Coolant Flow and Heat Transfer in PBMR Core With CFD · 2012-03-26 · Coolant Flow and Heat Transfer in PBMR Core With CFD Coolant Flow and Heat Transfer in PBMR Core With CFD Heikki

Coolant Flow and Heat Transfer in PBMR Core With CFD

Coolant Flow and Heat Transfer in PBMR CoreWith CFD

Heikki Suikkanen

Lappeenranta University of TechnologyDepartment of Energy and Environmental Technology

GEN4FIN

Heikki Suikkanen GEN4FIN 3.10.2008 1/ 27


Contents

1 Pebble-Bed Modular Reactor (PBMR)

2 Computational Fluid Dynamics (CFD)

3 Modeling Approach

4 Example Case

5 Discussions



Pebble-Bed Modular Reactor (PBMR)

Contents



3 Modeling Approach

4 Example Case

5 Discussions




The PBMR Project

PBMR-400

Figure source:http://metnet.files.wordpress.com/2008/06/pbmr.jpg

Pebble-Bed Modular Reactor (Pty) Limited

Founded by Westinghouse, EskomHoldings Limited, and the IndustrialDevelopment Corporation of SouthAfrica Limited in 1999

Headquarters in Centurion, SouthAfrica

Mission is to develop commercialhigh-temperature reactors for theproduction of electricity and processheat

Demonstration plant to be built inKoeberg near Cape Town (2010→)




Spherical Fuel Elements

PBMR fuel design

Figure sources:http://blogs.princeton.edu/chm333/f2006/nuclear/trisoball.jpghttp://www.ne.doe.gov/images/trisoFuelPellet.gif

TRISO coated particle

Fuel design together with the useof gas coolant and non-metalliccore structures allows highoperating temperatures




Power Plant Design

PBMR Brayton cycle layout

Figure source:http://www.schillerinstitute.org/graphics/conferences/070915_Kiedrich/ferreira/pbmr_schematic.jpg

Demonstration plant

Reactor thermal power 400 MW(165 MWe)

Recuperative helium gas-turbinecycle

Dedicated for electricity generation




Reactor Unit

PBMR reactor unit

Figure source:http://www.schillerinstitute.org/graphics/conferences/070915_Kiedrich/ferreira/power_conversion_unit.jpg

6.2 m diameter, 28 m high

Fixed centre and side reflectorsconstructed from graphite blocks

Graphite structures supported by asteel core barrel

Three de-fueling chutes connected tocore unloading devices

Reactivity control system andreactivity shutdown system

Two coolant flow inlets and one outlet




Reactor Core

Core vertical cross section

Annular core region surrounded bygraphite reflectors

Control rod channels in the side reflector

Channels for small absorber spheres inthe centre reflector

High thermal capacity and other designfeatures make passive decay heatremoval possible

Figure sources:Venter, P. J. et al. Integrated design approach of the pebble bed modular reactorusing models. Nuclear Engineering and Design, 2007. Vol. 237: 12-13. pp. 1341-1353.




Reactor Core

Main parameters

Reactor thermal power 400 MW

Reactor inlet temperature 500 ◦C

Reactor outlet temperature 900 ◦C

System pressure 9.0 MPa

Coolant mass flow rate 192 kg/s

Core outer diameter 3.7 m

Core inner diameter 2.0 m

Core height 11 m

Number of fuel pebbles 452 000

Core horizontal cross section

Source:Venter, P. J. et al. Integrated design approach of the pebble bed modular reactor usingmodels. Nuclear Engineering and Design, 2007. Vol. 237: 12-13. pp. 1341-1353.



Computational Fluid Dynamics (CFD)

Contents



3 Modeling Approach

4 Example Case

5 Discussions




Basics of CFD

Geometry under investigation isdefined

The geometry is discretized (meshed)

Boundary conditions are defined

Governing equations are written for each cell inalgebraic form

Numerical methods are used to obtain the solution

Results are post-processed and analyzed

Discretized flow region

Source:Lectures of numerical methods in heat and mass transferby Professor Timo Hyppänen (LUT 2008)




Computer Software

A UDF for defining inertial resistance profile

DEFINE_PROFILE(inertial_res,t,i){

cell_t c;

begin_c_loop(c,t){

F_PROFILE(c,t,i) = 3.5*(1 - C_POR(c,t))/(d_p*pow(C_POR(c,t),3));

}end_c_loop(c,t)

}

A variety of commercial and freesoftware for pre-processing,solving and post-processingexists

In this work a commercialsoftware Fluent by Ansys Inc. isused for solving andpost-processing

Fluent has a good range ofbuilt-in models and schemes

User coding via user definedfunctions (UDFs)



Modeling Approach

Contents



3 Modeling Approach

4 Example Case

5 Discussions



Modeling Approach

Porous Medium Approximation

Packing fraction = VspheresVtotal

A random pack of spheres

Figure Source:http://cherrypit.princeton.edu/rcp64.gif

The large number of fuel pebbles makes it impossible tomodel the whole core with individual pebbles (computingpower limitations)

A Porous medium approximation is used

Pebble-bed can be considered a packed bed of sphericalparticles

Parameter that describes the packing’s properties is thevoid/packing fraction

A constant value or a position dependent profile can beused for the packing/void fraction

Fluent includes a simple porous medium model by default



Modeling Approach

Core Flow and Heat Transfer Details

It is not necessary to take pebble motion intoaccount in coolant flow and heat transfercalculations (very slow speed)

Coolant gas flows through the pebbles

Pebbles generate heat

Convection heat transfer (coolant-pebble)

