Influence of Hot Streak and Swirl Clocking Position on Aerothermal Performance of High-Pressure Turbine

Abstract

In modern civil aeroengines, the hot streak and swirl at the exit of the combustor have a significant impact on the aerothermal performance of the high-pressure turbine (HPT). Due to the different design purposes of the combustor and the turbine, hot streak (HS) and swirl (SW) have different spatial distributions at the turbine inlet. This paper conducts a transient simulation of the GE E3 first-stage HPT, considering the swirl and hot streak facing the middle of the passage and the leading edge of the nozzle guide vane, respectively, and also explores the impact of positive and negative swirl. The results show that different clocking positions and swirl directions will change the incident angle and streamline distribution of the vane, thereby affecting the migration of the hot streak, the temperature and the Nusselt number distribution on the stator surface. In positive cases, the hot streak gathers in the upper part of the passage, and in negative cases, it is in the lower part. In middle cases, high-temperature areas appear in both vanes, and the distributions are opposite. Affected by the swirl, when facing the passage center, the pressure side stagnation lines of the two vanes are also different, so the Nusselt number distribution is opposite. When facing the leading edge, only one vane appears. Due to the insensitive interference of the rotor–stator, the transient migration of the hot streak in the rotor is mainly affected by the inherent secondary flow and the temperature at the inlet of the rotor (especially the conditions facing the leading edge), while the upstream residual swirl is less affected. Unlike the middle case, in leading edge cases, the hot streak is separated and needs to be re-mixed before entering the blade passage, so the temperature change in the blade cascade is relatively gentle. Based on this, the Nusselt number distribution on the surface of the blade is similar. In order to obtain the most favorable operating conditions for the engine, the turbine efficiency is used to compare the aerothermal performance under different conditions. Ultimately, it was found that the turbine with the hot streak and positive swirl directly facing the leading edge was the most efficient.

1. Introduction

As one of the most critical components of an aero-engine, the HPT not only has to face high-temperature and high-pressure gas, but it also needs to output sufficient power. Therefore, in order to protect the high-pressure turbine, the blade and its end wall adopt an efficient cooling system to ensure that the turbine can operate smoothly under these conditions. Since the cylinder wall of the combustion chamber contains cooling holes and there is a swirler in the combustion chamber, there is a radial and axial gradient in the outlet temperature (i.e., HS [1,2]), and a vortex is generated at the inlet of the HPT.

In order to explore the influence of HS and SW on the aerothermal performance of HPT, a large number of experiments (EXP) and numerical simulations have been carried out. Povey et al. [3] conducted experiments and simulations on HPT nozzle guide vanes (NGVS). This study compared the facing leading edge (LE) versus the channel center under non-uniform inlet conditions and HS conditions and found that the heat transfer rate across the suction side (SS) increased significantly in 50% of the span (relative to the results under non-uniform inlet temperature), while the heat transfer rate across the SS decreased slightly when the HS was aligned with the passage center. Gaetani et al. [4] explored the HS migration in the first-stage HPT and found that the shape and position of the HS at the outlet of the vane was related to the initial position of the injection. The change to the HS is the least when the HS is facing mid passage, and it is the most is when the HS facing the LE. On the contrary, compared with other boundary conditions, the secondary flow loss of the HS aligned mid is the smallest. This is caused by highly turbulent migration in the region close to the end wall, affecting the secondary flow generation process. Similarly, Kortikov et al. [5] also conducted research on the aerodynamic effects of HS on first-stage turbines. It was found that when the HS is facing the stator SS, the secondary flow in the turbine is more intense, and the efficiency of the stage is reduced by 1.26%. Wang et al. [6] was not only focused on the changes of HS on the stator but also carried out research on rotors. Ultimately, it was found that the HS migrated stably with the main flow in the NGV channel and gradually separated into two high-temperature areas located at 60% span of the blade and the blade tip in the rotor channel. Due to the migration of the HS, multiple high-temperature regions appear on the leading edge and suction surface of the NGV as well as the pressure side (PS), LE, and trailing edge (TE) of the rotor blade. Zhao et al. [7] explored the influence of the inlet HS temperature ratio and found that the increase of the HS temperature ratio tends to increase the relative Mach number at the outlet of the HPT and reduce the relative flow angle at the outlet of the HPT from 25% span to 75% span. In the other regions of the HPT outlet (from the bottom to 25% span and from 75% span to the tip), the relative flow angle increases with increasing HS temperature ratio. Additionally, the isentropic efficiency of the turbine blade decreases when the HS temperature ratio increases.

