Exploring the application of digital twin in the field of micro turbine engine core components

Abstract

The micro turbine engine (MTE) plays a vital role in the aerospace sector. However, traditional research and design models no longer suffice to accommodate the highly complex operating conditions of the MTE. Therefore, this paper briefly analyzes the concept and development process of digital twin technology and integrates it into the research and design of the MTE. This integration takes into account the recent leapfrog developments in information technology and digital intelligence technology. Utilizing digital twin technology to model the core components of the MTE allows for effective structural optimization, online monitoring, and timely problem detection in support of extending the overall lifespan of the engine. Multiple algorithms are used throughout the development, design, and usage phases of each component to merge into a cohesive whole, providing robust support for the MTE's overall development, production, and manufacturing. Digital twin technology facilitates accurate performance prediction, reliability evaluation, and advanced design optimization for the MTE. This, in turn, reduces the design cycle and research design cost more effectively. Lastly, we propose the future application and development trend of digital twin technology in the core components of the MTE.

INTRODUCTION

In recent years, countries around the world have been responding to changes in the global situation by increasing their focus on their own territorial security and ensuring the stability of the surrounding areas. The protection of their territorial integrity has become increasingly important, especially in the naval, land, and air domains where the risks are high. This has resulted in the miniaturization of equipment in the aviation industry, playing a crucial role in electronic air warfare, environmental monitoring, and precision detection. Additionally, aircraft now require higher performance in terms of endurance, stealth, and other factors, making micro turbine engines (MTE) particularly noteworthy due to their unique characteristics. As a result, MTEs have garnered attention from scholars both domestically and internationally, becoming a significant focus of research.¹ MTE has the potential to serve as a portable energy source in the future, owing to its lightweight and small size.² Furthermore, refueling is a more convenient way to supplement energy. Chemical cells, fuel cells, and solar cells are the main power sources used in micro air vehicles, but they have significant drawbacks, including limited range. Hydrogen and hydrocarbon fuels have an energy density that is 10–100 times greater than the best chemical lithium battery, making them more efficient for use in MTE. The development of micro-electro-mechanical systems (MEMS) and micro-processing technology has created favorable conditions for the advancement and manufacturing of MTE technology.^3–6 This paper focuses on the advancements in digital twin technology within the MTE field, as well as the technical challenges that the technology faces. Additionally, the paper explores the potential future development trends of digital twin technology in manufacturing.

DOMESTIC AND INTERNATIONAL RESEARCH PROGRESS

The MTE, initially proposed by Epstein at MIT, is a representative power MEMS device with great potential for future aerospace development due to its inherent capability for high power density, which is 20–100 times greater than existing lithium batteries.^7–11 By the 1950s, various prominent research and design organizations such as Williams International and Microturbo S A had emerged, leading to decades of development that have since matured the technology and produced various product types.¹² In the early 1970s, the American company Teledyne Turbine Engines designed the J402 series of engines for cruise missiles used by the US Navy, laying the foundation for small aero engines. In the 1990s, Microturbo in France developed the latest engine in the 350 daN thrust class, which improved boost ratio and efficiency.^13,14

In the 1970s, Russia developed the TRDD-20 twin-rotor turbofan engine with the structure illustrated in Figure 1, while Japan started developing a small turbojet engine for use in UAVs during the same period.^15–17 In the 1990s, China conducted research and development, and the Institute of Micro Aero Engines of Northwestern Polytechnic University designed and developed the first micro turbojet engine principle prototype, W²P-1 (Figure 2), filling a gap in China.¹⁸ Due to its advantages of small size, low vibration and noise, low NOx generation, and low environmental pollution, MTE has gained global attention and sparked a surge of research. This review summarizes MTE components from both domestic and international sources, briefly discusses overall design, cost control, application fields, and key components, and offers future prospects.

