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Progress in Nuclear Energy 53 (2011) 48e58

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Progress in Nuclear Energy

journal homepage: www.elsevier .com/locate/pnucene

An object-oriented approach to simulation of IRIS dynamic response

Antonio Cammi a,*, Francesco Casella b, Marco E. Ricotti a, Francesco Schiavo b

a Politecnico di Milano, Department of Energy, CeSNEF-Nuclear Engineering Division, via Ponzio, 34/3, 20133 Milano, Italyb Politecnico di Milano, Department of Electronics and Information, via Ponzio, 34/5, 20133 Milano, Italy

a r t i c l e i n f o

Article history:Received 19 March 2010Received in revised form27 August 2010Accepted 10 September 2010

Keywords:SimulationModellingObject-orientedControlIntegral reactors

* Corresponding author. Tel.: þ39 02 2399 6397; faE-mail address: antonio.cammi@polimi.it (A. Cam

0149-1970/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.pnucene.2010.09.004

a b s t r a c t

In this paper the development of an adequate modelling and simulation tool for Dynamics and Controltasks is presented. The key features of the developed simulator are: “Modularity” e the system model isbuilt by connecting the models of its components, which are written independently of their boundaryconditions; “Openness” e the code of each component model is clearly readable and close to the originalequations and easily customised by the experienced user; “Efficiency” e the simulation code is fast; “Toolsupport” e the simulation tool is based on reliable, tested and well-documented software.

To achieve these objectives, the Modelica language was used as a basis for the development of thesimulator. The Modelica language is the result of recent advances in the field of object-oriented, multi-physics, dynamic system modelling. The language definition is open-source and it has already beensuccessfully adopted in several industrial fields.

The test bed for the application of the object-oriented approach has been the new generation, integraltype, IRIS nuclear reactor. IRIS (International Reactor Innovative and Secure) is a pressurized light watercooled, small/medium power (335 MWe) reactor reactor, under development by an internationalconsortium of nineteen organizations from ten countries. The preliminary design has been completed andthe pre-application licensing process with the US-Nuclear Regulatory Commission (NRC) is underway.

To provide the required capabilities for the analysis, specific models for the nuclear reactor compo-nents have been developed, to be applied for the dynamic simulation of the IRIS integral reactor, albeitkeeping general validity for PWR plants. The following Modelica models have been written to satisfy theIRIS modelling requirements and are presented in this paper: point reactor kinetic, fuel heat transfer,control rods model, and a once-through type steam generator, thus obtaining a specific library of nuclearmodels and components. As far as other classical power generation plant components are concerned, theThermo Power open library, developed at Politecnico di Milano as well, has been adopted and is brieflypresented in the paper. Originally conceived for conventional, fossil-fired plants, the highly modularapproach allowed to effectively reuse the models of the balance of plant systems, which have beenconnected to the models of the nuclear power generation process, to obtain a system simulator for theIRIS reactor.

Finally, preliminary results of the code validation process and the reactor dynamics are presented.� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Dynamic simulation plays a key role in the design phase of themain systems for nuclear reactors. This is further emphasized whenthe study of an innovative, integral reactor is undertaken. Suitabledynamic models must be set up in order to evaluate differentdesign solutions during the phase of concept development, tosimulate the behaviour of the reactor in nominal and accidentconditions as well as the control system strategy.

x: þ39 02 2399 6309.mi).

All rights reserved.

In this frame, several codes for safety analysis are alreadyavailable, e.g. RELAP (Carlson et al., 1990), TRAC (Liles and Mahassi,1986), ATHLET (Lerchl and Austregesilo, 1995), CATHARE (Micaelliet al., 1988), while, on the contrary, adequate modelling andsimulation tools at the system level are still required for theDynamics & Control task, the tools being sufficiently accurate so asto represent a wide range of operating conditions and transients, ata viable computational effort.

As a statement of general validity, the key features for anoptimal reactor system simulator appear to be: “Modularity” e thesystem model should be built by connecting the models of itscomponents, which have to be written independently of their

A. Cammi et al. / Progress in Nuclear Energy 53 (2011) 48e58 49

boundary conditions; “Openness” e the code of each componentmodel should be clearly readable, close to the original equationsand easily customised by the experienced user; “Efficiency” e thesimulation code should be fast running; “Tool support” e thesimulation tool should be based on reliable, accurate, tested andwell-documented software.

Few simulation environments and tools fulfilling all the above-mentioned characteristics seem to be currently available for nuclearapplications. Recent advances in the field of object-oriented, multi-physics, dynamic system modelling led to the definition of theModelica language, representing a viable path to achieve the above-mentioned goals. The language definition is open-source and it hasalready been successfully adopted in different fields, such as auto-motive, robotics, thermo-hydraulic and mechatronic systems.

In this frame, specific models for nuclear reactor componentshave been developed, to be applied for the dynamic simulation ofthe IRIS integral reactor albeit keeping general validity for PWRplants. The IRIS, International Reactor Innovative and Secureproject (Carelli et al., 2005, 2004) involves 19 organizations from 10countries and refers to the design of an innovative, light waterreactor with a modular, integral primary system configuration. Thereactor pressure vessel houses not only the nuclear fuel, controlrods and control rods drive mechanisms, and support structures,but also all the major reactor coolant system components includingthe coolant pumps, the steam generators and the pressurizer, asdepicted in Fig. 1.

