Numerical Study on the Influence of Inlet Turbulence Intensity on Turbine Cascades

Abstract

The turbulence intensity of the high-pressure turbine inlet plays an important role in the development of secondary flow and boundary layer evolution in the turbine passage. Unfortunately, current research often overlooks the coupling effect between boundary layer separation and endwall secondary flow, and lacks comprehensive exploration of loss variation. To complement existing research, this study utilizes numerical simulation techniques to investigate the evolution of the boundary layer and secondary flow in high-pressure turbine cascades under varying turbulence intensities, with experimental research results as the basis. Furthermore, the relationship between profile loss and endwall secondary flow loss is analyzed. The research results indicate that higher turbulence intensity can enhance the anti-separation ability of the boundary layer, thereby reducing the blade profile loss caused by separation in the boundary layer. However, higher turbulence intensities (Tu) enhance the development of secondary flow within the cascade, leading to a significant increase in secondary flow losses. Q-criterion methods are employed to display the vortex structures within the passage, while loss decomposition is leveraged to uncover the variations of different losses under different turbulence intensities (Tu of 1% and 6%).With the exception of a minor decrease in total pressure loss (Yp) when Tu increases from 1% to 2%, Yp demonstrates a substantial increase in all other cases with increasing Tu. Additionally, this study explains why the loss of high-pressure turbine cascades shows a trend of first increasing and then decreasing with the increase in inlet turbulence intensity.

1. Introduction

Improving the thrust-to-weight ratio of aircraft engines has always been one of the main goals in aircraft engine research [1]. In recent years, with the emergence of small unmanned aerial vehicles, the development of compact aircraft engines has become an important research trend [2,3]. Due to the reduction in size of aircraft engines, the coupling effect between the combustion chamber and the turbine has become increasingly apparent [4]. Modern combustion chambers adopt rich burn–quick quench–lean burn technology and lean-premixed combustion technology, resulting in non-uniform temperature distribution (hot spots), strong swirling flow, and high turbulence intensity at its outlet, which significantly affects the aerothermal performance of the high-pressure turbine stage [5].

Turbulence intensity is one of the important flow characteristics of the exhaust flow from the combustion chamber, which not only has a significant influence on the heat transfer on the surface of the high-pressure turbine, but also affects the aerodynamic performance of the high-pressure turbine and cannot be ignored [6,7]. Art et al. [8] conducted a detailed study on noncooled transonic linear blade cascades with an outlet Reynolds number of 0.5 × 10⁶ < Re < 2 × 10⁶, an outlet Mach number of 0.7–1.2, and turbulence intensity of 1% to 6%. When the outlet Reynolds number is 590,000, the inlet turbulence changes from 1% to 6%, causing the transition position on the suction side to shift by 10% of the surface length. Nix et al. [9] have shown through experiments that increasing Tu from 2% to 16% increases heat transfer on the pressure side by 50%, while having little effect on the suction side surface. This indicates that the strong acceleration of the suction surface airflow reduces the local turbulence intensity to a sufficiently low amplitude, thus not affecting the transition characteristics. The impact of turbulence levels on flow physics has been reported in the literature and has received renewed attention [10,11]. Therefore, the effects of turbulence on blades have always been a research focus. It is necessary to study the effects of turbulence intensity on boundary layer separation and secondary flow.

Researchers have conducted extensive studies on surface boundary layer separation of blades. Factors such as blade surface roughness [12,13], Reynolds number [14], incoming flow turbulence intensity [15], blade loading distribution [16], upstream wakes [17,18], and pressure gradient [19] all affect the development of the boundary layer on the blade surface. Van Treuren et al. [20] studied the flow characteristics of turbine blades under three low Reynolds numbers (60,000, 108,000, and 165,000) and fifteen turbulence intensities (1.89~19.87%) in a steady-state cascade wind tunnel to predict the effects of Reynolds number and turbulence intensity on the onset of flow separation, flow separation region, and reattachment location. By quantifying the changes in separated flow caused by variations in Reynolds number and turbulence intensity, the operational conditions of the turbine under different turbulence intensity environments were described well. The research results show that separation and transition locations are related to Reynolds number and upstream free stream turbulence intensity (FSTI), and can be predicted. These studies illustrate that boundary layer separation is a common phenomenon in turbine operation, and suppressing boundary layer separation can effectively reduce profile loss, which can be achieved by increasing turbulence intensity. Thole et al. [21] explored the influence of large-scale high-intensity turbulence on secondary flow losses, blade exit losses, and outlet turbulence characteristics based on experiments using four-blade linear cascades. The results show that increasing free stream turbulence leads to significantly higher secondary flow losses and dissipation losses. Qu et al. [22] and others found in their study of turbine cascades that the generation of separation bubbles inhibits the separation flow near the center of the endwall, which has a certain influence on the endwall secondary flow. Additionally, a thick boundary layer leads to a stronger vortical structure within the cascade passage, exacerbating turbulent dissipation losses.

