6.1 Effect of winglet width on efficiency

The effect of winglet width on efficiency is showed in Fig. 8. The turbine efficiency is defined as Equation (1). In Fig. 8, there exists an inflection point at w/p = 2.1%. Before w/p = 2.1%, the efficiency increases linearly with the w/p. For a better illustration of this linear relation, a blue dash line is added toFig. 8. After w/p = 2.1%, the curve in Fig. 8 deviates down from this blue dash line, which means that the increment of the efficiency benefited from per unit increment of winglet width is smaller than that before w/p = 2.1%. In the following content, the mechanism of this inflection point in Fig. 8 will be explained by quantitative calculations of tip leakage flow loss, then illustration of the tip leakage flow mixing process and finally the inspection of the vortex structures inside the gap tip.

Figure 8.

Efficiency versus w/p.

The main factor for the increment of the efficiency is further revealed through investigations on the variations of tip leakage flow loss with winglet width. The flow loss is calculated using the mass-weighted integral of the relative total pressure loss, as Equation (4). The tip leakage flow loss is obtained by subtracting the loss at the rotor exit of the blade without tip clearance gap from that of the blade with tip gap, as Equation (5). The tip leakage flow loss can be divided into the internal gap loss and the external mixing loss. The internal gap loss is calculated from the tip gap exit using Equation (6) on the tip gap exit which is illustrated in Fig. 9. Then, the external mixing loss is calculated by subtracting the internal gap loss from the tip leakage loss using Equation (7). The normalised difference of internal gaploss is defined as Equation (8), and the normalised difference of external mixing loss is defined as Equation (9). The variations of them with winglet width are shown in Fig. 10.

(4) \begin{align}\zeta = \int {{{{P_{1 - rel}} - {P_{rel}}} \over {{P_{1 - rel}}}}} dm\end{align}

(5) \begin{align}{\zeta _L} = {\zeta _{wt}} - {\zeta _{nt}} = \int\limits_{wt - 2} {{{{P_{1 - rel}} - {P_{rel}}} \over {{P_{1 - rel}}}}dm} - \int\limits_{nt - 2} {{{{P_{1 - rel}} - {P_{rel}}} \over {{P_{1 - rel}}}}dm} \end{align}

(6) \begin{align}{\zeta _{IG}} = \int\limits_{wt - ga{p^{}}exit} {{{{P_{1 - rel}} - {P_{rel}}} \over {{P_{1 - rel}}}}dm} \end{align}

(7) \begin{align}{\zeta _{EM}} = {\zeta _L} - {\zeta _{IG}}\end{align}

(8) \begin{align}\Delta {\zeta ^*}_{IG} = ({\zeta _{IG - Improved}} - {\zeta _{IG - Original}})/{\zeta _{IG - Original}}\end{align}

(9) \begin{align}\Delta {\zeta ^*}_{EM} = ({\zeta _{EM - Improved}} - {\zeta _{EM - Original}})/{\zeta _{EM - Original}}\end{align}

Figure 9.

Illustration of tip gap exit.

Figure 10.

The variations of normalised leakage flow loss with winglet width. (a) Normalised internal gap loss, and (b) normalised external mixing loss.

The increment of internal gap loss (normalised by the tip leakage loss of original blade) with w/p is presented in Fig. 10(a). The internal gap loss increases with w/p, which is probably resulted from more contact area and time of the friction process between the gas flow and blade wall on the blade tip, as an effect of the winglet.

The decrement of external gap loss (normalised by the tip leakage loss of original blade) with w/p is presented in Fig. 10(b). The decrement of the external gap loss is about 20 times more than the increment of the internal gap loss, resulting in a net reduction of the tip leakage flow loss, thereby contributing to the increment of the efficiency in Fig. 8. At w/p = 2.1%, normalised by the tip leakage flow loss of the original blade, the external mixing loss is decreased by 5.3%, and the internal gap loss is increased by only 0.17%. This makes the decrement of the external mixing loss a critical contributor for the increment of the efficiency. Thus, the decrement of the external mixing loss in Fig. 10(b) shows a similar trend with the increment of the efficiency in Fig. 8, and there also exits an inflection point at w/p = 2.1% for the decrement of the external mixing loss in Fig. 10(b). After w/p = 2.1%, the decrement of the external mixing loss benefited from per unit increment of w/p is smaller than that before w/p = 2.1%. The main reason for this inflection point will be further explained step by step to the end of this section.

