5. NATURAL CIRCULATION EXPERIMENT: NACIE

5. NATURAL CIRCULATION EXPERIMENT: NACIE

The present chapter reports about the conceptual design of the NACIE facility, a Heavy Liquid Metal Loop, built up to carry out experimental tests needed to characterize the natural and gas enhanced circulation flow regimes, and to qualify components for HLM applications, especially in support of the ICE activities (see chapter 4) [1].

In fact, since the Fuel Pin Simulator FPS under design for the ICE activity is based on the use of prototypical electrical heaters, a preliminary characterization of their thermal and electrical performance is required; this characterization will be accomplished by the NACIE loop.

5-1. AIM OF THE NACIE ACTIVITY

The aim of NACIE loop is to set up a support facility able to qualify and characterize components, systems and procedures relevant for HLM nuclear technologies.

Moreover, by the this facility it will be possible to perform several experimental campaigns in the field of the thermal-hydraulics, fluid-dynamics, chemistry control, corrosion protection and heat transfer, allowing to obtain correlations essential for the design of the nuclear power plant cooled by heavy liquid metal.

More in detail, the NACIE loop has been built up to:

characterize the natural circulation flow regime in a HLM loop;

obtain experimental data on natural circulation heat transfer coefficient in a rod bundle assembly;

characterize the gas enhanced circulation in a HLM loop;

evaluate the global heat transfer coefficient inside the HX (HLM-water);
simulate several operational and accident transients inside a HLM loop;

establish a reference experiment for the benchmark of commercial codes when employed in HLM loop;

Finally, the possibility to test four prototypical pin simulators as well as all their ancillary systems and mechanical connections is mandatory in order to confirm the design of the ICE test section.

For this reason the NACIE loop is prepared to house a bundle made with four prototypical pin simulators in full scale to the ones which will be manufactured for the ICE test section.

5-2. GENERAL DESCRIPTION OF THE NACIE LOOP

NACIE is a HLM rectangular loop which basically consists of two vertical pipes (O.D. 2,5”) working as riser and downcomer, connected by means of two horizontal branches (O.D. 2,5”) [2].

The adopted material is stainless steel (AISI 304) and the total inventory of LBE is about 1000 kg; the design temperature and pressure are 550 °C and 10 bar respectively.

In the bottom part of the riser a heat source is installed through an appropriate flange, while the upper part of the downcomer is connected to an heat exchanger.

The difference in level between the thermal centre of the heat source and the one of the heat sink was fixed to reproduce the same height that characterises the ICE test section (H = 4.5 m).

The loop is completed by an expansion vessel, installed on the top part of the loop, coaxially to the riser.

The general layout of the loop is depicted in figure 1, while the geometrical data which characterize the NACIE facility are reported in table 1.

A view of the NACIE loop head (expansion vessel) is also reported in figure 2 .

5-2.1 HEATSOURCE

For the NACIE activity two different bundles are foreseen, named “high flux bundle” and “low flux bundle”.

High Flux Bundle

The high flux bundle consists of four prototypical pins; the characteristics of the bundle are reported in table 2 .

Total Vertical Length [mm] 9231

Horizontal Length [mm] 1000

Pipe Inner Diameter [mm] 62.7

Pipe Thickness [mm] 5.16

Expansion Vessel Height [mm] 765 Expansion Vessel Inner Diameter [mm] 254.5 Heat Exchanger Length [mm] 1500 Heat Source Active Length [mm] 1000

Table 1 NACIE Main Geometrical Data

Cover Gas Inlet Cover Gas Outlet Gas Injection Heat Exchanger Water Outlet Water Inlet Ultrasonic Flow Meter Heat Source Expansion Vessel Riser Downcomer Cover Gas Inlet Cover Gas Outlet Gas Injection Heat Exchanger Water Outlet Water Inlet Ultrasonic Flow Meter Heat Source Expansion Vessel Riser Downcomer

Figure 2. Top view of the NACIE expansion vessel. In the foreground the injection pipe adopted for the gas lift

A-type Prototypical Pin (see chapter 4)

Number 2

Diameter [mm] 8.2

Active Length [mm] 1000

Total Length [mm] 2760

Heat Flux [W/cm2] 100

Flux Distribution Uniform

Thermal Power [kW] 25

B-type Prototypical Pin (see chapter 4)

Number 2

Diameter [mm] 8.2

Active Length [mm] 1000

Total Length [mm] 8380

Heat Flux [W/cm2] 100

Flux Distribution Not-uniform

Thermal Power [kW] 25

Table 2 . High Flux Bundle Characteristics

The pins are arranged in a triangular lattice with a pitch to diameter ratio of 1.8, as envisaged for the ICE bundle. The total installed power is 100 kW, even if during the tests only two pins (one for each type) will be active.

Figure 3. View of the High Flux Bundle

The aim of the tests planned using the high flux bundle is to characterize the pins, in term of performance of the active length as well as cold length, reliability and thermal fatigue.

The results carried out should allow choosing the more suitable technical solution for the pins to adopt in the ICE bundle.

Low Flux Bundle

The low flux bundle consists of three electrical cartridges placed on triangular lattice with a pitch to diameter ratio of 1.4; the total thermal power installed is 30 kW.

The main parameters of the low flux bundle are reported in the table 3.

Number 3

Diameter [mm] 19.05

Active Length [mm] 1000

Total Length [mm] 2380

Heat Flux [W/cm2] 16.8

Flux Distribution Uniform

Thermal Power [kW] 10

Table 3 Low Flux Bundle Characteristics

In figure 4 a sketch of the low flux bundle is reported.

