Computer codes in Nuclear Reactor Thermal-Hydrauli- 123docz.net

The 12 The 12 self-powered detectors fingers contain each 6 self-powered detectors

C. Aeroball system for monitoring power distribution in the reactor core. The fundamental function of that movable nuclear fixed

XXI. Computer codes in Nuclear Reactor Thermal-Hydraulics Computer codes in Nuclear Reactor Thermal-Hydraulics

From early days of the usage of nuclear technology, computer codes From early days of the usage of nuclear technology, computer codes have been used to support design and safety analyses. The raison for have been used to support design and safety analyses. The raison for that is twofold: on the one hand nuclear engineering is an excellent that is twofold: on the one hand nuclear engineering is an excellent example of a multi-physics domain, where strong interactions between example of a multi-physics domain, where strong interactions between different fields (e.g. neutron physics, multi-phase flows, structural different fields (e.g. neutron physics, multi-phase flows, structural dynamics, chemistry, etc.) exists. On the other hand nuclear industry dynamics, chemistry, etc.) exists. On the other hand nuclear industry applies very high standards as far as the operational safety of NPPs is applies very high standards as far as the operational safety of NPPs is concerned, which, in turn, requires high accuracy in estimation of the concerned, which, in turn, requires high accuracy in estimation of the

operational conditions.

The currently used codes can be divided in the following groups:

Reactor simulation codes: Such codes have well developed neutronic Reactor simulation codes: Such codes have well developed neutronic modules (diffusion theory, transport theory, Monte Carlo theory) and modules (diffusion theory, transport theory, Monte Carlo theory) and somewhat more crude thermal-hydraulic modules. Examples of such somewhat more crude thermal-hydraulic modules. Examples of such codes are POLCA (Westinghouse, earlier ABB-Atom), SIMULATE, etc.

codes are POLCA (Westinghouse, earlier ABB-Atom), SIMULATE, etc.

Transport codes are used to obtain the macroscopic neutron cross- Transport codes are used to obtain the macroscopic neutron cross- sections which are later used as input to the diffusion theory codes.

sections which are later used as input to the diffusion theory codes. 334334

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Reactor kinetics codes: Example such is the PARCS code that solves the Reactor kinetics codes: Example such is the PARCS code that solves the time dependent two-group neutron diffusion equation in three- time dependent two-group neutron diffusion equation in three- dimensional Cartesian geometry using nodal methods to obtain the dimensional Cartesian geometry using nodal methods to obtain the transient neutron flux distribution. The code may be used in the transient neutron flux distribution. The code may be used in the analysis of reactivity initiated accidents in light water reactors were analysis of reactivity initiated accidents in light water reactors were spatial effects may be important. It may be run in the stand-alone spatial effects may be important. It may be run in the stand-alone

mode or coupled to other codes such as RELAP5.

Thermal-hydraulic system codes: Thermal-hydraulics codes are used to Thermal-hydraulic system codes: Thermal-hydraulics codes are used to analyse loss of coolant accidents, LOCAs, any system transients in analyse loss of coolant accidents, LOCAs, any system transients in light water reactors. There is a variety of TH system codes used in light water reactors. There is a variety of TH system codes used in nuclear engineering. The best know are the RELAP5, CATHARE and nuclear engineering. The best know are the RELAP5, CATHARE and the TRACE codes, which primary goal are to predict small break Loss- the TRACE codes, which primary goal are to predict small break Loss- Coolant Accident (LOCA) and the large break LOCA thermal- Coolant Accident (LOCA) and the large break LOCA thermal-

hydraulics, respectively hydraulics, respectively..

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Thermal hydraulic fuel analysis codes: The most important group are so Thermal hydraulic fuel analysis codes: The most important group are so called sub-channel analysis codes, which are using flow averaging on called sub-channel analysis codes, which are using flow averaging on the sub-channel level and apply mixing models to account for the the sub-channel level and apply mixing models to account for the mass, momentum and energy exchange between sub-channels.

mass, momentum and energy exchange between sub-channels.

Examples such codes are, THINC-IV, COBRA, VIPRE, COMETHE, Examples such codes are, THINC-IV, COBRA, VIPRE, COMETHE, THYC, FLICA, BUNGLE, MONA-3, FRAPCON, etc. Typical application THYC, FLICA, BUNGLE, MONA-3, FRAPCON, etc. Typical application of such codes I to predict void distributions, pressure drops and the of such codes I to predict void distributions, pressure drops and the

margins to CHF.

