Numerical Investigation of the Effects of Lattice Array Structures on Film Cooling Performance

Abstract

To better understand the mechanism influencing the periodic lattice structures in gas turbine blade cooling, these numerical simulations present a systematic comparison of the effects in cases involving pin-fin, Kagome, and BCC lattice arrays on film-cooling effectiveness under three blowing ratios (i.e., M = 0.5, 1.0, and 1.5). The results indicate that the introduction of lattice array structures improves film-cooling effectiveness within the whole streamwise range, especially downstream of the film hole. With an increase in the blowing ratio, the superiority of lattice array structures relative to those without a lattice becomes increasingly evident. The local film-cooling effectiveness can be increased, to a maximum of about 100%, under a blowing ratio of 1.5. The secondary flow induced by the lattice array structure at the internal flow channel increases the TKE and accelerates the development of vortices in the film cooling hole. Using the lattice array model, the improvement of the Kagome and BCC lattice arrays in terms of film cooling is better than those of pin-fins. In addition, the effect of lattice arrays on film-cooling effectiveness is different at various blowing ratios, and the lattice array structures have little impact on the film cooling at a relatively low blowing ratio.

1. Introduction

Increasing the turbine inlet temperature is a common way to improve the performance of aero engines and gas turbines. According to one analysis, the thrust of an aero engine can be increased by 10% with an increase in the turbine inlet temperature of 55 K [1]. Therefore, it is particularly important for turbine blades to improve their thermal protection performance, as in the case of challenges induced by the continuous increase of turbine inlet temperature [2]. Film cooling is a traditional and effective thermal protection technology, involving a cooling film layer near the blade surface to isolate the high-temperature mainstream away from the blade. Many numerical and experimental investigations have been carried out by a broad spectrum of researchers, to understand the fundamental physics of film cooling and to improve the state of the art [3,4].

Internal cooling is also important for the thermal protection of turbine blades. Traditional internal cooling technologies mainly include impingement cooling [5], serpentine-ribbed cooling, and pin-fin cooling [6,7]. There have also been many previous studies focused on turbulence flow and heat transfer enhancement in rib- or pin-fin-equipped channels. Hsieh et al. [8] have studied the heat transfer coefficient and loss coefficient of ribbed rectangular channels with staggered and parallel arrangements of the ribs. Rau et al. [9] have investigated the flow and heat transfer characteristics in ribbed cooling channels and found that the heat transfer coefficient of the ribbed wall was enhanced by the secondary flow, which is generated by the ribs when at an attack angle of 45°. Those investigations indicated that the heat transfer could be enhanced by the secondary flow, which is generated by the cooling structures of the internal channel [10,11]. Generally, the film cooling holes and convective cooling structures have been designed together with the cooling channel, and the film cooling jets would be influenced by the internal flow, which is generated by the internal cooling structures. Thurman et al. [12] have investigated the flow of heat transfer from the ribs and film cooling hole-equipped channel. It was found that with the flow extraction of film cooling holes, the overall heat transfer of the internal channel wall was enhanced, especially the region around the entrance of the film cooling holes. Bunker et al. [13] have investigated the flow structure in rib-equipped channels with the film hole in different positions and found that the ribs have a great impact on the outflow of the film cooling hole. Agata et al. [14] have numerically investigated the effect of the ribs’ angle on the film cooling performance. It is found that the separated flow generated by the ribs will affect the effecting structures of the film cooling process and film cooling effectiveness.

The lattice array structures are a type of complicated periodic porous structure. With the development of three-dimensional printing technology, the application of micro-lattice array structures in high-temperature components has become possible. Previous research has shown that lattice array structures can achieve good cooling performance because of the large surface area per unit volume and have an excellent capacity for enhancing turbulence flow [15,16,17]. Moreover, the pressure loss caused by the lattice array structure [18] is less than that of foam metal with the same heat transfer capacity [19]. Shen et al. [20] have compared the heat transfer enhancement of Kagome and pin-fin array structures in wedge-shaped channels and suggested that the heat transfer enhancement from a Kagome lattice is better than that in a pin-fin structure. Bai et al. [21] investigated the heat-transfer performance of the lattice core sandwich panel structures. They reported that multiple lattice array structures can enhance heat transfer efficiency.