Details of distributions of the external mixing loss can be illustrated by contours of viscous entropy generation rate [Reference Greizer, Tan and Graf28, Reference Zlatinov, Tan, Montgomery, Islam and Harris29]. The viscous entropy generation rate(VRGR) is defined as Equation (10).

(10) \begin{align} VEGR & = \mu \left[{\left({{\partial {V_y}} \over {\partial x}} + {{\partial {V_x}} \over {\partial y}}\right)^2} + {\left({{\partial {V_z}} \over {\partial y}} + {{\partial {V_y}} \over {\partial z}}\right)^2} + {\left({{\partial {V_z}} \over {\partial x}} + {{\partial {V_x}} \over {\partial z}}\right)^2}\right] \nonumber\\ & \quad + {2 \over 3}\mu \left[{\left({{\partial {V_x}} \over {\partial x}} - {{\partial {V_y}} \over {\partial y}}\right)^2} + {\left({{\partial {V_y}} \over {\partial y}} - {{\partial {V_z}} \over {\partial z}}\right)^2} + {\left({{\partial {V_z}} \over {\partial z}} - {{\partial {V_x}} \over {\partial x}}\right)^2}\right] \end{align}

Figure 11 shows the entropy generation rate at different streamwise locations. The shear layers due to the tip leakage flow mixing with mainstream can be identified by high value regions of viscous entropy generation rate far away from the suction side blade surface. Similar distributions are found for both blades. An obvious difference is that the viscous entropy generation rate at w/p = 2.1% blade is lower than that of original blade which is indicated by the enlarged part of Plane 2. This indicates that the existence of winglet probably only weakens the strength of the interaction between the tip leakage flow and the mainstream, but it does not change the pattern of this interaction.

Figure 11.

Contours of viscous entropy generation rate at different streamwise locations.

Further details of the mixing process between the tip leakage flow and the mainstream can be gained in Fig. 12 which shows the viscous entropy generation rate at 90% span. The shear layers due to the tip leakage flow mixing with mainstream can be identified by high value regions of viscous entropy generation rate starting from the suction side leading edge. It is found that, near the front part of the blade, the shear strength of the w/p = 2.1% blade is obviously reduced, highlighted by a dotted circle. Near the mid part of the blade, the winglet of the w/p = 2.1% blade puts the leakage vortex more far from the suction side surface, and the interaction between leakage vortex and suction side boundary layer would be weaker. This will reduce the heat flux through the suction side surface, which will be discussed in Section 6.2. Near the aft part of the blade, the difference between these two cases is not significant. The strength of the suction side trailing edge shock of the w/p = 2.1% blade shows a little reduction. Thus, the mixing loss reduction is mainly attributed to the weakened shearing between tip leakage flow and mainstream near the front part of the blade where the flow is subsonic. It could be inferred that, for the subsonic turbine blade, the suction side winglet design method maybe also have potential to reduce the tip leakage flow loss.

Figure 12.

Viscous entropy generation rate at 90% span.

Having interpreted the changes in details of the mixing process between the tip leakage flow and the mainstream, we refer to the root causes of the reduction in external mixing loss. The mixing loss can be estimated based on a control volume analysis with constant-pressure mixing assumption [Reference Denton30], as in Equation (11).

(11) \begin{align}MixingLoss = Cp(\gamma - 1){{{m_{injected}}} \over {{m_{main}}}}\left(1 - {{{V_{injected}}} \over {{V_{main}}}}\cos \alpha \right){M_{main}}\end{align}

This 1D model is originally used for the mixing progress between the injected flow and the mainstream. There is a clear boundary between the injected flow and the mainstream. The flow parameters on both sides of this boundary are discontinuous, so it is easy to distinguish the flow parameters for the injected flow or the mainstream before the mixing process. This makes it convenient to calculate the mixing loss using Equation (11).