In summary, although a considerable amount of research has focused on the impact of turbulence intensity on surface boundary layer separation, transition, and secondary flow losses, there is still relatively little research on the surface boundary layer and secondary flow of high-pressure turbine blades, particularly regarding the interaction between boundary layer separation bubbles and secondary flows. Therefore, further investigation and analysis are required. Taking high-pressure turbine cascades [23] as the research object, this paper studied the separation and transition of the cascade surface boundary layer under different turbulence intensity inlet conditions. It also employs vortex identification methods to extract the three-dimensional secondary vortex structure in the cascade passage, and conducts a detailed analysis of the development and evolution of the endwall secondary flow and the reasons for the increase in secondary flow losses. Finally, the losses of the cascade surface boundary layer and endwall secondary flow are correlated through total pressure loss for further discussion.

2. Materials and Methods

The research object of this study is the Harrison high-pressure turbine rotor cascade [23], as shown in Figure 1. The detailed parameters of Harrison cascade are shown in

Table 1. Geometric and aerodynamic parameters of Harrison cascade [24].

Design Parameters	Symbol	Value
Chord length (mm)	C	278
Axial chord length (mm)	Cax	223
Blade height L (mm)	L	300
Pitch (mm)	S	230
Inlet flow angle (°)	α	40
Outlet flow angle (°)	β	−66.8
Outlet Mach number	Ma	0.14
Outlet Reynolds number	Re	8.5 × 105~9 × 105

. C and Cax are chord length and axial chord length, respectively, S is pitch, L is blade height, and α and β are inlet and outlet airflow angles, respectively. Under design conditions, outlet Mach number is 0.14, Re is 7.8 × 10⁵, and the flow field in the cascade passage maintains subsonic speed.

Mesh quality has an important influence on numerical simulation results, so adopting reasonable mesh topology and fully structured mesh division is the key to reduce the number of elements and improve the calculation accuracy and efficiency. In this paper, the commercial software Numeca-IGG17.1 is used to construct a fully structured mesh for the flow domain of high-pressure turbine (HPT) cascade passage to ensure the mesh quality. In this study, the minimum mesh orthogonality of all cascade computational domain models is greater than 45, the maximum mesh aspect ratio is less than 1000, and the maximum mesh extension ratio is less than 1.6. The mesh division of the computational domain is shown in Figure 2. The distance from the inlet to the leading edge of the cascade is 1.5 times the axial chord length, and the distance from the outlet to the trailing edge of the blade is 2 times the axial chord length of the blade. On the spanwise boundary, adiabatic no-slip wall condition is applied; on the periodic surface boundary, periodic boundary conditions are applied; the blade surface is modeled as an adiabatic no-slip wall; the fluid model adopts ideal gas model; the total inlet pressure is 1.016 atm, and the outlet static pressure is 1 atm.

The number of grid cells has a certain influence on the accuracy of numerical calculation. In order to verify the independence between the results and the number of grids, different numbers of grids are built, including 2 million, 3 million, 4 million, 5 million, and 6 million. By comparing the change in total pressure loss coefficient (Yp) at cascade outlet, the influence of different grid numbers on numerical simulation results was evaluated. As shown in Figure 3, when the number of grids reaches 5 million, the change in total pressure loss coefficient at cascade outlet is small, and the relative deviation is about 0.22%. Therefore, considering the calculation cost and calculation accuracy, grids with a total number of 4 × 10⁶ are used in this research.

