De

Ma

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rbomtnaeP

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Nuclear Engineering and Design 297 (2016) 276–290

Contents lists available at ScienceDirect

Nuclear Engineering and Design

jou rn al hom epage : www.elsev ier .com/ locate /nucengdes

esign by theoretical and CFD analyses of a multi-blade screw pumpvolving liquid lead for a Generation IV LFR

arcello Ferrinia,1, Walter Borreanib,c, Guglielmo Lomonacoa,c,∗, Fabrizio Maguglianib

GeNERG - DIME/TEC, University of Genova, via all’Opera Pia 15/a, 16145 Genova , ItalyAnsaldo Nucleare S.p.A., Corso F.M. Perrone 25, 16152 Genova, ItalyINFN, Via Dodecaneso 33, 16146 Genova, Italy

r t i c l e i n f o

rticle history:eceived 2 July 2015eceived in revised form7 November 2015ccepted 7 December 2015

a b s t r a c t

Lead-cooled fast reactor (LFR) has both a long history and a penchant of innovation. With early workrelated to its use for submarine propulsion dating to the 1950s, Russian scientists pioneered the develop-ment of reactors cooled by heavy liquid metals (HLM). More recently, there has been substantial interestin both critical and subcritical reactors cooled by lead (Pb) or lead–bismuth eutectic (LBE), not only in Rus-sia, but also in Europe, Asia, and the USA. The growing knowledge of the thermal-fluid-dynamic propertiesof these fluids and the choice of the LFR as one of the six reactor types selected by Generation IV Interna-tional Forum (GIF) for further research and development has fostered the exploration of new geometriesand new concepts aimed at optimizing the key components that will be adopted in the Advanced LeadFast Reactor European Demonstrator (ALFRED), the 300 MWt pool-type reactor aimed at proving the fea-sibility of the design concept adopted for the European Lead-cooled Fast Reactor (ELFR). In this paper, atheoretical and computational analysis is presented of a multi-blade screw pump evolving liquid Leadas primary pump for the adopted reference conceptual design of ALFRED. The pump is at first analyzedat design operating conditions from the theoretical point of view to determine the optimal geometryaccording to the velocity triangles and then modeled with a 3D CFD code (ANSYS CFX). The choice of a3D simulation is dictated by the need to perform a detailed spatial simulation taking into account thepeculiar geometry of the pump as well as the boundary layers and turbulence effects of the flow, which

are typically tri-dimensional. The use of liquid Lead impacts significantly the fluid dynamic design of thepump because of the key requirement to avoid any erosion affects. These effects have a major impact onthe performance, reliability and lifespan of the pump. Albeit some erosion-related issues remain to befully addressed, the results of this analysis show that a multi-blade screw pump could be a viable optionfor ALFRED from a thermo-fluid-dynamic point of view.

. Introduction

The perspectives of nuclear energy changed significantly in theecent years (IAEA, 2013). Before 2011, an enthusiastic feelingoosted what was usually called as a “renaissance”: the numberf plants approaching their end of life and requiring a replace-ent, the intentions of several nations to adopt the nuclear option,

ogether with the many new ideas on the long-term future ofuclear energy represented the driving reasons of this enthusi-

stic period. This climate has been abruptly interrupted by thevents occurred in March 2011 at the Fukushima Dai-ichi Nuclearower Plant (NPP) and the following great impact to the worldwide

∗ Corresponding author. Tel.: +39 0103532867; fax: +39010311870.E-mail address: guglielmo.lomonaco@unige.it (G. Lomonaco).

1 Present address: A.S.EN. (Ansaldo Sviluppo Energia) S.r.l., Italy.

ttp://dx.doi.org/10.1016/j.nucengdes.2015.12.006029-5493/© 2015 Elsevier B.V. All rights reserved.

© 2015 Elsevier B.V. All rights reserved.

public opinion through the media. Following the Fukushima events,the way set out by the nuclear community has been a thoroughanalysis of the safety approach for the design and the operation ofNPPs, along with a significant rethinking of the design processes.In this new orientation, concepts like sustainability and safety havebecome mandatory in drawing the future of nuclear energy to over-come the safety issues dramatically highlighted at Fukushima. Thisgeneral point of view had already been put forward by the GIF,through the identification of the four areas (also in a combinedfashion, see as an example (Cipollaro and Lomonaco, 2016)) wherebreaking-through innovations might have allowed for a rebirthof nuclear energy: sustainability, economics, safety and reliabil-ity, and proliferation resistance and physical protection. The goalsadopted by GIF provided the basis for identifying and selecting six

nuclear energy concepts for further development. The six selectedconcepts employ a variety of core types, reactor coolants, energyconversion and fuel cycle technologies. Their designs feature

ering and Design 297 (2016) 276–290 277

twost

csmcctbd(

pttt

2D

s(fc

e

arppttfiwmn

Fig. 1. ALFRED configuration.

Table 1ALFRED data (Alemberti et al., 2013).

