1. Introduction
The gas turbine engine, a sophisticated piece of thermal equipment with symmetrical geometry, plays an important role in the aerospace industry [
1]. To promote the rapid development of the gas turbine, researchers urgently need a good performance model to replace many real engine tests with numerical simulations, which could make the development process more efficient and economical [
2]. Additionally, an accurate performance model is crucial for good gas engine controls, diagnostics, and prognostics [
3,
4].
Generally, the accuracy of a performance model mainly depends on accurate component characteristic maps. However, it is sometimes difficult to obtain the real component maps of an engine due to many different reasons, such as lacking bench testing, performance degradation, and engine-to-engine variations [
5,
6,
7]. Against this limitation, multiple-point performance adaptation methods have drawn more and more attention in recent years [
8]. These methods suggest a tuning of generic component maps to make an engine performance model match all measured performances. Typical published work is briefed as follows.
In the early 1990s, Stamatis et al. introduced an adaptation method that was able to calibrate existing component maps by optimizing scaling factors [
9,
10]. In 2009, Li et al. used a genetic algorithm method to search for an optimal set of scaling factors [
11]. In the following years, such a method was further developed by applying variable scaling factors to achieve a nonlinear multiple-point adaptation [
12,
13]. In 2014, Alberto and Benini performed map modifications in the neighborhoods of the multiple experimental points [
14]. An optimization algorithm was applied to seek optimal sets of perturbations on the map in order to minimize the deviation between experimental and predicted performance. Tsoutsanis et al. introduced a novel map representation and an optimization algorithm for the adaptation [
15,
16]. By employing elliptic curves to generate compressor maps, they refined gas turbine models with improved accuracy. Recently, Pang et al. proposed a joint adaptation method that added a transient performance adaptation procedure following the steady-state counterpart [
17]. After a two-step optimization process, engine models can be calibrated to have more accurate transient performance predictions.
The published work for multiple-point performance adaptations involves complex numerical searching and optimizations. Facing such problems, most researchers prefer to employ metaheuristics, such as genetic algorithms [
11,
12,
13,
15,
16] and evolutionary computation [
17]. The metaheuristics can often find good solutions over a huge set of feasible solutions with less computational effort than other optimization methods and proved to be useful approaches for optimization problems [
18,
19]. However, some drawbacks exist, such as long computing time when the number of points included in the adaptation is large. In addition, metaheuristics do not guarantee that a globally optimal solution can be found [
20]. Many heuristic methods contain stochastic procedures so that the solution found is dependent on the set of random variables generated [
21]. Furthermore, it is very tricky to specify the appropriate search domain for the adaptation calculations in practice. Therefore, Li et al. explored a non-heuristic method for performance adaptation problems [
22]. The method was applied to an industrial gas turbine engine and demonstrated by the comparison results. However, this approach is only suitable to the design point.
This paper proposes a deterministic approach to deal with the multiple-point performance adaptation of gas turbine engines. At first, engine measurements are employed as input information to estimate actual engine performance by a numerical iterative solution process. Next, we compare that performance with the predicted one (using the model with initial component maps) and summarize the comparison using scaling factors. Finally, an interpolation-based algorithm is developed to determine the overall modification of all major component maps. The proposed approach is applied to a model turbofan engine similar to the General Electric CF6 series. Simulation is carried out to demonstrate the capability of the proposed performance adaptation method. The results, discussions, and conclusions are made accordingly.
Compared to the heuristic methods, the novelty of this approach is that a deterministic calibration procedure replaces the searching algorithms to obtain some scaling factors and thus achieves performance adaptation with high accuracy, low computational complexity, and deterministic results.
The remainder of this paper is organized as follows:
Section 2 describes the methodology of the proposed deterministic calibration method.
Section 3 details the simulation results to demonstrate the effectiveness of the method.
Section 4 discusses the method’s advantages in three aspects. The final section provides a summary of this paper.
5. Conclusions
This paper presents a deterministic approach for multiple-point performance adaptation, specifically designed to calibrate the off-design performance of gas turbine models. In contrast to the well-developed optimization-based methods, this approach advocates for determining the shift of the initial characteristic maps in a straightforward manner. This concept is realized by calculating each Scaling Factor (SF) set at its corresponding measured condition and subsequently employing an interpolation-based algorithm to ascertain the precise shift of each map.
As discussed in
Section 4, this approach offers three primary advantages:
- (1)
The time complexity of this approach is notably low.
- (2)
The prediction error of the adapted model can be guaranteed at a relatively low level.
- (3)
In contrast to optimization-based approaches that entail stochastic procedures, the deterministic approach eliminates the need for a searching procedure and consistently delivers a reliable outcome.
The effectiveness of the proposed approach is demonstrated through its application to a model high-bypass turbofan engine. Following the adaptation process, a significant enhancement in the prediction accuracy of the model is observed, with the prediction error index decreasing from approximately 9% to about 0.6%. Owing to the modification of component maps, the method can be easily transplanted to other engine types and configurations. And with its assured results and minimal computational burden, this approach holds promise as a valuable tool for the calibration of gas turbine models.
The limitation of the proposed deterministic approach is that it is currently suitable for steady-state performance adaptation. The related dynamic performance adaptation and transient analysis need further research. Additionally, only simulated data are used in this paper to illustrate the effectiveness of the method. Applying real engine measurements for verification will be considered in future research. What is more, the impact of measurement uncertainties on model predictions is a direction worth exploring. Uncertainty analysis techniques such as Monto Carlo simulations are an optional solution for conducting future research.