Thermal Hydraulic Design Requirements –

Steady State Design

1. PWR Design

2. BWR Design

Course 22.39, Lecture 3 Professor Neil Todreas

Un l e ss sp e c if i e d ot h e rwis e, t h e f i gu res in t h is presentat ion are f rom: Shuffl er, C. , J . Trant,

N. Todreas, and A. Roman o . "App licat i on of H y dri d e Fuels to Enhance Pre ssuri ze d Wate r R e ac t o r Performan c e." MIT-NFC-TR-077. Ca mbridg e, MA: MIT CANES, January 20 06. Courte sy of MIT CANES. Use d wi th pe rmission.

PWR Design

Components of Margin for MDNBR Overpower Transient

3800 MW th

4456 MW th

Summary of Steady-State Thermal Hydraulic Design Constraints

MDNBR vs Power

9/13/06 C ourse 22.39, Lecture 3

Profes sor Neil Todreas

Source: Blair, S., and N.E. Todreas.

"Thermal Hydraulic Performance Analysis of a Small Integral Pressurized Water Reactor Core."

MIT-ANP-TR-099 . Cambridge MA: MIT CANES, December 2003. Courtesy of MIT CANES. Used with permission.

Flow-Induced Vibration Mechanisms

Vibrations Analysis Assumptions

• The fuel rod is modeled as a linear structure

• Changes to the fuel assembly structure over time are not considered

• Only the cladding structure is considered in the fuel rod model

• Only the first vibration mode is considered

• Core power is the only operating parameter affecting the vibrations performance of new designs

Summary of Steady-State Thermal Hydraulic Design Constraints

Vortex Shedding

The vortex shedding margins in the lift and drag directions are defined as:

VSM

VSM

lift

 f 1  f s f s



where, f

> 0.3

: f undamental frequency of the rod

(3.18)

(3.19)

drag

2 f s

The vortex s h edding frequenc y is given b y :

f  S  V cross s D

where the Strouhal n u m ber, S, was f o und b y Weaver and Fitzpatrick to depend on the P/D ratio and channel shap e. F o r square arra ys,

S  1

2  P D  1 

(3.15)

(3.16)

and f o r hexagonal arra ys ,

S  1

1.7 3  P D  1 

(3.17)

Fluid Elastic Instability

The ratio of the m a xi mu m effective cr oss-flow velocity in the hot asse m b l y , V eff , to the critical velocit y f o r the bundle geo m etr y V critica l :

FIM  V eff < 1

V critica l

(3.21)

The most widel y accepted correla tion f o r estim a ting the critical velo cit y f o r a tube bundle is C o nnor’s equation:

V critical

   f

n

(3.23)

where P e ttigrew s u ggested a P/D ef f ect on C o nnors’ constant:

  4.76   P 

 D

  0.76



(3.24)

The critical velocit y is constant for a fixed ge o m etr y and, with the exception of s m all changes in coolant densit y, does not depend on the power and f l ow conditions in the core.

Fretting Wear

W ˙ fretting , new

 f 3  m

 y 2 

T c , ref

W  

1 t

f 3  m

rms

 y 2

new 

T

(3.39)

fretting , ref

1 t rms

ref

c , new

where y rm s is turbulence induced vibratio n fro m axial and cross flow, m t is total linear mass, and f 1 is fundamental frequency of fuel rod.

The wear rate ratio is the constrained parameter, and the ratio of the cycle lengths is the design lim it.

If a new design has a shorter cycle length than the reference core, then it can safely accom m odate a higher rate of wear.

The wear rate limit, due to its dependence on cycle length, will depend on both the power and the fuel burnup. The power, however, depends on the wear rate limit, and the burnup, when limited by fuel perfor mance constraints, depends on the power.

