A flow model is formulated to investigate the hydrodynamic structure of the boundary layers of incompressible fluid in a rotating cylindrical cavity with steady radial inflow. The model considers mass and momentum transfer coupled between boundary layers and an inviscid core region. Dimensionless equations of motion are solved using integral methods and a space-marching technique. As the fluid moves radially inward, entraining boundary layers develop which can either meet or become non-entraining. Pressure and wall shear stress distributions, as well as velocity profiles predicted by the model, are compared to numerical simulations using the software OpenFOAM. Hydrodynamic structure of the boundary layers is governed by a Reynolds number, Re, a Rossby number, Ro, and the dimensionless radial velocity component at the periphery of the cavity, Uo. Results show that boundary layers merge for Re < < 10 and Ro > > 0.1, and boundary layers become predominantly non-entraining for low Ro, low Re, and high Uo. Results may contribute to improve the design of technology, such as heat exchange devices, and turbomachinery.

1.
M. C.
Breiter
and
K.
Pohlhausen
, “
Laminar flow between two parallel rotating disks
,”
Technical Report No. 275562
,
ARL, USAF
,
1962
.
2.
W.
Rice
, “
An analytical and experimental investigation of multiple-disk turbines
,”
J. Eng. Power
87
,
29
(
1965
).
3.
K. E.
Boyd
and
W.
Rice
, “
Laminar inward flow of an incompressible fluid between rotating disks, with full peripheral admission
,”
J. Appl. Mech.
35
,
229
(
1968
).
4.
B. E.
Boyack
and
W.
Rice
, “
Integral method for flow between corotating disks
,”
J. Basic Eng.
93
,
350
(
1971
).
5.
D. N.
Wormley
, “
An analytical model for the incompressible flow in short vortex chambers
,”
J. Basic Eng.
91
,
264
(
1969
).
6.
M.
Firouzian
,
J.
Owen
,
J.
Pincombe
, and
R.
Rogers
, “
Flow and heat transfer in a rotating cavity with a radial inflow of fluid. Part 1: The flow structure
,”
Int. J. Heat Fluid Flow
6
,
228
(
1985
).
7.
J.
Owen
, “
Air-cooled gas-turbine discs: A review of recent research
,”
Int. J. Heat Fluid Flow
9
,
354
(
1988
).
8.
D.
May
,
J. W.
Chew
, and
T. J.
Scanlon
, “
Prediction of deswirled radial inflow in rotating cavities with hysteresis
,”
J. Turbomachinery
135
,
041025
(
2013
).
9.
B. G.
Vinod Kumar
,
J. W.
Chew
, and
N. J.
Hills
, “
Rotating flow and heat transfer in cylindrical cavities with radial inflow
,”
J. Eng. Gas Turbines Power
135
,
032502
(
2013
).
10.
R. T.
Deam
,
E.
Lemma
,
B.
Mace
, and
R.
Collins
, “
On scaling down turbines to millimeter size
,”
J. Eng. Gas Turbines Power
130
,
052301
(
2008
).
11.
V. D.
Romanin
and
V. P.
Carey
, “
An integral perturbation model of flow and momentum transport in rotating microchannels with smooth or microstructured wall surfaces
,”
Phys. Fluids
23
,
082003
(
2011
).
12.
V. G.
Krishnan
,
V.
Romanin
,
V. P.
Carey
, and
M. M.
Maharbiz
, “
Design and scaling of microscale Tesla turbines
,”
J. Micromech. Microeng.
23
,
125001
(
2013
).
13.
A.
Pfenniger
,
R.
Vogel
,
V. M.
Koch
, and
M.
Jonsson
, “
Performance analysis of a miniature turbine generator for intracorporeal energy harvesting
,”
Artif. Organs
38
,
E68
(
2014
).
14.
M.
Ruiz
and
V. P.
Carey
, “
Experimental study of single phase heat transfer and pressure loss in a spiraling radial inflow microchannel heat sink
,”
J. Heat Transfer
137
,
071702
(
2015
).
15.
S.
Sengupta
and
A.
Guha
, “
A theory of Tesla disc turbines
,”
Proc. Inst. Mech. Eng., Part A
226
,
650
(
2012
).
16.
S.
Sengupta
and
A.
Guha
, “
Analytical and computational solutions for three-dimensional flow-field and relative pathlines for the rotating flow in a Tesla disc turbine
,”
Comput. Fluids
88
,
344
(
2013
).
17.
A.
Guha
and
S.
Sengupta
, “
The fluid dynamics of the rotating flow in a Tesla disc turbine
,”
Eur. J. Mech., B: Fluids
37
,
112
(
2013
).
18.
A.
Guha
and
S.
Sengupta
, “
The fluid dynamics of work transfer in the non-uniform viscous rotating flow within a Tesla disc turbomachine
,”
Phys. Fluids
26
,
033601
(
2014
).
19.
A.
Guha
and
S.
Sengupta
, “
Similitude and scaling laws for the rotating flow between concentric discs
,”
Proc. Inst. Mech. Eng., Part A
228
,
429
(
2014
).
20.
P. R.
Tatro
and
E. L.
Mollö-Christensen
, “
Experiments on Ekman layer instability
,”
J. Fluid Mech.
28
,
531
(
1967
).
21.
E.
Serre
,
S.
Hugues
,
E.
Crespo del Arco
,
A.
Randriamampianina
, and
P.
Bontoux
, “
Axisymmetric and three-dimensional instabilities in an Ekman boundary layer flow
,”
Int. J. Heat Fluid Flow
22
,
82
(
2001
).
22.
F.
Marques
,
A. Y.
Gelfgat
, and
J. M.
Lopez
, “
Tangent double hopf bifurcation in a differentially rotating cylinder flow
,”
Phys. Rev. E
68
,
016310
(
2003
).
23.
J.
Mizushima
,
G.
Sugihara
, and
T.
Miura
, “
Two modes of oscillatory instability in the flow between a pair of corotating disks
,”
Phys. Fluids
21
,
014101
(
2009
).
24.
Y.
Do
,
J. M.
Lopez
, and
F.
Marques
, “
Optimal harmonic response in a confined Bödewadt boundary layer flow
,”
Phys. Rev. E
82
,
036301
(
2010
).
25.
C.
Panades
,
F.
Marques
, and
A.
Meseguer
, “
Mode competition in cylindrical flows driven by sidewall oscillations
,”
Phys. Rev. E
87
,
043001
(
2013
).
26.
J. M.
Lopez
and
F.
Marques
, “
Rapidly rotating cylinder flow with an oscillating sidewall
,”
Phys. Rev. E
89
,
013013
(
2014
).
27.
H.
Schlichting
and
K.
Gersten
,
Boundary-Layer Theory
(
Springer
,
2000
).
28.
A.
Mager
, “
Generalization of boundary-layer momentum-integral equations to three-dimensional flows including those of rotating system
,”
Technical Report No. 1067
,
NACA
,
1952
.
29.
J. M.
Owen
,
J. R.
Pincombe
, and
R. H.
Rogers
, “
Source-sink flow inside a rotating cylindrical cavity
,”
J. Fluid Mech.
155
,
233
(
1985
).
You do not currently have access to this content.