# The Effects of Multistage Fuel-Oxidation Chemistry, Soot Radiation, and Real Gas Properties on the Operation Process of Compression Ignition Engines

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}O

_{2}with the formation of OH. Hot flames are caused by the chain branching reaction between atomic hydrogen and molecular oxygen with the formation of OH and O. So-called “double” cool flames correspond to the sequential appearance of a separated cool flame and a low-intensity blue flame rather than two successive cool flames. The use of a one-dimensional model of fuel droplet heating, evaporation, autoignition, and combustion at temperatures and pressures relevant to compression ignition engines shows that the thermal radiation of soot during the combustion of small (submillimeter size) droplets is insignificant and can be neglected. The use of real gas caloric and thermal equations of state of the matter in a three-dimensional simulation of the operation process in a diesel engine demonstrates the significant effect of real gas properties on the engine pressure diagram and on the NO and soot emissions: real gas effects reduce the maximum pressure and mass-averaged temperature in the combustion chamber by about 6 and 9%, respectively, increases the autoignition delay time by a 1.6 crank angle degree, increase the maximum heat release rate by 20%, and reduce the yields of NO and soot by a factor of 2 and 4, respectively.

## 1. Introduction

#### 1.1. Multistage Autoignition

_{2}CO∗. The flames corresponding to these two domains are called a “double” cool flame and a single cool flame, respectively. In [5], based on the review of a large experimental material, a generalization was made and the concept of multistage autoignition with individual cool, blue, and hot flames was introduced. Modeling the kinetics of the autoignition of hydrocarbons under laboratory conditions using a DKM indicates that cool flames are caused by the decomposition of alkyl hydroperoxide, during which a very reactive radical, OH, is formed, and blue flames are caused by the decomposition of H

_{2}O

_{2}with the formation of OH [6].

_{20}containing thousands of species and tens of thousands of elementary reactions have been proposed. For example, the authors of [7] proposed such a DKM composed of 7182 species and 31,721 reactions by merging two mechanisms reported in [8,9]. Later, this mechanism was reduced to contain 2277 reactions and 522 species [10]. Many of the proposed DKMs are capable of describing the low-temperature oxidation of hydrocarbons and predicting the formation of both cool and blue flames. The blue flames are often referred to as “intermediate temperature heat release” [11,12,13,14,15] or “intermediate temperature ignition” [16,17].

#### 1.2. Soot Formation and Radiation

#### 1.3. Real Gas Effects

^{3}[37]). Localized regions with low temperatures and high pressure in an engine cylinder can be critical. For example, the maximum pressure in an engine cylinder can reach 200–300 bar, while the temperature in the vicinity of the cooled walls can be quite low (400–550 K). Under such conditions, the real gas effects may manifest themselves. Thus, real gas effects can significantly affect the behavior and structure of the flow in the region of diesel spray [37,38,39,40] and change ignition delay times in diesel engines, particularly in the region of the negative temperature coefficient [40,41].

## 2. Materials and Methods

#### 2.1. Reaction Mechanism

_{8}H

_{18}and isomerized alkanes: iso-butane (2-methylpropane), iso-pentane (2-methylbutane), and iso-hexane (2-methylpentane). Their reactions with each other and other species available in the DKM are also added. The leading role is assumed to be played by deisomerization reactions to form stable intermediate isomerized molecules of 2,2-dimethylpentane, 2-methylpentane, 2-methylbutane, and 2-methylpropane and the corresponding normal-structure hydrocarbons, including methane. All of the other reactions leading to the increase in the “linear” five-membered portion of an iso-octane molecule are assumed to have no effect on the iso-octane oxidation rate. The resulting DKM of iso-octane oxidation is fairly compact: it includes 763 reactions involving normal-structure species and 987 reactions involving isomerized species. The total number of species involved in the DKM is 144.

#### 2.2. Droplet Autoignition and Combustion

^{3}, then ${S}_{\mathrm{r}\mathrm{a}\mathrm{d}}\approx 3\times {10}^{6}$ m

^{2}/kg [50].

