Investigation of the film cooling performance of ceramic matrix composites plate with different braided structures

The ceramic matrix composite (CMC) materials have been gradually applied in the high temperature components, due to its excellent heat resistance and mechanical performance. The CMC component still need cooling to protect its safe operation in the high temperature environment of aero engine, such as film cooling structure. This study focuses on the influence of braided structure on the film cooling effect over a three-dimensional braided CMC plate. The full-size calculation model reflecting the internal mesoscale structure of CMC plate was established. The thermal properties of fibers and matrix are also introduced in mesoscale. The geometric parameter which is braided angle of braided structure is changed in different models, to analyze its impacts on the comprehensive film cooling effect. The results show that the fiber bundles inside the CMC plate are the main heat transfer channel, due to its relatively higher thermal conductivity. The different braided angles affect the anisotropic thermal conductivity of CMC on the three main directions. There exists an optimal braided angle near 40° that maximizes the heat dissipation effect in the region near the film cooling holes. While in the downstream region away from holes, the influence of braided angle is weak.


Introduction
The thrust-to-weight ratio is an important indicator to measure the performance of modern highperformance aviation gas turbine engines, and increasing the gas temperature of the combustion chamber outlet is one of the effective ways to improve the thrust-to-weight ratio [1], however, the gradually increasing turbine inlet temperature puts forward strict requirements for the temperature resistance of high-temperature component materials, and traditional metal alloy materials are increasingly difficult to meet the requirements of improving the thrust-to-weight ratio of aircraft engines in terms of weight reduction and temperature resistance.Ceramic Matrix Composite (CMC) has exceptional properties, such as high-temperature resistance [2], and the toughened fibers in CMC materials greatly improve the overall mechanical properties of the material, making its practical engineering application under high thermal load and high mechanical load possible.Among them, the three-dimensional braided composite yarn bundle extends in multiple directions in space and interweaves with each other to form an overall network structure, which fundamentally overcomes the fatal weakness of low interlayer strength and easy delamination of laminated composites, while CMC materials have superior mechanical and physical properties such as oxidation resistance, ablation resistance, thermal shock resistance, insensitivity to cracks, and no catastrophic damage [3][4], and are gradually applied to high-temperature parts of aero-engines [5][6][7][8].
However, in order to meet the turbine gas inlet temperature of more than 2100K for highperformance aero engines [9], efficient heat evacuation and cooling technology is still required to ensure the safe operation of the hot end parts of CMC materials.Considering the low thermal conductivity of CMC materials and the complexity of processing technology, air film cooling is a feasible and efficient cooling structure.For example, NASA [10] applied gas film cooling technology to CMC material blades, successfully passing 50h steady state and 102 thermal cycling tests from 1173K to 1713K.Zhong et al [11] showed through experiments that opening air film pores in CMC materials has high cooling efficiency.
When carrying out the design and analysis of the air film cooling structure of CMC materials, it is necessary to accurately estimate the comprehensive cooling efficiency and the internal temperature field of the structure.Heidmann et al [12] compared and analyzed the cooling effect of turbine blades of high thermal conductivity superalloy and low thermal conductivity ceramic two materials, and the results show that in the complex conjugate heat transfer process of blade air film cooling, the heat transfer process is not only a simple one-dimensional process from the hot gas side wall to the cold gas side wall.Due to the internal heterogeneity and thermal conductivity characteristics, the braided CMC material is quite different from the traditional homogeneous metal material, which will further affect the heat conduction process inside the air film cooling structure, and then affect the cooling effect of the air film.At present, there are two main methods for the thermal analysis of anisotropic CMC material components, one is to characterize the internal structural characteristics of CMC material components by homogenization of anisotropic equivalent thermophysical parameters, and the other is to solve the problem by establishing a physical model reflecting the internal structure of CMC materials combined with numerical simulation.For the first method, Tu Zecan, Mao Junkui et al [13] revealed for the first time the influence mechanism of thermal anisotropy of CMC materials on the cooling effect of air films, and the differences between the implementation effect of air film cooling of traditional metal material components, and mastered the co-design criteria of flat-walled air film cooling and anisotropic CMC materials.Chen Qihao [14] et al. based on the thermodynamic analysis and using the method based on the effective thermal conductivity to equivalently equate the thermal conductivity of the CMC plate to the macroscopic effective thermal conductivity in the three directions of X, Y, and Z, The relationship between the angle of main heat transfer direction and the mainstream and the cooling efficiency distribution of the plate end wall is studied, and it is found that when the thermal conductivity of the plate shows anisotropic thermal conductivity, the cooling band of the plate end wall surface is twisted in the direction of main heat transfer.However, the above homogenization method is difficult to reflect the heat transport characteristics caused by the internal meso-scale structure of CMC materials, Dong et al. [15] firstly calculate the thermal conductivity of the representative volume element (RVE) of braided yarn at the microscale, and then calculate the thermal conductivity of mesoscale RVE and full-scale composites, respectively, and the results showed that the heat flow propagation mainly follow the fiber trend.In the research of Zhao et al. [16], a full-scale geometric model reflecting the real braided structure of the composite material was established, according to the geometric parameters of the weave structure of the 2.5 D braided composite sample.The anisotropic thermal conductivity of each component was introduced from the yarn scale in the calculation, and the results showed that the braided structure significantly affected the internal heat transfer path, and at the same time, the film holes and the composite braided structure interfered with each other, which had a significant impact on the cooling effect within about 2 D range downstream of the air film holes.Tu et al. [17] established a model based on effective thermal conductivity and a model based on internal micro braided structure, respectively, to verify the influence of braided structure on cooling performance, and the results showed that the internal braided structure had a significant impact on the cooling effect and internal heat conduction of the composite panel.Hou Yadong [18] et al. carried out experimental research on the film cooling performance of composite flat by different braided methods, and the results showed that the 2.5D braided method had the highest cooling efficiency of composite materials and the lowest cooling efficiency of 3D braided composites.
In summary, most of the current research on the film cooling performance of braided CMC materials is based on the homogenization equivalent method, and a few scholars have established an film cooling structure model based on mesoscale braided structure, and preliminarily explored the influence of mesostructure on the film cooling effect, but the affecting mechanism of geometric parameters of braided structure on the internal heat transfer and cooling efficiency of CMC plate has not yet been systematically clarified.Therefore, for the typical film cooling structure of three-dimensional five-way braided CMC materials, an analysis model reflecting the characteristics of meso-scale braided structure is established, and the anisotropic thermal conductivity of each component is introduced from the mesoscale.The influence of the braiding angle and fiber bundle cross-sectional size on the film cooling effect is analyzed, which can provide guidance for the further engineering application of CMC material in aero-engine high-temperature parts.

