Introduction

Air pollution from year to year is becoming a large-scale and serious issue of global significance. Continuous development and population growth in urban areas and many problems related to the environment, such as deforestation, toxic materials emission, solid waste emissions and air pollution attract more attention than ever before. The industry develops all over the world, resulting in a growing number of factories, thermal power plants, nuclear power plants, which produce large amounts of pollutants. Emissions lead to different environmental problems, which are harmful to the environment and the human health. The air pollution problem in cities has become so serious that there is a need for immediate information about changes in the contamination level (WHO 2002).

Each year, millions of tons of gaseous sulfur oxides and nitrogen oxides are disposed of into the environment. The share of anthropogenic emissions of these oxides from thermal power plants is 45–65% and 15–45%, respectively (WHO 2002). Further development of the thermal energy is highly dependent on ensuring an acceptable level of power plants’ impact on the environment and their safety for the ecology. Moreover, these emissions get into the atmosphere and they are distributed by the air, chemically react and fall in the surrounding ground surfaces in the dry form and liquid precipitation (plants, soil, water, buildings). The ambient pollutants can settle at a distance of 100–1000 km from the source depending on chemical, meteorological and various physical factors (Fay and Rosenzweig 1980). This distance increases mainly in proportion to the velocity of the emission source and depends on density, temperature, wind speed, humidity (Zavila 2012; Kozic 2015; Barbero et al. 2015). In the whole world, about 63% of all electricity is generated by thermal power plants (El-Sharkawi 2013; Olaguer et al. 2016). During the operation of the TPP, fuel is burned and various polluting substances emit into the atmosphere. Many of these contaminations are toxic and, despite the relatively low concentrations, have a negative impact on nature. Air pollution can have a negative impact on human health, the surrounding climate, flora and fauna. Flora is a group of indigenous plants in an ecosystem of a geographical zone, and fauna is a group of indigenous animals of any geographical zone. Contaminants include carbon, sulfur, nitrogen, as well as aerosols and carcinogens. As a result of organic fuel burning in the TPP, carbon dioxide and water formed the main emission components. In addition to the above contaminations from incomplete fuel combustion, the different dust compositions such as sulfur oxides, nitrogen oxides, fluoride compounds, metal oxides and gaseous products are included. After getting into the atmosphere, they cause significant damage not only to the surrounding biosphere but also to buildings, architectural objects, the municipal economy buildings, transport and the nearby area population. About 50% of the pollution from thermal power plant is sulfur dioxide, 30%—nitrogen oxide, and 25%—fly ash (Abbaspour et al. 2005).

The documents regulating the work of TPP are updated every year, in which the permissible norms of emissions into the air basin and reservoirs and solid particle emissions are prescribed. Nowadays various ways are known to reduce emissions from thermal power plants. For example, to limit sulfur dioxide so-called scrubbers (gas scrubbers) are used, which carry out desulfurization of the exhaust gas from the chimneys and remove up to 95% of sulfur dioxide (US Environmental 2016). Direct combustion process is modified in many countries around the world to limit nitric oxide emissions, thereby reducing the nitric oxide release by 30–50% (Environmental, Health, and Safety Guidelines for Thermal Power Plants 2017). There is also a selective catalytic purification method, which allows reducing the nitric oxide release by 80–90%. The advanced technologies for reducing emissions include the CCS (carbon capture and storage) method. At the heart of its principle lies the trapping the carbon dioxide (CO2) process, after which it is compressed and deposited into underground layers for storage, without letting it out into the atmosphere. Despite the fact that the above technologies provide an instant reduction in air pollution, it does not guarantee a complete exhaustion of the problem. For capturing the CO2, it can be done also by other technologies. Broadly, three different types of technologies exist: post-combustion, pre-combustion and oxy-fuel combustion.

The study of this process in the Republic of Kazakhstan is especially important. The Republic of Kazakhstan has large reserves of energy resources (oil, gas, coal, uranium). About 80% of exports are raw materials, and the share of industrial exports decreases annually. According to statistics, Kazakhstan’s energy consists of almost 87% coal, and by 2020, the hard fuel proportion will be about 66% of the total volume in the emission generation (Annual report. SAMRYK ENERGY 2015). Thus, the energy sector is a most polluter of the air basin of the Republic of Kazakhstan.

