Introduction

The Lead-cooled Fast Reactor (LFR) is one of the six Gen IV nuclear energy systems [1]. Lead or Lead-Bismuth Eutectic (LBE) is usually applied as a coolant for an LFR owing to its high boiling point, satisfactory heat transport performance, and compatibility with air or water [2-4]. Because of the chemical inertness of lead/LBE to water/steam in an LFR, setting intermediate heat transport loops is not necessary; in other words, the primary pumps and steam generators can be directly installed inside the primary vessel, which substantially simplifies the reactor system and increases thermal efficiency [2, 5]. However, in such a design, a Steam Generator Tube Rupture (SGTR) accident is possible, considering the high temperature, corrosion, and significant pressure difference between the secondary and primary sides [6]. In a hypothetical LFR SGTR accident, secondary subcooled water at high pressure contacts the primary coolant (liquid lead or LBE) at a higher temperature but much lower pressure than the secondary water [7].

The literature has divided the evolution of an LFR SGTR accident into four stages [5, 8, 9]. In stage I, highly pressurized water injected into the molten lead or LBE pool from the break instantaneously flashes and expands owing to the sudden pressure loss, with instantaneous pressure waves growing in the heavy liquid metal pool, which causes large loads on the internal structure and might rupture neighboring steam generator tubes. In stage II, the water jet is fragmented owing to the hydraulic instability and dispersed in the molten pool. In this process, the expansion of the mixing zone causes displacement of the liquid metal and the resultant sloshing of the molten pool, which might cause mechanical damage to structures inside the reactor. In stage III, although the water discharged into the primary circuit from the secondary circuit partly evaporates owing to flashing and heat exchange, a possibility is that some liquid water droplets will slowly evaporate inside the bubbles because the vapor layers could prevent water droplets from touching the molten lead or LBE [10]. Under the action of some triggers, such as pressure waves, the vapor layers may collapse; subsequently, internal water droplets fragment and directly contact molten lead/LBE, namely, a Coolant-Coolant Interaction (CCI), which could lead to violent evaporation and the possibility of steam explosion. In stage IV, some of the vapor bubbles are entrapped and transported toward the core along with the liquid metal flow. The bubbles that remain in the core sometimes lead to reactivity disturbances and deterioration of the heat exchange.

Many experimental, theoretical, and numerical studies have been conducted to simulate the scenario of secondary water injected into the primary loop in an LFR SGTR accident. For instance, based on EFIT reactor design, Wang et al. conducted Two-Dimensional (2D) numerical simulations of SGTR accidents using the SIMMER-III code [11]. In addition, based on the LIFUS 5 experimental facility, a series of experiments have been conducted by injecting high-pressure (6-70 bar) subcooled water (130℃-240℃) from the bottom of a reaction vessel containing molten LBE (350℃-400℃), with numerical simulations conducted using the SIMMER-III code [12-14]. Furthermore, Huang et al. performed a simulation of the LIFUS5/Mod2 experiment using MC3D code and obtained a good agreement [15]. Based on the KYLIN-II-S facility, Zhang et al. conducted an experiment by injecting high-pressure subcooled water (20 bar and 200℃) into molten LBE (~408℃) from a tube installed on top of the reaction vessel, with a numerical simulation performed using the NTC code developed by the FDS team [16]. In addition, Zhang et al. performed a numerical investigation on the influence of rupture position and secondary pressure on core voiding in an LFR SGTR accident [17]. To conduct visual research on the water-LBE interface fragmentation phenomenon, Huang et al. conducted many experiments by injecting molten LBE into a water pool from the pool surface and found that explosive interaction is more likely to occur at low water temperatures than at high water temperatures [18, 19]. Recently, Cheng et al. and Tan et al. conducted experimental investigations on the fragmentation behavior of lead, LBE, or lead-bismuth non-eutectic alloy (LBNE, 70% Pb-30% Bi) injected into a water pool and established maps that forecast the sphericity and porosity of fragments according to the temperatures of water and melt [20-22]. In addition to experiments and numerical calculations, Iskhakov et al. proposed an approach to approximately calculate the forces loaded on neighboring tubes at the initial stage of an LFR SGTR accident [8].

