Characterisation of Sodium Aerosol in Cover Gas Region of SILVERINA Loop

Sodium aerosols are continuously being generated in the cover gas region of Sodium cooled Fast Reactor (SFR) from the hot sodium pool and they play major role in heat and mass transfer to the roof top plug and side walls. In order to characterize the sodium aerosols, a study has been initiated by conducting experiments in one of the sodium loop facility SILVERINA of IGCAR. This paper describes design and installation of aerosol sampling system in SILVERINA loop, results and analysis of sodium aerosol characteristics, measurement of temperature profile of cover gas region, theoretical simulation of sodium aerosols mass concentration for the given pool (loop) condition and validation of the model with experimental results. The sodium aerosol size distribution in cover gas region is found to be mono-model. The Mass Median Diameter (MMD) of sodium aerosol is found to be varying from 1.5–11.5 μm as a function of sodium pool temperature and found to increase linearly with increase of sodium pool temperature. The sodium aerosol mass concentration is found to be varying from 0.026–35.6 g m as a function of sodium pool temperature and it is found to follow 3 order polynomial regression with increase of sodium pool temperature. The sodium aerosol mass concentration and MMD are found to be higher near the sodium pool compared to middle of the cover gas region and near the roof top. A theoretical simulation has been carried out to predict the sodium aerosol mass concentration with respect to pool temperature for a given geometry of the vessel and the theoretical and experimental mass concentration of sodium aerosols found to have good agreement.