However, for a tip leakage flow in a turbine rotor, even though it is reasonable to treat this tip leakage flow as an injected flow, there is no clear boundary between the tip leakage flow and the mainstream because the flow parameters are continuous in tip gap exit in 3D viscous simulations. For this reason, at the tip gap exit, the mixing process has probably begun, which makes it difficult to calculate the mixing loss directly using Equation (11).

Thus, in this study, only mass flow and flow angle at the tip gap exit are used to characterise the strength of mixing process. According to Equation (11): (1) a less mass flow at the gap exit implies less mixing loss; (2) a larger flow angle at the gap exit implies a smaller angle between the tip leakage flow and the mainstream, and hence less mixing loss.

At the gap exit, the local mass flow and the flow angle (relative to the axial direction) measured at the mid-gap height (0.993span) are plotted with the variation of the streamwise location, as shown inFig. 13. The blades with no winglet, w/p = 2.1% and w/p = 4% are chosen for illustration. It is found that the changes of the local mass flow rate and the flow angle are limited before 40% streamwise location. As the winglet width increases, the mass flow rate of leakage flow is reduced and the leakage flow exits the tip gap in a more streamwise direction (streamwise direction angle measured from axial direction equal to 75.02 deg), mitigating the external mixing loss of the tip leakage flow.

Figure 13.

Local mass flow rate and flow angle at the tip gap exit. (a) Local mass flow rate, and (b) flow angle.

Next, it is necessary to consider the flow field inside the tip gap in order to trace the dominated flow structure which plays a crucial role in mitigating the external mixing loss. For this purpose, the original blade and blade with w/p = 2.1% are chosen for comparisons. The streamlines to trace the dominated flow structure are shown in Fig. 14. Red streamlines are released from the suction side of leading edge, and the gray ones are released from the pressure side of leading edge.

Figure 14.

Streamlines released from leading edge.

On the tip surface near the leading edge, a pair of horseshoe vortexes are formed due to separation when the flow from the mainstream is entrained into the tip gap. The pressure arm of tip leading edge horseshoe vortex (PHV) can be identified by blue streamlines, and the suction arm of tip leading edge horseshoe vortex (SHV) can be identified by black streamlines. These vortexes have also been reported in previous studies [Reference Krishnababu, Newton and Dawes31, Reference El-Ghandour, Mori and Nakamura32]. The SHV moves along the suction side edge, and then exits in a certain distance to shear with the mainstream. This shear stress is the force for the roll-up and the formation of the tip leakage vortex. The onset of the roll-up of leakage vortex occurs further downstream in the blade with w/p = 2.1% due to SHV exiting suction side edge at a further downstream location.

The effect of this SHV on the leakage vortex is illustrated by the contours of streamwise vorticity on the 1% and 10% streamwise locations, as shown in Fig. 15. The flow is entrained from pressure side with positive streamwise vorticity (rotates clockwise), and this flow goes through the tip gap to formed the leakage vortex with the positive streamwise vorticity. On the contrary, the SHV rotates anticlockwise with the negative streamwise vorticity.

Figure 15.

Contours of streamwise vorticity at 1% and 10% streamwise locations. (a) 1% streamwise location, and (b) 10% streamwise location.

This opposite streamwise vorticity between the SHV and the leakage vortex makes the former an obstructive factor to the latter. The SHV postpones the onset of the leakage vortex and weakens the strength of it. These two effects are more severe in the blade with winglet. This is because the winglet offers more space for the generation of SHV. In the blade with winglet, the SHV stays longer time on the blade tip and leaves it at a further downstream location. This increases the time and the contact area of the interaction between the SHV and the leakage vortex, so the leakage vortex is further weakened. At 1% streamwise location, the SHV in the blade with w/p = 2.1% effectively postpones the onset of the leakage vortex, so the onset of leakage vortex is only observed in the original blade. At 10% streamwise location, the area of streamwise vorticity of the leakage vortex is smaller in w/p = 2.1% blade, implying that the strength of the leakage vortex is weakened due to the stronger SHV upstream of it.