The simulation of this process can be carried out in two ways: The first is to use a Gaussian model or use the complete momentum and the continuity equations. The Briggs plume rise equations and Gaussian model are often used for contaminants distribution simulation (Fatehifar et al. 2008; Igbokwe et al. 2016; Tomiyama et al. 2016; Gousseau et al. 2011; Ebrahimi and Jahangirian 2013). However, it does not allow a sufficiently accurate smoke movement nature determination. These models showed a good result only in the flat and linear terrain. As a consequence, it is necessary to use a numerical turbulent model that will allow for taking into account the roughness and terrain topography in which the contamination source is located. A two-dimensional pollution spreading model was constructed at the earth’s surface level. In the papers (Olivera et al. 2013; Sanín and Montero 2007; Grazia et al. 2017; Kho et al. 2007; Walvekar and Gurjar 2013), a “box model” was constructed, which takes into account the wind direction and terrain relief. The emission substance SO2 was considered and was used the k–epsilon turbulence model.

To simulate the spread of contamination from two chimneys of Ekibastuz SDPP-1, several test problems were first considered and solved numerically. This procedure is carried out in order to validate the numerical algorithm and the mathematical model. In the first test problem, a two-dimensional problem was examined. The obtained computational values were compared with the results from Schonauer and Adolph 2005 and Falconi et al. 2007, and good matches were obtained. In the second test problem, a three-dimensional jet in crossflow problem was examined. The obtained results were validated and compared with the numerical values from the paper (Keimasi and Taeibi-Rahni 2001), and measured values (Ajersch et al. 1995) showed a more accurate matching with the measured values than the data from computation (Keimasi and Taeibi-Rahni 2001). After solving the 2D and 3D test problems and validating the numerical algorithm, the distribution of atmospheric pollution from the Ekibastuz SDPP-1 was considered.

Ekibastuz SDPP-1 (Fig. 1) is the largest TPP in the Republic of Kazakhstan which is located in Ekibastuz city, which is between the Pavlodar and Semey cities. The design capacity of TPP is 4000 MW, and the working capacity is about 3500 MW. The Ekibastuz SDPP-1 is located on the northern shore of Zhyngyldy Lake, at 16 km north from the Ekibastuz city. The building dimensions: height—64 m, width—132 m and length—500 m. This TPP has two chimneys with heights are 300 m (built in 1980) and 330 m (built in 1982).

Fig. 1
figure 1

Satellite image of the TPP and the distance between the two chimneys [250 (m)]. Ekibastuz SDPP-1, Ekibastuz city, Republic of Kazakhstan

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Two-dimensional test problems

Scheme and dimensions of the computational domain

Figure 2 illustrates the scheme and the computational area dimensions. Substance A enters through the left side (inlet 1), substance B across the pipe input (inlet 2) and the output is on the right side (outlet). All computational domain size is indicated in Fig. 2.

Fig. 2
figure 2

Scheme and dimensions of the computational domain

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Materials and methods

Mathematical model

A detailed description of recent works devoted to the study of the contamination flow from a pipe in a transverse flow can be found in Su and Mungal (2004), Shan and Dimotakis (2006), Hasselbrink and Mungal (2001), Muppidi and Mahesh (2005, 2007, 2008), Chochua et al. (2000), Acharya et al. (2001), Camussi et al. (2002), Schluter and Schonfeld (2000), Chai et al. (2015), Livescu et al. (2000). In paper (Kelso et al. 1996), the authors numerically modeled the velocity field, while in papers (Su and Mungal 2004; Shan and Dimotakis 2006) the passive scalar mass fraction field was considered. For solving such problems are almost always used numerical simulations. In papers (Hasselbrink and Mungal 2001; Muppidi and Mahesh 2008), Reynolds-averaged Navier–Stokes equations (RANS) were applied and the data were matched with the measured data. In papers (Chochua et al. 2000; Acharya et al. 2001; Camussi et al. 2002), a more accurate correspondence between numerical results was obtained by using the direct numerical simulation (DNS) method and real measurements. These problems were also examined in many papers (Schluter and Schonfeld 2000; Chai et al. 2015; Livescu et al. 2000). However, the direct numerical simulation method claims high computational costs, which is expensive for simulating the problems in actual sizes. That is why in this paper the k–epsilon turbulent model was used. The main equations representing these processes are the Navier–Stokes equations (Ferziger and Peric 2013; Issakhov et al. 2018, 2019; Issakhov and Mashenkova 2019), which consist of the continuity and momentum equations:

