Biliaiev N.N.,

Doctor of Technical Sciences, Professor of Hydraulics and Wastewater Department, Dnipropetrovsk National University of Railway Transport

named after academician V. Lazaryan

Rusakova T.I.,

Candidate of Technical Sciences, Associate Professor of Aerodynamics and Energy Mass Transfer Department, Dnipro National University

named after Oles Honchar

Біляєв Микола Миколайович,

Доктор технічних наук, професор кафедри гідравліки та водопостачання, Дніпропетровський університет залізничного транспорту
імені академіка В. Лазаряна

Русакова Тетяна Іванівна,

Кандидат технічних наук, доцент кафедри аерогідродинаміки та енергомасопереносу, Дніпровський національний університет

імені Олеся Гончара



Summary: The regularities of the formation of pollution zones during the emission of a liquid and dust pollutant at different heights, taking into account vegetation and in the case when its «equivalent» – a porous plate is used instead of vegetation, were studied by the laboratory method. In mathematical modeling, a potential flow model was used to calculate the local velocity field with allowance for vegetation near the motorway, and the mass transfer equation for calculating the impurity dispersion.

Key words: vegetation, porous plate, mathematical modeling, computational experiment.

Анотація: За допомогою лабораторного методу вивчено закономірності формування зон забруднення при викидах забруднюючої рідини і пилу на різних висотах з урахуванням рослинності та у випадку, коли замість рослинності використовується його «еквівалент» – пориста пластина. У математичному моделюванні була використана модель потенційного потоку для розрахунку локального поля швидкості з урахуванням рослинності поблизу автомагістралі, а також рівняння масопереносу для розрахунку домішкової дисперсії.

Ключові слова: рослинність, пориста пластина, математичне моделювання, обчислювальний експеримент.

Introduction. One of the main tasks of urban ecology is to ensure conditions for environmentally comfortable living in the zones of dense residential buildings in large cities with the rational use of natural resources. The sources of environmental hazard for atmospheric air in large cities are industrial enterprises, heating boiler houses and road transport. The concentration of road transport emissions at a low level, the specificity of hydrodynamic flow around buildings of dense residential buildings, the emergence of powerful vortex zones and regions of recurrent flow lead to the emergence of stable pollution zones with a significant excess of the maximum admissible concentration of impurities. Lowering the level of air pollution can be achieved by regulating the flow of vehicles, improving their technical condition, as well as green plantations along motorways.

Air pollution is a major environmental problem in urban areas, and epidemiological studies show adverse effects on human health [1-2]. Urban planning and design strategies should be aimed at reducing the level of air pollution from vehicle emissions, so integration and selection of vegetation plays a major role in improving air quality and urban design.

Formulation of the problem. There is a sufficiently large number of works devoted to mathematical modeling of the process of pollutants dispersion from vehicles taking into account green plantations along motorways in residential areas of the city. However, all these studies are not systematized and are devoted to individual issues, for example, the sorption of pollutants by leaves, the study of planting plantations to reduce noise. A wide survey of the influence of vegetation growth, its porosity, absorptivity and deposition is presented in the work [3]. Focus on the greening of streets, instead of urban parks, which require empty spaces in densely built cities [4]. The characteristics of vegetation (leaf area, porosity, etc.) are considered, which play a key role and should be taken into account when designing green plantations. Based on the experiments carried out in the wind tunnel [5], a technique for modeling the effects of vegetation in the study of aerodynamics of buildings based on the theory of similarity and dimensional analysis was developed. This technique makes it possible to simulate the effect of various types of vegetation on impurity propagation at small scales. Experiments have shown that trees in the center of the canyon create unfavorable conditions that interfere with natural ventilation, which leads to the accumulation of harmful substances from the leeward side of the canyon. Parametric studies of the influence of crown porosity on the air flow have been carried out, which showed that the porosity in this case does not have a significant effect on the air flow and the concentration field. One of the options for reducing the concentration of pollutants is the use of green walls in urban canyons. This alternative was investigated in [6] using the model of chemical interaction and sedimentation in street canyons called CiTTy-Street. A numerical model implemented in COMSOL Multiphysics 5.2 is proposed, which can be applied to assess the influence of green plantations on pollution reduction in urban canyons. The model can be easily adapted to different plant species and the shape of green spaces [7].

