1. Introduction
In the design and development of modern aviation gas turbine engines, the temperature before the turbine is a critical indicator of engine performance. A higher turbine inlet temperature provides more powerful thrust, becoming a key factor that limits engine performance [
1]. Turbine blades are subjected to direct impacts from high-temperature gases in the combustion chamber. Compared to the forces exerted by gas flows and the vibrational loads during operation, thermal loads are the primary form of load on the blades during operation. A higher turbine inlet temperature means that the blades need to withstand greater thermal loads. The study of blade resistance to thermal damage is vital for enhancing engine overall performance and has become one of the hotspots in engine design research [
2]. As turbine inlet temperatures rise, relying solely on the heat-resistance of the blade materials is no longer sufficient. Continuous research by scholars globally has led to the gradual adoption of various efficient cooling techniques in blade design and use [
3,
4], such as convective cooling, impingement cooling, film cooling, effusion cooling, and thermal barrier coatings. Blades have evolved from solid to hollow structures, incorporating intricate internal cooling channels. Introducing cool air inside turbine blades effectively reduces the duration of high temperatures experienced by the blades, alters the temperature gradient, and diminishes the thermal stress on the blades, thereby enhancing their fatigue life. Gas film cooling technology (GFCT) is increasingly used in the design of turbine blades due to its effective cooling performance.
Although GFCT is effective in cooling, it has structural flaws that can lead to cracks around the holes after prolonged use, resulting in damage or even destruction of the blades [
5]. Montomoli [
6] introduced the concept of “thermal gradient”, revealing that an important cause of structural damage under transient temperature loads is the temperature difference at different structural positions, not merely the maximum temperature load. There are typically two reasons for the temperature differences within the blade: (1) the imbalance of temperatures in different directions before reaching thermal equilibrium and (2) the temperature differences caused by a stable thermal exchange at the boundaries after reaching thermal equilibrium. The flow of cooling gas from within the blade through small holes increases the thermal flow at the blade boundaries, exacerbating the stress concentration within the holes. It is necessary to study the impact of the amount of cooling air on the thermal stress within the holes caused by cooling gases. Peng Zhi yong [
7] conducted thermal shock fatigue tests on air-film-cooled blades, finding that the flow of cooling air from the holes creates a significant temperature gradient and substantial thermal stresses towards the interior of the blade, leading to cracks around the holes.
Ai xing [
8] conducted high-temperature tensile tests on perforated metal plates to study their high-temperature creep properties. The results showed that at the same stress level, the presence of cooling holes significantly reduced the high-temperature long-term fracture life of the specimens from about 100 h to about 50 h, with a maximum reduction of 52%. It is evident that cracks are prone to occur around the holes, and analyzing the cooling efficiency and temperature of the air film alone is insufficient to ensure an improvement in thermal strength. Kim [
9] conducted studies on various air foil-cooled blades, calculating the convective heat transfer coefficient and thermal stress distribution using finite element simulation methods, and found significant stress concentration around the cooling holes in the blades. Wang Zhan [
10] investigated the thermo-mechanical coupling characteristics of flat plate air film cooling structures and analyzed the factors affecting thermal stress, but the results lacked experimental validation. The amount of cooling air significantly affects the efficiency of the air film cooling [
1]. If the cooling air volume is too low, the blades may not achieve the desired cooling effect, leading to excessively high blade temperatures and potentially uneven air film distribution which creates temperature differences on the blade surface. If the cooling air flow is too high, it can affect the main combustion gas, reduce the gas temperature inside the turbine and affect turbine efficiency; furthermore, since the cooling air is generally drawn from the compressor, excessive cooling air flow can also impact the compressor’s seal integrity. Goldstein [
2] developed the first empirical formula for predicting air film cooling efficiency, which indicates that the cooling efficiency increases with the increase in blowing ratio. However, this formula is only applicable under the condition of low blowing ratios without airflow separation. Afterwards, Baldauf [
11] developed a more complex semi-empirical formula to reflect the relationships between various factors affecting air film cooling efficiency. This formula provides significant references for the study of air film cooling, but is still not capable of predicting models with high blowing ratios.
