1. Introduction
Because of climate change and the rapidly growing transport demand, it is urgent for the aviation industry to control its green-house gas (GHG) emissions [
1]. Plenty of researchers have devoted their efforts to studies related to reducing aviation GHG emissions through various technical approaches, including optimizing operational strategies, developing advanced aircraft/engine designs, and finding sustainable energies [
2]. The first two of these strategies could effectively slow down the growth rate of GHG emissions. It is also necessary to find sustainable energies to seek net-zero carbon emissions or carbon neutralization for the aviation industry. Sustainable energies are supposed to have low emissions, high safety, and high energy density. Several attempts have been made to employ hydrogen, electrical batteries, and sustainable aviation fuels (SAFs) in the aviation industry [
3,
4]. Represented by bio-fuels and other eco-friendly synthesized carbon-based fuels [
5], SAFs have the most promising potential to achieve life-cycle net-zero or even negative carbon emissions [
6,
7], since the ingredients may sequestrate the carbon dioxide from the atmosphere. In addition, SAFs have better compatibility with the current propulsion systems and infrastructure [
8] than other novel energies, requiring minimal changes in aero-engines and ground facilities. SAF’s moderate energy density is also beneficial for widely applying them in various situations with different flying distances and passenger capacities [
9]. Because of these advantages, SAFs are widely recognized as an effective solution to achieve carbon neutralization within the short and midterm.
SAFs’ influence on aero-engines safety is the decisive factor in whether it has an acceptable application risk. With the growing numbers of novel feedstocks and refining pathways [
10,
11], SAFs may have diverse compositions and properties compared to fossil fuels, such as a higher heat value, fewer aromatics, and a more concentrated carbon distribution [
12,
13]. These differences may lead to different burning behaviors and result in non-neglectable influences on aero-engine operation. These influences are closely related to passenger safety, which should be thoroughly considered and carefully evaluated.
Technically, both experimental and numerical approaches can be used for SAF’s engine-level safety assessment and certification. Industrial practice usually utilizes well-established component and engine tests [
14] to validate whether the SAF can support the engine’s safe operation. These tests provide a practical pathway for SAF safety assessment. They have guaranteed the safety application of several types of SAFs. However, these approaches may also be quite costly and time-consuming [
15]. Numerical or model-based approaches are considered an effective supplement to these tests and a promising way to reduce the costs. They may also support researchers in quantifying SAFs’ influences on aero-engine safety and reveal the underlying mechanisms. These advantages may be beneficial for SAF’s development. Therefore, there is a great demand to establish a reliable model-based approach to evaluate SAF’s impacts on aero-engine safety [
16].
It is quite challenging to quantitively evaluate SAFs’ influence on aero-engine safety via model-based approaches, since this involves multiple research levels and space scales. Published SAF research includes studies on the aero-engine system, component/subsystem, and fundamental process [
17,
18] levels. Analysis on each level is supported by the next level, as indicated in
Figure 1. Engine-level safety researchers are usually concerned about SAFs’ influences on the engine’s safety-critical parameters (SCPs) [
19], such as the rotor axial load safety margin and turbine entry temperature. Researchers prefer low-fidelity aerodynamic models [
20] to rapidly acquire the entire engine’s response and evaluate the SCPs’ deviation. Meanwhile, component-level research pays close attention to component performances, such as the combustor efficiency. Researchers prefer to utilize high-fidelity computational fluid dynamics (CFD) models to closely observe the combustion process and detailed flow field in a combustor [
21]. It is challenging to combine these models with different resolutions to establish the mapping relationship between SAFs’ properties and the aero-engine’s SCPs.
Moreover, engine models in published engine-level research may be insufficient for analyzing SAFs’ influences on aero-engine safety. These models usually only consist of gas flow path (GFP) components (such as the compressor, combustor, and turbine), because researchers mainly focus on the engine’s performance (such as thrust and specific fuel consumption) rather than safety. Nevertheless, evaluating the engine’s SCPs involves massive secondary air system (SAS) components [
22]. It is necessary to consider SAS components for SAFs’ engine-level safety assessment. The importance is twofold. On the one hand, the characteristics of SAS components determine the air bleeds from the GFP, which may significantly deviate the co-work point of GFP components and the engine’s operation state. Published research has shown that a 1% increase in air bleeds requires an increase of 11K in the turbine entry temperature to maintain the same thrust level [
22]. In addition, the compressed air in modern gas turbines bleeds at a rate of up to 20% [
23]. The effect of air bleeds through the SAS components on the SCPs is non-neglectable. On the other hand, the SAS components are also closely related to the integrity of the life-limited parts [
24]. For instance, the turbine disk is immersed in the air flow within the SAS. The flow and heat transfer characteristics of SAS components directly affect the thermal load and fatigue life of the life-limited parts [
25], which are vital to aero-engine safety and airworthiness. Therefore, it is also of great importance for SAF’s engine-level safety assessment to introduce SAS component modeling techniques, solving both the GFP and SAS components simultaneously.
