Uncertainties Treatment in the Nuclear Research Reactor Thermal Design

8/14/2019 Uncertainties Treatment in the Nuclear Research Reactor Thermal Design

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Uncertainties Treatment in the Water-Cooled Nuclear

Research Reactor - Thermal Design and Analysis

F. M. Bsebsu1

TNRC, Tajoura Nuclear Research CenterP. O. Box 30878, Tajoura (Tripoli) Libya

Fax: +218 21 360 4143, Phone +218 21 360 4141

) ( uncertainties

(WWR-M2 )10

.

.

.

. .

AbstractThis paper describes methods of uncertainties and its calculation

procedures for the water-cooled nuclear research reactor (i .e. WWR-M2)

with a 10 MWth, and its fuel type is coaxial annular, in the thermal design

and analysis, where the uncertainties are due to the reactor fuel coolant

channel design fabrication defects (fuel meat and clad thickness

uncertainties). As an example, well study the effects of the fuel meat and

cladding thickness may have a great influence on the distribution of the axial

temperatures (cladding surface, and fuel centerline) and other parameters in

1Dr. BSEBSU, Farag Muftah

P. O. BOX 30324, Tajoura (Tripoli), Libya, GJ

Fax: +218 21 360 4142, Phone +218 21 369 3518

Email: [email protected]
mailto:[email protected]:[email protected]


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the reactor core (reactor core thermal preformance) and more intense in the

reactor thermal design. The final results of this study are: the selection of

new reactor core operating conditions and parameters due to the fuel coolant

channel fabrication defects, and after that well calculate the new values of

the hot spot and hot temperatures of the WWR-M2 reactor by using different

methods.

1. IntroductionIn designing a nuclear reactor, the engineer is constrained to meet a

set of requirements, such as time of completion, power output, and cost,

achievement of a certain flux level for experimental purpose. Thefundamental choice of a reactor type is governed by such initial aims,

however, a further set of design requirements such as maximum fuel

centerline temperature, maximum cladding surface temperature, maximum

enthalpy rise in the coolant, or maximum local heat flux. These could be

related to melting of the fuel with release of an excessive amount of fission

gases, to reaching an unacceptable rate of creep in the cladding material, to

boiling in the coolant of a liquid cooled reactor, or to the occurrence of

burnout condition. In order to achieve the realization of these requirements,

the designer engineer has at his disposal a number of engineering variables.

These may include the choice of the materials, which constitute the fuel,

cladding and coolant, the composition of the fuel, the geometrical

arrangement of the various materials. In general, the design concentrates onsafeguarding against one or all of these features; in any case, it is important

to study the most likely malfunctions and to estimate their probability. It

should be incorporated in this design or redesign calculation the

uncertainties, which may result from the use of theoretical computational

methods or experimental data. Uncertainties in core materials and operating

condition affect the achievement of designer goals. These uncertainties from

two main sources as uncertainties from randomness inherent in a

manufacturing process, and uncertainties are from imperfect modeling or

estimating of parameters. Thus, for example, two major design criteria were

setup for the water-cooled nuclear research reactor core thermal hydraulic.

The first is to avoid nucleate boiling of coolant anywhere in the reactor core

in order to give enough allowance (The allowance in surface temperature offuel elements for the Onset Nucleat Boiling temperature was evaluated at the

hottest spot in the reactor core, using hot channel factors as described later)

against the burnout of the fuel element even at the hottest spot in the reactor

core to avoid any flow instability induced by partial boiling in the reactor

core and to obtain stable neutron fluxes for experiments. The second is to

give enough margins against the burnoutitself of the fuel element under the


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conditions of normal operation so that there may be enough margins also for

operational transients.

2. Methods of CalculationThe hot spot sub-factors may be combined into an overall hot spot

factor by one of two schemes (Deterministic and Statistical methods) [1-5].

The procedure of combining these sub-factors depends on the nature of the

individual variables. Several methods of combination of the sub-factors have

been suggested and they will be critically reviewed in this section as follows:

2.1 Deterministic MethodsIn this method (and this method was introduced by LeTourneau and

Grimble) all the sub-factors that tend to increase the temperature are

supposed to take place simultaneously and at the same point, the extreme

values of the uncertainties such as the worst deviations in fuel loading and

dimensions will occur in the same fuel element which will be located in the

channel with the poorest coolant flow condition which in turn will be located

in the region of highest deviation from the core average flux, so on. In this

method, there are two approaches of combination of hot-spot sub-factors as:

(Product approach and Sum approach).

