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TECHNICAL PAPERS

# Large-Eddy Simulation of Unsteady Surface Pressure Over a Low-Pressure Turbine Blade due to Interactions of Passing Wakes and Inflexional Boundary Layer

[+] Author and Article Information
S. Sarkar1

Department of Mechanical Engineering, Indian Institute of Technology, Kanpur 208016, Indiasubra@iitk.ac.in

Peter R. Voke

School of Engineering, University of Surrey, Guildford GU2 7XH, UKp.voke@surrey.ac.uk

1

To whom correspondence should be addressed.

J. Turbomach 128(2), 221-231 (Feb 01, 2005) (11 pages) doi:10.1115/1.2137741 History: Received October 01, 2004; Revised February 01, 2005

## Abstract

The unsteady pressure over the suction surface of a modern low-pressure (LP) turbine blade subjected to periodically passing wakes from a moving bar wake generator is described. The results presented are a part of detailed large-eddy simulation (LES) following earlier experiments over the T106 profile for a Reynolds number of $1.6×105$ (based on the chord and exit velocity) and the cascade pitch to chord ratio of 0.8. The present LES uses coupled simulations of cylinder for wake, providing four-dimensional inflow conditions for successor simulations of wake interactions with the blade. The three-dimensional, time-dependent, incompressible Navier-Stokes equations in fully covariant form are solved with $2.4×106$ grid points for the cascade and $3.05×106$ grid points for the cylinder using a symmetry-preserving finite difference scheme of second-order spatial and temporal accuracy. A separation bubble on the suction surface of the blade was found to form under the steady state condition. Pressure fluctuations of large amplitude appear on the suction surface as the wake passes over the separation region. Enhanced receptivity of perturbations associated with the inflexional velocity profile is the cause of instability and coherent vortices appear over the rear half of the suction surface by the rollup of shear layer via Kelvin-Helmholtz (KH) mechanism. Once these vortices are formed, the steady-flow separation changes remarkably. These coherent structures embedded in the boundary layer amplify before breakdown while traveling downstream with a convective speed of about 37% of the local free-stream speed. The vortices play an important role in the generation of turbulence and thus to decide the transitional length, which becomes time dependent. The source of the pressure fluctuations on the rear part of the suction surface is also identified as the formation of these coherent structures. When compared with experiments, it reveals that LES is worth pursuing as an understanding of the eddy motions and interactions is of vital importance for the problem.

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## Figures

Figure 1

Computational grid for the T106 blade profile and zoomed view of leading and trailing edges

Figure 2

Iso-surface of vorticity ∣ω∣ at an instant of time through the wake passing cycle

Figure 3

Time-averaged wall static-pressure coefficient Cp: Present LES; DNS by Wu and Durbin (24) and experiment by Stadtmüller and Fottner (28)

Figure 4

Phase-averaged Cp distributions on the T106 blade: Present LES and experiment (16)

Figure 5

S-T diagram of phase-averaged Cp over the suction surface of the T106 blade; (a) LES, (b) experimental (16)

Figure 6

Traces of phase-averaged Cp over the rear of the suction surface: Trajectories A and B represent local peaks of free-stream velocity, U and C represents 0.37U

Figure 7

Phase-averaged contours nondimensional streamwise component of velocities at different sections of boundary layer on the suction surface: Trajectories A and B represent local peaks of free-stream velocity, U and C drawn from 0.37U

Figure 8

Phase-averaged streamlines on rear half of the suction surface at selective phases during the wake passing cycle: The location of wake centerline is marked by a triangle

Figure 9

Phase- and time-averaged nondimensional velocity profiles on the suction surface during the wake passing cycle

Figure 10

Streamwise component of phase-averaged velocity perturbations ⟨U⟩−U¯ at different sections of boundary layer over the suction surface. Arrows indicate the maximum and minimum velocity by the negative jet

Figure 11

Instantaneous velocity vectors, streamline, iso-contour of spanwise vorticity over the rear of the suction surface

Figure 12

Instantaneous iso-surface of spanwise component of vorticity on the rear half of the suction surface

Figure 13

Schematic illustrating coherent vortices formation mechanism

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