Turbulent Modeling of the Plumes of a Single Stack

Copyright © 2004 by the Kuwait Society of Engineers. All rights reserved.

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Proceedings of IMEC2004 International Mechanical Engineering Conference

December 5-8, 2004, Kuwait

IMEC2004-FM176-CP

Turbulent Modeling of the Plumes of a Single Stack

Ahmed F. Abdel Azim1*, Ahmed F. Abdel Gawad2& Mostafa M. Ibrahim3 1Chairman and Professor, Mech. Power Eng. Dept., Zagazig Univ., Egypt, [email protected] 2Associate Prof., Mech. Power Eng. Dept., Zagazig Univ., Egypt, [email protected] 3Demonstrator, Mech. Power Eng. Dept., Zagazig Univ., Egypt, [email protected]

Abstract

Due to the continuous increase of inhabitants needs, developing countries are forced to

construct more industrial facilities. However, air quality management is one of the serious problems that face the developing countries. Thus, an understanding of the plume behavior, emitting from an industrial stack, is essential for the process of planning and constructing of new industrial cities. Among others, the approach of computational fluid dynamics (CFD) modeling seems to be attractive in describing the plume behavior. This study is a parametric investigation of the characteristics of the pollution plumes emitting from a single stack. Two- and three-dimensional turbulent flow fields are solved by k-ε model and large eddy simulation (LES), respectively. The influence of main parameters, such as wind speed (0–20 m/s), stack height (10–100 m), stack outlet diameter (1–3 m), and gas-exit speed (2–10 m/s), is discussed. The results cover the plume characteristics (maximum distance, height, and width) and the concentrations of pollutants (gaseous and/or solid) as well as the tracks of the emitted particles, refer to Fig. (1). Valuable conclusions and suggestions can be drawn from the present work to determine the optimum health-safe distance away from an industrial stack. Key words: air pollution – stacks – plumes – wind shear – LES / k–ε model. Nomenclature 2-D Two-dimensional. 3-D Three-dimensional. C Concentration due to emissions from the stack, micro-gram/m3. CFD Computational Fluid Dynamics. CO Carbon monoxide. CO2 Carbon dioxide. CD Drag coefficient. D Stack diameter, m. DC Molecular diffusion coefficient. DT Thermophoretic coefficient. dp Particle diameter, m.

DF Drag force, N.

gF Gravity force, N. ___________________________________________ * Corresponding author: [email protected]


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LF Saffman’s lift force, N.

pF Pressure gradient force, N. g Gravitational acceleration, m/s2. H Stack height, m. K Fluid thermal conductivity. Kp Particle thermal conductivity. Ky Diffusion coefficient in the y–direction. Kz Diffusion coefficient in the z–direction. k-ε A turbulence model. k Turbulence kinetic energy. LES Large Eddy Simulation. LPD Lagrangian Particle Dispersion model. mp Particle mass, kg. NOx Nitrogen oxides. P Fluid static pressure, N/m2 (Pa). PM Particulate Matter. Pr Prandtl number. Re Reynolds number. S Actual surface area of the particle, m2. SO2 Sulpher dioxide. Tambient Ambient air temperature, K. Tgas Temperature of exit gas, K. U Mean velocity of the wind in x-direction. Up Particle velocity, m/s. ui Instantaneous wind velocity vector. Vgas Gas-exit velocity, m/s. Vwind Wind speed, m/s. X Downwind distance, measured from the stack centerline, m. Xmax Plume maximum-distance downwind of the stack, m. Y Horizontal distance, normal to the wind direction, measured from plume centerline, m. Ymax Plume maximum-width (diameter), m. Z Vertical distance from ground level, m. Zmax Plume maximum-height, m. Greek Symbols ε Turbulence dissipation rate. Φ Shape factor. ϕ The percentage of mass concentration of gases that exit from stack. κ Von Karman constant. µ Dynamic (absolute) viscosity, Pa.s. υ Kinematic viscosity, m2/s. ρ Density, kg/m3. ρp Particle density, kg/m3. τij Subgrid-scale stress. τw Wall shear stress, N/m2.


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Introduction Pollution is one of the serious problems that face the developing countries since air

pollution may reach unacceptable limits. This situation affects greatly the health and overall activities of humans. Air pollutant is defined as any gaseous, liquid or solid substance, which when introduced into the atmosphere at sufficient concentrations, due to the activities of mankind, may interfere directly with human health, safety and comfort. Also, it may cause damage or destruction to both plant and animal life. There are various kinds of air pollutants, which may be particulate or gaseous; organic or inorganic; visible or invisible; submicroscopic, microscopic, or macroscopic; toxic or harmful.

