The remaining components of the PCS were modeled using basic Apros process components such as heat exchangers, various valves, pumps, tanks, and turbine elements.

#### *3.3. Small Energy Storage System*

The small ESS has been modeled explicitly featuring the elements described in §2.3. The recirculation line of the discharge pump enabled a soft control of the salt flow rate, where the motor speed is kept at a constant 100%. During the pulse phase, the Control Valve (CV) of the recirculation line is fully open; in dwell, the CV closes, directing the total salt flow to the primary inlet port of the MSSG. In Section 3, it was noted that the salt loop used the homogeneous solution for its TH nodes; nonetheless, due to the uncertainties of auxiliary systems (e.g., geometry, pressure control), the salt tanks have been modeled by boundary conditions where dynamic enthalpy calculations simulated the adequate transient behaviour. The pressure of the tanks was set to 8 bar, providing a reasonable pressure profile over the system. The general parameters of the small ESS model can be found in Table 5, where *mdisch*. refers to the cold pump flow rate (cold tank → MSEH/hot tank) and *mch*. denotes the hot pump flow rate (hot tank → recirc. line/MSSG/cold tank).

**Table 5.** Main steady state parameters of the small ESS in Apros.

#### *3.4. Logics*

Considering power deposition, the reactor model used an asymptotic time-dependent curve for plasma ramps as the boundary condition, simultaneously in the blanket segments and secondary power sources as well.

The PHTS flow control's development is still in progress; the model introduced hereby describes the recent iteration of the logics, which fulfills the established requirements. The control scheme envisages Cold Leg (CL) flow rate modulation according to reactor power with the constraint of the *Tin*,*comp* compressor inlet temperature, that is to keep *Tin*,*comp* as close as reasonably possible to its nominal value. This has been achieved by integrating a recirculation line on each compressor station. As the compressors are running at 100% at all times, this recirculation line adjusts the flow rate that is being sent to the blanket or fed back to the compressor's inlet. Since the compressor power is relatively large (∼11 MWe/pair), an intercooler was also installed on the recirculation lines in the form of a boundary condition. This cooler decreases gas enthalpy in order to prevent the overheating of the machine and the recirculated gas.

On the secondary side, the turbine main control valve was following the reference heat balances' steady-state pressures (123.5↔119.0 bar in pulse↔dwell transitions), as the turbine unload commenced bleed lines took over the preheater line heat exchangers' pressurization from the extraction lines. Bypass lines of the FWHXs, DIV, and VV HXs guaranteed that the primary side average temperatures remained around the pulse phase values. The deaerator pressure was maintained at 3.5 bar throughout the entire operation.

#### **4. Results**

The Apros calculation envelopes two consecutive pulse–dwell cycles with a 1200 s pulse phase at the beginning. The pulse phase is 7200 s including two plasma ramps before and after the pulse period, and the dwell phase lasts 600 s; thus, one full cycle is 7800 s. The figures of §4.1 to 4.3 show this sequence of events with grey areas marking the dwell periods.

#### *4.1. Primary System Behaviour*

The breeding blanket, the lumped curve of DIV, and the VV loops (secondary) are compiled in Figure 7, featuring also pumping power demands and steam turbine gross power.

**Figure 7.** Power trends.

The Loop #1 helium temperatures are depicted in Figure 8, denoting measurements in the hot and cold legs, the collectors, and the compressor inlet. The upper limit for hot leg temperatures was set at 550 ◦C due to the Eurofer creep temperature, while another restriction was defined for the circulator inlet temperature. During transients and dwell, the inlet temperature has to be kept as close as possible at its pulse phase value (296 ◦C). The transient showed that gas temperatures could reach 532–533 ◦C in the HL, yielding a narrow safety margin considering the earlier mentioned limit (HL1 and hot collector trends overlap in Figure 8). The compressor inlet temperature reached 316 ◦C, giving a mild 20 ◦C increase compared to the pulse phase. Since even higher HL temperatures are permissible, the mentioned maximum compressor inlet temperature could be further lowered, should the compressor operation require so.

**Figure 8.** Helium temperatures in the PHTS.

The PHTS pressures showed that during transients, the CL and HL pressures decreased ∼3 bar and ∼1.6 bar, respectively, while no significant change could be observed at the circulator inlet. This indicated that the recirculation line did not induce perturbations

apart from a momentary 0.6 bar depression when the recirculation valve opened at a nominal loop flow rate.

Gas flow rates in the coolant loops varied between 45 kg/s and 229 kg/s; the Loop #1 trends are shown in Figure 9. The ramp-down and ramp-up were rather asymmetric, governed by the thermal inertia of the blanket and steam generators. As for the rampup, the recirculation line throttled gas flow rates in the cold legs in order to ensure low circulator inlet temperatures, still maintaining acceptable HL temperatures. Cold and hot leg flow rates overlap in Figure 9, since in the pulse phase, the recirculation line is closed; in addition, the recirculation line is connected to the compressor suction; hence, the bypassed gas does not appear in the HL trends in dwell.

**Figure 9.** Helium flow rates in Loop #1.

The primary side temperatures of the DIV and VV heat exchangers are compiled in Figure 10, highlighting a notable change in the ΔT values. As the DIV and VV powers shift, from 100% to dwell time levels of ≈1%, the PCS (secondary) side flow rates of the corresponding HXs decrease as the bypass lines are activated. When HeSG chains restarted and flow rates rose in the feedwater collectors, the DIV-CAS and VV outlet temperatures decreased accordingly.

**Figure 10.** Divertor and vacuum vessel HX primary side temperatures.

#### *4.2. Secondary System Behaviour*

The MSL pressure was maintained at 119.0 bar during dwell, while the HP1 inlet pressure varied between 10 bar and 28 bar; the steam side pressures are given in Figure 11. The steam generators represent a substantial source of thermal inertia (∼401 t dry mass/HeSG) aside from the BB heat capacity; eventually, a significant part of the secondary inventory was evaporated; consequently, collapsed water levels decreased in the helices by 95% by the end of dwell. The surplus steam was delivered to the main condenser via the Dump Line (DL) during turbine (un)loading, resulting in a smoother pressure regulation upstream from the turbine. The dump line was closed at the end of the ramp-down period; thus, the HP1 inlet pressure followed strictly the inlet steam flow rate.

**Figure 11.** Steam pressures in the secondary system.

The transient trends showed steam qualities 99% in the collectors. As the fresh steam pressures and temperatures were sufficiently high in the MSL, the bleed lines could maintain hot conditions on the preheater line, as illustrated in Figure 12. During the unloading process, the maximum feedwater temperature *TFH*4,*out* fell ∼15 ◦C, although as flow rates stabilized on the preheater line, the *TFH*4,*out* recovered, and the dwell phase values varied between 230–233 ◦C.

**Figure 12.** Feedwater temperatures in the PCS.

The deaerator collapsed water level varied between 3.0 m and 3.7 m corresponding to an ∼44 m3 inventory displacement between plasma ramps. The pressure control was maintained at 3.5 bar during dwell with a ±0.1 bar margin; thus, no significant disturbance was prompted on the preheater line; the DEA behaviour is depicted in Figure 13 with respect to the mentioned properties. Despite satisfying the PCS pressure control, the collapsed water level resembled notable variation during the transients, and such deviations could be mitigated by tuning the capacities of the DEA/condenser let-down lines and their corresponding logics.

**Figure 13.** DEA pressure and collapsed water level trends.

The Apros cycle net efficiency for the PCS (*ηcy*) in pulse and dwell was calculated as 37.6% and 21.9%, while the overall plant net average efficiency (*ηo*) was 30.7% integrated over one cycle.

#### *4.3. Small ESS Behaviour*

The salt temperatures are depicted in Figure 14a, the electrical heater outlet temperature remained around 500 ◦C within a range of ±4 ◦C, implying that the current control scheme was ample. Due to the small salt tank volume and MSSG warm-up, the cold tank temperature varied by ±5 ◦C. In this layout, each tank has a volume of 418 m3, which is much smaller compared to the 1362 m3 tank volume in the small ESS of the WCLL plant. This disparity in salt inventories already indicates that the HCPB small ESS has indeed a smaller heat capacity compared to its WCLL counterpart. Figure 14b illustrates the molten salt levels with the top of the tanks, the level trends highlight a ±2.7 m and ±2.5 m variation for the hot and cold tank, respectively. The available free volumes above the salt highlight the challenge of future pressure control, albeit that the hereby described trends will assist developers. The results also showed that the minimum salt level at the end of the (dis)charge period yields ∼0.66–1.04 m (18–28% fill level).

**Figure 14.** Temperatures in the small ESS (**a**) and salt levels (**b**).

#### **5. Synopsis**

Modeling efforts and transient analysis were presented considering Apros activities related to the HCPB small ESS configuration of the DEMO. A novel helical coil steam generator was introduced as the primary–secondary side interface with helium as the primary and water as the secondary coolant. The transient simulation, composed of two consecutive dwell–pulse periods, revealed that the HeSG design in its current state is a feasible option with proper gas circulator logics. It was emphasized that the various restraints, with respect to primary system operation, have a profound impact on optimization freedom regarding control logics, moreover on the PCS behaviour. The power conversion system showed noticeable, but manageable transients during plasma ramps and dwell (e.g., coolant inventory displacement), corresponding pressure and temperature variations can be considered acceptable keeping in mind the pressure decrease exceeding 100 bar at the inlet of the high-pressure turbine section.

#### **6. Outlook**

The circulator control scheme's optimization will be a high priority task in the upcoming conceptual design phase. Due to the high degree of uncertainty considering, e.g., manufacturer and component characteristics, the logics will have to be further tailored. Hence, secondary side control systems will also have to be monitored and adjusted, should the PCS performance suggest otherwise. It has to be noted that no heat losses have been taken into consideration thus far, due to the maturity of the design. Nonetheless, based on the substantial surface area and length of the primary and secondary system piping (∼6.1 km and ∼3.5 km, respectively), when compared to commercial nuclear power plants, one has to pay close attention to the optimization of plant efficiency. One action in this direction was the addition of a pair of recuperative heat exchangers to the condenser–deaerator let-down line (see Figure 3), where the dumped steam heats the condensate, delivered to the DEA as a result of the condenser level control. Other areas can be also identified where energy could be recovered, for instance valve stations as the large steam dump valve where the integrated enthalpy loss amounts to ≈423 kWh over a cycle. Regarding the evolution of the small ESS, the implemented boundary conditions, responsible for dynamic enthalpy calculation, will be removed as the soon-to-be published Apros service pack will provide an upgraded iteration loop, dedicated to molten salt–inert gas systems.

**Author Contributions:** Conceptualization, formal analysis, data curation, writing, M.S.; supervision, S.N. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was carried out within the framework of the EUROfusion Consortium and received funding from the Euratom research and training program 2014–2018 and 2019–2020 under Grant Agreement No. 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

#### **Variables**

The following variables are used in this manuscript:

#### **References**

## *Article* **Model Development and Transient Analysis of the WCLL BB BOP DEMO Configuration Using the Apros System Code**

**Marton Szogradi \* and Sixten Norrman**

**\*** Correspondence<EMAIL_ADDRESS>
**Abstract:** Extensive modelling and analytical work has been carried out considering the water-cooled lithium–lead breeding blanket (WCLL BB) balance of plant (BOP) configuration of the demonstration power plant (DEMO) using the Apros system code, developed by VTT Technical Research Centre of Finland Ltd. and Fortum. Contributing to the BOP work package of the EUROfusion Consortium, the integral plant model for dynamic analyses of the WCLL BB configuration has been updated with special attention to primary system components. Following trends of relevant neutronics modelling, a new BB model has been implemented in 2020 with the aim to obtain higher resolution output data and a more realistic thermalhydraulic feedback from the primary system. Once-through steam generator user components have been built based on CAD models conceived by BOP partners. Transient analyses have been performed providing a better picture regarding the behaviour of main components, e.g., the BB and the OTSGs, whilst highlighting possible ways to optimise the control scheme of the plant.

**Keywords:** DEMO; WCLL BB; small ESS; transient; Apros

**Citation:** Szogradi, M.; Norrman, S. Model Development and Transient Analysis of the WCLL BB BOP DEMO Configuration Using the Apros System Code. *Energies* **2021**, *14*, 5593. https://doi.org/10.3390/en14185593

Academic Editors: Alessandro Del Nevo and Marica Eboli

Received: 26 July 2021 Accepted: 27 August 2021 Published: 7 September 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

#### **1. Introduction**

The balance of plant (BOP) work package of the EUROfusion Consortium is responsible for the development of cooling systems comprising the primary heat transfer system (PHTS), the intermediate heat transfer system (IHTS), and the power conversion system (PCS) concerning their technical description and control logics. Equipment and layouts of systems rely on designs used in conventional power plants albeit a stark departure can be highlighted with respect to the fusion power plant's normal operation. The initial break-down of hydrogen into plasma, afterwards the plasma current in the tokamak (Acronym for *toroidal chamber with magnetic coils*, Rus.: ТОроидальная КАмера с МАгнитными Катушками) are driven by the discharge of the central solenoid (located in the bore of the torus), until the plasma current reaches its opposite peak current. This means that the tokamak has to operate in pulsed mode, where a pulse period is followed by a dwell time when only decay heat is produced (∼1–3% *Pnom*). The pulsed operation brought forth challenges in the design for producing electricity in a commercially and technically viable way.

