Dipartimento di Ingegneria dell’Energia, dei Sistemi, del Territorio e delle
Tesi di Laurea
Influence of the 3
during a ULOF accident in the MYRRHA reactor
RELATORI
_________________________
Prof. Ing. Nicola Forgione
__________________________
Prof. Ing. Walter Ambrosini
__________________________
Dott. Ing. Francesco Belloni
__________________________
Dott. Guy Scheveneels
Dipartimento di Ingegneria dell’Energia, dei Sistemi, del Territorio e delle
Costruzioni
Tesi di Laurea Magistrale in Ingegneria Energetica
Influence of the 3-D phenomena on the safety
during a ULOF accident in the MYRRHA reactor
IL CANDIDATO
______
____________________
Prof. Ing. Nicola Forgione
Francesco Andreoli
______
Prof. Ing. Walter Ambrosini
______
Dott. Ing. Francesco Belloni
__________________________
Anno Accademico 2013/2014
Dipartimento di Ingegneria dell’Energia, dei Sistemi, del Territorio e delle
in Ingegneria Energetica
D phenomena on the safety parameters
during a ULOF accident in the MYRRHA reactor
IL CANDIDATO
____________________
1 The present thesis work, carried out during an internship at the nuclear research center SCK·CEN situated in Mol (Belgium), concerns the research activity performed for the MYRRHA (Multi-purpose hYbrid Research Reactor for High-tech Applications) reactor.
This reactor has been selected as the pilot plant for the lead-cooled fast reactor (LFR) technology by the European Sustainable Nuclear Industrial Initiative (ESNII), which addresses the need for demonstration of Generation IV Fast Neutron Reactor technologies, together with supporting research infrastructures, fuel facilities and R&D work.
The objective of this work is to assess the shortcomings of system codes in predicting the response of the MYRRHA reactor to a LOF (Loss Of Flow) event and to identify the 3-D safety-relevant phenomena that influence the transient evolution. Indeed, in a pool-type liquid metal cooled reactor like MYRRHA, the influence of 3-D thermal-hydraulic phenomena during LOF transients can have an important impact on safety-relevant parameters.
The adopted strategy is comparing the transient simulation results of the RELAP5 thermal-hydraulic system code with reference CFD estimations. An ANSYS-CFX coarse-mesh CFD model and a RELAP5 1-D model of the MYRRHA primary system were built to perform the transient analysis.
The scenario selected for this study is an Unprotected Loss Of Flow (ULOF) caused by the blockage of the two primary pumps: no coast-down is considered.
The CFD results were post-processed and averaged values of the main safety parameters were compared with the ones predicted by the system code. The good agreement between the results obtained from the two codes shows that the 3-D thermal hydraulic phenomena have not an important influence on the safety-relevant parameters and that RELAP5-3D is a good tool for the simulation of the transient analysis of MYRRHA. Moreover, it has been verified that the design of MYRRHA has a high intrinsic level of safety for the analyzed accident.
2 Desidero ringraziare tutti coloro che mi hanno aiutato nella realizzazione della mia Tesi. Tengo a specificare che tutte le persone citate in questa pagina hanno svolto un ruolo fondamentale nella stesura della tesi, ma desidero precisare che ogni errore o imprecisione è imputabile soltanto a me.
Il primo pensiero va sicuramente ai miei genitori cui dedico questa Tesi per ringraziarli del supporto, della pazienza e della fiducia che mi hanno mostrato durante tutto il percorso universitario.
Ringrazio il Professor Forgione e il Professor Ambrosini per avermi offerto quest’opportunità e per avermi dimostrato grande disponibilità e cortesia nell’aiutarmi durante la stesura della Tesi. Un sentito ringraziamento va ai miei Tutor Francesco e Dario per il notevole supporto e la fiducia che mi hanno dimostrato fin da subito. Senza il loro aiuto questa Tesi non esisterebbe. Grazie a Diego per i suoi consigli e per avermi aiutato nella parte finale del lavoro.
I want to thank Dr. Scheveneels for his precious suggestions that have guided me until the end of the work.
Desidero inoltre ringraziare tutti gli amici: i nuovi conosciuti durante questa esperienza con i quali ho condiviso momenti indimenticabili e gli amici di sempre per essermi stati vicini ed aver contribuito a fare di me quello che sono oggi.
L’ultimo ringraziamento, non sicuramente per importanza, è dedicato a Vania, una persona speciale senza la quale non sarei riuscito ad affrontare con serenità e coraggio questo lungo percorso. Con il suo amore e affetto è stata al mio fianco sia nei momenti più difficili che in quelli felici.
È stata un’esperienza speciale che non dimenticherò mai. It was a special experience that I will never forget.
3 ABSTRACT ... 1 TABLE OF CONTENTS ... 3 LIST OF ABBREVIATIONS ... 5 1. INTRODUCTION... 7 2. MATHEMATICAL MODELS ... 10 2.1. RELAP5-3D© ... 10 2.1.1. Mass Continuity ... 11 2.1.2. Momentum conservation ... 12 2.1.2.1. Wall Friction ... 16 2.1.3. Energy conservation... 17 2.1.3.1. Dissipation Term ... 18 2.1.4. Semi-Implicit Scheme ... 19 2.1.5. Nearly-Implicit Scheme ... 21
2.1.6. Heat structure model ... 21
2.2. ANSYS CFX ... 25
2.2.1. Multiphase flow ... 25
2.2.1.1. Continuity Equation ... 25
2.2.1.2. Momentum Equation ... 25
2.2.1.3. Thermal Energy Equation ... 26
2.2.2. Flow in Porous Media ... 27
2.2.2.1. Full Porous Model... 28
2.2.2.2. Porous Momentum Losses ... 29
2.2.2.2.1. Isotropic Loss Model ... 29
2.2.2.2.2. Directional Loss Model ... 30
3. MYRRHA PRIMARY SYSTEM ... 32
3.1. Introduction ... 32
3.2. Primary System ... 32
3.2.1. Reactor Vessel ... 33
4
3.2.5. Primary Heat Exchangers ... 39
3.2.6. Primary Pump ... 41
4. CODE MODELING AND IMPLEMENTATION ... 42
4.1. ANSYS CFX ... 42 4.1.1. Components description... 43 4.1.2. Mesh ... 51 4.2. RELAP5-3D© ... 55 4.2.1. Hydrodynamic components ... 57 4.2.2. Heat Structures ... 63
5. RESULTS AND COMPARISON ... 67
5.1. SHUT-DOWN state ... 67
5.2. STEADY-STATE condition (normal operation) ... 67
5.3. TRANSIENT ANALYSIS ... 81
5.3.1. ULOF with pump rotor pressure drop (CASE A) ... 83
5.3.1.1. Pump mass flow ... 84
5.3.1.2. Free surface levels... 86
5.3.1.3. Max LBE temperature... 87
5.3.1.4. Core mass flow ... 90
5.3.1.5. Average lower and upper plenum temperature ... 93
5.3.2. ULOF without pump rotor pressure drop (CASE B) ... 95
5.3.2.1. Pump mass flow ... 95
5.3.2.2. Free surface levels... 97
5.3.2.3. Max LBE temperature... 98
5.3.2.4. Core mass flow ... 100
5.3.2.5. Average lower and upper plenum temperature ... 101
6. CONCLUSIONS ... 102
5 ACS Above Core Structure
ADS Accelerator Driven System BPLU Border Profile Lower Upper CAD Computer-Aided Design CEL CFX Expression Language CFD Computational Fluid Dynamics
CR Control Rod
DHR Decay Heat Removal
ESNII European Sustainable Nuclear Industrial Initiative ETPP European Technology Pilot Plant
FA Fuel Assemblies HLM Heavy Liquid Metal
GIF Generation IV International Forum INL Idaho National Laboratory
InnDUMM Inner Dummies IPS In-Pile Section
IVFHM Inner Vessel Fuel Handling Machine IVFS Inner Vessel Fuel Storage
LOF Loss Of Flow
LBE Lead-Bismuth Eutectic LFR Lead-cooled Fast Reactor
LP Lower Plenum
6 OutDUMM Outer Dummies
PHX Primary Heat exchanger R&D Research and Development
SCK•CEN StudieCentrum voor Kernenergie - Centre d'etude de l'Energie Nucleaire SFR Sodium-cooled Fast Reactor
SR Safety Rod
ULOF Unprotected Loss Of Flow
UP Upper Plenum
7 Nowadays, the importance of designing nuclear system with the highest levels of safety and reliability has become essential [1]. Therefore, to meet this challenge, further development of nuclear technology and constant research activities are needed.
