Vortex Unsteadiness in the Endwall Region of a High-Lift Low-Pressure Turbine Passage

A major focus of turbine aero research is on the flow along the endwalls (i.e., flow adjacent to the hub and case), which is comprised of secondary fluid motion to the through-flow. The endwall flow region is characterized by three-dimensional vortical flow structures that affect both the aerodynamic performance and the heat transfer characteristics of the turbine design.

Numerous descriptions of the general, time-averaged, endwall flow topology can be found in the literature, which conveys the position and orientation of the major vortices found in a turbine passage, see Refs. [1–5]. There is consensus on the existence of several key flow structures, such as a horseshoe vortex structure that forms near the leading-edge junction, a large passage vortex, and a counter-rotating trailing edge shed vortex.

While the flow has been studied broadly in a time-average sense, the endwall flow structures exhibit a temporal behavior that is not well understood. For example, the horseshoe vortex at the leading-edge junction exhibits an unsteady behavior [4]. Endwall vortices through the middle of the passage also fluctuate in position and strength over time, which has been postulated to be related to the leading-edge dynamics [6]. It is important to consider the temporal characteristics in order to better relate the flow physics in the endwall region to improved heat transfer/thermal designs and aerodynamic efficiency.

The leading-edge junction flow about symmetric airfoil shapes has been studied by a number of researchers—see for example the summary by Gand et al. [7]. A leading-edge vortex forms and extends along the wing forming a horseshoe vortex structure. Some authors have reported various phenomena downstream from the leading-edge region, such as vortex meandering [7,8] and a corner separation [9]. The junction flow exhibits bimodal behavior, as first reported by Devenport and Simpson [10]. The authors described the flow as having two preferred states—termed zero-flow and backflow modes. An irregular transition between the states was observable in the velocity traces near the leading edge. The two flow states corresponded to periods of time when there were large and small vortical structures at the leading-edge junction. It was proposed that the transition to the backflow state was related to turbulent boundary layer events, such as the formation of hairpin vortices, which interact with the horseshoe vortex [10,11]. The frequency of state switching was determined by creating a histogram of the time period between switching events—finding a peak and mean corresponding to fδ/U_∞ = 0.12 and 0.05, respectively [10]. Other researchers have also reported low-frequency unsteadiness at the leading edge over a similar range including Rood [12] 0.04–0.13, Gand et al. [7] 0.05–0.1 and simulations by Gross and Robison [13] 0.1. Gand et al. [7] studied the meandering of the vortex in the transverse plane finding large-scale oscillations roughly twice the frequency as those at the leading edge—in the range fδ/U_∞≈ 0.2–0.3, thought to be triggered by the bimodal fluctuations at the leading edge. Though the dynamics at the leading edge were believed to be responsible for the horseshoe vortex (HV) meandering, there were no bimodal histograms of velocity observed in the meandering region [7].

Leading-edge flow unsteadiness has also been noted in turbine cascades. Wang et al. [4] observed periodic switching of the horseshoe vortices in a low-speed linear turbine cascade. Gross et al. [14] performed an eddy-resolved simulation of the flow through a high-lift front-loaded low-pressure turbine (LPT) cascade, and described leading edge and passage vortex transient behavior in Refs. [6,15]. Similar passage vortex fluctuations were described in early experiments by Veley et al. using surface-mounted hot-films and high-speed flow visualization [16,17].