The low flux bundle will be instrumented to allow HTC measurement under natural circulation flow regime as well as under gas-injection enhanced circulation.

5-2.2 EXPANSION VESSEL

The expansion vessel, located at the top of the riser, has the twofold purpose to allow for expansion of the fluid during transient operation and to separate the injected gas from the liquid in case of gas-injection enhanced circulation.

The free level of the LBE is maintained under an Argon atmosphere, with a slight overpressure (about 200-300 mbar).

The upper flange of the expansion vessel will be arranged to install the argon feeding pipe to be housed in the riser during the test for the qualification of the enhanced circulation.

To characterize the fluid-dynamic behaviour of the expansion tank and evaluate its equivalent pressure loss coefficient, several CFD simulations were performed, adopting the FLUENT code. Figure 5 shows the adopted grid for the domain discretization; 1/2 of the overall domain has been analyzed exploiting the vessel symmetry.

The cover gas inside the vessel has not been simulated; a wall with no shear has been utilized to simulate the interface between the HLM free level and the cover gas.

Figure 6 Velocity Magnitude inside the expansion vessel (LBE Flow Rate of 10 kg/s)

To perform the simulations also parts of the vertical inlet pipe as well as the horizontal outlet pipe were considered (see figure 5 ).

For the discretization of the overall domain, more than 500,000 cells have been adopted. A segregated implicit approach has been chosen. A steady state analysis was performed.

The adopted model for the simulation of the turbulence is RNG k-ε model, with standard wall treatment.

The calculations have been performed assuming different values of the LBE flow rate through the domain, and calculating the pressure difference between the inlet and outlet sections, ∆p_{in out,} .

Then, the pressure loss coefficient has been calculated applying the following equation: 2 , 2 2 _{LBE in} in out A k p M

ρ

where A is the inlet flow area (or outlet flow area), equal to 0.0031 min

2

. The obtained results are reported in the table 4.

Figure 6 shows the velocity magnitude field as computed in the expansion vessel for an imposed flow rate of 10 kg/s.

LBE Flow Rate [kg/s] Inlet Pressure [Pa] Outlet Pressure [Pa] , in out p ∆ [Pa] k [-] 10 100818 99806 1020 2.00 7 101076 100534 545 2.18 5 101198 100938 263 2.06 3 101279 101179 101 2.21 1 101320 101307 13 2.61

Table 4 .Results of the CFD calculations performed on the expansion vessel

In the following, an average value of 2.2 is assumed for this parameter.

Besides the fluid dynamic function, the expansion vessel has also a structural purpose; in fact, by three appropriate wings welded on the external surface, it takes on the overall facility (see fig. 7).

As a consequence, the expansion vessel results to be the more stressed mechanical component in the facility, and in order to verify its mechanical stability a numerical calculation was performed by the ANSYS code.

Figure 7 shows the expansion vessel discretization performed by the finite elements technique.

The applied loads are reported in table 5.

Temperature [°C] 550

Weight of the Facility [N] 15000

Table 5. Applied Loads on the Expansion Vessel for the Numerical Calculation

The obtained results are plotted in the figure 8; as it can be noted the maximum equivalent stress calculated by the criteria of Von Mises is about 37 MPa, well below the value of 90 MPa, that is the admissible stress for the AISI 304 steel at 550 °C.

Figure 8 . Plot of the Von Mises equivalent stress on the expansion vessel calculated by the ANSYS code

5-2.3 PUMPING SYSTEM

To promote the LBE circulation along the loop, a gas lift technique will be adopted; a pipe having inner diameter of 10 mm is housed inside the riser, connected through the top flange of the expansion tank to the argon feeding system.

At the other end of the pipe the injection nozzle is mounted, located just downstream the heating section. The gas will be injected in the riser through the nozzle, enhancing the liquid metal circulation. In the expansion tank the separation between the phases will take place.

In this way the possibility to have a two phase mixture flowing through the heat source is avoided.

The gas injection system is able to supply Argon flow rate in the range [1-75 Nl/min] with a maximum injection pressure of 5.5 bar.

5-2.4 CHEMISTRY CONTROL AND OXYGEN MONITORING

The design of a chemistry control and oxygen monitoring system for HLM pool facility was already described in the chapter 4.

For a HLM experimental loop facility the requirements are the same: 1. lead oxide (PbO) contamination has to be avoided;

2. corrosion and dissolution must be reduced.

Also for the NACIE loop, as well as for CIRCE operation, the oxygen control system must be designed defining:

 the upper limit for the oxygen concentration to avoid the contamination by coolant oxides;

 the lower limit for the oxygen concentration to enhance the corrosion protection by self-healing oxide layer.

Its main functions must also be taken into account:

 purification from oxygen during start-up or restart to prevent the formation of lead oxide;

 active oxygen control for corrosion protection during the normal operating mode, and, at the initial stage, to promote the formation of a protective oxide layer.

For the measurement of the oxygen concentration in NACIE, the same sensors adopted for the ICE test section will be available.

They consist of an electrochemical galvanic cell, indicated as

2 3 2 2 3

, / (reference) // // / ,

Mo Bi Bi O ZrO +Y O Pb PbO steel (2)

and the theoretical response of the sensor can be written as follows: (mV) 119.8 0.0539 (K) 0.0431 (K) ln O

E = − ⋅T − ⋅T ⋅ a (3)

for E>E_sat, while under saturation condition:

( ) 119.8 0.0539

sat K

E = − ⋅T (4)

Adopting the notation E T C

(

)

These relationships allow representing the theoretical values of E vs. T (with CO as

parameter) as illustrated in figure 9, allowing to compare the relative position of the oxygen when compared to the PbO saturation line, defining the lower potential value achievable to avoid the contamination of the system by lead oxide precipitation.

