Heat transfer in nuclear fuel rods bundles- 123docz.net

N.3. Transients at hot nil power (Design DNBR criterion)

XVI.3. Heat transfer in nuclear fuel rods bundles

a)Laminar Flow

Laminar flow occurs during reactor shutdown and removes Laminar flow occurs during reactor shutdown and removes

the residual power (less than 0.5% of the nominal power).

Although it is mainly of academic interest, laminar flow Although it is mainly of academic interest, laminar flow equations have been analytically resolved (without spacer equations have been analytically resolved (without spacer grids) and lead to some constant Nusselt Numbers in grids) and lead to some constant Nusselt Numbers in steady-state and fully developed flow [Lach (1986)], steady-state and fully developed flow [Lach (1986)], depending on the pitch to diameter ratio P/D (see following depending on the pitch to diameter ratio P/D (see following

table).

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Table . Nusselt Numbers (constant heat flux) for fully Table . Nusselt Numbers (constant heat flux) for fully

developed laminar flow in rod bundles.

1.02 1.05 1.10 1.20 1.30 1.40 1.50 Equilateral

triangular Spacing

0.40 1.05 2.90 6.90 9.05

Square

spacing 0.52 0.84 1.72 4.58 6.40 9.43 15.0 5

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b) b) Single-Phase Turbulent FlowSingle-Phase Turbulent Flow

This is the most usual case encountered in normal Pressurized This is the most usual case encountered in normal Pressurized Water Reactor (PWR) operation. It is important to know the Water Reactor (PWR) operation. It is important to know the temperature field in the reactor core not only in order to be temperature field in the reactor core not only in order to be able to calculate the neutron flux field, but also because a able to calculate the neutron flux field, but also because a difference of some degrees may have noticeable difference of some degrees may have noticeable consequences in the long term on the chemical and consequences in the long term on the chemical and

metallurgical behavior of the cladding of the fuel rods.

Usually, the single phase turbulent heat transfer coefficients Usually, the single phase turbulent heat transfer coefficients are estimated using the same correlations as for tubes, are estimated using the same correlations as for tubes, using the equivalent hydraulic diameter instead of the tube using the equivalent hydraulic diameter instead of the tube diameter. According to many authors, this approach diameter. According to many authors, this approach underestimates the actual heat transfer coefficient. Tong et underestimates the actual heat transfer coefficient. Tong et al. (1979) proposed modifying the constant C = 0.023 in al. (1979) proposed modifying the constant C = 0.023 in

the well-known Dittus-Boelter the well-known Dittus-Boelter

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* For a triangular lattice :

C = 0.026P/D - 0.006

* For square pitch lattice:

C = 0.042P/D - 0.024 Where P/D is the pitch over diameter ratio.

This increase in the heat transfer coefficient seems to be This increase in the heat transfer coefficient seems to be due mainly to the mixing grids that enhance the turbulence due mainly to the mixing grids that enhance the turbulence downstream, and, consequently, the heat transfer; some downstream, and, consequently, the heat transfer; some local measurements have demonstrated that the heat local measurements have demonstrated that the heat transfer coefficient decreases as the distance to the mixing transfer coefficient decreases as the distance to the mixing grid increases. A precise heat transfer correlation in this grid increases. A precise heat transfer correlation in this geometry would depend closely on the grid geometry and geometry would depend closely on the grid geometry and so would probably be proprietary. However, the so would probably be proprietary. However, the overestimation of the wall temperature obtained by a tube overestimation of the wall temperature obtained by a tube correlation is probably less than the inaccuracy due to the correlation is probably less than the inaccuracy due to the

THERMAL-HYDRAULIC IN NUCLEAR REACTOR

c)c) Nucleate Boiling FlowNucleate Boiling Flow

Nucleate boiling occurs in the hottest locations of a PWR core Nucleate boiling occurs in the hottest locations of a PWR core in normal operation and in the greater part of a BWR core.

in normal operation and in the greater part of a BWR core.

It may also occur in the greater part of a PWR core during It may also occur in the greater part of a PWR core during

transients associated with accidents.

As long as nucleate boiling occurs, the wall temperature is As long as nucleate boiling occurs, the wall temperature is TTsatsat + ΔT + ΔTsatsat, and ΔT, and ΔTsatsat is only a few degrees. The correlations is only a few degrees. The correlations

used for calculating ΔT

used for calculating ΔTsatsat are usually the same as for the are usually the same as for the tubes. The

tubes. TheOnset of Nucleate BoilingOnset of Nucleate Boiling (ONB) may be (ONB) may be calculated as the point at which the wall temperature, as calculated as the point at which the wall temperature, as estimated by a single-phase turbulent heat transfer estimated by a single-phase turbulent heat transfer

correlation, reaches T

correlation, reaches Tsatsat + ΔT + ΔTsatsat; a subchannel analysis code ; a subchannel analysis code is needed to estimate this position. For more details on is needed to estimate this position. For more details on

nucleate and saturated boiling flow.