The design of the MYRRHA reactor is one of the research projects conducted in the Belgian Nuclear research center SCK·CEN. MYRRHA is a multi-purpose flexible fast spectrum irradiation facility, for Research and Development (R&D) applications. It is conceived as an accelerator driven system (ADS), able to operate in sub-critical and critical modes. It contains a proton accelerator of 600 MeV, a spallation target and a multiplying medium with MOX fuel, cooled by liquid lead-bismuth eutectic (LBE). It shall be designed to use to the largest extent possible passive safety systems and to have inherent safety characteristics [2] [3].
Because MYRRHA is based on the heavy liquid metal technology (HLM), it will be able to significantly contribute to the development of Lead Fast Reactor (LFR) Technology, and in critical mode, MYRRHA will play the role of the European Technology Pilot Plant (ETPP) in the roadmap for LFR [4].
Heavy-liquid metal cooled fast reactors are indeed considered to play an important role in the future of nuclear energy production because of their possible efficient use of uranium and the possibility to reduce the volume and lifetime of nuclear wastes [5] [6] [7].
The typical design of LFRs is a pool-type configuration without an intermediate heat exchanger system. Because of the chemical inertness of the coolant, the secondary side system (delivering high-pressure superheated water) can be interfaced directly with the primary side using steam generators immersed in the pool. For these reasons, the LFR system is well positioned to fulfill the goals of the GIF (Generation IV International Forum) defined in its “Technology Roadmap” [8]. The advantages offered by the inherent characteristics of the coolant such as its chemical inertness as well as thermodynamic and neutron diffusion properties permit the use of passive safety systems.
Considering the new requirements for nuclear safety after the Fukushima accident, thermal hydraulics is fundamental in designing passive and safety-inherent systems.
8 The objective of this work is to study the influence of the 3D phenomena, occurring during one of the most jeopardizing accident like a ULOF (Unprotected Loss Of Flow), on the main thermodynamic safety parameters of MYRRHA reactor. Indeed, in a pool-type liquid metal cooled reactor, the influence of these phenomena during this kind of accident could have an important impact on reactor safety. 3-D temperature distributions and local pressure gradients may affect the evolution of the coolant mass flow during the transition from forced to natural convection, with the possible generation of flow instabilities and dissipating flows. Furthermore, the presence of stagnant volumes may influence the characteristic propagation time of perturbations through the system.
One of the most important safety parameter for a reactor is the cladding temperature that has to be maintained under a certain value. The temperature of the cladding is directly correlated to the temperature of the coolant (LBE) passing through the active zone of the core. Thus, the proper coolability of the core also after an ULOF accident is primarily determined by the mass flow evolution and flow paths passing from forced to natural convection condition. The cladding is directly in contact with the liquid coolant and a maximum critical value of 600°C for the LBE has been conservatively estimated. This value is indeed the maximum temperature below which the creep phenomenon of the cladding can be neglected.
This study is carried out using the system code RELAP5-3D [9] and the computational fluid dynamic (CFD) code ANSYS CFX 15.0 [10].
System codes as RELAP5 were originally conceived as one-dimensional codes for loop-type reactors in which the coolant flows in ducts so that the energy losses are mainly due to wall friction effect. Therefore, an investigation on the validity of this class of codes in simulating the physics of a pool-type reactor is needed. On the other hand, a coarse mesh CFD model has been set up in order to simulate as well as possible the real behavior of the reactor. Indeed, as the experimental data are hard and expensive to obtain, a CFD simulation is used to create reliable reference data. To validate the transient results of the RELAP5-3D thermal-hydraulic system code, a comparison analysis with the CFD model of MYRRHA reactor has been carried on. Firstly, a general overview of the modeling approach of the two codes and the main basic differential equations of flow are presented highlighting the major differences between the two. Then, a short description of the primary system of MYRRHA reactor follows, to better understand the modeling approaches of RELAP5-3D and ANSYS CFX described in chapter 3.
9 The scenario studied for the ULOF accident is the complete blockage of the two pump rotors, so that no coast-down is considered. Two different cases have been chosen to simulate the blockage of the pump rotors: the first considers different pressure losses for forward and reverse flow through the rotors of the pumps; the second case takes into consideration an ULOF transient analysis without any imposed pressure drop through the impeller surfaces of the pumps as if the rotors are not present. In the latter, however, to take into consideration the pressure losses coming from the particular shape of the pumps (abrupt and smooth flow area changes, bends, etc.), two different additional friction factors coefficients respectively for forward and reverse flow have been imposed in the RELAP5-3D pumps components.
The CFD results were post-processed and compared to the ones coming from the system code and the main differences were then explained based on the different equations implemented in the two codes. A comprehensive CFD post-process analysis of temperatures, velocities and flow paths distributions of the LBE in the pools of the reactor reveals all the occurring 3-D phenomena that cannot be evaluated by the mono-dimensional system code.
The good agreement between the results obtained from the two codes shows that, even if RELAP5-3D is not developed for this type of reactor, it is however a valid tool for the simulation of the transient analysis of MYRRHA reactor. The effect of the turbulence and energy losses in the pool of the reactor as well as the stagnant volumes, mixing and flow recirculation of coolant liquid, have not an important impact on the relevant safety-parameters.
The second transient simulation represents the most conservative ULOF scenario, and, by analyzing the results, also some consideration on the inherent safety characteristics of MYRRHA reactor has been made.
10
2.
MATHEMATICAL MODELS
2.1.
RELAP5-3D
©The RELAP5-3D© hydrodynamic code is a transient, two-fluid component code simulating a two-phase vapor-liquid mixture that can contain noncondensable components in the gas phase. A one-dimensional as well as a multi-dimensional hydrodynamic problem can be solved by the code.
The governing equations of fluid flow and heat transfer (mass, momentum and energy balance equations) that are used as the basis for the RELAP5-3D© hydrodynamic model are formulated in terms of volume and time-averaged parameters of the flow. Phenomena that depend upon transverse gradients, such as friction and heat transfer, are formulated in terms of the bulk properties using semi-empirical transfer coefficient formulations or with additional models specially developed for the particular situation.