Numerical models
Figure 1 shows the internal RVE model of the three-dimensional five-way braided film cooling structure, in which the light yellow part is the shaft yarn, the dark yellow part is the braided yarn, and the blue part is the matrix.The fiber arrangement inside the braided yarn and the shaft yarn tends to be hexagonal, the fiber filling factor is ε1=ε2=0.8.The axial thermal conductivity of the fiber bundle kFA=9.37W/(m.k), the transverse thermal conductivity is kFT=2.34W/(m.k),and the thermal conductivity of the matrix is 0.3W/(m.k).The data is provided by the material supplier.
Figure 2 is a schematic diagram of the internal structure of the cell.The solid line in the figure represents the braided yarn, and each cell contains 14 braided yarns with 4 different orientations.The shaft yarn is parallel to the braided direction, and each cell contains 9 shaft yarns, of which the other shaft yarns are shared by adjacent cells except for the central shaft yarn as a whole.The height of the cell h is one flower node length.The width and thickness are the same, and it is Wi.Define the inner weave angle γ which is the angle between the inner braided yarn and the forming direction of the fabric.In this paper, the key geometric parameters such as the braided angle γ of braided yarn and the crosssectional size of fiber bundle were changed to explore their influences on the film cooling effect.In different cases, the braided angle γ is 20°, 30°, 40°, 50°, and the cross-sectional size S of the fiber bundle is 0.1414mm2, and the parameters in different RVE models are shown in Table 1.Based on the RVE parametric model shown in Figure 1, a computational model of the braided CMC flat air film cooling structure was constructed, as shown in Figure 3.The geometric sizes of the film cooling plates with different braided structures are the same, with a length of 18mm, a width of 3.6mm, and a thickness of 2.6327mm.The air film hole is a vertical circular hole, the pore diameter is d=0.6mm, the center of the hole is 4.2mm away from the gas intake, and the hole spacing is 2d.
The origin of the calculation model is located at the junction of the air film holes in the middle and the air film plate in the flow direction, as shown at location ① in Figure 3(a).The X direction is the spreading direction of the plate, that is, the width direction of the plate.The Y direction is the normal direction of the plate, that is, the thickness direction of the plate, and the Z direction is the mainstream direction, that is, the length direction of the plate.

