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THERMAL-HYDRAULIC IN NUCLEAR REACTOR GS Trần Đại Phúc THERMAL-HYDRAULIC IN NUCLEAR REACTOR Summary Introduction 2.Energy from fission 3.Fission yield 4.Decay heat 5.Spatial distribution of heat sources 6.Coolant flow & heat transfer in fuel rod assembly 7.Enthalpy distribution in heated channel 8.Temperature distribution in channel in single phase 9.Heat conduction in fuel assembly 10.Axial temperature distribution in fuel rod 11.Void fraction in fuel rod channel 12.Heat transfer to coolant THERMAL-HYDRAULIC IN NUCLEAR REACTOR   I Introduction An important aspect of nuclear reactor core analysis involves the determination of the optimal coolant flow distribution and pressure drop across the reactor core On the one hand, higher coolant flow rates will lead to better heat transfer coefficients and higher Critical Heat Flux (CHF) limits On the other hand, higher flows rates will also 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 THERMAL-HYDRAULIC IN NUCLEAR REACTOR 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 THERMAL-HYDRAULIC IN NUCLEAR REACTOR  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     THERMAL-HYDRAULIC IN NUCLEAR REACTOR      Rods to the coolant fluid in normal operation and incidental conditions The thermal-hydraulic design is not under specific design requirements However, the assured safety functions requires the application of a Quality Assurance programme on which the main aim is to document and to control all associated activities 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 THERMAL-HYDRAULIC IN NUCLEAR REACTOR   The primary coolant rate and the drop time of the control rod clusters must be measured regularly The main aim of the thermal-hydraulic design is principally to guarantee the heat transfer and the repartition of the heat production in the reactor core, such as the evacuation of the primary heat or of the safety injection system (belong 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 THERMAL-HYDRAULIC IN NUCLEAR REACTOR  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 rapid increase of the clad temperature of the fuel rod   THERMAL-HYDRAULIC IN NUCLEAR REACTOR    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 thermalhydraulic and neutron behaviour of the reactor core  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 speed then Snv is the number of neutron falling on m2 of target material per second THERMAL-HYDRAULIC IN NUCLEAR REACTOR    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: Σf nv = ΣfФ , where Σf =nv is the neutron flux (to be discussed later) and Σf= Nσf , N being the number of fissile nuclei/m3 and σf 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 Σf Ф fissions, where Σf and Ф are the average values of the macroscopic fissions cross section and the neutron flux, respectively THERMAL-HYDRAULIC IN NUCLEAR REACTOR         B Neutron aspects The distribution of the power in the core is not uniform & large disparities exist betwwen the different zones, resulting from the non_uniform of the neutron flux in the core due to nuclear physics To recall, neutron flux is expressed in n/cm2 and is related at each point in the fuel to the thermal power release by the equation: q’’’ = ∑f Øth x 3.2 x 10 -11 Where :∑f is the effective fission cross-section in cm-1 & the Ø th is the thermal flux in n/cm2.s Or : P(W) = (VΣf Фth) / 3.1x1010 Shape of the neutron flux In considering the form of the neutron flux, one distinguishes between 1) the radial distribution & 2) the axial distribution THERMAL-HYDRAULIC IN NUCLEAR REACTOR    a) Radial flux distribution: For a homogeneous reactor (a theoretical case), the radial flux distribution is a Bessel function J0 (shape 1) Because of the presence of a neutron reflector (the water surrounding the core or a metallic structure installed & because of different fuel enrichment zones loaded according to a certain fuel loading pattern the flux distribution as function of the radius is in reality more complex than the Bessel function as shown in the following figure According to the fuel management strategies used in 80s & the fuel loading patterns which followed from these, the most enriched fuel assembly are loaded at the periphery of the core & the lowest at the centre in order to get a flatned power distribution (shape 2) Modern fuel management strategies currently