Empirical Modeling of Synthetic Fuel Combustion in a Small Turbofan

Abstract

Drop-in fuels for aviation gas-turbine engines have been introduced recently to mitigate global warming. Despite their similarity to the fossil fuel Jet A-1, their combustion in traditional combustors should be thoroughly analyzed to maintain engine health and low emissions. The paper introduces criteria for assessing the impact of the chemical composition of fuels on combustion in the DEGN 380 turbofan. Based on previous emission-test results, the power functions of carbon monoxide and its emission index were adopted as the model of combustion. Based on the general notation of chemical reactions leading to the production of CO in combustion, the regression coefficients were given a physical meaning by linking them with the parameters of the kinetic equations, i.e., the reaction rate constant of CO and CO₂ formation expressed as exponential functions of combustor outlet temperature and the concentration of O₂ in the exhaust gas, as well as stoichiometric combustion reactions. The obtained empirical functions show that, in the entire range of engine operating parameters, synthetic components affect the values of the rate constants of CO and CO₂ formation. It can be explained by the change in activation energy determined for all chain-of-combustion reactions. The activation energy for the CO formation chain changes in the range between 8.5 kJ/mol for A0 and 24.7 kJ/mol for A30, while for the CO₂ formation chain between 29.8 kJ/mol for A0 and 30.8 kJ/mol for A30. The reactivity coefficient lnα_iCOA_COD_CO changes between 2.29 for A0 and 6.44 for A30, while lnα_iCO2A_CO2D_CO2 changes between 7.90 for A0 and 8.08 for A30.

1. Introduction

Since the mid-20th century, jet fuels for gas-turbine engines, based on kerosene, have been produced with the two technologies of crude-oil processing: hydrorefining and Merox. Hydrorefining is based on a catalytic hydrogen process, in which sulfur is removed and double bonds are saturated between bonds. Merox technology is the catalytic oxidation of sulfur compounds. These two technologies, which differ significantly in the processes involved, make it possible to obtain fuels with a similar hydrocarbon composition and similar physicochemical properties. The following groups of hydrocarbons are basic components of jet fuels: paraffin~25%, isoparaffins~35%, cycloparaffin~20%, and flavors~20%. Conventional jet fuels have proven themselves in flight in terms of performance and safety. The need to reduce the emissions of greenhouse gases also from the aviation sector resulted in undertaking efforts to develop alternative fuels for aviation, most of which include components derived from biomass [1]. Biofuels produced using biomass are regarded as a renewable energy source and part of a closed carbon cycle in nature, so the CO₂ emitted during their combustion is not taken into account. Sustainable aviation fuels (SAF) are standardized biofuels for gas-turbine engines that have been introduced to mitigate global warming [2,3,4]. They are assumed to be essentially identical to the standard jet fuel (Jet A-1) and referred to as drop-in fuels [5]. SAF fuels contain a dozen hydrocarbons belonging to paraffins and isoparaffins, while Jet A-1 fuel contains about a thousand hydrocarbons, including aromatics and naphthenes.

Differences in chemical composition between SAF and regular jet fuel cannot be completely ignored for safety reasons. Therefore, using these biofuels in civil aviation requires approval by both engine and aircraft manufacturers. The ASTM D4054 standard established the system for the certification of alternative jet fuels [6]. For each platform, a four-tier qualification process has to be followed for an individual alternative fuel [7]. In its wake, blends up to 50% SAF are approved by many original equipment manufacturers (OEMs) [8]. Recent efforts are focused on moving towards 100% SAF, but they are hampered by insufficient feedstock availability [9].

The development of aeroengines mainly involved their design and materials. Fuel was treated as a fixed element. Hence, in various engine models, the properties and chemical composition of the fuel are considered to a small extent. Nowadays, when biofuels and electrofuels [10,11,12] are introduced to aviation, the chemical composition and properties of the propellant cannot be assumed as fixed. Therefore, there was a need to develop new and improved tools for testing and modeling combustion when fuels of varied chemical composition are used [13,14,15,16,17].

Testing alternative jet fuels relies on a limited set of sensors for engine performance and emissions. Consequently, combustion is characterized by a small number of macroscopic parameters, which do not indicate subtle effects related to the chemical composition of fuels. In our prior tests [18,19], some minor deviations of engine operational parameters and emissions from the reference were found, but the reasons for the observed regularities were not well explained. To assess the impact of biofuels on engine operation, the mechanism and kinetics of the combustion reaction need to be considered. For combustion modeling in jet engines, several kinetic-based approaches are used, e.g., [20,21]. However, these models do not describe the cause-and-effect relationships between the kinetics of combustion and engine operation. Some teams conduct research in this direction [22], but the proposed models either require a description of individual reactions in fuel combustion chains or are based on statistical methods. In this case, empirically determined parameter values cannot be physically interpreted, and these values refer only to a limited group of fuels.