Various techniques are used in studying the air pollution problem. These techniques include field records, experimental measurements (in laboratories) and numerical investigations. Field records are actual measurements of real cases. Examples of these measurements include the work of Yoshikado and Kondo [1]. They carried out observations about the structure of the sea breeze over the urban and suburban areas of Tokyo for four summer days. Desiato and Ciminelli [2] studied the suspended particulates in the atmosphere by using the satellite sensors. A number of LANDSAT TM images, presenting the evidence of the pollutant plumes emitted from the stacks of the electric power plants located at two Italian coastal sites, has been selected for their investigation.

Experimental measurements are employed to simulate actual cases using scaled models in wind tunnels. Examples of experimental measurements include the work of Seifert and Shemer [3] who studied the effect of using a nozzle with an elongated exit cross-section as a passive device for increasing the jet penetration into cross flow. They found that the smoke plume dispersion and jet penetration are governed not only by the ratio of flow velocities in the stack and in the cross flow, but also by the shape of the exit cross-section and its orientation with respect to the cross flow. Kumar and Wehrmeyer [4] described an experimental system to investigate the feasibility of using laser Raman spectroscopy to detect stack gas pollutants. They stated that the delectability limit presently obtained is inadequate for continuous emission monitoring. However, improvements in baseline reduction and/or signal enhancement should lower its delectability limit to the extent that such applications are possible.

Numerical investigations are divided into two categories; either employing commercial codes or designing and developing codes by the researchers. The first category, which is based on studies of industrial cases using verified commercial codes, includes the work of Uliasz and Pielke [5] who examined the possible simplifications of the Lagrangian particle dispersion model (LPD) in order to develop an efficient tool for mesoscale applications. They presented the computer time requirements for different model versions. Craig et al. [6] used computational fluid dynamics (CFD) and mathematical optimization techniques to minimize pollution due to industrial sources like stacks. The CFD simulation uses the STAR–CD code. They investigated a simplified two–dimensional case of the minimization of pollutant stack distance to a street canyon with or without barrier for a prescribed maximum ground-level concentration of pollutants in the street canyon. Abdel Azim et al. [7] carried out a parametric study of the different factors that affect the plume characteristics of a single or multiple stacks. They studied the concentration and distribution of pollution emissions from industrial chimneys located in the neighborhood of the main campus of Zagazig University, Egypt. Their investigations were based on the Cornell Mixing Zone Expert System (CORMIX, version 3) software. They presented useful remarks that may help in reducing the pollution effect in the university campus. Lopez and Salcido [8] carried out an empirical parameterization to estimate friction velocity in stacks and the covariance from wind speed and temperature under tropical–rural conditions.


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In the second category, numerical pollution models are developed. Examples include the work of Khan and Abbasi [9] who proposed an analytical model for gases dispersion based on modifications in the plume path theory. They carried out a study to simulate the effect of the wind speed, density of the gas, and venting speed on dispersion. They developed a set of empirical equations for describing the plume characteristics. Mangia et al. [10] proposed a general formulation for the eddy diffusivity in atmospheric boundary layer. They showed that their dispersion model produces a good fitting of the measured ground-level concentration. Liu and Hong [11] applied the dust–diffusion–model method in environmental impact assessments and in establishing national environmental standards in China. This method was used to prejudge the ground-level dust concentration downwind of the sources and to estimate the source strength, especially the emission rate from fugitive dust sources, according to the ground-level dust concentration in downwind. Cipollone and Sciarretta [12] proposed a quantitative Lattice Gas model for the prediction of the interaction between pollutant emissions from power plant stacks and the surrounding environment. They reported a comparison between the results obtained by the model and those provided by the Gaussian plume equation.

In all the above studies, it is noticed that there is a shortage in the parametric study of the effect of the different parameters on the pollutant diffusion. Most of the publications cover specified (special) cases with fixed operating and atmospheric conditions. The present study is a parametric investigation of the pollution plumes emitting from a single stack. Two numerical methods were used to solve the turbulent flow field, namely: k-ε model and large eddy simulation (LES). The two methods were employed to solve two- and three-dimensional, steady and unsteady, incompressible flow to find the distributions of gaseous and particulate matter (PM) pollutants in the downwind direction of the stack. The results include the effect of wind speed, stack height, stack outlet diameter and the speed of exhaust gases on the plume characteristics (maximum distance, height, and diameter), concentrations of pollutants, and tracks of the particles emitted from the stack. Generally, the present study belongs to the second category of numerical investigations.

In the succeeding sections, we will present the computational models together with the results of the examined cases.

