Tài liệu tiếng anh Thủy nhiệt của lò phản ứng hạt nhân

I Effect of the manufacturing tolerances of the spacer grids on CHF J Effect of the fuel rod bowing in the reactor on the CHF k Correlation between the heat transfer and the void coeff

THERMAL-HYDRAULIC IN

NUCLEAR REACTOR

GS Trần Đại Phúc

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Summary

I Introduction

I.1 Safety Functions & Requirements

I.2 Basis of thermal-hydraulic core analysis

I.3 Constraints of the thermal-hydraulic core design

II Energy from nuclear fission

III Fission yield

IV Decay heat

V Spatial distribution of the heat sources

VI Coolant flow and heat transfer in fuel rod assembly

VII Enthalpy distribution in heated channel

VIII Temperature distribution in channel in single phase

IX Heat conduction in fuel assembly

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Summary

X Axial temperature distribution in fuel rods

XI Void fraction in boiling channels

XI.1 Homogeneous Equilibrium Model (HEM)

XI.2 Drift-flux model

XI.3 Sub-cooled boiling region

XII Heat transfer to coolant

XII.1 Single phase

XIII Two-Phase flow

XIV Pressure drops

XIV.1 Single-phase flows

a) The Darcy Weisbach equation

b) The Moody diagram

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Summary

XV Critical Heat Flux (CHF)

XV.1 Departure from Nucleate Boiling (DNB)

XV.2 Dry-out

XV.3 Protection against boiling crisis

A. Fuel temperature

B Reactor core coolant mass flow rate

C Hydro-dynamic stability of the reactor core

D.Technology of the DNBR or Critical Heat Flux ratio and Mixing effect

D.1.Technology of the DNBR

a) Critical Heat Flux (CHF) – Correlation

E)Definition of the DNBR

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SummaryG) Uncertanties relative to the manufacturing parameters

H) Effect of the eccentricity of the fuel pellets and the ovality

of the cladding on the CHF.

I) Effect of the manufacturing tolerances of the spacer grids

on CHF

J) Effect of the fuel rod bowing in the reactor on the CHF

k) Correlation between the heat transfer and the void

coefficient to the radial distribution of the nuclear power

l) E Hydro-dynamic instability

m) F Defect of distribution of the rate at pressure-vessel inlet

n) G Pressure drops in the pressure-vessel

o) H Hydraulic forces

p) I Hydraulic Dimensioning of the internal components 5

e) Uncertainties relative to the manufacturing tolerances

f) Uncertainty relative to the design computer code

g) Uncertainty of the transient conditions versus the steady state conditions

b) Uncertainties due to the defect of the repartition of the

inlet mass flow rate

c) Uncertainties relative to the mass flow rate

d) Uncertainties relative to the hydraulic forces

e) Uncertainties relative to the hydraulic dimensioning of the internal components

N Methods of analysis and study data

N.1 Methods utilized to analyse the transients

O Hot channel factors

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SummaryXVI.2 Axial power distribution

XVI.3 Heat transfer in nuclear fuel rods bundles

a)Laminar Flow

b) Single-Phase Turbulent Flow

c) Nucleate Boiling Flow

d) Boiling Crisis

e)Quenching in Rod Bundles

f) Steam and water cross-flows

g) Ballooning and grid effects

h) Cold rod effects

XVI.4 Limitations of power distribution

XVI.5 Reactivity coefficients

XVI.6 Reactivity control

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Summaryb) Functional criteria

j)The command system of the control rods clusters

k) Chemical & Volume Control System (CVCS) & Emergency Boration System (EBS)

l) Emergency Core Coolant System (ECCS) 9

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Summaryn) Evaluation of the design

XVI.6 Fuel temperature coefficient (Doppler effect)

XVI.7 Moderator coefficient

XVI.7a Density moderator coefficient

XVI.7b Void moderator coefficient

XVI.7c Heat flux limitations

XVI.7.d The behaviour of the DNB correlations

XVI.7e Requirements relative to the instrumentation

XVI.7.f Operations at high linear power

XVI.7.g Other criterion

XVIII The corresponding core protection channels

XVIII.1 Limiting conditions of operation

XVIII.2 PWR nuclear instrumentation 10

XIX Protection chains ΔTe & ΔTOP

XIX.1.Steady state ΔI = 0

XIX 2.Transient conditions

XIX.3 Instrumentation & setting errors

XIX.4 Taken into account of the unbalance of the axial power XIX.5 Mass flow reductions