Activities of the work package have been organised around two candidate blankets during the pre-conceptual design phase of DEMO, namely the helium-cooled pebble bed (HCPB) and the water-cooled lithium–lead (WCLL) breeding blanket (BB) configurations [1,2]. The various blanket concepts offer different benefits and challenges compared to one another, thus several plant configurations have been developed in order to explore the various aspects of primary-secondary system coupling.

Depending on the PHTS and PCS interface one can separate direct and indirect coupling schemes, in case of the direct layout the PHTS is directly connected to the PCS via steam generators (SGs) whereas the indirect adjective implies that PHTS-PCS coupling is realised by an IHTS [3]. Such an intermediate system utilises molten salt energy storage

VTT Technical Research Centre of Finland Ltd., 02044 Espoo, Finland<EMAIL_ADDRESS>
technology in a similar fashion as solar power plants and other large scale applications of the chemical industry.

The direct coupling branch has two further variants, one operating an auxiliary boiler (AUXB) and another adopting a small energy storage system (ESS). A former variant represented a benchmark case, with the purpose to verify the feasibility of the pulsed operation regime of the DEMO plant using a gas-fired boiler during dwell periods [4]. AUXB studies confirmed that the envisaged operation scheme can be implemented, although results underlined the necessity to develop further, e.g., SG and feedwater inventory management. In the small ESS configuration, the auxiliary boiler was replaced by a molten salt steam generator (MSSG) as the interface between the salt loop and the PCS.

VTT has been taken part in the development of the mentioned plant variants using the Apros system code [5], present article will report the results of the modelling and analytical work related to the WCLL BB small ESS configuration. Section 2 will introduce the architecture of the PHTS (§2.1), the PCS with an emphasis on the true OTSGs and corresponding control logics (§2.2) setting out the general small ESS design as well in §2.3. Section 3 will give a depiction of the integral Apros model detailing the main subsystems in a similar manner as Section 2 with more focus on the mentioned key components (§3.1–3.4). The results of the transient analysis are outlined in Section 4, finally, leading the reader to the conclusions and outlook of the work within Sections 5 and 6, respectively.

#### **2. WCLL Small ESS BOP Configuration**

The WCLL small ESS BOP features a pressurised water-cooled primary system with two separate loops representing the first wall (FW) and the breeding zone (BZ) cooling circuits. Both loops are connected to the PCS via two OTSGs giving four steam generators in total. Secondary power sources, namely the divertor casette (DIV-CAS), divertor plasma facing unit (DIV-PFU), and the vacuum vessel (VV) coolant loops have been connected to the PCS via three pairs of heat exchangers, where the DIV-PFU units are located on the low-pressure (LP), the DIV-CAS and VV units are placed on the high-pressure (HP) feedwater preheater line. The fresh steam is fed via the main steam line (MSL) to the steam turbine (ST) that consists of two high- and four low-pressure stages. Ultimately, the exhaust steam is condensed in the main condenser, closing the imperfect Rankine cycle of the power conversion system. The small ESS and the MSSG with their auxiliary systems are installed in between the tokamak and turbine islands. The CAD layout of the facility is depicted in Figure 1 highlighting the enlisted subsystems.

**Figure 1.** CAD layout of the WCLL small ESS DEMO.

Transient scenarios enveloped two consecutive pulse-dwell phases where the pulse (*Pf us* = 100%, *PMSEH* = 100% (molten salt electrical heater), *PMSSG* ≈ 5%) and dwell periods (*Pf us* = 1%, *PMSEH* ≈ 40%, *PMSSG* = 100%) lasted 7200 and 600 s, respectively. The plasma ramps represent asymptotic time-dependent power functions describing the reactor's thermal power variation between 1–100% under 100 s.

Prior to the plasma ramp-down the unloading of the turbine is initiated 500 s before the reactor rundown in order to achieve a permissible power gradient on the machine around −10%/min. As dwell commences the power load rapidly decreases in the blanket and secondary power sources. In order to compensate the diminishing enthalpy difference between primary and secondary systems, the small ESS discharge line is activated loading the molten salt SG. The synchronisation of the OTSG and turbine unloading with MSSG control is a crucial aspect of successful pulse-dwell transition, where numerous safety requirements have to be fulfilled simultaneously, e.g., pressure restrictions in feedwater heat exchanger (FWHX) shells and the deaerator (DEA), hot leg (HL) temperature limitations in the PHTS (*Tw*,*max Tsat*,*HL*). On the top of these requirements, various goals pose challenges as well, for instance a 10% load has to be maintained on the turbine throughout dwell by a suitable re-alignment of the whole PCS.

#### *2.1. Primary Heat Transfer System*

The primary system is responsible for the cooling of the BB, divertor, and VV components of the reactor. The coolant enters the FW and BZ inlet collectors at ∼295 °C, 155 bar, hereafter the flow is distributed among 16 sectors via the cold fingers that connect the segments' inlet ports and the collectors. As the 1/16 flow reaches the cold manifolds, the coolant is redistributed further among two inboard (IB) and three outboard (OB) segments. The cold water enters the segment at the top (IB) or ∼2/3 height (OB) of the segment, then the coolant passes downward via the FW and BZ spinal cords. In the lower section of each segment the flow path takes a U-turn, filling the FW and BZ inlet manifolds. As the coolant rises in the segments the inlet manifold flow rates gradually decrease in subsequent breeding units (BUs) whilst the outlet manifold flow rates increase correspondingly. In the head of the IB segments, the total segment inlet flow appears at the FW and BZ outlet ports, for OB segments the coolant takes another U-turn in the upper mixing volume, reverting finally to the water port at ∼2/3 height. The outlet flow enters the outlet manifolds at ∼328 °C eventually mixing the IB and OB loops' coolant inventory in the hot collectors. The hot leg piping connects these collectors to the steam generators' inlet junction on the top of the SGs at 152 bar. In the BZ loop each OTSG has a pair of pumps, while on the FW side one SG has one pump. Considering both loops, the pumps are running at a constant 100 % speed during the entire operation. Relevant thermalhydraulic properties are tabulated in Table 1 with respect to pulse and dwell phase values.

**Table 1.** Main parameters of the WCLL PHTS.

\* *The values refer to loop-wise flow rates hence the multiplication by a factor of two.*

Each 22.5° sector accommodates two, nearly identical left and right IB segments (left-LIB, right-RIB) and three, more distinct outboard segments (left-LOB, center-COB, right-ROB). In addition to upfront differences in waterport arrangements and structures, the breeding units also show noticeable variation in terms of material inventories, i.e., geometry, power loads, and TH conditions. The current 2020 design is depicted in Figure 2 below, where the left side was dedicated to the IB design while the right side to the COB segment, featuring the layout of the equatorial BU (region #4). Volumes marked with yellow contain PbLi eutectic, the blue, purple and red manifolds refer to water junctions with increasing temperature. All manifolds are enclosed by the back support structure (BSS), made of Eurofer alloy.

**Figure 2.** The CAD layout of the IB (**left**) and the COB segments (**right**) with flow paths.

Depending on the location, each segment contains 94–106 BUs stacked over each other between the lower mixing volume and the top of the segment. The layout of the equatorial COB unit is shown in Figure 2 featuring three arrays of coolant tubes (Σ22), the FW coolant channels (Σ20), the BZ filled with PbLi17 (90 at.% 6Li) and the coolant manifolds with the Eurofer skeleton. The PbLi coolant (yellow in Figure 2) enters the BZ via oval perforations in the manifold wall, the heated alloy exits the BZ via the outlet manifolds. Considering BZ loops, the cold water enters the inlet manifold (blue in Figure 2) before passing through the Eurofer heat exchanger tubes which lay across the PbLi manifolds and the BZ, leading the hot coolant to the outlet manifolds (red in Figure 2).

#### *2.2. Power Conversion System*

As mentioned before the PCS design was strongly influenced by commercial nuclear power plant architecture, where a two-stage feedwater preheater line supplies the boiler section with 228 °C water at 75 bar (see layout in Figure 3). The first stage incorporates the two LP heat exchangers (fed by the LP ST stages) and the twin DIV-PFU HXs. The coolant is collected in the DEA at ∼140 °C with a tank fill level at 45%.

Apart from a major role in coolant inventory management a proper DEA pressure control is also capable of preventing undesired transients in the secondary system. The feedwater pump (FWP) delivers the coolant to the SG collectors via the two HP heat exchangers (fed by the HP ST stages and the reheaters) and the DIV-CAS and VV HX pairs. Bypass lines were also installed on the HP preheater section in order to achieve better temperature and flow rate control during dwell. The feedwater collectors divide the total flow into three branches: (1) MSSG line, (2) FAR, and (3) NEAR collectors. Two latter lines are connected to the OTSG chains, the designation of the branches is a reminder of the 168 m difference in length. The main steam line gathers the fresh steam (67–70 bar, 300–330 °C) from the SG collectors supplying the turbine and the bleed lines. During ST (un)loading the bleed lines pressurise the feedwater preheaters' shells in order to maintain the nominal feedwater temperature at the end of the preheater line throughout the entire operation.

**Figure 3.** Power conversion system of the WCLL small ESS DEMO plant.

#### *2.3. Small Energy Storage System*

As mentioned earlier, the small ESS design was conceived based on the principles of large scale industrial molten salt storage system technology, the current configuration's coolant is HITEC®, an eutectic mixture of water-soluble, inorganic salts composed of NaNO3–NaNO2–KNO3 [6]. Since the small ESS has no connection to the PHTS a molten salt electrical heater increases the enthalpy of the salt, this heater receives electricity from the plant as an onsite consumer, alike coolant pumps. The pulse phase operation principle is as follows: the charging pump delivers the coolant of the cold tank (282 °C) to the electrical heater, after the heating of the salt (to 330 °C) the coolant arrives at the hot tank. The discharge pump supplies the MSSG with fresh hot salt, after passing through the SG the salt is collected in the cold tank. For the depiction of the system the reader is advised to return to Figures 1 and 3.

#### **3. Apros Model**

The advanced process simulation (Apros) system code has been developed by VTT Technical Research Centre of Finland Ltd. and Fortum since 1986. The code provides three- and six-equation solutions for one-dimensional thermalhydraulic problems utilising a staggered space discretisation scheme. State variables are calculated in the center of the mesh cells (nodes), flow related variables are derived at the border of adjacent cells. Considering heat transfer modelling, a vast array of analytical and empirical correlations is available, in addition new formula can be implemented using Simantics Constraint Language (SCL) scripts. As a result of the EUROfusion-related work, nested user components were developed on top of the basic process component library of Apros, providing higher-fidelity solution with respect to the WCLL blanket and OTSGs. The homogeneous model has been applied considering nodes of the small ESS while the six-equation solution has been used in every other node filled with water or steam.

The general structure of the integral model can be seen in Figure 3 featuring some complementary elements compared to Figure 1, such elements were necessities to obtain satisfying plant control (e.g., steam dump line, make-up and let-down piping and steam bleed lines).

In order to provide basis for further comparison with other plant configurations the cycle net efficiency (*ηcy*) has been derived for pulse and dwell phase, as given in [3] by:

$$\eta\_{cy} = \frac{\mathcal{W}\_{\text{gross}} - \mathcal{W}\_{\text{PCS,pump}}}{P\_{BB} + P\_{DIV} + P\_{VV} + P\_{MSSG}} \tag{1}$$

where *Wgross* is the gross power on the ST shaft, *WPCS*,*pump* is the total pumping power of the PCS, *PBB*, *PDIV*, *PVV* and *PMSSG* are heat inputs from the *BB*, *DIV* (PFU and CAS), *VV,* HXs, and *MSSG*, respectively. Furthermore the overall plant net average efficiency (*ηo*) was also calculated as:

$$\eta\_o = \frac{\int\_0^{t\_{cy}} (W\_{\text{gross}} - W\_{\text{plant}}) \, dt}{\int\_0^{t\_{cy}} (P\_{BB} + P\_{DIV} + P\_{VV} + P\_{MSSG}) \, dt} \tag{2}$$

where *tcy* is the length of a full cycle (7800 s), *Wplant* is the total power of onsite consumers (total pumping power and MSEH).

#### *3.1. Primary Heat Transfer System*

The blanket model was rebuilt in 2020 following the spatial discretisation principles of relevant plasma physics and neutronics models, also taking into account given CAD specifications. The complexity of the structure had to be tackled on a system code level whilst preserving the novelty of certain aspects, e.g., power deposition schemes, coolant, and dry mass inventories. In order to fulfil such requirements nested process components were created, with respect to the aforementioned factors, representing an interface between boundary conditions (BCs) and the thermalhydraulic model of the PHTS. The underlying algorithm of this BB model can be characterised as a non-linear onion scheme where the outermost shell is the interface between the PHTS/BC modules and the segments. Unlike in classical onion structures, process components on the lowest level receive information from the top (e.g., power) bypassing all the shells in between, thus the output information is directly affected by the input. As §2.1 pointed out, in total 5 segments compose one 22.5° sector, thus the reactor model contains 5 segment components (2nd shell). Each segment accommodates 7 BU components, corresponding mixing volumes, water ports, and interfaces between the BUs (3rd shell).