Computational Models

The flow that emits from a stack is a rather complex one. It is a turbulent flow with

several constituents including gases and particulate matter (PM) pollutants. For handling such a complicated flow, the viscous flow equations are employed together with two turbulent models; namely:

(a) K–ε model. (b) The Large Eddy Simulation (LES) model.

The k-ε model was employed for solving the two-dimensional, steady, incompressible flow to define the distribution of the gaseous pollutants downstream of the stack. However, modeling was extended by using large eddy simulation (LES) to solve the three-dimensional, unsteady, incompressible flow for the gaseous and particulate matter (PM) pollutants.

K–ε Model: “Governing Equations of the Pollution (Impurity) Model

and Computational Aspects” General Navier–Stokes equations together with continuity equation comprise a closed

set of equations suitable for any fluid mechanics problem [13]. The solution of which provides a valid description for any laminar or turbulent flow. However, because of the


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difficulty of solving these equations directly for the turbulent flow, it is better to take a statistical approach. This approach is suitable for the engineering applications where the details of fluctuating motion are not important. This is achieved by averaging the equations over a time scale, which is long compared to that of the turbulent motion. Thus, a form of turbulence modeling is obtained.

Here, k–ε turbulence model is considered for a two-dimensional, steady, incompressible air flow containing a scalar impurity [14]. Air is assumed to be viscous and heat conducting in rather slow turbulent motion. Thus, the model of an air flow is the following:

0=⋅∇−V (1)

−−−∇=

∇+⎟⎟

⎠

⎞⎜⎜⎝

⎛∇⋅ VPVV 2 ν

ρ (2)

ji i ti t

i j i j j k i

UU Uk kUx x x x x x

νν εσ

⎛ ⎞∂ ⎛ ⎞∂ ∂∂ ∂ ∂= + − −⎜ ⎟ ⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂ ∂ ∂⎝ ⎠⎝ ⎠

(3)

1 2jt i i

i ti i i j j i

UU UU C Cx x x k x x xε ε

ε

νε ε ε νσ

⎡ ⎤⎛ ⎞∂∂ ∂∂ ∂ ∂= + + −⎢ ⎥⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂ ∂ ∂⎢ ⎥⎝ ⎠⎣ ⎦

(4)

TTV 2

Pr∇=⎟⎟

⎠

⎞⎜⎜⎝

⎛∇⋅

− ν (5)

2 CV Dϕ ϕ−⎛ ⎞⋅∇ = ∇⎜ ⎟

⎝ ⎠ (6)

Where ρ is the air density, −

V is the flow velocity vector, ν is the kinematic viscosity, νt is the eddy viscosity (= Cµ k2/ε), P is the pressure, T is the temperature, Pr is the Prandtl number, ϕ is the mass concentration of an impurity, Dc is the molecular diffusion coefficient, k is the turbulence energy, and ε is the turbulence dissipation rate. σk, σε, Cε1, Cε2, and Cµ are the model coefficients. The above equations (Eqs. (1)-(6)) are approximated by a second-order-accurate central difference on a two-dimensional staggered, rectangular; structured grid. The grid is fine near solid boundaries and is stretched gradually away to the far field. The no penetration and no slip conditions were applied at the solid boundaries. The approaching velocity profile is prescribed by the well known power law. Appropriate treatments of the values of k and ε at the domain boundaries were applied [13]. The Large Eddy Simulation (LES) Discrete Model

The following section gives details of the governing equations of LES for both

gaseous and particle flow.

Filtered Navier-Stokes Equations (for Gaseous Flow) Turbulent flows are characterized by eddies with a wide range of length and time

scales. The largest eddies are typically comparable in size to the characteristic length of the mean flow. The smallest scales are responsible for the dissipation of turbulence kinetic energy. The governing equations employed for LES are obtained by filtering the time-dependent Navier-Stokes equations in either Fourier (wave-number) space or configuration (physical) space [15].


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Filtering the incompressible Navier-Stokes equations, one obtains

Continuity equation ( ) 0=∂∂

+∂∂

ii

uxt

ρρ (7)

Momentum equation ( ) ( )j

ij

ij

i

jji

ji xx

Pxu

xuu

xu

t ∂

∂−

∂∂

−⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

∂∂

=∂∂

+∂∂ τ

ρρµ

ρ111 (8)

Where ui is the instantaneous velocity vector, and τij is the subgrid-scale stress defined by )( jijiij uuuu −= ρτ (9)

As for the thermal field, energy equation takes the form:

TTVtT 2

Pr∇=⎟⎟

⎠

⎞⎜⎜⎝

⎛∇⋅+

∂∂ − ν (10)

The diffusion equation of air pollution in the atmosphere; a statement for conservation of the suspended material, can be written for a non–reactive species as:

2

2

2

2

zCK

yCK

xCU

tC

zy∂

∂+

∂

∂=

∂∂

+∂∂ (11)

Where, U is the mean velocity of the wind, C is the concentration at any point of the domain, and Ky and Kz are the diffusion coefficients. Particle Flow Models (Equations of Motion of Particles)

Particle–Fluid interaction defines the trajectory of particles emitted from the stack.