$$\frac{{\partial u_{j} }}{{\partial x_{j} }} = 0$$
(1)
$$\frac{{\partial \rho u_{i} }}{\partial t} + \frac{\partial }{{\partial x_{j} }}(\rho u_{i} u_{j} ) = - \frac{{\partial p^{\prime}}}{{\partial x_{i} }} + \frac{\partial }{{\partial x_{j} }}\left[ {\mu_{\text{eff}} \left( {\frac{{\partial u_{i} }}{{\partial x_{j} }} + \frac{{\partial u_{j} }}{{\partial x_{i} }}} \right)} \right] - \rho \vec{g}\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{n}$$
(2)

where \(\mu_{\text{eff}}\)—the effective viscosity, \(p^{\prime}\)—the modified pressure. Here \(p^{\prime} = p + 2\rho k/3 + 2\mu_{\text{eff}} /3\partial u_{k} /\partial x_{k}\) and \(\mu_{\text{eff}} = \mu + \mu_{t}\), where \(\mu_{t} = C_{\mu } \rho k^{2} /\varepsilon\)—the turbulence viscosity, p—the pressure, g—the gravity force, \(\rho\)—the density, \(u_{j}\)—the velocity components, \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{n}\)—the normal vector. In order to close this equation system, a \(k - \varepsilon\) turbulent model was used

$$\frac{\partial k}{\partial t} + \frac{\partial }{{\partial x_{j} }}(u_{j} k) = \frac{\partial }{{\partial x_{j} }}\left[ {\left( {\mu + \frac{{\mu_{t} }}{{\sigma_{k} }}} \right)\frac{\partial k}{{\partial x_{j} }}} \right] + P_{k} - \rho \varepsilon + P_{kb}$$
(3)
$$\frac{\partial \varepsilon }{\partial t} + \frac{\partial }{{\partial x_{j} }}(u_{j} \varepsilon ) = \frac{\partial }{{\partial x_{j} }}\left[ {\left( {\mu + \frac{{\mu_{t} }}{{\sigma_{\varepsilon } }}} \right)\frac{\partial \varepsilon }{{\partial x_{j} }}} \right] + \frac{\varepsilon }{k}(C_{\varepsilon 1} P_{k} - C_{\varepsilon 2} \rho \varepsilon + C_{\varepsilon 1} P_{\varepsilon \,b} )$$
(4)

Pk—turbulence production due to viscous forces, which is presented as: \(P_{k} = \mu_{t} \left( {\frac{{\partial u_{i} }}{{\partial x_{j} }} + \frac{{\partial u_{j} }}{{\partial x_{i} }}} \right)\frac{{\partial u_{i} }}{{\partial x_{j} }} - \frac{2}{3}\frac{{\partial u_{k} }}{{\partial x_{k} }}\left( {3\mu_{t} \frac{{\partial u_{k} }}{{\partial x_{k} }} + \rho k} \right)\), where \(P_{kb} ,\,P_{\varepsilon b}\)—the buoyancy forces, where \(P_{kb} = - \frac{{\mu_{t} }}{{\rho \sigma_{\rho } }}\rho \beta g_{i} \frac{\partial T}{{\partial x_{i} }}\) and \(P_{\varepsilon b} = C_{3} \hbox{max} (0,P_{kb} )\). \(\beta\) is the coefficient of thermal expansion, \(\sigma_{\rho } = 0.9\), \(C_{\mu } = 0.09\), \(C_{\varepsilon 1,\,} C_{\varepsilon 2} ,\,\,\sigma_{k} ,\,\sigma_{\varepsilon }\)—are constants.

To solve the species transport equations, ANSYS Fluent computes the local mass fraction of each species Yi, by the solution of a convection diffusion equation for the ith species.

$$\frac{\partial }{\partial t}(\rho Y_{i} ) + \nabla \cdot (\rho \,\vec{u}Y_{i} ) = - \nabla \cdot \vec{J}_{i} + R_{i} + S_{i}$$
(5)

where Si is the rate of creation by addition from the dispersed phase plus any user-defined sources and Ri is the net rate of i species production by chemical reaction.

