HOT CHANNEL FACTORS DETERMINATION AND EVALUATION FOR WATER-COOLED NUCLEAR RESEARCH REACTORS PERFORMANCE

ألداء الح����ادة القن���اة مع�����امالت وتق���ييم حس���اببالماء المبردة الن��ووية البح�وث مفاع�الت

BSEBSU, F. M.1

TNRC, Tajoura Nuclear Research CenterP.O. BOX 30878, Tajoura (Tripoli) Libya, GJ.Tel.: +218 21 361-4241, Fax: +218 21 361-4243

الخالصة العام���ة الخط���وط وتس���تعرض تق���دم الورق���ة ه���ذه

ال��ذروة مع��امالت وتط��بيق وحساب واختيار لتقييم والعريضة وكمث��ال النووي��ة، البح��وث )الحارة( لمف��اعالت الحادة للقناة ان��ه حيث الح��رارة، انتق��ال معام��ل في الش��ك أو العيب لذلك أمان وحدود أداء إنقاص في واألكبر الرئيسي المساهم يكون

ه��ذه إن حيث النووي��ة، البح��وث بمف��اعالت الهيدروحراري��ة األخط���اء نتيج���ة تك���ون العي���وب ( أوuncertainties) الش���كوك )مث��ل والوق��ود التبري��د قن��اة تص��نيع عملي��ات في الص��ناعية

المغلف(. ومادة الوقود مادة سمك في األخطاء ح��ول المت��وفرة المعلوم��ات جل تكون المجال هذا في

ج��دا مفي��دة والمغل��ف الوق�ود م��ادة س��مك وقياس��ات تصنيع ال��ذروة مع��امالت ولحس��اب العي��وب، ه��ذه من والحد إلنقاص

الوق��ود وح��دة ل��ذلك، كمث��ال أخ��دنا حس��ابها طريق��ة وفهم نوع النووية البحوث بمفاعل ( الخاصةFuel Assembly) والتبريد

(WWR-M2روسي ) .الصنعAbstract

This paper presents the general outlines of the evaluation, selecting, determination, and applying peaking hot channel factors for nuclear research reactors. As an example, the uncertainty in the heat transfer coefficient is a major contributor to the reduction in nuclear research reactor performances and thermal hydraulic safety margins, where the uncertainties are due to the reactor fuel coolant 1 Dr. BSEBSU, Farag MuftahP. O. Box 30324, Tajoura (Tripoli), Libya, GJ.Email: bsebso@yahoo.com

channel design fabrication defects (fuel meat and clad thickness uncertainties), and the fuel element’s heterogeneity. Both the uncertainties are important contributors and an area where more information may be useful in reducing this uncertainty. In this case we take the WWR-M2 nuclear reactor (Russian type) fuel coolant channel (Fuel Assembly) as sample problem for applying and determination the peaking factors, and understanding this method. 1. INTRODUCTION

There are many quantities affecting the nuclear reactor core thermal hydraulic design and analysis as nuclear quantities, FN

(Macroscopic distribution of power in the core, Local radial and angular power distribution, difference in power distribution, fuel burn up in fuel assembly and fuel element, etc.) and engineering quantities, FE (Flow distribution in plenum chamber, and variations in coolant inlet temperature and pressure, coolant flow rate, and steady-state fluctuation, etc.).

The selections of engineering hot channel factors for the reactor thermal-hydraulic analysis of the limiting (hottest) channel have a significant impact on reactor safety margins.

Some reactor designs have large safety margins, and large uncertainties can be assumed without any particular difficulty. Even in these cases the choice of overly conservative peaking factors can unnecessarily limit the range and usefulness of the reactor.

The safety documents for the current reactors show a variety of choices for peaking factors and often with little justification for those choices. There seems to be no generally accepted method for the selection of hot channel factors. A method for the selection and application of hot channel factors is proposed here for consideration. The assumption here is that the fuel element design has been set (perhaps through standardization), and the reactor operator must now evaluate this fuel for this reactor based on the given fabrication tolerances and uncertainties.