INTRODUCTION
In the pool type Sodium cooled Fast Reactor (SFR), the pool design has an argon gas blanket (cover gas region) sandwiched between the surface of hot sodium pool and the roof structure of the reactor vessel (Sinai et al., 1993).In the normal operating condition of SFR, the temperature difference between the sodium pool and the bulk gas temperature leads to considerable evaporation of sodium from the pool surface and subsequent condensation results in the formation of sodium aerosol within the cover gas region (Ford et al., 1993) either by heterogeneous nucleation or self-nucleation (homogeneous nucleation).When these aerosols have sufficient concentration, would modify the total heat transfer to the cooled roof structure by absorption and scattering mechanisms.Further, the mass transfer occurs due to condensation of sodium aerosols on the cooler surfaces like annular gaps, roof top, control plug, rotating plug and fuel handling machine resulting deposition of aerosols, which hinders the rotational movement of rotating plug and operation of fuel handling machine (Robert et al., 1995).The aerosol mass concentration influences the operation of cover gas purification system and reduces its efficiency (flow through cold trap circuit).The aerosols with sufficient concentration reduce the visibility of cover gas region [Core inspection facility in RAPSODIE, France and Fast Breeder Test Reactor (FBTR), India].
The designer of the roof structure need to know heat and mass transfer rate to the roof in order to assess cooling requirements, thermal stress within the structure and the possible influence of sodium aerosol deposition (Sinai et al., 1993).In the reactor design, necessary care (conservative estimate -without taking into account of aerosols) has been taken to account for the heat and mass transfer phenomena.However, it is at most important to know the aerosol concentration and aerosols size distribution in order to predict effectively the heat and mass transfer phenomena, which may get changed due to interaction of thermal radiation with aerosols and mass transfer due to condensation of aerosols.At this juncture, in order to account for the role of aerosols, it is important to consider the sodium aerosol properties, which would get modified due to (i) temperature difference between the sodium pool surface and bottom of the roof top plug, (ii) spatial variation of aerosol mass concentration and size distribution in cover gas region, (iii) effect of geometric dimension (diameter of the sodium pool surface, height of the argon cover gas and shape of roof top) of the cover gas system, and (iv) possible enhanced coagulation of sodium aerosols upon interaction with gamma radiation, resulting increase in sizes (It is important to note that in the reactor environment, sodium aerosols are immersed in the sea of bi-polar charges (generated by gamma radiation) and get charged upon interaction with ions.The aerosol properties (size and mass concentration, coagulation coefficient and deposition rate etc.) would get modified due to enhanced coagulation of charged sodium aerosols (Subramanian et al., 2008(Subramanian et al., , 2012))).Hence, information on mechanism of aerosol formation, the kinetics and its characteristics is needed in the design of reactor top shield and to help in eliminating the potential operating problem caused by aerosols during steady state reactor operation.
The determination of sodium aerosols characteristics from a cover gas region requires special sampling procedure, in which sampling is to be carried out without exposing the aerosols to atmosphere (the sodium aerosols undergo chemical changes and properties would get modified when exposed to atmosphere).In some of the earlier studies, sampling of sodium aerosols from the cover gas region was carried out by using Andersen multistage Impactor, which gives mass-size distribution cumulatively over a period of time (Yamamoto et al., 1991;Minges andSchutz, 1991, 1993;Jackson et al., 1993).In another experiment, stainless steel wire mesh filter (kept in the open atmosphere) was used, which gave size distribution based on sieve size (Himeno and Takahashi, 1980;Himeno and Yamagishi, 1982;Frukawa et al., 1984;Yamamoto et al., 1991;Newson et al., 1993).It is to be noted here that, the sodium aerosols undergo reaction with atmospheric constituents (oxygen, moisture and CO 2 ) to form various compounds like oxide, hydroxide and carbonate resulting changes in both physical and chemical characteristics.Hence, the measurement in open atmosphere could not be a true evaluation of sodium aerosol characteristics in the cover gas region.Glockling et al. (1991) used Malvern 2600C (based on Franhofer diffraction) and Dantec particle dynamic analyzer for characterizing sodium aerosol in the cover gas region, but the results obtained in both techniques were found different for the same experimental condition.Laser mist concentration meter and sintered stainless steel filter were used for sodium aerosol mass concentration measurements (Yoshiaki andTakahashi, 1980, Yoshiaki andYamagishi, 1982).The methodologies adopted in their measurements were not dealt in details.In one of the experiment, atomic absorption spectroscopy was used for measurement of mass concentration and laser scattering technique was used for determination of size distribution of sodium aerosols (Roberts et al., 1995).In our earlier work, a suitable technique has been developed and sodium aerosols were characterized using Mastersizer (M/s Malvern, UK).The sampling of sodium aerosols is accomplished by (i) drawing aerosols from the cover gas region, (ii) trap them in a suitable medium without exposing them to the atmosphere, and (iii) analyze the trapped aerosols for its characteristics (Amit et al., 2014).The technique has been qualified in Aerosol Test Facility (Baskaran et al., 2004;Misra et al., 2012) and validated in SILVERINA loop facility.
It was observed from the literature survey, the size distribution of aerosols ranges from 1-16 µm and mass concentration ranges from 1-40 g m -3 (Yoshiaki and Takahashi, 1980;Yoshiaki and Yamagishi, 1982;Frukawa et al., 1984;Glockling et al., 1991;Yamamoto et al., 1991;Minges andSchutz, 1991, 1993;Ford et al., 1993;Jackson et al., 1993;Newson et al., 1993;Robert et al., 1995).It is further noted from the literature, the sodium aerosol mass concentration increases with the increasing of difference between roof to pool temperatures whereas, there is no definite correlation of aerosol size distribution with the variation of pool and roof temperatures.Taking into consideration of all the above aspects and towards ongoing SFR program of our country, we are involved in the characterization of sodium aerosols in the cover gas region from one of the sodium loop facility, called SILVERINA Loop, in Fast Reactor Technology Group (FRTG), IGCAR.The characterization of sodium aerosols includes experimental determination of aerosol characteristics and theoretical modeling to predict the aerosol mass concentration in the cover gas region.The theoretical simulation is carried out with the purpose that, it can be useful and extended to the reactor geometry and serves as input in the reactor design.
In this paper, the design, fabrication and installation of aerosol sampling system and temperature profiling system for the cover gas region of SILVERINA loop, experimentation, results and analysis of sodium aerosol characteristics, theoretical simulation of sodium aerosols mass concentration for the given pool temperature and geometry and validation of the model with experimental results are presented.

