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1
Proceedings of the 37th
International & 4th
National Conference on Fluid Mechanics and Fluid Power
December 16-18, 2010, IIT Madras, Chennai, India
FMFP10 - AM - 04!!
FLUID FLOW SIMULATIONS WITHIN ROTATING ANNULUS
Arun K Sukumaran
College of Engineering Thiruvananthapuram, Kerala
Reji R.V
College of Engineering Thiruvananthapuram, Kerala
K.S.Santhosh College of Engineering
Thiruvananthapuram, Kerala
ABSTRACT
The fluid flow associated with heat transfer in
rotating annuli exists in many engineering
applications. The present study presents the
effect of the variation of rotational Reynolds
number (ReΩ) and axial Reynolds number (Rea)
on heat transfer and fluid flow in rotating
annulus for a radius ratio (j= ri/ro) 0.5. The
computational work using a CFD software
FLUENT is validated with experimental work.
The wall of inner rotating cylinder is kept at
constant heat flux and stationary outer wall is at
operating temperature. Results for various ReΩ
and Rea are presented. Axial velocity, swirl
velocity, inner wall temperature profiles and
Nusselt number variations are also presented.
Keywords- CFD, rotating annulus, heat transfer,
Nusselt number, rotational Reynolds number.
INTRODUCTION
The study of fluid flow coupled with heat
transfer in rotating annuli is of great importance
because of its many engineering applications in
electrical, mechanical and nuclear engineering
field. The rotating annulus means two concentric
or eccentric cylinders with an annular gap in
which one or both of the cylinders rotate with a
angular velocity. The applications of the rotating
annulus include rotating extractors, rotating
membrane filters, co-axial rotating heat pipes,
cylindrical bearings, rotating power transmission
systems and drilling operation of oil and gas
wells etc.
In rotating extractors the extracted material hold
in the annulus and the inner cylinder rotating
with a uniform angular velocity. If the inner
cylinder has small holes in its periphery, due to
rotation of inner cylinder the extracted material
going into inside of inner cylinder and flow
axially to the storage tank. In co-axial rotating
heat exchanger the hot fluid flows into the inner
cylinder and cold through the annulus. To
enhance heat transfer the inner cylinder rotate
with a constant angular velocity, due to the
thermal boundary layer disturbance more heat is
transferred from hot fluid to cold fluid. This type
of heat exchangers are used where the space
constrain are very important. In journal bearing
the annulus is the space between the rotating
shaft and bearing case. In turbo machine, the
shaft which is connected in between the
compressor and turbine has extreme temperature
difference in their two ends. Typically a liquid
hydrogen pumping turbopump system,
compressor end of the shaft is at cryogenic
temperature about 30K and the turbine end has
temperature about more than 650K. So the shaft
has high axial temperature gradient and it
rotate at high speed. Due to this high
temperature gradient exists in the shaft may lead
to failure. To avoid this failure, a coolant (air or
Proceedings of the 37th National & 4th International Conference on Fluid Mechanics and Fluid Power
December 16-18, 2010, IIT Madras, Chennai, India.
FMFP10 - AM - 04
2
liquid) is passed axially through annulus in
between the gap of shaft and casing. During
drilling operations liquid are pumped from a
surface mud tank via the drill pipe, through
nozzle in the rotating drill bit, and back to the
mud tank through the annular space between the
well and the drill pipe. Rotating electric
machines are subjected to very severe heating
phenomena resulting from electric losses
occurring in their different constituents. In large
electrical machines proper cooling a fluid is
flowing axially through the annulus in between
rotor and stator.
Literature Review
Convective heat transfer from a horizontal
rotating cylinder has been studied by many
authors. Most of them concluded that rotation
has no significant effects on the heat transfer
coefficient for low rotational speeds and that the
heat transfer is governed by free convection.
However, for very high rotational speeds, the
forced convection is the predominant heat
transfer regime and the average Nusselt number
on the cylinder surface is often obtained with
correlations such as Nu=aReb where a and b
being constants.