A simplified schematic of prominent endwall flow structures in a high-lift front-loaded cascade of blades is shown in Fig. 1, consistent with experiments and the simulations described in Refs. [14,18]. Vortical structures are colored either blue or red to signify either clockwise, or counterclockwise rotation when viewed from downstream looking in the upstream direction. Similar to symmetric junction flows, the incoming boundary layer separates due to an adverse pressure gradient. A separation line S1 extends across the passage. The separated shear layer extends across the passage from near the leading-edge region of one blade toward the suction surface (SS) of the adjacent blade due to the cross passage pressure gradient. A HV structure forms at the leading-edge junction with the endwall. An important vortical flow structure extends from the pressure-side leg of the horseshoe vortex (PSHV) across the passage along the separated shear layer toward the adjacent suction surface forming a vortex line. A secondary separation line S2 corresponds to the lift-off line of the vortex and is very evident in oil flow visualization. The strength of PSHV is enhanced by the cross passage secondary flow and referred to here as the passage vortex (PV) within the passage. The PV interacts with a strong three-dimensional suction side corner separation vortex (SSCSV) along the suction surface near the trailing-edge generating losses and reducing aerodynamic efficiency. A second leg of the HV structure extends from the leading edge toward the suction surface; however, the vortex quickly dissipates due to vortex stretching from the large acceleration along the SS of a high-loaded blade.

Many factors that affect the leading-edge junction flow dynamics have been identified in the literature, such as the Reynolds number, bluntness of the obstacle, boundary layer characteristics, freestream turbulence level, and surface roughness [7,9,19,20]. Several parameters have been proposed to relate the horseshoe vortex to shape and flow parameters, including Re_θ, and two by Fleming et al. [21]: bluntness factor (BF), and momentum deficit factor (MDF). The bulk of the studies focus on the junction of a symmetric wing; however, in a turbine, the endwall flow dynamics are further influenced by blade loading, pressure gradient, interaction between vortices of adjacent blades, and unsteady blade row interaction.

The push to open the design envelope beyond traditional blade designs to higher lift profiles, including front-loaded geometries, means that the secondary flow becomes increasingly important. The present work focuses on elucidating the unsteady behavior of the passage vortex in a low-speed linear cascade of front-loaded high-lift airfoils. High-speed measurements in the passage are used to visualize and describe key unsteady phenomena. The data are further analyzed to determine the time scales associated with the phenomena. Finally, the temporal characteristics of the vortex are compared to canonical junction flow papers in the literature.

All experiments were conducted in the Air Force Research Laboratory's Low Speed Wind Tunnel Facility (Fig. 2). The test section was configured as a seven-blade LPT linear cascade. The linear cascade was fitted with a high-lift front-loaded LPT profile, designated L2F [22]. A splitter plate with an elliptic leading edge was used to generate a clean incoming boundary layer. The plate extended 4.97 C_x upstream from the cascade, and 4.27 C_x downstream. Reynolds number was 1.0 × 10⁵ based on blade axial chord and inlet velocity. The incoming reference velocity was measured using an upstream (2 C_x) Pitot-static probe, connected to a 0–0.4 in-H₂O Druck pressure transducer. The incoming boundary layer thickness was 9.3% C_x. It should be noted that the large scale of the tunnel results in a large AR of 4.17 and a relatively thin boundary layer compared to span 2.2% H. This configuration is ideal for studying the endwall flow characteristics with minimal interaction between the endwall and midspan flows.

An upstream bar turbulence grid increased the incoming freestream turbulence intensity (FSTI) to 3.0%, which is more representative of the elevated turbulence in turbomachinery flows. A summary of the linear cascade parameters is listed in Table 1.

High-speed stereo particle image velocimetry (SPIV) measurements were acquired using two high-speed Phantom VEO 640L cameras fitted with Scheimpflug adapters. A Photonics Industries DM30 Dual Head 527 nm laser (Nd:YLF) with sheeting forming optics was used to illuminate seeding particles. A LaVison programmable timing unit and DaVis 8 software were used to synchronize the laser and cameras, calibrate, acquire images, and calculate the velocity vector fields from each raw image pair. Additional post-processing data analysis was performed using in-house codes.

The final spatial resolution was typically 1.1 vectors/mm (167.8 vectors/C_x). The in-passage SPIV plane (Fig. 3) was aligned along the secondary coordinate system (x′,y′) based on the exit flow angle so that the velocimetry data captured the cross section of the dominant PV. Analysis in subsequent sections is based on datasets of 12,500 or more instantaneous image pairs (spanning 273 T⁺), acquired at 2.5 kHz (F⁺ = 45.8). Using the above-mentioned setup, the motion of large-scale structures, such as the passage vortex, was highly resolved.

