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	<title>Электронный научно-практический журнал «Современная техника и технологии» &#187; artursauc</title>
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		<title>Solution of problems of air protection in the Comsol Multiphysics (for example, diffusion of biogas from landfills). Using Comsol Script ™</title>
		<link>https://technology.snauka.ru/en/2013/10/2412</link>
		<comments>https://technology.snauka.ru/en/2013/10/2412#comments</comments>
		<pubDate>Mon, 14 Oct 2013 13:04:30 +0000</pubDate>
		<dc:creator>artursauc</dc:creator>
				<category><![CDATA[Common rubric]]></category>
		<category><![CDATA[air dynamics.]]></category>
		<category><![CDATA[air pollution]]></category>
		<category><![CDATA[biogas]]></category>
		<category><![CDATA[Comsol Multiphysics]]></category>
		<category><![CDATA[Comsol Script]]></category>
		<category><![CDATA[Convection and diffusion]]></category>
		<category><![CDATA[finite element/volume analysis]]></category>

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		<description><![CDATA[ The software package Comsol Multiphysics, which implements the numerical solution of equations of mathematical physics, partial (PDE) by finite element/volume, is now widely used to solve problems in various fields of science and technology. The advantages of this package is that it supports a programming language Comsol Script, which allows you to specify non-trivial initial [...]]]></description>
			<content:encoded><![CDATA[<p><span> The software package Comsol Multiphysics, which implements the numerical solution of equations of mathematical physics, partial (PDE) by finite element/volume, is now widely used to solve problems in various fields of science and technology. The advantages of this package is that it supports a programming language Comsol Script, which allows you to specify non-trivial initial and boundary conditions , the physical parameters of the environment , to work together various modules package Comsol Multiphysics [1] . In this paper, the language of the Comsol Script written a program using which in Comsol Multiphysics solved urgent task of Applied Ecology &#8211; Mathematical modeling of air pollution biogas , outstanding in the decomposition of solid waste and industrial waste in landfills.<br />
</span></p>
<p style="text-align: justify;"><span style="color: black;">Dissipation in the atmospheric surface layer with a passive tracer concentration, mg per m<sup>3</sup>, described by unsteady turbulent diffusion equation:<br />
</span></p>
<p style="text-align: right;"><img style="margin-top: -10px; margin-bottom: -10px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu1.png" alt="" width="216" height="48" /><span style="color: black;">                                                                                          (1)<br />
</span></p>
<p style="text-align: justify;"><span style="color: black;">there <img style="margin-top: -15px; margin-bottom: -15px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu2.png" alt="" width="77" height="36" /> is vector velocity, m per sec; <em>w<sub>s</sub></em> is sedimentation rate impurities: for light inert gas impurities <em>w<sub>s</sub></em>=0 m per sec; for heavy <em>w<sub>s </sub></em>= 0,001 m per sec; for aerosols <em>w<sub>s</sub></em> = 0,008 m per sec [2]; <em>k<sub>хуz</sub></em> is coefficient of turbulent viscosity in different directions, m<sup>2</sup> per sec; <img style="margin-top: -19px; margin-bottom: -19px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu3.png" alt="" width="38" height="32" /> is function emissions of impurities in the atmosphere, which is determined by the equation:<br />
</span></p>
<p style="text-align: right;"><img style="margin-top: -20px; margin-bottom: -20px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu4.png" alt="" width="148" height="47" /><span style="color: black;">                                                                                                (2)<br />
</span></p>
<p style="text-align: justify;"><span style="color: black;">There <em>I<sub>i</sub></em> is function emissions from <em>i</em>-th source; <em>f<sub>i </sub></em>(<em>t</em>) and <img style="margin-top: -20px; margin-bottom: -20px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu5.png" alt="" width="39" height="39" /> are functions describing the mode of operation and location of stationary sources, connected to the radius-vector <img style="margin-top: -19px; margin-bottom: -19px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu6.png" alt="" width="10" height="34" /> and <img style="margin-top: -19px; margin-bottom: -19px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu7.png" alt="" width="74" height="34" />. For continuously operating sources <em>f<sub>i </sub></em>(<em>t</em>) = 1.<br />
</span></p>
<p style="text-align: justify;"><span style="color: black;">Because the movement of air is a subsonic, in accordance with the approximation of the Boussinesq approximation can be described by a system of equations of the Navier-Stokes equations for an incompressible viscous fluid:</span></p>
<p style="text-align: justify;"><span style="color: black;"><br />
</span></p>
<p style="text-align: right;"><img style="margin-top: -40px; margin-bottom: -40px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu8.png" alt="" width="277" height="83" /><span style="color: black;">                                                                            (3)<br />
</span></p>
<p style="text-align: justify;"><span style="color: black;"><span>There </span><span>n is dynamic viscosity, Pa·sec; </span><span><em>р</em></span><span> is piezometric pressure, Pa;  p </span><span>is the density of the medium (air), kg per m<sup>3</sup>; <img style="margin-top: -18px; margin-bottom: -18px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu9.png" alt="" width="13" height="31" /> is specific force field, N/m<sup>3</sup>.<br />
</span></span></p>
<p style="text-align: justify;"><span style="color: black;">Density of air can be found using the equation of state of an ideal gas:<br />
</span></p>
<p style="text-align: right;"><img style="margin-top: -20px; margin-bottom: -20px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu10.png" alt="" width="112" height="41" /><span style="color: black;">                                                                                                            (4)<br />
</span></p>
<p style="text-align: justify;"><span style="color: black;"><span>There </span><span><em>р</em><sub>атм</sub></span><span> is atmospheric pressure, Pа; </span><span><em>R</em><span><sub>m</sub></span></span><span> is gas constant, for air </span><span><em>R</em><sub><span>m </span></sub></span><span>= 3,464<span>×</span>10<sup>-3 </sup>J per kg<span>×</span>K<span>×</span>mol;</span><span><em> Т</em><sub>ф </sub></span><span>is background temperature, K.<br />
</span></span></p>
<p style="text-align: justify;"><span style="color: black;">Kinematic viscosity can be found using the approximation [3]:<br />
</span></p>
<p style="text-align: right;"><span style="color: black;"><span><span>h</span> = 6<span>×</span>10<sup>-6 </sup>+ 4<span>×</span>10<sup>-8</sup><span>×</span><em>Т</em><sub>ф</sub>.                                                                                                     </span><span>(5)<br />
</span></span></p>