The poloidal power distribution has been defined for 7 regions, separately for IB and OB segments (uniform for OBs), thus the breeding units of these regions have been collapsed into 7 representative BUs, each corresponding to the average BU of its region. Inside the BU model three further user components have been placed: (1) FW (2) BZ, and the (3) VV components with their dependent interfaces (4th shell). These modules contain the heat structures (HSs), piping and power boundary conditions. The general structure can be seen in Figure 4 opening up the information flow and the shells of the reactor. Such an approach made it possible to customise FW, BZ, and VV compartments, independently from one another, in terms of nodalisation and power deposition. The radiative power distribution was derived by EUROfusion partners using the ASTRA transport code [7] developed by IPP for core radiative flux, the SOLPS code [8] for the scrape-off-layer radiative flux and the CHERAB code [9] developed by Culham Centre for Fusion Energy (CCFE). Nuclear heating deposition schemes were obtained with Monte Carlo N-particle analyses [10,11] concerning W, PbLi, water, Eurofer, and SS316L (VV) domains.

**Figure 4.** Structure of the BB sector user component.

#### *3.2. Power Conversion System*

The secondary system was built using basic Apros process components, such as heat exchangers, various valves, pumps, tanks, and turbine elements. Concerning the once-through steam generators, two new user components were dedicated to the coupling of the FW and BZ loops to the PCS. The BZ OTSG design was set up by the University of Napoli, as a member of the BOP work package, utilising a modified Babcock and Wilcox layout as a template while incorporating Westinghouse-type tubesheets. The SG is modified in the sense that no recirculation takes place between the downcomer annuli and riser volume, unlike in the generic layout. The development of the component is still in progress exploring alternatives as an attempt to find the most suitable configuration for the needs of the primary system, nonetheless present paper will discuss the behaviour of the first prototype. Taking into account foreseeable limitations in terms of geometry and TH parameters the BZ OTSG was scaled down by VTT to derive the FW OTSG. Since DEMO de jure represents a nuclear power plant, the ASME boiler and pressure vessel code standard's class 1 relevant section was applied during the sizing of both components [12].

The cross section of the BZ OTSG can be seen in Figure 5 also depicting the Apros component, note that FW and BZ OTSG components share their topology. The feedwater enters the riser volume via the downcomer annuli, the coolant is heated to its boiling point, evaporated, and superheated while rising through the 15 broached tube plates. The fresh steam leaves the SG via the outlet manifold connecting the OTSGs to the steam collectors (NEAR and FAR). General properties of the SGs are given in Table 2 with respect to nominal values, dwell phase powers, and flow rates are reduced to 1%.

**Figure 5.** OTSG layout with Westinghouse-type broached plates.

#### *3.3. Small Energy Storage System*

The small ESS has been modelled explicitly featuring the elements described in §2.3. Earlier it was found that a recirculation line, installed on the discharge line, could enhance control quality significantly, thus an additional pipeline was connected to the discharge and suction points of the discharge salt pump. During pulse phase the control valve (CV) of this line is in fully open position, as for dwell the recirculation line closes, i.e., the full flow is directed to the MSSG. This control scheme was proven to be very reliable in terms of TH parameters throughout the pulse-dwell cycle. Referring back to Section 3, the molten salt loop used a homogeneous solution for its TH nodes filled with salt. Nonetheless due to uncertainties of auxiliary systems (pressure control), the salt tanks have been modelled by boundary conditions where dynamic enthalpy calculations have ensured that the tanks' proper transient behaviour is accounted for. The pressure of these tanks was set to 8 bar in order to provide a sufficiently high back pressure for salt pumps. General parameters of the small ESS model can be found in Table 3 where mdisch. refers to the cold pump flow rate (cold tank→MSEH/hot tank) and mch. denotes the hot pump flow rate (hot tank→recirc. line/MSSG/cold tank).

**Table 3.** Main parameters of the small ESS in Apros.

#### *3.4. Logics*

The control scheme of the plant revolves around the needs of the blanket, i.e., the main goal of the PHTS and PCS logics is to ensure the cooling of the BB at all times. In the current arrangement the PHTS pumps are running at full speed also in dwell according to design specification. The design objective, to maintain a constant average temperature on the SGs primary side (*TSG*,*p*), has been simplified in the simulation with the requirement to preserve a ∼17 °C subcooling in hot legs until a comprehensive regulation scheme is realised. Whilst providing a robust heat sink, a secondary objective of PCS logics is to keep the PCS in a low-load regime during dwell, ready for the subsequent plasma ramp-up. Due to the large, periodic displacement of the coolant inventory the DEA pressure is controlled, in this model, by a bleed line (maintaining 3.5 bar), FWHX shell pressures are also controlled from the bleed line since turbine extractions close down at the beginning of turbine unloading and open up only after reaching nominal conditions on the MSL.

#### **4. Results**

The transient analysis entails two consecutive pulse-dwell cycles with a 1200 s pulse phase at the beginning. The complete pulse phase is 7200 s including two plasma ramps before and after the flat-top period (100 s + 7000 s + 100 s), the dwell phase lasts 600 s thus one full cycle is 7800 s. Figures in Sections 4.1–4.3 follow this sequence of events where grey rectangles mark the two dwell periods. The reported results were recorded after driving several cycles and adjusting parameters, e.g., molten salt tank levels, valve driving times, and controller characteristics.

#### *4.1. Primary System Behaviour*

Power trends are depicted in Figure 6 featuring the blanket, secondary power sources and the molten salt SG. As the reactor power decreases from 100 to 1% the small ESS discharge line activates increasing the salt flow rate on the primary side of the MSSG, thus bringing its power up to 271 MW. As an improvement the MSSG loading time was shortened by 10 s (to 90 s) in order to achieve a smoother feed-transition on the MSL. Due to PHTS thermal inertia and OTSG behaviour, the MSSG unloading process had to be extended in order to supply the turbine for some extra time after dwell. As a solution, the discharge line CV followed a 200 s long asymptotic flow rate curve.

**Figure 6.** Power trends.

Regarding BB coolant loops and the primary side of DIV-VV loops, pressure deviations were in the range of 1 to 2 bar, illustrated in Figure 7, thus no significant perturbation was observed while BZ and FW loop trends practically overlapped. Therefore, it was concluded that the continuous pump operation and the pressurisers of the mentioned systems effectively damped perturbations coming from the reactor chamber and the PCS.

**Figure 7.** BB, DIV, and VV coolant loops' primary pressure trends.

FW and BZ coolant temperatures are given in Figure 8 with respect to hot and cold collector temperatures, i.e., SG inlet and outlet temperatures of the OTSGs where three distinct sections can be defined according to governing control logics. During turbine unloading temperatures varied by 1–2 °C, however, as plasma ramp-down commenced, HL temperatures (OTSG inlet) started to drop significantly. As the secondary coolant inventory of the SGs was reduced substantially, this cool-down trend constituted section #1 (1700–2000 s). Shortly after the beginning of dwell SG feedwater inventories stabilised as flow rates on the PCS-side feedwater collectors reached their dwell phase set-points, i.e., heat transfer rates saturated as primary side ΔT values nearly halved in both FW and BZ loops.

**Figure 8.** OTSG primary side inlet and outlet coolant temperatures.

In section #2 (2000–2400 s), hot leg temperatures continued to fall as OTSG water levels gradually recovered, nonetheless the primary FW OTSG ΔT did not change noticeably compared to #1 due to tranquil TH conditions in the SGs. In section #3 (2400–3000 s), the

OTSG feedwater flow rates were briefly decreased in order to increase primary ΔT prior to SG reload, thus the SG feedwater logic does not overcool the primary system while flooding the heat exchangers. After the short decrease, the feedwater flow rates were once again increased following the average primary loop temperatures until reaching nominal conditions around the end of the ST reload. The hereby outlined protocol highlighted that PHTS primary control was mainly realised by OTSG feedwater control, more light will be shed on the reason of such practice and its further consequences in §4.2 where the OTSG operation will be discussed in detail.

#### *4.2. Secondary System Behaviour*

Using Equation (1) the cycle net efficiency for the PCS (*ηcy*) in pulse and dwell was calculated as 30.3% and 25.6%, respectively, while Equation (2) yielded an overall plant net average efficiency (*ηo*) of 26.7%.

To some degree, pulse phase control schemes have relied on the output of preliminary (steady state) heat balance analyses, e.g., with respect to MSEH power, FWHX shell pressures, etc., while in other cases logics had to be tailored to meet the requirements of both phases. The OTSG feedwater control valves directly controlled PHTS coolant temperatures as described earlier, during pulse the average primary coolant temperature of the given OTSG was the control variable for the SG feedwater control valves. If negative discrepancy appeared (*TSG*,*p* < 311.5 °C) the valves decreased flow rates, otherwise vice versa.

This method was a simple and robust solution to mitigate smaller anticipated perturbations during pulse, yet the challenges posed by plasma ramps had to be tackled using a more thorough approach that takes into account the following three main interdependent factors, affecting general system stability: (1) PHTS hot leg temperature has to remain well below saturation (*THL Tsat*,*HL*), (2) the collapsed water level in OTSG risers has to be maintained above the upper rim of the waterports to avoid serious downcomer voiding (*Lcoll* > *Lwp*—see in Figure 5), and (3) the steam quality in the MSL has to be kept as high as possible in order to prevent erosive damage on the turbine blades (*qMSL* > 99%). One can see that the enlisted variables can oppose one another, for instance a higher HL coolant temperature would induce flow rate increase on the SG secondary side, albeit process could lower steam qualities or even flood the SG under far-out operating conditions. Considering another scenario, one can assume that low HL temperatures would force the SG control valves to close, ultimately decreasing collapsed water levels in the riser. This action could lower the water level below the waterports' upper rim leading to rapid downcomer voiding further propagating and amplifying an initially minor perturbation (It has to be noted though that the process and automation design of the BOP model does not yet account for possible safety feature design aspects, thus the hereby considered factors represent a preliminary and conservative take on future safety criteria.).

In order to avoid unintentional transients and optimisation pitfalls of such a complex system, a workbench solution was conceived offering a helping hand to developers of the WCLL plant and control systems during the upcoming conceptual development phase of DEMO. The solution is based on a steam generator feedwater CV logic, following a flow rate function, hence decoupling primary and secondary side response from the OTSGs during plasma ramps and dwell. The normalised flow rate function is depicted in Figure 9 below with respect to FW and BZ OTSG control loops.

**Figure 9.** OTSG secondary side flow rate function.

The motivation behind the functions can be understood best by studying OTSG collapsed water levels, Figure 10 depicts OTSG-averaged riser and DC water levels. At 0 s the reactor rundown initiates and the dwell phase FW OTSG logic takes over, however pulse phase flow rates are maintained for an additional 50 s on the BZ branches in order to compensate PHTS inertia. At 50 s in the plasma ramp the dwell phase logic seizes control on both FW and BZ control branches, setting a constant flow rate on every OTSG feedwater CV. At 400 s after the start of dwell the flow rates are decreased on each SG reducing the cooling of the PHTS. Such action was necessary to decrease the difference between the after-dwell and pulse phase value of the average primary coolant temperature (311.5 °C).

**Figure 10.** Averaged collapsed water levels in riser and DC volumes.

At the end of dwell feedwater flow rates are increased as plasma power rises between 700 and 800 s, ensuring also that collapsed water levels remain above the waterports' upper rim. This post-dwell protocol is enabled for 150 s in case of FW OTSGs and 250 s for BZ OTSGs, where the difference is due to the different inertia of the two loops. By maintaining acceptable water levels in the risers the primary coolant temperature inevitable decreases by the end of dwell to some extent. Lowering flow rates, then gradually increasing them at a lower gradient leaves time for the blanket to warm up the hot legs and approach pulse phase primary side coolant ΔT. At 850 s the FW OTSG dwell logic is disabled, the FW OTSG feedwater control valves are driven only by the pulse phase logic afterwards. Correspondingly at 950 s (250 s after dwell end) the BZ OTSG dwell logic hands over the control to the pulse phase logic. The closer the primary side ΔT and hot leg temperature to their nominal values the smoother the transition into the period where pulse phase logics have full control over OTSG CVs.

Steam flow rates are depicted in Figure 11 with respect to HP, LP stages, and the steam dump line (DL). At the beginning of the unloading process (600 s before dwell) extraction lines close along the shaft, thus the steam flow rate at the 4th LP stage (LP4) outlet converges to the value taken at HP1 inlet. As dwell is reached (Δ*pMSL* = −4.5 bar) the steam dump-line remains open to divert the excess flow to the main condenser while the thermal inertia of the BB provides some surplus steam in addition to the molten salt SG. In Figure 11, the LP2 flow rate is identical to LP1, this is due to the fact that earlier the LP1 extraction was used as primary feed for deaerator pressure control. Preliminary calculations showed that the periodic turbine operation posed challenges on the mentioned control loop, thus the extraction line was closed and the DEA bleed line was activated for pulse, consequently simplifying and improving control.