The system model is solved numerically using a semi-implicit finite-difference technique (section 2.1.4). The user can also select an option for solving the system model using a nearly-implicit finite-difference technique (section 2.1.5), which allows violation of the Courant limit number. This option is suitable for steady-state calculations and for slowly varying, quasi-steady transient calculations.
The basic two-fluid differential equations that form the basis for the hydrodynamic model are:
• mass continuity equation;
• momentum conservation equation;
• energy conservation equation.
11
2.1.1. Mass Continuity
The phasic continuity equations are:
+1 = Γ (2.1) for the liquid phase, and
+1 = Γ (2.2) for the vapor/gas phase, where:
= cross-section area ( )
= vapor volume fraction (void fraction) = liquid volume fraction
= vapor density
= liquid density
= vapor velocity
= liquid velocity
Γ = total volumetric mass transfer rate
These equations come from the one-dimensional phasic mass equations in reference [4]:
( )
+ ( )= Γ (2.3) where the term is reduced to .
12 Generally, the flow does not include mass sources or sinks, and overall continuity consideration yields the requirement that the liquid generation term be the negative of the vapor generation, that is:
Γ = −Γ (2.4) The interfacial mass transfer model assumes that total mass transfer can be partitioned into mass transfer at the vapor/liquid interface in the bulk fluid (Γ" ) and mass transfer at the vapor/liquid interface in the thermal boundary layer near the walls (Γ#); that is:
Γ = Γ" + Γ# (2.5)
2.1.2. Momentum conservation
A guiding principle used in the development of the RELAP5-3D©momentum formulation is that momentum effects are secondary to mass and energy conservation in reactor safety analysis and a less exact formulation (compared to mass and energy conservation) is acceptable. Indeed, in nuclear reactors flows are dominated by large sources and sink of momentum (i.e., pumps, abrupt area change), and for this reason an expanded form of the momentum equations is used, that is more convenient for development of the numerical scheme.
The RELAP5-3D©
expanded form of the phasic momentum conservation equation can be written as:
+12 =
− %+ &' − ()( ∙ − Γ +− −
(,( ∙ − − - . − + − /
(2.6)
13
+12 =
− %+ &' − ()0 ∙ − Γ +− −
(,0 ∙ − − - . − + − /
(2.7)
for the vapor/gas phase, where:
&' = body acceleration 1
- = coefficient of virtual mass ()0 = vapor wall drag coefficients ()( = liquid wall drag coefficients (, = interphase drag coefficient
% = pressure (%2)
+ and + = velocity at interface between vapor and liquid
The left sides of equations (2.6) and (2.7) describe the time rate of change of velocity and momentum flux, while on the right side of the equations, the force terms are, respectively, the pressure gradient, the body force (i.e., gravity and pump head), wall friction, momentum transfer due to interface mass transfer, interface frictional drag, and force due to virtual mass. The terms FWG and FWF are part of the wall frictional drag, which are linear in velocity, and are products of the friction coefficient, the frictional reference area per unit volume, and the magnitude of the fluid bulk velocity. The interfacial velocity in the interface momentum transfer term is the unit momentum with which phase appearance or disappearance occurs. The coefficient FI is part of the interface frictional drag; two different models (drift flux and drag coefficient) are used for the interface friction drag, depending on the flow regime. The coefficient of virtual mass C is calculated according to the flow regime.
14 ( &')+ ( - )= − % + 3 (4'' + 4''56 )7+ &'− ∆%9 9 ∙ :'− ∆%# # ∙ :'+ Γ ;+ <9=>+ <9=?+ <9@? ∙ :'+ <#=>+ <#=? + <#@? ∙ :' (2.8)
with the following simplifications:
• the Reynolds term stress and the phasic viscous stresses are neglected,
A 4'' + 4''56 B → 0
(2.9)
This approximation represent one of the most important difference between the implementation of RELAP5-3D© and CFX code equations. The absence of the shear stress implies that there are no terms to model the influence of viscous stress between adjacent fluid layers.
Moreover, the absence of the Reynolds stress term causes the total absence of the turbulent stresses. This does not mean that turbulence effects are totally neglected; the more significant radial or transverse turbulent diffusion effects are included within the wall heat transfer and wall friction correlations.
• the phasic pressures are assumed equal,
% → % EF %
(2.10)
• the interfacial pressure gradient is neglected,
∆%9 9 ∙ :' → 0 (2.11)
%9 is defined only at the interface while % is defined everywhere within phase G.
15
∆%# # ∙ :' → 0 (2.12)
• the covariance terms are universally neglected (unity assumed for covariance multipliers),
- → 1 (2.13) • The phasic continuity equations are multiplied by the corresponding phasic velocity, and the resulting equations are subtracted from the momentum equations. The vapor/gas momentum Equation (2.7) is the same as the resulting vapor/gas momentum equation from Equation (2.8) using k = g; the liquid momentum Equation (2.6) is the same as the resulting liquid momentum equation from Equation (2.8) using k = f.
• virtual mass term
<9=>∙ :' → - . − + − / (2.14) isthe inertia added to a system because an accelerating or decelerating body must move (or deflect) some volume of surrounding fluid as it moves through it.
• wall friction term
<#=>+ <#=? + <#@? ∙ :'→ ()( ∙ (2.15)
represents the wall shear pressure losses, in which:
<#=> takes into account the momentum variation due to the local pressure difference. <#=? and <#@? represents, respectively, the normal and tangential components of the
viscous wall stress.
• interphase friction terms
16 represent the interfacial pressure losses, in which the terms <9=? and <9@? are representative, respectively, of normal and tangential components of the viscous interfacial stresses.
Since the flow through the whole reactor is single-phase (liquid LBE), the terms that involve the vapor/gas phase are not hereafter illustrated.
2.1.2.1. Wall Friction
The wall friction term is in terms of the Relap5-3D wall friction coefficients but it could also be expressed in term of wall shear stresses as:
()( ∙ = 4 H (2.17) where HI is the liquid wetted perimeter.
Chisholm postulated that the wall shear stress could be determined using the Darcy-Weisbach friction factor computed from the Reynolds number based on liquid properties as:
4 =J(KL )4 2 (2.18) where J(KL ) is the Darcy friction factor, KL is the Reynolds number, the liquid density and
the liquid velocity.
The Darcy-Weisbach friction factor is computed from correlations for laminar and turbulent flows with interpolation in the transition regime. Two different turbulent friction factors models can be used: The first model computes the turbulent friction factor using an engineering approximation to the Colebrook-White correlation, while the second model uses an exponential function with users’ input coefficients.
The laminar friction factor is calculated as:
J =KLO64
P IEF 0 ≤ KL ≤ 2200 (2.19)
where OR is a user-input shape factor for noncircular flow channels (OR is 1.0 for circular channels).
17 The turbulent friction factor is calculated as:
1
SJT= −2 log XY
Z
3.7^ +2.51KL `1.14 − 2 log Xa^ +Z 21.25KLX.bcde IEF 3000 ≤ KL (2.20) where ε is the surface roughness and D the hydraulic diameter.
The friction factor in the transition region between laminar and turbulent flows is computed by reciprocal interpolation as:
J ,T= a3.75 −8250KL c JT,hXXX− J , XX + J , XX IEF 2200 ≤ KL ≤ 3000 (2.21) where JT,hXXX is the turbulent friction factor calculated at a Reynolds number of 3000 and J , XX is the laminar friction factor calculated at a Reynolds of 2200.