Although several previous studies have investigated the flow and heat transfer characteristic of a cooling channel equipped with a lattice array structure, the effect of the complex flow induced by lattice array structures on film cooling is still not clear. In this paper, an integrated cooling model, combined with lattice array structures and film cooling, has been described and numerical investigations have been performed to study the interaction of the lattice array structure and the film cooling, especially the influence of internal flow on the film cooling performance. This paper is expected to serve as a reference for the cooling optimization of gas turbine blades.

2. Physical Model and Grid Independence Study

Three types of typical lattice array structures, Kagome, BCC, and pin-fin, are applied in an integrated cooling model; the geometry of the unit cell is shown in Figure 1. The unit cell is the smallest-volume element in the lattice array; the different volumes of the lattice structure have different blocking ratios and heat exchange areas. In order to compare the internal flow and heat transfer in different lattice array structures, the volume of each lattice structure type is set to be equal.

To simulate the film cooling on the turbine blades, a film cooling hole is added above the internal cooling channel, and the inlets of the film cooling holes are evenly distributed in the middles of the lattice gaps. The main flow channel is perpendicular to the internal flow section. The diameter of the film hole is 6 mm, the aspect ratio of the film hole is 3, the spacing of the film hole is 22 mm, and the inclination angle and compound angle of the film hole are 30°and 0°, respectively, as shown in Figure 1.

A tetrahedral computational mesh is used that is generated by the ANSYS ICEM software. To increase the accuracy of calculation, a dense mesh is used at the wall of the film cooling hole and the lattice structure surface. An O-grid is used to surround the film cooling hole to keep orthogonality, as shown in Figure 2. Meanwhile, the height of the first prism layer elements near the surface is adjusted to ensure that the dimensionless wall distance (y⁺) is less than 1.

The grid independence study has been carried out for a pin-fin array model, with a grid number ranging from 2.9 million to 12.5 million. As shown in Figure 3, the laterally averaged film cooling effectiveness in a grid number of 7.59 million shows good agreement with that of 12.5 million, with a maximum deviation of less than 1%. Therefore, the grid number of 7.59 million was chosen for numerical study, and the grid number for all the models was around 10 million.

The film cooling effectiveness is defined as follows:

$${\eta }_{adiabatic}=\frac{T-T_{\infty }}{T_C-T_{\infty }}$$

(1)

Among them, T is the adiabatic wall temperature, T_∞ is the mainstream temperature, and T_c is the temperature of the coolant.

3. Numerical Method and Boundary Conditions

The numerical simulation was conducted using the ANSYS CFX19.0 commercial software. The analysis of the fluid flow and heat transfer is achieved by solving the compressible RANS equations, based on the finite-volume method under steady-state conditions [22,23]. The standard SST k-ω turbulence model is used; it has been proven that the SST k-ω turbulence model could give a good prediction of film cooling effectiveness in a scenario with a ribbed crossflow coolant channel [24]. The mainstream inlet conditions are maintained as constants. The inlet and outlet of the internal cooling channel are set as the mass flow-rate boundary conditions, and the difference of the mass flux between the inlet and outlet is adjusted to meet the blowing ratio requirement. The condition of symmetry is applied at the sidewalls of the mainstream channel, and the top of the mainstream channel is set as an open boundary condition. The other walls are set as adiabatic, with no-slip boundary conditions. The specifications of the boundary condition are summarized in

Table 1. The boundary conditions in the numerical simulation.

	Inlet velocity (m/s)	Inlet temperature (K)	Inlet mass flow (kg/s)	$M=\frac{{\rho }_c{u}_c}{{\rho }_{\infty }{u}_{\infty }}$	DR	MR	Tuin
Mainstream	20	300			0.97		5%
Coolant		310	0.001	0.5		0.26
				1		1.03
				1.5		2.32

.

