1. Introduction
Corner separation is a typical flow phenomenon occurring at the junction of blade suction surfaces and end-walls in axial compressors [
1]. This phenomenon significantly deteriorates compressor performance by inducing passage blockage, reducing static pressure rise, increasing total pressure loss, and lowering overall efficiency. The achievement of high-pressure ratios, a critical requirement for high-performance compressor stages, necessitates the effective control of internal flow separation during the design process. Effective flow control can mitigate corner separation, reduce aerodynamic losses, and enhance the overall efficiency of axial compressors.
Flow control techniques are implemented in the corner regions of the cascade and are generally divided into active and passive categories. Active flow control technologies include methods like plasma actuation [
2], end-wall suction [
3], pulse jets [
4], and synthetic jets [
5]. These methods involve controlling the flow field by adding energy through auxiliary equipment, such as fluid injection or external force application. Nonetheless, this also increases the complexity of the design and manufacturing process. Alternatively, passive flow control technologies encompass non-axisymmetric end-walls [
6], vortex generators [
7], blade tip winglets [
8], end-wall fences [
9], and blade ribs [
10].
Natural organisms possess specific flow control mechanisms for them to adapt to changes in their environment. These mechanisms have served as inspiration for the construction of passive flow control devices. Wang et al. [
11] examined aerodynamic performance cascade configurations featuring smooth and non-smooth surfaces, inspired by the microgroove structures found in shark skin, under varying pressure gradients. Their simulation indicated that the non-smooth structure effectively reduced skin friction and turbulence intensity within the flow channel, leading to a significant reduction in total pressure loss. Dong et al. [
12] proposed a novel technique profiling leading-edge tubercles based on attenuation functions and sine waveforms inspired by the morphology of Humpback whale flippers. Their approach allowed for the adjustment of tubercle amplitude and wavelength through a sine function, revealing that smaller amplitudes could minimize additional losses in the mid-span region, while larger wavelengths promoted separation vortex formation. Lu et al. [
13] explored the impact of ellipsoidal dimples arranged in columns on cascade performance. Their findings showed that the inclusion of these dimples enhanced energy exchange between the mainstream flow and the low-energy region within the boundary layer near the wall, improving overall aerodynamic performance. This improvement enhanced the fluid’s anti-separation capability. It reduced total pressure loss by suppressing the migration of spanwise secondary and transverse flows, thereby decreasing the range and intensity of the corner and passage vortices. In their study, the authors designed bio-inspired structures of the cascade to reduce losses, but they discovered that the microgroove structure and the surface of the tubercles were excessively complex and expensive to machine.
Benner et al. [
14,
15] proposed an empirical approach to predict secondary losses in turbine cascades. Their analysis highlighted the influence of spanwise penetration depth, defined as the spanwise distance between the separation line and the end-wall at the trailing edge, on total pressure loss. Total losses were attributed to secondary losses, profile losses, and tip-leakage losses, with a strong positive correlation identified between profile losses and total losses. A reduction in the spanwise penetration depth of the climb secondary flow was found to decrease total pressure loss, thereby enhancing cascade performance. Shan et al. [
16] investigated the application of a micro-vortex generator upstream of the corner vortex (CV), particularly at a larger incidence angle, which effectively delayed stall onset. For the baseline cascade, this delay was noted at an incidence angle of 7.9°. Moreover, the addition of a vortex generator not only eliminated the stall behavior but also significantly reduced the total pressure loss. Cao et al. [
17] examined the control mechanism of an end-wall passage vortex generator (EVG) on the corner stall of a high-load cascade. They utilized vortex visualization to determine the position of the vortex structure. They used three-dimensional streamlines to observe the trajectory of the vortex and understand how the end-wall passage vortex generator improved the flow field in the cascade passage. In their study, they placed the end-wall passage vortex generator upstream of the corner vortex. This technique effectively mitigated the secondary flow losses in the cascade’s flow field.
Overall, we examined the literature on the effects of vortex structures on the distribution of total pressure loss. Many studies employ advanced vortex visualization techniques combined with projected 2D streamline analyses to thoroughly investigate the formation, development, and evolution of vortical structures within the flow field. These approaches enable researchers to clearly reveal complex 3D vortex structures and to better understand how such structures influence fluid dynamic characteristics and the spatial distribution of energy losses. This multifaceted analysis provides an important theoretical foundation and valuable references for the present study.
