2.2.2. Option *ii*: C2H5O–Air Mixture

For this option, the same system of equations is solved as for option *i*, but in Equations (20) and (21) everywhere in the rows and in the indices, C2H<sup>5</sup> must be replaced by C2H5O. To solve the problem for these two options, a special computational code has been developed.

#### *2.3. Experimental Setup*

Before designing the experimental setup, it was implied that the self-ignition delay, *τi* , of the TEA/TEB spray in ambient air could be estimated experimentally either by measuring the time delay between the start of spray injection and the appearance of selfignition luminosity, if TEA/TEB is sprayed in a short pulse mode, or by measuring the width of the dark zone between the injector nozzle face and the luminous combustion plume, if the TEA/TEB is sprayed continuously. It could be assumed that ignition occurs much later than the pulsed injection of TEA/TEB. During this time, TEA/TEB droplets slow down, causing the ignition to occur in a virtually quiescent and spatially homogeneous mixture. With an average droplet path of around 10 cm and a speed of escape from the

injector nozzle of the order of 10<sup>4</sup> cm/s, the deceleration time is around 1 ms. This time is much shorter than the expected self-ignition delay time, even at the lowest estimated value of activation energy in Equation (17), *ε* ≈ 2 kcal/mol. With the continuous spraying of TEA/TEB into the ambient air, one could expect the appearance of a quasi-stationary luminous combustion plume. In this case, TEA/TEB droplets ignite due to the air flow around them, and the self-ignition delay, *τ<sup>i</sup>* , of the spray is determined by the time given to a droplet to enter the zone of the luminous combustion plume. The value of *τ<sup>i</sup>* can be estimated experimentally based on the width, *L*, of the dark zone between the injector nozzle face and luminous combustion plume measured along the spray axis. The value *τ<sup>i</sup>* is related to *L* and the speed of the TEA/TEB spray at the nozzle exit, *U*, as *τ<sup>i</sup>* ≈ *L*/*U*.

Based on these implications, the experimental setup for fuel spraying in air was designed and manufactured. The experimental setup consisted of an electromagnetic fuel injector (BOSCH 0 280 158 017) and a system for ensuring its operation (hydraulic system and microprocessor control unit), an optical system, a high-speed camera (Phantom Miro LC310), and a safety system. The elements of the setup are shown in Figure 1a. The injector nozzle had 4 holes with a diameter of 0.2 mm. The microprocessor control unit monitored the current through the injector and the voltage applied, and issued synchronization and trigger signals for the high-speed video camera. In the preliminary experiments, the standard 13%TEA–87%TEB mixture provided by the production company was used. The density of the TEA–TEB mixture was 0.703 g/cm<sup>3</sup> . To prevent clogging of the setup communications by the condensed reaction products of the TEA–TEB mixture with air, the injector was sprayed with n-heptane before and after each experiment. n-heptane (density 0.684 g/cm<sup>3</sup> ) was also used for estimating the flow rate and characteristic droplet size in the spray at different injection pressures. The nominal flow rate of n-heptane at an overpressure of 3 and 6 atm was 2.55 ± 0.08 mL/s (1.74 ± 0.05 g/s) and 5.1 ± 0.2 mL/s (3.5 ± 0.1 g/s), respectively. The droplet diameter in n-heptane sprays at the injection overpressure of 3 and 6 atm measured by the slide sampling method [29,30] was ~80–120 and ~30–50 µm, respectively. The operation frequency of the injector in the pulsed mode as well as the injection duration time were varied (see below). *Micromachines* **2022**, *13*, x FOR PEER REVIEW 7 of 17

**Figure 1.** (**a**) Experimental setup and (**b**) the hydraulic scheme of fuel supply. **Figure 1.** (**a**) Experimental setup and (**b**) the hydraulic scheme of fuel supply.

Figure 2 shows two options used for fastening the injector in the housing, which differed in the means of supplying argon and the geometry of the insulating cavity. The first series of experiments was performed using the recessed injector of Figure 2a and direct video registration of spray self-luminosity during ignition and combustion in ambient air (see Section 3.3). As the dark zone between the flame and the nozzle mouth could be quite short, the second series of experiments was performed using the flat Injector of Figure 2b (see Section 3.3). In the latter case, spray self-ignition and combustion was registered both Figure 1b shows the hydraulic scheme of the experimental setup. The experimental procedure was as follows. (i) Before supplying the TEA–TEB mixture to the injector, all communications were thoroughly purged with argon; (ii) liquid n-heptane was poured into the transparent measuring tank through the funnel and pressurized by argon to an overpressure of 3 atm using valve 1; (iii) with valves 2, 4, and 5 closed, valve 3 open, and the injector turned on, the communications were spilled with n-heptane; (iv) valve 3 was closed and the pressure was relieved by briefly turning on the injector; (v) valves 6 and 7

(**a**) (**b**)

Before conducting the calculations for options *i* and *ii*, we calculated the self-ignition delays for stoichiometric C2H5–air and C2H5O–air mixtures in the absence of heterogene-

4C2H<sup>5</sup> + 13O<sup>2</sup> → 8CO<sup>2</sup> + 10H2O.