Regarding stage III, that is, the circumstance of a water droplet immersed inside a liquid lead/LBE pool, there are also limited experimental, numerical, and theoretical studies. For example, Cheng et al. conducted experiments at the Japan Atomic Energy Agency (JAEA), in which a glass flask containing water was transported into a pool with liquid Bi-Sn-In alloy and then broken by a crushing cone placed inside the pool [23]. Cheng et al. conducted numerical calculations using the SIMMER-III code to acquire further knowledge of the physical processes in the experiments [24]. The numerical calculations well reproduced the finite pressure buildup with increasing water volume, as observed from experiments, and confirmed that the finite pressure buildup may be due to the hindrance effect of the steam generated at the interface of water and melt [23, 24]. Iskhakov et al. calculated the mechanical energy released in multiphase systems (melt-liquid water-vapor) and compared the calculated results with the data from the literature [23, 24], with good agreement obtained only for the cases with water volume not exceeding 20 mL because of the assumption that all water participates in this interaction [9].

However, according to the analyses by Zhang et al. and Cheng et al. [24-26], there are some defects in the experimental facility used in the literature [23]. For example, the shape of the released water is difficult to maintain owing to the use of a crushing cone. To obtain more reliable experimental data on water droplet-melt interactions than using the experimental facility at JAEA, Cheng et al. and Zhang et al. set up an experimental facility called Pressurization Characteristics In Melt-Coolant Interaction (PMCI) at Sun Yat-sen University (SYSU), which has been confirmed to be adequate for remedying the deficiency of the experimental facility established at JAEA [23, 25, 26]. Zhang et al. conducted many experiments by releasing water lumps at the bottom of the molten pool using the same material as that used at JAEA (i.e., Bi-Sn-In alloy) [26]. Through detailed analysis, a consistent conclusion was obtained that the limited pressure buildup was due to the isolation effect of the vapor layer, as found in the literature [24]. As shown in Table 1 [27], the thermophysical properties of Bi-Sn-In alloys differ from those of lead-based alloys (esp. thermal conductivity and thermal diffusivity); therefore, the findings from the Bi-Sn-In experiments might create uncertainty in the LFR SGTR safety analysis. Recently, to deepen the understanding of the CCI in stage III of an LFR SGTR accident, Cheng et al. performed experiments using the LBE based on the PMCI facility, and a limited pressure buildup with an increase in water volume was also observed [28, 29]. In addition, probably because the higher melt density of LBE than that of Bi-Sn-In could promote melt piercing through the steam layer, the pressure buildup in the LBE experiments was much higher than that in the Bi-Sn-In experiments [28].

The aforementioned discussion demonstrates that the experimental research on water-melt interaction in an LFR SGTR accident remains insufficient (especially stage Ⅲ), and most of these experimental studies were conducted using LBE or other low melting point alloys. Pure lead is a more promising coolant choice for LFR than LBE because the former has a much lower cost and substantially lower radiological concern (especially ²¹⁰Po) than the latter does [2, 4]. Although the difference in the thermophysical properties between LBE and lead is slight, molten lead is more likely to solidify in a water-lead interaction experiment than LBE because the former has a much higher melting point, which may lead to different experimental results. For instance, in Sa et al., by releasing molten LBE or lead droplets from a certain height above the water pool, the fragmentation behavior of the melt droplet was studied. They observed that as the droplet temperature increased, the peak pressure in the LBE experiment increased from 5 to 8 kPa, and for the lead experiment, the peak value was maintained at approximately 2 kPa [30]. Therefore, meaningful experimental data on lead for future safety analysis of LFR SGTR accidents is urgently necessary.

In this work, in an endeavor to understand the pressure-buildup characteristics of a water droplet immersed inside a liquid lead pool during an LFR SGTR accident, based on the PMCI experimental facility, many experiments were conducted by releasing water lumps inside a liquid lead pool at SYSU. In addition, to increase the knowledge of the impact of the melt material, the lead experiments were compared with LBE experiments performed by Cheng et al. [28, 29]. In Sect. 2, details of the PMCI facility and experimental conditions are presented. In Sect. 3, the lead experimental data from this study are analyzed and compared with the LBE experimental data in detail.

Experimental details

The following is a detailed introduction to the PMCI experimental facility, the schematic of which is shown in Fig. 1. The interaction vessel in which the CCI occurs is a stainless steel cylindrical container with an inner diameter of 250 mm, a height of 750 mm, and a design pressure of 40 MPa. As shown in Fig. 1, many sensors are installed on the interaction vessel wall to obtain the temperature and pressure trends of the melt pool and cover gas. Moreover, for obtaining the temperature of the water lump, a thermocouple is inside the drive rod (Fig. 1). In addition, because of the risk of high temperature and pressure buildup during the experimental run, the reaction vessel is isolated by the outer vessel.