As research progressed, subsequent researchers began to study the impact of the shape of air film holes on cooling efficiency. Chen Wei [
12] conducted comparative studies on cylindrical and diffuser hole models, discovering that the blowing ratio has a significant impact on the cooling efficiency of diffuser holes, with higher efficiencies at higher blowing ratios. Wu Xiang yu [
13] conducted thermal cycle load tests on three different types of typical laminar cooling structures. The results indicated that thermal fatigue cracks appeared near the exhaust plate cooling holes and extended longitudinally along these holes, with a greater extent of expansion on the inner surface than on the outer surface. Although the temperature gradient was greater at the baffles during the test, they were not damaged. It is evident that compared to other methods of enhancing heat transfer, the presence of air holes actually weakens structural strength. Whether it is possible to achieve better cooling effects while maximizing structural strength in a thermal shock environment is a question that warrants significant attention. Mazur [
14] analyzed the general characteristics of surface crack distribution on first-stage guide vanes after long-term use in engines. As the operating environment of the blades is consistent, the results are quite reference-worthy. The locations of heat stress concentration on the blades were primarily found at the connections between the leading edge and the inner and outer rings, the trailing edge and the outer ring, the cooling air inlet, and inside the cooling holes at the blade trailing edge.
Elnady [
15] conducted research on the cooling efficiency of air film holes at the leading edge of turbine blades, which were of an expanding shape. The study showed that the cooling efficiency of these expanding holes increases with the rising blowing ratio. In recent years, with the extensive application of multi-porous and composite cooling structures, there has been an increase in the thermal stress load on guide vanes under thermal shock conditions. Due to the dense air film cooling holes on the surface of the blades, the flow of cool air from these holes creates a small concentrated cooling zone around them, leading to an increased temperature gradient around the holes and significant thermal stress at their edges. Practical observations indicate that various air film-cooled blades have experienced cracking originating from the air film holes (
Figure 1).
From the research outcomes, it is evident that although film cooling provides an effective cooling performance, the openings on the blade surface facilitate fatigue damage at the locations of the film holes. Many studies have attempted to enhance cooling efficiency by modifying the position, size, and shape of these holes, and the flow rate of the cooling air, sometimes overlooking issues related to structural strength and fatigue damage. This paper begins with the temperature and pressure of the cooling airflow to comprehensively study the effects of cold air parameters on the cooling performance, strength, and fatigue life of turbine blades, identifying optimal cold air parameters for a typical film-cooled blade, and thus providing insights for the cooling design of film-cooled blades. As the focal point of this research is on the effect of cold air parameters on the thermal fatigue life of the blades, there is less emphasis on the cooling efficiency of the film-cooled blades themselves. Instead, the blade temperature, which significantly affects fatigue life, is chosen as the standard measure of cooling effectiveness (
Figure 2).
2. Thermal Shock Fluid–Solid Thermal Coupling Analysis of Gas Film Cooling Blade
Film cooling blades feature film holes in specific parts of the blade body. As the cooling air passes through the internal cooling channels of the blade and reaches these holes, it flows through the film holes to the blade’s surface and then mixes with the mainstream gas, flowing towards the blade’s trailing edge. Due to the mainstream pressure, the cooling air flowing out of the film holes travels along the blade’s surface, forming a protective layer of cold air over the blade. The cold air inside the film holes mixes and collides with the surrounding combustion gases. Since there is a significant temperature difference between the cooling air and the combustion gases, intense heat exchange occurs, creating areas with large temperature gradients around the film holes. Due to the temperature differences, thermal stresses develop around the film holes (
Figure 3). During engine operation, the film holes at the blade’s leading edge are directly impacted by the mainstream hot combustion gases and the internal cooling air. During changes in engine operating conditions, such as acceleration-deceleration and starting-stopping, the temperatures of the mainstream and cooling air change accordingly, causing the thermal stresses near the film holes to fluctuate. After numerous cycles of loading, cracks can be found at the film holes of the blade, exacerbated by prolonged exposure to high temperatures. The complex plasticity and creep changes within the pores can lead to various forms of cracking or deformation of the metal material [
8].
2.1. Heat Flow Coupling Governing Equation
2.1.1. Continuity Equation
Fluid flow problems adhere to the law of mass conservation. For mainstream gases flowing around turbine blades, the flow state around the blades can be described using turbulent differential control equations:
In the equation,
,
and
are velocity components in
x,
y, and
z directions, respectively. Introducing the Hamiltonian operator:
Then Equation (2) is expressed as:
2.1.2. Momentum Conservation Equation
Energy conservation is one of the fundamental laws of thermodynamics. As hot gas flows over turbine blades, heat exchange occurs between the blades, the hot gas, and the cooler air exiting from the film cooling holes in the cooling channels; however, the total energy remains constant. Its differential equation expression is as follows:
In the equation, represents the pressure on the fluid element; is the velocity tensor; is the identity tensor; represents the fluid’s viscosity; and stands for the mass force.