**Figure 11.** Steam flow rates on the ST and dump line.

Considering the main condenser the observed pressure transient was in close agreement with heat balance analysis where shell pressure varied between 27.2 to 50.0 mbar. In addition to incorporating the flow of the dump line, the condenser served also as a pressure buffer of the DEA. Originally the DEA was pressurised by an LP1 extraction however as turbine operation had been tested, such arrangement was not deemed to be feasible during transients thus the DEA feed was moved to the MSL, where no significant pressure transient was postulated. Since DEA inventory shows substantial change (±39 t between pulse-dwell) a stable steam source (MSL) and a reliable low-pressure point (main condenser) are essential for a firm DEA pressure control. DEA collapsed water level and pressure trends are shown in Figure 12. It can be seen that the current system handled the DEA pressure with a margin of ±0.08 bar despite the 0.7 m level variation.

**Figure 12.** Deaerator collapsed water level and pressure.

Preheater line temperatures were adjusted via preheater HX shell pressures, considering FH1HX the pulse phase pressure was maintained in dwell, as for FH2HX the pressure was increased by 50%. Moving onto the high-pressure stage larger relative pressure corrections had to be made due to the order of HXs in the preheater chain. Since secondary power sources ramped down, their bypass lines opened up meaning that the pulse phase ΔT had to be preserved only by FH(3,4)HXs, hence the FH3HX shell pressure was increased by 45%, while maintaining pulse phase pressure in FH4HX. The feedwater temperature trends are depicted in Figure 13 indicating a ±5 °C variation in FH4HX outlet temperature.

**Figure 13.** Feedwater temperatures along the preheater line.

#### *4.3. Small ESS Behaviour*

Considering the periodic, high amplitude variation in salt flow rates, as shown in Figure 14a, concerns might be raised regarding mechanical stresses of components located on the discharge line. Comparing flow rate gradients (*Fg* [kg/s2] = [N/m]) to weight forces (*Fw* [N/m]) on the unit length it was found that the induced stresses were negligible. Corresponding tank levels are depicted in Figure 14b, where a ∼5.5 m (∼2300 t) displacement can be seen between charge and discharge periods. Such a trend implies that the current 1362 m3 salt inventory was mostly depleted leaving a residual salt reserve of

∼440 t per tank per period. Note that in this configuration the cover gas volume was not taken into consideration, such parameters will be defined later on during the conceptual development phase.

**Figure 14.** Flow rates in the small ESS (**a**) and molten salt tank levels (**b**).

#### **5. Synopsis**

Development and analytical work, carried out for the DEMO WCLL small ESS integral Apros thermalhydraulic model has been discussed. A new blanket concept was introduced utilising a layered structure where the segments' spatial discretisation and power deposition schemes follow the trends of neutronics models. Once-through steam generators have been implemented in Apros using a similar, nested architecture as the breeding blanket model. The transient simulations outlined the complexity of the challenges facing the control logics, where engineering solutions have to be derived respecting all safety criteria. In order to provide a reference case for future development a simplified OTSG control scheme was obtained highlighting the narrow operating margins of both PHTS and PCS.

#### **6. Outlook**

Carrying on with the development of the BB model the power deposition schemes have to be refined. In the current setup each material compartment has a homogeneous volumetric power distribution that is adjusted only in the toroidal direction, neglecting radial gradients. As the BU design matures, with respect to certain components, e.g., FW, BSS or in a broader context on segment level, the blanket model shall follow the specifications in any case. The OTSG design is still under development where alternative options are being considered, e.g., allowing internal circulation between riser and DC volumes. Model performance will be benchmarked during 2021–2022 and additional finite element method analyses will support the system code results. Keeping in mind the dimensions of the PHTS and PCS, where the total piping length yields ∼6.9 km and ∼2.1 km for primary and secondary systems, respectively, the issues of heat and pressure losses will have to be tackled as well. Aside from mitigating such losses, energy can still be recovered in various aspects, e.g., from dumped steam via recuperative heat exchangers (FHd(1,2)) on the condenser-deaerator let-down line, where the dumped steam heats the cold condensate before it enters the DEA (see Figure 3). This small system recycles only a portion of the total enthalpy loss on the steam dump valves, ≈168 kWh/cycle is still being ejected from the PCS via the main condenser. In recent Apros 6.11 release a new iteration scheme, dedicated to molten salt-inert gas systems will be available, thus the small ESS model will be refined accordingly, removing obsolete boundary conditions.

**Author Contributions:** Data curation, M.S.; Validation, S.N.; Writing—review & editing, M.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Euratom research and training programme 2014–2018 and 2019–2020 under grant agreement No 633053.

**Acknowledgments:** This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 and 2019–2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:

#### **References**

## *Article* **Loss of Liquid Lithium Coolant in an Accident in a DONES Test Cell Facility**

**Danilo Nicola Dongiovanni 1,\* and Matteo D'Onorio 2**

**\*** Correspondence<EMAIL_ADDRESS>
**Abstract:** A Demo-Oriented early NEutron Source (DONES) facility for material irradiation with nuclear is currently being designed. DONES aims to produce neutrons with fusion-relevant spectrum and fluence by means of D–Li stripping reactions occurring between a deuteron beam impacting a stable liquid lithium flowing film implementing the target. Given the hazard constituted by the liquid lithium inventory and the potential risk of reactions with water, air, and concrete eventually resulting in fire events, the Target Test Cell (TTC) is filled with helium and the reinforced concrete walls forming the bio-shield are covered with steel liners. A loss of Li in TTC, due to a large break in the Quench Tank, is postulated, and consequences are deterministically studied. With the TTC liner being water-cooled, the impact of the liner temperature rise following a leakage event is evaluated. Two separate MELCOR code models have been defined for the liquid lithium loop and water-cooled loop and are numerically coupled. The amount of leaked inventory dependent on the implemented safety logic and impact on TTC containment is evaluated. The water pressurization pattern within the liner cooling loop is studied to highlight possible risks of lithium–water/concrete reactions.

**Keywords:** fusion; DONES; liquid lithium; LOCA; Melcor; numeric coupling

#### **1. Introduction**

Special materials able to withstand outstanding neutronic loads will be required for the exploitation of nuclear fusion energy. However, there is limited experience relating to materials exposed to such load conditions. In particular, in-vessel components will be subject to thermal and neutron loads with energy up to around 14.1 MeV and fluence leading to 5–15 displacements per atom (dpa) [1,2] in the irradiated components (first wall, divertor) able to alter their structural and functional behavior.

The IFMIF-DONES (International Fusion Material Irradiation Facility-DEMO Oriented NEutron Source) facility for material irradiation is currently being designed within the EUROfusion programme [3] to fill this knowledge gap in view of a DEMOnstration fusion power plant expected for the mid-2040s [4]. DONES achieves the production of neutrons with fusion–relevant spectrum and fluence through D–Li stripping reactions occurring between a 125 mA and 40 MeV deuteron beam impacting a stable liquid lithium flowing film implementing the target.

A safety analyses campaign [5] is ongoing within the DONES project to assess the DONES system ability to handle any abnormal event ensuring safe conditions for workers and the population. To reach the goal, a selection of the analyses has been done using the FMECA plan and FMEAs studies.

As part of the conceptual design, a selection of accident events has been studied deterministically for lithium systems and or the test systems interface either by MELCOR code [6] or RELAP code [7].

The exploitation of liquid lithium within the facility constitutes a hazard with potential risk of reactions with air, water, and concrete, eventually resulting in fire events [8].

**Citation:** Dongiovanni, D.N.; D'Onorio, M. Loss of Liquid Lithium Coolant in an Accident in a DONES Test Cell Facility. *Energies* **2021**, *14*, 6569. https://doi.org/10.3390/ en14206569

Academic Editors: Dan Gabriel Cacuci and Marica Eboli

Received: 30 July 2021 Accepted: 4 October 2021 Published: 12 October 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Therefore, great attention has been paid to the DONES design to avoid any direct contact between reactants (air, water, concrete) such as the use of an inert atmosphere (helium, argon) or double-stage heat removal systems lithium–oil/oil–water. Safety mitigation provisions are also in place to prevent the possible reaction of lithium and the reinforced concrete TC walls forming the bio shield. In particular, all TC is covered by a steel liner layer to prevent liquid lithium–concrete reactions in the case of a loss of liquid lithium in an accident. Despite such provisions, deterministically assessing the consequences of possible accidents is of paramount importance in the early phases of the design to identify safety concerns. Assessments have been performed in the past for other test facilities exploiting liquid lithium [9,10]. Therefore, a preliminary analysis on the consequences of postulating fire events in the DONES lithium system has also been performed [11].

In the present analysis, a loss of Li in TTC (LTTC1 Postulated Initiating Event) due to large break in the Quench Tank is postulated and consequences deterministically studied with MELCOR [12–14]. In particular, the amount of leaked inventory and its impact on TTC containment and the atmosphere is evaluated. The TTC liner is cooled by a cooling water loop, and the effect of the temperature rise due to leaked lithium inventory on the liner floor and underlying cooling lines is evaluated. To overcome the MELCOR limitation for two cooling fluids contemporary usage, two different MELCOR models have been defined for the liquid lithium loop and water-cooled loop and are numerically coupled by means of external data exchange for interfacing heat structures. Possible water pressurization within the cooling loop has been studied.

#### **2. Materials and Methods**

#### *2.1. System Description*

The DONES facility is composed of three main systems (Figure 1) and several auxiliary systems [3]. The accelerator system is in charge of accelerating and focusing deuteron ions into a beam with a 125 mA current and 40 MeV energy. The beam flies within a vacuum conduit entering the Test Cell within a beam duct until a vacuum chamber (Figure 2) where it impacts the lithium film to have D-Li striping reactions and produces fusion-spectra neutrons [15]. A backplate (BP) is placed between the lithium film and the High Flux Testing Module [16]. The lithium system [17] main lithium loop provides liquid lithium flowing film for striping reactions. The lithium main loop is composed of the Target Assembly (TA) [18] located in the TC, which in turn is composed of pipework leading the lithium to the vacuum chamber area where the thin liquid lithium film is created by means of a flow straighter and reducing nozzle (ST-NZ). Below the target area where the beam impacts the lithium film, lithium is collected in a quench tank (QT) before exiting the TC towards the lithium system room. In order to obtain liquid lithium film, specific velocity/mass flow rate and thermodynamic conditions need to be maintained in the loop. This task is in charge of the part of the lithium main loop located in the lithium room. In particular, lithium flow is provided by an Electromagnetic Pump (EMP) and is measured by an EM flow meter. A Dump Tank (DT) collecting lithium at shutdown is also located therein. The Lithium System (LS) includes three main systems; a Heat Removal System (HRS) is deployed in two rooms housing the main Li loop. Beam heat deposited on the lithium film is exhausted within a primary Heat Exchanger (HX) exploiting a secondary oil loop to prevent lithium–water reactions and is located in the lithium main room. In turn, heat transferred to the oil secondary loop is transferred to a tertiary water loop located in a separate room, considered out of scope. The TC Atmosphere [19] is He at a pressure of 20 kPa, with a free volume of 47.1 m3. The Lithium System (LS) [17] is Ar buffered during normal operation and is slightly depressurized (−140 Pa) with respect to standard atmospheric pressure.

**Figure 1.** IFMIF-DONES plant system configuration.

**Figure 2.** (**a**) Building layout and rooms in scope (light blue). (**b**) Related Melcor model elevations for considered systems.

#### *2.2. Accident Specification for the LTTC1 Event*

Accident Analysis Specifications for the accident have been developed to define the analysis scope, methodology, and expected goal. The PIE event considered is LTTC1 Loss of Li in TTC due to a large break in the Quench Tank. The transient sequence initiated by the rupture in the lithium loop running inside the TTC induces the release of liquid metal into the TTC. The TTC atmosphere is filled with inert (Helium) gas and kept at "sub-atmospheric/or slight" pressure; then, no Li–air reaction occurs. Nevertheless, the rupture of the QT induces the release of a large amount of hot lithium in the TTC floor. A liner is foreseen to prevent contact between Li and the concrete of the TTC structures to mitigate the risks of reactions between Li and the concrete elements (e.g., water humidity and air). Under the liner, incorporated in the concrete structure, a water-cooling circuit is

foreseen to prevent heat-up of the TTC during the facility operations. The release of the large Li mass over the liner will start the heat exchanging between the hot lithium and the cold TTC structures. Over-heating and over-pressurization of the water cooling could occur, impairing the cooling loop integrity. The objective of the analysis is to study overpressurization of the TTC volume because of the heating of the He gas contained inside the TTC, the over-heating of the TTC structures (liner and concrete), and the over-heating and over-pressurization of the TTC water cooling system.

Note that no Loss of Off-Site power is assumed to co-occur in the selected initiating event. As safety mitigation system assumptions, the EMP stop and BEAM shutdown have been assumed. The beam power switches off and EMP fully stops after 0.1 s and 5 s from the event detection, respectively. The accelerator beam duct is isolated from the target after beam shutdown. Note that in compliance with diversity criterion for safety important classified detection systems, several accident condition detection systems are currently being considered in design (e.g., QT level, pressure in selected volumes, etc.) and are expected to have different detection times depending on the accident.

No valves for the lithium main loop isolation are foreseen, so in order to investigate the possibility of reducing the lithium leaked inventory, the exploitation of a dump tank (normally used to store lithium during loop maintenance or off-line operation) to be opened as a consequence mitigation solution is still under discussion.

