Effect of Hot Streak on Aerothermal Performance of High Pressure Turbine Guide Vane under Different Swirl Intensities

Abstract

In advanced civil aero-engine, the gas exiting combustor typically features hot streak (HS) and swirl that affect the aerothermal performances of the high pressure (HP) nozzle guide vane (NGV). The purpose of this paper is to study the influences of HS on HP NGV aerothermal behaviors under swirl with various intensities. The numerical investigations were conducted on the first NGV of GE-E3 HP turbine. Four swirl intensities (|SN| = 0, 0.25, 0.50, 0.75) and two swirl orientations (positive and negative) were considered. The result indicates that the relative strengths between the swirl and its induced radial pressure gradient dominate the flow patterns on vane surfaces. Thus, the diverse streamlines distributions appear on the surfaces and the dominated factor on each surface does not vary with swirl intensity. The swirl redistributes the cold and hot fluid and thus generates the relatively hot oblique strip and cold region at the upstream of vane. The heat load on the vane that is not directly impinged by HS is dictated by the radial migration of the fluids originating from the regions aforementioned at |SN| = 0.25 and 0.50. However, at |SN| = 0.75, the transverse movement of HS due to the intense swirl causes additional thermal load. The heat load on the vane that faces HS is mainly determined by the radial migration of HS. The swirl alters the heat transfer distribution on vane surfaces remarkably. With positive swirl, the heat transfer coefficients at the lower span of suction side and pressure side are enhanced and weakened respectively. As expected, the opposite trends are observed in the negative swirl case. Swirl also affects boundary layer transition, and then affecting heat transfer. Positive and negative swirls both advance the transition on the suction side of vane directly impinged by the swirl, and with the increase of swirl intensity, transition onset shifts toward upstream.

1. Introduction

In order to improve the aero-engine performance, an extremely high turbine entry temperature is adopted, which is far greater than the melting point of advanced nickel base single crystal alloy . Consequently, the highly effective cooling system is designed to protect the blade from severe operating conditions. Due to the discrete fuel injectors and coolant for the combustion liner wall, a highly distorted temperature profile (hot streak, HS) appears at the turbine inlet. More recently, aero-engine tends to use lean-burn combustor to meet the legislative requirement for NOx emissions [1], which results in an aggressive swirl at the turbine inlet. These characteristics bring challenges to the design of the high pressure (HP) nozzle guide vane (NGV) cooling system. Thus, the detailed knowledge of aerothermal performances of HP NGV under the influence of total temperature distortion (hot streak, HS) and swirl is great significant to improve and design cooling scheme.

A large number of experimental and numerical investigations have been conducted to reveal the effect of hot streak on the aerothermal performances of high pressure (HP) turbine. Povey et al. [2] experimentally investigated the high pressure nozzle guide vane (NGV). The analyses revealed that in comparison with results obtained with uniform inlet conditions, the heat transfer rate at the midspan of the suction side (SS) is higher when HS aligns with the leading edge and slightly lower when HS aligns with the passage, but such variations are not observed on the pressure side (PS). Butler et al. [3] studied numerically the hot streak redistribution within the large scale rotating rig through solving three-dimensional Euler equations. It was found that hot and cold fluids tend to migrate toward the PS and SS of the rotor blade individually, resulting from the preferential migration effect [4]. Numerical work by He et al. [5] indicated that the preferential migration effect can be weakened by adjusting the clocking position of HS with respect to NGV: when the hot streak aligns with NGV leading edge (LE), the effect is minimal. Jenny et al. [6] developed an advanced hot streak generator that can produce dimensionless temperature profile which is identical to that in the realistic combustor. With it, the hot streak migration inside the 1.5-stage turbine was examined. The time-resolved measurements indicated that hot fluid travels towards the hub through interaction with secondary flows, which causes the accumulation of hot fluid at the rotor hub-pressure side corner region. Aiming at this issue, Ong [7] describes a method that utilizes the unsteady vortex to transport the coolant originating from the hub slot at the upstream of vane toward the hot region. It was found that newly introduced coolant weakens the peak time-averaged temperature by a similar degree as the film cooling but using only a sixth of the coolant used for film cooling. The investigations above focus on hot streak only and do not take the effect of inlet swirl into consideration. Consequently, the related conclusions are not fully applicable to turbines operating at realistic conditions.

Besides, the impact of swirl-only on the aerothermal performance of NGV has also been investigated in previous studies. Schmid et al. [8] numerically studied the swirl intensities on the aerothermal performance on the NGV endwall. The stronger swirl is observed to expand more quickly and impinge on the endwall earlier. The heat transfer on the impinging region is enhanced due to the increasement of turbulence level induced by the swirl. Similar results can also be found in the work by Werschnik et al. [9]. The authors experimentally investigated the endwall film cooling performance on a large scale turbine rig. Experimental results indicated that swirl enhances heat transfer and reduces film cooling effectiveness, and the corresponding variations show a strong dependence on the swirl clocking position. Jacobi et al. [10] conducted an LES simulation on the effect of the realistic combustor exit flow on the steady and unsteady aerothermal behavior of the NGVs. Results showed that the interaction of the passage vortex and adjacent NGV’s horse-shoe vortex occurs at a certain phase. This unsteadiness impact induced fluctuations in heat flux on NGV surfaces. Qureshi et al. [11,12] conducted experimental investigations for the effect of inlet aggressive swirl on the heat transfer characteristics of a high-pressure turbine. The inlet swirl was found to redistribute the boundary layer fluid on NGV and thus affect the heat transfer distribution. Following the work of Qureshi, the influence of swirl on turbine stage efficiency was examined by Beard et al. [13], it was found that the inlet swirl decreases turbine efficiency due to its induced additional secondary flow.