Urban vegetation can help reduce the concentration of pollutants in cities, although the current percentage removal of impurities is very low. Coniferous trees capture pollutants better than deciduous trees, since they retain their foliage all year long and have very high surface areas.

Some studies show that planting trees in close proximity to a source of pollution (motorways) is more effective than at a distance from it. Later studies show a decrease in the dispersion of pollutants when too many trees are placed in a street canyon. The total concentrations of pollutants can even be increased to 40 %, depending on the diameter and volume of the crown, the height of the trunk and the permeability of the deciduous cover. Wood species and green plants are studied that contribute to reducing city air pollution and improving its quality [8-9].

Much attention is paid to the study of aerodynamic processes [10] associated with the flow of buildings, since the formation of vortices and their intensity to affect significantly the process of removal of impurities from the residential zone. A mathematical model describing mass transfer processes on an inhomogeneous surface in a porous medium is developed and theoretically investigated. The mechanical effect of the boundary surfaces and the structure of the porous medium on the mass transfer process is considered and included in the model [11].

There are CFD models for assessing the influence of vegetation on reducing the level of air pollution, but they require a large expenditure of computer time for practical implementation, which is not convenient for serial calculations.

For practical purposes it is important to have certain methods for assessing the influence of vegetation on reducing the level of air pollution. It is very important that these methods meet the requirements: convenience of practical application, a small base of initial data, speed of calculation, convenience in processing and interpretation of quantitative results. An analysis of the literature indicates the need to develop such methods.

The purpose of this work is to study the patterns of impurity penetration through vegetation and the development of a methodology for calculating local pollution zones near motorways in the presence of vegetation.

General part. Increased attention is paid to mathematical modeling of the process of pollutants dispersion from vehicles taking into account green plantations along motorways in urban residential areas of the city.

In this paper, the studies were carried out in two stages: at the first stage, the regularities of the formation of pollution zones in the presence of vegetation were studied in a laboratory way; at the second stage, a mathematical model was developed to calculate local pollution zones from vehicle emissions in the presence of vegetation.

The analogy method was used. The investigations were carried out in a hydraulic tray (Fig. 1, a), which is located in the laboratory of the Hydraulic and Water Supply Department of the DNURT. The purpose of the work was to study the process of formation of contamination zones during the emission of impurities near the hedge model from trees located near each other.

Fig. 1 – Experimental installation: 1 – the chute of the hydraulic tray; 2 – weirs; 3 – investigated model of vegetation (a), the model of Pīcea pūngens (b)

On a separate section of the tray two spillways were installed which formed a space that simulates a section of the street. Vegetation was located inside this space: branches of blue spruce (Pīcea pūngens) arranged in 2 rows (Fig. 1, b). Plants of the first row 13 cm in height were located at a distance of 1.5 cm from each other, plants of the second row 6 cm in height were placed between plants of the first row. The entire hedge was attached on the bottom of the tray, an admixture (sodium chlorine solution) was put in through a needle, paint was added to the solution to visualize the contamination zone, and the supply was carried out for 3 s. This process simulated an ejection from cars on the road.

During the experiments video recording was carried out. Reynolds number of the moving fluid flow was Re=1596>500, which in the case of open channels corresponds to the turbulent flow regime. The arrow in the figures shows the direction of the flow. Two scenarios of pollutant emission were considered: in the first scenario a low emission was simulated – the emission was at a depth of 0.3 cm from the bottom, in the second scenario – the average outburst, the emission was at a depth of 3 cm from the bottom.