Figure 1. TRDD-50AT engine structure.15

Figure 2. The first micro-turbojet engine in China.18

MTE working principles

The working principle of MTE is similar to that of conventional gas turbine engines, as shown in Figure 3, consisting primarily of a compressor, combustion chamber, turbine, and accessories. The working process involves starting the engine, where the impeller does work on the gas after the high-speed rotation of the compressor, sucking in and compressing air, flowing through the air duct into the combustion chamber where reaction fuel is mixed. After the chemical reaction, a large amount of gas and heat is produced, ejected through the combustion chamber outlet, and the gas impacts the turbine blades via kinetic energy, driving them to rotate at high speed. The turbine drives the output shaft to produce a certain torque, and the gas ejected through the nozzle at high speed produces a reaction force on the engine, ultimately generating thrust.¹⁹

Figure 3. Micro turbine engine working principles.

Proposal and development of the digital twin

The concept of the digital twin was first introduced by Grieves in 2003 at the University of Michigan's Office of Product Lifecycle Management. It is defined as the part that establishes linkages between physical and digital entities, and the relationships between them.²⁰ By integrating various data from the digital twin physical system, the entire life cycle of the physical system is comprehensively mapped and co-evolved or optimized using parsing algorithms.²¹ Figure 4 represents the development process based on the digital twin. Siemens is well-known for advocating the concept of the digital twin,²² which uses the information space to build a system model of the manufacturing process, digitizing the entire product design phase to the manufacturing phase in the physical space. This, in turn, can predict product performance in the research and design phase and provide auxiliary decisions for the system operation.^23,24 Other companies, such as ANSYS,²⁵ IBM²⁶ have also defined related digital twins, essentially expanding and upgrading on Grieves' original definition.

Figure 4. Digital twin development process and application areas.22

Digital twinning technology is widely used in the aerospace industry for full lifecycle management. By incorporating all models, including physical entities, into a virtual world that corresponds to the real world, the digital twin model enables product lifecycle management, improves product quality, reduces costs, and enhances performance. This technology offers a new development direction for the field and provides new ideas and methods for designing, producing, and maintaining aerospace products. MTEs are an important power unit for turbofan engines used in micro air vehicles due to their simple structure, light mass, and low noise. However, limitations such as complex engine structure, small size, and complicated design and manufacturing processes hinder their practical applications.^27,28 To overcome these limitations, the MTE is simulated, analyzed, and optimized using digital twin technology, and the resulting numerical model is validated by experiments. Compared with traditional simulation techniques, digital twin technology offers several advantages²⁹ (Table 1).

Table 1 Advantages of digital twinning technology.

Advantages	Content
Efficient	By simulating and optimizing the engine in a virtual environment, calculations become more efficient. Additionally, digital twinning enables full lifecycle management of engine performance, allowing for continuous monitoring and improvement throughout the engine's lifespan;
Accuracy	Digital twinning technology enables the simulation of real-world physical entities in a virtual environment, allowing for optimization and verification of their performance. This technology provides effective support for quality control of products during actual production and use, ensuring that products meet or exceed expected performance standards;
Interactive	Compared with traditional simulation technology, a digital twin model based on data has several advantages. It not only simulates the product's structure, process, and performance but also interacts with the product design and production process. This technology provides guidance and advice to the product throughout its subsequent use, enabling continuous improvement and optimization;
Intelligent	The digital modeling method adopts digital simulation of physical objects to enable on-line monitoring and diagnosis of real physical objects. This allows for real-time monitoring and timely detection of potential hidden dangers in physical objects;
High real-time	Digital twinning technology uses digital modeling to simulate complex behavior during engine operation, resulting in shorter simulation times. Additionally, there is a one-to-one correspondence between the simulation model and the real physical object, allowing for real-time simulation and optimization analysis. This technology enables efficient and accurate analysis of engine performance, allowing for timely adjustments and improvements.