In order to deepen into the aerothermal behaviors of the high-pressure turbine with realistic inlet condition, a considerable literature has grown up around the theme of the combined effect of hot streak and swirl. Mansouri et al. [14] studied the aerothermal performances of NGV under the comprehensive influence of hot streak and swirl. The hot region is seen to follow the trajectory of the vortex induced by swirl. Khanal et al. [15] and Wang et al. [16] simulated the impact of the swirl on hot streak migration within high- pressure turbine. The results revealed that the swirl induces hot streak to migrate radially on the pressure side of rotor, and its direction is related to swirl orientation, not to clocking position. A similar investigation was also conducted by Rahim et al. [17], whose work focused on the heat transfer under the hot streak and swirl. Li et al. [18] examined the impact of the mismatch between combustor and HP NGV. Results indicated that the clocking position of inlet non-uniformity profile relative to the NGV dominates the heat load difference among the neighboring vanes and swirl orientations dominate radial transport of the hot streak along rotor blade. The aerothermal behavior of a fully film cooling 1.5-stage turbine under inlet non-uniformities was examined by Adams et al. [19]. The swirl was found to alter the heat load of HP NGV by redistributing the film coolant. Unsteady RANS simulations with non-uniformity inlet were conducted on the HP turbine by Wang et al. [20]. The film cooling behavior on the rotor blade leading edge is found to be mainly determined by the variation of inlet incidence angle, while that at the mid-chord region is dictated by the unsteady cooling discharge associated with pressure perturbation.

As reviewed above, the inlet non-uniformities result in the remarkable changes in aerothermal behaviors of high-pressure turbine, especially when swirl and hot streak appear at inlet simultaneously. Swirl intensity would vary with the aero-engine operating conditions. It can be expected that the NGV aerothermal behaviors will vary with swirl intensity. Thus, it is necessary to study the effect of hot streak on the NGV under different swirl intensities. In addition, such knowledge is also critical for the integrated design of combustor and high-pressure turbine [10,21]. A strong swirl is beneficial for combustion but may result in the excessive heat load on NGV at the same time. Therefore, the optimal swirl configuration for both combustion and aerothermal performances of high-pressure turbine is necessary. The influence of swirl intensity on aerodynamic losses, secondary flow pattern, and heat transfer has been highlighted by Schmid et al. [8]. However, the effect of hot streak is neglected in their work. Recent work reported by Mansouri et al. [14] involved the combined effects of hot streak and swirl intensity. However, the authors assumed that aerothermal performances of all NGVs are identical and the NGV clocking position relative to the combustor is not considered, although the difference in aerothermal performances among vanes has already been confirmed in previous studies [13,18]. Therefore, it is incapable of reflecting the aerothermal performance difference of NGVs under different swirl intensities.

Based on the viewpoints above, numerical simulations were carried out on the first NGV of GE-E3 HP turbine with swirl and hot streak inlet, which took the realistic clocking position of NGV relative to the inlet non-uniform profile into consideration. Thus, the difference between neighboring vanes could be distinguished. The influence of the swirl intensities and orientations on the flow structure, aerodynamic loading and temperature distribution, and heat transfer coefficient on each vane surface were analyzed. The main findings of the present work will contribute not only to the design of an effective cooling scheme for NGV, but also to the integrated design of combustor and HP turbines [10,21].

2. Numerical Methodology

In present study, the numerical simulations were carried out with the commercial software ANSYS CFX 19.1 which discretize the calculated domain and Reynolds-averaged Navier-Stokes equations based on the element-based finite volume method. In the current high pressure turbine stage, the vane exit Mach number is less than 1 and thus the strong shock interaction between vane and rotor blade does not occur. The unsteadiness inside the stator passage is merely induced by the potential field interactions, such that unsteady characteristics are comparatively weak inside current vane passage. Even with the inlet swirl, the same continues [18,22,23]. Hence, the steady and compressible Reynolds-averaged Navier-Stokes equations were used as governing equations. The total energy model which considers the transport of enthalpy, kinetic energy effects and the effect of viscous work was applied to solve the temperature. The overall accuracy of the current simulations was second order. The interface between stator and rotor blade is modelled with Stage (mixing plane method). These simulations were assumed to be converged after the root mean square residual level of the computed parameters were lower than 1 × 10⁻⁵ and the monitored parameters were stable with the increase of the iteration time steps.

2.1. Computational Model and Boundary Conditions

The first NGV of GE-E3 HP turbine was utilized in the current work. Geometry model has been established referring to the NASA reports [24,25], as presented in Figure 1. The validations of geometry established were conducted through comparison of Mach number at midspan between numerical results and experimental data [25], as presented by Figure 2 (note that the Mach number here is not an isentropic value and is the one of the mainstream closest to vane wall). Obviously, a good agreement between numerical results and experiment data was obtained, except for the region at about Z/Bx = 0.55. The reason for the deviation may be test errors. Therefore, the current geometry profile is consistent with the that described in the reports [24,25].

The realistic clocking position of NGV relative to the inlet non-uniform profiles was considered in the current investigation. There exist 30 fuel injectors in the combustor and 46 HP NGVs in GE-E3 engine, and thus the count ratio between HS or swirl and NGV is 30:46 which is close to 2:3. To reduce calculated cost and minimize the effect caused by domain scaling, the number of NGVs in full scale was amplified by the factors of 46/45, i.e., the two hot streaks and swirl profiles for every three NGVs. Thus, the computational domain consists of three NGVs. Simultaneously, the other parts of GE-E3 HP turbine were also modelled to provide back pressure for the NGV, but with coarse grids, as revealed in Figure 1. The simulation boundary conditions were specified according to the GE-E3 turbine performance test report [25]. The rotational period boundary condition was specified for domain of every blade-row. The inlet was assigned with the swirl and HS (mass-flow averaged total temperature is 709 K). The inlet turbulence level is 10% with the eddy viscosity ratio of 100, static pressure at outlet was 62 kPa and the angular velocity for rotor blade-row was 8349 rev/min⁻¹. Nonslip boundary conditions were specified for the solid wall. Adiabatic wall and isothermal wall with temperature of 0.7 times inlet-averaged total temperature (496.3 K) were set for different cases to obtain heat transfer distribution.