= Ψ<sup>C</sup>2H5<sup>O</sup> = 0. The overall reaction of C2H<sup>5</sup> with oxygen reads

*3.1. Self-Ignition of Stoichiometric C2H5–Air and C2H5O–Air Mixtures at NPT Conditions*

**Figure 2.** Two options of injector housing: (**a**) recessed injector and (**b**) flat injector.

by direct video registration of self-luminosity and by the schlieren method.

**3. Results and Discussion**

ous reactions, i.e., at Ψ<sup>C</sup>2H<sup>5</sup>

were opened and the TEA–TEB tank was pressurized by argon to the overpressure of 3 to 6 atm; valve 8 was used to control the pressure level; (vi) valves 6 to 8 were closed and valves 1, 4, and 5 opened; (vii) using a rotameter, a small flow rate of argon (around 1 L/min) was established around the injector nozzle to avoid nozzle clogging by the condensed reaction products of the TEA–TEB mixture with air available in the vicinity of the nozzle face; and (viii) the injector was turned on and operated for a preset time either in the pulsed or continuous injection mode. (**a**) (**b**) **Figure 1.** (**a**) Experimental setup and (**b**) the hydraulic scheme of fuel supply. Figure 2 shows two options used for fastening the injector in the housing, which dif-

*Micromachines* **2022**, *13*, x FOR PEER REVIEW 7 of 17

Figure 2 shows two options used for fastening the injector in the housing, which differed in the means of supplying argon and the geometry of the insulating cavity. The first series of experiments was performed using the recessed injector of Figure 2a and direct video registration of spray self-luminosity during ignition and combustion in ambient air (see Section 3.3). As the dark zone between the flame and the nozzle mouth could be quite short, the second series of experiments was performed using the flat Injector of Figure 2b (see Section 3.3). In the latter case, spray self-ignition and combustion was registered both by direct video registration of self-luminosity and by the schlieren method. fered in the means of supplying argon and the geometry of the insulating cavity. The first series of experiments was performed using the recessed injector of Figure 2a and direct video registration of spray self-luminosity during ignition and combustion in ambient air (see Section 3.3). As the dark zone between the flame and the nozzle mouth could be quite short, the second series of experiments was performed using the flat Injector of Figure 2b (see Section 3.3). In the latter case, spray self-ignition and combustion was registered both by direct video registration of self-luminosity and by the schlieren method.

**Figure 2.** Two options of injector housing: (**a**) recessed injector and (**b**) flat injector. **Figure 2.** Two options of injector housing: (**a**) recessed injector and (**b**) flat injector.

#### **3. Results and Discussion 3. Results and Discussion**

#### *3.1. Self-Ignition of Stoichiometric C2H5–Air and C2H5O–Air Mixtures at NPT Conditions 3.1. Self-Ignition of Stoichiometric C2H5–Air and C2H5O–Air Mixtures at NPT Conditions*

Before conducting the calculations for options *i* and *ii*, we calculated the self-ignition delays for stoichiometric C2H5–air and C2H5O–air mixtures in the absence of heterogeneous reactions, i.e., at Ψ<sup>C</sup>2H<sup>5</sup> = Ψ<sup>C</sup>2H5<sup>O</sup> = 0. The overall reaction of C2H<sup>5</sup> with oxygen reads Before conducting the calculations for options *i* and *ii*, we calculated the self-ignition delays for stoichiometric C2H5–air and C2H5O–air mixtures in the absence of heterogeneous reactions, i.e., at ΨC2H<sup>5</sup> = ΨC2H5<sup>O</sup> = 0. The overall reaction of C2H<sup>5</sup> with oxygen reads

$$\text{4C}\_2\text{H}\_5 + 13\text{O}\_2 \to 8\text{CO}\_2 + 10\text{H}\_2\text{O}.$$

The stoichiometric composition of the C2H5–air mixture is *X*C2H<sup>5</sup> = 0.061; *X*O<sup>2</sup> = 0.197; and *X*N<sup>2</sup> = 0.742. Self-ignition delays were calculated for the C2H5–air mixture of stoichiometric composition for NPT conditions: *T*<sup>0</sup> = 300 K and *p* = 1 atm.

The self-ignition delays obtained using the developed kinetic code were compared with the results of calculations using the standard kinetic code KINET, developed by M. G. Neigauz at the Institute of Chemical Physics of the Russian Academy of Sciences for homogeneous gas mixtures [31]. In both cases, the same kinetic mechanism was used: the detailed kinetic mechanism of combustion and oxidation of alkanes up to C4 [26]. It should be noted that the KINET code applies somewhat different thermodynamic data than [28]: the polynomial dependence of heat capacity on temperature has fewer terms.