However, the above article does not take into account the influence of SW on an HPT. Bacci et al. [8] explored the cooling efficiency, pressure loss, and secondary flow of HPTs under the condition of SW through experiments. The SW flow produces strong uplift at the PS and downflow at the SS, which can separate cold fluid from most areas of the blade. Especially on the SS, it helps to enhance the secondary flow of the end wall, which intensifies the separation of cold fluid from the inside of the SS. Johansson et al. [9] compared the results of computational fluid dynamics (CFD) calculation and EXP. The clocking position of the swirl relative to the HPT vanes affects the radial gas pressure mixing distribution in adjacent vane channels. The total pressure distribution at the outlet of the HPT rotor is further affected by the effect of the SW on the HPT rotor. The SW also leads to lower HPT blade loading, resulting in higher HPT blade exit Mach numbers. Xing, Yang et al. [10] adopted a combustor (no HS) and NGV coupling method without considering the cooling effect. By changing the position of the swirler, it was concluded that the flow in the vane channel is strongly affected by the spatial position of the inlet SW and the direction of the SW. Positive (Pos) vortices are more likely to move in the direction of the circumferential pressure gradient, while negative (Neg) vortices have the ability to migrate against the pressure gradient. Moreover, the inlet vortices create distortions in the gas flow that lead to a very non-uniform distribution of the heat flux rate across the vanes. According to the EXP results, Giller et al. [11] concluded that, due to the incidence of swirl flow, the stagnation line of the vane is inclined, which causes the surface cooling air film to flip to the other side of the vane in some areas. Werschnik et al. [12] measured the pressure loss coefficients of different boundary conditions at the outlet of the NGV and concluded that the SW would increase the pressure loss coefficient and be less affected by the vane wake. Qureshi et al. [13] explored the effect of SW on the rotor. It was found that the increase of the Nusselt number (Nu) on the surface of the SS was due to the SW enhancing the intensity of inlet turbulence. The Nu increasing at the PS is that because the SW aggravates the secondary flow, leading to stronger tip leakage flow and tip streamline divergence.

In order to examine the influence of real inlet conditions on the aerothermal performance of the turbine, many studies simultaneously focus on the mixing effect brought by the HS and the SW. Mansouri et al. [14] studied the migration of HS of different shapes and cascade flow from the intensity and direction of the SW. The SW has a significant effect on the pressure ratio of the blade, and SWs of different directions and intensities will change the incident angle of the blade. Zhang et al. [15] found through numerical simulation that the relative strength between the SW and the radial pressure gradient it causes determines the flow on the blade surface. The interaction of the SW and the secondary flow in the cascade produces a high-temperature oblique strip and two cold zones upstream of the blade. Adams et al. [16] investigated HS and SW effects on a 1.5-stage HPT and compared CFD and experimental results. It was found that under the varying HS and SW conditions, the pressure loss coefficient at the stator outlet and the film flow on the vane surface changed little. Due to the temperature non-uniformity at the inlet, the incident angle of the rotor is reduced, and the local load on the blade becomes smaller. Although the intermediate-pressure (IP) vanes are less affected, the IP vanes’ loading and secondary flow structure are changed, and significant overall temperature non-uniformity persists at the outlet. Zhang et al. [17] adopted the method of transient numerical simulation and explored the HS migration of the rotor channel at different times, which was mainly affected by the inherent vortices and SW in different directions. Due to the strong interference between the stator and the rotor, the heat transfer on the surface of the rotor is not significantly changed. By coupling the combustor and turbine, Zhang et al. [18] concluded that in the NGV channel, the interaction between the combustor vortex and the NGV changes the secondary flow structure and causes an HS and radial migration of cold fluid. The SW changes the streamline of the blade and its end wall, and the accumulation and transition of the boundary layer change, which enhances the heat transfer of the PS end wall.

However, the investigation of HSs and SW should also consider the mismatching of the number of combustion chambers and blades. During the design process of the combustion chamber, the main concern is environmental protection and continuous and stable operation, then the number of downstream blades needed to achieve the best results. Therefore, the combustion chamber and the number of downstream blades is significantly different, and multiple blades will face a combustion chamber. As a result, the temperature and velocity distributions are different between adjacent blades. This point of view was confirmed experimentally by Koupper et al. [19]. Some numerical studies [20,21] only use the same number of combustion chambers as the number of turbine blades in order to simplify the calculation, but this causes the calculation results to be unable to reflect the actual flow.

Based on the above point of view, a transient numerical simulation of the GE-E3 first-stage HPT with SW and HS inlet conditions was carried out with consideration of the influence of the clocking position of the HS and SW on the aerodynamic and heat transfer properties of turbine blades. Therefore, it is possible to distinguish the differences at different locations and moments. The time-averaged effects of different positions and SW directions on the flow, temperature distribution, and heat transfer of each blade surface are analyzed.

2. Numerical Methodology

2.1. Computational Model and Boundary Conditions

This paper adopts a GE-E3 first-stage HPT as the research object. According to the NASA research report [22,23], the research object was established as shown in Figure 1. The turbine has a total of 46 stator vanes and 76 rotor blades. In order to simplify the calculation, the ratio of the number of stator vanes to rotor blades is 2:3 (the blades become 69/76 times the original). According to the NASA document [23], the tip clearance is 1% of the blade height.

The calculation of this model uses the commercial CFD software ANSYS CFX, and the calculation fluid is Ideal Gas. Considering that the subsequent heat transfer calculation uses the total energy, the residual error of the calculation is 10⁻⁶. Referring to the experimental standard [23], the rotor speed is 8283 r/min, the inlet reference total pressure is 344,740 Pa, the total temperature is 709 K, and the outlet static pressure is 143,641.67 Pa. The inlet turbulence intensity is 10%, and the eddy viscosity ratio is 100. The blade surface is set into no-slip walls under adiabatic and isothermal conditions. The surface temperature of the stationary blade is set to 496.3 K, and that of the rotor blade is 455 K (i.e., 0.7-times the temperature of the inlet and interface averaged). The interface between the vanes and the blades adopts the stage mixing plane in the steady state and the transient rotor stator in the transient state.