Moreover, in the figure 9 the working area for the NACIE loop is reported; in fact, as already mentioned, for a non isothermal system operating between 300 °C and 600 °C (minimum and maximum wall temperature foreseen in the NACIE operation when LBE is adopted) the intersection of the two ranges defined by vertical lines plotted respectively for the cold and hot temperatures defines the oxygen range.

0 100 200 300 400 500 600 250 300 350 400 450 500 550 600 650 T [°C] E [ m V ] 1E-9 10 1 0.1 0.01 1E-3 1E-4 1E-5 1E-6 1E-7 1E-8 PbO saturation Fe3O4 threshold

Figure 9. Diagram E vs. T for oxygen sensors reading in LBE

For the NACIE operation, no solid phase control will be adopted; the control of oxygen concentration will be achieved only by the gas phase control by the gas mixture injections (Ar-H2 or Ar-O2).

The conditioning of the LBE will be performed before the tests start, to avoid any interference with the thermal hydraulic behaviour of the system.

5-3. NACIE LOOP THERMAL HYDRAULIC DESIGN

In the following, the thermal hydraulic design of the NACIE loop is described, reporting also the CFD calculations made in support of it.

5-3.1 ENHANCEDCIRCULATIONFLOWREGIME

As already mentioned, the gas lift technique will be utilized to promote the LBE circulation along the NACIE loop.

Assuming a maximum average void fraction in the riser of 0.1, the maximum driving force available for the tests can be evaluated as follow:

DF r

p

ρ

∆ = ∆ (6)

where H is the riser height, and: _r

(

)

(

)

, 1

LBE r TP LBE g LBE LBE g

ρ ρ ρ ρ αρ α ρ α ρ ρ

∆ = − = − − − = − (7)

where ρ_{r TP,} indicates the two phase flow density inside the riser. Because ρ_g <<ρ_LBE the following approximation is made:

(

)

By equation (9), the maximum driving force available for the primary circulation is max

55 kPa DF

p

∆ = (10)

being the riser 5.5 m tall and assuming a LBE average temperature in the loop of 350 °C. By the momentum transport equation [4] for a closed loop in steady state conditions, it is possible to write the following relationship:

DF fric

p p

∆ = ∆ (11)

where ∆p_fric indicates the overall pressure drops along the primary flow path; for its evaluation the following correlation will be adopted (see also chapter 4):

2 2 1 2 fric eff eff eff M p K A

ρ

 Mɺ is the primary flow rate,  A is the effective flow area, eff



ρ

The effective flow area and density were chosen as the riser actual flow area A and _r the LBE average density

ρ

Dividing the flow path into several branches, (heating section, heat exchanger, riser, downcomer, etc) for the i-th ones it is possible to define a local pressure drop coefficient,

, eff i

K , referred to the effective parameters, A and _eff

ρ

The i-th local pressure drop coefficient can be written as : 2 , , 2 , eff eff i eff i i i l l h i i i A L K f k D A

ρ

ρ

∑

where k is a coefficient taking into account the l-th singular pressure drop (entrance _{i l,} effect, change of direction, orifice, mass flow transducer, etc.) placed along the flow path inside the i-th branch.

By equations (13) the effective pressure drop coefficient can be written as: ,

eff eff i i

K =

∑

In the following, the equation (13) will be applied, assuming the following effective parameters: 2 3087.6 mm eff Α = 3 10271.2 kg/m eff

ρ

where Μɺ is a tentative flow rate for the NACIE loop.

Upper and Lower Horizontal Pipe

Applying equation (13), in the first term the Darcy-Weisbach factor f must be H evaluated. In this aim the Churchill Correlation [4] was again adopted.

(

)

(

)

(

)

ε

where

ε

2 3087.6 mm H A = D_{h H,} =62.7 mm L =_H 1000 mm 0.50 m/s H w = Re_H =1.9E+05

By the Churchill Correlation it is possible to obtain:

1 21 A= E+ B=4E−12 and so: 0.019 H f =

Along the upper horizontal pipe no singular pressure drop are placed, and so: , 0

H l l

k =

∑

Finally, it is possible to write:

1 eff H

ρ

ρ

ρ

ρ

Heat Source (Low Flux Bundle)

For the Heat Source the following parameter results: 2 2232.6 mm HS A = D_{h HS,} =23.7 mm L_HS =1800 mm 0.7 m/s HS w = Re_HS =1.0E+05

Applying the Churchill Correlation to the Heat Source (see equation (15)) it is possible to obtain: 2 20 A= E+ B=1E−07 and so: 0.023 HS f =

Along the Heat Source no singular pressure drop will be considered; for the low flux bundle no spacer grids are installed. So, for the HS the following assumption will be made:

, 0 HS l l

k =

∑

Finally, because the LBE average temperature along the HS and flow path are equal, it is possible to write:

1 eff HS

ρ

ρ

ρ

ρ

For the downcomer (because the HX is a tube in tube type, the downcomer takes in account in this evaluation also the HX) the following parameter results:

2 3087.6 mm DW A = Dh DW, =62.7 mm LDW =7500 mm 0.50 m/s DW w = Re_DW =1.9E+05

By the Churchill Correlation it is possible to obtain:

1 21 A= E+ B=4E−12 and so: 0.019 DW f =

Along the downcomer no singular pressure drop are placed, and so: , 0

HS l l

k =

∑

Finally, it is possible to write:

1 eff DW

ρ

ρ

ρ

ρ

Riser

Due to the gas injected to promote the LBE circulation during the tests, a two phase flow subsists along the riser; to evaluate the two phase pressure drop, equation (13) has to be rewritten as follow [4] (neglecting the singular pressure drop term):

2 2 2 , 2 2 , , eff eff m r eff r lo lo h r l r r A M H K f D A M

ρ

ρ

In this relationship, Mɺ indicates the mixture flow rate along the riser, _m f is the _lo Darcy-Weisbach friction factor evaluated considering a “liquid only” single phase at the same flow rate of mixture,

ρ

lo

Φ is the two phase factor multiplier.