Steam generator (Cioncolini et al., 2003) and pressurizer (Popovand Yoder, 2008) components, together with the internal controlrod drive mechanism (Conway et al., 2004), represent innovativefeatures with respect to current PWRs, thus requiring a furthereffort in terms of modelling. In particular: (i) the steam generatorsare of once-through type, framed into modules and made up byhelical coil tube bundles 30 m long, with the secondary two-phasemixture generated inside the tubes and flowing upward, while theprimary flow rate is in downward crossflow on the external side;(ii) the pressurizer is placed into the reactor pressure vessel,

Fig. 1. IRIS reactor view and main components (arrows show primary fluid path).

therefore it represents a large volume of saturated steam andsaturated or subcooled liquid, with a nonregular geometry andwithout sprays as one of the pressure control systems; (iii) theinternal control rod drive mechanism (ICRDM) considered for thisstudy has been the hydraulically driven type (Ricotti et al., 2003),with an external pump system supplying the required flow rate andpressure to sustain the hydraulic piston, to which the control rodsare linked, and with a set of valves needed to temporarily modifythe equilibrium pressure, thus allowing the withdrawal and inser-tion steps. Notwithstanding the IRIS design has recently movedtowards a different technological solution, i.e. an ICRDM based onelectro-magnetic motors and devices, the models library includesalso this type of component, the adoption of which is foreseen inother integral type reactor designs (Xiaotian and Shuyan, 2006;Fukami and Santecchia, 2000).

Besides the inherent distinctive design characteristics of themain components, other features affect the dynamic response ofthe reactor and significantly differ from current plants: the largewater inventory of the integral reactor is three times that of anequivalent PWR of the same power, resulting in an increasedthermal inertia of the primary fluid; the large volumes of theprimary side, mainly the riser and the downcomer, lead to a widecharacteristic period for the primary circuit transit time, one orderof magnitude bigger than current plants; on the other hand, theonce-through type steam generators allow a quick response of thecomponent on the secondary side, because of the reducedsecondary fluid inventory and thermal inertia.

As a consequence of the above-mentioned considerations,a dynamic simulator of an innovative, integral reactor has been setup, in order to study the dynamic response of IRIS, by adopting theModelica object-oriented language. The primary and secondarysystems of the reactor have been simulated, by assemblingcomponent models already available in a specific thermal hydrauliclibrary and suitable nuclear component models developed for thisspecific purpose. Both the language and themodels are described inthe following sections, with preliminary results of test transientsreported as well.

2. Modelica object-oriented language for system and plantsimulation

The Modelica language (Mattsson et al., 1998; ModelicaAssociation web site, 2007; Fritzson, 2004) was first introducedin 1997, as the product of an international cooperative effort towardthe definition of an object-oriented language for the modelling ofgeneral physical models, described by algebraic and differentialequations. The key features of the language are briefly summarised.

2.1. A-causal modelling

The equations of each model are written independently of theactual boundary conditions, without deciding a-priori which arethe inputs and which are the outputs. The causality of the model isdetermined automatically by the Modelica model interpreter orcompiler at the aggregate level, when a systemmodel is assembledout of elementary ones. In this way, models are much easier towrite, document, and reuse, while the burden of determining theactual sequence of computations required for the simulation isentirely left to the compiler.

2.2. Code transparency

Equations written in Modelica models tightly match the waythey are written on paper, so that it is very easy to understandwhat’s inside a given model, as well as to modify or enhance it.

A. Cammi et al. / Progress in Nuclear Energy 53 (2011) 48e5850

2.3. Encapsulation

The models of a system components are connected throughrigorously defined interfaces or “connectors” corresponding to thephysical interactionwith the outside whole. For example: electricalconnectors carry a voltage and a current, thermal connectors carrya temperature and a heat flow, and so on. As long as two differentcomponents have compatible connectors, they can be boundtogether, regardless of their inner details. This feature is essential forthe development of libraries of reusablemodels;moreover, it allowsto easily replace a part of a system model with a more detailed ora more simplified one, without affecting the rest of the model.

2.4. Inheritance

Model libraries can be given a hierarchical structure, in whichmore complex models are obtained from basic models by addingspecific variables, equations or even models. For example, it ispossible to write the equations describing the flow of a generic gasin a tube; the model of the flow of a particular, e.g. a multi-component ideal gas mixture, can be obtained by inheriting fromthe general one and by adding the specific model of the ideal gas.

2.5. Multi-physics modelling

The Modelica language is general in scope, as it providesmodelling primitives such as generic algebraic, differential anddifference equations, and is not tied to any specific engineeringdomain, such as mechanics, electrical engineering, or thermody-namics. It is then quite straightforward to model systems havinga multi-disciplinary nature, such as mechatronic systems, resultingfrom the interaction of mechanical, electrical and control sub-systems, or nuclear plants, resulting from the interaction ofthermo-hydraulic, nuclear and control sub-systems.

2.6. Reusability

A-causal modelling and encapsulation are a strong incentivetowards the development of libraries of general-purpose reusablemodels for different engineering domains. Some basic standardlibraries are already included in the definition of the Modelicalanguage, while others are being developed for more specificdomains, either as open-source or as proprietary codes.

TheModelica language has already been applied to awide rangeof system modelling problems in different engineering domains, asdemonstrated by the topics in the annual international conferencespecifically devoted to it (Otter, 2002; Fritzson, 2003; Schmitz,2005; Kral, 2006).

When developing a new application using Modelica, it is oftenthe case that some, or most, of the needed models are alreadyavailable in some previously developed library, so that it is possibleto concentrate the effort on the writing of the fewer models whichare not already available. In the case of the project illustrated in thispaper, it has been possible to develop the model of a completenuclearpowerplant byonlywriting themodelsof thenuclearpowergeneration processes, and then connecting them to taken from theThermoPower library (Casella and Leva, 2003, 2006), whichwas notoriginally conceived to deal with nuclear power plants.

As to the efficiency of the actual simulation code obtained froma complex Modelica model, one may wonder whether the possi-bility of describing the process with a high-level modellinglanguage has to be paid in terms of increased computationalburden. It turns out that this is usually not the case: Modelicacompilers incorporate sophisticated symbolic manipulation algo-rithms, which allow, among other things, to obtain index-1 systems

of differential-algebraic equations from higher-index ones, tosymbolically solve both linear and nonlinear model equations, andto find efficient calculation sequences through sorting and auto-matic tearing of system equations; the resulting code is then linkedto state-of-the-art numerical integration codes such as DASSL(Brenan et al., 1989). All of this process is completely transparent tothe user, and the resulting efficiency is often comparable, or evenhigher, than that of laboriously hand-crafted Fortran, C or Matlabcode, which is error-prone and hard to document and reuse.