Other relationships include a correction of the friction factor to take into account the variation of the fluid viscosity near a heated surface.
2.1.3. Energy conservation
The phasic thermal energy equations are:i +1 i =
−% −% + j# + j" + Γ" ℎ∗+ Γ#ℎm + ^,RR
(2.22)
for the gas/vapor phase, and:
i +1 i =
−% −% + j# + j" − Γ" ℎ∗− Γ#ℎm + ^,RR
(2.23)
18 The previous equations come from the one-dimensional phasic thermal energy equation in reference [12] ( i ) + ( i )= % . + ( )/ + Γ ai +% c 9− A n' + n'56 B+ n9 9+ n# # + j + o Φ (2.24)
with the following simplification:
• The turbulent heat flux is neglected
A n' + n'56 B→ 0 (2.25)
As for the momentum equation, this is the biggest difference between RELAP5-3D©
and CFX code implementation. Indeed, neglecting the turbulent heat flux means that all the thermal energy contributes transported by fluctuations in internal energy and velocity are neglected; then, also the turbulence kinetic energy related to the fluctuations of the velocity is neglected.
• The covariance terms are universally neglected.
• The interfacial energy storage is neglected.
• The internal phasic heat transfer is neglected.
As for the momentum equation, only the terms that involve the liquid phase are next illustrated.
2.1.3.1. Dissipation Term
The energy dissipation term DISS is the sum of wall friction, pump and turbine effects. While in the momentum equations, the interface mass transfer, interface friction and virtual mass are important, in the energy equation these terms are small in magnitude compared to the effects of wall friction, pump and turbine, and so they are neglected.
19 If there is no presence of pump and turbine components, the dissipation term can be expressed as:
^,RR = ()( (2.26) where ()( has been discussed previously.
When a pump or turbine component is present, the associated energy dissipation is included in the dissipation terms.
As an example, for the pump component, the associated dissipation term is:
^,RR>q >= 4r − st( ) (2.27)
Where 4 is the pump torque and r is the pump angular rotational speed.
2.1.4. Semi-Implicit Scheme
The previous basic equations of motion, mass continuity (2.1) and (2.2), momentum conservation (2.6) and (2.7) and energy conservation (2.22) and (2.23) can be presented in an expanded form that constitutes a more convenient set of differential equations upon which to base the numerical scheme.
The semi-implicit numerical solution scheme is based on replacing the system of differential equations with a system of finite difference equations partially implicit in time. The implicit terms are formulated to be linear in the dependent variables at new time, so that a linear time advancement-matrix is obtained. The method used for solving the matrix is the BPLU solver (border-profile lower upper solver). Moreover, an important feature of the scheme is that implicitness is selected such that the field equations can be reduced to a single equation per fluid control volume or mesh cell, which is in term of the hydrodynamic pressure. Thus, a matrix N x N is obtained (where N is the number of the cell of the system).
A well-posed and stable numerical algorithm results from employing several stabilizing techniques. These include the selective implicit evaluation of spatial gradient terms at the new time, donor formulations for the mass and energy flux terms, and use of a donor-like formulation for the momentum flux terms. Donor-like formulations for these flux terms are used because of the well-known instability of an explicit centered finite difference scheme.
20 The scheme is solved using a staggered mesh (see Figure 2-1), in which mass continuity equation and energy equation are computed within the center of the cell (K or L), while the momentum equation is computed in the cell centered on the boundaries of the mass and energy cell (centered on the junction between each cell). Thus, averaged scalar properties, like pressure, specific internal energies and void fraction, are defined at the center of the mass and energy control volume, while knowledge of phase velocities is required at the volume boundary cell (vector quantities).
Figure 2-1 Staggered mesh nodalization scheme [11]
The discretised equations for each cell are obtained by integrating the mass and energy equations with respect to the spatial variable, x, from the junction at xjto xj+1. The momentum equations are
integrated with respect to the spatial variable from cell center to adjoining cell center (xK to xL,
21
2.1.5. Nearly-Implicit Scheme
The Nearly-implicit Scheme could be used for problems where the flow is expected to change very slowly with time, so that it is possible to use a very large time step. The use of a fully implicit method scheme requires a very large number of calculations and so, others method (called multiple or fractional step), like the Nearly-implicit, have been tried. One of the most important differences between the Semi-implicit and Nearly-implicit methods is that in the last one a violation of the Courant limit number is permitted for all nodes. As the Semi-implicit scheme, the Nearly-implicit method makes use of the BPLU linear equation solver to calculate the solution to the discrete hydrodynamic system for time step advancement.
The Nearly-implicit method consists of two steps:
• In the first step, all the seven conservation equations are solved. These finite difference equations are exactly the expanded ones solved in the semi-implicit scheme with one major change: the convective terms in the momentum equations are evaluated implicitly (in a linearized form) instead of in an explicit donored way as is done in the semi-implicit scheme.
• During the second step, the unexpanded form of mass and energy equations are solved.
2.1.6. Heat structure model
In RELAP5-3D© the heat transfer is modeled using the heat structure components: solid structures that could be coupled with the hydrodynamics volumes. Temperatures and heat fluxes are computed from the one-dimensional heat conduction equation based on heat conduction code HEAT-1 developed at the INL [13].
Finite differences are used to advance the heat conduction solutions.
The following is the equation of the one-dimensional heat conduction in the integral form that is resolved by RELAP5-3D every time a heat structure is present:
u ->(v, ̅) v( ̅, )x = y G(v, ̅)∇{v( ̅, ) ∙ x| + u R( ̅, )x (2.28) where
22 -> = volumetric heat capacity
v = temperature ̅ = space coordinate = time = volume | = surface G = thermal conductivity R = heat source
For heat structure boundaries attached to hydrodynamic volumes, a heat transfer correlation package is typically used to define the boundary conditions. In addition, symmetry or insulated conditions are provided, and for special situations, tabular based conditions or control variable based conditions can be specified.
Heat Transfer Correlation Package Conditions
The heat transfer correlation package contains correlations for convective, nucleate boiling, transition boiling, and film boiling heat transfer from the wall to the fluid, and it contains reverse heat transfer from the fluid to the wall including correlations for condensation.
The heat transfer correlation package partitions the total heat flux at the heat structure surface into two heat fluxes: one from (or to) the liquid phase and the other from (or to) the vapor/gas phases.
n# = ℎ# v}− v + ℎ# T v}− vP(%)
n# = ℎ# v}− v + ℎ# T v}− vP(%) + ℎ# > v}− vP(%P)
n~ = n# + n#
(2.29)
in which n# is the heat flux between the wall of the heat structure and the liquid phase, while n# is the the heat flux between the wall of the heat structure and the vapor/gas phase and where the other parameters are:
23 ℎ# = heat transfer coefficient between wall and liquid
ℎ# T = heat transfer coefficient between wall and liquid at saturation temperature calculated at the total pressure
ℎ# = heat transfer coefficient between wall and vapor
ℎ# T = heat transfer coefficient between wall and vapor at saturation temperature based on total pressure
ℎ# > = heat transfer coefficient between wall and vapor at saturation temperature
based on partial pressure of the vapor/gas phase v} = surface temperature
v = liquid temperature v = vapor/gas temperature
vP(%) = saturation temperature based on total pressure
vP(%
P) = saturation temperature based on partial pressure
n~ = total heat flux
Insulated and Tabular Boundary Conditions
The other boundary conditions implemented in RELAP5-3D are given by the following relationships: −G v= 0 −G v= nT ( ) −G v= ℎT (v − vT ) v = vT ( ) (2.30)
The first two conditions are flux-specified conditions: the first condition is a symmetry or insulated condition and is just a special case of the second condition. The third condition is a convection condition similar to that used with the correlation package except that only a total heat transfer coefficient which is a tabular function of time or surface temperature is used. The fourth condition directly specifies the surface temperature.