This approach is based on treating the particles as sources of mass, momentum, and energy to the gaseous phase [3]. The equation of motion for a particle takes the following form:

∑= ip F

dtUd

(12)

Where, pU is the particle velocity, ∑ iF is the sum of all forces acting on the particle per unit mass of particle, which are in general drag, lift and gravitational forces as follows.

(a) Drag Force ( DF )

( )pD

ppD UUC

dF −

∗

∗=

24Re18

2ρµ (13)

Where, U is the fluid phase velocity, pU is the particle velocity, µ is the viscosity of the fluid, ρ is the fluid density, pρ is the density of the particle, and dp is the particle diameter, Re is the Reynolds number, which is defined as

µ

ρ UUd pp −=

Re (14)

The drag coefficient, CD, can take the form, [15],

( )Re

ReRe11Re24

4

32+

+∗+=bbbC b

D (15)

where ( )2

1 4486.24581.63288.2exp Φ+Φ−=b Φ+= 5565.00964.02b

( )323 2599.104222.188944.13905.4exp Φ−Φ+Φ−=b


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( )324 8855.157322.202584.124681.1exp Φ+Φ−Φ−=b

The shape factor, Φ, is defined as sS

Φ =

Where, s is the surface area of a sphere having the same volume as the particle and S is the actual surface area of the particle.

(b) Gravity Force ( gF )

( ) pg

p

gF

ρ ρ

ρ

−= (16)

Where, g =gravitational acceleration.

(c) Pressure Gradient Force ( pF ) It is a force due to pressure gradient in the fluid.

xUUF p

pp ∂

∂= ρρ (17)

(e) Saffman’s Lift Force ( LF )

1__ __22

L pp p

KF U Udυ ρ

ρ⎛ ⎞= −⎜ ⎟⎝ ⎠

(18)

Where, K=2.594. The subgrid-scale stresses (Eq. (9)), resulting from the filtering operation, are

unknown, and require modeling. The Smagorinsky-Lilly model, which is a form of eddy viscosity models [15], was adopted in the present investigation. The above equations (Eqs. (7)-(18)) were solved using an unstructured (tetrahedral or quadrilateral) grid. The grid was generated to be fine near the solid boundaries. Boundary and initial conditions were properly prescribed allover the computational domain.

Results and Discussion Results of k–ε Model

In this study, concentration is focused on the plume maximum-height (Zmax), and the

plume maximum-distance downstream of the stack (Xmax). The results demonstrate the important relations between the basic parameters of air pollution problem (such as the wind speed, and the exhaust gas speed) and the maximum-distance, the maximum-height of the uniform plume, and the concentration of pollutants at any location. Emission angle is kept at 90 deg. (vertical emission).

The variations of the non–dimensional plume maximum-distance (Xmax/H), traveled by the plume and the non–dimensional maximum-height (Zmax/H) with wind speed are shown in Figs. 2 and 3, respectively, at different emission speeds (from 3 to 10 m/s) for a stack height of 50 m and diameter of 1.5 m. Generally, the characteristic values increase with the emission speed (Vgas). Figure 2 shows that there is a peak value for the non–dimensional maximum-distance (Xmax/H). The corresponding wind speed for this peak depends on the emission speed. This peak moves in the direction of increasing the wind speed as the emission speed increases. Figure 3 illustrates that the non–dimensional maximum-height (Zmax/H) is reached when the air is stagnant (Vwind=0 m/s). Increasing the wind speed decreases the non–dimensional maximum-height reached by the plume. The effect of stack height (from 10 to