2.1.3. Energy Equation
Conservation of energy is one of the fundamental laws of thermodynamics. As high-temperature gas flows over turbine blades, the blades simultaneously exchange heat with the high-temperature gas and the gas within the cooling channels, yet the total amount of energy remains unchanged. Its differential equation expression is as follows:
represents the rate of change in the total enthalpy per unit volume with respect to time. takes into account the influence of the change in pressure over time. is the net outflow of energy through the surface of the control volume per unit time, reflecting the divergence of the energy flux resulting from fluid flow. indicates the divergence of the energy flux caused by the temperature gradient through heat conduction, where K is the thermal conductivity coefficient in Fourier’s law. is the energy dissipation generated by the work performed by viscous forces. is the work performed by viscous forces, which can be neglected in most cases. is the internal heat source.
2.2. Turbulence Model
Turbulence is a common physical characteristic in fluid flow processes, and different turbulence models are suitable for different situations. Therefore, in the finite volume method calculations, selecting the appropriate turbulence model is crucial for improving the accuracy of results. Currently, widely used turbulence models include the k-
ε model and the k-
ε model, as well as the modified RNG k-
ε model and SST k-
ω model, which further enhance the simulation accuracy of the models [
16]. As this paper employs the SST k-
ω model for calculations, that model will be mainly introduced. It assumes that the Reynolds stress is directly proportional to the mean velocity gradient:
In the equation,
,
, and
represent the three-dimensional indices, taking the values of 1, 2, and 3;
represents density,
;
represents a geometric point in the spatial coordinates;
represents velocity;
represents turbulent viscosity; and
K represents turbulent kinetic energy. The k-ω model assumes that the turbulent viscosity is related to the turbulent kinetic energy and turbulent frequency. The expression for
is as follows:
Given a limiting series, the SST model expression is as follows:
In the equation, is an estimated value of the strain rate, represents the kinematic viscosity of the fluid, and represents the distance to the nearest wall.
2.3. Solid Domain Control Equations
In the calculations, it is assumed that the material is isotropic, and the effects of body forces and external loads on the system are not considered. The constitutive equations for stress, deformation, and temperature can be represented under conditions of small deformations as follows:
Assuming parameters within the element follow a linear distribution, the relationship between stress vector
and strain vector
in finite elements is as follows:
In the equation, is the elasticity matrix, depending on the material’s modulus of elasticity and Poisson’s ratio.
The expression for the strain vector
is defined as follows:
In the equation,
represents the total strain, and
represents the thermal strain. According to Equations (9) and (10), the total strain can be expressed as follows:
In the equation, is referred to as the flexibility matrix.
For isotropic materials, changes in temperature can only cause normal strain and not shear strain. The thermal strain
induced by temperature can be expressed as follows:
is a function of temperature change and
is the coefficient of thermal expansion. Substituting Equation (9) into (10) yields the constitutive equation for thermal stress as follows:
In the equation, represents the shear modulus. represents the Poisson’s ratio.
Guo Zhao yuan [
17] used a simple model to verify the correctness of a multi-field coupled finite difference program for turbine blades, considering the similarity in calculation methods, a similar approach can be adopted to verify the accuracy of thermal stress calculations. Reference [
18] provides the theoretical calculation formula for thermal stress in perforated thin-walled circular disks:
represents the modulus of elasticity, measured in Gpa. represents the Poisson’s ratio; represents the coefficient of thermal expansion. represents radial stress, and represents circumferential stress, both measured in MPa. and represent the inner and outer diameters of the disk, respectively, measured in mm.
4. Calculation of Turbine Blades’ Fatigue Life
4.1. Fatigue Life Calculation Based on the Local Stress–Strain Method
In 1961, Neuber proposed the relationship between nominal stress–strain and local stress–strain in notched parts, known as the Neuber formula. The strain–life equations proposed by Coffin and Manson have gradually developed into a method for estimating the life span of part cracks, namely, the local strain method. This method has been widely applied in the design of structural fatigue strength in fields such as aviation and automotive. Based on the strain–life relationship, the damage caused by the full cycles extracted can be calculated. The relationship between strain amplitude and life, namely, the Manson–Coffin equation is as follows:
represents the strain amplitude, which is a dimensionless quantity. It denotes the difference between the maximum and minimum values of strain in a stress cycle. is the elastic strain amplitude, indicating the difference between the maximum and minimum elastic strains of a material during the elastic deformation stage. is the plastic strain amplitude. The total strain range should be the sum of the elastic and plastic strain ranges, and the half strain range also follows this rule.
