A three-scale k–ε turbulence model was recently developed for complex flows such as the rotor–rotor and rotor–stator cavities found in gas turbine engines. The three-scale model is a logical extension of the previous two-scale k–ε model of Ko and Rhode (1990). Both multiscale turbulence models are presented and assessed via comparison with measurements for possible adoption in future cavity computations. A single computer code solving the two-dimensional axisymmetric Navier–Stokes equations with a “switch” for selecting among the various turbulence models being compared was used. It was found for both cavity cases that the three-scale model gives a marginal improvement over the two-scale model. Further, both multiscale models give a substantial improvement over the standard k–ε model for the rotor–stator case, especially in the near-wall region where different eddy sizes are found. However, the feasibility of using a multiscale model for the rotor–rotor case is unclear since it gives improved values over the standard high-Re model in some regions but worse values in other regions. In addition, the solutions provide enhanced insight concerning the large changes in flow pattern previously photographed in the rotor–rotor case as rotation increases. In particular, it is shown how: (a) the number of recirculation zones increase with increasing rotation rate and (b) the recirculation zones decrease in size with a decreasing G ratio.

1.
Avva, R. K., Ratcliff, M. L., and Leonard, A. D., 1989, “CFD Analysis of Rotating Disk Flows,” Proc. ASME Winter Annual Meeting, O. Baysal, ed., ASME FED-Vol. 103, pp. 99–105.
2.
Backshall
R. G.
, and
Landis
F.
,
1969
, “
The Boundary-Layer Velocity Distribution in Turbulent Swirling Pipe Flow
,”
ASME Journal of Basic Engineering
, Vol.
91
, pp.
728
733
.
3.
Capp, S. P., 1983, “Experimental Investigation of the Turbulent Axisymmetric Jet,” Ph.D. Thesis, State University of New York, Buffalo, NY.
4.
Carmody
T.
,
1964
, “
Establishment of the Wake Behind a Disk
,”
ASME Journal of Basic Engineering
, Vol.
86
, pp.
869
882
.
5.
Chen
C. P.
, and
Guo
Kuan-liang
,
1991
, “
A Non-isotropic Multiple-Scale Turbulence Model
,”
Applied Mathematics and Mechanics
[English ed.], Vol.
12
, No.
10
, pp.
981
991
.
6.
Daily, J. W., Ernst, W. D., and Asbedian, V. V., 1964, “Enclosed Rotating Disks With Superposed Throughflow,” Hydrodynamics Laboratory, MIT, Report No. 64.
7.
Durao
D. F. G.
, and
Whitelaw
J. H.
,
1978
, “
Velocity Characteristics of the Flow in the Near Wake of a Disk
,”
Journal of Fluid Mechanics
, Vol.
85
, Part 2, pp.
369
385
.
8.
Fabris, G., Harsha, P. T., and Edelman, R. B., 1981, “Multiple-Scale Turbulence Modeling of Boundary Layer Flows for Scramjet Applications,” NASA CR-3433.
9.
Farthing
P. R.
,
Long
C. A.
,
Owen
J. M.
, and
Pincombe
J. R.
,
1992
, “
Rotating Cavity With Axial Throughflow of Cooling Air: Flow Structure
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
114
, pp.
237
246
.
10.
Guo, Z., 1995, “Development and Assessment of a Three-Scale k–ε Turbulence Model for Turbomachinery Applications,” Ph.D. Thesis, Texas A&M University, College Station, TX.
11.
Hanjalic, K., Launder, B. E., and Schiestel, R., 1980, “Multiple-Time-Scale Concepts in Turbulent Transport Modeling,” Turbulent Shear Flows, L. J. S. Bradbury et al., eds., Springer-Verlag, New York, Vol. 2, pp. 36–49.
12.
Jones
W. P.
, and
Launder
B. E.
,
1973
, “
The Prediction of Laminarization With a Two-Equation Model of Turbulence
,”
Int. J. Heat Mass Transfer
, Vol.