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100 m) on the non–dimensional plume maximum traveling distance and height is shown in Figs. 4 and 5, respectively, for different emission speeds. Figure 4 shows that the non–dimensional maximum-plume-distance (Xmax/H) decreases with the increase of stack height. The non–dimensional maximum-plume-height (Zmax/H) decreases with increasing the stack height. Figures 6–9 display comparisons of the important characteristics at an emission speed of 5 m/s for stack diameters of 1.5 and 3 m. Figure 6 displays the non–dimensional maximum-plume-distance (Xmax/H) with the wind speed. It shows that the non–dimensional maximum-distance (Xmax/H) increases with the increase of the stack diameter. Figure 7 displays the non–dimensional maximum-plume-height against the wind speed. It is clear that the non–dimensional maximum-height increases with the increase of the stack diameter. Figure 8 illustrates the maximum-plume-distance against the stack height. It can be seen that the non–dimensional maximum-distance (Xmax/H) increases by a small amount with the increase of the stack diameter. Figure 9 displays the non–dimensional maximum-plume-height (Zmax/H) with the stack height. It appears that the non–dimensional maximum-height (Zmax/H) increases by a small amount with the increase of the stack diameter. Figure 10 shows the variation of the temperature of the exit gases relative to ambient temperature (Tgas/Tambient) at the centerline of the plume against the distance along the centerline of the plume at different emission speeds from 3 to 10 m/s. Figure 11 shows the variation of the concentration of the exhaust pollutant gases relative to maximum concentration (C/Cmax %) at the centerline of the plume with the distance along the centerline of the plume at different emission speeds from 3 to 10 m/s. It takes about 2000 m for C/Cmax to drop to about 5%.

Results of LES Model

Investigation covers different test cases for a single stack. Wind speed is assumed to

obey the power law. The emission angle of discharge is taken to be 90 deg. relative to the wind direction (i.e., the exhaust gases exit uniformly in the vertical direction). Stack height (H) varies from 10 to 100 m. Discharge temperature is kept constant at the value of 420 K (147 oC). The plume characteristics (maximum-distance, Xmax, maximum-height, Zmax, and maximum-width or diameter, Ymax) are presented firstly. These characteristics are determined when the plume starts to dissipate in the surrounding atmosphere. This study is also concerned with gas temperature distribution and the distribution of the pollutant concentrations at any location downstream the stack. Concentrations of the components of the pollutant exhaust gas (CO2, CO, SO2, and NOx) are calculated. Also, trajectory of solid particles of different sizes (diameters) will be displayed.

The variations of the non–dimensional maximum-plume-distance (Xmax/H), traveled by the plume, the non–dimensional maximum-height (Zmax/H) and the non–dimensional maximum-width (diameter) of the plume (Ymax/D) with wind speed are shown in Figs. 12–14, respectively, for different gas emission speeds (from 2 to 10 m/s) and a stack of 50 m–height and a diameter of 1.5 m. Generally, the characteristic values increase with the emission speed (Vgas). Figure 12 shows that there is a peak value for the non-dimensional maximum-distance (Xmax/H). Similar behavior of the results of the k–ε model is noticed. Figure 13 illustrates that the non-dimensional maximum-height (Zmax/H) is reached when the air is stagnant (Vwind=0 m/s). Increasing the wind speed, at the same gas-exit speed, decreases the non-dimensional maximum-height reached by the plume. Figure 14 shows that the increase of the wind speed above a certain limit decreases the non-dimensional maximum-plume-width (diameter). This may be attributed to the rapid dissipation of the plume. The effect of stack height (from 10 to 100 m) on the plume maximum traveling distance, height, and width (diameter) are shown in Figs. 15–21, respectively, for different emission speeds. Figure 15 shows that the non-dimensional maximum-plume-distance (Xmax/H) decreases with the increase of stack height.


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The non-dimensional maximum-plume-height (Zmax/H) decreases with increasing the stack height, Fig. 16. In Fig. 17, the behavior of the non-dimensional plume-maximum-width (diameter) (Ymax/D) changes by small amounts with the increase of the stack height.

Figures 18–23 display comparisons between the important relations at an emission speed of 5 m/s for stack diameters of 1.5 and 2.5 m. Figure 18 displays the non–dimensional maximum plume distance against the wind speed. It shows that the non-dimensional maximum-distance (Xmax/H) increases with the increase of the stack diameter for a range of wind speed from 2 to 14 m/s. Figure 19 displays the non-dimensional maximum-plume-height (Zmax/H) with the wind speed. It shows that the non-dimensional maximum-height (Zmax/H) increases with the increase of the stack diameter. When the wind speed reaches 16 m/s, the effect of stack diameter begins to vanish. Figure 20 shows the non-dimensional maximum-plume-width (Ymax/D) against the wind speed. It shows that the non-dimensional maximum-width (Ymax/D) decreases with the increase of the stack diameter. Figure 21 illustrates the non-dimensional maximum-plume-distance (Xmax/H) against the stack height. It shows that the non-dimensional maximum-distance (Xmax/H) increases slightly with the increase of the stack diameter. This means that the increase of gas discharge has a slight effect on Xmax. Figure 22 shows that the non-dimensional maximum-height (Zmax/H) increases with the increase of the stack diameter. Figure 23 shows that the non-dimensional maximum-plume-width decreases with the increase of the stack diameter. However, stack height has a slight effect on Ymax.