2.2 Statistical Methods

The probability that the most unfavorable value of all theuncertainties occurs at the same positions, at the same time is extremely

small. This fact is origin to the statistical methods.[2] In this method all the

uncertainties are combined statistically and the hot spot factors no longer an

absolute factor and are functions of a certain confidence level. This

confidence level depends upon the necessary safety margin assigned to the

reactor core: ).z(FF yy , where z and are defined as the desiredconfidence level and the standard deviation of the property y, respectively.

The statistical procedure of combining the hot spot or hot channel sub-

factors depends on the statistical distributions of these sub-factors. The most

common distributions are the Gaussian and the rectangular distributions. The

two procedures that were developed for combining factors by this methodas: (Product-statistical method, and Sum - statistical method). Table 1summarizes the general formula for combinational methods of hot spot

factors and temperatures analysis [2 -15].

Table 1. Formula for combinational methods of hot spot analysis


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Method Hot spot factor Hot spot temperature

Cumulativ

e

Product =

=n

1i

y,iy fF =

+=M

1y

nom.yyinM T.FTT

Sum =

+=n

1i

y,iy )1f(1F =

+=M

1y

nom.yyinM T.FTT

Statistical

Vertical

+=

=

n

1i

2y,iy )1f(1F

=

+=M

1y

nom.yyinM T.FTT

Horizonta

l nom,y

1JJy

T

TTF

=

=

=

+

++=

n

i

nomyyi

M

y

nomyinM

Tf

TTT

1

2.,

1

.

]).1[(

3. Sample ProblemThe WWR-M2 water-cooled nuclear research reactor is a cylindrical

tank type reactor. The reactor core is placed 5.145 m below the surface of the

reactor tank (in order to minimize the radioactive exposure to the personnel),

which is open to atmospheric pressure. The diameter of the tank is 2300 mm,

and its height is 5685 mm. The heavy concrete reactor-shielding block is

situated in a rectangular semi-hermetically sealed reactor hall. The base of

the reactor core is a hexagonal grid plate, with 397 identically formed holes.

The fuel assemblies and the beryllium displacers can be put into these holes,

as well as the guide tubes of the 18-absorber rods. A fixed beryllium

reflector of 20-cm average thickness surrounds the core. The fuel assembly

type consists of 3 coaxial fuel elements, the innermost is a Tube, this is

followed by a second fuel element with an annulus cross-section, and the

third fuel element (outer) is a hexagonal shape, with active length is 60 cm.

[16-22].

4. Calculation Results

In this section the methods described in previous section are appliedto the WWR-M2 nuclear research reactor thermal hydraulic analysis. The

coolant and clad surface temperatures will be analysed for several values of

temperature limits.

4.1 Fuel element fabrication defects


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The fuel elements type WWR-SM has a high ratio of heat transfer

area to elements volume, thereby permitting operation at high heat fluxes.

This configuration is particularly attractive for the reactors high neutron

fluxes in research reactors as in WWR-M2 and of high specific power in

compact reactors. Usually the high ratio of cladding-plus-fuel diluents to

fuel makes it advisable that the fuel to high enriched uranium. Since WWR-

M2 reactor fuel element geometry is an effective means of improving heat

removal, it reduces the central temperature of a fuel of low conductivity. The

principal problem in the design and fabrication of WWR-M2 reactor fuel

assemblies is the mechanical stability of the plates. These plates have to be

thin enough, generally 2.5 mm or less, to provide the advantage of thisgeometry for heat removal and yet strong enough to maintain a stable

configuration, notably in permitting flow of coolant through the small water

channels between fuel elements.