The static pressure coefficient is defined as:

$$\mathrm{C}\mathrm{p}={\displaystyle \frac{{\mathrm{P}}_{0,\mathrm{i}\mathrm{n}}-{\mathrm{P}}_{\mathrm{s},\mathrm{l}\mathrm{o}\mathrm{c}}}{{\mathrm{P}}_{0,\mathrm{i}\mathrm{n}}-{\mathrm{P}}_{\mathrm{s},\mathrm{i}\mathrm{n}}}}$$

(1)

The total pressure loss coefficient is defined as:

$$\mathrm{Y}\mathrm{p}={\displaystyle \frac{{\mathrm{P}}_{0,\mathrm{in}}-{\mathrm{P}}_{0,\mathrm{loc}}}{{\mathrm{P}}_{0,\mathrm{in}}-{\mathrm{P}}_{\mathrm{s},\mathrm{in}}}}$$

(2)

In the formula, ${\mathrm{P}}_{0,\mathrm{i}\mathrm{n}}$, ${\mathrm{P}}_{\mathrm{s},\mathrm{i}\mathrm{n}}$, ${\mathrm{P}}_{\mathrm{s},\mathrm{l}\mathrm{o}\mathrm{c}}$, ${\mathrm{P}}_{0,\mathrm{loc}}$ correspond to the average total pressure at the inlet, the average static pressure at the inlet, the local average static pressure, and the local average total pressure, respectively. The above average method adopts mass average.

ANSYS CFX 18.1 was used to solve the Reynolds-averaged Navier–Stokes equation of the HPT. The finite volume method was used as the numerical method; the second-order upwind scheme was adopted for spatial discretization; the second-order backward Euler difference was used for time discretization. The shear stress transport (SST) turbulence model and γ-θ transition model [25] were used to calculate the separation and transition of the boundary layer. To meet the requirements of the SST turbulence model, the maximum nondimensional wall distance (y+) was less than 1 at the first node from the solid walls (blade and hub endwall). When calculating convergence, the root mean square of residuals decreases to 10⁻⁶. In order to verify the reliability of the numerical method in this paper, the results were compared with the experimental data. The distribution of the static pressure coefficient (Cp) on the blade surface is illustrated in Figure 4, comparing numerical results with experimental data. The predicted Cp distribution closely matches the experimental findings along the blade’s span. Numerical analysis indicates a small separation bubble on the suction side of the blade beyond 80% axial chord, a feature not clearly represented in the experimental Cp data. Figure 5 presents the limit streamlines on the blade’s suction side using an oil flow method, with the numerical results accurately predicting the location, size of the separation bubble, and the vortex structure. To further validate the computational accuracy of the turbine near-endwall region, the computed results using the aforementioned numerical methods were compared with experimental results under identical boundary conditions. Figure 6 compares the vorticity cloud maps at 103% Cax and 123% Cax downstream of the blade exit, showing prominent corner vortex, counter vortex, and passage vortex at the blade exit. The computed results exhibit good agreement with the experimental data, effectively capturing almost all the flow characteristics of the HPT blade, including the size and location of the counter vortex and passage vortex. However, the predicted vortex core strength exceeds the experimental results, likely due to inconsistencies between the inlet endwall boundary layer state and the experimental data. The present RANS simulations effectively capture the flow conditions on the blade surfaces and the distribution of endwall vortices, meeting the requirements for general research. It can be concluded that the present computations are reliable.

3. Results and Discussion

3.1. The Results of the Effect of Turbulence Intensity on Cascades

Total pressure loss coefficient (Yp) is widely regarded as a key parameter for reflecting the energy consumption and flow characteristics inside a turbine. In turbine research, reducing turbine losses is a goal that is pursued. The total pressure loss coefficient is defined in Formula (2). As shown in Figure 7, with the increase in turbulence intensity, the total pressure loss of the blade row significantly increases. When turbulence intensity increases from 1% to 26%, the total pressure loss increases by 14.6%. Under high turbulence intensity, the increase in loss is progressive. An anomaly occurs at low turbulence intensity, where the total pressure loss peaks at Tu = 2%, but at Tu = 4%, 6%, and 8%, the total pressure loss coefficients are significantly lower than at Tu = 2%, decreasing by 6.7%, 2.6%, and 0.8%, respectively. Given the above circumstances, this paper selects several special operating conditions at low turbulence intensity for investigation.

In the cascade passage, due to the influence of turbulence intensity, variations not only exist in secondary flow loss but also in profile loss across different spanwise and circumferential regions. Figure 8 and Figure 9 depict the distribution of total pressure losses downstream of the cascade. These figures clearly demonstrate that areas with high losses are predominantly concentrated in the boundary layer along the suction surface, as well as in the secondary flow and corner regions. Through analysis of the spanwise distribution curve of circumferential average total pressure loss, it is evident that blade profile loss decreases with increased turbulence intensity. However, secondary flow losses exhibit a noticeable increase. Comparing these findings, it is apparent that as turbulence intensity increases, the high-loss region associated with secondary flow moves closer to the blade. This trend becomes less pronounced when Tu > 2%, indicating that turbulence intensity also influences the spanwise migration of the secondary flow.