Severe accident codes: Severe accidents codes are used to model the Severe accident codes: Severe accidents codes are used to model the progression of accidents in light water reactor nuclear power plants.

progression of accidents in light water reactor nuclear power plants.

Three examples of such codes are MELCOR, SCDAP/RELAP5, TRACE, Three examples of such codes are MELCOR, SCDAP/RELAP5, TRACE,

ATHLET and CATHARE.

THERMAL-HYDRAULIC IN NUCLEAR REACTOR

XXII. Hydraulic loading in reactor core XXII. Hydraulic loading in reactor core

Five flow-induced vibration mechanisms are addressed here:

Five flow-induced vibration mechanisms are addressed here: Buckling Buckling instability, Vortex-induced vibration, Acoustic resonance, Fluid-elastic instability, Vortex-induced vibration, Acoustic resonance, Fluid-elastic

instability, and Turbulence induced vibration . instability, and Turbulence induced vibration .

Buckling instability is a static instability by bending. Since the internal Buckling instability is a static instability by bending. Since the internal cladding is a very long hollow tube, buckling due to internal flow in the cladding is a very long hollow tube, buckling due to internal flow in the

annular fuel produces stresses by a bending moment.

Periodic wake shedding occurs immediately downstream of structures Periodic wake shedding occurs immediately downstream of structures subjected to cross flow. Periodic wake shedding generates periodic subjected to cross flow. Periodic wake shedding generates periodic fluid forces. When the structural natural frequency is close enough to fluid forces. When the structural natural frequency is close enough to the vortex-shedding frequency, a phenomenon known as lock-in the vortex-shedding frequency, a phenomenon known as lock-in occurs whereby the shedding frequency coincides with the structural occurs whereby the shedding frequency coincides with the structural natural frequency. As a result, resonant vibration by lock-in can natural frequency. As a result, resonant vibration by lock-in can

potentially lead to fuel failure.

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Acoustic pulsations, such as those generated by coolant Acoustic pulsations, such as those generated by coolant pumps, can potentially cause large responses if standing pumps, can potentially cause large responses if standing pressure waves are produced in the coolant channels.

pressure waves are produced in the coolant channels.

Standing waves are of non-propagating nature and result Standing waves are of non-propagating nature and result from a reflected wave that is superimposed onto the from a reflected wave that is superimposed onto the original wave, forming interference patterns which have original wave, forming interference patterns which have amplified deflections. One of the most detrimental acoustic amplified deflections. One of the most detrimental acoustic problems for the fuel is induced when one or more of the problems for the fuel is induced when one or more of the lower acoustic modes are excited by vortex-shedding in the lower acoustic modes are excited by vortex-shedding in the fuel bundle. The acoustic cavity resonance correlated with fuel bundle. The acoustic cavity resonance correlated with shedding causes intense acoustic noise, which can lead to shedding causes intense acoustic noise, which can lead to

severe structural damage.

THERMAL-HYDRAULIC IN NUCLEAR REACTOR

Fluid-elastic instability is one of the main mechanical damage Fluid-elastic instability is one of the main mechanical damage mechanisms and should be absolutely avoided. Fluid-elastic mechanisms and should be absolutely avoided. Fluid-elastic instability produces excessive vibration amplitudes by instability produces excessive vibration amplitudes by negative damping resulting from coupling between fluid- negative damping resulting from coupling between fluid- induced dynamic forces and the motion of the structures.

induced dynamic forces and the motion of the structures.

Instability occurs when the flow velocity is sufficiently high Instability occurs when the flow velocity is sufficiently high so that the energy absorbed from the fluid forces exceeds so that the energy absorbed from the fluid forces exceeds

the energy dissipated by damping.

The minimum velocity at which instability occurs is called the The minimum velocity at which instability occurs is called the

critical velocity for fluid-elastic instability.

Turbulence-induced excitation generates random pressure Turbulence-induced excitation generates random pressure fluctuations around the fuel surfaces forcing them to fluctuations around the fuel surfaces forcing them to vibrate. Turbulence-induced excitation is the primary vibrate. Turbulence-induced excitation is the primary vibration excitation mechanism in axial flow. Turbulence- vibration excitation mechanism in axial flow. Turbulence- induced excitation may cause sufficient vibration response induced excitation may cause sufficient vibration response

to cause long-term fretting-wear damage.

to cause long-term fretting-wear damage. 339339

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The life-time wear of the fuel cladding should be less than a The life-time wear of the fuel cladding should be less than a critical wear, at which cladding failure may be expected.

critical wear, at which cladding failure may be expected.