<p style="text-align: justify;"><span style="color: black;">Turbulent flow structure, which cannot be solved explicitly for the numerical solution of a system of Navier-Stokes equations, are approximated using the subgrid turbulence Smagorinsky model. This approach proposed by Deardorff and developed in the works of Smagorinsky, involves the allocation of the scale, smaller grid, which is approximated by the turbulence [4]. The preference of this model is given to the fact that it takes into account the presence of turbulence, formed a small vortices while flowing wind flow walls of buildings, structures and other obstacles, but the vortices don&#8217;t need to approximate the «wall-functions». This approach due to the reduction of the dimension of the matrix equations by a sequence of calculations reduces the requirements to computing resources of a computer.<br />
</span></p>
<p style="text-align: justify;"><span style="color: black;"><span>The scale of small eddies in the Smagorinsky model determined time-measures </span><span><span>D</span><em>х</em></span><span>, </span><span><span>D</span><em>у</em></span><span>, </span><span><span>D</span><em>z</em></span><span> three-dimensional cell:<br />
</span></span></p>
<p style="text-align: right;"><img style="margin-top: -21px; margin-bottom: -21px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu11.png" alt="" width="104" height="37" /><span style="color: black;">                                                                                                           (6)<br />
</span></p>
<p><span style="color: black;">The coefficients of turbulent viscosity is determined using the system:</span><span style="color: black;"><br />
</span></p>
<p style="text-align: right;"><img style="margin-top: -10px; margin-bottom: -10px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu12.png" alt="" width="133" height="99" /><span style="color: black;">                                                                                                            (7)</span></p>
<p style="text-align: justify;"><span style="color: black;"><span>There </span><span><em>k</em><sub>баз</sub></span><span> is basic coefficient of turbulent viscosity, and contempt of the temperature gradient low altitude and temperature of the discharged impurities determined the approximate equation:</span></span></p>
<p style="text-align: justify;"><span style="color: black;"><span><br />
</span></span></p>
<p style="text-align: right;"><img style="margin-top: -20px; margin-bottom: -20px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu13.png" alt="" width="131" height="62" /><span style="color: black;">                                                                                                  (8)<br />
</span></p>
<p style="text-align: justify;"><span style="color: black;"><span>There </span><span><em>k</em><sub>ф </sub></span><span>is background coefficient of turbulent viscosity, </span><span><em>k</em><sub>ф</sub></span><span> = 1-15 м<sup>2</sup>/с; </span><span>ε</span><span> = 0,1-0,4; </span><span><em>Def </em>(<em>x</em>; <em>y</em>; <em>z</em>)</span><span> is function of deformation or dissipation defined by the equation:<br />
</span></span></p>
<p style="text-align: center;"><img class="aligncenter" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu14.png" alt="" width="477" height="72" /><br />
<span style="color: black;">At the upstream boundary of the computational domain profile of wind speed is given by Karman. Since wind flow can be directed at an angle of the input boundary of the computational domain, the velocity components of the system are given by:</span></p>
<p style="text-align: center;"><span style="color: black;"><br />
</span></p>
<p style="text-align: right;"><img style="margin-top: -20px; margin-bottom: -20px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu15.png" alt="" width="234" height="89" /><span style="color: black;">                                                                    (9)<br />
</span></p>
<p style="text-align: justify;"><span style="color: black;"><span>There </span><span><em>u*</em></span><span> is dynamic speed, m per sec; <em>z</em><sub>0</sub> is argument of a roughness; <img style="margin-top: -15px; margin-bottom: -15px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu16.png" alt="" width="9" height="28" /> is Karman`s constant,<img style="margin-top: -19px; margin-bottom: -19px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu17.png" alt="" width="41" height="31" />; <em>Н</em><sub>ср</sub> is the average height of wind barriers; </span><span><em>С</em></span><span> is coefficient of resistance;</span></span><span><br />
</span><span>α</span><span> is the angle between the direction of the wind on the input in the computational domain boundary and the x-axis, radian.<span style="color: black;"><br />
</span></span></p>
<p style="text-align: justify;"><span style="color: black;">At the downstream boundary of the computational domain is given the type of border Outlet, the boundary condition Normal flow / zero pressure:<br />
</span></p>
<p style="text-align: right;"><span style="color: black;"><span><em>р</em> = 0.                                                                                                         </span><span> (10)<br />
</span></span></p>
<p style="text-align: justify;"><span style="color: black;">On the surfaces of buildings and structures, landfill, land for the components of the wind speed is given by the condition of impermeability and adhesion:<br />
</span></p>
<p style="text-align: right;"><img style="margin-top: -20px; margin-bottom: -20px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu18.png" alt="" width="33" height="32" /><span style="color: black;"><span>                                                                                                            (11)<br />
</span></span></p>
<p style="text-align: justify;"><span style="color: black;"><span>If the streamlined surface is the area where is blowing (suction) air velocity components </span><span><em>u</em><sub>в</sub></span><span>, </span><span><em>v</em><sub>в</sub></span><span>, </span><span><em>w</em><sub>в</sub></span></span><span style="color: black;">, then the area is given by the boundary condition Moving /Leaking wall:<br />
</span></p>
<p style="text-align: right;"><span style="color: black;"><span><em>и</em> = <em>и</em><sub>в</sub>; <em>v = v</em><sub>в</sub>;<em> w = w</em><sub>в</sub>.</span><span>                                                                                          (12)<br />
</span></span></p>
<p style="text-align: justify;"><span style="color: black;">On the lateral boundaries of the computational domain is specified Symmetry boundary, meaning the absence of leaks and tangential stresses:<br />
</span></p>
<p style="text-align: right;"><img style="margin-top: -15px; margin-bottom: -15px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu19.png" alt="" width="216" height="34" /><span style="color: black;">                                                                               (13)<br />
</span></p>
<p style="text-align: justify;"><span style="color: black;">There <img style="margin-top: -15px; margin-bottom: -15px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu20.png" alt="" width="11" height="29" /> and <img style="margin-top: -15px; margin-bottom: -15px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu21.png" alt="" width="10" height="29" /> is normal and tangential unit vector to the boundary surface, unit vector <img style="margin-top: -15px; margin-bottom: -15px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu22.png" alt="" width="11" height="29" /> directed outward from the boundary region.<br />
