**Numerical code**

ANSWER is a finite volume based CFD software (Patankar 1980; Runchal 1987; Versteeg and Malalasekara 2007) that solves the 3-D Navier-Stokes equations, for incompressible and compressible fluid flows with arbitrary polyhedral grids. This code (ACRi 2016) also has various turbulence models including Reynolds Averaged Navier-Stokes (RANS) based models, Reynolds stress models, \(k\)-\(\epsilon\) and *LES* (Large Eddy Simulation), and the CFD framework of this code has been coupled to the modules written for aerosol transport and dynamics. It handles the aerosol dynamical processes such as coagulation and removal mechanisms as described in Eq. (1). Eq. (1) is an integro-differential equation where the integral terms are due to the coagulation process of particles that appear on the right-hand side as shown below:

where \({d}_{p}\) and \({d{\prime }}_{p}\) are particle diameters, \(n({d}_{p},r,t)\) is the spatially (\(r\)) and temporally (\(t\)) varying number concentration distribution function for particle diameter \({d}_{p}\),\(U\) is the gas phase velocity,\(D{\prime }\)is the particle diffusivity,\(K\left({d}_{p},{d}_{p}^{{\prime }}\right)\) is the collision frequency between particles of different sizes,\(S\) is the source term and \({U}_{drift}\) is the total drift velocity of the aerosol particles due to various mechanisms like gravitational settling, thermophoresis and turbophoresis. Second and third term on R.H.S. of the above equation describes the formation and loss of particle size dp by coagulation.

The particle diffusivity used in Eq. (1) is also a function of particle size and is given by,

$$D{\prime }=\frac{{K}_{b}T{C}_{c}}{3\pi {\mu }_{g}{d}_{p}}$$

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where, \({K}_{b}\) is the Boltzmann constant, \(T\) is the temperature, \({\mu }_{g}\) is the gas viscosity, and \({C}_{c}\) is the Cunningham slip factor (Cunningham 1910, Davies 1966)

$${C}_{c}=1+{K}_{n}*(2.514+0.8*\text{e}\text{x}\text{p}(-0.55/{K}_{n}\left)\right)$$

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where,\({K}_{n}\) (Knudsen number) is the ratio of the mean free path of the gas particles (\(\lambda\)) to the particle diameter (\({d}_{p}\)) and is given as,

$${K}_{n}=\frac{2\lambda }{{d}_{p}}$$

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The aerosol general dynamic equation (Eq. 1) is solved for each aerosol particle size class *d**p* at every time step (the particle size range being divided into *m* classes in the discrete domain) with the necessary inputs from flow field simulation results by CFD part of the software.

The master equation handling aerosol dynamic equation has different sub modules, each of which have been validated with respect to their analytical and/or experimental solutions by Rajagopal et al. (2018). For coagulation sub module, analytical validation was done through the time evolution of an initial log-normal distribution of aerosols (Lee et al. 1984). In addition to above-described analytical validation for coagulation, a numerical validation against NGDE software (Prakash et al. 2003) was done with initially homogenously mixed lognormal size distribution and with continuous injection of particles into the chamber. Details of these validation exercises have been presented elsewhere (Mariam et al. 2021).

**Experimental set-up**

A controlled experiment was carried out in a stainless-steel chamber of dimension (0.8x0.8x0.8) m3 (Figure.1) to verify the numerical output of the ANSWER software. Aerosols were generated using a nebulizer, TOPAS aerosol generator ATM 226, which generates NaCl polydisperse aerosols mainly below 1 µm with constant particle size distribution. Condensation Particle Counter (GRIMMCPC 5.403) and Scanning Mobility Particle Sizer (SMPS) were used for the measurement of aerosol number concentration and size distribution respectively. GRIMM SMPS (model 5.403C) associated with a Vienna type DMA was used which can detect particle size in the range (11.1-1083.3) nm at a flow rate 0.3 Lpm.

**Evolution of aerosols in a closed chamber – problem description and CFD set up for Comparison of simulation results with experimental observations**

Aerosols were injected continuously into the experimental chamber using a nebuliser at the rate of 1010 s− 1. Experiments were conducted with five different flow rates (10, 20, 30, 40 and 50 Lpm respectively) and the corresponding Reynolds number were estimated for each of the flow rates (ex. Re ~ 1956 for 10 Lpm). Both laminar and turbulent flows were simulated depending upon the ventilation rate. In case of turbulent flow, *k*-ε model was implemented. The chamber was discretised with total number of mesh elements of 87,472 with grid clustering near the walls. Global residue was taken to be 10− 8 for all the variables for the termination of iteration. No-slip condition was taken during the simulation. More details on the experimental set up are shown in Figure.1. Aerosol total number concentration in the chamber is measured using CPC and its temporal evolution is monitored up to 3000 s during the experiment.