#### 2.3. Real Gas Equation of State

_{2}, N

_{2}, H

_{2}O, CO, CO

_{2}and H

_{2}in wide ranges of pressure (from 0.5 to 200 bar) and temperatures (from 280 to 3000 K). As an example, Table 1 demonstrates the accuracy of Equation (16) for n-hexane and other mentioned gases at some selected isobars and isotherms. It turns out that the error in calculating the pressure according to Equation (16) does not normally exceed tenths of a percent, even in the vicinity of the critical point. Note that Equation (16) is used in the gas-dynamic calculation to determine the density $\rho $ from the known values of pressure $P$ and temperature $T$, as well as from the known composition of the gas mixture. To solve Equation (16) with respect to density, one has to use numerical methods.

#### 2.4. Solution Procedure of the Zero-Dimensional Problem

#### 2.5. Solution Procedure of the One-Dimensional Problem

_{2}H

_{2}. As an example, Figure 6 compares the soot yields predicted by the OM with those predicted by the DKM of [72] for the oxidation of homogeneous fuel-rich n-heptane–air mixture with a fuel-to-air equivalence ratio of $\mathsf{\Phi}=$ 2. Soot yield refers to the ratio of the mass of carbon contained in soot to the initial mass of carbon contained in the hydrocarbon fuel. As seen, the OM of Table 2 provides satisfactory qualitative and quantitative agreement with the results predicted by the DKM [72].

#### 2.6. Solution Procedure of the Three-Dimensional Problem

_{7}H

_{16}), O

_{2}, N

_{2}, CO

_{2}, H

_{2}O, CO, and H

_{2}. The formation of nitrogen oxides and soot is described by the Zel’dovich [80] and Kennedy–Hiroyasu–Magnussen [81] standard models. Due to the low concentrations, nitrogen oxides, soot, and active radicals present in the combustion model are not included in the material balance.

## 3. Results and Discussion

#### 3.1. Multistage Fuel-Oxidation Chemistry

_{3}C(CH

_{3})

_{2}CH

_{2}CH(CH

_{3})CH

_{2}O

_{2}H), and hydrogen peroxide (H

_{2}O

_{2}) in the engine cylinder at an air-to-fuel equivalence ratio $\alpha =$ 1.5 ($\mathsf{\Phi}=$ 0.667) and different compression ratios $\epsilon $: 12 (Figure 9a); 13 (Figure 9b); 13.5 (Figure 9c); 13.75 (Figure 9d); and 14 (Figure 9e). In all plots, the time is plotted along the X-axis in terms of the crankshaft rotation angle $\theta $ (in CAD). The extreme position of the piston (TDC, 0 CAD) is shown by the dashed vertical line. For the sake of convenience, the pressure $P$ (in bar), temperature $T$ (in K), and volume fractions of OH, CH

_{3}C(CH

_{3})

_{2}CH

_{2}CH(CH

_{3})CH

_{2}O

_{2}H, and H

_{2}O

_{2}are all plotted along the Y-axis with some scaling factors indicated near the corresponding curves. The mixture composition with $\alpha =$ 1.5 ($\mathsf{\Phi}=$ 0.667) is chosen for calculations because the boundaries of single cool flame, “double” cool flame, blue flame, and hot flame domains for this mixture in the experiments are well separated (see the dashed vertical line in Figure 1). All other calculation conditions are the same as in the experiments.

_{2}O

_{2}), rather than two successive cool flames. In other words, in this parametric domain, the multistage nature of the low-temperature autoignition of hydrocarbons manifests itself. In laboratory conditions, multiple cool flames can only occur when strong cooling is applied to the reactor walls and the reaction progress is insignificant. In this case, almost identical conditions can be reproduced for restarting the cool-flame reactions. In the internal combustion engines, such conditions are not realized.

_{2}O

_{2}is only accumulated, but, probably, the inverse process of H

_{2}O

_{2}decomposition is already beginning to noticeably proceed.