The vortex of interest extends along a core line adjacent to S2, from near the pressure-side leading edge and across the passage toward the adjacent blade suction surface, as described in Fig. 1. High-speed measurements in the passage show that the vortex fluctuates in strength and time. These fluctuations are associated with two phenomena: an intermittent loss of coherence and an undulation (transverse movement) of the core line. Both phenomena were noted in high-order numerical simulations Ref. [15], which are compared with instantaneous flow visualization in Fig. 4. During the loss of coherence event, the vortex rapidly changes from a large coherent rotational structure, item A in Fig. 4(c), to a region of unorganized turbulent flow depicted in Fig. 4(d). When coherent, the vortex rotates clockwise with a clearly discernable core. The rotational region reached a diameter greater than 10% C_x (8.2% of the pitch) in the experiments. The vortex rollup is located at the end of the separated shear layer, marked item B in Fig. 4(c), which extends from S1. The lift-off line S2 is located at point C.

At least one secondary vortex, marked D, with an opposite sense of rotation, is located adjacent to the vortex. Evident from the flow visualization is the large degree of flow entrainment between the secondary flow along the endwall and the high-momentum 2D bulk flow.

The undulation of the vortex core line results in vortex positional change in the pitchwise and spanwise directions. Velocity measurements at four instances of time are shown in Fig. 5, depicting the unsteady vortex behavior. The velocity field is flooded with Q-criterion to highlight the regions of the strong rotational flow. Note that this view is aft-looking-forward with the SS designated with a thick black vertical line on the left side of the figure.

Visualizing the time series of the secondary flow shows a strong coherent vortex in the center of the passage at t₀, along with an occasional smaller vortex that forms near the endwall closer to the SS. Often, these smaller vortices navigate toward the PV and become entrained in the rotationally dominant vortex. Observations of the smaller vortices using the high-speed data suggest their unsteady dynamics occur at smaller time scales compared to the larger PV. The PV exhibits pitchwise movement, migrating closer to the passage/pressure side (PS) as shown at t₁, and toward the SS at t₂. The total distance that the vortex position fluctuates in the y′ direction is about 0.2 C_x. Aperiodically, the vortex rapidly loses rotational strength, becoming incoherent, which is evidenced by low levels of Q and an unidentifiable central core at t₃. Additionally, unsteady dynamics of the vortex which cannot be captured using a single 2-D plane of velocity data includes the vortex filament weaving into and out of alignment with respect to the data plane and streamwise undulation.

While these temporal changes associated with the vortex are not periodic, the progressions have been observed to follow a similar pattern over time. The vortex is strengthened by the secondary flow in the passage and then moves through a process of strengthening as it shifts toward the PS of the passage. The vortex shifts back toward the SS, and in some instances loses strength followed by fluctuations in the pitch direction. In other instances, the vortex rapidly loses coherence. During the positional shifts, the length of the separated shear layer increases and decreases. It is hypothesized that the separation line S2 also fluctuates over time, e.g., shifting downstream and toward the PS of the passage as the separated shear layer length increases, influencing the interaction of the endwall flow with the suction surface.

The time-averaged velocity field flooded by Q is shown in Fig. 6(a), highlighting the mean vortex position. Note that the contour levels of Q-criterion are significantly lower than those used in the instantaneous results of Fig. 5. This conveys the degree of the vortex undulation and fluctuating strength, which causes depleted time-averaged values. It is therefore imperative that researchers consider these unsteady phenomena so that they do not misinterpret the vortex strength from time mean data, while the vortex wandering goes unidentified as a causality.