Primary lead temperature 400÷480 ◦CSecondary side pressure 180 barSteam generator Once-throughWater/steam temperature 335–450 ◦COverall efficiency 42%

M. Ferrini et al. / Nuclear Engine

hermal and fast neutron spectra, closed and open fuel cycles and aide range of reactor sizes from very small to very large. Depending

n their respective degrees of technical maturity, the Generation IVystems are expected to become available for commercial introduc-ion around 2030–2040.

LFRs (lead-cooled fast reactors), one of the six nuclear energyoncepts, are Pb- or Pb–Bi-alloy-cooled reactors operating at atmo-pheric pressure and at high temperature because of the highelting point of the coolant (up to 227 ◦C for Pb). The core is

haracterized by a fast-neutron spectrum. Pb and Pb–Bi-alloyoolants are chemically inert and show several attractive proper-ies (OECD/NEA, 2007a). However, one important drawback muste addressed: the requirement for low velocities of the coolant inirect contact with the surfaces to avoid erosion of the surfacesZhang, 2009; Del Giacco, 2013; Jianu, 2011).

It is therefore mandatory to develop a design for the primaryump, the steam generator and any components in contact withhe flowing coolant which minimizes the relative velocity but, athe same time, makes it possible for these components to performheir functions at best.

. ALFRED (Advanced Lead Fast Reactor Europeanemonstrator)

The goal of ALFRED (Fig. 1) is to develop a totally representativecale demonstrator of the industrial European Lead Fast ReactorELFR, defined within the LEADER project), representing a guidelineor its licensing and construction in terms of safety aspects, costs,omponents and technologies.

The main features of ALFRED are shown in Table 1 (Alembertit al., 2013).

Because of the requirements of inspection and removability ofll the major components of the reactor, all the components of theeactor are carefully designed to be removed from the system inde-endently and separately. The design of the primary (mechanical)umps is such that the primary pump is enclosed in a hot ducthat will allow for its removal from inside the inner vessel, con-ributing to the compactness of the primary system. In order to

nd the optimal solution both at the single component level asell as at the whole reactor level, alternative configurations for theain components of ALFRED are currently explored, including a

ew design and location of the steam generators, of the ancillary

Fig. 2. Different ALFRED configurations: (a) standard config

Primary pumps Mechanical, removable located in hotleg inside the inner vessel

equipment and of the primary pumps. With respect to the develop-ment of the primary pump, different configurations are currently

under evaluation: this paper deals the theoretical investigation andnumerical simulations of the multi-blade screw pump. Fig. 2 showssome of the alternative configurations for the major components of

uration, (b) and (c) configurations under evaluation.

278 M. Ferrini et al. / Nuclear Engineering and Design 297 (2016) 276–290

Screw

Awt

lhtlcrfamrpnc

pvmpdeugd((

3

Glpht(waCaNbafic

Fig. 3.

LFRED. The main differences between configurations (b) and (c)ith respect to the standard configuration (a) are the location of

he steam generators and of the primary pumps.Configuration (c) shows the multi-blade screw pump as ana-

yzed in this paper: the pump is mounted vertically inside a (fixed)ot duct and the coolant flows through the pump from the topoward the bottom, where a properly-sized pressure chamber col-ects the flows coming from the 8 primary pumps and creates theonditions for the coolant to flow (upwards) through the core. Withespect to the development of the primary pump, as already doneor alternative solutions (Mangialardo et al., 2014), the rationale fornalyzing in detail the screw pump is related to the safety require-ents mandated for the primary pump design of a Generation IV

eactor: minimize the pressure losses of the coolant flowing in theump in accidental conditions (to allow for the establishment ofatural circulation of the coolant) and remove the heat from theore in the case of failure of one or all the pumps.

This paper will present a theoretical investigation of the screwump (using the operational conditions for ALFRED) based on theelocity triangles, the conservation of mass, energy and angularomentum in order to assess the optimal geometry, show the com-

arison between the theoretical predictions and the results of aetailed 3D computational fluid dynamic (CFD) analysis (Jiyuant al., 2012; Anderson, 1995; Versteeg and Malalasekera, 2007)sing ANSYS CFX V15 (ANSYS, 2015) , and finally optimize theeometry of the screw pump to reduce any unwanted performanceegradation caused by unsteady flow phenomena (e.g. turbulenceWilcox, 1998; Tennekes and Lumley, 1972) and flow recirculationKarassik et al., 2015)).

. Lead properties

Generation IV fast reactors are cooled by liquid metals or gas.EN-IV LFR chain reaction is governed by fast neutrons because

ead has a very small absorption cross-section and low scatteringroperties due to the high atomic number: the fuel efficiency isigh since the so called “closed cycle” can be implemented andhus strongly reduces the production of highly radioactive wasteArtioli et al., 2010; Cerullo and Lomonaco, 2012), analogously tohat already proposed for other GEN-IV concepts (e.g. (Cerullo

nd Lomonaco, 2012; Bomboni et al., 2008; Bomboni et al., 2009;hersola et al., 2015; Cerullo et al., 2014)). Lead has the considerabledvantage of not reacting with water and not burning in air (as fora), and, from the point of view of basic safety features, it has high

oiling point, very low vapor pressure and high shielding capacitygainst � radiation, when compared with Na; moreover lead retainsssion products like cesium and iodine released from the core inase of cladding failure. The likelihood of core damage is very low

pump.

because lead has good characteristics with regards to heat transferand thermal capacity. In OECD/NEA (2007b) a comprehensive list isreported of existing data for lead–bismuth Eutectic Alloy and lead;(GEN-IV, 2015) and Cerullo and Lomonaco (2012) list the benefitsand challenges of using different coolants for GEN-IV reactors.