Vibrations and rod grid wear (response to flow turbulence, Vibrations and rod grid wear (response to flow turbulence,

instabilities, baffle jetting..).

XXII.1. Recall laminar flow & turbulent flow XXII.1. Recall laminar flow & turbulent flow

Heterogeneities in the coolant flow map in the PWR cores Heterogeneities in the coolant flow map in the PWR cores are one of the mechanisms involved in fuel assembly are one of the mechanisms involved in fuel assembly deformation detected after core unloading. Cross flows deformation detected after core unloading. Cross flows between fuel assemblies in the core generate hydraulic between fuel assemblies in the core generate hydraulic forces. The hydro-mechanic forces generated in the FA are forces. The hydro-mechanic forces generated in the FA are mainly by axial and cross flows through the reactor core.

mainly by axial and cross flows through the reactor core.

The pressure drop of the rod bundle generates hydro- The pressure drop of the rod bundle generates hydro- mechanic forces. The pressure drop coefficient depends on mechanic forces. The pressure drop coefficient depends on the mass flow rate and on the slope angle between the flow the mass flow rate and on the slope angle between the flow

and the fuel bundle.

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At low velocity, the flow within a boundary proceeds along At low velocity, the flow within a boundary proceeds along stream lines and hence is of laminar type (see following stream lines and hence is of laminar type (see following figure). However, with sufficient length, disturbances figure). However, with sufficient length, disturbances within flow appear, leading to variable velocity (in direction within flow appear, leading to variable velocity (in direction as well as magnitude) at any position: thus the flow as well as magnitude) at any position: thus the flow

becomes

becomes “turbulent”. “turbulent”.

The higher the flow velocity, the shorter is the purely The higher the flow velocity, the shorter is the purely laminar flow length. With turbulent flow, eddies are formed laminar flow length. With turbulent flow, eddies are formed that have random velocity, which destroys the laminar flow that have random velocity, which destroys the laminar flow lines. However, even for turbulent flow, the flow near the lines. However, even for turbulent flow, the flow near the

wall (where the velocity is small) appears to have a

wall (where the velocity is small) appears to have a laminar laminar region

region or sub-layer, as illustrated in following figure. or sub-layer, as illustrated in following figure.

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For most practical flow conditions, the effects of viscosity on For most practical flow conditions, the effects of viscosity on the flow over a surface can be assumed as confined to a the flow over a surface can be assumed as confined to a

“thin” region close to the surface. This region is called the

“boundary layer

“boundary layer”. The velocity of the fluid at the surface is ”. The velocity of the fluid at the surface is taken to be zero. Thus by definition, the boundary layer is taken to be zero. Thus by definition, the boundary layer is taken as the region in which the velocity changes from a taken as the region in which the velocity changes from a

free stream velocity to zero at the surface.

The cooling flow pass through from lower end to the upper The cooling flow pass through from lower end to the upper plate of the fuel assembly in the reactor core will induce plate of the fuel assembly in the reactor core will induce

many

many hydraulic loadshydraulic loads. These later will affect the mechanical . These later will affect the mechanical behavior of the fuel assembly. This chapter will pass behavior of the fuel assembly. This chapter will pass through all aspects related to the induced loads by through all aspects related to the induced loads by

turbulent flow

turbulent flow to the fuel assembly in the reactor core. to the fuel assembly in the reactor core.

THERMAL-HYDRAULIC IN NUCLEAR REACTOR

XXII.2. Vortex-Shedding Issues XXII.2. Vortex-Shedding Issues

Turbulent flow-induced vibration mechanisms are addressed Turbulent flow-induced vibration mechanisms are addressed

here:

Buckling instability, Buckling instability,

Vortex-induced vibration, Acoustic resonance, Fluid-elastic Vortex-induced vibration, Acoustic resonance, Fluid-elastic

instability, and Turbulence induced vibration.

Buckling instability is a static instability by bending. Since the Buckling instability is a static instability by bending. Since the internal cladding is a very long hollow tube, buckling due to internal cladding is a very long hollow tube, buckling due to internal flow in the annular fuel produces stresses by a internal flow in the annular fuel produces stresses by a

bending moment bending moment..