The relationship between strain amplitude and life is decomposed into elastic and plastic parts:
is the fatigue strength coefficient. is the elastic modulus. refers to the fatigue life, indicating the number of stress cycles that a material undergoes from the start of loading until fatigue failure occurs. is the fatigue ductility coefficient, reflecting the proportional relationship of the material’s plastic deformation ability during the fatigue process.
Under cyclic external loading, if the material is within the elastic deformation range, the mean stress will have a significant impact on fatigue life. If the material is in the plastic deformation range, the influence of mean stress will be greatly weakened due to the stress relaxation effect. The Manson–Coffin equation is obtained under symmetric cycles, so when the external load cycle is asymmetrical, its elastic part should be corrected. According to the Goodman equation, the equivalent stress amplitude for symmetric cycles is as follows:
In the equation,
is the stress amplitude,
is the mean stress of the cycle,
is the equivalent stress amplitude. Hence, the modified strain–life equation is:
Inserting the Smith formula (Smith–Watson–Topper formula) [
22], this method is used as a parameter for damage calculation, reflecting the influence of mean stress:
4.2. Based on Ncode Fatigue Simulation Analysis
Ncode, developed by a member company of the AEA Technology listed group, is a powerful software solution capable of visualizing and processing large volumes of signal data. It captures the most viable results and enhances data processing efficiency. It offers mature time–domain and frequency–domain analysis methods, integrating timestamp, spectral planning, rain flow counting, and finite element damage results, thus enabling rapid life prediction through internal software matrices and equations. The fatigue life solution process employs the Standard strain fatigue analysis method, utilizing the Coffin-Manson–Basquin strain life curve method. This equation corrects the mean stress using the SWT method. The calculation is performed using a multiaxial evaluation method based on the maximum principal strain criterion (
Figure 14).
As shown in the life distribution cloud diagram in
Figure 15, the areas near the top of the blade at the film cooling holes have the shortest lifespan, and smaller lifespan points also occur near the dovetail at the blade’s trailing edge. The points of minimum lifespan correspond to the areas of maximum equivalent stress discussed earlier. Due to the presence of the film cooling, the lifespan of the blade parts protected by the cooling film is significantly increased.
In the figure, the red bullet represent thermal fatigue life at critical locations of the blade From the fatigue life distribution contour maps in
Figure 16 and
Figure 17, it can be observed that when the cooling gas temperature is less than 500 K, the fatigue life of the blades decreases as the cooling gas pressure increases, and increases as the cooling gas temperature rises. Under the condition of 300 K cooling gas, when the cooling gas pressure increases from 0.71 Mpa to 0.9 Mpa, the blade life decreases from 2900 times to 1900 times; and as the cooling gas temperature increases, the trend of life reduction becomes gradually slower. Under the condition of 500 K cooling gas, when the cooling gas pressure increases from 0.71 Mpa to 0.9 Mpa, the blade life decreases from 3140 times to 2700 times.
When the cooling gas temperature is greater than 600 K, the fatigue life of the blades first decreases and then increases with the cooling gas pressure, and decreases with the increase in the cooling gas temperature. Under the condition of 600 K cooling gas, when the cooling gas pressure increases from 0.71 Mpa to 0.9 Mpa, the fatigue life of the blades increases from 3300 times to 3500 times at 0.75 Mpa, and then decreases to 3100 times. After the cooling gas temperature exceeds 600 K, the fatigue life of the blades decreases as the cooling gas temperature increases. Under the condition of 0.75 Mpa cooling gas, when the cooling gas temperature increases from 600 K to 800 K, the fatigue life of the blades decreases from 3500 times to 3200 times.
