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Flows in Complex Systems

Low Pressure Turbine Relaminarization Bubble Characterization using Massively-Parallel Large Eddy Simulations

[+] Author and Article Information
Shriram Jagannathan1

Department of Mechanical Engineering,Texas A&M University, College Station, TX 77843shriramjegan@tamu.edu

Markus Schwänen, Andrew Duggleby

Department of Mechanical Engineering,Texas A&M University, College Station, TX 77843

1

Corresponding author.

J. Fluids Eng 134(2), 021102 (Mar 19, 2012) (13 pages) doi:10.1115/1.4006065 History: Received March 04, 2011; Revised February 08, 2012; Published March 16, 2012; Online March 19, 2012

The separation and reattachment of suction surface boundary layer in a low pressure turbine is characterized using large-eddy simulation at Ress  = 69000 based on inlet velocity and suction surface length. Favorable comparisons are drawn with experiments using a high pass filtered Smagorinsky model for sub-grid scales. The onset of time mean separation is at s/so  = 0.61 and reattachment at s/so  = 0.81, extending over 20% of the suction surface. The boundary layer is convectively unstable with a maximum reverse flow velocity of about 13% of freestream. The breakdown to turbulence occurs over a very short distance of suction surface and is followed by reattachment. Turbulence near the bubble is further characterized using anisotropy invariant mapping and time orthogonal decomposition diagnostics. Particularly the vortex shedding and shear layer flapping phenomena are addressed. On the suction side, dominant hairpin structures near the transitional and turbulent flow regime are observed. The hairpin vortices are carried by the freestream even downstream of the trailing edge of the blade with a possibility of reaching the next stage. Longitudinal streaks that evolve from the breakdown of hairpin vortices formed near the leading edge are observed on the pressure surface.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 4

A fairly constant slope on a semilog plot of error versus polynomial order signifies an exponential convergence for the hemisphere DNS. Data is acquired at a polynomial order of 14.

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Figure 5

Streamwise velocity profiles at 0.5D, 1.5D, 2.5D downstream of the hemisphere, offset by 0.5, respectively. The profiles are in good agreement with the DNS, except at 2.5D where Filter1 performs better predicting the boundary layer growth in accordance with the DNS.

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Figure 6

Streamwise fluctuation velocity profiles at 0.5D, 1.5D, 2.5D downstream of the hemisphere, offset by 0.2, respectively. The filtered rms profiles are in fair agreement following the trend predicted by the DNS.

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Figure 7

A nearly constant slope in semilog plot of error versus polynomial order signifies an exponential convergence. A polynomial order of 10 is used for the present study since an error close to 10-5 is achieved.

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Figure 8

Contour plot of spanwise vorticity with the turbulence generating bars and blade. Only one-half of the domain shown is simulated.

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Figure 9

The fluctuating components decay from grid to cascade resulting in a nearly isotropic turbulence before the cascade

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Figure 23

Variation of separation based Reynolds Number. Reθ is fairly constant in the laminar regime up to s/so  = 0.73, but increases sharply in the transitional and turbulent regime.

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Figure 24

The plots show time functions (first, second and third subplot from left to right) and Power Spectral Density estimate via Welch’s method (Welch [42] (fourth, fifth and sixth subplot from left to right) of modes 3, 28, 30, and 34 from top to bottom. The PSD is scaled by the highest absolute coefficient magnitude occurring in one of the three components of one mode.

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Figure 25

Isosurfaces at -0.8 (blue) and 0.8 (red) of scalar spatial basis function of mode 3 (a), 28 (c), 30 (b), and 34 (d). The larger plot shows the x/y view whereas the inset shows a x/z plane looking at the blade suction side.

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Figure 1

Strong scaling of NEK5000 for two different computer architectures: (square) EOS at Texas A&M Supercomputing Center and (circle) Ranger at Texas Advanced Computing Center(TACC). When the number of processor is doubled, the computational time per step should decrease by one-half for ideal scaling (dashed lines).

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Figure 2

Flow over a flat plate with a hemisphere for testing the High Pass Filtered Smagorinsky model. The figure shows the nonperiodic faces in the domain. The freestream turbulence is generated by a recycling and rescaling technique. A recycling plane downstream of the inflow plane is defined from which all velocity components are copied back to the inflow. The velocities at the recycling plane are scaled to match the chosen turbulence intensity inside the recycling box.

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Figure 3

The filter transfer functions are set similar to a cosine function that filters the large scales and leaves the small scales unfiltered. A stabilizing filter is used for all simulations (DNS and LES) where the last 4 modes are filtered with a weight of 0.05.

