of which are presented in
Figure 5. The maximum error does not exceed 5–7%.
Based on the results of MM calibration, the ways and limitations of its rational use in parametric analysis were identified, as well as directions for improvement.
3.2. Analysis of the Combustion Cycle Factors That Determine ηi
Methods for improving energy performance,
ηe, ηi, through parametric analysis have been extensively studied, particularly in the 1980s, with the onset of the energy crisis [
49]. Researchers attributed the improvement of
ηi to the degree of compression (
ε), excess air coefficient (
α), process dynamics (degree of pressure increase (
λ),
(pmax) maximum cycle pressure, air pressure after compression (
pk), ambient air (
Tat), charge air temperature (
Tk)), and other secondary factors [
37,
38]. Studies have been performed to determine the analytical dependences in the state of linear equations
ηi = (ε, α, λ, pk, Tk) for a certain class of DEs [
58]. The constants of the linear equations that determine the accuracy of the calculations in most cases were determined from statistical experimental data and by providing analytical or graphical formulas for the dependencies of the operational parameters. Analogous solutions have been implemented for DEs of V. Yuzhin ships [
38]. The main disadvantage of this method is the need to update the information base constantly with the values of the factors that influence energy indicators [
36,
39].
Several studies on the characteristics of the physical process—heat release—occurring within the cylinder and determining the COP of the combustion cycle and, largely, the energy efficiency have been conducted [
40,
41,
57,
59]. The methods developed in these studies and the statistical methods for processing experimental data have served as foundations for identifying the influence of heat release duration and variation in the value of the COP of the combustion cycle [
60,
61,
62]. Furthermore, to substantiate this relationship analytically for analysis of the cycle of the dual-fuel engine, Stechkin’s study should be used as a reference [
59]. Stechkin [
59] investigated the relationship between the theoretical cycle,
, and the combustion process rate and provided a series of analytical solutions (
Figure 6).
(Q3: heat release in the cycle; y0 field center abscissa; F(y) heat release curve; xτ heat release duration).
The analytical solutions provided can be compared based on their nature, thereby enabling evaluation of the COP for the rapid combustion cycle in accordance with the analytical equations of the law of thermodynamics (11):
The difference between the theoretical cycle with finite combustion rate, ηt, and the rapid combustion cycle efficiency ratio is determined by three parameters of the heat release law: xτ, Δ, and y0 (Δ: area under the curve of heat release). The final ηt correction depends on the combustion time (, expressed in parts of the CC volume, v0, and parameter Ω is the heat release law factor in studies related to the heat release characteristics of the area under the curve of center mass location. As a result of a series of simplifications, the following final expression is generated: . Under Ω = invar, correction for the selected ε is determined only by the heat release duration, χτ. This statement has been used as one of the bases for the analysis of multivariate MM results.
In modern DEs, with a relatively short
xτ, the correction is not significant. However, the more than four-fold increase in
xτ noticed during the experimental study on the DE has a significant effect on
and
ηi. The finite element method has been used for Equations (12) and (13) [
63]:
, or the shape of the proposed finite elements in the expression of the equation; the product of the first and second factors of the additive sum is equal to the area of the elementary element, (
φi−1 − φi), from the third factor to the ordinate of the centers of mass of the elements (
φi−1 − φi). In the structural expression of Equation (12), the third factor of the product equals the centers of mass of the elements (
φi−1 − φi):
Fragments of the results of the study on the dynamics of the heat release characteristics at different engine loads with dual-fuel D-NG during the center mass change cycle are presented in
Figure 7.
The implemented analytical solutions shown in
Figure 7 demonstrate the dynamics of the change in the center of mass of the heat release characteristic during the cycle. Essentially, the dynamics of change in the abscissa (
φc according to Stechkin [
54]) of the centers of mass for modes BEMP = 2, 4, and 6 bar and the final value of
φc remain constant for all variants examined from D to D20-NG80, with minor exclusions. Analysis of the diagrams indicates that with the engine operating in the dual-fuel mode, where NG is responsible for a significant share of energy, increasing
φinj within the range analyzed, and possibly within a wider range, may become an effective tool for increasing the energy cycle.
Advancing the diesel fuel injection phase, φinj, significantly increases the heat release dynamics in the expansion cycle when pmax and Tmax are reached. It was found that the ordinate values of the center of mass, and accordingly the current values of Xi, are higher when the engine is running on dual fuel compared to running on diesel. When the engine is running on diesel, the increase in heat release dynamics at higher φinj values is characteristic of the initial heat release headers. In the range of 25‒40° CA after TDC, the values of Xi become equal, and the ordinates of the values of the higher center of mass (Xi) continue to prevail at lower φinj. Thus, when the engine is running on diesel, it is reasonable to expect a lower ηi, leading to a further decrease in the combustion cycle dynamics.
