Ruben Avila

A 3-D Lagrangian stochastic model for the meso-scale atmospheric dispersion applications

Abstract A fully 3-D Lagrangian stochastic particle trajectory model is presented and applied to the meso-scale atmospheric dispersion and ground concentration calculations. The use of Gaussian plume model (GPM) with Pasquill–Gifford σ s for downwind distances exceeding 10 km is critically viewed. Further, the effect of variation in release height on the ground concentration and dispersion parameters ( σ y , σ z ) is studied for continuous releases. A continuous release of a non-buoyant gas in a neutral stratified atmosphere is simulated for various stack heights. The turbulent atmospheric parameters like vertical profiles of the fluctuating wind component and the eddy lifetimes for the horizontal and vertical directions, etc. were calculated using a semi-empirical mathematical model and compared with a E – ϵ model. The numerically calculated horizontal and vertical dispersion coefficients ( σ y , σ z ) are compared with the Pasquill–Gifford empirical σ s and with the Pasquill-modified σ y . The ground concentration values as a function of downwind distance, have been compared with the Green Glow data and with a GPM for various release heights. The comparison of the results demonstrate a need of using a 3-D model over the simple GPM for meso-scale atmospheric dispersion applications. The GPM overpredicts the ground concentration because it cannot take into account the vertical wind shear, which is observed in the atmosphere under all stability conditions. A weak dependence on the release height in the numerically calculated dispersion coefficients σ s, is also observed.

A 3-D Lagrangian (Monte Carlo) Method for Direct Plume Gamma Dose Rate Calculations

A fully 3-D Lagrangian particle method has been presented for calculating the direct gamma dose rates due to a radionuclide plume in the atmosphere. A continuous release of radionuclides into the atmosphere was simulated by liberating a large number of Lagrangian particles whose trajectories were tracked for about 25 h in a turbulent atmosphere with a known wind field. The atmosphere turbulent/stability characteristics like wind velocity fluctuations, eddy lifetime, etc., were obtained from the reported data in the published literature. For calculating the direct plume gamma dose rates a point isotropic source formula has been used with appropriate attenuation and build-up factors for the air medium. Each Lagrangian particle represented a point source of radioactivity with a known strength. The dose rates at ground due to the radionuclide cloud were calculated by adding the contribution from each Lagrangian particle in the domain. The numerically calculated dose rates were compared with the already reported results. An excellent comparison was observed for a uniform atmosphere with the Gaussian plume model predictions. However, if the wind shear (change in wind direction with height) is taken into account, we observed that for distances exceeding 20 km, the numerical data were below the reported Gaussian Plume Model (GPM) results. This indicated the need of using a modified GPM for extended distances.

Conjugate Natural Convection in a Square Cavity Heated From Below

This paper presents numerical results for two-dimensional steady-state natural convection in a square cavity. The upper and lower walls are kept at different constant temperatures, whereas the lateral walls have certain thickness and thermal conductivity and are externally insulated. Under these conditions we deal with a conjugate natural convection problem in which the heat conduction in the lateral walls is coupled with the internal convection. The continuity, momentum and energy equations were solved by using the finite volume method. The results here presented include: (i) the temperature distribution in the lateral walls and in the fluid, (ii) the velocity field, and (iii) the average Nusselt number at the upper and lower walls. It was found that the steady state fluid flow is strongly dependent on the initial temperature condition, when the fluid is initially at rest. The PIV technique allowed us to get some experimental data by measuring the velocity field in a two-dimensional square cavity. A good agreement between numerical and experimental results was found.Copyright

A Comparison of Direct Gamma Dose Rates from a Stationary Gaussian Plume Using Different Models

