The work is devoted to the study of the flow structure and the nature of the impurities distribution in a street canyon, depending on the location of a constant intensity pollution source. The paper considers three cases when the source of the impurity is located: in the center at the bottom of the street canyon, at the bottom under leeward wall and at the bottom under windward wall

Danilkin, Evgeniy A.

Leshchinskiy, Dmitriy V.

Starchenko, Alexander V.

English

Tomsk State University Repository

МИНИСТЕРСТВО НАУКИ И ВЫСШЕГО ОБРАЗОВАНИЯРОССИЙСКОЙ ФЕДЕРАЦИИНациональный исследовательскийТОМСКИЙ ГОСУДАРСТВЕННЫЙ УНИВЕРСИТЕТДЕСЯТАЯСИБИРСКАЯ КОНФЕРЕНЦИЯПО ПАРАЛЛЕЛЬНЫМ ИВЫСОКОПРОИЗВОДИТЕЛЬНЫМВЫЧИСЛЕНИЯМС Б О Р Н И К  С Т А Т Е ЙТомск, 5–7 октября 2021 г.ТОМСК«Издательство НТЛ»202147Influence of the pollution source locationon the concentration of the impurity in street canyon*D.V. Leshchinskiy, E.A. Danilkin, A.V. StarchenkoTomsk State University, Tomsk, RussiaThe work is devoted to the study of the flow structure and the nature ofthe impurities distribution in a street canyon, depending on the location ofa constant intensity pollution source. The paper considers three caseswhen the source of the impurity is located: in the center at the bottom ofthe street canyon, at the bottom under leeward wall and at the bottom un-der windward wall.Keywords: street canyon, mathematical modeling, turbulent flow, impu-rity concentration.This work is devoted to the construction and testing of a mathematicalmodel for studying the processes of transport of impurities in street canyons.Studies of this kind are relevant for understanding the microclimate of cities,are useful in planning new buildings and assessing areas of increased envi-ronmental hazard. Based on the developed original micro-scale mathematicalmodel M2U [1], a study was carried out of the influence of the location ofthe pollution source on the flow structure and the nature of the distribution ofimpurities inside the street canyon. The mathematical model is based on theReynolds-averaged Navier-Stokes equations. The system of differentialequations is closed using a two-parameter model, which takes into accountthe influence of buoyancy forces on the turbulent flow structure, and theBoussinesq gradient-diffusion hypothesis. The numerical solution is carriedout based on the finite volume method, a monotonized scheme for approxi-mating convective terms, and the SIMPLE algorithm for matching the veloc-ity and pressure fields [2].In this work, the emphasis is on the study of changes in the maximum andaverage concentration in the breathing zone of a person (up to 2 m from theground) and in the canyon as a whole. Three cases of the location of the pol-lution source were considered: in the center at the bottom of a street canyon,at the bottom at the leeward wall, and at the bottom at the windward wall.                                                       * This work was supported by the Ministry of Science and Higher Education of Russia (agree-ment No. 075-02-2020-1479/1).48This study will help to understand how strongly the pollution source loca-tion will affect the accumulation of impurities in the street canyon. Thus, thedata obtained can be used in the design of residential areas and parking lots.Physical and mathematical formulation of the problemStationary isothermal turbulent air movement in the surface layer over aninhomogeneous underlying surface with elements of large-scale roughness isconsidered. Roughness elements are fixed, flow-tight obstacles (buildings).A point source of harmful emissions of constant intensity (vehicles) is con-sidered. The dimensions of buildings are commensurate with the dimensionsof the study area (Figure 1).WHDWFig. 1. Physical statement of the problemThe mathematical model includes Reynolds-averaged continuity equa-tions, Navier-Stokes equations, impurity transport [2, 3] and heat transfer:0;iiux∂=∂(1)1 ;i j i jij i j j ju u u uupx x x x x′ ′∂ ∂⎛ ⎞∂∂ ∂= − + ν −⎜ ⎟⎜ ⎟∂ ρ ∂ ∂ ∂ ∂⎝ ⎠(2)S; , 1,2,3.j jj j j ju C u CCD i jx x x x′ ′∂ ∂⎛ ⎞∂ ∂= − + =⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠(3)49Here iu , iu′  – averaged and ripple projections of the velocity vector on thecoordinate axis, p  – pressure, ρ  – density, ν  – kinematic viscosity of air,C  – averaged impurity concentration, S  – function describing the distribu-tion of impurity sources, i ju u′ ′  – Reynolds stress tensor, D v Sc=  – diffu-sion coefficient, Sc  – Schmidt number.The closure of the system of equations (1) – (3) is carried out using the two-parameter «k−ε» model and the Boussinesq gradient-diffusion hypothesis [2, 4]:2 ;3jii j T ijj iuuu u kx x∂⎛ ⎞∂′ ′ = −ν + + δ⎜ ⎟⎜ ⎟∂ ∂⎝ ⎠ ;Ti jT jCC uSc xν ∂′ ′ = −∂(4)2;TkCμν = ε ;ii jjuP u ux∂′ ′= −∂(5);j Tj j k ju k k Px x x∂ ⎛ ⎞ν⎛ ⎞∂ ∂= ν + + − ε⎜ ⎟⎜ ⎟⎜ ⎟∂ ∂ σ ∂⎝ ⎠⎝ ⎠(6)( )1 2 ,j Tj j juC P Cx x x k ε εε∂ ε ⎛ ⎞ν⎛ ⎞∂ ∂ε ε= ν + + − ε⎜ ⎟⎜ ⎟⎜ ⎟∂ ∂ σ ∂⎝ ⎠⎝ ⎠(7)where νT – turbulent viscosity, k – kinetic energy of turbulence, ε  –dissipation of turbulent kinetic energy. Turbulence model coefficients:1.0kσ = , 1.3εσ = , 1 1.44Cε = , 2 1.92Cε = , 0.09Cμ = , 0.5TSc =  – turbu-lent Schmidt number.A full description of the mathematical model used and the numericalmethod for its solution is given in [5].Simulation of flow and parametric calculationsThe analysis of the influence of the location of the pollution source in thestreet canyon on the maximum concentration of the impurity in the breathingzone (up to 2 m from