Referring to the calculation results of Wang et al. [24], this paper also adopts a similar distribution of hot spots, as shown in Figure 2. Referring to the results of Povey T. et al. [25], an appropriate ratio of the maximum temperature to the average temperature was selected. T_max/T_ref is 1.097, and T_min/T_ref is 0.955. The center of the HS is located at 60% of the vane heights, which is similar to the temperature core distribution of a real combustion chamber.

By setting the boundary conditions of the velocity inlet and inputting different parameters of axial, tangential, and radial in cylindrical coordinates, the non-uniform distribution of the inlet velocity is finally obtained. The configuration of the inlet swirl refers to the results of Schneider et al. [26]. The center of the swirl coincides with the center of the HS. Based on this, the distribution of inlet tangential velocity is determined by Formula (1):

$$V^S\left(R\right)=d^s\frac{\Gamma }{2\pi R}\left[1-\exp \left(-\frac{4R^2}{{\left(D_{core}^S\right)}^2}\right)\right]$$

(1)

where R is the radial distance from any position of the inlet section to the center. Through the size of d^s (±1), to control the positive and negative swirl direction. $D_{core}^S$ represents the size of the center diameter of the vortex core, which is set to 23.348 mm in this paper, which is about 33% of the arc length at 60% of the entrance height. According to the size of the swirl number (SN), reasonably set the swirl intensity. The calculation of swirl number is based on Formula (2):

$$SN=\frac{V_{\theta }}{W}$$

(2)

The size of SN is specified according to the experimental data of Werschnik et al. [27]. SN is about 0.496, which is very close to 0.5, and this swirl strength is regarded as a design reference value. Based on this, swirl intensity is 2.857 m²/s.

After obtaining the calculation results of the steady state, it is carried out using the initialization conditions of the transient calculation. The transient calculation utilized is second-order backward Eurler. The duration of time needed for the rotor blades to rotate through the passage of the stator vane is taken as a period, and there are 36 time steps in a period and 20 periods in total. Figure 3 shows the pressure changes of the monitoring point located at the interface over the course of 20 periods under the conditions of HS and swirl at the inlet. After the tenth period, the pressure fluctuation became stable. Therefore, the time-averaged result will be obtained from the data read from the 10th to the 20th period.

2.2. Numerical Verification

In order to verify the accuracy of the numerical simulation, refer to the EXP data and boundary conditions of the NASA report [23]. In this paper, the Mach number near the midspan of the stator vane is selected as the comparison. Figure 4 shows the comparison between the experimental data and the CFD calculation results. It can be seen that the comparison between the EXP and simulation results is good, except for the chord length of 19 mm. The reason for the deviation may be testing error. Therefore, the current geometric profile is basically consistent with the results described in reports [22,23].

Since this paper deals with heat transfer, the calculation of the heat transfer on the blade surface is very dependent on the turbulence model. Considering that the GE-E3 turbine has no experimental data on heat transfer, the turbulence model verification was carried out using the C3X vane, which has a large amount of heat transfer experimental data under real turbine operating conditions. According to the NASA report [28], the No. 4311 of data on the C3X vane was selected for steady-state heat transfer calculation. Its computing grid is shown in Figure 5, with a total of 1.78 million grid cells. The mesh size is small enough, the dimensionless wall distance y+ in the range of 30 to 100 for high-Re-number models and y+ less than 2 for low-Re-number models, to ensure that the boundary layer is resolved by wall function or wall integral modeling. When the inlet is set to uniform (UNF) flow, the pressure is 244763 Pa, the Mach number is 0.17, the temperature is 802 K, and the turbulence intensity is 6.5%. The outlet pressure is 131,800 Pa, and the wall temperature is set to 585.46 Pa. Figure 6 compares the difference between the heat transfer coefficient (HTC) calculated by $SST$$\gamma -\theta$, $SST$, $K-\omega$, $K-\epsilon$ and the four turbulence models and the experimental data. Most turbulence models can calculate the HTC of the PS more accurately, but the HTC predicted by the SS has a certain deviation from the experimental data. Compared with the other three models, the calculated results of may have a more similar trend with the experimental data after 25% of the chord length. Before 25% of the chord length, there is still a certain deviation. Therefore, the calculation result is closer to the experimental data, so we chose $SST$$\gamma -\theta$ as the numerical simulation turbulence model.

2.3. Grid and Grid Independence Verification

The Autogrid5 module of the CFD software NUMECA 15.1 used the O4H method to generate the computational domain-structured grid in Figure 1. Since this paper is meant to evaluate the influence of the spatial position of the HS and SW on the aerothermal performance of the HPT, the verification of grid independence must include not only pressure, but also Nu. The calculation of Nu is shown in Equation (3):

$$N\mathrm{u}=\frac{q_w\cdot Bx}{\left(T_{aw}-T_W\right)\cdot \lambda }$$

(3)

$q_w$ is the wall heat flux under isothermal wall conditions, $Bx$ is the chord length of the blade, $T_{aw}$ is the temperature of the blade under adiabatic conditions, $T_W$ is the temperature of the isothermal wall, and $\lambda$ is the thermal conductivity. A total of three groups of grids are divided, and the numbers of cells are 5.57 million, 8.42 million, and 11.09 million (corresponding to coarse, medium, and fine). The area average y+ values in these grids are all less than 1.5, meeting the calculation requirements of $SST$$\gamma -\theta$.