Table 1 shows the values of the self-ignition delays *τ<sup>i</sup>* , the temperature of the reaction products *T<sup>e</sup>* , volume fractions of C2H<sup>5</sup> radical, *X*C2H<sup>5</sup> *e* , oxygen, *X*O<sup>2</sup> *e* , and water, *X*H2<sup>O</sup> *e* , in the reaction products, as well as the maximum value of methane volume fraction, *X*CH<sup>4</sup> max , obtained by calculations using the two indicated codes. Figure 3a shows the calculated time histories of temperature obtained by the two indicated codes. Both the data in Table 1 and the curves in Figure 3a are in satisfactory agreement with each other. The slight differences in the results seem to be caused by the differences in the thermodynamic data used. the calculated time histories of temperature obtained by the two indicated codes. Both the data in Table 1 and the curves in Figure 3a are in satisfactory agreement with each other. The slight differences in the results seem to be caused by the differences in the thermodynamic data used.

, in the reaction products, as well as the maximum value of methane volume frac-

, obtained by calculations using the two indicated codes. Figure 3a shows

= 0.742. Self-ignition delays were calculated for the C2H5–air mixture of stoichi-

) 

The self-ignition delays obtained using the developed kinetic code were compared with the results of calculations using the standard kinetic code KINET, developed by M. G. Neigauz at the Institute of Chemical Physics of the Russian Academy of Sciences for homogeneous gas mixtures [31]. In both cases, the same kinetic mechanism was used: the detailed kinetic mechanism of combustion and oxidation of alkanes up to C4 [26]. It should be noted that the KINET code applies somewhat different thermodynamic data than [28]: the polynomial dependence of heat capacity on temperature has fewer terms.

**Table 1.** Estimated values of the main variables.

and <sup>N</sup><sup>2</sup>

products

tion, (CH<sup>4</sup>

) max

(<sup>H</sup>2<sup>O</sup>) 


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The stoichiometric composition of the C2H5–air mixture is <sup>C</sup>2H<sup>5</sup>

ometric composition for NPT conditions: <sup>0</sup> = 300 K and = 1 atm.

Table 1 shows the values of the self-ignition delays

, volume fractions of C2H<sup>5</sup> radical, (<sup>C</sup>2H<sup>5</sup>

= 0.061; <sup>O</sup><sup>2</sup>

, the temperature of the reaction

)  , and water,

, oxygen, (<sup>O</sup><sup>2</sup>

= 0.197;

**Figure 3.** Calculated time histories of temperature during self-ignition of C2H5–air (**a**) and C2H5O– air (**b**) mixtures of stoichiometric composition at NPT conditions using two codes: new code and KINET [31]. **Figure 3.** Calculated time histories of temperature during self-ignition of C2H5–air (**a**) and C2H5O– air (**b**) mixtures of stoichiometric composition at NPT conditions using two codes: new code and KINET [31].

Then, the self-ignition delays of the stoichiometric C2H5O–air mixture were calculated under NPT conditions: <sup>0</sup> = 300 K and = 1 atm. The overall reaction of C2H5O with oxygen reads Then, the self-ignition delays of the stoichiometric C2H5O–air mixture were calculated under NPT conditions: *T*<sup>0</sup> = 300 K and *p* = 1 atm. The overall reaction of C2H5O with oxygen reads

$$\text{4C}\_2\text{H}\_5\text{O} + 11\text{O}\_2 \to 8\text{CO}\_2 + 10\text{H}\_2\text{O}.$$

The stoichiometric composition of the C2H5O–air mixture is <sup>C</sup>2H5<sup>O</sup> = 0.063; <sup>O</sup><sup>2</sup> = 0.172; and <sup>N</sup><sup>2</sup> = 0.765. Figure 3b shows the calculated time histories of temperature for the stoichiometric C2H5O–air mixture. The self-ignition delays obtained with the new code and KINET are 118 and 124 s, respectively, i.e., the results differ by less than 5%. Thus, calculations show that the self-ignition delay of a stoichiometric C2H5O–air mixture is much longer than that of a stoichiometric C2H5–air mixture at NPT conditions. This The stoichiometric composition of the C2H5O–air mixture is *X*C2H5<sup>O</sup> = 0.063; *X*O<sup>2</sup> = 0.172; and *X*N<sup>2</sup> = 0.765. Figure 3b shows the calculated time histories of temperature for the stoichiometric C2H5O–air mixture. The self-ignition delays obtained with the new code and KINET are 118 and 124 s, respectively, i.e., the results differ by less than 5%. Thus, calculations show that the self-ignition delay of a stoichiometric C2H5O–air mixture is much longer than that of a stoichiometric C2H5–air mixture at NPT conditions. This indicates the much greater reactivity of the C2H<sup>5</sup> radical in air compared to the C2H5O radical. In view of this, the option with the C2H5O radical can be omitted.