For the turbulent flows, the mass diffusion is computed as:

$$\vec{J}_{i} = - \left( {\rho D_{i,m} + \frac{{\mu_{t} }}{{Sc_{t} }}} \right)\nabla Y_{i}$$
(6)

where \(Sc_{t} = \mu_{t} /\rho D_{t}\)—turbulent Schmidt number (Dt—the turbulent diffusivity and \(\mu_{t}\)—the turbulent viscosity). The default Sct is 0.7. In this work, it was defined as 1.

The energy equation is computed as:

$$\frac{\partial }{\partial T}(\rho E) + \nabla \cdot (\vec{v}(\rho E + p)) = \nabla \cdot \left( {k_{\text{eff}} \nabla T - \sum\limits_{j} {h_{j} \vec{J}_{j} } + (\overline{\overline{\tau }}_{eff} \cdot \vec{v})} \right) + S_{h}$$
(7)

where \(\vec{J}_{j}\)—the diffusion flux of species j, \(k_{\text{eff}} = k + k_{t}\)—the effective conductivity, kt—the turbulent thermal conductivity, set according to the turbulence model. The first three components on the RHS of (7) express energy transfer due to conduction, species diffusion and viscous dissipation, respectively. Sh take into account the chemical reaction energy, \(E = h - \frac{p}{\rho } + \frac{{v^{2} }}{2}\), here \(h = \sum\limits_{j} {Y_{j} } h_{j} + \frac{p}{\rho }\), Yj is the mass fraction of species j, \(h_{j} = \int_{{T_{\text{ref}} }}^{T} {c_{p,j} \;{\text{d}}T}\), where \(T_{\text{ref}} = 298.15\,{\text{K}}\).

Mesh

There are a lot of different studies concerning the choice of optimal grid size. For instance, in the papers (Schonauer and Adolph 2005; Falconi et al. 2007) a computational result analysis for three different grids is carried out. According to these data, the main part of the channel grid had 2561 × 641 dimensions; the pipe grid had 161 × 321 dimensions. As a result, the total number of elements was 1,693,121.

For the numerical simulations, which carried out at ANSYS Fluent, all values were set in meters; geometry was built in ANSYS Geometry. The grid for simulations by the TFS-MCM software has been built by using the Pointwise program. Details on the grid generation process and further details and application to various flow problems can be found in Issakhov (2014, 2015a, b, 2016a, b; 2017a, b). For the numerical algorithm was chosen the SIMPLE algorithm. Convergence condition was set as \(\varepsilon = 0.00001\). For numerical solving the distribution of the species mass fraction in the ANSYS Fluent, the species transport option was used.

Inlet conditions for the main pipe and the crossflow velocity are described by the different profiles. The velocity ratio is expressed through ratio \(R = U_{\text{jet}} /U_{\text{crossflow}} = 1.5\). The results of different velocity profiles and their influence on the substances movement were compared. Substance B, outgoing from the pipe, reacts with the main flow substance A, thereby forming C. There each mass fraction of them has been studied. The species mass fraction is the species mass per unit of the mixture mass (e.g., kg of species in 1 kg of the mixture). The substances are selected for the purpose that the Damköhler number was 1. The flow was presented as incompressible due to the small Mach number and weak wind velocity. A similar study was conducted by the papers (Schonauer and Adolph 2005; Falconi et al. 2007), and the aim of this study was to compare the obtained numerical data with the previous results.

Boundary conditions

Boundary conditions were defined as follows: for the walls—“Wall,” for the outlet—“Pressure outlet,” for inlet 1 and inlet 2—“Velocity inlet.”

For the main channel input (inlet 1) were considered the different velocity profile u types (where u is the horizontal velocity component):

$$u1:u = u^{*}$$
(8)
$$u2:u = u^{*} \left( {1 - e^{{ - 4.5\,\left( {1 - \frac{{r^{2} }}{4}} \right)}} } \right),\quad r = y$$
(9)
$$u3:u = u^{*} \left( {1 - e^{{ - 5\left( {1 - \frac{{r^{2} }}{4}} \right)}} } \right),\quad r = y$$
(10)
$$u4:u = u^{*} \left( {1 - e^{{ - 5.5\,\left( {1 - \frac{{r^{2} }}{4}} \right)}} } \right),\quad r = y$$
(11)

