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 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,
CPloss, which is defined by Equation (3) where the
Pt,inlet and
Pt,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
CPloss 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.
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.