The thermal-hydraulic limits of the fuel are not used to establish what tolerances can be allowed in the fuel fabrication. The method is illustrated by example, and the sensitivity to some of the choices is examined.

In order, to achieve the high average surface heat flux and maximum enthalpy rise, and the extreme importance, these ratios are also called hot channel factors. Hot spot and hot channel factors are used to express the extent to which actual reactor performance may depart from its nominal performance, owing to the cumulative effect of variations of all primary design variables from their nominal values. Engineering hot channel factors may be broken into three separate components corresponding to: [1,2]1. Uncertainties that influence the heat flux: Heat flux hot factor,

Fq, was used, defined as the ratio of the highest heat flux which could possible occurs any where in the reactor core to the average heat flux.

2. Uncertainties in the heat transfer coefficient: Heat transfer coefficient hot factor, Fα, was defined as the ratio of the maximum heat transfer coefficient, which could possibly occurs any where in the reactor core channel to the average heat transfer coefficient.

3. Uncertainties in the temperature rise or enthalpy change in the channel: Coolant temperature rise or enthalpy change in the channel hot factor, Fc, was defined as the ratio of the maximum coolant temperature rise which could possibly occur in any fuel assembly of the reactor core to the average temperature rise.

2. CALCULATION METHODThe basic method for determining the hot channel factors

associated with the manufacturing tolerances is to consider a channel of nominal (design) dimensions in a region of average heat flux parallel with a channel of minimum or maximum average dimensions.

The basic assumptions will use in this calculation are that the pressure drops across the nominal and hot channel are equal, and the constructed dimensions deviate statistically from the nominal dimension according to Gaussian distribution and that 99.865 % confidence limit, equivalent to three times the standard deviation was chosen to determine the hot sub-factors.

Engineering hot channel factors were broken into three separate components (factors) corresponding to uncertainties that influence the coolant temperature rise Fc, heat flux Fq, and heat

transfer coefficient Fα. These factors should be introduced into the analysis procedure as:

(1)

(2)

(3)where q" is the heat flux, coolant mass flow rate, the notation n refers to the nominal channel value, and h refers to the hot channel value.

These components of Equations 1 – 3 can be broken down further into sub-factors. The sub-factors may be combined (The procedure of combining these sub-factors depends on the nature of the individual variables) into an overall hot factor by one of two schemes as Deterministic (Product and Sum approaches), and/or Statistical (Statistical Vertical approach) methods as follows: [1]

(4)

(5)

(6)Where Fx is combined hot channel factor, and ƒx sub-factors may determine from the uncertainties (tolerances) in the specifications of reactor fuel element (fuel density, fuel meat thickness, cladding thickness, coolant channel spacing, fuel loading, etc.), and other reactor related components. Other sub-factors may be determined

from the limitations in the ability to measure certain parameters accurately (temperatures, coolant flow rates, etc.).

Table 1 summarizes the general contribution and effect of the uncertainties in reactor core parameters on the peaking hot factors.

Table 1. General contribution and effect of the uncertainties in reactor core parameters on the peaking hot factors.

Uncertainties Sources Fuel Meat Thickness ● � ●Coolant Flow Rate ● ● �Heat Transfer Coefficient � ● �Power Measurement ● � ●Power Density ● � ●Coolant Channel Spacing ● ● �235U Loading ● � ●235U Homogeneity ● � ●Data fitting � ● �

Combination Methods(Cumulative & Statistical)

▲ ▲ ▲

A complete method for calculation the hot channel sub-factors is completely descried in Ref. 1, with the pressure drop across the hot channel is assumed to be equal to that of the nominal channel.

The specifications for the fuel elements and elements that are used in the fabrication of the reactor fuel usually contain tolerances on the fuel loading, the fuel density variation, fuel element thickness, and channel spacing. The tolerances on fuel element and channel dimensions may be extracted from the associated blue print used in the fuel fabrication.