</span></p>
<p style="text-align: justify;"><span>At presence on a surface of the polygon of ground insulation filling and absence of gas drainage wells circuit equations emissions and diffusion components of biogas is produced with the help of the derived equations [5]:</span></p>
<p style="text-align: justify;"><span><span style="color: black;"><br />
</span></span></p>
<p style="text-align: right;"><img style="margin-top: -15px; margin-bottom: -15px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu23.png" alt="" width="193" height="55" /><span style="color: black;">                                                                                     (14)<br />
</span></p>
<p style="text-align: justify;"><span>There<em> D</em> is diffusivity of landfilling (insulating the outside waste), m<sup>2</sup> per sec; <em>h</em> is thickness of landfilling, m; <em>n</em><sub>отх</sub> is porosity of waste, <em>n</em><sub>отх </sub>= 0,33; γ is permeation coefficient, for gases γ = 0,01-0,015 m per sec; <em>с</em><sub>пов,возд</sub> is the concentration of component biogas at the upper side of air filling, mg per <span style="color: black;">m<sup>3</sup></span>.<span style="color: black;"><br />
</span></span></p>
<p style="text-align: justify;"><span style="color: black;">On the surface of the landfill to calculate the concentration of a component of biogas in the absence of gas drainage wells gets <img style="margin-top: -18px; margin-bottom: -18px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu24.png" alt="" width="59" height="31" /> and sets boundary condition:<br />
</span></p>
<p style="text-align: right;"><span style="color: black;"><span><em>c </em>= <em>с</em><sub>пов,возд</sub></span><sub><span>.</span></sub><span>                                                                                                 (15)<br />
</span></span></p>
<p style="text-align: justify;"><span style="color: black;">If the emission biogas through gas drainage wells or surface landfill, which has no insulating filling, the consideration of the effect of each of them by using boundary condition Flux:<br />
</span></p>
<p style="text-align: right;"><img style="margin-top: -20px; margin-bottom: -20px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu25.png" alt="" width="124" height="39" /><span style="color: black;">                                                                                        (16)<br />
</span></p>
<p style="text-align: justify;"><span style="color: black;"><span>On impervious surfaces flow of impurities (</span><span><em>I<sub>i</sub></em> = 0</span><span>) is given by boundary condition Isolation/Symmetry:<br />
</span></span></p>
<p style="text-align: right;"><img style="margin-top: -20px; margin-bottom: -20px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu26.png" alt="" width="121" height="41" /><span style="color: black;">                                                                                         (17)<br />
</span></p>
<p style="text-align: justify;"><span style="color: black;">On the other boundaries of the computational domain is given by the boundary condition Convective flux:<br />
</span></p>
<p style="text-align: right;"><img style="margin-top: -20px; margin-bottom: -20px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu27.png" alt="" width="99" height="37" /><span style="color: black;">                                                                                              (18)<br />
</span></p>
<p>When determining the scale of small eddies in the model of the radical work of Smagorinsky D<em>х</em>D<em>у</em>D<em>z</em> can be interpreted as the volume of the rectangular cell using MCS . When using the finite element method with the most common type of cells &#8211; tetrahedral most famous software packages such as Ansys CFX, Fluent, Flow Vision, etc. In this case, the volume of each cell is calculated by means of numerical methods. To determine the scale, the following simpler approach. The maximum linear dimension of the finite element and should be much smaller than the calculated area, the growth rate of the element responsible for the degree of condensation, taken strictly to 1. These options allow you to get a thick, almost uniform grid consisting of a set of tetrahedral that are close to correct. Then, in our case for small scale vortices can be approximated as the cube root of the volume of the tetrahedron:</p>
<p><img style="margin-top: -20px; margin-bottom: -20px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101813_1645_1.png" alt="" width="209" height="39" />                                                                     (19)<br />
Then, using the approximation<img style="margin-top: -20px; margin-bottom: -20px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101813_1645_2.png" alt="" width="99" height="33" />, we obtain:<em><br />
</em></p>
<p><img style="margin-top: -20px; margin-bottom: -20px;" src="https://technology.snauka.ru/wp-content/uploads/2013/10/101813_1645_3.png" alt="" width="226" height="40" />                                                                 (20)</p>
<p>In our case, made ​​<em>a</em> = 4 m. At this density grid in [6] by the method of successive approximations for calculating the concentrations of methane emitted at the site &#8221; Centralny&#8221; in Volgograd , the optimal values ​​of <em>k</em><sub>ф</sub> = 4 m<sup>2</sup>/s ; ε = 0,2. This approach eliminates the calculation of sub-grid scale using tetrahedral finite element mesh, thereby simplifying the numerical (software) implementation of the turbulence model and reduces the requirements for compute-intensive computer.</p>
<p>From a practical point of view is suitable stationary statement of the problem. In this case, a method of determining where the problem is solved on a large time interval that the process leads to stationary. Implicit scheme allows to get rid of restrictions to the size of the time step. Stationary statement of the problem significantly reduces the number of iterations, and the consumption of computing resources of a computer.</p>
<p>The solution of the discrete analogues of the differential equations made by bi-conjugate gradients with the stabilization of the solution. The whole program code is more than a dozen pages, so in an article for the sake of brevity, it shows only the main conclusions:</p>
<p style="text-align: justify;"><span><span style="color: forestgreen;">% COMSOL Multiphysics Model M-file</span><br />
</span></p>
<p><span><span style="color: forestgreen;">% Generated by COMSOL 3.4 (COMSOL 3.4.0, $Date: 2007/10/03 17:02:19 $)</span><br />
</span></p>
<p><span style="color: black;"><span>flclear <span style="color: #a020f0;">fem</span></span><br />
</span></p>
<p><span><span style="color: forestgreen;">% COMSOL version</span><br />
</span></p>
<p><span style="color: black;"><span>clear <span style="color: #a020f0;">vrsn</span></span><br />
</span></p>
<p><span style="color: black;"><span>vrsn.name = <span style="color: #a020f0;">&#8216;COMSOL 3.4&#8242;<span style="color: black;">;</span></span></span><br />
</span></p>
<p><span style="color: black;"><span>vrsn.ext = <span style="color: #a020f0;">&#8216;a&#8217;<span style="color: black;">;</span></span></span><br />
</span></p>
<p><span><span style="color: black;">vrsn.major = 0;</span><br />
</span></p>
<p><span><span style="color: black;">vrsn.build = 603;</span><br />
</span></p>