Finally, it is worth noting that the definition of the Modelicalanguage, owned by the non-profit Modelica Organization, is in thepublic domain, so it is not tied to any specific simulation toolvendor. As of today, there are two commercial tools supporting thislanguage: Dymola (2008), which was used in this project, andMathModelica (2008). An open-source tool, OpenModelica (2008),has been under development for several years, and is expected tobe usable for industrial-strength projects in a few years. Othersimulation tool vendors, such as LMS-Imagine and ITI, are currentlydeveloping Modelica-compatible front-ends for their tools. It istherefore expected that good support for this language will beavailable and improved in the long term.

3. Library strategy: “Thermo Power” components and models

The complete model of the IRIS reactor has been built usingmodels from two different libraries: Thermo Power and NUKOMP.

The Thermo Power library has been developed as an open-source library for the modelling of thermal power plants at thesystem level, to support the design and validation of controlsystems. The library has been developed according to the followingguidelines:

(a) models are derived from first principle equations wheneverpossible, e.g. mass, momentum, and energy dynamic balanceequations, or from acknowledged empirical correlations;

(b) the level of detail of the models is flexible, up to the maximumfidelity which is compatible with a system-level simulation,e.g. ruling out complex models with 3-dimensional CFD;

(c) the structure of the model interfaces is as simple as possibleand is independent of the modelling assumptions inside eachmodel (lumped-parameter vs. distributed-parameter model,one-phase vs. two-phase flow, homogeneous vs. non-homo-geneous flow, inertial effects accounted for or neglected, etc.),so that models of specific parts of the process can be effort-lessly replaced with more accurate or more simplifiedcounterparts;

(d) the library is structured with a limited use of the inheritancemechanism, so that the code of a particular physical compo-nent is not scattered through many different classes; in thisway, it is straightforward to understand the equations ofa specific model by just looking in a single place in the code;

(e) the library is an open-source software and available on theWeb(Thermo Power Home Page, 2008).

As for the simulator of the IRIS integral reactor, several ThermoPower models have been used without modification. Theirmodelling principles are summarised here; for further details, thereader is referred to (Casella and Leva, 2003, 2006), as well as to theonline documentation in (Thermo Power Home Page, 2008). As anexample, the detailed equations and the corresponding Modelicacode given in the solving system Eq. (1) and Fig. 2 refer to theheader, a thermal hydraulic basic component corresponding toa control volume in the best estimate system codes. This givesa flavour of the way models are formulated in an object-orientedcontext.

Fig. 2. Modelica language: connection type definition and component modellingexamples.

A. Cammi et al. / Progress in Nuclear Energy 53 (2011) 48e58 51

The model of the fluid flow in a cylindrical conduit is based onthe dynamicmass, energy, andmomentum conservation equations,which are originally given as one-dimensional, partial differentialequations. Since Modelica can only describe systems of ordinarydifferential-algebraic equations, the original distributed-parametermodel is first discretised by using either the finite-volume method(Casella, 2006), or a Petrov-Galerkin finite-element method(Schiavo and Casella, 2007). The model is formulated in order tocorrectly handle possible flow reversal conditions. A homogeneousmodel, i.e. same velocity for the liquid and vapour phases, isadopted for two-phase flow conditions. The heat transfer coeffi-cients are computed using Dittus-Boelter’s and Chen’s correlations.

The fluid flow model is used both for the primary side, i.e. thecore coolant loop, and for the secondary side, i.e. the once-throughsteam generators.

The heat transfer model computes the actual heat flow betweentwo 1-dimensional interacting objects, usually a fluid and a metalwall. The heat transfer coefficient can be assumed either asconstant, or supplied by the fluid flow model.

A cylindrical metal wall is modelled by a simplified 1-dimen-sional version of Fourier’s equations: the thermal resistance iscomputed according to the formulation of Fourier’s equation incylindrical coordinates, while the heat capacity terms are lumpedin the middle of the tube thickness. This model is used to representthe steam generator pipe walls.

A turbulent, lumped pressure drop model is assumed, propor-tional to the kinetic pressure.

Other specific models refer to typical power plant components.As an example, the coolant pump model is based on the charac-teristic curves of the centrifugal pumps, the first relating head, flowrate and shaft speed, the second to compute the mechanical power

consumption; the thermal effects of the pump on the fluid are thuscorrectly represented.

The header is modelled as a rigid plenum filled with waterexchanging heat, with a metal wall having a finite thermal capac-itance. If the pressure P and the specific enthalpy h of the fluid andthe wall temperature Tm are chosen as the state variables, it ispossible to write the mass, energy and momentum balances for thefluid and the energy balance for the metal wall as:8>>>>><>>>>>:

V�vrvP

dPdt

þvr

vhdhdt

�¼wiþwo

Vh�

hvr

vP�1

�dPdt

þ�rþh

vr

vh

�dhdt

�¼wihiþwoho�gSðT�TmÞ

CmdTmdt ¼gSðT�TmÞ

P¼PoPo�Pi¼rgH

(1)

where r is the fluid density, P is the fluid pressure,wi andwo are theinlet and outlet flow rates (assumed positivewhen entering), Pi andPo the corresponding pressures, hi and ho the corresponding specificenthalpies, T is the fluid temperature, Cm is the metal wall thermalcapacity, g is the fluidemetal heat transfer coefficient, S is thefluidemetal interface area, H the height of the inlet over the outlet.

The model is connected to the outside world through twoconnectors of type referred as “FlangeA” and “FlangeB”, having theModelica code definition as reported in Fig. 2.

When an A-type connector is bound to a B-type connector,connection equations are generated automatically: the sum of theflow variables is zero while the remaining variables having thesame name are equalled to each other.

The Modelica corresponding to Eq. (1) can be written as shownin Fig. 2.

The actual code is slightly more complex, in order to providefeatures such as a replaceable fluid model, whose description ishowever beyond the scope of this paper.

