3.1. Model Validation
Figure 3 shows the numerical results for stoichiometric mixtures at 300 K and 0.1 MPa, obtained by using the kinetic models of
Table 2 and compared with several measurements [
4,
11,
17,
18,
19,
20,
21,
22]. The figure shows that LFS increases exponentially with H
2 molar content in the fuel blend, in agreement with Ref. [
4]. Both experimental data and the simulations give similar results for low values of X(H
2), whereas some discrepancies arise as hydrogen content increases. The mechanism proposed by Singh et al. [
13] predicts the highest values of LFS for any value of X(H
2), whereas Otomo et al. [
10] mechanism predicts the lowest values of LFS for X(H
2) less than 0.6. For pure hydrogen, the mechanism by Gotama et al. [
11] provides the lowest LFS. However, the dispersion of the numerical data is comparable to the variability of the measurements by different authors.
Figure 4 shows the comparison between the experimental data and the present numerical results in terms of LFS as a function of hydrogen mole fraction of the NH
3/H
2 mixture, in the range 0.0–0.6, at T = 300 K, ϕ = 1 and different pressures, namely 0.1, 0.3 and 0.5 MPa. The conditions used for the experiments are listed in
Table 4.
Figure 4 shows an additional set of experimental data by Han et al. [
5] with pressure equal to 0.1 MPa. For the sake of clarity, this set is not reported in
Figure 3. For all the selected pressures, the numerical results fall between those obtained with the mechanism of Singh et al. [
13] and those obtained with the mechanism of Otomo et al. [
10]. With a hydrogen molar content equal to 60%, the numerical values of LFS range from 56.6 to 71.7 cm/s at 0.1 MPa, from 38.1 to 51.3 cm/s at 0.3 MPa, and from 29.5 to 40.6 cm/s at 0.5 MPa. At 0.3 and 0.5 MPa, although all mechanisms give reasonable results, Zhang et al. [
9] mechanism provides the best agreement with measurements [
4,
11,
22] for any hydrogen molar content.
Thus, the results have been analyzed to assess the influence of pressure on LFS. For this purpose, the percentage reduction in LFS with pressure,
, as a function of the H
2 mole fraction has been evaluated for each of the mechanisms from
Table 2. The expression used to compute
by increasing pressure from
to
reads:
where
and
are the laminar flame speeds for the lower and the higher values of pressure, respectively.
Two different data sets have been considered to analyze the influence of pressure increase from 0.1 to 0.3 MPa and from 0.1 to 0.5 MPa. The mean percentage reduction in LFS has been computed across the five mechanisms for each H
2 mole fraction. Such a percentage reduction is shown in
Figure 5 together with the bars that represent the variability between the maximum and minimum percentage reduction across the five mechanisms. The figure shows that this percentage reduction is less pronounced as pressure increases. For example, at X(H
2) equal to 0.4, where the maximum decrease occurs, reductions of 35% and 48% are observed with a pressure increase by a factor of 3 and 5, respectively. Moreover, the figure shows that, for a molar fraction of H
2 equal to 0.2, the mean values are closer to the upper limit of the range of variability. This is because the mechanism of Otomo et al. [
10] gives a percentage reduction in LFS by increasing pressure from 0.1 to 0.3 MPa and from 0.1 to 0.5 MPa close to 16% and 30%, respectively, whereas higher and closer values are predicted by the other mechanisms. The highest percentage reduction in LFS is predicted by using Gotama et al.’s [
11] mechanism for all X(H
2) values, except for X(H
2) = 0.4. For such a case, the highest reduction is observed by using Singh et al. [
13] mechanism.
In the next section, the influence of pressure will be analyzed to assess whether a further increase in pressure provides the same behavior discussed here.
Several simulations have been carried out in order to study the LFS of different NH
3/H
2 fuel mixtures as a function of equivalence ratio at 0.1 MPa by using the kinetic mechanisms from
Table 2. Six H
2 mole fractions, i.e., 0.0, 0.05, 0.3, 0.4, 0.5 and 0.6, and three temperatures, i.e., 298, 373 and 473 K, have been considered.