The near-endwall flow structure exhibits significant differences under varying inlet turbulence intensities. Figure 10 compares the total pressure loss distribution downstream of the cascade at different axial positions for turbulence intensities of 1% and 6%. It is evident that with higher turbulence intensity, the high-loss region downstream of the cascade becomes more extensive. Specifically, Figure 10c shows that at an axial position of Cax = 140% in the near-end zone, there is only one high-loss region under low turbulence intensity (Tu = 1%). However, under higher turbulence intensity (Tu = 6%), the high-loss region expands significantly, presenting two closely spaced high-loss cores corresponding to the counter vortex and passage vortex. The development of endwall secondary flow has always been a focal point in turbine aerodynamic research.

Figure 11 uses the flood of secondary kinetic energy (C_SKE) to illustrate the distribution of secondary kinetic energy intensity downstream of the turbine cascade. Regions with higher secondary kinetic energy closely coincide with areas of higher total pressure loss, and the intensity of secondary kinetic energy exhibits a positive correlation with turbulence intensity. As the distance from the cascade exit increases, the intensity of secondary kinetic energy gradually decreases.

Figure 12 displays the distribution of vorticity downstream of the cascade. The counter-rotating vortex and passage vortex are precisely located in regions of high total pressure loss. With an increase in turbulence intensity, the vorticity intensity also increases, causing the distance between the cores of the two vortices to expand. This results in the two high-loss cores observed in Figure 10f. Under low turbulence intensity, due to the lower vorticity intensity, the high total pressure loss core is positioned exactly in the middle region between the two vortices.

Ref. [26] provides a detailed definition of the coefficient of secondary turbulent kinetic energy (C_SKE).

The SKE is defined as

$$\mathrm{S}\mathrm{K}\mathrm{E}={\displaystyle \frac{1}{2}}\mathsf{\rho }\left({\mathrm{v}}_{\mathrm{S}\mathrm{E}\mathrm{C}}^2+{\mathrm{u}}_{\mathrm{S}\mathrm{E}\mathrm{C}}^2\right)$$

(3)

$${\mathsf{\nu }}_{\mathrm{S}\mathrm{E}\mathrm{C}}=-\mathrm{w}\sin \mathsf{\phi }+\mathsf{\nu }\mathrm{c}\mathrm{o}\mathrm{s}\mathsf{\phi }$$

(4)

$${\mathrm{u}}_{\mathrm{S}\mathrm{E}\mathrm{C}}=\mathrm{u}$$

(5)

where $\mathrm{u}$, $\mathrm{v}$, and $\mathrm{w}$ are the velocity components in the spanwise, pitchwise, and axial directions, respectively. ${\mathrm{v}}_{\mathrm{S}\mathrm{E}\mathrm{C}}$ and ${\mathrm{u}}_{\mathrm{S}\mathrm{E}\mathrm{C}}$ and are the secondary (SEC) velocities. φ is the mass averaged exit flow angle in a plane. The non-dimensional secondary kinetic energy is defined as

$${\mathrm{C}}_{\mathrm{S}\mathrm{K}\mathrm{E}}={\displaystyle \frac{{\mathsf{\nu }}_{\mathrm{S}\mathrm{E}\mathrm{C}}^2+{\mathrm{u}}_{\mathrm{S}\mathrm{E}\mathrm{C}}^2}{{\mathrm{U}}_{\mathrm{i}\mathrm{n}}^2}}$$

(6)

where ${\mathrm{U}}_{\mathrm{i}\mathrm{n}}$ is the mass averaged velocity at the inlet.

The streamwise vorticity coefficient is defined as:

$${\mathrm{w}}_{\mathrm{s}}={\displaystyle \frac{{\mathrm{w}}_{\mathrm{x}}\mathrm{u}+{\mathrm{w}}_{\mathrm{y}}\mathrm{v}+{\mathrm{w}}_{\mathrm{z}}\mathrm{w}}{\sqrt{{\mathrm{u}}^2+{\mathrm{v}}^2+{\mathrm{w}}^2}}}$$

(7)

$${\mathrm{C}}_{\mathrm{w}\mathrm{s}}={\displaystyle \frac{{\mathrm{w}}_{\mathrm{s}}\times \mathrm{C}\mathrm{a}\mathrm{x}}{\sqrt{{\mathrm{u}}^2+{\mathrm{v}}^2+{\mathrm{w}}^2}}}$$

(8)

where $w_x$, $w_y$, and $w_z$ are the vorticity of spanwise, pitchwise, and axial directions.