Asmentioned above, two important features areworth stressingagain: the model code tightly resembles the way equations arewritten on paper, and the model equations are written using theboundary conditions provided by the two connectors, withoutintroducing artificial causality, and without bothering how thespecific model equations, coupled with the outside world equa-tions, will be actually solved by the final simulation code.

4. “NUKOMP” library: components and models

The models available in the Thermo Power library allowed a fastassembling of the largest part of the reactor primary and secondarysystems. The remaining components, i.e. the pressurizer, thereactor core and the hydraulically driven ICRDM, have been ad-hocsimulated by writing suitable models, derived from elaboratingopen literature (Todreas and Kazimi, 2001) or previous works(Brega et al., 1996; Vitulo, 2003), thus leading to a first release of theNUKOMP library of Nuclear Components and Models, specific fornuclear reactor components.

The pressurizer model has beenwritten by considering a separatephases approach. The core has been simulated by assemblinganeutronkineticsmodel anda thermalmodel for the fuel. Thenuclearcomponentmodels are briefly described in the following paragraphs.

4.1. Pressurizer model

The physical model is based on a non-equilibrium, two regionsformulation of the fluid balance equations with a control volumeapproach, as shown in Fig. 3. The two regions are supposed to be

Fig. 3. Conceptual scheme for a typical pressurizer component.

A. Cammi et al. / Progress in Nuclear Energy 53 (2011) 48e5852

isobaric and singularly isothermal, and will be referred to as liquidzone and vapour zone, respectively. The mathematical model isa system of coupled, nonlinear equations in five primaryunknowns, namely the liquid zone mass (Ml) and the vapour zonemass (Mv), the corresponding enthalpies (hl and hv) and the systempressure (pv). The solving system refers to the mass and energybalance equations for the liquid zone (Eqs. (2) and (3), respectively)and the vapour zone (Eqs. (4) and (5)), plus a congruence equationon the control volume, as in Eq. (6).

dMldt

¼ Gsl þ Gcnd þ Gspr � Geva � Gl;rel � Gl;saf (2)

ddtðMlhlÞ ¼ GslhslþGcndhl;satþGsprhl;sat�Gevahv;sat�Gl;relhl

�Gl;saf hlþWprhþWbh�Wl;wallþVldpvdt

(3)

dMv

dt¼ Geva � Gcnd � Gv;rel � Gv;saf (4)

ddtðMvhvÞ ¼ Gevahv;sat � Gcndhl;sat � Gv;relhv � Gv;saf hv

� Gspr�hl;sat � hspr

��Wv;wall þ Vvdpvdt

(5)

V ¼ Mlrl

þMv

rv(6)

where the variables are: M for mass, h for specific enthalpy, p forpressure, G for mass flow rate,W for thermal power, V for volume, rfor density, t for time, while the following subscripts hold: l forliquid, v for vapour, sat for saturation condition, sl for surge line, cndfor condensation, eva for evaporation, spr for sprays (note thatalbeit spray and relief valves are not included in the simulation

presented in this paper, the pressurizer model was developed to begenerically applicable to PWRs), rel for relief valves, saf for safetyvalves, prh for proportional heaters, bh for backup heaters, wall forpressurizer wall heat losses. The closure equations needed are theevaporation and condensation flow rates, as read in Eq. (7) whereseva and scnd are the bubble rising time and the droplet falling time,and the state equations (Eq. (8)), as obtained from the IAPWS IF97water properties correlations (Wagner et al., 2000):

Geva ¼ Ml�hl � hl;sat

�seva

�hv;sat � hl;sat

�; Gcnd ¼ Mv

�hv;sat � hv

�scnd

�hv;sat � hl;sat

� (7)

hl;vjsat ¼ f ðpvÞ; rl;v ¼ g�hl;v; pv

�(8)

4.2. Point kinetics neutronic model

The neutronic power generated into the fuel is proportional tothe neutronic population n, which responds to the point reactorkinetics balance equations (Eqs. (9) and (10)):

dndt

¼�r� b

L

�nþ

X6i¼1

lici (9)

dcidt

¼�biL

�n� lici i ¼ 1;.;6 (10)

where c is the precursor concentration leading to a delayed neutronsource, r is the total reactivity of the core, b is the fraction ofdelayed neutrons, l is the decay constant of the precursors and L isthe mean neutron generation time. The model set up for theNUKOMP library is able to treat enriched uranium, plutonium orthorium-based fuels.

Reactivity feedbacks are taken into account as well, by consid-ering linear or nonlinear feedback coefficients, for the coolantdensity effect (ac), the fuel Doppler effect (af), the effect of theboron concentration (aB) into the primary fluid as a neutronicpoison and the level of insertion of the control rod banks into thecore (rCR).

These relations are reported in Eq. (11):

8>><>>:

r ¼ rCR þ rf þ rc þ rB

rf ¼ af

�Teff � Teff0

�rc ¼ acð1=vc � 1=vc0ÞrB ¼ aBðC � C0Þ

(11)

where Teff and Teff0 are the instantaneous and reference effective fueltemperature, respectively, obtained from the fuel model describedin the next paragraph, vc and vc0 are the instantaneous and referencespecific volumes of the coolant, C and C0 are the instantaneous andreference boric acid concentration in the coolant. The referencevalues are those corresponding to the nominal, full power operationof the reactor.

4.3. Fuel model

The time dependent Fourier equation in one-dimensionalcylindrical geometry is applied to the three fuel rod zones: pellet,gap and cladding. The main assumption of the model is to consideronly the radial heat transfer, thus disregarding both the axial andthe circumferential diffusions.