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d)d) Boiling CrisisBoiling Crisis

The boiling crisis, or

The boiling crisis, or Departure from Nucleate BoilingDeparture from Nucleate Boiling (DNB) is (DNB) is one of the phenomena limiting the power of a water nuclear one of the phenomena limiting the power of a water nuclear

reactor.

Although some boiling crises, like

Although some boiling crises, like dryoutdryout, lead to only , lead to only moderate temperature rises, others, like

moderate temperature rises, others, likeBurnoutBurnout at low at low

quality, may result in a dramatic and very rapid increase of quality, may result in a dramatic and very rapid increase of the rod wall temperature. Consequently, in many countries, the rod wall temperature. Consequently, in many countries,

the rules are that all boiling crises must be avoided in the rules are that all boiling crises must be avoided in

normal and abnormal situations, up to incidental transients normal and abnormal situations, up to incidental transients

of class 2.

The basic boiling crisis phenomena have been modeled in The basic boiling crisis phenomena have been modeled in

tubes (ex. Whalley for dryout, Weissman et al. or Katto for tubes (ex. Whalley for dryout, Weissman et al. or Katto for

burnout), but the phenomenon is far more complicated in burnout), but the phenomenon is far more complicated in

rod bundles due to the presence of crossflows, mixing rod bundles due to the presence of crossflows, mixing

grids, complex geometry, nonuniform heat-flux, and the grids, complex geometry, nonuniform heat-flux, and the tube models give only a very rough approximation of the tube models give only a very rough approximation of the 230230

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There are several ways to obtain a local

There are several ways to obtain a local Critical Heat Flux, Critical Heat Flux, CHFCHF, prediction:, prediction:

a quick-and-approximate method is to use a tube CHF a quick-and-approximate method is to use a tube CHF prediction and adjust the result to the appropriate rod prediction and adjust the result to the appropriate rod bundle geometry using correcting factors. Among the bundle geometry using correcting factors. Among the

several hundreds of existing

several hundreds of existing CHFCHF correlations for tubes, correlations for tubes, annular space and other simple geometry the Groeneveld annular space and other simple geometry the Groeneveld

(1993) CHF tables are recommended.

a more accurate method is to use a specific CHF correlation a more accurate method is to use a specific CHF correlation (or table, smoothing splines, etc.) especially fitted for the (or table, smoothing splines, etc.) especially fitted for the specific geometry and mixing grids used. This involves car specific geometry and mixing grids used. This involves car rying out several CHF tests with the specific geometry and rying out several CHF tests with the specific geometry and the appropriate parameter range, analyzing these tests the appropriate parameter range, analyzing these tests with the same subchannel computer code and building a with the same subchannel computer code and building a CHF predictor. Since these experiments are difficult, CHF predictor. Since these experiments are difficult, expensive and long, and apply only to specific mixing grids expensive and long, and apply only to specific mixing grids and geometries, most of the CHF predictors are proprietary and geometries, most of the CHF predictors are proprietary

and not openly published.

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An intermediate method is to use a reference general An intermediate method is to use a reference general purpose rod bundle CHF correlation, perform some CHF purpose rod bundle CHF correlation, perform some CHF tests with the appropriate geometry and mixing grid, tests with the appropriate geometry and mixing grid, calculate the average and standard deviations of the calculate the average and standard deviations of the experimental results with respect to the reference CHF experimental results with respect to the reference CHF correlation, and then use these deviations to modify the correlation, and then use these deviations to modify the safety margin. The use of this methodology seems safety margin. The use of this methodology seems surprising as it is less efficient than the former one, and the surprising as it is less efficient than the former one, and the missing step—the construction of a specific CHF predictor missing step—the construction of a specific CHF predictor based on expensive and hard-won experimental data—is based on expensive and hard-won experimental data—is relatively easy, quick, cheap and more precise. However, relatively easy, quick, cheap and more precise. However, this methodology is very commonly used, especially for this methodology is very commonly used, especially for new fuel to be loaded into existing plant, because the on- new fuel to be loaded into existing plant, because the on- line computer software and, above all, the existing line computer software and, above all, the existing regulations (including the reference CHF correlation) seem regulations (including the reference CHF correlation) seem

very difficult to modify very difficult to modify

THERMAL-HYDRAULIC IN NUCLEAR REACTOR

The geometry and the grid spacer have a considerable The geometry and the grid spacer have a considerable influence on the CHF values. For the same thermohydraulic influence on the CHF values. For the same thermohydraulic local conditions (pressure, mass velocity, quality), the CHF local conditions (pressure, mass velocity, quality), the CHF may vary by a factor of 2 or 3! The most obvious effects on may vary by a factor of 2 or 3! The most obvious effects on

the CHF are due to:

the grid spacing: the CHF increases significantly as the grid the grid spacing: the CHF increases significantly as the grid

spacing decreases;

the geometry of the mixing grid, especially that of the mixing the geometry of the mixing grid, especially that of the mixing vanes: it may have a considerable influence on CHF vanes: it may have a considerable influence on CHF especially at low quality and high heat flux but most of the especially at low quality and high heat flux but most of the

results in this field are proprietary;

the guide thimble: it influences CHF and acts both as a cold the guide thimble: it influences CHF and acts both as a cold

wall effect and as a hydraulic diameter effect;

the equivalent hydraulic diameter: as in tubes, CHF generally the equivalent hydraulic diameter: as in tubes, CHF generally increases when the hydraulic diameter decreases for increases when the hydraulic diameter decreases for constant local thermal-hydraulic conditions. This sensitivity constant local thermal-hydraulic conditions. This sensitivity is usually greater for low quality and tends to zero for is usually greater for low quality and tends to zero for

higher quality.