Figure 24 shows the trajectory of the solid particles of different sizes (1 – 100 micro–meter) that exit from the stack. The material of these particles is carbon, which has an average density of 2885 Kg/m3. Naturally, the distance traveled by the solid particle decreases as the particle size increases. For very light particles (From 1 to 9 micro–meter), the particle may travel to distances that exceed 24 Km downstream the emitting stack. Heavy particles (dp= 100 micro–meter) fall to the ground in less than 1.0 km. Figure 25 shows cross–sections in the plume at different locations downstream the stack with the distribution of the particles according to their sizes. These results are very useful in the planning of the construction of new industrial projects nearby urban or sub–urban areas. Figure 26 shows the contour maps of the temperature of the exhaust gases downwind the stack in two planes (horizontal and vertical). The shown planes pass through the centerline of the plume. It is noticed that the temperature of the plume needs 1600 m to drop by about 150 K. Thus, it is expected that the presence of many tall stacks (e.g., in a modern industrial complex) may lead to considerable changes in the weather temperature and cloud formation in the surrounding area. Figure 27 shows the contour maps of the concentration of the pollutant gases (CO2, CO, SO2, and NOx) that exit from the stack, in the horizontal plane. Gas concentration is measured in milli-gram/m3. It is noticed that maximum concentration is that of CO2. However, other gasses (CO, SO2 & NOx) are found by considerable amounts for a distance of 15 km downstream the stack. Thus, proper choice of the stack specifications is extremely important to lower the hazards to human health.

Comparisons (a) Comparison between Present Models

Comparisons between the two employed computational models ((k–ε) and large eddy

simulation (LES)) are displayed in Figs. 28–31 for a stack of height 50 m, and diameter 1.5 m. Figure 28 displays the maximum-plume-distance for the two models for a wide range of wind speed while the gas–exit speed is 3 m/s. It is observed that the two models have the same trend and that the steady state model (k–ε model) has higher values compared to the large eddy simulation (LES). Figure 29 displays the maximum-plume-height for the two models. It is observed that the two models have the same trend and that the k–ε model (two–dimensional


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model) has smaller values of the maximum-height of the plume. Figure 30 displays the maximum-plume-distance for the two models for a wide range of stack height at a wind speed of 5 m/s and a gas-exit speed of 3 m/s. It is observed that LES has smaller values than the k–ε model. Figure 31 displays the maximum-plume-height for the two models. It is observed that the k–ε model has smaller values of plume height than the other model for different stack heights. The differences between the predictions of the two models may be attributed to many reasons, namely: (i) k-ε model was applied to a steady flow in a 2-D domain, whereas, LES was applied to an unsteady flow in a 3-D domain. (ii) The impurity (pollution) representation in the k-ε model is simpler than that of LES. (iii) Due to the nature of LES, its grid dependence is less than that of k-ε model especially near the solid boundaries. (b) Comparison between Present Models and Others

Figure 32 shows a comparison between the two present models and the published

experimental and numerical results of Ref. [9] for the plume temperature. Temperature is recorded along the centerline of the plume. These results are for a stack of height 13 m, and diameter of 1.2 m at a wind speed of 5 m/s, and ambient temperature of 300 K. Figure 34 shows the relative error of the k–ε and large eddy simulation (LES) results w.r.t. experimental results. Thus, large eddy simulation is nearer to the published data as it has maximum relative error of 6.5%, whereas k–ε model has a maximum relative error of 17%. Figure 36 shows the relative error of k–ε and large eddy simulation (LES) method w.r.t. the numerical results of Ref. [9] also. Large eddy simulation (LES) is the closer to the published data as it has a maximum relative error of 3.8% while the k–ε model has a maximum relative error of 18%.

Figure 33 shows a comparison between the two present models and the experimental and numerical published results of Ref. [9] for the normalized plume velocity (U/Ua) along the centerline of the plume where (Ua = wind speed). Figure 35 shows the relative error of k–ε model and large eddy simulation (LES) w.r.t. the experimental results. Large eddy simulation is closer to the published data as it has a maximum relative error of 9% but k–ε model has a maximum relative error of 37%. Figure 37 shows the relative error of k–ε model and LES w.r.t. the numerical results. Again, large eddy simulation (LES) is advantageous over k–ε model .It has a maximum relative error of 3% while the k–ε model has a maximum relative error up to 33%. The comparisons of Figs. 32-37 show that the predictions of LES are much closer to the experimental results. Thus, the present methodology of using LES is reliable. However, the two-dimensional k-ε model is beneficial in giving an overall, as well as quick and low-cost, idea of the plume behavior. It is worth mentioning that 2-D k-ε model is much simpler than the 3-D LES and needs much less computer run-time.

