3 SIMMER-III CODE OVERVIEW

3 SIMMER-III CODE OVERVIEW

SIMMER-III is a two-dimensional, multi-velocity field, multi-phase, multi-component, Eulerian, fluid-dynamics code coupled with a structure model (fuel pin) and a space- time and energy-dependent neutron kinetics model. The conceptual overall framework of the code is shown in Fig. 3.1. The fluid-dynamic portion, which constitutes about two thirds of the code, is interfaced with the structure model through heat and mass transfer at structure interfaces, while the neutronics portion provides nuclear heat sources based on the mass and energy distributions calculated by the other code elements [1].

The basic geometric structure of SIMMER-III is a two-dimensional R-Z system (Fig. 3.2), although optionally an X-Z system can be also used for various fluid-dynamics calculations.

Fig. 3.1 – SIMMER-III overall code structure (Ref.[1]).

3.1.1 Code features

The SIMMER-III code models five basic LMFR core materials. For each one the operator

can choose a different sub material already implemented in the code. Moreover, the

material can exist as different physical states, so the user can choose between 7 different

phases. Thus, the material mass distributions are modeled by 30 density components in

the current version of SIMMER-III, 12 for solid phase, 13 for liquid phase and 5 for vapor

phase. The energy distributions are modeled by only 16 energy components since some

density components are assigned to the same energy component, 9 for solid phase, 7 for

liquid phase and only 1 for the vapor phase.

Fig. 3.2 – SIMMER-III geometric framework (Ref.[1]).

3.1.2 Fluid-dynamics and FCI models

The fundamental equations of the fluid dynamics are based on a so-called multi-fluid model in SIMMER-III. Material density and energy component distributions are obtained through mass, momentum, and energy conservation equations:

• Mass equation

𝜕𝜌̅ _𝑚

𝜕𝑡 + ∇ ∙ (𝜌 ̅̅̅̅𝑣 _𝑚 ⃗⃗⃗⃗ ) = −𝛤 _{𝑞 𝑚} (3.1)

