The impact of the distribution of the condensation energy adsorbed in the water pool on the DCC efficiency at sub-atmospheric pressure

The safety of a fusion reactor like ITER relies on the reliability of the pressure suppression system (for keeping pressure below 0.15 MPa during accidental scenarios), and, in turn, on the efficiency of Direct Contact Condensation (DCC). In this study, the role played by the distribution of the condensation energy in the water is analysed considering the experimental results of temperature and pressure recorded during steam condensation tests in a closed volume at sub-atmospheric conditions. The investigation of the mechanisms involved in the condensation at the water-steam interface is fundamental to verify that the subcooled water mass fully participates into the steam condensation for all the foreseen condensation regimes. Particularly, the paper analyses the distribution of the condensation energy in a water pool for different test conditions and with reference to the large-scale facility under operation at the DICI-University of Pisa. The subcooled water volume of the condensation tank in this system was assumed subdivided in 104 annular discrete volumes corresponding to the location of temperature and pressure sensors (testing monitoring points). Moreover, this discretization was used to implement a model to visualize the experimental data and in particular the accumulation of the condensation energy in the different part of the water pool and of the vacuum space. The experimental results showed that most of the tests had a participating fraction of water mass greater than 50%. Nevertheless, the non-uniformity and stratification of the temperature in the water pool requires a greater water mass for condensing a given steam mass. The analyses of steady state pure steam condensation tests determined that it needs to increase 1.39 times the water mass respect to the case of full participation of the water at the steam condensation.


Introduction
The International Thermonuclear Experimental Reactor (ITER), which is under construction in Saint Paul Lez Durance (France), manages Loss of Coolant Accidents (LOCA) in the Vacuum Vessel (VV) by means of a Pressure Suppression System (PSS).This safety system is made of four tanks partially filled with water working at sub-atmospheric pressure.The steam flows inside the tanks through multiholed tubes (spargers) one for each tank [1].Conceptually the PSS is similar to system used in the fission reactors (particularly in the Boiling Water Reactor), although it differs substantially from this in terms of the steam condensation that occurs in a closed volume starting from a sub-atmospheric pressure.
These steam condensation conditions have not been tested previously and very few experimental studies can be found in the scientific literature.An extensive experimental test campaign, funded by The qualification of the pressure suppression system consists in the demonstration of the ability to condense the steam mass, foreseen in the accidental scenario, without to overcome the pressure limit of 0.15 MPa.In this context, it is necessary to verify that the water mass fully participates to the steam condensation for all the possible expected condensation regimes.Obviously, the temperature stratification contrasts with this requirement.This paper illustrates the distribution of the condensation energy in the water pool for different LSF test conditions and for the two spargers' configurations.The ETT has been subdivided in discrete volume correspondent to the location of the temperature and pressure sensors in the horizontal and vertical direction.The water pool and the vacuum space have been discretized in ring volumes for implementing a model of accumulation of the steam condensation.

Steam condensation regimes in a closed volume at sub-atmospheric pressure
The steam condensation tests, performed in the LSF employing 100 holes and 1000 holes spargers, experimentally analysed the following conditions: -Steam mass flow rate, Q: up to 0.5 kg/s -Water temperature, Tw: 15-100°C -Pressure in front of the sparger holes (downstream pressure), P: 0.25-1.2bars Moreover, tests were performed injecting steam flux mixed with a non-condensable gas flux (up to a 20% fraction in mass).Tests were performed at constant (steady state tests) or variable (transient tests) steam mass flow rate.The map of steam condensation regimes (CR) at atmospheric pressure is defined in the plane Tw -Qh being Tw, the water temperature and Qh, the steam mass flow rate per area of one hole [6]- [7].In the steam direct contact condensation in a closed volume starting from a sub-atmospheric pressure, the parameter which defines the condensation regimes is, instead, the ratio Qh/P (Kg/(sm 2 kPa)) between the steam mass flow rate per hole (Qh) and the downstream pressure (P) [5].In particular, the following steam condensation regimes can be identified (Figure 2):