4. The screw pump

The screw pump or Archimedean screw pump, from the nameof its inventor, is the oldest type of rotating pump (Nesbitt, 2015;Chris, 2000). Even though this device was invented in ancient times,it has been adapted throughout time and still today there are sev-eral applications of it. The Archimedean screw is used mainly forlifting water from a lower to higher level. As shown in Fig. 3, thelowest portion of the screw just dips into the water, and as it isturned a small quantity of water is scooped up into the tube. Asthe screw turns, the water slides along the tube. Meanwhile morewater is scooped up at the end of the tube and then it slides along,and so on until the water comes out the top of the tube.

Recently, the Archimedean screw has also found a new appli-cation when operating in reverse as a turbine and in this case theprinciple is the same but acts in reverse. The water enters the screwat the top and the weight of the water pushes on the helical flights,allowing the water to fall to the lower level and causing the screwto rotate. An electrical generator connected to the main shaft of thescrew can then extract this rotational energy.

4.1. Classic model of the screw pump

Focusing on the Archimedean screw as a pump for lifting fluid,from the theoretical analysis it can be demonstrated that a certainslope of the screw is requested in order for the fluid to be trapped inthe screw. In particular, it is necessary that the sinusoidal curve inFig. 4 defining the outer edge of a blade tilts downward as it crossesthe axis of the screw. In terms of the angles � and in Fig. 4, it isnecessary that: � ≤ (Chris, 2000).

In the envisioned use in the ALFRED reactor, this condition is aproblem because inside the reactor the pump will be vertical andtherefore will be never greater than �. Moreover, in the classicArchimedean screw the flow rises along the pump, while in theenvisioned use in the ALFRED reactor the pump has to push thecoolant downward. For these reasons, the ‘classic’ model of thescrew pump does not apply to our conditions and geometry; there-fore an ad-hoc theoretical model for the vertical, downward flowing

pump has to be developed. A one-dimensional approach based onthe analysis of the velocity triangles and on the conservation ofmass, energy and angular momentum is developed specifically forthis geometry to predict the performance of the pump.

M. Ferrini et al. / Nuclear Engineering a

F

4

tos

fmour

constraints of the reactor.

ig. 4. Profile view of segment of two-bladed Archimedean screw (Chris, 2000).

.2. Theoretical analysis

The theoretical, isothermal and non-viscous model is based onhe law of conservation of mass, energy, angular momentum andn the velocity triangles. In particular, two simplified forms of con-ervation of energy have been used:

ptotabs= constant

ptotabsin= ptotabsout

ps out + 12

∗ � ∗ V2out = ps int + 1

2∗ � ∗ V2

in

(1)

ptotrel= constant

ptotrelout= ptotrelin

psout + 12

∗ � ∗ W2out − 1

2∗ � ∗ U2

out = psint + 12

∗ � ∗ W2in − 1

2∗ � ∗ U2

in

(2)

with:V = velocity in the absolute reference frame [m/s]W = velocity in the relative reference frame [m/s]ps = static pressure [Pa]Eqs. (1) are the equations of energy in the absolute reference

rame, therefore applicable in the fluid region where there are notoving parts (the stator of the pump). Eqs. (2) are the equations

f energy in the relative reference frame; these equations will besed to analyze the fluid region where there are moving parts (theotor of the pump).

Fig. 5. Kinematical analysis of

nd Design 297 (2016) 276–290 279

The conservation of angular momentum has been appliedin a simplified form, called Euler’s turbine equation (Ferrini,2014):

Lsp = (Uout ∗ vtout) − (Uin ∗ vtin) (3)

with:Lsp = specific work [J/kg]Uout,Uin = circumferential velocityvout,vtin = tangential component of the absolute flow velocity in

the outlet and inlet sectionEq. (3) states that the specific work transferred from the pump to

the flow is related to its deflection between the inlet sections andthe outlet section of the control volume. According to the equa-tions mentioned above, a classic Archimedean screw pump hasbeen analyzed.

