Application of a Turbulent Jet Flame Flashback Propensity Model to a Commercial Gas Turbine Combustor

Carbon emissions from the combustion of fossil fuels are a concern within the energy generation sector. As a result, while natural gas is currently plentiful, strategies for using fuels derived from renewable sources (i.e., alternative fuels) must still be pursued if a reduction in carbon signature is to be achieved. Many of these potential fuels contain some level of hydrogen. In the development of modern power generation systems, gas turbines have been continuously evolving to cope with the operability issues associated with alternative fuels [1,2]. While the combustion of high hydrogen content fuels reduces carbon-containing pollutants, NO_x emissions are still an inevitable result of fuel/air combustion. Hence, lean premixed combustion of high hydrogen content fuels has been implemented along with a precise control of combustion temperatures to achieve a reduction in all the pollutant species. Considering the narrow operating range of the combustor to meet these requirements, further attention needs to be given to addressing the operability issues (e.g., lean blow off, flashback, and dynamic stability) associated with alternative fuels [1]. In the case of high hydrogen content fuels, curtailing the high propensity for flashback is of primary concern. Gas turbines fed by high hydrogen content fuels are especially prone to flashback due to the high flame speed and low quenching distance associated with these fuels [2].

Flashback propensity of fuel/air mixtures is the likelihood of flashback occurring as a result of a change in the parameters studied. Four mechanisms for flashback of premixed flames have been identified [2]: (1) core flow flashback, (2) boundary layer flashback, (3) combustion-induced vortex breakdown (CIVB), and (4) combustion instability induced flashback. Boundary layer flashback is considered the primary mode of flashback in jet/Bunsen flames. Despite the fact that the boundary layer flashback of jet flames has been frequently studied in the literature, further verification is needed for high hydrogen content fuels at gas turbine relevant conditions. Hence, boundary layer flashback is the focus of the current study.

Numerous studies of boundary layer flashback can be found in the literature, which typically characterize behavior in terms of a “critical velocity gradient.” Boundary layer flashback occurs when the burning velocity exceeds the flow velocity near the wall surface. The bulk velocity at which the flashback occurs corresponds to a critical velocity gradient calculated at the wall. As a result for a given equivalence ratio, higher flashback propensity is associated with higher critical velocity gradients. Similarly, the flashback propensity increases with a decrease in equivalence ratio for a given bulk velocity. The earliest studies investigated the effects of various parameters including preheat temperature, fuel composition, burner diameter, and burner material on flashback of laminar flames [3–15]. The correlations developed under laminar conditions are in good agreement with the experimental data, which indicates the ability of the velocity gradient concept to predict flashback [10]. While the critical velocity gradient theory neglects the interaction between the flame and incoming reactants, it is nevertheless capable of predicting experimental results. The existence of a reverse flow region near the wall boundary has been recently observed even for the laminar case prior to the onset of flashback [16–18], confirming the nonphysical nature of critical velocity gradient theory for confined flames.

In an effort toward understanding flashback behavior for a wider range of applications, a limited number of flashback studies have been performed under turbulent conditions [19–24]. While these studies investigated the effects of turbulence on flashback, the range of Reynolds numbers covered (⁠$1800<ReD<104$⁠) is still not representative of practical gas turbines (i.e., $104<ReD<106$⁠). Indeed, the turbulent combustion regime of a particular flame is largely determined by the turbulent characteristics of reactants at the flame front.

In terms of application to gas turbine premixers, material temperatures must be considered as the ambient temperature will be elevated in general. The effect of thermal coupling between the burner head and flame on flashback of turbulent hydrogen flames was first studied by Bollinger and Edse [22], who observed that uncooled burners have greater flashback propensity than cooled burners. This was attributed to a decrease in quenching distance at higher temperatures. Furthermore, they concluded that burners constructed of materials with higher thermal conductivity reduced the propensity of boundary layer flashback. It is evident that the tip temperature of a particular burner head is a function of the total heat transfer balance. The heat transfer rate to the burner head increases significantly as quenching distance decreases resulting in higher tip temperatures, which in turn further decreases the quenching distance. In addition to being affected by heat transfer to the burner head, tip temperature is also affected by the thermal properties of the burner material. Quenching distance is a function of various parameters including mixture thermal properties, combustion properties, burner material, tip temperature, preheat temperature, and pressure. An increase of pressure or equivalence ratio increases the heat release rate and results in a lower quenching distance [25]. The temperature profile near the wall surface has a direct impact on the quenching distance and is influenced by the wall temperature. Furthermore, using burner material with a lower thermal conductivity increases the maximum wall heat flux and tip temperature resulting in lower quenching distance [26].