• Momentum equation

𝜕𝜌̅ _𝑚 𝑣 ⃗⃗⃗⃗ _𝑞

𝜕𝑡 + ∑ ∇ ∙ (

𝑚∈𝑞

𝜌 _𝑚

̅̅̅̅𝑣 ⃗⃗⃗⃗ 𝑣 _𝑞 ⃗⃗⃗⃗ ) + 𝛼 _{𝑞 𝑞} ∇𝑃 − 𝜌̅ _𝑔 𝑔 + 𝐾 _𝑞𝑠 𝑣 ⃗⃗⃗⃗ − ∑ 𝐾 _{𝑞 𝑞𝑞} ^′ (

𝑞 ^′

𝑣 _𝑞 ^′

⃗⃗⃗⃗⃗ − 𝑣 ⃗⃗⃗⃗ ) − 𝑉𝑀 _𝑞 ⃗⃗⃗⃗⃗⃗⃗⃗⃗ _𝑞

= − ∑ 𝛤 _𝑞𝑞 ^′

𝑞 ^′

[𝐻(𝛤 _𝑞𝑞 ^′ )𝑣 ⃗⃗⃗⃗ + 𝐻(−𝛤 _{𝑞 𝑞𝑞} ^′ )𝑣 ⃗⃗⃗⃗⃗ ] (3.2) _𝑞 ^′

• Energy equation

𝜕𝜌̅ _𝑀 𝑒 _𝑀

𝜕𝑡 + ∑ ∇ ∙ (

𝑚∈𝑀

𝜌 _𝑀

̅̅̅̅𝑒 _𝑀 𝑣 ⃗⃗⃗⃗ ) + 𝑃 [ _𝑞 𝜕𝛼 _𝑀

𝜕 _𝑡 + ∇ ∙ (𝛼 _𝑀 𝑣 ⃗⃗⃗⃗ )] _𝑞

− 𝜌̅ _𝑀

𝜌̅ _𝑞 [∑ 𝐾 _𝑞𝑞 ^′

𝑞 ^′

(𝑣 ⃗⃗⃗⃗ − 𝑣 _𝑞 ⃗⃗⃗⃗⃗ )(𝑣 _𝑞 ^′ ⃗⃗⃗⃗ − 𝑣 _𝑞 ⃗⃗⃗⃗⃗⃗⃗ ) − 𝐾 _𝑞𝑞 ^′ _𝑞𝑠 𝑣 ⃗⃗⃗⃗ (𝑣 _𝑞 ⃗⃗⃗⃗ − 𝑣 _𝑞 ⃗⃗⃗⃗⃗ ) − 𝑉𝑀 _𝑞𝑠 ⃗⃗⃗⃗⃗⃗⃗⃗⃗ (𝑣 _𝑞 ⃗⃗⃗⃗⃗ − 𝑣 _𝑞 ^′ ⃗⃗⃗⃗⃗⃗ ) _𝐺𝐿

= 𝑄 _𝑁,𝑀 + 𝑄 _{𝑀𝐹,𝑀} + 𝑄 _{𝑉𝐶,𝑀} + 𝑄 _{𝐻𝑇,𝑀} (3.3)

where m, q (or q ^’ ), and M denote the components of density, velocity, and energy, respectively; 𝜌̅, α, 𝑣 , e, and 𝛤 represent macroscopic (smeared) density, volume fraction, velocity, specific internal energy, and mass transfer rate, respectively; P, t, 𝑔̅, and H(x) are pressure, time, gravity, and Heaviside unit function, respectively; 𝐾 _𝑞𝑠 is the momentum exchange function between q and q ^’ , respectively; 𝑄 _𝐻𝑇 , 𝑄 _𝑀𝐹 , 𝑄 _𝑁 and 𝑄 _𝑉𝐶 are rates of energy interchange due to heat transfer, melting/freezing, nuclear heating rate (not present in this case), and vaporization/condensation, respectively; and, finally, 𝑉𝑀 ⃗⃗⃗⃗⃗⃗⃗⃗⃗ _𝑞 and 𝑉𝑀 ⃗⃗⃗⃗⃗⃗⃗⃗⃗ (𝑣 _𝑞 ⃗⃗⃗⃗⃗ − 𝑣 _𝑞 ′ ⃗⃗⃗⃗⃗⃗ ) are virtual mass terms in momentum and internal energy _𝐺𝐿 equations, respectively.

The interfacial area convection model improves the flexibility of SIMMER-III by tracing transport and history of interfaces, and thereby better represents physical phenomena.

Ishii [2] proposed a convection equation for the interfacial areas per unit volume in a general form:

𝜕𝐴 _𝑀

𝜕𝑡 + ∇ ∙ (𝑣 𝐴 _𝑀 ) = ∑ 𝑆 _𝑀,𝑘

𝑘 (3.4)

where A M is the interfacial area of component M per unit volume and S M,k denotes the source terms of the interfacial area.

In SIMMER-III there are two different types of interfacial area [3]:

• A i : convectible interfacial area (areas associated to moving energy components), assigned to each component;

• a i : binary contact areas, through which the heat and mass exchange occurs. This area is determined from A i and the flow regime.

During a FCI process, a multi-phase flow state may change from single phase (liquid) to a high void fraction regime. In SIMMER-III, multiple flow regimes are modeled for both pool flow and channel flow [3].

The flow regime model is one of the important constitutive models for numerical simulation of multiphase flows. The flow regime representation is rather simple. As shown in Fig. 3.3, bubbly, dispersed and in-between transition regimes are modeled for the pool flow; the upper limit of the bubbly regime and the lower limit of the dispersed regime are defined by user-specified void fractions 𝛼 _𝐵 and 𝛼 _𝐷 , respectively, with typical values being 0.3 and 0.7. In SIMMER-III flow regime modeling, it is generally assumed that a cell consists of two local regions, bubbly and dispersed regions, as shown in Fig.

3.4.

Fig. 3.3 – Pool flow regime map in SIMMER-III (Ref.[1]).

Fig. 3.4 – Schematic concept of separating bubbly and dispersed regions (Ref.[1])

For what concern the channel flow regime, the model is the same but it is more complicate due to the effect of the structure, as shown in Fig. 3.5.

Fig. 3.5 – Channel flow regime map in SIMMER-III.

The change of interfacial areas due to the processes of fragmentation, flashing, turbulence-driven breakup, coalescence, and droplet or bubble production are treated as “source terms” in the interfacial area convection equation.