<p><span style="color: black;"><span>vrsn.rcs = <span style="color: #a020f0;">&#8216;$Name: $&#8217;<span style="color: black;">;</span></span></span><br />
</span></p>
<p><span style="color: black;"><span>vrsn.date = <span style="color: #a020f0;">&#8216;$Date: 2007/10/03 17:02:19 $&#8217;<span style="color: black;">;</span></span></span><br />
</span></p>
<p><span><span style="color: black;">fem.version = vrsn;</span><br />
</span></p>
<p><span><span style="color: forestgreen;">% Constants</span><br />
</span></p>
<p><span style="color: black;"><span>% Constants<br />
fem.const = {&#8216;W_s&#8217;,&#8217;0&#8242;, &#8230;<br />
&#8216;k_f&#8217;,&#8217;4&#8242;, &#8230;<br />
&#8216;epsilon&#8217;,&#8217;0.2&#8242;, &#8230;<br />
&#8216;Mcomp&#8217;,&#8217;5&#8242;, &#8230;<br />
&#8216;h_iz&#8217;,&#8217;0.2&#8242;, &#8230;<br />
&#8216;Vpol&#8217;,&#8217;100000&#8242;, &#8230;<br />
&#8216;Diffusiv&#8217;,&#8217;3.4e-5&#8242;, &#8230;<br />
&#8216;gamma&#8217;,&#8217;0.001&#8242;, &#8230;<br />
&#8216;Ccomp&#8217;,&#8217;50&#8242;, &#8230;<br />
&#8216;Pamb&#8217;,&#8217;1e5&#8242;, &#8230;<br />
&#8216;T_amb&#8217;,&#8217;25&#8242;, &#8230;<br />
&#8216;Udin&#8217;,&#8217;3&#8242;, &#8230;<br />
&#8216;Hsr&#8217;,&#8217;10&#8242;, &#8230;<br />
&#8216;Z0&#8242;,&#8217;0.2&#8242;, &#8230;<br />
&#8216;C&#8217;,&#8217;0.0115&#8242;, &#8230;<br />
&#8216;alpha&#8217;,&#8217;0&#8242;, &#8230;<br />
&#8216;a&#8217;,&#8217;4&#8242;};</span></span></p>
<p>% Geometry</p>
<p>% (Default values are not included)</p>
<p>% Application mode 1<br />
clear appl<br />
appl.mode.class = &#8216;FlNavierStokes&#8217;;<br />
appl.shape = {&#8216;shlag(1,&#8221;u&#8221;)&#8217;,'shlag(1,&#8221;v&#8221;)&#8217;,'shlag(1,&#8221;w&#8221;)&#8217;,'shlag(1,&#8221;p&#8221;)&#8217;};<br />
appl.gporder = 2;<br />
appl.cporder = 1;<br />
appl.assignsuffix = &#8216;_ns&#8217;;<br />
clear prop<br />
prop.analysis=&#8217;static&#8217;;<br />
appl.prop = prop;<br />
clear pnt<br />
pnt.p0 = {};<br />
pnt.name = {};<br />
pnt.pnton = {};<br />
pnt.ind = [];<br />
appl.pnt = pnt;<br />
clear bnd<br />
bnd.U0out = {};<br />
bnd.v0 = {};<br />
bnd.opentype = {};<br />
bnd.u0 = {};<br />
bnd.Fbnd = {};<br />
bnd.p0 = {};<br />
bnd.type = {};<br />
bnd.velType = {};<br />
bnd.walltype = {};<br />
bnd.w0 = {};<br />
bnd.inttype = {};<br />
bnd.vw = {};<br />
bnd.U0in = {};<br />
bnd.ww = {};<br />
bnd.uw = {};<br />
bnd.name = {};<br />
bnd.outtype = {};<br />
bnd.f0 = {};<br />
bnd.intype = {};<br />
bnd.stresstype = {};<br />
bnd.ind = [];<br />
appl.bnd = bnd;<br />
clear equ<br />
equ.eta = &#8217;6e-6+T_amb*4e-8&#8242;;<br />
equ.name = &#8216;physical parameters of the atmosphere in the zone of landfill&#8217;;<br />
equ.rho = &#8216;Pamb*3.464e-3/T_amb&#8217;;<br />
equ.ind = [];<br />
appl.equ = equ;<br />
fem.appl{1} = appl;</p>
<p>% Application mode 2<br />
clear appl<br />
appl.mode.class = &#8216;FlConvDiff&#8217;;<br />
appl.assignsuffix = &#8216;_cd&#8217;;<br />
clear prop<br />
prop.analysis=&#8217;static&#8217;;<br />
clear weakconstr<br />
weakconstr.value = &#8216;off&#8217;;<br />
weakconstr.dim = {&#8216;lm5&#8242;};<br />
prop.weakconstr = weakconstr;<br />
appl.prop = prop;<br />
clear bnd<br />
bnd.d = {};<br />
bnd.Dbnd = {};<br />
bnd.c0 = {};<br />
bnd.name = {};<br />
bnd.N = {};<br />
bnd.type = {};<br />
bnd.ind = [];<br />
appl.bnd = bnd;<br />
clear equ<br />
equ.D = &#8217;4.160167646*k_f+0.707106781*epsilon*(a^2)*((ux)^2+(vy)^2+(wz)^2+0.5*((vx+uy)^2+(wy+vz)^2+(uz+wx)^2))^0.5&#8242;;<br />
equ.w = &#8216;w-W_s&#8217;;<br />
equ.v = &#8216;v&#8217;;<br />
equ.u = &#8216;u&#8217;;<br />
equ.name = &#8216;physical parameters of the atmosphere in the zone of landfill&#8217;;<br />
equ.ind = [];<br />
appl.equ = equ;<br />
fem.appl{2} = appl;<br />
fem.sdim = {&#8216;x&#8217;,'y&#8217;,'z&#8217;};<br />
fem.frame = {&#8216;ref&#8217;};<br />
fem.border = 1;<br />
clear units;<br />
units.basesystem = &#8216;SI&#8217;;<br />
fem.units = units;</p>
<p>% Scalar expressions<br />
fem.expr = {&#8216;profil_u&#8217;,&#8217;2.5*Udin*log((z-Hsr+Z0/C)/Z0)*cos(alpha)&#8217;, &#8230;<br />
&#8216;profil_v&#8217;,&#8217;2.5*Udin*log((z-Hsr+Z0/C)/Z0)*sin(alpha)&#8217;, &#8230;<br />
&#8216;Cpov&#8217;,'(Mcomp*z_iz*h_izol/Vpol+0.33*Diffusiv*Ccomp)/(Diffusiv+gamma*h_iz)&#8217;, &#8230;<br />
&#8216;Mud&#8217;,'Mcomp*z/Vpol&#8217;};</p>
<p>% Descriptions<br />
clear descr<br />
descr.expr= {&#8216;Mud&#8217;,'emission component of biogas from the landfill area, mg / (kv.m.sek) (boundary condition of the 2nd kind is used in the absence of landfilling)&#8217;,'Cpov&#8217;,'concentration of the component of biogas at the landfill surface (boundary condition of the 2nd kind is used in the absence of landfilling)&#8217;,'profil_v&#8217;,'y-oic wind component on the input boundary of the computational domain&#8217;,'profil_u&#8217;,'x-oic wind component on the input boundary of the computational domain&#8217;};<br />
fem.descr = descr;</p>
<p>% Descriptions<br />
descr = fem.descr;<br />
descr.const= {&#8216;h_iz&#8217;,'thickness of the insulating filling (default made ??0.2 m)&#8217;,'Pamb&#8217;,'atmospheric pressure Pa&#8217;,'Vpol&#8217;,'volume occupied by the solid waste landfill or softwareб cubic m&#8217;,'Hsr&#8217;,'average height of wind barriers, m&#8217;,'Diffusiv&#8217;,'diffusivity of the soil from which the filling,square m/seс&#8217;,'a&#8217;,'maximum line size tetraedricheskogo finite element, m&#8217;,'C&#8217;,'roughness parameter&#8217;,'k_f&#8217;,'background coefficient eddy viscosity Smagorinsky model, square m/sec (default is assumed to be 4)&#8217;,'Mcomp&#8217;,'emission component of the biogas emitted from around the landfill or software mg/sec&#8217;,'Udin&#8217;,'dynamic speed, m/s&#8217;,'Z0&#8242;,&#8217;resistance coefficient, m&#8217;,'W_s&#8217;,'settling velocity of the impurities in the atmosphere for light inert gas impurities 0; Heavy 0.001, 0.008 for aerosols m/sec&#8217;,'Ccomp&#8217;,'the concentration of the components in the biogas at the time of its release in the body of the landfill, mg/cubic m&#8217;,'gamma&#8217;,'coefficient of gas seepage through the soil, m/sec (default is 0.001)&#8217;,'alpha&#8217;,'angle between the direction of the wind at the entrance to the settlement area boundary and the x axis, radian&#8217;,'epsilon&#8217;,'constant in the Smagorinsky model (the default is assumed to be 0.2)&#8217;,'T_amb&#8217;,'background air temperature, K&#8217;};<br />
fem.descr = descr;</p>
<p>% ODE Settings<br />
clear ode<br />
clear units;<br />
units.basesystem = &#8216;SI&#8217;;<br />
ode.units = units;<br />
fem.ode=ode;</p>
<p>% Multiphysics<br />
fem=multiphysics(fem);<span><br />
</span></p>
<p style="text-align: justify;"><span style="color: black;">The settlements were made on the computer AMD FX™-4100 Quard-Core Processor, RAM 4 Gb, 3,2 GHz, OS MS Windows 7 Ultimate SP1. The calculation time for landfill «Centralny» was about 30 hours. The results of calculations are shown in figures 1-2 (unit mol per m<sup>3</sup> treated as mg per m<sup>3</sup>).<br />
</span></p>
<p style="text-align: center;"><img src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu30.jpg" alt="" /><span style="color: black;"><br />
</span></p>
<p style="text-align: center;"><span>Figure<span style="color: black;"> 1 – The field of wind speed, m per sec, at the height of 1.8 m above the top of the landfill site landfill PTO-3 «Novosyolki» 26.08.2001<br />
</span></span></p>
<p style="text-align: center;"><img src="https://technology.snauka.ru/wp-content/uploads/2013/10/101413_1304_SautsAVSolu31.jpg" alt="" /><span style="color: black;"><br />