A.Thermal aspect

B Neutron aspects

1 Shape of the neutron flux

a) Radial flux distribution:

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Summaryb) Axial neutron flux distribution.

c) The Xenon effect

XXI Computer codes in Nuclear Reactor Thermal-Hydraulics XXII Hydraulic loading in reactor core

XXII.1 Recall laminar flow & turbulent flow

XXII.2 Vortex-Shedding Issues

XXII.3 Basic Theory

XXII.4 Acoustic Resonance Issue due to Vortex Shedding

XXII.5 Acoustic Resonances of the Inner Channel Due to

Pump Blades Pass

XXII.6 Fluid-Elastic Instability

XXII.7 Discussion of Connor’s Equation Connor’s constant β

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SummaryXXII.9.Turbulence Induced Vibration

XXII.10 Axial Flow Induced Vibration

XXII.11 Cross Flow Induced Vibrations

XXII.12 Wear Analysis in the Fuel Assembly

XXII.13 Archard theory of adhesive wear

XXII.14 Impact Wear

XXII.15 Sliding Wear

XXII.16 Fretting Wear

XXII.17 Turbulent flow inside a channel

XXII.18 Turbulent friction factor

XXII.19 Pressure drop in rod bundles

XXII.20 Friction Along Bare Rod Bundles

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SummaryXXII.22 Pressure drop at spacers

XXII.23 Lateral resistance across bare rods arrays

in large pressure drops across the reactor core, hence larger required pumping powers and larger dynamic loads

on the core components Thus, the role of the hydrodynamic and thermal-hydraulic analysis is to find proper operating conditions that assure both safe and economical operation of the nuclear power plant.

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This chapter presents methods to determine the distribution

of heat sources and temperatures in various components of nuclear reactor In safety analyses of nuclear power plants the amount of heat generated in the reactor core must be known in order to be able to calculate the temperature distributions and thus, to determine the safety margins Such analyses have to be performed for all imaginable conditions, including operation conditions, reactor startup and shutdown,

as well as for removal of the decay heat after reactor shutdown The first section presents the methods to predict the heat sources in nuclear reactors at various conditions The following sections discuss the prediction of such parameters

as coolant enthalpy, fuel element temperature, void fraction, pressure drop and the occurrence of the Critical Heat Flux (CHF) in nuclear fuel assemblies

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I.1 Safety Functions & Requirements

The safety functions guaranteed by the thermal-hydraulic design are following:

Evacuation via coolant fluid the heat generated by the nuclear fuel;

Containment of radioactive products (actinides and fission products) inside the containment barrier.

Control of the reactivity of the reactor core: no effect on the thermal-hydraulic design.

Evacuation of the heat generated by the nuclear fuel: The aim

of thermal-hydraulic design is to guarantee the evacuation

of the heat generated in the reactor core by the energy transfer between the fuel

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Preliminary tests: The basic hypothesis on scenarios adopted

in the safety analyses must be control during the first physic tests of the reactor core Some of those tests, for example the measurements of the primary coolant rate or the drop time of the control clusters, are performed regularly Other tests are performed in totality only on the head of the train serial.

For the following units, only the necessary tests performed to guarantee that thermal-hydraulic characteristics of the reactor core are identical to the ones of the head train

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to each case) assures the respect of safety criteria.

I.2 Basis of thermal-hydraulic core analysis

The energy released in the reactor core by fission of enriched uranium U235 and Plutonium 238 appears as kinetic energy

of fission reaction products and finally as heat generated in the nuclear fuel elements This heat must be removed from the fuel and reactor and used via auxiliary systems to convert steam-energy to produce electrical power. 19

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I.3 Constraints of the thermal-hydraulic core design

The main aims of the core design are subject to several important constraints.

The first important constraint is that the core temperatures remain below the melting points of materials used in the reactor core This is particular important for the nuclear fuel and the nuclear fuel rods cladding.

There are also limits on heat transfer are between the fuel elements and coolant, since if this heat transfer rate becomes too large, critical heat flux may be approached leading to boiling transition This, in turn, will result in a

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The coolant pressure drop across the core must be kept low to minimize pumping requirements as well as hydraulic loads (vibrations) to core components.