To get a quantitative assessment of this weakening effect of SHV on the leakage vortex, a normalised streamwise vorticity decrement outside the suction side tip edge is calculated from Equation (12). The flow field at 10% streamwise location is chosen as the calculation domain to represent this effect of SHV. The results are shown in Fig. 16 with variation of w/p. From Fig. 16, the decrement of the streamwise vorticity varies nearly linearly with winglet width before w/p = 2.1%, and the slope of it reduces rapidly after w/p = 2.1%. The w/p = 2.1% is the inflection point of the decrement of leakage vortex strength benefiting from per unit increment of w/p. This is in accordance with the trend of the increment of efficiency with w/p in Fig. 8. This similarity makes it clear that, the interaction between the SHV and the leakage vortex is a crucial contributor for the increment of efficiency.

(12) \begin{align}\Delta {\omega _{\rm{s}}}^{\ast} = {{\int\limits_{Original} {{\omega _{\rm{s}}}dA} - \int\limits_{Improved} {{\omega _{\rm{s}}}dA} } \over {\int\limits_{Original} {{\omega _{\rm{s}}}dA} }}\end{align}

Figure 16.

The normalised decrement of streamwise vorticity at 10% streamwise location.

To explain the reason for the inflection point at w/p = 2.1% in Fig. 16, the contours of wall shear near the leading edge on the tip of the original blade, and blades with w/p = 2.1%, w/p = 3.2% and w/p = 4.3% are shown in Fig. 17. The trace of SHV is labeled with white dash arrow, and the angle of this trace is labeled as ‘θ’, measured from the streamwise direction. The strength of SHV can be characterised by the value of wall shear. To illustrate the vortexes on the tip, red streamlines are released from the suction side of leading edge to show SHV, and the gray ones are released from the pressure side of leading edge to show PHV.

Figure 17.

Contours of wall shear on blade tip.

From Fig. 17, for all blades, the distribution of SHV strength keeps a high similarity in a same normal distance, and the SHV evolves in a nearly equal direction. The evolution of SHV is mainly driven by the flow from the pressure side due to shearing, and near the pressure side, the flow angle and wall shear in the blade with winglet keep nearly the same as that in the original blade. This implies that the driving force of turning the SHV in the blade with winglet keeps nearly the same as the one in the original blade. Thus, for all blades, the distribution of SHV strength keeps a high similarity in a same normal distance. However, it should be noted that, for blades with different winglet widths, some slight differences in distributions of SHV strength are still observed. This is mainly because the velocity and pressure fields near the suction side leading edge are changed by different winglet profiles.

A closer inspection of Fig. 17 shows that the strengths of SHV in blades with w/p = 3.2% andw/p = 4.3% start to decrease after a normal distance equal to L (labeled in Fig. 17). This normal distance is also equal to that of the blade with w/p = 2.1%. The decrease of the strength of SHV is mainly resulted from the conflict between the flow from the suction side and the one from the pressure side. The flow from the suction side is supplied into SHV with negative streamwise vorticity. On the contrary, the flow from the pressure side with positive streamwise vorticity weakens the strength of SHV. After the normal distance equal to L, the latter factor surpasses the former factor, and hence the strength of SHV starts to decrease.

As an important effect of this decay of the SHV, the interaction between the SHV and the leakage vortex is weakened. This is evidenced by the rapid reduction of the slope of streamwise vorticity decrement after w/p = 2.1% in Fig. 16. The decay of the SHV is also responsible for the inflection point at w/p = 2.1% of the increment of efficiency in Fig. 8, since the weakening effect of SHV on the strength of leakage vortex is a crucial contributor for the increment of efficiency.

6.2 Effect of winglet width on heat load

The winglet increases the blade surface area, and therefore it tends to increase the blade heat load. This section will examine the relation between the winglet width and the blade heat load, and then analyse the distribution of heat flux over the blade surface.

Figure 18(a) shows the relation between the winglet width and the normalised blade surface area increment, and Fig. 18(b) shows the relation between the winglet width and the normalised heat load increment which is defined as Equation (13). It should be noted that, the blade surface area, used to calculated the heat load, includes the surface area of pressure side, suction side and tip, that is, the whole blade surface. In each plot, a linear fitting through least square method is marked with a red dash straight line. The linear determination coefficient and slope of the straight line are also marked.

Figure 18.

