Radiological Concentration Distribution of 134 Cs and 137 Cs Due to a Hypothetical Accident of TRIGA Research Reactor

The assessment of the radiological concentration of 134 Cs and 137 Cs owing to hypothetical accident of TRIGA Mark-II research Reactor at AERE, Savar, Bangladesh is presented here in this work. The concentration of 134 Cs and 137 Cs was estimated in different pathways consisting of the ingestion of plants, milk, and meat. The highest air concentration has been determined at 65 m distance from the core of the reactor. The maximum concentration passed off without delay simply after the accident in various directions. Local meteorological information such as average wind velocity and wind frequency were analyzed. Considering all directions, the highest concentration has been observed in the “S” direction. The concentrations of 134 Cs and 137 Cs were determined in ground, vegetation, milk and meat. The concentration of 137 Cs is investigated to be higher than the 134 Cs. The concentration of 134 Cs and 137 Cs was found to be lower in vegetation, milk, and meat than that of ground concentration. Overall, in this study, the concentration in meat has been investigated to be lower. In case of a reactor accident, the concentration assessment due to the ingestion of vegetables, milk, and meat will be a valuable guide for insuring radiological protection across the research reactor at AERE, Savar, Bangladesh.

hypothetical or probable release of radio nuclides are crucial for background radiation information and licensing necessities for the choice of a site prior to nuclear activities which includes nuclear facility. The reactor operation license is executed as per global selected criteria by means of the local regulatory authorities [1]. It's been shown that nuclear research reactors, under their normal operation, release no massive quantity of radioactivity to the surroundings. However, under accidental situations with severe core damage to the nuclear reactor, some meaningful quantity of radio nuclides may be released into the atmosphere.
Radio nuclides that are genuinely anticipated to be emitted through the stack can bring about direct radiation exposure to the population and the atmosphere in downwind distance and that also be deposited on ground and vegetation [2] [3].
In the event of a release of radioactive substance into the atmosphere, the dispersion takes place relying on climate situations, resulting in deposition in-ground and other environ mental media such as vegetables, meat, and milk and finally accumulated in human beings. The dispersion additionally depends upon several parameters inclusive of the release condition (release height from the ground, the leak rate), topography (soil, presence of boundaries), and nature of the source. In this work, we focus on the behavior of ground deposition, vegetation, milk, and meat because radio nuclides are predictable to be released considering hypothetical accident of TRIGA Mark-II research reactor, Atomic energy research establishment (AERE), Savar, Dhaka, Bangladesh. When cattle (cows, oxen, and so on) are fed vegetation, their milk and meat turn out to be contaminated. The radioisotopes along with 134 Cs and 137 Cs just after the accident show the maximum severe risks [2]. To evaluate doses, it's no doubt to make up the concentration of radio nuclides is important. Various methodologies and assumptions have been taken to determine concentration suggesting the necessity of site-precise meteorological information. In this regard, IAEA generic methodologies to evaluate the radiological consequence due to the discharge of radioactive substances in the environment have been taken into consideration [4] [5]. A computational code has been developed to predict the concentration of 134 Cs and 137 Cs based on methodologies and hypothetical accidental scenario. In this work, 40% of radioactive cesium was considered to be released from the core of the reactor to the surrounding environment [5].

Source Term and Accident Scenario
The source term represents the amount of the radioactive materials which are released to the containment. Source term is a very important term to determine the radioactive concentration in a nuclear research reactor. An approximate principle giving activity A i (t) of an isotope i at time t after the beginning of irradiation (t = 0) whose fission yield is γ and its decay constant be i The Release rate is the exhaust rate from the stack. It is an essential factor that has to be determined in the case of assessing air concentration. The equation can be represented by [5]: where F P is the fraction release the fuel to building, F B is the fraction remaining airborne and available to be released from the building to the atmosphere, A i is the Activity term, 1 λ is the lake rate parameter, sec −1 , and r λ is the radioactive decay constant, sec −1 . Considering the above assumptions, the activity of cesium 134 Cs and 137 Cs were by using of Equation (1). The estimated activity and release rate of radio cesium along with their uncertainty for 10 days continuous operation at 3 MW (t) power level is given in Table 1.