24 In this work, for the MYRRHA reactor modeling, the heat structures are used in the core to simulate the nuclear power source of the pins, in the Primary Heat Exchanger to simulate the power ''sink" of the water tubes and in the upper region of the reactor to simulate the heat exchange between the LBE in the upper plenum and the cold LBE in the annulus structure.
25
2.2.
ANSYS CFX
ANSYS CFX is a general purpose Computational Fluid Dynamics (CFD) software suite that combines an advanced solver with powerful pre and post-processing capabilities.
To better understand the comparison with the RELAP5-3D© mathematical models, the multiphase flow equation model of ANSYS CFX [14] will be presented.
2.2.1. Multiphase flow
The multiphase flow equations for inhomogeneous flow are presented in the next sections. 2.2.1.1. Continuity Equation
( • •) + ∇ ∙ ( • • •) = S•‚ƒ+ Γ•„ (2.31) where the subscripts and … stands for the different phases (liquid and vapor/gas). The previous equation is the same of the RELAP5-3D© phasic mass continuity equations (2.1) and (2.2) except for the term S•‚ƒ that represent the user-specified mass source.
The term Γ•„ is the mass flow rate per unit volume from phase … to phase and occours only when interphase mass transfer takes place. It can be expressed, as equation (2.5), as:
Γ•„= Γ•„† − Γ„•† (2.32)
where Γ•„† > 0 represents the positive mass flow rate per unit volume from phase to phase ….
2.2.1.2. Momentum Equation
The CFX phasic momentum equation can be expressed as:
( • • •) + ∇ ∙ ( •( • •× •)) =
− •∇pƒ+ ∇ ∙ ( •o•(∇ •+ (∇ •)T)) + Γ•„† „− Γ„•† •+ RŠ‹+ <•
(2.33)
that is similar to the RELAP5-3D© phasic momentum equations (2.6) and (2.7) except for some terms next presented:
26
• The terms ∇ ∙ ( •o•(∇ •+ (∇ •)T)) represent the turbulent and shear stresses that, as just said in section 2.1.2, are both neglected in the RELAP5-3D© implementation.
• The term Γ•„† „− Γ„•† • is the same of Γ +− in equation (2.6) and represents the momentum transfer per unit volume induced by interphase mass transfer.
• The term RŠ‹ describes momentum sources due to external body forces and user defined momentum sources, and is equal to the body force term &' of equation (2.6).
• The term <• describes the interfacial forces acting on phase due to the presence of other phases. It contains the RELAP5-3D© terms (,( ∙ − and - `Œ ?•Ž?•
Œ@ + Œ?•
Œ' − Œ?•
Œ' d that are respectively the interphase frictional
drag and the force due to virtual mass which, in CFX, are calculated in the same way of the RELAP5-3D© formulation.
2.2.1.3. Thermal Energy Equation
The CFX multiphase thermal energy equation is written as:
( • •i•) + ∇ ∙ ( • • •i•) =
∇ ∙ ( •J•∇v•) + •4•: ∇ •+ R‘•+ j•+ (Γ•„†L„’− Γ„•† L•’)
(2.34)
in which:
• i• , v• and J• are respectively the internal energy, temperature and thermal conductivity
of phase .
• •4•: ∇ • is always positive and is called viscous dissipation. This models the internal heating by viscosity in the fluid, and it is negligible in most flows.
• R‘• describes external heat sources.
27
• (Γ•„† L
„’− Γ„•† L•’) is the heat transfer induced by interphase mass transfer.
Despite of the very different notation between the RELAP5-3D and CFX terms for the energy conservation equations, there are no other substantial differences comparing the two implementations of the equations of motion.
2.2.2. Flow in Porous Media
A full detailed fine mesh CFD simulation of the entire primary system of MYRRHA is not possible due to the huge amount of computational time needed for the calculation. Moreover, due to a large range of scales and the diversity of the physical phenomena involved, several simplifications and modeling assumptions must be made. For these reasons, it is necessary to model some "critical parts" of the primary system as a "Porous Media''. With the word "critical" are intended that parts in which the fluid flows in regions with intimately immersed solid, such as the Core, the Primary Heat Exchangers and the ACS (Above Core Structure).
In ANSYS CFX there are two possible ways of modeling flow in porous media:
• Fluid Domain and momentum loss:
The region of interest is treated as a fluid domain together with a model for momentum loss. The effects of porosity are accounted for only through this loss term by modifying the source momentum term RŠ‹ in the momentum equation (2.33); all other terms in the governing equations are not changed.
• Porous Domain or so called "Full porous model":
The region of interest involves one or more fluids and an optional solid. Porosity modifies all terms in the governing equations as well as the loss term. This method supports solid models (for example, for modeling thermal conductivity of the solid), and models for the interaction between the fluid and solid parts of the domain.
As only the ''Full Porous Model'' is used in this work, the "Superficial Velocity Formulation Model" (Fluid Domain and momentum loss) will not be described.
28 2.2.2.1. Full Porous Model
The Full Porous Model is a generalization of the Navier-Stokes equations and the Darcy's law. It can be used to model flows where the geometry is too complex to resolve with a grid. The model retains both advection and diffusion terms and can therefore be used for flows in rod or tube bundles where such effects are important.
The general scalar advection-diffusion equation in a porous medium becomes:
(“ Φ) + ∇ ∙ ( ” ∙ iΦ) − ∇ ∙ (Γ” ∙ ∇Φ) = “R (2.35) where the source term R will contain, in addition, transfer terms from the fluid to the solid part of the porous medium; γ is the volume porosity defined as the ratio of the volume V′ available to flow in an infinitesimal control cell surrounding the point, and the physical volume V of the cell and ” is the area porosity:
“ = ′ ” = m
(2.36)
In particular, the balance equations become:
“ + ∇ ∙ ( ” ∙ i) = 0 (2.37)
for the continuity equation, and,
(“ i) + ∇ ∙ ( (” ∙ i) × i) − ∇ ∙ —o6” a∇i + (∇i)T−23 ˜ ∙ ic™ = “RŠ− “∇H (2.38) for the momentum equation, in which, o6 is the effective viscosity, RŠ is the momentum source term and i is the so called “true velocity” (actual fluid velocity through the full area ).
Energy balance is modeled with a similar equation:
(“ t) + ∇ ∙ ( ” ∙ it) − ∇ ∙ (Γš” ∙ ∇t) = R› (2.39) where Γš is an effective thermal diffusivity and Sœ contains a heat source or sink to or from the porous medium.