the bottom of the canyon) and in the canyon as a whole iscarried out. The geometric characteristics of the street canyon are: height (H)and width (W) 20 meters, depth (L) – 30 meters. The calculations were carriedout on a structured Cartesian grid 110 62 100 along the axes Ox, Oy and Oz,respectively. The mesh was compacted at the border nodes. The size of 5 bor-der cells in the direction normal to the solid boundary was 0,1 m. This is doneto get the dimensionless y+ into the recommended range of 30 to 300.50The source of constant-intensity admixture was located in the center, atthe leeward wall and at the windward wall of the street canyon, near thebottom.The viscosity of the medium is considered to be v = 15·10−6 m2/s, whichcorresponds to the viscosity of the air at 20 °C. The boundary conditionswere set as follows: at the inlet boundary, the horizontal velocity Uin = 1 m/s;at the outlet boundary, the normal velocity derivatives are equal to zero; no-slip conditions were considered on the generators of the street canyon and onthe roofs of buildings; sliding conditions are set on the upper wall. Initialconditions: the longitudinal velocity is equal to the inlet velocity (1 m/s), andthe vertical velocity and pressure are zero.As can be seen from the vector velocity fields (Figure 2), the wind flowpassing over the canyon affects the air masses inside the canyon, settingthem in motion. Thus, one large vortex is formed within the canyon, which,in turn, acts on the source of the impurity, setting the impurity in motion.Thus, the weathering process begins.Fig. 2. Vector velocity field and the contour fields of concentrationwith center location of the pollution source. The width, height anddepth of the street canyon are 20 m, 20 m and 30 m, respectively51As a result of modeling the transport of impurities in a street canyon, thefollowing pictures of the distribution of its concentration were obtained (Fig-ure 2, 3).a bFigure 3. Contour fields of concentration in a street canyon with a) left and b) right locations of the pollution sourceIn all three cases, the admixture is weathering from the canyon. When thesource is displaced to any of the street canyon generators, the deterioration ofthe admixture weathering is observed. This fact is confirmed by the follow-ing integral characteristics of the maximum concentrations of impurities inthe breathing zone (Table).Maximum impurity concentrations in the breathing zoneSource location Left Middle RightC 1,919602 0,15369 0,51267The maximum impurity concentrations in case of left source location areseveral times higher than the maximum impurity concentrations in the caseof right location, which is explained by poor ventilation, which depends onthe velocity and direction of the wind. In case of central source location, theimpurity does not have time to accumulate and is well weathered.ConclusionA microscale model of turbulent air movement and impurity transport in astreet canyon is presented. For isothermal turbulent air flow in the canyon, itwas investigated how different variants of the location of the pollution sourceaffect the accumulation of the incoming admixture inside the street canyon(Figure 2, 3). The integral characteristics of the impurity concentration in the52street canyon in general and in the breathing zone (up to 2 m from the bottomof the canyon) are calculated and analyzed.The location of the source of the impurity directly depends on how theimpurity will accumulate in the street canyon. The case of the central sourcelocation showed the best weathering of the admixture, the left is the worst.REFERENCES 1. Nuterman R., Starchenko A., Baklanov A. Numerical model of urban aerodynamics andpollution dispersion // International Journal of Environment and Pollution. – 2011. –V. 44. – P. 385−393. 2. Starchenko A.V., Nuterman R.B., Danilkin E.A. Numerical study of turbulent flows andpollution transport in street canyons. – Tomsk: Tomsk University Press, 2015. – 252 p. 3. Danilkin E.A., Starchenko A.V. Modelling the transfer of road transport emissions in astreet canyon // Computational technologies. – 2020. – V. 22(4). – P. 4−21. 4. Henkes R.A.W.M., Van Der Flugt F. F., Hoodendoorn C. J. Natural convection flow ina square cavity calculated with Low-Reynolds-number turbulence models // Int. J. HeatMass Transfer. – 1991. – V. 34(2). – P. 377−388. 5. Danilkin E.A., Lechshinskiy D.V., Starchenko A.V. Natural Numerical research of theinfluence of wall heating on the turbulent flow pattern in an idealized street canyon //J. Phys.: Conf. Ser. – 2020. – 1715 012015.__________Leshchinskiy Dmitriy Victorovich, junior research assistant of The Regional Scientific andEducational Mathematical Center of Tomsk State University; 360flip182@gmail.com;Danilkin Evgeniy Alexandrovich, Candidate of Physical and Mathematical Sciences, seniorresearch assistant The Regional Scientific and Educational Mathematical Center of TomskState University; ugin@math.tsu.ru;Starchenko Alexander Vasilyevich, Doctor of Physical and Mathematical Sciences,professor, leading scientific worker of The Regional Scientific and Educational MathematicalCenter of Tomsk State University; starch@math.tsu.ru.

Influence of the pollution source location on the concentration of the impurity in street canyon

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Influence of the pollution source location on the concentration of the impurity in street canyon

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