1. Introduction
As an important energy power device, the gas turbine offers advantages such as high power density and strong maneuverability, and its development is crucial to a nation’s construction and development strategy in both military and civilian sectors [1]. With the application of integrated power systems in naval gas turbines, higher performance and harsher operating conditions have placed more stringent practical demands on aspects such as cycle efficiency, output power, and service life [2,3]. Gas turbines are hailed as the “jewels on the crown of advanced manufacturing”. They are not only used for power generation but also widely serve as the main or auxiliary power source in aviation, ships, missiles, tanks, heavy-duty locomotives, as well as in general industrial fields such as metallurgy, exploration, chemical engineering, and civil engineering. It can be said that gas turbines are a symbol of a country’s advanced manufacturing level of major equipment. Therefore, developed countries all support advanced gas turbine technology as the most important industry of their countries in the long term. Advanced gas turbine technology is of great significance for defending national sovereignty, security, and development interests, promoting the comprehensive utilization of energy, and achieving the “dual carbon” goals [4].
Improving thermal efficiency and output power is the primary goal in the development of advanced gas turbines [5]. Looking at the global history of gas turbine technology, since the 1880s, the United States [6] and various European countries [7,8] have implemented a series of gas turbine research and development programs, adopting transformative technological approaches to significantly enhance gas turbine performance while reducing research and development and manufacturing costs [9]. China’s gas turbine development has gone through three stages: introduction and imitation, independent research and development, and system establishment [10]. Since 2016, China has launched the national “Aviation Engines and Gas Turbines” major scientific and technological project, breaking foreign technological monopolies and continuously improving the domestic production level of gas turbines [11].
Currently, the integrated power system of naval gas turbines is an inevitable trend in the development of naval power systems worldwide. To meet the rapid response and high-speed maneuverability of ship platforms, as well as the high-energy pulsed energy supply for directed energy and kinetic energy weapons, the gas turbines within the integrated power system must possess the ability to rapidly adapt to varying operating conditions and even sudden load changes. This poses significant challenges to maintaining the operational stability of hot-end components such as the turbine casing, guide blades, and nozzles [12]. As critical hot-end components of the gas turbine, high-pressure turbine guide blades must withstand high loads and sudden load increases while coping with high temperatures, large temperature gradients, and thermally fluctuating stresses, all while maintaining good structural integrity [13]. Therefore, high-performance gas turbines place higher demands on the high-temperature alloy materials, thermal barrier coatings, and cooling technologies for guide blades [14]. However, the development of high-temperature materials is nearing its limits, and they still struggle to meet the operational requirements of advanced turbines [15]. Figure 1 illustrates the distribution of high-temperature regions in a specific turbine guide blade during operation, as well as the cracking and end-region erosion caused by thermal protection failure. Extensive erosion and fracture in turbine areas indicate that there is still a gap between the current turbine cooling technologies and the demands of high-dynamic-performance ship power platforms. Therefore, breakthroughs in turbine thermal protection technology are urgently needed [16,17]. To effectively overcome the limitations of turbine thermal protection technologies, conducting optimization research on turbine cooling techniques is of great military and economic significance for enhancing the maneuverability of gas turbines and supporting the nation’s strategy of building a strong maritime power.
In the field of turbine thermal protection, researchers have continuously explored two key technologies: cooling and thermal barrier coatings, to bridge the gap between the material’s allowable temperature and the turbine’s operating temperature [18]. Figure 2 shows the development history of the turbine operating temperature in gas turbines. Prior to the 21st century, there was still a certain gap between China and developed countries in terms of the maximum working temperature of high-temperature alloys. However, with the development of third-generation single-crystal alloys, this gap has been significantly reduced [19]. Currently, the stable working temperature limit of the most advanced high-temperature alloys is between 1400 and 1420 K, which exceeds 90% of the melting point of the high-temperature alloy [20]. In the future, the temperature tolerance of the next generation of nickel-based single-crystal alloys will approach the thermal limit of metal materials, with an annual increase of 1 to 3 K [21]. Therefore, efficient thermal protection technology is crucial, as it ensures the safe and stable operation of turbines in high-temperature environments [22,23].
Figure 3 shows a typical turbine blade with an integrated thermal protection system, which primarily consists of cooling technologies and thermal barrier coatings. Turbine cooling technologies can be categorized into internal and external cooling. Internal cooling includes leading-edge convective impingement, serpentine channel cooling in the blade body, and turbulators, while external cooling is mainly achieved through film cooling. By adding internal cooling to the turbine blades, they can operate at temperatures exceeding the melting point of high-temperature alloys. When thermal barrier coatings are applied, the operating temperature of the hot-end components can be elevated to 1800 K. Currently, the combined use of cooling technologies and thermal barrier coatings can achieve a temperature reduction of 600 K, which has become an essential aspect of advanced gas turbine design. As shown in Figure 4, film cooling is the most commonly used cooling technology for hot-end components [24,25]. Its function is to lower the temperature of the fluid near the wall, mitigate the thermal shock from high-temperature gases, and facilitate convective heat transfer between the low-temperature film and the solid surface, ultimately reducing the thermal load [26].
Overall, the goal of turbine film cooling technology is to lower the blade temperature, since higher metal temperatures can lead to shortened component lifespan or even burnout. The injection of cooling gas requires the design of film hole channels inside the blade to reach the outer surface, covering the blade surface to form a layer of cooling film, thereby separating the high-temperature gas from the blade surface and achieving the purpose of cooling. Film cooling combines the dual functions of heat insulation and heat absorption, and can achieve a temperature drop of 600 K. Additionally, it is necessary to reduce the internal temperature gradient of the hot-end components as much as possible to minimize thermal stress and avoid issues related to strength degradation and shortened lifespan. The cooling air for film cooling is sourced from the compressor, with advanced gas turbines now drawing up to 20% of the air for this purpose, leading to performance decline due to the high consumption of air. Therefore, it is crucial to enhance the performance of film cooling while reducing the amount of cooling air used, which is essential for turbine thermal protection [28]. A challenge for many scholars is how to design film cooling units to improve cooling efficiency or reduce cooling air consumption while maintaining cooling performance. Moreover, film cooling is the result of the combined action of multiple rows of film holes, where the cooling jets from same-row and adjacent-row holes interact and their cooling effects are compounded. In terms of hole arrangement, whether in turbine blades or end-wall regions, the traditional design relies on the designer’s experience and lacks fixed design guidelines for film hole layout. Optimizing the arrangement of film holes on the hot-end component surfaces can improve film cooling effectiveness at a relatively low cost, offering a promising optimization approach. Therefore, conducting optimization research on film cooling, addressing issues through the design of hole configurations and layouts, is critical to solving the current limitations in turbine cooling performance for next-generation gas turbines. This will provide crucial technical support for the thermal protection design of naval gas turbines, playing a significant role in advancing the leapfrog development and innovative breakthroughs of China’s naval power platforms. This study mainly summarizes the research deficiencies on turbine cooling performance at home and abroad and the future development trends, aiming to provide new ideas for the optimal design of the cooling system and further improve the power and efficiency of gas turbines.
2. Development of Configuration Design of Turbine Film Holes
2.1. Shaped Hole
In earlier studies, the factors influencing film cooling were classified into three categories [29]: (1) the geometric structure of the hot-end components; (2) the geometric parameters and layout of the film holes; (3) the flow parameters of the jets and mainstream [30]. The ideal form of film cooling is the two-dimensional slot gap, a structure commonly used in combustion chamber flame tubes. This structure can create a continuous cooling film on the surface of the protected object, effectively blocking high-temperature gases. However, the two-dimensional slot gap significantly reduces structural strength, posing substantial safety risks. Figure 5 illustrates the failure of the two-dimensional slot gap cooling in the combustion chamber and the short-slot cooling structure at the trailing edge of the guide vane. Therefore, two-dimensional slot gaps are not suitable for hot-end components, such as the blade body, which need to withstand large loads [31].
Currently, the film cooling units applied in practical engines mainly use discrete cylindrical holes [32]. The cylindrical hole structure is simple, easy to manufacture, and has minimal impact on structural strength, with its film cooling performance differing significantly from that of two-dimensional slot gaps. Blair et al. [33] experimentally verified the film cooling performance of cylindrical holes and further revealed the heat transfer mechanism of film cooling. In addition, researchers have conducted extensive and detailed exploration of cylindrical hole applications, systematically studying the effects of geometric parameters (inclination angle, compound angle, aspect ratio, hole spacing) and flow parameters (blow ratio, turbulence intensity, Reynolds number, Mach number) [34]. In subsequent numerical simulations and experimental studies, researchers found that the cooling jet from cylindrical holes interacts with the mainstream flow, forming complex combined vortex systems [35]. Within these vortex systems, kidney-shaped vortices are the primary factor influencing the film cooling effectiveness. As shown in Figure 6, these large-scale vortices can lift the cooling film off the surface, limiting its coverage. Additionally, kidney-shaped vortices can entrain high-temperature gases into the bottom of the cooling film, obstructing the lateral extension of the cooling jet [36]. Worse still, at high blow ratios, kidney-shaped vortices lead to a sharp deterioration in film cooling performance [37]. With the development of gas turbines, the cooling capability of traditional cylindrical holes has become limited. The momentum of the cooling jet in the lateral direction is small, and the coverage of the cooling film on the turbine surface is poor, making it difficult to meet the thermal protection requirements of new turbine blades. Therefore, finding more efficient film hole designs has become a popular research topic.
The key to enhancing film cooling performance lies in reducing the impact of kidney-shaped vortices. The most used and representative method is to modify the hole shape of the film holes [38]. As early as 1974, Goldstein et al. conducted research on shaped hole designs and introduced the concept of expansion holes for the first time [39]. Expansion holes are formed by enlarging the lateral exit of cylindrical holes. With the use of expansion holes, the penetration of the cooling jet is reduced, the lateral coverage is enhanced, and the cooling performance is improved. This also laid the foundation for the design of fan-shaped holes.
In modern advanced gas turbines, cylindrical holes are predominantly used for the leading edge of turbine blades, while fan-shaped holes are used in part on the pressure and suction surfaces. Fan-shaped holes can suppress the separation phenomenon of the cooling jet at the outlet, allowing the cooling film to closely adhere to the surface, thereby improving cooling efficiency. Gritsch et al. investigated the influence of structural parameters of fan-shaped holes, with the results indicating that hole spacing is a critical factor affecting cooling performance [40]. Zhou and Lee et al. [41,42] optimized the geometric parameters of fan-shaped holes (including streamwise/lateral expansion angles and expansion positions), further enhancing the lateral coverage of the cooling gas and reducing the penetration of the cooling jet [43]. The research also found that the film cooling efficiency of fan-shaped holes increases with the increase in cold air consumption [44], achieving lower aerodynamic losses [45]. Based on a summary of fan-shaped hole designs, researchers proposed the 7-7-7 baseline fan-shaped hole with better cooling performance. Figure 7 shows a schematic of the 7-7-7 baseline fan-shaped hole, with both the forward expansion angle and lateral expansion angle set at 7°. The 7-7-7 baseline fan-shaped hole has been widely used for numerical validation and comparative studies on the cooling performance of shaped holes, which has also led to the extensive development of various new shaped hole designs [46,47].
Researchers have invested significant effort in the design of novel film hole configurations. With the deepening of research, a large number of structurally innovative shaped hole designs have emerged. Figure 8 summarizes the schematic diagrams of various shaped holes from the past few decades. Based on the variation in the cross-sectional area of the cooling gas from the inlet to the outlet centerline, these designs can be classified into three categories: (1) sharp-edged holes and laterally expanding holes with a constant centerline cross-sectional area [48]; (2) backward-expanding holes [49], conical holes [50], heart-shaped holes [51], slit holes [52], arrow-shaped holes [53], convergent inlet holes [54], W-shaped holes [55], and leaf-shaped holes [56], all of which have an increasing centerline cross-sectional area; (3) inlet fan-shaped holes [39], scaled slot holes [57], and crescent-shaped holes [58], which have a decreasing centerline cross-sectional area.
The shaped holes are all developed based on cylindrical holes, with the aim of further enhancing cooling performance by altering the momentum distribution of the cooling jet at the hole exit. Some of these shaped holes can generate anti-kidney vortices, providing new insights for the optimization and design of subsequent film hole configurations.
Among the shaped holes, the scaled slot-cavity hole most closely resembles the ideal two-dimensional slot structure [59], with a cylindrical inlet and a two-dimensional slot outlet. This design allows for the preservation of the cooling performance of the two-dimensional slot while reducing the structural impact on strength [60]. Research by Sargison et al. [61] indicates that, compared to the fan-shaped hole, the scaled slot-cavity hole achieves a more uniform lateral film coverage and lower aerodynamic losses. Additionally, due to the strong lateral expansion capability of the cooling jet, a reverse kidney-shaped vortex structure, as shown in Figure 9, was observed on both sides of the scaled slot-cavity hole outlet [62]. Yao et al. [63] evaluated the aerodynamic losses of the scaled slot-cavity hole and found that when it is positioned upstream of the vane throat, the aerodynamic losses are smaller than those of a cylindrical hole; however, when placed downstream of the throat, the results are the opposite. On one hand, the scaled slot-cavity hole weakens the penetration of the cooling jet, thus reducing the mixing losses between the mainstream and the cooling gas [64]. On the other hand, its complex geometric structure increases the losses within the internal cooling passages. Ultimately, the overall loss depends on the combined effects of these two factors. The reduction in kidney vortices by shaped holes occurs through two main mechanisms: one involves the lateral expansion of the shaped hole outlet, which reduces the momentum of the cooling jet at the exit. The decrease in the coolant-to-mainstream momentum ratio weakens the jet’s penetration ability into the mainstream. Meanwhile, the spanwise coverage capabilities improves. The second mechanism is the induced Coanda effect. The Coanda effect, also known as the wall attachment effect, refers to the phenomenon where due to the viscous effects of the fluid, the flow tends to adhere to the solid wall. In film cooling, the arrangement of structures with different geometries downstream of the film holes can control the flow, causing the jet to better adhere to the wall and produce a more effective cooling performance.