29 It is possible to define a heat transfer formulation through the fluid and the solid using a non-thermal equilibrium model (the current porous solid heat transfer formulation allows a finite temperature difference between the fluid and the solid phases). Therefore, there are separate energy equations for the fluid phase and the solid phase:
For the fluid phase:
(“ t) + ∇ ∙ ( ” ∙ it) − ∇ ∙ (Γš” ∙ ∇t) = “R•ž+ j (2.40) and for the solid phase:
(“P P- v ) + ∇ ∙ ( ”P∙ iP-PvP) − ∇ ∙ (J”P∙ ∇vP) = “PRPT+ j (2.41) where “P= 1 − “ and the interfacial heat transfer between the fluid and the solid, j , is determined using an overall heat transfer coefficient model using:
j = −j = ℎ (vP− v ) (2.42)
The convective heat transfer coefficient ℎ comes from the Kazimi - Carelli correlation used in the Core Fuel Bundle and from the Ushakov correlation used in the Primary Heat Exchangers. A detailed description of the heat transfer modeling is described in chapter 4.
2.2.2.2. Porous Momentum Losses
In ANSYS CFX, when a porous domain is used together with a Porous Momentum Losses model, an appropriate momentum source term is implemented in the momentum equation (2.33) as a force per unit volume acting on the fluid. Two different options can be used, the Isotropic Loss Model and the Directional Loss Model, respectively described in sections 2.2.2.2.1 and 2.2.2.2.2.
2.2.2.2.1. Isotropic Loss Model
The momentum loss through an isotropic porous region can be formulated using permeability and loss coefficients as follows:
30 RŠ,' = −”o >6} '− ”Ÿ 2 |¢| ' RŠ,£ = −”o >6} £− ”Ÿ 2 |¢| £ RŠ,¤= −”o >6} ¤− ”Ÿ 2 |¢| ¤ (2.43)
where ”>6} is the permeability and ”Ÿ is the quadratic loss coefficient. The linear component of this source represents viscous losses, while the quadratic term represents the inertial losses. A preliminary calculation of these terms let us to say that the viscous losses can be neglected. The sink momentum term expressed before in equation (2.38) represents thepressure losses due to friction in the porous media:
RŠ
¥¥¥¥¥¦ = ∇H> } q (2.44)
Once the expected pressure drop ∆H> } q along the reference length }6 is known, ”Ÿ can be estimated according to the estimated flow rate as follows:
”Ÿ =∆H> } q FLI2 §
(2.45)
where § is the superficial velocity equal to the equivalent velocity in a fully open media. It is calculated by multiplying the real velocity by the media porosity.
2.2.2.2.2. Directional Loss Model
The Directional Loss Model could be used for modeling anisotropic porous region in which a streamwise direction of the flow must be specified. Considering a streamwise-oriented coordinate system with x' as the streamwise flow direction, the momentum losses term could be written as: RŠ,'m = −”P>6} 'o − ”PŸ 2 |¢| 'm RŠ,£m = −”T>6} £o − ”TŸ 2 |¢| £m RŠ,¤m= −”T>6} ¤o − ”T Ÿ 2 |¢| ¤m (2.46)
31 where ”P>6} and ”T>6} are the streamwise and transverse permeability coefficients, while ”P
32
3.
MYRRHA PRIMARY SYSTEM
3.1.
Introduction
MYRRHA (Multi-purpose Hybrid Research Reactor for High-tech Applications) is a flexible fast spectrum irradiation facility, currently under the design stage at SCK•CEN in Mol (Belgium), operating as a sub-critical (accelerator driven) or critical system for material and fuel developments for GEN IV and fusion reactors and in a back-up role for radioisotopes production. This reactor is also meant to contribute to the objectives of developing an alternative to the sodium fast reactor technology due to its heavy liquid metal based coolant technology (Lead-Bismuth Eutectic).
Since this work focuses on the physics and behavior of the LBE contained into the primary system during an ULOF accident scenario, the secondary and tertiary system have not been modeled. Therefore, the following paragraphs describe only the main parts of the primary system of the MYRRHA reactor.
3.2.
Primary System
MYRRHA-FASTEF 1.6 is a pool-type Accelerator Driven System (ADS) reactor cooled by liquid lead-bismuth eutectic. The core consists of 211 positions that are filled by Fuel assemblies, control rods, safety rods, in-pile sections and LBE dummies. The LBE coming out from the core, rise up in the above core structure and then it flows in the upper plenum passing through the holes in the core barrel. The two pumps allow the LBE to flow through the four primary heat exchangers and to reach the cold plenum to close the “loop”. An overview of the MYRRHA FASTEF 1.6 reactor is represented in Figure 3-1. The main components of the primary system that have been considered and are used as computational domains in this work are presented in the next paragraphs.
33 Figure 3-1 Overview of the MYRRHA-FASTEF reactor
A - Reactor vessel B - Reactor Cover C - Diaphragm
D - Primary Heat Exchanger E - Primary Pump
F - In-Vessel Fuel Handling Machine
G - Core Barrel
H - Above Core Structure I - Core Restraint System
3.2.1. Reactor Vessel
As a pool-type reactor, the vessel houses all the components of the primary system with the reactor cover closing it from above and supporting the penetrating components. It is a welded structure without nozzles, made of a cylindrical shell with a torispherical bottom head.
The reactor vessel constitutes the main confinement barrier of the primary system and has to guarantee the integrity of the system itself
The material is AISI 316L Stainless Steel and the corresponding allowable stress at design temperature is 110 MPa.
34 Figure 3-2 represents the 3D layout of the reactor vessel.
Figure 3-2 3D of the reactor vessel
3.2.2. Core
A critical model of the Core has been studied. In particular, the Core has 100 MW of power produced by 108 Fuel Assemblies. In total, the core is composed by 211 positions that are subdivided as follow (referring to Figure 3-3):
• 108 Fuel Assemblies - FA (dark-yellow positions)
• 4 In-Pile-Structures - IPS (light-yellow positions)
• 6 Control Rods - CR (green positions)
• 3 Safety Rods - SR (white positions)
• 42 Inner Dummies - InnD (sky-blue positions)
35 Figure 3-3 Critical Core Layout 108 FA – 100 MW
An additional conservative heat up of 10 MW is considered due to additional heat sources such as the polonium decay, the heat dissipation of the pumps and the heat production in the in-vessel fuel storage. So, a total core power of 110 MW is implemented in both the codes.
While the presence of Safety Rods and Control Rods is very well known, the In-Pile-Sections are foreseen to allow the introduction of samples to be irradiated in different conditions and of monitoring instruments to check, directly from inside, the main parameters and conditions of the Core. The Inner Dummies have the same hexagonal shape of Fuel Assemblies but without fuel inside, while the Outer Dummies have YZrO instead of the fuel pellet in order to reduce the radiation damage induced by the neutron flux on the core barrel. The flow area through the inner and outer Dummies is considered a "By Pass" for the core because the LBE flows in this area without receiving any considerable heat flux, so that the LBE flows from the lower to the upper plenum remaining at the constant temperature of the cold plenum (270 ˚C).
The fuel assembly (FA) design is similar to the typical design used in fast spectrum reactors cooled by liquid sodium (SFR) [15]. Each FA contains a hexagonal bundle of 127 cylindrical
36 fuel pins, surrounded by a hexagonal wrapper. The upper and lower ends of the wrapper are connected to the inlet and outlet nozzles guiding the LBE coolant through the FA.