According to the Lockart-Martinelli approach [5], the two phase flow multiplier can be expressed as:

(

)

X is the Lockart-Martinelli parameter defined as:

(

)

(

)

2

,

/ friction pressure gradient in the liquid phase

friction pressure gradient in the gas phase /

frict l frict g dp dz X dp dz = = (18) evaluated as 0.2 1.8 2 g 1 l l g x X x

ρ

µ

ρ

µ

where x is the flow quality:

g g m g l M M x M M M = = + ɺ ɺ ɺ ɺ ɺ (20)

Since the Argon flow rate envisaged to be utilized during the tests is in the range of 1-75 Nl/min (about 0.00003-0.002 kg/s), it is possible to assume that:

(

)

ρ

ρ

ρ

µ

µ

from equation (19) it is possible to get the value for 2

X , and as a consequence, by equation (17), the two-phase flow multiplier is evaluated to be:

(

)

2

1.00 1.03

lo

Φ = ÷ (21)

for a gas flow rate in the range of

(

)

To evaluate the “liquid only” friction factor f , the Churchill correlation (see equation lo (15)) was adopted; in that equation Re is substituted with Re_lo , that is the Reynolds number obtained considering a single phase flow rate equal to the mixture one. So, considering that , 62.7 mm h r D = 2 3087.6 mm r A = H =_r 5500 mm it is possible to get: , , Re_lo m h r h r 1.9 5 l r l r M D MD E A A

µ

µ

Finally, by equation (16), (considering the maximum estimated value of 1.03 for the two phase factor multiplier), :

, 1.72 eff r

K =

having the ratio 2 2

/ 1

eff r

A A = .

Bends

The flow area, hydraulic diameter and length foreseen for the bends, are: 2 3087.6 mm B A = D_{h B,} =62.7 mm 0.50 m/s B w = Re_B =1.9E+05 From the [6] 0.27 B k = Finally, because 1 eff B

ρ

ρ

2 , 2 0.27 eff eff eff B B B B A K k A

ρ

ρ

On the basis of the above described CFD calculation, it is possible to write: , 2.2

eff EV

K =

since it is already referred to the riser flow area and velocity.

Effective Pressure Loss Coefficient

To evaluate the effective pressure drop coefficient a summation of all the previous contributions is made:

, , 3 , 2 , , , 10.13

eff eff DW eff r eff B eff H eff EV eff HS

K =K +K + K + K +K +K =

and so, the overall pressure drop along the flow path can be estimated applying equations (12); 2 2 1 13.2 kPa 2 fric eff eff eff M p K A

ρ

Applying equation (9), it is possible to estimate the void fraction needed into the riser to promote a LBE flow rate circulation of 16 kg/s:

0.024 frict LBE r p gH

α

ρ

In the figure 10 the behaviour of the NACIE loop under the enhanced circulation flow regime is illustrated; the effective pressure loss coefficient as well as the average void fraction in the riser, calculated by the procedure illustrated above, are reported as function of the LBE flow rate.

In the figure 11, the thermal difference between the inlet and outlet section of the low flux bundle, as well as the velocity through the bundle, are reported as a function of the LBE flow rate.

9.0 9.5 10.0 10.5 11.0 11.5 12.0 0 10 20 30 40

LBE Flow Rate [kg/s]

K [ -] 0.000 0.020 0.040 0.060 0.080 0.100 0.120 A v e ra g e V o id F ra c ti o n [ -] K Void Fraction

Figure 10 . Effective Pressure Loss Coefficient and Average Void Fraction in the Riser, calculated for the NACIE loop (Tav=350°C; Low Flux Bundle)

0 5 10 15 20 25 30 35 40 45 0 10 20 30 40

LBE Flow Rate [kg/s]

∆ T [ K ] 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 L B E V e lo c it y [ m /s ] ∆Τ w

Figure 11. Thermal Difference and LBE velocity through the NACIE Low Flux Bundle (Tav =350°C)

5-3.2 NATURAL CIRCULATION FLOW REGIME

The available driving force under the natural circulation flow regime, can be expressed as follows, in similarity with the equation (6):

,

DF *C HS

p

ρ

∆ = ∆ (24)

Here, H indicates the elevation between the thermal centre of the heat source and the heat sink.

Since the heat flux inside the HS as well as in the HX is uniform (see paragraph 5-3.4), their thermal centres can be considered coincident with the geometric ones.