Atmospheric Dispersion and Radiological Concentration Calculation Model
For estimating downwind concentrations of airborne material released into the atmosphere, the Gaussian Plume Model (GPM) is the maximum widely used method. Inside the utility of this version, which has been validated under widely different kinds of meteorological conditions. It's assumed that the plume will spread each laterally and vertically in accordance with a Gaussian distribution. For a continuous release from an elevated point source under consistent diffusion conditions (i.e. wind route, wind velocity, and atmospheric balance) and taking into account plume reflection at ground level, the concentration x (x, y, z) is given by means of [3].
where, x (x, y, z) = air concentration (Bq/m 3 ) at a point with co-ordinates x, y, z, x= downwind distance (m), y = crosswind distance (m), z = height above the ground (m), Q = release rate (Bq/s), , y z σ σ = diffusion parameters (m) which are a function of downwind distance, x, and atmospheric stability, h = effective release height (m).
For radiological concentration assessment, ground-level concentration is required and therefore, Z can be assumed to be zero and Equation (3) can be written as The average concentration for release that happens over a time period can be calculated by making use of the above equation. If the radiological substance has a massive exit velocity (or if it's far at a high temperature), it's going to move up to a higher stage than the actual stack height. Hence the effective stack height may be written as [6] wherein D = 0.26 m, is the outlet stack diameter, v = 16.15 ms −1 , is the exit speed, ∆T is the distinction between ambient and effluent gas temperature, T is the absolute temperature of the effluent on the other hand for a research reactor like a TRIGA Mark-II at AERE, Savar, the temperature distinction, ∆T can be considered to 0 due to energetic operation of the ventilation system. Here, u = 1.56 It is vital to convert the velocity into an effective stack height implementing the subsequent formula [3] , where u z is the speed at ground level at a height z = 10 m and m is the wind coefficient depending on underlying surface and diffusion category.   dispersion is expected to follow to a protracted distance depending on the stability class around the site and release height. Then again, air concentration can be high in a path if the wind frequency is excessive in that path. From this result, the leading stability class of the site is discovered to be "A" in keeping with the Pasquill-Gifford stability category. Parameters required for radiological concentration assessment need to be taken for this stability class.
The strategies offered in this phase to be used in instances that don't include building wake outcomes.
In this case, the arena averaged from of the GPM may be used with the following simplifying assumptions: 1) For each air concentration calculation, a single wind velocity and frequency are to be taken.
2) A single long-term average wind speed for every route.
3) An impartial atmospheric stability class (Pasquill-Gifford stability class (A) World Journal of Nuclear Science and Technology [3].
Based on the above assumptions, the version for atmosphere dispersion may be represented via the equation [4] 1 exp , where C A is the ground level concentration at downwind distance x in sector p (Bq/m 3 ), P P is the fraction of the time during the year that the wind blows towards the receptor of interest in sector p, u a is the geometric mean of the wind speed at the height of release, F is the Gaussian diffusion factor appropriate for the height of release H and the downwind distance x being considered (m −2 ), Q i is the annual average discharge rate for radionuclide i (Bq/s).
where z P and qz x are two parameters depending on the stability class and on the effective stack height, and x is the downwind distance.
Here for stability class "A", 0.151 z P = and 1.291 z q = [3]. The relationship between gaussian plume diffusion factor and downwind distance for a given release height (H) is shown in Figure 3.

Radiation Concentration Calculation
The concentration calculation methodologies using GPM are described elsewhere [7]. The methodologies of concentration calculation in pathways are given in the following segments.

Ground Deposition
Activity concentrations of radio nuclides on the ground may be calculated certainly where i d is the total daily average deposition rate on the ground of a given radionuclide i from both dry and wet processes, including deposition either on to impervious surfaces or on to both vegetation and soil (Bq•m −2 •d −1 ); v d is the dry deposition coefficient for a given radionuclide (m/d); v w is the wet deposition coefficient for a given radionuclide (m/d). ( ) where, d i is the total ground deposition rate (Bq  is the time period that crops are exposed to contamination during the growing season (d). t e = 60 (d) [4], w λ is the rate constant for reduction of the concentration of material deposited on the plant surfaces owing to processes other than radioactive decay (d −1 ). i λ is the rate constant for the radioactive decay of radionuclide i (d −1 ).