Fig. 1Full-screen View

Schematic of PMCI experimental facility [28].

In the experiments in this study, an electromagnetic induction heater with a power of approximately 40 kW, in which the induction coil was installed on the interaction vessel wall, was employed to heat and melt the lead. The mass of lead blocks required was calculated by multiplying the molten lead density by the volume of the lead pool (corresponding to the target depth). Inhibiting the lead from oxidizing during the heating process was achieved by feeding inert gas into the interaction vessel.

In order to simulate a CCI with a water droplet immersed inside a liquid lead pool, a spherical glass flask for holding water was installed at the bottom of the drive rod. Compared with the two volumes of flask (i.e., V_F = 50 or 100 ml) employed in the literature [23], the spherical glass flasks had a series of capacities (V_F:0–100 ml) in our experiments based on the PMCI facility. When the volume of the water lump was the same as the capacity of the flask, the shape of the water lump remained almost spherical [26].

During the heating process, the temperature inside the interaction vessel is expected to be high. In order to avoid a rapid increase in water temperature, the spherical glass flask was placed inside a stainless steel inner cylinder with the cooling water flowing inside its hollow wall, which was hung on the interaction vessel (Fig. 1). Moreover, a thin aluminum film was used to seal the bottom of the inner cylinder, obstructing the heat convection. In addition, the aluminum film was so thin that it could be easily punctured by the drive rod and therefore did not interfere with the movement of the drive rod.

When the temperatures of the melt and water attain target values, along with the movement of the drive rod (controlled by a motor), the glass flask can move downward at a velocity of approximately 100 mm/s and finally break as it collides with the bottom of the interaction vessel. According to our previous work based on PMCI, such a small descending speed is sufficient to rupture the thin flask (without the help of a crushing cone) and realize an instant release of water lump inside the molten pool [26, 29]. Owing to the low velocity of the drive rod, the fluctuation of the molten pool (owing to the movement of the drive rod) can be reduced to an acceptable level [25, 26, 29]. Consequently, the stability of the initial shape of the discharged water lump should increase, even if it cannot be guaranteed to be absolutely spherical [26, 29].

To ascertain the pressure-buildup characteristics underlying CCI in LFR SGTR accidents, Cheng et al. successfully performed many LBE experiments using the PMCI facility [28, 29]. In this work, some experiments were conducted using pure lead with various parameters employed as in LBE experiments, namely, water temperature/subcooling (T_w/ΔT_sub), water volume (V_w), water lump shape, melt temperature (T_m), and molten pool depth (H_m). In order to understand the impact of the thermophysical properties of the melt on the experimental results, the lead experiments in this study were compared with LBE experiments in the literature, and the details of the experimental conditions are listed in Table 2.

In addition, the boiling mode has a significant impact on the evaporation rate when the water lump contacts the melt. For example, in the film boiling mode, a stable steam film is formed between water and melt, which can seriously hinder heat transfer. According to the literature, a criterion for film boiling was proposed, which is an instantaneous contact interface temperature Ti higher than the minimum film boiling temperature T_mfb [31-33]: $\frac{T_{\text{i}}-T_{\text{c}}}{T_{\text{h}}-T_{\text{i}}}={\left(\frac{K_{\text{h}}{\rho }_{\text{h}}{C}_{\text{h}}}{K_{\text{c}}{\rho }_{\text{c}}{C}_{\text{c}}}\right)}^{1/2},$ (1) $T_{\text{mfb}}=T_{\text{sat}}+\left(101+8\Delta T_{\text{sub}}\right),$ (2) where K, ρ, and C denote thermal conductivity, density, and specific heat, respectively. The subscripts c and h represent the cold and hot liquids, respectively. For water, the saturation temperature T_sat was 373 K at atmospheric pressure, and ∆T_sub is the water subcooling. According to this criterion, the boiling mode can be predicted under different thermal conditions (Fig. 2).

Fig. 2Full-screen View

Boiling mode for different thermal conditions. (a) LBE; (b) Lead.

Analyses of experimental result

3.1

Transient temperature and pressure trend during CCI

Similar to LBE experiments in the literature, the lead experiments in this study have two interaction mechanisms: steam explosion and non-steam explosion [28, 29]. Because the water-melt interaction process cannot be directly observed visually, the interaction mechanism in each case was mainly evaluated according to the pressure variation in the melt pool. To improve the understanding of the differences in transient temperature and pressure trends during CCI resulting from different interaction mechanisms, this section discusses the measured temperature and pressure data of representative runs in the LBE and lead experiments under both interaction mechanisms.