Formation zone of pollution for two consecutive times of 2 s and 6 s after starting the pollutant is shown in Fig. 2. When analyzing these figures, it is possible to come to the following conclusions: at the initial moment the tree creates an obstacle and pollution on the windward side stops (Fig. 2, a), then the pollution zone extends upwards along the model (Fig. 2, b), the tree is a natural barrier, that’s why at the same time begins the penetration of the contaminant in the lower part of the vegetation, where the resistance of the medium is minimal, because there are tree trunks.


Fig. 2 – Dynamics of formation of pollution zones when the source of pollution is at a low level: 1 – zone of pollution; 2 – investigated model of vegetation, t=2 s (a), t=6 s (b)

Zones of pollution for the second scenario when the average height for emission was considered are presented in Fig. 3. As it can be seen, when the ejection is located at medium altitude, as in the previous scenario, the trees form an obstacle in the path of the moving contamination zone. Over a very short period of time, the contamination zone is inhibited (Fig. 3, a) and begins to develop up and down (Fig. 3, b), and only after a few seconds the contaminant penetrates through the vegetation, a contamination zone is in the form of a «tongue» directly for the vegetation model. This process occurs most intensively in the lower part of the obstacle (Fig. 3, c).

Fig. 3 – Dynamics of formation of pollution zones when the source of pollution is at an average level: 1 – zone of pollution; 2 – investigated model of vegetation, t=2 s (a), t=4 s (b), t=7 s (c)

At the second step of laboratory studies, a dust pollutant entered the stream instead of the paint and studied the law of its subsidence in the presence of vegetation. The white contour shows the pollution zone of the dust pollutant, it is clearly visible that in the upper region (Fig. 4 a) the pollution intensity is higher than in the lower region of this zone, this is directly related to the fact that the dust has a settling velocity, and also in the region of location the dust penetrates more easily, that dissipates quickly. The areas of the settled dust pollutant after its entry into the stream, partial flow displacement and flow dissipation have been obtained (Fig. 4, b). It can be observed that a significant part of this contaminant has settled directly in front of the vegetation, which effectively prevents the movement of the dust pollutant.

Fig. 4 – Dynamics of formation of dust pollution zones: 1 – zone of pollution; 2 – investigated model of vegetation; 3 – model of building, t=6 s (a), t=22 s (b)

At the third step stage of laboratory studies the regularities in the formation of pollution zones were studied, when instead of vegetation its «equivalent» – a plate is used. However in contrast to other studies, we use not a solid plate, but a porous plate, where porosity was understood as the ratio of clearance to cross-sectional area of the plant zone. The dynamics of the formation of contamination zones is shown in the case of liquid contamination entering the flow in the presence of a porous plate with such characteristics (Fig. 5): the diameter of the holes is d=3 mm, the distance between the holes is 5 mm.

Fig. 5 – Dynamics of formation of pollution zones when the source of pollution is at a low level, t = 6 s: 1 – zone of pollution; 2 – porous plate; 3 – model of building

Comparison of the dynamics of pollution zones formation when the source of pollution is at a low level in the case of vegetation (Fig. 2, b) and a porous plate (Fig. 5) shows similarities in the development of pollution zones. Carrying out full-scale experiments is a laborious process and takes a long time, therefore it is more relevant to replace it with a numerical experiment. The results of laboratory studies served as a prerequisite for using the «equivalent» of these plantations – the porous plate for mathematical modeling of the calculation of pollution zones near vegetation (Fig. 6). Of course, this is a simplified assumption, but with this approach it is possible to build a model for carrying out «pilot» or estimated calculations.

Fig. 6 – The scheme for flowing a porous plate: 1 – source of pollution; 2 – porous plate; 3 – model of building.

