The paper presents the numerical simulation of the dispersion of biogas from landfills using the solutions of the equations of diffusion and Navier-Stokes equations. The results can be used for the assessment of the pollution of the atmospheric air in the area of influence of landfill sites, in choosing the location of future landfill, in substantiation of the size of the sanitary protection zones of landfill, remediation and evaluation of the effectiveness of measures to reduce air pollution biogas.

For modeling of the dispersion of biogas invited to the numerical solution of differential equations of convective-diffusion transfer of contaminants in the atmospheric air, which has the form:

here u, v, w are wind velocity components along the axes x, y, z; k_x, k_y, k_z are coefficients of the turbulence along the axes х, у, z;

  I(r, t) is function of the emission of pollutants. To simplify the calculations in the future in equation (1) and accounting of emission of biogas is produced with the help of boundary conditions – concentration on the surface of landfill [4].

Coefficients of turbulence it is expedient to define by means of Smagorinsky model that takes into account the additional turbulence caused by the vorticity, with the help of equations [3]:

here is the scale of the smaller eddies is determined by the width of three-dimensional cell, k_based is the basic coefficient of turbulence, is determined as:

here k_backgr is background coefficient of turbulence, k_backgr=1-15 м²/с; ε=0,1-0,4;

Def(x; y; z; t) is the function of dissipation or deformation, which is determined using the equation:

 Ri is local number Richardson, which is determined using equation:

here T is the temperature; γ_backgr(z) is the gradient of temperature background, γ_а is adiabatic temperature gradient.

Thermal imaging survey of various landfills, which was made by author in [5] showed that release of biogas at landfill can be considered “cold”, i.e.:

here Т_biogas is the temperature of the exhaust of biogas; Т_backgr is background temperature.

In modeling dispersion of emissions from low sources of greatest interest is the lower boundary of the surface layer of the atmosphere, to which the lower 50-100 m in it vertical fluxes of heat and momentum are constant in height and are resistant to the atmosphere. Given small vertical extent of the layer, you can take the equilibrium condition (indifferent) stratification, when the vertical heat flux is zero, and temperature change occurs adiabatically. [1] In this case, the vertical temperature gradient is adiabatic g_a = 0,01ºC per meter.

For neutral stratification of the atmosphere of “cold” emissions

And system (3) is simplified:

Rough, chemically active surface capable of partial retention of biogas on the surface with further absorption. Under aerobic processes in biogas composition dominates the carbon dioxide absorbed during photosynthesis. The rest of the components poison soils and plants. Diffusion of gas at the “air-to-ground” can be expressed by equation:

here β is constant of interaction (for smooth, chemically inert surface β≈0).

At the initial moment of time (without background) concentrations of impurities of biogas are equal to zero. The infinite distance from the landfill of impurity concentration is equal to zero:

For modeling of turbulent motion of the gas is used direct modeling «DNS», based on the decision of non-stationary Navier-Stokes equations for incompressible fluids and gases:

here ν is the kinematic viscosity, p is pressure,

For the free stream pressure p equals the atmospheric, v=w=0, the profile of wind speeds at neutral stratification of atmosphere is described by Karman [3]:

here H is average height of wind obstructions (buildings, forest plantations); C is coefficient of resistance. Values ​​of z₀ and C for some surfaces are given in Table 1.

Table 1 – The values of z₀ and C for some types of surfaces [3]

Wind velocity profile is also convenient to define the equation, use the simulation in wind tunnels [3]:

here u* is dynamic speed, m/s; ϛ is constant Karman, ϛ = 0,4; z₀ is the desired height; u₀ is the speed of the wind at a given height z₀.

To solve the problems associated with the transfer of turbulent scalar substances in solution of differential equations using the scheme of splitting into physical processes. According to the principles of splitting finite-difference integration of the equations of hydrodynamics and convective-diffusive transport of scalar substance at each time step Dt is carried out in two stages. At the first stage the hydrodynamic parameters. In the second phase, based on the calculated hydrodynamic fields solved the diffusion equation.

As an example, we present dispersion modeling of methane (main component of biogas) in the landfill “Centralny” of Volgograd region of Russian Federation in 2007. The modeling was made in the software environment «Mat lab / Femlab». Profile free-stream passed logarithmic, values ​​ k_backgr=4 m²/s; ε=0,2. In Figure 1 we show the velocity field of the wind and concentrations of methane.

Figure 1 – The velocity field of the wind flow around the polygon (left) and the field of methane in the landfill area of ​​influence “Central” (right)

Table 2 – Comparison of values of concentration of methane in the zone of influence of the landfill «Central» in 2007, received a variety of ways

So, modeling based on the solutions of Navier-Stokes equations and diffusion yielded result is significantly better than the method OND-86. The results of calculation using the proposed model are close to experimental data. Modeling emissions of biogas on stage at the stage of operation, reclamation landfills can be considered as an aspect of information modeling, to ensure environmental safety in the handling of waste.

Figure 1 – The scheme of the bridge [1]

Technical inspection of bridge was carried out periodically at intervals of 10-15 years. Since 1969, the discovered characteristic defect, which represents a tilted position-roller support parts of the farm on the first (left-Bank) way. The slope of rollers is 11,5º  to the left coast, the offset is55 mm. This also manifested strain cones embankment foundations in the form of breakdown and collapse of the soil in the river bed. Attempts to restrict the movement of the movable end of the span setting plates movable bearings in normal position, installation of metal pinching gave only a temporary effect, and eventually encounter the rollers tilt state (Figure 2).

Figure 2 – Tilt position-roller support parts of the farm

The most likely cause of this defect is loss of stability of the left pillar of the subsidence of the soil under the influence of load and education floating earth.

Perform a numerical simulation of deformation of bridge from own load and away from traffic on him train (Figure 3). Profiles section take from the old assortments of GOST 14-1932 «Corners equal», GOST 15-1932 «the Corners of unequal», GOST 16-1932 «Goods of equal». The value of load on the composition, conical mounds take from the SN 200-62* «Specifications for design of railway, road and city bridges and pipes», SN 35.13330.2011 «Bridges and pipes». Because of the shrinkage of the pillars in the soil is inelastic character, in the estimated model, we consider them as a relation of the form «the Deformable bottom».

Figure 3 – The deflection of the bridge under the action of a load

Graphical results of a numerical experiment here in Fig. 4, where there is also a shift of skating rinks farm in the direction of the left Bank, and it is56,902 mm, that practically coincides with the experimental data.

Figure 4 – Scheme of strain-bridge, obtained in the «Scad Office»

According to the results of modal analysis in «Scad Office» Lanczos method on an interval of 6.1-8.3 Hz identified the movement of elements of the bridge, as shown in Figure 5.

Figure 5 – Patterns of movement of the bridge structures under dynamic loading at a frequency of 7.9 Hz

A similar pattern was observed in experimental studies [4], in which the same pattern is observed at a frequency of 8.3 Hz, the results of numerical and field experiment are approximately equal. The deviation of the calculated value from the pilot due to the structural heterogeneity of time-children of the bridge, add new parts (triggers stairs, railings, etc.).

Thus, thanks to the «Scad Office» determined that the cause of the offset rollers fermions we cause uneven subsidence pillars (mostly left) under high loads. Further investigation of the model will help in the development of measures for elimination of the defect.