For the non-steam explosion cases, No. 9 (LBE) and No. 71 (lead) were selected for analysis, and the measured transient pressure and temperature histories are depicted in Fig. 3. A consistent trend was observed in the measured temperature and pressure histories, despite the difference in melt materials. When the spherical flask was broken at the bottom of the interaction vessel, the measured water temperature increased significantly. According to Fig. 3(b), the CCI event starts at approximately 2.9 s. At the end of the CCI event, the significantly increased water temperature was still lower than the bulk temperature of the lead pool. The reason for the low water temperature may be that thermocouple TW12 touches the bottom of the interaction vessel [26]. Unlike the water temperature change trend, the molten pool temperature and cover gas temperature are almost constant during the CCI, which is mainly due to the large size of the molten pool and the effective water cooling system, respectively [25, 26, 29].

Fig. 3Full-screen View

Transient pressure and temperature change trend in non-explosion cases. (a) LBE_No. 9: H_m = 180 mm, T_m = 573 K, T_w = 293 K, V_w = 30 ml, V_F = 30 ml [29]; (b) Lead_No. 71: H_m = 100 mm, T_m = 673 K, T_w = 293 K, V_w = 20 ml, V_F = 20 ml

Regarding pressure history, Fig. 3 shows that after the CCI starts, the water evaporates rapidly, and then a series of pressure pulses is generated in the molten pool (generally, the first pressure pulse is the most violent). According to the enlarged view of the molten pool pressure during CCI, the evolution of a CCI event can be divided into three phases [25, 26, 28, 29]: in phase (1), water and melt are mixed with a relatively slow steam generation rate; in phase (2), after part of/all the water is dispersed into the melt, instant water evaporation occurs, causing violent pressure buildup; in phase (3), the generated steam is expanded. The pressure buildup in the molten pool during CCI can be characterized by the two-phase pressure involved in phase (2). In the cases shown in Fig. 3, the peak values of the two-phase pressures are relatively large (approximately 0.3-0.4 MPa) with short durations. However, the cover gas pressure increasing velocity is relatively slow because of the efficient water-cooling system and large volume of the cover gas region [25, 26, 29].

Regarding the interaction mechanism of the steam explosion, No. 33 (LBE) and No. 60 (lead) were selected for analysis, and the measured pressure and temperature histories are depicted in Fig. 4. As shown in Figs. 3 and 4, although the interaction mechanism differs, the temperature and pressure change trends in the steam explosion cases are qualitatively similar to those in the non-steam-explosion cases. In addition, for the lead and LBE experiments, owing to the much higher evaporation rate under the steam explosion interaction mechanism than under the non-steam explosion interaction mechanism, the peak values of the two-phase pressures have increased (up to approximately 1.5MPa), and the cover gas pressure increasing velocities have increased.

Fig. 4Full-screen View

Transient pressure and temperature change trend in steam explosion cases. (a) LBE_No. 33: H_m = 180 mm, T_m = 673 K, T_w = 333 K, V_w = 60 ml, V_F = 60 ml [29]; (b) Lead_No. 60: H_m = 180 mm, T_m = 673 K, T_w = 293 K, V_w = 70 ml, V_F = 70 ml

3.2

Impact of experimental parameters on pressure buildup

By employing the quantitative analysis method used in experimental investigations [23, 26, 28, 29], the impact of experimental parameters on pressure-buildup characteristics in the present lead experiments was analyzed in detail. Because steam explosion has occurred in few experimental cases (Table 2), the analysis was conducted mainly considering the non-steam explosion cases. As a supplement, in the last part of this section, the impact of the interaction mechanisms on pressure buildup is analyzed.

According to the discussion in Section 1, in an LFR SGTR accident, the evaporation and expansion of water lead to the generation of pressure waves and sloshing of the molten pool, which is likely to damage internal structures. As demonstrated in Section 3.1, a series of pressure pulses are generated in the melt pool during CCI, especially the first two-phase pressure (corresponding to phase (2) depicted in Figs. 3 and 4) is the most dangerous. For this reason, with regard to the molten pool pressure, impulse I of the first two-phase pressure is employed for the analysis: $I=A\int P\left(t\right)\text{d}t,$ (3) where A is the cross-sectional area of the interaction vessel, t is time, and P is the pressure in the molten pool.