</span></p>
<p style="text-align: center;"><span>Figure 2<span style="color: black;"> – Field concentrations of methane, mg per m<sup>3</sup>, at the height of 1.8 m above the top of the landfill site PTO-3 «Novosyolki» 26.08.2001</span></span></p>
<p><span><br />
</span></p>
]]></content:encoded>
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		</item>
		<item>
		<title>Subgrid isotropic turbulent viscosity, determined by the Smagorinsky model for an isothermal environment</title>
		<link>https://technology.snauka.ru/en/2013/11/2634</link>
		<comments>https://technology.snauka.ru/en/2013/11/2634#comments</comments>
		<pubDate>Fri, 29 Nov 2013 15:27:59 +0000</pubDate>
		<dc:creator>artursauc</dc:creator>
				<category><![CDATA[Common rubric]]></category>
		<category><![CDATA[Lagrangian finite element]]></category>
		<category><![CDATA[Smagorinsky model]]></category>
		<category><![CDATA[Subgrid modeling]]></category>
		<category><![CDATA[tetrahedral grid]]></category>
		<category><![CDATA[turbulence]]></category>
		<category><![CDATA[turbulent viscosity]]></category>

		<guid isPermaLink="false">https://technology.snauka.ru/?p=2634</guid>
		<description><![CDATA[Subgrid modeling is now widely used in the calculation of atmospheric processes and phenomena at large settlement areas. Grid spacing at the subgrid modeling can reach 300 km. Among the most popular models of subgrid model acquired Joseph Smagorinsky. This article examines the Smagorinsky model for an isothermal environment. Subgrid modeling is characterized by a [...]]]></description>
			<content:encoded><![CDATA[<p>Subgrid modeling is now widely used in the calculation of atmospheric processes and phenomena at large settlement areas. Grid spacing at the subgrid modeling can reach 300 km. Among the most popular models of subgrid model acquired Joseph Smagorinsky. This article examines the Smagorinsky model for an isothermal environment.</p>
<p>Subgrid modeling is characterized by a kind of subgrid scale D. The most common definition of subgrid scale dimensions for rectangular cells Dx, Dy, Dz at a moderate anisotropy of the grid as follows:</p>
<p style="text-align: center;"><img style="margin-top: -25px; margin-bottom: -25px;" src="https://technology.snauka.ru/wp-content/uploads/2013/12/120213_2112_1.png" alt="" width="95" height="35" />                                                                                                  (1)</p>
<p style="text-align: center;">and for strong anisotropy of grid as follows:</p>
<p style="text-align: center;"><img style="margin-top: -25px; margin-bottom: -25px;" src="https://technology.snauka.ru/wp-content/uploads/2013/12/120213_2112_2.png" alt="" width="140" height="36" />                                                                                         (2)</p>
<p style="text-align: center;">Turbulent air flow occurring at subsonic speeds, in accordance with the «hypoacoustic» Boussinesq approximation can be described by the Navier-Stokes equations consisting of equations of motion and continuity for an incompressible viscous fluid:</p>
<p style="text-align: center;">
<p style="text-align: center;"><img class="alignnone" style="margin-top: -25px; margin-bottom: -25px;" src="https://technology.snauka.ru/wp-content/uploads/2013/12/120213_2112_3.png" alt="" width="293" height="86" />                                                               (3)</p>
<p style="text-align: center;">Here <img class="alignnone" style="margin-top: -15px; margin-bottom: -15px;" src="https://technology.snauka.ru/wp-content/uploads/2013/12/120213_2112_4.png" alt="" width="74" height="34" /> is velocity vector;<br />
h is dynamic viscosity, Pa∙s; <em>р</em> is piezometric pressure, Pa; <img style="margin-top: -15px; margin-bottom: -15px;" src="https://technology.snauka.ru/wp-content/uploads/2013/12/120213_2112_5.png" alt="" width="12" height="28" /> is specific force field, N per cubic m; p is air density, kg per cubic m.</p>
<p>The system (1) is applicable for finding eddies of various scales in its analytical solution, but it is an unsolved mathematical problem. Among the numerical methods for the solution is the most accurate direct numerical simulation (DNS) &#8211; the solution of unsteady Navier-Stokes equations with a small time step on the dense grid , but it is now possible computing still do not allow the DNS to the large settlement areas. Therefore , in practice, often authors suggest solving Reynolds averaged in the system (2) the equation of motion (RANS):</p>
<p style="text-align: center;"><img style="margin-top: -25px; margin-bottom: -25px;" src="https://technology.snauka.ru/wp-content/uploads/2013/12/120213_2112_6.png" alt="" width="325" height="63" />                                                  (4)</p>
<p>There h<em><sub>t</sub></em> is dynamic coefficient of turbulent viscosity, Pa∙s, h<em><sub>t </sub></em>= r<em>k<sub>хуz</sub></em>; <em>k<sub>хуz</sub></em> is eddy viscosity in different directions, m<sup>2</sup></p>
<p>&nbsp;</p>
<p>per s, for an anisotropic medium is given by the matrix <img style="margin-top: -27px; margin-bottom: -27px;" src="https://technology.snauka.ru/wp-content/uploads/2013/12/120213_2112_7.png" alt="" width="148" height="107" />.</p>
<p>The coefficients of turbulent viscosity in subgrid Smagorinsky model defined by the system:</p>
<p>&nbsp;</p>
<p style="text-align: center;"><img style="margin-top: -27px; margin-bottom: -27px;" src="https://technology.snauka.ru/wp-content/uploads/2013/12/120213_2112_8.png" alt="" width="160" height="70" />                                                                             (5)</p>
<p style="text-align: center;">Here<em> k</em><sub>баз</sub> – is basic coefficient of turbulent viscosity, and contempt of the temperature gradient low altitude and temperature of the discharged impurities determined the approximate equation:</p>
<p style="text-align: center;"><img style="margin-top: -25px; margin-bottom: -25px;" src="https://technology.snauka.ru/wp-content/uploads/2013/12/120213_2112_9.png" alt="" width="176" height="48" />;                                                                          (6)</p>
<p style="text-align: center;">Here <em>k</em>ф is background coefficient of turbulent viscosity, <em>k</em>ф = 1-15 м2/с; ε = 0,1-0,4; <em>Def</em> (<em>x</em>; <em>y</em>; <em>z</em>) is function of</p>
<p>deformation or dissipation defined by the equation:</p>
<p>&nbsp;</p>
<p style="text-align: center;"><img class="aligncenter" style="margin-top: -26px; margin-bottom: -26px;" src="https://technology.snauka.ru/wp-content/uploads/2013/12/120213_2112_10.png" alt="" width="544" height="87" /></p>
<p>Most software packages such as Ansys CFX, Fluent, Flow Vision for the calculation for anisotropic media digested TBE on sub-elements within each of which can be regarded as an isotropic medium (Figure 1). To simplify the calculation of turbulent flow structure, the present author proposed a model to produce isotropization subgrid of turbulent viscosity determined by Smagorinsky model for an isothermal environment.</p>
<p><img class="aligncenter" src="https://technology.snauka.ru/wp-content/uploads/2013/12/120213_2112_11.jpg" alt="" width="289" height="241" /></p>
<p style="text-align: center;">                                                      Figure 1 &#8211; Example of splitting finite element on the sub-elements [1]</p>