Based on
Figure 18, the following conclusions can be drawn: the trend of the lifespan of the gas film holes does not exactly match the trend of the stress changes with the cooling air. The reason is that if the cooling air temperature is too high and the pressure is too low, the cooling effect of the blades will deteriorate, causing the blade temperature to be too high. The fatigue resistance performance of the material will significantly weaken when the temperature is too high [
19]. When the cooling air pressure is too high, the temperature difference in the blade body will increase, causing the stress at the gas film hole to increase, thereby reducing the lifespan. Based on the calculation results of the fatigue lifespan, it is found that there is an optimal cooling air parameter that maximizes the blade lifespan. The optimal cooling air parameters are a cooling air temperature of 600 K and a cooling air pressure of 0.75 MPa.
4.3. Experimental Results Verification
Thermal Shock Tester. The actual working environment of turbine guide vanes is complex, and existing equipment cannot achieve thermal shock fatigue testing of blades under real working conditions. Therefore, it is necessary to modify and construct the existing thermal shock test equipment in the laboratory to conduct thermal shock fatigue tests under specific conditions. The thermal shock test system is complex and the experimental equipment occupies a significant amount of space, thus requiring a re-layout of the laboratory. The laboratory includes a distribution room, pump room, power room, fuel room, exhaust tower, and the main experimental area where the experimental pipelines and heater are placed (
Figure 19).
The thermal shock tester comprises six main systems: the gas supply system, oil supply system, heating system, cooling system, data acquisition system, and control system, built upon the improvements of existing testing equipment.
Principle of Thermal Shock Test. As shown in
Figure 20, the core components of the tester, including the combustion chamber and the thermal shock test section. As indicated by 4 in the figure below, it shows the blade installation position within the test section. Inside the installation section, to ensure that the external flow field around the blade matches the flow field within the blade cascade channel, a blade is added next to the test blade as a reference blade, to ensure the flow field experienced by the blade conforms to reality, and by connecting the end plates of the reference blade and test blade, circumferential constraints on the test blade are applied, with a local magnification of the blade cascade channel formed by the reference and test blades shown in the right part of the figure above.
Initially, the blade is placed into the tester simulating the blade cascade environment for the adjustment of experimental equipment. The external air compressor was activated to supply stable high-pressure air. Aviation kerosene was ignited by an electronic igniter, generating high-temperature, high-pressure combustion gases for the external gas thermal shock under specified load boundary conditions. Subsequently, an electric heater was turned on to introduce a portion of the air stream from the compressor, providing internal cooling air for the blade during the experiment. The blade temperature was determined using thermocouples attached to the blade, allowing for comparison and analysis with simulated results. This informed adjustments to the experiment parameters by the control system, aligning them more closely with the simulated outcomes. High-temperature thermocouples were placed within the test blade array to measure the temperatures of the hot and cold gases, feedback was sent to the data acquisition system. This allowed for real-time adjustments of the hot and cold gas ratios for heating and cooling via the experimental spray system, thereby controlling the temperature variations in the external gas and cooling air throughout the entire experimental cycles [
23].
Before testing, the turbine blade surface is smooth and free of foreign objects. The blade undergoes a thermal shock fatigue test, and the damage to various parts of the blade is observed using an optical microscope. Due to the high cost of thermal shock tests which require substantial amounts of fuel and time and necessitate an intact turbine blade, analysis is limited to examining the fatigue failure of film-cooled blades under thermal shocks at a coolant temperature of 600 K and a pressure of 0.75 MPa. It was found that the most severe fatigue damage occurs at the film cooling holes, hence special attention was paid to observing these areas. Film cooling holes were examined after cyclic impacts of 1000, 2000, and 3000 cycles.
As shown in the figure below (
Figure 21), magnified images of the fatigue damage at the film cooling holes at various cycles of impacts are presented. Test results reveal that the edges of the film cooling holes suffered the most severe fatigue damage, particularly at the rear edges of the holes where the film is formed, as this is where the hot gas and cooling airflow intersect. After 1000 thermal shock cycles, fatigue damage signs were observed around the film cooling holes of the blade; after 2000 cycles, the damage was more severe, especially near the top holes of the blade, as the leading edge holes are the first region where the coolant passes through. This area has a lower coolant temperature compared to later sections, resulting in a larger thermal gradient; After 3000 cycles, significant fatigue damage was observed around the blade’s film cooling holes, compromising their integrity. These results slightly deviate from the predicted film cooling hole lifespan of 3485 cycles under these conditions, but with an error margin within 20%. This falls within the acceptable range for fatigue life calculation errors and confirms the accuracy of the fatigue life calculations.