Sliding Wear

˙

slidin g , new

W ˙ sliding , ref

 D  y rms 



f 1  new  





1

A cl

1

 D 2

4 I cl

D 2





 ref



 T c , re f

T c , new

(3.44)

 D  y rms 

f 1  ref

 

 A cl



4 I cl



 new

where A cl is cladding cross-sectional area,

I cl is cladding moment of inertia,

D is cladding outside diameter

P/D vs H/HM for Square and Hexagonal arrays of UZrH 1.6 and UO 2

3. 50

3. 25

3. 00

2. 75

2. 50

2. 25

2. 00

1. 75

1. 50

1. 25

1. 00

0. 75

0. 50

0. 25

0. 00

1 . 0 0 2 . 0 0 3. 00 4 . 0 0 5. 00 6. 00 7. 00 8. 00 9. 00 1 0. 00 1 1. 00 1 2. 00 13. 00 1 4. 00 15. 00 16. 0 0 17 .0 0 18 . 0 0 19 .0 0 20 . 0 0 21 . 00 2 2. 00 2 3. 00 2 4. 00 2 5. 00 2 6. 00

H/H M

H y dr i de H ex Hy dr id e Sq ua re Ox i d e He x O x id e Sq ua re

Maximum Achievable Power for Square

Note: The following figures, slides 14-19, ca me f r om the paper, E. Gre enspan, N. Todreas, et a l , “Opti m izati on of UO 2 Fu e l e d P W R Core Design,” P r oce e dings of ICA PP ‘ 05, Seoul, Korea, Ma y 15-19, 2005, Paper 5569

9/13/06 C ourse 22.39, Lecture 3

(c) 2005 by the American Nuclear Society, La Grange Park, Illinois. Courtesy of the American Nuclear Society. Used with permission.

Profes sor Neil Todreas 14

Maximum Achievable Power for Square Arrays of UO 2 at 60 psia

Maximum Achievable Power at 29 psia Accounting for Fuel Rod Vibration and Wear

Maximum Achievable Power at 60 psia Accounting for Fuel Rod Vibration and Wear

Maximum Permissible Cycle Length. 29 psia

Maximum Permissible Cycle Length. 60 psia

9/13/06 C ourse 22.39, Lecture 3

(c) 2005 by the American Nuclear Society, La Grange Park, Illinois. Courtesy of the American Nuclear Society. Used with permission.

Illustration of Porosity in a Wire-Wrapped Bundle

S o u r c e : Shuffle r , C . , J . T r a n t , N . T o d r e a s , a n d A . R o ma no. "Ap p l icat io n o f Hydr ide F u e l s to E n ha nce Pressurized Water Reactor Performan c e . " M I T - NFC- TR -07 7 . C a m b ri dg e, MA : M I T CANE S , J a nu a r y 200 6 . Co urtesy o f M I T C A N E S. Used w i th permi s si o n .

THV-Induced Wear Data with Otsubo’s Wear Constraint

where P i is the pitch, P is the poro sit y , d w is the wire diameter, R is the num b er of rings in the bundle,  T i s the tem p er ature drop across the bundle in  C, H is the axial pitch, and L is the leng th of the as s e mbly .

The region above this line (label ed wear mark region ) is the re gion where Otsubo’s constraint predic ts that wear will occur. In th e region below the dott e d line, Otsubo’s c onstraint predi c ts that no sign ificant we ar will occur. The point s m a rked with a  represent re actors in which no we ar has been observed, while the poi nts ma rked with a * represent reactors in which wear marks occurred. The horizontal lines identi f y the range over whic h the subje ct fuel t ests were conduct ed. The red dots,  , used for BN-350, BN-600, and BOR-60, represent Russian fa st reactor data not used b y Otsub o .

BWR Core Design

GE9×9 Fuel Bundle

Thermal-Hydraulic Constraints

The Hench-Gillis correlation has the general form:

x  AZ

 2 

J   F

C B  Z P

Pin-by-Pin Power-to-Average Power Ratio at BOL for a BWR GE 9×9 Single Bundle – N o PLFRs, with Gd

J 1 Factors

Bundle Loss Coefficients

Coefficients for Frictional Pressure Drop Correlations

Peak Vibration Ratio Dependence on Quality and Mass Flux, Païdoussis C orrelation

9/13/06 C ourse 22.39, Lecture 3

Profes sor Neil Todreas

Source: Ferroni, P., and N. E. Todreas.

"Thermal Hydraulic Analysis of Hydride Fueled BWRs" MIT-NFC-TR-079.

Cambridge, MA: MIT CANES, February 2006. Courtesy of MIT CANES.

Used with permission. 30

Païdoussis C orrelation – Quinn’s Data Comparison

Païdoussis - T sukuda P eak Vibration Ratio Comparison (Restricted G Range)

Final Vibration Ratio Comparison

Locations of the Assembly Configurations Examined for Power/Flow Ratio Investigation

Comparison between “Relative” Maximum Power and “Overall” Maximum Power

Core Radial Power Distribution

5 core types are considered*:

1) Ox-Backfit-5: existing BWR/5 vessel (D cor e = 5.2 m ) , UO 2 fueled, crucif.CRs, WRs, fixed fuel channel size.