3.2. Separation and Transition of Suction Surface Boundary Layer in Different Tu

Boundary layer separation on the surfaces of turbine cascades has a detrimental impact on turbine efficiency. Therefore, accurately determining the position of boundary layer separation is crucial before exploring methods to prevent or mitigate separation. Researchers have utilized different approaches to identify boundary layer separation, including analyzing the constant region (highlighted in the red box area in Figure 13a of the cascade suction surface load (Cp) distribution and determining the position where the blade surface friction coefficient (Cf) becomes negative (as shown in Figure 14)) [22,23,24,27]. In this section, these two methods are combined with the velocity distribution of the suction surface flow field to precisely capture the transition characteristics of boundary layer separation on the suction surface, considering variations in inlet turbulence intensity.

Figure 13a illustrates the distribution of the blade surface static pressure coefficient (Cp) along the axial direction (z) at the 50% spanwise position for five different levels of incoming turbulence intensity. Remarkably, the load distributions on the blade surface exhibit high consistency across the different turbulence intensities, indicating that the main flow structures within the flow passage are not significantly influenced by variations in incoming turbulence intensity.

As shown in Figure 13, it is evident that at the 50% spanwise position, the load distribution on the blade surface fluctuates significantly at x/Cax = 80%. The red line (Tu = 1%) and black line (Tu = 2%) exhibit the most significant changes, followed by the green line (Tu = 4%). Taking the black line as an example, its load distribution curve displays a distinct gradient decline, forming a so-called “constant pressure platform” [28]. This phenomenon is attributed to boundary layer separation on the blade surface, where the boundary layer exhibits weak backflow in the separation region. If separation is severe and large-scale, it significantly impacts the flow efficiency. Many researchers utilize the size and length of separation bubbles to define the extent of separation regions. Figure 13 (right) also reveals that the separation bubbles formed by the incoming flow corresponding to the black line are larger than those formed by the red line. This indicates that turbulence intensity of the incoming flow influences the development of the boundary layer on the blade surface. As turbulence intensity increases, the boundary layer separation bubble becomes smaller. When Tu = 4%, the separation bubbles practically disappear, indicating smoother development of the boundary layer under this condition. When Tu > 4%, the separation bubble completely vanishes.

After boundary layer separation occurs, low-energy fluid accumulates and backflows on the surface of the cascade. As a result, the friction coefficient (Cf) of the cascade surface in the boundary layer separation region becomes negative. Figure 14 illustrates the distribution of friction coefficient along the blade surface under different incoming flow conditions with varying turbulence intensities. The transition from positive to negative friction coefficient indicates boundary layer separation, while the transition from negative to positive signifies the reattachment of separated flow. Furthermore, it can be observed that when the incoming turbulence intensity is 1%, the boundary layer separates at approximately 80.7% of the axial chord (x/Cax = 0.807), and the separated flow reattaches at 88.6% of the axial chord (x/Cax = 0.886). Similarly, for an incoming turbulence intensity of 2%, the boundary layer separates at around 81.1% of the axial chord (x/Cax = 0.811), and reattachment occurs at 86.7% of the axial chord (x/Cax = 0.867). Conversely, at turbulence intensities of 6%, 8%, and 10%, no boundary layer separation is observed.

In summary, higher turbulence intensity in the incoming flow reduces the likelihood of boundary layer separation. Conversely, lower turbulence intensity makes it easier for the boundary layer to separate, resulting in a larger separation area. These findings indicate that in the analysis of Figure 13, the sudden flattening of the static pressure coefficient gradient and the formation of a “constant pressure platform” effectively reflect the degree of boundary layer separation and the size of the separation area formed.