<p>The radical product D<em>х</em>D<em>у</em>D<em>z</em> in definition (1) can be interpreted as the volume of the rectangular cell, equal to the amount that would be occupied with the cubic cell edge D. In practice, the most common use is not rectangular and tetrahedral cells. Scale D cells form a regular tetrahedron volume Ω, by analogy with definition (1) can be found as:</p>
<p style="text-align: center;"><img style="margin-top: -30px; margin-bottom: -30px;" src="https://technology.snauka.ru/wp-content/uploads/2013/12/120213_2112_12.png" alt="" width="266" height="50" />                                                                  (7)</p>
<p style="text-align: center;">Here <em>а</em> is edge of tetrahedral cell.</p>
<p style="text-align: center;">Then coefficients of turbulent viscosity for grid with small anisotropy will be determined as:</p>
<p style="text-align: center;"><img style="margin-top: -20px; margin-bottom: -20px;" src="https://technology.snauka.ru/wp-content/uploads/2013/12/120213_2112_13.png" alt="" width="289" height="43" />                                                             (8)</p>
<p style="text-align: center;">For computational domains with real geometry to build isotropic mesh is practically impossible. Therefore, by analogy with definition (2) is physically more correctly we only consider the maximum size of the cell edge:</p>
<p style="text-align: center;"><img style="margin-top: -25px; margin-bottom: -25px;" src="https://technology.snauka.ru/wp-content/uploads/2013/12/120213_2112_14.png" alt="" width="335" height="48" />.                                                  (9)</p>
<p style="text-align: center;">Here <em>а</em><sub>mах </sub>is maximum element size.</p>
<p>The expression (9) for example tetrahedral mesh is a kind of generalization of the two definitions scale D. This eliminates the need to calculate the subgrid scale for each grid cell.</p>
<p>Example of constructing a structured mesh for the computational domain of landfill PTO-1 (St. Petersburg) is shown in Figure 2.</p>
<p style="text-align: center;"><img class="aligncenter" src="https://technology.snauka.ru/wp-content/uploads/2013/12/120213_2112_15.jpg" alt="" width="755" height="461" /></p>
<p style="text-align: center;">Figure 2 &#8211; Example of a structured grid (built in Comsol Multiphysics)</p>
<p>To construct the proposed structured grid should adhere to the following rules:</p>
<p>1. The growth rate of TBE tetraedricheskoy grid responsible for the degree of thickening, taken strictly equal to 1.</p>
<p>2. The maximum line size amah given considerably smaller than the calculated area to get a thick, close to the isotropic mesh.</p>
<p>To subgrid turbulent viscosity considered isotropic must comply with condition <em>k</em><em><sub>хуz </sub></em>= const. This condition can be performed using the calculation of velocity field Lagrangian finite elements with linear approximation. In this case, within each end element derivatives of the velocity components <em>и</em>, <em>v</em> и <em>w</em> on the coordinate axes are constants then <em>Dеf</em> = const then <em>k</em><em><sub>хуz </sub></em>= const.</p>
<p>Asking subgrid isotropic of turbulent viscosity and reduces the computation time for the approximation of the finite element method of the differential equation of turbulent diffusion, as eddy viscosity within a finite element can be considered constant.</p>
]]></content:encoded>
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		</item>
		<item>
		<title>Reducing air pollution and energy saving achieved by improving gas supply systems using biogas from landfills</title>
		<link>https://technology.snauka.ru/en/2014/02/3141</link>
		<comments>https://technology.snauka.ru/en/2014/02/3141#comments</comments>
		<pubDate>Thu, 27 Feb 2014 11:06:19 +0000</pubDate>
		<dc:creator>artursauc</dc:creator>
				<category><![CDATA[Common rubric]]></category>
		<category><![CDATA[air regime building]]></category>
		<category><![CDATA[biogas]]></category>
		<category><![CDATA[gas supply]]></category>
		<category><![CDATA[landfill]]></category>

		<guid isPermaLink="false">https://technology.snauka.ru/?p=3141</guid>
		<description><![CDATA[Under the conditions of the sealing of building construction are increasingly made of various buildings around the landfills. Long people stay in such buildings leads to the risk of respiratory diseases, cancer, diseases of the circulatory system, complications during pregnancy, as biogas is a mixture of poisonous methane, carbon dioxide, benzene, xylene, ammonia, hydrogen sulphide [...]]]></description>
			<content:encoded><![CDATA[<p>Under the conditions of the sealing of building construction are increasingly made of various buildings around the landfills. Long people stay in such buildings leads to the risk of respiratory diseases, cancer, diseases of the circulatory system, complications during pregnancy, as biogas is a mixture of poisonous methane, carbon dioxide, benzene, xylene, ammonia, hydrogen sulphide and other substances.</p>
<p>To determine the external and internal contamination of the air environment of buildings near landfills biogas components developed mathematical model, the equations of which are given below.</p>
<p>Because air movement is a subsonic, it can be described by a system of Navier-Stokes equations in the Boussinesq approximation:</p>
<p style="text-align: right;"><img style="margin-top: -27px; margin-bottom: -27px;" src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_1.png" alt="" width="292" height="94" />;                                                                       (1)</p>
<p>here r<sub>0</sub> is background density of air at a certain equilibrium temperature, kg/m<sup>3</sup>; <img style="margin-top: -20px; margin-bottom: -20px;" src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_2.png" alt="" width="84" height="39" /> is velocity vector of air (wind); h= h(<em>Т</em>) is dynamic viscosity of air, Pa×sec.</p>
<p>Specific power load for interior subregion is defined as:</p>
<p style="text-align: right;"><img style="margin-top: -21px; margin-bottom: -21px;" src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_3.png" alt="" width="94" height="35" />                                                                                                   (2)</p>
<p>outdoor subdomains:</p>
<p style="text-align: right;"><img style="margin-top: -21px; margin-bottom: -21px;" src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_4.png" alt="" width="66" height="35" />                                                                                                       (3)</p>
<p>here r = r(<em>Т</em>) is air density, kg/m<sup>3</sup>.</p>
<p>Density and background density of the air can be found using the equation of state for an ideal gas:</p>
<p style="text-align: right;">r = <em>р</em><sub>атм </sub>/(<em>R</em><sub>m</sub><em>Т</em>);                                                                                                              (4)</p>
<p style="text-align: right;">r<sub>0</sub> = <em>р</em><sub>атм </sub>/(<em>R</em><sub>m</sub><em>Т</em><sub>ф</sub>);                                                                                                            (5)</p>
<p>here <em>R</em><sub>m</sub> is gas constant of air, <em>R</em><sub>m </sub>= 287 J/(kg×K×mol); <em>Т </em>– temperature , К; <em>Т</em><sub>ф </sub>– background temperature, К.</p>
<p>For the calculation of the temperature fields, the system (1) is supplemented by the heat equation:</p>