Fig. 5 shows that from the kinematic point of view theArchimedean screw can be considered as an axial pump withstraight blades. According to the theory, this pump cannot gen-erate work because the velocity triangles in the sections in screwand out are the same. Indeed, in the non-viscous case and accordingto Eq. (2), if the velocity vector does not change between the inletand outlet sections the (total and static) pressure remains constant.Therefore, in order to generate the required head, the pumpingdevice has to deflect the flow field in the operating part of the pumpwith respect to the inlet conditions. There are two possible optionsto deflect the flow:

• The first option is an axial screw pump with increasing pitch ofthe screw (Fig. 6). In this case, the relative velocity W is reducedinside the device and hence, according to Eq. (2), the staticpressure increases from the inlet to the outlet sections of thepump

• The second option to deflect the flow is to change the hub diam-eter of the screw pump (Fig. 7). In this case, the flow increases itsabsolute velocity from the section in bulb to the section in screw.Then, according to Eq. (1), the static pressure decreases in thispart of the machine, but from the section in screw to the sectionout screw the static pressure increases and increases more thanthe previous decreasing. Therefore, this screw pump with vari-able hub diameter may generate the head required by the design

Both geometries present innovative design which, as far as theAuthors know, have not been analyzed as per their use in nuclear

an Archimedean screw.

280 M. Ferrini et al. / Nuclear Engineering and Design 297 (2016) 276–290

Fig. 6. Screw pump with increasing pitch and velocity triangles.

ra

bd6p

do

-

--

hrodtatm

Fig. 8. Section along the pump duct and pump.

Table 2Initial data – pump dimensions.

Sectionin bulb

Sectionin screw

Sectionout screw

Sectionout

D duct 0.65 m 0.65 m 0.65 m 0.65 mD pump ext 0.63 m 0.63 m 0.63 m 0.63 mD hub 0.2 m 0.5 m 0.3 m 0 mD centerline 0.415 m 0.565 m 0.465 m 0.315 mA pump ext 0.312 m2 0.312 m2 0.312 m2 0.312 m2

2 2 2 2

ptot in = 12

∗ �Pb ∗ V2in = 225, 000 Pa (6)

Fig. 7. Screw pump with variable hub diameter and velocity triangles.

eactors; this paper focuses the fixed-pitch screw pump with vari-ble hub diameter.

A mono-dimensional, isothermal and non-viscous design haseen performed to estimate the exact dimension of the pumpingevice as shown in Fig. 8. The requirements are to evolve450 kg/s of mass flow rate and generate 1.5 bar of differentialressure.

The imposed external constraints (due to reactor geometricalesign and/or compatibility between lead and structural materials)f the problem are:

Rotational speed: the velocity inside the pump shall not exceed10 m/s

Pump duct diameter: the diameter shall be smaller than 1.5 m Pump length: into the reactor vessel there are about 5 m availableto locate vertically the pump

According to these inputs parameters, a preliminary analysisas been performed to estimate the pump duct diameter and theesults of the analysis show that the optimal value for the diameterf the pump duct is between 0.65 m and 0.8 m. Hence, a mono-

imensional design has been developed for different diameters ofhe hub and as a function of the rotational speed. Structural evalu-tions impose a minimum of 0.2 m for the diameter of the hub;herefore this dimension will be used in the first section of the

achine.

A hub 0.031 m 0.196 m 0.071 m 0 mA flow 0.281 m2 0.116 m2 0.241 m2 0.312 m2

The design is carried out as follows:Initial data (see Table 2)1:

pstatin = 200, 000 Pa (4)

Vin = vax in = mass flow rate

Aflow ∗ �Pb= 2.2

ms

(5)

1 The values in Table 2 have been calculated as a function of rotational speed (RPM)in order to achieve 6450 kg/s of mass flow rate and generate 1.5 bar of differentialpressure

M. Ferrini et al. / Nuclear Engineering and Design 297 (2016) 276–290 281

ta

a

a

p

r

p

p

p

p

p

p

v

abl

˛

ˇ

p

a

r

t

p

io

Fig. 9. Velocity triangle in the section in screw.

From the initial data mentioned above, as a function of the RPM,he velocity triangles and the pressure values can be calculated inll the sections along the pump as follows2:

ngular velocity = ω = RPM ∗ 2 ∗ �

60= 29.32

rads

(7)

Section in screw:

bsolute velocity = Vcent = mass flow rate

Aflow ∗ �Pb= 5.3

ms

(8)

eripheral velocity = ucent = rcent ∗ ω = 8.3ms

(9)

elative velocity = Wcent =√

u2cent + V2

cent = 9.8ms

(10)

abstot= ptot in = 225, 000 Pa (11)

absdyn= 1

2∗ �Pb ∗ V2

cent = 150, 000 Pa (12)

stat = pabstot− pabsdyn

= 75000 Pa (13)

reldyn(W)= 1

2∗ �Pb ∗ W2

cent = 510, 000 Pa (14)

reldyn(u)= 1

2∗ �Pb ∗ u2

cent = 510, 000 Pa (15)

reltot= pstat + preldyn(W)

− preldyn(u)= 225, 000 Pa (16)

Hence in section in screw all parameters are known and theelocity triangle can be plotted as shown in Fig. 9.