The inlet total temperature profiles were set according to the work by Povey et al. [26], as shown in Figure 3. Figure 3a shows the total temperature contour at the inlet. The ratio between the maximum T_t and mean T_t is 1.14 and the ratio between the maximum T_t and minimal T_t is 1.58, both of which are slightly less than these in realistic aero-engine (the former is 1.21 and the latter is 1.64 [26]). Figure 3b presents the circumferential averaged total temperature distributions used in the current work and two total temperature profiles from the Ref. [26]. The hot streak center is at 60% span, which is consistent with one at realistic combustor exit.

The swirl were imposed at the HP NGV inlet, referring to the literature [9]. Yaw angle and pitch angle defined in Ref. [27] were utilized to characterize swirl distribution characteristics, as shown in Figure 4a. Figure 4b displays the comparison of circumferentially-averaged yaw angle distributions between the present work and the experimental data in Ref. [9]. The current swirl profile has greater angle at the region above 50% span, which is resulting from the fact that current swirl center is at 60% span. The swirl number (SN) was introduced to characterize the swirl intensity, which is defined by Equation (1) where V_θ and W are the averaged tangential velocity and averaged axial velocity individually [14] (note that current equation for the swirl number is a simplified expression, the more exact expression can be found in reference [14,28]). The SN of swirl specified according to the experimental data in Ref. [9] is about 0.496 which is perfectly close to 0.5, and this swirl intensify is regarded as the design point. Based on it, the effect of four swirl intensities (0, 0.25, 0.50, 0.75) and two swirl orientations (clockwise and anticlockwise) on NGV aerothermal performances is considered in this paper. Figure 4c shows the circumferential averaged yaw angles under different swirl intensities.

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

(1)

2.2. Turbulence Model Verifications

The verification of turbulence models was conducted on GE-E3 stator and Mark II cascade. The turbulence models tested in current work include high-Re k-ε, RNG k-ε, and low-Re k-ω, SST, and SST γ-Re_θ transition mode. In order to meet the requirements of various turbulence models on mesh, the height of the first grid node from the wall was adjusted to achieve the y⁺ < 1.5 for low-Re turbulence models and the y⁺ > 15 for high-Re turbulence models.

The design value of stator exit angle was used to check the ability of turbulence models as the detail aerodynamic test data was not provided in the NASA reports [24,25]. Figure 5 is the comparison of circumferential averaged stator exit angle between numerical results and design value. The basic trends of the exit angle along spanwise are similar with that of the design intent, but with smaller angle (one degree smaller). Moreover, it can be observed that the numerical results obtained using the different turbulence closure approaches are nearly identical. This is mainly resulting from the mainstream flow field being insensitive to the turbulence model in the case that there is no aggressive flow separation. Hence, only based on these, the optimum turbulence model for the current work cannot be distinguished, and further validations should be conducted.

Due to the lack of experimental data in term of heat transfer on GE-E3 HP turbine, the further examination for turbulence models used the experimental results of the MarkII vane [29], which is with ten radial internal cooling channels and has extensive experimental data under the realistic turbine operation conditions. Steady conjugate heat transfer (CHT) simulations were performed under the experimental condition No. 5411 with the inlet Mach number equal to 0.19. The CHT mesh of the Mark-II vane was generated by POINTWISE, as revealed in Figure 6. The turbulence models checked were the same as before and the grids adjustments were also conduced to adapt to them. The measured vane surface pressure and temperature were utilized to examine the turbulence models.

Figure 7a presents the pressure distributions at midspan obtained by simulation and experiment. The numerical results obtained with different turbulence models are found to be identical with each other and show a good consistency with the experimental data at most region. The comparatively remarkable deviation is observed at the Z/Bx = 0.55, which is resulting from the flow separation induced by the shock originating from the neighboring vane. Figure 7b gives the temperature distribution at midspan. From the figure, all turbulence models except for SST γ-Re_θ transition model are observed to overestimate the wall temperature near leading edge and the result predicted by SST γ-Re_θ transition model shows a good agreement with experimental data. Note that the SST γ-Re_θ transition model overestimate wall temperature at the rear of suction side as well, this may be caused by the excessive production of turbulent kinetic energy after boundary layer transition. On the whole, the SST γ-Re_θ transition model has the most superior performance in predicting aerothermal characteristics under such scenario. Moreover, the transition model has been extensively applied to simulate flow inside turbine and it can give an acceptable prediction of aerothermal performances [30,31,32]. Therefore, the SST γ-Re_θ transition model was selected for the subsequent simulations.

Note that the turbulence model validations above focus on the aerothermal performances at midspan, therefore, the ability of these turbulence models in terms of simulating flow near endwall which is dominated by the secondary flow has not been verified. In fact, k-ω and SST have been extensively proven to simulate the flow and heat transfer characteristic near endwall relatively accurately [33,34]. As expected, the SST γ-Re_θ transition model has good performances in predicting aerothermal performances at such regions as well [35,36].