The extent of the vortex positional and strength change are further visualized in Figs. 6(b) and 6(c). The position of the vortex was tracked in every instantaneous vector field by locating the maximum Q-criterion (Q_max). The search region was restricted to the range of vortex meandering. The time history of the vortex Q_max indicated that the strength can fluctuate by greater than 70% over short periods of time. The tracked vortex spatial distribution over time is plotted in Fig. 6(b). The distribution is elliptical in shape spanning ∼20% C_x in the pitch direction. Spanwise movement also occurs but the extent of the movement is about half that of the pitchwise wandering. The average of Q_max at each position in the distribution is shown in Fig. 6(c), which illustrates a correlation between vortex strength and position. The trend clearly indicates that the vortex strength is highest when located towards the PS of the passage, at which point the separated shear layer length is the longest.

Early measurements in Ref. [16] using endwall surface-mounted thin-film sensors adjacent to the vortex core line detected low-frequency fluctuations in frequency bands centered around F⁺ ≈ 0.38. The fluctuations were assumed to be associated with intermittent loss of coherence events, which were evident in the flow visualization shown in Fig. 4, based on the findings and in agreement with numerical simulations [6]. To better visualize and quantify the complex temporal fluctuations observed in the passage, space-time plots of the vortex movement were developed using the new high-speed SPIV measurements. Isosurfaces of Q-criterion are presented in Fig. 7, which clearly depicts three-dimensional vortex motion over time. The motion demonstrates the range of time scales involved with the PV movement. Some undulations occur over a period of one convective time, while other fluctuations occur over a fraction of the convective time.

Several segments of time are displayed in Fig. 8, viewed from a two-dimensional perspective. The undulation of the vortex in the pitch direction is evident in Fig. 8(a). The vortex wandering occurs at multiple wavelengths, ranging from short periods of ∼0.2 T⁺ or less, to long-period fluctuations of 3.1 T⁺. The longer period fluctuations vary over time, with multiple periods of spatial fluctuation superimposed upon one another. Positional changes also occurred in the spanwise direction but were not as pronounced.

A series of loss of coherence events is apparent in Fig. 8(b). In this sample, the events are in coordination with the long-period spatial fluctuation, with a time period of ∼2.7 T⁺, although the events did not consistently repeat at a fixed frequency. During each event, the vortex remained incoherent for a time period of ∼0.6–0.8 T⁺. The duration of the loss of coherence events varied throughout the data sets from less than 0.2 T⁺ to as long as 1 T⁺. Figure 8(b) also illustrates the large positional change of the vortex that often occurs during the loss of coherence events.

In Fig. 8(c), the vortex is visualized over a longer time segment of 15 T⁺. Several loss of coherence events are highlighted with arrows. The large positional shifts in the pitch direction were typically followed by a loss of coherence event. When the vortex loses coherence on the pressure side of the passage (bottom of Fig. 8(b)), it frequently regains coherence toward the suction side. This behavior is hypothesized to not only indicate an unsteady change in the length of the separated shear layer, but also an unsteady variation of the topology—such as a change in positions of the S1 and S2 separation lines with time. Sieverding [1] described a strong and weak interaction of the flow between S1 and S2 with the suction surface and related it to the corner separation along the surface. These unsteady changes to the flow topology are important to better understand, as they would affect the instantaneous heat transfer and influence the loss generation in the endwall region.

The guiding philosophy of applying VITA in this manner takes advantage of the event being manifested by a rapid loss of vortex strength. An example of the results is displayed in Fig. 9, demonstrating the VITA technique implemented to identify loss of coherence events (vertical lines on plots). Using these visualizations of the PV, the VITA parameters were tailored to ensure that loss of coherence events was being appropriately detected.

The VITA method was applied to sets of 25,000 instantaneous SPIV measurements that were acquired at 2.5 kHz—accounting for nearly 550 flow convective times. The time interval between loss of coherence events was calculated from the VITA analysis and plotted as a histogram, presented in Fig. 10. A probability density function (PDF) estimate was fitted and overlaid on the histogram. The time period between events is skewed toward shorter periods, such as a large number of occurrences at ∼0.35. However, the histogram shows that the events tended to occur over a range of longer time periods. The mean of the distribution was ΔT⁺ = 1.62, and the median was 1.13, with a peak occurrence of 0.5 based on the estimated PDF. Visual inspection of the space-time plots indicated that the duration of the events typically ranged from ∼0.2 to 0.8; however, in some instances, the vortex remained incoherent for as long as one convective time. The frequencies associated with peak, mean, and median times between events are 2, 0.62, and 0.88, respectively, as summarized in Table 2.