Figure 6,
Figure 7 and
Figure 8 show the numerical results obtained at 298, 373 and 473 K, respectively, together with the measured data in
Table 4. Once again, for cases with many available measurements, the dispersion of the numerical data obtained by using different mechanisms is comparable to the variability of measurements by different authors. For all temperatures, numerical results show that the maximum value of LFS is obtained for rich mixtures, with ϕ close to 1.1 or higher, and X(H
2) equal to 0.6.
For lower hydrogen mole fractions, i.e., 0.0 and 0.05, the M3 mechanism predicts higher values of LFS as the equivalence ratio is lower than 1.1, whereas, for richer mixtures, M4 gives higher LFS than the other mechanisms. On the other hand, the M2 mechanism gives the lowest values of LFS, except for lean mixtures, where the lowest values are found with the M1 mechanism. For other H2 mole fractions, M2 gives the lowest LFS, whereas the highest values are obtained by using M5 for most cases. Specifically, M3 and M4 give higher values of LFS than M5 for X(H2) = 0.3 with an equivalence ratio less than 0.8 for each temperature of interest; this is also the case for hydrogen mole fraction equal to 0.4 with the temperature equal to 298 K.
Figure 9 shows the percentage increment of LFS with temperature,
, as a function of equivalence ratio for three values of X(H
2), namely 0.0, 0.3 and 0.6, at 0.1 MPa. Increasing the temperature from
to
,
is evaluated as follows:
where
and
are the laminar flame speeds for the lower and the higher values of temperature, respectively.
is computed for each mechanism, and the mean value is shown in
Figure 9. The bars represent the range of variability for the entire set of reaction mechanisms. Two data sets are plotted. The first set refers to an increase in temperature from 298 to 373 K, and the second set refers to an increase in temperature from 373 to 473 K.
An increase in temperature by 75 K starting from 298 K results in a lower percentage increase in LFS with respect to that obtained with an increase of 100 K starting from 373 K. However, the trends as a function of equivalence ratio are similar for the two data sets, regardless of the mole fraction of hydrogen. The only exception is the case with X(H2) = 0.3 and ϕ equal to 0.7, for which the largest differences are obtained depending on the kinetic mechanism. For each H2 mole fraction, the highest increase in LFS is found for either ϕ = 0.7 or ϕ = 0.8, whereas the minimum occurs at about ϕ = 1.1.
The influence of temperature on LFS decreases with increasing H2 mole fractions, therefore the case with pure ammonia provides the highest increase. Finally, with X(H2) = 0.6, the lowest variability of the numerical results is found. In the next paragraph, the influence of temperature on LFS has been investigated for hydrogen/ammonia mixtures under engine-like thermodynamic conditions.
3.2. A Parametric Analysis
A parametric study has been carried out to analyze the laminar flame speed of NH
3/H
2 mixtures under engine-relevant thermodynamic conditions. Three mechanisms, namely Zhang et al. [
9], Gotama et al. [
11] and Stagni et al. [
12], have been chosen since they provide results that are in better agreement with available experimental data at pressure (
Figure 4) and temperature (
Figure 7 and
Figure 8) conditions above the ambient. Hence, the M2 and M5 mechanisms have not been employed for the parametric analysis discussed in this section. Indeed, for the stoichiometric mixtures of
Figure 4, the M5 mechanism [
13] overpredicts LFS measurements at 300 K with pressure equal to 0.1 and 0.3 MPa and a molar fraction of H
2 greater than 0.4. For cases at ambient pressure and temperature equal to 373 K (
Figure 7) and 473 K (
Figure 8), the M5 mechanism overestimates the measurements when the H
2 molar fraction is higher than 0.3 for all equivalence ratios considered in this work. On the other hand, the M2 mechanism [
10] underestimates the experimental data of
Figure 7 and
Figure 8 with a molar fraction of H
2 higher than 0.3 for all equivalence ratios.