The blow ratio M is defined in Equation (2):

$$M=\frac{{\rho }_c{u}_c}{{\rho }_{\infty }{u}_{\infty }}$$

(2)

The coolant-to-mainstream density ratio DR is defined in Equation (3):

$$DR=\frac{{\rho }_c}{{\rho }_{\infty }}$$

(3)

The momentum flux ratio MR is determined through Equation (4):

$$M=\frac{{\rho }_c{u}_c^2}{{\rho }_{\infty }{u}_{\infty }^2}$$

(4)

Among them, u_c and ρ_c are the average flow velocity and average density at the outlet of the film hole, respectively. u_∞ and ρ_∞ are the average flow velocity and average density of the mainstream inlet, respectively.

4. Numerical Validation

In order to verify the accuracy of the numerical method, numerical verification has been carried out. In this section, the effectiveness of the laterally averaged film cooling at the measurement region and the end wall-averaged Nu in the channel equipped with a Kagome lattice are discussed and compared with the experimental results.

4.1. Film Cooling Performance

The numerical validation for flat-film cooling was carried out with several turbulence models, k-ε, RNG k-ε, and SST k-ω, and then compared with the experimental results reported by Sinha et al. [25]. As the results show in Figure 4, there were some deviations between the numerical result and experimental data, which were due to under-prediction by the turbulence model of the lateral diffusion of the film coolant. The numerical result using the SST k-ω model showed a relatively better agreement (the average deviation is less than 25%) with the experimental data among the tested models. Therefore, further calculations were performed using the SST k-ω model.

4.2. Flow and Heat Transfer in a Lattice Array Structure Equipped with a Channel

The numerical verification for the turbulence flow and heat transfer in the lattice array structure equipped with a channel is carried out and compared with the experimental result [26]. Figure 5 presents the comparison of the experimental and numerical Nu distribution on the bottom end wall at Re = 9500. In the case of a Kagome lattice, the heat transfer characteristic of the numerical result is similar to the experimental distribution; the entrance effects are mainly concentrated in the first two rows of units, the arch-shaped heat transfer augmentation is formed at the front vertices of the units, and the low heat transfer zone is formed at the downstream of the unit back vertices. However, from the third row, there are some deviations between the experimental and numerical results. The first reason for this is the slight heat conduction on the channel surface in the experiment. The second reason is the under-prediction of mixing intensity for vortex flow with the SST k-ω model. In the case of the BCC lattice, the numerical and experimental results have a similar situation as in the scenario with a Kagome lattice.

Figure 6 presents the comparison of the end wall-averaged Nu at different Re between the numerical and experimental data [26]. It can be seen that the numerical result shows good agreement (the biggest deviation is less than 20%) with the experimental results. Therefore, it is possible to apply this numerical method in the study.

5. Results and Discussion

5.1. The Effect of Lattice Array on Film Cooling

In order to investigate the effect of different lattice array structures on film cooling, the film cooling effectiveness contours of the mainstream channel bottom for all cases at M = 1 are shown in Figure 7. It can be seen that the introduction of lattice array structures improves the film cooling effectiveness within the whole streamwise range, especially downstream of the film hole. In the case of the model with no lattice, the coolant crossflow has little effect on the film cooling, and the film-cooling effectiveness at the exit of the film hole is relatively high. However, due to the weak spanwise expansion of the coolant jet, the film cooling lateral coverage area is small. In the scenario with a pin-fin array, the lateral film coverage near the exit of the film hole is narrower than that without a lattice. As the film jet develops along the mainstream, the lateral film coverage becomes wider, and the coverage area in the scenario with a pin-fin array is wider than that of the no-lattice model. In addition, with the model affected by the crossflow of the internal coolant and the mainstream flow of the coolant, the film coverage shifted in the spanwise direction in the pin-fin array scenario. In the scenario with a Kagome array, the distribution trend of film coverage is similar to that seen with the pin-fin array, while the lateral film coverage near the exit of the film-cooling hole shows contraction. In the case of the BCC array, the film cooling performance is better than that of the other lattice array structures, and the distribution trend of the film coverage is similar to that of the Kagome lattice array.