Blade surface area and heat load versus w/p. (a) Blade surface area versus w/p, and (b) heat load versus w/p.

(13) \begin{align}\Delta H^{\ast} = {{{H_{Imroved}} - {H_{Original}}} \over {{H_{Original}}}} = {{\int\limits_{Improved} {qdA} - \int\limits_{Original} {qdA} } \over {\int\limits_{Original} {qdA} }}\end{align}

It is found that, the winglet increases the blade surface area and the heat load. The linear determination coefficient for each plot exceeds 0.99, indicating that the relation between blade surface area increment and winglet width and the relation between heat load increment and winglet width are approximately linearity. This implies that, the increase of blade surface area due to the winglet might be an important contributor for the heat load increment.

To further analyse the effect of winglet on heat load, the contours of surface heat flux on the blade tip and suction side surface are shown in Fig. 19. The original blade and the blade with w/p = 2.1% are chosen for comparisons.

Figure 19.

Heat flux on tip and suction side surface. (a) Original, and (b) w/p = 2.1%.

From Fig. 19, on the blade tip surface, the high heat flux region is related to the development of pressure arm of tip leading edge horseshoe vortex (PHV) and the suction arm of tip leading edge horseshoe vortex (SHV), as mention in Section 6.1. The high heat flux related to PHV and SHV reduces along streamwise direction due to the flow acceleration. The region near the SHV in the blade with w/p = 2.1% shows a longer distance due to the winglet.

From Fig. 19, on the suction side surface, there is a reduction of heat flux on the region from leading edge to mid-chord at about 90% span for the w/p = 2.1% blade. This is because, the winglet of the w/p = 2.1% blade puts the leakage vortex more far from the suction side surface, as seen from Fig. 12, and the interaction between leakage vortex and suction side boundary layer is weaker, reducing the heat flux through the suction side surface. The rest regions are similar for both blades. Combined with the finding from Fig. 18(b), it could be concluded that, even though the winglet can put the leakage vortex far from the blade to reduce the heat flux in a small region, this reduction of heat flux is smaller than the increment of heat flux due to the increased blade surface area, leading to a net increment of heat flux.

Except for the above differences, the distributions of heat flux on the tip surface and suction side blade surface of these two blades show a similar pattern.

6.3 Trade-off between efficiency and heat load

From Section 6.1 and Section 6.2, it is found that, as the winglet width increases, the efficiency is improved at the expanse of a more severe heat load. Further, the main factors responsible for the increment of efficiency and that of heat load have been revealed. In the Section 6.3, the design space of the winglet width will be explored based on a point view of the trade-off between the efficiency and the heat load.

Since the increment of efficiency is a positive effect of the winglet and the increment of heat load is a negative effect, this paper defines a ratio of the increment of efficiency to the increment of the normalised heat load (Δη/ΔH*), Equation (1) divided by Equation (13), in order to quantify the trade-off between the efficiency and the heat load. The higher value of Δη/ΔH* means that more increment of efficiency is achieved at the expanse of per unit increment of heat load, that is, a better choice of winglet width for the winglet design in the present paper. The Δη/ΔH* versus w/p is plotted in Fig. 20.

Figure 20.

Trade-off relation between efficiency and heat load.

It is found that, the Δη/ΔH* gradually changes above 0.65 before w/p = 2.1%, but dramatically drops below 0.65 after w/p = 2.1%. This means that, after w/p = 2.1%, at the expanse of each 1% heat load increment, the efficiency improvement is less than 0.65%.

This dramatic drop of Δη/ΔH* after w/p = 2.1% in Fig. 20 is mainly resulted from the same inflection point of efficiency increment in Fig. 8. For the increment of heat load it keeps a great linear relation with the w/p(from Fig. 18(b) in Section 6.2), because it is primarily driven by the increment of the blade surface area due to the winglet. For the increment of the efficiency, however, it inflects down from the linear relation after w/p = 2.1%(from Fig. 8 in Section 6.1). This inflection point of efficiency improvement may be attributed to the reduction in the strength of SHV, as explained in Section 6.1.