First, the influence of pressure, in the range 0.1–3.0 MPa, has been investigated by considering different NH
3/H
2 mixtures, with three equivalence ratios, namely 0.8, 1.0 and 1.2, at 300 K. The results obtained with the M1 mechanism are shown in
Figure 10. Similar trends are obtained with the M3 and M4 mechanisms, though they are not shown for the sake of conciseness. A semi-logarithmic scale is used in order to assess whether a linear trend between the logarithm of LFS and the H
2 mole fraction, as proposed by Ichikawa et al. [
4] based on experimental data up to 0.3 MPa for stoichiometric mixtures, occurs for higher pressures and lean/rich mixtures. Furthermore, for each pressure, X(H
2) ranges from 0.0 to 1.0, whereas in Ref. [
4] the upper limit of the H
2 molar fraction has been reduced as pressure increases. Specifically, in Ref. [
4], X(H
2) ranges from 0.0 to 1.0 at 0.1 MPa, from 0.0 to 0.6 at 0.3 MPa, and from 0.0 to 0.4 at 0.5 MPa.
From
Figure 10, a quasi-linear dependence between the logarithm of LFS and the H
2 mole fraction is observed, according to the following equation:
where LFS
0 is the laminar flame speed of pure ammonia and α is the slope of the linear interpolation of the numerical data, computed by means of the method of the least squares. The coefficient of determination, R
2, has also been considered to assess the accuracy of such a fitting. R
2 is evaluated as:
where n is the number of data,
is the i-th laminar flame speed,
is the corresponding fitting value and
is the mean value of the computed LFSs.
For all mechanisms, R
2 decreases as pressure increases for any equivalence ratio, thus suggesting that the accuracy of the linear correlation worsens with increasing pressure. In order to address this issue, α and R
2 have been computed by fitting the numerical data, obtained by using the M1 mechanism, up to X(H
2) equal to 0.6. Indeed,
Figure 10 shows that linear correlations (solid lines) accurately fit the numerical data with H
2 mole fraction ranging from 0 to 0.6. The results are summarized in
Table 5, where the determination coefficient is denoted as
, which is also given in
Figure 11 as a function of pressure for the three equivalence ratios under consideration. For each equivalence ratio, α monotonically decreases as pressure increases, which suggests that the influence of hydrogen addition to the mixture is reduced. This is because, as a matter of fact, with more hydrogen in the fuel mixture, mass diffusivity should increase but this is counterbalanced by the increase in pressure. For each pressure value, α decreases with increasing equivalence ratio, since the H
2 Lewis number increases and thermal diffusion plays a more important role. On the other hand,
is always higher than 0.99, it decreases as ϕ increases and approaches 1.0 for lean mixtures and low pressures, as shown in
Figure 11.
decreases with increasing pressure for the lean case, reaches a minimum value at 1.0 MPa under stoichiometric conditions, and only slightly changes for the rich case.
A further improvement on the fitting of the numerical data for the entire range of H
2 mole fractions is proposed as a second-degree polynomial fit, which reads:
where β
1 and β
2 are the correlation coefficients, given in
Table 5 together with the coefficients of determination,
, which are also shown in
Figure 11. The second-degree polynomial regressions are shown as dashed lines in
Figure 10. Such regressions are computed by using the method of least squares, i.e., by minimizing the sum of the squares of the difference between the numerical value of LFS for each X(H
2) and the value provided by the polynomial fit. The figure shows a very good fitting of the numerical data for the entire range of H
2 mole fractions. Moreover,
Table 5 and
Figure 11 show that
is always higher than
, thus suggesting that the second-degree polynomial fit is also an improved approximation in the range [0.0–0.6]. β
1, like α, decreases as pressure and equivalence ratio increase, whereas β
2 has the opposite trend, i.e., it increases as pressure and equivalence ratio increase. It is worth noting that β
2, which represents the concavity of the second-degree polynomial, is negative for cases with pressure equal to 0.1 MPa and ϕ equal to 0.8 and 1.0. Moreover,
Figure 11 shows that
has a maximum value of 1.0 MPa for all the three equivalence ratios under consideration.