The relationship between leading-edge junction flow dynamics and the mid-passage vortex was studied numerically in Ref. [6]. Bimodal behavior at the leading-edge junction was associated with a frequency of 0.65 (ΔT⁺ = 1.5) and vortex oscillations in the passage corresponded to 0.52 (ΔT⁺ = 1.92) when normalized by SSL and average passage velocity, as in the present work. The frequencies in the simulation are in good agreement with the experimental mean frequency of loss of coherence from the VITA of 0.62, and in the range of long-period vortex undulation, 0.3 > F⁺ > 0.7. Devenport and Simpson [10] analyzed velocity at the leading-edge junction of a Rood wing and developed histograms of the time between transitions of back- and zero-flow modes. It is interesting to note that the histogram was best represented by a log-normal distribution similar to the distribution in Fig. 10. They reported a mean frequency of f·δ/U_∞ = 0.05. The mean frequency of the vortex loss of coherence in the passage in the present cascade experiments, f·δ/U_in = 0.045, is in good agreement, supporting the hypothesis that the loss of coherence observed in the passage is related to the leading-edge dynamics.

To gain a sense of the dominant periodic modes of the PV, the power spectral density (PSD) was computed for several components and shown in Figs. 11 and 12. First, the vortex position was tracked through time over the entire data set. This resulted in a time series that captures the changes in vortex position and strength with time. The PSDs were calculated using the time series of vortex strength (Q_max) and pitchwise position (y′) over time, plotted in Figs. 11(a) and 11(b). These two plots give a sense of the frequencies associated with fluctuations in vortex strength and position. Second, the PSDs were calculated from a fixed spatial position in the flow. The time-average position of the vortex was chosen as the fixed position, and the PSD of the time series of pitchwise and spanwise velocity is presented in Figs. 12(a) and 12(b).

Looking at the PSD of different parameters, repeated baseline runs, and viewing the results on log–log versus linear plots, several takeaways emerged regarding the unsteady characteristics of the vortex. One takeaway is that significant energy was manifested through low-frequency (F⁺ < 0.6) unsteadiness. While peaks at specific frequencies were often not consistent between repeated runs, distinguishable bands of peaks at certain frequencies were reproducible between runs. Figure 11(a) shows that there are several dominant peaks from F⁺ = 0.3 to 0.6. The PSD is presented on a log–log scale in Fig. 11(b). The low-frequency fluctuations, centered at about 0.4 in the PSD, occur at longer periods, 1.5 < ΔT⁺ < 3.1, showing good agreement with the undulations in the vortex presented in the space-time plots of Fig. 8. The long-period undulations, along with a range of ΔT⁺ between loss of coherence events, correspond with a frequency band in the range of 0.3 < F⁺ < 0.6. The peaks in the higher frequency band, F⁺ > 0.6, are believed to be associated with the short duration undulations of the PV which are visible in Fig. 8(a).

When comparing the results from the VITA method (Table 2) with the PSD of in-plane velocities in Fig. 12, there are peaks in the spectrum occurring near the median (0.88) and average (0.62) frequencies, indicating fluctuations in velocity associated with the loss of coherence events. A significant amount of energy is contained in the low-frequency band, 0.1 < F⁺ < 0.3 (Fig. 12(b)). There is uncertainty as to the physics associated with peaks in this range but it does appear that estimates of the PV rotational frequency (within the Eulerian sense) for when the vortex is coherent are found to be in this range. It is reasonable to suggest that the mixing and entrainment of the high-momentum 2D flow with the secondary flow would cause significant fluctuations along the endwall and manifest as high-energy periodic modes at low frequencies.