Experimental distribution of condensation energy in the water pool of the ETT
The ETT volume has been subdivided in the radial and axial direction by means of discrete volumes, to be consistent and considering the position of the temperature and pressure sensors.Radially the volumes have annular shape, the internal and external radius correspond to the average distance between the sensors.Along the height, the ETT volume is subdivided in fourteen layers (ten in the water pool and four in the vacuum space).
Generally, four temperature sensors are located along the radius except in the holed area of the sparger where six sensors have been installed.Moreover, in this zone, the axial layers (6 and 7) have been subdivided in further two sublayers to locate a greater number of sensors.This same volume discretization was used for implementing the numerical model to study the accumulation of the condensation energy in the different parts of the water pool and vacuum space.The water pool was discretized by 104 ring volumes, while the vacuum space by 55 ring volumes.The energy released in the ETT, EV(  ), until an instant tJ, is determined by the summation of the steam mass flow rate (  ) per the time span and per its enthalpy, H022(  ), calculated at the temperature and pressure of the steam in the inlet nozzle (T022(  ) and P022(  )): For each water volume, Vwi, the correspondent mass Mwi(t J ) and thermal capacity CWi(t J ) are calculated by:   (  ) =     (  (  )) (  ) =   (  )  (  (  )) being i(Twi(t J )) and cpi(Twi(t J )) the density and the specific heat of the generic i-th water volume, respectively.They are calculated at the instantaneous value of temperature, Twi(t J ), of the generic i-th water volume.The accumulated condensation energy CAEi(t J ) in the Vwi is given as: where Twi( −1 ) is the temperature of i-th volume at the previous step j-1.At each instant, the percentage of the injected steam energy accumulated as condensation energy in each volume, is calculated by: In the vacuum space, where is globally accumulated an energy smaller than 0.5% of the total one, the calculation starts with the determination of the initial masses of steam and non-condensable gas (air).From the initial average temperature of vacuum space, Tvs(to), we derived the initial saturation pressure psatvs(to) and the initial steam mass Msvs(to): where Vvs(to) is the initial value of the vacuum space volume.The initial mass of air, Mavs(to) contained in vacuum space is obtained known the initial average pressure of vacuum space pvs(to) as: At a generic instant tJ, the steam mass Msvs (tJ) and the air mass Mavs (tJ) are always calculated from the same equations 4) and 5) substituting the instantaneous values of Tvs(tJ), psatvs(tJ), pvs(tJ) and Vvs(tJ).The instantaneous values of the vacuum space volume, Vvs(tJ) is given as: Vvs(tJ)=Vtot-Vw(tJ), being Vtot the total volume of ETT, Vw(tJ) the instantaneous value of the water volume which changes for the variation of the water density, w(Twave(tJ)) and for the condensation of steam mass Ms(tJ) according to the following formulas: Twave(tJ) is the average temperature of the water at the instant tJ.In each volume of the vacuum space, Vvsi, the masses of air, Mavsi(tJ), and of steam, Msvsi(tJ), are assigned proportionally to the relative volumes: Defining the thermal capacity of the steam and air in each i-th volume of the vacuum space at a generic instant t: the energy accumulated in each volume of the vacuum space, Vvsi, is given by:   (  ) = ∑ (  (  ) +   (  ))(  (  ) −   ( −1 )) 1 (8) where cpsi and cpai the specific heat of the steam and air calculated at the temperature Tvsi(tJ), respectively.The percentage of the injected steam energy that is accumulated as condensation energy in each volume can be obtained from the equation 3).The elaboration of the huge amount of data was performed by implementing in-house programs in Fortran 90: they allowed also to visualize the results by contour bands using the post-processor of a FEM code (MSC-Mentat [8]).

Experimental Results and Discussion
Figure 3 provides the results obtained with the sparger B in a condensation test defined by the parameter Qh/P= 0.171 Kg/(s m 2 kPa).The condensation regime is Chugging (Figure 3-a) that is characterized by an intermittent steam flux.A large temperature stratification occurred in this test (see Figure 3-b).At the final instant of the test, the water in front of the sparger holes has a temperature of about 59 °C while in the lower zone the temperature ranges between 16-17°C.Figure 3-c) shows the percentage of energy accumulated in the discretized volumes at the final instant, tf.In this test, the water participating to the steam condensation is a fraction of the whole water pool.To determine the actual participating water mass, FMw, all the volumes in which the adsorbed energy is smaller than 10 -5 Ev(tf) were discarded (considered not participating).This limit, assuming during the test an injection of 3.5 t steam mass, corresponds at a temperature increase of 0.005°C and 0.1°C in the greatest or smallest volume, respectively.Based on that, the participating water mass in the test N.152, shown in Figure 3, was the 57.9 % of the total mass in the ETT.IOP Publishing doi:10.1088/1742-6596/2685/1/0120596 condition, a large part of the water participates to the steam condensation as shown in Figure 4-c).On the base of previous assumption, the participating water mass at the steam condensation is the 86 % of the total mass in the ETT.The elaboration of all experimental data permitted to determine the distribution of the participating water fraction, FMw, versus Qh/P for both the spargers and for all the test conditions (condensation of pure steam and of the mixture of steam and non-condensable gas in transient and steady state operation).FMw=1 is obtained for very low water temperatures.In these conditions, large turbulence is produced by degassing effects.In fact, the water temperature increase reduces the air solubility and air bubbles move vertically in the water towards the vacuum space.FMw ranges between 0.25 and 0.8 for most of the tests, the minimum values correspond to higher temperatures.-FMw ranges between 0.5 and 1 per 0.2< Qh/P <1.6.Also, for these tests FMw=1 is obtained at low temperatures and due to degassing effects.Discarding these tests, FMw ranges between 0.5 and 0.8.-FMwp=1 per Qh/P >1.6.All the water mass participates to the steam condensation.CRs are CO or SC.The determination of the experimental value of the participating water mass to the steam condensation permitted to calculate global parameters to assess the efficiency of the steam condensation, in particular the average temperatures of the actual and participating water mass and the correspondent average increment of the temperature for a given injected steam energy.Figure 5 (b) shows, for the sparger A and steady state tests with pure steam, the experimental data, and the derived correlation between the participating water average temperature, Twp, and the average temperature of the water pool, Twave.A linear best fit of experimental data is given by: Twave = 0.8877 Twp.The average temperature of the water pool, Tave, is 11.23% and smaller than Tpw (error bands -30%-+20%).The coefficient of linear best fit can be interpreted as the inverse of an average effective value of the water specific heat.The average value of the water specific heat in the temperature range 40-100°C is 4.188 kJ/kg°C and the inverse value is 0.2388 Kg °C/kJ.This value is almost equal to the coefficient of the correlation relative to the participating water mass.In the other case (normalizing the steam energy at the actual water mass) the coefficient is 1.39 times greater.This means that fixed the maximum pressure in the vacuum space and, therefore, the maximum temperature of the water, the non-uniformity and stratification of the temperature in the pool required a water mass 1.39 times greater than that that occurring in the case of full participation of the water into the steam condensation.