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e) e) Quenching in Rod BundlesQuenching in Rod Bundles

Quenching of the core may occur after a Loss Of Coolant Quenching of the core may occur after a Loss Of Coolant Accident. Here the specificity of the rod bundle case is Accident. Here the specificity of the rod bundle case is directly related to radial steam and water crossflows, to the directly related to radial steam and water crossflows, to the complex geometry and heterogeneities of the core. (See complex geometry and heterogeneities of the core. (See

Blowdown

Blowdown and Reflood and Reflood.).)

f) Steam and water cross-flows f) Steam and water cross-flows

Analytical experiments in large 2D test sections have Analytical experiments in large 2D test sections have demonstrated that strong steam and water crossflows demonstrated that strong steam and water crossflows occur between neighboring assemblies with different occur between neighboring assemblies with different residual powers (radial peaking factor as high as 1.8).

residual powers (radial peaking factor as high as 1.8).

Considering, for instance, a "hot" assembly between two Considering, for instance, a "hot" assembly between two

"cold" ones [Deruaz et al. (1984) and Housiadas et al.

(1989)] perfect steam radial mixing is observed in the (1989)] perfect steam radial mixing is observed in the rewetted region indicating existence of steam crossflows rewetted region indicating existence of steam crossflows from the hot to the cold assemblies. At the same time, from the hot to the cold assemblies. At the same time, water cross-flows occur from the cold to the hot assembly water cross-flows occur from the cold to the hot assembly with an intensity which can reach values of up to 60% of with an intensity which can reach values of up to 60% of

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Liquid crossflows are negligible in the dry region whereas Liquid crossflows are negligible in the dry region whereas steam escapes to the cold assemblies due to the flow steam escapes to the cold assemblies due to the flow resistance inherent in a larger amount of liquid in the dry resistance inherent in a larger amount of liquid in the dry zone of the hot assembly. This complex behavior has a zone of the hot assembly. This complex behavior has a noticeable impact on quench front progression and heat noticeable impact on quench front progression and heat transfer in the assemblies. In the hot assembly, quench transfer in the assemblies. In the hot assembly, quench velocity is lower and precursory cooling is enhanced due to velocity is lower and precursory cooling is enhanced due to

the larger amount of liquid in the dry zone.

In steady or quasi-steady situations (boil-up or boil-off In steady or quasi-steady situations (boil-up or boil-off cases), level swell is uniform and depends only upon the cases), level swell is uniform and depends only upon the averaged residual power (and not upon its distribution averaged residual power (and not upon its distribution between the assemblies). This result is consistent with the between the assemblies). This result is consistent with the

existence of perfect steam radial mixing.

If exit steam velocities are not too large an additional If exit steam velocities are not too large an additional possible 2D phenomenon could be preferential fall back of possible 2D phenomenon could be preferential fall back of water from the upper plenum to the cold assemblies. Due to water from the upper plenum to the cold assemblies. Due to mixing of steam in the core this type of phenomenon does mixing of steam in the core this type of phenomenon does

not occur.

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g)g) Ballooning and grid effectsBallooning and grid effects

Extensive experiments have shown that both spacer grids Extensive experiments have shown that both spacer grids [Clement et al. (1982) and Hochreiter et al. (1992)] and [Clement et al. (1982) and Hochreiter et al. (1992)] and flow blockages (Hochreiter et al., 1992) (due flow blockages (Hochreiter et al., 1992) (due to ballooningto ballooning of some heater rods) can significantly alter of some heater rods) can significantly alter post-CHF heat transfer. Similarly, they exhibit local post-CHF heat transfer. Similarly, they exhibit local precursory rewetting and induce downstream effects due to precursory rewetting and induce downstream effects due to convection enhancement of the continuous phase and convection enhancement of the continuous phase and

breakup of entrained droplets.

h) Cold rod effects h) Cold rod effects

The presence of unheated rods in a bundle (control rod guide The presence of unheated rods in a bundle (control rod guide thimbles in the standard PWR for example) has a significant thimbles in the standard PWR for example) has a significant effect on the cooling efficiency viewed in terms of overall effect on the cooling efficiency viewed in terms of overall quench time (the time necessary to quench the full bundle) quench time (the time necessary to quench the full bundle) or of maximum wall temperature [Veteau et al. (1994)].

or of maximum wall temperature [Veteau et al. (1994)].

The cold rods exhibit very early quenching, modifying The cold rods exhibit very early quenching, modifying hydrodynamics in the subchannels and enhancing radiative hydrodynamics in the subchannels and enhancing radiative 236236

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Heat transfer in nuclear fuel rods bundles

Constraints of the thermal-hydraulic core design

Heat conduction in fuel assembly