For quantitative evaluation, the film cooling effectiveness at the centerline of the mainstream wall is plotted in Figure 8. In the case of the Kagome and BCC lattice arrays, the film cooling effectiveness at the centerline along the mainstream direction is significantly higher than that of the pin-fin array and the channel without a lattice, and the local film cooling effectiveness can be increased by a maximum of about 100%. In the case of the pin-fin array, at the area near the exit of the film hole, the film cooling effectiveness decreases drastically to lower than that of the no-lattice model. However, in the area downstream of the film hole, the change of film cooling effectiveness tends to be gradual and is higher than that of the no-lattice model, with the film jet developing in the mainstream direction.

The streamline and dimensionless temperature distribution in several representative y-z cross-sections along with the mainstream flow are shown in Figure 9. Among them, the definition of dimensionless temperature θ is the same as that of film cooling effectiveness, and T_a is the fluid temperature.

$$\theta =\frac{T_{\mathrm{a}}-T_{\infty }}{T_{\mathrm{c}}-T_{\infty }}$$

(5)

At the near-wall region of the mainstream bottom wall, the kidney vortices are induced by the film cooling jets. In the case of the no-lattice model, the kidney vortices are in good symmetry. At the area near the exit of the film cooling hole, the kidney vortices stay close to the mainstream wall, resulting in a good film cooling coverage. Due to the continuous action of the shear stress between the mainstream and coolant flows, the kidney vortices tend to deviate from the mainstream wall and the film cooling effectiveness decreases. In the case of the pin-fin array model, due to the influence of the crossflow between the internal coolant flow and the mainstream flow, the coolant film jet shifts in the spanwise direction, and the symmetry of the kidney vortices is destroyed. At the area near the exit of the film cooling hole, the kidney vortices close to the mainstream wall at the central zone rise in the spanwise area, resulting in the lateral gas film coverage being narrowed in this area, as shown in Figure 7. Downstream of the film cooling hole, the distance between the vortex core and the mainstream wall is closer than that of the no-lattice structure. This strong vortex structure effectively transports the coolant to the target surface via entrainment, resulting in stronger heat transfer and a better film cooling cover over the mainstream wall. The kidney vortices’ distribution in the case of the Kagome and BCC array models is similar to that of the pin-fin array model, but the strength is different. In the case of the Kagome and BCC array models, the scale of the kidney vortices and the lateral spacings between two vortex cores are smaller than that of the no-lattice structure. This vortex characteristic shows a strong trend of driving more coolant, converging at the central area of the mainstream wall to form entrainment of the vortex, which results in a better film-cooling performance in this area, as in the dimensionless temperature distribution shown in Figure 9.

The velocity streamlines the distribution in several elaborately selected y-z cross-sections along with the mainstream flow, as shown in Figure 10. In the case of the no-lattice model, the distribution range of the kidney vortices at the cross-section is wider than that of the lattice array structures, which results in a greater area of contact between the coolant and the mainstream flow. This flow characteristic gradually moves the coolant away from the mainstream wall to mix with the gas in the mainstream flow by entrainment of the kidney vortices. Thus, such a flow characteristic contributes little to enhance the film cooling performance. In the case of lattice array structures, the lower-velocity area is wider than in the no-lattice structure near the mainstream bottom wall. Thus, the period of heat exchange is prolonged in this area. This is beneficial to promoting flow-mixing and enhancing the film-cooling performance, as revealed by the dimensionless temperature distribution in Figure 9.

