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```					Thermal-Hydraulics Uncertainties As
Applied to DNB Anaylsis and Best-
Estimated LOCA Calculations
Presented by
L. E. Hochreiter
Professor of Nuclear and Mechanical Engineering
The Pennsylvania State University

ACE Uncertanity Workshop
North Carolina State University
May 31 – June 1, 2006
Outline
    Introduction

    Departure from Nucleate Boiling (DNB)
Methodology
- Original Analysis Methods
- Current Statistical Approaches
- Margin Gain

   Loss of Coolant Accident (LOCA)
Methodology
- Original Analysis Approach
- Best-Estimate LOCA Approach
- Margin Gain

    Conclusions                             2
 Introduction
• Initial Design analysis was performed
in a conservative manner
- uncertainties were bounded
- little or no statistical methods were
used
- resulting analysis and plant limits
were very conservative
3
• As operating Manufacturing and Licensing
Experience was gained
- uncertainties could be determined,
controlled and quantified
LOCA) were performed to quantify
uncertainties in phenomena and
methods
- Analysis Methods (T/H codes) were
significantly improved

4
 Design Methods now employ statistical
Methods to determine plant operating
limits in a conservative manner

5
 Departure from Nucleate Boiling (DNB)
Methodology
• Sub-Channel T/H Analysis Methods are
used to Determine DNB limits (PWR) for
Transients

6
• Analysis is performed in a conservative
manner to:
(power distributions)
- Account for manufacturing
uncertainties
- Account for uncertainties in plant
conditions/states
- Account for uncertainties in initial boundary
conditions
- Account for uncertainties in predicting DNB
7
• Original Design Approach was to bound
nearly all the uncertainties
- Some manufacturing data was
statistically combined (enrichment,
pellet OD, pellet density)
- DNB correlation used statistical limit
(95/95)

8
 DNB Methodology – con’t
• Current Methods
- Conservatism is retained, but
more quantified
- Uncertainties are assessed and
separated into:
> statistical parameters
> non-statistical parameters (bias)

9
• Plant Parameters and Uncertainties
- Reactor Flow (statistical)
- By-pass Flow (bias)
- Core inlet Flow Distribution (bias)
- Out let pressure (statistical)
- Core power (statistical,bias)
- Core geometric parameters, (pitch
reductions, rod bow) (statistical)
10
• Plant Parameters and Uncertainties, con’t.
- Fuel Fabrication Parameters
(statistical)
- Fuel Pellet Stock height (bias)
- Mixing Coefficient (bias)
- Pin Power uncertainties
(statistical/bias)
- DNB Correlation/Code uncertainties
(statistical)
11
12
Fuel Rod Pellet Stack Weight Distribution

13
Distribution of Observed Uncertainties in FNH for
Fuel Rods

14
Measured CHF Versus Predicted CHF Mark-BW
Data Base

Predicted CHF (mBu/Hr-ft-2)
15
Measured to Predicted CHF Versus Mass Velocity
Mark – BW Data Base

16
   Method of Uncertainty Combinations
• Simple statistical approach was used for
uncertainty combinations (KISS)

• Uncertainties were assumed to be independent

• Taylor Series approach was used to represent
y-DNBR (variable)/DNBR (normal) as a function of Xi
(design variables)

17
• Final Expression is

2        2        2
y        21      2 2   23 
   S1 
    S 2    S3      ...
y
1 
 
 
 2
 
 3

18
where

y   is variance of the normalized DNBR

y

1  2
,
1  2   is variance of the design parameter normalized on its mean value

19
and
S1, S2, S3 . . . are the DNBR sensitivity
coefficients determined from Sub-Channel
code calculations over the range of the
design variable

20
21
• In this case, the limiting DNBR can not be lower than
1.54 for a typical cell or 1.46 for a thimble cell such that
the 95% percentile point would have a limit DNBR of
1.3.

• The difference between the DNBR of 1.54 and 1.3 are
the effects of statistically combining the uncertainties
and using the nominal condition as the basis.

• Gain for the utility is using of nominal conditions rather
than bounded conditions.

22
• These simpler statistical approaches
have been improved using Monte Carlo
techniques and Response Surfaces
(CE/ABB).

• General Electric has a similar approach
as Westinghouse for MCPR.

23
• Statistical Approaches do indicate that
some fuel rods could experience DNB or
Boiling transition.

• Vendors have calculated (estimated) the
number of fuel rods that could
experience DNB or Boiling transition

24
• The number is typically very small
~ 9-12 rods out of 50,000.

• Methods have been accepted by US
NRC.