#### *3.2. Self-Ignition of TEA Droplets in Air at NPT Conditions*

The problem for option *i* (see Section 2.2) was solved numerically for several values of *ε*, from 2 to 6 kcal/mol (see Equation (17)), to compare the calculated self-ignition delays with the experiment. For the sake of definiteness, the parameters entering Equation (21) were assumed to have the following values: *<sup>λ</sup>* = 0.1; *<sup>u</sup>*O<sup>2</sup> <sup>=</sup> 4.46·10<sup>4</sup> cm/s; *r<sup>d</sup>* = 50 µm; *<sup>S</sup>* <sup>=</sup> 3.14·10−<sup>4</sup> cm<sup>2</sup> ; *N* = 210 cm−<sup>3</sup> ; *<sup>c</sup><sup>p</sup>* <sup>=</sup> 1.33·10−<sup>3</sup> J/(cm3K) (see Appendices A and B). Initial NPT conditions are *t* = 0; *T* = *T*<sup>0</sup> = 300 K; pressure *p* = 1 atm; volume fractions of oxygen and nitrogen *X*O<sup>2</sup> = 0.21 and *X*N<sup>2</sup> = 0.79. All other components: *X<sup>j</sup>* = 0; *n*C2H<sup>5</sup> = 0; *n*O<sup>2</sup> = *X*O<sup>2</sup> /22,400 = 9.37 · <sup>10</sup>−<sup>6</sup> mol/cm<sup>3</sup> .

Calculations show that the self-ignition delay *τ<sup>i</sup>* depends very strongly on *ε* (Table 2). Figure 4 shows the calculated time histories of temperature within 0 ≤ *t* ≤ *τ<sup>i</sup>* at *ε* = 5 and 6 kcal/mol. The upper limit of the specified time interval is chosen equal to *τ<sup>i</sup>* because, at *t* > *τ<sup>i</sup>* , the reactions leading to the complete burnout of TEA, which are not included in

the reaction scheme, become significant. Figure 5 shows the calculated time history of the C2H<sup>5</sup> radical concentration, *n*C2H<sup>5</sup> (*t*), at *ε* = 6 kcal/mol. at > , the reactions leading to the complete burnout of TEA, which are not included in the reaction scheme, become significant. Figure 5 shows the calculated time history of the C2H<sup>5</sup> radical concentration, <sup>C</sup>2H<sup>5</sup> (), at = 6 kcal/mol. at > , the reactions leading to the complete burnout of TEA, which are not included in the reaction scheme, become significant. Figure 5 shows the calculated time history of the C2H<sup>5</sup> radical concentration, <sup>C</sup>2H<sup>5</sup> (), at = 6 kcal/mol.

indicates the much greater reactivity of the C2H<sup>5</sup> radical in air compared to the C2H5O

indicates the much greater reactivity of the C2H<sup>5</sup> radical in air compared to the C2H5O

The problem for option *i* (see Section 2.2) was solved numerically for several values of , from 2 to 6 kcal/mol (see Equation (17)), to compare the calculated self-ignition delays with the experiment. For the sake of definiteness, the parameters entering Equation

The problem for option *i* (see Section 2.2) was solved numerically for several values of , from 2 to 6 kcal/mol (see Equation (17)), to compare the calculated self-ignition delays with the experiment. For the sake of definiteness, the parameters entering Equation

; = 1.33 ∙ 10−3

; = 1.33 ∙ 10−3

Calculations show that the self-ignition delay depends very strongly on (Table 2). Figure 4 shows the calculated time histories of temperature within 0 ≤ ≤ at = 5 and 6 kcal/mol. The upper limit of the specified time interval is chosen equal to because,

Calculations show that the self-ignition delay depends very strongly on (Table 2). Figure 4 shows the calculated time histories of temperature within 0 ≤ ≤ at = 5 and 6 kcal/mol. The upper limit of the specified time interval is chosen equal to because,

B). Initial NPT conditions are = 0; = <sup>0</sup> = 300 K; pressure = 1 atm; volume fractions

B). Initial NPT conditions are = 0; = <sup>0</sup> = 300 K; pressure = 1 atm; volume fractions

cm/s; = 50

cm/s; = 50

=

=

J/(cm3K) (see Appendixes A and

J/(cm3K) (see Appendixes A and

= 0.79. All other components: = 0; <sup>C</sup>2H<sup>5</sup>

= 0.79. All other components: = 0; <sup>C</sup>2H<sup>5</sup>

radical. In view of this, the option with the C2H5O radical can be omitted.

radical. In view of this, the option with the C2H5O radical can be omitted.

(21) were assumed to have the following values: = 0.1; <sup>O</sup><sup>2</sup> = 4.46 ∙ 10<sup>4</sup>

(21) were assumed to have the following values: = 0.1; <sup>O</sup><sup>2</sup> = 4.46 ∙ 10<sup>4</sup>

.

.

= 0.21 and <sup>N</sup><sup>2</sup>

= 0.21 and <sup>N</sup><sup>2</sup>

; = 210 cm–<sup>3</sup>

; = 210 cm–<sup>3</sup>


μm; = 3.14 ∙ 10−4

μm; = 3.14 ∙ 10−4

= <sup>O</sup><sup>2</sup>

= <sup>O</sup><sup>2</sup>

0; <sup>O</sup><sup>2</sup>

0; <sup>O</sup><sup>2</sup>

of oxygen and nitrogen <sup>O</sup><sup>2</sup>

of oxygen and nitrogen <sup>O</sup><sup>2</sup>

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*3.2. Self-Ignition of TEA Droplets in Air at NPT Conditions*

*3.2. Self-Ignition of TEA Droplets in Air at NPT Conditions*

cm<sup>2</sup>

cm<sup>2</sup>

/22400 = 9.37 10−6 mol/cm<sup>3</sup>

/22400 = 9.37 10−6 mol/cm<sup>3</sup>


6 11.1

**Figure 4.** Calculated time histories of temperature during self-ignition of stoichiometric C2H5–air mixture with the heterogeneous reaction at NPT conditions and = 5 and 6 kcal/mol. **Figure 4.** Calculated time histories of temperature during self-ignition of stoichiometric C2H5–air mixture with the heterogeneous reaction at NPT conditions and *ε* = 5 and 6 kcal/mol. **Figure 4.** Calculated time histories of temperature during self-ignition of stoichiometric C2H5–air mixture with the heterogeneous reaction at NPT conditions and = 5 and 6 kcal/mol.

