Flow measurements were made on a highly loaded low pressure turbine blade in a low-speed linear cascade facility. The blade has a design Zweifel coefficient of 1.34 with a peak pressure coefficient near 47% axial chord (mid-loaded). Flow and surface pressure data were taken for Rec = 20,000 with 3% inlet freestream turbulence. For these operating conditions, a large separation bubble forms over the downstream portion of the blade suction surface, extending from 59% to 86% axial chord. A Single-element hotfilm measurements were acquired to clearly identify the role of boundary layer transition in this separated region. Higher-order turbulence statistics were used to identify transition and separation zones. Similar measurements were also made in the presence of unsteady forcing using pulsed vortex generator jets just upstream of the separation bubble (50% cx). Measurements provide a comprehensive picture of the interaction of boundary layer transition and separation in this unsteady environment. Similarities between pulsed flow control and unsteady wake motion are highlighted.

Particle image velocimetry (PIV) measurements were made on a highly loaded low-pressure turbine blade in a linear cascade. The Pack B blade has a design Zweifel coefficient of 1.15 and a peak Cp at 63% axial chord on the suction surface. Data were taken at Rec = 20K with 3% inlet freestream turbulence and a wake passing flow coefficient of 0.8. Without unsteady wakes, a non-reattaching separation bubble exists on the suction surface of the blade beginning at 68% axial chord. The time averaged separation zone is reduced in size by approximately 35% in the presence of unsteady wakes. Phase-locked hot-wire and PIV measurements were used to document the dynamics of this separation zone when subjected to synchronized, unsteady forcing from a spanwise row of vortex generator jets (VGJs) in addition to the unsteady wakes. The phase difference between VGJ actuation and the wake passing was optimized. Both steady state Cp and phase-locked velocity measurements confirm that the optimal combination of wakes and jets yields the smallest separation.

The synchronous application of flow control in the presence of unsteady wakes was studied on a highly-loaded low pressure turbine blade. The L1A blade has a design Zweifel coefficient of 1.34 and a suction peak at 58% axial chord, making it an aft-loaded pressure distribution. Velocity and pressure data were acquired at Rec = 20,000 with 3% incoming freestream turbulence. Unsteady wakes from an upstream vane row are simulated with a moving row of bars at a flow coefficient of 0.76. At this Reynolds number, the blade exhibits a non-reattaching separation bubble beginning at 57% axial chord under steady flow conditions without upstream wakes. The separation zone is modified substantially by the presence of unsteady wakes, producing a smaller separation zone and reducing the area-averaged wake total pressure loss by more than 50%. The wake disturbance accelerates transition in the separated shear layer but stops short of reattaching the flow. Rather, a new time-averaged equilibrium location is established for the separated shear layer, further downstream than without wakes. The focus of this study was the application of pulsed flow control using two spanwise rows of discrete vortex generator jets (VGJs). The VGJs were located at 59% Cx, approximately the peak cp location, and at 72% Cx. The most effective separation control was achieved at the 59% Cx location. Wake total pressure loss decreased 60% from the wake only level and the cp distribution fully recovered its high Reynolds number (attached flow) performance. The VGJ disturbance dominates the dynamics of the separated shear layer, with the wake disturbance assuming a secondary role only. When the pulsed jet actuation (30% duty cycle) was initiated at the 72% Cx location, synchronization with the wake passing frequency (10.6Hz) was key to producing the most effective separation control. A 25% improvement in effectiveness was obtained by aligning the jet actuation between wake events. Evidence suggests that flow control using VGJs will be effective in the highly unsteady LPT environment of an operating gas turbine, provided the VGJ location and amplitude are adapted for the specific blade profile.

The synchronous application of flow control in the presence of unsteady wakes was studied on a highly loaded low pressure turbine blade. At low Reynolds numbers, the blade exhibits a nonreattaching separation bubble under steady flow conditions without upstream wakes. Unsteady wakes from an upstream vane row are simulated with a moving row of bars. The separation zone is modified substantially by the presence of unsteady wakes, producing a smaller separation zone and reducing the area-averaged wake total pressure loss by more than 50%. The wake disturbance accelerates transition in the separated shear layer but stops short of reattaching the flow. Rather, a new time-averaged equilibrium location is established for the separated shear layer. The focus of this study was the application of pulsed flow control using two spanwise rows of discrete vortex generator jets. The jets were located at 59% Cx, approximately the peak cp location, and at 72% Cx. The most effective separation control was achieved at the upstream location. The wake total pressure loss decreased 60% from the wake-only level and the cp distribution fully recovered its high Reynolds number shape. The jet disturbance dominates the dynamics of the separated shear layer, with the wake disturbance assuming a secondary role only. When the pulsed jet actuation was initiated at the downstream location, synchronizing the jet to actuate between wake events was key to producing the most effective separation control. Evidence suggests that flow control using vortex generator jets (VGJs) will be effective in the highly unsteady low pressure turbine environment of an operating gas turbine, provided the VGJ location and amplitude are adapted for the specific blade profile.

We obtain the real singularities and corresponding discontinuities of a class of multiple integrals over real contours. Our aim is to give a unified treatment, obtaining, by elementary mathematical methods. both previously known results and some new generalizations. In a subsequent paper the results are applied to unitarity integrals.