#### *2.3. Simulation Models and Approaches*

MELCOR is a code originally developed for the safety analysis of light water fission reactors. Over the past twenty years, a series of modifications have been implemented to account for nuclear fusion–relevant phenomena [12,13,20,21]. This new MELCOR version validated against available fusion experimental data or benchmarked against validated codes [22–25] has become a reference code for safety analysis in nuclear fusion studies. It has also been adopted for accident analyses exploited for licensing purposes in fusion facilities, the most representative example being ITER [13,26].

More recently, the MELCOR Fusion adapted version 1.8.6—2017 computer code [12] has been exploited for the analysis of integrated HTS containment as part of preliminary safety assessments in pre-conceptual designs of European DEMO concepts [27–30] as well as in Korean DEMO [31]. Being able to model phenomena relevant for fusion safety applications such as radionuclide transport (e.g., tritiated water) in the presence of a variety of cooling fluids (helium, water, liquid metals) as well as pressure conditions (e.g., vacuum), the MELCOR code has been considered for deterministic safety analyses aimed at the licensing of the DONES plant [5,6], showing good agreement with RELAP5 results [7,32,33].

Considering thermal–hydraulic analyses performed within the DONES/IFMIF facilities context, most of the studies have focused on CFD modeling of liquid lithium target with a focus on correctly modeling phenomena such as liquid metal flow, free surface flow under vacuum [34–37] or specific effects resulting from beam/target interactions [38]. This is justified by the many requirements for facility operation relying on the specific conditions that the flowing liquid lithium film will stably achieve. The present application assesses the impact on the containment of a liquid lithium large spillage event. Therefore, despite that liquid metal flow and free surface flow under vacuum are relevant phenomena to reproduce a steady-state regime before the postulated initiating event, the focus is on the heat transfer phenomena occurring at the lithium/liner (Figure 3) and liner/cooling pipe (Figure 4) interfaces.

**Figure 3.** TC-LS Melcor model nodalization.

**Figure 4.** TC-WCS Melcor nodalization.

The MELCOR code has been reputed to be suitable for the present application modeling purpose. In fact, the MELCOR fusion version when lithium is selected as a working fluid includes in the model the thermodynamic and transport properties of lithium other than lithium/air reactions possibly occurring after spills events [10]. In particular, the Equation of State (EOS) was modified to integrate the liquid lithium properties from [39], extrapolation below the triple point, and film formation on cold structures. Refer to [40] for further details on numerical models. These modifications were validated by using Hanford Engineering Development Laboratory (HEDL) experimental data [41,42] as a benchmark.

An additional feature available in MELCOR fusion exploited in the present analysis is the user-defined function FUN1 to model direct heat transfer (radiation and conduction) between heat structures. Heat power exchanged across heat structures is equal to

$$Q = \mathcal{S} \cdot \left( f \cdot \frac{k\_s}{dx} \right) (T\_1 - T\_2) + (1 - f) \cdot \varepsilon \cdot \sigma \cdot \left( T\_1^4 - T\_2^4 \right) \qquad [W]\_1$$

with S surface of heat exchange across structures, *T*1 and *T*2 are the considered heat structure surface temperatures, *f* is the fraction of such surfaces in conductive contact, *ε* is emissivity, the Stefan-Boltzmann constant is *σ*, dx is the distance across a solid, and *ks* is the thermal conductivity. In the present analysis, the DBA version of the MELCOR code has been used.

Unfortunately, the current MELCOR version does not allow for contemporary usage of two cooling fluids such as lithium (used in the LS main loop) and water (used in TC -WCS). Therefore, to have a preliminary study providing future reference for the upcoming Melcor-TMAP integrated version able to treat multiple fluids [42], the exploited approach was:

Details about the MELCOR model nodalization and coupling approach are provided in the following subsections.

#### 2.3.1. Nodalization of TC and LS with the Lithium Working Fluid

With reference to Figure 2, the first implemented model considered TC and TCLIC rooms with a Helium atmosphere and LS main loop room filled with an Argon atmosphere. As outlined in (Figure 3), the adopted nodalization includes a TC room, TA volumes, LS main loop volumes, beam duct (0.8 m3), vacuum chamber (0.36 m3), and some service volumes such as the environment or vacuum supply volume.

The main lithium loop has a total inventory (Table 1) of 7.4 m3 of lithium in the liquid phase at 523.15 K, set as the working fluid for the MELCOR code. The loop initially contains an argon atmosphere; then, the vacuum is pumped at start-up and EMP is started. After start-up, the loop reaches a reference operative parameter, i.e.,: 49.8 kg/s of lithium mass flow rate, 1.43 m liquid level within QT. Then, the beam is operated and injects 5.E6 W power into the lithium film, increasing the liquid lithium temperature from 523.15 K at the HX outlet to 546.15 K within QT. Note that for comparability's sake and whenever possible, the same CV names and safety logic were used as in [6]. The break was assumed to occur at the bottom of the QT in correspondence with the QT outlet flange. The break area was assumed to be the outlet pipe section (0.0314 m2), assumed to open at t = 1000 s after a stationary operation period. Figure 3 also shows the considered heat structure general scheme and heat transfer coupling phenomena. Each CV within the main lithium loop was provided with heat structures representing stainless steel piping or component walls. Pipes were covered with 0.04 m of MICROTHERM® pipe-insulating material (shown in Figure 3 with a yellow contour) to reduce lithium loop heat losses towards the room atmosphere in the TC and lithium area. A set of additional structures representing TC structures were also defined. In particular, BP and HFTM structures (made of Eurofer) and TA and TC support structures (made of Stainless Steel) and assumed to be in thermal conductivity with the liner floor. LSP Cladding acting as a TC ceiling and HTFM module were helium-cooled. Since the helium cooling loop is not considered within scope, those HSs were modeled as boundary condition structures with a fixed temperature. Test cell heat structure details

are reported in Table 2. Convective and radiative heat exchange between heat structures and the surrounding atmosphere was considered. A conductive coupling was considered across selected structures (as shown in Figure 3) and modeled using MELCOR FUN1. Two heat structures modeled the TC lateral wall, one upstream target plane with respect to the beam source and one downstream. This choice was made to account for different nuclear heating and decay heat conditions [43,44] in the two zones.

**Table 1.** Lithium inventory. \* DT volume is empty during operation.

2.3.2. Nodalization of TC Walls Water Cooling Loop

A second MELCOR model was implemented for the TC-WCS loop using water as a working fluid. Figure 4 shows the adopted nodalization for the TC/TC-WCS model, heat structures, and heat transfer phenomena. Table 3 reports control volume data. Liner and bio shield walls are cooled by parallel branches. In particular, a main distributor manifold splits the nominal 25 kg/s water mass flow into 23.2 kg/s flow for the bio shield concrete walls cooling branch and the remaining 1.8 kg/s for the liner wall cooling branch. Such branches converge into a unique collector after two separate delay tank volumes allowing for activated water decay before entering HX. An HX removes about 109 kW power, of which 90 kW is from the bio shield and the remaining part from the liner. Water at the HX outlet is at 283.15 K and 0.6 MPa. A pump compensates for an estimated pressure drop of 4500 hPa along the loop. Cooling pipes volumes were provided with a 2-mm-stainless steel wall representing pipe walls with which the liner and concrete walls have conductive exchange.

**Table 3.** Control Volumes in the TC-WCS loop.

#### 2.3.3. Numerical Coupling of the Two Models

Several working fluids are available in the MELCOR 1.8.6 code; however, for a given problem, only one of these fluids can be used (together with non-condensable gases). Thus, obvious challenges have been encountered during the modeling phase of the DONES facility since both lithium and water coolants could not be used in a single run.

A possible solution is represented by the external coupling through a Python script of two separate MELCOR input decks, one working with lithium and the other one with water. The two models run concurrently, and information is exchanged between them. Figure 5 represents the approach implemented to couple the TC-LS and TC-WCS Melcor models.

**Figure 5.** Scheme of numerical coupling between TC-LS and TC-WCS Melcor models.

In the Python script, information regarding the heat exchange between the two fluids is collected. In each MELCOR input, a heat structure and two control volumes are present. One of the control volumes contains the working fluid, while the other is a time-dependent control volume that simulates the other fluid involved in the heat transfer. In this control volume, as previously described, the properties are specified as a function of time.

During each MELCOR run, the update on the exchanged heat flux is passed from one input to the other, reporting the new heat transfer coefficients and the new temperatures in the heat structure and in the time-dependent control volume, respectively. Indeed, the temperature of the time-dependent volume will be the temperature assumed by the fluid of the other input at the previous time step. The exchange of information between the MELCOR inputs is obtained by writing in external files (External Data File or EDF) the variables of interest, i.e., temperatures and heat transfer coefficients in this case, after they have been saved in the Python script after a single run. Thus, the heat transfer coefficients are given as a type of boundary condition applied at the left or right boundary surface of the heat structure. In this case, a convective boundary condition is applied with the heat transfer coefficients specified by the Control Function in which the value is reported through the EDF. Instead, the temperatures are directly introduced into the time-dependent volumes directly through the EDF. To clarify this with an example referring to Figure 5 (left side), CV800H2Oinput is the time-dependent volume representing the CV containing lithium in the H2O input and the HS80001 heat structure simulating the liner, and the power transferred to HS80001 is equal to Q = HTCLiInput (TLIQLiInput−THS80001) AHS80001.

Note that the current design of liner wall cooling considers cooling coils welded to the liner surface. Therefore, cooling power is extracted by means of conduction between the coil pipe surface and liner surface. This was implemented in MELCOR (Figure 5) using a FUN1 function assuming a thermal conductivity ks = 10 W/mK (order of SS316, accounting for thermal contact resistance) and a distance dx over which the thermal gradient was calculated to be 8 mm.

The MELCOR execution maximum time step parameter "dt" was set to 0.1 s as a trade-off between the computational time and amount of power exchanged within each time step across heat structures by means of FUN1 functions. In fact, higher values of time steps have been observed to lead to numerical instabilities. The coupling dtcoup for data extraction was then set accordingly.

Note that a 60,000 s stationary regime simulation period was considered to reach a steady-state for the TC-WCS loop before the PIE event in the TC-LS simulation. Numerical coupling starts at 60,000 s for the TC-WCS loop, 1000 s before PIE occurrence set at 61,000 s.

#### **3. Results and Discussion**

Model validation in the two cases was at first performed on the basis of selected parameters. For the main lithium loop, the adopted parameters were (i) Li temperature at target inlet 522.68 K (523 K nominal), (ii) Li mass flow rate 49.5 kg/s (49.8 kg/s nominal), (iii) Li level in QT 1.39 m (1.43 m nominal at steady state), and iv) Li temperature in QT at 546 K (546.7 K nominal). Concerning the TC-WCS cooling loop, it should be noted that its design stage is pre-conceptual and not detailed. Thus, the model validation during the stationary regime was performed on available dimensioning parameter expected values: (i) mass flow rate at distributors: 1.8 kg/s and 22.5 kg/s for liners and concrete distributors, respectively (in good agreement with nominal values reported in Section 2.3.2); (ii) liner temperatures (HS-80001, HS-80003, HS80004) within ±1% from nominal value of 283.15 K.

After model validation, a first assessment of the LTTC1 event in terms of released inventory and consequences on the TC atmosphere was performed. After a steady-state period with the loop fully active and beam operating, the PIE occurred at time t = 1000 s. A sensitivity analysis was performed on PIE detection sensors and the mitigation device. Note that for the considered PIE, detections upstream QT might result in late detection, since perturbation of the main LS loop parameters is firstly propagated to downstream QT. A selection of the main accident detection sensors considered to initiate the beam stop procedure is reported in Table 4.

**Table 4.** Accident detection.

Given the goal of this simulation (i.e., to investigate the liner temperature rise and underlying cooling loop pressurization), the results from the case with a slower detection were conservatively considered.

Figure 6 shows the mass flow rate transient at PIE for selected flow paths judged relevant (break flow path, straightener inlet, and EMP outlet). Note that after EMP stop triggered by accident detection, the mass flow rate in the loop gradually decreases from the steady-state value (49.5 kg/s) until an inversion occurs due to relative elevations of EMP and the target (refer to Figure 2). This limits the released lithium mass inventory to about 729 kg (Figure 7), slightly more than the steady-state inventory within the QT (562 kg).

**Figure 6.** Mass flow rate for selected flow paths for break (FL801), removable ST-NZ inlet (FL852), and EMP (FL350).

**Figure 7.** Inventory in QT(CVH850) and released in TC (CVH800).

The pressure wave form of the TC containment after PIE is shown in Figure 8. The pressure peak reaches 33 kPa within 8 s, then starts a decreasing pattern within 100 s from PIE.

**Figure 8.** Pressurization of TC after PIE.

Figure 9 focuses on the temperatures on the liner floor and related cooling systems. Leaked lithium is released at a temperature of 546 K and then quickly cools down once in contact with the liner floor. In turn, the liner floor quickly passes from the 287 K temperature before PIE, to 463 K within 50 s, peaking at 472 K within 220 s. As a consequence, the underlying cooling pipe HS and water coolant reach 460 K.