25
 Statistical Methods For Large-Break
Loss-of Coolant Accident (LOCA)
Analysis
• Before 1988, very bounding LOCA
Analysis was performed (10CFR50.46-
Appendix K)

26
• In 1988
-10 CFR 50.46 revised to allow use of
realistic calculations, however
○ Uncertainties in computer code and model
must be considered
○ Uncertainties in the plant state, accident
initial and boundary conditions must be
considered
○ 95th percentile peak cladding temperature
became licensing limit
○ Must show high probability that ECCs
acceptance criteria not exceeded
27
○ The new rule was effective on 10/17/88.
The key features of the new rule are:
□ No specific models/correlations specified
□ Code must be realistic representation of
the plant and LOCA process
□ Rule requires calculation of nominal, 50th
percentile PCT, and an accurate
estimate of the 95th percentile PCT
considering uncertainties in the plant,
accident conditions, and the computer code.
□ Current EM models are still permitted

28
   Phenomena Identification and Ranking Table
(PIRT)
• PIRTs were developed for LB-LOCA, on a
plant type basis
- identified key phenomena that require
accurate code modeling
- phenomena ranked by impact on Peak
- identified/grouped phenomena into
statistical uncertainties and bias
- identified computer code validation needs

29
• NRC Research Division sponsored and led
the Code Scaling And Uncertainty (CSAU)
- Objective was to develop the licensing framework
for approving best-estimate safety analysis codes
and methodology
- Perform a sample analysis to assess
uncertainties
- Examine code uncertainties, bias, and
performance
- Address issues such as uncertainty propagation
and compensating errors.

30
   CSAU LOCA Calculations
• Developed a (PIRT) to identify dominate effects

• Performed limited number of system calculations with TRAC-
PF1, varying most important parameters

• Fitted PCT results by regression and analysis to obtain three
(3) response surface equations (RS)

• Used Monte Carlo sampling of RS, to obtain PCT distributions

• Calculated 50th and 95th percentile PCTs

31
Blowdown PCT

32
Blowdown PCT

33
First Reflood Peak PCT

34
Second Reflood Peak PCT

35
36
 Best-Estimate Methodologies
• Initial licensing submittals followed CSAU
approach
• Response surfaces were developed and used
for sampling to obtain 50th and 95th percentile
PCTs
• Newer approach is to use ordered statistics as
proposed by GRS
• Both Framatome and Westinghouse have proposed
this approach
• Canadians are also considering this approach
37
    LOCA Statistical Methods

• Westinghouse and General Electric followed the NRC-CSAU
Approach and developed PCT response surfaced, used Monde-
Carlo techniques

-Calculated PCT distribution, CPT, 50th and 95th
percentile PCTs
-Methodology included several conservative bias’s
to simplify method, account for code inaccuracies.
-Separate code uncertainity was added to plant
calculation from code validation

• Method was too complex, difficult to use and implement

38
• Framatome ANP licensed its realistic LBLOCA methodology (2003)

-Follows CSAU approach, but uses ordered statistics method
(eliminates need for response surfaces)
-95/95 criterion used as PCT acceptance criterion

• Advanced Statistical Treatment of Uncertainty Method
(Westinghouse ASTRUM, 2004)

-Uncertainty methodology uses ordered statistics
-Follows CSAU Approach, Just Statistical Approach is different
-Approved for all Westinghouse and Combustion Engineering
designs

39
Current Best-Estimate LOCA Statistical Methods
Ordered Statistical Approach
• Originally suggested by GRS (Germany)
• Approach is based on the Wilks’s formula/equation.
• Wilks’s equation determines the minimum number of
trials, N, needed to guarantee that the maximum
value PCT of the sample (PCTi) i=1, ..N exceeds for a
given b-level confidence the desired g-quantile of the
variate:

40
Ordered Statistical Approach (cont’d)
• Guba et. al. (2003) generalized the Wilks’s Method for
cases when p>1 (multivariate). The size of the sample
is determined by the following equation:

• Where:
•       b = confidence level
•       N = sample size (number of runs)
•       p = number of output variables desired
•       g = tolerance interval

41
• Guba results reduce to Wilks’s when
p=1(one variate)
• In particular for b = 0.95 and g = 0.95, we
obtain:
– p = 1 (i.e. PCT)             N = 59
– p = 3 (i.e. PCT, LMO, CWO)  N = 124
(Local Maximum Oxidation/Core Wide Oxidaton)

42
• Guba approach is based on most generic
assumptions:
– Nothing is known relative to the distribution
function of the sample
– Nothing is known on the degree of correlation
among the sampled variables (PCT, LMO,
and CWO)

43
 Debate on Use of Order Statistics in Recent Literature

• A significant debate has taken place in the technical
community regarding the practical implementation of
Order Statistics
– The focus of this debate has been on the actual number of runs
required to satisfy the LOCA licensing criteria
– In this framework, Westinghouse approach has been considered
(overly) conservative
– Various authors have suggested that a reduced number of runs
(compared to 124) may be sufficient to develop a ‘statistical
statement’ which satisfies the LOCA licensing criteria

44
Debate on Use of Ordered Statistics (cont’d)
• A 95/95 statistical statement is required
on three independent variables: PCT,
LMO, and CWO
• This is the most general approach, and
results in a requirement of 124 runs

45
Conclusions

• Statistical methods for DNB Analysis are well
established, no issues remain

• Statistical methods for LBLOCA still have some
issues but there is general acceptance

• Application of statistical methods has allowed greater
design margins/flexibility and has resulted in
improved economic operation of US reactors
46

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