Figure 7 shows the difference in calculation results reflected by different elements of grids. It can be seen that the pressure is not sensitive to the change of the elements of grids, but the distribution of Nu in the NGV and blade is mostly dependent on the number of grid elements. It can be seen from Figure 7 that the Nu calculation results of 8.42 million and 11.09 million have little difference. This shows that verification of grid independence is achieved within the current grid range. Therefore, in order to ensure the calculation economics, a grid with 8.42 million elements was finally selected for subsequent simulation. The blade spanwise has 73 grid layers, and the tip of the blade is divided into 33 grid layers using O2H topology. There are 21 nodes in the boundary layer, and its growth rate is 1.1, which meets the needs of the transition model. Figure 8 shows the calculation grid and its details.

3. Results and Discussion

In this paper, the effects of different swirl directions and clocking positions on the aerothermal performance of high-pressure turbines are considered. As shown in Figure 9, this spatial position is based on the fact that the HS and SW are facing the middle of the passage (mid) and the LE of NGV1. In addition, there are two types of SW directions, positive and negative, specifically clockwise and counterclockwise. There are a total of four non-uniform inlet conditions. Along with considering the conditions of non-uniform inlet and blade surface, as shown in

Table 1. Boundary conditions under different calculation examples.

Case No.	Inlet BC	Thermal BC
1	Uniform	Ad/Iso
2	Pos Mid	Ad/Iso
3	Pos LE	Ad/Iso
4	Neg Mid	Ad/Iso
5	Neg LE	Ad/Iso

, there are a total of 10 sets of simulation calculations.

3.1. Influence of Inlet Non-Uniformity on the Aerothermal Performance of NGV

In this section, the aerodynamic characteristics of the HS and its impact on the thermal performance of the NGV will be presented. The redistribution of hot and cold fluids due to swirl-induced pressure distribution and swirl direction will first be discussed. On this basis, the thermal load distribution on the surface of each vane is analyzed. Finally, the effect of the SW on the heat transfer characteristics of each vane surface is studied.

3.1.1. Migration of Hot and Cold Fluids in the Vane Passage

Figure 10 and Figure 11 show the overall temperature distribution at different axial positions along the stator channel. It can be seen from the figure that the swirl direction and different spatial positions have a significant effect on the migration of HS in the passage. As shown in Figure 10, at Z/Bx = 2.5%, when the HS and SW are facing the NGV1 LE, they are directly divided into two parts by the blade. When facing the center of the channel, the shape of the HS is well maintained.

When the center of the positive swirl and HS is in NGV1 LE, the main part of the HS gathers in SS1 and PS2 and the upper half of the channel of SS2 and PS1. This is due to the flow field distribution around NGV1 caused by the positive swirl. As shown in Figure 12, the incident angle of the S1 shroud is negative, and the incident angle of the hub is positive. The stagnation line on the shroud shifts toward the PS, and that on the hub shifts toward SS, so the pressure on the vane shroud SS decreases and the pressure on the vane hub PS increases. As shown in Figure 10, the swirl field produces a pressure gradient in the channel (the blue arrow in Figure 13), and the part below 85% of the channel height is significantly affected by the pressure gradient. The central region of the leaf is affected by the coupling of swirl and pressure field, and the HS moves upward obviously (white arrow). The stator shroud is affected by the swirling flow and the positive horseshoe vortex (HV) generated by the vane, as shown in Figure 14, making the fluid move downward (black arrow in Figure 13). The cold fluid migrates down until about 85% span, so the HS is mainly concentrated in the channel at 50% to 75% of the vane height. Unlike Pos mid, the position of Pos LE’s HS is higher. The reason for this is that the HS is closer to the blade and is more affected by the pressure gradient in the SS, while the PS is not only affected by the inherent upwash flow, but also by the swirling flow further aggravates the upward migration of the HS.

When the swirl direction is negative, a negative HV is generated at the hub, as shown in Figure 14, and the superposition of the negative swirl enhances the flow of cold fluid at the hub, resulting in accumulation of the HS at 40% to 50%; compared with Pos LE, no significant downshift occurred. With the change of the flow field in the channel, as shown in Figure 12, at Z/Bx = 50%, the pressure around the SS gets lower, and the cold fluid in the channel gradually flows to the SS. Additionally, the effect of the pressure gradient near the SS results in the area of the hot spot within the SS1 and PS2 channels being reduced. In addition, due to the high pressure of the S1 PS, less SS2 cold air migrates there, as shown in Figure 10, which causes the HS area and temperature between SS2 and PS1 of Pos LE to be larger than those of SS1 and PS2. Therefore, in Neg LE, due to the directional effect of the swirl, the HSs are mainly concentrated in the middle and lower regions of the Z/Bx = 50% channel. When the SW is facing the mid, little heat is absorbed by the blades, and the shape of the HS in the channel is maintained well. At Z/Bx = 2.5%, it can be seen that, due to the effect of pressure, the cold fluid below migrates upwards, and the HS at the center is affected by the combined effect of swirl direction and pressure gradient. As shown in Figure 11, the HS has moved noticeably upwards. At the SS1 shroud, the swirling flow and the stator shroud generate a positive HV, which induces the gas to flow downward and finally meets the hot fluid at the position of 70% span. Under negative conditions, a negative HV is generated at the hub, and under the actions of negative swirling flow and a gradient downward pressure field, hot and cold fluids gather at the position of 30% of the vane height.