**Figure 5.** Calculated time history of the C2H<sup>5</sup> radical concentration in a heterogeneous reaction at NPT conditions; *ε* = 6 kcal/mol.

#### *3.3. Experimental Results*

Figures 6 and 7 show selected video frames of TEA–TEB spray self-ignition during pulsed (Figure 6) and continuous (Figure 7) spraying from the recessed injector of Figure 2a at injection overpressure 3 atm. The duration of the single-shot pulsed spray in the experiment of Figure 6 is 20 ms. After the termination of spray injection in Figure 6, one can see the successive appearance of haze and smoke in the spray core, followed by the formation of a luminous self-ignition spot of a green color, characteristic of TEB combustion (see frame #35 in Figure 6). The first hot spot is located at a distance of around 130 mm from the nozzle face. Subsequently, while this hot spot rapidly grows with time, several other hot spots appear, grow, and overlap with each other, moving in lateral, downstream, and upstream directions and forming a luminous combustion plume. The evolution of the continuous spray in Figure 7 has much in common with that of Figure 6, but the first hot spot is located somewhat closer to the nozzle face (at around 100 mm) and the luminous combustion plume looks more elaborated. The characteristic spray velocity at the nozzle

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NPT conditions; = 6 kcal/mol.

*3.3. Experimental Results*

exit estimated based on the mass flow rate and injector nozzle diameter is approximately 20 m/s. the nozzle exit estimated based on the mass flow rate and injector nozzle diameter is approximately 20 m/s.

**Figure 5.** Calculated time history of the C2H<sup>5</sup> radical concentration in a heterogeneous reaction at

Figures 6 and 7 show selected video frames of TEA–TEB spray self-ignition during pulsed (Figure 6) and continuous (Figure 7) spraying from the recessed injector of Figure 2a at injection overpressure 3 atm. The duration of the single-shot pulsed spray in the experiment of Figure 6 is 20 ms. After the termination of spray injection in Figure 6, one can see the successive appearance of haze and smoke in the spray core, followed by the formation of a luminous self-ignition spot of a green color, characteristic of TEB combustion (see frame #35 in Figure 6). The first hot spot is located at a distance of around 130 mm from the nozzle face. Subsequently, while this hot spot rapidly grows with time, several other hot spots appear, grow, and overlap with each other, moving in lateral, downstream, and upstream directions and forming a luminous combustion plume. The evolution of the continuous spray in Figure 7 has much in common with that of Figure 6, but the first hot spot is located somewhat closer to the nozzle face (at around 100 mm) and the luminous combustion plume looks more elaborated. The characteristic spray velocity at

**Figure 6.** Sequence of video frames of pulsed TEA–TEB spray self-ignition and combustion in ambient air at NPT conditions: recessed injector. Frame numbers correspond to time in milliseconds from the start of injection. Injection overpressure is 3 atm. Frame size is 672 × 456 pixels (213 × 145 mm<sup>2</sup> ), frame rate 1000 fps, shutter speed 400 μs. **Figure 6.** Sequence of video frames of pulsed TEA–TEB spray self-ignition and combustion in ambient air at NPT conditions: recessed injector. Frame numbers correspond to time in milliseconds from the start of injection. Injection overpressure is 3 atm. Frame size is 672 <sup>×</sup> 456 pixels (213 <sup>×</sup> 145 mm<sup>2</sup> ), frame rate 1000 fps, shutter speed 400 µs. *Micromachines* **2022**, *13*, x FOR PEER REVIEW 11 of 17

**Figure 7.** Sequence of video frames of continuous TEA–TEB spray self-ignition and combustion in ambient air at NPT conditions: recessed injector. Injection overpressure is 3 atm. Frame size is 672 × 456 pixels (213 × 145 mm<sup>2</sup> ), frame rate 3200 fps, shutter speed 300 μs, injection duration 500 ms. The measured self-ignition delays in Figures 6 and 7 are approximately 30 and 20 ms, **Figure 7.** Sequence of video frames of continuous TEA–TEB spray self-ignition and combustion in ambient air at NPT conditions: recessed injector. Injection overpressure is 3 atm. Frame sizeis <sup>672</sup> <sup>×</sup> 456 pixels (213 <sup>×</sup> 145 mm<sup>2</sup> ), frame rate 3200 fps, shutter speed 300 µs, injection duration 500 ms.