Research on improving cooling performance by altering the geometric structure of scaled slot holes has also become a key focus [65]. Liu et al. [66] experimentally investigated the impact of geometric parameters of scaled slot holes on film cooling efficiency. The results indicated that reducing the outlet-to-inlet area ratio of the scaled slot hole could improve cooling performance, but it also led to a decrease in the flow coefficient of the cooling jet, thereby increasing the injection pressure drop. Huang et al. [67] defined scaled slot holes with a gradually decreasing cross-sectional area from inlet to outlet as convergent slot holes, and those with a gradually increasing cross-sectional area as divergent slot holes. The study showed that the cooling jet accelerates in convergent slot holes and decelerates in divergent slot holes. Convergent slot holes provided better cooling performance at low blowing ratios, while divergent slot holes performed better at high blowing ratios. Zhu et al. [68] maintained cylindrical holes on the leading edge of the blade and optimized scaled slot holes on the suction and pressure surfaces. The research found that the flow coefficient of convergent slot holes was the lowest, and the reduced cooling gas flow resulted in a decrease in both overall cooling efficiency and loss coefficient. In contrast, divergent slot holes increased the cooling gas flow, leading to higher cooling efficiency and loss coefficient. Scaled slot holes with an equal-area transition were able to balance the positive effects of improved cooling efficiency and the negative effects of increased loss coefficient, showing promising application prospects.
The research is derived from the original fan-shaped holes, primarily aiming to reduce the penetration ability of the cooling jet by altering the structure of the film holes while enhancing their lateral spreading capacity [69]. The innovation in the configuration of the film holes aims to eliminate the adverse effects of kidney-shaped vortices and offers unique advantages in terms of heat transfer and aerodynamics [70]. Unlike standard fan-shaped holes, the manufacturing process of shaped holes is complex. Although significant progress has been made in current processing technologies, shaped holes still have a long way to go before they can be applied in gas turbines [71]. Apart from designing shaped holes, other approaches to improving film cooling performance can be broadly classified into three categories, as shown in Table 1: first, enhancing film cooling performance through external auxiliary structures; second, exploring combinations of cylindrical holes by increasing the number of cylindrical holes and adjusting their relative positions to weaken kidney-shaped vortices or generate anti-kidney vortex structures through hole interference; third, optimizing the arrangement of film holes on the surfaces of hot-end components.
Shaped holes typically feature complex geometries, which are difficult to accurately produce using conventional machining methods. Additionally, the high precision required often exceeds the capabilities of traditional machining equipment. The economic cost of manufacturing shaped holes is high, and the technical expertise required further increases investment and operational costs. In practical engineering applications, the dimensions and shapes of shaped holes may lack standardized consistency, making large-scale production challenging. Therefore, in turbine film cooling technology, the challenges of manufacturing shaped holes involve multiple aspects, including both technical machining difficulties and economic and engineering limitations. These issues can be addressed to some extent through advancements in manufacturing technologies (such as precision machining and laser processing), optimization of design schemes, enhanced adaptability of equipment and materials, and improvements in the production process.
2.2. Film Hole with Auxiliary Structure
Another major direction in the development of film hole configurations is the integration of film holes with auxiliary structures to reduce or eliminate the negative effects of kidney-shaped vortices, thereby generating favorable effects on the cooling jet [72]. Figure 10 illustrates external and internal auxiliary structures used to enhance film cooling performance, which can be primarily categorized into three types: First, external auxiliary structures, such as the placement of ramps upstream of the film hole [73], crescent-shaped sand dunes [74], micro-ribs downstream [75], lateral rib grooves [76], crescent-shaped vortex generators [77], and protruding plates at the film hole exit [78]; second, internal auxiliary structures within the film hole, such as the addition of a ridge at the hole leading edge [79]; and third, placing the film hole within a recessed auxiliary structure, mainly consisting of grooves [80], slots [81], and pits [82].
Protruding plates are a type of simple vortex generator, and the placement of a leading-edge ridge inside the film hole can induce disturbances in the downstream flow field [83]. The flow direction towards the ridge causes a rapid increase in boundary layer thickness, while an outward ridge forms a protrusion in the boundary layer, with the thickness at the protrusion reaching a local maximum. Moreover, by altering the position and orientation of the ridge, a significant impact on film cooling efficiency can be achieved.
Among the auxiliary devices for enhancing film cooling performance, the upstream ramp is the most successful. This technology originates from vortex generators in passive flow control schemes [84]. With a vortex generator, the fluid near the boundary layer undergoes flow separation, forming a localized static pressure region downstream, which allows fluid to recirculate within the static pressure zone [85]. The ramp induces normal deflection of the mainstream, thereby reducing the impact of the mainstream on the cooling jet. Additionally, the ramp in front of the film hole affects the flow state inside the film hole, increasing the high-speed region and reducing the low-speed region, which weakens the jetting effect at the film hole exit and enhances the lateral diffusion of the cooling jet. The shape of the ramp is an important factor influencing film cooling effectiveness. Generally, at higher blowing ratios, the larger the ramp angle, the more significant the improvement in film cooling performance [86]. However, ramps with larger angles also cause greater boundary layer separation, thereby increasing the aerodynamic losses in film cooling [87]. The position of the ramp is another key factor affecting film cooling performance. When the upstream ramp is located farther from the film hole, if the separation shear layer attachment region it generates coincides with the area above the film hole, it will have an adverse effect on the film cooling performance [88].
In recent years, various ramp shapes have emerged, such as pyramid-shaped ramps [89], segmented step ramps [90], curved/wavy ramps [91], variable height ramps [92], dune-shaped ramps [93], and curved steps [94]. Altering the shape of the ramp can influence the motion state of the boundary layer fluid, thereby affecting the interaction patterns between the mainstream flow and the cooling jet, ultimately achieving a balance between cooling performance and aerodynamic losses. Among the various ramp shapes, the dune-shaped ramp has garnered significant attention from researchers due to its streamlined structure. This design is inspired by the crescent-shaped dunes commonly found in deserts, which can alter the near-surface air pressure distribution, create vortices on the leeward side, and prevent sand particles on the ground from being blown away by the oncoming airflow. Zhou et al. [86] measured the adiabatic film cooling efficiency and flow field structure of film holes with crescent-shaped dunes on a flat plate using Particle Image Velocimetry (PIV) and Pressure Sensitive Paint (PSP). Additionally, they explored the effects of the position and height of the crescent-shaped dunes on film cooling performance. Their research indicates that the crescent-shaped dunes can induce the formation of reverse kidney-shaped vortices. These vortices can roll the separated cooling jet back toward the wall, eliminating the negative effects of kidney-shaped vortices, thereby ensuring a wider and more uniform distribution of the cooling film on the flat plate.
Unlike changing the hole configuration itself, the methods involve adding auxiliary structures around the film hole, which work in conjunction with it. Although these auxiliary structures improve the cooling performance of the film hole to some extent, they can damage the blade surface and disrupt the flow field, leading to boundary layer flow separation and increased aerodynamic losses. Placing the film hole within a recessed groove, trench, or pit structure is a successful solution, as it allows the discrete holes to achieve a configuration like a two-dimensional slot. By embedding the film hole in a recessed structure, the cooling jet can diffuse prior to interacting with the mainstream, enhancing its lateral coverage [95]. More importantly, the transverse grooves, trenches, or pits can simulate changes in the shape of the thermal barrier coating, greatly improving the feasibility in engineering applications [96]. Through the rational design of auxiliary structures such as lateral grooves, channels, or pits, the performance of thermal barrier coatings in turbine film cooling can be significantly improved, enhancing the film cooling effect, prolonging the service life of turbine blades, and increasing overall thermal efficiency. However, these designs also face challenges such as manufacturing process complexity, the interaction between airflow and heat flux, coating durability, and optimization of the design. Therefore, when designing these structures, it is essential to deeply understand their effects on airflow and heat flux, and to optimize the design through advanced simulations and experiments to ensure they can deliver maximum benefits in practical applications.
The transverse grooves are the most common recessed auxiliary structures, with the depth and width of the grooves being key factors influencing cooling performance. Studies have shown that grooves with smaller depths and widths offer better cooling enhancement effects [97]. In recent years, the shape of grooves has evolved to include beveled/rounded grooves, swept grooves [98], and wavy grooves [99], among others. Groove holes have been proven to eliminate kidney-shaped vortices downstream of film holes and achieve excellent film cooling effects under high blowing ratios. However, the addition of such auxiliary structures can compromise the continuity of the thermal barrier coating, making it prone to peeling and detachment [100]. Additionally, this recessed structure can increase turbulence and flow separation, thereby increasing pressure losses to some extent [101].
2.3. Combined Film Hole
The third aspect of film hole configuration optimization involves the exploration of combined film holes. Existing literature indicates that increasing the number of cylindrical holes and adjusting their relative positions can induce the formation of anti-kidney vortices in the cooling jets. This method has been applied to design various combined film hole structures, with the basis being the dual-shear film hole. The dual-shear film hole is a relatively simple combined structure, where two cooling jets generate an anti-kidney vortex. As shown in Figure 11, modifications to the dual-shear film hole have led to the development of new combined film hole designs in recent years, such as anti-kidney vortex film holes [102], triangular-frame anti-kidney vortex holes [103], sister holes [104], and trunk-branch film holes [105].
However, these combined film holes require the addition of one or two extra holes, which can have a certain impact on the structural strength of the turbine. To address this issue, the fusion of two film holes in the dual-shear film hole has led to the creation of geometric structures such as cat-ear holes [106], dumbbell-shaped holes [107], and bean-shaped holes [108]. These types of combined film holes maintain the geometric characteristics and cooling performance of the dual-shear film hole while reducing the impact on turbine structural strength. However, the complex geometric structures also limit their development [109].
The performance of combined film cooling holes is influenced by various flow parameters, including jet angle, jet velocity, and the temperature of the cooling air. These flow parameters significantly affect the formation, stability, and uniformity of the film. The rational selection and optimization of these parameters can greatly enhance the stability and uniformity of the film cooling, thereby improving the thermal protection capability of turbine blades. However, the design process requires a comprehensive consideration of the interactions between these parameters and the potential challenges to ensure the optimal performance of film cooling.
2.4. Development Trend of Film Hole Configuration
A comparative summary to contrast different film cooling designs regarding thermal efficiency, aerodynamic loss, and manufacturability is shown in Table 2. The development of film hole configurations has reached a certain level, and the next focus is to optimize the balance between cooling effectiveness and aerodynamic losses. This work is primarily conducted through the optimization of the target parameters for cooling units. Parameter optimization of shaped holes can effectively unlock their potential, which is one of the directions for the future development of shaped holes [110]. Lee et al. [111] conducted multi-objective optimization of fan-shaped holes using the average adiabatic cooling efficiency and aerodynamic loss coefficient as objective functions, deriving three optimal solutions. Huang et al. [112] performed multi-objective optimization of fan-shaped holes on the suction side of turbine blades with a blowing ratio (M) of 1.5, using average adiabatic cooling efficiency and flow coefficient as two independent objective functions. The optimization yielded the maximum spatially averaged adiabatic cooling efficiency, the maximum flow coefficient, and the optimal solution balancing both. Among them, fan-shaped holes with a larger inclination angle and moderate forward expansion angle achieved the highest spatially averaged adiabatic cooling efficiency; fan-shaped holes with a smaller inclination angle and moderate forward expansion angle achieved the highest flow coefficient; while fan-shaped holes with both smaller inclination and forward expansion angles balanced both aspects. Wang et al. [113] optimized the flow direction/spanwise expansion angle and hole diameter ratio of fan-shaped holes using a neural network and genetic algorithm with the surface-averaged cooling efficiency as the objective function, obtaining the optimal film hole structure.
In terms of optimizing auxiliary structures, Kim et al. [114] conducted a single-objective optimization study on the hole-pit structure by altering three geometric parameters (major axis length, minor axis length, and depth), achieving a 20% improvement in film cooling efficiency when M was 0.5. Using surface-averaged cooling efficiency as the objective function, Feng optimized the structural parameters (groove width, groove depth, and groove bend angle) of serrated-slot film holes with support vector machines and genetic algorithms [115]. This led to an 8.75% and 70.5% increase in cooling efficiency under low and high operating conditions, respectively. However, research on the impact of auxiliary structure parameters on enhancing film cooling performance is still insufficient. Specifically, previous studies have primarily focused on adiabatic film cooling effects, with less attention given to additional flow losses and reduced net heat flux. Furthermore, the effect of energy losses caused by film cooling with auxiliary structures on heat transfer enhancement is not yet clear. That is, there is no publicly available quantitative method to describe the relationship between the negative effects (energy loss) and positive effects (improvement of heat transfer and cooling of wall surfaces) caused by cooling. These two aspects require further investigation to gain a more comprehensive understanding of the role of auxiliary structures in film cooling performance and to achieve optimal design solutions.