According to the analyses in our previous articles regarding Bi-Sn-In and LBE experiments, employing impulse I instead of peak value greatly alleviated the probable impact of noise in pressure data owing to the time-cumulative effect of I [23, 26, 28, 29]. For analyzing the pressure-buildup characteristics of the cover gas, the pressure increasing velocity has been employed, that is, the ratio of the maximum pressure to the time necessary to reach the value [23, 25, 26, 28, 29].

3.2.1

Impact of water volume

The change trends of impulse for the molten pool and cover gas pressure increasing velocity, with water volume increasing, are depicted in Fig. 5 at representative melt and water temperature (673 K and 293 K, respectively) for the LBE and lead experiments. According to Fig. 2, all the cases in Fig. 5 are involved in the non-film boiling mode, and film boiling could theoretically occur only in case No. 65 with a water temperature of 358 K, which is discussed in Sect. 3.2.4.

Fig. 5Full-screen View

Impact of water volume on pressure buildup (H_m = 180 mm, T_m = 673 K, T_w = 293 K, V_F = V_w). (a) Impulse in molten pool; (b) Cover gas pressure increasing velocity

As shown in Fig. 5, the pressure buildup of the melt and cover gas regions has an analogous change trend with increasing water volume, that is, it initially rises and then becomes saturated at relatively large water volumes. The similarity of the change trends is easy to understand because, theoretically, both the impulse on the melt pool and the cover gas pressure increasing velocity are positively related to the steam generation rate. Notably, the main concern in this work is impulse I on the molten pool, considering the relatively slow cover gas pressure increasing velocity (Section 3.1). For example, in Wang et al., according to the result of a simulation of an SGTR accident with 91 damaged tubes (full bundle), although peak pressure values of approximately 50-60 bar were detected near the rupture of SG, the cover gas pressure increased almost linearly at a relatively low rate of approximately 4.5 bar/s [11]. In addition, according to the discussion in Section 1, regarding the generated steam in an LFR SGTR accident, the main concern is its potential consequences within the melt region (e.g., pressurization, resultant sloshing, reactivity disturbance, and deterioration of core heat exchange), rather than in the cover gas region, because pressurization in this region can be mitigated comparatively simply (e.g., by using pressure relief valves). In addition, there are uncertainties in the cover gas pressure increasing velocity in the experiments owing to the influence of experimental conditions (e.g., different cover gas region volumes corresponding to different molten pool depths, the steam condensed by the water cooling system, and different cover gas temperatures due to the unfixed heating time). Considering the aforementioned analysis, for brevity and accuracy, only the impulse on the melt pool is discussed later.

For the lead cases in Fig. 5, there is an insufficient of large water volume experimental data, because the steam explosion occurs in cases with water volumes of 70 ml and 80 ml. For the lead experiment, to improve the understanding, keeping other conditions consistent, two additional series of cases at melt temperatures of 648 K and 698 K are depicted in Fig. 6(a). An additional series of LBE cases at a melt temperature of 573 K is shown in Fig. 6(b). As expected, for the lead and LBE cases, a limited pressure buildup as the water volume increased was observed regardless of melt temperature.

Fig. 6Full-screen View

Impact of water volume on pressure buildup (H_m = 180 mm, T_w = 293 K, V_F = V_w). (a) Impulse on molten lead pool; (b) Impulse on molten LBE pool

Based on our previous studies [24, 26, 28, 29], three probable factors in such a saturated pressure buildup were proposed: (1) when the volume of water lump released inside the molten pool is relatively large, the initial cooling effect of the liquid water lump on the surrounding melt is strong; (2) the steam generated at the water-melt interface during CCI is likely to prevent the remaining liquid water from directly contacting with the melt, deteriorating the heat transfer; and (3) when the water volume is relatively large, the water lump cannot evaporate completely in an instant, and part of the generated steam may be cooled and condensed by the remaining liquid water (before leaving the initial position). For a violent CCI event in our experiments, in theory, factor (3) should not play a primary role [23, 26, 28, 29].

Regarding factor (1), if the limited pressure buildup is caused by the cooling role of the water lump on the surrounding melt, as the melt temperature decreases, the minimum water volume required to reach the saturated pressure buildup is believed to decrease to a smaller value. However, as shown in Fig. 6, for different melt temperatures in the lead or LBE experiments, the critical volume of water seems to be fixed, which proves that factor (1) is not the main reason for the limited pressure buildup. Based on the aforementioned discussion, at least under the current experimental conditions, factor (2), that is, the hindrance effect of the generated steam on the heat exchange between the water and melt, is probably responsible for the limited pressure buildup.