Each fuel pin contains fuel pellets and free space for filling and fission gases. The helical wire-spacers wound on the outer surface of fuel pins keep them separated one from another in the bundle.
Figure 3-4 represents a well-detailed layout of the Fuel Assembly section:
3.2.3. Core Barrel
The core Barrel is a big cylindrical tube
mm that stands at the center of the reactor and contains the Above Core structu the core plug. As shown in Figure
order to permit the LBE coming from the Core Upper Plenum.
The Core Barrel is considered a
Indeed, it has to withstand upward flow forces and flow induced motion coming from the fuel assemblies pushing on the core support plate, which is connected to the barrel
barrel has to resist to the hydrostatic coming from the thermal gradient region next to the cold plenum to 325 The barrel has a thickness of 30 mm and t
Core Barrel
ndrical tube of 8903 mm of height and an internal diameter of that stands at the center of the reactor and contains the Above Core structu
Figure 3-5, the top part of the Barrel has a large number of holes in coming from the Core to flow from the Above Core structure into the
Figure 3-5 Core Barrel
The Core Barrel is considered a safety class 1 component due to its important structural purpose. Indeed, it has to withstand upward flow forces and flow induced motion coming from the fuel
on the core support plate, which is connected to the barrel
hydrostatic forces due to buoyancy in LBE and to the thermal stresses coming from the thermal gradient along the length of the barrel (ranging from 270
on next to the cold plenum to 325 ˚C in the upper part next to the hot plenum). barrel has a thickness of 30 mm and the considered material is AISI 316L steel.
37 nd an internal diameter of 1732 that stands at the center of the reactor and contains the Above Core structure, the Core and of the Barrel has a large number of holes in to flow from the Above Core structure into the
safety class 1 component due to its important structural purpose. Indeed, it has to withstand upward flow forces and flow induced motion coming from the fuel on the core support plate, which is connected to the barrel. Moreover, the forces due to buoyancy in LBE and to the thermal stresses along the length of the barrel (ranging from 270 ˚C in the
C in the upper part next to the hot plenum). he considered material is AISI 316L steel.
38
3.2.4. Diaphragm
The Diaphragm is a mechanical welded structure, composed by two plates in order to separate the stresses caused by the pressure difference over the cold and hot plenum on one side, and the stresses induced by the thermal gradient due to the temperature difference between the cold and hot plenum on the other side. Figure 3-6 and Figure 3-7 show the shape and the functions of the diaphragm:
Figure 3-6 3D of the diaphragm
39 The main functions of the Diaphragm are:
• Separate the cold, high pressure LBE plenum form the hot, low pressure LBE plenum;
• Support the Inner Vessel Fuel Storage
• Ensure a coolable geometry for the fuel assemblies in the Inner Vessel Fuel Storage
• Foresee feedthroughs of components to the cold plenum
3.2.5. Primary Heat Exchangers
Four primary heat exchangers are foreseen to remove the total heat generated into the reactor. The design power of each PHX is 27.5 MW because an additional power heat generation of 10 MW coming from all the other sources (polonium decay, IVFS, pumps) is considered. So, they have been designed for 110% of the nominal core power, in order to take into account all the additional heat sources.
The main functions of the PHX are:
• In normal operation the PHX must be able to remove all the total heat generated into the reactor (forced circulation regime)
• In case of accidental situation, the whole reactor (primary, secondary and tertiary system) must be able to operate in passive condition (natural circulation) in order to guarantee the Decay Heat Removal (DHR) function (estimated conservatively as ~7% of the total core power)
• During shutdown periods, the PHX must be able to operate in a "reverse" mode during which, the LBE is heated in order to prevent freezing.
The adopted solution in the design of MYRRHA/FASTEF is to have a counter-current heat exchanger with straight tubes, organized in a triangular lattice and enclosed into a cylindrical shroud, in which the LBE flows downwards outside the water tubes and saturated water flows upwards inside the tubes. The secondary system pressure and temperature are always kept constant at respectively 16 bar and 200 ˚C (saturation temperature), while the primary system
temperature vary, according to the core power, between 200 the operational temperatures at maximum power
At full core power, the PHX
temperature is 270 ˚C with a nominal LBE mass flow of about 3450 kg/s.
In Figure 3-8 the design chosen for the PHX is represented. The right part of the active part of the heat exchanger.
vary, according to the core power, between 200 ˚C (safe shutdown temperature) and the operational temperatures at maximum power (in normal operation).
core power, the PHX maximum LBE inlet temperature is 325 with a nominal LBE mass flow of about 3450 kg/s. the design chosen for the PHX is represented. The right part of the active part of the heat exchanger.
Figure 3-8 FASTEF PHX layout
40 ˚C (safe shutdown temperature) and
inlet temperature is 325 ˚C and the outlet
41 Table 3-1 represents the main geometrical and thermal-hydraulic parameters of the PHX:
Parameter Unit Revised Value Comments
Power in one PHX MW 27.5 1/4 of the total power
PHX LBE inlet temperature ˚C 325
PHX LBE outlet temperature ˚C 270
LBE safe shutdown temperature ˚C 200
PHX LBE mass flow rate ˚C 3450 1/4 of the total mass flow
PHX water inlet temperature ˚C 200
PHX water outlet temperature ˚C 201.4
PHX water mass flow rate kg/s 47
PHX water pressure bar 16
Table 3-1 PHX main geometrical and thermal-hydraulics parameters
3.2.6. Primary Pump
The design of the pump is still under development. The actual choice will be determined by a series of constraints such as available space, velocity of the LBE in the impeller of the pump (erosion), cavitation and the need for the flow not to be bent too much when flowing through the pump in natural circulation to avoid high pressure losses. Furthermore, the need of maintaining a good pump efficiency during all the pump working conditions has to deal with the importance of having a mechanical simplicity of the assembly.
For such reasons, an axial design has finally been selected as better suited, although mixed-flow shape could have brought better efficiency.
Since the nominal value of the mass flow is 6900 kg/s and the nominal head requested is about 2.8 ÷ 3 m, the best option seems to be a centrifugal pump. A hypothetical design of the pump is shown in Figure 3-9.
Figure 3-9 General layout of the pump
42
4.
CODE MODELING AND IMPLEMENTATION
In this chapter the two model developed will be discussed. For a clearer understanding, the CFD model will be analyzed first in section 4.1 and, later on, the Relap5 model will be presented in section 4.2.
4.1.
ANSYS CFX
The model created in Ansys CFX aims to represent as well as possible the real geometrical layout and physical behavior of the whole reactor. However, as already said in chapter 2, a full detailed CFD simulation of the entire primary system of MYRRHA is not possible due to the huge amount of computational resources and time needed for the calculation. For these reason, the parts of the reactor in which the fluid flows in regions with intimately immersed solid have been simulated by the use of porous media. Moreover, solid parts and some other regions that are not important for the thermodynamic behavior of the reactor (for example the Inner Vessel Fuel Storage) have been excluded from the calculation domain.
Figure 4-1 shows the complete model of the MYRRHA reactor simulated in ANSYS CFX where the main components have been colored for a clearer understanding.
The red cylinder represent the core and it is subdivided in 5 porous domains each one characterized by a different sub-assembly structure (more details are presented later). Above the core, colored in orange, there is the barrel from which the LBE flows through the holes from the above core structure to the upper plenum. The light purple elliptical structures are the wall of the inner vessel fuel handling and the LBE is allowed to flow inside them only from the bottom (from the lower plenum volume). The opaque green and yellow structures are respectively the primary heat exchangers and the pumps.