THEORETICAL SIMULATION
In the cover gas space, aerosol particles are formed by a single source term (evaporation and condensation) and removed continuously by several mechanisms (gravitational, wall plating, and ventilation).Since, all the removal mechanisms are dependent on particle size, a theoretical model is developed using mass and number concentration decay equation by including the effect of continuous source term and various removal mechanisms (Sheth et al., 1975).A first order differential equation is formulated to predict the equilibrium mass and number concentration of the aerosols in cover gas region over a period of time.Taking initial size of the aerosols as an input from the experimental results, the equilibrium mass concentration is evolved by solving rate equation of mass concentration and number concentration numerically by finite difference method.In this model, the inputs parameters are (i) temperature of sodium pool surface, bottom surface of roof top and bulk cover gas, (ii) geometry of the vessel (diameter of the pool surface and height of the cover gas region) and (iii) initial radius of aerosol.The rate equations for mass concentration, number concentration and inter-relating equation of mass and number concentration of the aerosols are given below: where C -Mass concentration (g cm -3 ) λ-Decay rate (gravitational, wall plating and ventilation) (1 s -1 ) δ -Convective source rate (1 s -1 ) S e -Evaporative source term (g cm -3 s -1 ) N -Number concentration (1 cm -3 ) S n -Source term for number concentration (no. of particles cm -3 s -1 ) K -Coagulation rate (1 s -1 ) ρ -Particle density (g cm -3 ) r -Radius of particle (cm) t -Time (s) The correlation λ, δ and K are given below: where λ1-Decay rate due to gravitational (1 s -1 ) λ2-Decay rate due to wall plating (1 s -1 ) λ3-Decay rate due to ventilation (1 s -1 ) where g -Gravitational constant (cm 2 sec -1 ) H -Height of cover gas region (cm) η-Viscosities of argon cover gas (g cm -1 sec -1 ) φ -Cunningham correction factor k -Boltzmann's constant (erg K -1 ) Tm -Bulk Cover gas temperature (K) Aw -Area of walls (cm 2 ) Δ -Wall platting parameter V -Volume of cover gas region (cm 3 ) Q -Ventilation Rate (cm 3 sec -1 ) ρc -Density of cover gas (g cm -3 ) Dem -Diffusion coefficient of sodium vapour (cm 2 sec -1 ) ΔT -temperature difference between sodium pool surface to roof surface (K) Pp -Partial Pressure of sodium vapor (Torr) M -Sodium molecular weight R g -Gas Constant (Torr cm 3 K -1 mol -1 ) Tp -Sodium pool temperature (K) Due to evaporation of sodium vapour from the sodium pool, the concentration of sodium vapour is more near the pool boundary than bulk cover gas region.The flux of sodium vapour across the sodium pool is written as: where Ce -Sodium vapour concentration (g/cm 3 ) and x-Thickness of pool boundary layer (cm) The source term due to evaporation (S e) is defined as: Se = J × A p /V, where, A p -Surface area of sodium pool (cm 2 ) 1.823 0.424 642.83 The source term for number concentration (S n ) is calculated by using S e , density and volume of particle In our modeling, to begin with the concentrations C and N are set to zero.The initial particle radius is fed from the experimental results.In the next time step, for the initial particle radius, the convection source rate (δ), the collision kernel rate K (coagulation), the particle decay rate constant λ are calculated.Then for these conditions the mass concentration C and the number concentration N are calculated.In the next time step from the calculated value of C and N, the new particle radius is calculated.The particle radius in this step is different from the initial radius.Subsequently all parameters are calculated until the convergence of mass concentration value is reached.At this time, the mass and number concentrations reached steady state value, while the particle radius also reaches steady state value.Hence, the measured mass concentration and the theoretically calculated mass concentrations are equilibrium values.

Descriptions of SILVERINA Loop
SILVERINA sodium loop was constructed and commissioned at Engineering Hall-I, FRTG, IGCAR to conduct various experiments related to Prototype Fast Breeder Reactor (PFBR) and general Sodium Technology (Chandramouli et al., 2006).The loop consists of three cylindrical test pots namely Test Pot-1(TP-1), Test Pot-2 (TP-2) and Test Pot-3(TP-3).This is a dynamic sodium loop with an electromagnetic pump, cold trap, plugging indicator, sodium sampler, heater vessel, interconnecting pipe lines, bellows sealed valves, flow meters and cover gas purification circuit.Sodium is filled in to the loop from a storage tank (capacity of 1300 kg).The sodium aerosol characterization experiments are carried out in TP-1.The height and internal diameter of the TP-1 are 2235 mm and 750 mm respectively and the height of the cover gas region is 820 mm.The total volume and quantity of sodium holdup in the TP-1 are 1.04 m 3 and 0.512 m 3 respectively.The top flange of TP-1 is provided with three nozzles for sodium level indication (low, middle and high levels) and a spare nozzle.The internal diameter of spare nozzle is 60.3 mm which is used for the experiments.The salient features of SILVERINA Loop are as follows: (i) the loop consists of a sodium tank in which liquid sodium could be maintained at various temperatures from 200-550°C and it simulates the reactor pool condition, (ii) the region above the sodium pool is filled with cover gas (Argon).