It is evident from Figure 14 that each curve of the friction coefficient (Cf) follows a similar three-stage pattern: a descending stage, a sudden rise with a steep gradient, and a subsequent gradual decline. The wall shear stress is often used to assess the flow conditions near the wall. Many researchers define the region where shear stress increases sharply as the boundary layer transition zone. In Figure 14, the points marked with red five-pointed stars can be approximately regarded as the start points of boundary layer transition. As for the end points of transition, it can be identified as the extreme point where the Cf curve rises sharply and the gradient reaches zero at the onset of transition. It is evident that as the incoming turbulence intensity increases, boundary layer transition occurs earlier. This is because higher turbulence intensity corresponds to a significant increase in turbulent kinetic energy. When the laminar boundary layer develops to a certain extent, it becomes more influenced by the strong momentum of the mainstream flow, which promotes early boundary layer transition. This has a positive impact on the flow structure within the passage. Overall, these observations contribute to a better understanding of the flow behavior and provide insights into the promotion of flow structure.

The development of the boundary layer is closely associated with the flow structure on the blade surface. To effectively visualize the evolution of the boundary layer near the separation region on the suction surface, this paper presents a comparative analysis of the velocity along the wall of the suction surface for four different turbulence levels, as illustrated in Figure 15. This figure clearly demonstrates the changes in separation bubble size, the axial location of the separation starting point, and the reattachment point of the boundary layer.

At a turbulence level of 1% in the incoming flow, the separation bubble attains its maximum thickness and length. The boundary layer initiates thickening from approximately 0.7 times the axial chord length, resulting in the accumulation of low-energy fluid on the wall area and the formation of separation bubbles characterized by backflow. This substantially raises the extent to which the boundary layer is lifted. The presence of low-energy fluid within the boundary layer has a direct impact on the flow passage, causing it to narrow and influencing the mainstream flow. The separation phenomenon concludes at an axial chord length of 0.94, with the boundary layer reattaching to the blade surface. At this point, the previously adhered layer of low-energy fluid on the blade surface becomes significantly thinner, transitioning into a turbulent boundary layer. This transition occurs due to the intense momentum exchange between the boundary layer and the mainstream flow following the lifting of the boundary layer, facilitating the transfer of energy from the mainstream to the low-energy fluid and resulting in the formation of a turbulent boundary layer.

However, the accumulation of low-energy fluid in the separation bubble region causes a constriction in the flow passage, adversely affecting the mainstream flow and leading to increased energy loss. This hampers the achievement of an optimal flow state within the cascade. Therefore, it is imperative to minimize such occurrences in order to maintain a favorable flow structure.

To validate the transition of the boundary layer near the separation bubble region, Figure 15 offers a visual representation, while Figure 16 presents velocity profiles at five axial positions for four different turbulence levels. At x/Cax = 0.78, the velocity patterns clearly indicate a laminar boundary layer across all turbulence levels. However, at x/Cax = 0.81, the velocity profile curve for Tu = 6.0% gradually shifts towards a turbulent boundary layer, exhibiting a fuller profile. This suggests the initiation of boundary layer transition. By x/Cax = 0.84, the velocity pattern of the boundary layer with Tu = 6.0% has completely transitioned into a turbulent boundary layer, consistent with the earlier analysis in Figure 14, where the rise in the Cf curve gradient was identified as the transition starting point. Similarly, at x/Cax = 0.87, the velocity pattern of the boundary layer with Tu = 4.0% starts to show a saturation trend, indicating the onset of transition. Finally, at x/Cax = 0.90, the velocity pattern of the boundary layer with Tu = 4.0% has fully transformed into a turbulent boundary layer, resembling the behavior observed for Tu = 6.0%. This further validates the proposed transition starting and ending points and affirms the accuracy of this study.

In conclusion, the precision of the boundary layer transition analysis put forth in this study is reinforced by examining the distribution of velocity profiles. Additionally, the analysis presented in Figure 16 establishes the starting points of the transition, aligning with previous research findings.

3.3. Flow Characteristics in the Blade Endwall in Different Tu

Different inlet turbulence intensities result in a thickening of the boundary layer upstream of the cascade leading edge. As shown in Figure 17, when the turbulence intensity increases from 1% to 6%, the boundary layer thickness more than triples. Figure 18 compares the turbulent kinetic energy coefficients under different turbulence intensities. The turbulence intensity increased from 1% to 4%, and the peak of C_SKE increased by more than three times. The turbulence intensity increased from 1% to 4%, and the peak of C_SKE increased by more than three times. The significant increase in C_SKE is concentrated in the downstream area of 50% x/Cax, which is also the location where secondary flow is rapidly developing.