Application of digital twins in industry

Digital twinning technology is an advanced method for managing digital assets, production activities, and asset lifecycles in intelligent manufacturing for industrial applications. It involves the entire process from design to production, and the entire lifecycle of a product from concept to delivery to consumers. Digital twins can be utilized in many ways throughout these stages. For example, during the development of a new manufacturing system, differences in machine tools across different mechanisms, controllers, and communication interfaces require significant time and resources for debugging, equipment transportation, assembly, integration, verification, and testing. To address this issue, digital twin technology can be used to design, configure, and operate an intelligent manufacturing system based on a new method of remote semi-physical debugging, resulting in significant time and cost savings.^30,31

With the onset of the industry 4.0 era, intelligent manufacturing has become the global trend in manufacturing. Zhang et al.³² integrate digital twinning technology into manufacturing system design. In the manufacturing process, whether upgrading process equipment or researching and designing new products, a significant number of experiments are conducted, which is a major contributor to the high cost of manufacturing products. Taking the manufacturing process as an example, NC machine tools, robots, and other intelligent devices require numerous experiments to validate their performance. Therefore, a large number of experiments are needed to ensure the feasibility of manufacturing before production. In the traditional approach, these experiments are often conducted after product development has been completed, resulting in wasted human and material resources, as well as economic loss to the enterprise. Digital twinning, a new technology, simulates physical entities by establishing mapping relationships between physical and virtual entities, and conducts experiments in virtual environments to confirm that physical entities meet the expected requirements. For instance, Chai et al.³³ demonstrated the fabrication technology for casting process samples and prototypes, which includes data sensing and visual operation monitoring of condensing shell furnace equipment, as well as high throughput preparation of casting performance and standard specimens. By utilizing modular, standardized, and process-oriented intelligent design of titanium alloy fittings, process simulation technology and automated data collection, an algorithmic model for regulating the heat treatment process in the processing and production of sample parts is proposed. Digital twin technology offers full life cycle management, reusability, and scalability, making it possible to create virtual models that significantly reduce the time needed for new product development.

Mahmoud and Grace,³⁴ proposed a digital twin-based simulation approach for configuring smart manufacturing systems (SMS) after reviewing existing development models. They argue that creating a digital twin at the design stage of an SMS has numerous advantages over traditional simulations, including continuous digitization, realistic models, and interdisciplinary interactions. SMS are complex integrated systems that involve multiple domains and are made possible by the coupling of intelligent machines, products, materials, and other elements. In another study, Leng et al.³⁵ utilized digital twin technology to build prototype SMS and plan system test scenarios during the configuration phase. This approach helps to reduce the number of trial and error experiments and more accurately identify areas that require intelligent systems. The most significant advantage of digital twin technology is its ability to replace the purely physical tuning phase, serving as a novel design method and effectively improving design efficiency.^36,37

In system operation, by creating a digital twin of the roller conveyor line, the CPS (cyber-physical systems) technology enables real-time monitoring and optimization of the conveyor line's performance, including sorting accuracy, throughput, and energy consumption. The digital twin also allows for predictive maintenance, as it can simulate the wear and tear of equipment and alert operators to potential failures before they occur. Overall, the use of digital twin technology in CPS can greatly improve the efficiency and productivity of SMS logistics operations.³⁸

Review aim and novel contributions

The aim of this paper is to explore the use of digital twinning in the aeronautical field to reduce design cycle times, monitor real-time status, and predict maintenance requirements for MTE. To achieve this objective, a comprehensive literature review is conducted, focusing on the development process of digital twinning, the historical evolution of MTE, and the challenges and opportunities for future research in breaking through new technology barriers. The paper's innovation lies in the creation of a digital twin of MTE and the implementation of real-time health monitoring and fault prediction for MTE. By modeling the digital twinning of the core components of the MTE, effective integration of the components into a whole allows for more effective structural optimization, online monitoring, and timely detection of problems to meet the extended overall life of the MTE. Using digital twinning technology, the health status of key components of MTE is predicted, and active early warning, control, and protection mechanisms are implemented to avoid engine downtime due to failure.

MAIN CORE COMPONENTS

The main components of the MTE are the compressor, the turbine, the bearings and the combustion chamber. The details are shown in Figure 5.