**Estimation of CPP for a typical workplace environment using coupled A-CFD**

*CAM Placement Parameter (CPP)*

Locations for placing sensors in a workplace environment are primarily decided based on few factors. They generally are taken downwind, should have higher probability of occupancy of workers i.e. within the breathing zone, should avoid any potential dead zone, it shouldn’t be too close to the potential source location. Further quantitatively the best possible locations among the initially chosen CAM locations is decided based on the assigned CPP value. The quantity CPP is estimated based on the peak number concentration in the indoor environment and lag time. CPP for *i**th* sampling locations is defined by Geraldini et al. (2016) as,

$${CPP}_{i}=\sum _{j=1}^{n}{M}_{i,j}=\sum _{j=1}^{n}\left(\frac{{CR}_{i}}{{\tau }_{i,j}}\right)$$

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where *i* and *j* represent specific sampling and potential release locations, \({M}_{i,j}\) is the contribution of *j**th* release location towards *i**th* sampling location in evaluating *CPP*, \(n\) is the total number of potential sources/release locations.\({CR}_{i}\) is the concentration ratio term defined as,

$${CR}_{i}=\frac{{C}_{i,peak}}{{C}_{peak}}$$

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where *C**i,peak* is the peak aerosol concentration found at the sampling location *i* at time *t* and *C**peak* is the peak aerosol concentration observed in the room following a release at the same time *t*. *τ**ij* is the lag time defined as the time at which the total number concentration of particles in that sampling location attains a value of \({10}^{10}\)m−3 following a release from a specific location *j* inside the room. Eq. (5) shows that CPP is s a measure of suitability of the CAM location *i* for releases from any of *j* release points since many potential release locations exist and the optimum location of placement of CAMs shall account for all of them. To find out the most suitable location for placing the CAM, one should compare the CPPs for each of the proposed sampling locations and choose the \({CPP}_{i}\) having the largest value.

*Flow field simulation*

To illustrate the application of this model, we simulated the airflow dynamics and particle transport in a chamber of dimension (3x2x1) m3 as shown in Figure.2. Two blocks of dimension (1.5x 0.3x 0.3) m3 and (0.15x 1x 0.3) m3 were added in the chamber geometry to simulate the presence of obstacles to the air flow. The area was ventilated via an inlet, of area 0.04\({ \text{m}}^{2}\) at a height of 0.9 m, on the left sidewall and two outlets of same dimensions close to the ground on the right sidewall. As boundary condition, the velocity components at the inlet area were chosen to be 0.1, 0.0, -0.1 ms− 1 respectively along X, Y, Z directions and it was assumed that 60% of the total flow was through outlet-2 while 40% (outlet flow fraction, given as input) was through outlet-1. This distribution of exhaust flow was to make the flow well distributed throughout the whole geometry to avoid any biasness in choosing the sampling location, as both the sides of the 3D block2 were assumed to be the potential breathing zone. The Reynolds number (\(Re\)) for this condition was estimated as 2160. The airflow pattern within the geometry is governed by the locations of the inlet and outlet. A partitioning wall divides the simulation area into two compartments connected through a door of area 0.08 \({\text{m}}^{2}\). \({\text{R}}_{7 }\),\({\text{R}}_{8}\),\({\text{R}}_{9},{\text{R}}_{11}\) denoted in red colour on the left compartment were chosen to be the potential aerosol release locations due to large quantity radioactive material handling in powder form and \({\text{R}}_{4 }\),\({\text{R}}_{5}\), \({\text{R}}_{6},{\text{R}}_{10}\), \({\text{R}}_{13}\) were the five sampling points denoted in green colour. Right part of the compartment was chosen for sampling locations due to the higher occupancy of workers in this area. The computational domain was discretised with total 11,088 number of mesh elements. Global residue for momentum was set to be 10− 8. An incompressible fluid of density 1 kg.m− 3 and viscosity of 0.00153 m2s− 1 was considered in these simulations. An aerosol emission rate of \({10}^{14}\) s− 1 for 40 s (total of 4x1015 particles) from each of the release locations were assumed into the geometry with an air-exchange rate of 3.5 h− 1. The aerosol size distribution at the emission location was considered to be lognormally distributed with a count median diameter (CMD) of 30 nm and geometric standard deviation (GSD) of 1.3. Thermophoresis was not considered in this simulation due to the assumption of uniform temperature throughout the chamber. No-slip condition was taken throughout the simulation.

The authors did not receive support from any organization for the submitted work. The authors have no relevant financial or non-financial interests to disclose.

Background particle concentration in ambient air as well as at the inlet is assumed to be zero. So, we ignored any interparticle interaction between ambient and radioactive aerosols in our study. The outlets are set as open boundaries with zero particle gradient. Apart from the simulated puff release scenario, we neglected any other background aerosol source term for simplicity.

For different size class, gravitational settling responsible for deposition has been taken for the floor surface only.

**Application of CPP estimation methodology to a ****typical radiological laboratory **

The A-CFD model was applied to a typical laboratory of dimension (18.6x10.9x5.0) m3 as shown in Figure.3. The laboratory had six rectangular inlets of different dimensions in the ceiling. Each of the inlets was accompanied with diffusers below them for flow dilution purpose. The areas of inlet-1, 2, 3, 4, 5 and 6 are 0.95 m2, 1.05 m2, 0.84 m2, 0.91 m2, 1.25 m2, 1.03 m2 respectively, and the laboratory had an air-exchange rate of 6 h-1. Velocity components at each of the inlets were taken as 0.0 ms-1, 0.0 ms-1, -0.3 ms-1 respectively along X, Y and Z directions. Five fume hoods, each having a length of 1.35 m, width 0.75 m and height 3 m were mounted on the wall at a height of 2 m. A partition up to the ceiling divides the laboratory in to two parts connected through a door area of 2.18 m2. Based on the operating experience and available sources, R2, RDC3 and R3FH7 are identified as the potential release locations, and S6, Sfh3, S5, S4, Sfh7, S2 and S3 were selected as the probable sampling locations.