Other parameters were defined as constant: \(w = 0\) (vertical velocity component), \(Y_{A} = 1,\,Y_{B} = 0.\)

For the pipe inlet (inlet 2): \(Y_{A} = 0,\,Y_{B} = 1;\)

$$u = 0,\,w = 2R\,u^{*} \,(1 - 4\,l^{2} ),\quad l = x$$
(12)

where \(u^{*}\) changes depending on the selected material. In this case for substances A and B was set the oxygen O2. To obtain the necessary Reynolds number \(Re = \frac{{\rho \,u_{\text{crossflow}} \,D}}{\mu } = 25\) and taking into account the fact that the dynamic viscosity of the oxygen is \(\mu = 1. 9 1 9 {\text{e}} - 0 5\;{\text{kg}}\;{\text{m}}^{ 2} /{\text{s}}\), the density \(\rho = 1. 2 9 9 8 7 4\;{\text{kg/m}}^{ 3}\), the velocity was determined as \(u^{*} = 0. 0 0 0 3 6 9 0 7 4 2 3 3\,\,{\text{m/s}}\), temperature considered constant and the value set as \(T = 3 0 0\;{\text{K}}\). The pipe diameter was \(D = 1\;{\text{m}}\). In order to get the Schmidt number equal to 1, the diffusion coefficient was defined as the \(0. 6 7 7{\kern 1pt} {\text{ m}}^{ 2} /{\text{s}}\).

In the ANSYS Fluent, all simulations are made in real size, so the actual parameters have been specified in the present case. In the simulations by the TFS-MCM (Issakhov 2014, 2015a, b, 2016a, b, 2017a, b) were used dimensionless parameters. The boundary conditions are given in Table 1.

Table 1 Boundary conditions
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Results and discussion

Numerical results

Next, the numerical computational values and comparative analysis of the following parameters are presented: the velocity, mass fraction and temperature fields.

Velocity

Figure 3a–d) shows the results for the horizontal and vertical velocity profiles at the initial velocity profile u3 for the main channel. Below there are the velocity profiles u for different initial velocities at different distances x/D = 0.0, x/D = 1.5, x/D = 3.0, x/D = 4.5. Furthermore, Fig. 3e–h clearly shows that the difference between the profiles u2, u3 and u4 approximately similar, but the profile u1 is different from others. These results show that it is significant to define the velocity profile as a function, rather than uniform, since it greatly influences the value and more accurately describes the real physical processes.

Fig. 3
figure 3

Profiles of vertical and horizontal velocity components (m/s): ax/D = 0.0, bx/D = 1.5, cx/D = 3.0, dx/D = 4.5; and comparison of velocity profiles at different distances: ex/D = 0.0, fx/D = 1.5, gx/D = 3.0, hx/D = 4.5

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Figure 4a–c shows the flow streamlines and velocity magnitude values throughout the computational domain. Moreover, Fig. 4d–i illustrates the contours of u and w velocity components, respectively.

Fig. 4
figure 4

Contour of velocity magnitude and streamlines: a results of (Schonauer and Adolph 2005; Falconi et al. 2007), b results obtained by calculations on TFS-MCM software, c results obtained by ANSYS. Contour of the u velocity component: d results of (Schonauer and Adolph 2005; Falconi et al. 2007), e results obtained by calculations on TFS-MCM software; f results obtained by ANSYS. The contour of the w velocity component: g results of (Schonauer and Adolph 2005; Falconi et al. 2007), h results obtained by calculations on TFS-MCM software, i results obtained by ANSYS

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Differences in the numerical results are explained by the fact that physical values are specified in ANSYS, and dimensionless values are set in TFS-MCM. The obtained numerical results for velocity magnitude, horizontal velocity components and vertical velocity components were compared with numerical results from papers (Schonauer and Adolph 2005; Falconi et al. 2007). While Figure 4a, d, g shows the results from the paper (Schonauer and Adolph 2005; Falconi et al. 2007), in Fig. 4b, e, h, numerical results can be found obtained with the TFS-MCM, whereas Fig. 4c, f, i describes the numerical results obtained with the ANSYS Fluent.

Mass fraction

Figure 5a–l illustrates the mass fraction profile results of substances A, B and the resulting reactant C at different sections (x/D = 0.0, x/D = 1.5, x/D = 3.0, x/D = 4.5), respectively. They also clearly show that the difference between the velocity profile u1 and others has the influence to the species mass fraction distributions too.