used require that the highest fuel-enrichment zone be loaded at the centre and the lowest at the periphery in order to decrease the amplitude of the neutron leakage & then increase the initial core reactivity & consequently the fuel cycle length (shape 3) THERMAL-HYDRAULIC IN NUCLEAR REACTOR   Obviously, the immediate consequence is an increase in the core peaking factors The safety analysis must be reviewed to demonstrate that the safety margins are still acceptable Figure XX.1: Radial distribution of neutron flux THERMAL-HYDRAULIC IN NUCLEAR REACTOR      b) Axial neutron flux distribution When the core is homogenous & at the beginning of the life (BOL) & zero power (shape 1), the curve of the flux distribution has the shape of a cosinus function The reactor power level increasing to full power, the coolant temperature being higher towards the top of the core while being roughly constant towards the bottom (according to the core average temperature variation versus the power level), neutron moderation is more effective towards the bottom of the core where the water density is the highest (less effective towards the top where the density is the lowest) This leads to an axial gradient of reactivity that induces a slight bulge in the axial flux distribution towards the base of the core (shape 2) After few months of operation at full power, the fuel is burned up faster in the region where the neutron flux is higher i.e a little bit lower than the mid-axis On the other hand, the fuel is burned up more slowly at the axial core extremities The consequence is a so-called THERMAL-HYDRAULIC IN NUCLEAR REACTOR  XX.2 : Axial distribution of the neutron flux THERMAL-HYDRAULIC IN NUCLEAR REACTOR     As indicated in the following figure, insertion of the control rods modifies the shape of the axial flux distribution curve by moving the position of maximum flux clearly into the lower half of the core This movement is accompanied by an increase in the value of the maximum flux in the same region It is therefore necessary, as we will see later on, to verify that the thermal flux at this point does not exceed certain limiting values The situation also makes it necessary to operate at normal rated reactor power with minimum insertion of the control rods in the core, which allows more homogeneous fuel burn-up & ensures a greater negative reactivity reserve in case of reactor trip Nevertheless, the fast reactivity variations, related to rapid changes in the power level must be compensated for by the RCCA That means a compromise must be looked for & a certain insertion is acceptable THERMAL-HYDRAULIC IN NUCLEAR REACTOR      To be able to keep the control rod clusters at the position indicated in the figure, which is in the so-called « reference » zone, these must be another means of reactor control available soluble boron This element is present in the form of boric acid, diluted in the reactor coolant Thus, slow reactivity variations, in particular those related to progressive burn-up of the fuel, shift over from cold shutdown to hotshutdown, & scheduled slow reactor power changes are compensated for by causing the boron concentration to vary correspondinly This adjustment is quite slow (some 10 minutes is necessary to change the boron concentration but homogeneous i.e does not influence the power distribution This drawback relates to the quantity of liquid effluents produced at each change in the boron concentration of the reactor coolant Immediately after the first power escalation after reactor fueling, at full power, the boron concentration is approximatively 1000 ppm according to the fuel management strategy and the fuel loading pattern THERMAL-HYDRAULIC IN NUCLEAR REACTOR   Normal fuel burn-up reduces the concentration by to ppm per day Figure XX.3: Axial neutron flux distribution with RCCA insertion THERMAL-HYDRAULIC IN NUCLEAR REACTOR      c) The Xenon effect Some of the fission products formed strongly capture free neutrons & are known as « poisons » This particularly the case of the Xenon 135, which can cause considerable variations in the core reactivity within the space of few hours, thus leading to difficulties in controlling the reactor power (overall effect) & in controlling the power distribution (local effect) The Xenon effect is responsible for the following phenomena: - Start-up: If one starts the reactor from a situation where no Xenon is present (after a shutdown lasting for several days), the progressive formation of Xenon 135 makes it necessary to withdraw the RCCA or to reduce the concentration of the soluble boron in order to maintain the desired neutron flux or power level, until the Xenon has attained its equilibrium concentration - Power increase: Starting from a situation where the Xenon is in a state of equlibrium, it is necessary to temporarily increase the boron concentration or to insert the control rod clusters, whereas power THERMAL-HYDRAULIC IN NUCLEAR REACTOR    - Power decrease: Starting from a situation in which the Xenon is in equilibrium, one obtains an opposite effect from that mentioned just above, but one that is much more pronounced This is called « the Xenon peak » After a reactor trip, it can limlit the return to criticality and then the full reactor power for periods of several hours - Stable power distribution: The production of Xenon depends upon the disappearance of the iodine 135, the local quantity of the Xenon depends on the evolution of the flux at the point under consideration The distribution of Xenon in the core influence the power distribution & can cause instabilities in the later The following figure shows the evolution of the negative reactivity due to the Xenon over time, as function of the power level variations) THERMAL-HYDRAULIC IN NUCLEAR REACTOR  Figure XX.4: Evolution of the Xenon negative effect THERMAL-HYDRAULIC IN NUCLEAR REACTOR     XX1 Computer codes in Nuclear Reactor Thermal-Hydraulics From early days of the usage of nuclear technology, computer codes have been used to support design and safety analyses The raison for that is twofold: on the one hand nuclear engineering is an excellent example of a multi-physics domain, where strong interactions between different fields (e.g neutron physics, multi-phase flows, structural dynamics, chemistry, etc.) exists On the other hand nuclear industry applies very high standards as far as the operational safety of NPPs is 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 modules (diffusion theory, transport theory, Monte Carlo theory) and somewhat more crude thermal-hydraulic modules Examples of such codes are POLCA (Westinghouse, earlier ABB-Atom), SIMULATE, etc Transport codes are used to obtain the macroscopic neutron crosssections which are later used as input to the diffusion theory codes THERMAL-HYDRAULIC IN NUCLEAR REACTOR   Reactor kinetics codes: Example such is the PARCS code that solves the time dependent two-group neutron diffusion equation in threedimensional Cartesian geometry using nodal methods to obtain the transient neutron flux distribution The code may be used in the analysis of reactivity initiated accidents in light water reactors were 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 analyse loss of coolant accidents, LOCAs, any system transients in light water reactors There is a variety of TH system codes used in nuclear engineering The best know are the RELAP5, CATHARE and the TRAC codes, which primary goal are to predict small break LossCoolant Accident (LOCA) and the large break LOCA thermalhydraulics, respectively THERMAL-HYDRAULIC IN NUCLEAR REACTOR   Thermal hydraulic fuel analysis codes: The most important group are so called sub-channel analysis codes, which are using flow averaging on the sub-channel level and apply mixing models to account for the mass, momentum and energy exchange between sub-channels Examples such codes are, THINC-IV, COBRA, VIPRE, COMETHE, THYC, FLICA, BUNGLE, MONA-3, etc Typical application 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 progression of accidents in light water reactor nuclear power plants Three examples of such codes are MELCOR, SCDAP/RELAP5 and CATHARE THERMAL-HYDRAULIC IN NUCLEAR REACTOR THANKS FOR YOUR ATTENTION ... drop in a fuel rod cross-section is represented in following figure IX.2 THERMAL-HYDRAULIC IN NUCLEAR REACTOR Figure IX.1: Cross section of a square fuel lattice THERMAL-HYDRAULIC IN NUCLEAR REACTOR. .. coolant temperature with cosines heat flux distribution THERMAL-HYDRAULIC IN NUCLEAR REACTOR  IX Heat conduction in fuel assembly   Modern nuclear power reactors contain cylindrical fuel elements... /W.Cp.cos(πz /H) (VIII.4) THERMAL-HYDRAULIC IN NUCLEAR REACTOR  Figure VIII.2: Heated channel with cosines power distribution THERMAL-HYDRAULIC IN NUCLEAR REACTOR  After intergration, the coolant