After determining flow regime, IFAs and consequently binary interfacial areas, momentum exchange equation has to be resolved, before resolving intra-cell mass and energy transfer equations. Then, the heat transfer coefficients (HTCs) between fluids are required to perform the heat- and mass-transfer calculations. The last step is to solve the conservation equations without convection for intra-cell heat and mass transfer, including non-equilibrium process such as Melting/Freezing and Vaporization/Condensation, coupled with the Equation of State (EOS) [4].

A comprehensive and systematic program of code assessment [5] was conducted in two steps: phase 1 for fundamental assessment of individual code models and phase 2 for integral code assessment. The scope of the latter phase was to find key accident phenomena, directly relevant to the CDA analysis, and include boiling pool dynamics, fuel relocation and freezing, material expansion, Fuel Coolant Interactions (FCI), and disrupted core neutronics.

Concerning the FCI, Morita et al. [6] analysed a series of experiments and performed SIMMER-III simulations to validate and assess the code.

Recently, a code assessment campaign for the application of CCI to the interaction between HLM and water was performed by ENEA/Università di Pisa [7]-[12].

On the basis of all these considerations, the availability of tools for simulating the overall interaction in its complexity is very limited because most of them are strictly focused on simulating a single aspect of the entire interaction process. Despite of this, SIMMER-III may be considered one of the most complete and flexible codes for dealing with liquid metal-coolant interaction, being able to simulate pressure trends, pressure peaks and wave propagation during a FCI transient. However, the current version of the code is not able to simulate the chemical reaction between lithium lead and water, therefore it is necessary to implement and validate a new code model, as illustrated in the next section.

3.1.3 Implementation of the chemical model in SIMMER-III code

The original chemical model has been modified to manage the PbLi/water chemical reaction [14] and the modifications have been made in SIMMER-III Ver. 3F of the code [15]. Two different equations are considered and implemented in the source code [16]:

𝑃𝑏 ₈₃ 𝐿𝑖 ₁₇ + 8.5𝐻 ₂ 𝑂 → 8.5𝐿𝑖 ₂ 𝑂 + 8.5𝐻 ₂ + 83𝑃𝑏 + 19.0 𝑘𝐽

𝑚𝑜𝑙 𝑃𝑏𝐿𝑖 (3.5) 𝑃𝑏 ₈₃ 𝐿𝑖 ₁₇ + 17𝐻 ₂ 𝑂 → 17𝐿𝑖𝑂𝐻 + 8.5𝐻 ₂ + 83𝑃𝑏 + 25.8 𝑘𝐽

𝑚𝑜𝑙 𝑃𝑏𝐿𝑖 (3.6) 3.1.4 Code verification and validation

After the implementation of the chemical reaction model, a verification phase for code

has been addressed, verifying the correct behaviour in calculation performances. Making

use of BFCAL tool [19] for post processing of calculations, it is possible to obtain the

errors between the theoretical and calculated value of hydrogen mass. A simple simulation with SIMMER-III code has been addressed and the results, in terms of material composition, are illustrated in Fig. 3.6. If we take into account Li 2 O product, the considered reaction is the first and the maximum error obtained is 0.32%;

𝜀 = 𝑥 _𝑆𝐼𝑀 − 𝑥 _𝑇𝐻

𝑥 _𝑇𝐻 ∗ 100 = 0.32%

(3.7) if the reaction considered produces LiOH, maximum code error is -0.55%.

𝜀 = 𝑥 _𝑆𝐼𝑀 − 𝑥 _𝑇𝐻

𝑥 _𝑇𝐻 ∗ 100 = −0.55%

(3.8)

Fig. 3.6 – Material composition at the end of simulations.

A validation campaign of the code against LIFUS5 tests has been performed in ENEA Brasimone. Results of reference calculation are briefly explained in the following and compared with experimental data. Reaction vessel of facility can be modelled as in Fig.

3.7.

Fig. 3.7 – SIMMER-III nodalization of LIFUS5 reaction vessel.

Transient can be divided into four main phases, and these are shown in Fig. 3.8 (for sake of brevity only pressure trend is reported).

Fig. 3.8 – Pressure trends of reference case in reaction vessel.