In chemistry, reactivity is understood as an impulse by which a substance reacts with a complete release of energy. We introduced a so-called α_i reactivity model, which combines the parameters related to the flow of energy with the quantities describing the kinetics of chemical reactions [23]. The general nature of the model, which considers both the flow of energy across the system boundaries (thermodynamic processes) and the kinetics of chemical reactions, makes it possible to describe combustion in gas-turbine engines. Attempts to apply the α_i reactivity model to analyze the combustion of fuel blends containing synthetic components were performed at the GTM 140 microturbine, which acted as an instrumented combustion rig. The reactivity model stands out by linking a thermodynamic process, such as engine operation, with a function that characterizes the kinetics of chemical reactions, enabling the process to occur.

This article applies the reactivity model in a turbofan engine to describe the combustion of fuel blends containing SAF in various concentrations and assesses the impact of fuel composition on turbine operation. The specific objective is to empirically determine the value of activation energy for the reaction chains of complete and partial combustion, as well as the values of reactivity coefficient α_i for blends of Jet A-1 fuel and the tested SAF.

2. Combustion Modeling

2.1. Chemical Kinetics in Combustion

Fuel combustion in gas-turbine engines is a chain of chemical reactions that vary greatly with the operating point of the engine. There are several modeling approaches based on physics and chemistry, e.g., [24]. While thermodynamics, fluid dynamics, and other physical processes play a key role in achieving optimum combustion performance, chemical processes are important mainly for their impact on pollutant emissions and the limits of lean light off and lean blowout at high altitudes [25]. For a chemical reaction, its reaction rate v depends on the concentration of each reactant X and Y. The exponents p and q are reaction orders, which depend on the reaction mechanism:

v = k[X]^p[Y]^q

(1)

The reaction rate constant k is expressed by the Arrhenius equation as an exponential function of the temperature at which the reaction occurs. This is a fundamental formula for chemical kinetics based on the concept of activation energy E_a:

k = A exp(−E_a/RT)

(2)

where: A is the Arrhenius pre-exponential factor, R is the universal gas constant, E_a is the activation energy for the reaction, and T is the absolute temperature.

The Arrhenius equation is often used in the linear form:

ln k = −E_a/RT + ln A

(3)

The Rice–Ramsperger–Kassel–Marcus (RRKM) model is based on the theory of chemical reactivity [26,27]. This method enables the computation of simple estimates of the unimolecular reaction rates from a few characteristics of the potential energy surface. The RRKM model describes the energy dependencies that determine the course of chemical reactions much better than the Arrhenius model. The microcanonical rate constant is expressed as:

k(E) = σN⁺⁺(E − E₀)/h ρ(E)

(4)

where k(E) is the microcanonical rate constant and σ is the degeneracy of the reaction pathway. E is the internal energy of the system, E₀ is the activation energy for the reaction, N⁺⁺(E − E₀) is the sum of states of the transition state from E₀ to E, ρ(E) is the density of states of precursors at energy E, and h is Planck’s constant.

Other well-known models are dedicated to fuel combustion processes in internal combustion engines. For example, the SAE Aerospace Recommended Practice ARP 1533 [28] introduces a procedure for analyzing and evaluating the chemical composition of gaseous emissions from aircraft engines. Measurements of the CO₂, CO, NO_x, and C_xH_y emissions are used to determine:

• emission indices;
• fuel–air ratio;
• combustion efficiency;
• thermodynamic properties of exhaust gases.

The SAE procedure has been developed for turbine aircraft engines, but it can be applied to any other machines in which fuel combustion occurs. The basis of this model is the following chemical reaction:

C_nH_mOpN_qS_r + X[R(O₂) + S(N₂) + T(CO₂) + h(H₂O) + U(CH₄)]−> P1(CO₂) + P2(N₂)
+ P3(O₂) + P4(H₂O) + P5(CO) + P6(C_xH_y) + P7(NO₂) + P8(NO) + P9(SO₂)

(5)

The SAE procedure considers only a few selected properties of the fuels, which are mixtures of numerous individual chemical compounds. It is known, however, that combustion consists not only of the combustion reaction chains but of several sub-processes, e.g., the atomization of fuel. This process can be described by the Weber number defining the conditions for droplet atomization when aerodynamic forces and surface tension equalize [27]. The atomization of the fuel stream into drops takes place when We ≥ We_cr, where We is described by the equation:

We = ρw²d/σ

(6)

where w is the initial droplet speed, ρ is the fluid density, d is the initial droplet diameter, and σ is the surface tension.