Recent numerical and experimental studies have focused on the interaction between the flame and incoming reactants at the onset of flashback [27–29]. The presence of a back flow region ahead of upstream propagating flame prior to the onset of flashback is different from the previous simplified assumption neglecting the interaction of the flow field with premixed flame. The height of the back flow region (⁠$y+=20$⁠) is considerably larger (approximately ten times for the studied cases) than the quenching distance (⁠$y+=2$⁠) based on direct numerical simulation of turbulent boundary layer flashback [28,29]. A similar value of y⁺= 25–30 was reported for the height of reversal flow region in the experimental study of boundary layer flashback for hydrogen flames confined in ducts [16–18]. The existence of the reverse flow region near the wall boundary contributes to higher flame propagation velocity. Although the existence of the back flow region height in the buffer layer has been observed from both numerical and experimental studies of confined flames, the extension of this conclusion to higher Reynolds number requires further investigation [16,28]. Indeed, analysis of this recent phenomenological concept of flashback needs to be studied at higher pressures and higher Reynolds numbers in order to make a general conclusion.

The turbulent boundary layer flashback of syngas at atmospheric pressure has been recently studied in more detail by considering different compositions of hydrogen, carbon monoxide, and methane [30,31]. The thermal coupling effect between the burner and flame was also studied in these papers. However, the range of Reynolds number covered in all the previous studies of high hydrogen content fuels is small compared to practical gas turbine premixer applications.

While a considerable amount of work has been performed to characterize flashback, very little has been done to quantify the effects of pressure. Fine studied the flashback propensity of turbulent hydrogen–air flames at subatmospheric pressures [20]. Daniele et al. investigated the flashback propensity of turbulent syngas jet flames at high pressure [32]. Although these studies have shed some light on understanding the effects of varying pressure on flashback propensity, until very recently, no comprehensive research had been conducted to fully characterize flashback propensity of jet flames at elevated pressures. To address this deficiency, new data on flashback propensity of turbulent hydrogen–air jet flames at elevated temperatures and pressures and for various burner materials were gathered by the authors of the present paper [33]. The range of Reynolds number studied in this experiment is $5×104<ReD<3×105$⁠.

Figure 1 illustrates the facility used to gather these recent flashback data. The full description of the experiment can be found elsewhere [33]. The air is heated to the desired preheat temperature, and the rig is pressurized by the compressed air entering through two flanges located at the top section in Fig. 1. The air enters the venturi in which the fuel is injected at the low-pressure section leading to a high mixing level. The mixture passes through a perforated plate located immediately after the exit section of venturi to create a uniform velocity profile as illustrated in Fig. 1. The mixture enters the premixing tube with the inner diameter of 35 mm and length of 30 cm. The premixing tube is long enough to achieve a uniform concentration and fully developed flow at the exit of the burner head (inner diameter of 25.4 mm), where the mixture is injected into the combustor. The flame is contained inside the quartz tube combustor liner (15 cm in inner diameter and 19 cm in length). Two thermocouples (TCs) were cemented to the opposite sides of the burner tip to measure the tip temperature continuously. A pressure transducer was used to record the pressure drop across the flame (i.e., between the premixer and combustion chamber). Along with visual observation, these measured values are used simultaneously to detect flashback. The flame propagates upstream of the flow at the onset of flashback causing a clear peak in both tip temperature and pressure difference measured by thermocouples and pressure transducer.

The laminar flame speed varies inversely with pressure (⁠$SL∝P−bp$⁠) [34,35]. Consequently, the laminar flame speed reduces as the pressure increases. In other words, the penetration distance remains as the dominant parameter in increasing flashback propensity at higher pressure from this perspective.

Previous work shows that Eq. (1) provides promising performance for the data gathered in a single burner jet flame [33] and that it matched the limited data set of Daniele et al. [32]. However, it was not evaluated against practical configurations. As a result, the objectives of the present work are to:

• compare predicted flashback propensity in an annular combustor configuration as found in a commercial 60 kW gas turbine

• provide additional interpretation of the flashback propensity at high pressure as a function of the parameters studied

The approach taken in the present effort is to analyze experimental results from two different test platforms: a combustor from a commercially available microgas turbine operating at atmospheric pressure and a commercial 60 kW gas turbine engine/generator (i.e., a Capstone C-60 microturbine generator).