5
, pp.
301
314
.
13.
Kim, S.-W., and Chen, C.-P., 1987, “A Multiple-Time-Scale Turbulence Model Based on Variable Partitioning of Turbulent Kinetic Energy Spectrum,” NASA CR-179222.
14.
Kim, Y. W., and Metzger, D. E., 1992, “Comparison of Central Axis and Jet Ring Coolant Supply for Turbine Disk Cooling on a SSME-HPOTP Model,” Paper No. AIAA 92-0255.
15.
Ko, S. H., and Rhode, D. L., 1990, “Derivation and Testing of a New Multi-scale k–ε Turbulence Model,” Paper No. AIAA-90–0243.
16.
Ko
S. H.
, and
Rhode
D. L.
,
1992
, “
Thermal Details in a Rotor-Stator Cavity at Engine Conditions With a Mainstream
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
114
, pp.
446
453
.
17.
Launder, B. E., and Spalding, D. B., 1972, Mathematical Models of Turbulence, Academic Press, London.
18.
Leonard
B. P.
,
1979
, “
A Stable and Accurate Convective Modeling Procedure Based on Quadratic Upstream Interpolation
,”
Computer Methods in Applied Mechanics and Engineering
, Vol.
19
, pp.
59
98
.
19.
Owen
J. M.
, and
Bilimoria
E. D.
,
1977
, “
Heat Transfer in Rotating Cylindrical Cavities
,”
Journal of Mech. Engr. Sci.
, Vol.
19
, pp.
175
187
.
20.
Owen
J. M.
, and
Onur
H. S.
,
1983
, “
Convective Heat Transfer in a Rotating Cylindrical Cavity
,”
ASME JOURNAL OF ENGINEERING FOR POWER
, Vol.
105
, pp.
265
271
.
21.
Owen, J. M., and Rogers, R. H., 1989, Flow and Heat Transfer in Rotating-Disc Systems: Vol. 1, Rotor–Stator Systems, Research Studies Press, Taunton.
22.
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York.
23.
Phadke
U. P.
, and
Owen
J. M.
,
1988
, “
Aerodynamic Aspects of the Sealing of Gas-Turbine Rotor-Stator Systems, Part 1: The Behavior of Simple Shrouded Rotating-Disk Systems in a Quiescent Environment
,”
Int. J. Heat Fluid Flow
, Vol.
9
, No.
2
, pp.
98
105
.
24.
Pratte
B. D.
, and
Keffer
J. F.
,
1972
, “
The Swirling Turbulent Jet
,”
ASME Journal of Basic Engineering
, Vol.
94
, pp.
739
748
.
25.
Samuel
A. E.
, and
Joubert
P. N.
,
1974
, “
A Boundary-Layer Developing in an Increasingly Adverse Pressure Gradient
,”
Journal of Fluid Mechanics
, Vol.
66
, pp.
481
505
.
26.
Schiestel
R.
,
1983
, “
Multi-Scale Concept in Turbulence Modeling
,”
Journal de Mechanique Theorique et Appliquee
, Vol.
2
, pp.
417
449
.
27.
Virr, G. P., Chew, J. W., and Coupland, J., 1993, “Application of Computational Fluid Dynamics to Turbine Disc Cavities,” ASME Paper No. 93-GT-89.
28.
Williams
M.
,
Chen
W. C.
,
Bache
G.
, and
Eastland
A.
,
1991
, “
An Analysis Methodology for Internal Swirling Flow Systems With a Rotating Wall
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
113
, pp.
83
90
.
29.
Yu
J. M.
,
Sparrow
E. M.
, and
Eckert
E. R. G.
,
1973
, “
Experiments on a Shrouded, Parallel Disk Systems With Rotation and Coolant Throughflow
,”
Int. J. Heat Mass Transfer
, Vol.
16
, pp.
311
328
.
This content is only available via PDF.
You do not currently have access to this content.