**Figure 9.** Liner floor, underlying water pipes, and water coolant temperature after PIE.

Figure 10 shows that water within the liner floor cooling loop vaporizes after about 350 s, causing a temporary loss of coolant mass from the CV880 volume, as shown in Figure 11. The mentioned vaporization results in the pressurization pattern shown in Figure 12, though gradually absorbed by the loop within 500 s from PIE.

**Figure 10.** Water steam quality within liner floor cooling loop water pipes.

**Figure 11.** Flow mass rate at the liner floor cooling volume inlet/outlet.

**Figure 12.** Water coolant pressure in the liner cooling loop water pipes after PIE.

#### **4. Conclusions**

An analysis of the impact of a liquid lithium spillage event on room containment has been proposed. In particular, the purpose of this study was to investigate consequences on the water-cooled steel liner floor of the containment room with a possible breach of the liner barrier enabling lithium to contact the underlying concrete or water itself in the case of cooling pipe rupture. Considering the impact of presented transients in terms of safety consequences, the TC pressurization does not appear to be a concern for the TC containment. In fact, despite the occurrence of water vaporization transient in the cooling loop under the floor liner, the reached pressure peak at about 1.14 MPa appears withstandable within the cooling pipe design pressure. Therefore, the break of cooling pipes and consequent release of water appear unlikely. Given the high temperature difference between released liquid lithium inventory (546 K) and liner temperature (287 K), the temperature rise has a steep pattern reaching more than 3 K/s temperature rise velocity. Future work shall investigate liner structural resistance to such thermal shock events [45–47], possibly leading to liner failure and lithium contacting the concrete. However, even in the case of such a concrete–lithium contact event, lithium at such an interface point would likely be in solid phase or below the minimal observed ignition point (453.15 K) [8], making a consequent fire event unlikely. Future work will also investigate model sensitivity [48] to specific parameters impacting the liner model as the interface point (e.g., thermal conductivity at the liner/cooling pipe contact point, cooling pipe exchange surface).

**Author Contributions:** Conceptualization, D.N.D.; methodology, D.N.D. and M.D.; software, D.N.D. and M.D.; validation, D.N.D. and M.D.; writing—original draft preparation, D.N.D.; writing—review and editing, D.N.D. and M.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 and 2019–2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **Nomenclature**

#### **References**

## *Article* **CFD Optimization of the Resistivity Meter for the IFMIF-DONES Facility**

**Ranieri Marinari \*, Paolo Favuzza, Davide Bernardi, Francesco Saverio Nitti and Ivan Di Piazza**

ENEA, ENEA Brasimone Research Centre, Department of Fusion and Nuclear Safety Technology, 40032 Camugnano, BO, Italy<EMAIL_ADDRESS>(P.F<EMAIL_ADDRESS>(D.B<EMAIL_ADDRESS>(F.S.N<EMAIL_ADDRESS>(I.D.P.)

**\*** Correspondence<EMAIL_ADDRESS>Tel.: +39-0534-801-114

**Abstract:** A detailed study of lithium-related topics in the IFMIF-DONES facility is currently being promoted and supported within the EUROfusion action, paying attention to different pivotal aspects including lithium flow stability and the monitoring and extraction of impurities. The resistivity meter is a device able to monitor online non-metallic impurities (mainly nitrogen) in flowing lithium. It relies on the variation of the electric resistivity produced by dissolved anions: the higher the concentration of impurities in lithium, the higher the resistivity measured. The current configuration of the resistivity meter has shown different measuring issues during its operation. All these issues reduce the accuracy of the measurements performed with this instrument and introduce relevant noise affecting the resistance value. This paper proposes different upgrades, supported by CFD simulations, to optimize lithium flow conditions and to reduce measurement problems. Owing to these upgrades, a new design of the resistivity meter has been achieved, which is simpler and easier to manufacture.

**Keywords:** DEMO-EU fusion reactor; IFMIF-DONES facility; lithium technology; CFD; thermofluid dynamics

#### **1. Introduction**

Knowledge regarding the purity of liquid lithium flowing inside metal pipes, such as those typically constituting the loops used in fusion applications, is of primary importance, since it is well known [1–6] that the presence of impurities, particularly non-metallic elements, greatly enhances the corrosion action exerted by lithium itself on wet pipe surfaces. Therefore, it is necessary to keep as low as possible the concentration of nonmetallic elements in lithium such as carbon, oxygen, hydrogen and, particularly, nitrogen, which is the most corrosion-affecting element among them. For this purpose, a device or a technique able to quantify their concentrations is necessary.

In the IFMIF (International Fusion Materials Irradiation Facility) project, the maximum allowed concentration value for each of the aforementioned elements had been set to 10 wppm [7]. The same value was also chosen for the IFMIF-DONES (Demo-Oriented NEutron Source) plant [8], even if the possibility to allow a higher nitrogen limit is under evaluation, for instance 30 wppm or more, depending on the results of the corrosion validation activities [9], which are still ongoing.

Unfortunately, the quantification of the non-metals concentration in lithium is not possible for almost all of them. Only for nitrogen has a specific procedure been implemented, but it is in any case an offline procedure, the sample entailing a small amount (a few grams) of lithium from the loop and the performance of a batch chemical analysis on it. This requires many hours and the availability of a chemistry-trained operator [10].

An online (real-time) individual analysis of nitrogen as well as of the other nonmetallic elements is not available. Nonetheless, an overall evaluation of the amount of total impurities can be given by the Resistivity Meter (RM). The RM measures the electrical

**Citation:** Marinari, R.; Favuzza, P.; Bernardi, D.; Nitti, F.S.; Di Piazza, I. CFD Optimization of the Resistivity Meter for the IFMIF-DONES Facility. *Energies* **2021**, *14*, 2543. https:// doi.org/10.3390/en14092543

Academic Editor: Hiroshi Sekimoto

Received: 23 March 2021 Accepted: 26 April 2021 Published: 28 April 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

resistance of lithium and relates it to the purity of the alkaline metal, since the higher the concentration of total impurities, the higher the electrical resistance.

The first part of this paper describes the measurement principle of the RM and the issues presently encountered with the instrument. The second part deals with the design and the constructive details of a new, improved RM, possibly giving a more stable, precise and sensitive measurement output; this new RM, once constructed, will be then tested, installed and employed in the IFMIF-DONES Impurity Control System (ICS) loop.

#### **2. The Current Resistivity Meter**

The Resistivity Meter is a device able to online monitor the electric resistance of flowing lithium. It was developed at the University of Nottingham in collaboration with ENEA Brasimone and relies on the variation of the metal resistivity produced by the dissolved anions: the higher the concentration of impurities in lithium, the higher the resistivity (α) [11–15]. Clearly, each kind of impurity affects the resistivity value to a different extent. However, taking into account their relative effects and their solubility in lithium, it is possible to almost entirely ascribe the variation of α to hydrogen and nitrogen, the latter being the most corrosion-affecting non-metal impurity.

The current RM, shown in Figure 1, has been installed and operated inside the Lifus 6 plant at the ENEA Brasimone Centre since 2014 [16,17]; its particular location (the purification loop upstream of the Cold Trap), permits one to analyse the less purified lithium flowing throughout the plant so as to avoid underestimation of the total impurities' concentration value.

**Figure 1.** Picture of the current resistivity meter.

Lifus 6 RM is made of AISI 316L and is an all TIG welded assembly. The main components are:

The electrical resistance is measured between two metal plates (40 mm × 40 mm, 2 mm thickness, 150 mm one from the other), which intersect the measurement capillary and where silver electrical leads are connected both to bring the electrical current and to acquire the voltage drop (BINT 20024 Precision Nano-ohmmeter is employed for this purpose). From Figure 1, it is also possible to see that all the apparatus is housed inside a steel parallelepiped box, and that along the lateral inner walls of this box are mounted four heating elements (two on each side), which permit one to control the desired temperature inside. The box, open in the figure, is closed during normal operation in order to minimize the heat losses to the external environment.

During plant operation, the current configuration of the resistivity meter has evidenced two relevant issues [18]:

All of these issues reduce the accuracy of the measurements performed with this instrument and introduce a relevant noise affecting the resistance value.

#### **3. Upgrade Strategy**

The component upgrades have followed three parallel lines:

For the replacement of the electromagnetic pump, an appropriate analytical design of the Venturi suction was performed by keeping the 1 s travel time of lithium inside the capillary (i.e., mass flow in the capillary) and minimizing the irreversible pressure drop through the Venturi. Owing to this effort, the general dimensions of the pipes were fixed (Figure 2). The Venturi geometry foresees an inlet pipe of ¾ ࡌsch 40 followed by a sudden restriction to a ¼ ࡌsch 40 and a 10◦ angle divergent to the ¾ ࡌsch 40 outlet pipe.

The inlet sudden flow area restriction was chosen instead of a smooth one for reducing both the Venturi length and lithium pressure drop in the component. The adoption of a slow convergent one would have required the adoption of a smaller pipe diameter in the suction region to grant the nominal flow rate in the capillary; on the other hand, the smaller pipe would have increased the pressure drop in the divergent downstream region.

The other two phases (assessment of the thermal losses and reduction of the thermal stratification in the box) require a CFD numerical approach; then, a CFD model of the upgraded component was developed.

**Figure 2.** Sketch of the Venturi suction designed for the resistivity meter; pipe capillary with its main dimensions and air box are illustrated.

#### **4. CFD Analysis: Models and Methods**

A CFD computational model of the upgraded resistivity meter was built to perform CFD simulations. The general-purpose code ANSYS CFX (V.19.2, Canonsburg, PA, USA) was used for all the numerical simulations presented in this paper [19].

The code employs a coupled technique, which simultaneously solves all the transport equations in the whole domain through a false time-step algorithm. The linearized system of equations is preconditioned in order to reduce all the eigenvalues to the same order of magnitude. The multi-grid approach reduces the low frequency error, converting it to a high frequency error at the finest grid level; this results in a great acceleration of convergence. Although with this method a single iteration is slower than a single iteration in the classical decoupled (segregated) SIMPLE approach, the number of iterations necessary for a full convergence to a steady state is generally of the order of 102, against typical values of 103 for decoupled algorithms.

The discretization scheme of the convective terms used for energy and momentum equation variables was the high-resolution scheme (second order-like scheme) [20].

The SST (Shear Stress Transport) *k-ω* model by Menter [21] is extensively used in this paper. It is formulated to solve the viscous sub-layer explicitly and requires several computational grid points inside this latter. The model applies the *k-ω* model close to the wall, and the *k-ε* model (in a *k-ω* formulation) in the core region, with a blending function in between. It was originally designed to provide accurate predictions of flow separation under adverse pressure gradients, but it was applied to a large variety of turbulent flows and is now the default and most-used model in CFX-19 and other CFD codes.

The CFD model developed (Figure 3) includes the Venturi suction described in the previous paragraph, the U tube capillary (the pipe inner/outer diameter of 3/4.8 mm and the curvature radius of 32 mm were kept from the previous configuration) with the two steel measuring plates (again at a distance of 150 mm from each other) and the air in the box surrounding both the capillary and the main pipe. The RM box is a parallelepiped flat oriented 30 cm long and 10 cm × 6 cm rectangular rounded base. The whole model includes three main domains: the lithium flowing in the RM, the piping steel inside the box and the air inside the RM box. The conjugate heat transfer between lithium, steel and air is set owing to the General Grid Interface (GGI) algorithm that links nodes on different domains (solid and fluid) facing each other. No heat source was included in the RM air box looking for an estimation of the thermal losses.

**Figure 3.** Sketch of the CFD model developed: lithium domain in red, steel domain in grey, and air domain in blue. The measuring length between the two slabs (kept from the former configuration) is highlighted.

Liquid lithium properties were implemented as temperature dependent in ANSYS CFX code according to [22] while air and piping steel were set as constant property materials in the code.

The RM box has a horizontal orientation for limiting the thermal stratification of the air inside it.

On the external surfaces of the air domain, a constant heat transfer coefficient boundary condition of 1.5 W/m2/K was set (considering 30 mm thermal insulator and stagnant outside air) and an outside temperature of 15 ◦C. Buoyancy forces were set in the air domain (Boussinesq approximation) for heat exchange between the hot pipes and the cold external walls.

Being interested in average thermal-hydraulic results (pressure drop, heat transfer rate, temperature gradients) and not in point values, full convergence of the simulation is declared when all the Root Mean Square (RMS) residuals reach 1E-5 (according to the CFX User Manual [19] for simulations focused on reliable average quantities but not on detailed point values) and the monitoring points on: lithium pressure drop, thermal loss from air and local velocity values attain a stable value.

Regarding the boundary conditions adopted in the model, it has to be highlighted that the new RM is supposed to be installed inside the future IFMIF-DONES lithium loop. Therefore, its operative parameter will be different from those adopted in Lifus 6 experiments. Unfortunately, a stable definition of the new loop parameters has not been performed yet; thus, two limit cases have been considered here.

The first case assumes the original values set for the IFMIF-DONES plant. These imply a lithium inlet temperature equal to 273 ◦C (i.e., the same temperature of the plant hot leg, the cold leg being set at 250 ◦C) and a flow rate of 0.065 L/s (i.e., 10% of the total lithium flow rate trough the ICS, with the residual 90% going through the traps system).

The second case reflects instead the change in the IFMIF-DONES main lithium loop operating parameters, which was proposed to minimize the possible 7Be accumulation inside the loop. The new values for the temperature and the flow rate of lithium entering the RM circuit are, respectively, 330 ◦C and 0.108 L/s (1/9 of the lithium flow rate through the trap system).