Abstract The direct gamma dose rates due to a stationary Gaussian plume of radionuclides in the atmosphere have been calculated using different models [Lagrangian dose model (LDM), Gaussian plume model (GPM), and uniform cloud model (UCM)], and the results are compared. The atmospheric parameters (used in the Lagrangian model) like mean and fluctuating wind components, etc., were obtained from the published field data on a neutral atmosphere. In the LDM, a continuous release of radionuclides into the atmosphere was simulated by liberating a large number of Lagrangian particles, whose trajectories were tracked for various hours in a three-dimensional computational domain. A point isotropic source formula was used for calculating the direct gamma dose contribution from all Lagrangian particles constituting the plume. Each particle represented a point source of radioactivity, whose strength was calculated from the known release rate and was subsequently allowed to decay as a function of time. The comparison of the LDM results with the GPM indicated that both models predict comparable results in a homogeneous atmosphere. The LDM is, however, more versatile, as it can incorporate variation in meteorological data in space and time (of course when available). The UCM also compared well for ground releases; however, it cannot be used for elevated releases and short downwind distances. The purpose of this work was to test the LDM for simulating the transport, dispersion, and decay of a radionuclide plume. The LDM shall later be used for complex topographic and meteorological conditions, where the GPM is not suitable.

Simulation of atmospheric dispersion of radionuclides using an Eulerian–Lagrangian modelling system

In this paper we present an atmospheric dispersion scenario for a proposed nuclear power plant in Pakistan involving the hypothetical accidental release of radionuclides. For this, a concept involving a Lagrangian stochastic particle model (LSPM) coupled with an Eulerian regional atmospheric modelling system (RAMS) is used. The atmospheric turbulent dispersion of radionuclides (represented by non-buoyant particles/neutral traces) in the LSPM is modelled by applying non-homogeneous turbulence conditions. The mean wind velocities governed by the topography of the region and the surface fluxes of momentum and heat are calculated by the RAMS code. A moving least squares (MLS) technique is introduced to calculate the concentration of radionuclides at ground level. The numerically calculated vertical profiles of wind velocity and temperature are compared with observed data. The results obtained demonstrate that in regions of complex terrain it is not sufficient to model the atmospheric dispersion of particles using a straight-line Gaussian plume model, and that by utilising a Lagrangian stochastic particle model and regional atmospheric modelling system a much more realistic estimation of the dispersion in such a hypothetical scenario was ascertained. The particle dispersion results for a 12 h ground release show that a triangular area of about 400 km(2) situated in the north-west quadrant of release is under radiological threat. The particle distribution shows that the use of a Gaussian plume model (GPM) in such situations will yield quite misleading results.

Time-integrated thyroid dose for accidental releases from Pakistan Research Reactor-1.

The two-hourly time-integrated thyroid dose due to radio-iodines released to the atmosphere through the exhaust stack of Pakistan Research Reactor-1 (PARR-1), under accident conditions, has been calculated. A computer program, PAKRAD (which was developed under an IAEA research grant, PAK/RCA/8990), was used for the dose calculations. The sensitivity of the dose results to different exhaust flow rates and atmospheric stability classes was studied. The effect of assuming a constant activity concentration (as a function of time) within the containment air volume and an exponentially decreasing air concentration on the time-integrated dose was also studied for various flow rates (1000-50000 m3 h(-1)). The comparison indicated that the results were insensitive to the containment air exhaust rates up to or below 2000 m3 h(-1), when the prediction with the constant activity concentration assumption was compared to an exponentially decreasing activity concentration model. The results also indicated that the plume touchdown distance increases with increasing atmospheric stability.

Simulation of Monsoon Precipitation over South-Asia Using RegCM3

The objective of this study is to explore the capability of the Regional Climate Model (RegCM3), to predict the extreme weather events in south-Asian region with particular reference to precipitation during monsoon season (July, August and September) over northern mountainous and southern plain regions of Pakistan. Different cumulus parameterization schemes in RegCM3 for prediction of convective precipitation are tested for monsoon period during the years 1998 and 2001. The model results are compared with the Climate Research Unit (CRU) observational data and the surface synoptic data of the Pakistan Meteorological Department (PMD). The year 1998 was a dry year and proved to be the beginning of a severe drought lasted up to the year 2000. While in year 2001 the precipitation over some parts of the country exceeded the normal, especially the northern parts of the country observed exceptionally high rainfall rate. The results indicate that some convective parameterization schemes of RegCM3 well captured the summer monsoon precipitation over Pakistan. However, the schemes need to be selected carefully depending upon the region of interest. It was found that the Grell scheme with both closures: Arakawa-Schubert (AS) and Fritsch-Chappell (FC) satisfactorily captured the monsoon phenomenon in Pakistan specially for the northern mountainous regions.