Governing equations
The numerical research part of this paper uses the non-isothermal flow and conjugate heat transfer models in COMSOL software, and the governing equations include the continuity equation, momentum equation and energy equation of compressible gas in steady state [19]: ① ③ ② Formula: ρ and u represent density and velocity, p and μ represent pressure and dynamic viscosity, F represents volumetric force, T represents temperature, and k is thermal conductivity.According to the research conclusions in the literature [16], the k-ω turbulence model has good accuracy in predicting the overall cooling effect of the gas film, so the k-ω turbulence model is also used in the simulation calculation in this paper.

Thermal conductivity setting
Since the main direction of thermal conductivity of the fiber bundle in the three-dimensional five-way braided composite material is the axial direction of the fiber bundle, which changes with the braiding direction and has inclined angles with the global coordinate system.So the anisotropic thermal conductivity matrix keeps changing inside the plate, and it needs to be calculated and converted in the global coordinate system.If the width direction of the braided structure is X-axis, the thickness direction is the Y axis, and the braided axis is the Z-axis, the computational coordinate system is established, as shown in Figure 5, the thermally conductive isotropic matrix can be considered to be consistent with the global coordinate system, and the axial yarn direction is consistent with the Z-axis of the global coordinate system.In the calculation of this section, the braided yarn in the RVE model has four spatial directions (as shown in Figure 5 Nos. 1, 2, 3, and 4), and the coordinate system of the main direction of the braided yarn is inconsistent with the global coordinate system, that is, it has four local coordinate systems, in order to complete the overall numerical calculation of the thermal conductivity of the single cell, it is necessary to convert the thermal conductivity in the non-principal direction of the braided yarn.The detail method for the thermal conductivity setting is shown in our previous published paper [20]， and will not be repeated here.

Calculate operating conditions and boundary conditions
As shown in Figure 6, the boundary ① is the mainstream inlet, the inlet temperature is 393.15k, the mainstream flow velocity is 33.62m/s, the boundary ② is the coolant flow inlet, the inlet temperature is 293.15k, the blowing ratio is 0.25, that is, the coolant flow inlet speed is 0.1088m/s.The coolant flow enters the coolant flow channel from the coolant flow inlet, and then enters the mainstream channel through the film hole, and after mixing with the mainstream, it flows out from the outlet ③.The boundary ③ is the pressure outlet boundary condition, the absolute pressure at outlet is 101325Pa.The other boundaries are adiabatic boundary conditions.

Meshing and mesh independence verification
In this study, COMSOL software was used to mesh the computational model.Taking the plate of case2 as an example, the mixed grids are applied in the simulations, in the solid regions, a tetrahedral grid is used, and then the meshes on the plate's top and bottom surface are swept in the mainstream and coolant regions respectively.The junction of fiber and matrix is encrypted by mesh and the boundary layer encryption grid is constructed in the fluid domain near the gas side wall.
In the study, the independence of the grids was first verified, and the total number of grids was 1049233, 2189891, and 3147647, which were recorded as Normal, Fine, Finer, respectively.Figure 7 shows the variation curve of cooling efficiency on the downstream central line with different grid numbers.The results show that, when the grid number increases from 2189891 to 3147647, the maximum relative variation of the cooling efficiency is less than 5%, so the grid and its division strategy are adopted 2189891 in this study.The maximum cell size is 0.21514mm, the minimum is 0.09439mm, the maximum cell growth rate is 1.35, the boundary layer grid size change rate is 1.10, and the grid diagram is shown in Figure 8.

Experimental system
In order to verify the simulation accuracy of the calculation model in this paper, the film cooling experiment was carried out for the typical three-dimensional five-way braided CMC plate.Figure 9 is the schematic diagram of the experimental system, which consists of main and secondary flow air compressors, air storage tanks, regulating valves, flow meters, electric heaters, rectifier wind tunnels, transfer sections, test sections, pressure and temperature measurement systems, etc.The mainstream air is provided by the air compressor, which first enters the high-pressure gas storage tank to stabilize the pressure, and then flows through the regulating valve and mainstream flow meter that control the flow of the mainstream channel into the electric heater, which is heated to the temperature required for the test in the electric heater, and rectified through the rectifier wind tunnel, and supplied to the test section after passing through the transfer section.The secondary flow cooling air is supplied by another air compressor and flows sequentially through the flow control valve and the secondary flow meter before entering the test section.In addition to the main and secondary flow channels, the core part of the test section is an air film orifice plate made of three-dimensional five-way braided composite material.The main purpose of the test is to obtain the temperature distribution of the gas side wall of the gas film flat plate, and then calculate the comprehensive cooling efficiency of the gas film, verify the accuracy of the numerical simulation model in this paper, and mainly use the infrared thermal imager to measure the surface temperature field.The overall test system is divided into four parts: gas supply system, heating system, measuring system and test section.

