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Comparison of Two Methods to Predict Boundary Layer Flashback Limits of Turbulent Hydrogen-Air Jet Flames

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Abstract

Flame flashback into the premixer is a serious issue in gas turbine combustion, especially for high hydrogen content fuels. Of particular interest is the risk of upstream flame propagation inside the wall boundary layer. Consequently, methods to predict the minimum flow velocities to prevent boundary layer flashback are sought by designers. In the first part of this paper two methods to predict boundary layer flashback limits are summarized and compared. The first method is a Damköhler correlation based on non-dimensional parameters developed at University of California Irvine (UCI). The correlation was developed based on the gathered experimental data at elevated pressures and temperatures (i.e. p = 3–7 bar, T u = 300–500 K, ϕ = 0.3–0.6) and successfully applied to a commercial gas turbine combustor. Due to its simplicity the Damköhler correlation is attractive for the design of gas turbine burners. But its applicability is limited to the turbulent combustion regime for which it was originally designed. The second method is called the “flame angle theory”. It was developed at Technische Universität München (TUM) and is based on a description of the physical process of boundary layer flashback. This method has been validated with experimental data at atmospheric pressure and a wide range of preheating temperatures and equivalence ratios (T u = 293–673 K, ϕ = 0.35–1.0). Since it describes the physical process of boundary layer flashback based on a set of sub-models it should be generally applicable to all operating conditions if the sub-models are appropriate. To verify this, the flame angle theory is applied to high pressure conditions in the second part of this paper. A comparison with results from the Damköhler correlation shows that the predicted flashback limits are in a reasonable range. However, the degree of agreement between Damköhler correlation and flame angle theory strongly depends on equivalence ratio because the Damköhler correlation does not account for the changing susceptibility of different hydrogen-air mixtures to flame stretch. For that reason, a modified Damköhler correlation has been derived at TUM from the flame angle theory and is presented in the third part of this paper. This correlation combines the advantages of the other two methods as it features high usability and is generally applicable to all operating conditions.

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Notes

  1. In an e-mail conversation with Law and Liang it was assured that the method used by [23] delivers a similar maximum if the region around stoichiometry is resolved.

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Acknowledgements

This publication has been produced with support from the BIGCCS Center, performed under the Norwegian research program Centers for Environment-friendly Energy Research (FME). The authors acknowledge the following partners for their contributions: ConocoPhillips, Gassco, Shell, Statoil, TOTAL, GDF SUEZ and the Research Council of Norway (193816/S60).

Furthermore, the U.S. Department of Energy and the University Turbine Systems Research program (Contract No. DE-FE0011948; Steven Richardson Contract Monitor; Rich Dennis Program lead) supported the generation of some of the results shown in this paper.

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Correspondence to Vera Hoferichter.

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Appendix A: Changes Made in Flame Angle Theory

Appendix A: Changes Made in Flame Angle Theory

Compared to the original publication of the flame angle theory by [16], the following changes were made: The turbulent macroscale is set to Λ = 0.5 h in order to account for symmetrically evolving flow structures at the burner exit. Furthermore, the global activation energy is defined as introduced in Appendix A. In order to compensate the effect on the turbulent burning velocity, the model constant C S is modified to 2.6. Apart from that, the flame generated turbulence correlation in Eq. 16 is here based on S l,0 instead of \(\overline {S}_{\text {l,s}}\) in order to stay closer to the original correlation proposed by [21] (cf. [16]). Therefore, the coefficients G 1G 3 had to be changed to obtain the same velocity fluctuations.

1.1 A.1 Unstretched laminar burning velocity

In this work, the unstretched laminar burning velocity at preheated and high pressure conditions is calculated from one-dimensional free flames in Cantera 2.2 [19] with the reaction mechanism of [20] instead of using the power law approach from [16]. The resulting unstretched burning velocities at atmospheric pressure are presented in Fig. 15. The experimental values by [22] used at ambient temperature are shown as well. It should be noted that at ϕ = 0.35 the burning velocity at 473 K seems low compared to the 293 K case. A reason might be the fact that S l,0 is underestimated by the free flame calculations at low equivalence ratios. This has to be kept in mind regarding the model validation in Section 3.2.