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XXII.3. Basic Theory XXII.3. Basic Theory

As the tube bundle is subjected to cross flow, the vortices will As the tube bundle is subjected to cross flow, the vortices will shed alternately from one side and then the other side of shed alternately from one side and then the other side of the cylindrical tubes. The frequency of the vortex shedding, the cylindrical tubes. The frequency of the vortex shedding, s f s f , has been found proportional to the cross flow velocity, , has been found proportional to the cross flow velocity, V V , and inversely proportional to the diameter of the tube , and inversely proportional to the diameter of the tube DD. .

Thus, Thus,

f SV / D f SV / D

where S is the proportionality constant, and is defined by where S is the proportionality constant, and is defined by

[Weaver and Fitzpatrick, 1988]

In-line square array:

S = 1/(2(P/D – 1)) S = 1/(2(P/D – 1))

THERMAL-HYDRAULIC IN NUCLEAR REACTOR

The above equation is based on the maximum approach The above equation is based on the maximum approach

velocity defined by velocity defined by

VVapproachapproach = ((P – D)/P)V = ((P – D)/P)Vpp where

where

P P : pitch of tube bundle: pitch of tube bundle D: outer diameter of tubeD: outer diameter of tube V p:

V p: :velocity within the narrowest gap distance:velocity within the narrowest gap distance V approach

V approach :velocity at the sub-channel frontal area:velocity at the sub-channel frontal area

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As the vortices shed from the tube, a fluctuating force will be As the vortices shed from the tube, a fluctuating force will be generated. It has two components. The lift direction generated. It has two components. The lift direction (perpendicular to the flow direction) has a frequency equal (perpendicular to the flow direction) has a frequency equal

to the vortex-shedding frequency

to the vortex-shedding frequency s f s f . The drag direction (in . The drag direction (in the direction of flow) has a frequency equal to twice the the direction of flow) has a frequency equal to twice the

vortex-shedding frequency 2

vortex-shedding frequency 2 fs fs ..

If the fluctuating force frequency is close to one of the tube If the fluctuating force frequency is close to one of the tube natural frequency modes, a phenomenon called lock-in will natural frequency modes, a phenomenon called lock-in will occur, which can take place both in the lift direction and in occur, which can take place both in the lift direction and in the drag direction, resulting in a much larger amplitude of the drag direction, resulting in a much larger amplitude of

resonance vibration of the tube.

The most important rule in designing components against The most important rule in designing components against vortex-induced vibration damage is to avoid the lock-in vortex-induced vibration damage is to avoid the lock-in

condition.

THERMAL-HYDRAULIC IN NUCLEAR REACTOR

Although there are several alternate rules, the most common Although there are several alternate rules, the most common one is the separation rule. If the structural modal frequency one is the separation rule. If the structural modal frequency is at least 30% below or 30% above the vortex-shedding is at least 30% below or 30% above the vortex-shedding

frequency, i.e., if frequency, i.e., if

f f nn< 0.7 f< 0.7 fs s ,or, f,or, fnn >1.3 f >1.3 fss

then lock-in in the lift direction is avoided in the nth mode.

Likewise, if Likewise, if

f < 0.7 × 2 f

f < 0.7 × 2 fss ,or, f ,or, fnn > 1.3× 2 f > 1.3× 2 fss

the lock-in in the drag direction is avoided in the nth mode.



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When the vortex-shedding frequency is well separated from When the vortex-shedding frequency is well separated from the natural frequency of tubes, based, for example, on the the natural frequency of tubes, based, for example, on the 30% rule, the magnitudes of forced tube vibration are 30% rule, the magnitudes of forced tube vibration are usually small and are bounded by turbulence-induced usually small and are bounded by turbulence-induced vibration. The main concern of vortex-shedding in a tube vibration. The main concern of vortex-shedding in a tube bundle is its potential to excite the acoustic modes in the bundle is its potential to excite the acoustic modes in the

flow cavity.

XXII.4. Acoustic Resonance Issue due to Vortex Shedding XXII.4. Acoustic Resonance Issue due to Vortex Shedding

Theoretically, once the vortex-shedding frequency is above Theoretically, once the vortex-shedding frequency is above the lowest acoustic mode in the tube bundles, the acoustic the lowest acoustic mode in the tube bundles, the acoustic resonance is very easily excited. The acoustic resonance resonance is very easily excited. The acoustic resonance normally causes intense acoustic noise, which can lead to normally causes intense acoustic noise, which can lead to

severe structural damage.

Computer codes in Nuclear Reactor Thermal-Hydraulics Computer codes in Nuclear Reactor Thermal-Hydraulics

Constraints of the thermal-hydraulic core design

Heat conduction in fuel assembly