2.3. Meshing and Grid Independence Validations

In order to eliminate the influence of mesh on the simulation of compressible flow inside NGV passages, mesh sensitivity analyses based on the static pressure and Nusselt number (Nu) distributions at three spans of NGV have been conducted. Nu is calculated using Equation (2) where q_w is isothermal vane wall heat flux, T_aw and T_w are vane temperature for adiabatic and isothermal condition individually and λ is thermal conductivity and Bx is vane axial chord. The commercial software NUMECA was employed to generate structured mesh for computational domains shown in Figure 1. Four different meshes of the HP NGVs were generated, consisting of about 1.23, 2.48, 3.11, and 3.95 million nodes for three guide vanes (respectively, refer to as Mesh1, Mesh2, Mesh3 and Mesh4). In these meshes, the height of the first grid node from the wall is set as 0.001 mm to model boundary layer and the y⁺ is less than 1.50 at most region of HP NGV. Steady simulations with uniform inlet boundary conditions were conducted to check mesh independence.

$$Nu=\frac{q_{\mathrm{w}}\cdot Bx}{(T_{\mathrm{a}\mathrm{w}}-T_{\mathrm{w}})\cdot \lambda }$$

(2)

The effect of the mesh refinement on the pressure at three spans is shown in Figure 8a–c. From the three sub-figures, it can be observed that there are no substantial differences in pressure distributions at the three spans which are assessed with different meshes. This indicates that static pressure field is insensitive to mesh refinement in the current stator. Compared with the pressure distributions, the heat transfer distributions are more dependent on the number of mesh nodes, especially on suction side where boundary layer transition occurs, as manifested by Figure 8d–e. On pressure side, the results of the four meshes reveal the same distribution in both trend and value, while on suction side, the results obtained with Mesh2, Mesh3, and Mesh4 almost have the same value. Moreover, with the increase of nodes number, the difference in Nu calculated by the adjacent meshes is seen to become less, such that differences in results obtained using Mesh2, Mesh3, and Mesh4 are negligible at most axial locations. This indicates that continuing to increase the nodes number does not cause substantial variations in terms of pressure and Nu. Thus, Mesh2 or Mesh3 can be the mesh independent solution of the current work. Considering that the demand for computational resources of the steady simulation is not large, Mesh3 was adopted for the subsequent simulations. It has 25 nodes within boundary layer and the expansion factor within boundary layer is 1.1, which thoroughly satisfies the requirements for the transition model [37,38]. Figure 9 presents some details of the meshes utilized. This figure also show the numbering rule for the nozzle guide vanes.

3. Results and Discussions

The inlet of the three NGVs face two fuel injectors in GE-E3 engine, i.e., there exist two non-uniform profiles at computational domain inlet, as shown by Figure 10. In this study, one integrated clocking position was studied, which includes the two relative positions of NGV with respect to the inlet non-uniform profiles. Taking the NGV2 leading edge (LE) as reference, this clocking position is that one non-uniform profile directly faces NGV2 and another is aligned to passage consisting of NGV1 SS and NGV3 PS. The current configuration considers two the most extreme relative positions between inlet non-uniform profiles and NGVs simultaneously (in some investigation [6,9,12,18], these two extreme relative positions are studied, individually). The effect of the interactions between the two adjacent swirls was embodied. Four swirl intensities are evaluated at each swirl orientation (clockwise or anticlockwise). When facing NGV LE, swirl rotating in the anticlockwise direction is positive swirl (PSW) and vice versa (negative swirl, NSW). These distributions are detailed by Figure 10.

Table 1. Simulation matrix.

No. of Cases	Thermal BC	HS	Swirl Intensity
1	Ad/Iso	Yes	0
2	Ad/Iso	Yes	0.25
3	Ad/Iso	Yes	0.50
4	Ad/Iso	Yes	0.75
5	Ad/Iso	Yes	−0.25
6	Ad/Iso	Yes	−0.50
7	Ad/Iso	Yes	−0.75

presents a summary of simulation matrix.

3.1. Effect of Swirl on Main Flow and Vane Loading

The interactions between the swirl and the NGV’s potential flow field alter the primary flows within NGV passage significantly, which can be seen from the limited streamlines on NGV surfaces, as shown in Figure 11. As seen in the figure, vertical stagnation lines (red lines) and the almost parallel streamlines from leading edge to trailing edge (TE) are observed at all three NGVs of the no-swirl case. Again, there is little difference among them, which is consistent with the Munk and Prim substitution principle: the introduction of hot streak does not induce additional flow in stationary blade row [39]. However, for the swirl cases, stagnation lines (black dotted lines) become inclined, and streamlines of each NGV are distinctive and are found to converge at different degrees. In positive swirl case (SN = 0.5), the streamlines on pressure sides of NGV2 and NGV3 are downwash and converge toward lower span, while the one of NGV1 is slightly upwash. There exist reverse streamlines patterns on the suction sides, i.e., streamlines on suction sides of NGV2 and NGV3 are upwash and converge toward higher span. Moreover, the flow along the NGV3 suction side seem not to be affected remarkably. The opposite is evident for the reversed swirl case (SN = −0.50). The current streamline distributions characteristics are similar with these obtained by LES [10] and SAS model [40].

The combined influences of swirl and the changes in the inlet incidence angle due to the swirl are responsible for the flow patterns above. For the incidence angle effect, positive swirl inflow with anticlockwise tangential momentum generates the positive and negative incidence angles at shroud and hub individually, as revealed in Figure 12. The positive incidence angle shifts the stagnation points at shroud toward PS and generate high static pressure, induces flow to aggressively accelerate toward SS and therefore results in the lower static pressure, as shown in Figure 13. Analogously, the negative incidence angle at hub shifts stagnation points toward SS and regions with high static pressure form, causes acceleration toward PS and therefore leads to the lower static pressure. The incidence angles increase monotonically with spanwise, thus resulting in a spanwise pressure gradient, i.e., pressure gradient from shroud to hub along PS and the exactly opposite pressure gradient along SS. The spanwise pressure gradients have the same orientation with swirl within the passage consisting of NGV1 SS and NGV3 PS, which enhances the upwash/downwash flow on NGV1 SS/NGV3 PS, as presented in Figure 13. Meanwhile, around NGV2, spanwise pressure gradients are opposite to the swirl and have more remarkable impacts on the flow. Thus, it is the spanwise pressure gradients that induce the streamlines on the surfaces toward endwall. However, the incidence angle effect has comparatively slight impacts on static pressure distributions on NGV1 PS and NGV3 SS. Hence, the streamlines on NGV1 PS are dictated by swirl flow and thus show upwash characteristics, and those on NGV3 SS are similar to that of the no-swirl case. Nearly opposite streamlines distributions are observed for the negative swirl case (SN = −0.50) and the analogous reasoning can be applied.