For the pellet, gap and cladding the corresponding balanceequations read:

CORE

RISER

PRESSURIZER

SECONDARY SIDE

STEA

M G

ENER

ATO

R

T

T

Tp

p

F

CORE

PUMPS

STEA

M

GEN

ERAT

OR

S

PRESSURIZER

RIS

ER

CRodsSG-Pin

SG-Pout

T Steam

PRZ levelPRZ press

Heaters

FlowHin

a

b

A. Cammi et al. / Progress in Nuclear Energy 53 (2011) 48e58 53

rpcp;pvTpvt

¼ 1r

v

vr

�rkp

vTpvr

�þ q

000(12)

v

vr

�r kg

vTgvr

�¼ 0 (13)

rccp;cvTcvt

¼ 1r

v

vr

�r kc

vTcvr

�(14)

where r is the density, cp is the specific heat, T is the temperature, kis the thermal conductivity, q0 00 is the volumetric source term, r isthe radial dimension and t the time, while the subscripts stand for:p, the pellet, g, the gap, c, the cladding. Note that the heat capacityof the gap region has been neglected in this model.

The heat transfer model is represented in Fig. 4, with the pelletdiscretized into three zones of equal volume. Eqs. (12)e(14),together with the conditions of heat flux vanishing at the pelletcentre and the continuity of the temperatures and heat fluxes at thethree boundaries pellet-gap-cladding-coolant allow the determi-nation of Tpðr; tÞ, Tcðr; tÞ and Tgðr; tÞ.

In particular, the condition at the claddingecoolant interfacereads:

�kvTcvr

jr¼Rc;o

¼ H�TRc;o � Tm

�(15)

in which the rhs of Eq. (15) refers to the coolant mean values intothe core, i.e. H is the convective heat transfer coefficient and Tm isthe mean water temperature over the entire core height L:

Tm ¼

Z L

0Tf ðzÞdzL

(16)

Thecoolant temperatureprofileTmðzÞ is obtained fromthesolutionof the thermalhydraulicmodel. Inaddition to theaboveequations,fivecorrelations synthesizing the dependences of cp;p; cp;c; kp; kc asa function of the temperature and kg as a function of both the reactorpower and the burn-up have been adopted.

The effective fuel temperature, used to evaluate the Dopplerfeedback contribution on neutronics, is defined as follows:

Teff ¼ 4=9Tr¼0 þ 5=9Tr¼R (17)

Fig. 4. Fuel pellet radial scheme for heat transfer modelling.

NeutronicsTcold Thot

Prim.Flow

Fig. 5. RELAP nodalization scheme (a) and Modelica simulator (b) for the IRIS reactor.

5. IRIS simulator: comparison with RELAP code results

A Modelica-based simulator has been obtained by assemblingthe required components from Thermo Power and NUKOMPlibraries, as shown in Fig. 5. Both the primary and the secondarysystems of the IRIS integral reactor have been simulated, the

Table 1Main IRIS reactor design data at full power, nominal operating conditions, andcorresponding values obtained by the RELAP code and the Modelica simulator.

Parameter IRIS designdata

RELAPmodel data

MODELICAmodel data

Thermal Power MW 1000 999.998 1000.000Primary Flow Rate Kg/s 4500 4512.120 4588.752Core Inlet Temp. K 565.15 565.181 565.402Core Outlet Fluid Temp. K 603.15 603.082 602.716Secondary Flow Rate Kg/s 502.8 502.801 502.800Steam Temperature K 590.15 590.893 590.993Secondary Pressure bar 58 58.004 58.007

Fig. 6. Modelica vs. RELAP comparison e Core Thermal Power, Core Reactivity, Primary Temperature and Primary Flow Rate for the Feed Water flow rate step reduction (�20%)transient.

A. Cammi et al. / Progress in Nuclear Energy 53 (2011) 48e5854

boundary conditions for the reactor being the steam generator feedwater flow rate, temperature and pressure and the condenserpressure on the secondary side, and the control rod banks level ofinsertion into the core on the primary side.

The simulator has been validated against the well established,best estimate code RELAP, based on more complex and detailedthermal hydraulic models. Moreover, a comparisonwith a simulatorSIMULINK-based, which represents one of the most popular andwidely adopted tool for dynamic simulation and control, has beencarried out as well. The results are encouraging: the computationaltime required for the transient computation of 2000 s transient isreducedbya factorabout 300 (fromabout7h to less than1min)withthe Modelica model; the effort required to implement the samecomponent models and the whole plant simulator is roughly oneorderofmagnitude lower for theModelicamodel than theSIMULINKmodel, roughly equivalent to someman-months in the latter case. As

0 400 800 1200 1600 2000

time [s]

RELAPMODELICA

585

590

595

600

605

610

Step

meT

maera

tur

[e

K]

Transient: FeedWater Step (-20% nominal mass flow rate)

Fig. 7. Modelica vs. RELAP comparison e Steam Generator Steam Temperature and

far as the accuracy of the results is concerned, the same degree ofaccuracyhasbeenobtainedbybothsimulators,withbetter results forthe Modelica model when transients with stiff parameters orboundary conditions are to be simulated.

As part of this validation process, a set of open-loop transientshas been analysed for the IRIS plant, namely the responses of thereactor to instantaneous step variation of (i) the Feed Water flowrate, (ii) the Control Rods position and (iii) the Turbine AdmissionValve opening. Note that at this stage of the investigation, theinterest was more on the simulator performance and benchmarkwith different models than on the accurate and realistic analysis ofvarious operating sequences.

During the transients, no plant controls are in operation and thepressure in the primary side is kept to constant. At the beginning ofthe transient, all the neutronic and thermal hydraulic parametersare at values corresponding to the plant nominal, full power,

0 400 800 1200 1600 2000

time [s]

RELAPMODELICA

400

440

480

520

]s/gk[eta

RwolF

maetS

Transient: FeedWater Step (-20% nominal mass flow rate)

Feed Water Flow Rate for the FW flow rate step reduction (�20%) transient.