Prior to any CFD case simulation, an appropriate mesh sensitivity analysis was performed. Three different meshes were generated adopting the same mesh strategy but different element sizes. Mesh A has a coarse grid resolution, both in the lithium and in the air domain; it has about 398,000 elements and 294,000 nodes. Mesh B is an average mesh with 1.4 million elements and 866598 nodes. Mesh C has a fine mesh, both in the air and lithium domain; it has 2.65 million elements and 1.87 million nodes.

The first case boundary conditions are imposed on the three meshes for the mesh sensitivity analysis (0.182 m/s inlet lithium velocity, 273 ◦C inlet lithium temperature, 0 bar relative pressure on the lithium outlet surface).

Different data were compared: the pressure drop across the whole model (Δp), the heat losses through the RM box (Q), the average lithium velocity inside the capillary (u), the average lithium outlet temperature from the capillary (Tout). The general comparison between the meshes is reported in Table 1. As illustrated in the table comparison, the outlet temperature from the capillary is not affected by the mesh. Heat losses and lithium velocity in the capillary are marginally affected with about 1% difference between coarse mesh A and average mesh B. The most interesting comparison seems to be the total pressure drop across the CFD model that tends to converge between average mesh B and fine mesh C with a percentage difference of 1.6. s

**Table 1.** Comparison of the main mesh data and results between the three grids (A, B and C) developed and run; results are also reported as percentage difference.

> Due to the very good convergence of the heat losses, average capillary velocity, outlet temperature and the negligible pressure drop difference (barely measurable or not measurable with the instruments) between mesh B and mesh C, mesh B was selected for all the simulations presented in this paper.

> As an insight into the selected mesh B (Figure 4), the grid is fully structured in the lithium domain (red) and in the capillary pipe, while it is unstructured in the solid domain (grey) that includes the pipes and the measuring plates on the capillary.

> For the air domain in the box, the mesh is unstructured with node inflation on the surface boundaries. Other interesting mesh details are reported in Table 2. Mesh parameters such as skewness, orthogonal quality and aspect ratio are declared excellent for the structured domain lithium and good for the tetrahedral/unstructured domains air and steel [19].

**Figure 4.** Sketch of the mesh developed for the resistivity meter simulation.

**Table 2.** Orthogonal quality, skewness and aspect ratio of the mesh developed in the three domains.

#### **5. Results and Discussion**

*5.1. First Case: Boundary Conditions and Results*

The boundary conditions imposed are:

The first parameter to assess in the post-processing phase is the pressure drop of the upgraded component. As we can see in Figure 5, the overall pressure drop is about 308 Pa (3 mbar), but it is not possible to calculate from the contour plot the different contributions due to the variation of the kinetic/hydrostatic energy component in the pipes. Considering both the pressure and the kinetic energy variation in the lithium between two generic sections *i* and *j*, it is possible to obtain the pressure drop Δ*p* with the following expression (Bernoulli equation):

$$
\Delta p = p\_i + \rho \frac{v\_i^2}{2} - p\_j - \rho \frac{v\_j^2}{2} \tag{1}
$$

where *pi* (*pj*) is the pressure on the generic section i (*j*), *ρ* is the lithium density and *vi* (*vj*) is the lithium velocity. It was found that:

• 142.1 Pa (46% of the total pressure drop) is lost in the 10◦ enlargement and in the outlet section.

**Figure 5.** Pressure contour in the lithium domain.

Concerning the velocity field inside the lithium fluid, it must be highlighted that:

It must be highlight that the pressure drop inside the model is mainly concentrated in the 10◦ enlargement section due to the lithium entrainment from the capillary and the recirculation vortex produced (Figure 6). The only possible way to reduce this effect would be to increase the ¼ ࡌpipe length downstream of the capillary to reach a fully developed flow (at least tripling the current length), but this solution would increase both the pressure drop inside the ¼ ࡌpipe and the resistivity meter length, obtaining a negligible effect on the total pressure drop.

Regarding lithium velocity, the maximum lithium velocity inside the model (1.3 m/s) is not a concern for the IFMIF-DONES loop, where the average lithium velocity in the main loop is 5–6 m/s.

Regarding the temperature field (Figure 7), the lithium flowing inside the main pipe (Venturi suction) is kept at the inlet temperature, while the lithium flowing in the capillary loses about 2 ◦C because of the thermal losses in the box.

**Figure 6.** Velocity streamline of lithium flow inside the resistivity meter.

**Figure 7.** Temperature contour of lithium flow inside the resistivity meter.

The higher lithium cooling inside the capillary has two root causes: one is the reduced dimensions of the capillary pipe that give rise to a remarkable volume to surface ratio for the lithium flowing inside, the other is due to the two measuring plates along the capillary that act as thermal bridge enhancing the heat exchange like a finning surface (Figure 8).

**Figure 8.** Temperature contour on the steel surface of the capillary.

Regarding the temperature field in the air domain, the temperature contour of Figure 9 highlights a high temperature gradient from 82 ◦C on the lower surface to about 170 ◦C on the upper one; this remarkable temperature gradient is a perfect example of how natural circulation works. In the upper air region, the buoyancy forces produce air convective vortices over the capillary (granting a temperature mixing), while the lower air volume under the capillary is stagnant because the cold box surface is under the hot capillary and natural circulation cannot take place.

**Figure 9.** Temperature contour in the air domain (resistivity meter box).

Owing to its horizontal orientation, the capillary pipe is surrounded by a constant temperature of about 175 ◦C that avoids an uneven heat exchange along the capillary (one of the issues of the previous configuration characterized by a vertical capillary).

The heat losses, mainly concentrated in the upper surface of the box, are estimated as 18 W.

The small heat losses do not require any heating element inside the box; however, a heating cable or infrared device should be installed in the box for the pre-heating (start-up) phase of the facility to avoid lithium freezing inside the capillary.

#### *5.2. Second Case: Boundary Conditions and Results*

The boundary conditions imposed in this case are the following:

The total pressure drop of the resistivity meter is about 777 Pa. Applying Equation (1) as in the previous case, it was found that (Figure 10):

**Figure 10.** Pressure contour in the lithium domain (new IFMIF-DONES settings).

301.3 Pa (39% of the total pressure drop) is lost in the sudden flow area reduction;

If we compare first case and second case pressure drop results, it is possible to preliminarily assess the hydraulic behavior of the component. A velocity/mass flow increase (from 0.182 m/s to 0.303 m/s) through the resistivity meter leads to a redistribution of the percentage pressure drop contributions inside the component. The sudden flow area reduction percentage increases (+3%) against the 10◦ enlargement one, perhaps because it is more sensitive to mass flow variation, while the distributed pressure loss in the ¼ ࡌpipe keeps the same percentage contribution.

Moving to the velocity field inside the lithium fluid (Figure 11), the folowing must be highlighted:

• The maximum lithium velocity inside the model is 2.1 m/s, and it is reached in the ;pipeࡌ 1/4

**Figure 11.** Streamline velocity of lithium flow (new IFMIF-DONES settings).

As previously mentioned, the 2.1 m/s peak velocity inside the ¼ ࡌpipe is not a concern for erosion and corrosion issues for the IFMIF-DONES due to the low lithium velocity inside the capillary (0.64 m/s). This second case set-up shows a favorable effect on the measuring device granting a better lithium sampling; in fact, by keeping the 1 Hz sampling frequency of the current RM configuration, it is possible to always measure a different lithium sample in a normal operation phase.

Regarding the temperature field (Figure 12), lithium flowing inside the main pipe (Venturi suction) keeps its inlet temperature, while lithium flowing in the capillary experiences about 1.5 ◦C decrease because of the thermal losses in the box, 25% less if compared with previous results but with a higher velocity (mass flow) through the capillary. As for the previous case, in Figure 12 one can clearly observe, from the contour bands across them, the thermal effect of the steel plates on the flowing lithium enhancing thermal losses to the surrounding air.

As for the temperature field in the air domain, the temperature contour of Figure 13 highlights a high temperature gradient (104 ◦C, +18% increase), ranging from 96 ◦C on the lower surface to about 200 ◦C on the upper one. This higher gradient is mainly due to the higher lithium circulation temperature (imposed as a boundary condition) inside the instrument that generates a better natural circulation of heat transfer with the upper "cold" surface of the box; this phenomenon increases the upper air temperature, while it has only minor effect on the lower air temperature because no circulation takes place here. In conclusion, the thermal gradient increase inside the box is not symmetric but unbalanced towards the hot region.

**Figure 12.** Temperature contour of lithium flow inside the RM pipe (new IFMIF-DONES settings).

**Figure 13.** Temperature contour in the air domain inside the RM box (new IFMIF-DONES settings).

The heat losses mainly concentrated in the upper surface of the box (due to the natural circulation of air in the upper air region) are estimated as 19.4 W (7% more than the previous test case); this is due to the combination of three opposed effects (compared to the first case): the higher velocity inside the capillary, the lower density due to the higher inlet/circulation temperature, the lower temperature difference across the capillary.

#### **6. Conclusions**

The purity of liquid lithium flowing inside a loop pipe is of primary importance, especially in fusion applications such as the IFMIF-DONES plant, due to corrosion issues

on contact surfaces. An appropriate device called the "Resistivity Meter" was developed by the University of Nottingham and procured by ENEA to monitor lithium impurities in Lifus 6 loop. Unfortunately, the device has shown some measuring issues during its operation that reduce its accuracy and introduce relevant background noise.

An upgrade strategy is proposed in this paper to overcome the aforementioned problems, and a CFD assessment of the fluid-dynamic behavior of the new layout was developed. Without fixed parameters for the boundary condition of the device, two limit cases have been considered: a low mass flow and low temperature case (first case) and a high mass flow and high temperature case (second case).

The CFD simulations of both the situations have demonstrated that it is possible to move lithium through the capillary measurement without using a dedicated electromagnetic pump upstream of the capillary. This will permit one to suppress the noxious noise introduced by the pump on the resistivity meter signal, which was largely evidenced with the old configuration. The resulting lithium speed inside the capillary is, in both cases, largely enough to completely replace all the lithium inside the capillary during the time span between two successive signal acquisitions (set as 1 s).

The comparison of the two simulation results was also adopted as sensitivity analysis to better understand the component behavior with different lithium mass flow and inlet temperature. Regarding mass flow, the comparison highlighted that the sudden flow restriction placed at the inlet is more sensitive to the mass flow variation if compared to the 10◦ enlargement placed at the outlet. As for temperature sensitivity, the comparison points out that an inlet temperature increase leads to a higher non-symmetric thermal gradient (+18%) inside the air box.

The simulations have additionally shown that during the operations there is no need to employ an external heating element to keep the proper lithium temperature inside the capillary.

Since the residence time of lithium will be very short (about 1 s or 0.5 s, depending on its flow rate), its thermal losses will be limited to about 2 or 1.5 ◦C and will be constant over time, provided a good thermal shielding of the RM box may be assured.

Nonetheless, an external heater will be necessary and employed in the following situations:

**Author Contributions:** Conceptualization, P.F.; software, R.M. and I.D.P.; data curation, R.M. and P.F.; writing—original draft preparation, R.M. and P.F.; writing—review and editing, R.M.; visualization, P.F.; supervision, D.B. and F.S.N., project administration, D.B.; funding acquisition, D.B. and F.S.N. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 and 2019–2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors wish to thank all the ENEA's technicians involved in the implementation and operation of the Lifus 6 experimental facility.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **References**

## *Article* **Wake Shape and Height Profile Measurements in a Concave Open Channel Flow regarding the Target in DONES**

**Björn Brenneis 1,\*, Sergej Gordeev 1, Sebastian Ruck 1, Leonid Stoppel 2 and Wolfgang Hering 1**

	- 2 Institute for Thermal Energy Technology and Safety, Karlsruhe Institute of Technology, 76344 Eggenstein-Leopoldshafen, Germany<EMAIL_ADDRESS>	- **\*** Correspondence<EMAIL_ADDRESS>
**Abstract:** Wakes appearing downstream of disturbances on the surface of a water flow in a concave open channel were examined experimentally. The investigated channel geometry was similar to the liquid lithium target in DONES (Demonstration fusion power plant Oriented NEutron Source). The objective of the measurements was to analyze the effect of a disturbance on the downstream layer thickness. For measuring the height profiles in the channel, an optical measurement system based on laser triangulation was developed. It was shown that the wake of the undisturbed flow emerged from the nozzle corner, which was in accordance with analytical solutions. For sufficiently large disturbances at the nozzle edge, the height profiles located downstream showed symmetrical minima and maxima on both sides of the disturbance. The wake depth strongly depended on the diameter and penetration depth of the disturbance, as well as the circumferential position in the channel, which yields to a critical wake depth of one millimeter for the lithium target in DONES.