The critical value of Weber number We_cr is reached for critical droplet speed (maximum speed of a drop in a stationary gaseous medium, above which decay occurs) and depends mainly on liquid viscosity. The Weber number is a useful tool for estimating the droplet size in steady flows when the injection takes place into a medium in which there is no flow. In the case of unsteady flows, it was necessary to introduce corrective factors.

d = 6σE_p − A₁ηv

(7)

where E_p is the fuel pulsation energy, A₁ is the constant volume, η is the dynamic viscosity, and v is the fuel flow velocity.

To a greater extent, the physicochemical properties of the fuel can be modeled in Ansys Chemkin-Pro software. For the simulation of reactions involving fuels, the model is supported by a fuel data library. Using this model, it is possible to calculate the thermodynamic effects of fuel combustion, i.e., the amount of heat released, the change in pressure in the combustion chamber, the flame propagation rate, and temperature in the combustion chamber. However, this model is based on relationships formulated using a large amount of experimentally obtained data. These data were used to determine the values of the relationship parameters using statistical methods. As a result, this model can be applied to a specific, relatively narrow group of fuels, and the introduction of new, yet unexplored, components may cause even large discrepancies between the model and the empirical data.

The models presented above are statistically formulated relationships combining, on the one hand, the physicochemical properties (e.g., density, distillation, and calorific value) of the fuel with the engine’s operating parameters (e.g., thrust) and emissions of exhaust gas components. These models seem to bypass the combustion process and its chemistry. Cuoci et al. [29] reviewed models describing combustion in turbine engines. Among other things, the relationship between the mass flow rate and exp(E_a/RT) is presented, but the descriptions of the combustion process are either related to the chemical kinetics of the combustion reaction or describe the relationship between the engine operating (pressure, thrust, and temperature). A similar kinetic-based approach was proposed for propanol combustion by Wang et al. [30].

A number of advanced models have been developed to describe the kinetics of fuel combustion reactions, which take place in reactors of various designs. These models are formulated on the basis of tests of simple fuels in terms of chemical structure, such as hydrogen, methane, and single hydrocarbons. Curran et al. [20] reviewed models describing the combustion of hydrogen and individual hydrocarbons. They showed that some models describe chemical kinetics to a satisfactory extent and possibly combine them with elements of thermodynamics but do not allow for connecting combustion kinetics with engine operating parameters.

The concept that seems to be useful in combustion modeling is reactivity. In chemistry, it is understood as an impulse by which a substance reacts with a complete release of energy. Reactivity covers both thermodynamic factors and kinetic factors, which are actually different, and both usually depend on the temperature. Often, however, in chemistry, reactivity is equated with the rate of reaction.

2.2. Reactivity Model for Combustion

In this paper, the chemical reactivity of fuel blends containing synthetic components and the α_i model were used to describe combustion in an aviation turbine engine. The α_i reactivity model:

• links the function describing the flow of energy across the boundaries of the system with the function describing the change in the internal energy of the system resulting from chemical reactions taking place in the system;
• introduces a quantitative measure of reactivity in the form of the reactivity coefficient α_i.

The basic criterion for the model is the possibility of adopting one independent variable, e.g., fuel mass flow rate, on which the reactivity coefficient α_i will depend; all other quantities appearing in the model are functions of this variable. In general, the reactivity model can be presented as:

L = α_i kD + L₀

(8)

where L is generalized work done by the system (e.g., by engine proportional to thrust F) or on the system, L₀ is the constant value for the certain system and group of fuels, k is the constant rate of reaction taking place in the system, e.g., combustion reaction; and D is the change in the internal energy of the system caused by a chemical reaction undergoing with the rate appropriate to the unit value of the k.

A gas-turbine engine was adopted as the system studied in this work, and the dominant chemical reactions occurring in this system are related to fuel combustion. It can be assumed that the produced thrust F is linearly dependent on fuel flow:

F = a m_f + F₀

(9)

where m_f is the fuel consumption, F₀ is the reference thrust value, constant for a given engine and fuel set, and a is the empirically determined proportionality coefficient.

If the α_i reactivity model describes the combustion of fuels blended in various concentrations, then the chain of chemical reactions taking place in the system can be expressed as:

• CO₂ and H₂O formation reaction:

  C_xH_y + (x + y/4) O₂ → x[CO₂] + y/2 H₂O

  (10)
• CO and H₂O formation reaction:

  C_xH_y + (x/2 + y/4) O₂ → x[CO] + y/2 H₂O

  (11)
• CO–to-CO₂ reaction:

  CO + ½ O₂ → CO₂

  (12)

The dominant reaction is the CO₂ formation, so Equation (8) can be presented as:

α_iCO2 = (L − L₀)/k_CO2 D

(13)

where α_iCO2 is the reactivity coefficient related to combustion to CO₂.