In internal cooling, swirl cooling has gradually gained the attention of researchers due to its outstanding cooling performance. The cooling gas in the swirl chamber rotates at high speed, generating a high radial pressure gradient that thins the thermal boundary layer, thereby enhancing the heat transfer effect and improving the heat transfer capability of internal passages. This has become a promising method for enhancing cooling [116]. Reference [117] points out that applying swirl cooling in pipes can increase the wall heat transfer coefficient by eight times, marking the first application of vortex cooling for the internal cooling of turbine blades. Based on the above research, the application of swirl cooling structures in turbine blades has also been validated.
With in-depth research in the field of combined film holes, the coupling relationship between film cooling and internal cooling has become a popular topic, making significant progress [118]. Bruce-Black et al. [119] proposed a cooling structure that combines internal impingement cooling and external discrete groove cooling. This combination can induce the formation of anti-kidney vortices beneath the kidney-shaped vortex. Additionally, researchers have applied swirl to enhance film cooling performance [120], combining internal swirl cooling with external film cooling to form swirl film cooling. This method uses a cold air chamber or film holes to generate a swirl cooling film that isolates high-temperature gases, providing thermal protection. Existing literature on the interaction between swirl cooling and film cooling has shown that proper swirl can enhance cooling performance, though this effect is not always beneficial [121,122,123]. Swirl cooling jets can disrupt traditional kidney-shaped vortices, significantly expanding the coverage area of the cooling gas and improving the adhesion of the cooling film.
As shown in Figure 12, the methods for generating swirl film cooling can be categorized into two types: the first involves using a special configuration of the cold air chamber to perform the cooling gas into a swirl within the chamber, which is then ejected through cylindrical holes [124,125]. Jiang et al. [126] achieved a good cooling effect by altering the shape of the cold air chamber to generate swirls of varying intensities and structures, resulting in effective combined configurations. After the swirl cooling gas is ejected from the film holes, it exhibits strong lateral extension and wall adhesion capabilities. Subsequently, Yang et al. [121] also utilized swirl cold air chambers to enhance the film cooling effectiveness of cylindrical holes, cloverleaf holes, and compound angle holes. However, the cold air chamber structure is quite complex, and its aerodynamic losses are significantly increased. Like shaped holes, these geometries face a common challenge, namely the limitations of manufacturing techniques. The second type of method for generating swirl film cooling is to directly use the special internal passage shape of the film holes, such as spiral channel holes, which cause the cooling gas to form a swirl directly after entering the film hole and then be ejected outside the hole [127]. Spiral channel holes can be obtained by tapping cylindrical holes with appropriately sized drill bits, which is simple in structure, easy to process, and holds promising application prospects [128,129].
Generally, improving the film hole cooling performance inevitably leads to an increase in aerodynamic losses. Finding a balance between these two factors is a crucial research topic. Additionally, there is limited research on the optimization of combined film hole structural parameters, so applying intelligent optimization algorithms to the design of key parameters for combined film holes holds significant development potential. Furthermore, there are many evaluation criteria for film cooling performance. In addition to cooling efficiency, heat transfer coefficient and net heat flux loss are also critical thermal parameters. Using only cooling efficiency as the objective function cannot determine the optimal solution. Therefore, it is also necessary to incorporate these key parameters affecting film cooling into the scope of multi-objective optimization when defining the objective function.
Film cooling is a thermal protection measure that comes at the cost of work and efficiency. On one hand, the cooling gas is introduced by the compressor, which results in a reduction in airflow, further diminishing the compressor’s ability to do work. On the other hand, the temperature of the cooling gas introduced from the compressor is much lower than that of the combustion gas, and its mixing with the combustion gases increases entropy and losses, thereby reducing thermal efficiency. Therefore, when cooling the turbine, it is essential to balance the adverse effects of film cooling on work and efficiency to achieve optimal cooling performance.
3. Development of Turbine Film Hole Arrangement
3.1. Arrangement of Film Holes in Turbine Blades
Optimizing the arrangement of film holes on the hot-end component surfaces can improve film cooling efficiency at a relatively low cost, making it a promising approach for enhancing cooling performance. For the optimization of film hole layout on turbine blade surfaces, current research mainly focuses on the influence of single-row film hole positioning or the cooling performance of multiple rows of film holes. From the perspective of turbine blade position, the leading edge experiences the most intense high-temperature gas impact, and the high-pressure horizontal gas may also cause combustion gas backflow into the film holes. The curvature variations in the pressure and suction surfaces lead to differences in fluid velocity and the centrifugal force acting on the fluid, resulting in different dissipation processes for the cooling gas. Additionally, the trailing edge has relatively low structural strength, and the velocity of the hot mainstream reaches its maximum at this location, leading to high heat transfer intensity, which is a weak point of film cooling.
In terms of the influence of film hole positioning, Li et al. [130] studied the impact of film hole spacing and the radial angle of the leading edge on the leading edge cooling efficiency. The turbulence intensity of the mainstream at the leading edge is 8%, the density ratio of secondary flow to mainstream is 1.5, and the momentum ratio varies from 0.5 to 4. The radial angles are 0°, 45°, and 65°, and the ratios of hole spacing to hole diameter are 2, 3, and 4, respectively. Under the conditions of a mainstream inlet Reynolds number of 3.7× 105, outlet Mach numbers of 0.81, 0.91, and 1.01, and a blowing ratio of 0.6 to 2.1, Wang et al. [131] explored the film cooling performance of scoop holes at different positions on the suction surface and found that the greater the curvature at the film hole position, the better the wall attachment of the cooling jet, but this also leads to a faster decay in cooling efficiency. Yao et al. [132] conducted cooling experiments on the expansion holes on the pressure surface of turbine guide vanes in a transonic wind tunnel, where the test specimen was equipped with four rows of film holes. The study revealed that the cooling jet increases the local heat transfer coefficient downstream of the film holes, and the mixing between the cooling gas and the mainstream becomes more intense near the trailing edge on the pressure surface. The cooling effect deteriorates as the distance from the trailing edge decreases. Therefore, film holes should be placed more frequently on the front part of the pressure surface, and the flow angle should be minimized as much as possible. These studies all used thermocouples as the measurement method. Colban et al. [133] investigated the effect of the streamwise position of fan-shaped holes on the cooling effectiveness of the suction and pressure surfaces of guide vanes using infrared thermography, and found that high-curvature positions lead to a decrease in film cooling efficiency, while leading edge cooling jets mitigate the impact of curvature on cooling efficiency.
The film cooling performance on the blade surface is the result of the interaction between multiple rows of film holes, which involves coupled cooling between adjacent and interspersed film holes. Therefore, studying only single-row film holes is insufficient, and a comprehensive consideration of the specific structure of the gas turbine blades and the number of film hole rows is necessary. Sreedharan et al. [134] studied the cooling performance of three rows of cylindrical holes at the leading edge and found that increasing the blowing ratio initially increased the cooling efficiency in the stagnation region, which then decreased, while the downstream cooling efficiency continued to increase. Drost et al. [135] used transient liquid crystal technology to measure the cooling efficiency of double-row cylindrical holes on the suction and pressure surfaces of guide vanes, and examined the impact of mainstream parameters on cooling efficiency. Guo et al. [136] studied the cooling performance of fan-shaped holes in blades with a full film hole layout. The research indicated that, compared to cylindrical holes, fan-shaped holes provide higher cooling efficiency on the suction surface but lower efficiency on the pressure surface, resulting in a lower overall heat transfer coefficient. Gao et al. [137] employed PSP technology to measure the cooling efficiency of the blade surface when multiple rows of fan-shaped holes were used together. Four rows of film holes and two rows of film holes were arranged on the pressure and suction surfaces, respectively. The study found that the cooling efficiency downstream of the film holes increased with the blowing ratio. The existence of hot streak will decrease the suction side time-averaged film effectiveness by a factor of 10%. In comparison, swirl has shown a negative effect on PS film effectiveness by a factor of 6%. Furthermore, based on this, they arranged three rows of cylindrical holes at the leading edge of the blade, creating a composite cooling blade. The research showed that the cooling efficiency of the blade surface significantly improved after increasing the leading edge cooling [138].
The studies primarily explore the effects of various parameters (such as blowing ratio, inlet and outlet Mach numbers, density ratio of coolant to mainstream, inlet turbulence intensity, and blade wall thickness) on the cooling performance of blades with fixed film hole positions. Several patterns have been identified, such as the fact that Mach number has little effect on the film cooling coverage area on the blade surface [139]; increasing the coolant-to-mainstream density ratio can improve film cooling performance [140]; an increase in inlet turbulence intensity negatively impacts the film cooling effectiveness of cylindrical and fan-shaped holes [141]; and blade thickness affects the film cooling performance on the pressure surface, but has little to no impact on the leading edge and suction surface of the blade [142]. Despite the research on the cooling performance of blades with fixed film hole positions, there is a relative lack of studies on the optimization of film hole layout on the blade.
3.2. Flow Characteristics of Cascade Channel Region
Currently, research on endwalls generally focuses on flat endwalls [143], where the hub and casing are assumed to be flat plate structures, and the upper blade row adopts an equivalently stretched 2D airfoil. A thorough understanding of the flow characteristics of flat endwalls is fundamental to the study of turbine endwall film cooling. The secondary flow present in the endwall passage interacts under the influence of spanwise pressure gradients and large-angle flow, affecting each other and developing into a complex system of interacting vortices [144]. The system of vortices in the blade passage is the focal point of research, and as the research progresses, a clearer, more precise, and complete model of the vortex system structure has gradually been developed.
In 1955, Hawthorne et al. [145] proposed the classical secondary flow theory, in which they first divided the vorticity components of the non-uniform flow through the blade rows into three parts: (1) distributed secondary circulation, (2) wake flow field circulation, and (3) trailing vortex filament circulation. The distributed secondary circulation is caused by the flow curvature in the curved regions or the passage between the blades; the wake flow field circulation is induced by the cyclic variation along the blade, like the flow of a uniform fluid around a finite-span wing; and the trailing vortex filament circulation results from the stretching of vortex filaments carried by the flow between the upper and lower stagnation streamlines in the wake of each blade. Additionally, through secondary flow calculations based on “channel” theory and the application of simple disturbance theory to determine the vorticity components, the trailing vortex filament circulation is subtracted, further revealing the wake flow field circulation, thus determining the cyclic variation in the secondary flow at the blade’s trailing edge.
Langston et al. [146] conducted detailed measurements in the axial planes ahead of, inside, and behind the subsonic blade row and described the secondary or three-dimensional flow structures in large-size, low aspect ratio turbine blade rows. They found that the boundary layer region of the endwall is characterized by small crossflow near the pressure side of the passage and large crossflow near the suction side. At the blade row inlet, the boundary layer separates at the leading edge of the blade, forming a horseshoe vortex. The two branches of the horseshoe vortex (the pressure side leg and the suction side leg) are in adjacent passages. The passage vortex is composed of the pressure side leg of the horseshoe vortex (from the inlet boundary layer), the crossflow within the blade row (from the endwall boundary layer), and the fluid entrained in the mainstream within the blade passage [147]. The suction side leg of the horseshoe vortex spirals around the passage vortex, rotating to the suction surface endwall corner, with its rotation direction opposite to that of the passage vortex. This is referred to as the counter-rotating vortex. The size and strength of the counter-rotating vortex are relatively small and can dissipate gradually through viscosity.
Sharma and Butler [148] provided a more detailed explanation of the classical secondary flow theory for axial-flow turbine blade rows and further expanded on Langston et al.’s model. They discovered that most of the fluid from the inlet boundary layer is trapped within the two legs of the horseshoe vortex. Once the fluid enters the blade row, before the mainstream achieves most of its turning, the normal component of vorticity associated with the inlet boundary layer is transformed into a flow component. The two legs of the horseshoe vortex entering the blade row rotate in opposite directions, and if both legs contain equal amounts of fluid and there is no friction, the net flow component of vorticity in the exit plane of the blade row will be zero. However, the fluid closest to the wall in the inlet boundary layer does not become part of the horseshoe vortex; this fluid flows towards the suction side of the endwall and meets the blade surface near the minimum pressure point. It then climbs along the blade surface and separates from the blade at the top of the passage vortex. As the flow develops downstream, the suction side leg of the horseshoe vortex rotates around the outer edge of the passage vortex, maintaining its flow characteristics, and the position of the suction side leg in the blade row’s exit plane depends on both its own size and vorticity and that of the passage vortex.
The secondary flow in turbine blade rows generally increases the convective flow in the passage and leads to a complex distribution of convection coefficients, with variations on the endwall exceeding one order of magnitude. Therefore, a two-dimensional boundary layer analysis cannot accurately describe the convection changes across the entire passage.