43 Figure 4-1 Simplified CAD model of the CFX MYRRHA simulation
4.1.1. Components description
The tool used to create the geometry of MYRRHA FASTEF 1.6 is the Cad software plug-in of Ansys: "Design Modeler".
44 Figure 4-2 ¼ CAD geometry of MYRRHA FASTEF 1.6
Figure 4-2 shows a quarter of the CAD geometry model created for the simulation. Some details of the implementation of the simulation are next described:
• Core
A detailed image of the Core implemented in the CAD geometry is highlighted in Figure 4-3. The five rings represent the different groups of elements present in the reactor. Indeed, each group has its own structure layout that governs both porosity and pressure losses (each of these zones is characterized by a certain value of the porosity γ (see section 2.2.2)). Figure 4-4 shows better the subdivision of the core elements into
rings. However, it should be noted
between the FA, thus approximating this area to a single ring is a non terms of momentum and heat transfer.
For simplicity, the height of the cylinder is equal to the vertical distance between the two plenums (2.62 m) even if the real core height is shorter
rings, the pressure losses and the power have been set depending on the vertical coordinate
Figure 4-5
However, it should be noted that in reality the IPS, SR and CR are arranged separately between the FA, thus approximating this area to a single ring is a non-negligible assumption in terms of momentum and heat transfer.
Figure 4-4 Core nodalization
For simplicity, the height of the cylinder is equal to the vertical distance between the two plenums (2.62 m) even if the real core height is shorter (Figure 4-5). So, especially for the FA rings, the pressure losses and the power have been set depending on the vertical coordinate
Cross section of the Core implemented in CFX
45 that in reality the IPS, SR and CR are arranged separately negligible assumption in
For simplicity, the height of the cylinder is equal to the vertical distance between the two . So, especially for the FA rings, the pressure losses and the power have been set depending on the vertical coordinate f (z).
46 In the Fuel Assemblies sections of the core, the expected pressure drop is calculated using the Rehme correlation for a fuel bundle as a function of the local Reynolds number:
∆H> } q = I^H¨:
Ln2 (4.1)
where is the local flow velocity, >"= corresponds to the pin length, ^6© is the equivalent diameter and I is the friction factor given by:
I = aKL √( +64 0.0816KLX. hh(X.bhh«c¬}-(^}+ ^#)
%#6@@6® (4.2)
in which ¬} is equal to the number of pins, ^} is the clad outside diameter and ^# is the wire diameter and %#6@@6® is the wetted perimeter. The geometrical factor ( is expressed as:
( = ¯xH >"=+ °7.6 (x>"=+ x#"}6) t —xH>"=™ ± . ² (4.3)
where t is the pass of the wires.
Once the expected pressure drop is known, it is possible to calculate the ”PŸ factor (see equation (2.45)). At the inlet of the Fuel Assembly element, to account for the constriction of the LBE flow passage, a constant ”PŸ is entered considering that the total pressure drop must be 1.75 bar.
The ”PŸ factors in the other rings of the core do not depend on the vertical coordinate z and are calculated using the Darcy-Weisbach equation knowing the mass flow rate per each ring and that the total pressure drop has to be 1.75 bar. Therefore, for the IPS+CR+SR, Inner and Outer DUMMIES ring the Rehme correlation is not used.
Porous Zone Porosity γ Axial resistance C2,y (/m)
FA inner (FA 1) 0.44 0.875 / f(Re)
IPS+CR+SR 0.15 220.0
FA outer (FA 2) 0.44 0.875 / f(Re)
LBE DUMM 0.44 21.4
OUT DUMM 0.28 35.9
47 Table 3-1 reports a summary of the porosities and friction characteristics of all the rings of the core.
Actually, due to the presence of various instrumentation tubes and guiding vanes, the flow is blocked in the radial direction in all of these porous media rings. This condition is imposed numerically by assigning a very high value to ”TŸ (1000 /m) in the core region.
The cross sections of the rings are determined with respect to the fractions of core positions taken. In critical configuration, the core of MYRRHA is made up of 108 fuel assemblies, 48 inner dummies, 42 outer dummies, 3 SR, 6 CR and 4 IPS . The mass flow rate distribution for this simplified model can then be determined based on the number of the elements and the nominal mass flow rates per each different kind of structure. The expected mass flow distribution can be found in Table 4-2.
Porous Zone Number of elements Total area (mm2) Mass flow rate per unit (kg/s)
Mass flow rate (kg/s)
Mass flow rate per area (kg/m2) (considering the porosity) FA inner (FA 1) 36 296679.5 71.40 2570.4 19536.0 IPS+CR+SR 13 107134.3 22.84 296.9 18456.8 FA outer (FA 2) 72 593359.0 71.40 5140.8 19536.0 LBE DUMM 48 395572.7 64.355 3089.0 17747.6 OUT DUMM 42 457198.8 64.355 2702.9 21113.8 TOTAL 211 1849944.2 - 13800.0
Table 4-2 Core area and mass flow discretization
Note: The area considered for the Outer Dummies is the sum of the area of the 42 elements and the total interwrapper flow area.
Core Power distribution:
The radial power distribution is based on the sum of the total power production in the different batches of the Core. A total power of 51.25 MW and 58.75 MW are foreseen respectively in the Inner FA and Outer FA zones. The axial power distribution is implemented following the theory
48 of the power distribution in an homogeneous unreflected core as in [16], using a CEL expression (CFX expression language).
The heat transfer is implemented using the Kazimi-Carelli correlation (shown after in section 4.2.2) to calculate the heat transfer coefficient ℎ between the LBE liquid phase and the MOX solid phase. In CFX, the pin structure is not modeled and the solid inside the porous zone of the Fuel Assemblies is MOX.
• Above Core Structure
The design of the Above Core Structure is still under work. Anyway, to simulate the ACS, the same specifications of the design procedure have been used. In particular, a total pressure drop of 0.3 bar is expected. Due to the numerous and geometrically complicated structures present inside the Barrel, once again the porous media approach is used to model the ACS. By taking into account the presence of all guiding tubes, a porosity of 0.91 is calculated.
As first approximation, the axial pressure losses have been neglected in order to find a proper value of ”TŸ (radial loss factor). The other objective of the design is to have an LBE profile velocity at the outlet of the holes barrel as uniform as possible. For this reason an optimization of the pressure losses has been done implementing also an axial pressure loss factor ”PŸ .
The final expression used to model the axial pressure losses is the following, given in 1/m:
¨I ³ < 1.8 ”PŸ = 7
¨I ³ > 1.8 ”PŸ = 3.111³ − 20.533³ + 33.880 (4.4) The radial factor loss ”TŸ is kept constant and has a value of 54.
Porous Zone Porosity γ Axial resistance C2,y (1/m) Radial resistance C2,r (1/m)
ACS 0.91 7.0 / f(z) 54.0
Table 4-3 Porous media definition in the Above Core Structure
• Primary Heat Exchangers
The primary heat exchangers consist in four porous media cylinders that go from the upper plenum to the pump boxes. The inlet area is simplified without drawing the inlet windows after having verified that these elements constitute a negligible effect in terms of pressure drop.
