Numerical Investigation of

Mixed Convection in AGRs

ByBy

Amir KeshmiriAmir Keshmiri

Supervisors:Supervisors: Prof. Dominique Laurence and Dr. Mark Cotton Prof. Dominique Laurence and Dr. Mark Cotton

School of Mechanical, Aerospace & Civil Engineering (MACE)School of Mechanical, Aerospace & Civil Engineering (MACE)

The University of ManchesterThe University of Manchester

Internal Seminar at the University of Manchester – 07/11/2007Internal Seminar at the University of Manchester – 07/11/2007

OutlineOutline

• Introduction to AGRs

• Ascending/Descending Flows

• The Geometry Studied

• Some Results

• Conclusions

• Future Work

[http://gt-mhr.ga.com]

[http://www.gen-4.org]

Advanced Gas-Cooled ReactorsAdvanced Gas-Cooled Reactors (AGRs) (AGRs)

[The Safety of the AGR by J M Bowerman (1982)]

Advanced Gas-Cooled ReactorsAdvanced Gas-Cooled Reactors (AGRs) (AGRs)

Advanced Gas-Cooled ReactorsAdvanced Gas-Cooled Reactors (AGRs) (AGRs)

[The Safety of the AGR by J M Bowerman (1982)]

Ascending/Descending Flows; Ascending/Descending Flows; Enhancement/Impairment of Heat TransferEnhancement/Impairment of Heat Transfer

2w

4qgDGr

8.0425.34108

PrReD

DGrBo

UD

D Re

ehD

Nu

pCPr

Solution MethodsSolution Methods

• In-House Code (CONVERT)In-House Code (CONVERT)

• Commercial CFD Package (STAR-CD)Commercial CFD Package (STAR-CD)

• Industrial Code (Code_Saturne)Industrial Code (Code_Saturne)

• or

• Radius=0.1 m

• Ascending Flow

• Constant Heat Flux BC

• ‘Boussinesq’ Approximation

180Reτ 5300ReD

Key Features of the Flow ProblemKey Features of the Flow Problem

The Governing EquationsThe Governing Equations

0)(1

z

W

r

rV

r

Continuity:

zt gTTr

Wr

rr

dz

dpW

zrVW

rr

)0

2

(1)(1

)()(1

Momentum:

r

Tr

rrWT

zrVT

rr t

t )Pr

(1

)()(1

Energy:

The Geometry Used in ‘CONVERT’The Geometry Used in ‘CONVERT’

RUN1=‘approximate turbulent flow’

RUN2=‘fully developed flow’

R Marching

• An in-house Fortran77 Code, ‘CONVERT’ (for Convection in Vertical Tubes)

• Finite Volume/Finite Difference Code

• Parabolic governing equations i.e. Marching problem

RANS ResultsRANS Results

The Turbulence Models Tested by CONVERT :

• Launder-Sharma k-ε model [1]

• Cotton-Ismael k-ε-S model [2]

• Suga NLEVM [3]

The Results are validated against:

• DNS of You et al (2003) [4]

• LS of Kim et al (2006) [5]

The analysis focuses on 4 cases:

• Gr/Re^2=0.000 Forced Convection

• Gr/Re^2=0.063 Early onset Mixed Convection

• Gr/Re^2=0.087 Laminarization

• Gr/Re^2=0.241 Recovery

RANS ResultsRANS Results

Gr/Re^2=0 – Forced ConvectionGr/Re^2=0 – Forced Convection

Gr/Re^2=0 – Forced ConvectionGr/Re^2=0 – Forced Convection

Gr/Re^2=0 – Forced ConvectionGr/Re^2=0 – Forced Convection

Gr/Re^2=0 – Forced ConvectionGr/Re^2=0 – Forced Convection

Gr/Re^2=0.087 – LaminarizationGr/Re^2=0.087 – Laminarization

Gr/Re^2=0.087 – LaminarizationGr/Re^2=0.087 – Laminarization

Gr/Re^2=0.087 – LaminarizationGr/Re^2=0.087 – Laminarization

Gr/Re^2=0.087 – LaminarizationGr/Re^2=0.087 – Laminarization

Budgets of Turbulent Kinetic EnergyBudgets of Turbulent Kinetic Energy

Gr/Re^2=0.087Gr/Re^2=0.087Gr/Re^2=0.0Gr/Re^2=0.0

Heat Transfer Enhancement/ImpairmentHeat Transfer Enhancement/Impairment

Heat Transfer Enhancement/ImpairmentHeat Transfer Enhancement/Impairment

Heat Transfer Enhancement/ImpairmentHeat Transfer Enhancement/Impairment

Nu and Cf DevelopmentsNu and Cf Developments

Nu and Cf DevelopmentsNu and Cf Developments

Effects of Reynolds NumberEffects of Reynolds Number

Effects of Reynolds NumberEffects of Reynolds Number

ConclusionsConclusions

• Mixed convection in an ascending flow in a heated pipe, is a very complex phenomenon, despite its simplicity; Thus requires more research.

• Most of the turbulence models successfully predict the flow field at relatively low heat loading i.e. small Gr/Re^2

• Only very few turbulence models (only Linear k-ε) can predict the Re-laminarization Phenomena.

• There is a close agreement between the results of Code_Saturne and STAR-CD for the tested models.

• The relatively more advanced turbulence models, such as Non-Linear k- of Suga and V2f models are observed to suffer from convergence problems at high Gr/Re^2.

• The few available DNS data are not sufficient to carry out in depth validation of the RANS models, particularly at the maximum heat transfer impairment point.

• Development of Code_Saturne by implementing some advanced wall functions such as Analytical and Numerical Wall Functions.

• Cross examination of Code_Saturne with TEAM and STREAM Codes.

• Testing more complex geometries such as rib roughened surfaces, etc.

Future WorkFuture Work

AcknowledgementsAcknowledgements

This work was carried out as part of the TSEC programme KNOO and as such we are grateful

to the EPSRC for funding under grant EP/C549465/1

ReferencesReferences

[1] Launder, B.E. and Sharma, B.I., 1974, “Application of the energy dissipation model of turbulence to the calculation of flow near a spinning disc”, Lett. Heat Mass Transfer, 1, pp. 131-138.

[2] Cotton, M.A., Ismael, J.O., 1998, “A strain parameter turbulence model and its application to homogeneous and thin shear flows”, Int. J. Heat Fluid Flow 19, pp. 326–337.

[3] Craft, T.J., Launder, B.E. and Suga, K. 1996, “Development and application of a cubic eddy-viscosity model of turbulence”, Int. J. Heat Fluid Flow, 17, pp. 108-115

[4] You, J., Yoo, J.Y. and Choi. H., 2003, “Direct Numerical Simulation of Heated Vertical Air Flows in Fully Developed Turbulent Mixed Convection”, Int. J. Heat Mass Transfer, 46, pp.1613-1627

[5] Kim, W.S., Jackson, J.D. and He, S. (2006), “Computational Investigation into Buoyancy-Aided Turbulent Flow and Heat Transfer to Air in a Vertical Tube”, Turbulence, Heat and Mass Transfer, 5, (Hanjalić, K., Nagano, Y. and Jakirlic, S. (Editors))

THE ENDTHE ENDTHANK YOUTHANK YOU