Additionally, examining the PSD plots of Fig. 11, calculated by tracking the vortex over time, shows some agreement in the fluctuations of strength (dark blue) and pitchwise position (light blue). This is especially noticeable at F⁺ < 1. On the contrary, the PSD of velocity components calculated at a fixed position in Fig. 12 shows less agreement in the range F⁺ = 0.3–0.6. The agreement in frequency spectrums in Fig. 11 is consistent with the observed relationship between vortex strength and pitchwise spatial position.

The analysis of time scales associated with the passage vortex unsteady events in the high-lift LPT cascade indicates that they are related to the leading-edge junction flow behavior. Results are consistent with numerical simulations of the linear cascade passage flow [6] and with junction flow experiments in literature [10]. Note that the presented results involve a dramatically different flow environment (e.g., freestream turbulence, flow turning, strong passage pressure gradients, secondary flow) and geometry (e.g., cascade of turbine blades, asymmetrical profile) than the classical junction flow configurations. The unsteady fluctuations in strength and position occur at both long and short periods, often superimposed on each other. Low-frequency fluctuations observed in prior experiments correspond to long-period oscillations in position, which are sometimes accompanied by loss of coherence events.

Experimental efforts focused on obtaining high-speed measurements of endwall vortical structures in a high-lift front-loaded linear cascade of LPT blades. The vortical structures have been shown to be a major contributor to aerodynamic losses and heat transfer in high-lift turbine passages. The measurements were used to better understand both the unsteady phenomena associated with the passage vortex, such as strength and positional fluctuations, as well as the time scales of each type of event. Key findings include the presence of both long-period and short-period positional fluctuations in the vortex core line with time, often superimposed on one another. Low frequencies of F⁺ ∼0.35 were consistently observed in spectral analysis, as well as over the broader range of 0.3–0.7, which are associated with long-period fluctuations. Loss of coherence events were also observed, which often accompanied the strong pitchwise positional shifts. The VITA method was applied to better understand the loss of coherence events. Histograms of the time period between the loss of coherence events were developed using the VITA technique. The distribution was skewed toward shorter periods; however, the mean of the distribution agreed well with the frequencies reported in the literature that are associated with the bimodal behavior of leading-edge junction flows. The findings in this paper support the hypothesis that in-passage vortex unsteady characteristics are influenced by leading-edge junction flow dynamics. Analysis of the temporal fluctuations in position and strength of the passage vortex, such as the dominant low-frequency long-period fluctuations and relationship with leading-edge dynamics, provides new insight into unsteady endwall physics. Knowledge of the time scales associated with the endwall flow dynamics are an important factor necessary to further the development of endwall loss reduction techniques; however, additional work is necessary to better understand the global dynamics, and the relationship between unsteady flow fluctuations and endwall loss production mechanisms.

Distribution Statement A: Approved for Public Release; Distribution is Unlimited. PA# AFRL-2021-4338. This material is based upon work supported by the Air Force Office of Scientific Research under award number 21RQCOR016. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Air Force.

There are no conflicts of interest.

Data provided by a third party are listed in Acknowledgment.

f =

frequency

t =

time

u =

in-plane lateral velocity component

v =

in-plane vertical velocity component

w =

out-of-plane velocity component

x =

axial coordinate

y =

pitchwise coordinate

z =

spanwise coordinate

H =

blade span

Q =

Q-criterion

S =

pitch spacing

U =

velocity magnitude

C_x =

axial chord

F⁺ =

non-dimensional frequency

T⁺ =

non-dimensional time

Re =

Reynolds number

Δ =

change in or difference in

δ =

boundary layer thickness

γ =

pressure loss coefficient

ρ =

density

τ =

VITA integration window size

∞ =

freestream or edge

C_x =

with respect to axial chord

in =

inlet reference

PS =

passage/pressure-surface

T =

with respect to thickness

θ =

with respect to momentum thickness

¯ =

time-averaged

′ =

secondary coordinate system

^ =

VITA applied quantity