1. Introduction

2. The Approach of the Closed Constant Volume Combustion in Otto Engine Cycles

2.1. The Assumptions for the Otto Cycle, See Figure 1

Let’s suppose the general basic Otto cycle interrelating with the environment by heat, mass and power transfers, see Figure 1. The engine cycle used to describe truthfully the constant volume combustion of a homogeneous mixture of CH₄ and H₂ and to evaluate the flue gases composition and harmful emissions, is consisting of below processes:

• 1 – 2 isentropic compression of a mixture CH₄/H₂/air prepared by a carburetor technique;
• 2 – 3 closed constant volume combustion:
• 3 – 4 isentropic expansion of flue gases and,
• 4 – 5 exhaust of flue gases, assimilated to a throttling process (succession of 4 – 4t isentropic expansion through flow section of exhaust valves and 4t – 5 constant pressure stagnation);
• 5 – 1 final constant pressure exhaust of flue gases.

Figure 1. The basic Otto cycle.

Figure 1. The basic Otto cycle.

2.2. The Isentropic Compression of a Mixture of CH₄/H₂/Air, Prepared by a Carburetor, See Figure 2

The assumptions were related to 1 kmole fuel with different mole composition and mixed with air having different values of excess oxygen:

−

they were considered 1 kmole fuel with x kmole H₂ and (1 – x) kmole CH₄;

−

the needed air for combustion was evaluated by the imposed excess oxygen, exo, respectively (1 + exo)(2 – 1.5x) kmole O₂ and 3.7619(1 + exo)(2 – 1.5x) kmole N₂;

−

the imposed x and exo, x = (0, 0.25, 0.5, 0.75); exo = (0, 0.25, 0.5, 0.75, 1, 1.5, 2);

−

the volumetric compression ratio, π₁₂ = V₂/V₁ = 10.

Figure 2. The isentropic compression 1 – 2. O_2min and N_2min correspond to stoichiometric combustion.

Figure 2. The isentropic compression 1 – 2. O_2min and N_2min correspond to stoichiometric combustion.

The parameters for the state 2 were evaluated through equations 1, 2 and 3

$$\begin{gathered} \mathrm{isentropic} \mathrm{exponent} \\ k12=\frac{r_{CH4}·\left({\sout{h}}_{2,CH4}-{\sout{h}}_{1,CH4}\right)+r_{H2}·\left({\sout{h}}_{2,H2}-{\sout{h}}_{1,H2}\right)+r_{O2}·\left({\sout{h}}_{2,O2}-{\sout{h}}_{1,O2}\right)+r_{N2}·\left({\sout{h}}_{2,N2}-{\sout{h}}_{1,N2}\right)}{r_{CH4}·\left({\sout{u}}_{2,CH4}-{\sout{u}}_{1,CH4}\right)+r_{H2}·\left({\sout{u}}_{2,H2}-{\sout{u}}_{1,H2}\right)+r_{O2}·\left({\sout{u}}_{2,O2}-{\sout{u}}_{1,O2}\right)+r_{N2}·\left({\sout{u}}_{2,N2}-{\sout{u}}_{1,N2}\right)} \end{gathered}$$

(1)

$$\begin{gathered} \mathrm{isentropic} \mathrm{compression} \mathrm{ending} \mathrm{temperatures} {\mathrm{T}}_2 \mathrm{and} {\mathrm{T}}_1 \\ {T}_2=T_1·{\pi }_{12}^{k12-1}, T_1=298 \mathrm{K} \end{gathered}$$

(2)

$$\begin{gathered} \mathrm{isentropic} \mathrm{compression} \mathrm{ending} \mathrm{pressures} {\mathrm{p}}_2 \mathrm{and} {\mathrm{p}}_1 \\ {p}_2=p_1·{\pi }_{12}^{k12}, p_1=1 \mathrm{bar} \end{gathered}$$

(3)

where $r,\sout{h},\sout{u}=\sout{h}-R·\left(T-T_1\right)$ are the mole composition of wholly mixture CH₄/H₂/air [kmole/kmole], and the relative physical enthalpies and internal energies [kJ/kmole] that were interpolated by 5^th order polynomials function of temperatures, see Table 1, R= 8.3145 kJ/kmole.K is the universal constant of ideal gas;

2.3. The Closed Constant Volume Combustion, See Figure 3

The closed constant volume combustion was designed in two successive steps. The first step gives the energy input for the second one, respectively the higher heating value, HHV, and the physical enthalpy of intaking chemical species, see Figure 3. This first step develops a fictitious combustion without dissociation, and performed at the constant pressure p₂ and the constant temperature T₁. The chemical reactions pertaining to this first step are those of direct oxidation of the fuel:

(1-x)CH₄ + 2(1 – x)O₂ → (1 – x)CO₂ +2(1 – x)H₂O

(4)

xH₂ + 0.5xO₂ → xH₂O

(5)

Figure 3. The first step of combustion giving the heat input for the second one. HHV is higher heating value, O_2min and N_2min values for stoichiometric combustion.