The work done by the system L is proportional to thrust F. So, assuming that L is related to the unit distance, the (a m_f) obtained from Equation (9) can be equal to (L − L₀).

L − L₀ = a m_f

(14)

Then

α_iCO2 = a m_f/k_CO2 D

(15)

Based on Equation (1), the rate of fuel combustion to CO₂ and H₂O can be presented as:

d[CO₂]/dt = k_CO2 m_f^p[O₂]^q

(16)

After integration in the limits <0, t>, the following relationship was obtained:

[CO₂] = k_CO2 m_f^p[O₂]^qt

(17)

where p and q are effective reaction orders, t is the reaction time, m _f is the concentration of reaction substrates expressed as fuel flow, and O₂ is the oxygen concentration in the air flowing through the engine.

To estimate the reactivity coefficient α_iCO2 for individual fuel blends, it was assumed that complete combustion takes place in the tested engine, so the entire amount of fuel is oxidized to CO₂.

By substituting k from the Arrhenius Formula (2) to Equations (15) and (17), the following was received:

α_iCO2ch A_CO2 exp(−E_aCO2ch/RT) = (a/D_CO2)m_f

(18)

[CO₂] = A_CO2 exp(−E_aCO2ch/RT₄) m_f^p[O₂]^qt

(19)

To model the dilution of combustion products by air flowing through the engine, the following functions are used:

[CO₂]_meas = [CO₂]_ch/(AF)
ln[CO₂]_meas = ln[CO₂]_ch − ln(AF)

(20)

where AF is the air flow. Consequently, Equation (20) can be expressed as follows:

ln[CO₂]_meas = −E_aCO2ch/RT₄ + p ln(m_f[O₂]^q A_CO2t) − ln(AF) =

−E_aCO2meas/RT₄ + p ln(m_f[O₂]^q A_CO2t)

(21)

−E_aCO2meas/RT₄ = −E_aCO2ch/RT₄ − ln(AF)

(22)

where [CO₂]_meas is the CO₂ concentration measured in exhaust gases, E_aCO2ch is the activation energy resulting from the kinetics of the combustion reaction, without the effect of CO₂ dilution with air; E_aCO2meas is the activation energy determined on the basis of [CO₂]_meas measurements, and AF is the air low.

Equation (17) contains four measurable quantities. Three of them are dependent variables, namely thrust F, [CO₂], and [O₂], and one is an independent variable, namely fuel flow m_f. For a given fuel blend, the following dependencies can be empirically determined for engine operating points:

$$\{\begin{array}{l}\mathrm{F}=\mathrm{f}\left({\mathrm{m}}_{\mathrm{f}}\right)\\ \left[{\mathrm{CO}}_2\right]=\mathrm{g}\left({\mathrm{m}}_{\mathrm{f}}\right)\end{array}$$

(23)

where f(m_f) and g(m_f) are the functions of fuel flow. By solving the system of equations, it will be possible to experimentally determine the value of α_iCO2 for each tested fuel.

Respectively, for the fuel combustion reaction to CO, the following relationship can be formulated:

α_iCO = (L − L₀)/k_CO D = am_f/k_CO D

(24)

where α_iCO is the reactivity coefficient related to the fuel combustion reaction to CO. The rate of fuel combustion to CO and H₂O can be presented as:

d[CO]/dt = k_CO m_fⁿ[O₂]^r

(25)

After integration within the limits <0, t>, the following relationship was obtained:

[CO] = k_CO m_fⁿ[O₂]^r t

(26)

If CO can be treated as an intermediate product of the follow-up reactions in (10) and (11), the relationship between CO and mf can be expressed as:

[CO] = {c₂k_CO[1 + e^t]/e^t c₅k_CO2} m_fⁿ

(27)

After substituting Equation (13) into (9), the following was obtained:

α_iCO = (L − L₀)/D([CO]m_f⁻ⁿ[O₂]^−r t⁻¹)

(28)

As described by Åkerblom et al. [12], the kinetic of the CO creation during the combustion process can be described by the following kinetic equations:

(a)

for parallel reactions:

[CO] = c₂k_CO t m_f⁻ⁿ⁺¹

(29)

(b)

for follow-up reactions:

[CO] = {c₂k_CO [1 + e^t]/e^t c₅k_CO2 }m_fⁿ

(30)

where c₂ is the coefficient determining the participation of [O₂]^{np(x/2 + y/2)} in the rate of reaction (10) and c₅ is the coefficient determining the participation of [O₂]^{np(x/2 + y/2)} in the rate of reaction (11).