The flow characteristic at the entrance of the film cooling hole is shown in Figure 11. The coolant flow boundary layer is interrupted by the Kagome lattice upstream of the film hole, resulting in a low-momentum flow region near the entrance of the film hole; the interruption by the Kagome lattice of the coolant flow is stronger than that of the pin-fin array. Compared with the Kagome lattice scenario, the lower momentum near the entrance of the film cooling hole in the case of the pin-fin array and the no-lattice model implies the lower momentum of the jet at the hole exit. The strong shear flow and impingement of the mainstream flow impose a stronger effect on the lower-momentum coolant flow, changing the coolant jet flow direction, and cover the mainstream channel bottom. The film-cooling effectiveness of the Kagome lattice is significantly higher than that of the pin-fin array and no-lattice model, downstream of the mainstream wall. Among these flows, turbulent kinetic energy (TKE) is characterized by the measured root-mean-square velocity, which provides information regarding flow-mixing intensity [23]. In the case of the no-lattice model, the flow boundary layer develops smoothly at the cooling channel. Due to the suction effect of the film cooling hole, the flow velocity of the coolant is increased drastically; the flow direction of the coolant will also change drastically to enter the film cooling hole. Notable kidney vortices are formed inside the film cooling hole, due to the combined effects of centrifugal force relative to the hole axis and the suction effect of the film cooling hole. At the entrance of the film cooling hole, the flow direction is shifted at the negative Z semi-axis, which is affected by the crossflow between the internal flow and mainstream flow. In addition, the distribution of turbulent kinetic energy creates significant differences around the film hole. The turbulent kinetic energy is high near the entrance of the film cooling hole and has an obvious vortex structure. The large-velocity gradient enhances the shear stress between the inside and outside of the vortex system, resulting in a significant difference in the distribution of turbulent kinetic energy in the film hole. In the case of the lattice array model, the coolant flow is interrupted by the lattice array structures upstream of the film hole, which results in strong secondary flow and a low-momentum flow region near the entrance of the film hole. As is shown in Figure 11, the secondary flow induced by the array structure changes the flow characteristics, so that the flow field is complex at the entrance of the film cooling hole. Thus, high TKE exists at the entrance of the film cooling hole, and early asymmetric kidney vortices appear. The above results show that the asymmetric kidney vortex in the lattice array model is formed earlier than that in the no-lattice model in the film hole.

The asymmetry of the flow in the film cooling hole is caused by the crossflow between the internal coolant flow and mainstream. At the entrance of the film cooling hole, the coolant flow impinges on the downstream lip of the film cooling hole, which is affected by the crossflow between the internal flow and mainstream flow. Thus, the mass flow rate downstream of the film cooling hole is higher. At the entrance of the film cooling hole, the flow seems to be asymmetric due to the non-uniform mass flow rate. The scale of the early vortex is larger in the downstream area of the film cooling hole. With the development of the coolant flow along the film cooling hole, the mass flow rate trend is relatively uniform near the exit of the film cooling hole. The momentum of the vortex is higher, due to the higher velocity upstream of the film cooling hole. With reference to Figure 10, this high-momentum vortex is easily lifted off the mainstream wall.

5.2. The Influence of Different Blowing Ratios

High blowing ratios will lead to a waste of coolant and will contribute little to the film cooling near the exit of the film cooling hole, as in the jet detachment. Low blowing ratios will lead to insufficient cooling. We also investigated the flow characteristics in different cases with blowing ratios M = 0.5, 1.0, and 1.5. The Reynolds number at the entrance of the internal flow channel is restricted to 3400, and the suction flow rate in the case of blowing ratios M = 0.5, 1.0, and 1.5 are 0.26, 0.53, and 0.8, respectively.