Thus, the generated results support the application of the method of parametric analysis of the combustion cycle in association with the indicators of the heat release characteristic. In contrast, based on the theoretical analysis, Equation (14) [
59] describes the relationship between the engine cycle,
ηe, and heat release characteristics as a function of x
τ duration and shape parameters:
A similar conclusion was reached in the study by Lebedev et al. [
47], in which the main factors influencing the engine duty cycle efficiency factor
ηi were based on the change in fuel burn duration and
pmax in the cylinder. Thus, the value of
pmax, under the condition
pmi, α, is described by the amount of heat when
Q (pmax) is reached while
° CA. Considering this, the value of
Q (pmax) at the optimal start phase of combustion depends directly on the dynamics of the combustion process or, in other words, on the shape of the heat release characteristic.
Based on this, the value of
pmax/pk [
51] in this work represents the influence of the shape of the law of heat release on the value of
ηi. In contrast, the
pmax/pk ratio is the product of
, the two other indicators that determine the level of
ηi, together with α [
56,
64]. According to statistics summarising a number of experimental studies [
52,
53], the influence of the excess air coefficient,
α, on
ηi is expressed as an analytical dependence (15):
where
is the heat release time according to the I. Vibe model; the value
characterizes the duration of heat release during operation of the motor in the basic numerical mode, which is usually accepted as the nominal power mode. The equation shows
, which also indicates the dependence of
ηi change on the α and
n parameters in the presence of the form factor
m [
51] and
Ω [
59]; otherwise, the mass of the center of the heat release characteristic is the same.
3.3. Optimization of DE Combustion Cycle Parameters
In the works by Ivanchenko [
42,
64], the MM of the relationship between
ηi and characteristic indicators of the combustion cycle were applied to highly supercharged DEs, forced according to
pmi. Practical application of the model essentially consists of a numerical multivariate experiment that serves as the basis for developing the generalized graphic dependences of the combustion cycle parameters. The influence of the
pmax limitation of the cycle on the fuel cost efficiency and engine heat stresses, described by
ηi and α, respectively, is assessed. Simultaneously, the selection of the rational combination of cycle indicators to achieve the anticipated value of the engine energy efficiency
ηi is addressed.
The method is characterized by the convenience of its practical application; however, one of the limitations is the set of accepted fixed indicators of the heat release law: the heat release duration and heat release shape parameters. In fact, the variation in the forcing rate according to pmi determines significant changes in this important indicator in relation to the energy efficiency of the cycle. Moreover, it is not only pme but also the combination of the combustion cycle parameters (ε, λ, α, etc.) that have a fairly large influence on the heat release duration and shape.
Variational modeling of the duty cycle was performed at different values of ε0, α, and pmax/pk. Based on the MM results, generalized graphical dependences were obtained that represented the relationships between the indicated efficiency factor, complex forcing according to the pmi parameter, and α, pmax/pk parameters. The obtained generalized graphical dependences allow to evaluate the methods of rational in-cylinder engine process execution (ε, p Tk, α, φinj) for the specific structural configuration engine model in order to achieve energy efficiency under acceptable constraints.
This method is easy to apply, however, one of its provisions limits its practical application to convertible operation for dual-fuel engines. The method implementation algorithm adopts fixed heat release law indicators: heat release time and heat release law parameter φc. The burning time, according to the accepted accuracy of 0.3%, was determined in the form of a constant equal to 8 φc, and φc was assumed to be 12.4 ± 4° CA BTDC.
The application of this parametric analysis method to dual-fuel engines in relation to the significant changes in the parameters of the heat release characteristic should be supported by analytical, experimental, and MM research development. Indeed, the change in the forcing level, according to
pmi, leads to the perceived changes in this important indicator for the energy efficiency of the cycle. Experimental studies have also demonstrated a significant increase in burning time when the engine is running on dual fuel, particularly in the LLM [
43]. Thus, considering the significant influence of the burning time, the use of real values of the heat release time in the studies became an essential change in the method used in the parametric analysis. The method used in parametric analysis of the combustion cycle was approved through multivariate numerical research using the IMPULS software.
3.4. Investigations of the Optimization of Dual-Fuel D-NG Engine Combustion Cycle Parameters
We investigated the ranges of change of the initial data:
α = 1.7–4.0;
ε = 15.5–23.5;
φin j = 1–35° CA BTDC (differentiated with different
pmi values).
Figure 4 and
Figure 5 present the results of the parametric analysis of the operating process at the limit values of
pmi = 4.2 bar and
pmi = 8.2 bar in the load range with the engine running on diesel fuel and dual fuel, respectively. The sufficient accuracy of the MM results for solving practical problems is confirmed by their comparison with the experimental data. The results of the experiment in the diagrams are presented in the form of local points in the coordinates of
α–pmax/pk. The differences in
do not exceed 2–4%.