A commercially available microgas turbine combustor was configured to investigate the flashback propensity for mixtures of H₂/CO and H₂/NG operating at atmospheric pressure and preheat temperatures between 300 K and 700 K. Measurements were performed at injector bulk velocities between 20 m/s and 45 m/s.

In addition, flashback data were obtained for a full commercial C-60 engine operated on mixtures of H₂/NG as well as H₂/CO at different engine loads. Flashback in the engine was detected using instrumented injectors.

Finally, the paper is concluded with an interpretation of the high-pressure data and a critical evaluation of the developed correlation.

A combustor from a Capstone C-60 microturbine, indicated in Fig. 2, was adapted to be operated at 1 atm and to provide visual access to the reaction [36]. To achieve this goal, the combustor was extracted from the engine, and some turbomachinery parts required for operation in the engine were removed to make the annular combustor visually and physically accessible. The engine normally operates on natural gas at a pressure of approximately 4 atm. A manifold was developed to feed air to the combustor as it would be in the engine, and a fuel blending system was utilized to vary the fuel content and flow rate fed to the combustor.

The fuel/air mixture enters the combustor through the six injectors located tangentially at two different planes along the combustor axis according to Fig. 2. The inner diameter of the burner head for all the injectors is 25.4 mm with Reynolds number varied between $1×104<ReD<3×104$⁠. Air inlets ports were adapted to simulate the actual flow field and primary zone structure found in the microturbine generator. The incoming air was heated to reach the desired preheat temperatures of 300 K and 672 K. Two sets of experiments were conducted with two injectors on plane A (Fig. 3(a)), while other injectors on plane B (Fig. 3(b)) were not fueled and preheated air constantly entered through them. Air mass fractions entering from different holes in the primary and dilution zones were modified to represent the actual values for this gas turbine engine.

For the first case, natural gas was injected through one injector at constant equivalence ratio of 0.7, while the equivalence ratio of the other injector was varied for two fuel mixtures, H₂/CO and H₂/NG, to approach flashback. The preliminary result of this experiment was presented in a previous publication, which did not focus on the critical velocity gradient aspect [36]. For the second case, the equivalence ratio of the two injectors was varied simultaneously to reach the onset of flashback. In this case, both injectors were instrumented and whichever flashed back first was considered as flashback for the test.

Fuel/air mixtures were prepared by four Alicat^® mass flow controllers, enabling the operator to independently adjust the equivalence ratio of the two injectors. Control of the fuel/air mixing was done with the existing C-60 injector basically designed for natural gas, as it is illustrated in Fig. 4. The air mass flow rate and preheat temperature were independently controlled by proportional-integral-derivative controllers.

Two thermocouples (TC-A and B) were placed at the burner head to continuously report the tip temperature. Two measured tip temperatures at opposite sides were different due to the location of the burner rim relative to the primary zone. Indeed, the side of the burner which is closer to the primary zone is exposed to the higher temperature, while the opposite side located close to the combustion liner experiences a lower temperature. Tip temperature is a crucial parameter in triggering flashback and can also be used to detect flashback by reporting a sudden increase in its value. The TC-air is placed in injector air hole (Fig. 4) to report the temperature of the mixture right before the injection and was also used as a flashback indicator.

Furthermore, a pressure probe is used to measure the pressure at indicated location inside the premixing tube, see Fig. 4. Flame propagation into the burner head results in a pressure rise, used as the second method along with tip temperature measurements to detect flashback. Additionally, since this experiment is conducted at atmospheric pressure, the audible sound with a clear pitch can be used as an indicator of flashback for the operator. The experiment was conducted at two preheat temperatures of 300 K and 672 K with various fuel compositions, i.e., H₂/CO with variation of CO from 0% to 70% and H₂/NG with variation of NG from 0% to 60% based on the volume concentration.

Prior to each experiment, preheated air was allowed to flow through the combustor and injectors for a sufficiently long time to ensure thermal equilibrium. Thermal equilibrium was verified through measurements of injector tip temperatures and combustor surface temperature. Between tests, the burner head was cooled back to its initial temperature by running the preheated air through the combustor without fuel. A standard procedure was used for the experiment to approach flashback. The air mass flow rate is set to the desired value corresponding to the specific velocity at the burner head, and then, the equivalence ratio is gradually increased to reach flashback.