Fortunately, advanced aero-engine modeling techniques could be introduced into SAFs’ engine-level safety assessment to address the abovementioned difficulties. Firstly, researchers proposed the integrated engine model [
26] to calculate the coupling of the GFP and SAS components, which are strongly inter-related and co-determine the engine’s working state. This model solves the GFP and SAS components via the component method and network method, respectively, and matches them with bleeding/returning modules. This method has been used to evaluate the aero-engine SCPs when adopting fossil fuels. It may also be applicable for evaluating SAF’s influence on aero-engine safety, especially the load of life-limited parts. Secondly, the data-zooming method could embed high-fidelity component models into the low-fidelity engine system model [
27,
28] to effectively improve the engine model’s resolution. This method may apply to the combustor to improve the engine model’s compatibility with different fuels, thus evaluating SAFs’ impact on engine-level SCPs. These aero-engine modeling techniques may support us in establishing model-based approaches for SAFs’ engine-level safety assessment with necessary improvements.
In summary, there is very limited published research simulating and quantitively discussing SAFs’ engine-level influences from a safety perspective. Published engine-level research [
29,
30,
31,
32] mainly focuses on SAFs’ influence on aero-engine performance, and barely considers the conservation and coupling relationships between the combustor and the engine. The reason for this deficiency is the lack of effective approaches to achieve conservation throughout the engine flow field and to integrate simulation models with different fidelities.
Therefore, the main scope of this research work is to develop a model-based approach to evaluate SAF’s influence on aero-engine safety. A multi-fidelity integrated engine model (MF-IEM) is proposed to establish the mapping relationships between SAFs’ properties and aero-engine SCPs. The MF-IEM solves unified aerodynamic conservation relationships for both GFP and SAS components. In addition, the combustor part of the MF-IEM was modified using a high-fidelity CFD model with a novel surrogate-based iteration strategy, achieving the conservation between the combustor and the engine model. The MF-IEM is proven to have sufficient resolution to discriminate SAFs’ influences on aero-engine safety. There is also the promising potential to develop a comparative assessment approach for SAF’s safety based on the MF-IEM.
The rest of this paper is organized as follows:
Section 2 describes the modeling approaches and multi-fidelity iteration strategy, establishing the relationship between fuel-level properties and engine-level SCPs.
Section 3 applies the proposed approach to a study case, evaluating SAF’s influences on engine’s safety quantitively.
Section 4 discusses the potential of utilizing the model-based approach for SAF certification.
Section 5 summarizes this paper and puts forward future research directions.
2. Materials and Methods
2.1. Integrated Engine Modelling
A low-fidelity integrated engine model (IEM) was first established to evaluate engine SCPs at the co-work point of massive engine components. The IEM was designed to have two categorized modules: the node and the component module. The former guarantees the global conservation of massive components, including the fluid and the mechanical nodes, while the latter describes the detailed behaviors of each component, including the GFP and SAS components.
As the connector of adjacent or related components, the node module solves various GFP and SAS components simultaneously with a unified conservation criterion. The fluid node ensures mass and energy conservations at each interface between adjacent components. The momentum transfer at the interface is neglected, assuming that the volumes between the components are sufficiently large. Under the steady states of aero-engines, the fluid nodes ensure conservation by solving Equations (1) and (2):
where the enthalpy flowrate is calculated as
for related components.
It is also important for aero-engine spools to guarantee the power balance between power-generating (such as the turbine) and power-consuming components (such as the compressor). Under the steady states of aero-engines, the mechanical nodes ensure energy conservation by solving Equation (3):
where the power flowrate
equals the enthalpy flowrate rise over each related component.
For convergence consideration, it is preferred to solve these conservations using the time-marching method [
33]. Therefore, Equations (1)–(3) could be transformed into the dynamic form by adding the term at the right side of the equations, indicated as Equations (4)–(6):
where Equations (4) and (5) represent the aerodynamic conservations achieved by fluid nodes, and Equation (6) represents the rotor-dynamic conservation achieved by mechanical nodes. Under constant aero-engine boundary conditions and fuel flows, the solution of Equations (4)–(6) would converge with the solution of Equations (1)–(3) as the solving time
enlarges. These conservation relationships are generally applicable for both GFP and SAS components with great convergency.