Fig. 5
figure 5figure 5

Profiles of mass fraction for the reaction product C at different distances for various initial velocity profiles: ax/D = 0.0, bx/D = 1.5, cx/D = 3.0, dx/D = 4.5. Profiles of substance B mass fraction at different distances for various initial velocity profiles: ex/D = 0.0, fx/D = 1.5, gx/D = 3.0, hx/D = 4.5. Profiles of substance A mass fraction at different distances for various initial velocity profiles: ix/D = 0.0, jx/D = 1.5, kx/D = 3.0, lx/D = 4.5

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Figure 6a–i illustrates a comparative analysis of the mass fractions spread obtained in this work by TFS-MCM and ANSYS with the results obtained from papers (Schonauer and Adolph 2005; Falconi et al. 2007), where C1, C2 and C3—the mass fraction of substances A, B and C, respectively.

Fig. 6
figure 6

Comparative analysis of the substance A distribution: a results of Schonauer and Adolph (2005, Falconi et al. (2007), b results obtained by calculations on TFS-MCM software; c results obtained by ANSYS. Comparative analysis of the substance B distribution: d results of Schonauer and Adolph (2005), Falconi et al. (2007), e results obtained by calculations on TFS-MCM software; f results obtained by ANSYS. Comparative analysis of the substance C distribution: g results of Schonauer and Adolph (2005), Falconi et al. (2007), h results obtained by calculations on TFS-MCM software; i results obtained by ANSYS. Comparative analysis of the temperature field: j results obtained by calculations on TFS-MCM software; k results obtained by ANSYS

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Figure 6j, k shows the temperature distribution results obtained by performing calculations on the TFS-MCM and ANSYS.

The three-dimensional test problem

The computational domain

The simulation region of the test problem is a three-dimensional channel with the pipe entering into it. The transverse channel length is 45D, the width is 3D, the pipe center is located at 5D from the inlet, the crossflow channel height is 20D, and the pipe height is 5D (Fig. 7).

Fig. 7
figure 7

Computational domain parameters

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Characteristics of the flow

The flow velocity ratio from the pipe to the vertical flow velocity is marked by R and is calculated as follows:

$$R = V_{\text{jet}} /V{}_{\text{crossflow}}$$
(13)

In the study (Keimasi and Taeibi-Rahni 2001), different Rs (0.5, 1.0 and 1.5) were studied. The crossflow pipe velocity was 5.5 m/s. In this work, the ratio R = 0.5 was tested, so the flow velocity in the vertical flow was defined as 11 m/s. The pipe diameter was \(D = 12.7\;{\text{mm}}\). On the basis of the considering velocity, the Reynolds number was \(Re_{\text{jet}} = {{\rho V_{\text{jet}} D} \mathord{\left/ {\vphantom {{\rho V_{\text{jet}} D} \mu }} \right. \kern-0pt} \mu } = 4700\). The air was chosen as the substance material.

Boundary conditions

As shown in Fig. 7, the following boundary condition types were used for solving the problem: inlet, wall, outlet, periodic, no flux. Based on the measured value, the boundary layer width is 2D. To characterize the initial transverse velocity profile in the boundary layer was used 1/7 power law wind profile.

$$\frac{u}{{u_{r} }} = \left( {\frac{z}{{z_{r} }}} \right)^{\alpha }$$
(14)

where α is an empirically derived coefficient that varies due to the atmosphere stability and ur is the known wind velocity at a reference height zr and u is the wind velocity at height z. The neutral stability conditions are given as α = 1/7. Above the boundary layer, the velocity is defined as a uniform (11 m/s) (Keimasi and Taeibi-Rahni 2001).

The obtained numerical results

In this work, the case R = 0.5 was studied. Figure 8 illustrates the matching of values for the lateral velocity component at jet center plane (z/D = 0) for R = 0.5 with the measured values (Keimasi and Taeibi-Rahni 2001) and the experimental values (Ajersch et al. 1995) for the cross section x/D = 3 and x/D = 0. The results of present work are marked by the red solid line, round-shaped measured values (Ajersch et al. 1995), and the rest illustrates the obtained numerical data (Keimasi and Taeibi-Rahni 2001) by using various turbulent models. Also, the values obtained by using the SST \(k - \omega\) turbulent model are illustrated. From these figures, it can be seen that the selected \(k - \varepsilon\) model and SIMPLE method allow obtaining the values closest to the experimental results.