2) Hyd-Backfit-5: existing BWR/5 vessel (D core = 5.2 m ) , U-ZrH 1.6 fueled, crucif.CRs, no WRs, fixed fuel chan. size.

3) Hyd-NewCore-5: existing BWR/5 vessel (D core = 5.2 m ) , U-ZrH 1.6 fueled, control fingers, no WRs, variable fuel chan. size.

4) Ox-Backfit-ES: ESBWR vessel (D cor e =6.1 m), UO 2 fueled, crucif. CRs, WRs, fixed fuel channel size.

5) Hyd-NewCore-ES: ESBWR vessel (D core =6.1 m), U- ZrH 1.6 fueled, control fingers, variable fuel channel size.

* Each core type has been model ed 400 times, i.e. each time with a d ifferent assembly configuration.

Core structural changes resulting from the implementation of U-ZrH 1.6 …

The greater design freedom for the hydride cores is limited by the application of 2 Structural Constraints:

* to limit the refueling time.

** due to the limited load capacity of the cr ane in an existing plant. Not applied to the Hydride New Core since a reactor d esigned specifically to utilize U-ZrH 1. 6 is assumed to be provided with a crane of sufficient load capacity.

Ox-Backfit-5 Powermap ( Δ p lim =36 psia)

Power, LHGR and Number of Rod Ratios Between the Exa m ined Ox-

Backfit-5 Core Configuration and the Ref. Core, Δ p lim =36 psia (the lines represent unity ratios)

Whole Core Flow Rate (Ox-Backfit-5, Δ p lim =36 psia)

Case Ox-Backfit-5: What are the limiting parameters and where do they apply

Ox-Backfit-5 (p lim =24.5 psia) O x-Backfit-5 (p lim =36 psia)

NOTE: Clad Surface T and fuel centerline T are never limiting.

Limiting Effect Exerted by Constraints (Ox-Backfit-5, Δ p lim =36 psia)

Core Average Exit Quality and Hot Bundle Exit Quality (Ox-Backfit-5, Δ p li m =36 psia )

Bypass Flow Percentage (Ox-Backfit-5, Δ p li m = 36 psia)

Oxide Core Fuel Matrix ( n × n ) Size

(the col o red scale indicates the matri x index n ; black upper line: n =7, black lower line: n =12; green line: high power region)

Power comparison: Ox-Backfit-5 vs Hyd-Backfit-5 ( Δ p limit =36 psia)

Ox-Backfit-5

Hyd-Backfit-5

By comparing the two cores for the same D-P/D pair, the Hy dride Backfit Core deliv ers around 6-9% more power.

Power comparison: Ox-Backfit-5 vs Hyd-NewCore-5 ( Δ p limit =36 psia)

Ox-Backfit-5 Hyd-NewCore-5

By comparing the two cores for t he same D-P/D pair, the Hy dride NewC ore delivers around 25-30% more power

Power, LHGR and Rod Ratios Between Hyd-NewCore a nd Oxide Ref. Core, Δ p lim =36 psia (continuous lines represent unity ratios)

Power comparison: Ox-Backfit-ES vs Hyd-NewCore-ES ( Δ p li mi t =11 psia)

Power gain percentages: up to + 37% for the same D-P/D pair, up to +70% with respect to the reference ESBWR (4500 MW t) .

Reason for higher power gain % with respect to BWR/5 backfit-newcore comparison: smaller flow rate → vibrations are not limiting

Limiting Constraints for Ox-Backfit-ES and Hyd-NewCore-ES

NO TE: 1) vibrations are not limiting, 2) Δ p more limiting for Hy d t han Ox because of larger number of rods per bundle (Hyd does not contain WRs)

Effect of Neutronic Constraints: feasibility regions for Hydride

• F easible region: 1.1 ≤ P/D ≤ 1.2. In this region there are no limitations due to the reactivity coefficients, and the theoretical burnup can be achieved.

• F easible region but with limited burnup: 1.2< P/D ≤ 1.35. These geometries can safely reach only a fraction of the theoretical burnup.

• Non feasible region: P/D >1.35. These geometries are not feasible due to limitations on the reactivity coefficients.