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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

[email protected]

Reji R.V

College of Engineering Thiruvananthapuram, Kerala

[email protected]

K.S.Santhosh College of Engineering

Thiruvananthapuram, Kerala

[email protected]

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

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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

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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.

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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

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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.

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Figure 6. Axial velocity distribution at 0.8L


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


Figure 8. Swirl velocity distribution at 0.8L


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.

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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

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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

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