Abstract

The Rotor-Stator cavity (R-S cavity) is a prototype model in many engineering applications such as gas turbine secondary air systems. The flow characteristics of the R-S cavity are relatively complex considering the rotation effect. A radial through flow is usually superposed in the R-S cavity, further complicating the fluid motion. The flow inside an R-S cavity with a superposed radial throughflow can be divided into four regions based on flow characteristics: a source region, a rotor entrainment layer, a rotating core, and a mixing region. In the present work, a one-dimensional (1-D) radial swirl ratio predictive model is built and verified based on computational fluid dynamics (CFD) results in the rotor entrainment layer and rotating core region. A swirl ratio gradient governing equation is deduced at first. The equation involves two scale factors CS and CR which are related to the stator and rotor friction correspondingly. The governing equation in the rotor entrainment layer is further simplified by neglecting the stator friction factor CS where the rotor friction prevails. Then, based on the discretized governing equation, CR and CS are determined via approximation with CFD results. Correlations between CR, CS, and nondimensional radial through flowrate cw are determined and verified. The obtained correlations and the discretized governing equation together form the complete swirl ratio, predictive model. The model accuracy is described by cross-correlation coefficients, which show a good agreement. The 1-D model is then implemented to different rotating speed cases, based on which the model portability is discussed.