The component module describes the nonlinear responses of mass, enthalpy, and power flowrate under the boundary conditions set by the node module, such as the total pressure
, total temperature
, and rotor speed
. Notably, the combustor’s preliminary response is acquired by means of a semi-analytical model. Since the combustor is the stationary part of the aero-engine, it does not involve the power balance with the rotating parts or the spools. Therefore, the model mainly includes mass and energy change over the combustor, indicated as Equations (7)–(8):
where the fuel’s enthalpy flow is neglected in Equation (8) since it is relatively small compared to its internal energy. The air flow at the combustor inlet
and the combustion efficiency
are dependent on aerodynamic parameters of the upstream and downstream fluid nodes. They can be interpolated by the combustor’s characteristic map and modified by the experience coefficients
Cw and
Cη.
This low-fidelity model can be solved by non-linear algorithms, such as the N+1 algorithm [
34]. At each pseudo time step, the algorithm first guesses the boundary conditions on the fluid and mechanical nodes. Then, the algorithm may obtain the components’ responses and calculate the residuals of Equations (4)–(6). Next, the algorithm modifies the guess values until the result reaches acceptable accuracy.
Compared to the conventional engine modeling approaches [
26], the proposed integrated modeling approach with the unified criterion can achieve the conservation of GFP and SAS components without extra blending/returning modules. This convenience provides a better consistency between the model and the engine structure and simplifies the modeling complexity. In addition, the proposed model can solve the engine components simultaneously under the unified criterion without assigning different numerical solvers for GFP and SAS components, respectively. This may be beneficial for achieving better numerical efficiency for engine model calculation, which is important for the multi-fidelity iteration.
This low-fidelity IEM could effectively calculate the SCPs throughout the engine flow field, considering the GFP and SAS components’ impacts on the aero-engine’s operation state. It not only shows excellent numerical convergency, but also has the capacity to be modified by high-fidelity models. Therefore, the low-fidelity IEM can be recognized as an adjustable surrogate model for further detailed analysis.
2.2. Multi-Fidelity Iteration Strategy
This paper proposed a multi-fidelity iteration strategy to embed the combustor’s high-fidelity CFD model into the engine’s low-fidelity model, establishing the mapping relationship between SAFs’ properties and the engine’s SCPs through the combustor’s performances.
The objective of this strategy was to seek accurate SCP values at the engine’s co-work point influenced by SAF’s properties. The multi-fidelity strategy is indicated in
Figure 2. Firstly, the low-fidelity IEM provides rough aerodynamic boundary conditions to the combustor’s CFD model, including combustor inlet total pressure
total temperature
outlet mass flowrate
, and fuel flowrate
. These boundary conditions may not be accurate enough until a few iterations have been made. The reason for this is that the low-fidelity IEM estimates the combustor’s performances via the semi-analytical model, which may be insufficient for considering SAF properties and the combustor’s structure.
Secondly, the CFD model may analyze the detailed combustion process, flow pattern, and combustor performances under the abovementioned boundary conditions calculated by the IEM. The impacts of SAF properties and combustor structure are considered. Concerned performance parameters in this paper include the combustor’s pressure recovery coefficient
, outlet temperature (also known as the turbine entry temperature)
, and outlet pressure non-uniform coefficient
[
35]. In other words, the CFD model outputs
, and
in each multi-fidelity iteration for further engine-level simulation.
Next, the CFD model returns the combustor’s performance to modify the IEM’s low-fidelity surrogate model by adjusting the coefficients . The outlet pressure non-uniform coefficient is directly set to the high-pressure turbine, which is located adjacently downstream of the combustor, considering the influence of the pressure inlet non-uniformity on the turbine efficiency. After the modification, the low-fidelity model would be able to provide more accurate boundary conditions for the next iterations. Guided by the multi-fidelity iteration strategy, the engine-level SCPs at co-work points would converge to accurate values as the residual error of the combustor’s performances reduces to an acceptable value .