Due to the tangential momentum proportional to the absolute value of SN, the corresponding incidence angle effect and induced spanwise pressure gradient both increase with the |SN|. Thus, streamlines characteristics under other swirl intensities are found to be similar with that at |SN| = 0.5. This indicates that the factors dominating flow around each NGV surface are the same at the different swirl intensities. This is the reason why the limited streamlines and pressure contour under other swirl intensities are not shown hereby.

The effects of variable swirl intensities can be quantified by the pressure distributions along the NGVs, as shown in Figure 14. These three NGVs have diverse pressure distributions, resulting from different clocking locations relative to the swirls. For the NGV1, static pressure on PS of swirl cases is almost independent on swirl, thus the flow near NGV1 PS has the similar behavior with that of no-swirl case, as described above. However, static pressure on SS is dependent on swirl, especially near endwalls. At 10% span of NGV1, static pressure is found to increase with SN at the forward region of SS and declines with SN at the rear portion, which is a consequence of the incidence angle effect varying with SN. The exactly opposite trends are observed at 90% span. Contrary to NGV1, it can be seen that swirl has considerable influence on the static pressure of NGV3 PS and little influence on that of NGV3 SS. The static pressure at 10% span of PS is observed to decrease with SN and that at 90% span shows the exactly reversed trend. The reasons responsible for such distribution are similar with that on NGV1. Different from the NGV1 and NGV3, the NGV2 is directly subjected to swirl and thus the static pressure distributions on both pressure and suction sides are found to vary with swirl intensity. The static pressure on SS reveals similar distributions with these of NGV1, and static pressure on PS has the same trend with that of NGV3. Moreover, when comparing static pressure on PS and SS, it is found that the latter is more significantly affected by swirl.

Variations in the pressure distribution on NGV must lead to the change in blade loading. A lumped parameter, Zweifel coefficient [41], was introduced to represent blade loading under different swirl intensities. In the current work, Zweifel coefficients of swirl cases are normalized by that of the no-swirl case and named it loading coefficient. NGV loadings under variable swirl intensifies are indicated by Figure 15. As expected, loading coefficients at 10% and 90% spans of NGV2 increases and declines with the SN respectively, resulting from the fact that the enhanced SN increases the incidence angle at tip and decreases incidence angle at hub. The relative change in blade loading is about 9% at lower span and 10% at upper span, which is mainly due to the core of swirl locating at 60% span. For the same reason, the loading coefficients at 50% span present the same trend with that at 10%.

Different from the NGV2, the changes in blade loading of NGV1 and NGV3 are mainly caused by the static pressure varying on SS1 and PS3 respectively. For NGV1, the loading coefficients at 10% span are seen to increase with SN and that at 90% span decreases with SN. Moreover, the loading at 50% is observed to first decrease and then increase, this may be caused by that the higher SN cause more aggressive flow acceleration at the rear part of SS and thus decrease the static pressure. A similar trend is observed at the 50% span of NGV3 and the analogous reasoning is applied. The loading coefficient variation at 90% span of NGV3 is the result of the incidence angle effect, similar with that of NGV1. The loading coefficient at 10% is found to first increase with the SN and then decline, which may be due to the variation in static pressure at PS as revealed in Figure 14h. Furthermore, when comparing blade loadings of NGV1 and NGV3, it can be found that the change of the former (maximum variation of around 15%) is greater than that of the latter (maximum variation of around 6%). This is mainly caused by the fact that static pressure on the suction side is more sensitive to swirl intensities.

3.2. Secondary Flows under Different Swirl Intensities

In this section, the flows at endwall under different swirl intensities are presented, which features the evolutions of horseshoe vortex and passage vortex. Figure 16 presents an iso-surface of the Q-criterion inside the vane passages for the no-swirl case. After impinging the leading edge, one horseshoe vortex (HV) is divided into two parts which are suction side leg of horseshoe vortex (HV_SS) and pressure side leg of horseshoe vortex (HV_PS). These vortexes appear at hub and shroud regions simultaneously. The HV_PS migrates toward the suction side of the adjacent vane but does not interact with HV_SS to form passage vortex, which is different from the classic secondary flow structure described by textbook. It is stretched along transverse direction while passing downstream, which leads to the decrease in vorticity (showing agreement with Helmholtz vortex law for vorticity conservation [42]). Thus, the iso-surface is observed to disappear at the furthest part of pressure side. Then, it interacts with the adjacent HV_PS and wake vortex downstream of the trailing edge.

Compared to the no-swirl case, distinctive secondary flow structures are observed at the swirl cases, as illustrated by the Figure 17 which includes vorticity difference contours in the cross section of Z/Bx = 50% relative to the no-swirl case. The notable changes in vortex system are observed near shroud. With positive swirl, the HV_PS and HV_SS of NGV3 are both enhanced by the swirl, and their intensities increase with the swirl intensities. While horseshoe vortex of NGV1 and NGV2 is weakened near leading edge and then reinforced at downstream of suction side. The iso-surfaces for horseshoe vortexes of NGV1 and NGV2 are thus found to disappear near leading edge due to the lower vorticity, and then arise at the downstream of suction sides. Note that HV_SS values of all NGVs are intensified at the downstream when compared to the no-swirl case; for brevity, only the vorticity contours of NGV3 are shown hereby, which has the most significant change in vorticity. Furthermore, additional vortex structures appear near the upper span of NGV1 SS and NGV2 SS at SN = 0.75. These are generated by the interaction of swirls. The flow has the opposite tangential velocities at the boundary between two adjacent swirls and thus a new vortex is generated at triangle area near shroud, as shown in Figure 10 (red triangle dashed box). Then, the new vortexes are convected downstream, enhanced as the flow accelerates along suction side, and transported toward upper span by the upwash flow. It should be stated that the similar vortex structures also arise at the lower span, but with much smaller strength (one small core of this new vortex can be seen near the lower span of NGV2 SS), originating from the triangle area near hub. With negative swirl, a reinforced HV_SS and a diminished HV_PS are observed near NGV1. The intensity of the former increases with |SN|, while the intensity of the latter declines with it and finally disappear at SN = −0.75. Moreover, a newly formed vortex is seen near the midspan of NGV1 SS and NGV2 SS respectively (with extremely small-scale vortex core). This is resulting from the similar mechanisms to those in the positive swirl case.