Different turbulence intensities have varying effects on the migration characteristics of secondary flow and the pressure distribution on the cascade surface. To study these patterns more accurately, Figure 19 presents the load coefficient distribution at three positions (10% span, 30% span, and 50% span) on the high-pressure turbine cascade under different turbulence intensities. A significant change in load distribution is observed at the 10% span position compared to the other positions (as shown by the black dashed line in Figure 19). Specifically, the load factor at the leading edge of the blade decreases, while the load on the cascade surface near the trailing edge increases. This indicates a decrease in the pressure difference between the suction and pressure surfaces at the leading edge, resulting in increased pressure on the suction surface while maintaining the pressure on the pressure surface unchanged. Conversely, the suction surface pressure decreases at the trailing edge. Importantly, these phenomena become more pronounced with increasing turbulence intensity. This is because turbulence and vortices are generated as the airflow passes through the cascade passage, and these disturbances accumulate at the trailing edge of the blade, forming larger vortex structures. These structures impede airflow into the trailing edge, creating a lower static pressure area at the root of the blade. With higher turbulence intensity, the vortex structure becomes more distinct, resulting in even lower static pressure and increased load coefficient at the trailing edge of the cascade.

Figure 20 illustrates the static pressure distribution on the suction surface and endwall of the cascade. The large bending curvature of the cascade leads to the formation of a low-pressure zone in the flow passage. This region is typically located at the throat of the cascade and is influenced by a significant velocity gradient. As the fluid passes through the throat, it gradually slows down, leading to an increase in pressure. Near the trailing edge, a reverse pressure gradient forms, often causing an elevated risk of boundary layer separation. This phenomenon contributes to the formation of separation bubbles, as mentioned earlier.

Observing and analyzing fluid flow trajectories on the turbine blade’s surface provides valuable information about secondary flow, centrifugal force effects, and energy dissipation. Such knowledge plays a crucial role in turbine design optimization and performance analysis. Figure 21 presents the distribution of limit streamlines on the endwall and suction surface to demonstrate flow trajectories on the blade surface and the influence of turbulence intensity on the development of separation bubbles and secondary vortex in the endwall. The limit streamline on the suction surface describes three-dimensional flow separation in the cascade passage, showing the migration path of the horseshoe vortex suction surface branch (S1), passage vortex (S2), and corner vortex (S3) from the endwall to the blade center. The image provides intuitive information on the size and position of separation bubbles on the suction surface. It can be observed that the spanwise length of separation bubbles accounts for approximately 40% of the cascade’s span under low turbulence intensity. Figure 22 shows the change in the ratio of radial velocity to axial velocity, which indicates that the velocity of secondary migration from the suction surface to the center of the blade is proportional to turbulence intensity.

However, due to the closed separation bubbles on the suction surface at low turbulence intensities, the migration of S1 to the center of the blade is impeded. Consequently, the distance between S1 and S2 is relatively small at the trailing edge of the cascade. However, as the turbulence intensity increases and the separation bubble disappears, S1 loses its blocking effect, causing S1 and S2 to approach each other and then gradually separate as they migrate to the center of the blade. This has an impact on the subsequent development of the trailing filament vortex, and the follow-up Figure 21 proves this conclusion. Therefore, the separation state of the boundary layer on the suction surface is closely related to the secondary flow in the endwall.

To further investigate the influence of inlet turbulence on the energy loss in the endwall of a high-pressure turbine cascade, Figure 23 presents the results of static entropy at different axial positions within the cascade passage, and provides a three-dimensional streamline distribution in the endwall. The static entropy distribution shows that higher turbulence intensity results in greater energy loss. Conversely, in the high-loss region (red region), high turbulence intensity inhibits boundary layer separation, resulting in a reduction in the area of profile loss region (as shown by the black rectangle in Figure 23). Generally, higher turbulence intensity can decrease profile loss caused by separation but introduces higher secondary flow loss.

The strip streamlines in the Figure 24 demonstrate the trajectory of the passage vortex’s formation. The passage vortex originates from the suction surface branch of the horseshoe vortex at the cascade’s leading edge. As the mainstream enters the cascade passage, the flow passage gradually narrows, and the fluid begins to accelerate. Under the shear stress of the endwall, the streamlines near the endwall interweave, indicating the emergence of numerous vortex mechanisms. With increased turbulence intensity in the flow field, the vortex system becomes more prominent, migrates along the suction surface towards the cascade center, and gradually separates from the cascade surface.