These fuel element (fuel element) and channel tolerances can be translated into subfactors in most cases without difficulty. The presence of a higher fuel loading in a fuel element will result in both an increase in the heat flux from the fuel element and a temperature rise in the channel. And also we can note the potential reduction in the flow channel spacing results in both a bulk temperature rise over the channel and a reduction in the heat transfer from the clad surface

to the coolant. Table 2 provides a summary of the proposed sub-factors.

Table 2. Summary of Hot Channel Sub-factors Expressions and formals.

Sources of Hot channel sub-factors

Uncertainty

Fuel Loading / FE(M±Δm)

��

Fuel density: Local(±UL%)

�� ��

Fuel density: axial variation (± Ua %)

�� ��

Channel Spacing(b±Δb)

y = k=

��

Fuel Element Thickness (t±Δt)

�� ��

Heat Transfer Coefficient: (± Uα%)

�� ��

Flow Rate(± UF %)

��

Power & Power Density (± UP %)

��

Data Fitting(± UDF %)

�� ��

In the above we discussed the evaluation method of hot channel factor due to the uncertainties in the fuel fabrication defects. Most of the other uncertainties can be related to uncertainties in measurements or tolerances in equipments.

1. Fuel loading based upon final weight of the final compact and chemical and isotopic analysis of the constituents.

2. The homogeneity specifications for the fuel material (density), local or variation density along the fuel elements.

3. The uncertainties in the coolant flow can result from tolerances in pumping rate as the pump speed may vary with voltage fluctuation or load, or uncertainties in the instruments used to measure flow itself.

4. The uncertainties in the power level and the power density may be attributed to the various sources. As it due to limitations in the calibration of the instrumentations or in the sensitivity of the equipment used for measurements.

5. Uncertainties from imperfect modeling or estimating of parameters (as an example the experimental data generally fit within a band of ± 20 % for any of the single-phase correlations commonly used).

3. SAMPLE PROBLEM AND APPLICATIONThe WWR-M2 reactor is a tank type reactor, moderated and

cooled by light water. The base of the reactor core is a hexagonal grid fuel element with 397 identically formed holes.

The fuel assemblies and the beryllium displacers can be put into these holes, the guide tubes of the control rods as well. The equilibrium core size consists of 223 fuel assemblies, with a lattice pitch of 35 mm; the control rods, beryllium displacers and isotope production channels occupy the remaining core positions. Stationary beryllium reflector of 20 cm average thickness surrounds the core.

The cooling water is flowing down stream across the reactor core. The fuel of the reactor is of the WWR-SM type. It is an alloy of aluminum and uranium-aluminum eutectic with aluminum cladding. The uranium enrichment is 36%, and the average 235U content is 39 (g/fuel element). The fuel assembly contains three fuel tubes, the outer tube is of hexagonal shape, while the two inner ones are cylindrical. The active length of fuel elements is 60 cm. The design specifications of this reactor are shown in Table 3.4. APPLICATION AND RESULTS

The fuel meat thickness with cladding = 2.553 ± 0.473 mm, coolant channel spacing = 3.063 ± 0.444 mm, and 235U loading per

fuel element = 39 ± 0.18 gm for the fuel specifications of the WWM-M2 reactor. Since some data were not available for uncertainty (± U %) as an example, in power, power density, flow measurement, local density, and axial density variation in this case; the following assumptions were made:

Uncertainty in local density variation = ± 5 %Uncertainty in axial density variation = ± 20 % Uncertainty in flow rate measurement = ± 13 %Uncertainty in power measurement = ± 6.5%Uncertainty in power density measurement = ± 13 %

Table 3. The elements of the design specifications of the WWR-M2 reactor core.