#### 3.2. Droplet Autoignition

#### 3.3. Real Gas Effects

## 4. Conclusions

- (1)
- reduces the maximum pressure and mass-averaged temperature in the combustion chamber by about 7 bar (6%) and 150 K (9%), respectively;
- (2)
- increases the autoignition delay time by a 1.6 crank angle degree;
- (3)
- increases the maximum heat release rate by 20%; and
- (4)
- reduces the yields of NO and soot by a factor of 2 and 4, respectively.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

0D | Zero-dimensional |

1D | One-dimensional |

3D | Three-dimensional |

CAD | Crank angle degree |

CFD | Computational fluid dynamics |

CIE | Compression ignition engines |

CV | Compensation volume |

DKM | Detailed kinetic mechanism |

EoS | Equation of state |

OM | Overall mechanism |

RANS | Reynolds-averaged Navier–Stokes |

SIMPLE | Semi-implicit method for pressure linked equations |

TDC | Top dead center |

TVD | Total variation diminishing |

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**Figure 1.**The boundaries of the single and “double” cool flames, blue flame, and hot flame domains during compression induced the autoignition of iso-octane–air mixtures in a compression ignition engine [4] (legends are taken from [5]). Initial temperature ${T}_{0}=$ 343 K, initial pressure ${P}_{0}=$ 1 bar, engine rotation speed $n$ = 1500 rpm. The red dashed vertical line at $\alpha =$1.5 corresponds to the composition of the fuel–air mixture examined in Section 3.1.

**Figure 2.**Comparison of predicted (curves) and measured (symbols) ignition delay times for the homogeneous stoichiometric iso-octane–air (

**a**) and n-heptane–air (

**b**) mixtures in wide ranges of initial conditions in terms of pressure and temperature: (

**a**) circles, triangles [48]; (

**b**) circles, triangles [49].

**Figure 5.**Comparison of predicted (curve) and measured (symbols) dependences of the autoignition delay time of n-heptane droplets on pressure. The curve is obtained for ${d}_{0}=$ 700 µm, ${T}_{d0}=$ 293 K, and ${T}_{g0}=$ 1000 K. Triangles correspond to ${d}_{0}=$ 700–750 µm [60], circle to ${d}_{0}=$ 700 μm, ${T}_{g0}=$ 940 K [61] (the vertical bar shows the scatter of experimental data).

**Figure 7.**Base (

**a**) and fine (

**b**) computational meshes of the diesel segment at a top dead center (TDC); Base mesh contains 30,000 cells, average cell size 0.5 mm; Fine mesh contains 250,000 cells, average cell size 0.25 mm.

**Figure 9.**Calculated time histories of pressure $P$, temperature $T$, and volume fractions of OH, CH

_{3}C(CH

_{3})

_{2}CH

_{2}CH(CH

_{3})CH

_{2}O

_{2}H, and H

_{2}O

_{2}at an air-to-fuel equivalence ratio of 1.5 and different compression ratios $\epsilon $: (

**a**) 12; (

**b**) 13; (

**c**) 13.5; (

**d**) 13.75; (

**e**) 14.

**Figure 10.**Calculated dependences of the maximum gas temperature in the vicinity of a droplet on the reduced time during the autoignition of droplets of different initial diameters (50 mm; 100 mm; and 200 mm) in air at ${T}_{g0}$ = 1000 K and $P$ = 100 bar.

**Figure 11.**Calculated instantaneous spatial distributions of temperature (

**a**) and soot mass fraction (

**b**) around a droplet of initial diameter ${d}_{0}$ = 50 μm during its autoignition at ${T}_{g0}$ = 1000 K and $P$ = 100 bar: 1—$t$ = 1.5 ms; 2—2 ms; 3—$t$ = 3 ms.