3.2.2

Impact of molten pool depth

To study the impact of the molten pool depth on the pressure-buildup characteristics, this study depicted experimental data at different molten pool depths (180 and 100 mm) (Fig. 7). As shown in Fig. 7, when the molten pool depth decreased from 180 to 100 mm, there was a significant reduction in the pressure buildup on the molten pool for lead and LBE. Similar to Figs. 5 and 6, a limited pressure-buildup tendency was observed at a molten pool depth of 100 mm.

Fig. 7Full-screen View

Impact of molten pool depth on pressure buildup (T_m = 673 K, T_w = 293 K, V_F = V_w).

As shown in Fig. 7, for both depths of the molten pool, a slightly more violent pressure buildup was observed in the lead experiments than in the LBE experiments, which contrasts with the findings of the lead alloy droplet fragmentation experiment conducted by Sa et al. [30]. According to the analysis of Sa et al., the significantly lower melting point of LBE than that of lead makes the LBE droplet remain liquid for an increased amount of time, combined with lower surface tension of LBE than that of lead, which may be the main reason for the increased pressure peak in the fragmentation of LBE droplets [30]. However, in our water droplet-molten pool experiment, the quantity of melt was sufficient to maintain the liquid. According to the thermophysical property data in Table 1, it can be inferred that the higher thermal conductivity of lead than that of LBE (approximately 26.5% higher) results in an increased water evaporation rate, that is, an enhanced pressure buildup.

SIMMER-III calculations in the literature [24] confirmed that only a small part of the melt (near the water lump) changes the temperature during a rapid melt-water interaction. In addition, as shown in Figs. 3 and 4, the melt temperatures detected by thermocouple TM0 (Fig. 1) remain almost unchanged during the CCI. Based on the aforementioned analysis, for such an instant CCI event, only a small amount of melt near the water lump plays a role in the evaporation of water (i.e., pressure buildup). In other words, with a decrease in the molten pool depth, the significant reduction in the impulse on the molten pool is not due to the thermal effect.

Combined with the conclusion drawn in Section 3.2.1 (i.e., the limited pressure buildup is most likely due to the generated steam), the significant increase in pressure buildup as the molten pool depth increases can be explained reasonably. As a result of the large density difference between the melt and steam layers, the melt tends to pierce through the steam layer and contact the water lump. In theory, an increase in the molten pool depth could strengthen the trend of melt piercing through the steam film, enhancing pressure buildup.

3.2.3

Impact of melt temperature

For lead experiments (623-698 K) and LBE experiments (473-793 K), the impact of melt temperature on the pressure-buildup characteristics is shown in Fig. 8 at a water temperature of 293 K and molten pool depth of 180 mm.

Fig. 8Full-screen View

Impact of melt temperature on pressure buildup (H_m = 180 mm, T_w = 293 K, V_F = V_w).

As shown in Fig. 8, regardless of melt material and water volume, the impulse on the molten pool increases as melt temperature increases. Because all cases in Fig. 8 do not involve film boiling or steam explosion, theoretically, when the water-melt interaction maintains the non-film boiling state, an increase in melt temperature could lead to an increase in water evaporation rate.

As pointed out in Sect. 3.2.2, a stronger impulse on the molten pool exists in lead experiments than in LBE experiments under the same experimental conditions (Fig. 7), owing to the better thermal performance of lead than that of LBE. However, as shown in Fig. 8, a more violent pressure buildup in lead cases than in LBE cases is observed only in the cases with melt temperatures higher than 648 K, and the impulses in lead cases with a melt temperature of 623 K are even lower than those in LBE cases with a melt temperature of 573 K. Thus, it can be inferred that because the melt temperature of 623 K is relatively close to 600.6 K (i.e., the melting point of lead), local solidification of lead may occur and restrict the pressure buildup.

3.2.4

Impact of water subcooling

Some experimental cases with different water subcooling temperatures (15–80 K) are shown in Fig. 9, including the only case with the theoretical possibility of film boiling (Fig. 2). Film boiling can cause a much weak impulse in the molten pool.

Fig. 9Full-screen View

Impact of water subcooling on pressure buildup (H_m = 180 mm, T_m = 673 K, V_F = V_w).