From the velocity triangle the angles � and � can be evaluatednd therefore the angle of attack of the blades of the screw wille designed equal to � to avoid incidence angle and minimize the

osses (Fig. 10). Hence, from geometrical calculation:

cent = arctanucent

Vcent= 57.4◦ = ˛blade (17)

cent = 90◦ − 57.4◦ = 32.6◦ = ˇblade (18)

itch = 2 ∗ � ∗ rcent ∗ tan ˇcent = 1.1 m (19)

Section out screw:

xial velocity = vax = wax = mass flow rate

Aflow ∗ �Pb= 2.5

ms

(20)

elative velocity = Wcent = wax

cos ˛blade= 4.7

ms

(21)

angential relative velocity = wtancent = tan ˛blade ∗ wax = 4.0ms(22)

eriferal velocity = ucent = rcent ∗ ω = 6.8ms

(23)

2 The values shown in this section relate to 280 RPM, because this rotational veloc-ty, with the geometrical values in Table 2, seems to be sufficient to generate 1.5 barf differential pressure

Fig. 10. Velocity triangle and attack angle of the blades of the screw.

tangential absolute velocity = vtancent = wtancent − ucent = −2.8ms(24)

absolute velocity = Vcent =√

v2ax + v2

tancent= 3.8

ms

(25)

preltot= preltot in screw

= 225, 000 Pa (26)

preldyn(W)= 1

2∗ �Pb ∗ W2

cent = 117, 000 Pa (27)

preldyn(u)= 1

2∗ �Pb ∗ u2

cent = 245, 000 Pa (28)

pstat = preltot− preldyn(W)

+ preldyn(u)= 353, 000 Pa (29)

pabsdyn= 1

2∗ �Pb ∗ V2

cent = 77, 000 Pa (30)

pabstot= pstat + pabsdyn

= 430, 000 Pa (31)

As before, the velocity triangle can be now plotted in sectionout screw because all parameters are known (Fig. 11).

Sectionout:From the section out screw to the section out the flow reduces

only its axial velocity due to the increase of the cross section. Hence:

tangential absolute velocity = vtancent = vtancent out screw = −2.8ms

(32)

axial velocity = vax = mass flow rate

Aflow ∗ �Pb= 2.0

ms

(33)

absolute velocity = Vcent =√

v2ax + v2

tancent= 3.5

ms

(34)

pabstot= pabstot out screw

= 430, 000 Pa (35)

pabsdyn= 1

2∗ �Pb ∗ V2

cent = 64, 000 Pa (36)

pstat = pabstot− pabsdyn

= 364, 000 Pa (37)

Applying the procedure previously described, several geome-tries for the pump with different initial data (Table 2) have been

evaluated, and the results confirm that, in an isothermal and non-viscous case, the screw pump sizing according to Table 2 cangenerate above 1.6 bar of differential pressure. Therefore this geom-etry will represent the reference case for the simulations.

282 M. Ferrini et al. / Nuclear Engineering and Design 297 (2016) 276–290

4

(t

Fto

Table 3Boundary conditions.

Inlet Outlet

Fig. 11. Velocity triangle in the section out screw.

.3. CFD simulations

The CFD model of the pump (Fig. 12) consists of a pump ductgray transparent volume) divided in two fluid domain: one sta-ionary domain and one rotational domain.

ig. 12. Screw pump into the pump duct and mesh of fluid domains. (For interpreta-ion of the references to color in this figure, the reader is referred to the web versionf this article.)

Option 1 Total pressure Mass flow rateOption 2 Total pressure Static pressure

The two fluid domains are shown at the right side of Fig. 12, thestationary domain in green and the rotating domain in purple. Inthis way, the 3D CFD solver (ANSYS, 2013a) will compute the flowgenerated from the motion of the rotating fluid domain inside thepump, instead of the motion generated by the rotation of the pumpblades (ANSYS, 2013b).

In order to perform the simulations, the appropriate boundaryconditions have to be specified. The inlet and outlet boundary con-ditions are closely linked and there are two possible options asshown in Table 3.

The total pressure inlet condition is an appropriate conditionwhen the machine is drawing fluid directly from a static reser-voir. The mass flow rate at outlet is recommended practice forANSYS CFX V15 (ANSYS, 2013b) and suits the requirement to havea constant and fixed mass flow rate feeding the pressure chamber:therefore this condition has been used to perform the simula-tions presented in this paper (Fig. 13) . Last but not least, the totalpressure inlet – mass flow rate outlet conditions ensure a fasterconvergence of the simulation without affecting the validity of theresults (ANSYS, 2013b).

ANSYS CFX V15, the selected 3D CFD package (ANSYS, 2015)provides the Frozen Rotor model which treats the flow from one

component to the next by changing the frame of reference whilemaintaining the relative position of the components. Due to thepresence of two fluid domains there will be two interfaces to

Fig. 13. Inlet and outlet boundary conditions.

M. Ferrini et al. / Nuclear Engineering and Design 297 (2016) 276–290 283

Table 4Boundary conditions.