The fabrication of the WWR-SM fuel elements by using Hot Roll-

bonding technique, which is the predominant method for fabrication of the

fuel elements, this technique versatile enough to be applicable to a variety of

fuel-cladding combinations and to permit the performance of a series of fuel

elements differing in composition and in any of several dimensional. This

technique is using for the fabrication of WWR-M2 reactor fuel elements may

be produce a lot of fabrication errors or uncertainties in the fuel elements

dimensions. These errors are depending on the accuracy and operating

conditions of the fabrication machines. The our example of the fabricationdefects in the fuel elements dimensions (40 cases of fuel elements)

comparing to the design fuel elements dimensions, and the comparison

between statistical calculations due to fabrication defects and design are

shown in Table 2.[1, 16].

Table 2. The comparison between statistical calculations due

fabrication defect and design value for WWR-M2 reactor fuel

elements thickness, [mm].Variable

Thickness

[mm]

Fuel Element I Fuel Element II Fuel Element III

DesignStatistica

lDesign

Statistica

lDesign Statistical

Clad 0.9 0.750.26 0.9 0.770.25 0.94 0.780.31Meat 0.7 1.040.13 0.7 1.020.12 0.74 1.020.13

Clad 0.9 0.760.19 0.9 0.760.17 0.94 0.760.18

FETH 2.5 2.550.48 2.5 2.550.54 2.62 2.560.62

Using the fuel elements dimensions as given in Table 2 as input date

file of THMOD2 code [1] well get the results of WWR-M2 reactor

operating parameters (Hydraulic diameter, coolant velocity, heat transfer


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WWR-M2 Fuel ElementsFuel

maxT , Maximum Fuel Centerline Temperature, [oC]

Fuel Element 1Design 141.86

Statistical 147.4 11.3





4.2 Results of fuel element fabrication defectsFinally, according to the results of the fuel element thickness

(fabrication defects), and according to design limits of the WWR-M2 reactor

(Fuel centerline temperature 150 C, and max. cladding surface

temperature 104 C), and from Figure 1, We can select the fuel meat and

cladding thickness (the fuel meat thickness = 0.86 mm, and the cladding

thickness = 1.021 mm) for all fuel elements (new design).

Using the new design thickness for the WWR-M2 reactor fuel

elements, we shall calculate the thermal hydraulic parameters for this type of

nuclear research reactor, and by using THMOD2 code. Figure 2 shows the

calculated results for both cases (new design and vendor (old) design) of fuel

axial centerline temperature, cladding surface temperature, and coolant

temperature as a function of channel axial distance of sub-channel D in the

WWR-M2 reactor fuel coolant channel as an example. Table 6 shows the

calculated results of hydraulic diameter, channel spacing, channel inletcoolant velocity, channel inlet coolant heat transfer coefficient, and the

channel coolant outlet temperature for both cases.

Figure 1. Maximum fuel

centerline temperature as afunction of fuel meat and

cladding thickness.

Figure 2. Temperature

distribution along fuelcoolant channel for new

and old design.


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Finally, and according to the operating limits of WWR-SM reactor

core for the maximum centreline temperature of the fuel elements ( 150 oC)

and maximum surface temperature for the fuel cladding ( 104 oC) we can

conclude that the new design (statistical) fuel meat thickness and cladding

thickness are better than the old design as shown in the Table 7 and Table 8,

respectively.

Table 6. The calculated results of Thermal hydraulic Parameters.

Sub-channels Parameter Old design New Design

Channel A

Dh [mm] 6.00 5.60

Cs [mm] 3.00 2.80

V [m/sec] 2.78 3.21 [W/cm2 K] 1.60 1.83Tout [

oC] 64.38 64.74

Channel B

Dh [mm] 6.00 5.20

Cs [mm] 3.00 2.60

V [m/sec] 2.78 3.04 [W/cm2 K] 1.60 1.78Tout [

oC] 67.71 69.27

Channel C

Dh [mm] 6.36 5.68

Cs [mm] 3.18 2.84

V [m/sec] 2.90 3.24

[W/cm2 K] 1.64 1.83Tout [oC] 63.73 63.63Channel D

Dh [mm] 6.62 6.00

Cs [mm] 1.58 1.44

V [m/sec] 2.98 3.37 [W/cm2 K] 1.66 1.87Tout [

oC] 65.11 64.23

Table 7. Maximum cladding surface temperatures [oC].

Cladding Surface Old design New Design

1 100.21 100.73

2 93.98 92.383 98.50 98.67

4 92.68 90.50

5 108.57 103.82

6 109.34 103.24


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Table 8. Maximum fuel centerline temperatures [oC].