Data were also gathered from a commercial Capstone C-60 60-kW natural gas fired microturbine generator (MTG) as shown in Fig. 5. The same combustor configuration used for the atmospheric studies was also used in the full engine tests. Experiments were conducted for H₂/CO with variation of CO from 60% to 90% and H₂/NG with variation of NG from 30% to 70% at operating conditions summarized in Table 1. The engine operated at Reynolds number of $3×104<ReD<6×104$ in this experiment. The engine control system automatically varies the fuel flow rate in order to maintain turbine exit temperatures and control engine speed; therefore, equivalence ratio could not be varied during these tests to induce flashback. To approach flashback, the concentration of hydrogen in the fuel was increased until flashback occurred. More details regarding the engine test bed can be found elsewhere [37,38].

For the engine tests, the same instrumented injectors shown in Fig. 4 were used in the engine. Data from the thermocouples were used to detect flashback and to monitor injector tip temperature. A specially developed fuel mixing system was used to blend mixtures of natural gas and hydrogen as well as hydrogen and carbon monoxide. Additional details on the mixing system can be found elsewhere [37–39].

Figure 6 illustrates the variation of equivalence ratio at flashback as a function of hydrogen concentration in H₂/CO mixture. The results are presented for the two sets of experiments (one-injector or two-injector) described in the previous section, Atmospheric Test. The mass flow rate was kept constant resulting in the same velocity at the injector exit for a given preheat temperature. Increasing the preheat temperature decreases the mixture density and consequently causes higher velocity for a constant mass flow rate. As indicated in Fig. 6, increasing the hydrogen concentration in the fuel mixture leads to higher flashback propensity for a given mass flow rate. An increase of preheat temperature results in flashback at lower equivalence ratios indicating higher flashback propensity. Some discrepancy between the result of different tests at preheat temperature of 300 K is observed. This is due to the difficulty of stabilizing a nonpreheated flame at such high velocities.

As shown in Fig. 6, the results with two injectors simultaneously varying are in good agreement with the results obtained with only one injector varying. Overall, a linear trend between the variation of hydrogen concentration and equivalence ratio at flashback is observed.

The variation of equivalence ratio at flashback with hydrogen concentration for H₂/NG mixture is shown in Fig. 7. The overall trend for both preheated and nonpreheated cases is similar to H₂/CO mixture except for the two-injector case. Indeed, a clear difference between the results of the one-injector and two-injector cases is observed. The main reason is that the premixed flame preserved its original conical shape for the two-injector case resulting in higher tip temperatures and hence lower quenching distance. Consequently, the equivalence ratio at flashback decreases compared to the single injector case which has lower tip temperatures. The results for 73% hydrogen for the 300 K preheat case are quite varied again due to the difficulty in stabilizing the flame in the absence of preheat. The effect of hydrogen concentration on flashback propensity is pronounced for nonpreheated mixture. This can be seen in Figs. 6 and 7, where the slope of the hydrogen concentration versus equivalence ratio at flashback curves is steeper for the nonpreheated cases.

As a first step toward applying the correlation in Eq. (1), Fig. 8 shows the variation of critical velocity gradient as a function of adiabatic flame temperature. The critical velocity gradient is calculated using the Blasius correlation developed for smooth pipes, by the following equation [40]:

The thermodynamic properties required are calculated based on the fuel/air mixture at the injector inlet conditions. Figure 8 presents the critical velocity gradient as a function of adiabatic flame temperature. Both equivalence ratio and hydrogen concentration affect the critical velocity gradient. The critical velocity gradient increases with an increase of adiabatic flame temperature. The slope of each trend line is indicated by m in Fig. 8. The H₂/CO mixture has a higher slope compared to H₂/NG mixtures for both preheated and nonpreheated cases, indicating a stronger dependency on hydrogen concentration. Higher flashback propensity is associated with H₂/CO mixtures for a given adiabatic flame temperature. It is also evident that the preheat temperature significantly increases the flashback propensity of both fuel mixtures.

As shown in Fig. 8, the adiabatic flame temperature alone cannot capture the effects of preheat temperature and fuel composition. This is consistent with previous observations [33]. The traditional way to compare flashback propensity of different fuels is to keep the equivalence ratio fixed and observe at which particular velocity flashback occurs. However, both fuel and air mass flow rates should be varied simultaneously to keep the equivalence ratio constant, which makes this approach challenging for the present data.