Figure 12 shows LFS as a function of pressure in a semi-logarithmic scale for different H
2 mole fractions in the fuel mixture and different equivalence ratios using the M1 mechanism from
Table 2 at T = 300 K. As expected, LFS decreases as pressure increases for all cases. The reduction is almost linear when pure hydrogen is used, while for the other cases, a more noticeable influence of pressure is observed especially with pressures lower than 0.5 MPa.
In order to assess the influence of pressure,
Figure 13 shows the percentage reduction in LFS, with respect to the case at 0.1 MPa, as pressure increases for three equivalence ratios. As previously, the lines represent the mean reduction across the three mechanisms used for the computations, i.e., M1, M3 and M4, whereas the bars represent the range of variability between the maximum and the minimum reduction for each H
2 molar fraction. The figure shows that the variability of the numerical results is generally lower for intermediate values of X(H
2). This is less evident for ϕ = 1.2, but it still occurs, especially for higher pressures.
The figure shows that the largest LFS reduction is observed with X(H2) in the range [0.4–0.6], depending on the value of pressure and ϕ. For the highest H2 mole fractions, the LFS percentage reduction decreases and reaches the minimum for the combustion of pure hydrogen.
Furthermore, the influence of pressure on LFS is more pronounced at lower pressures. For instance, for ϕ = 0.8 and X(H2) = 0.0, by increasing pressure from 0.1 to 0.3 MPa and from 0.1 to 1.0 MPa, LFS decreases by about a factor of two, i.e., 30% and 58%, respectively. For the same case, at 2.0 MPa and 3.0 MPa, the LFS percentage reduction is about 70% and 75% compared to LFS under atmospheric conditions.
Finally, stoichiometric mixtures of NH
3/H
2 with X(H
2) up to 0.8 with temperature equal to 800 K and pressure varying from 0.5 to 8.0 MPa, which represent engine-like thermodynamic conditions, have been investigated. For the sake of conciseness, the simulations have been performed using only the mechanism by Zhang et al. [
9]. The results are shown in
Figure 14, where numerical data are given by symbols, whereas the correlations are plotted by using a solid line for the first-degree polynomial and a dashed line for the second-degree polynomial. The first-degree polynomial has been calculated for 0.0 ≤ X(H
2) ≤ 0.6, whereas the second-degree polynomial has been extended to the entire range of the hydrogen molar fraction.
Table 6 summarizes the correlation coefficients, as well as the coefficients of determination of such fittings. The table shows that
is less than that obtained with temperature equal to 300 K, indicating that the first-degree approximation is even less accurate as temperature increases. On the other hand, the coefficient of determination obtained with the second-degree polynomial is always higher than 0.999, thus suggesting that the proposed fitting model is adequate and very accurate. Both correlation coefficients α and β
1 show a monotonic decrease with increasing pressure, as already seen at T = 300 K, whereas β
2 increases up to 2.0 MPa and then decreases. By comparing α and β
1 with those computed at lower temperature for the same pressure, it is noticeable that both coefficients decrease as temperature increases. In
Figure 15, the determination coefficients as a function of pressure are given. The figure shows that
and
have opposite trends, with a minimum and a maximum value, respectively, at 2.0 MPa.