Figure 5. Micro turbine engine.39

Air compressor

The construction of compressors can generally be classified into three types based on the flow characteristics of air: axial, centrifugal (also known as radial), and a combination of both types. Based on the evolution and development of these three categories, centrifugal compressors are used more frequently due to their superior single-stage pressure ratio and relatively compact structure, making them particularly suitable for micro engines.⁴⁰ The importance of the compressor is self-evident, as it mainly draws in air to reach a certain pressure value and provide the gas source for the operation of the combustion chamber. The impeller design of the compressor is typically classified into front and rear curved and radial types based on the impeller exit angle. Each type has its own advantages and disadvantages,⁴¹ as shown in Table 2. With the continual advancement of science and technology, the production of miniature components is becoming increasingly accessible, thanks to the emergence of advanced technologies such as MEMS and additive manufacturing, which enable the manufacture of three-dimensional miniature structures.

Table 2 Impeller efficiency, processing comparison.

Classification	Efficiency	Ease of processing
Forward curved impeller	Minimum	Easy
Radial impeller	Moderate	Medium
Backward curved impeller	Highest	Difficult

Compressor under digital twin

The concept of digital twin has been discussed earlier, and it is now widely used in the engineering field. Nowadays, digital twin technology is also used for compressor testing, as shown in Figure 6. Hosseinimaab and Tousi⁴³ utilized neural networks to optimize the geometry of centrifugal compressors through approximate modeling of the design space, resulting in space savings and decreased design costs. Meanwhile, Yang Kang proposed that detuning characteristics arise on the physical leaf disc, and suggested utilizing digital twin technology to non-contactly measure blade dynamic strain. Given the critical role and complex nature of the blade, real-time acquisition of dynamic strain and stress levels can allow for early warning failure detection and adjustments to promote blade health.⁴⁴ Yan⁴⁵ proposed a blade fault diagnosis method based on Support Vector Machine (SVM) and a hybrid model to overcome the limitations of not having performance data available or when the accuracy is low. The diagnosis flow chart is illustrated in Figure 7. The increasing performance requirements and design complexity of compressors have made traditional research methods more challenging. The hybrid model-based gas turbine blade fault early warning and diagnosis addresses several crucial issues and proposes an automatic blade diagnosis method based on an improved similarity algorithm that can automatically identify blade fault types, leading to enhanced stability, economy, and operational safety. However, the integration of digital twin technology has the potential to address many of these issues. By simulating real-time online conditions in a virtual environment, digital twin technology can effectively improve compressor development to meet new challenges and demands, the virtual-real interaction in reliability digital twin, model self-correction, and high-fidelity simulation support real-time condition monitoring, reliability design, process control, failure mode analysis, and prediction, as well as reliability assessment. These capabilities aid in enhancing the reliability of engine design, manufacturing, and usage.⁴⁶ The digital twin technology provides various functions such as predictive maintenance, performance prediction, and fault diagnosis. It allows the integration of various technologies such as neural networks and vector machines throughout the product development, production, and sales management processes. It is an outcome of technological innovation, product innovation, research and development, and quality improvement in manufacturing.

Figure 6. Current status and needs of compressor testing.42

Figure 7. Flow chart of blade fault diagnosis method based on SVM and hybrid model.45

Bearings

With advancements in modern science and technology, traditional bearings face challenges in achieving high precision and high speed performance. This is especially true in the field of MTE, where small size and high speed are crucial requirements. In this context, lubrication and support become critical factors that need to be addressed.⁴⁷ The proposed air bearing provides a solution to the aforementioned difficulties to a certain extent. Air bearings utilize air as a lubrication medium, minimizing the influence of material friction and fully embodying their advantages in the field of high precision and high speed. The use of air bearings is very versatile and has been applied in various industries such as the machine tool, electronics, and precision machinery industries.^48,49