Conclusions

The present investigation aims to describe the dispersion of air pollutants from a

single stack into the surrounding atmosphere. A wide parametric study, of the different factors that affect the plume characteristics, was carried out. The results of two computational models (k-ε & LES) were reported. Based on the previous results and discussion, the following points can be summarized:

1- The numerical techniques that were applied in the present study proved to be very effective tools in investigating the plume behavior of a single stack. Full details (real-time views) of the development of the plume can be recorded and investigated.


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2- The present predictions of large eddy simulations (LES) compare very well to the published numerical and experimental data. Thus, 3-D time-dependent simulations with a detailed impurity (pollutant) model are more suitable for the present problem.

3- There is a peak value for the non-dimensional maximum-distance of the plume (Xmax/H) that depends on both the wind speed (Vwind) and gas-exit speed (Vgas). Naturally, (Xmax/H) increases with the increase of the amount of discharge from the stack.

4- The non-dimensional maximum-height of the plume (Zmax/H) increases with gas-exit speed (Vgas) but decreases with wind speed (Vwind).

5- The non-dimensional maximum-width of the plume (Ymax/H) increases with wind speed (Vwind) until it reaches a maximum value then it starts to decrease rapidly.

6- The stack height has a small effect on the non-dimensional maximum-distance (Xmax/H) and -width (Ymax/H). However, it has an observed effect on the non-dimensional maximum-height (Zmax/H).

7- The dissipation of pollutants (gaseous or solid) is a complex process that depends on the different operating and atmospheric conditions (e.g. wind speed, gas-exit speed, particle size, etc.).

Generally, the present work highlights the way to determine the optimum health-safe distance, away from an industrial stack, according to the local environmental regulations. The authors wish that this effort would help in the planning and constructing of the new industrial zones throughout Egypt. References 1. H. Yoshikado and H. Kondo, Inland Penetration of the Sea Breeze over the Suburban

Area of Tokyo, Boundary–Layer Meteorology, 48, pp. 389–407, 1989. 2. F. Desiato and M. G. Ciminelli, Plume Dispersion Investigated by LANDSAT Imagery,

Atmospheric Environment, Vol. 25A, No. 5/6, pp. 965–978, 1991. 3. A. Seifert and L. Shemer, Plume Rise from a Chimney with an Elongated Exit Cross

Section, Atmospheric Environment, Vol. 29, No. 6, pp. 709–713, 1995. 4. P. C. Kumar and J. A. Wehrmeyer, Stack Gas Pollutant Detection Using Laser Raman

Spectroscopy, J. Applied Spectroscopy, 51(6), pp. 849–855, 1997. 5. M. Uliasz and R. A. Pielke, Implementation of Lagrngian Particle Dispersion Model for

Mesoscale and Regional Air Quality Studies, Proc. of the 93th Int. Conf. on Air Pollution, Mexico, Computational Mechanics Publications, Ashurst, UK, pp. 157–164, 1993.

6. K. J. Craig, D. J. De Kock and J. A. Snyman, Using CFD and Mathematical Optimization to Investigate Air Pollution due Stacks, Int. J. Numer. Meth. Eng., 44, pp. 551–565, 1999.

7. A. F. Abdel Azim, A. F. Abdel Gawad and M. M. Ibrahim, Study of Air Pollution due to Industrial Spots nearby the Campus of Zagazig University (Egypt), Proc. of the 9th Int. Conf. on Modelling, Monitoring and Management of Air Pollution, Italy, WIT press, Southamton, UK, pp. 233–242, 2001.

8. J. Lopez and A.Salcido, Air Pollution Modeling with Turbulence Data Estimated from Conventional Meteorological Parameters in an Urban Tropical Region, Proc. of the 9th Int. Conf. on Modelling, Monitoring and Management of Air Pollution, Italy, WIT press, Southamton, UK, pp. 45–56, 2001.

9. F. I. Khan and S. A. Abbasi, Modelling and Simulation of Heavy Gas Dispersion on the Basis of Modifications in Plume Path Theory, J. of Hazardous Materials, A80, 15-30, 2000.


12

10. C. Mangia, I. Schipa, D. M. Moreira, T. Tirabassi, G. A. Degrazia and U. Rizza, A New Eddy Diffusivity Parameterisation for Dispersion Models: Evaluation in Different Atmospheric Conditions, Proc. of the 9th Int. Conf. on Modelling, Monitoring and Management of Air Pollution, Italy, WIT press, Southamton, UK, pp. 105–112, 2001.