Specific outcomes from the reference post-test analyses of the LIFUS5 Test#8 by are outlined below:

• During Phase 1, SIMMER-III code predicts very well the first pressure peak due to

water flashing. The pressure trend is qualitatively in line with the experimental

results, even though the pressure increase rate are overestimated. Some differences

occur during Phase 2; indeed, the code calculates an anticipated onset of S5 pressurization. The fragmentation and jet-breaking model affect the behavior.

• The code results are satisfactory also during Phase 3. The pressures calculated by the code align with the injection pressure imposed as PT3. Differences less than 10 bar are due to the code modeling choices and unavoidable assumption and simplifications. However, the code results are perfectly aligned with the experimental trends. Moreover, it worth pointing out that differences of about 5 bar are recorded also by PT themselves. The PT3 trend is probably affected by its position in the injection line and by the possibility of PbLi falling, while the PT in S1 vessel are probably affected by the reset which was not done before the experiment.

• From the qualitative behavior of the temperature trends, SIMMER-III reasonably predicts the experimental results. Indeed, the code correctly predicts the zones where the temperatures are higher, i.e. the expansion vessel and the zone 1 of the mock-up.

However, the temperatures are underestimated in S1 and overestimated in S5. The likely reasons for the discrepancy are due to the U-tube modeling and fragmentation:

1) not modeling the elbow curve, the water jet is easily transported towards S5 reacting with PbLi in the expansion vessel, 2) not modeling the U-tube curves, the fragmentation is lower diminishing the interfacial area between the fluids and therefore the interaction/reaction itself.

Due to the poor accurateness of the test procedures, the validation of the code is not exhaustive on this experimental campaign; as example, the injected mass of water is calculated by experimentalists a posteriori because direct measurement is not available.

The values have been reviewed and more realistic quantification is derived thanks the code simulations. Then, a verification of the code prediction has been evaluated by means of theoretical considerations.

Nevertheless, the calculations permitted to improve the knowledge of tests procedure and tests operating conditions (i.e. the injected pressure trend and the pressure at which the injector cap breaks do not correspond to the design specifications).

The correct knowledge of initial and boundary conditions largely affects the SIMMER-III code results. However, the code has demonstrated promising capability in predicting phenomena connected with PbLi/water interaction, considering also the chemical reaction and the hydrogen production.

Therefore, it is necessary to design the new LIFUS5/Mod3 campaign, in order to obtain reliable data and complete the validation phase of the code.

3.1.5 Implementation of PbLi properties in SIMMER-III code

Properties and the correlations of the PbLi in SIMMER code are preliminary and based on CEA data used in [17], while the properties of the lithium compounds were set with the available information (Perry’s chemical handbook [18]) starting from the properties of the sodium compounds [13].

EOS properties of PbLi alloys are directly implemented in SIM05 input file under the

XEOS flag.

Past and recent studies have been carried out in order to determine the most important properties of this compound, but also nowadays the discrepancy between these studies are in some cases very consistent. It is therefore necessary to make extensive studies on this argument in near future to “level” every calculation made using this kind of alloy; for sake of completeness are here reported some of the most important properties of Pb 83 Li 17 alloy, according to available references [20].

PROPERTY EXPRESSION RANGE [K] ERROR SCATTERING

Density [kg/m ³ ] ρ(17.0 at. % Li)

= 10520.35 − 1.19051

∗ T[K]

508-880 0.3% 4.39%

Specific heat [J/(g*K)]

cp(16.8 at. % Li)

= 0.195 − 9.116 ∗ 10 ⁻⁶

∗ 𝑇[𝐾]

508-800 ±3%* 31.39%

Thermal diffusivity [cm ² /s]

α(17.0 at. % Li) = 3.46 ∗ 10 ⁻⁴ ∗ 𝑇[𝐾] − 1.05 ∗ 10 ⁻¹

508-773 ≤ 5∙10 ^-3 cm ² /s*

37.35%

Thermal conductivity [W/(cm*K)]

λ (17.0 at. % Li)

= 0.1451 + 1.9631

∗ 10 ⁻⁴ ∗ T [°C]

508-873 n.d. 37.72%

Dynamic viscosity [mPa*s]

μ (16.8 at. % Li)

= 0.187 ∗ 𝑒 11640 R∗T[K]

508-625 n.d. 14.75%

Volumetric thermal expansion coefficient [K ^-1 ]

β(17.0 at. % Li)

= (11.221 + 1.531

∗ 10 ⁻³ ∗ T [K]) ∗ 10 ⁻⁵

508-880 3% 49.41%

Tab. 3.1 – Suggested PbLi properties (Ref.[20]).