Aerodynamic model. To calculate the local velocity field in the presence of vegetation near the motorway, the potential flow model is used [12]:

, (1)

where P – the velocity potential, the Y axis is directed vertically upwards. The following boundary conditions are imposed [13] to solve Eq. 1:

— on the wall of the porous plate and on other hard surfaces, a boundary condition is imposed, where is the only vector of the outer normal to the solid wall;

— on the boundary of the airflow inlet to the design area , where is the known value of the airflow velocity;

— on the boundary, where the stream leaves the computational domain (Fig. 11) is a certain number (the Dirichle condition).

Mass transfer model. To calculate the dispersion of gaseous and dust pollution near the motorway in the presence of vegetation (porous plate), the equation of mass transfer is used [12]:


where C – concentration of the pollutant; – air velocity vector components; – velocity of gravitational sedimentation of the pollutant, – coefficient of turbulent diffusion; – coordinates of the pollutant release source; – intensity of pollutant source at a point ; – Dirac delta-function, which simulates the flow of pollutant.

Numerical model. Numerical integration of modeling equations is carried out using a rectangular difference grid. For the numerical integration of the Laplace Eq. 1 the Libman method is used. In this case the approximating equation has the form:


The unknown value of the velocity speed potential is determined from the following relationship:


To begin the calculation using the Libman method, the «initial» value of the velocity potential in the computational domain is given. The calculation is terminated when the condition is performed, where ε=0.001, n – is the iteration number. The obtained values of the velocity potential allow us to calculate the components of the velocity vector on the verges of the difference cells with respect to the dependences:


Numerical integration of the mass transfer Eq. 2 is carried out using an implicit alternate-triangular difference splitting scheme [13–14]. The statement of the boundary conditions for Eq. 2 was considered in the works of G. Marchuk and A. Samarskii. The initial data for the calculation are: the wind velocity profile at the entrance to the calculated region , where  m/s is the wind velocity on high  m, ; the state of the atmosphere (inversion, convection), that is, the value of the vertical diffusion coefficient ; the average CO of pollution from one car is 0.058 g/s; the position of the pollution source is the position of the vehicle exhaust pipe.

Results of mathematical modeling. The developed program code was used to calculate local pollution zones using the proposed mathematical model. The dynamics of the formation of pollution zones for different time points is presented (Fig. 7), calculated using the proposed approach, when the position of the vegetation is modeled by the placement of a porous plate.

Comparing these figures with the results of laboratory studies on the distribution of paint and dust in the stream, it can be seen that agreement is being made on the shape and structure of the formed zone near the green plantations and the porous plate. The pollution subzone is clearly distinguished, which at the initial stage of the interaction of the air stream with vegetation is pulled upwards (Fig. 7, a), and then the impurity penetrates through the porous barrier (Fig. 7, b-d). The obtained results show that the mathematical model «traces» the process of impurity penetration through a porous plate according to the same principle (Fig. 5), as penetration of pollution through green spaces (Fig. 3).

The proposed mathematical model makes it possible to calculate the formation of pollution zones near motorways in the presence of green spaces.

Conclusions. As a result of the research, the following results were obtained:

— a number of laboratory experiments were conducted to study the dynamics of the formation of pollution zones during the emission of liquid and dust pollutants at different heights, taking into account vegetation;

— based on the conducted laboratory studies, the patterns of formation of pollution zones is were identified when the source of pollution is located at a low and an average level in the presence of green spaces;

— the analogy of the pollutant behavior in the case of vegetation and the porous plate is shown, which serves as an obstacle to the moving of pollution zones;

— a mathematical express model for the calculation of pollution zones in the presence of vegetation is proposed, which makes it possible to quickly assess the formation of pollution zones near the motorway;

— a computer program was developed to perform numerical calculations of pollution zones when a porous plate is located near the source of pollution; the results of the calculation and their satisfactory agreement with the results of laboratory experiments are shown.

The prospect of development of this direction is the development of a 3D numerical model for predicting the formation of pollution zones, taking into account the location of vegetation near the motorway.


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