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Figure 10

The time and spanwise averaged pressure distribution around the blade is shown on the left. The onset of separation is at s/so  = 0.61 and reattachment at s/so  = 0.81. The onset of separation is illustrated by the constant pressure coefficient regime. The experimental data are taken from Schobeiri [8] with error bars of experimental uncertainty (2.2%).

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Figure 11

Time mean streamwise velocity profiles on the suction surface. An inflectional velocity profile can be seen at s/so  = 0.61 when the flow beings to separate. The boundary layer is laminar up to s/so  = 0.73, after which it becomes turbulent and reattaches at s/so  = 0.81.

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Figure 12

The instantaneous velocity profiles at y/l = 0.015 (top), near shear layer at y/l = 0.045 (bottom), at four different time instants. Here, l is the bubble length. t (square), t + Δt1 (circle), t + 2Δt1 (diamond), t + 3Δt1 (star). At both locations, the spanwise oscillations seem to be violent after s/so  = 0.725 reaching more than 30% of freestream velocity. The freestream velocity is defined as the velocity at which the change in velocity is less than 1% outside the boundary layer.

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Figure 13

The maximum reverse flow velocity is less than 15% of the freestream velocity and the associated instability could be classified as convective according to Alam and Sandham [1]

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Figure 14

Time mean streamwise velocity profiles on the suction side at s/so  = 0.49, 0.57, 0.61, 0.73, 0.77, 0.85 from left to right. The velocity profiles are in excellent agreement with the experiment in the laminar flow regime as far as s/so  = 0.61. Minor differences in the growth of boundary layer can be observed in the transitional regime at s/so  = 0.73, 0.77. The experimental data is taken from Schobeiri [8], with uncertainty of 4%.

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Figure 15

Time mean streamwise fluctuation rms at s/so  = 0.49, 0.57, 0.61, 0.73, 0.85 from left to right. The profiles are offset by 0.2 for clarity. The computed streamwise rms velocity follows the trend predicted by the experiment, but fails to comply with the experiment towards the turbulent flow regime at s/so  = 0.73, 0.85. The experimental data is taken from Schobeiri [8].

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Figure 16

Spanwise vorticity along the suction surface at different time instants. The contours are superimposed on isolines of spanwise vorticity. Blue indicates a negative value and red represents a positive value. (a), (b): The separated shear layer is unstable and sheds vortices downstream that appear like hairpin structures. (c): The growth of recirculation region beneath the shear layer can be seen. Circles indicate the physical phenomenon discussed.

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Figure 17

Velocity contours near the suction surface boundary layer at different time instants. The contours are superimposed on isolines of spanwise vorticity. (a)-(c): Flapping of the separated shear layer and formation of roll-up vortex is clearly seen. (c): The shear layer is stabilized possibly by the growth of the recirculation zone underneath. Circles indicate the physical phenomenon discussed.

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Figure 18

(a) Hairpin vortex structures can be seen near the leading edge of pressure surface, but due to the flow acceleration, gets elongated by the freestream and appear as long streamwise streaks.(b) Hairpin vortices near the trailing edge of the blade are marked with arrows. A nearly hairpin structure can be seen even downstream of the blade.

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Figure 19

AIM Map at different suction surface locations (s/so  = 0.57, 0.65, 0.73, 0.77) aptly tracks the changes in the form of turbulence as one traverses from onset to end of separation. The circles denote the form of turbulence until the shear layer and the dots represent the behavior of turbulence away from the shear layer.

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Figure 20

Streamwise and pitchwise velocity fluctuations on the suction surface at s/so  = 0.49, 0.57, 0.61, 0.65, 0.73, 0.77, 0.85 with each profile offset to the right. The flow is calm as far as s/so  = 0.61 when minor streamwise fluctuations occur but it is only at s/so  = 0.73 that the fluctuations begin to grow.

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Figure 21

Spanwise velocity fluctuations (a) and Reynolds stress (b) on the suction surface at s/so  = 0.49, 0.57, 0.61, 0.65, 0.73, 0.77, 0.85 with each profile offset to the right. Very minor spanwise fluctuations can be observed from s/so  = 0.49, however the growth is pronounced at s/so  = 0.77. This phenomenon near the reattachment region could be attributed to the highly unsteady boundary layer.

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Figure 22

(a) Variation of displacement and momentum thickness inside the boundary layer. The displacement thickness is maximum at s/so  = 0.73 and decreases further downstream which can be envisioned due to the transition to turbulence. (b) A similar trend can be seen for the form factor. The form factor reduces after s/so  = 0.73 that is typical of turbulent boundary layers.

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