In our previous study [
18], we developed a single array of grass carp fish scales positioned upstream of the corner vortex to control corner separation and improve compressor cascade performance. This design aimed to reduce geometric complexity and computational demands while effectively addressing flow losses. This study builds on previous work by employing a fish scale array with low viscous friction drag to further control corner separation and improve compressor cascade performance. Using a combination of numerical simulations and wind tunnel experiments, we analyzed secondary flow structures through techniques such as vortex visualization, helicity analysis, axial velocity density (AVD), projected 2D streamlines, and spanwise penetration depth measurements. The cascade flow field was divided into four regions—the end-wall, passage, blade profile, and wake—to quantify total pressure loss and optimize the cascade configuration. These findings offer insights into applying additional bio-inspired features to mitigate adverse effects like stall, passage blockage, and flow separation, thereby enhancing compressor efficiency and performance.
3. Results and Discussion
To determine the influence of secondary flow losses and total pressure loss, we use helicity (with positive values represented counterclockwise and negative values represented clockwise), as well as projected 2D streamlines, to visualize the direction of rotation of the vortex. These metrics are combined to assess the contribution of vortex structures to flow losses.
Figure 10 illustrates the total pressure loss distribution at
x/
c = 1.1 downstream of the cascade outflow, along with helicity and the secondary flow distribution. In Case 1 and Case 2, the high total pressure loss region exhibited minor changes, indicating that the fish scale structure did not effectively suppress the passage vortex, leaving the total pressure loss distribution essentially unchanged. In contrast, Case 3 showed a significant reduction in the high-total-pressure-loss region. A detailed comparison of the helicity and projected 2D streamline distributions in Case 3 revealed that the passage vortex (PV) and concentrated shedding vortex (CSV) were influenced by the fish scale structure, which in turn caused the vortex structure to decrease and move toward the end-wall.
Figure 11 compares the spanwise variation in the pitch-averaged total pressure loss coefficient for the four cascade configurations. The results indicate that placing the fish scales near the leading edge of the suction surface (Case 1) failed to suppress the passage vortex, increasing total pressure loss. In Case 2, a mild suppressive effect on the passage vortex was observed, with a slight decrease in the total pressure loss coefficient in the spanwise direction from
z/
s = 0 to
z/
s = 0.1. In Case 3, the passage vortex structure was significantly suppressed, resulting in a notable decrease in the total pressure loss coefficient over the corresponding spanwise range.
Various vortex structures were identified in the flow field, namely the passage vortex (PV), corner vortex (CV), wall vortex (WV), concentrated shedding vortex (CSV), and trailing edge vortex (TEV). To investigate the impact of the fish scale array on cascade performance, the underlying mechanisms of these vortices were examined.
Figure 12 shows the vortex structure near the corner region in the cascade, visualized using
Q = 2.5 × 10
4 s
−2 and color-coded based on helicity. The horseshoe vortex (HV) was formed due to the presence of an adverse pressure gradient, causing the boundary layer fluid to roll up at the leading edge. The HV divided into two branches in front of the stagnation line at the leading edge (LE) of the blade. The stronger branch of the HV flowed over the pressure surface (PS), while the weaker branch flowed over the suction surface (SS). When the pressure-side horseshoe vortex (HV
ps) interacted with the cross-flow in the passage channel, it created what is known as the PV. The PV induced the WV on the SS. Therefore, the CSV formed near the trailing edge (TE). A comparison of Case 1 with the ORI case revealed minimal changes in the passage vortex region, with similar results observed in Case 2. However, in Case 3, the placement of the fish scale array significantly reduced the size of the passage vortex and shifted it closer to the end-wall. Additionally, Case 3 showed a smaller wall vortex (WV) on the suction surface compared to the ORI case, a phenomenon not observed in Cases 1 and 2.
To investigate the suppression effects of secondary flow produced by the fish scale structure on the cascade blade, further analyses of the projected 2D streamlines and the velocity distribution were conducted to understand the mechanism of flow loss.
Figure 13 shows a cross-section velocity distribution at a blade height of
z/
s = 4%, while
Figure 14 illustrates the local flow structure and the projected 2D streamlines of the cascade. The results indicate that the climbing vortex generated by the fish scale structure produced excitation in the near flow field. In Case 1 and Case 2, the fish scale structure was not optimally positioned, leading to an increase in the region of low-energy fluid, similarly to the ORI case. By contrast, Case 3 exhibited the most substantial reduction in the region with low-energy fluid, demonstrating the lowest loss of the fish scale cascade. Under this condition, the fish scale structure generated climbing vortex rolls that extracted energy from the wall boundary layer and injected it into the passage vortex region. The kinetic energy near the passage vortex could enhance the energy transfer around it, thereby reducing the volume of the low-energy-fluid region and mitigating flow losses caused by the passage vortex.
