Techniical Paper of

5 th Int.Symp.on Computational

Fluid Dynamics – Sendal, 1993

P.Aniruddha, K.Charan and S.Tripathi

Transoft International, Epinay/Seine, France

The propagation and accumulation of a transient plume, over a standard urban location, in an uinstable atmosphere, has been investigated jusing a second order accurate CFD package Fluidyn-PANACHE. The code Fluidyn-PANACHE solves the complete system of navier-Stokes’ equations over any arbitraty domain. Results are presented in the form of ground level concentration of various components at different time intervals along with the plume growth in the atmosphere.

With the increasing awareness about our threatened environment and the pace at which instustrialisation is taking place, a need has arisen to have prior warning about the spread of hazardous pollutants in the atmosphere. Due to a large number of varying parameres, it is neither feasible nor economical to predict atmospheric dispersion using experimental setup. Much work has been done in the past few decades by Pasquil, Turner, Briggs, etc.. for statistical estimation of pollutant dispersion into the atmosphere. However, such models solve for the diffusion equation only and are hence insufficient in many cases since they do not incorporate the complete fluid dynamics. This has led to the identification of CFD as a means of carrying out such simulations. Considerable research has been devoted towards the development of reliable CFD tools to simulate complex atmospheric flows incorporating the effects of vaious factors like wind speed and direction, terrain topology , location and nature of cloud cover, condensation – rainfall, gas-particle intercation, evaporation, dissolution of gasesd in water droplet – wash down, etc... as well as proper modelling of atmospheric turbulence. Unfortunately, till date there is no commanly available, economical and user-friendly CFD package capable of simulating these difficult tasks. The development of Fluidyn-PANACHE is a step towards achieving this goal.

In Fluidyn-PANACHE, for different species, the respective species conservation equations are solved along with the Navier-Stokes’ equations. The solution procedure is based on the well known ALE (Arbitrary Lagrangian-Eulerian) formulation of the Los Alamos group ( Hirt et al : 1974. Pracht : 1975). A second order MUSCL based scheme (van Leer – 1977) is used to spatially discretize the convective part.

The planetary boundary layer is characterized by a two layer model, viz. An unstable convective boundary layer close to he ground with a stable capping inversion layer. The height of the boundary layer is computed using Deardorff’s (1979) formulation. Atmospheric turbulence is estimated using a K-model for the unsteady, horiwontally homogeneous, unstable boundary layer. The K-model parameters are determined from Nieuwstadt and Van Ulden’s (1978) formulation in terms of surface layer similarity relations and Businger’s (1971) velocity profile. For mixed layer Hunna’s (1968) relations are used for the determination of K-model parameters.

The effect of Vegetation on the surface fluxes of heat and humidity are modelled using Deardoff’s (1978) method.

The problem considered is that of transient plume over a slowly sloping semi-urban area. The computational domain extends to 2 km. In the downwind direction (Z-axis) and 500 mt. in the crosswind direction (Y-axis). Based on approximate plume rise calulations, the height of the computational domain is limited to 800 mt.(X-axis). Since the simulation was on local scale , it was felt that the recirculation and its effects around buildings be also modelled. This resulted in a grid of 14 x 19 x 51 (X,Y,Z). The terrain slopes from 58 mt. Gradualy to 200 mt. In the downwind direction. Fig. 1 gives a plan view of the computational domain with terrain altitide contours and obstacles.

The plume was considered to be emitted continuosly for 600 sc. After which it was switched off. The flow rate from the stack is assumed to be 30 kg/sc. With an initial Sulphur dioxide concentration of 30000 ppm the remainder being air. The wind velocity for this unstable case was 9 mt/sc., assumed uniform. The ground level concentrations (GLC) ploted, shown in figures 2 to 7, correspond to 30 sc., 550 sc., 600 sc., 727 sc., 770 sc. 1120 sc. And 1700 sc. respectively.

Figures 2 to 4 correspond to the case of continuos emission of the plume, the remainder showing the GLC due to the plume which has got detached from the stack and is slowly diffusing and rapidly convecting in the downwind direction. Figure 2 represents the intial development of the GLC due to the plume. Figure 3 and 4 slow that the GLC contours have stabilised. The effect of recirculation behind the buidings and a loacl increase in concentration due to the recirculation is clearly seen in them. Further a building that presents a broader frontal area to the wind has a greater pollutant trapped in its recirculation zone.

Figures 5 to 8 show the gradual diminution of the GLC value , as the detached plume is diluted and convected aways by the wind. In approximately 20 minutes, it is seen that the GLC drops to 1c12 ppm. Further downstrem, particularly near the exit plane of the computational domain the GLC drop is not very drastic. This probably due to the sloping up of the terrian.

Figure 9 to 10 represent the variation of GLC along the stack centerline with distance for different instances of time. Figure 9 represents this development for the continuos plume. The detached plume convection is clearly visible in fig. 10, while fig.9 shows the build up of GLC as long as the pollutant is pumped into the atmosphere.

The crosswind direction evolution of the plume is shown in figure 11 and 12. From fig. 12 it can be seen that due to the convection in the downwind direction, the concentrations in the crossiwnd direction in the visinity of the stack (i.e. at 62m) decreases ater 10 seconds of switching off. Where as, at 250 mt. The plume GLC is still to be significantly affected. The concentrations at 25 mt. Upwind of the stack have also reduced, since the plume on switching off is convected further downstream.

Figure 13 and 14 are the surface plots corresponding to the continuous and the detached plumes, for a concentration value of 1 ppm. The effcet of upward sloping is to make the surface contours plot of the buoyanat plume to appear as if it is sinking. Figure 14 shows the detached plume after 85 sc. of switching off of the plume. The downwind travel of the plume due to convection of the wind corresponds well with the wind velocity.

The results produced by Fluidyn_PANACHE seem to be quit inpressive in giving correct

Picture of transient pollutant dispersion on uneven terrain with obstacles. It is thus a economical tool for prediction of the spread of hazardous gases, either accidental or deliberate, and a helpful package for city planners, environmental engineers and a host of other professionals involved in the task of maintaining our fragile and increasingly theratened environment.

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