For other cases with non-film boiling, regardless of melt material, a decrease in water subcooling could only lead to a slight variation in the impulse on the molten pool. Considering the thermal aspect, because the specific heat capacity of water (approximately 4.2 kJ·kg^-1·K^-1) is much lower than its vaporization heat (approximately 2257 kJ·kg^-1), the reduction in water subcooling only leads to a negligible reduction in the required heat for evaporation. Therefore, when the boiling mode was unchanged, the decrease in water subcooling had no obvious effect on pressure buildup.

3.2.5

Impact of water lump shape

The effect of the water lump shape on the pressure-buildup characteristics is shown in Fig. 10. In this part, the shape of the water lump was changed by loading a certain volume of water in a flask with a larger capacity. For example, when the capacity of the flask was twice the volume of water, the water lump was almost hemispherical.

Fig. 10Full-screen View

Impact of water lump shape on pressure buildup (H_m = 180 mm, T_m = 673 K).

When the capacity of the flask is larger than the volume of the water lump, additional non-condensable gas may be entrapped, which may prevent the initial contact between the water lump and the surrounding melt, weakening the pressure buildup. However, as shown in Fig. 10, for both the lead experiments and LBE experiments, the impulse on the molten pool increases as the flask capacity increases. According to this analysis, the additional non-condensable gas does not play a major role in the CCI. Theoretically, when water is loaded into a larger spherical flask, the surface area of the water lump increases. In other words, the increase in the spherical flask capacity could enlarge the heat transfer area during CCI, increasing water evaporation intensity.

3.2.6

Impact of interaction mechanism

For the analysis of the impact of the interaction mechanism on the pressure-buildup characteristics, the steam explosion and non-explosion cases with nearby water volumes or water temperatures are shown in Fig. 11. Regarding steam explosion, according the literature [5, 30], the occurrence of energetic melt-water interaction requires some conditions: first, premixing of sufficient water and melt; second, the vapor film between water and melt collapses under the action of some triggers; and finally, the interface temperature is higher than the spontaneous nucleation temperature of water, initiating explosive boiling.

Fig. 11Full-screen View

Impact of interaction mechanism on pressure buildup (T_m = 673 K, V_F = V_w).

As shown in Fig. 11, the steam explosion generally causes a much greater impulse on molten pool for both lead experiments and LBE experiments than the non-explosion cases do. In addition, all steam explosion cases occurred at a melt temperature of 673 K and water temperature of 293 K (except for a steam explosion case with a water temperature of 333 K). Thus, a steam explosion is likely to occur in some cases with specific initial melt/water temperature conditions. However, the experimental cases (especially the cases of steam explosion) are too few to clarify how a steam explosion is triggered in the lead and LBE experiments in this study.

3.3

Melt kinetic energy conversion efficiency

Melt kinetic energy can reflect the speed of melt; in other words, the melt kinetic energy can be used to analyze melt pool sloshing. Therefore, an analysis of the melt kinetic energy conversion efficiency would facilitate LFR SGTR accident evaluation. In theory, the momentum of melt is equal to the impulse; therefore, melt kinetic energy E_k can be estimated as [23, 25, 29, 34, 35] $E_{\text{k}}=\frac{I^2}{2m_{\text{pl}}},$ (4) where m_pl is the mass of melt.

The melt kinetic energy conversion efficiency η could be calculated as $\eta =\frac{E_{\text{k}}}{E_{\text{ther}}},$ (5) where E_ther is the thermal energy transferred from molten pool to water during CCI.

If the mass of evaporated water is known, the thermal energy E_ther can be estimated as [25, 29] $E_{\text{ther}}=m_{\text{s}}\left[c_{\text{w}}\left(T_{\text{sat}}-T_{\text{w}}\right)+h_{\text{lg}}+c_{\text{s}}\left(T_{\text{m}}-T_{\text{sat}}\right)\right],$ (6) where m_s and c_s are the mass and specific heat of the generated steam, respectively, and T_sat and h_lg are the saturation temperature and vaporization heat of water, respectively.

m_s can be estimated according to the pressure change in the cover gas region [25, 29]: $m_{\text{s}}=n_{\text{s}}\times M_{\text{s}}=\left(\frac{P_1{V}_{\text{cg}}}{R{T}_1}-\frac{P_0{V}_{\text{cg}}}{R{T}_0}\right)\times M_{\text{s}}=\left(P_1-P_0\right)\times \frac{P_1{V}_{\text{cg}}}{R{T}_1}{M}_{\text{s}},$ (7) where n_s and M_s are the molar quantity and molecular weight of the steam, respectively; V_cg is the volume of the cover gas region; T and P are the temperature and pressure of the cover gas, respectively; subscripts 0 and 1 signify the start and end of CCI, respectively; and R is the gas constant, 8.314 J/(mol·K). In the experiments in this study, owing to the use of an efficient water-cooling system, T₁ is almost equal to T₀ during CCI (Sect. 3.1).