The values were verified by comparison with the test results
Figure 11 shows the change of cooling efficiency on the central line based on the experimental data and numerical data under the same operating conditions.The results show that, in the range of 2.5D to 15D, the numerical results are slightly greater than the experimental results, and after 15D, the numerical results are basically consistent with the experimental values.The maximum error between the experimental data and numerical data is 4.48%, which indicated that the mesoscale numerical model of the braided CMC film cooling structure established in this paper is reliable [16] .

Analysis of numerical simulation results
In Figure 12, (a), (b), (c) and (d) are the surface cooling efficiency clouds of case1-case4, respectively.In the flow direction, the film cooling efficiency gradually decreases along the flow direction, and in the direction of the direction, the film cooling efficiency at the center is the highest, and the cooling efficiency decreases as it moves away from the central line.In this paper, the area with the film cooling efficiency higher than 0.4 is defined as the area with high cooling efficiency.By comparing (a), (b), (c) and (d) in Figure 12, it can be found that the area with high film cooling efficiency in case 1 and 3 is relatively larger.Compared with case1 and 3, the areas with high film cooling efficiency in case2 and case4 are smaller, only reaching about 2D downstream of the air film holes.Figure 13 shows the temperature distributions on the plane X=0 in case 1-case 4.Among them, the size of the red arrow indicates the magnitude of the conduction heat flux inside the plate, and the direction of the red arrow indicates the direction of heat transfer.It can be found that the characteristics of the heat transfer direction on case 1-case 4 are consistent.Since the upstream region is not covered by the cooling film, the heat inside this region is gradually transferred from the hot-side-wall to the coldside-wall and the wall of film holes.In the downstream of the air film holes, because the upper wall surface is protected by cooling gas, the lower wall surface is directly in contact with the cooling gas, in the solid domain downstream of the air film holes, the temperature distribution shows a lower temperature close to the upper wall and the lower wall, and the middle part of the temperature is higher.
Table 2 is the equivalent thermal conductivity of the plate on the Y direction and Z direction under different braided angles, it can be found that with the increase of the braided angle, the equivalent thermal conductivity on the Y direction increases.The heat transfer on the Y direction is enhanced, and the temperature in the middle part is low.In the region near the holes, as shown in the red circle in Figure 14, the temperature of this area increases with the increasing braided angle.The reason is that, the heat is mainly transferred from the plate to the wall of holes in this region, the equivalent thermal conductivity on the Z direction gradually decreases with the increasing braided angle.So the thermal resistance on the Z direction is greater, the heat is not easy to dissipate, and the temperature is higher.Although the direction of heat transfer in case 1-case 4 is globally consistent, there are still differences of the specific heat transfer path.The direction of the red arrow in Figure 13 is deflected vertically with the increase of the braided angle, it can be found that the angle of the braided structure obviously affects the path of heat propagation.With the increase of the braided angle, the isotherm changes accordingly, and the isotherm is basically consistent with the braided angle of the briaded yarn near the air film hole.This is mainly caused by the thermal anisotropy of the braided yarn and the difference of the thermal conductivity between the yarn and the matrix.The thermal conductivity of the braided yarn is significantly higher than the matrix, so the heat transfer is more intense in the direction of the braided yarn.Figure 14(a) shows the change curves of the film cooling efficiency on the central line in downstream region.The influence of braided angles on the cooling efficiency is obvious, and the film cooling efficiency in case1 and case3 is relatively higher than that of case2 and case4.
In the range of Z/D less than 10, the film cooling efficiency on the central line with different braided angles has slight variation, because the covering effect of the cooling film is obvious in this region, the influence of the anisotropic thermal conductivity and braided angle is weaker comparing the cooling film.The cooling effect on the central line in case3 is relatively better, because the heat dissipation of the film cooling plate is mainly divided to two parts, one is the heat exchange with the holes wall, the larger the equivalent thermal conductivity on the Z direction, the more heat is transferred and taken away by the cooling airflow.the other one is the heat transfer on the thickness direction, the greater the equivalent thermal conductivity on the Y direction, the more heat is transferred and taken away by the cooling airflow.Therefore, in the region near the holes, the cooling effect depends on both of the thermal conductivity on the Z and Y directions.Therefore, there will be an optimal angle to maximize the cooling efficiency of the air film plate, this angle is around 40° under the operating conditions in this paper.
Figure 14(b) shows the change of film cooling efficiency along the extension direction at Z=4d downstream of the air film holes.In terms of the development direction, the cooling efficiency is highest at the center, and the cooling efficiency decreases as it moves away from the center line.At the Z=4d position, case3 has the highest cooling efficiency.Therefore, when the braiding angle is 40°, the air film plate has a better cooling effect.