Above mentioned constraints must be analyzed over the core live, for all the reactor core components, since as the power distribution in the reactor changes due to fuel burn-up or core management, the temperature distribution will similarly change.

Furthermore, since the cross sections governing the neutron physics of the reactor core are strongly temperature and density dependent, there will be a strong coupling between thermal-hydraulic and neutron behaviour of the reactor core.

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 Thermal hydraulic considerations are important when selecting overall plant charac-teristics Primary system temperature and pressure are key characteristics related to both the coolant selection and plant thermal performance This thermal performance is dictated by the bounds of the maximum allowable primary coolant outlet temperature and the minimum achievable condenser coolant inlet temperature Because this at-mospheric heat sink temperature is relatively fixed, improved thermodynamic per- formance requires increased reactor coolant outlet temperatures Figure 2-1 illustrates the relation among reactor plant temperatures for a 22

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Bounds on the achievable primary outlet temperature depend

on the coolant type For liquid metals, in contrast to water, the saturated vapor pressure for a given temperature is low, i.e., less than atmospheric pressure at outlet temperatures of interest of 500° to 550°C.

For water-cooled reactors, on the other hand, high primary outlet temperatures require correspondingly high system pressures (7 to 15 MPa), which increases the stored energy

in the primary coolant and requires increased structural piping and component wall thicknesses Single-phase gas coolants offer the potential for high outlet temperatures without such inherently coupled high pressures

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For these reactors the system pressure is dictated by the desired core heat transfer capabilities, as gas properties that enter these heat transfer correlations are strongly dependent on pressure The resulting pressures are moderate, i.e., 4 to 5 MPa, whereas achievable outlet temperatures are high, i.e., 635° to 750°C The nu-merical value of the plant thermal efficiency depends on the maximum temperature in the secondary or power- generation system This temperature is lower than the reactor coolant outlet temperature owing to the temperature difference needed to trans-fer heat between the primary and secondary systems in the steam generator

or inter-mediate heat exchanger

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In the boiling water reactor a direct cycle is employed The reactor outlet temperature is therefore identical (neglecting losses) to the inlet tem-perature to the turbine This outlet temperature is also limited to the saturation con-dition, as BWRs do not operate under superheat conditions In a typical BWR, how-ever, the average outlet enthalpy achieved corresponds to an average quality of 15% The PWR and BWR reactors achieve approximately equal thermal efficiencies, as the turbine steam conditions are comparable even though the primary system pressure and temperature conditions significantly differ (Table 2-1) Note that because of detailed differences in thermodynamic cycles the example PWR plant achieves a slightly higher

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Relations among reactor plant temperatures for typical PWR.

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Other plant characteristics are strongly coupled with thermal hydraulic consid-erations Some notable examples are as follows.

- Corrosion behavior, though strongly dependent on water chemistry control, is also temperature-dependent.

- The reactor vessel resistance to brittle fracture degrades with accumulated neu-tron fluence Vessel behavior under low-temperature, high-pressure transients from operating conditions is carefully evaluated to ensure that the vessel has retained the required material toughness over its lifetime.

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Primary system inventory

- The time response during accidents and less severe transients strongly depends on coolant inventories The reactor vessel inventory above the core is important to behavior in primary system rupture accidents For a PWR,

in particular, the pressurizer and steam generator inventories dictate transient response for a large class of situations.

- During steady-state operation the inlet plenum serves as

a mixing chamber to homogenize coolant flow into the reactor The upper plenum serves a similar function in multiple-loop plants with regard to the intermediate heat exchang-er/steam generator while at the same time protecting reactor vessel nozzles from thermal shock in 28

- Orientation of pump shafts and heat exchanger tubes coupled with support designs and impingement velocities

is important relative to prevention of trou-blesome vibration problems.

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II Energy from nuclear fission

Consider a mono-energetic neutron beam in which n is the neutron density (number of neutrons per m3) If v is neutron

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Since s is the effective area per single nucleus, for a given reaction and neutron energy, then S is the effective area of all the nuclei per m3 of target Hence the product Snv gives the number of interactions of nuclei and neutrons per m3 of target material per second.

In particular, the fission rate is found as: Σ f nv = Σ f Ф , where

Σ f =nv is the neutron flux (to be discussed later) and Σ f =

Nσ f , N being the number of fissile nuclei/m3 and σ f m2/nucleus the fission cross section In a reactor the neutrons are not mono-energetic and cover a wide range of energies, with different flux and corresponding cross section.