respectively. The distance between the nozzle face and luminous plume in a continuous spray appeared to be variable with time (Figure 8) rather than quasi-stationary, as was expected. Thus, while the first ignition event in Figure 8 appeared at a distance of ~100 mm from the nozzle face, it dropped to zero in 100 ms after the start of injection (see Figure 8). This means that the apparent velocity of self-ignition spreading toward the nozzle face The measured self-ignition delays in Figures 6 and 7 are approximately 30 and 20 ms, respectively. The distance between the nozzle face and luminous plume in a continuousspray appeared to be variable with time (Figure 8) rather than quasi-stationary, as was expected. Thus, while the first ignition event in Figure <sup>8</sup> appeared at a distance of ~100 mmfrom the nozzle face, it dropped to zero in 100 ms after the start of injection (see Figure 8).

was higher than the spray velocity (~20 m/s).

This means that the apparent velocity of self-ignition spreading toward the nozzle face was higher than the spray velocity (~20 m/s).

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**Figure 8.** Sequence of video frames of continuous TEA–TEB spray combustion in ambient air at NPT conditions: recessed injector, the same test fire as in Figure 7. Injection overpressure is 3 atm. Frame size is 1280 × 456 pixels (406 × 145 mm<sup>2</sup> ), frame rate 3200 fps, shutter speed 300 μs, injection duration 500 ms. **Figure 8.** Sequence of video frames of continuous TEA–TEB spray combustion in ambient air at NPT conditions: recessed injector, the same test fire as in Figure 7. Injection overpressure is 3 atm. Frame size is 1280 <sup>×</sup> 456 pixels (406 <sup>×</sup> 145 mm<sup>2</sup> ), frame rate 3200 fps, shutter speed 300 µs, injection duration 500 ms.

Consider Figure 9 for a better understanding of the circumstances of TEA–TEB spray self-ignition. This figure shows a sequence of synchronized schlieren (left column) and self-luminosity (right column) video frames of TEA–TEB spray injection by the flat injector of Figure 2b, followed by spray self-ignition and combustion. The injection overpressure is 6 atm, and the spray velocity is ~40 m/s. The schlieren images in the left column are superimposed by the self-luminosity images reflected from the mirror of the schlieren system. Schlieren images contain thin droplet trajectories. After a certain delay, the trajectories inflate, forming cloud-like swellings, which can be attributed to the liquid mist and gas, self-heated due to the spontaneous reaction in air. The latter is substantiated by the fact that the luminous self-ignition plume is located exactly in these swellings of the droplet trajectories. Furthermore, Figure 10 shows the pulsed injection of the TEA–TEB spray into the ambient air at NPT conditions with a very short pulse duration of 0.7 ms. Similar to Figure 9, the schlieren images here are also superimposed by the self-luminosity images reflected from the mirror. One can see the appearance of the cloud-like trajectory swellings lagging behind the moving droplets and growing with time in the form of conical tongues of hot matter. It is seen from the schlieren images that the luminous self-ignition plume is also located exactly in these swellings. Consider Figure 9 for a better understanding of the circumstances of TEA–TEB spray self-ignition. This figure shows a sequence of synchronized schlieren (left column) and self-luminosity (right column) video frames of TEA–TEB spray injection by the flat injector of Figure 2b, followed by spray self-ignition and combustion. The injection overpressure is 6 atm, and the spray velocity is ~40 m/s. The schlieren images in the left column are superimposed by the self-luminosity images reflected from the mirror of the schlieren system. Schlieren images contain thin droplet trajectories. After a certain delay, the trajectories inflate, forming cloud-like swellings, which can be attributed to the liquid mist and gas, self-heated due to the spontaneous reaction in air. The latter is substantiated by the fact that the luminous self-ignition plume is located exactly in these swellings of the droplet trajectories. Furthermore, Figure 10 shows the pulsed injection of the TEA–TEB spray into the ambient air at NPT conditions with a very short pulse duration of 0.7 ms. Similar to Figure 9, the schlieren images here are also superimposed by the self-luminosity images reflected from the mirror. One can see the appearance of the cloud-like trajectory swellings lagging behind the moving droplets and growing with time in the form of conical tongues of hot matter. It is seen from the schlieren images that the luminous self-ignition plume is also located exactly in these swellings.

*Micromachines* **2022**, *13*, x FOR PEER REVIEW 13 of 17

**Figure 9.** Sequence of schlieren (left column) and self-luminosity (right column) video frames of continuous TEA–TEB spray self-ignition and combustion in ambient air at NPT conditions: flat injector. Injection overpressure is 6 atm. Frame size is 590 × 392 pixels (192 × 127 mm<sup>2</sup> ), frame rate 12,000 fps, shutter speed 81.5 μs, injection duration 100 ms. **Figure 9.** Sequence of schlieren ((**left**) column) and self-luminosity ((**right**) column) video frames of continuous TEA–TEB spray self-ignition and combustion in ambient air at NPT conditions: flat injector. Injection overpressure is 6 atm. Frame size is 590 <sup>×</sup> 392 pixels (192 <sup>×</sup> 127 mm<sup>2</sup> ), frame rate 12,000 fps, shutter speed 81.5 µs, injection duration 100 ms. **Figure 9.** Sequence of schlieren (left column) and self-luminosity (right column) video frames of continuous TEA–TEB spray self-ignition and combustion in ambient air at NPT conditions: flat injector. Injection overpressure is 6 atm. Frame size is 590 × 392 pixels (192 × 127 mm<sup>2</sup> ), frame rate 12,000 fps, shutter speed 81.5 μs, injection duration 100 ms.