The induced secondary flows inevitably cause additional aerodynamic losses. The losses were evaluated using the total pressure loss coefficient, CP_loss, which is defined by Equation (3) where the P_t,inlet and P_t,outlet are the total pressure at inlet and outlet, individually. As expected, the no-swirl case has the minimum aerodynamic losses of 4.23% and the CP_loss are seen to raise with the swirl intensity, as shown by Figure 18. At the low and medium swirl intensities, the positive swirl cases have little smaller aerodynamic losses than these at negative swirl, however, at high swirl (|SN| = 0.75), the opposite is true. This may be due to the fact that in comparison with case at SN = −0.75, one additional vortex appears near NGV2 SS at SN = 0.75. Thus, the strong positive swirl generates the maximum aerodynamic losses, which is around 10% higher relative to the no-swirl case.

$$C{P}_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}}=\frac{P_{\mathrm{t},\mathrm{i}\mathrm{n}\mathrm{l}\mathrm{e}\mathrm{t}}-P_{\mathrm{t},\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{l}\mathrm{e}\mathrm{t}}}{P_{\mathrm{t},\mathrm{i}\mathrm{n}\mathrm{l}\mathrm{e}\mathrm{t}}}$$

(3)

3.3. Temperature Distributions on Nozzle Guide Vane Surfaces

Figure 19a present the interactions between the swirl and the cross flow inside NGV passages at different axial planes and their combined influences on total temperature distributions. At the upstream of NGV LE, convection effects due to the swirl generates some oblique regions with relatively high temperature, and these regions always exist as passing downstream. More significantly, swirl combined with high pressure at the upstream of leading edge generates two cold regions near shroud. The reasons for forming the two cold regions are different. This can be seen from the relative position between the cold region and the pressure distribution near LE, as Figure 19b reveals. For the positive swirl (SN = 0.5), the cross flow induced by high pressure (blue arrow at plane of Z/Bx = −25%) and swirl (red arrow) meet with the opposite velocity at the right of NGV1 LE. This results in the accumulation of cold fluid originating from shroud and thus the cold region near NGV1 LE establishes. The cross flow meets swirl with the same velocity at the left of NGV1 LE, the confluent flow transports cold fluid toward NGV3 LE and is blocked by the higher pressure at the region. This generates the cold region near NGV3 LE. Similar temperature distributions are observed for the reversed case and the analogous reasoning could be applied. However, note that, under the negative swirl, reasons for generating cold regions near NGV1 LE/NGV3 LE are consistent with those for inducing cold region near NGV3 LE/NGV1 LE at the positive swirl.

The interaction effect for generating the cold region will vary with the swirl intensities. Figure 19c presents the total temperature distributions at 75% span of Z/Bx = 2.5% plane under the different swirl intensities. The total temperature at the core of the cold region is observed to decrease with the swirl intensity, which indicates enhanced accumulation of cold fluid. Importantly, the cold regions maintain through passages and continue to extend toward mid-span as the increase of swirl intensity, which will weaken the heat load of NGVs near them.

The interactions of the swirl and primary flow within NGV passage dominate the migration of HS, especially in radial direction. The spanwise pressure gradient caused by the positive swirl generates the downwash flow at NGV2 PS and upwash flow at NGV2 SS (see Figure 11). Thus, hot streaks adjacent to NGV2 PS and SS are transported toward tip and hub individually, as shown by the total temperature distributions of outlet in Figure 19a. HS aligned to passage migrates with cross flow from PS to SS, become close to the NGV1 SS, and is thus transported toward tip by the upwash flow. The exactly opposite migrations are observed for the reversed swirl case and the related reasons are analogous. These basic trends of radial migration of hot streak are identical with the existing experimental result [21] and numerical investigation [14,15].

The hot streak migration inside passage will be affected by the swirl intensities, this can be seen from the pitch-averaged total temperature at NGV outlet, as indicated by Figure 19d. Compared with no-swirl case, more uniform total temperature distributions are observed for the swirl cases due to the additional mixing effect caused by the swirl. As the increase of the absolute value of swirl intensity, the positive swirl tends to transport hot fluid toward upper span and the negative swirl has the exactly opposite effect. Therefore, the intense negative swirl may produce beneficial total temperature profiles, which results in lower heat load at the rotor blade tip.

The redistribution of hot and cold fluid caused by the swirl has a remarkable influence on the heat load on NGV surfaces. Figure 20 shows the total temperature distributions on NGV surfaces under different swirl intensities. For the no-swirl case, there exist hot areas around midspan. However, for swirl cases, such areas are found to move toward tip or hub.

The heat load on NGV1 of the positive swirl case are mainly determined by the oblique strips with relatively high temperature and the upwash flow. These oblique strips load up upper half of NGV1 with hot fluid, and then the hot fluid migrates with the upwash flow (see Figure 11) as travelling downstream. Thus, hot regions are found to be located at the upper span and to be moving up towards the tip, as shown in Figure 20. From this figure, it can also be found that, as the increase of swirl intensity, hot regions decrease and their cores continue to approach NGV1 tip, especially on pressure side. These are associated with the two effects caused by the stronger swirl. Specifically, the former is caused by the enhanced convection effect which declines the scale of the oblique strips of high temperature, and the latter is mainly due to the intense upwash flow.