Goldstein and Spores [149] used local mass transfer techniques to identify regions of high turbulent transport on the endwall and obtained three-dimensional flow details of the turbine passage. Their study confirmed the presence of three distinct flow features in the turbine blade row: the corner vortex at the pressure side-endwall connection, the counter-vortex at the suction side-endwall connection, and the leading-edge corner vortex. The secondary flow in the endwall region results from two primary pressure gradients in the passage. The first pressure variation, at the leading edge-endwall connection (due to the boundary layer velocity distribution and flow stagnation at the blade leading edge), forces the fluid to flow downstream along the endwall and into the horseshoe vortex. The mainstream turning between the blades generates a pressure gradient across the passage, leading to the second pressure variation. This gradient influences the low-momentum flow near the leading-edge horseshoe vortex and the adjacent endwall, resulting in an upward flow on the suction surface and a downward flow on the pressure surface. The pressure side leg of the horseshoe vortex combines with the low-momentum flow near the endwall to form the passage flow. Upon reaching the suction side, the passage vortex departs from the endwall and continues downstream along the suction side. In contrast, the suction side leg of the horseshoe vortex flows along the blade-endwall connection from the start, until it reaches the separation line of the endwall boundary layer. At the separation line, the suction side leg climbs above the passage vortex and continues downstream along the blade’s suction surface. The average velocity is high and pressure is low far from the endwall on the suction surface, causing both the pressure side and suction side legs of the horseshoe vortex to detach from the endwall surface. Additionally, they observed a set of corner vortices in the lower corner region of the passage vortex, which rotate in the opposite direction to the horseshoe vortex.
The primary difference among the three models mentioned above lies in the determination of the position and flow state of the suction side leg of the horseshoe vortex. In 1997, Wang et al. [150] performed flow visualization on the endwall of a high aspect ratio linear blade row using smoke wire experiments and proposed a more comprehensive secondary flow model. During the experiment, they discovered that the pressure side leg of the horseshoe vortex flows through the passage toward the suction surface, becoming a major part of the passage vortex. Approximately one-quarter of the distance from the leading edge on the blade surface, it merges with the suction side leg. The passage vortex then moves toward the suction side, strengthening itself by entraining the mainstream flow. When the pressure side leg of the horseshoe vortex merges with the passage vortex, the suction side leg formed before the leading edge moves above the passage vortex. Due to the high strength of the passage vortex, the suction side leg wraps around the passage vortex, becoming a branch of the entire passage vortex system. The wall vortex induced by the passage vortex is very close to the suction surface, originating near the merging point of the suction side and pressure side legs of the horseshoe vortex, and rotates in the opposite direction to the passage vortex. Additionally, although the corner vortices are smaller in scale, they are very strong.
In terms of flow losses in turbine blade rows, Dring and Heiser [151] pointed out that aerodynamic losses in the endwall region account for 35% to 40% of the total losses. As gas turbines continue to evolve and the loads on the turbine increase, the aerodynamic losses in the blade row endwall region will also increase. Therefore, a deep understanding of the loss mechanisms induced by secondary flow is crucial in the study of endwall film cooling. Researchers have categorized the aerodynamic losses in the turbine blade row endwall region into five aspects [152]: first, the losses due to entropy increase in the endwall surface boundary layer; second, losses caused by fluid mixing within the boundary layer at the leading edge of the blade; third, losses due to the increase in secondary kinetic energy; fourth, losses caused by flow separation; and finally, losses in the blade surface boundary layer due to secondary flow. The generation mechanism of aerodynamic losses in the turbine endwall region is highly complex, influenced not only by the geometry of the blade row passage but also by the flow conditions within the passage. In real gas turbines, leakage flows at the turbine–combustor interface, cooling jets in the endwall region, and cooling jets on the turbine blades all affect the secondary flow structure in the endwall region, subsequently impacting the aerodynamic losses at the endwall. Therefore, clarifying the coupled interactions between these factors will significantly advance research on endwall film cooling.
3.3. Arrangement of Film Holes on Turbine Endwall
The endwall, connected to the blade root, is extensively exposed to high-temperature gases, and the thermal load it experiences continues to increase, significantly reducing its service life and making it a weak link in the turbine components of gas turbines [153]. In this context, while developing new heat-resistant materials and thermal barrier coatings, advanced endwall cooling technologies must also be developed to ensure the stable and efficient operation of gas turbines [154]. Film cooling, as a common cooling technique, has been successfully applied to turbines. However, its application in the blade row passages is more complex than on the blades themselves, exhibiting a three-dimensional flow pattern. The interaction between secondary flows and boundary layers in the endwall region is more pronounced. In particular, the presence of secondary flows, such as horseshoe vortices, passage vortices, and corner vortices, makes it easy for cooling jets to couple with induced vortices on the endwall, thus negatively affecting the film cooling performance [146]. Additionally, aerodynamic losses in the blade row passages are influenced by the shape and position of the film holes. Therefore, finding an appropriate and effective endwall film cooling design has been a popular topic of research.
The optimization of endwall cooling performance primarily focuses on two aspects: First, optimizing the configuration of the film holes, including the study of shaped holes, enhancing the cooling performance of cylindrical holes through auxiliary structures, and adjusting the relative positioning of cylindrical holes to form combined film holes. Research in this area is generally combined with studies on shaped holes on the blades, and will not be further elaborated here. However, despite the application of these optimization techniques in relatively simple endwall configurations, there remains the challenge of significant machining difficulty. Therefore, cylindrical holes without auxiliary structures are still the most widely used hole type for endwall film cooling. Second, optimizing the arrangement of film holes on the endwall surface to achieve a more uniform and efficient distribution of the cooling film.
In hot-end components, film cooling results from the combined effect of multiple rows of film holes [155]. The cooling jets from holes in the same row and those in parallel affect each other, with their cooling effects adding up. Regarding the arrangement of film holes, both for turbine blades and endwall regions, design has traditionally relied on the experience of the designers, leading to a lack of unified guidelines for film hole design. The staggered arrangement of film holes along the flow direction is the earliest and most widely used configuration. It is structurally simple, easy to arrange, and can provide good cooling for the endwall under uniform flow conditions. However, in practical situations, secondary flows significantly affect the cooling performance of staggered film holes. The cooling gas is confined within the three-dimensional separation line on the endwall, leading to large uncovered areas and making endwall erosion more likely [156]. Upstream of the three-dimensional separation line, the original cooling structures have already provided sufficient coverage of cooling gas, so the cooling demand in this region is relatively small. However, when secondary flows interact with the radially incoming fluid, the high-temperature mainstream is swept onto the endwall surface. Additionally, the formation of a new thin boundary layer downstream of the three-dimensional separation line increases the heat transfer coefficient. As a result, achieving better cooling gas coverage downstream of the three-dimensional separation line becomes more difficult, and improving cooling performance in this region remains a challenge, necessitating further optimization of the film hole arrangement.
To address the adverse effects caused by secondary flows, many film hole arrangement designs have been proposed. These designs include: arranging film holes along isentropic Mach number lines [157], distributing film holes in regions downstream of the three-dimensional separation line [158], placing film holes along constant velocity lines [159], arranging film holes based on heat transfer coefficient distribution [160], positioning film holes along isobaric lines, and using locally enhanced hole arrangements [161]. The optimized film hole arrangement design aims to provide more uniform cooling gas coverage on the endwall surface downstream of the three-dimensional separation line. The design goal is to achieve complete cooling gas coverage downstream of the three-dimensional separation line while maintaining the same cooling gas consumption as the baseline film hole arrangement. Furthermore, the aerodynamic losses should be less than or equal to those of the baseline arrangement. Table 3 summarizes the optimized arrangement mode of film holes. In numerical simulations and experimental validations, cooling gas is typically supplied to the cooling cavity at a constant pressure, and uneven blowing ratios can cause some of the cooling jets to detach from the protected surface, resulting in a loss of cooling capability.
In low Mach number flow fields, the distributions of the Mach number lines and pressure lines are essentially the same. The film holes arranged along the Mach number lines can achieve a uniform momentum flux ratio, and the blowing ratio remains constant for different density ratios. This design eliminates the pressure fluctuations caused by crossflow inside the cooling air chamber, resulting in a more uniform outflow of the cooling gas [162]. Friedrichs et al. [158] proposed a regionally distributed film hole arrangement scheme by considering the interaction between secondary flows and cooling jets. Based on flow visualization techniques, the film holes were individually arranged in four regions, aimed at providing more comprehensive cooling to the endwall surface downstream of the three-dimensional separation line. The results show that, for the same cooling gas consumption, the improved film hole arrangement increases the average film cooling efficiency of the endwall by 19.4%, essentially eliminating the uncooled regions, while also achieving lower aerodynamic losses [163]. In the presence of a leading-edge slot, Knost and Thole [159] proposed a film hole arrangement distributed along the isovelocity lines. When the cooling gas flow through the slot was low, the leading-edge film holes distributed along the isovelocity lines failed to effectively cool the blade root region. However, when the cooling gas flow was increased to 0.75%, the cooling performance of the film holes improved, but this caused a deterioration in the cooling performance at the connection between the pressure side endwall and the blade.
In 1974, Blair et al. [33] were the first to measure the convective heat transfer coefficient distribution on the turbine endwall using embedded thermocouples. Through thermochromic liquid crystal technology, they found that the heat transfer coefficient downstream of the throat of the blade passage was the highest, indicating that this region requires the greatest coverage by the cooling film. Satta and Tanda [164] proposed a film hole arrangement scheme based on the heat transfer coefficient distribution, which improved the film cooling efficiency by 29% in the high heat transfer coefficient regions of the endwall, while achieving more uniform and broader cooling gas coverage [160]. Another optimization method is the arrangement of film holes along isobaric lines [165]. The characteristic of film holes arranged along isobaric lines is that the local static pressure at the exit of the same row of holes is uniform, thus ensuring identical blowing ratios, density ratios, and momentum flux ratios for the holes in the same row. Compared to film holes arranged in the flow direction, the adiabatic film cooling efficiency of holes arranged along isobaric lines is more uniformly distributed downstream of each row of holes. Furthermore, to address the issue of limited cooling film coverage near the leading edge and pressure side of the endwall with uniformly distributed film holes, Su et al. [161] proposed a new method of local enhancement hole arrangement. This local enhancement arrangement adjusted the position, number, and compound angle of the film holes near the endwall leading edge and pressure side. Infrared thermal imaging results indicated a significant improvement in cooling efficiency.
Based on the assumption of an adiabatic wall or the flow parameter analysis when the temperature difference between the mainstream and cooling gases is small, the above-mentioned arrangement schemes can improve the film coverage area or the adiabatic cooling efficiency of the endwall to some extent. However, during actual operation, the turbine endwall is affected by both convective and radiative heat transfer from the gas flow and solid conduction, with its surface temperature being the conjugate heat transfer temperature [166]. The reliability of the endwall is related to the conjugate temperature distribution, with the maximum temperature and temperature gradient within the endwall being critical factors determining its reliability. A large temperature gradient can cause rapid changes in internal stresses, leading to deformation and cracking of the metal material. In extreme cases, it may even result in severe thermal fatigue failure. Therefore, while optimizing the film hole arrangement to achieve uniform film coverage, it is essential to also ensure a uniform conjugate temperature distribution, thereby improving the service life of the endwall. As a result, designing the film hole arrangement based on the conjugate temperature distribution of the endwall, in conjunction with the flow characteristics within the blade passage, has become a prevailing trend.
4. Research Status and Development Trend Analysis
The structural optimization research of turbine film holes in gas turbines primarily focuses on two aspects: first, optimizing the film hole configuration, including the design of shaped holes, enhancing the cooling performance of cylindrical holes through auxiliary structures, and utilizing a single combined film hole to form a “reverse kidney-shaped vortex” structure. However, even for relatively simple structures such as the endwall, the above optimization methods still face significant challenges in processing. As a result, the most widely used hole type for film cooling applications remains the cylindrical hole without auxiliary structures. The second aspect involves optimizing the arrangement of film holes on the turbine surface to achieve a more uniform and efficient cooling film distribution while minimizing the temperature gradient inside the turbine, thus reducing thermal stresses.
The progress in film cooling optimization research can be divided into two dimensions: The first dimension involves the transition from studies on simple models to those on complex, real-world models. For example, early studies on film cooling performance used an adiabatic wall assumption, followed by coupled heat transfer analysis methods. The research objects have progressively evolved from simple flat plate models to two-dimensional straight blades and flat endwalls, and then to curved, twisted gas-cooled turbine blades and non-axisymmetric endwall models that consider operational environments. The second dimension concerns the shift from mechanism research to performance enhancement studies. Early work focused mainly on the flow mechanisms of film cooling and performance characterization, while current research is centered on methods to enhance film cooling performance. Research has gradually moved from simply improving the effects of film cooling performance to rationally balancing cooling efficiency with energy loss, ultimately considering the improvement of both film cooling performance and heat transfer performance.
The analysis suggests that the inadequacy of turbine cooling performance research, both domestically and internationally, and the future development trends are primarily reflected in the following aspects: Various types of shaped holes, auxiliary devices, and combined film holes can improve film cooling performance; however, they still face numerous challenges in practical applications, such as stress concentration, processing technology, and processing costs. This has led many studies to remain at the basic research stage, making it difficult to apply them to engineering practices. Furthermore, the optimized film hole arrangements typically perform well only under specific operating conditions. When geometric structure or inlet conditions change, the performance tends to degrade, leading to poor versatility and stability. Therefore, designing new, easily manufacturable, high-efficiency film hole configurations and further expanding their stable operating range is an important development direction. There is a significant discrepancy between experimental studies and real-world operating conditions. Due to the difficulty of simulating actual high-temperature conditions in experimental setups, many researchers adopt reverse heat transfer methods for experimental studies, where secondary flow is heated to create a temperature difference between the mainstream and the secondary flow [167]. However, the extent to which reverse heat transfer affects cooling performance prediction, and how to more accurately assess the comprehensive cooling performance of turbines under experimental conditions, are critical issues that must be addressed in turbine cooling structure design for engineering applications. Therefore, it is essential to validate the reverse heat transfer method, assess its applicable range, and, when experimental conditions exceed the applicable range, use related theories to correct its predictive performance. This is key to overcoming the bottleneck in film cooling prediction. The film hole arrangement of turbine components is generally designed separately for blades and endwalls, which cannot integrate multiple critical factors. In particular, the effects of coupled heat transfer conditions and the mechanisms of inter-row cooling jet interactions remain unclear, leading to design guidelines for turbine component film hole arrangements still relying primarily on traditional operational experience. Therefore, it is urgent to develop a film hole arrangement guideline that is suitable for various types of film holes and components with temperature differences at the thermal end, to fill the gap in future film cooling optimization design technologies.