<p style="text-align: right;"><img style="margin-top: -27px; margin-bottom: -27px;" src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_5.png" alt="" width="225" height="55" />                                                                                              (6)</p>
<p>here <em>С<sub>р </sub></em>= <em>С<sub>р</sub></em>(<em>Т</em>) is isobaric heat capacity of air, J/(kg×K); λ = λ(<em>Т</em>) is thermal conductivity, W/(m∙K); <em>Q<sub>heat</sub></em> is source or sink of heat, W/m<sup>3</sup>.</p>
<p>Dispersion of passive tracer with concentration c, mg/m<sup>3</sup>, described unsteady turbulent diffusion equation:</p>
<p style="text-align: right;"><img style="margin-top: -27px; margin-bottom: -27px;" src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_6.png" alt="" width="246" height="50" />                                                                                       (7)</p>
<p>here <em>k<sub>хуz</sub></em> is turbulent viscosity coefficient, m<sup>2</sup>/s, for anisotropic media <em>k<sub>хуz </sub></em>= diag{<em>k<sub>х</sub></em>; <em>k<sub>у</sub></em>; <em>k<sub>z</sub></em>};  <em>w<sub>s</sub></em> is sedimentation rate of the impurity, m/s;  <em>I</em> (<em>r</em>; <em>t</em>) is emission function impurities into the atmosphere.</p>
<p>To calculate the field of impurity concentrations given amount of air in the room is possible, which can be determined by converting the equation Lang in the following form [1]:</p>
<p style="text-align: right;"><img style="margin-top: -27px; margin-bottom: -27px;" src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_9.png" alt="" width="153" height="39" />                                                                                                        (8)</p>
<p>here <em>с</em><sub>прист</sub> is concentration on the surface of the outer wall of the building, mg/m<sup>3</sup>; <em>i</em><sub>вп </sub>is coefficient of permeability of the fencing construction, kg/m∙s∙Pa; <em>S</em><sub>ок </sub>is area enclosing structure, m<sup>2</sup>; δ is material thickness, m; ρ<sub>н</sub> is average density of the external and internal air, kg/m<sup>3</sup>.</p>
<p>Computer implementation of the mathematical model is made using the software Comsol Multiphysics. The results of calculations on the outer subdomains fields of wind speed, pressure and concentration of the components of biogas near landfill &#8220;Centralny&#8221; of Volgograd listed in the overview chapter are shown in Figures 1-3. Unit mol/m<sup>3</sup> treated as mg/m<sup>3 </sup>concentration fields are calculated without taking into account the background levels.</p>
<p>&nbsp;</p>
<p style="text-align: center;"><img src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_10.jpg" alt="" /></p>
<p style="text-align: center;">Figure 1 – Field of annual average wind speed, m /sec, near landfill &#8220;Centralny&#8221; at a height of 2 m</p>
<p style="text-align: center;"><img src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_11.jpg" alt="" /></p>
<p style="text-align: center;">Figure 2 – The pressure field, Pa, near the landfill &#8220;Centralny&#8221; at a height of 2 m</p>
<p style="text-align: center;"><img src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_12.jpg" alt="" /></p>
<p style="text-align: center;">Figure 3 – Field of annual average surface concentrations of methane mol/m<sup>3</sup> in landfill &#8220;Centralny&#8221; in 2007</p>
<p>Figures 7-9 shows the results of the velocity fields of movement, temperature and ammonia concentrations in the indoor air of the building near landfill &#8220;Central&#8221; of Volgograd. For calculations considered office space on the ground floor area of 18 m<sup>2</sup>, volume of 46 m<sup>3</sup>, equipped and unframed walling vent diameter of 100 mm (eg HL 900N NECO). Pressure difference between indoor and outdoor air adopted 56 Pa, outdoor temperature adopted +7 °C, thermal resistance of the outer wall and the window unit to the exterior wall <em>R</em><sub>с</sub> = 3,59 m<sup>2</sup>∙K/W, window <em>R</em><sub>ок </sub>= 4,089 m<sup>2</sup>∙K/W [2]. Dimensions of the window unit taken 1,7х1,4 m. Heat exchange with the adjacent spaces are not taken into account. The heater is regarded as a cuboids length 1,3 m, width 0,15 m, height 0,5 m on the surface of the device temperature of 66 °C. The adopted Remove air from the room through a slit height of 0,01 m under the closed door.</p>
<p>&nbsp;</p>
<p style="text-align: center;"><img src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_13.jpg" alt="" /><strong><br />
</strong></p>
<p style="text-align: center;">Figure 4 – The velocity field of air, m/sec, in a room with a vent on the ground floor near the landfill &#8220;Centralny&#8221;</p>
<p>&nbsp;</p>
<p style="text-align: center;"><img src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_14.jpg" alt="" /><strong><br />
</strong></p>
<p style="text-align: center;">Figure 5 – Temperature field, K, in a room with a vent on the ground floor near the landfill &#8220;Centralny&#8221;</p>
<p>&nbsp;</p>
<p style="text-align: center;"><img src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_15.jpg" alt="" /><strong><br />
</strong></p>
<p style="text-align: center;">Figure 6 – Field of ammonia concentrations, mg/m<sup>3</sup>, in a room with a vent on the ground floor near the landfill &#8220;Centralny&#8221;</p>
<p>&nbsp;</p>
<p style="text-align: center;"><img src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_16.jpg" alt="" /><strong><br />
</strong></p>
<p style="text-align: center;">Figure 7 – The velocity field of air, m/s, in a room without air vent on the ground floor near the landfill &#8220;Centralny&#8221;</p>
<p><strong><br />
</strong></p>
<p style="text-align: center;"><img src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_17.jpg" alt="" /></p>
<p style="text-align: center;">Figure 8 – The temperature field, K, in a room without air vent on the ground floor near the landfill &#8220;Centralny&#8221;</p>
<p style="text-align: center;"><img src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_18.jpg" alt="" /><strong><br />
</strong></p>
<p style="text-align: center;">Figure 9 – Field methane concentrations, mg/m<sup>3</sup>, in a room without air vent on the ground floor near landfill &#8220;Centralny&#8221;</p>
<p>To reduce air pollution biogas system has been improved its production, purification and collection.</p>
<p>Extraction of biogas produced from gas drainage wells. Assuming that the pressure on the surface of the landfill does not differ from the atmospheric sectional area wells <em>S</em><sub>скв</sub> and amount <em>n</em><sub>скв</sub> can be defined as:</p>
<p style="text-align: right;"><img style="margin-top: -27px; margin-bottom: -27px;" src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_19.png" alt="" width="209" height="58" />                                                                                                (9)</p>
<p>there <em>m<sub>l</sub></em> is weight <em>l</em>-th component of biogas, tons/year;<em> р</em><sub>атм</sub> is atmospheric pressure, Pa; <em>R<sub>l</sub></em> is gas constant, J/(kg×K×mol); <em>N</em> is the number of components of biogas, which is being payment; <img style="margin-top: -20px; margin-bottom: -20px;" src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_20.png" alt="" width="40" height="36" />is speed biogas wells, m/s, not more than 0,1 m/s.</p>
<p>Specific mass of component of biogas <em>m</em><sub>уд</sub>, g/s, emitted from each well is defined as:</p>