When CO is an intermediate product of fuel oxidation to CO₂, Equation (30) can be expressed as:

ln[CO] = lnc_CO − E_aCO/RT₄ + E_aCO2/RT₄ + nlnm_f

(31)

where c_CO = c₂[1 + e^t]/e^tc₅.

The description of the kinetic of CO formation should consider the dilution of combustion products by air:

[CO]_meas = [CO]_ch/(AF)
ln[CO]_meas = ln[CO]_ch − ln(AF)
[CO]_meas = {c₂k_CO [1 + e^t]/e^t c₅k_CO2}m_fⁿ/(AF)
[CO]_ch = (AF) [CO]_meas = (k_CO/k_CO2)_ch {c₂[1 +e^t]/e^t c₅}m_fⁿ

(32)

ln[CO]_meas = (−E_aCOch + E_aCO2ch)/RT₄+ ln{c₂[1 + e^t]/e^t c₅} + lnm_fⁿ − ln(AF)

(33)

The values of E_aCOch/RT₄₁ and am_f can be used for the α_iCOA_COD_CO calculation.

α_iCO = am_f/k_CO D_CO
α_iCO = am_f/D_CO A_CO exp[(−E_aCO/R)(1/T)]
lnα_iCO = ln(am_f) − ln(D_CO A_CO) + E_aCO/RT
E_aCO/RT = lnα_iCO D_CO A_CO − ln(am_f)

(34)

For a given fuel blend, the following dependencies can be empirically determined for the engine operating points:

$$\{\begin{array}{l}\mathrm{F}=\mathrm{f}\left({\mathrm{m}}_{\mathrm{f}}\right)\\ \left[\mathrm{CO}\right]=\mathrm{h}\left({\mathrm{m}}_{\mathrm{f}}\right)\end{array}$$

(35)

where f(m_f) and h(m_f) are the functions of fuel flow. By solving the system of equations, it will be possible to experimentally determine the value of α_iCO for each tested fuel.

The proposed αi reactivity model describes the impact of the fuel chemical composition on the engine operation. Equations (2), (9), (13), and (24) will be used to characterize combustion and determine to what extent it is affected by adding biofuels to Jet A-1. Figure 1 and Figure 2 summarize the methodology of E_aCO2, E_aCO, αi_CO2, and αi_CO determination as quantities characterizing fuel behavior during the combustion process. The parameters shown in Figure 1 and Figure 2 were used to model the impact of component A on combustion in the DGEN 380 engine.

3. Materials and Methods

3.1. Fuels

Blends of the commercial Jet A-1 fuel with synthetic components approved by ASTM D7566 (

Table 1. Volumetric composition of tested fuel blends.

Blend	Jet A-1	SAF
A0	100%	0%
A5	95%	5%
A20	80%	20%
A30	70%	30%
A	0%	100%

) were prepared. They were tested in the laboratory for their compliance with ASTM D7566 (

Table 2. Fuel lab-testing results.

Property	Unit	Requirement	Lab-Test Result
			A0	A5	A20	A30	A
Density at 15 °C	kg/m3	775–840	798	796	790	786	759
Viscosity at −20 °C	mm2/s	max 8.0	3.40	3.45	3.57	3.66	4.78
Net heat of combustion	MJ/kg	min 42.8	43.2	43.3	43.4	43.4	44.0
Aromatics	(v/v)%	max 25	16.7	15.7	13.0	11.3	0
Naphthalenes	(v/v)%	max 3	0.58	0.55	0.46	0.40
Flash point	°C	min 38	49.5	49.0	49.0	49.0	47.5
Freezing point	°C	max −40	−63.5	−65.5	−66.5	−66.8	−67.5
Smoke point	mm	min 18	20	23	25	28

).

3.2. Engine Testing

The reactivity model was used to study the fuel combustion at the WESTT test cell with a Price Induction DGEN 380 engine. It is a small and high bypass ratio (7.6) geared turbofan (Figure 3), producing 255 daN (

Table 3. Technical specification of the DGEN 380 turbofan [32].

Maximum Thrust	255 daN
Specific Fuel Consumption (for maximum thrust)	12.4 g/kN·s
Bypass ratio	7.6
Weight	85 kg
Lifetime	3600 h

) of thrust while maintaining emissions and fuel consumption at a low level. It was developed by the French company Price Induction for educational and general aviation applications using modern, high-performance materials to ensure optimal performance and life. The turbofan design follows the more electric engine concept since it uses electrically driven oil and fuel pumps and an electrical starter–generator. The data-acquisition system of the WESTT test cell [31] enables data acquisition and the analysis of several engine performance parameters, such as thrust, fuel consumption, temperature, and pressure.