Film cooling is a cooling measure carried out at the expense of power generation and efficiency. On the one hand, because the cooling gas is introduced from the compressor, the mainstream flow rate is reduced, resulting in a decrease in power generation capacity. On the other hand, the cooling air ejected from the film holes has a temperature much lower than that of the gas. During the blending process with the gas, it leads to entropy increase and flow loss, thereby reducing the thermal efficiency. Therefore, while cooling the turbine blades, the influence of the cooling gas on thermal efficiency and power should also be considered to ensure that the negative effects on thermal efficiency and power are minimized as much as possible when improving the cooling effect. The positive effect of increasing the initial temperature of the gas on the gas turbine (improving thermal efficiency and power) is greater than the negative effect (reducing thermal efficiency and power) brought by the additional cooling measures due to the increase in temperature.
5. Conclusions
In the pursuit of higher power and efficiency for next-generation naval gas turbines, the cooling technology of turbine vanes has become one of the core technologies of interest to researchers, in response to the need for rapid increases in the initial gas temperature. As an advanced and efficient cooling technology, film cooling plays a crucial role in this process, with the key determining factor for its cooling performance being the configuration and arrangement of the film holes. This paper outlines the research background and significance of turbine thermal protection systems, reviews the current state and progress of turbine film hole configuration design and arrangement studies, and discusses the development trends of turbine cooling technologies, while summarizing the advantages and disadvantages of the current research techniques.
The optimization of film cooling performance is mainly approached from two aspects: one is the optimization of film hole configurations, including the study of shaped holes, enhancing the cooling performance of cylindrical holes through auxiliary structures, and utilizing single combined film holes to form a “reverse kidney-shaped vortex” structure. The second is the optimization of the arrangement of film holes on the turbine surface to achieve a more uniform and efficient cooling film distribution. This study summarized the structural forms and cooling performance improvement effects of 16 types of shaped holes, 12 types of film holes with auxiliary structure, and 9 types of combined film holes. In addition, the arrangement patterns of six types of film holes on the endwall and the principles they follow were analyzed.
In the future, balancing cooling effectiveness with aerodynamic losses, designing new high-efficiency film hole configurations that are easy to manufacture, and further expanding their stable operational range are important development directions. Researching a set of guidelines for film hole arrangements suitable for various film hole types and components with conjugate temperature differences at the thermal end is key to filling the gap in future film cooling optimization design technologies and overcoming the bottleneck in film cooling performance. Through the analysis of this study, new ideas and methods can be better provided for the critical and difficult issues that need to be urgently solved in the real world, such as how to improve the cooling efficiency of the gas film and how to design film holes.
Y.J.: Conceptualization, Investigation, Writing—original draft preparation, Writing—review and editing, Software. Y.L.: Conceptualization, Methodology, Resources, Data curation, Writing—review and editing, Project administration, Funding acquisition. X.H.: Conceptualization, Software, Formal analysis, Writing—review and editing. G.X.: Validation, Visualization, Formal analysis. Z.S.: Writing—review and editing. All authors have read and agreed to the published version of the manuscript.
The raw data supporting the conclusions of this article will be made available by the authors on request.
Anonymous referees are thankfully acknowledged for insightful comments on the first draft of this manuscript.
We declare that there is no conflict of interest.
Footnotes
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Figure 1 The surface temperature distribution and ablation of vanes. (a) Surface temperature of a turbine guide vane. (b) Vane cracking and endwall ablation (the red circle represents the crack).
Figure 2 The development history of operating temperature of gas turbine. (The rows of different colors represents the increase in temperature).
Figure 3 The turbine blade with thermal protection system [
Figure 4 The film cooling structure of turbine guide vane. (The red arrows represent hot air and the blue arrows represent cooling air. The red square box represents the film hole zone).
Figure 5 The 2-D slot cooling of combustor and structural failure of vane trailing edge. (The red circles represent that the structure has been damaged).
Figure 6 The typical kidney vortex structure.
Figure 7 The structure of 7-7-7 baseline fan-shaped hole.
Figure 8 The structure diagram of various shaped holes.
Figure 9 The flow structure at the film hole outlet.
Figure 10 The external auxiliary structures for enhanced film cooling.
Figure 11 The new combined film holes.
Figure 12 The swirl film cooling structure. (a) Swirl coolant chamber. (b) Segmented swirl structure. (c) Spiral-channel hole.
Approaches to improving film cooling performance.
| Approaches | Hole Type |
|---|---|
| Shaped Hole | Heart-shaped holes, W-shaped holes, scaled slot holes |
| Film Hole with Auxiliary Structure | Hole-grooves, hole-slots, hole-pits |
| Combined Film Hole | Triangular-frame anti-kidney vortex holes, sister holes, and trunk-branch film holes |
Performance comparison of different film cooling designs.
| Approaches | Thermal Efficiency | Aerodynamic Loss | Manufacturability |
|---|---|---|---|
| Shaped Hole | Good | Good | Average |
| Film Hole with Auxiliary Structure | Average | Poor | Good |
| Combined Film Hole | Poor | Average | Poor |
A brief survey of film holes arrangement.
| Reference Study | Hole Arrangement Type |
|---|---|
| Harasgama S P et al. [ | Arranging film holes along isentropic Mach number lines |
| Friedrichs S et al. [ | Distributing film holes in regions downstream of the three-dimensional separation line |
| Knost D G et al. [ | Placing film holes along constant velocity lines |
| Satta F et al. [ | Arranging film holes based on heat transfer coefficient distribution |
| Su H et al. [ | Using locally enhanced hole arrangements |
1. Kang, Y.J.; Jeong, J.Y.; Kim, H.J.; Kim, G.M.; Kwak, J.S. Effect of Relative Location of Film Cooling Hole With Internal Angled Ribs on the Film Cooling Effectiveness of a Gas Turbine Blade. Proceedings of the ASME Turbo Expo 2024; London, UK, 24–28 June 2024; 87998.
2. He, Y.; Yao, R.; He, F.; Ma, L.; Chen, J.; Song, W.; Pu, J.; Wang, J. Effect of pulsed coolant injection on unsteady film cooling characteristics with serrated trench design. Int. J. Therm. Sci.; 2024; 201, 108997. [DOI: https://dx.doi.org/10.1016/j.ijthermalsci.2024.108997]
3. Jia, Y.H.; Liu, Y.B.; He, X.; Meng, Z.W.; Zhao, S. Investigation on the arrangement guideline of film holes along the conjugate temperature difference in turbine guide vane. Chin. J. Aeronaut.; 2024; 103400.
4. Jia, Y.H.; Liu, Y.B.; Meng, Z.W.; Yin, W.T.; Hua, W.Z. Numerical study on film cooling effectiveness from spiral-channel hole. Int. Commun. Heat Mass Transf.; 2023; 143, 106716. [DOI: https://dx.doi.org/10.1016/j.icheatmasstransfer.2023.106716]
5. Mansouri, Z. Unsteady simulation of flow and heat transfer in a transonic turbine stage under non-uniform inlet conditions. Int. Commun. Heat Mass Transf.; 2021; 129, 105660. [DOI: https://dx.doi.org/10.1016/j.icheatmasstransfer.2021.105660]
6. Sounik, J.L.; Wright, L.M. Analysis of the Instantaneous Film Cooling Effectiveness on Showerhead Film Cooling Using Fast Response Pressure Sensitive Paint (Fast-PSP). Proceedings of the ASME Turbo Expo 2024; London, UK, 24–28 June 2024; 87998.
7. Li, M. Analysis to Ultra High Bypass Ratio Turbofan Engine Roadmap of ATI. Aerosp. Power; 2023; 39, pp. 10-15. (In Chinese)
8. Park, J.; Park, S.J.; Bang, K.M.; Jin, H. Influence of external thermal resistance on thermoelectric cooling in thermal management systems: Operating modes and material selection. Energy Convers. Manag.; 2025; 333, 119806. [DOI: https://dx.doi.org/10.1016/j.enconman.2025.119806]
9. Chen, W.H.; Zhang, H.G. Current situation and future development prospect of aero-engine manufacturing industry in Russia. Def. Ind.; 2015; 2015, pp. 73-80. (In Chinese)
10. Jeong, J.Y.; Jo, Y.R.; Kang, M.S.; Kang, Y.J.; Kwak, J.S. Film Cooling Effectiveness and Flow Structures of Butterfly-Shaped Film Cooling Hole Configuration. Proceedings of the ASME Turbo Expo 2023; Boston, MA, USA, 26–30 June 2023; 87004.
11. Barigozzi, G.; Perdichizzi, A.; Abba, L.; Pestelli, L. Platform film cooling investigation on an HP nozzle vane cascade with discrete shaped holes and slot film cooling. Proceedings of the of the ASME Turbo Expo 2020; Virtual, 21–25 September 2020; 84171.
12. Wang, B.; Wang, F.; Zhang, X.; Wang, J.; Xue, T. Numerical analysis of cooling efficiency for turboshaft engines with converging-diverging film holes. Int. J. Therm. Sci.; 2023; 185, 108044. [DOI: https://dx.doi.org/10.1016/j.ijthermalsci.2022.108044]
13. Meetham, G.W. High-temperature materials—A general review. J. Mater. Sci.; 1991; 26, pp. 853-860. [DOI: https://dx.doi.org/10.1007/BF00576759]
14. Meng, Z.W.; Liu, Y.B.; Li, Y.J.; Zhang, Y.S. An analytical model for predicting residual stress in TBC-film cooling system considering non-uniform temperature field. J. Appl. Phys.; 2021; 129, 135301. [DOI: https://dx.doi.org/10.1063/5.0045148]
15. Zhang, W.; Zeng, R.; Lu, J.; Liu, S.; Cha, H.; Li, G. Investigation of cooling performance degradation of impingement/effusion structure on pressure side of nozzle guide vane. Case Stud. Therm. Eng.; 2022; 33, 101991. [DOI: https://dx.doi.org/10.1016/j.csite.2022.101991]
16. Jia, Y.H.; Liu, Y.B.; Meng, Z.W.; He, X.; Liu, Y. The film cooling performance of spiral-channel holes on turbine guide vane. Case Stud. Therm. Eng.; 2024; 53, 103846. [DOI: https://dx.doi.org/10.1016/j.csite.2023.103846]
17. Jia, Y.; Liu, Y.; He, X.; Meng, Z.; Liu, Y. Effects of blowing ratio, hole position, and mainstream Reynolds number on film cooling effectiveness and energy loss of spiral-channel holes. Int. J. Therm. Sci.; 2024; 195, 108662. [DOI: https://dx.doi.org/10.1016/j.ijthermalsci.2023.108662]
18. Li, G.; Wan, L. Film cooling improvement of dovetail hole compared to cylindrical hole at different hole row locations on nozzle guide vane. Case Stud. Therm. Eng.; 2023; 45, 103015. [DOI: https://dx.doi.org/10.1016/j.csite.2023.103015]
19. Wang, J.; Cui, P.; Vujanović, M.; Baleta, J.; Duić, N.; Guzović, Z. Effects of surface deposition and droplet injection on film cooling. Energy Convers. Manag.; 2016; 125, pp. 51-58. [DOI: https://dx.doi.org/10.1016/j.enconman.2016.03.038]
20. Wang, Y.; Zhou, L.; Kang, X.; Huang, Q.; Shi, X.; Wang, C. Experimental and numerical optimization of direct-contact liquid film cooling in high concentration photovoltaic system. Energy Convers. Manag.; 2017; 154, pp. 603-614. [DOI: https://dx.doi.org/10.1016/j.enconman.2017.11.014]
21. Krishna Anand, V.G.; Parammasivam, K.M. Thermal barrier coated surface modifications for gas turbine film cooling: A review. J. Therm. Anal. Calorim.; 2021; 146, pp. 545-580. [DOI: https://dx.doi.org/10.1007/s10973-020-10032-2]
22. Zhang, X.; Zhao, Y.; Yang, C. Recent developments in thermal characteristics of surface dielectric barrier discharge plasma actuators driven by sinusoidal high-voltage power. Chin. J. Aeronaut.; 2023; 36, pp. 1-21. [DOI: https://dx.doi.org/10.1016/j.cja.2023.04.016]
23. Fu, Z.; Zhu, H.; Cheng, L.; Jiang, R. Experimental investigation on the effect of mainstream turbulence on full coverage film cooling effectiveness for a turbine guide vane. J. Therm. Sci.; 2019; 28, pp. 145-157. [DOI: https://dx.doi.org/10.1007/s11630-019-1085-9]
24. Ni, H.; Jiang, P.; Peng, W.; Sun, X.; Zhu, Y. An innovative design for measuring the enhanced mixing effect of a shock wave on supersonic film cooling. Int. Commun. Heat Mass Transf.; 2021; 122, 105132. [DOI: https://dx.doi.org/10.1016/j.icheatmasstransfer.2021.105132]
25. Pu, J.; Zhang, T.; Wang, J. Experimental study of combined influences of wall curvature and compound angle on film cooling effectiveness of a fan-shaped film-hole. Int. Commun. Heat Mass Transf.; 2022; 130, 105834. [DOI: https://dx.doi.org/10.1016/j.icheatmasstransfer.2021.105834]
26. Zhang, J.Z.; Zhang, S.C.; Wang, C.H.; Tan, X.M. Recent advances in film cooling enhancement: A review. Chin. J. Aeronaut.; 2020; 33, pp. 1119-1136. [DOI: https://dx.doi.org/10.1016/j.cja.2019.12.023]
27. Yeranee, K.; Yu, R.A.O. A review of recent studies on rotating internal cooling for gas turbine blades. Chin. J. Aeronaut.; 2021; 34, pp. 85-113. [DOI: https://dx.doi.org/10.1016/j.cja.2020.12.035]
28. Cui, Y.; Shi, X.; Huang, Q.; Kang, X. Experimental study on direct-contact liquid film cooling simulated dense-array solar cells in high concentrating photovoltaic system. Energy Convers. Manag.; 2017; 135, pp. 55-62.