Fig. 8
figure 8

Comparison of the lateral velocity component values at jet center plane (z/D = 0) for R = 0.5 with the numerical data (Keimasi and Taeibi-Rahni 2001) and the measured values (Ajersch et al. 1995): ax/D = 0; bx/D = 3

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So it can be observed from the figures that the computational values of the horizontal and vertical velocity components describe the motion character well in comparison with the measured values (Ajersch et al. 1995). These results can be explained by the fact that for a given numerical simulation the finer computational grid was used, which clustered near the wall than for simulation in the work (Keimasi and Taeibi-Rahni 2001).

The three-dimensional problem in real physical scale

In this section, a three-dimensional problem in actual physical size is considered. The comparative analysis was carried out with work (Zavila 2012). The results of Zavila 2012 were checked by a measured performed in a low-speed wind tunnel.

Computational area and mesh

The three-dimensional box with a chimney was selected as the computational area. The emissions are emitted from the chimney hole. Figure 9a, b illustrates the geometry and computational mesh. The dimensions are represented in Table 2. For precise modeling, the computational mesh was non-uniform and was clustered close to the ground, near the chimney outlet and approximately along the pollution motion trajectory. The total number of three-dimensional element number is 568,486. Furthermore, it should be noted that according to Chang et al. 2011 and Saeed et al. 2017, the RNG \(k - \varepsilon\) and the standard \(k - \varepsilon\) models give nearly the equal values for the similar problem. So, the test problem was simulated using the Standard \(k - \varepsilon\) model, but in this work RNG \(k - \varepsilon\) model was used. It was done in order to match the obtained values with results of Zavila (2012).

Fig. 9
figure 9

Three-dimensional problem in actual physical size: a geometry of calculating domain; b unstructured grid. The He distribution values: data of Zavila (2012) (c) and present paper data (wind velocity is 5 m/s) (d)

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Table 2 Geometry parameters
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The boundary conditions and comparison of obtained numerical results

Boundary conditions were defined as the “Wall” for chimney walls and the ground, “Velocity inlet” for the wind inlet and the chimney hole, “Symmetry” for the side walls and the top wall and “Pressure Outlet” for the outlet.

In the paper (Zavila 2012), the author assumed the He dispersion for various wind velocities: 1, 3 and 5 m/s. For matching with the paper, it was selected the third case (\(v_{\text{air}} = 5\;{\text{m/s}}\)) (see Fig. 9c). In the test problem for species movement simulation was used species transport model. It was considered that discharged concentration do not react with air. The gravitational force impact was taken into account. The convergence criterion and temperature were defined as \(\varepsilon = 0.0001\) and 300 K, respectively. All characteristics were specified similar to Zavila (2012).

Figure 9d illustrates good correspondence with the numerical values (see Fig. 9c) (Zavila 2012). The numerical values were illustrated as pollutant concentrations iso-surfaces and the high mass fraction value was defined as 0.00003.

The Ekibastuz SDPP-1

Next, the pollution distribution of the real physical model for the Ekibastuz SDPP-1, in the Ekibastuz city, was considered. The Ekibastuz SDPP-1 species emits from two chimneys with heights 330 m and 300 m. The space between the two chimneys is about 250 m (see Fig. 1). The chimneys diameters were set as 10 m. For simulation were considered two cases with various wind velocities: 1.0 m/s and 1.5 m/s (Fig. 10a, b). The pollutant emission velocity from chimneys is 5 m/s. In order to characterize the boundary layer, the following wind velocity profile was set \(v_{x} = v_{\text{wind}} \cdot \left( {0.2371 \cdot \ln \left( {{\text{Y}} + 0.00327} \right) + 1.3571} \right)\,({\text{m}}/{\text{s}})\). In this case, the CO2 was defined as a pollutant (see Fig. 10a, b). Figure 10a, b shows that at strong wind velocity drops down the pollution on the ground surface much farther from the source than at weak wind velocities. Further, height effect of the thermal power plant chimney was investigated. For this aim, mass fraction profiles from two chimneys were matched at various distances from the source [1750 and 2150 (m) (see Fig. 10c, d)] with wind velocity 1.5 m/s.