Sampling System
A schematic diagram of sodium aerosol sampling system installed in TP-1 is shown in (215, 415 and 715 mm) to enable the sampling at three different levels.Before starting the experiment the required length tube is attached with the flange and inserted into the TP-1.The aerosol sampling tube is made of SS316 with internal diameter of 10 mm (1.5mm wall thickness).The maximum particle diameter that can be collected is 20 µm, without having bias due to wall deposition by impaction for a flow rate of 2 L min -1 (Hinds, 1982).
(b) Aerosol sampling bottle: The schematic diagram of sodium sampling bottle is shown in Fig. 2. The capacity of the sampling bottle is 1.0 L and made of Perspex.The height and diameter of the bottle are 306 and 80 mm respectively.The bottle is closed on top side with perspex flange arrangement.The flange is provided with two opening for the insertion of inlet and outlet tubes.The inlet tube is inserted upto bottom and it is connected to sampling tube by means of KF coupling and ball valve/gate valve.The paraffin oil will be drained by using a tube and needle valve arrangement at the bottom.
The sampling bottle is filled with paraffin oil (~600 mL) and maintained at ambient temperature.The sodium aerosol laden cover gas is made to pass through the bottle, thus solidification of aerosol particles would occur as the cover gas enters into the paraffin oil.The residence time of the cover gas is increased due to baffle arrangement, which ensures that all sodium aerosols get trapped from the cover gas before it goes out of the bottle.The cover gas coming out from the sampling bottle #1 is made to pass through sampling bottle #2 so as to remove aerosols escaped if any, from the 1 st bottle.After sampling, the sample bottles are removed from the loop and paraffin oil is drained for analysis.(c) Line heaters and controller: To prevent sodium aerosol solidification within the sampling tube during experimental measurements, the wall temperature of the sampling tube is maintained at 110°C.The heating coils are wound on the sampling tube along with insulation and the current through the heating coils was controlled by using PID (proportionalintegral-derivative) controller.The temperature along the sampling tube was monitored by 2 thermocouples.In order to have a redundancy in heating, a spare heater is also provided.The heater controller set-up consists of a panel board mounted with one PID controller, temperature display units, 3 pole rotary switches for double heaters and allied PCBs.
(d) Aerosol flow control device: In order to regulate the gas flow through the sampling bottles a rotameter is connected after the 2 nd bottle followed by a filter paper holder (25 mm diameter).The pressure of the cover gas region is maintained at 34 kPa above atmosphere.The cover gas is drawn from the cover gas space of TP-1 and made to bubble through the paraffin bottles.The cover gas flow rate was maintained at 2 L min -1 using the rotameter and found to be maintained upto 30 minutes.A glass fiber filter of 25 mm was used to prevent aerosols escaped, if any, after the 2 nd bottle.
Before the experiment, pressure holdup test for sampling tube and gate valve has been carried out by pressurizing TP-1 up to 50 kPa above atmosphere.The functioning of surface heaters, PID temperature controller and thermocouples has been checked by heating the heater up to 110°C.

Temperature Measurement System
The pool, roof and cover gas temperature are important parameters for the theoretical simulation of aerosol mass concentration in cover gas region of SILVERINA loop.A temperature measurement system has been fabricated, installed in top flange of SILVERINA loop TP-1 (spare nozzle) and measurements were carried.A schematic diagram of the temperature measurement system is shown in Fig. 3.The system consists of matched top flange for the aerosol port, a vertical cylindrical shaft welded below the top flange and six grooves to insert 6 thermocouples which are terminated at six different heights.Temperature was measured by using chromel-aluminium K-type thermocouples at the six locations in the cover gas region.The material used for the fabrication of cylindrical soft and flange is SS316.The diameter and length of the cylindrical shaft is 60 mm and 820 mm respectively.Proper O-ring arrangements were made to prevent leakage of cover gas through thermocouple holes.The temperature measurement locations from the top of flange are (i) the pool surface (820 mm), (ii) near to the pool (790 mm), (iii) two locations on the middle of the cover gas region with 300 mm difference in height (400 mm and 100 mm).(iv) near to the roof surface (20 mm) and (v) roof surface (0 mm).Accordingly, the thermocouples were terminated at 820 mm, 790 mm, 400 mm, 100 mm, 20 mm, and 0 mm from bottom surface of the top flange.Each thermocouple is connected with 3½ -digit digital indicator.