In thermal reactor with volume V there will occur V Σ f Ф fissions, where Σf and Ф are the average values of the macroscopic fissions cross section and the neutron flux,

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To evaluate the reactor power it is necessary to know the average amount of energy which is released in a single fission The table below shows typical values for uranium- 235.

Table II.1: Distribution of energy per fission of U-235.

10-12 J = 1 MeV

Kinetic energy of fission products 26.9 168

Instantaneous gamma-ray energy 1.1 7

Kinetic energy of fission neutrons 0.8 5

Beta particles from fission products 1.1 7

Gamma rays from fission products 1.0 6

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As can be seen, the total fission energy is equal to 32 pJ It

means that it is required ~3.1 1010 fissions per second to generate 1 W of the thermal power Thus, the thermal

power of a reactor can be evaluated as:

P (W) = VΣfФ / 3.1x10 10 (W) Thus, the thermal power of a nuclear reactor is proportional

to the number of fissile nuclei, N, and the neutron flux f

Both these parameters vary in a nuclear reactor and their correct computation is necessary to be able to accurately calculate the reactor power.

Power density (which is the total power divided by the

volume) in nuclear reactors is much higher than in

conventional power plants Its typical value for PWRs is 75 MW/m3, whereas for a fast breeder reactor cooled with

sodium it can be as high as 530 MW/m3.

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III Fission yield

Fissions of uranium-235 nucleus can end up with 80 different primary fission products The range of mass numbers of products is from 72 (isotope of zinc) to 161 (possibly an isotope of terbium) The yields of the products of thermal fission of uranium-233, uranium-235, plutonium-239 and a mixture of uranium and plutonium are shown in following figure III.1.

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Figure III.1: Fission yield as a function of mass number of the fission product.

As can be seen in all cases there are two groups of fission

products: a “light” group with mass number between 80

and 110 and a “heavy” group with mass numbers between

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Figure III.2: Illustration of the 6 formula:

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IV Decay heat

A large portion of the radioactive fission products emit gamma rays, in addition to beta particles The amount and activity of individual fission products and the total fission product inventory in the reactor fuel during operation and after shut-down are important for several reasons: namely

to evaluate the radiation hazard, and to determine the decrease of the fission product radioactivity in the spent fuel elements after removal from the reactor This information is required to evaluate the length of the cooling period before the fuel can be reprocessed.

Right after the insertion of a large negative reactivity to the reactor core (for example, due to an injection of control rods), the neutron flux rapidly decreases according to the

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Φ(t) = Ф 0 {(β / β – ρ) e (λρ / β – ρ)t - (ρ / β – ρ))e (β – ρ / l)t }

(IV.1)

Here f (t ) is the neutron flux at time t after reactor

shut-down, 0 f is the neutron flux during reactor operation at full power, r is the step change of reactivity, b is the fraction of delayed neutrons, l is the prompt neutron lifetime and l is the mean decay constant of precursors of delayed neutrons For LWR with uranium-235 as the fissile material, typical

values are as follows: l = 0.08 s-1, b = 0.0065 and l =

10-3s.

Assuming the negative step-change of reactivity r = -0.09, the relative neutron flux change is given as:

Ф(t) / Ф0 = 0.067 e -0.075t + 0.933 e -96.5t (IV-2)

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The second term in Eq (4-3) is negligible already after t =

0.01s and only the first term has to be taken into account in calculations As can be seen, the neutron flux (and thus the generated power) immediately jumps to ~6.7% of its initial value and then it is reduced e-fold during period of time T = 1/0.075 = 13.3 s.

After a reactor is shut down and the neutron flux falls to such

a small value that it may be neglected, substantial amounts

of heat continue to be generated due to the beta particles and the gamma rays emitted by the fission products FIGURE 4-2 shows the fission product decay heat versus the time after shut down The curve, which covers a time range from 1 to 106 years after shut down, refers to a hypothetical pressurized water cooled reactor that has operated at a constant power for a period of time during which the fuel (with initial enrichment 4.5%) has reached

50 GWd/tU burn-up and is then shut down instantaneously Contributions from various species which are present in the spent fuel are indicated.

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Figure IV.1: Fission product decay heat power (W/metric ton

of HM) versus time after shutdown.