Conclusion
In this paper, the mesoscale model of film cooling plate with three-dimensional five-way braided CMC materials is established considering the internal structure characteristics.The anisotropic thermal conductivities of fiber bundles and matrix are introduced from the mesoscale structure.The influences of the braided angle and the cross-sectional size of fiber bundles on the film cooling efficiency are obtained.The main conclusions reached are as follows: (1) The film cooling efficiency gradually decreases along the flow direction.In the cases with different braided structures, there are significant differences in the specific heat transfer path.The heat is mainly transferred and changed along the fiber direction.(2) When the braided angle changes, the heat transfer in the region near the holes mainly has two parts.The one is the heat exchange with the wall of hole, and the other one is the heat transfer on the thickness direction.Therefore, the film cooling effect depends on both of the thermal conductivities on the Y and Z directions.There is an optimal angle with best cooling effect, this optimal angle is 40° under the operating conditions in this paper.

Figure 1 .
Figure 1.Three-dimensional five-way braided composite RVE.The fiber arrangement inside the braided yarn and the shaft yarn tends to be hexagonal, the fiber filling factor is ε1=ε2=0.8.The axial thermal conductivity of the fiber bundle kFA=9.37W/(m.k), the transverse thermal conductivity is kFT=2.34W/(m.k),and the thermal conductivity of the matrix is 0.3W/(m.k).The data is provided by the material supplier.Figure2is a schematic diagram of the internal structure of the cell.The solid line in the figure represents the braided yarn, and each cell contains 14 braided yarns with 4 different orientations.The shaft yarn is parallel to the braided direction, and each cell contains 9 shaft yarns, of which the other shaft yarns are shared by adjacent cells except for the central shaft yarn as a whole.The height of the cell h is one flower node length.The width and thickness are the same, and it is Wi.Define the inner weave angle γ which is the angle between the inner braided yarn and the forming direction of the fabric.

Figure 2 .
Figure 2. Schematic diagram of the internal structure of the cell.

Figure 4 .
Figure 4. Schematic diagram of the calculation domain.

Figure 7 .Figure 8 .
Figure 7.The variation curve of cooling efficiency under the three sets of grids.

Figure 9 .
Figure 9. Schematic diagram of the experimental system.Figure 10 shows the photograph and size diagram of the test piece, and the specific dimensions of the gas film plate are 35 mm × 19 mm × 3 mm.The film holes are vertical, and the spreading distance of adjacent film holes is 3D.The center of the film holes is 9mm from the upstream boundary, and the distance from the left and right boundaries is equal to 1.1mm.Under typical test conditions, the Reynolds number Re is 180000, the characteristic length L in the Re definition is the equivalent diameter of the experimental section of the mainstream transfer channel, and the air-conditioning blowing ratio M=0.5.

Figure 10
Figure 9. Schematic diagram of the experimental system.Figure 10 shows the photograph and size diagram of the test piece, and the specific dimensions of the gas film plate are 35 mm × 19 mm × 3 mm.The film holes are vertical, and the spreading distance of adjacent film holes is 3D.The center of the film holes is 9mm from the upstream boundary, and the distance from the left and right boundaries is equal to 1.1mm.Under typical test conditions, the Reynolds number Re is 180000, the characteristic length L in the Re definition is the equivalent diameter of the experimental section of the mainstream transfer channel, and the air-conditioning blowing ratio M=0.5.

Figure 10 .
Figure 10.Schematic diagram of the experimental plate.

Figure 11 .
Figure 11.The results of experimental and simulation.

Figure 12 .
Figure 12.Cloud diagram of cooling efficiency on the surface of gas film plate with different braided angles.

Figure 13 .
Figure 13.Temperature distribution cloud of the plane X=0 in the solid domain.

Table 1 .
Basic dimensions of flat plates.

Table 2 .
Equivalent thermal conductivity of flat plates in different directions at different braiding angles.