29. Bogard, D.G.; Thole, K.A. Gas turbine film cooling. J. Propuls. Power; 2006; 22, pp. 249-270. [DOI: https://dx.doi.org/10.2514/1.18034]
30. Zhou, Z.; Li, H.; Xie, G.; You, R. Film Cooling Performance on Turbine Blade Suction Side With Various Film Cooling Hole Arrangements. Proceedings of the ASME Turbo Expo 2020; Virtual, 21–25 September 2020; 84171.
31. Wang, L.; Chu, T.; Yuan, S.; Zhou, P.; Zhao, W.C.; Zheng, X.B.; Xia, M.P. Advances and future perspectives in thermoelectric cooling technology. Energy Convers. Manag.; 2025; 332, 119621. [DOI: https://dx.doi.org/10.1016/j.enconman.2025.119621]
32. Goldstein, R.J.; Eckert, E.R.G.; Ramsey, J.W. Film cooling with injection through holes: Adiabatic wall temperatures downstream of a circular hole. J. Eng. Gas Turbines Power; 1968; 90, pp. 384-393. [DOI: https://dx.doi.org/10.1115/1.3609223]
33. Blair, M.F. An Experimental Study of Heat Transfer and Film Cooling on Large-Scale Turbine Endwalls. Proceedings of the ASME Turbo Expo 1974; Zurich, Switzerland, 31 March–4 April 1974.
34. Wang, Y.P.; Jiang, P.X. The separation vortex model is used to calculate the gas film cooling of inclined cylindrical holes. J. Eng. Thermophys.; 2005; 26, pp. 668-670. (In Chinese)
35. Andreopoulos, J. Measurements in a jet-pipe flow issuing perpendicularly into a cross stream. J. Fluids Eng. Trans. ASME; 1982; 104, pp. 493-499. [DOI: https://dx.doi.org/10.1115/1.3241892]
36. Walters, D.K.; Leylek, J.H. A detailed analysis of film-cooling physics: Part I-Streamwise injection with cylindrical holes. J. Turbomach.; 2000; 122, pp. 102-112. [DOI: https://dx.doi.org/10.1115/1.555433]
37. Kusterer, K.; Bohn, D.; Sugimoto, T.; Tanaka, R. Double-jet ejection of cooling air for improved film cooling. J. Turbomach.; 2007; 129, pp. 809-815. [DOI: https://dx.doi.org/10.1115/1.2720508]
38. He, J.; Yao, J.; Yang, X.; Zhang, K.; Lei, J.; Xie, G. Investigation on overall performance of double-jet film holes with various spanwise distance. Int. J. Therm. Sci.; 2023; 183, 107841. [DOI: https://dx.doi.org/10.1016/j.ijthermalsci.2022.107841]
39. Goldstein, R.J.; Eckert, E.R.G.; Burggraf, F. Effects of hole geometry and density on three-dimensional film cooling. Int. J. Heat Mass Transf.; 1974; 17, pp. 595-607. [DOI: https://dx.doi.org/10.1016/0017-9310(74)90007-6]
40. Gritsch, M.; Colban, W.; Schär, H.; Döbbeling, K. Effect of hole geometry on the thermal performance of fan-shaped film holes. J. Turbomach.; 2005; 127, pp. 718-725. [DOI: https://dx.doi.org/10.1115/1.2019315]
41. Zhou, W.; Peng, D.; Wen, X.; Liu, Y.; Hu, H. Unsteady analysis of adiabatic film cooling effectiveness behind circular, shaped, and sand-dune-inspired film holes: Measurement using fast-response pressure-sensitive paint. Int. J. Heat Mass Transf.; 2018; 125, pp. 1003-1016. [DOI: https://dx.doi.org/10.1016/j.ijheatmasstransfer.2018.04.126]
42. Lee, K.D.; Kim, K.Y. Surrogate based optimization of a laidback fan-shaped hole for film-cooling. Int. J. Heat Fluid Flow; 2011; 32, pp. 226-238. [DOI: https://dx.doi.org/10.1016/j.ijheatfluidflow.2010.08.007]
43. Huang, Y.; Zhang, J.; Wang, C. Multi-objective optimization of round-to-slot film holes on a flat surface. Aerosp. Sci. Technol.; 2020; 100, 105737. [DOI: https://dx.doi.org/10.1016/j.ast.2020.105737]
44. Colban, W.; Thole, K. Influence of hole shape on the performance of a turbine vane endwall film-cooling scheme. Int. J. Heat Fluid Flow; 2007; 28, pp. 341-356. [DOI: https://dx.doi.org/10.1016/j.ijheatfluidflow.2006.05.002]
45. Barigozzi, G.; Benzoni, G.; Franchini, G.; Perdichizzi, A. Fan-shaped hole effects on the aero-thermal performance of a film-cooled endwall. J. Turbomach.; 2006; 128, pp. 43-52. [DOI: https://dx.doi.org/10.1115/1.2098788]
46. Liu, J.H.; Liu, Y.B.; Liu, L. Film cooling modeling of a turbine vane with multiple configurations of holes. Case Stud. Therm. Eng.; 2018; 11, pp. 71-80. [DOI: https://dx.doi.org/10.1016/j.csite.2018.01.001]
47. Oliver, T.A.; Bogard, D.G.; Moser, R.D. Large eddy simulation of compressible, shaped-hole film cooling. Int. J. Heat Mass Transf.; 2019; 140, pp. 498-517. [DOI: https://dx.doi.org/10.1016/j.ijheatmasstransfer.2019.04.119]
48. Liu, Z.; Yang, X.; Feng, Z.P. Heat transfer and cooling of gas turbine blades: Film cooling. Therm. Turbine; 2014; 43, pp. 1-9. (In Chinese)
49. Jackson, D.J.; Lee, K.L.; Ligrani, P.M.; Johnson, P.D.; Soechting, F.O. Transonic aerodynamic losses due to turbine airfoil, suction surface film cooling. J. Turbomach.; 2000; 122, pp. 317-326. [DOI: https://dx.doi.org/10.1115/1.555455]
50. Zhang, G.; Liu, J.; Sundén, B.; Xie, G. Comparative study on the adiabatic film cooling performances with elliptical or super-elliptical holes of various length-to-width ratios. Int. J. Therm. Sci.; 2020; 153, 106360. [DOI: https://dx.doi.org/10.1016/j.ijthermalsci.2020.106360]
51. Yusop, N.M.; Ali, A.H.; Abdullah, M.Z. Computational study of a new scheme for a film-cooling hole on convex surface of turbine blades. Int. Commun. Heat Mass Transf.; 2013; 43, pp. 90-99. [DOI: https://dx.doi.org/10.1016/j.icheatmasstransfer.2013.02.011]
52. Sargison, J.E.; Oldfield, M.L.G.; Guo, S.M.; Lock, G.D.; Rawlinson, A.J. Flow visualisation of the external flow from a converging slot-hole film-cooling geometry. Exp. Fluids; 2005; 38, pp. 304-318. [DOI: https://dx.doi.org/10.1007/s00348-004-0892-1]
53. Okita, Y.; Nishiura, M. Film effectiveness performance of an arrowhead-shaped film-cooling hole geometry. J. Turbomach.; 2007; 129, pp. 331-339. [DOI: https://dx.doi.org/10.1115/1.2437781]
54. Kim, J.H.; Kim, K.Y. Performance evaluation of a converging-diverging film-cooling hole. Int. J. Therm. Sci.; 2019; 142, pp. 295-304. [DOI: https://dx.doi.org/10.1016/j.ijthermalsci.2019.04.027]
55. Fu, Z.; Zhu, H.; Liu, C.; Wei, J.; Zhang, B. Investigation of the influence of inclination angle and diffusion angle on the film cooling performance of chevron shaped hole. J. Therm. Sci.; 2018; 27, pp. 580-591. [DOI: https://dx.doi.org/10.1007/s11630-018-1070-8]
56. Lee, K.D.; Kim, K.Y. Performance evaluation of a novel film-cooling hole. J. Heat Transf.; 2012; 134, 101702. [DOI: https://dx.doi.org/10.1115/1.4006752]
57. Azzi, A.; Jubran, B.A. Numerical modelling of film cooling from converging slot-hole. Heat Mass Transf.; 2007; 43, pp. 381-388. [DOI: https://dx.doi.org/10.1007/s00231-006-0115-9]
58. Dai, P.; Lin, F. Numerical study on film cooling effectiveness from shaped and crescent holes. Heat Mass Transf.; 2011; 47, pp. 147-154. [DOI: https://dx.doi.org/10.1007/s00231-010-0692-5]
59. Sargison, J.E.; Guo, S.M.; Oldfield, M.L.G.; Lock, G.D.; Rawlinson, A.J. A converging slot-hole film-cooling geometry-Part 1: Low-speed flat-plate heat transfer and loss. J. Turbomach.; 2002; 124, pp. 453-460. [DOI: https://dx.doi.org/10.1115/1.1459735]
60. Yao, Y.; Zhang, J.Z.; Wang, L.P. Film cooling on a gas turbine blade suction side with converging slot-hole. Int. J. Therm. Sci.; 2013; 65, pp. 267-279. [DOI: https://dx.doi.org/10.1016/j.ijthermalsci.2012.10.004]
61. Sargison, J.E.; Guo, S.M.; Oldfield, M.L.G.; Lock, G.D.; Rawlinson, A.J. A converging slot-hole film-cooling geometry-Part 2: Transonic nozzle guide vane heat transfer and loss. J. Turbomach.; 2002; 124, pp. 461-471. [DOI: https://dx.doi.org/10.1115/1.1459736]
62. Liu, C.L.; Zhu, H.R.; Bai, J.T.; Xu, D.C. Film cooling characteristics of converging-expanding hole with equal exit-entry area. J. Propuls. Technol.; 2009; 30, pp. 666-672.
63. Yao, Y.; Zhang, J.Z.; Tan, X.M. Numerical study of film cooling from converging slot-hole on a gas turbine blade suction side. Int. Commun. Heat Mass Transf.; 2014; 52, pp. 61-72. [DOI: https://dx.doi.org/10.1016/j.icheatmasstransfer.2014.01.008]
64. Meng, Z.W. Study on Cooling Performance and Life Prediction of Thermal Barrier Coating on Turbine Guide Vane of Marine Gas Turbine. Ph.D. Thesis; Naval University of Engineering: Wuhan, China, 2023; (In Chinese)
65. Tang, H.; Guo, C.; Zhao, X.; Fan, F.; Lu, R.F.; Zhao, D.L. Guidance for combining radiative cooling and evaporative cooling: A heat and mass transfer analysis. Energy Convers. Manag.; 2025; 325, 119385. [DOI: https://dx.doi.org/10.1016/j.enconman.2024.119385]
66. Liu, C.L.; Zhu, H.R.; Bai, J.T.; Xu, D.C. Film cooling performance of converging-slot holes with different exit-entry area ratios. J. Turbomach.; 2011; 133, 011020. [DOI: https://dx.doi.org/10.1115/1.4000543]
67. Huang, Y.; Zhang, J.Z.; Wang, C.H. Shape-optimization of round-to-slot holes for improving film cooling effectiveness on a flat surface. Heat Mass Transf.; 2018; 54, pp. 1741-1754. [DOI: https://dx.doi.org/10.1007/s00231-017-2272-4]
68. Zhu, X.D.; Zhang, J.Z.; Tan, X.M. Numerical assessment of round-to-slot film cooling performances on a turbine blade under engine representative conditions. Int. Commun. Heat Mass Transf.; 2019; 100, pp. 98-110. [DOI: https://dx.doi.org/10.1016/j.icheatmasstransfer.2018.12.008]
69. Ingle, N.; Mohan, R.V.; Mogbolu, J. Effect of Cooling Rate on Gas Diffusion in Metal Additive Manufacturing. Proceedings of the ASME International Mechanical Engineering Congress and Exposition 2024; Portland, OR, USA, 17–21 November 2024; 88612.