Case Fuel Element I Fuel Element II Fuel Element III

New Design 137.53 131.49 143.79

Old Design 138.20 133.27 154.82

4.3 Determination of the hot spot and hot temperatures

In this section, well summarize the calculated values [the completedescription of this calculation is described in ref. 1] of hot spot sub-factors,

overall hot spot factors and the hot spot temperature of coolant, cladding

surface, and fuel centerline by using the combinational methods (section 2,

and Table 1), with using the following nominal temperatures values (coolant

- T1,nom = 25C, clad - T2,nom = 26

C, fuel - T3,nom = 30C, and Tin= 50

C), the final results of this calculation are given in Table 9.

Table 9. Results Summary for hot spot and hot temperature of WWR-

M2 reactor

Method Hot spot

Coolant

y =1

M =1

Clad

y = 2

M = 2

Fuel

y = 3

M = 3

Deterministic

ProductFyTM, [

C]

1.84

96

1.38

130.5

1.26

168.3

SumFyTM, [

C]

1.66

91.5

1.35

125.2

5

1.25

162.75

Statistical

VerticalFyTM, [

C]

1.33

83.25

1.26

114.75

1.22

151.35

HorizontalFyTM, [

C]

1.33

83.25

1.095

111.74

1.063

143.64

5. Calculation of Uncertainties

It is useful to report the significant uncertainties interval of theTHMOD2 code for calculating WWR-M2 reactor coolant channel heat

transfer coefficients using Dittus-Boelter correlation as an example. The

Root-Sum-Square (RSS) method is more precise method of estimating

uncertainty intervals: [1, 15]


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21

2

i

2

11

w..........w

++

=i

Rx

R

x

RW

Where R is the result and xn independent variables, i number of independent

variables, wi are the uncertainties if independent variables, and calculated as

following.

Nw ii

3=

Where n is the standard deviation of independent variables, and N is the

total number of calculation cases.

The uncertainty interval calculations for heat transfer coefficients,

which were calculated by using Dittus-Boelter correlation, are given in the

Table 10.

Table 10. The overall uncertainties results of heat transfer coefficient.

Heat Transfer coefficient uncertainty interval, WR [ %]Channel A Channel B Channel C Channel D

1.5 1.0 0.45 0.46

Conclusions

From the previous results, it is clear that the manufacturing defectsof the fuel element dimensions has great effects on the thermal hydraulic

performance of the reactor, therefore, must take our great care before loading

the fuel assemblies in the reactor, we should measure and selecting them,

which had the same dimensions (if it possible) to getting the good neutron

flux distribution in the reactor core, and also to overlook the maximum

design parameters which must keeping under design value limits (i.e. clad

surface temperature).

The uncertainties determination in the nuclear reactor thermal

hydraulic analysis and design are very important tools sbecause they are

giving and showing us the possibilities of errors points in our system and

whereabouts those errors. The selection of hot channel factors has a large

influence on the thermal-hydraulic performance and impacts the design andsafety margins of the reactor. Thus, these factors should be selected with

great care. The proposed uncertainties determination methods are asn

attempt to provide some guidance and rational for this task.

NomenclatureCs = Channel spacing, [mm]


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Dh = Equivalent hydraulic diameter, [mm]

y,if = Single hot spot factor for property, y and I independent variables

yF = Overall hot spot factor for property, y

M = Material type = (1 = coolant, 2 = clad, 3 = fuel, 4 = film)

maxq = Maximum cladding surface heat flux, [W/cm2]Tin = Coolant inlet temperature

TM = Hot spot temperatureclad

maxT = Maximum cladding surface temperature, [C]

Fuel

maxT = Maximum Fuel Centerline Temperature, [o

C]Tout = Channel outlet temperature, [

oC]

V = Coolant velocity, [m/sec]

iw = Uncertainty of independent variables i

RW = Overall uncertainty interval, [ %]xi = Independent variables

Z = Desired confidence level

TM,nom = Nominal temperature of material M = Heat transfer coefficient, [W/cm2. K]i = Standard deviation of independent variables i

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Uncertainties Treatment in the Nuclear Research Reactor Thermal Design

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