Figure 12 presents the film cooling effectiveness at the central line of the mainstream wall for all cases. In the case of M = 0.5, the adiabatic film cooling effectiveness is high in all cases. The adiabatic film cooling effectiveness at the central line of the mainstream wall is impacted little by the lattice array structures; the film cooling effectiveness at the central line of the mainstream wall in all cases shows good agreement with a maximum deviation of less than 10%. With the increase in the blowing ratio, the adiabatic film cooling effectiveness at the centerline of the mainstream wall in all cases is reduced drastically. This is because the jet momentum increases as the blow ratio increases, resulting in the coolant flow gradually deviating from the mainstream wall and mixing with the mainstream flow by entrainment, reducing the film cooling effectiveness of the mainstream wall. However, the superiority of lattice array structures relative to the case of no-lattice becomes increasingly evident. In the case of M = 1, the adiabatic film cooling effectiveness at the central line of the mainstream wall of the lattice array is significantly different from that in the case of the no-lattice model. Increasing the blowing ratio to 1.5, continuously, the improvement of the lattice array structure on film cooling effectiveness is increased significantly, and the film cooling effectiveness maximum is increased to twice that of the no-lattice model. Among them, the effect of the pin-fin array structure is changed visibly as the blowing ratio increases. The improvement of the pin-fin array on film cooling effectiveness is better with an increased blowing ratio; the improvement even surpasses the Kagome and BCC lattice arrays downstream of the mainstream wall with a blowing ratio of 1.5. As the results show in Figure 13, with the increase in the blowing ratio, the turbulent kinetic energy and momentum in the film cooling hole are increased, and the jet’s velocity at the exit of the film cooling hole increases sharply. Thus, the coolant jet tends to deviate from the mainstream wall downstream of the film cooling hole. Among them, in the case of the lattice array, the coolant flow boundary layer is interrupted by the lattice array upstream of the film hole. It can also be observed that a secondary flow, initiated by the lattice array at the region near the entrance of the film hole, results in increased TKE at the entrance of the film cooling hole. At the entrance of the film cooling hole, the coolant flow impinges on the downstream lip of the film cooling hole and is affected by the crossflow of the internal coolant flow. In the case of different blowing ratios, all the high TKE regions are generated near the lower wall of the film cooling hole, which is closely related to the more complex flows mixing in this area. Furthermore, as shown in Figure 14, with the increase in the blowing ratio, a more complex flow field and higher TKE are induced in the internal coolant channel. In the case of the no-lattice model, with the increase in the blowing ratio, the TKE is increased significantly near the lower wall of the film cooling hole. As the results of cross-section 3 of the film cooling hole show, with the increase in blowing ratio, the kidney vortices develop more fully in the high TKE region. The influence of the crossflow between the internal flow and the crossflow of the internal coolant flow gradually disappears with an increase in the blowing ratio. In the case of the lattice array model, due to the complex flow field and high TKE at the area near the entrance of the film cooling hole, a high TKE area exists at the entrance to the film cooling hole with early asymmetric kidney vortices. As the results show in Figure 14, the asymmetric kidney vortices in the lattice array model are formed earlier than those in the no-lattice model. In addition, in conditions with the same blowing ratio, the Kagome and BCC array models show better development of early kidney vortices along the film cooling hole than those of the pin-fin array model. Combined with the results in Figure 12, the Kagome and BCC array models show a better optimization effect on film cooling performance. The results show that the secondary flow induced by the lattice array structure is conducive to the formation and development of early kidney vortices in the film cooling hole and that the film cooling performance at the mainstream wall increases with the full development of kidney vortices.

6. Conclusions

In this paper, numerical simulations were employed to investigate the influence mechanism of the periodic pin-fin, Kagome, and BCC lattice arrays on film cooling effectiveness at different blowing ratios (i.e., M = 0.5, 1.0 and 1.5). The conclusions can be summarized as follows:

With a blowing ratio M = 1.0, the introduction of lattice array structures improves film cooling effectiveness within the whole streamwise range, especially downstream of the film hole. In the case of Kagome and BCC lattice arrays, the film cooling effectiveness at the centerline in the mainstream direction is significantly greater than that of the pin-fin array and the no-lattice structure, and the local film cooling effectiveness can be increased by a maximum of about 100%.

It is revealed that relative to the pin-fin and no-lattice structures, a more complex flow field, and higher TKE are induced in the area near the entrance of the film cooling hole in both the Kagome and BCC lattice arrays. The early asymmetric kidney vortices in the lattice array model are formed earlier and are more fully developed than those in the no-lattice model. Such a characteristic makes a great contribution to enhancing film cooling performance.

With the increase in the blowing ratio, the adiabatic film cooling effectiveness at the centerline of the mainstream wall in all cases is reduced drastically. However, the superiority of the lattice array structures relative to the no-lattice structure becomes increasingly evident. The film cooling effectiveness of a lattice array structure is increased by a maximum of twice that in the no-lattice model, with a blowing ratio of 1.5.