0 100 200 300 400 500

time [s]

6.00x108

7.00x108

8.00x108

9.00x108

1.00x109

]W[

rewoPla

mrehT

RELAPMODELICA

Transient: Control Rod Step (-20% nominal worth)

0 100 200 300 400 500

time [s]

RELAPMODELICA

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

]$[ytivitcae

R

Transient: Control Rod Step (-20% nominal worth)

0 100 200 300 400 500

time [s]

RELAPMODELICA

5.3x106

5.4x106

5.5x106

5.6x106

5.7x106

5.8x106

5.9x106

Pmaet

Sr

usser

]aP[e

Transient: Control Rod Step (-20% nominal worth)

0 100 200 300 400 500

time [s]

RELAPMODELICA

480

490

500

510

]s/gk[eta

RwolF

maetS

Transient: Control Rod Step (-20% nominal worth)

Fig. 8. Modelica vs. RELAP comparison e Core Thermal Power, Core Reactivity, Steam Generator Steam Pressure and Steam Flow Rate for the Control Rod step insertion (�20%)transient.

0 100 200 300 400 500

time [s]

9.60x108

1.00x109

1.04x109

1.08x109

1.12x109

1.16x109

]W[

rewo

Plamreh

T

RELAPMODELICA

Transient: Control Rod Step (+5% nominal worth)

0 100 200 300 400 500

time [s]

RELAPMODELICA

-0.04

0

0.04

0.08

0.12

]$[ytivitcae

R

Transient: Control Rod Step (+5% nominal worth)

0 100 200 300 400 500

time [s]

RELAPMODELICA

5.70x106

5.75x106

5.80x106

5.85x106

5.90x106

StP

maer

usser

]aP[e

Transient: Control Rod Step (+5% nominal worth)

0 100 200 300 400 500

time [s]

RELAPMODELICA

502

504

506

508

510

]s/gk[eta

RwolF

maetS

Transient: Control Rod Step (+5% nominal worth)

Fig. 9. Modelica vs. RELAP comparison e Core Thermal Power, Core Reactivity, Steam Generator Steam Pressure and Steam Flow Rate for the Control Rod step withdrawal (þ5%)transient.

A. Cammi et al. / Progress in Nuclear Energy 53 (2011) 48e58 55

0 100 200 300 400 500

time [s]

9.90x108

1.00x109

1.01x109

1.02x109

1.03x109

1.04x109

]W[ re

woP lamreh

TRELAPMODELICA

Transient: TAValve Step (+10% nominal opening)

0 100 200 300 400 500

time [s]

RELAPMODELICA

-0.004

0

0.004

0.008

0.012

]$[ ytivitcaeR

Transient: TAValve Step (+10% nominal opening)

0 100 200 300 400 500

time [s]

RELAPMODELICA

5.3x106

5.4x106

5.5x106

5.6x106

5.7x106

5.8x106

5.9x106

]aP[ erusserP maetS

Transient: TAValve Step (+10% nominal opening)

0 100 200 300 400 500

time [s]

RELAPMODELICA

480

500

520

540

560

]s/gk[ etaR

wolF maetS

Transient: TAValve Step (+10% nominal opening)

Fig. 10. Modelica vs. RELAP comparison e Core Thermal Power, Core Reactivity, Steam Generator Steam Pressure and Steam Flow Rate for the Turbine Admission Valve step opening(þ10%) transient.

0 100 200 300 400 500

time [s]

9.00x108

9.20x108

9.40x108

9.60x108

9.80x108

1.00x109

1.02x109

]W[

rewoP

lamreh

T

RELAPMODELICA

Transient: TAValve Step (-20% nominal opening)

0 100 200 300 400 500

time [s]

RELAPMODELICA

-0.04

-0.03

-0.02

-0.01

0

0.01

]$[ytivitcae

R

Transient: TAValve Step (-20% nominal opening)

0 100 200 300 400 500

time [s]

RELAPMODELICA

5.6x106

6.0x106

6.4x106

6.8x106

]aP[erusserP

maetS

Transient: TAValve Step (-20% nominal opening)

0 100 200 300 400 500

time [s]

RELAPMODELICA

400

440

480

520

]s/gk[eta

RwolF

maetS

Transient: TAValve Step (-20% nominal opening)

Fig. 11. Modelica vs. RELAP comparison e Core Thermal Power, Core Reactivity, Steam Generator Steam Pressure and Steam Flow Rate for the Turbine Admission Valve step closure(�20%) transient.

A. Cammi et al. / Progress in Nuclear Energy 53 (2011) 48e5856

A. Cammi et al. / Progress in Nuclear Energy 53 (2011) 48e58 57

steady-state operating conditions. A first comparison between theModelica simulator and the RELAP code has been performed on thesteady state, nominal conditions for the reactor. Table 1 summa-rizes the main data, showing a good agreement both between thecodes and with respect to the design data for the IRIS reactor. Themismatch in the primary flow rate is due to the different correla-tions for water/steam properties used in Modelica and RELAP.

5.1. Plant dynamics e steam generator feed water flow rate stepreduction (�20%)

The first event considered to benchmark the Modelica simulatorto the RELAP5 mod3.2 plant model (Grgic et al., 2003) has beena step reduction in the steam generator feedwater flow rate by 20%.During the transient the control rod system was assumed notavailable, thus the core neutronics response depends only on theneutronic feedbacks. The expected plant response in these condi-tions is that following the reduction in feed water flow, the heatremoval rate from the steam generators will decrease and thereactor coolant system temperature will increase as more heat isgenerated in the system than is removed by the steam generators.Due to the core negative feedback, the power of the reactor willdecrease until a new equilibrium condition is reached at a lowerpower level.

The results reported in Figs. 6 and 7 show an excellent agree-ment between theModelica simulator and the detailed RELAP plantmodel.

During the transient the core inlet temperature increases bye6 Kand the core outlet temperature decreases from 603.1 K to 602.6 K.Thefinal equilibriumpower at the endof the simulation is a functionof the feedback coefficients: the more negative the doppler andmoderator density coefficients, the power will be more reduced. Inthe presented simulation the neutronic feedback coefficients havebeen assumed equal to 8.86 pcm/kg m�3 for the mean coolantdensity and to �3 pcm/�C for the effective fuel temperature. Notethat to allow a meaningful comparison the RELAP model wasmodified to adopt the same core feedback model of the Modelicasimulator, since the RELAPmodel is devoted to safety analysis, not tooperational-like transient analysis.