Sheng-Chung Tzeng, 2006 experimentally
investigated the local heat transfer of a co-axial
rotating cylinder. The test rig is designed in such
a way that to make the inner cylinder rotating
and the outer cylinder stationary. The inner
surface of the inner cylinder is heated with a
film heater. The local temperature distributions
of the inner and outer cylinder on axial direction
were measured using thermocouple. Under the
experimental condition, the ranges of the
rotational Reynolds number are 2400 ≤ ReΩ ≤
45,000. Experimental results reveal that the heat
transfer coefficient will increases with increase
in rotational Reynolds number. They develop an
empirical relations for average rotational Nusselt
number and the ratio of average rotational
Nusselt number to the Nusselt number without
rotation; correlations are
NuΩ=8.854Pr0.4×ReΩ0.262 and Ω
Ω respectively.
Seghir-Ouali et al., 2006 conducted an
experimental identification technique for the
convective heat transfer coefficient inside a
rotating cylinder with an axial airflow. The
experiments were carried out for a rotational
speed ranging from 4 to 880 rpm corresponding
to rotational Reynolds numbers (ReΩ) varying
from 1.6 × 103 to 4.7 × 10
5 and an air flow rate
varying from 0 to 530 m3/ h which corresponds
to an axial Reynolds numbers (Rea) ranging
from 0 to 3 × 104. They got a correlation
connecting for Nusselt number in terms of the
axial and rotational Reynolds numbers. The
correlation is Nu = 0.01963Rea0.9285
+ 8.5101 x
10-6
ReΩ 1.4513
, 0 < Rea< 3 x 104 and 1.6 x 10
3<
ReΩ < 2.77 x 105.
Escudier et al., 1995 experimentally investigated
axial, radial and tangential component of
velocity and root mean square velocity
fluctuations in concentric annular flow for
Newtonian and a shear thinning polymer in
laminar, transitional and turbulent flow region
with a rotating center body of radius ratio is
0.506. The influence of center body rotation on
pressure drop in concentric annular flow is
negligible under turbulent flow conditions for
both fluids.
Tzer-MingJeng,2007experimentally investigated
the heat transfer characteristics of Taylor–
Couette–Poiseuille flow in an annular channel
by mounting longitudinal ribs on the rotating
inner cylinder. The ranges of the axial Reynolds
number (Rea) and the rotational Reynolds
number (ReΩ) are Rea = 30 to1200 and ReΩ = 0
to 2922 respectively.
Joo-Sik Yoo, 1998 numerically investigated the
effect of mixed convection of air with Pr = 0.7
between two horizontal concentric cylinders.
The inner cylinder is hotter than the outer
cylinder. The forced flow is induced by the cold
outer cylinder which is rotating slowly with
constant angular velocity with its axis at the
center of the annulus. Investigations are made
for various combinations of Rayleigh number
based on the gap width, rotational Reynolds
number and ratio of the inner cylinder diameter
to gap width in the range of
Ra≤5×104, Re≤1500 and .
Ming et al., 1998 conducted numerical
computation for turbulent mixed convection of
3
air in a horizontal concentric annulus between a
cooled outer cylinder and a heated, rotating,
inner cylinder. Numerical results are obtained
for the Rayleigh number, Ra, ranging from 107
to 1010
, the Reynolds number, Re, from 0 to 105
and the radius ratio from 2.6 to 10 for a constant
Prandtl number of 0.7. Results show that the
mean Nusselt number, Nu, increases with an
increase in Ra, but decreases with an increase in
Rea or radius ratio.
As evident from the literature review, numerical
simulations validated with experimental results
will provide useful information for designing
annular rotating systems associated with fluid
flow and heat transfer.