**Figure 10.** Sequence of schlieren (upper raw) and self-luminosity (lower raw) video frames of selfignition and combustion of the pulsed TEA–TEB spray in ambient air at NPT conditions: flat injector. Injection overpressure is 6 atm. Frame size is 480 × 320 pixels (156 × 104 mm<sup>2</sup> ), frame rate 5000 fps, shutter speed 190 μs, injection duration 0.7 ms. **Figure 10.** Sequence of schlieren (upper raw) and self-luminosity (lower raw) video frames of selfignition and combustion of the pulsed TEA–TEB spray in ambient air at NPT conditions: flat injector. Injection overpressure is 6 atm. Frame size is 480 × 320 pixels (156 × 104 mm<sup>2</sup> ), frame rate 5000 fps, shutter speed 190 μs, injection duration 0.7 ms. **Figure 10.** Sequence of schlieren ((**upper**) raw) and self-luminosity ((**lower**) raw) video frames of self-ignition and combustion of the pulsed TEA–TEB spray in ambient air at NPT conditions: flat injector. Injection overpressure is 6 atm. Frame size is 480 <sup>×</sup> 320 pixels (156 <sup>×</sup> 104 mm<sup>2</sup> ), frame rate 5000 fps, shutter speed 190 µs, injection duration 0.7 ms.

Tables 3 and 4 show the statistics of self-ignition events in the case of four successive injection pulses with a pulse duration of 10 ms and time interval between pulses of 1000 ms

(Table 3) and six successive pulses with a pulse duration of 5 ms and time interval between pulses of 400 ms (Table 4). The mean self-ignition delay is seen to be shorter for the conditions of Table 4, thus indicating that the shorter interval between pulses (400 ms vs. 1000 ms) promotes self-ignition, presumably due to the availability of hot residual air on the spray path, which is in line with Equation (14). The results of Figures 6–8, as well as Tables 3 and 4, indicate that the activation energy of TEA–TEB mixture self-ignition in Equation (7) is approximately *ε* ≈ 2 kcal/mol (see Table 2).

**Table 3.** Measured self-ignition delays in the test fire with 4 successive injection pulses with a pulse duration of 10 ms and time interval between pulses 1000 ms; injection overpressure is 3 atm.


**Table 4.** Measured self-ignition delays in the test fire with 6 successive injection pulses with a pulse duration of 5 ms and time interval between pulses 400 ms; injection overpressure is 3 atm.


Tables 5 and 6 show the statistics of self-ignition events in the case of 15 successive injection pulses with a pulse duration of 1 and 2 ms, respectively, and a time interval between pulses of 100 ms. Contrary to Tables 3 and 4, the injection overpressure for the test fires of Tables 5 and 6 was 6 atm rather than 3 atm. The mean self-ignition delay is seen to be around 6 ms, which is shorter than that for the lower injection overpressure by a factor of 3 to 5. This result is also in line with Equation (14) as the characteristic droplet size decreases with the injection pressure.

**Table 5.** Measured self-ignition delays in the test fire with 15 successive injection pulses with a pulse duration of 1 ms and time interval between pulses 100 ms; injection overpressure is 6 atm.


**Table 6.** Measured self-ignition delays in the test fire with 15 successive injection pulses with a pulse duration of 2 ms and time interval between pulses 100 ms; injection overpressure is 6 atm.


#### **4. Discussion**

The proposed kinetic model of the self-ignition of TEA–TEB droplets at NPT conditions, implying the intrusion of oxygen to the condensed phase with the formation of (C2H5)2Al–O–O–(C2H5) and (C2H5)2B–O–O–(C2H5) molecules, seems plausible due to the indisputable experimental fact of the self-ignition of liquid TEA, TEB, or TEA–TEB mixture upon contact with air. The model shows that the rate of decomposition of these molecules with the formation of the active ethyl radical depends on the size of the liquid droplets, as well as the local instantaneous oxygen concentration and temperature in the environment, implying that the ignition delay is shorter for the higher injection pressure and hotter air. The results of preliminary experiments on the self-ignition of pulsed and continuous TEA–TEB sprays in air at NPT conditions have confirmed these implications and provided the data for estimating the activation energy of the rate-limiting reaction, which appeared to be close to 2 kcal/mol.