**Keywords:** wakes; open channel flow; experimental methods; DONES

#### **1. Introduction**

For fusion power plant technology, specific materials withstanding the harsh environment of high-energy neutron fluxes are necessary [1]. The neutron irradiation facility for fusion materials, DONES, is intended to be built for this purpose. In DONES, a deuteron beam (125 mA, 40 MeV) hitting the lithium target produces a high-energy neutron flux. The target is a liquid lithium free surface flow on a concave backplate, as depicted in Figure 1. In order to contain the heat released by the beam within the liquid lithium (Bragg peak at 19 mm [2]) and to avoid an introduction of the heat in the backplate, a stable configuration of the free surface flow with a setpoint layer thickness of 25 ± 1 mm is crucial. Stable wave structures, so-called wakes, which occur from accumulated impurities at the nozzle edge [3], can cause a local decrease in the layer thickness of more than one millimeter.

The free surface of the lithium flow without wakes is sufficiently stable [4]. Wakes occuring next to the side walls do not reach the beam footprint (Figure 1) and are therefore not critical [5]. Wake structures caused by stationary lithium droplets sticking at the nozzle were observed by Kondo et al. [3]. Their experimental setup was a horizontal 70 mm wide open channel flow at 15 m/s. The wake structures were temporally and spatially stable and could be described by analytical Kelvin wake equations presented in Section 2, neglecting the gravitational force. The observed area was up to 50 mm downstream of the nozzle.

In a subsequent work by Kondo et al. [6], they used pattern projection to measure the height profile of the liquid lithium flow. The measurements were limited to an area of 5 × 3 mm. They observed a relatively smooth surface up to a velocity of 6 m/s. At higher flow velocities, the amplitude of the wake increased.

**Citation:** Brenneis, B.; Gordeev, S.; Ruck, S.; Stoppel, L.; Hering, W. Wake Shape and Height Profile Measurements in a Concave Open Channel Flow regarding the Target in DONES. *Energies* **2021**, *14*, 6506. https://doi.org/10.3390/en14206506

Academic Editors: Alessandro Del Nevo and Marica Eboli

Received: 3 August 2021 Accepted: 6 October 2021 Published: 11 October 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

**Figure 1.** Sketch of the liquid lithium target in DONES. (**a**) Side view on the cross-section through the channel center. (**b**) Front view. (**c**) Cross-section perpendicular to the flow direction at the nozzle outlet. The coordinate axes are *y* for the channel width, *x'* parallel to the channel floor in streamwise direction and *z'* perpendicular to the channel floor. The origin is at the nozzle outlet.

Originally, wakes were examined in the context of ship waves, due to their impact on the wave drag [7]. Kelvin wake equations [8] describe the shape of wakes analytically. The wake shape is defined by the angle of the wave front with maximum amplitude. Measurements showed that the wake angle depends on the Froude number [7,9–11]. Moisy and Rabaud [10] systematically examined wakes behind partially immersed cylinders moving through water at different velocities. The wake angle depended on the Froude number, Bond number and minimal phase velocity. Pethiyagoda et al. [11] showed a dependency of the wake angle on small Froude numbers. Therefore, the originally constant Kelvin angle is limited to Froude numbers around one. Another explanation for these phenomena of smaller wake angles is given by Noblesse et al. [12] considering an interference of multiple wakes.

The deformation of the water surface directly at the cylinder due to run-up upstream and depression downstream was analyzed by Ageorges et al. [13] and Chaplin and Teigen [14]. Koo et al. [15] analyzed the flow past a surface piercing cylinder numerically. They also evaluated the height profile downstream near the disturbance.

An integrated approach was applied to examine the development of wakes downstream of a disturbance in a concave open channel flow. Wake shape and profile measurements were conducted in the test facility FIDES ("Facility for experimental Investigation of a 3D FreE Surface flow") presented in Section 3. The operating point was selected using the analytical equations of Kelvin wakes (Section 2). Therefore, the measured wake shapes (Section 4.3) can be transferred quantitatively to the lithium flow and compared to other published wake shape results. The observed wake profiles in water (Section 4.2) provide a qualitative insight in the development of the wake amplitude along the channel in lithium.

#### **2. Analytical Wake Equations**

Waves behind a moving disturbance in calm water or behind a stationary disturbance in a steady flow can be described by the following equations [8]:

$$\begin{aligned} x' &= p \cdot \cos(\theta) - \frac{dp}{d\theta} \cdot \sin(\theta) \\ y &= p \cdot \sin(\theta) + \frac{dp}{d\theta} \cdot \cos(\theta) .\end{aligned} \tag{1}$$

The disturbance moves along the negative *x* -axis or water streams around the stationary disturbance in the positive *x* direction with the velocity, *u*. A line of length *p* connects the disturbance with points on the constant phase line with the angle *θ* in between *p* and *x* . The points with a constant phase are at the position (*x* ,*y*). The phase velocity *c* = *u* · cos(*θ*) is defined by the dispersion relation [16]:

$$\mathbf{c} = \sqrt{\left(\frac{\lambda\mathbf{g}}{2\pi} + \frac{2\pi\sigma}{\lambda\rho}\right) \cdot \tanh(2\pi h/\lambda)}.\tag{2}$$

The wavelength is defined as *λ* = *p*/*n*. The variable *n* can be chosen as a multiple of 0.5. Wave troughs are given by a positive integer value of *n* = 1, 2, 3 ...; otherwise, wave crests are described. In addition, the density *ρ* and surface tension *σ* of the fluid have an influence.

With regard to the flow in DONES (FIDES), it is assumed that the wavelength is much smaller than the layer thickness of *h* = 25 mm (10 mm). Therefore tanh(*h*/*λ*) ≈ 1, which causes an error smaller than 3% for *λ* < 3.6 *h* [17]. Additionally, gravity, *g*, is substituted by the centrifugal acceleration, *u*2/*R* [3]. This is justified, because gravity is mostly in the streamwise direction and, therefore, the centrifugal acceleration is more than one order of magnitude bigger considering the perpendicular acceleration on the free surface. Without any assumptions about the dominant forces (surface tension, *σ*, and centrifugal forces) the equations have two solutions, which depend on the curvature radius, *R*, the Weber number, *We* = *u* #*ρL*/*σ*, and the Froude number, *Fr* = √*R*/*L*. The characteristic length, *L*, is either the nozzle height, *h*, or for the flow with the cylindrical disturbance, the diameter, *D*, of the cylinder. For different flow facilities with the same curvature radius, the equations have the same wake curves as long as the product *We* · *Fr* is constant, which is equivalent to 2·*U*2, where *U* = *u*/*cmin* is the velocity ratio and *cmin* = 4*u*2*σ*/(*Rρ*) 1/4 is the minimal phase velocity. The flow velocity for the reference lithium flow was *u* = 15–20 m/s (velocity range in DONES) with a constant curvature radius of *R* = 250 mm for the vertical concave channel, which results in the velocity range *u* = 4.7–6.2 m/s in water (20 ◦C).

The solution of Equations (1) and (2) for *n* = 1, *u* = 15 m/s in lithium without the assumption of a dominant force is shown in Figure 2. The blue dashed line in the diagram represents the capillary wake line dominated by the surface tension and the red lines are the centrifugal wake dominated by centrifugal forces. Considering the analytical solutions, it was concluded that wakes from the nozzle corners do not reach the beam footprint [3] and, thus, the accumulation of impurities at the nozzle edge are the main source for a film thickness decrease. For the prediction of the wake shape, the solution for *n* = 0.5 was used, which describes the position of a wave crest and was compared to the experimental results.

**Figure 2.** Solution of the Kelvin wake Equations (1) and (2) for *n* = 1 and *u* = 15 m/s in lithium. The blue dashed line (capillary line) represents the wake line dominated by surface tension. The red solid line (centrifugal line) is the wake line dominated by the centrifugal acceleration.

#### **3. Experimental Setup**

The experiments were conducted at the water flow test facility FIDES at KIT (Karlsruhe Institute of Technology). The general layout of the facility is shown in Figure 3. A pump provided a constant water mass flow to the top end of the test section, which was

measured using a magnetic inductive flow meter. The test section made of plexiglass was geometrically similar to the layout of the liquid lithium target in DONES, as depicted in Figure 4. The water in the test section flowed through a flow straightener into a two-stage nozzle with an outlet cross-section of 100 × 10 mm. A maximum flow velocity at the nozzle outlet of *u* = 20 m/s could be reached. Downstream of the nozzle, water flowed through the concave open channel with a curvature radius of *R* = 250 mm before it returned to the separator.

**Figure 3.** Scheme of the FIDES test facility.

**Figure 4.** Sketch of the FIDES test section showing the position of the measurement system (camera and laser) and the position of the disturbance with the diameter, *D*. The test section is a concave open channel with a curvature radius of *R* = 250 mm. The measuring position is described by the angle *β*. On the right side, the view on the back wall of the test section with the three reflected lines l1, l2 and l3 is shown.

Stable wave structures were generated by an artificial disturbance at the nozzle outlet. This disturbance was a metal cylinder with different diameters *D* (1.2, 2, 3 mm). The penetration depth of the cylinder into the water could be varied by a linear stage. A camera ("Basler ac2040-55uc" camera [18] and "KOWA LM16JC3M2" objective [19]), placed as depicted in Figure 4 with a back wall distance of 213 mm, was used to observe the wake structures with an exposure time of 1 s. To measure the layer thickness, a laser line was projected in the camera's field of view. The camera observed three reflected lines from the channel outside wall (l1), the channel floor (l2) and the water surface (l3). Figure 4 shows the arrangement of the disturbance, the camera and the laser, as well as the view on the

channel back wall with the three reflected lines. To measure the height profile at different positions, the camera and laser could be moved by keeping a constant distance to the back wall. The relative position of the laser and camera remained constant. The measured circumferential positions were *β* = 35◦, 40◦, 45◦ and 50◦ downstream of the nozzle. The vertical channel position corresponded to *β* = 45◦.

MATLAB [20] was used for the image evaluation. Three horizontal areas were defined where the laser lines were expected to be. Those were further subdivided into vertical segments. In every segment, the laser lines were detected by defining threshold values for the pixel intensity. Therefore, the pixel positions of the three lines in the image were known. By using pictures of measuring tapes at the channel outside wall (*R0* = 270 mm), the pixel position could be assigned to a circumferential position at the outside wall (the nozzle outlet was zero). The layer thickness was calculated via triangulation with the known circumferential position, the camera position, the refractive indices and the back wall thickness of 20 mm. Laser line l1 was the reflection from the back wall. With the camera position, l2 had to be corrected via refraction through the 20 mm back wall to obtain the position of the laser line on the channel floor. Using the known position of l1 on the back wall, l2 on the channel floor and the laser line through the back wall, the incidence angle on the channel floor and the ray further through the water could be calculated. With the observed reflection on the water surface (l3), the viewing line of the camera to the water surface was calculated. The intersection point of the viewing line and the laser line resulted in the point on the water surface. The difference between the channel floor curvature radius and the distance of the point on the water surface to the center point of the curvature was the output of the algorithm (the thickness of the water flow at this location).

To validate the measurement system, the layer thickness in the area 0–2 mm downstream of the nozzle was measured. The expected thickness was the nozzle height of 10 mm. The average layer thickness along the channel width was 9.99 mm, with a standard deviation of <0.09 mm. In addition, undisturbed profiles were measured with a chromatic confocal sensor (KEYENCE CL-3000 with CL-LP070 optical head [21]). The mean deviation of the undisturbed absolute height profile in between the side wall wakes measured by the two sensors for *β* = 45◦ (*u* = 5 m/s) was smaller than 0.1 mm.

#### **4. Experimental Results**

The presented analytical solutions of Kelvin wakes in Section 2 were used to set the boundary conditions for the tests in water and to be able to transfer the results to DONES. Under the assumption of a constant product *Fr* · *We*, the velocity range of *u* = 15–20 m/s in lithium (250 ◦C) is similar to the velocity range of *u* = 4.7–6.2 m/s in water (20 ◦C). In this range, the wake shape in water is similar to the shape in a lithium flow with the same curvature radius of *R* = 250 mm.

#### *4.1. Undisturbed Height Profile Measurements*

In the first step, the layer thickness of the undisturbed water flow in FIDES was analyzed. Figure 5 shows the averaged measured height profile at *u* = 5 m/s, *β* = 45◦ downstream of the nozzle. In the images of the reflected laser lines, 1 px in the height was equivalent to a height change of 0.043 mm. The standard deviation of the measured undisturbed profile was <0.11 mm. In addition, the calculated systematic error of the absolute height measurements was 0.13 mm. The considered errors were the uncertainty of the camera distance, the measuring tape position and the uncertainty of the threshold value in the laser line detection algorithm. In *y*-direction, the point to point distance was 0.729 mm, across which the measured heights were averaged.

**Figure 5.** Height profile of the undisturbed flow at *u* = 5 m/s, *β* = 45◦ downstream of the nozzle. The standard deviation is represented as the area behind the line.

The profile of the undisturbed flow in Figure 5 showed a slight bulge in the center of the channel. Near both side walls, the wakes that occurred from the nozzle corners were visible as a maximum and minimum. The measured maximum had a side wall distance of 11.82 mm, which corresponds to the first maximum (*n* = 0.5) of the centrifugal Kelvin wake line (Section 2). The first 8 mm from both side walls could not be measured. Laser light scattered by the side wall prevented the measurements. Directly at the wall, the film thickness reached another maximum due to wetting. Between the wake maximum and the wall, another minimum was indicated. The average layer thickness of the measured profile shown in Figure 5 was 9.88 mm.