In this simulation, at the end of the transient after about 800 swhen the overall reactivity is again at zero, the thermal powerdecreased from the nominal value of about 1 GW down to0.827 GW, with a 17.3% reduction.

On the secondary side, the decrease of the feed flow rate leads toa decrease of the steam pressure, from the nominal value of 58 barto 48 bar. The superheated steam temperature is instead increasedfrom 591 K to 603 K.

5.2. Plant dynamics e control rod step insertion and withdrawal(�20%, þ5%)

The second event considered for the benchmark has beena control rod step insertion by 20% of the nominal worth. Duringthe transient the core neutronics response depends only on theneutronic feedbacks. The expected plant response in these condi-tions is that following the insertion of the control rod, the thermalpower will decrease as well as the reactor temperatures (coolantand fuel); because of the core negative feedback, the power of thereactor will increase until a new equilibrium condition is reached ata lower power level. The results are reported in Fig. 8.

The results of control rod step withdrawal simulation (insertionof 5% of nominal control rod worth) are shown in Fig. 9.

The results reported in Figs. 8 and 9 show an excellent agree-ment between theModelica simulator and the detailed RELAP plantmodel.

5.3. Plant dynamics e turbine admission valve step opening (�20%,þ10%)

As a further example of transient analysis and comparison,useful to gain knowledge about the dynamic response of thereactor, a step opening (10% with respect to nominal value) anda step closing (�20% with respect to nominal value) of the TurbineAdmission Valve has been simulated (Figs. 10 and 11). The transientdoes not represent a real operational transient for the plant, since inthis case also the controls are supposed not to be in operation, but isa preliminary, valuable insight in order to identify the optimumstrategy and configuration of the control system.

The step opening of the turbine valve allows the steam flow rateto follow with a sudden increase, due to the depressurization andcorresponding flashing of the secondary fluid. The effect on theprimary side is a slight overcooling, with a decrease of the coolanttemperatures at core inlet (from 565.4 K to 564.6 K) while the coreoutlet temperature does not change (e601 K). The neutronic feed-backs push the core power to about 1.02 GW with an overallincrease of 2% with respect to the nominal value. The very mildresponse of the integral reactor is due to the limited inventory inthe steam generators, that limit the amount of steam generated tothe available feed water flow into the steam generators (that is keptconstant during the simulation), except for the very short spikeshown in Fig. 11, where the results for the Turbine Admission Valvestep closing (�20%) are reported.

6. Conclusions

The development of a plant simulator with Modelica for controlstudies on integral reactor and for the IRIS reactor in particular hasbeen presented in this paper.

The development cycle of the simulator has been shorteneddramatically compared to alternative approaches, due to the reuseof existing models and to the object-oriented approach to write themodel code. Moreover, the system model can be easily modified toimprove the modelling of the nuclear generation process, withoutaffecting the remaining parts of the code.

The simulation time for one transient is reduced by almost threeorders of magnitude, while keeping the fundamental dynamicbehaviour of the plant. This makes the model usable for controlsystem studies.

The model presented in this paper has been successfullyemployed for a preliminary assessment of the control strategy(Cammi et al., 2005a), and further restructured in order to allowa more flexible level of detail in the overall plant model (Cammiet al., 2005b). This will allows to use the model also for thedetailed engineering design of the control system.

Finally, it is planned to further validate this model againstexperimental results obtained from scaled laboratory models ofparts of the plant.

The final objective of these activities is to complete a fast andreliable tool for the IRIS reactor dynamics simulation, that can beused to support both the investigation of the plant control strate-gies and probabilistic safety assessment (PSA) analysts in theirefforts to identify a realistic physical status for the reactor, withrespect to several accident configurations for the plant.

References

Brega, E., Lombardi, C., Ricotti, M.E., Sordi, R., 1996. Development and initial vali-dation of fast-running simulator of PWRs: TRAP-2. In: IAEA-TECDOC-872. IAEA,Vienna, pp. 341e352.

Brenan, K.E., Campbell, S.L., Petzold, L.R., 1989. Numerical Solution of Initial-valueProblems in Differential Algebraic Equations. North-Holland Ed.

A. Cammi et al. / Progress in Nuclear Energy 53 (2011) 48e5858

Cammi, A., Casella, F., Ricotti, M.E., Schiavo, F., Storrick, G.D., 2005a. Object-orientedsimulation for the control of the IRIS nuclear power plant. In: Proceedings 16thIFAC World Congress, Prague, Czech Republic, Jul. 3e8.

Cammi, A., Casella, F., Ricotti, M.E., Schiavo, 2005b. Object-oriented modeling,simulation and control of the IRIS nuclear power plant with modelica. In:Proceedings 4th International Modelica Conference, Hamburg, Germany, Mar.7e8, pp. 423e432.

Carelli, M.D., Conway, L.E., Kling, C.L., Oriani, L., Petrovic, B., Lombardi, C.V.,Ricotti, M.E., Barroso, A.C.O., Collado, J.M., Cinotti, L., Todreas, N.E., Grgic, D.,Boroughs, R.D., Ninokata, H., Oriolo, F., 2005. Design and safety of IRIS, anintegral water cooled SMR for near term deployment. In: Kuznetsov, V. (Ed.),Innovative Small and Medium Sized Reactors: Design Features, SafetyApproaches and R&D Trends. IAEA-TECDOC-1451. IAEA, Vienna, pp. 51e74.

Carelli, M.D., Conway, L.E., Oriani, L., Petrovic, B., Lombardi, C.V., Ricotti, M.E.,Barroso, A.C.O., Collado, J.M., Cinotti, L., Todreas, N.E., Grgic, D., Moraes, M.M.,Boroughs, R.D., Ninokata, H., Ingersoll, D.T., Oriolo, F., 2004. The design and safetyfeatures of the IRIS reactor. Nuclear Engineering and Design 230, 151e167.