Sampling and Analysis
The pot is filled with sodium up-to a particular level before starting the experiment.The argon is filled above the sodium surface at pressure 34 kPa above the atmosphere.The temperature of the sodium is raised by heater and monitored continuously by using thermocouples.There is no ventilation path other than sampling line.Aerosols are drawn from the cover gas region and allowed to get trapped in liquid paraffin oil medium without exposing them to atmosphere.After isolating the bottles from the system the sampling bottles were taken for analyzing the samples.The size distribution of sodium aerosols is determined by using Mastersizer (M/s Malvern Instruments, UK).The instrument measures the particle size distribution (sodium aerosol) hovered in a liquid dispersant (paraffin oil) by using ensemble diffraction technique.The measurement of sodium aerosol mass concentration is carried out by conductivity method (M/s Metrohm, 856 conductivity module, Switzerland).The mass of sodium aerosols trapped in the liquid paraffin is measured by transferring them into a water medium (to become NaOH) and measuring the change in conductivity of the NaOH solution.The sodium aerosol mass concentration is estimated by using a pre-established calibration graph between changes in conductivity as a function of concentration of NaOH (Amit et al., 2014).
The sodium pool temperature was varied from 250-550°C.The cover gas (argon gas) is made to bubble through liquid paraffin oil at a flow rate of 2 L min -1 .The sampling time is varied from 20 minute to 2 minute according to sodium pool temperature.Since the sodium aerosol mass concentration increases with increase of sodium pool temperature and in order to avoid coagulation of aerosol trapped in the paraffin oil, the sampling time was kept for 20 minutes for the pool temperature 250°C and progressively reduced to 2 minutes when pool temperature is 550°C.The maximum volume of sample would be 40 L when the sodium pool temperature is 250°C and the minimum volume of sample is 4 L when sodium pool temperature is 550°C.The total volume of cover gas is 500 L at 34 kPa pressure inside the cover gas region.The maximum pressure drop in the cover gas region is from 34 kPa to 25 kPa during 40 L sampling.Test runs showed that, up to 50 mg of trapped sodium aerosol mass in the bottle, the coagulation of aerosols was not noticed for next 24 hrs after sampling.It is observed that, total sampled aerosol mass is found to get trapped in the first bottle itself for the sampling temperature upto 350°C, while, for the temperature of 400-550°C, there exists trapping of aerosols mass in the second bottle upto a maximum of 10% of the first bottle.There is no trapping of aerosol is observed in filter paper in all the runs.