NUMERICAL ANALYSIS
In the present work, numerical analysis of fluid
flow and heat transfer in a rotating annulus with
various radius ratios and various axial flow is
considered. The inner cylinder rotates with a
uniform angular velocity while outer cylinder is
kept stationary. The surface of the inner
cylinder is subjected to uniform heat flux and
surface of outer cylinder is in isothermal
(operating) condition. A validation study was
conducted to check the compatibility of CFD
software FLUENT 6.3 for predicting heat
transfer in rotating annulus. The experimental
study mentioned in Sheng-Chung Tzeng, 2006
was taken and the dimension and boundary
conditions are being exactly same as that in
experimental setup. The present analysis
presents how the variation of rotational
Reynolds number (ReΩ) and axial Reynolds
number (Rea) influence the heat transfer and
fluid flow in rotating annulus.
Physical Model
The present study is the fluid flow and heat
transfer through rotating annulus with axial
flow. Figure 1 shows the physical model of the
present study, the inner cylinder is rotating with
an angular velocity ω rad/sec and outer cylinder
is kept stationary. Assuming the flow is
incompressible and steady, the outer cylinder is
kept in isothermal condition and inner cylinder
wall subjected to constant heat flux. The inlet
velocity of the fluid is uniform ui and entering at
operating temperature and exit through the other
side of the annulus.
Figure. 1. Physical Model.
Computational Model
The assumptions made for numerical analysis is
incompressible, two dimensional axi-symmetric
steady flow. Figure 2 shows the computational
domain of the annulus.
Figure 2. Computational model for the present
study.
The boundary conditions of the computational
domain are shown in the Table 1.
Table 1. Boundary conditions of the annular
flow
Zone Type
Flow inlet Velocity
inlet 300k
Flow outlet Out flow Flow rate
weighting 1
Fixed outer
wall Stationary Isothermal
Rotating inner
wall Rotating
Constant heat
flux
Solver settings and material properties are given
in tables 2 and 3 respectively.
4
Governing equations
The incompressible Navier-Stokes equations,
energy equation coupled with k-e turbulence
model in single rotating frame were considered
for this case. Additional terms originated from
the relative frame formulation were treated a
source terms in the FLUENT formulations.
Table 2. Solver settings of the annular flow
Space Axisymmetric swirl
Time Steady
Viscous Standard k-epsilon
turbulence model
Pressure-velocity
coupling
Simple (semi implicit
pressure linked equation)
Fluid Air
Inner wall Copper
Outer wall Copper
Table. 3. Material properties used
Mate
rial
name
Property Unit Method Value
Air
Density Kg/m3 Boussin
esq 1.225
Specific
heat J/kg-K Constant
1006.
43
Thermal
conductivit
y
W/m-
K Constant
0.024
2
Viscosity Kg/m-
s Constant
1.789
x10-05
Thermal
expansion
coefficient
1/K Constant 0.003
Copp
er
Density Kg/m3
Constant 8978
Specific
heat J/kg-K Constant 381
Thermal
conductivit
y
W/m-
K Constant 387.6
Bake
lite
Density Kg/m3
Constant 1280
Specific
heat J/kg-K Constant 1590
Thermal
conductivit
y
W/m-
K Constant 0.23
The discretization of flow domain is done using
a commercial software GAMBIT with
quadrilateral structured mesh and defined
appropriate boundary conditions. Numerical
analysis has been carried out using commercial
software FLUENT 6.3.26. k-ε model for
turbulence, second order upwind for modeling
momentum, swirl velocity and first order
upwind for energy and segregated implicit
scheme was used to obtain steady state solution.
Validation
The experimental work of Sheng Chung Tzeng,
2006 was taken for validation of the
methodology.
Figure.3. Computational domain for validation
Figure 3 shows the computational domain for
the validation case. The dimension of the
computational domain length is 120 mm, inner
and outer diameter is 60 mm and 67 mm
respectively. The boundary conditions, solver
settings and material properties used for
validation are given in tables 4, 5.
Table.4 Boundary conditions for heat transfer in
a small gap between co-axial rotating cylinders.
Zone Type
Wall 1 Stationary Isothermal
Wall 2 Stationary Isothermal
Inner
cyl wall Rotating
Constant heat flux
850 W/m2
Outer
cylinder
wall
Stationary Isothermal
5
Table.5 Solver settings for heat transfer in a
smallgap between co-axial rotating cylinders.