Notably, this paper proposed a control-theory-analogy training algorithm when modifying the low-fidelity IEM. Governed by Equations (4)–(8), the IEM can be regarded as a non-linear system or an aerodynamic-conservative network model. The components can be regarded as the flow and power links between the nodes. The experience coefficient
can be regarded as an adjustable parameter to be trained by the algorithm. The training algorithm for the IEM regards the high-fidelity model’s results
as the control targets. The error between the models is defined as Equation (9):
Analogized to the control theory [
36], the adjustable coefficients can be modified by the proportional, integral, and derivative values of the error, as shown in Equation (10):
Under steady engine operating conditions and constant fuel flows, the adjustable coefficient would converge to appropriate values. The error between the low-fidelity and high-fidelity models would approach acceptable accuracy at the same time, outputting the well-trained IEM. This control-theory-analogy training algorithm does not depend on the gradient calculation. It shows great convergence with appropriate values of the coefficients , , and . This is beneficial for embedding the high-fidelity combustor model into the low-fidelity engine model.
The conventional approach to embedding the combustor’s CFD model into the engine model has to acquire the combustor’s characteristic map before the engine-level calculation. Obtaining the characteristic map requires massive CFD calculations over a wide range of the combustor’s boundary conditions. The higher the accuracy required for the map and the engine-level matching calculation, the denser the sampling point of the combustor CFD calculation. The calculation time also increases according to the power law when considering the fuel properties as the independent variable of the combustor’s characteristic map and the input of CFD simulation. The proposed multi-fidelity algorithm only needs to compute the combustor’s CFD model near the engine-level matching state, attributed to the rough guess of boundary conditions provided by the engine model in each multi-fidelity iteration. The multi-fidelity algorithm shows great convergence, and it can usually obtain the co-work point within ten iterations and CFD calculations with appropriate initial values. This convenience is beneficial for reducing the computation resource costs when evaluating an SAF’s engine-level safety impacts, achieving the same engine-level matching calculation accuracy as the conventional approach. In addition, the proposed approach is beneficial for considering the impact of the combustor’s high-dimensional characteristics on aero-engines, such as the outlet pressure’s non-uniformity or the aerodynamic parameters’ distribution.
Combining the IEM and the multi-fidelity iteration strategy, the proposed MF-IEM could not only effectively evaluate the SCPs through the engine flow field, but also recognize the SAF’s property differences in detail. It may be applicable for quantifying SAFs’ influences on aero-engine safety.
4. Discussion
The MF-IEM represents an engine-level scope and tool to evaluate SAF’s safety. Based on the MF-IEM, an engine-level comparative safety criterion could be established for SAF safety assessment and airworthiness certification. Current SAF safety requirements, such as ASTM D7566 [
47], impose fuel-level restrictions on SAFs’ compositions and physical properties. These restrictions mainly refer to service experiences with fossil fuels. However, these fuel-level restrictions may be neither sufficient nor necessary for novel SAFs’ safety assessment within the engine-level systematic scope. For instance, SAFs’ lignin content may significantly influence carbon deposition on the gas flow path and deteriorate turbine blades’ cooling. However, there is no corresponding requirement in published SAF safety standards, which may lead to safety risks in aero-engine operation. Meanwhile, ASTM D7566 clearly restricts SAFs’ aromatic content, because it may influence rubber ring swelling and oil sealing performance [
48]. However, recent research reveals that cycloparaffins may implement the same functionality [
49]. Similar over-restrictions derived from experiences with fossil fuels may impose unnecessary limitations on developing SAFs with novel ingredients and refining pathways. This deficiency may lead to higher SAF prices and fewer applications. Engine-level evaluation has the potential to comprehensively consider the influences of SAFs’ various physical properties and their interrelationships. It is suggested to evaluate SAFs’ safety on the engine level.
Within the systematic scope, the criterion for SAF safety assessment is supposed to be the capacity to support the continuing operation of aero-engines. Aero-engine SCPs when adopting SAF should be safer than when adopting fossil fuels or other certificated fuels. As shown in
Figure 5, the aero-engine SCPs based on certificated fuels are considered as the benchmark or the safety boundary. These boundaries can be obtained using databases of certificated fuels’ properties and usage experiences. Thereby, fuel producers and aero-engine designers can evaluate SAF’s engine-level safety comparatively. If SAF-based SCPs are similar enough or comparatively safe, the SAF may have the potential to achieve engine-level safety. Therefore, fuel producers and aero-engine designers are encouraged to expand their production and applications after further validations, such as engine and flight tests. Otherwise, they could conduct detailed research to judge whether the SCPs’ deviation is acceptable. If the detailed research shows that the influence is acceptable for the aero-engine operation, the SAF could still be a candidate for further evaluation. Otherwise, fuel producers are supposed to make the necessary adjustments, such as blending the SAF with certificated fuels with an appropriate blending ratio or improving the refining process.