Carlson, K.E., Berta, V.T., Lenglade, C.E., Riemke, R.A., Lintner, M.A., Schultz, R.R.,Fletcher, C.D., McKenzie, C.C., Shieh, A.S.-L., Jenkins, E.E., Mesina, G.L.,Shumway, R.W., Johnsen, E.C., Miller, C.S., Slater, C.E., Johnsen, G.W.,Mortensen, G.A., Sloan, S.M., Kelly, J.M., Murray, P.E., Warnick, M., Kuo, H.-H.,Nielson, R.B., Weaver, W.L., Larson, N.S., Paik, S., Wilson, G.E., 1990. RELAP5/MOD3 code manual. NUREG/CR-5535, INEL-95/0174, vol. IeIV Rev. 1.

Casella, F., 2006.Object-orientedmodellingof two-phasefluidflowsby thefinite volumemethod. In: Proceedings 5th Mathmod Vienna, Austria, Sep. 6e8, pp. 631e640.

Casella, F., Leva, A., 2003. Modelica open library for power plant simulation: designand experimental validation. In: Proceedings of Modelica Conference 2003,Linköping, Sweden, Nov. 3e4, pp. 41e50. http://www.modelica.org/Conference2003/papers/h08_Leva.pdf.

Casella, F., Leva, A., 2006. Modelling of thermo-hydraulic power generationprocesses using modelica. Mathematical and Computer Modeling of DynamicalSystems 12 (1), 19e33.

Cioncolini, A., Cammi, A., Cinotti, L., Castelli, G., Lombardi, C., Luzzi, L., Ricotti, M.E.,2003. Thermal hydraulic analysis of iris reactor coiled tube steam generator. In:ANS Topical Meeting in Mathematics & Computations (M&C), April 6e10,Gatlinburg, TN, USA.

Conway, L.E., Petrovic, B., Kanagawa, T., Ricotti, M.E., 2004. Internal control rod drivemechanism, design options for IRIS. In: Proceedings of ICAPP’04, Paper 4315,Pittsburgh, June 13e17.

Dymola, 2008. Dymola User’s Manual. DynasymAB.Fritzson, P. (Ed.), 2003. Proceedings of the 2003 Modelica Conference, Linköping,

Sweden, Nov. 3e4. http://www.modelica.org/events/Conference2003.Fritzson, P., 2004. Principles of Object-oriented Modeling and Simulation with

Modelica 2.1. Wiley-IEEE Press.Fukami, M.V.I., Santecchia, A., 2000. CAREM project: innovative small PWR. Prog-

ress in Nuclear Energy 37 (1e4), 265e270.

Grgic, D., Bajs, T., Oriani, L., 2003. Development of RELAP5 nodalization for IRIS non-loca transient analyses. In: Proceedings of ANS Topical Meeting in Mathematics& Computations, Gatlinburg, USA, April 6e10.

Kral, C. (Ed.), 2006. Proceedings of the 2006 Modelica Conference, Vienna, Austria,Sep. 4e5. http://www.modelica.org/events/modelica2006/Proceedings/.

Lerchl, G., Austregesilo, H., 1995. The ATHLET code documentation package. User’sManual, GRS-P-1 Vol. 1.

Liles, D.R., Mahassi, J.H., 1986. TRAC-PF1/MOD1: An Advanced Best EstimateComputer Program For Pressurized Water Reactor Thermal Analysis. NUREG/CR-3858.

MathModelica, 2008. MathModelica User’s Manual. Mathcore Engineering AB.Mattsson, S.E., Elmqvist, H., Otter, M., 1998. Physical system modeling with mod-

elica. Control Engineering Practice 6, 501e510.Micaelli, J.C., Bestion, D., Bernard, M., Porracchia, A., Miraucourt, J.M., Catalani, L.,

1988. CATHARE. Best estimate thermal hydraulic code for reactor safety studies,last developments. In: Proceedings of the International ENS/ANS Conference onThermal Reactor Safety, Avignon, October 2e7.

Modelica Association web site, 2007. http://www.modelica.org/.OpenModelica, 2008. Open Modelica project. http://www.ida.liu.se/labs/pelab/

modelica/OpenModelica.html.Otter, M. (Ed.), 2002. Proceedings of the 2002 Modelica Conference, Oberpfaffen-

hofen, Germany, March, 18e19. http://www.modelica.org/Conference2002/papers.shtml.

Popov, E., Yoder, G., 2008. IRIS pressurizer fluid dynamics and heat transfer anal-yses. Nuclear Engineering and Design 238, 81e89.

Ricotti, M.E., Cammi, A., Carelli, M., Colombo, E., Lombardi, C., Passoni, M., Rizzo, C.,2003. Hydraulically driven control rod concept for integral reactors: fluiddynamic simulation and preliminary test. In: Proceedings of GENES4/ANP2003,Paper 1028, Kyoto, Sept. 15e19.

Schiavo, F., Casella, F., 2007. Object-oriented modelling and simulation of heatexchangers with finite element methods. Mathematical and ComputerModelling of Dynamical Systems 13 (3), 211e235.

Schmitz, G. (Ed.), 2005. Proceedings of the 2005 Modelica Conference, Hamburg,Germany, March 7e8. http://www.modelica.org/events/Conference2005.

Thermo Power Home Page, 2008. http://home.dei.polimi.it/casella/thermopower/.Todreas, N., Kazimi, M., 2001. Nuclear Systems I & II. Taylor & Francis Education,

USA.Vitulo, A., 2003. Development of the Internal Hydraulically Driven Control Rod

Concept for the IRIS reactor. Master thesis, Politecnico di Milano.Wagner, W., Cooper, J.R., Dittmann, A., Kijima, J., Kretzschmar, H.J., Kruse, A.,

Mare�s, R., Oguchi, K., Sato, H., Stöcker, I., �Sifner, O., Takaishi, Y., Tanishita, I.,Trübenbach, J., Willkommenet, T., 2000. The IAPWS industrial formulation 1997for the thermodynamic properties of water and steam. ASME Journal of Engi-neering for Gas Turbines and Power 122, 150e182.

Xiaotian, L., Shuyan, H., 2006. Dynamic behavior of upper hydraulic drive controlrod. Nuclear Engineering and Design 236, 2556e2566.