Space Axisymmetric swirl
Time Steady
Viscous Standard k-epsilon
turbulence model
Pressure-
velocity
coupling
Simple (semi implicit
pressure linked equation)
Fluid Air
Inner wall Bakelite
Outer wall Copper
Wall 1 Copper
Wall 2 Copper
For numerical analysis, the conditions and
material properties are same as that of the
experimental setup. The numerical work is
carried out in the range of 3000≤ Rea≤45,000 .
Nusselt number calculated from the
experimental correlation (Sheng, 2006,
, 2400 ReΩ
45,000.) and obtained from the numerical
analysis is shown in fig. 4. The numerical results
are slightly over predicted for all cases of
Reynolds number. The error of numerical value
with correlated value in between 4 to 15%.
Reason of this error may be due to discretization
and numerical errors.
Figure.4 Comparison of Nusselt number with
Sheng (2006)
RESULTS AND DISCUSSIONS
Axial Velocity Distribution
Figure 5 and 6 shows the axial velocity
distribution at 0.8L from inlet of annulus for
axial Reynolds number 3000 and 11000
respectively. The analysis has to be done for
rotational Reynolds number ranging from 5000
to 18000 and axial Reynolds number varying
from 3000 to 11000. When rotational Reynolds
number increases, the magnitude of axial
velocity decreases, this is due to the rotation.
That is, the rotation effect reduces the axial
velocity component. From these two graphs, it is
clear the rotation has significant effect only at
low axial Reynolds numbers. At high axial
Reynolds numbers the effect of rotation will
diminish and the magnitude of axial velocity is
almost same.
Figure 5. Axial Velocity Distribution at 0.8L
from inlet of annulus for Rea 3000.
6
Figure 6. Axial velocity distribution at 0.8L
from inlet of annulus for Rea 11000.
Swirl Velocity Distribution
Figure 7 and 8 shows the swirl velocity
distributions at 0.8L from the inlet of annulus
for axial Reynolds number 3000 and 7000
respectively As the rotational Reynolds number
increases from 4000 to 18000 the hydrodynamic
boundary layer become thinner at inner rotating
wall. . From these graphs it is evident that the
axial Reynolds number has no effect on swirl
velocity.
Figure 7. Swirl velocity distribution at 0.8L
from inlet of annulus for Rea 3000.
Figure 8. Swirl velocity distribution at 0.8L
from inlet of annulus for Rea 7000.
Temperature Distribution
Figure 9 and 10 shows the temperature
distribution of inner wall of the annulus for axial
Reynolds number 3000 and 11000 respectively.
As rotational Reynolds number increases, wall
temperature decreases which may due to high
rate of transfer of thermal energy transfer from
the inner wall to fluid. Form these graphs it is
evident that when axial Reynolds number
increases more heat is transferred from inner
rotating wall to fluid flowing through annulus.
Figure 9. Dimensional Temperature distribution
of inner wall for Rea 3000.
7
Figure 10. Non Dimensional Temperature
distribution of inner wall for Rea 3000.
Nusselt Number
Figure 11 shows the variation of Nusselt number
with the rotational Reynolds number for
different axial Reynolds number.
Figure.11 Variation of Nusselt number with
Rotational Reynolds number
From this graph it is evident that as rotational
Reynolds number increases, Nusselt number
increases for constant axial Reynolds number
and at high axial Reynolds number the effect
diminishes. This is because due to the
disturbance of boundary layer. That is when
axial Reynolds number increases both thermal
and hydrodynamic boundary layers become
thinner, so more heat is transferred from solid to
liquid. As in the case of higher axial Reynolds
number, rotational Reynolds number has less
significance. This is due to the fluid particle has
higher axial velocity compared to rotational
velocity.
CONCLUSIONS
A numerical study and a detailed parametric
analysis on the problem have been conducted on
the rotating heated annulus. The current
problem is validated using an experimental work
and the analysis is in good agreement with
correlation. The parameters like axial and swirl
velocity components, temperature distribution
and Nusselt number variations are studied and
discussed.