It must be noticed that the existence of reactions (5) and (6) and their supposed role in the TEA self-ignition process still remain questionable. For example, in [4], on the basis of molecular dynamics simulation of the reaction of TEA (in the condensed phase) with gaseous oxygen at a temperature above 2000 K, it is assumed that the reaction begins with the rapid removal of a hydrogen atom by an oxygen molecule, with the formation of the HO<sup>2</sup> radical in the gas phase, and subsequently H<sup>2</sup> molecules (the latter is associated with air humidity), i.e., the rapid occurrence of reactions in the gas phase is associated with the high reactivity of hydrogen. For the kinetic parameters *A* and *ε* in the analogue of formula (7), the values 9.67·10<sup>9</sup> s <sup>−</sup><sup>1</sup> and 0.3 kcal/mol, respectively, were obtained. Another example is Ref. [19], where the priority is given to the channel of TEA decomposition through the breaking of the bond between oxygen atoms in the (C2H5)2Al–O–O–(C2H5) molecule with the formation of the C2H5O radical. In this case, the total process of oxygen intrusion and (C2H5)2Al–O–O–(C2H5) molecule decomposition is exothermic and proceeds with the release of 15.4 kcal/mol, whereas the same process proceeding through the C2H<sup>5</sup> radical is claimed to be endothermic. The question of which mechanism is actually implemented can only be answered after systematic experiments, which are planned for the future. Note that the model proposed herein, even if it is not implemented in relation to the self-ignition of TEA, TEB, and TEA–TEB mixtures, can be applied to other reactions, the rate constant of which depends on temperature according to the Arrhenius law.

### **5. Conclusions**

A novel scheme of the heterogeneous interaction of gaseous oxygen with liquid TEA– TEB droplets accompanied by the release of light hydrocarbon radicals C2H<sup>5</sup> and/or C2H5O into the gas phase was used for calculating the self-ignition of a spatially homogeneous mixture of TEA–TEB droplets in ambient air at normal pressure and temperature conditions. Calculations were performed with the variation of the activation energy of the rate-limiting reaction intended for comparison with experiments. Calculations showed that the selfignition delay of a stoichiometric C2H5O–air mixture was much longer than that of a stoichiometric C2H5–air mixture, indicating the much greater reactivity of the C2H<sup>5</sup> radical compared to the C2H5O radical in air. The proposed kinetic model with the formation of (C2H5)2Al–O–O–(C2H5) or (C2H5)2B–O–O–(C2H5) molecules seems plausible due to the indisputable experimental fact of the self-ignition of liquid TEA, TEB, and TEA–TEB mixtures upon contact with air. Experiments on the self-ignition of pulsed and continuous TEA–TEB mixture sprays in air at normal pressure and temperature conditions provided the data for estimating the activation energy of the rate-limiting reaction, which appeared to be close to 2 kcal/mol. The ignition delay was shown to decrease with the decrease in the droplet size, both in the model and in the experiment.

**Author Contributions:** Conceptualization, S.M.F.; methodology, S.M.F., I.O.S. and V.S.A.; investigation, V.Y.B., A.A.B., I.O.S., V.S.A., F.S.F., P.A.S. and S.L.G.; data curation, A.A.B., I.O.S. and V.S.A.; writing—original draft preparation, S.M.F.; writing—review and editing, S.M.F.; visualization, I.O.S. and V.S.A.; supervision, S.M.F.; project administration, S.M.F.; funding acquisition, S.M.F.; resources, S.L.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by a subsidy given to Semenov Federal Research Center for Chemical Physics of the Russian Academy of Sciences to implement the state assignments with registration numbers 122040500073-4 and 122040500068-0.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors offer a tribute of respect to the late Nickolai N. Kuznetsov for his valuable contribution to this study.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A. Heat Capacities of TEA–Air Mixture**

According to reaction (1), there are 10.5 moles of O<sup>2</sup> per 1 mole of TEA. The heat capacities *c<sup>v</sup>* and *c<sup>p</sup>* of 1 cm<sup>3</sup> of air under normal conditions are 5 2*R* 22,400 <sup>=</sup> 9.3 <sup>×</sup> <sup>10</sup>−<sup>4</sup> J/(cm3K) and 7 2*R* 22,400 <sup>=</sup> 1.3 <sup>×</sup> <sup>10</sup>−<sup>3</sup> J/(cm3K). Moreover, 1 cm<sup>3</sup> contains 0.21 22,400×10.5 <sup>=</sup> 8.9·10−<sup>7</sup> moles of TEA. The heat capacity of such an amount of TEA is much less than the heat capacity of air, and it can be taken into account approximately, equating it to the heat capacity of, e.g., oil. The heat capacity of oil is roughly half that of water and is approximately 4.5*R* per mole. Hence, in terms of the number of moles in 1 cm<sup>3</sup> , one obtains <sup>9</sup> <sup>×</sup> 4.18 <sup>×</sup> 8.9 <sup>×</sup> <sup>10</sup>−<sup>7</sup> <sup>=</sup> 0.33 <sup>×</sup> <sup>10</sup>−<sup>4</sup> J/(cm3K). The heat capacities of the mixture are

$$\mathbf{c}\_{\upsilon} = 9.6 \times 10^{-4} \,\mathrm{J/(cm^3 \,\mathrm{K})} \,\mathrm{s}$$

$$\mathbf{c}\_{p} = 1.33 \times 10^{-3} \,\mathrm{J/(cm^3 \,\mathrm{K})} \,\mathrm{s}$$