Conduction heat transfer (pebble-pebble,pebble-reflector, all solids)

Radiation heat transfer (pebble-pebble,pebble-reflector walls, core barrel-RPV wall)

Heat transfer details



Example Case

Contents



3 Modeling Approach

4 Example Case

5 Discussions



Example Case

Computational Domain

Axisymmetric geometry used inthe computations

The active core region bounded by thepressure vessel is studied

A simplified geometrical representation ofthe core

Axisymmetric geometry without additionalcooling or leakage flow paths

Constant temperature boundary conditionat the pressure vessel outer wall

Porous medium approximation of the fuelregion



Example Case

Material Properties

Thermal conductivity of H-451 graphite

0 200 400 600 800 1000 1200 1400 160040

60

80

100

120

140

160

Temperature [ °C ]

The

rmal

con

duct

ivity

[W

/m ⋅

K]

Original data (axial)Original data (radial)Polynomial fit (axial)Polynomial fit (radial)

Appropriate material properties are issued

Helium: density(ideal gas law), specificheat f(T), thermal conductivity f(T),viscosity f(T)

Graphite (both reflector and fuel):constant density, specific heat f(T),thermal conductivity f(T), constantemissivity

Steel (core barrel and RPV): constantdensity, specific heat f(T), thermalconductivity f(T), constant emissivity



Example Case

Fluid Flow Equations

Fluid flow in a domain is governed by the conservation laws of mass andmomentum

Fuel pebbles form a volume blockage that is taken into account by adding lossterms to the momentum equations

Continuity equation

∂ρ∂t +∇ · (ρu) = 0

Momentum equation in x-direction

∂∂t (ρu)+∇·(ρuu) = ∇·(µ∇u)− ∂p

∂x +Bx +Vx

Viscous losses

−∇pvisc = µK U

+Inertial losses

−∇piner = Fρ|U|U√K

=Pressure drop over the pebble-bed

|4p|L = 150µ

d2p

(1−ε)2

ε3 u + 1.75ρdp

(1−ε)ε3 u2



Example Case

Porosity Variation

Porosity profile

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.80.3

0.4

0.5

0.6

0.7

0.8

0.9

1

r [m]

Voi

d fr

actio

n

⇐

Increase in void fraction near the reflectorwalls is taken into account by using acorrelation suggested in literature

Larger void fraction near the walls affects flowand heat transfer

Radial variation of void fraction

ε (r) = ε∞h1 + c1e−c2(r−ri)/dp

i, ri 6 r 6 ro+ri

2 ,

ε (r) = ε∞h1 + c1e−c2(ro−r)/dp

i, ro+ri

2 < r 6 ro



Example Case

Energy Equation in the Pebble-Bed

A mixture model is used for heat transfer in the fuel/flow region

Local thermal equilibrium between fuel and coolant is assumed

Correlation suggested in literature is used for conduction + radiation heat transferbetween the fuel pebbles

Energy equation in porous mediumˆ(ρcp)s (1− ε) + (ρcp)f ε

˜ “∂T∂t +∇ · (uT )

”= ∇ · (keff∇T ) + Sh, keff = εkf + (1− ε) ks

Correlation for pebble-bed thermal conductivity (conduction + radiation)

ks = 4σT 3dp

(`1− α0.5´ (1− α) + α0.5

2ε−1

hBz+1

Bz

i »1 + 1

( 2ε−1)kp

–−1),

Bz = 1.25 ·“

α1−α

”10/9



Example Case

Nuclear Heat Source

Chopped cosine power profile

0 1 2 3 4 5 6 7 8 9 10 111

2

3

4

5

6

7

Axial position [m]

Hea

t gen

erat

ion

rate

per

uni

t vol

ume

[MW

/m3 ]

Nuclear heat source is added to theenergy equation as an additionalsource term

A chopped cosine approximation forvertical power distribution

No available data about what the"real" profile would be like

Total heating power of 400 MW



Example Case

Results of Steady-State Computations

Contours of temperature in ◦C Velocity profile

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.80

1

2

3

4

5

6

7

8

9

10

Radial position [m]

Vel

ocity

[m

/s]

Pressure drop over the core 401 kPa

Average outlet temperature 897 ◦C



Discussions

Contents



3 Modeling Approach

4 Example Case

5 Discussions



Discussions

Improving the Accuracy and Reliability

Use of a more detailed 3D geometry

Power profile mapped from a reactor physics code

Studying the validity and accuracy of correlations

Using a two energy equation model in the fuel region (especially intime-dependent cases)

Energy equation for the fluid phase

ε (ρcp)f∂Tf∂t + (ρcp)f [∇ (uTf )] = ∇ · (kf∇Tf ) + hfsafs (Ts − Tf ) + Sh,f

Energy equation for the solid phase

(1− ε) (ρcp)s∂Ts∂t = ∇ · (ks∇Ts) + hfsafs (Tf − Ts) + Sh,s



Discussions

Further Research Interests

Randomly packed pebbles

Figure: Doctor Payman Jalali (LUT)

Using Discrete ElementMethod (DEM) to studythe packing behavior nearthe walls

Using the two energyequation model incomputations (alreadydone but there are someproblems in implementingthe model properly toFluent)



Discussions

Thank you for listening!Any questions?


Documents

Coolant Flow and Heat Transfer in PBMR Core With CFD · 2012-03-26 · Coolant Flow and Heat Transfer in PBMR Core With CFD Coolant Flow and Heat Transfer in PBMR Core With CFD Heikki