URANS Simulations of RotorStator Cavity Flow

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URANS Simulations of Rotor-Stator Cavity Flow

• T. J. Craft, S. E. Gant, H. Iacovides, B. E.
  Launder

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Contents

• Introduction
• Experiments
• Numerical Methods
• 2-D Steady RANS Results
• 3-D URANS Results
• Conclusions

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Rotor-Stator Cavity

• Two discs rotor and stator
• Bottom disc rotates
• Top disc and walls stationary
• No through-flow
• Centrifugal forces induce radial outflow near
  rotor and inflow near stator
• Relevant to cooling systems in gas turbines

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Rotor-Stator Cavity Experiments

• Czarny, Iacovides Launder, 2002
• Ink injected using hypodermic needle into
  water-filled cavity
• Coherent structures at certain rotational
  Reynolds numbers/cavity heights

ReWRH/n166,000 H/R0.195
ReWRH/n112,000 H/R0.126
Aim to reproduce coherent structures observed
experimentally using URANS.
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Numerical Methods 2D Steady Flow

• TEAM code
• Finite-volume
• Staggered velocity/pressure nodes
• Launder-Sharma k-e turbulence model
• Numerical wall function which solves
  thin-boundary-layer equations across embedded
  grid.

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Rotor-Stator 2D Steady Simulations

• Itoh et al. test case ReWR2/n106, H/R0.08
• Numerical wall function results agree well with
  full low-Re model
• No problem with internal corner cells.

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Rotor-Stator 3D Simulations

• STREAM code parallelized using domain
  decomposition and MPI
• 2-block axisymmetric grids running on local linux
  cluster
• 8-block version running on SGI Origin/Altix at
  CSAR
• Number of main-grid nodes in (R,q,Z) (60,50,37)
  plus 30 subgrid nodes on each wall.
• Reynolds Number ReWRH/n112,000
• Disc spacing H/R0.126

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Rotor-Stator Quasi-LES
Using laminar viscosity only (deactivating
turbulence model)
Radial velocity isocontours (yellowpositive
bluenegative)
Axial velocity contours near stator surface (at
z/H 0.79)
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Rotor-Stator Quasi-LES
Using laminar viscosity only (deactivating
turbulence model)
Radial velocity
Tangential velocity
(Profiles taken at r/R0.79, towards the outer
rim of the cavity)
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Rotor-Stator URANS
Realizable k-e model
Eddy-viscosity contours (red, yellow, green) ?
(40?, 30?, 20?)
Axial velocity contours near stator surface
(scale WRmax 1.0)
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Rotor-Stator URANS
Realizable k-e model
Radial velocity
Tangential velocity
(Profiles taken at r/R0.79, towards the outer
rim of the cavity)
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Rotor-Stator URANS

• Models Tested
• Linear k-e with/without Yap
• Realizable k-e
• Cubic non-linear k-e
• Linear Production (LP) (Laurence Guimet)
• Organized Eddy Simulation (OES) (Braza) with Cm
  0.02
• Filter-based URANS (Johansen et al.)

• Different Initial Conditions
• Lower initial turbulence levels
• Zero initial turbulence levels in core of domain

• Periodic Disturbances
• Rotor velocity sinusoidal function or spiked
  profile for W
• Eccentric axis of rotation (in progress).

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Rotor-Stator OES
(The only model to show continued presence of
turbulent structures)
Axial velocity near stator surface (at z/H 0.79)
Radial velocity at r/R 0.79
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Concluding Remarks

• Standard RANS models are too dissipative to
  simulate 3-D turbulent structures in rotor-stator
  cavity (grid resolution? numerical viscosity?).

• Eddy structures can be resolved by decreasing the
  eddy-viscosity by a factor of 4.5 (OES) or
  removing it entirely (mt 0) (rigorous model
  definition?).

Future Work

• Investigate further filter-based LES/URANS model
  of Johansen et al.

• Grid refinement (although this is costly!)

• Investigate other LES approaches (LNS, DES etc.)

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Filter-Based URANS

• Standard k-e model with clip on mt based on the
  grid dimension, D

where the filter width, D, is given by
L is a characteristic dimension and cD 0.15

• In the rotor-stator the above formulas lead to
  steady, axisymmetric flow.
• Testing with cD 0.06 and different formulations
  for smaller D

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Filter-Based URANS
Using cD 0.15
Radial velocity isocontours (yellowpositive
bluenegative)
Radial velocity at r/R 0.79
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Subgrid Transport Equations
Simplified low-Re transport equations for U, k,
and T in plane Cartesian coordinates (convection
terms in non-conservative form).
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Wall Function Generalization to 3-D Flows

• Generic form of subgrid transport equations (f ?
  U, V, k, e)

where (U, V, W) are grid-aligned contravariant
subgrid velocity components in the (x, h, z)
directions, J is the Jacobian (equivalent to cell
volume), gii and gjj are metric tensors and the
source term C includes pressure gradient,
turbulence-equation sources and geometric terms.

• Multi-block implementation using subgrid halo
  cells
• Efficient interpolation scheme to minimize cost
  of calculating geometric terms

z
z
y
h
x
x