In summary, even though the efficiency monotonically increases with the winglet width, the inflection point at w/p = 2.1% limits the increment of efficiency at the expense of per unit increment of heat load. The ZISTR designed with the winglet width equal to 2.1% blade pitch achieves a great trade-off between efficiency and heat load that the efficiency is improved by 0.85% at an expense of 1.2% increment of the heat load.

6.4 Effect of winglet on blade weight and mechanical stress

Winglets are small plates extending from the tip of the blade. This would add the blade weight and affect the mechanical performance of the rotor, which would prevent to implement these winglets. In this section, the effect of winglet on blade weight and mechanical stress are discussed. Based on the maximum working temperature of the ZISTR, that is 1200K, K465 superalloy is chosen as the material of the ZISTR for the mechanical simulation in this investigation. Since the blade with winglet of w/p = 2.1% has been proved to be a great design from Section 6.3, the original blade and the blade with winglet of w/p = 2.1% are chosen for comparisons in this section.

The weights of single blade of the original blade and the blade with w/p = 2.1% are listed inTable 3. The winglet of w/p = 2.1% increases the blade weight by about 0.183%, from 32.71g to 32.77g. To eliminate the added weight resulted from winglet, there are some ways, such as decreasing the blade numbers, reducing the blade chord length and so on. For simplicity, the way of reducing the blade chord length is chosen for investigation in this paper. To obtain a reduced-chord blade, the blade geometry is scaled down at the same proportion in axial direction and it is kept unchanged in spanwise direction. After some trials, it is found that, the blade with w/p = 2.1% reduced by 0.174% of chord length has the same weight as the original blade, as listed in Table 3. The efficiency of the reduced-chord blade with w/p = 2.1% decreases by 0.05%, from 84.16% to 84.11%. This decrement of efficiency is acceptable because the efficiency of reduced-chord blade with w/p = 2.1% is still higher than that of the original blade by 0.8%. Thus, the added blade weight caused by the winglet on the blade with w/p = 2.1% could be eliminated by means of reducing the blade chord length by 0.174%, and the efficiency improvement decreases from 0.85% to 0.8%.

Table 3.

Blade weight and turbine efficiency

To quantify the effect of the winglet on the blade mechanical stresses, a static structural analysis has been performed on the original blade and the blade with w/p = 2.1%. The ANSYS Workbench Static Structural Analysis is employed for mesh generation and finite element analysis. To simplify the structure modeling, the blade and its disk are assumed to be integrated into a turbine disk. A 1/18th sector of the turbine disk is created based on the blade number, as shown in Fig. 21. On the frame of reference, displacement constraints in axial and tangential directions are applied to the surface marked with dash circle in Fig. 21. Three different kinds of loads have been applied, including: 1) a centrifugal load resulting from rotational speed, 2) an aerodynamic load extracted from the blade surface pressure, and 3) a thermal load decided by the blade surface temperature. The Von Mises stress distributions on the suction side and hub surface are shown in Fig. 22.

Figure 21.

Blade models for finite element analysis.

Figure 22.

Von Mises stress distributions on blade surface.

From Fig. 22, it is found that the distributions of Von Mises stress on the suction side and hub surface of these two blades are similar. The maximum of stress appears at the blade root near the leading and trailing edge, marked with dash circles. To quantify the difference between the original blade and the blade with w/p = 2.1%, the distributions of Von Mises stress at the blade root and the 95% blade span are plotted in Fig. 23. The blade root is chosen to compare the maximum value of the Von Mises stress. The 95% blade span is chosen, because it is near the interface between the winglet and the blade.

Figure 23.

Von Mises stress at the blade root and 95% blade span. (a) Blade root, and (b) 95% blade span.

From Fig. 23, the distributions of Von Mises stress at the blade root of these two blades are nearly the same. The maximum of the Von Mises stress is below 750Mpa, which is under the allowable stress of K465 superalloy. At 95% blade span, before 50% blade chord, the Von Mises stress of the blade with w/p = 2.1% is higher than that of the original blade by only about 2Mpa, which is acceptable for the engine application [Reference Zhou and Zhong23]. Thus, for blade with w/p = 2.1%, the added mechanical stress due to the centrifugal, aerodynamic and thermal load may not pose a severe problem for its application.