According to Eqs. (4)-(7), the melt kinetic energy conversion efficiency η can be estimated. The η values of the lead experiments and previous experiments (using Bi-Sn-In alloy and LBE) are shown in Fig. 12.

Fig. 12Full-screen View

Comparison of melt kinetic energy conversion efficiency.

As shown in Fig. 12, the melt kinetic energy conversion efficiency η of the lead, LBE, and Bi-Sn-In experiments varied in the range of approximately 0-1.4%, 0-1.6%, and 0-0.6%, respectively. In Cheng et al., the mechanical energy conversion efficiencies of the LBE and Bi-Sn-In experiments were estimated to be in the range of 2.5-5.5% and 2.9-5.0%, respectively, where the mechanical energy comprises the melt kinetic energy and the compression work of the cover gas [29]. This discussion suggests that the melt kinetic energy only accounts for a small part of the total thermal energy and is far less than the compression work of the cover gas.

A further comparison demonstrated that the η value and impulse on the molten pool were positively correlated to some extent. For example, the impulse in lead cases is generally close to the impulse in LBE cases, as analyzed in Sect. 3.2, and the η values in the lead and LBE experiments are in a consistent range. As found by Cheng et al., the impulse in LBE experiments is usually much higher than that in Bi-Sn-In experiments [29]. Similarly, compared with those in the Bi-Sn-In experiments, the η values in the LBE experiments were larger.

Concluding remarks

In an LFR SGTR accident, water-melt interaction involves a series of complex thermal hydraulic phenomena (e.g., the flash of pressurized water, the sloshing of the melt pool, steam explosion, and vapor entering the core). Understanding the mechanism of interaction between water and the melt pool (lead or LBE) is meaningful for improving the evaluation of LFR SGTR accidents. In this work, based on the circumstance of a water droplet immersed inside a liquid lead pool, which can occur in an LFR SGTR accident, many experiments were performed by releasing water lumps inside a molten lead pool, with many of experimental parameters employed (e.g., water lump volume, water lump shape, molten pool depth, and temperature of water and melt). Through a detailed analysis of the present lead experiments and previous LBE experiments, the following conclusions were obtained:

(1) Like the findings in the LBE experiments, a consistent trend of measured temperature and pressure histories and a similar effect of the experimental parameters on pressure-buildup characteristics were observed for the lead experiments, which confirms to some extent the findings of LBE experiments in the literature.

(2) Per the lead experiments and LBE experiments, a steam explosion is likely to occur under some specific initial water/melt temperature conditions, which usually strengthen pressure buildup. Similarly, under some specific initial water/melt temperature conditions corresponding to a sufficiently high instantaneous contact interface temperature, film boiling is likely to occur with a much weaker pressure buildup than that of non-film boiling cases.

(3) Similar to LBE and Bi-Sn-In experiments in the literature, probably because of the hindrance effect of the generated steam on the heat transfer between water and melt, there is a saturated trend in pressure buildup with increasing water lump volume.

(4) Compared with that in the LBE experiments, a slightly more violent pressure buildup is usually observed in lead experiments under the same experimental conditions, which may be due to the higher thermal conductivity of lead than of LBE. However, owing to the high melting point of lead, in some experimental runs at relatively low melt temperatures, a possibility is that local solidification of molten lead occurs, weakening pressure buildup.

(5) The calculated melt kinetic energy conversion efficiency η had a relatively small value (not exceeding 1.6%), and the η value had an overall positive correlation with the impulse on the molten pool.

A wider range of experimental parameters than is used in this study and the literature should be employed to conduct further investigations of LFR SGTR accidents. For example, to determine the thermal conditions required for a steam explosion, additional experimental runs should be conducted at different melt/water temperature conditions. In addition, the opacity of lead/LBE makes visualizing such water-melt interactions difficult; therefore, a numerical simulation of the CCI process is necessary.