RESULTS AND DISCUSSION
Temperature Profile: The temperature profile of cover gas region in SILVERINA loop was measured by varying sodium pool temperature from 250-550°C.The temperature profiles of the cover gas region with cover gas height for various pool temperatures are shown in Fig. 4. It is observed that, temperature profile is found to follow a similar pattern as found in the literature (Roberts et al., 1995).The temperature started decreasing from the pool surface (820-790 mm) -region C, then has uniform temperature region (790-20 mm) for about 770 mm height -region B, and decreases towards roof temperature (20-0 mm) -region A. The temperature of the roof top found to vary from 90 to 150°C for the sodium pool temperatures from 250 to 550°C respectively.The decrease of temperature in the region A varies according to the temperature of the bottom surface of the roof top from bulk gas temperature.
Size Distribution: The liquid paraffin oil sampled after each measurement is analyzed and mass-size distribution and MMD were determined.The size distribution and MMD were obtained for all the three sampling heights (probe length) and for all the pool temperatures.A typical steady state size distribution at middle region of cover gas for 400°C pool temperature is shown in Fig. 5.It is observed from Fig. 5, that particles are found in the range of 1 to 16 µm with MMD around 7.0 µm (σ g = 1.5).The MMDs obtained for three different sampling levels for  various pool temperatures are shown in Fig. 6.It is observed from Fig. 6, that, MMD found to increase linearly with increase of sodium pool temperature.It is also noted from the figure, for all the pool temperatures, the value of MMD is found to be higher near the pool surface (715 mm) when compared with that of near the roof (215 mm) and middle level of cover gas region (415 mm).
Mass concentration: The mass of trapped sodium aerosols in the bottles for all the samples was determined and found to vary from 0.026-35.6 g m -3 .The variation of sodium aerosol mass concentration for various pool temperatures is shown in Fig. 7.It is observed that, the mass concentration increases with increase of sodium pool temperature and found to fit in 3 rd order polynomial regression.It is also observed from the figure, for all the pool temperatures, the sodium aerosol mass concentration is higher near the pool than that of near the roof and middle level of cover gas region.
Theoretical simulation: Fig. 8 shows the MMD of sodium aerosols measured in the middle region of cover gas for various pool temperatures along with fitted equation (linear regression).This fitted equation is used as an input for calculating mass concentration of the sodium aerosols for various pool temperatures in the cover gas region.Since sodium aerosols are continuously generated in the pool when rising the pool temperature, to calculate the mass concentration of aerosols for a particular temperature, the initial particle size is taken for the temperature below that particular temperature by using the fitted equation.For example, if we want to calculate the mass concentration at pool temperature of 300°C, the initial radius is taken from fitted equation at 290°C.It is observed that, the mass concentrations predicted for pool temperature of 250°C and 300°C did not show significant difference when the initial particle size is taken for the temperature difference of more than 10°C, but it shows significant variation  (> 15%) in the range of 400°C and above.(It is to be noted that aerosol mass concentration is very less in 250°C and 300°C, when compared with 400°C and above).Fig. 9 shows the simulated and experimentally measured mass concentration for various pool temperatures at the middle level of the cover gas region.It is noted from the figure that, mass concentration predicted by the simulation is found to be underestimated by 10-15% with experimental value for the temperatures between 250°C and 450°C.Afterwards the trend begins to change and at 550°C the mass concentration is overestimated by 15%.The variation of 10-15% in the lower temperature region (250-450°C) is attributed to the spatial variation of concentration in the actual scenario, whereas, it is assumed to be uniform in the theoretical estimation.As the evaporation rate increases with increase of temperature, the mass concentration as well as MMD gets increased.Due to higher concentration, the higher sized particles undergo cloud settling resulting the difference in the measured concentration by about -15% from the predicted value for 550°C; whereas, the simulation deals with individual particle settling.It is to be noted here that, similar trend is observed between the predicted mass concentrations and measured concentrations for other two levels (lower and upper cover gas regions).The experimental error associated due to flow rate, sampling time and analysis is 7-10%.
The role of aerosols in the cover gas region: The thermal radiation from the pool surface is scattered by the presence of aerosols in the cover gas region and it reduces the heat flux reaching the bottom of the roof top.The modified Stephan's law for heat transfer including aerosols between two surfaces is given below:   It is further observed that, particle size plays important role in the forward scattering (Mie Scattering) of thermal radiation.It is noted that, the thermal radiation transfer is unique feature to a particular geometry (Roberts et al., 1995).
It is observed in literature, the mass transfer occur mainly due to condensation of aerosol reaching the bottom of roof surface.The mass transfer rate found to increase with increase of roof temperature with corresponding decrease in bulk to roof temperature difference upto 100°C.At higher roof temperature, the mass transfer rate decreases and mass deposited on the roof bottom surface also begin decrease.It is noted that, the sodium aerosols begin to condense in the bulk gas region before reaching the roof surface.

SUMMARY
The sodium aerosol size distribution is found to be monomodel.Both, MMD and mass concentration of sodium aerosols increases with increase of sodium pool temperature.The sodium aerosol mass concentration and MMD are found to be higher near the sodium pool compared to middle of the cover gas region and near the roof top.The simulated and experimental measured mass concentration of sodium aerosol in cover gas region is found to have good agreement.The modeling is found useful in predicting the sodium aerosol mass concentration for a given geometry and pool temperature.
Fig. 1.A schematic diagram of sodium aerosol sampling system installed in TP-1 of SILVERINA loop.

Fig. 3 .
Fig. 3.A schematic diagram of the temperature measurement system.

Fig. 4 .
Fig. 4. The variation of temperature in cover gas region with cover gas height for various pool temperatures.

Fig. 5 .
Fig. 5. Volume -size distribution of sodium aerosol at the middle level of cover gas region for 400°C pool temperature.
where σ-Stefan-Boltzmann constant; εp-Emissivity of sodium pool surface; εr-Emissivity of roof bottom surface; Tr-Roof bottom surface temperature.Optical thickness -τ = κ × L (13)where κ-extinction coefficient of aerosol = C × Kc, where Kc is the mass extinction coefficient and to be determined experimentally by conducting experiments for the absorption of black body radiation for a various known concentration C; L -Height of cover gas region.