**Figure 12.**Calculated dependences of the maximum gas temperature ${T}_{max}$ around the n-heptane droplet during its autoignition and subsequent combustion; ${T}_{d0}$ = 293 K; ${T}_{g0}$ = 1000 K: (

**a**) ${d}_{0}$ = 40 µm, $P$ = 25 bar; (

**b**) ${d}_{0}$ = 20 µm, $P$ = 100 bar; 1—calculation with thermal radiation of soot; 2—calculation without thermal radiation of soot.

**Figure 13.**Estimated instantaneous temperature distributions in a droplet and in a gas depending on the distance from the droplet center; ${T}_{d0}$ = 293 K; ${T}_{g0}$ = 1000 K: (

**a**) ${d}_{0}$ = 40 μm, $P$ = 25 bar, $t$ = 2.35 ms; (

**b**) ${d}_{0}$ = 20 µm, $P$ = 100 bar, $t$ = 0.425 ms; 1—calculation with thermal radiation of soot; 2—calculation without thermal radiation of soot.

**Figure 14.**Calculated time histories of the squared droplet diameter during droplet autoignition and subsequent combustion; ${T}_{d0}$ = 293 K; ${T}_{g0}$ = 1000 K: (

**a**) ${d}_{0}$ = 40 µm, $P$ = 25 bar; (

**b**) ${d}_{0}$ = 20 μm, $P$ = 100 bar: 1—calculation with thermal radiation of soot; 2—calculation without thermal radiation of soot.

**Figure 15.**Predicted dependences of pressure (

**a**), mass-averaged temperature (

**b**), and the total heat release rate (

**c**) in the diesel cylinder on the crank angle in test calculations I–III.

**Figure 16.**Predicted instantaneous temperature distributions in the combustion chamber at different instants of time obtained in calculation I: (

**a**) 721 CAD; (

**b**) 722 CAD; (

**c**) 723 CAD; (

**d**) 724 CAD; (

**e**) 725 CAD; (

**f**) 726 CAD; (

**g**) 727 CAD; and (

**h**) 728 CAD.

**Figure 17.**Predicted instantaneous temperature distributions in the diesel combustion chamber at different instants of time obtained in calculation III: (

**a**) 721 CAD; (

**b**) 722 CAD; (

**c**) 723 CAD; (

**d**) 724 CAD; (

**e**) 725 CAD; (

**f**) 726 CAD; (

**g**) 727 CAD; and (

**h**) 728 CAD.

**Figure 18.**Predicted dependences of the mass fractions of nitrogen oxides (

**a**) and soot (

**b**) in the combustion chamber on the crank angle obtained in calculations I–III.

**Figure 19.**Predicted instantaneous distributions of the mass fractions of NO (

**a**) and soot (

**b**) in the diesel combustion chamber obtained in calculations I (left column) and III (right column) at 745 CAD. White arrow shows the location in the vicinity of the cylinder wall where soot forms.

**Figure 20.**Predicted instantaneous distributions of the relative excess heat capacity ${C}_{p,\mathrm{e}\mathrm{x}\mathrm{c}}/{C}_{p0}$ (left column) and the relative excess pressure ${P}_{\mathrm{exc}}/{P}_{0}$ (right column) in the combustion chamber at different times obtained in calculation III: (

**a**) 721 CAD; (

**b**) 725 CAD; and (

**c**) 729 CAD.

**Table 1.**Comparison of predicted pressure, ${P}_{\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{c}}$, given by the EoS of Equation (16) with measured pressure, ${P}_{\mathrm{e}\mathrm{x}\mathrm{p}}$, for n-hexane, oxygen, nitrogen, water, carbon monoxide, carbon dioxide, and hydrogen at some selected isobars and isotherms.

n-Hexane | ||||

$T$, K | $\rho $, mol/dm^{3} | ${P}_{\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{c}}$, MPa | ${P}_{\mathrm{e}\mathrm{x}\mathrm{p}}$, MPa [63] | $\left|{P}_{\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{c}}-{P}_{\mathrm{e}\mathrm{x}\mathrm{p}}\right|/{P}_{\mathrm{e}\mathrm{x}\mathrm{p}}$, % |