The proposed model-based approach provides a preliminary screening before costly tests, which may be beneficial to reduce the dependency on various tests and reducing the certification cost. Instead of carrying out engine-level tests that require a large amount of fuel for each certification trial, SAF producers only need to produce small volumes of the fuel sample to acquire the necessary properties required by the model’s input, such as the heat value. Then, producers may obtain SAF’s engine-level safety influences from the proposed model. The results may support producers in deciding whether to carry out further certification processes. The quantitative evaluation results may also guide SAF producers in making targeted adjustments. These conveniences may reduce trail-and-error costs when developing the novel SAF. In the future, as the models continue to be validated and become increasingly reliable, it is also promising that the certification authority may allow SAF producers to use an analysis approach supported by the simulation results to show compliance with the safety standards, substituting parts of the tests and reducing the certification cost.
In addition, the newly tested SAFs may also enlarge the safety boundary and renew the safety assessment benchmark. Since the proposed criterion focuses on SAF’s influences on engine-level impacts rather than strictly imposing restrictions on fuels’ physical properties, the proposed certification process may reduce the probability of failing the SAFs that exceed the current fuel-level restrictions yet would not degrade engine-level safety parameters. This convenience may allow SAFs with a broader range of fuel physical properties and blending ratios for further validation. If these validations show no deterioration in aero-engine safety, the results may support researchers in proposing amendment suggestions for fuel safety requirements, enlarging the fuel property restrictions or blending ratio limits referring to these SAFs.
The proposed comparative safety criterion does not concern whether adopting SAFs can push aero-engines beyond their absolute safety boundary. Instead, this criterion examines the deviation in engine SCPs when using SAFs compared to fossil fuels or other certificated fuels. Under this criterion, the proposed model plays a role in providing a consistent platform or mapping relationships between fuel properties and engine SCPs for both SAFs and fossil fuels. The model’s inherent uncertainties, such as the applicability to the novel SAF to be certificated, would not significantly influence the assessment conclusions in SCPs’ deviation trends. As the model continues to be validated and improved, it will be able to assess the deviation magnitude more precisely.
5. Conclusions
This paper proposed a model-based approach to evaluate SAF’s safety at the aero-engine level. The proposed MF-IEM could effectively establish the mapping relationship between the SAF’s physical properties and the aero-engine’s safety-critical parameters. The contributions of this paper can be summarized into the following two points.
First, the proposed MF-IEM can effectively evaluate SAF’s influence on aero-engines’ SCPs. The MF-IEM first establishes a unified criterion to ensure the aerodynamic conservations of both the GFP and SAS components of aero-engines. Thereby, SCPs throughout the engine flow field can be evaluated under the co-work point. A surrogate-based multi-fidelity iteration strategy is then proposed to embed the high-fidelity combustor model into the engine model. A control-theory-analogy training algorithm is used to train the aero-engine network model by regarding the high-fidelity model’s results as the control targets and the low-fidelity models’ adjustable coefficients as manipulated handlers. The proposed model-based approach shows great numerical convergence and sufficient accuracy for SAF safety assessment.
Second, the proposed approach is applied to an F-T SPK safety assessment case. The effects of fuel flow and the SAF’s blending ratio with Jet A are discussed. The results prove the necessity to assess the SAF’s safety on the engine level. The case study shows that only researching SAF’s impact on the component level may underestimate the severity of the turbine entry temperature increase by 33.3%. In addition, the results show that adopting the F-T SPK will improve thrust and specific fuel consumption. However, it will also increase the turbine entry temperature, which may be detrimental for the hot-section and engine life-limited parts. Notably, the influences of SAFs on SAS-related SCPs show an equivalent severity compared to the GFP-related SCPs, which also need to be aware of for SAF safety assessment.
Based on the proposed MF-IEM, the SAF producers and aero-engine designers could effectively evaluate SAFs’ influences on engine safety compared to fossil fuels. This may be beneficial for reducing certification costs and expanding SAF’s application. In the future, we will extend our research to the transient modeling of MF-IEM and evaluate SAFs’ safety influence during an engine’s accelerating and decelerating process, such as take-off and landing. It is also of interest to evaluate SAFs’ influence on the failure risk of aero-engine’s life-limited parts corresponding to the airworthiness requirements, which requires investigating the SAF’s properties uncertainty caused by product instability and conducting SCP probabilistic analysis.