In the engine test, a finite amount of fuel in the tank was used to maintain a constant blend ratio throughout the test. The engine dwelled at the selected operating points for a minute at least. Exhaust gases were measured with the Semtech DS analyzer through a probe maintaining the temperature of 191 °C. The concentration measurement of CO and CO₂ was performed with a non-dispersive infrared (NDIR) analyzer. The test procedure and emission measurements are presented in detail in [23]. The engine test profile is presented in

Table 4. Test profile of DGEN 380 engine.

Step	Thrust [%]	Thrust [daN]	NH [%]	NL [%]	PLA [%]	Fuel Flow [L/h]	Operating Mode
1	10	26.4	52.7	33.5	0	32	Idle
2	13	33.8	57.8	37.8	11	37
3	20	50.9	66.2	45.8	29	44	Cruise
4	26	65.8	74.9	57.3	57	49
5	40	100.9	81.1	65.3	61	66	Max
6	56	141.6	87.7	75.3	75	86
7	72	183.5	93.3	86.1	87	112
8	97	246.3	99.3	99.4	100	151	Take-off

.

4. Results

4.1. E_aCO2 and α_iCO2 Determined from Engine Operating Parameters

The calculated activation energy and reactivity coefficients are based on the operational parameters of the engine, such as thrust, fuel flow, mass air flow, combustor outlet temperature and the emissions of CO, and CO₂. Figure 4 shows the linear dependency of mass flow m_f on thrust F (Equation (9)), while

Table 5. Regression results for thrust vs. mass flow.

Fuel	a	F0	R2
A0	6.123	18.7	0.9978
A5	6.384	25.11	0.9980
A20	6.397	24.7	0.9976
A30	6.374	24.98	0.9982

presents the regression results. The obtained slope and intercept indicate that the A0 fuel (Jet A-1) has a slightly different thrust vs. the m_f function than its blends with component A. This may be due to the difference in the calorific value of the tested fuels, as well as a different hydrocarbon structure, which is visible already at 5% wt of component A.

4.2. E_aCO2ch and αi_CO2ch Determined from Emission Measurements

For the tested blends, fuel flow was related to the inverted combustion temperature (Figure 5). The regression results are presented in

Table 6. Regression results for fuel flow vs. inverted temperature.

Fuel	R2	EaCO2ch/R	EaCO2ch [kJ/mol]	(αiCO2chACO2D/a)	(αiCO2chACO2DCO2)	ln(αiCO2chACO2DCO2)
A0	0.9979	3480	29.8	438.38	2684	7.90
A5	0.9977	3525	29.3	440.32	2811	7.94
A20	0.9973	3556	29.5	445.71	2851	7.96
A30	0.9978	3705	30.8	509.79	3249	8.08

.

The values of A_CO2 and D_CO2 should be constant for all tested fuels. A_CO2 is a pre-exponential factor in the Arrhenius equation. Its value should be constant for a given reaction. In this research, it was assumed that the A_CO2 value is constant for the chains of reactions undergone during the combustion process. D_CO2 is the proportional coefficient describing the change in the internal energy of the system caused by a chemical reaction undergone at the rate appropriate to the unit value of the k. It was assumed the constant value of this coefficient for the tested fuels. Consequently, the differences in (α_iCO2A_CO2D_CO2) result from different values of α_iCO2. The obtained results confirm that the reactivity coefficient α_i does not depend on the fuel mass flow rate and is a characteristic quantity for fuel with a specific chemical composition.

The values of the constant reaction rate of the combustion reaction of the tested fuels to CO₂ were also estimated from Equation (18). However, introducing the empirically determined concentrations of CO₂ and O₂ in the exhaust gases and m_f. The values of a_CO2;T = A_CO2 m_fO₂^pt, and E_aCO2meas/R were empirically determined. The results are presented in Figure 6 and

Table 7. Empirically obtained values of the parameters of function (25) for the tested blends.

Fuel	R2	ACO2mfpO2qt	EaCO2meas/R	EaCO2meas
A0	0.9589	0.2293	−840	−6972
A5	0.9505	0.2425	−850	−7055
A20	0.9641	0.2259	−924	−7669
A30	0.9635	0.205	−1022	−8483

. The curve for the A0 fuel has a different trend than the ones for blends containing component A. The values of EaCO2meas, quite different than those shown in Table 6, are the result of the dilution of combustion products by air flowing through the engine.

Figure 7 confirms that the A concentration in the tested fuels has a notable impact on EaCO2ch/EaCO2meas. Since a linear relationship between E_aCO2ch/E_aCO2meas and the SAF concentration was confirmed, E_aCO2ch/E_aCO2meas can be expressed by the following transformation of Equation (21):

−RT[ln(AF)]/E_ameas + 1 = E_aCO2ch/E_aCO2meas

(36)

and

−RT[ln(AF)]/E_aCO2meas + 1 = −0.0213c_SAF + 4.2659

(37)

where c_SAF is the concentration of SAF in the tested fuels.

