In the present work, nine modification steam turbine low-pressure last blades with tubercles and the baseline geometry were simulated by a three-dimensional CFD analysis. Each of the modified blades was characterized by wavelength, amplitude, position, and thickness values defined by OTM. The results in terms of the blade axial torque of the nine modified tests were compared with the baseline value, and a physical explanation of the mechanism was given by looking at the flow characteristics around the bionic tubercles.
3.1. Blade Axial Torque
In order to better visualize the evolution in the blade axial torque given by bionic tubercles under different mass flow rate conditions, the non-dimensional blade axial torque was generated as follows:
which is the difference between the OTM test blade axial torque and the baseline value at the same mass flow rate condition normalized by the original blade axial torque.
Table 5 shows the non-dimensional blade axial torque comparison between the nine modified blades with bionic tubercles and the original blade. As illustrated in
Table 4, from the calculated blade axial torques of the nine different modified blades with bionic tubercles, these all have a visible positive effect on the blade axial torque at case 2. The maximum effect could increase the output torque by 33.32%. Thus, as the mass flow rate decreased, the corresponding flow rate was reduced when the blade axial torque of the turbine last stage became negative, demonstrating that those tubercles could effectively delay the turbine from entering the windage conditions, thereby improving the working capacity of the turbine unit.
For all nine tests, the blade axial torque of the last stage blade with tubercles also slightly increased correspondingly at case 1 when compared with the increment of the blade axial torque at case 2 and case 1. Test 3 achieved a maximum increase of output torque at33.32% for case 2, while the effect of the increase was the worst for case 1, only 0.90%, and the tendency seemed to reverse at test 1. Therefore, for this kind of steam turbine last stage tubercle modification, if the tubercles greatly improved the working capacity at low load, this may sacrifice the working capacity under the design conditions. Thus, when considering the specific bionic tubercle structure, the annual operating load of the turbine should be fully considered.
We now discuss the resulting non-dimensional blade axial torque of the nine tested blades with tubercles at case 2, since the bionic tubercles are supposed to can work even better under low load conditions. In order to study the influence of the four parameters of the bionic tubercles, including the wavelength, amplitude, position, and thickness on the output torque of the last stage blade, the blade axial torque of test 1, test 6, and test 7, corresponding to level 1 (1.09%) of the wavelength, has been added to calculate the average value. Similarly, the average value of different parameters at different levels can be calculated. The discrepancy between the average values could be considered as the effect of different parameters on the blade axial torque at different levels. In addition, the results revealed the effect of each level selected by the factor on the axial torque by comparing the magnitude of the
R. The greater the
R, the greater the change in the level of a factor and the greater effect on the axial shaft torque. The analysis results are illustrated in
Table 6.
From
Table 6, the amplitude of the tubercle had the largest influence on the blade axial torque of the turbine blade and the minimum thickness. Therefore, the amplitude of the bionic tubercle can be increased appropriately, and the thickness can be reduced appropriately. Moreover, within the parameter range of this study, if the wavelength, amplitude, and position of the tubercle increased, the blade axial torque value increased gradually, and as the thickness of the tubercle increased, its value decreased gradually. Within the scope of this study, the optimal tubercle parameters were when the wavelength was 2.19%, the amplitude was 0.77%, the position was 10%, and the thickness was 3%, which was when the blade axial torque could reach the maximum value.
3.2. Physical Mechanism Analysis
Next, we analyzed the flow characteristics of the best tubercle configuration (test 3) to reveal the physical mechanism.
Figure 8 is a schematic diagram of the limiting streamlines on the surface of the original blade and modified blade with bionic tubercles. As shown in this figure, under low load conditions, there was a large radial flow in the low-pressure last stage of the steam turbine. The steam at the blade root was affected by the backflow and flowed in the direction of the spanwise to discharge the last stage domain. The radial speed made the blade surface limiting streamlines develop at the root of the blade along the direction of the spanwise, which is why the present article considered putting the bionic tubercle on the blade tip.
There were two obvious reattachment lines above the middle part of the blade, and the distance between the two reattachment lines was larger in the middle span, which means that there was a larger separation vortex. Comparing the limiting streamlines of the baseline with a modified blade after the bionic tubercles were set on the suction side, there was a strong disturbing effect on the side, and small turbulent vortices were formed around the tubercles, which could strengthen the energy exchange between the mainstream and the pressure side boundary layer. The tubercles also shortened the distance between the two reattachment lines on the blade, which means that they could reduce the separation vortex in the flow channel to a certain extent.
For the purpose of analyzing the development of turbulent vortices formed by bionic tubercles, the present paper analyzed the axial velocity distribution on different streamwise sections, which are shown in
Figure 9, and cloud plots of the axial velocity distribution are illustrated in
Figure 10. As shown in the figure, the flow field in the rotor cascade was changed by the turbulent vortices, which formed on the upper and lower sides of the bionic tubercle. The axial velocity component of the fluid in the boundary layer was reduced accordingly for low-energy fluids converging here, while high-energy fluids in the mainstream supplemented the two sides of the tubercle by the suction effect of the turbulent vortices. Looking at the static pressure distribution comparison (
Figure 11), the accumulation of low-energy fluid in the turbulent vortex reduced the pressure on the suction side surface relative to the regular, and the reduced pressure propagated toward the trailing edge of the blade at a tubercle wavelength. The decrease in pressure increased the axial torque of the blades and the output power of the steam turbine.
On the other hand, the existence of turbulent vortices squeezed the mainstream fluid and moved the mainstream to the pressure side of the blade, thereby increasing the energy exchange between the mainstream and the pressure side boundary layer. Therefore, there was less low-energy fluid on the pressure side, which increased the axial velocity of the fluid near the pressure side. In the streamwise direction, the turbulent vortex generated by the bionic tubercle structure gradually developed toward the center of the flow domain, and its intensity gradually decreased.
The surface streamline distribution of the original type and the modified blade with bionic tubercles on 89.5% and 87.5% spanwise sections are reported in
Figure 12 where 89.5% of the span corresponded to the tubercle position, while 87.5% of the span was located between two adjacent tubercles, As shown in
Figure 13.
At 89.5% of the spanwise section, compared with the original blade, the modified blade formed a convergence of low-energy fluid after the tubercles, which developed from the boundary layer and then squeezed the mainstream. At 87.5% of the span, the flow boundary layer of the suction blade surface was thicker than the regular one affected by the two adjacent tubercles above and below, and this also squeezed the mainstream flow, enhancing the energy exchange between the mainstream and the separation vortex. Therefore, the larger the amplitude of the bionic tubercle, the more obvious the squeeze effect on the mainstream, which explained that the amplitude was the most important factor affecting the blade axial torque. The existence of the tubercles is similar to a kind of vortex generator passively controlling the flow.