Reactor power, [MW] 10Fuel assemblies / core 223Fuel element / fuel assembly 3Array shape HexagonalActive core length, [cm] 60Fuel meat thickness, [mm] 0.7Clad thickness, [mm] 0.9Clad material SAV-I Nuclear axial factor 1.2581Nuclear radial factor 1.7940Coolant and moderator material H2OAverage flow rate / FA, [m3/hr] 6.12Total core flow rate, [m3/hr] 1750Film heat transfer coefficient, [W/cm2. K] 1.99

The assumptions of turbulent flow forced convection, constant density and constant viscosity, and the flow rate in the channel changes as the heat flux changes will consider in this case, with the pressure drop across the hot channel is assumed to be equal to that of the nominal channel.

The hot channel factors and the hot channel subfactors derived from the uncertainties for the WWR-M2 reactor are summarized in the Table 4.

Table 4. Results summary of the hot channel sub-factors for the WWR-M2 nuclear research reactor thermal design.

Uncertainties sourcesFuel Loading / Fuel Element 1.20 ــ 1.20Fuel density: Local ــ ــ 1.15Fuel density: Axial variation 1.20 ــ ــChannel Spacing 1.30 1.05 ــFuel Element Thickness ــ ــ 1.19Heat Transfer Coefficient ــ 1.85 ــFlow Rate 1.13 1.10 ــPower measurement 1.07 ــ 1.07Power Density measurement 1.13 ــ 1.13Data Fitting (correlation) ــ 1.20 ــ

Combination MethodsCumulative: Product Approach

: Sum Approach2.561.21

2.571.78

1.991.12

Statistical: Vertical Approach 1.46 1.88 1.35

The cumulative methods of combining the sub-factors are conservative but somewhat unrealistic. The statistical method recognizes that all of these conditions do not occur at the same time and location. The combined hot channel factors with the statistical method are lower. The choice of hot channel factors strongly affects the reactor design and safety margins.5. CONCLUSIONS

From previous discussion in this paper, we can conclude that the proposed method here is an attempt to help and provide some guidance outlines to select the peaking (hot) channel factors for water-cooled nuclear research reactor thermal hydraulic design and analysis, and the peaking channel factors should be divided into three separate components: 1. Heat transfer coefficient,2. Temperature or enthalpy change in the channel, and

3. Heat flux. Also, these factors can be broken into several sub-factors

based on uncertainties in the manufacturing process of the reactor core fuel elements, specifications, methods of calculation, and measurements. These sub-factors may be combined by several methods as conservative or statistical.

The determination and evaluation of hot channel factors has a large contribution and influence on the reactor thermal hydraulic design and analysis (performance) and impacts the reactor core design and safety margins. Thus, these factors should be selected and determined with great care. Nomenclatureb : Channel spacing, [mm] Cp : Coolant specific heat, [kj/kg. oC]De : Equivalent diameter, [mm]ƒ : Hot channel sub-factorF : Combination hot channel factor

FA : Fuel AssemblyFE : Fuel ElementM : Nominal fuel loading / fuel element, [g]Q : Heat transfer amount, [W]t : Fuel element thickness, [mm]T : Temperature, [oC]U : Uncertainties value, [±%]

: Heat transfer coefficient, [W/m2. K]: Friction factor coefficient = 0.2 – 0.25: Mass flow rate, [kg/sec]

: Heat flux, [W/cm2]

(Subscripts): Axial: Coolant or bulk

F : Flow rate: Hot channel

L : Localn : Nominal channelP : Power or power densityq : Heat fluxs : Surface (clad)

: Heat transfer coefficient

6. REFRENCES1. BSEBSU, F. M.: Thermal Hydraulic Analysis of Water-

Cooled Nuclear Research Reactors, PhD. Thesis, Budapest University of Technology and Economic, Budapest-Hungary, (2000).

2. BSEBSU, F. M.: Uncertainties Treatment in the Water-Cooled Nuclear Research Reactor Thermal Design and Analysis, under press and submit to Journal of Nucleons. Tajoura Nuclear Research Center, Tripoli – Libya, Sept. 2003.

3. BSEBSU F. M. and Bede G.: Nuclear Reactor Channel Modelling Using the THMOD2 Code, Kerntechnik Journal, 64 (5-6), 269-273, (1999).