Conclusions
The paper described the implemented model for the analysis of the experimental results obtained in steam direct contact condensation in a closed volume starting from sub-atmospheric pressure.The measurements of temperature and pressure in the water pool and in the vacuum space permitted to determine the fraction of the water mass in which the condensation energy is accumulated, considering the non-uniformity and stratification of the temperature.Considering the experimental results obtained in pure steam steady state condensation tests, the provided elaboration model permits to assess the performances of the ETT and the sparger A. In fact, assuming that the final values of the vacuum space pressure and water temperature in ETT are 1.5 bar and 110°C, respectively, a pool of 60 m 3 of water at 20°C condenses with a temperature increment of T=90°C about 5800 kg of steam.This value is greater than that foreseen in the Large LOCA which could occur in the Vacuum Vessel of ITER.

Figure 2 .
Figure 2. Map of the CRs for steady state pure steam condensation tests with sparger A: the inclined straight lines and the numerical points represent the CRs boundaries and the test conditions, respectively.

Figure 3 .
Figure 3. Condensation test of pure steam with the sparger B (test n.152) for Qh/P=0.171kg/(sm 2 kPa): a) steam jet; b) temperature distribution (in °C) in the ETT at tf; c) percentage of condensation energy accumulated in the discretized water volumes.

Figure 4
Figure 4 provides results of test N.36 of pure steam condensation carried out with the sparger A. The test conditions correspond to the parameter Qh/P= 1.54 Kg/(s m 2 kPa).Therefore, the condensation regime is the Condensation Oscillation (CO).Figure 4-b) shows the distribution of the temperature in the water pool and in the vacuum space at the final instant of the transient.The temperature is almost uniform.The maximum temperature difference is 5.2°C (Tmin=36.5°, Tmax=41.7°C).In this test Figure 4 provides results of test N.36 of pure steam condensation carried out with the sparger A. The test conditions correspond to the parameter Qh/P= 1.54 Kg/(s m 2 kPa).Therefore, the condensation regime is the Condensation Oscillation (CO).Figure 4-b) shows the distribution of the temperature in the water pool and in the vacuum space at the final instant of the transient.The temperature is almost uniform.The maximum temperature difference is 5.2°C (Tmin=36.5°, Tmax=41.7°C).In this test

Figure 4 .
Figure 4. Condensation test of pure steam with the sparger A (test n.36) for Qh/P= 1.54 kg/(sm 2 kPa): a) steam jet; b) temperature distribution (in °C) in the ETT at tf; c) percentage of condensation energy accumulated in the discretized water volumes.

Figure 5 (
Figure 5 (a) shows the participating water fraction, FMw, versus Qh/P, for the tests of pure steam condensation with the sparger A. The orange line represents the minimum participating water fraction at different condensation regimes.This diagram can be considered a quantitative description of the performances of the ETT and of the sparger A in the direct contact condensation of pure steam.For the different CRs, the participating water fraction, FMw has the following values: -FMw ranges between 0.25-1 per Qh/P <0.2.CRs correspond to smallest values of steam mass flow rate or highest values of downstream pressure (pure steam tests after non condensable gases injection).FMw=1 is obtained for very low water temperatures.In these conditions, large turbulence is produced by degassing effects.In fact, the water temperature increase reduces the air solubility and air bubbles move vertically in the water towards the vacuum space.FMw ranges between 0.25 and 0.8 for most of the tests, the minimum values correspond to higher temperatures.-FMw ranges between 0.5 and 1 per 0.2< Qh/P <1.6.Also, for these tests FMw=1 is obtained at low temperatures and due to degassing effects.Discarding these tests, FMw ranges between 0.5 and 0.8.-FMwp=1 per Qh/P >1.6.All the water mass participates to the steam condensation.CRs are CO or SC.

Figure 5 .
Steady state pure steam tests with sparger A: (a) Participating water fraction versus Qh/P, (b) average temperature (Twave) versus the participating water average temperature Twp.

Figure 6
Figure 6 (a, b) show the water temperature increment versus the steam energy per unit of the actual or participating water mass, respectively.The experimental linear best fits are given by the following formulas: ∆ (°) = 0.3321  ()   ()

Figure 6 .
Trend of temperature increment vs. steam energy per unit of (a) actual water mass and (b) participating water mass.