Fig. 15
figure 15

Unstretched laminar burning velocities at atmospheric pressure used in flame angle theory

1.2 A.2 Global activation energy

In [16], the global activation energy was defined based on calculated data given by [23] for ambient temperature and pressure. According to [23], the global activation energy can be defined as

$$ E=-2 R \frac{\partial \ln(\rho_{\text{u}} S_{\text{l},0})}{\partial(1/T_{\text{b}})} \, . $$
(27)

For an assumed adiabatic system the product temperature T b can be set to the adiabatic flame temperature T ad. A variation of adiabatic flame temperature is achieved by varying the amount of nitrogen dilution \(X_{\text {N}_{2}}\) in the reactants from \(X_{\text {N}_{2}, 1}=X_{\text {N}_{2},\text {air}}-{\Delta } X_{\text {N}_{2}}\) to \(X_{\text {N}_{2}, 2}=X_{\text {N}_{2},\text {air}}+{\Delta } X_{\text {N}_{2}}\). It is assumed that the partial derivative in Eq. 27 can be replaced by

$$ E=-2 R \frac{\ln(\rho_{\text{u}}(X_{\text{N}_{2}, 1}) S_{\text{l},0}(X_{\text{N}_{2}, 1}))-\ln(\rho_{\text{u}}(X_{\text{N}_{2}, 2}) S_{\text{l},0}(X_{\text{N}_{2}, 2}))}{1/T_{\text{ad}}(X_{\text{N}_{2}, 1})-1/T_{\text{ad}}(X_{\text{N}_{2}, 2})} \, . $$
(28)

The required mixture parameters can be calculated with Cantera 2.2 ([19]) and the reaction mechanism of [20] for hydrogen-air mixtures.

The global activation energies of [23] are shown in Fig. 16 for two different pressures compared to results from the calculation approach presented in Eq. 28. At lean conditions, the global activation energy decreases with equivalence ratio. In the calculated data a local maximum at stoichiometry is observed which is not found in the results of [23]. However, this region was not fully resolved by [23] as they focused on rich conditions.Footnote 1 It is unclear if the observed maximum represents a physical effect. At rich conditions, the calculated activation energies match the data of [23] at both pressure levels.

Fig. 16
figure 16

Global activation energy of hydrogen-air mixtures

Based on Eq. 28 the preheating temperature and pressure dependence of E is illustrated in Fig. 17. At lean conditions preheating significantly reduces the global activation energy whereas at rich conditions only a small influence is found. At p = 20 bar and ϕ < 0.5 a drop of global activation energy can be seen for the lower preheating temperatures. As it does not seem reasonable that the activation energy should drop approaching the flammability limit, this drop might be a numerical artifact caused by the low unstretched laminar burning velocities at these conditions.

Fig. 17
figure 17

Global activation energy of hydrogen-air mixtures at different preheating temperatures and pressures calculated with Eq. 28

In the context of the flame angle theory, a correlation based representation of the global activation energy is beneficial to reduce the computational effort. Due to the low influence of preheating temperature on global activation energy above ϕ = 0.7 and the uncertainty in the results of Eq. 28 at lean conditions, the temperature and equivalence ratio dependence of E is neglected choosing a reference point at ϕ = 0.8. The dependence of global activation energy at ϕ = 0.8 on pressure as computed with Eq. 28 is illustrated in Fig. 18. It can be seen that the global activation energy can be represented with a logarithmic fit

$$ E[\text{kcal}/\text{mol}]= 8.4986\,\ln(p[\text{bar}])+ 30.1050 \, . $$
(29)
Fig. 18
figure 18

Pressure dependence of global activation energy of hydrogen-air mixtures. Values are calculated at ϕ = 0.8 and T u = 293 K

This different definition of the global activation energy compared to [16] only leads to small changes in the calculated Markstein length but significantly reduces the effort to apply the flame angle theory at varying pressure and preheating temperature.

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Hoferichter, V., Hirsch, C., Sattelmayer, T. et al. Comparison of Two Methods to Predict Boundary Layer Flashback Limits of Turbulent Hydrogen-Air Jet Flames. Flow Turbulence Combust 100, 849–873 (2018). https://doi.org/10.1007/s10494-017-9882-2

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