Figure 16 shows the percentage reduction in LFS with increasing pressure from 0.5 to 1.0, 2.0, 4.0 and 8.0 MPa, as a function of H
2 mole fraction for the stoichiometric fuel mixture at 800 K. Only the mechanism by Zhang et al. [
9] has been used; therefore, bars are not provided. For all pressure increments, the trends are similar: LFS reduction initially increases as H
2 mole fraction increases, reaches a maximum, and then decreases. As pressure increases from 0.5 to 1.0 MPa, LFS decreases by 15% with pure ammonia and reaches a maximum decrease of about 25% where X(H
2) is about 0.55. As pressure increases from 0.5 to 2.0 MPa, LFS reduction is about 30% with pure ammonia, whereas the maximum reduction is about 45% where X(H
2) is approximately 0.6. A further increase in pressure leads to a further reduction in LFS, up to about 50% for pure ammonia when pressure increases from 0.5 to 8.0 MPa, whereas the maximum shifts towards higher values of H
2 mole fraction, reaching a value of about 73%. Therefore, the more the pressure increases, the less it influences the LFS.
Finally, the influence of temperature on LFS has been analyzed by comparing the numerical results at 300 and 800 K. As expected, LFS increases with temperature for all pressures and mixture compositions.
Figure 17 shows the percentage increment of LFS as temperature increases from 300 to 800 K as a function of H
2 mole fraction in the fuel mixture for three different pressures, namely 0.5, 1.0 and 2.0 MPa, for ϕ = 1. The figure shows that the influence of temperature on LFS is higher for pure ammonia, and it reduces almost linearly as H
2 mole fraction increases. Furthermore, the increase in LFS with temperature is higher as pressure increases. As an example, for the case of pure ammonia at 2.0 MPa, the LFS at 800 K is 10.3 times the LFS at 300 K, whereas for the mixture with 80% by mole of H
2 at 0.5 MPa the LFS at 800 K is 6.4 times that at 300 K.
3.3. Structure of the NH3/H2 Flame
The steady laminar flame structure of stoichiometric NH
3/H
2 mixtures has been analyzed at 800 K and 4.0 MPa. These thermodynamic conditions are mostly encountered at spark timing of SI engines. Two cases with and without hydrogen addition have been compared, i.e., X(H
2) = 0.4 and X(H
2) = 0.0. The kinetic mechanism of Zhang et al. [
9] has been used for the simulations.
Figure 18 shows the temperature, reactants and major products profiles for the two cases.
The figure shows that the burnt gas temperature with hydrogen addition is above 2500 K, whereas a lower burnt gas temperature occurs for the pure ammonia case. The flame thickness
, has been evaluated by using the following relation:
where
and
are the burnt and unburned gas temperatures, respectively. The flame thickness is 21
and 42
for the cases with and without hydrogen, respectively. It means that, with 40% by mole of H
2 in the fuel blend, the thickness is halved compared to the case of pure ammonia.
Figure 19 shows the major intermediate species profiles of
flames for the cases with and without hydrogen addition. When hydrogen is added to the fuel blend, intermediate species are produced and depleted faster than those of the case of pure ammonia, and higher peak molar fractions occur.
The main oxidation reaction of ammonia is
, which produces
, which in turn is oxidized mainly by OH through the reaction
, as well as by H and O radicals. However, in the pre-heating zone, at low and medium temperatures,
is quickly converted to
through the reaction
. Indeed, as shown in
Figure 19 for both cases with and without hydrogen, in the pre-heating zone,
mole fraction is higher than that of the other chemical species. After the peak,
decomposes into lighter molecules such as NO, OH and H. On the other hand, at high temperature
is also depleted through the reaction
which produces HNO, which reacts with O, OH and O
2 to produce NO. NO is also produced by the reaction
. As shown in
Figure 18, hydrogen addition in the fuel mixture reduces the amount of ammonia, so NO consumption through the reactions with NH and
is reduced, leading to higher NO concentrations in the burnt gases, as shown in
Figure 19.
Furthermore, the presence of hydrogen increases the amount of H radicals through the reactions
and
, and, as a result, O radicals produced by
also increase. Thus, higher HO
2 concentrations occur in the pre-heating zone. Finally, both the role of H radicals in the conversion of ammonia to NH
2 and NH and the role of O radicals in the conversion of NH
2 and NH to HNO, NO and N
2O increase, as shown in
Figure 19, making the mixture more reactive and resulting in a higher laminar flame speed, as shown in
Section 3.2.