530 | 2.526 | 4.010 | 4 | 0.25 |

550 | 1.619 | 4.032 | 4 | 0.79 |

600 | 1.106 | 4.008 | 4 | 0.19 |

630 | 0.9741 | 4.0025 | 4 | 0.06 |

Oxygen | ||||

$T$, K | $\rho $, kg/m^{3} | ${P}_{\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{c}}$, MPa | ${P}_{\mathrm{e}\mathrm{x}\mathrm{p}}$, MPa [64] | $\left|{P}_{\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{c}}-{P}_{\mathrm{e}\mathrm{x}\mathrm{p}}\right|/{P}_{\mathrm{e}\mathrm{x}\mathrm{p}}$, % |

500 | 45.6 | 6.0008 | 6 | 0.013 |

500 | 60.51 | 8.0033 | 8 | 0.041 |

500 | 75.25 | 10.007 | 10 | 0.07 |

500 | 111.31 | 15.028 | 15 | 0.19 |

500 | 146.15 | 20.076 | 20 | 0.38 |

Nitrogen | ||||

$T$, K | $\rho $, mol/dm^{3} | ${P}_{\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{c}}$, MPa | ${P}_{\mathrm{e}\mathrm{x}\mathrm{p}}$, MPa [65] | $\left|{P}_{\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{c}}-{P}_{\mathrm{e}\mathrm{x}\mathrm{p}}\right|/{P}_{\mathrm{e}\mathrm{x}\mathrm{p}}$, % |

500 | 0.94635 | 4.0007 | 4 | 0.018 |

500 | 1.4070 | 6.0011 | 6 | 0.018 |

500 | 1.8590 | 8.0018 | 8 | 0.023 |

500 | 2.3020 | 10.002 | 10 | 0.022 |

500 | 3.3700 | 15.004 | 15 | 0.027 |

500 | 4.3806 | 20.004 | 20 | 0.022 |

Water | ||||

$T$, °C | $\nu $, dm^{3}/g | ${P}_{\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{c}}$, MPa | ${P}_{\mathrm{e}\mathrm{x}\mathrm{p}}$, MPa [66] | |

300 | 5.885 | 4.0066 | 4 | 0.17 |

300 | 4.532 | 5.017 | 5 | 0.34 |

300 | 3.616 | 6.033 | 6 | 0.55 |

300 | 2.976 | 7.0052 | 7 | 0.07 |

300 | 2.425 | 8.090 | 8 | 1.1 |

Carbon monoxide | ||||

$T$, K | $\rho $, mol/dm^{3} | ${P}_{\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{c}}$, MPa | ${P}_{\mathrm{e}\mathrm{x}\mathrm{p}}$, MPa [67] | |

500 | 0.94818 | 4.004 | 4 | 0.09 |

500 | 1.40962 | 6.002 | 6 | 0.04 |

500 | 1.86196 | 7.999 | 8 | 0.01 |

500 | 2.30518 | 9.994 | 10 | 0.06 |

500 | 2.73932 | 11.990 | 12 | 0.08 |

500 | 3.16448 | 13.988 | 14 | 0.09 |

500 | 3.58073 | 15.989 | 16 | 0.07 |

500 | 3.98813 | 17.994 | 18 | 0.03 |

500 | 4.38673 | 20.004 | 20 | 0.02 |

Carbon dioxide | ||||

$T$, °C | $\rho $, g/cm^{3} | ${P}_{\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{c}}$, MPa | ${P}_{\mathrm{e}\mathrm{x}\mathrm{p}}$, MPa [68] | |

300 | 56.42 | 6.000 | 6 | 0.00 |

300 | 75.59 | 8.000 | 8 | 0.01 |

300 | 94.89 | 10.000 | 10 | 0.00 |

300 | 114.26 | 12.000 | 12 | 0.00 |

300 | 133.67 | 14.001 | 14 | 0.01 |

300 | 153.09 | 16.006 | 16 | 0.04 |

300 | 172.4 | 18.009 | 18 | 0.05 |

300 | 191.6 | 20.014 | 20 | 0.07 |

Hydrogen | ||||

$T$, K | $\rho $, mol/dm^{3} | ${P}_{\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{c}}$, MPa | ${P}_{\mathrm{e}\mathrm{x}\mathrm{p}}$, MPa [69] | |