It is very important to clarify the development process of secondary flow to reduce the loss caused by secondary flow. Vortex identification adopts the Q-criterion method. The Q-criterion vortex identification method is currently recognized and widely accepted as a method for identifying turbulent vortex structures [29]. Figure 24 clearly shows that as the turbulence intensity increases, the identifiable vortex system becomes more obvious. When Tu = 1%, we can observe two tiny horseshoe vortices. However, these horseshoe vortices are so weak along the suction surface that they almost disappear when they migrate to the suction surface, which echoes the phenomenon that the proportion of low shear stress zone at the leading edge of the cascade is large. Usually, the high shear stress region of the endwall mainly occurs in the region affected by strong interference and strong secondary flow, which is related to the characteristics of higher turbulence intensity. The higher turbulence intensity will result in the formation of a stronger shear stress zone. After the passage vortex rises off, especially in the first half of the passage, the shear stress coefficient rises sharply. It can be observed that with the increase in turbulence intensity, the strong shear stress region extends to the region near the trailing edge, which means that the loss of the endwall boundary layer in this region also increases.

In order to further reveal the development characteristics of vortex structure in the passage of high-pressure turbine cascade under different turbulence intensities, Figure 25 shows the vortex iso-surface map identified by Q-criterion and the total pressure loss distribution perpendicular to the axial direction near the trailing edge of the cascade. Many researchers extensively use the Q-criterion for vortex identification in the study of turbomachinery [30,31]. It can be seen from the whole vortex system structure that the counter vortex developed from the pressure surfaces of adjacent blades is mixed with the angular vortex. Due to the insufficient driving force of the pressure surface branch of horseshoe vortex, the low-energy fluid in the endwall boundary layer has a small rolling amplitude. In contrast, the passage vortex develops from the horseshoe vortex along the suction surface, and develops rapidly due to the large transverse pressure gradient. Eventually, the passage vortex strengthens and begins to approach the mid-blade position in the A region. The above characteristics are the common characteristics of vortex system development in the flow passage.

In order to study the variation in different losses in the cascade passages in a turbine, including secondary loss (SEC), suction surface profile loss (SBL), free flow loss (FS), and endwall loss (EW), the main positions and methods of these losses are determined in Figure 26 according to the distribution relationship of the total pressure loss nephogram. Figure 27 shows the proportion of these losses at different axial positions (Cax = 0%, Cax = 33.3%, Cax = 66.6%, Cax = 100%) under Tu = 1% and Tu = 6% conditions.

By comparison, it can be found that the secondary flow loss caused by the vortex system increases gradually with the mainstream from leading edge to trailing edge of cascade, and the secondary flow loss is greater under high turbulence. This is closely related to the structural strength of the generated vortex system, which shows that the secondary flow loss is mainly contributed by the vortex system. The proportion of free flow loss and endwall profile loss decreases along the axial direction, not because their true losses decrease, but because the strong secondary flow leads to an increase in the proportion of loss at the same axial position, which makes the relative proportion of free flow loss and endwall profile loss decrease. It is worth noting that the performance of profile loss on suction surface is better at high turbulence than at low turbulence. This is because the high turbulence intensity inhibits the boundary layer separation, which is consistent with the previous analysis results.

4. Conclusions

By analyzing the influence of different turbulence intensities on the turbine inlet, this study investigates the development and evolution of the turbine cascade boundary layer and uncovers its underlying mechanism. Furthermore, it examines the effect of turbulence intensity on vorticity generation in the turbine passage and the loss characteristics of the vorticity system behind the cascade during the development process. Based on the research conducted, the conclusions can be summarized as follows:

• The separation of the boundary layer on the suction surface of the turbine cascade is a common occurrence. Severe separation results in the accumulation of low-energy fluid on the cascade surface, thus reducing the efficiency and aerodynamic performance of the turbine. However, higher turbulence intensity at the inlet of the high-pressure turbine cascade improves this separation phenomenon. Increased turbulence intensity restricts the size of boundary layer separation bubbles and induces an earlier transition, which positively affects the overall flow state of the cascade.
• Higher turbulence intensity corresponds to a more complex flow field, characterized by enhanced development of secondary flow near the endwall. This ultimately leads to a significant increase in loss within the turbine cascade passage.
• In terms of the total pressure loss generated from the leading edge to the trailing edge of the turbine cascade, within a certain range of turbulence intensity, higher turbulence intensity can reduce the total pressure loss. However, this is mainly attributed to the suppression of separation flow loss in the boundary layer of the cascade.