4.3. E_aCO and α_iCOch Determined from Emission Measurements

The relationship between [CO]_meas and m_f is shown in Figure 8 and

Table 8. The parameters of functions [CO]_meas = a_CO m_fⁿ.

Fuel	R2	aCOmeas	n
A0	0.9070	2918	−1.281
A5	0.8464	1153	−0.616
A20	0.8123	1036	−0.545
A30	0.8064	1007	−0.535

. The curve for the A0 fuel is clearly different than those for the blends, including SAF.

The relationship between CO and 1/T₄ was used for the determination of the (−E_aCO + E_aCO2)_ch/R values for the tested fuels.

As shown in Figure 9, the concentration of CO in exhaust gases decreases when the temperature increases in the combustion chamber. This tendency should result from the dilution of exhaust gases by the air flowing through the engine (like in the case of the CO₂ concentration in exhaust gases).

The relatively low values of R² for relationships CO vs. 1/T₄ in

Table 9. Empirically obtained parameters of the function from Equation (32).

Fuel	R2	(−EaCOch + EaCO2ch)/R	{c2[1 + et]/etc5}mfn/(AF)
A0	0.7411	2459	0.0017
A5	0.8464	1625	0.0049
A20	0.8123	1507	0.0059
A30	0.8064	734	0.0122

indicate that the term [ln{c₂[1 + e^t]/e^t c₅} + lnm_f^np − ln(AF)] in Equation (32) is not constant for various m_f. Based on the E_aCO2ch values shown in Table 6, the values of E_aCOch/R were calculated.

The E_aCOch/RT₄₁ and am_f values were used for the α_iCOA_COD_CO calculation.

The results are shown in Figure 10 and

Table 10. Empirically determined values of parameters that characterize the fuel’s tendency to generate CO in exhaust gases (Equation (33)).

Fuel	R2	(EaCOch − EaCO2ch)/R	EaCOch/R	EaCOch [kJ/mol]	lnαiCOACODCO	n1
A0	0.9973	2459	1021	8.5	2.29	0.29
A5	0.9980	1625	1900	15.8	4.30	0.54
A20	0.9968	1507	2049	17.0	4.58	0.57
A30	0.9989	734	2971	24.7	6.44	0.79

.

5. Discussion

The results presented above indicate that the synthetic component introduced into the fossil-fuel Jet A-1 does not noticeably affect the operation of the DGEN 380 engine, since the relationship between thrust and fuel flow for all the tested fuels is practically the same. But, it has a significant impact on the combustion chemistry and emissions, i.e., CO₂ and CO. Two criteria were used to assess the impact of SAF content on the combustion chemistry and engine operating parameters:

• activation energy E_a related to the whole chain of combustion reactions;
• coefficient of reactivity α_i related to thrust F, fuel flow m_f, and constant rate determined for all chain of combustion reactions k.

Table 11. Parameters characterizing the impact of SAF content on the kinetic of combustion and their reactivity related to this process.

Fuel	EaCO2ch/R	lnαiCO2chACO2DCO2	EaCO2meas/R	EaCOch/R	lnαiCOACODCO
A0	3590	7.90	−840	1021	2.29
A5	3528	7.94	−850	1900	4.30
A20	3554	7.96	−924	2049	4.58
A30	3707	8.09	−1022	2971	6.44

shows both criteria determined for fuels consisting of fossil Jet A-1 fuel (A0) and blends of this fuel and A synthetic component in concentrations of 5, 20, and 30 wt%.

The activation energy determined for the entire combustion reaction chain cannot be interpreted in the same way as for individual chemical reactions. However, when comparing the E_aCO2ch and E_aCOch (Table 11) values obtained for the fuels with different chemical compositions, this value can be treated as a criterion for the similarity of reaction chains. Using this method of assessing the similarity of combustion reaction chains of fuels with different SAF content, it was found that (Figure 11):

• SAF in a concentration between 5 and 20 wt% has a negligible impact on the kinetics of the entire fuel combustion chain, since the E_aCO2ch values for all tested fuels are similar;
• SAF affects the kinetics of the reaction chain ending with the formation of CO.

Considering that CO₂ formation is a subsequent reaction with CO as an intermediate product, the rate of the entire reaction chain is determined by the rate of the slowest reaction. Figure 11 indicates that, depending on SAF content, the activation energy of CO is from 70 to 20% smaller than that of CO₂. This suggests that:

• for CO₂ formation, the slowest stage is CO oxidation,
• for CO formation, the slowest is one of the reactions in the chain of fuel hydrocarbon oxidation to CO.