Concentration Is Vegetation
The concentration of radionuclide in vegetation resulting from indirect processes from uptake from the soil and from soil adhering to the vegetation-is λ is the rate constant for reduction of soil activity owing to processes other than radioactive decay; s λ is the great constant for reduction of the concentration of material deposited in the root zone of soils owing to process other than radioactive decay (d −1 ), t b is the duration of the discharger of radioactive material (d), ρ is a standardized surface density for the effective root zone in soil (kg/m 2 , dry soil). 260 ρ = [3].
The total concentration of the radionuclide on the vegetation at the time of consumption is

Concentrations in Animal Feed
The concentration of radionuclide i in animal feed is calculated with the aid of , a i C is the concentration of radionuclide i in the animal feed (Bq/kg, dry matter); , v i C is the concentration of radionuclide i for pasture, the calculated using Equations (12)-(15) with t h = 0 (Bq/kg, dry matter), , p i C is the concentration of radionuclide in stored feeds (Bq/kg, dry weight), calculated using Equations (12)-(15), and substituting

Concentrations in Milk
The concentration of a radionuclide in milk relies upon without delay the radioactivity concentration of the feed consumed with the aid of the lactating animal. With the value of

Concentrations in Meat
The radionuclide concentration in meat is calculated in the same way as the concentration in milk. The same constraints exist.
where, Q w = 0.06 (m 3 /d) [4], i λ is the rate constant for radioactive decay of radionuclide i (d −1 ), t f is the average between slaughter and human consumption of meat-a default value is 20 days [4].

Result and Discussion
To evaluate the concentration of each radionuclide a computational code has World Journal of Nuclear Science and Technology been developed using Math-CAD professional software program to find out mathematical expressions. Source term and concentration distribution were evaluated using the developed code. The meteorological parameters such as wind velocity and wind frequency were estimated for calculating concentration.
For different food-stuffs such as vegetation, milk, and meat owing to the accidental release of radiocesium from the TRIGA Mark-II reactor at AERE, Savar, Dhaka, Bangladesh was considered. The air concentration was estimated with respect to downwind distance. Concentration in vegetation, milk, and meat was evaluated for 8 cardinal directions as the function of time. Concentration was found to be higher in the south ("S") direction. Table 1 shows the inventory (source-term) with statistical uncertainty for 134 Cs and 137 Cs. Both the activity in the core and corresponding release rate are found to be higher for 137 Cs than that of 134 Cs. The meteorological parameters such as wind frequency and wind velocity are presented in Figure 1 and Figure   2, respectively. The highest air concentration has been investigated at a 65 m distance from the core of the reactor and it was observed to be maximum towards the "S" direction shown in Figure 4 and Figure 5. The concentrations of 134 Cs and 137 Cs have been calculated in the ground. The maximum ground concentration appeared simply after the accident in various media and is depicted in Table 2. Maximum ground concentration was found in the "S" direction. With the passes of time, the ground concentration is found to be reduced exponentially due to radioactive decay. The radioactive materials move via ingestion to   Table 4. The concentration in milk at t = 0 is highest after the accident. The concentration in milk to be decreased and the sequence of the concentration of cesium in milk is C milk 137 Cs > C milk 134 Cs.   By depending so on the consumption of contaminated food, the concentration in meat occurs in the same way as the concentration in milk occurred. The concentration in meat shows in Table 5 just after the accident in 8 dominant directions. And again, the maximum concentration in milk was found in the same "S" direction. The concentration is decreased with time. As a result, we have got the sequence of concentration in meat in this paper for cesium is C meat 137 Cs > C meat 134 Cs.

Conclusion
In this study, concentrations in different pathways such as ground, vegetation meat and milk were investigated and based on atmospheric dispersion phenomena due to release of radio cesium from the TRIGA Mark-II research reactor at site. This study obviously provides a proper guideline for nuclear research reactor on radiological safety measures that have to be considered for radiation protection from nuclear reactor site at AERE in case of radiological accident.