Bearings under digital twin

The theory of bearing condition monitoring and fault diagnosis based on deep learning has become a popular research topic in recent years. Previous methods relied on historical operation and maintenance data, but missing data often led to inaccurate results and other issues. To address this, a bearing condition digital twin model has been proposed.⁵⁰ Wang⁵¹ examined the viability and potential solutions for machine learning and deep learning approaches in various bearing fault diagnosis scenarios. These developments have widely promoted the application of data-driven fault diagnosis methods, though they typically require a sufficient amount of labeled data to train a highly accurate model. For fault diagnosis tasks under different task conditions and source domains of knowledge, exploring migration solutions utilizing data from different equipment conditions, different bearing objects, digital twin models, and multiple source domains. Meanwhile, Ma et al.⁵² obtained fault feature data by simulating faults in the digital twin of physical equipment and performed iterative learning of the aforementioned fault data using deep machine learning to analyze and assess operational conditions for aurora. This method generates and diagnoses fault features based on the digital twin model. By using model simulation to obtain fault feature data, the technique offers a virtual data source for fault diagnosis algorithms. The iteration and analysis of this “virtual data” via deep learning technology can produce a fault diagnosis model that accurately assesses the health condition of the equipment. The digital twin technology mainly interacts with the actual product virtual reality through deep product modeling, the use of the virtual-real mapping model in the whole-life reliability of the MTE involves establishing a physical-virtual mapping relationship in both the design and manufacturing/testing/operation/recycling phases. Since engine entities and actual operating environments do not exist during the design phase, the virtual-real mapping mechanism in both phases contain four links—modeling, description, diagnosis, and prediction, highlighting that building a digital twin technology brings certain effectiveness and ensures that the problem of data imbalance exists in the process of building a bearing monitoring system.^52–54

The research on bearing fault diagnosis based on digital twin technology still has problems such as low accuracy of bearing fault diagnosis, inability to perform big data analysis, not making full use of time series data, and less research on complex equipment fault diagnosis and intelligent decision support. To operate the equipment, various factors will affect the equipment status, such as vibration, temperature, current, displacement, and other parameters that have a direct relationship with the fault status of the bearings. Therefore, a comprehensive analysis of these data can obtain more information and provide better help for an intelligent decision support system.

Combustion chamber

The combustion chamber is one of the three core components of an engine and can be compared to the “heart” of the engine, playing a critical role in its operation.⁵⁵ The high temperature and pressure within the combustion chamber constitute a multidimensional and dynamic process, which necessitates extensive time for development and design to achieve relative stability. This requires numerous numerical simulations for analysis, significantly simplifying the cost and cycle time of the design process.^56,57 Reducing the size of the combustion chamber can lead to a decrease in the surface area ratio, which in turn can cause an increase in wall heat loss and flame instability.^58,59 Enagi et al.⁶⁰ designed and optimized a new combustion chamber geometry using a novel liquid biofuel combustion system. Manigandan et al.⁶¹ investigated the impact of various additive blends on the emissions and combustion performance of fuels. Yin⁶² utilized additive manufacturing technology to address the limitations of traditional manufacturing processes and designed a 50 kg class MTE reflux combustion chamber that maximizes the limited space of the combustion chamber and other components of the NK-10 engine combustion chamber, as shown in Figure 8. The research objectives of the combustion chamber include achieving higher combustion efficiency, reducing structural mass, and lowering fuel consumption rates.^63,64

Figure 8. NK-10 engine combustion chamber and other components.62

Combustion chamber under digital twinning

From both domestic and international perspectives, there are various research areas that integrate digital twin technology with combustion, offering new possibilities for combustion chamber design, optimization, and performance analysis. Liu et al.⁶⁵ employed cross-disciplinary incorporation of LSTM (Long Short-Term Memory) network-based machine learning to develop predictive models for microalgae hybrid fuel micro gas turbine engines. It is widely used in various applications such as signal processing, medical applications and other forecasting applications.⁶⁶ Figure 9 represents the simple architecture of LTSM. Ren et al.⁶⁷ constructed a direct numerical simulation (DNS) database of free-propagating premixed flames based on three different turbulence intensities. They developed a low-dimensional prediction model for flame-to-strain correlation using neural networks and random forests to enhance the efficiency and accuracy of flow field prediction. Pulga et al.⁶⁸ fully integrated neural networks with traditional combustion chemical reaction mechanisms, which not only improved computational accuracy but also reduced computational time. Pawar et al.⁶⁹ utilized eigenorthogonal decomposition and long-short time neural networks to model both known and unknown physical phenomena, incorporating data-driven machine learning methods to model residual residuals that may be concealed within the data, as shown in Figure 10. They achieved significantly higher accuracy compared to the conventional reduced-order method. Many studies have developed neural network models for flame strain measurement, which have been utilized for combustion simulation and optimization. The research on fusion combustion by domestic and foreign scholars reveals that the calculation method for fusion combustion based on digital twin technology is becoming a new trend with the continuous development of artificial intelligence and numerical simulation technology.