500 | 0.94818 | 3.998 | 4 | 0.05 |

500 | 1.40962 | 5.994 | 6 | 0.10 |

500 | 1.86196 | 7.990 | 8 | 0.13 |

500 | 2.30518 | 9.986 | 10 | 0.14 |

500 | 2.73932 | 14.990 | 15 | 0.07 |

500 | 3.16448 | 20.03 | 20 | 0.15 |

Reaction | ${\mathit{A}}_{\mathit{k}}$, (L, mol, s) | ${\mathit{E}}_{\mathit{k}}/\mathit{R}$, K | ${\mathit{n}}_{\mathit{k}}$ |
---|---|---|---|

C_{2}H_{2} + C_{2}H_{2} = C + C + C_{2}H_{4} | 2 × 10^{16} | 40,000 | 0 |

C + CO_{2} = CO + CO | 1 × 10^{15} | 40,000 | 0 |

C + H_{2}O = H_{2} + CO | 1 × 10^{15} | 40,000 | 0 |

C + OH = HCO | 1 × 10^{12} | 0 | 0 |

Parameter | Value |
---|---|

Rotation speed, rpm | 2000 |

Cylinder radius, mm | 42.5 |

Compression ratio | 16 |

Start of injection, CAD ** | 715.78 |

End of injection, CAD | 730.06 |

Injection angle, deg. | 150 |

Mass of injected fuel, kg | 2.8 × 10^{−5} |

Fuel temperature, K | 330.15 |

Mass fraction of exhaust gases | 0.233 |

Equivalence ratio in exhaust gases | 0.5606 |

Flow swirl, 1/min | 5800 |

**Table 4.**Calculated compression ratios $\epsilon $ and temperatures ${T}_{c}$ at the end of compression (${T}_{0}$ = 343 K, ${P}_{0}$ = 1 bar, $n$ = 1500 rpm, $\alpha $ = 1.5).

Reaction Type | $\mathit{\epsilon}$ | ${\mathit{T}}_{\mathit{c}}$, K | $\mathrm{Exp}.\mathrm{Range}{\mathit{T}}_{\mathit{c}}$, K |
---|---|---|---|

No apparent reaction | 12.00 | <786 | <703 |

Single cool flames | 13.00 | 808 | 703–838 |

Double cool flames | 13.50 | 816 | 838–882 |

Blue flames | 13.75 | 820 | 882–914 |

Hot flames | 14.00 | >826 | >914 |

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## Share and Cite

**MDPI and ACS Style**

Basevich, V.Y.; Frolov, S.M.; Ivanov, V.S.; Frolov, F.S.; Semenov, I.V.
The Effects of Multistage Fuel-Oxidation Chemistry, Soot Radiation, and Real Gas Properties on the Operation Process of Compression Ignition Engines. *Eng* **2023**, *4*, 2682-2710.
https://doi.org/10.3390/eng4040153

**AMA Style**

Basevich VY, Frolov SM, Ivanov VS, Frolov FS, Semenov IV.
The Effects of Multistage Fuel-Oxidation Chemistry, Soot Radiation, and Real Gas Properties on the Operation Process of Compression Ignition Engines. *Eng*. 2023; 4(4):2682-2710.
https://doi.org/10.3390/eng4040153

**Chicago/Turabian Style**

Basevich, Valentin Y., Sergey M. Frolov, Vladislav S. Ivanov, Fedor S. Frolov, and Ilya V. Semenov.
2023. "The Effects of Multistage Fuel-Oxidation Chemistry, Soot Radiation, and Real Gas Properties on the Operation Process of Compression Ignition Engines" *Eng* 4, no. 4: 2682-2710.
https://doi.org/10.3390/eng4040153