Fig. 10
figure 10figure 10

Distribution of CO2 from the thermal power for different wind velocities: a 1.0 m/s, b 1.5 m/s. Comparison of the CO2 mass fraction profiles at different distances for two chimneys [330 and 300 (m)]: c 1750 (m), d 2150 (m). Wind velocity: 1.5 m/s

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Figure 10a obviously illustrates that concentration from a lower chimney (300 m) drops down closer to the emission source. Figure 10c outlines comparison of CO2 concentration profiles for a distance of 1750 m from the emission source. From the obtained numerical solutions, it can be noted that the discharged concentration from a small chimney (300 m) already reaches the land surface. And the level of concentration from a high chimney (330 m) is approximately equal to zero. However, when comparing values at an altitude of 150–350 m, it is observed that the released substance from the lower chimney (300 m) has a high value, whereas for a high chimney (330 m) the concentration value has a lower value. This is due to the fact that in a given altitude range, the concentrations from the two chimneys are mixed because the space between the two chimneys is only 250 m, since the pollutions can dissipate well. From the obtained data, it can be noted that at a distance of 2150 m, the pollution from two chimneys is almost deposited on the land surface. It should be noted that the concentration (CO2) value has higher values on the surface of the land than at a height (~ 300 m), since at this height the diffusion effect is insignificant. This phenomenon is connected with turbulent vortex dissipation. In paper (Toja-Silva et al. 2017), the authors illustrated that the species change trajectory and settle below toward the land at a distance approximately 500 m from the chimney. Nevertheless, despite that, at a distance of approximately 700 m from the Ekibastuz SDPP-1, high concentration values can be noticed close to the ground level. However, this effect is also can be seen in the paper (Toja-Silva et al. 2017), but there are differences in the sedimentation distances due to different chimney heights.

Conclusion

The purpose of this work was to determine the distance at which the concentration from the chimney settles, and the factors affecting it, as well as the effect of the chimney height on the distribution of pollution. For this objective, a CFD modeling of dispersion and gaseous pollutant plume motion in real atmospheric conditions was conducted. The impact of different wind velocities and chimney heights was studied. To check the numerical algorithm and mathematical model, two test problems were simulated: two-dimensional and three-dimensional. The computational result of the three-dimensional test problems was compared with the measured data (Ajersch et al. 1995) and values from computation (Keimasi and Taeibi-Rahni 2001). The obtained values gave well agreement with the measured data. After proving the numerical algorithm and mathematical model, they were applied to the real-size problem. It should be noticed that numerical values in this paper were found to be almost the same as the measured values than numerical values obtained by other authors due to the improved computational mesh configuration and density. Next, a three-dimensional modeling of pollution spread in actual physical size was studied. Also the spread of the CO2 was considered. The fine computational mesh was used close to the ground, near the chimney outlet and along the pollution motion trajectory.

Additionally the actual physical model of the pollution spread from Ekibastuz SDPP-1 (Ekibastuz city) was considered. The extraordinary feature of this TPP is that the pollution discharges from two chimneys with various heights (330 and 300 m). From the computational values, it is clear that the height of the chimneys essentially impacts the concentration spread. Obviously, the construction of higher chimneys leads to more corresponding for the ecology safety. Furthermore, future increases in computational power will be accompanied by claims of researchers for increased number of mesh elements and the inclusion of additional physical characteristics. Therefore, new treatments are needed in order to decrease modeling computational costs. The ecology safeness distances (2150 m for the second chimney (330 m) and 1750 for the first chimney (300 m)) were also specified the concentration drop down from the two chimneys of the thermal power plant.

Future investigation should proceed to investigate knowledge in describing the spread of harmful substances in the air at different distances. It would help to minimize the harm caused by emissions to people, fauna and flora and to define the optimal location of new TPPs with respect to cities or towns in advance.

It is should be noticed that various limitations may exist in this study. The first limitation is the number of mesh elements: The lack of computer resources limited us in the mesh size. The second limitation is the complexity of implementing and analyzing measured researches at the Ekibastuz SDPP-1 (negligible differences between subjects, environmental factors and other unexpected changes during the experiment). These works are useful for those who are interested in gas pollutant spread in the environment.