3.2 References

[1] S. Cheng et al., SIMMER-III Analyses of Local Fuel-Coolant Interactions in a Simulated Molten Fuel Pool: Effect of Coolant Quantity, Science and Technology of Nuclear Installations, Article ID 964327, 2015.

[2] M. Ishii and N. Zuber, Drag coefficient and relative velocity in bubbly, droplet or particulate flows, AICHE Journal 25(5) pp. 843-855, 1979.

[3] D. Wilhelm, AFDM: an advanced fluid-dynamics model Volume II: topologies, flow regimes, and Interfacial areas, LA-11692-MS-Vol.2, 1990.

[4] AA.VV., AFDM: an advanced fluid-dynamics model Volume VI: EOS-AFDM interface, LA-11692-MS-Vol.6, 1994.

[5] S. Kondo, W. Maschek, et al., Current status and validation of the SIMMER-III LMFR safety analysis code, 7th International Conference on Nuclear Energy, ICONE-7249, 1999.

[6] K. Morita, et al., SIMMER-III applications to fuel-coolant interactions, Nuclear Eng.

Des., 189 (1999) 337-357.

[7] A. Ciampichetti, et. al., Experimental and computational investigation of LBE-water interaction n LIFUS5 facility, Nuclear Eng. Des., 239 (2009), pp. 2468-2478.

[8] A. Ciampichetti, et. al., LBE-water interaction in LIFUS5 facility under different operating conditions, Journal of Nuclear Materials, Vol. 415 Issue 3 (2011), pp. 449- 459.

[9] A. Pesetti, et. al., Experimental investigation and SIMMER-III code modelling of LBE- water interaction in LIFUS5/Mod2 facility, Nuclear Eng. Des., 290 (2015), pp. 119- 126.

[10] A. Pesetti, et. al., Water/Pb-Bi Interaction Experiments in LIFUS5/Mod2 Facility Modelled by SIMMER Code, 22 ^nd International Conference on Nuclear Engineering, Vol. 3, Prague, Czech Republic, July 7–11, 2014.

[11] A. Del Nevo, et. al., Addressing the heavy liquid metal – Water interaction issue in LBE system, Progress in Nuclear Energy, June 2015.

[12] A. Del Nevo, et. al., Experimental and Numerical Investigations of Interaction between Heavy Liquid Metal and Water for supporting the Safety of LFR Gen. IV Reactor Design, Proc. of the NURETH-16, Log Number: 13807 Hyatt Regency Chicago, Chicago, IL, USA, Aug. 30-Sept. 4, 2015.

[13] AA.VV., SIMMER-SW, Japan Nuclear Fuel Development Institute, JNC TJ9440 99- 009, 1999.

[14] M. Eboli, N. Forgione, A. Del Nevo, Implementation of the chemical PbLi/water reaction in the SIMMER code, Fusion Eng. Des. 109-111 (2016) 468-473.

[15] AA.VV., SIMMER-III (Version 3.F) Input Manual, O-arai Engineering Center, Japan Nuclear Cycle Development Institute, May 2012.

[16] K.A. McCarthy, Safety issues related to liquid metals, APEX meeting, Albuquerque,

July 1998.

[17] C. Blanchard, Modelling of the Lithium-lead / water interaction, improvement of the kinetics of the pressure evolution, CEA H0-200-5010-3090.

[18] R.H. Perry, D.W. Green, Perry’s chemical engineers’ handbook 8 ^th ed., McGraw-Hill, 2007.

[19] AA.VV., bfcal (Ver.4.5) manual, May 2012.

[20] A. Venturini, D. Martelli, Literature review of PbLi alloys properties, ENEA internal report, 2017.

[21] K. Kamiyama et al., Development of an evaluation methodology for the fuel- relocation into the coolant plenum in the core disruptive accident of sodium-cooled fast reactors, ICONE ’22, Vol. 3, Pag. 12, July 2014.

[22] H. Yamano et al., SIMMER-III: A Computer Program for LMFR Core Disruptive

Accident Analysis, Version 3.A Model Summary and Program Description, Japan

Nuclear Cycle Development Institute, 2003.