70. Du, K.; Li, Z.; Li, J.; Sunden, B. Effects of the swirling coolant jet from the upstream slot on the vane endwall cooling and the vane suction side phantom cooling. Int. J. Heat Mass Transf.; 2018; 121, pp. 952-966. [DOI: https://dx.doi.org/10.1016/j.ijheatmasstransfer.2018.01.068]
71. Bunker, R.S. Film cooling: Breaking the limits of diffusion shaped holes. Heat Transf. Res.; 2010; 41, pp. 627-650. [DOI: https://dx.doi.org/10.1615/HeatTransRes.v41.i6.40]
72. Chokhar, I.A.; Dyachenko, A.Y.; Pakhomov, M.A.; Philippov, M.V.; Terekhov, V.I. Experimental study of the effect of a transverse trench depth on film cooling effectiveness. Case Stud. Therm. Eng.; 2021; 25, 100934. [DOI: https://dx.doi.org/10.1016/j.csite.2021.100934]
73. Na, S.; Shih, T.I.P. Increasing adiabatic film-cooling effectiveness by using an upstream ramp. J. Heat Transf.; 2007; 129, pp. 464-471. [DOI: https://dx.doi.org/10.1115/1.2709965]
74. Zhang, S.C.; Zhang, J.Z.; Tan, X.M. Numerical investigation of film cooling enhancement using an upstream sand-dune-shaped ramp. Computation; 2018; 6, 49. [DOI: https://dx.doi.org/10.3390/computation6030049]
75. Meng, Z.W.; Liu, Y.B.; Li, Y.J.; Yu, Y.H. A study on cooling performance of surface-modified TBC-film cooling system with bio-inspired micro-riblets. Int. J. Therm. Sci.; 2022; 172, 107340. [DOI: https://dx.doi.org/10.1016/j.ijthermalsci.2021.107340]
76. Benabed, M. Computational optimization of Coanda effect on film-cooling performance. J. Thermophys. Heat Transf.; 2015; 29, pp. 757-765. [DOI: https://dx.doi.org/10.2514/1.T4487]
77. An, B.; Liu, J.; Zhang, C.; Zhou, S. Film cooling of cylindrical hole with a downstream short crescent-shaped block. J. Heat Transf.; 2013; 135, 031702. [DOI: https://dx.doi.org/10.1115/1.4007879]
78. Yang, C.F.; Zhang, J.Z.; Chen, J.Q. Experimental study on cooling effect of inclined gas film on leading edge ridge. J. Eng. Thermophys.; 2008; 7, pp. 1174-1176. (In Chinese)
79. Shih TI, P.; Lin, Y.L.; Chyu, M.K.; Wu, S.X. Computations of film cooling from holes with struts. Proceedings of the ASME Turbo Expo 1999; Indianapolis, IN, USA, 7–10 June 1999; Volume 3, 78606.
80. Bunker, R.S. Film Cooling Effectiveness due to Discrete Holes Within a Transverse Surface Slot. Proceedings of the Turbo Expo: Power for Land, Sea, and Air 2002; Amsterdam, The Netherlands, 3–6 June 2002; 36088.
81. Yang, C.F.; Zhang, J.Z. Experimental investigation on film cooling characteristics from a row of holes with ridge-shaped tabs. Exp. Therm. Fluid Sci.; 2012; 37, pp. 113-120. [DOI: https://dx.doi.org/10.1016/j.expthermflusci.2011.10.011]
82. Kistenmacher, D.A.; Todd Davidson, F.; Bogard, D.G. Realistic trench film cooling with a thermal barrier coating and deposition. J. Turbomach.; 2014; 136, 091002. [DOI: https://dx.doi.org/10.1115/1.4026613]
83. Bradbury LJ, S.; Khadem, A.H. The distortion of a jet by tabs. J. Fluid Mech.; 1975; 70, pp. 801-813. [DOI: https://dx.doi.org/10.1017/S0022112075002352]
84. Ni, Y.Q. Development of eddy current generator and its effect on Boundary layer. J. Aerodyn.; 1995; 1, pp. 110-116. (In Chinese)
85. Jia, Y.H.; Liang, H.; He, Q.; Su, Z.; Song, G. Flow separation control of nacelle in crosswind by microsecond pulsed surface dielectric barrier discharge plasma actuator. Flow Turbul. Combust.; 2021; 107, pp. 631-651. [DOI: https://dx.doi.org/10.1007/s10494-021-00247-0]
86. Zhou, W.W.; Hu, H. Improvements of film cooling effectiveness by using Barchan dune shaped ramps. Int. J. Heat Mass Transf.; 2016; 103, pp. 443-456. [DOI: https://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.07.066]
87. Barigozzi, G.; Franchini, G.; Perdichizzi, A. The effect of an upstream ramp on cylindrical and fan-shaped hole film cooling—Part I: Aerodynamic results. Proceedings of the ASME Turbo Expo 2007; Montreal, QC, Canada, 14–17 May 2007; Volume 4, pp. 105-113.
88. Rallabandi, A.P.; Grizzle, J.; Han, J.C. Effect of upstream step on flat plate film-cooling effectiveness using PSP. J. Turbomach.; 2011; 133, pp. 1-8. [DOI: https://dx.doi.org/10.1115/1.4002422]
89. Hammami, Z.; Dellil, Z.A.; Nemdili, F.; Azzi, A. Improving adiabatic film-cooling effectiveness by using an upstream pyramid. Comput. Therm. Sci.; 2016; 8, pp. 135-146. [DOI: https://dx.doi.org/10.1615/ComputThermalScien.2016016302]
90. Zheng, D.; Wang, X.; Zhang, F.; Yuan, Q. Numerical investigation on the effects of the divided steps on film cooling performance. Appl. Therm. Eng.; 2017; 124, pp. 652-662. [DOI: https://dx.doi.org/10.1016/j.applthermaleng.2017.06.019]
91. Zheng, D.; Wang, X.; Zhang, F.; Zhou, J.; Yuan, Q. The effect of upstream ramps with different shapes on film cooling efficiency. Proceedings of the ASME Turbo Expo 2017; Charlotte, NC, USA, 26–30 June 2017; 26–30 June
92. Zhang, F.; Wang, X.; Li, J. The effects of upstream steps with unevenly spanwise distributed height on rectangular hole film cooling performance. Int. J. Heat Mass Transf.; 2016; 102, pp. 1209-1221. [DOI: https://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.07.001]
93. Zhou, W.; Hu, H. A novel sand-dune-inspired design for improved film cooling performance. Int. J. Heat Mass Transf.; 2017; 110, pp. 908-920. [DOI: https://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.03.091]
94. Abdala, A.M.M.; Elwekeel, F.N.M. An influence of novel upstream steps on film cooling performance. Int. J. Heat Mass Transf.; 2016; 93, pp. 86-96. [DOI: https://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.10.007]
95. Kalghatgi, P.; Acharya, S. Improved film cooling effectiveness with a round film hole embedded in a contoured crater. J. Turbomach.; 2015; 137, 101006. [DOI: https://dx.doi.org/10.1115/1.4030395]
96. Jia, R.; Sundén, B.; Miron, P.; Léger, B. A numerical and experimental investigation of the slot film-cooling jet with various angles. J. Turbomach.; 2005; 127, pp. 635-645. [DOI: https://dx.doi.org/10.1115/1.1929821]
97. Lu, Y.P.; Dhungel, A.; Ekkad, S.V.; Bunker, R.S. Effect of trench width and depth on film cooling from cylindrical holes embedded in trenches. J. Turbomach.; 2009; 131, pp. 339-349. [DOI: https://dx.doi.org/10.1115/1.2950057]
98. Oguntade, H.I.; Andrews, G.E.; Alan, B.; Derek, B.I.; Mohammed, P. Improved Trench Film Cooling With Shaped Trench Outlets. J. Turbomach.; 2012; 135, pp. 1-10.
99. Zhang, B.L.; Zhu, H.R.; Liu, C.L.; Wei, J.S. Experimental Study on the Film-Cooling Characteristics of the Cylindrical Holes Embedded in Sine-Wave Shaped Trench. J. Eng. Gas Turbines Power; 2020; 142, 101003. [DOI: https://dx.doi.org/10.1115/1.4048326]
100. Sundaram, N.; Thole, K.A. Film-cooling flowfields with trenched holes on an endwall. J. Turbomach.; 2009; 131, pp. 1-10. [DOI: https://dx.doi.org/10.1115/1.3068316]
101. Kalghatgi, P.; Acharya, S. Flow dynamics of a film cooling jet issued from a round hole embedded in contoured crater. J. Turbomach.; 2019; 141, 081006. [DOI: https://dx.doi.org/10.1115/1.4043071]
102. Heidmann, J.D.; Ekkad, S. A novel antivortex turbine film-cooling hole concept. J. Turbomach.; 2008; 130, pp. 487-496. [DOI: https://dx.doi.org/10.1115/1.2777194]
103. Ramesh, S.; Ramirez, D.G.; Ekkad, S.V.; Alvin, M.A. Analysis of film cooling performance of advanced tripod hole geometries with and without manufacturing features. Int. J. Heat Mass Transf.; 2016; 94, pp. 9-19. [DOI: https://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.11.033]
104. Dhungel, A.; Lu, Y.; Phillips, W.; Ekkad, S.V.; Heidmann, J. Film cooling from a row of holes supplemented with antivortex holes. J. Turbomach.; 2009; 131, 021007. [DOI: https://dx.doi.org/10.1115/1.2950059]
105. Li, G.C.; Zhang, W. Improving film cooling performance by using one-inlet and double-outlet hole. J. Therm. Sci.; 2010; 19, pp. 430-437. [DOI: https://dx.doi.org/10.1007/s11630-010-0405-x]
106. Kusterer, K.; Tekin, N.; Reiners, F.; Bohn, D.; Sugimoto, T.; Tanaka, R.; Kazari, M. Highest-efficient film cooling by improved nekomimi film holes—Part 1: Ambient air flow conditions. Proceedings of the ASME Turbo Expo 2013; San Antonio, TX, USA, 3–7 June 2013; Volume 3, 95027.
107. Bunker, R.S. A review of shaped hole turbine film-cooling technology. J. Heat Transf.; 2005; 127, pp. 441-453. [DOI: https://dx.doi.org/10.1115/1.1860562]
108. Yang, X.; Liu, Z.; Feng, Z. Numerical evaluation of novel shaped holes for enhancing film cooling performance. J. Heat Transf.; 2015; 137, 071701. [DOI: https://dx.doi.org/10.1115/1.4029817]
109. Kusterer, K.; Tekin, N.; Kasiri, A.; Bohn, D.; Sugimoto, T.; Tanaka, R.; Kazari, M. Highest-efficient film cooling by improved nekomimi film holes—Part 2: Hot gas flow conditions. Proceedings of the ASME Turbo Expo 2014; Düsseldorf, Germany, 16–20 June 2014; Volume 3, 25845.