Another approach for comparing flashback propensity is to plot the variation of critical velocity gradient with laminar flame speed as shown in Fig. 9. The higher flame speed results in higher flashback propensity. Yet preheat temperature effects are not captured by this approach.

The critical velocity gradient can also be represented as a ratio of laminar flame speed to the penetration distance. The penetration distance is approximated by the quenching distance, which is proportional to thermal diffusivity divided by the laminar flame speed. Hence, the critical velocity gradient variation can be characterized by $SL2/α$⁠. This strategy is frequently used in the literature [3–15] and does a reasonable job of collapsing the effect of fuel composition, but it is not able to predict the preheat temperature effect as indicated in Fig. 10.

The inability of the strategies shown in Figs. 8–10 to fully capture the influence of the parameters studied was a motivating factor in the original development of Eq. (1) [33]. Hence, consistent with the objectives of the present work, Fig. 11 presents the application of Eq. (1) to the atmospheric annular combustor data presented above. Shown for reference are the data used to develop Eq. (1) [33]. The “high pressure” data include results for pure hydrogen used with three burners (inner diameter of 25.4 mm) constructed from stainless steel, copper, and ceramic with preheat temperatures from 300 to 500 K and pressures from 3 to 8 atm [33]. In addition, data obtained with a stainless steel burner with an inner diameter of 30.48 mm at preheat temperature of 400 K and pressure of 3 atm are also included. Also shown are the results from Daniele et al. [32], who reported the flashback propensity of H₂/CO at pressure up to 15 atm, and preheat temperature between 577 K and 674 K. As shown in Fig. 11, Eq. (1) captures the effects of various fuels, pressures, preheat temperature, and burner materials and is able to collapse the results from the atmospheric annular combustor study. It is noted that the effect of burner diameter on flashback propensity may be significant due to the tip temperature variation when the burner is not cooled during the experiment. In the present model, the presence of the tip temperature term in Eq. (1) takes into account the heat transfer between the burner rim and flame front and may mask any separate diameter effect. The solid points above the dashed line in Fig. 11 represent the atmospheric data with a preheat temperature of 672 K. The solid points below the dashed line represent the 300 K inlet temperature cases. As shown, the deviation from Eq. (1) increases for the nonpreheated case. The actual velocities in that experiment [36] were calculated based on an assumed constant airflow splits between the fuel injectors, the dilution jets, and leakage paths. In reality, this flow split likely changes with temperature, which could account for the deviation of the predicted and measured flashback values. The deviation is more pronounced for H₂/NG mixtures.

Similar to the results for the 1 atm annular combustor, the results from the engine test are difficult to analyze since many parameters must vary together according to the engine “cycle deck” [38]. Hence, it is impossible to simply fix inlet temperature and pressure and maintain the injector bulk velocity due to the parameters imparted by the engine control system. However, since all of these parameters were monitored as tests were conducted by slowly adding hydrogen to either natural gas or carbon monoxide until flashback was noted, it is possible to apply Eq. (1) to the data obtained. Noteworthy for the engine tests is that the injector tip temperature was monitored (recall Fig. 4) as a means to detect flashback. In the engine tests, no optical access to the combustor was available, hence the injector temperatures were the primary means of detecting flashback. For some cases, emissions measurements were also being obtained and when flashback was indicated by the injector temperatures, NO_x levels were also observed to spike.

The results for the engine data are shown in Fig. 12. As shown, the agreement is quite good. The data shown represent different engine loads from 20 to 60 kW conditions for various amounts of hydrogen added to either natural gas or carbon monoxide. The inlet pressures and temperatures corresponding to the set engine load conditions are used along with the measured injector tip temperature at flashback as inputs to Eq. (1). The injector bulk velocity is determined from the air flow corresponding to the engine load condition. As shown in Fig. 12, Eq. (1) is able to capture the impact of various effects on flashback propensity.

All of the data analyzed in the present work have benefited from knowing the tip temperature at flashback. The results shown above also capture the influence of ambient pressure. As a result, Eq. (1) allows for further understanding of the coupling of this parameter with other factors. This is explored in this section to add insight into the role of tip temperature and ambient pressure.