<p style="text-align: right;"><img style="margin-top: -27px; margin-bottom: -27px;" src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_21.png" alt="" width="208" height="58" />                                                                                            (10)</p>
<p>Surface proposed landfill cover with a film of thermoplastic elastomers. They have a high resistance to oil, fuel and water, exposure to the weather and climatic conditions. This film also has a high mechanical strength and wears resistance.</p>
<p>Figure 10 depicts a schematic diagram of the proposed production and collection of biogas emitted by landfills.</p>
<p><img src="https://technology.snauka.ru/wp-content/uploads/2014/02/022214_1505_1.jpg" alt="" /></p>
<p style="text-align: center;">Figure 10 – Scheme of extraction, purification and collection of biogas from landfills</p>
<p>Biogas from landfill gas drainage wells at open valves 1 enters the manifold 2, whence by the compressor 4 is fed into a centrifugal separator 5 for gas purification from moisture and dust. In view of explosion safety gas supply to a separator and subsequent separation of thermosensitive portions of the pipeline shut-off valve equipped with 3 and 6. The gas enters the purification unit of the carbon dioxide and hydrogen sulphide 7. Carbon dioxide is emitted into the air, and the hydrogen sulfide reacts with the iron oxide (III) and is absorbed. From halogenated hydrocarbons, ammonia, and residual gas is purified of other impurities zeolite filter 8 (Ме<sub>2/n</sub>О∙Аl<sub>2</sub>О<sub>3</sub>∙хSiО<sub>2у</sub>Н<sub>2</sub>О). Purified gas to acquire odor mixed ethyl mercaptan (СН<sub>3</sub>SН) by setting 9, and then liquefied by the compressor 10 and is supplied to the gas-holder 12, which is liquefied and after the pressure reducer gas is fed into a gas pipeline or refueling gas cylinders 15. In order to land a gas pipeline explosion safety before the gas holder and it is also equipped with temperature-sensitive shut-off valves 11 and 13. This system is a semi-automatic and does not require constant intervention of the staff and most of the elements may be located in the building of administrative area landfills. Water-dust mixture, the resulting separation, reaction products with zeolites is disposed at the landfill. Accumulated biogas meets the requirements for natural gas when used for gas supply. Since methanogens occurs at the site limited number of years, the gas supply system should be compact, in case of need to be dismantled relatively quickly.</p>
<p style="text-align: left;">Laying pipelines abroad housekeeping area landfill entails additional difficulties associated with construction works. Therefore, it is advisable to supply excess biogas in cylinders. Figure 11 as an example of a perspective diagram of proposed buildings gas housekeeping area landfill &#8220;Centralny&#8221;, where «<em>I</em>» crossing pipelines connected to the gas drainage wells acts as a collector (equalization) of the gas stream. Compressors, cleaning plant and adding ethyl mercaptan are located in the left building. Removing carbon dioxide from it by means of ventilation.</p>
<p style="text-align: center;"><img src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_23.jpg" alt="" /></p>
<p style="text-align: center;">Figure 11 – Scheme of gas supply buildings housekeeping area landfill &#8220;Centralny&#8221;</p>
<p>Landfill gas energy potential can be estimated <em>V</em><sub>прир.газа</sub>, thousand m<sup>3</sup>, showing how much you can save natural, if used for the entire gas evolved biogas:</p>
<p style="text-align: right;"><img style="margin-top: -20px; margin-bottom: -20px;" src="https://technology.snauka.ru/wp-content/uploads/2014/02/022114_2121_24.png" alt="" width="188" height="35" />                                                                                                   (11)</p>
<p>here χ is coefficient reflecting the gas leak from its production and supply (in Russia, USA, Germany and Netherlands adopted χ = 0,99); <em>k</em><sub>сж.газа</sub> = 1,57 and <em>k</em><sub>прир.газа</sub> = 1,154 are coefficients for conversion to tons of equivalent fuel.</p>
<p>When using biogas for gas supply buildings located near landfills, reduced pollution of air and concentrations of most pollutants contained in the biogas may be considered as the background (other than carbon dioxide). Table 1 shows as an example the values of surface concentration of methane in 2007, contained in the ambient air near buildings located near landfill &#8220;Centralny&#8221; From the warm period during 2006 and providence collection and treatment of biogas.</p>
<p>Table 1 – Surface methane concentration in 2007 in the outdoor air near buildings located at the landfill &#8220;Centralny&#8221;</p>
<div>
<table border="0">
<tbody valign="top">
<tr>
<td style="text-align: center;" rowspan="2" valign="middle">Outdoor air near buildings landfill &#8220;Centralny&#8221;</td>
<td style="text-align: center;" colspan="2" valign="middle">Methane concentration, mg/m<sup>3</sup></td>
</tr>
<tr>
<td style="text-align: center;" valign="middle">During collection and treatment of biogas</td>
<td style="text-align: center;" valign="middle">When not carrying out the collection and treatment of biogas (background)</td>
</tr>
<tr>
<td style="text-align: center;" valign="middle">Housekeeping area</td>
<td valign="middle">54,225-10,125</td>
<td valign="middle">0,125</td>
</tr>
<tr>
<td style="text-align: center;" valign="middle">Settlement &#8220;Ovrazhny&#8221;</td>
<td style="text-align: center;" valign="middle">34,125-21,165</td>
<td style="text-align: center;" valign="middle">0,125</td>
</tr>
<tr>
<td style="text-align: center;" valign="middle">Building on the south-west of the landfill</td>
<td style="text-align: center;" valign="middle">2,265</td>
<td style="text-align: center;" valign="middle">0,125</td>
</tr>
</tbody>
</table>
</div>
<p>Also reduce air pollution inside buildings. Table 2 shows the concentration of methane and ammonia inside the building premises calculated housekeeping area landfill &#8220;Centralny&#8221;.</p>
<p>Table 2 – Concentrations of pollutants in the air in the buildings of the estimated landfill near the &#8220;Centralny&#8221;</p>
<div>
<table border="0">
<tbody valign="top">
<tr>
<td style="text-align: center;" rowspan="2" valign="middle">Сompartment</td>
<td style="text-align: center;" rowspan="2" valign="middle">Pollutant</td>
<td style="text-align: center;" colspan="2" valign="middle">Сoncentration, mg/m<sup>3</sup></td>
</tr>
<tr>
<td style="text-align: center;" valign="middle">When not using the biogas for gas supply</td>
<td style="text-align: center;" valign="middle">When using biogas for gas (background)</td>
</tr>
<tr>
<td style="text-align: center;" valign="middle">With a vent</td>
<td style="text-align: center;" valign="middle">Ammonia</td>
<td style="text-align: center;" valign="middle">0,2465-0,2575</td>
<td style="text-align: center;" valign="middle">0,0025</td>
</tr>
<tr>
<td style="text-align: center;" valign="middle">Without vent</td>
<td style="text-align: center;" valign="middle">Methane</td>
<td style="text-align: center;" valign="middle">43,138-43,254</td>
<td style="text-align: center;" valign="middle">0,125</td>
</tr>
</tbody>
</table>
</div>
<p>Payback period is determined according to the schedule in Figure 12, which shows that it would be approximately 1,4 years.</p>
<p><img class="aligncenter" src="https://technology.snauka.ru/wp-content/uploads/2014/02/022214_1534_1.png" alt="" /></p>
<p style="text-align: center;">Figure 12 – Graph of the payback period</p>
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