The opposite high heat load distributions are observed on NGV1 of negative swirl cases (i.e., hot regions appear at hub and decrease with swirl intensity), and the related reason are analogical. However, in comparison with positive swirl cases, the heat loads on NGV1 under negative swirl are also influenced by the migration of cold fluid. NGV1 tip experiences the lower temperature because of the accumulation of cold fluid near shroud (see Figure 19a). These cold regions are seen to decline with the swirl intensities. This is mainly resulting from the enhanced mixing effect and radial transport of cold fluid (Figure 19b) due to the stronger swirl. These can be seen from the fact that the total temperature at midspan of SN = −0.50 is lower than that of SN = −0.25 (see Figure 20). Moreover, NGV1 of SN = −0.75 shows distinctive temperature distributions, which has two hot regions and one cold region (between two red dashed lines). Such distribution characteristics are detailed by Figure 21 which shows the total temperature distributions on NGV1 along the lines of Z/Bx = 75% (black lines on NGV1 in the Figure 20a). The hot region at hub is generated due to the same reason as that at SN = −0.25 or −0.50. Another hot region at midspan is caused by the transverse movement of hot streak core. The secondary flow is in line with negative swirl at upper half of span (see Figure 19a for reference) and is thus strengthened, which causes the hot fluid to reach NGV1 and to replace some cold fluids originating from shroud. This results in the thermally loaded midspan and thus cuts off the continuous cold region which can be observed at the lower SN. In fact, such a distribution also exists at NGV1 SS of SN = −0.50 (see Figure 21).

Radial migration of hot streak predominates the heat load on NGV2. With the positive swirl, the hot fluid is transported to PS tip by the upwash flow and to SS hub by the downwash flow, as previously mentioned. The hotter regions are thus observed to move up toward the tip on PS and toward the hub on SS, as shown by Figure 20. The reversed distributions are evident for the negative swirl cases and the analogous reasoning could be applied. As the increase of the swirl intensity, the hot regions are found to decrease due to the more aggressive mixing effect, and their cores are seen to become more adjacent to tip or hub, which is resulting from the reinforced incidence angle effect. In addition, cold fluid accumulating at shroud (between NGV1 PS and NGV2 SS) migrates with cross flow and reaches NGV2 SS (Figure 19a), which declines the total temperature at tip.

It is of interest to note that heat load distributions on NGV3 of positive and negative swirl are similar with these on NGV1 of negative and positive swirl respectively. The corresponding mechanisms responsible for these distribution characteristics are also analogous. More specifically, for the positive swirl, the hot region at hub is due to oblique strips with relatively high total temperature at lower half span of NGV3, while the tip region of low temperature is caused by the radial migration of cold fluid accumulating near shroud, as indicated in Figure 20. The temperature distributions at the strong positive swirl (SN = 0.75) are resulting from the interaction of the enhanced transverse displacement of heat streak and radial migration of cold fluid from the shroud, which is analogous with that on NGV1 of SN = −0.75. The hot tip regions under the negative swirl are generated by the hot fluid at the upper half of NGV3 and their movements toward tip with the upwash flow.

3.4. Heat Transfer on Nozzle Guide Vane Surfaces

In this section, the heat transfer characteristics under the different swirl intensities will be compared and discussed. Figure 22a show Nusselt number (Nu) distributions on NGV surfaces. As seen in this figure, the difference of Nu distributions on the three NGVs of the no-swirl case is slight, resulting from the same flow patterns among them. On the PS, Nu is seen to initially decline and then slightly increase with streamwise (detailed by Figure 23), corresponding to the change in boundary layer thickness due to the pressure gradient. The Nu on the SS experiences decrease, increase and another decrease successively, which is mainly caused by the boundary layer transition. In the current NGV, the boundary transition is achieved via bypass mode: the transition is activated by the increase in the boundary layer thickness which is principally caused by the adverse pressure gradient. The thermal performances near the endwalls are dominated by vortex behaviors. The vortexes at junctions between the SS and endwalls are stronger than those at the corresponding regions of PS. Also, the latter migrates with the cross flow toward SS as passing through passage. Therefore, the low and high Nu are found at the PS and SS endwalls individually.

The redistribution of flow due to the swirl have remarkable impact on the heat transfer behaviors of NGVs. Thus, the heat transfer characteristics on the three NGVs of the swirl cases are observed to be distinctive with each other, as presented by Figure 22, which is different with the no-swirl case.

For the NGV1, positive swirl increases Nu at the lower span of PS and decrease that near midspan, and such trends are reinforced by the swirl intensity. These are mainly resulting from the fact that upwash flow (Figure 11) cause the low momentum fluid originating from the boundary layer at lower span to accumulate near midspan. Under negative swirl, one region with low Nu is seen at the upper span, which is caused by the two reasons. The first is similar with one at positive swirl. The second is the incidence angle effect. Negative incidence angle at tip generates the lower static pressure, leads to smaller velocity at downstream, and thus weakens heat transfer.

These two factors also have significant effects on the heat transfer on NGV1 SS. The positive swirl is found to enhance Nu at the lower span and decline that at the upper span. Moreover, it advances boundary layer transition, especially at the upper span. Transition onset at 90% span is seen to move upstream with the increase of swirl intensity (Figure 23c). These are resulting from the similar mechanisms for the smaller Nu on PS, but with the opposite behaviors. Positive swirl generates higher pressure at the hub and lower pressure at the tip, as shown by Figure 14a,c. The former generates the more aggressive flow acceleration and thus increases the heat transfer at hub. Upwash flow caused by the radial pressure gradient transports the boundary layer outward and meet with the downwash flow from the upper endwall (see Figure 11). This leads to the accumulation of low momentum fluid and thus weaken the heat transfer at tip. The advanced transition at tip could be attributed to the lower pressure weakening acceleration and the migration of boundary layer, both of which induce thicker boundary layer. The roughly reversed distributions are observed for the negative swirl cases and the analogous reasoning could be applied. Note that the transition onset under negative swirl shifts toward the upstream at hub, with the opposite direction relative to that at tip, while under positive swirl, such behaviors are not observed. This may be result from the fact that boundary layer migration with the upwash flow is partly offset by the radial pressure gradient in passage (from tip to hub).