Using measured data from Ref. [33], Fig. 13 illustrates tip temperature variation as a function of equivalence ratio for a stainless steel burner head for different pressures and inlet temperatures. For each set, three points along the trend line represent a different flashback propensity of hydrogen according to the velocity at the burner head. At constant pressure, an increase of preheat temperature leads to flashback at a lower equivalence ratio and higher tip temperature. Lower equivalence ratio results in a lower adiabatic flame temperature, but an increase of preheat temperature compensates this effect and finally causes a higher tip temperature. At constant preheat temperature, an increase of pressure shifts the flashback point to lower equivalence ratios and higher tip temperatures. As the pressure increases, the quenching distance of the stabilized flame reduces and leads to higher tip temperature. As shown in Fig. 13, an increase of preheat temperature from 400 to 500 K caused a more significant increase in tip temperature at flashback than does an increase in pressure from 3 to 7 atm.

As an example, the critical velocity gradient has been predicted as a function of tip temperature for hydrogen using the further validated correlation in Eq. (1) at equivalence ratio of 0.5 and preheat temperature of 300 K, see Fig. 14. An increase of tip temperature leads to higher flashback propensity by reducing the quenching distance. The higher pressure enhances the effect of tip temperature, based on Fig. 14, and this observation is similar to the experimental data depicted in Fig. 13. Indeed, the slope of trend lines in Fig. 13 increases with an increase of pressure for a constant preheat temperature. Hence, the correlation is able to predict the physical bases underlying the thermal coupling effect. The results above as well as those from the previous studies have noted the importance of the burner tip temperature as a means of instigating flashback [22,31].

Experimental data obtained for hydrogen with the stainless steel burner head are shown in Fig. 15 and illustrate the effect of pressure on the critical velocity gradient. Each line of data represents a different velocity at the burner head. Higher velocities correspond to higher equivalence ratios at flashback for a given preheat temperature and pressure. At a constant preheat temperature, an increase of pressure causes a higher flashback propensity, i.e., higher critical velocity gradient and lower equivalence ratio. The critical velocity gradient variation rate increases with an increase of pressure. This observation is also according to the previous studies at subatmospheric pressure [19,20]. In fact, the effect of equivalence ratio is enhanced at higher pressure. Equation (1) can also be used to help interpret pressure effects on flashback. Similar behavior has been predicted by the developed correlation in the previous work (see Fig. 10 in Ref. [33]).

In terms of uncertainty, Fig. 16 indicates the percent uncertainty based on difference between the predicated velocity (Eq. (1)) and actual velocity at flashback divided by the actual velocity. As shown, the percent uncertainty is a function of bulk velocity at which flashback occurs. The range of velocities covered in all of the experimental data used varies from 20 to 65 m/s. The objective of the current research was to study flashback at gas turbines premixer conditions (i.e., elevated pressures and temperatures), consequently higher Reynolds numbers. As a result, it is expected that the accuracy of the correlation decreases for lower Reynolds numbers as clear from Fig. 16. The main reason is that the turbulent combustion regime is different at low Reynolds numbers as discussed in Ref. [33], influencing on the flame–turbulence interaction.

from the data obtained on a single jet burner operated at elevated pressures and temperatures on hydrogen [33] was applied to two sets of flashback data obtained using a combustor from a commercial gas turbine operated at both atmospheric pressure and within the commercial engine. The present results reaffirm the conclusions from Ref. [33] regarding increased flashback propensity with (1) higher injector tip temperature, (2) higher ambient pressures, and (3) CO added to H₂ versus CH₄ added to H₂. The current study also leads to the following additional conclusions:

• The slope of critical velocity gradient variation as a function of equivalence ratio increases at higher pressure for a constant preheat temperature indicating higher sensitivity to variation in fueling at elevated pressure.

• Higher pressure increases the tip temperature by reducing the quenching distance for a given preheat temperature and velocity.

Ultimately, the current study has confirmed the utility of the previously developed correlation by demonstrating its ability to predict flashback in actual engines.

The authors would like to acknowledge the support from the U.S. Department of Energy through a University Turbine Systems Research grant (Contract No. DE-FE0011948; Steven Richardson Contract Monitor; Rich Dennis Program lead). The assistance of Salvatore Danielle and Peter Jansohn in provision of their data and associated discussions is greatly appreciated. The data from the combustor and engine configurations were made possible by a subcontract from the Capstone Turbine Corporation and a grant from the U.S. Department of Energy (Contract No. DE-EE0001732). David Page and Brendan Shaffer provided guidance relative to interpretation of the combustor and engine data.