Under this hypothesis, for the NACIE loop it is: 5.25

H = m (25)

HS

ρ

∆ represents the variation of density that the liquid metal undergoes flowing through the heat source. In order to evaluate this term, the Boussinesq approximation [4] has been adopted:

( )

( , ) 1 ( )

LBE TLBE z LBE LBE TLBE z TLBE

ρ

ρ

β

where

β

ρ

β

ρ

By the equations (26) and (27), the ∆

ρ

, , , , ( , , , , )

HS LBE HS in LBE HS out LBE LBE TLBE out HS TLBE in HS LBE LBE THS

ρ

ρ

ρ

ρ β

ρ β

∆ = − = − = ∆ (28)

Then, the driving force term can be written as a function of the thermal power and the LBE flow rate:

, th HS DF LBE LBE HS LBE LBE

LBE Q p gH T gH MCp

ρ β

ρ β

By equation (11), (12), and (29), it is possible to get: 2 , 2 1 2 th HS

LBE LBE eff

LBE LBE eff

Q M gH K MCp A

ρ β

ρ

In the general case, the Keff coefficient is a function of the mass flow rate by the following relationship [4] :

( )

eff

where K is a proportionality constant; for highly turbulent flow, n=0.2, while for laminar flow, n= . 1

From equation (30) and (31):

1 2 3 2 , , 2 n eff th HS LBE HS A M gH Q Cp K

ρ β

Anyway, as it can be noted from the figure 10, in the case of NACIE loop the K _eff coefficient is quite independent from the flow rate; for a preliminary rough calculation the following assumption is made:

( )

eff eff *C

K Mɺ =K (33)

and the equation (32) can be write as follow:

1 2 3 2 , , , 2 eff _{th HS} eff *C LBE HS A M gH Q Cp K

ρ β

The assumption reported by the equation (33) results to be completely true when the form losses along the flow path are much higher than the friction ones [4].

Solving equation (34) by an iterative process, it is possible to obtain: , 10.8 eff *C K = (35) 6.4 / *C Mɺ = kg s (36) , , 32.7 th HS HS *C out in *C LBE Q T T T C M Cp ∆ = − = ° ɺ (37)

and the average LBE velocity through the Heat Source is about 0.3 m/s.

5-3.3 CFD NUMERICAL SIMULATIONS

The aim of the CFD numerical simulations was to perform a preliminary evaluation of the NACIE loop behaviour under the natural circulation flow regime, in terms of LBE flow rate, thermal difference through the HS, average velocity and maximum temperature on the pin walls.

As heat source, the low flux bundle is adopted; moreover, in order to reduce the CPU time, the expansion tank was not simulated, thus strongly reducing the number of cells needed to simulate the whole loop.

Exploiting the NACIE symmetry, only half of the loop was simulated, cutting it with a vertical plane (see figure 12). The spatial domain is divided in 10 sections, in order to optimize the meshing process.

Figure 12. Lateral view of the adopted domain for the NACIE loop.

To simulate the Heat Source, an appropriate heating volume is introduced; it consists of the fluid pipe volume plus the solid pin volumes (see figure 13); a surface

source on the pin walls was adopted.

An appropriate mesh was constructed for these volumes, as shown in figure 13, structured in the vertical direction with a pitch of 1 cm, as can be noted from figure 14.

For each wall, a boundary layer was created, to improve the performance of the mesh. For the discretization of the overall domain, about 260,000 cells were adopted. A segregated implicit approach has been chosen. A steady state analysis has been performed.

Figure 13. Mesh adopted in the Heat Source; the solid volume (pins) and the fluid volume are depicted.

Concerning the discretization of the governing equations, a first order upwind scheme was adopted for momentum, turbulence kinetic energy, turbulence dissipation rate and energy equations, while a body force weighted scheme was used for interpolating the pressure values. The model adopted for the simulation of turbulence is the RNG k-ε model, with standard wall functions [8] .The RNG k-ε model was derived using rigorous statistical technique (Renormalization Group Theory); it is similar in form to the standard k-ε model, but includes some refinements.

In particular, the RNG theory provides an analytical formula for turbulent Prandtl number ( Prt) (instead of a constant value as in the standard k-ε model), to take in account the experimental evidence indicating that the Prt varies with the molecular Prandtl number and turbulence; in fact, it is know that an accurate expression of the Pr_t is very important in simulating turbulent heat transfer in liquid metal flow [8] [9] [10] [11] [12].

Moreover, the RNG and standard k-ε models are isotropic [9] [10] [11]; as such, they cannot reproduce the secondary flows occurring in the flow channels with non circular cross section [10]; in this aim, second order closure turbulence models should be adopted, i.e. Reynolds Stress Model of Speziale (SSG model) [10]

Since the aim of this simulations is to get a preliminary overview of the fluid dynamics behaviour of the NACIE loop, the RNG model was chosen because of its robustness and widespread use, even if it is well know that it is not completely accurate for low molecular Pr numbers [9] [10] [11] [12].

To simulate the turbulent flow regime and heat transfer in the NACIE heating section and heat exchanger, more accurate simulations must be performed, paying greater attention to the meshing process, to the adopted turbulence model and to the evaluation of the turbulent Prandtl number.

Concerning the heat exchanger, its secondary side was not simulated; to take in account the heat sink, a cooled surface was simulated on the HX boundary wall.

A sensitivity analysis on the mesh was performed, changing the number of volumes (90,000 – 300,000) and the discretization schemes adopted for each section. The one here described (about 260,000 volumes) provided the best performances in terms of CPU time and insensitivity of the solution from the number of adopted cells.

Concerning the adopted discretization, the adopted mesh showed wall y+ values in accordance with the values suggested by the theory for the turbulence model (ref. value: 30-300).

The results carried out by the numerical simulation show a good agreement with the preliminary analytical evaluation.

In figure 15, the contours of the velocity in the outlet section (hottest section) of the NACIE heater are plotted. The maximum velocity inside the HS is about 0.4 m/s. The LBE flow rate computed by the FLUENT code is 7 kg/s, while the analytical estimated value is 6.4 kg/s (evaluated taking in account the expansion vessel pressure loss contribution).