Figure 3. The first step of combustion giving the heat input for the second one. HHV is higher heating value, O_2min and N_2min values for stoichiometric combustion.

The HHV was evaluated by the enthalpies of formation of involved chemical species, h_f0, see Table 2.

(6)

The physical enthalpy of intaking chemical species were given by a fictitious constant pressure cooling of the intaking gases.

ph = xh_2,H2 + (1 – x)h_2,CH4 + (1 + exo)(2 – 1.5x)h_2,O2 +3.6719(1 + exo)(2 – 1.5x)h_2,N2 [kJ/kmole fuel]

(7)

where the physical enthalpies of intaking gases correspond to T₂.

The second step of constant volume combustion, 2i – 3, is conceived as a heating with dissociation of flue gases and consuming the heat released in the first step, i.e. HHV and physical enthalpy of intaking chemical species (state 2), see Figure 4. The inlet chemical species have the temperature T₁ and pressure p₂. The outlet temperature and pressure, T₃ and p₃, were computed using the mass and energy conservation law and the Mendeleev – Clapeyron state equation.

Figure 4. The second step of combustion consuming the heat released in the first one.

Figure 4. The second step of combustion consuming the heat released in the first one.

The second step of combustion has counted the following chemical reactions, of dissociation and of recombination:

e CO₂ → e CO + 0.5 e O₂

(8)

0.5g H₂O → 0.5g H₂ + g OH

(9)

f H₂O → f H₂ + 0.5f O₂

(10)

0.5h O₂ → h O

(11)

0.5k N₂ → k N

(12)

0.5i H₂ → i H

(13)

0.5l N₂ + 0.5 O₂ → i NO

(14)

0.5m N₂ + m O₂ → m NO₂

(15)

The mass balance equations are stated by:

−

four equations related to the balance of kmoles number of major chemical species, CO₂ and H₂O and O₂ and N₂,

−

eight equations interrelating all chemical species through chemical equilibrium relations and,

−

one mass balance for the whole process 2i – 3.

The balance of kmoles number of major chemical species:

a = (1 – x) – e [kmole]

(16)

b = (2 – x) – g – f [kmole]

(17)

c = exo(2 – 1.5x) + 0.5e + 0.5f – 0.5h – 0.5l – m [kmole]

(18)

d = 3.7619(1 + exo)(2 – 1.5x) – 0.5k – 0.5l -0.5m [kmole]

(19)

For a chemical reaction ν_AA + ν_BB → ν_CC + ν_DD the equilibrium constant is $\mathrm{K}=\frac{{\mathrm{y}}_{\mathrm{C}}^{{\mathsf{\nu }}_{\mathrm{C}}}\cdot {\mathrm{y}}_{\mathrm{D}}^{{\mathsf{\nu }}_{\mathrm{D}}}}{{\mathrm{y}}_{\mathrm{A}}^{{\mathsf{\nu }}_{\mathrm{A}}}\cdot {\mathrm{y}}_{\mathrm{B}}^{{\mathsf{\nu }}_{\mathrm{B}}}}\cdot {\mathrm{P}}^{{\mathsf{\nu }}_{\mathrm{C}}+{\mathsf{\nu }}_{\mathrm{D}}-{\mathsf{\nu }}_{\mathrm{A}}-{\mathsf{\nu }}_{\mathrm{B}}}$where $\mathrm{P}=\frac{\mathrm{reaction}\mathrm{pressure}}{\mathrm{normal}\mathrm{pressure}\left(0.1\mathrm{MPa}\right)}$The natural logarithms of chemical equilibrium constants, for P = 1, were interpolated by polynomials of 7^th order, see Table 3, using values from [10] (p.773).

The equations interrelating all chemical species through chemical equilibrium relations:

(20)

(21)

(22)

(23)

(24)

(25)

(26)

(27)

The mass balance for the whole process 2i – 3

(28)

The energy balance equation:

(29)

The Mendeleev - Clapeyron state equation for gaseous mixtures:

(30)

2.4. The Isentropic Expansion 3 - 4, See Figure 5

During the isentropic expansion, the chemistry of flue gases is also prevailing due to high temperatures and pressures, and therefore the composition of flue gases is changing by variable temperature and pressure. This process was solved defining a proper isentropic exponent quantifying the variable chemical composition of flue gases. The equations defining a reactive isentropic expansion allowed the evaluation of parameters of state 4. The parameters for the state 4 were evaluated through equations 30, 31 and 32, evaluating the flue gases composition through two computational loops regarding relationship composition – temperature and pressure, similar as in the case of constant volume combustion.

(31)

(32)

(33)

3. The Numerical Solving and Results

Figure 7. The CO mole fractions in states 3, 4 and 5, function of excess of oxygen and x.

Figure 7. The CO mole fractions in states 3, 4 and 5, function of excess of oxygen and x.

Figure 10. The NO_x mass ppm [mg/kg] in states 3, 4 and 5, function of excess of oxygen and x.

Figure 10. The NO_x mass ppm [mg/kg] in states 3, 4 and 5, function of excess of oxygen and x.

4. Discussions

5. Conclusions

References

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