Transient thermal response in nuclear waste repositories

Abstract In this paper, it is shown that a previously reported non-linear, one-dimensional, theoretical approximation simplifies — from a computational point of view — the calculation of the time-decay temperature field in nuclear waste repositories (NWR). This conclusion has been reached after solving, by using the control volume numerical method, the full three dimensional, transient, non-linear heat diffusion equation. The transient thermal field in a rock salt repository, is analytically solved and numerically predicted, along 100 years, after the disposal of a high-level waste (HLW). The nuclear waste, with a half-life of 32.9 years, releases an exponentially time dependent heat flux with 12 W m−2 as the initial thermal load. Two cases are studied, in the first one it is assumed that the conductivity (k) and the volumetric heat capacity ρcp of the host rock (diffusion domain) remain constant (linear case), whereas in the second one, a more realistic situation is analysed. In this last case, the conductivity of the rock salt varies as a function of the temperature field and the product ρ×cp remains constant (non-linear case). In order to observe the effect of the salt conductivity (constant or variable) on the repository temperature distribution, a comparison of both cases is performed. It is concluded, that the theoretical model, which provides an analytical solution of the thermal fields may be a powerful low cost method for design purposes.

A Pressure Correction Approach Coupled with the MLPG Method for the Solution of the Navier-Stokes Equations

We present a pressure-velocity correction approach for the solution of the Navier-Stokes equations. The Meshless Local Petrov Galerkin (MLPG) method is used to solve the two dimensional, incompressible and steady, state viscous fluid flow equations. The weak form of these equations, which are formulated in the Cartesian coordinate system, are integrated in a local standard domain by the Gauss-Lobatto-Legendre quadrature rule. The Moving Least Square (MLS) scheme is used to generate the interpolation shape functions. The pressure-velocity correction approach (segregated solution procedure) follows an iterative process, in which the momentum equations are solved sequentially to obtain the velocities v 1 ** and v 2 ** from initial guessed values for the velocity (v 1 * and v 2 * ) and pressure (p *) fields. Using the corrected velocities v i=v i/**+v i ′ pressure p=p *+p ′ in the weak form of the continuity and momentum equations, we generate a system of three equations with three unknown variables (a fully implicit method): the velocity corrections (v 1/′ and v 2/′ and the pressure correction (p ′) Using the correction values the pressure is updated and the velocities are corrected to satisfy the continuity equation. The updated values are taken as the new guessed values, and the iterative process continues until convergence. We apply the method for the solution of four (low Rayleigh number and low Reynolds number) fluid flow problems. We conclude that the MLPG method coupled with an implicit procedure to calculate the corrections of pressure and velocities can be used as a reliable methodology for the solution of the Navier-Stokes equations.

The Influence of a Harmonic Motion on a Melting Process With Natural Convection

We study the heat transfer rate in an oscillatory, two dimensional solid-liquid system which is melted from below. As the phase change process takes place, the height of the fluid layer in the lower part of the cavity is continuously enlarged. The influence of the angular frequency of the motion (Taylor number) and the melting rate (Stefan number) on: (i) the heat transfer in the liquid (Nusselt number), (ii) the temperature field and (iii) the shape of the interface, is analyzed. The governing equations together with the Stefan condition at the interface are solved by using a spectral element method. It is observed that as the height of the liquid layer increases, a non-steady unicellular flow appears, and it leads to an oscillatory behaviour of the Nusselt number. As the height of the liquid layer increases further, the onset of the thermal convection and its instabilities modify the shape of the interface, and the heat transfer rate in the molten material. We find that (i) for large Stefan numbers, the heat is transported mostly along the inclined walls, while for low Stefan numbers, a Rayleigh-Benard type convection is dominant, and (ii) for large Taylor numbers, the motion induced by the oscillation is small, resulting in a Nusselt number that decreases monotonously as a function of time, in contrast, for small Taylor numbers, an oscillatory Nusselt number is displayed.Copyright