Location Options set

Inlet Total pressureOutlet Mass flow rateDuct Stationary wallPump surface (in stationary domain) Rotating wall

chtoqo(

thvc

Ittositskstecitaos

0.00E+00

5.00E+04

1.00E+05

1.50E+05

2.00E+05

2.50E+05

3.00E+05

3.50E+05

4.00E+05

0 1 2 3 4 5

Sta�

c pr

essu

re [P

a]

Pump height [m]

theore�cal analysis

non viscous CFD simula�on

Pump surface (in rotating domain) Stationary wall

ommunicate the data between them. The Frozen Rotor modelas the advantages of being robust, using less computer resourceshan other frame change models available in CFD packages;n the downside, the drawbacks of this model include inade-uate prediction of physics for local flow values and sensitivityf the results to the relative position of the rotor and statorANSYS, 2013b).

Table 4 summarizes the geometrical boundary conditions:In order to validate the results of the 3D CFD model against

he theoretical predictions shown in Section 4.2, a simulationas been performed in non-viscous conditions. Fig. 14 shows theelocity streamlines, the velocity contours and the static pressureontours.

As shown, the flow matches perfectly the theoretical analysis.n the first part of the duct the flow is completely axial, then takeshe same angle of the blades inside the rotor and finally main-ains the swirl acquired in the screw. In the section in screw andut screw the streamlines are bent due to the transition from thetationary domain to the rotating domain and then from the rotat-ng domain to the stationary domain. The static pressure alonghe pump predicted by the theoretical analysis and by the CFDimulations are shown in Fig. 15. As expected, the static pressureeeps constant in the first part of the machine, where the crossection is constant, then decreases when it enters in the reduc-ion of the cross section, increases inside the rotor because of thexpanding cross section and finally keeps constant because of theross section is constant. The analysis confirms that the theoret-cal design is matched by the non-viscous simulation. Thereforehe theoretical model can be used as a predictive tool for further

nalysis and then, viscous 3D simulations have to be executed inrder to evaluate detailed information about the flow fields, ashown in the following paragraph. As predicted, the pump evolves

Fig. 14. Non-viscous reference case: velocity streamlines (left), velocity contou

Fig. 15. Static pressure along the pump: theoretical analysis and CFD non-viscoussimulation.

a mass flow rate of 6450 kg/s and generates 1.6 bar of differentialpressure.

4.3.1. Viscous reference caseIn order to evaluate the impacts of the viscous effects on the

flow field, the transport propriety of the fluid are implemented inthe same geometry and with the same boundary conditions used forthe non-viscous simulation. The standard k–� turbulence model isused. In Section 4.3.3 a sensitivity analysis is shown with respect tothe turbulence model. This case will be considered as the reference(viscous) case. The velocity streamlines, the velocity contours andthe static pressure contours are shown in Fig. 16.

Fig. 16 shows the same behavior of the flow field, while theabsolute values of the variables are different, compared with thenon-viscous case.

Fig. 17 shows the velocity contours on a frusto-conical surface inthe middle of the rotor. Due to the viscous effects near the surface ofthe blades, there is a region where the velocity is close to zero. Theimage confirms the deceleration of the flow inside the rotor andshows the greater velocity in the suction side of the blades thanin the pressure side, because of the opposite behavior of the pres-sure generated by the forces on the fluid. Because of the impact

of the transport propriety of the fluid between the viscous andnon-viscous case, the absolute value of the total pressure showsa markedly different behavior, as shown in Fig. 18.

rs (middle) and static pressure contours (right) on a longitudinal plane.

284 M. Ferrini et al. / Nuclear Engineering and Design 297 (2016) 276–290

Fig. 16. Viscous reference case: velocity streamlines (left), velocity contours

Fig. 17. Velocity contours on a frusto-conical surface in the middle of the rotor.

0.00E+00

5.00E+04

1.00E+05

1.50E+05

2.00E+05

2.50E+05

3.00E+05

3.50E+05

4.00E+05

4.50E+05

5.00E+05

0 1 2 3 4 5

Tota

l pre

ssur

e [P

a]

Pump height [m]

non-viscous CFD simula�on

viscous CFD simula�on

Fig. 18. Total pressure along the pump: non-viscous and viscous CFD simulations.

(middle) and static pressure contours (right) on a longitudinal plane.

As expected, the curves have the same value in the first part andthen the differences increase along the pump due to the viscouseffect of the fluid. In particular, in Fig. 19, the velocity stream-lines on a longitudinal plane for the reference (viscous) case showa region below the end of the hub where the flow detaches fromthe wall and the vortices dissipate energy (hence total pressure)mainly because of viscous effects. This phenomenon is the mainreason for the reduction of total pressure from the cross sectionlocated at 3.1 m to the section located at 3.4 m, compared with thenon-viscous case (Fig. 18), and will be considered in the designoptimization phase in order to improve the performance of thepump.

This configuration generates 6447 kg/s of mass flow rateat 0.9 bar of differential pressure. Being the target 1.5 bar, anew design will be necessary to achieve the desired designobjective.