110. Farade, R.A.; Wahab, N.I.A.; Mansour, D.E.A.; Soudagar, M.E.M. The effect of nanoadditives in natural ester dielectric liquids: A comprehensive review on stability and thermal properties. IEEE Trans. Dielectr. Electr. Insul.; 2023; 30, pp. 1478-1492. [DOI: https://dx.doi.org/10.1109/TDEI.2023.3274089]
111. Lee, K.D.; Kim, S.M.; Kim, K.Y. Multi-objective optimization of a row of film holes using an evolutionary algorithm and surrogate modeling. Numer. Heat Transf. Part A Appl.; 2013; 63, pp. 623-641. [DOI: https://dx.doi.org/10.1080/10407782.2013.751316]
112. Huang, Y.; Zhang, J.Z.; Wang, C.H.; Zhu, X.D. Multi-objective optimization of laidback fan-shaped film hole on Turbine Vane Suction Surface. Heat Mass Transfe; 2019; 55, pp. 1181-1194. [DOI: https://dx.doi.org/10.1007/s00231-018-2500-6]
113. Wang, C.; Zhang, J.; Zhou, J. Optimization of a fan-shaped hole to improve film cooling performance by RBF neural network and genetic algorithm. Aerosp. Sci. Technol.; 2016; 58, pp. 18-25. [DOI: https://dx.doi.org/10.1016/j.ast.2016.08.004]
114. Kim, J.H.; Kim, K.Y. Surrogate-based optimization of a cratered cylindrical hole to enhance film-cooling effectiveness. J. Therm. Sci. Technol.; 2016; 11, JTST0025. [DOI: https://dx.doi.org/10.1299/jtst.2016jtst0025]
115. Feng, H.K. Research on Cooling Law and Optimization of Shallow Slot Air Film. Master’s Thesis; Nanjing University of Aeronautics and Astronautics: Nanjing, China, 2019; (In Chinese)
116. Zhang, R.; Zhou, L.; Xing, J.; Luo, C.; Du, X. Numerical evaluation of film cooling performance of transverse trenched holes with shaped lips. Int. Commun. Heat Mass Transf.; 2021; 125, 105326. [DOI: https://dx.doi.org/10.1016/j.icheatmasstransfer.2021.105326]
117. Hay, N.; West, P.D. Heat transfer in free swirling flow in a pipe. J. Heat Transf.; 1975; 97, pp. 411-416. [DOI: https://dx.doi.org/10.1115/1.3450390]
118. Zhu, R.; Terrence, S.; Li, S.; Xie, G. Film cooling performance and flow structure of single-hole and double-holes with swirling jet. Chin. J. Aeronaut.; 2022; 35, pp. 201-213. [DOI: https://dx.doi.org/10.1016/j.cja.2021.09.021]
119. Bruce-Black, J.E.; Davidson, F.T.; Bogard, D.G.; Johns, D.R. Practical slot configurations for turbine film cooling applications. J. Turbomach.; 2011; 133, 031020. [DOI: https://dx.doi.org/10.1115/1.4002413]
120. Takeishi, K.; Komiyama, M.; Oda, Y.; Egawayuta, Y. Aerothermal investigations on mixing flow field of film cooling with swirling coolant flow. J. Turbomach.; 2013; 136, 051001. [DOI: https://dx.doi.org/10.1115/1.4023909]
121. Yang, X.; Liu, Z.; Liu, Z.; Feng, Z. Numerical analysis on effects of coolant swirling motion on film cooling performance. Int. J. Heat Mass Transf.; 2015; 90, pp. 1082-1089. [DOI: https://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.07.055]
122. Seibold, F.; Ligrani, P.; Weigand, B. Flow and heat transfer in swirl tubes—A review. Int. J. Heat Mass Transf.; 2022; 187, 122455. [DOI: https://dx.doi.org/10.1016/j.ijheatmasstransfer.2021.122455]
123. Fan, X.; Li, L.; Zou, J.; Zhou, Y. Cooling methods for gas turbine blade leading edge: Comparative study on impingement cooling, vortex cooling and double vortex cooling. Int. Commun. Heat Mass Transf.; 2019; 100, pp. 133-145. [DOI: https://dx.doi.org/10.1016/j.icheatmasstransfer.2018.12.017]
124. Li, H.W.; Gao, Y.F.; Du, C.H.; Hong, W.P. Numerical study on swirl cooling flow, heat transfer and stress characteristics based on fluid-structure coupling method under different swirl chamber heights and Reynolds numbers. Int. J. Heat Mass Transf.; 2021; 173, 121228. [DOI: https://dx.doi.org/10.1016/j.ijheatmasstransfer.2021.121228]
125. Jiang, Y.; Yue, G.; Dong, P.; Gao, J.; Zheng, Q. Investigation on film cooling with swirling coolant flow by optimizing the inflow chamber. Int. Commun. Heat Mass Transf.; 2017; 88, pp. 99-107. [DOI: https://dx.doi.org/10.1016/j.icheatmasstransfer.2017.08.008]
126. Jiang, Y.; Zheng, Q.; Dong, P.; Yao, J.; Zhang, H.; Gao, J. Conjugate heat transfer analysis of leading edge and downstream mist-air film cooling on turbine vane. Int. J. Heat Mass Transf.; 2015; 90, pp. 613-626. [DOI: https://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.07.005]
127. Zhu, R.; Lin, E.; Simon, T.; Xie, G. Investigation and numerical simulation on film cooling performance with an anti-vortex hole design: Influences of diameter ratio. Int. Commun. Heat Mass Transf.; 2021; 121, 105118. [DOI: https://dx.doi.org/10.1016/j.icheatmasstransfer.2021.105118]
128. Jia, Y.H.; Liu, Y.B.; Xing, H.; Meng, Z.W.; Yin, W.T.; Zhao, S. Experimental and numerical investigations on film cooling performances with spiral-channel holes for a turbine vane. Appl. Therm. Eng. Elsevier Ltd.; 2024; 256, 124124. [DOI: https://dx.doi.org/10.1016/j.applthermaleng.2024.124124]
129. Li, H.L. Study on the Effect of Segmented Swirl Structure on the Cooling Characteristics of Gas Film. Master’s Thesis; Harbin Engineering University: Harbin, China, 2021; (In Chinese)
130. Li, G.C.; Zhu, H.R.; Bai, J.T.; Xu, D.C. Experiment on effect of gas film hole layout on cooling efficiency of leading edge gas film. Propuls. Technol.; 2008; 29, pp. 153-157. (In Chinese)
131. Wang, K.F.; Luo, J.X.; Tian, S.; Zhu, H.R.; Liu, C. Comparison of air film cooling characteristics at different positions of blade suction surface. J. Aerodyn.; 2017; 32, pp. 1281-1288. (In Chinese)
132. Yao, C.Y.; Zhu, H.R.; Liu, C.L.; Zhang, B.L.; Zhou, Y.D. Effect of gas film hole row position on Pressure Surface of turbine guide vane on cooling characteristics of gas film. Propuls. Technol.; 2020; 41, pp. 1560-1570. (In Chinese)
133. Colban, W.; Gratton, A.; Thole, K.A.; Haendler, M. Heat transfer and film-cooling measurements on a stator vane with fan-shaped cooling holes. J. Turbomach.; 2006; 128, pp. 53-61. [DOI: https://dx.doi.org/10.1115/1.2098789]
134. Sreedharan, S.S.; Tafti, D.K. Effect of blowing ratio in the near stagnation region of a three-row leading edge film cooling geometry using large eddy simulations. Proceedings of the ASME Turbo Expo 2009; Orlando, FL, USA, 8–12 June 2009; Volume 3, pp. 213-224.
135. Drost, U.; Böles, A. Investigation of detailed film cooling effectiveness and heat transfer distributions on a gas turbine airfoil. J. Turbomach.; 1999; 121, pp. 233-242. [DOI: https://dx.doi.org/10.1115/1.2841306]
136. Guo, S.M.; Lai, C.C.; Jones, T.V.; Oldfield, M.L.G.; Lock, G.D.; Rawlinson, A.J. The application of thin-film technology to measure turbine-vane heat transfer and effectiveness in a film-cooled, engine-simulated environment. Int. J. Heat Fluid Flow; 1998; 19, pp. 594-600. [DOI: https://dx.doi.org/10.1016/S0142-727X(98)10034-6]
137. Wang, Z.; Wang, Z.; Zhang, W.; Feng, Z. Numerical study on unsteady film cooling performance of turbine rotor considering influences of inlet non-uniformities and upstream coolant. Aerosp. Sci. Technol.; 2021; 119, 107089. [DOI: https://dx.doi.org/10.1016/j.ast.2021.107089]
138. Gao, Z.; Narzary, D.P.; Mhetras, S.; Han, J.C. Full-coverage film cooling for a turbine blade with axial-shaped holes. J. Thermophys. Heat Transf.; 2008; 22, pp. 50-61. [DOI: https://dx.doi.org/10.2514/1.31206]
139. Mhetras, S.; Han, J.C.; Rudolph, R. Effect of flow parameter variations on full coverage film-cooling effectiveness for a gas turbine blade. J. Turbomach.; 2011; 134, pp. 1-10.
140. Liu, K.; Yang, S.F.; Han, J.C. Influence of coolant density on turbine blade film-cooling with axial and compound shaped holes. J. Heat Transf.; 2014; 136, 044501. [DOI: https://dx.doi.org/10.1115/1.4025901]
141. Narzary, D.P.; Liu, K.C.; Rallabandi, A.P.; Han, J.C. Influence of coolant density on turbine blade film-cooling using pressure sensitive paint technique. J. Turbomach.; 2011; 134, 031006. [DOI: https://dx.doi.org/10.1115/1.4003025]
142. Li, W.; Li, X.; Ren, J.; Jiang, H. Experimental investigation of wall thickness and hole shape variation effects on full-coverage film cooling performance for a gas turbine vane. Appl. Therm. Eng.; 2018; 144, pp. 349-361. [DOI: https://dx.doi.org/10.1016/j.applthermaleng.2018.08.068]
143. Huang, W.; Huang, C.F.; Wang, Y.M. Non-axisymmetric end wall forming method based on parametric ridge line. Propuls. Technol.; 2017; 38, pp. 1294-1301. (In Chinese)
144. Chen, P.T. Flow Heat Transfer Mechanism of Gas-Cooled End Wall of Gas Turbine. Ph.D. Dissertation; Tsinghua University: Beijing, China, 2020; (In Chinese)
145. Hawthorne, W.R. Rotational flow through cascades Part I. the components of vorticity. Q. J. Mech. Appl. Math.; 1954; 3, pp. 266-279. [DOI: https://dx.doi.org/10.1093/qjmam/8.3.266]
146. Langston, L.S. Crossflows in a turbine cascade passage. J. Eng. Gas Turbines Power; 1980; 102, pp. 866-874. [DOI: https://dx.doi.org/10.1115/1.3230352]
147. Herzig, H.Z.; Hansen, A.G.; Costello, G.R. A Visualization Study of Secondary Flows in Cascades; National Advisory Committee for Aeronautics: Washington, DC, USA, 1954; 54.
148. Sharma, O.P.; Butler, T.L. Predictions of endwall losses and secondary flows in axial flow turbine cascades. J. Turbomach.; 1987; 109, pp. 229-236. [DOI: https://dx.doi.org/10.1115/1.3262089]
149. Goldstein, R.J.; Spores, R.A. Turbulent transport on the endwall in the region between adjacent turbine blades. J. Heat Transf.; 1988; 110, pp. 862-869. [DOI: https://dx.doi.org/10.1115/1.3250586]
150. Wang, H.P.; Olson, S.J.; Goldstein, R.J.; Eckert, E.R.G. Flow visualization in a linear turbine cascade of high performance turbine blades. Proceedings of the ASME Turbo Expo 1995; Houston, TX, USA, 5–8 June 1995; Volume 4, pp. 1-8.
151. Aungier, R.H. Turbine Aerodynamics; ASME: New York, NY, USA, 2006.
152. Denton, J.D. Loss mechanisms in turbomachines. J. Turbomach.; 1993; 115, pp. 621-656. [DOI: https://dx.doi.org/10.1115/1.2929299]
153. Zhang, F.; Liu, C.; Wang, W.; Ye, L.; Li, B.; Liu, F. Film superposition prediction method for film cooling layouts with same opening ratio on the turbine blade. Appl. Therm. Eng.; 2023; 233, 121105. [DOI: https://dx.doi.org/10.1016/j.applthermaleng.2023.121105]
154. Liu, R.; Li, H.; You, R.; Tao, Z.; Huang, Y. Numerical decoupling of the effect of internal cooling and external film cooling on overall cooling effectiveness. Appl. Therm. Eng.; 2023; 222, 119905. [DOI: https://dx.doi.org/10.1016/j.applthermaleng.2022.119905]
155. Zhou, Y.; Zhang, Y.; Su, X.R.; Yuan, X. Pore distribution of end-wall gas film resistant to swirling disturbance. J. Eng. Thermophys.; 2016; 37, pp. 2544-2548. (In Chinese)
156. Friedrichs, S.; Hodson, H.P.; Dawes, W.N. Distribution of film-cooling effectiveness on a turbine endwall measured using the ammonia and diazo technique. J. Turbomach.; 1996; 118, pp. 613-621. [DOI: https://dx.doi.org/10.1115/1.2840916]
157. Harasgama, S.P.; Burton, C.D. Film cooling research on the endwall of a turbine nozzle guide vane in a short duration annular cascade: Part 1-experimental technique and results. J. Turbomach.; 1992; 114, pp. 734-740. [DOI: https://dx.doi.org/10.1115/1.2928026]
158. Friedrichs, S.; Hodson, H.P.; Dawes, W.N. The design of an improved endwall film-cooling configuration. J. Turbomach.; 1998; 121, pp. 772-780. [DOI: https://dx.doi.org/10.1115/1.2836731]
159. Knost, D.G.; Thole, K.A. Adiabatic effectiveness measurements of endwall film-cooling for a first-stage vane. J. Turbomach.; 2005; 127, pp. 297-305. [DOI: https://dx.doi.org/10.1115/1.1811099]
160. Satta, F.; Tanda, G. Effect of discrete-hole arrangement on film-cooling effectiveness for the endwall of a turbine blade cascade. Appl. Therm. Eng.; 2015; 91, pp. 507-514. [DOI: https://dx.doi.org/10.1016/j.applthermaleng.2015.07.082]
161. Su, H.; Pu, J.; Wang, J.H.; Yuan, R.M.; Luan, Y.X.; Kang, B.P. An Experimental Investigation of Cooling Characteristics at a Vane End-Wall with a Locally Enhanced Hole-Layout. Experimental Thermal and Fluid Science; Elsevier: Amsterdam, The Netherlands, 2018; Volume 96, pp. 137-145.
162. Knost, D.G.; Thole, K.A. Computational predictions of endwall film-cooling for a first stage vane. Int. J. Turbo Jet Engines; 2005; 22, pp. 41-58. [DOI: https://dx.doi.org/10.1515/TJJ.2005.22.1.41]
163. Friedrichs, S.; Hodson, H.P.; Dawes, W.N. Aerodynamic aspects of endwall film-cooling. J. Turbomach.; 1997; 119, pp. 786-793. [DOI: https://dx.doi.org/10.1115/1.2841189]
164. Satta, F.; Tanda, G. Measurement of local heat transfer coefficient on the endwall of a turbine blade cascade by liquid crystal thermography. Exp. Therm. Fluid Sci.; 2014; 58, pp. 209-215. [DOI: https://dx.doi.org/10.1016/j.expthermflusci.2014.07.005]
165. Li, X.; Ren, J.; Jiang, H. Influence of different film cooling arrangements on endwall cooling. Int. J. Heat Mass Transf.; 2016; 102, pp. 348-359. [DOI: https://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.06.047]
166. Montomoli, F.; Massini, M.; Yang, H.; Han, J.C. The benefit of high-conductivity materials in film cooled turbine nozzles. Int. J. Heat Fluid Flow; 2012; 34, pp. 107-116. [DOI: https://dx.doi.org/10.1016/j.ijheatfluidflow.2011.12.005]
167. Yang, X.; Liu, Z.; Zhao, Q.; Liu, Z.; Feng, Z.; Guo, F.; Ding, L.; Simon, T.W. Experimental and numerical investigations of overall cooling effectiveness on a vane endwall with jet impingement and film cooling. Appl. Therm. Eng.; 2019; 148, pp. 1148-1163. [DOI: https://dx.doi.org/10.1016/j.applthermaleng.2018.11.116]
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