The change in the incidence angle caused by the swirl has a significant influence on the Nu at the NGV2 leading edge. Under positive swirl, the flows with positive and negative incidences impinges PS tip and SS hub, individually, which enhance Nu at the two regions. The reversed distributions are true for the negative swirl cases due to the similar reason. Moreover, such incidence angle effects will increase with swirl intensity. This can be seen from that the Nu of SN = 0.75 at 10% span is maximum and that of SN = −0.75 is minimum, as expected, the opposite is true for 90% span, as shown by the Figure 23d,f.

On the NGV2 PS, lower Nu is observed at the lower span for the positive swirl case and upper span for the negative swirl case, resulting from the similar reasons with that on NGV1 PS. In addition, due to the additional mixing effect generated by the swirl, the area with lower Nu declines with swirl intensity. It is of interest to note that, a sloping band with high Nu arises on PS and broadens near trailing edge under a strong swirl (|SN| = 0.75). The former is mainly caused by the more aggressive upwash or downwash caused by the enhanced incidence effect (it can be seen that the high Nu region is along trajectory of upwash or downwash streamline, see Figure 11). The latter may be due to the interaction of residual swirl and flow near trailing edge. For the analogical reasons, the Nu distribution on the NGV2 SS is similar with that on the NGV1. However, it should be stated that compared with NGV1, the related effects due to swirl are more aggressive on NGV2 (directly subjected to swirl). Therefore, the boundary layer transition at the three spans is found to vary with swirl intensity, particularly at midspan. With the stronger swirl, the transition onset at midspan is seen to continuously shift toward upstream. This can be explained by the fact that whether the boundary layer near endwall migrates with upwash or downwash, the low momentum fluid will accumulate near midspan, boundary layer based on momentum becomes thicker and the transition is advanced. Moreover, it may be affected by the interaction of induced vortexes and boundary layer [14].

The heat transfers on the NGV3 are less influenced by the swirl. The lower Nu on NGV3 PS at different swirl intensities are resulting from a similar reason with that on NGV1 PS. Significantly, the positive swirl reinforces the pressure side leg of the horseshoe vortex near the shroud (Figure 17), and thus raises the heat transfer at the tip region, especially near the trailing edge, as revealed in Figure 23i. Such an effect is seen to increase with swirl intensity. The changes in the heat transfer on NGV3 SS are mainly resulting from the additional mixing effect and limited transport of the boundary layer both of which are generated by swirl. Yet, it is worth noting that, under positive swirl, the Nu at the tip region is enhanced by the swirl and that at the hub it is weakened, and the opposite trends are observed under negative swirl. These are associated with the change in vortex intensity caused by the swirl. Similar trends also exist at the suction side endwall regions of NGV2.

4. Conclusions

Steady numerical simulations were performed to investigate the effect of swirl intensities combined with hot streak on the high-pressure nozzle guide vane. The realistic clocking position of NGV relative to the inlet non-uniform profile was considered. The flow structures at different swirl intensities and its impacts on aero-thermal performances of each vane surface were analyzed. The key findings are summarized as follows.

• The relative strength between the swirl and its induced radial pressure gradient dictates the flow patterns on vane surfaces. On the vane surface directly impinged by swirl or adjacent to it, the effect of radial pressure gradient dominates, while on other vane surface, swirl itself dominates. Thus, diverse flow patterns appear on the vane surfaces, and the dominant factor on each surface does not vary with swirl intensity.
• Swirl orientations have remarkable impacts on the vortex system at shroud. Positive swirl is found to intensify horseshoe vortex. Negative swirl enhances the HV_PS and weakens HV_SS simultaneously. Such trends become more significant with the increase of swirl intensity. Moreover, the interactions of swirl and secondary flow generates the new vortexes. These changes cause the additional aerodynamic loss. The total pressure loss at high swirl is around 10% higher, relative to the no-swirl case.
• Swirl’s induced incidence effect alters vane aerodynamic loading. The aerodynamic loading at 90% span of the vane which is directly impinged by swirl increases with the swirl intensities and that at 10% span shows the exactly opposite behaviors. The aerodynamic loading variations can also be observed on other two vanes. The aerodynamic loading on the vane whose suction side is adjacent to the swirl has the greater variation and is more sensitive to swirl intensities, relative to the vane whose pressure side is adjacent to swirl.
• The interactions of swirl and secondary flow generates the relatively hot oblique strips and the two cold regions at the upstream of vane. The heat loads on the vane which is not directly impinged by the hot streak are dictated by the radial migration of the fluids originating from the regions above. As the swirl intensity increases, the radial migration of cold fluid toward hub is reinforced, which weakens the heat load at the lower span under low and medium swirls (|SN| = 0.25 and 0.5). However, intense swirl(|SN| = 0.75) strengthens the transverse movement of hot streak simultaneously and thus leads to the additional thermally loaded on vane.
• Swirl’s induced incidence effects show significant effect on the heat transfer of the vane surfaces. With positive swirl, the heat transfers at the lower spans of suction side and pressure side are reinforced and weakened respectively. As expected, the exactly opposite distributions are observed under negative swirl. Such trends are enhanced with the swirl intensities. The swirl also affects the boundary layer transition, and then heat transfer. Both positive and negative swirls advance transition on the suction side of the vane directly impinged by the swirl, and with the increase of swirl intensity, transition onset keeps shifting toward upstream, particularly at midspan.