3.1.2. Temperature Distribution on NGV

As mentioned above, the SW and HS have obvious influence on the distribution of hot and cold fluid and pressure distribution in the passage. Therefore, the temperature distribution and flow on the surface of the vane are also affected by it. The streamlines of the vane surface in this paper are similar to those calculated by Jacobi et al. [29] with LES. As shown in Figure 13, due to the spatial position of the SW, the stagnation position of the NGV1 PS upwash flow in Pos LE is slightly higher than that in Pos mid; because the stagnation line at the bottom is closer to the SS and the pressure is higher, the upwash flow is more intense and the stagnation line on the shroud is closer to the PS, the pressure is lower, and the downwash amplitude is lower. On the contrary, because NGV2 is more affected by the downwash of the SW itself under the conditions of Pos mid, the stagnation position of the NGV2 PS upwash flow is lower and accompanied by a significant downwash flow. The NGV2 of Pos LE is less affected by the swirling flow, so only the upwash flow appears on the vane. Due to the diverse swirl direction, the stagnation position of the NGV1 PS in Neg mid and Neg LE is lower, and the downwash flow is unobvious. The confluence of the upwash and downwash of the NGV2 PS is also higher. The flow of NGV SS is not only affected by the swirl direction and spatial position, but also by the pressure gradient and vortex induced by the swirl. For Pos mid and Pos LE, due to the pressure gradient generated by the swirling flow, there is an obvious upwash flow in the middle and lower parts of the NGV1 SS. However, the HV on the shroud of Pos mid is stronger, and the position of the passage vortex (PV) is lower, as shown in Figure 15. Therefore, the confluence positions of the upwash flow and the downwash flow of Pos mid are also lower, which further affects the subsequent heat exchange results. Although Neg mid and Neg LE have opposite swirl directions and pressure gradients, their reasons are the same.

In Pos LE, NGV1 directly faces the HS, and the temperature of the blade surface is higher than that of Pos mid. Since the HS and SW are separated by the blades at this time, both the HS at the PS and SS are affected by SW. In addition, the SS is also affected by the pressure gradient generated by SW. Therefore, the high-temperature areas are mainly concentrated between 50% and 80% of the height of NGV1, while NGV2 is less affected by HS and SW. Similarly, the high-temperature region of Neg LE is mainly concentrated between 50% and 30% of the height of NGV1. Due to the spatial location of HS and SW, both NGV1 and 2 in the mid case are affected by the HS. Based on the effect of the swirl direction, under the influence of the positive swirl, the HS on the right side of the passage migrates downward, and the HS on the left side migrates upward, so the temperature distributions of NGV1 and 2 are opposite. In Pos mid, as shown in Figure 11 and Figure 14, the high-temperature area is closer to NGV2. Therefore, the high-temperature area mainly gathers in NGV2. NGV1 is also slightly affected by HS, given that the HS and SW are at mid passage. Therefore, the temperature of the high-temperature area of NGV1 is lower than that of NGV2, and its distribution area is also affected by SW, mainly concentrated at 55% to 75% span of NGV1. The distribution of the Neg mid temperature is opposite, due to the various swirl direction.

3.1.3. Heat Transfer on NGV Surfaces

Figure 16 shows the distribution of Nu on the vane surface under different cases. The PS of Pos mid and Pos LE have similar distributions. In Pos mid, the boundary layer thickened due to the accumulation of upwash and downwash at 75% to 85% of the vane height of the NGV1 PS. In contrast, other locations are affected by downwash and upwash to thin the boundary layer. Therefore, the Nu at the LE of 75% to 85% span is obviously lower than that at other positions. Due to the location effect of the HS and swirl, the distribution of NGV2 streamlines in Pos mid and Pos LE is changed. The reason for the distribution of NGV2 Nu in Pos mid is similar to that of the NGV1 PS. Since the NGV2 PS of Pos LE only has upwash flow, and most of the upwash flow gathers above 65% of vane height, its Nu is mostly 500.

Similarly, the Nu distribution of Neg mid and Neg LE is similar to that of Pos mid, but the areas with lower Nu migrate downward due to the effect of the swirl direction. Since the flow first touches the LE of the NGV and generates HV and corner vortices (CV) at the hub, which promotes heat transfer at the hub, its Nu is higher. There is an interaction of swirl flow and vane wake at the TE of the PS, so a region with higher Nu appears. Affected by the different clocking positions of the HS and SW, the TE of the NGV1 PS in Pos LE is more affected by swirl, so its high Nu area and Nu value are larger than those of Pos mid. On the contrary, the boundary layer thickens because the swirling flow changes the streamline of the NGV2 PS, allowing the upwash and downwash to converge in the 45% to 50% span. Therefore, the high-Nu region of the NGV2 PS TE of Pos LE is smaller than that of Pos mid. Similarly, the high-Nu region and Nu value of the NGV1 PS TE of Neg LE are larger than those of Neg mid. However, the confluence of up- and down-washing flow at the TE of the NGV2 PS in Neg mid is higher than that in Neg LE. Therefore, the high-Nu region in Neg mid is larger than that in Neg LE.