· As rotational Reynolds number increases
the magnitude of axial velocity will
decreases only at low axial Reynolds
number but at high axial Reynolds
numbers the effect of rotation will
diminish.
· The axial Reynolds number has no
significant effect on swirl velocity. As
the rotational Reynolds number increases
the hydrodynamic boundary layer
become thinner and is nearer to inner
rotating wall.
· As rotational Reynolds number
increases, wall temperature decreases
which may due to high rate of transfer of
thermal energy from the inner wall to
fluid.
· As axial Reynolds number increases
more heat is transferred from inner
rotating wall to the fluid which is
flowing through annulus.
· As rotational Reynolds number
increases, Nusselt number also increases
for low axial Reynolds number and at
high axial Reynolds number the effect
diminishes.
· As rotational speed increases more heat
is transferred from shaft to fluid, which
8
is due to the disturbance of thermal
boundary layer.
NOMENCLATURE
Rea- Axial Reynolds Number =ρ μ
ReΩ- Rotational Reynolds Number=ρω µ
Nu – Nusselt Number =
h – Heat Transfer Coefficient, W/m2K
d – Width of annulus ri−ro, m
ri – Radius of inner cylinder, m
ro – Radius of outer cylinder, m
k – Thermal conductivity of fluid, W/mK
Ui – Uniform inlet velocity, m/s
– Axial velocity at any point, m/s
– Swirl velocity at any point, m/s
– Swirl velocity corresponding to angular
velocity= riω
P– Pressure, N/m2
T – Temperature, K
L– Length, m
– Non- Dimensional axial velocity =
- Non- Dimensional swirl velocity =
T/Tot-Non-Dimensional temperature distribution
Tot- Operating temperature, K
j – Radius ratio = ri/ro
Greek symbols
ρ - Density of fluid, kg/m3
τw - Wall shear stress, N/m2
ω- Angular velocity of inner cylinder, rad/s
Subscripts/superscripts
a- Axial
Ω- Rotational
i – Inner, Inlet
o - Outer, Outlet
w – Wall
s – Swirl
ot – Operating temperature
REFERENCES
Escudier, I W Gouldson, 1995. Concentric
annular flow with center body rotation of a
newtonian and a shear- thinning liquid,
International Journal of Heat and Fluid Flow
Vol. 16, 156-162.
Joo-Sik Yoo, 1998. Mixed convection of air
between two horizontal concentric cylinders
with a cooled rotating outer cylinder,
International Journal of Heat Mass Transfer,
Vol. 41, pp. 293-302.
Ming-I Char, Yuan-Hsiung Hsu, 1998
Numerical prediction of turbulent mixed
convection in a concentric horizontal rotating
annulus with low-re two-equation models,
International Journal of Heat and Mass Transfer,
Vol. 41, pp. 1633-1643.
Seghir-Ouali et al., 2006. Convective heat
transfer inside a rotating cylinder with an axial
air flow, International Journal of Thermal
Sciences, Vol.45, 1166–1178.
Sheng-Chung Tzeng, 2006. Heat transfer in a
small gap between co-axial rotating cylinders,
International Communications in Heat and Mass
Transfer Vol. 33, 737–743.
Tzer-Ming Jeng et al., 2007. Heat transfer
enhancement of taylor–couette–poiseuille flow
in an annulus by mounting longitudinal ribs on
the rotating inner cylinder, International Journal
of Heat and Mass Transfer, Vol. 50, 381–390.
Molki, K. N. Astill, E. Leal., 1990. Convective
heat-mass transfer in the entrance region of a
concentric annulus having a rotating inner
cylinder, International Journal of Heat and Fluid
Flow, Volume 11, 120-128
Lee T.S., 1992. Numerical computation of fluid
convection with air enclosed between the annuli
of eccentric heated horizontal rotating cylinders,
Computers & Fluids, Vol 21, 355-368