To investigate the relationship between the low-energy-fluid region and the total pressure loss in the cascade, axial velocity density (AVD) and total pressure loss coefficient distribution were analyzed.
Figure 15 shows the flow distribution of the total pressure loss coefficient in the cascade passage, with the low-energy fluid in the corner region identified by the iso-surface with an AVD of 5 kg/(s·m
2). At 25% chord length, the total pressure loss in the cascade was concentrated near the end-wall due to the boundary layer. At 50% chord length, the PV and the WV expanded, leading to a flow loss region extending towards the blades and the emergence of a high-total-pressure-loss area closely associated with the vortex structures. Between 100% and 110% chord lengths, the concentrated shedding vortex (CSV) and trailing edge vortex (TEV) appeared in sequence, interacting at the trailing edge of the blade and intensifying the flow loss in the wake region. In this configuration, the low-energy-fluid regions near the fish scale structure were reduced, along with the areas of high total pressure loss. This result confirms the effectiveness of the fish scale structure in enhancing the kinetic energy of the fluid near the grooves and reducing total pressure loss.
In Case 1 and Case 2, no significant suppressive effect on the passage structure was discovered, leading to increased total pressure loss. However, in Case 3, the low-energy-fluid region was substantially reduced in the areas of the CSV and the PV, resulting in decreased spanwise penetration depth. The separation line (marked by a red dotted line) was closer to the end-wall in Case 3 than in the other cases, correlating with the lowest total pressure loss. Combined analysis of
Figure 12 and
Figure 15 revealed that low-energy-fluid regions were located precisely at the secondary flow positions, corresponding to high-total-pressure-loss areas. The findings demonstrate that the fish scale array greatly suppressed the PV and CV, reducing the total pressure loss in both the cascade and the groove.
Figure 16 shows the limiting streamlines on the suction surface; the solid orange line represents the separation line for the ORI case, the red dotted line indicates the separation line for the other cases, and
hpd represents the spanwise penetration depth. The spanwise penetration depths in Case 1 and Case 2 were nearly identical to that of the ORI case, indicating no significant improvement. Conversely, Case 3 demonstrated a substantially reduced spanwise penetration depth compared to the ORI case, indicating a lower total pressure loss in this configuration. Overall, cases with diminished low-energy-fluid region and decreased total pressure loss also exhibited reduced spanwise penetration depth. This is consistent with previous findings by Wang et al. [
30] and Benner et al. [
14,
15], highlighting the effectiveness of Case 3 in mitigating corner separation and enhancing cascade performance.
To analyze the distribution of the total pressure loss coefficient across all cases, eleven slices were created along the chord direction to obtain the total pressure loss distribution of the flow field, as illustrated in
Figure 17. In Case 1, the fish scale structure failed to suppress the passage vortex structure and instead increased the total pressure loss by 0.4%. Similarly, in Case 2, the fish scale structure caused a slight increase in the total pressure loss by 0.3%. In contrast, Case 3 effectively suppressed both the passage vortex structure and the corner vortex structure, leading to a reduction in the low-energy-fluid region and achieving a 5.69% reduction in total pressure loss.
The computational domain was divided into four distinct areas to assess the distribution of total pressure loss across the cascades. These areas included the end-wall region, the passage region, the wake region, and the zone near the blade surface representing the blade profile. This division is illustrated in the three-dimensional (3D) diagram in
Figure 18a.
Figure 18b illustrates the total pressure loss in four regions for three cases. Each value represents the proportion of fish scale cases to ORI cases in the total pressure loss coefficient. In Case 1, the total pressure loss decreased in both the end-wall and wake regions but increased in the blade profile region. Case 2 showed reductions in the end-wall and passage regions, though losses in the blade profile region also increased. Notably, case 3 effectively reduced total pressure loss across all regions, particularly with reductions of 9.7% in the passage region and 3.35% in the end-wall region, indicating it as the most effective design configuration. This improvement is attributed to the placement of the bio-inspired fish scale structure ahead of the CV, which reduced the volume of the PV structure and the low-energy-fluid region near the end-wall, thereby enhancing overall cascade performance.
Figure 19 compares the limiting streamlines on the blade’s suction surface in Case 3, derived from numerical simulations and validated through experimental oil-film visualization. When the fish scale array was positioned ahead of the CV, the separation line observed in the numerical simulation closely matched the results from the oil-film visualization experiment. A comparison of
Figure 7 and
Figure 19 indicate that the fish scale array greatly suppressed the process of corner separation. Furthermore, the spanwise penetration depth in Case 3 was lower than in the ORI case, indicating a reduction in total pressure loss.