Figure 15. Velocity contours in the outlet section of the NACIE HS, [m/s]

In figure 16, the contours of the temperature in the outlet section (hottest section) of the NACIE heater are plotted. The maximum temperature calculated on the pin walls is 371 °C.

The ∆T between the inlet and the outlet sections of the heater is 29.6 K evaluated by the code, while the one calculated analytically is 32.7 K.

5-3.4 HEAT EXCHANGER DESIGN

The Heat Exchanger designed for the NACIE loop is a “tube in tube”, counter flow type; the secondary fluid is water at low pressure (about 1.5 bar).

The Heat Exchanger is made by three coaxial tubes with different thicknesses (fig.17); the dimensions of tubes are reported in table 6.

Inner Pipe Middle Pipe External Pipe

Inner Diameter [mm] 62.68 84.9 102.3

Outer Diameter [mm] 73 88.9 114.3

Thickness [mm] 5.16 2.0 6.02

Length [mm] 1500 1500 1500

Material AISI 304 AISI 304 AISI 304

Table 6 . NACIE Heat Exchanger Pipes Dimension

LBE flows downward into the internal pipe, while water flows upwards into the annulus between the middle and external pipes (see fig.17).

The annulus created by the internal and middle pipe, that has a width of 5.95 mm, is filled by stainless steel powder. The aim of this powder gap is to guarantee the thermal flux towards water, since it has a good thermal conductivity, mitigating at the same time the thermal stresses on the pipes due to the differential thermal expansion along the axis during the operation.

In fact, the three pipes are welded together in the lower part by a plate, while in the upper part only the middle and external pipe are constrained together. In this way the internal pipe has no axial constraints with the HX and axial expansion is allowed.

The annulus containing the powder is closed on the top by a “stopper” made by graphite, in order to avoid the powder leakage.

Finally, on the external pipe an axial expansion joint is installed to compensate the different axial expansion between the middle and external pipe (see fig. 18 )

Figure 17 . Scheme of the NACIE Heat Exchanger

Figure 18. View of the expansion joint installed on the NACIE heat exchanger

Moreover, the powder gap allows reducing the thermal gradient through the thickness of the pipes; in fact, its thermal resistance is about the 30-50% of the overall one.

In the following, the thermal hydraulic design for the HX is illustrated, assuming a thermal duty of 30 kW; it is the case of the low flux bundle under the natural circulation flow regime.

The main parameters characterizing the NACIE-HX are reported in table 7.

For the HX design, the method of the logarithmic mean temperature was applied, by the following equation [13]:

th HX

Q = ⋅ ⋅S U F ⋅LMTD (38)

where:

 S: exchanger surface [m2];

 LMTD: logarithmic mean temperature difference [K];  U: overall heat transfer coefficient [W/m2 K];

 FHX: LMTD correction factor [-].

For a pure counter flow heat exchanger type, the LMTD can be evaluated as:

(

)

1 LBE in, wat out, 365 61 304

T T T C

∆ = − = − = ° (40)

1 LBE out, wat in, 335 35 300

T T T C

∆ = − = − = ° (41)

so, for the NACIE HX (see table 7) it is possible to get:

(

)

 Fluid Lead Bismuth Eutectic

 Inlet Temperature [°C] 365  Outlet Temperature [°C] 335  Flow Rate [kg/s] 7  Average velocity [m/s] 0.2 Secondary Side  Fluid Water

 Working Pressure [bar] 1.2-1.5

 Inlet Temperature [°C] 35

 Outlet Temperature [°C] 61

 Flow Rate [kg/s] 0.27

 Average Velocity [m/s] 0.14

Table 7 : NACIE Heat Exchanger Parameters adopted under the natural circulation flow regime with installed the low flux bundle

Considering that NACIE HX is a pure counter-flow one, for the correction factor F_HX a value equal to 1 is assumed [13].

To assess the overall heat transfer coefficient, U , it is necessary to evaluate the convective heat transfer coefficient for the LBE-side, hLBE, and for the water-side, hwat.

LBE-side (primary side)

For the LBE-side, the Maresca-Dwyer Correlation [12] is adopted: 0.8

5.0 0.025

*u= + Pe (42)

Since the average temperature of the LBE along the HX is 350 °C, the following value for the thermal and physical properties of the liquid metal are assumed:

3 10271.2 kg/m LBE

ρ

κ

µ

µ

κ

The LBE velocity inside the tube is

0.22 / LBE LBE HX M w m s A

ρ

and being the hydraulic diameter

, 62.7 mm h HX

D =

it is possible to estimate the Reynolds number as follows: , Re_HX LBE LBE h HX 8.5 4 LBE w D E

ρ

µ

(

)

and applying the Maresca correlation (see eq.(42)), it is possible to estimate the Nusselt number:

14 *u =

Finally, the convective heat transfer coefficient for the LBE side is evaluated as

2 , W 2905 m LBE LBE LBE h shell *u h D K

κ

Water-side (tube side)

For the water-side, the Gnielinski or the Seider and Tate correlations [4] are adopted to estimate the convective heat transfer coefficient; the choice among them is made on the basis of the flow regime (Reynold Number) inside the water annulus.