On account of the transition of the boundary layer on NGV SS, its Nu grew from small to large. Under the impact of SW, PV appeared in the SS of NGV1. Affected by the direction of the swirl, the direction of the PV is also positive, and a negative vorticity area is induced on the SS surface of NGV1, which inhibits the heat transfer of the vane. Therefore, Nu was lower at the TE from 30% to 50% vane height of the NGV1 SS in Pos mid. Due to the influence of the clocking position, the NGV1 streamline washing of Pos LE is more intense, which weakens the downwash flow at TE. Therefore, the low-Nu region moves up. However, due to the influence of the flow on the vane surface, as shown in Figure 12, the streamline at TE is relatively dispersed and the boundary layer becomes thinner, and a region with Nu higher than 1800 appears. Additionally, streamlines gathered in the direction of 80% to 95% vane height. In addition, as shown in Figure 10, the pressure of the NGV1 SS shroud is low, and the gas acceleration is slow, which is not conducive to the heat exchange of the fluid. In addition, unlike Pos mid, the PV of Pos LE is closer to the shroud. Therefore, the Nu after 50% of the chord length at 80% to 95% span is less than 1250 and is generally lower than that of the hub. Similarly, the NGV1 SS of Pos mid has a lower Nu behind 50% chord length at 70% to 95% vane height. Under negative swirl conditions, the pressure gradient on the surface of NGV1 SS is downward. The streamlines in the middle and upper half of NGV accumulated a lot, and the local Nu was low. Compared with Neg mid, Nu is larger in the lower part of the TE of Neg LE. This is due to stronger local downwash, thinning the boundary layer there.

Since NGV2 SS is less affected by swirl than NGV1 SS, the distribution of Nu in Pos mid and Pos LE is similar. After 50% of the chord length of NGV2 SS, there was a strong downwash at 40% to 95% vane height, and the streamlines gathered at 50% to 80% vane height. Therefore, the Nu here is lower. In the shroud and mid-low span, due to the intensive downwash, the Nu is greater than 1500. When the swirl direction is negative, affected by its direction, the downwash of NGV2 is weakened, the streamline is more dispersed than that of Pos, and the transition point of NGV2 is closer to the front. The reasons for the distribution of the NGV2 SS Nu in Neg mid and Neg LE are the same. However, the transition position in the vane at the midspan TE of Neg mid is more anterior than that of Neg LE. This is because, as shown in Figure 13, although the pressure of NGV2 SS in Neg mid is smaller, it is more affected by swirling flow, the intensity of downwash in the TE is weaker than that of Neg LE, and the local streamlines are not too dense. HV and CV appeared at the SS shroud and hub of NGV1 and NGV2, which caused the streamlines on vanes’ shrouds to shift downwards, and the streamlines on the NGV hub diverged upwards, thereby promoting heat transfer.

3.2. Influence of Inlet Non-Uniformities on the Aerothermal Performance of the Rotor Blade

In this section, the combined effects of the HS and SW on rotor blades will be investigated. Compared with the stator, the flow inside the rotor has unsteady characteristics due to the interaction between the rotor and stator. Therefore, the unsteady migration of cold and hot fluids in the rotor is analyzed first. On this basis, the time-averaged heat load of blades is studied. Finally, the time-averaged heat transfer performance of the rotor is discussed.

The inlet swirl is significantly weakened by the rotor–stator interaction. Unlike the streamlines in the stator channel determined by the incident angle effect, in the rotor passage, the secondary flow and pressure gradient caused by the residual swirl and the interference of the rotor–stator dominate, especially for the latter two. Figure 17 plots the time-averaged vortex structure and vorticity field in the GE-E3 rotor passage. Figure 17a shows the evolution of the vortex inside the rotor as it passes through the passage. Due to the impact of the flow on the blades, HVs appear near the blades, which are located on the SS and PS, respectively. The elevated lateral pressure gradient due to flow acceleration pushes the HV_PS towards the SS, and the two leg vortices gradually merge into a single PV [30,31]. Simultaneously, CV are formed in corner regions as an HV is generated, as shown in Figure 17. In addition, since the main flow flows from the PS to the SS through the tip clearance, a tip leakage vortex (TLV) is generated. The vortex has a significant effect on the hot or cold fluid migration and the distribution of Nu, especially on the SS.

3.2.1. Migration of Hot and Cold Fluids within the Rotor

Inside the rotor passage, the transient mechanism affecting the flow originates from the interaction of the rotor and stator and the migration effect of swirling flow. In this section, the transient flow characteristics are investigated in order to determine the mechanisms that dominate the unstable migration of hot and cold fluids in the rotor passages. To explore these properties, Figure 18 shows the instantaneous picture of the vector and temperature at z/Bx = 25% of the total period (T) through the vane passage.

In UNF, the influence of the vortex in the channel of the vane and the shedding vortex of the trailing edge on the secondary flow inside the rotor is weak. Therefore, in the rotor passage, the gas from the vane mainly interacts with the HV. The HV_PS at the shroud and hub interact significantly with the HV_SS due to the circumferential and radial pressure in the channel. Consequently, the intensity and position of the secondary flow and the shroud and hub HV vary over long durations. For the convenience of illustration, blue arrows represent swirl flow, and the HV and induced vortex are represented by white arrows.

In HS and SW, the flow in the passage is not only affected by the shroud and hub HV, but also by the swirl and its induced vortex. At 0T/6, HS and SW appear in the passage. Affected by the upstream swirl, HSs appear in the upper half of the passage under Pos mid. From 1T/6 to 3T/6, with the positive swirl and shroud-positive HV, the HS moves upward. The migration direction of the HS is consistent with the direction of the SW. At the same time, affected by the coupling of the shroud HV and the swirl, the HS and the cold fluid (indicated by the black arrow) gradually move towards the PS. Based on this, from 4T/6 to 6T/6, the influence of the HV and the migration of cold fluid and HS to the PS are more intense.