The procedure detailed in Section 4.2 will be used to developa new design. In the revised model of the pump, the hub diam-eter size along the machine is equal to the previous design, but

in order to increase the energy transferred to the flow the rota-tional speed has been increase to 315 RPM and consequently alsothe angle of attack and the pitch of the screw blades have beenmodified.

Fig. 19. Velocity streamlines on a longitudinal plane on a longitudinal plane alongthe pump.

M. Ferrini et al. / Nuclear Engineering and Design 297 (2016) 276–290 285

aTittb

tsssittds

tabg

0.00E+00

1.00E+05

2.00E+05

3.00E+05

4.00E+05

5.00E+05

6.00E+05

0 1 2 3 4 5

Tota

l Pre

ssur

e [P

a]

Pump height [m]

315 RPM (new d esign)

280 RPM (re fere nce ca se)

Fig. 22. Total pressure along the pump: new design (315 RPM) and reference case(280 RPM).

0.00E+00

5.00E+04

1.00E+05

1.50E+05

2.00E+05

2.50E+05

3.00E+05

3.50E+05

0 1 2 3 4 5

Sta�

c Pr

essu

re [P

a]

Pump height [m]

315 RPM (new d esign)

280 RPM (re fere nce ca se)

velocities in the active part of the pump are close to the threshold

Fig. 20. New design and velocity triangles.

The new design and its velocity triangles are shown in Fig. 20.The new design has a shorter pitch, hence a smaller angle of

ttack, in order to receive the increased tangential relative velocity.he length of the hub from the section out screw to the section outs greater than in the previous design, with the purpose to reducehe flow separation shown in Fig. 19. The boundary conditions arehe same as for the reference case, while the rotational speed haseen increased from 280 to 315 RPM.

The flow field at 315 RPM is shown in Fig. 21. Compared withhe case at 280 RPM and same geometry (Fig. 16), there is only amall difference after the section out screw: in the new design thetreamlines show a higher swirl, due to the increased rotationalpeed and the greater length of the last part of the hub. This behav-or generates an increase of absolute velocity, hence an increase ofotal pressure and a small reduction of static pressure. However,he new pump transfers more energy to the fluid, generating moreifferential static and total pressure between the inlet and outletection of the duct.

Figs. 22 and 23 show the comparison for the static and theotal pressure between the reference case (280 RPM) and the case

t 315 RPM. As expected, the case at 315 RPM performs better,ecause of the increased rotational speed as well as because to theeometrical modifications listed above.

Fig. 21. New design: velocity streamlines (left), velocity contours (mid

Fig. 23. Static pressure along the pump: new design (315 RPM) and reference case(280 RPM).

The differential static pressure for the new design is 1.2 barwhile the differential total pressure is 2.2 bar. One option to achievethe target differential static pressure (1.5 bar) could be increas-ing the rotational speed: this solution is not advisable because the

beyond which the erosion effects could severely impact the surfacesof the pump. A different strategy should be used: because the pumpchannels the coolant into the lower reactor plenum, a proper design

dle) and static pressure contours (right) on a longitudinal plane.

286 M. Ferrini et al. / Nuclear Engineering and Design 297 (2016) 276–290

Fig. 24. Velocity contours: k–� turbulent model (right), Shear Stress Transport Turbulent model (middle) and their difference (left).

Fig. 25. Three different positions of the rotating domain: reference case (left), 40◦ (middle) and 80◦ (right).

Fig. 26. (a) Static pressure and (b) total pressure along the pump.

M. Ferrini et al. / Nuclear Engineering and Design 297 (2016) 276–290 287

Fig. 27. (a) Detail of longitudinal section of the mesh at the end of the hub: finer (right) and reference case (left), (b) velocity contours: difference between finer and referencecase.

Fig. 28. (a) Static pressure and (b) total pressure along the pump: reference case and finer mesh.

0.00E+00

3.00E+04

6.00E+04

9.00E+04

1.20E+05

1.50E+05

1.80E+05

2.10E+05

2.40E+05

2.70E+05

4.00E+03 5.00E+03 6.00E+03 7.00E+03 8.00E+03 9.00E+03 1.00E+04

Diffe

ren�

al to

tal p

ress

ure

[Pa]

Mass flo w rate [kg /s]

e pum

oflo

4

b

Fig. 29. Static pressure of th

f the geometry of the plenum will considerably slows down theuid (because of the bigger cross section) and the dynamic pressuref the flow will be turned in static pressure.

.3.2. Sensitivity analysisThe simulation shown in Section 4.3.2 has used the k–ε tur-

ulence model. In order to demonstrate the results independence

p at off-design conditions.

from the turbulent model, a test has been run using the Shear StressTransport k–ω turbulent model. In literature, the k–ε and ShearStress Transport models are indicated to be appropriate choices for

modelling turbulence in geometries as in the case and the resultsshown in Fig. 24 confirm it. The differences between the two resultsare minimal and are located mainly in the region below the end ofthe hub.