Figure 9. Long Short-Term Memory architecture.65

Figure 10. A hybrid model order reduction method based on proper orthogonal decomposition and long short-term memory neural network.69

Constructing a digital twin of the combustion chamber that integrates both data-driven and physical constraints can expedite the development of combustion chamber technology, showcasing the advancement of digital and intelligent integration in traditional research and design models.⁷⁰

Turbines

The turbine is a crucial component of MTE and is typically used in both centripetal and axial flow types. Centripetal turbines have several advantages, including low cost, good strength, large work capacity under high-temperature conditions, and high efficiency under small flow rates. In comparison, axial flow turbines have stronger circulation capacity under the same structure and have accumulated rich technology and experience in leaf design, enabling them to meet the structural requirements for multistage tandem connection.^71–73 Axial turbine losses, including losses from blade shape, secondary flows, and wake, all increase with larger sizes, which can lead to decreased efficiency when compared to smaller structures.^74,75 The Technical University of Lodz in Poland conducted an experimental study using a bipolar axial turbine with curved blades.⁷⁶ The results showed a smoother pressure gradient at the tip of the blade, as shown in Figure 11, effective suppression of secondary flow losses, and an increase in turbine design point efficiency by 0.5%. In China, Harbin Institute of Technology et al.⁷⁷ conducted a study on the design of curved blades for axial turbines, focusing on the appropriate range of bending angles and identifying key parameters that impact the performance of the turbine through experiments.⁷⁸ Xiang et al.⁷⁹ studied the numerical simulation of hot strip (HS) pattern on a miniature axial turbine to reveal the heat deposition and heat migration phenomena, and Figure 12 is the blade surface temperature. Structures of turbine components are receiving more and more attention, and researchers are increasingly focusing on health monitoring theory.⁸⁰ This is because turbines are subjected to harsh environments of long-term high temperatures and high pressures, and their lifetimes directly affect the service life of MTE.

Figure 11. Blade surface static pressure distribution.76 (A) Static pressure distribution near the hub of the turbine of the first stator. (B) Static pressure distribution in the middle of the flow channel of the first stator. (C) Static pressure distribution near the shroud of the first stator.

Figure 12. Temperature distribution of the blade surface.79 (A) Temperature distribution of pressure side, (B) ISO surface of total temperature (1220K), and (C) temperature distribution of suction side.

Turbines under digital twin

As technology continues to advance, an increasing number of researchers are utilizing digital and intelligent technologies to design and develop turbines. Wang⁸¹ conducted a study on turbine blade temperature monitoring, utilizing feature extraction methods to design monitoring models. Feature vectors extracted from training and monitoring phases can be predicted and matched to achieve the goal of accurate monitoring. To enhance the prediction accuracy of the monitoring model, a hybrid algorithm that incorporated Elman networks, average influence value algorithm, genetic algorithm, and particle swarm algorithm with adaptive variation was employed. Matej⁸² used 5-axis milling simulation implemented in an in-house developed virtual machining software called MillVis. The software utilizes a mathematical approach to simulate the machining and manufacturing of thin-walled impeller blades, taking into account the combined effects of material removal, machine tool dynamics, and cutting forces of the cutting tool and workpiece. Finnegan et al.⁸³ developed a model for tidal turbine 1 MW power generation nacelle with full-size fiber-reinforced composite blades through numerical modeling, advanced manufacturing techniques, and state-of-the-art structural testing techniques, which yielded some results.

Based on the above research, it can be observed that there are many mainstream algorithms available for turbine blade analysis. However, the difference lies in the time taken by each algorithm. This is also the reason why traditional methods take longer to analyze blades compared to current optimization and intelligent design methods. Using traditional and intelligent methods for blade analysis can yield different results due to this time difference. The intelligent method is a supplement to the traditional method and will continue to evolve with advancements in technology.