References

1.
Rolls-Royce plc
.,
1996
The Jet Engine
, reprinted, 5th ed., Derby, UK.
2.
Lei
,
X.
,
RuoNan
,
W.
,
Guang
,
L.
,
ZengYan
,
L.
, and
Qiang
,
D.
,
2020
, “
Numerical Investigation on Unsteady Characteristics in Different Rim Seal Geometries: Part A
,”
ASME
Paper No. GT2020-14832
.10.1115/GT2020-14832
3.
von Karman
,
T.
,
1921
, “
Uber Laminare Und Turbulente Reibung
,”
Z. Fur Angew. Mathematik Und Mechanik
,
1
(
4
), pp.
233
252
.10.1002/zamm.19210010401
4.
Schlichting
,
H.
, and
Gersten
,
K.
,
2017
,
Boundary-Layer Theory
,
Springer
,
Berlin Heidelberg
.
5.
Bödewadt
,
U. T.
,
1940
, “
Die Dehstromung Uber Festem Grunde
,”
Z. Fur Angew. Mathematik Und Mechanik¨
,
20
(
5
), pp.
241
253
.10.1002/zamm.19400200502
6.
Ekman
,
V. W.
,
1905
, On the Influence of the Earth's Rotation on Ocean-Currents. Ark. Mat. Astron. 205 Fys., 2, pp.
1
52
.
7.
LINGWOOD
,
R.
,
1997
, “
Absolute Instability of the Ekman Layer and Related Rotating Flows
,”
J. Fluid Mech.
,
331
, pp.
405
428
.10.1017/S0022112096004144
8.
Lance
,
G. N.
,
Rogers
,
M. H.
, and
Howarth
,
L.
,
1962
, “
The Axially Symmetric Flow of a Viscous Fluid Between Two Infinite Rotating Disks
,”
Proc. R. Soc. London. Ser. A. Math. Phys. Sci.
,
266
(
1324
), pp.
109
121
.10.1098/rspa.1962.0050
9.
Batchelor
,
G. K.
,
1951
, “
Note on a Class of Solutions of the Navier-Stokes Equations Representing Steady Rotationally-Symmetric Flow
,”
Q. J. Mech. Appl. Math.
,
4
(
1
), pp.
29
41
.10.1093/qjmam/4.1.29
10.
Stewartson
,
K.
,
1953
, “
On the Flow Between Two Rotating co-Axial Discs
,”
Math. Proc. Cambridge Philos. Soc.
,
49
(
2
), pp.
333
341
.10.1017/S0305004100028437
11.
Daily
,
J. W.
, and
Nece
,
R. E.
,
1960
, “
Chamber Dimension Effects on Induced Flow and Frictional Resistance of Enclosed Rotating Disks
,”
J. Basic Eng.
,
82
(
1
), pp.
217
232
.10.1115/1.3662532
12.
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
.10.1016/0894-1777(92)90081-F
13.
Owen
,
J. M.
,
1989
, “
An Approximate Solution for the Flow Between a Rotating and a Stationary Disc
,”
J. Turbomach.
,
111
(
3
), pp.
323
332
.10.1115/1.3262275
14.
KUROKAWA
,
U.
,
TOYOKURA
,
T.
,
SHINJO
,
M.
, and
MATSUO
,
K.
,
1978
, “
Roughness Effects on the Flow Along an Enclosed Rotating Disk
,”
Bull. JSME
,
21
(
162
), pp.
1725
1732
. 10.1299/jsme1958.21.1725
15.
Will
,
B.-C.
,
2011
, “
Theoretical, Numerical and Experimental Investigation of the Flow in Rotor-Stator Cavities With Application to a Centrifugal Pump
,”
Ph.D. thesis
, University of Duisburg-Essen, Essen, Germany.https://d-nb.info/1017451427/34
16.
Kurokawa
,
J.
, and
Sakura
,
M.
,
1988
, “
Flow in a Narrow Gap Along an Enclosed Rotating Disk With Through-Flow
,”
JSME Int. J. Ser. 2, Fluids Eng., Heat Transfer, Power, Comb., Thermophys., Prop.
,
31
(
2
), pp.
243
251
.10.1299/jsmeb1988.31.2_243
17.
Debuchy
,
R.
,
Dyment
,
A.
,
Muhe
,
H.
, and
Micheau
,
P.
,
1998
, “
Radial Inflow Between a Rotating and a Stationary Disc
,”
Eur. J. Mech., B/Fluids
,
17
(
6
), pp.
791
810
.10.1016/S0997-7546(99)80014-4
18.
Owen
,
J. M.
, and
Rogers
,
R. H.
,
1989
,
Flow and Heat Transfer in Rotating-Disc Systems
,
United States
.
19.
Poncet
,
S.
,
Chauve
,
M.
, and
Le Gal
,
P.
,
2005
, “
Turbulent Rotating Disk Flow With Inward Throughflow
,”
J. Fluid Mech.
,
522
, pp.
253
262
.10.1017/S0022112004002046
20.
Daily
,
J. W.
,
Ernst
,
W. D.
, and
Asbedian
,
V. V.
,
1964
,
Enclosed Rotating Discs With Superposed Through-Flow
,
Massachusetts Institute of Technology
,
Cambridge, MA
, Report No. 64.
21.
Mearstone
,
L.
,
2015
, “Theoretical Modelling of Flow in Rotor-Stator Systems,”
Ph.D. thesis
, University of Bath, Bath, UK.https://researchportal.bath.ac.uk/en/studentTheses/theoretical-modelling-of-flow-in-rotor-statorsystems
22.
Poncet
,
S.
,
Facchini
,
B.
,
Joliot-Curie
,
F.
,
Stecco
,
S. S.
, and
Marta
,
S.
,
2010
, “
Rans Modeling of Flow in Rotating Cavity System
,” Paper No.
hal-00679124
.https://hal.archives-ouvertes.fr/hal-00679124/document
23.
Hu
,
B.
,
2018
, “
Numerical and Experimental Investigation on the Flow in Rotor-Stator Cavities
,”
Ph.D. thesis
,
University of Duisburg-Essen
,
Essen, Germany
. https://d-nb.info/1163534072/34
24.
Dorfmann
,
L. A.
,
1963
,
Hydrodynamic Resistance and the Heat Loss of Rotating Solids
,
Oliver and Boyd
,
Edinburgh, Scotland
.
25.
Schultz-Grunow
,
F.
,
1935
, “
Der Reibungswiderstand Rotierender Scheiben in Gehäusen
,”
Z. angew. Math. Mech.
,
15
(
4
), pp.
191
204
.10.1002/zamm.19350150403
26.
Peter R.N
,
C.
,
2011
,
Rotating Flow
,
Butterworth-Heinemann
,
Oxford, UK
.10.1016/C2009-0-30534-6
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