288 M. Ferrini et al. / Nuclear Engineering and Design 297 (2016) 276–290

0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

6.00E-01

7.00E-01

8.00E-01

9.00E-01

4.00E+03 5.00E+03 6.00E+03 7.00E+03 8.00E+03 9.00E+03 1.00E+04

Effici

ency

Mass flo w rate [kg /s]

Fig. 30. Efficiency of the pump at off-design conditions.

0.00E+00

2.00E+01

4.00E+01

6.00E+01

8.00E+01

1.00E+02

1.20E+02

1.40E+02

1.60E+02

1.80E+02

4.00E+03 5.00E+03 6.00E+03 7.00E+03 8.00E+03 9.00E+03 1.00E+04

Pow

er [k

W]

ss flo

orbed

tiAttaF

Flp

st

tpeotI

tbn

Fig. 32 shows the velocity streamlines on a frusto-conical surfacein the middle of the rotor in off-design points. In spite of a significantvariation of the mass flow rate, the flow field does not show any

Ma

Fig. 31. Pump power abs

In order to demonstrate the results independence with respecto the location of the blades, two simulations have been run rotat-ng the relative position of the rotor and stator of 40 and 80 degrees.lthough the pump studied in this paper do not have standard sta-

or blades, this analysis is necessary because of the sensitivity ofhe Frozen Rotor model to the relative position of the rotor bladesnd stator. The relative positions of the rotor blades are shown inig. 25.

The static and the total pressure along the pump are shown inig. 26. The results confirm the perfect match between the simu-ations and therefore the accuracy of the model irrespective of theosition of the blades.

One of the most important aspects that characterize a correctolution is the grid independence. It requires checking the estima-ion of the errors introduced by possible inadequate mesh.

Fig. 27a shows the differences between the two meshes usedo check the grid independence. In particular, in the finer case, therism layers are thinner than in the reference case in order to bettervaluate the near wall flow.3 The finer mesh has about 6 millions

f nodes while the reference case has about 2 millions of nodes. Aypical simulation runs in about 6 h in 8-way parallel mode on anntel E5-2995 based node.

3 In both the cases the scalable wall function has been used and has been verifiedhat the upper limit of y+ was always less than 200, whereas if the y+ values areelow the valid range of the wall functions, the model automatically ignores thatodes.

w rate [kg /s]

at off-design conditions.

Fig. 27b shows that there is a perfect match between the flowfield computed in the finer case as in the reference case, withonly negligible differences. Given that the grid independence hasbeen demonstrated, the simulations have been performed with thecoarser mesh because the results are sufficiently accurate and thecomputational time is reduced (Fig. 28).

4.4. Off-design performances

In order to better define the behaviour of the pump in a largerange of operating conditions, an off-design analysis has been per-formed changing the mass flow rate. Figs. 29–31 show respectivelythe differential total pressure, the pump efficiency4 and the pumppower consumption in the range from −30% to +40% of the nominalflow rate (4702-9042 kg/s).

detachment from the surface, therefore minimizing any unwantedperformance degradations.

4 The pump efficiency has been defined as: �pump = WrealWideal

=(m• �ptot

�

)from theoretical analysis(

m• �ptot�

)from CFD simulations

M. Ferrini et al. / Nuclear Engineering and Design 297 (2016) 276–290 289

ng con

5

AblettuAfs

Fig. 32. Velocity streamlines in design and off-design operati

. Conclusions and future work

The analysis of a liquid lead screw pump as primary pump forLFRED has been performed. A three-dimensional geometry haseen successfully modeled, adopting a relatively fine mesh which

eads to accurate results enabling the accurate modeling of thentire flow field of the coolant inside the pump. The validation ofhe design has been done initially comparing the numerical predic-ions with theoretical results in non-viscous conditions, and then

sing the same geometry coupled with the real properties for lead.

parametric analysis based on the mass flow rate has been per-ormed to understand the effects of the velocities and rotationalpeed of a screw pump.

ditions on a frusto-conical surface in the middle of the rotor.

The results of the CFD analysis on the multi-bladed screw pumpsupport the following conclusions:

• The multi-bladed screw pump geometry modeled in this papermatches the dimensional requirements imposed by the pump hotduct

• The tip of the blades may have a potential erosion problembecause of a velocity of about 10 m/s; special components andtreatments, which have to be tested experimentally, shall be

used

• While the target differential static pressure has not been achievedin the present design, the maximum performance has beenextracted according to the limitations in velocity (imposed by

2 ering a

•

A

tmMits

R

A

A

AAh

W

A

B

B

C

90 M. Ferrini et al. / Nuclear Engine

the requirement to avoid any erosion effects) and geometricalrequirementsA proper design of the lower reactor plenum could supplementthe performance of the pump achieving the target differentialstatic pressure.

cknowledgments

The work presented in this paper was partially performed withinhe FALCON (Fostering ALfred CONstruction) Consortium Agree-

ent. The authors would like express their gratitude to Luigiansani of Ansaldo Nucleare S.p.A., whose expertise, understand-

ng and patience added considerably to this paper. Finally we wanto thank Alessandro Alemberti of Ansaldo Nucleare S.p.A. for hisupport and suggestions.

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