A high-order numerical method is employed to investigate flow in a rotor/stator cavity without heat transfer and buoyant flow in a rotor/rotor cavity. The numerical tool used employs a spectral element discretization in two dimensions and a Fourier expansion in the remaining direction, which is periodic and corresponds to the azimuthal coordinate in cylindrical coordinates. The spectral element approximation uses a Galerkin method to discretize the governing equations, but employs high-order polynomials within each element to obtain spectral accuracy. A second-order, semi-implicit, stiffly stable algorithm is used for the time discretization. Numerical results obtained for the rotor/stator cavity compare favorably with experimental results for Reynolds numbers up to Re1 = 106 in terms of velocities and Reynolds stresses. The buoyancy-driven flow is simulated using the Boussinesq approximation. Predictions are compared with previous computational and experimental results. Analysis of the present results shows close correspondence to natural convection in a gravitational field and consistency with experimentally observed flow structures in a water-filled rotating annulus. Predicted mean heat transfer levels are higher than the available measurements for an air-filled rotating annulus, but in agreement with correlations for natural convection under gravity.

References

References
1.
Chew
,
J. W.
, and
Hills
,
N. J.
,
2007
, “
Computational Fluid Dynamics for Turbomachinery Internal Air Systems
,”
Philos. Trans. R. Soc., A
,
365
(
1859
), pp.
2587
2611
.
2.
Itoh
,
M.
,
Yamada
,
Y.
,
Imao
,
S.
, and
Gonda
,
M.
,
1992
, “
Experiments on Turbulent Flow Due to an Enclosed Rotating Disk
,”
Exp. Therm. Fluid Sci.
,
5
(
3
), pp.
359
368
.
3.
Serre
,
E.
,
Bontoux
,
P.
, and
Launder
,
B.
,
2002
, “
Direct Numerical Simulation of Transitional Turbulent Flow in a Closed Rotor-Stator Cavity
,”
Flow Turbul. Combust.
,
69
(
1
), pp.
35
50
.
4.
Poncet
,
S.
,
Serre
,
É.
, and
Le Gal
,
P.
,
2009
, “
Revisiting the Two First Instabilities of the Flow in an Annular Rotor-Stator Cavity
,”
Phys. Fluids
,
21
(
6
), p.
064106
.
5.
Séverac
,
É.
,
Poncet
,
S.
,
Serre
,
É.
, and
Chauve
,
M.-P.
,
2007
, “
Large Eddy Simulation and Measurements of Turbulent Enclosed Rotor-Stator Flows
,”
Phys. Fluids
,
19
(
8
), p.
085113
.
6.
Amirante
,
D.
, and
Hills
,
N. J.
,
2015
, “
Large-Eddy Simulations of Wall Bounded Turbulent Flows Using Unstructured Linear Reconstruction Techniques
,”
ASME J. Turbomach.
,
137
(
5
), p.
051006
.
7.
Bohn
,
D.
,
Deuker
,
E.
,
Emunds
,
R.
, and
Gorzelitz
,
V.
,
1995
, “
Experimental and Theoretical Investigations of Heat Transfer in Closed Gas-Filled Rotating Annuli
,”
ASME J. Turbomach.
,
117
(
1
), pp.
175
183
.
8.
Bohn
,
D.
, and
Gier
,
J.
,
1997
, “
The Effect of Turbulence on the Heat Transfer in Closed Gas-Filled Rotating Annuli
,”
ASME
Paper No. 97-GT-242.
9.
Sun
,
Z.
,
Kifoil
,
A.
,
Chew
,
J. W.
, and
Hills
,
N. J.
,
2004
, “
Numerical Simulation of Natural Convection in Stationary and Rotating Cavities
,”
ASME
Paper No. GT2004-53528.
10.
King
,
M. P.
,
Wilson
,
M.
, and
Owen
,
J. M.
,
2007
, “
Rayleigh–Bénard Convection in Open and Closed Rotating Cavities
,”
ASME J. Eng. Gas Turbines Power
,
129
(
2
), pp.
305
311
.
11.
Owen
,
J. M.
, and
Long
,
C. A.
,
2015
, “
Review of Buoyancy-Induced Flow in Rotating Cavities
,”
ASME J. Turbomach.
,
137
(
11
), p.
111001
.
12.
Lopez
,
J. M.
,
Marques
,
F.
, and
Avila
,
M.
,
2013
, “
The Boussinesq Approximation in Rapidly Rotating Flows
,”
J. Fluid Mech.
,
737
, pp.
56
77
.
13.
Blackburn
,
H. M.
, and
Sherwin
,
S.
,
2004
, “
Formulation of a Galerkin Spectral Element–Fourier Method for Three-Dimensional Incompressible Flows in Cylindrical Geometries
,”
J. Comput. Phys.
,
197
(
2
), pp.
759
778
.
14.
Karniadakis
,
G. E.
,
Israeli
,
M.
, and
Orszag
,
S. A.
,
1991
, “
High-Order Splitting Methods for the Incompressible Navier–Stokes Equations
,”
J. Comput. Phys.
,
97
(
2
), pp.
414
443
.
15.
Karniadakis
,
G.
, and
Sherwin
,
S.
,
2013
,
Spectral/HP Element Methods for Computational Fluid Dynamics
,
Oxford University Press
, Oxford, UK.
16.
Lewis
,
G. M.
, and
Nagata
,
W.
,
2004
, “
Linear Stability Analysis for the Differentially Heated Rotating Annulus
,”
Geophys. Astrophys. Fluid Dyn.
,
98
(
2
), pp.
129
152
.
17.
Pitz
,
D. B.
, and
Chew
,
J. W.
,
2015
, “
Numerical Simulation of Natural Convection in a Differentially Heated Tall Enclosure Using a Spectral Element Method
,” 23rd
ABCM
International Congress of Mechanical Engineering
, Associação Brasileira de Ciências Mecânicas, Rio de Janeiro, Brazil, Dec. 6–11.
18.
Trias
,
F.
,
Soria
,
M.
,
Oliva
,
A.
, and
Pérez-Segarra
,
C.
,
2007
, “
Direct Numerical Simulations of Two-and Three-Dimensional Turbulent Natural Convection Flows in a Differentially Heated Cavity of Aspect Ratio 4
,”
J. Fluid Mech.
,
586
, pp.
259
293
.
19.
Blackburn
,
H. M.
, and
Schmidt
,
S.
,
2003
, “
Spectral Element Filtering Techniques for Large Eddy Simulation With Dynamic Estimation
,”
J. Comput. Phys.
,
186
(
2
), pp.
610
629
.
20.
Busse
,
F.
, and
Carrigan
,
C.
,
1974
, “
Convection Induced by Centrifugal Buoyancy
,”
J. Fluid Mech.
,
62
(
03
), pp.
579
592
.
21.
Hollands
,
K.
,
Raithby
,
G.
, and
Konicek
,
L.
,
1975
, “
Correlation Equations for Free Convection Heat Transfer in Horizontal Layers of Air and Water
,”
Int. J. Heat Mass Transfer
,
18
(
7
), pp.
879
884
.
22.
Lloyd
,
J.
, and
Moran
,
W.
,
1974
, “
Natural Convection Adjacent to Horizontal Surface of Various Planforms
,”
ASME J. Heat Transfer
,
96
(
4
), pp.
443
447
.
You do not currently have access to this content.