We have received the traditional form of relations between the
ηi = f(pmax/pk, α, ε = invar.) and the motor forcing parameter
, Π = f(pmax/pk, α, ε = invar.). The curves of
ηi = f(pPmax/pk, α, ε = invar.) for different
ε are given by the lines of rounded shapes. The obtained data show that at
pmi = 8.2 bar (
n = 2000 rpm) and
α = 2.3,
ηi is close to its maximum achievable value at point 2. Increasing
pmax above 9 MPa (lines -1-2-3) has virtually no effect on
ηi. In addition, the increase of reserve
ηi is also used because of the increase in ε above the limit of 19.5 designed for the engine. Simultaneously
, pmax/pk increases above 74.5 pcs., and the increase in α has no effect on
ηi. An analogous conclusion can be reached by evaluating the LLM
pmi = 4.2 bar (
Figure 4). Increasing α above 4.5 units also does not affect the value of
ηi. An increase in ε and an extension of the
pmax limit (shift of line 1–2–3–4 to the 5–6–7–8 position) lead to a decrease in the value of
ηi (shift of line 1–4 to the 5–8 position). The results of the parametric analysis indicate that in the case of HLM, when the motor operation process execution is achieved and the
pmax limits are set, the achieved level of
ηi is close to the optimal one. It is known that radical engine improvements, such as the installation of a storage fuel injection system, would quantitatively change the relationships shown in
Figure 8 and expand the potential for energy efficiency improvements.
Increasing ε under φinj = invar. positively influences ηi throughout the range analyzed, which is ε =15.5‒23.5 units. However, the value implemented in the engine, which is ε =19.5, corresponds to the optimum value of ηi. In summary, from the analysis of the change of nomogram Π, ηi = f(pmax/pk, α = invar.), the following conclusions are drawn.
Considerable reduction in the heat release dynamics under the dual-fuel D-NG LLM operation of the engine strengthens the influence of the change in φinj on ηi within a wide range of ε and α, and, in parallel, reduces the influence of φinj on pmax/pk or pmax.
The range of change of φinj may be expanded with the aim of improving ηi without posing a risk of reaching the limit values of the reliability indicator, pmax.
The numerical analyses reveal a strong influence of the fuel injection timing phase,
φnj, on
ηi, and also have good correlation with the experimental research results. Irrespective of the load, the advancement of the injection timing,
φinj, within the range analyzed, which is
φinj = 1 to 13° CA BTDC, influences the increase in
ηi at different levels under diesel-fuel versus dual-fuel operation of the engine. The increase in the NG portion in the dual fuel from 0 to 80% leads to different effects of the change in
φinj: 1–18% under
pmi = 4.2 bar, 4–21% under
pmi = 6.2 bar, and 7–17.5% under
pmi= 8.2 bar load modes (
Table 5).
Owing to the low intensity of the fuel combustion kinetics and work process under D-NG-fuel engine operation, a relatively high share of heat is released at later phases of the expansion stroke. Hence,
φinj advancement to 13° CA BTDC led to an intensive increase in
ηi, both during the experiment and during the modeling. Under DE operation, the change in
φinj led to a 2% increase in
ηi (maximum
ηi achieved at
φinj was equal to 7° CA BTDC), whereas under dual-fuel D20-NG80,
ηi increased by 17%. In the numerical modeling, the advancement of
φinj to 30° CA BTDC had a positive influence on the increase in
ηi, but at a lower intensity than that of
ηi when the range was between 1 and 13° CA BTDC (see
Figure 8).
Investigation of the combination of optimum parameters of the engine combustion process under the
pmi = 4.2 bar mode essentially does not differ from the aforementioned HLMs; for example, the assessment of the rational combination of
ε, φinj, and α was performed under the condition of
pmax ≤ 6.9 MPa. Under
pmax = 6.9 MPa, the value of parameter
Π is
. The fields marked by points 1′–3′–6′–4′ graphically define the combinations of
ε, α, φinj that improve
ηi. Hence, the parametric
ηi analysis method has been analytically substantiated and verified through experiment and numerical investigation for the purposes of practical application with the aim to improve the energy efficiency parameters of an engine converted to dual-fuel operation. At the same time, the research showed rational aspects of further evaluation and improvement of the method, with a view to its real practical application. Among other things, attention must be paid to adapting it to the different speeds when assessing the operation of the engine over a wide speed range. It is expected that the qualitative dependence of
ηi on the main factors of the combustion cycle (
α, ε, μ, pk, Tk) should not change. However, it must be taken into account that the modification of the method was related to the actual use of the heat release characteristic duration
φz to form the nomogram in
Figure 8. On the other hand,
φz together with
α is determined by the engine speed (for example see Equation (8)). Meaning qualitatively unchanged for each engine speed, it will be necessary to use quantitatively separate nomograms. The partially made assumption is confirmed by the results of the authors’ previously studied engines 150/180 mm (2000–1300 rpm) and 165/185 mm (1850–1200 rpm) [
51,
60]. It is also important to adapt the dependences of heat release and heat exchange from the same basic calibration mode to different dual fuel compositions in G. Woschni’s analysis.