Gnielinski Correlation [4]

(

)

(

)

(

)

Seider and Tate Correlation [4]

0.14 0.38 1.86 Re Pr Pr 0.7 Re 2100 b D D w D D *u L

µ

µ

For water, because the predicted average temperature is 48°C, the following value for the thermal and physical properties of the coolant are assumed:

3 989 kg/m wat

ρ

κ

µ

31.34 mm Inner Radius of the Inner Pipe 36.50 mm Outer Radius of the Inner Pipe 42.45 mm Inner Radius of the Middle Pipe 44.45 mm Outer Radius of the Middle Pipe 51.13 mm Inner Ra r r r r r = ⇒ = ⇒ = ⇒ = ⇒ = ⇒ 6

dius of the External Pipe 57.15 mm Outer Radius of the External Pipe

r = ⇒

the water flow area is

(

)

5 4 2006 mm

wat

and the wetted perimeter is

(

)

, 2 5 4 600.5 mm w wat

P =

π

The water velocity and the hydraulic diameter are respectively:

0.14 m/s wat wat wat wat M w A

ρ

The Prandtl number for the water is:

Pr wat wat 4.8 wat wat Cp

ρ

κ

and the Reynolds number inside the annulus is: ,

Rewat wat wat h wat 2500

wat

w D

ρ

µ

= = (47)

As it can be noted, the flow inside the water annulus is laminar, and the correlation (44) will be applied, obtaining:

0.05 f = (48) 15 wat *u = (49) obtaining: 2 , 717 W/m wat wat wat h wat *u h K D

κ

Global Heat Transfer Coefficient

To evaluate the global heat transfer coefficient, U, the following equation is adopted:

(

)

(

)

(

)

LBE wall inner powder wall middle wat

U r r r r r r r r r r h

κ

κ

κ

Equation (51) is referred to the internal radius r of the inner pipe, while ₁

κ

κ

κ

By applying an iterative process to solve equation (51), it is possible to get: 2

405 W /

having as average operating temperature for the inner wall, middle wall and powder gap respectively: , , 290 230 173 wall inner powder wall middle T C T C T C = ° = ° = °

From equation (38), the exchanger surface is evaluated: 2 0.25 m th HX Q S U F LMTD = = ⋅ ⋅ (52)

and so the needed length required for the HX is:

1 1.25 m 2 HX S L r π = = (53)

When the procedure above described is applied to the system when the high flux bundle is installed, and the LBE circulation is promoted by the gas lift (see table 9-8 ), it is possible to obtain the following results.

Thermal Duty [kW] 51.5

Primary Side

 Fluid Lead Bismuth Eutectic

 Inlet Temperature [°C] 361  Outlet Temperature [°C] 339  Flow Rate [kg/s] 16  Average velocity [m/s] 0.5 Secondary Side  Fluid Water

 Working Pressure [bar] 1.2-1.5

 Inlet Temperature [°C] 35

 Outlet Temperature [°C] 53

 Flow Rate [kg/s] 0.7

 Average Velocity [m/s] 0.35

Table 9 : NACIE Heat Exchanger Parameters adopted under the gas enhanced circulation flow regime with installed the high flux bundle

So the heat exchanger of NACIE allows to perform the planned tests, both with low flux bundle and high flux bundle. The parameters adopted to change the performance of the HX are the water flow rate and average temperature.

To run test with Lead, which strongly increases the LMTD, a different powder with a lower thermal conductivity will be adopted.

LBE Primary Side

Correlation Eq. (42)  Average Temperature 350°C  Pr 0.018  Re 2E+5  Pe 3600  Nu 22.5  hLBE 4700 W/m 2 K

Water Secondary Side

Correlation Eq. (44)  Average Temperature 44°C  Pr 5.2  Re 6E+3  F 0.04  Nu 42.3  hwat 2000 W/m 2 K Global Heat Transfer Coefficient 572 W/m2 K

, wall inner T 290°C powder T 195°C , wall middle T 113°C S 0.29 m2 LHX 1.48

Table 10 Design Parameters for the NACIE HX with installed the high flux bundle, under the enhanced circulation flow regime.

5-4. TEST MATRIX

The test matrix for the NACIE activities has been defined; for each planned test the main operating parameters of the loop, as well as the aim of the tests are summarised hereafter.

1. Characterization of the enhanced circulation.

The tests will be performed in isothermal conditions, without thermal power supply by the bundle; in this first phase the high flux bundle will be installed.

The aim of this tests is to obtain a preliminary characterization of the hydraulic behaviour of the loop under gas-injection enhanced circulation, in order to define the test parameters to be adopted for the high flux bundle characterization.

The tests will be performed at different value of the LBE average temperature ( 250°C, 300°C, 350°C) and for different value of the argon injection flow rate in the riser (1-75 Nl/min).

2. Characterization of the high flux bundle.

The test will be performed under full power conditions (50 kW), promoting the LBE flow rate by the gas lift technique: a LBE flow rate of 16 kg/s is expected.

The average temperature will be 350 °C (similar to the conditions envisaged in ICE), and in the first phase of the tests, a long term (about 1 month) steady state condition will be simulated on the bundle.

Then several thermal cycles will be performed, in order to stress both the hot part and the cold part of the pins. In the first part of the tests, the air flow rate adopted to cool the cold part of the pins will be kept constant. Later on several thermal cyclea will be performed, stopping the air flow rate adopted to cool the cold part of the pins.

The aim of this test is to obtain a thermal and mechanical characterization of the prototypical pins to be adopted for the ICE bundle.

At the end of the tests, a choice between the A-type and B-type pins will be made, allowing to start with the construction of the ICE bundle.

3. Characterization of enhanced circulation.

The tests will be performed installing the low flux bundle.

The aim of these tests is to obtain a characterization of the enhanced circulation in a HLM loop. The isothermal tests will be performed at different values of the LBE average temperature (250 °C, 300 °C, 35 0°C) and for different values of the argon injection flow rate in the riser (1 - 75 Nl/min).

Later on, full power tests (30 kW) will be performed adopting an average LBE temperature of 350°C.