In Pos LE, the HS appears completely at 1T/6. As shown in Figure 19, the HSs are affected by the stator. Under different conditions, the distribution of the HS in the blade channels is varied. For Pos LE, since the HS is affected by the both the NGV1 separation and the rotor and stator interference, the remixing of the two high-temperature fluids and entering the 25% chord length rotor channel is slower than the entry of hot fluid, which is less affected by the stator in Pos mid. As shown in Figure 18, compared with Pos mid, the HS position of Pos LE is higher. This is because, due to the influence of the clocking position, the HS position of Z/Bx = 50% in the vane passage is higher. From 1T/6 to 3T/6, under the effect of positive swirl, the HS moves upward. However, from 4T/6 to 5T/6, due to the interference of the rotor–stator, as shown in Figure 20, the HS at the rotor inlet is partially deflected downward from the top. As a result, part of the HS at the top of the passage has moved downward significantly. Until 6T/6, the intensity of the secondary flow in the passage is further enhanced, so the HS gradually moves to the top of the PS and disappears under the influence of the shroud HV and the residual swirl.

In negative swirl, affected by its direction, the HS is located in the middle and lower areas of the passage. Under Neg mid conditions, the negative swirl mainly gathers in the middle of the passage, from 1T/6 to 3T/6, and the cold fluid in the SS moves to the PS under the influence of negative swirl. Compared with Pos mid, the HS area is smaller. Accompanied by the induced wall vortex (purple arrow) and secondary flow, as shown in Figure 18a,d, the HS migrates upward. Following this trend, from 4T/6 to 5T/6, HSs migrate upward and gradually disappear. Different from Neg mid, due to the clocking position and upstream HS being divided by NGV1 and the interference effect between rotor and stator, the HS and swirl position of Neg LE are lower. From 1T/6 to 3T/6, the evolution of HS is similar to that of Neg mid. However, from 4T/6 to 5T/6, similar to Pos LE, as shown in Figure 18, the HS of the rotor inlet is partially deflected upward from the hub. Therefore, part of the HS at the hub moves noticeably upwards. Until 6T/6, the intensity of the secondary flow in the channel is further enhanced so that the HS gradually moves to the PS and disappears under the influence of the hub HV and negative swirl.

3.2.2. Temperature Distribution on the Blade Surface

Figure 21 shows the time-averaged temperature and streamline distribution of the rotor blade. From this, it can be found that the streamline change of the SS is little. This is because the HV_PS merges with the HV_SS to create a PV of high vorticity. However, on the PS, the local distribution of streamlines is somewhat diverse due to the difference in clocking position and swirl direction. In Pos mid, the swirl is close to the middle and upper part of the passage, which makes the local negative wall-induced vortex shown in Figure 17 stronger. Therefore, the upper and middle streamlines are shifted downward and converge in the mid-span. In Pos LE, the swirl is closer to the blade tip, enhancing the TLV and making the shroud upwash flow more intensive. In negative cases, such as Neg mid, the swirl is closer to the middle and lower portions, and the wall is less affected by the swirl. Different from Pos mid, in Neg LE, although the swirl flow is located at the end wall close to the hub, the negative HV at the hub enhances the local negative vortex, making the position of streamline shift downward move upward. Therefore, the streamlines at the hub TE are denser compared to Neg mid.

Due to the difference in clocking position and swirl direction, the temperature distribution of the rotor blades in various cases has obvious differences. In Pos mid, the HS gathers in the middle and upper areas of the PS of the passage, so the temperature at the middle and upper portions of the PS is higher. In SS, the HV_PS at the hub moves to the SS to form PV, as shown in Figure 22. Due to the dissipation of the eddy current, the temperature at the PS hub becomes lower. On the shroud, the LE is cooler due to PV formation. However, as the high-temperature fluid of the PS flows toward the SS along the axial direction, the temperature of the TE at the SS shroud is higher than that of the LE. Due to the position of the HS, a high-temperature area appears in the middle of the blade. In Pos LE, since the HS is closer to the blade shroud and has a large downward movement, the high-temperature area is mainly at the shroud, and the temperature in the mid-span also increases. In the SS, due to the location of the HS and its migration to the SS, high-temperature regions appear on the LE and TE of the shroud. In negative cases, under the Neg mid condition, a high-temperature region appears in the PS mid-span, and the analysis results in Section 3.2.1 show that the shroud temperature also becomes higher. In the SS, due to the location of the HS, the high-temperature areas are mainly in the middle and lower parts. The formation of low-temperature regions at the shroud and hub is similar to Pos mid. Under the condition of Neg LE, the temperature in most areas of the PS is higher because the HS at the hub migrates upwards substantially. In SS, due to the clocking position, the high-temperature region is further down.