DIGITAL TWIN TECHNOLOGY IN MTE DEVELOPMENT TREND

The development of digital twin technology is fascinating and has brought about a paradigm shift. Its application is vast and encompasses industries such as healthcare, logistics, transportation, aerospace, and more. In the literature, a five-dimensional digital twin model has been proposed, which comprises physical entities (PE), virtual models (VM), services (Ss), digital twin data (DTD), and connections (CN). The mathematical representation of the five-dimensional relationship of the digital twin is illustrated in Figure 13. Using digital twin technology involves creating virtual models of physical entities, with the physical model serving as the foundation and the virtual model replicating its structure, dimensions, and other aspects. The key to handling multidimensional and multiple heterogeneous data is twin data, which prepares computations for follow-up processes, supports each link, and facilitates cooperative relationships between components, ultimately allowing for advanced simulation, operation, and analysis. The connection between the five dimensions is necessary for achieving data information and data sharing.^85–88 Digital twin technology allows for the creation of virtual models for physical entities, which can be used to simulate and analyze the performance of the MTE before it is actually built. This can help identify potential issues and improve the design, leading to better performance and reduced design cycles and costs. By establishing relationships between components, digital twin technology can help optimize the overall system and achieve performance goals.

Figure 13. Five-dimension digital twin model.84

Due to the unique structure of MTE, it is subject to various limitations in its application. Firstly, the complex and small size structure of MTE makes modeling more challenging. Secondly, MTE typically operates in high-speed flight conditions, and the aerodynamic characteristics of the flight conditions greatly affect the design of the digital twin model. Since it is difficult to determine the aerodynamic characteristics of MTE under high-speed flight conditions, the control algorithms and design requirements are higher. Third, the complex structure and aerodynamic characteristics of MTE require a more detailed digital twin model, which in turn requires more data for accurate modeling. This can be a significant challenge in terms of data acquisition, storage, and processing. However, the use of advanced sensors, data analytics, and machine learning techniques can help overcome these challenges and improve the accuracy of the digital twin model. Fourth, these three types of models are commonly used in combustion modeling for MTE and other applications. The flame surface model describes the combustion process as a thin surface where fuel and oxidizer mix and react, while the transport probability density function model uses probability distribution functions to describe the behavior of reacting species. The finite rate model considers the reaction rates of different species and their interactions, as well as the effects of temperature and pressure on the reaction rates. Each of these models has its advantages and disadvantages, and the choice of model depends on the specific application and the level of accuracy required. By combining multiple modeling techniques and machine learning methods, we can improve the accuracy and efficiency of combustion modeling for MTE. Multi-modal fusion digital twin technique can help to integrate different types of models to build a more comprehensive and accurate digital twin model of MTE, while efficient and general adaptive models based on machine learning methods can learn from large amounts of data to improve the accuracy of predictions and control strategies. These approaches have the potential to overcome the limitations of current combustion models and improve the performance of MTE. The development and promotion of intelligent digital twin technology is a global trend and requires collaboration and efforts from various fields and industries. With the increasing complexity of modern systems and the need for high efficiency and accuracy in their operation and maintenance, digital twin technology has become an important tool for achieving these goals. Its potential benefits in reducing costs, improving performance, and optimizing operations make it a highly valuable technology that can benefit various industries worldwide. Therefore, the advancement and widespread adoption of digital twin technology should be a global effort, with collaboration and cooperation between different countries, industries, and experts.

CONCLUSION

Indeed, the development of digital twin technology has brought about significant benefits in a wide range of applications, particularly in the field of MTE. With the advancements in information technology, the digital twin has the potential to revolutionize the way production and manufacturing are carried out. By integrating virtual space with real space, the digital twin can improve design solutions through data analysis, substantially reduce testing cycles, and improve overall efficiency. As information continues to lead digitalization and intelligence, it is clear that digital twin technology will play a crucial role in the future of intelligent design and manufacturing in MTE.

ACKNOWLEDGMENTS

This research is supported by the Chongqing Natural Science Foundation of China under Contract No. CSTB2022NSCQ-MSX1332, and Scientific Research Project of Education Department of Guangdong Province (2022KCXTD029).