4. Characterization of natural circulation.

The tests will be performed installing the low flux bundle.

The aim of this tests is to obtain a characterization of the natural circulation in a HLM loop.

The tests will be performed under full power condition, adopting different value of the average LBE temperature (250 °C, 300 °C, 350 °C).

5-5. Preliminary Experimental Results

In order to test the Data Acquisition System, Control System, Power Supply System, as well as to start the pins qualification, experimental tests have been performed on the NACIE facility, promoting the natural circulation flow regime.

In the preliminary test, only one pin, type B (see chapter 4), has been used inside the heating section, with a nominal power of 25 kW.

The Power Supply System has been successfully tested, as reported in figure 19, where the trend of the voltage and the current adopted to supply the pin is reported.

Figure 19 . Voltage and Current on the pin type-B

As it can be noted, the average voltage across the pin is 297 V, while the average current is about 74 A; by these values, in can be calculated that the electrical power supplied to the system is about 23.5 kW, nearly 95% of the nominal power. The time trend of the electrical power supplied to the heater is depicted in figure 20.

The test has been run supplying the power to the heat source by the activation of the pin.

The thermal difference arising between the inlet and outlet section of the heat source increases, thus promote the LBE natural circulation, which allows for the mixing of the HLM along the loop.

When an average temperature of about 350°C is achieved along the heat source, the air cooler installed in the secondary loop is started and the water flow rate is set to the nominal value.

During the transient the secondary pump is active, to avoid the boiling of water inside the heat exchanger, even if the flow rate is set at a value much lower than the nominal one.

Figure 20 . Electrical Power supplied to the loop, by the pin type-B.

In figures 21 and 22 the time trend of the LBE temperature at the inlet and the outlet section of the Heat Source and of the Heat Exchanger, are plotted. As it can be noted, after about 5000 seconds from the start of the experiment, a steady-state condition is achieved.

In figure 23 the water temperature under the steady state condition obtained for the preliminary test is reported. As shown in figure 24, across the Heat Source the LBE undergoes an increase in temperature of about 33°C, while the thermal difference through the HX is about 31°C.

This slight difference is mainly due to the heat losses through the expansion vessel (partially insulated) placed at the top of the facility, where a large inventory of LBE is placed.

Figure 21. LBE Temperature time trend at the Inlet and Outlet Section of the HS

Figure 23. Inlet and outlet temperature of water inside the Heat Exchanger.

Figure 25 . LBE flow rate calculated by an energy balance through the HS

Though the ultrasonic flow meter is not yet installed along the NACIE loop, an estimation of the LBE flow rate under steady state condition could be made applying an energy balance across the heat source, as in the following:

, , th HS *C LBE HS *C Q M Cp T = ∆ ɺ ₍₅₄₎

As it can be noted in figure 25, the estimated flow rate is about 5.5 kg/s, which matches very well with the value of that can be calculated by the equation (34):

1 2 3 2 , , , 2 eff _{th HS} 5.4 kg/s eff *C LBE HS A M gH Q Cp K ρ β  _{ }  = _{ }  =       ɺ

Moreover, as reported in the figure 24, the thermal difference through the HS is about 33°C, which well matches with the analytical estimate of 30°C.

The preliminary tests, performed to qualify the ancillary system as well as the pins behaviour, will be continued after the installation of the ultrasonic flow meter. Later on, the tests will be performed as indicated in the test matrix, as above reported, starting with the gas enhanced circulation characterization.

5-6. References

[1] Report ENEA ET-F-S-001, “Test Specification of the Integral Circulation Experiments (ICE)- DEMETRA D 4.15 (task4.5.3) ”, G Scaddozzo, M. Tarantino, 2006.

[2] Tarantino M., De Grandis S., Benamati G., Oriolo F., “Natural Circulation in a Liquid Metal One Dimensional Loop” Journal of Nuclear Materials 376, 2008, 409-414.

[3] Na and NaK Handbook, Liquid-Metal Heat Transfer, O.E. Dwyer, Brookhaven National Laboratory, Upton, New York, 1970.

[4] N. E. Todreas, M. S. Kazimi, Nuclear System II, Elements of Thermal Hydraulic Design, Taylor & Francis, 2001

[5] R. W. Lockart, R. C. Martinelli, “Proposed correlation of data for isothermal two-phase two-component flow in pipes”, Chem. Eng. Prog. 45:no. 39, 1949.

[6] I.E. Idelchick, Handbook of Hydraulic Resistance, 3rd Edition, Begell House.

[7] Pfrang W., Struwe D., “Assessment of Correlations for the Heat Transfer to the Coolant for Heavy Liquid Metal Cooled Core Designs” Forschungsentrum Karlsruhe, FZKA 7352, October 2007.

[8] FLUENT 6.2 User’s Guide, January 2005

[9] G. Grotzbach, Turbulence Modelling Issues in ADS Thermal and Hydraulic Analysies. IAEA Technical meeting on Theoretical and Experimental Studies of Heavy Liquid Metal Thermal Hydraulics, Karlsruhe, Germany, 2003

[10] X. Cheng, N.I. Tak, CFD Analysis of thermal-hydraulic behaviour of heavy liquid metals in sub-channels, Nuclear Engineering and Design 236 (2006), 1874-1885 [11] X. Cheng, N.I. Tak, Investigation on turbulent heat transfer to lead-bismuth eutectic

flows in circular tubes for nuclear applications, Nuclear Engineering and Design 236 (2006), 385-393

[12] O.E. DWYER, Na and NaK Handbook, Liquid-Metal Heat Transfer, Brookhaven National Laboratory, Upton, New York (1970).