3.2.3. Heat Transfer on the Blade Surface

Figure 23 shows the time-averaged Nu distribution on the blade. The strong interference between the rotor and the stator makes the heat transfer effect of the residual swirl flow on the blade surface less. In the SS, there was little difference in the distribution of Nu in different cases. As the curvature of the rotor SS is too large, the high-speed gas flowing through produces a boundary layer transition. Therefore, Nu is lower in the SS LE. At the SS shroud, due to the existence of the CV shown in Figure 17 and Figure 21, energy is dissipated for the high-temperature gas disturbance from the PS, so the Nu there is low. At the shroud, due to the formation of PV, the weakened HV and the accumulation of a large number of downwash streamlines makes a local high Nu appear. At the hub, although CV exists here, its Nu is very large. The reason for this is that the hub PV is formed here, which promotes streamline upwashing and suppresses the CV of streamline downwashing. At the TE, the Nu is lower due to the concentration of PV and mainstream streamlines.

In the PS, the distribution of the Nu is similar. Due to the existence of the shroud TLV, the boundary layer becomes thinner and the Nu is higher. However, in the mid-span region, the distribution of the Nu was slightly different. In Pos mid, a large number of streamlines accumulate in the mid-span region, where Nu is lower. For the other three cases, due to the difference in clocking position and swirl direction, the LE has low Nu caused by streamline accumulation at different positions. At the hub, the CV makes the local Nu low. However, for Neg LE, because the swirl is further down, the position where the streamlines start to wash down is lowered, resulting in the accumulation of streamlines at TE. Therefore, the area of the low-Nu region at the hub trailing edge is larger than that of the other three cases.

3.3. Effect of Inlet Inhomogeneity on Turbine Efficiency

In order to further analyze the influence of the HS and the spatial position of the swirl on the aerothermal performance of the turbine, Figure 24 shows the turbine efficiency under different cases. The total-to-total turbine efficiency [32] formula is as follows:

$$\eta =\frac{h_0^{*}-h_2^{*}}{h_0^{*}-h_{2,is}^{*}}$$

(4)

where h* represents the total enthalpy, the subscripts $0$ and $2$ represent the inlet and outlet, respectively, and are the isentropic conditions. Its formula is expressed as the ratio of the actual enthalpy drop to the isentropic enthalpy drop. As expected, the turbine is most efficient in UNF cases. This is due to HS and swirl effects. However, under conditions with HS and SW, the turbine efficiency of Pos LE is the highest, and that of Pos mid is the lowest. This is because, when the swirl flow is in the mid passage, the swirl flow is less affected by the vanes, thus generating more secondary flow. In the rotor blade, due to the strong interference of the rotor and stator, the influence of the swirling flow on the rotor blade is small. Therefore, considering the influence of HS and swirl, the design of high-pressure turbines should take Pos LE as the best condition.

4. Conclusions

Through URANS simulation calculation, the influence of HSs and positive and negative swirling flow on the aerothermal performance of GE E3 first-stage HPT at different clocking positions was explored. This paper is mainly devoted to analysis of the migration of HS and the heat load of the blade surface. The main conclusions are as follows:

(1)

Different clocking positions and swirl directions change the incident angle on the vane surface, thereby generating different pressure gradients on the vane surface. The pressure gradient is upward for positive swirl and opposite for negative swirl. With the positive and negative HV at the shroud and hub, the HS of the positive swirl is located in the upper-span of the passage, and the negative swirl is located in the lower portion. Due to the difference in clocking positions, HS appeared on both the left and right sides of the NGV1 passage in LE cases. In the mid cases, only NGV1 and NGV2 channels showed HS.

(2)

Due to the change in the incident angle of the blade, the stagnation line of the NGV in the positive swirling flow deviates to the PS at the shroud and to the SS at the hub. The stagnation line for negative swirl is in the opposite direction. As shown by the migration of the HS within the passage, a high-temperature region appears at the shroud of NGV1 in Pos LE, and a negative swirling flow is at the hub. When the HS and swirl are facing the mid passage, due to the direction of the swirl, the temperature of the NGV1 shroud and the temperature of the NGV2 hub are higher, and the reasons are the same for the negative swirl.

(3)

Based on the influence of swirl direction and different clocking positions on the distribution of vane streamlines, the heat transfer on the vane surface is also quite different. In the PS, due to the different aggregation positions of the streamlines, the low Nu regions are different. At SS, there is a boundary layer transition at LE, so Nu is lower. Due to the different swirling directions and spatial positions, the streamlines that allow PV and NGV1 to gather appear in different regions. Therefore, the low-Nu position of NGV1 SS is different. Less affected by the swirl, the Nu of NGV2 is relatively similar. Different from the positive swirl, the downwash of the NGV2 SS streamline under the influence of the negative swirl is relatively moderate, so the transition point is closer to LE.

(4)

The strong interference between the rotor and the stator makes the flow characteristics of the rotor transient. In the passage, the HS transferred from the stator is distributed in different positions due to the various clocking positions and swirl directions. Under the dominant effect of the secondary flow in the passage and the auxiliary effect of the residual swirl, the HS has a significant migration. However, in LE cases, the migration of the HS is less affected by the secondary flow and residual swirl due to the interference of the rotor. In the SS, due to the formation of PV, the discrepancy of temperature distribution in SS is small. However, in the PS, due to the different positions of HS transferred upstream, the temperature in the upper-span of the positive swirl cases is higher, and the temperature in the lower-span of the negative swirl cases is higher.

(5)

Based on the fierce interference of the rotor and the stator, the heat transfer distribution of the rotor blade is also relatively similar. There is only a slight difference due to streamline distribution. In order to further explore the optimal performance of the turbine under HS and swirl flow, by comparing the turbine efficiency in different cases, it is known that Pos LE is the most conducive to the operation of the turbine.