The above indicates that, regardless of the method for determining the value of E_a/R, the resultant activation energy of the combustion reaction to CO₂ increases with the increase in the concentration of component SAF. Conversely, the increase in the content of component SAF causes a decrease in the resultant activation energy of CO formation.

A comparison of the dependence of the calculated reactivity coefficient functions (lnα_iCO2A_CO2D_CO2) on the SAF content in the fuel leads to similar conclusions (Figure 12). Observing fuel combustion as one chain of reactions leading to the formation of CO₂ (this combustion product dominates quantitatively in the composition of exhaust gases), it can be concluded that the introduction of SAF in an amount of up to 30 wt% does not affect the reactivity coefficient. This seems obvious given the fact that the SAF component has been approved for use under the ASTM D4054 procedure. However, for CO emissions, an impact of the SAF content on the value of the reactivity coefficient function (lnα_iCOA_COD_CO) is noticeable.

The results presented in Table 10 directly indicate a significant impact of SAF on CO emissions, E_aCOch/R changes from 1021 K to 2971 K and lnαi_COA_COD_CO changes from 2.29 to 6.44, and indicate differences compared to Jet A-1 fuel in the kinetics of the reactions making up the fuel combustion chain in the DGEN 380 engine.

The regression results shown in Table 10 were used to formulate relationships between E_aCO2Ch/R, E_aCOCh/R, lnα_iCO2chA_CO2D_CO2, and lnα_iCOA_COD_CO and the SAF A concentration. On the basis of the results obtained for the A0, A20, and A30 fuels, the following relationships were formulated:

E_aCO2Ch/R = 0.57(SAF concentration)² − 13.2(SAF concentration) + 3590

(38)

E_aCOCh/R = 63.06(SAF concentration) + 962.7

(39)

lnα_iCO2chA_CO2D_CO2 = 0.0003(SAF concentration)² − 0.0021(SAF concentration) + 7.92

(40)

lnα_iCOA_COD_CO = 0.1349(SAF concentration) + 2.19

(41)

It should be emphasized that the formulated equations refer to fuels containing the SAF A component and combustion in the DGEN 380 turbofan. With these relationships, the values of E_aCO2Ch/R, E_aCOCh/R, lnα_iCO2chA_CO2D_CO2, and lnαi_COA_COD_CO were calculated for A5 fuel. The results are shown in

Table 12. The model validation results.

Parameter	Predicted	Empirically Determined
EaCO2Ch/R	3538	3525
EaCOCh/R	1278	1900
lnαiCO2chACO2DCO2	7.92	7.94
lnαiCOACODCO	2.86	4.30

. The models based on Equations (38) and (40) provided good agreement between the predicted and measured data. Meanwhile, those based on Equations (39) and (41) performed worse, since CO formation is not well modeled.

6. Conclusions

The paper attempts to model the impact of the concentration of synthetic fuel on combustion in a turbofan engine. For this purpose, the α_i reactivity model, developed and verified in earlier tribochemical studies, was used. The proposed approach uses linear regression to determine the reactivity coefficients α_iCO2 and α_iCO, describing the mechanism and kinetics of complete (to CO₂) and incomplete (to CO) combustion reactions. Due to the use of this model, quantities such as thrust and fuel flow were quantitatively related to the kinetics of the formation of exhaust gases.

To assess the impact of the synthetic component on combustion in the DGEN 380 engine, two criteria were used, namely the resultant activation energy determined for the entire chain of reactions ending with the production of CO₂ and CO function of the reactivity coefficient α_iCO2 and α_iCO. It was found that SAF in the concentration range of up to 30 wt% does not affect fuel combustion to CO₂, while its impact is significant in relation to the combustion reaction to CO. The reactivity model led to calculating the coefficient of reactivity α_i expressed as lnα_iCOA_COD_CO, whose value changes between 2.29 for A0 and 6.44 for A30, while lnα_iCO2A_CO2D_CO2 changes between 7.90 for A0 and 8.08 for A30. The above results indicate the impact of the tested biofuel A on combustion chemistry and propose the following criteria for biofuel evaluation: E_aCO2, E_aCO, ln(α_iCO2chA_CO2D_CO2), and lnα_iCOA_COD_CO. The critical values of these criteria will be determined via further testing.

The presented assessment of fuel combustion is of a comparative nature, i.e., the calculated values of the reactivity coefficients for the blends containing the SAF component are compared to the values obtained for the fossil Jet A-1 fuel. Future work will be focused on linking the reactivity coefficients with a greater number of operational parameters, including those affecting engine durability and reliability.