11. F. Liu and Y. Hong, Application of the Dust Diffusion Model Method in China, J. Aerosol Sci., 27(1), pp. S93–S94, 1996.

12. R. Cipollone and A. Sciarretta, A Lattice Gas Model for the Evaluation of Transport and Diffusion Parameters of Stack Emissions in Air, Proc. of the 9th Int. Conf. on Modelling, Monitoring and Management of Air Pollution, Italy, WIT press, Southamton, UK, pp. 153–162, 2001.

13. A. F. Abdel Gawad, Computational of Turbulent Flow and Heat Transfer in Rotating Non–Circular Ducts, Ph. D. Thesis, Mech. Power Eng. Dept., Faculty of Engineering, Zagazig University, Egypt, 1998.

14. A. P. Trunev, Similarity Theory and Model of Diffusion in Turbulent Atmosphere at Large Scales, Proc. of the 5th Int. Conf. on Air Pollution, Bologna, Italy, Modelling, Monitoring and Management, Computational Mechanics Inc., Billerica, MA, USA, pp. 423–432, 1997.

15. User’s manual, FLUENT–6.0, Fluent Inc., USA, 2001.

Fig. 1. Basic dimensions of a plume.

X

Y

Z Mean wind

Plume axis

Cross-section of Plume

Ky

Kz

H

Zmax Ymax

Xmax


13

Fig. 2. Relation between wind speed and Fig. 3. Relation between wind speed and normalized maximum-plume-distance for normalized maximum-plume-height for different gas-exit speeds, H=50 m, D=1.5 m. different gas-exit speeds, H=50 m, D=1.5 m. Fig. 4. Relation between stack height and Fig. 5. Relation between stack height and normalized maximum-plume-distance for normalized maximum-plume-height for different gas-exit speeds, different gas-exit speed, D=1.5 m and Vwind=5 m/s. D=1.5 m and Vwind=5 m/s.

Fig. 6. Comparison between the normalized Fig. 7. Comparison between the normalized maximum-plume-distance for two stack maximum-plume-height for two stack diameters in a wide range of wind speed, diameters in a wide range of wind speed, H=50 m, Vgas=5 m/s. H=50 m, Vgas=5 m/s.

Wind speed (m/s)

Nor

mal

ized

max

imum

plum

ehe

ight

(Zm

ax/H

)

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

3

3.5

4Vgas=10 m/sVgas=5 m/sVgas=3 m/s

Stack height (m)

Nor

mal

ized

max

imum

plum

edi

stan

ce(X

max

/H)

10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

120

140

160

180


Stack height (m)

Nor

mal

ized

max

imum

plum

ehe

ight

(Zm

ax/H

)

10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7


W ind speed (m/s)

Nor

mal

ized

max

imum

plum

edi

stan

ce(X

max

/H)

0 2 4 6 8 10 12 14 16 18 200

10

20

30

40

50

D=3 mD=1.5 m

W ind speed (m/s)

Nor

mal

ized

max

imum

plum

ehe

ight

(Zm

ax/H

)

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

3

3.5

4

D =3 mD =1 .5 m

Wind speed (m/s)

Nor

mal

ized

max

imum

plum

edi

stan

ce(X

max

/H)

0 2 4 6 8 10 12 14 16 18 200

10

20

30

40

50

60

70

80Vgas=10 m/sVgas=5 m/sVgas=3 m/sPeak Point


14

Fig. 8. Comparison between the normalized Fig. 9. Comparison between the normalized maximum-plume-distance for different maximum-plume-height for different diameters in a wide range of stack height, diameters in a wide range of stack height, Vwind=5 m/s, Vgas=5 m/s. Vwind=5 m/s, Vgas=5 m/s. Fig. 10. Normalized temperature distribution Fig. 11. Concentration of gases at plume for different gas-exit speeds, centerline for different gas-exit speeds, H=50 m, Vwind=5 m/s, D=1.5 m. H=50 m, D=1.5 m, Vwind=5 m/s.

Fig.12. Relation between wind speed and Fig.13. Relation between wind speed and normalized maximum-plume-distance for normalized maximum-plume-height for different gas-exit speeds, H=50m, D=1.5m. different gas-exit speeds, H=50m, D=1.5m.

Downwind distance (m)

Exi

tgas

tem

pera

ture

(T/T

a)

0 250 500 750 1000 1250 1500 1750 20001

1.1

1.2

1.3

1.4

1.5

1.6

Vgas=10 m/sVgas=5 m/sVgas=3 m/s


Con

cent

ratio

nat

plum

ece

nter

line

(C/C

max

)

0 250 500 750 1000 1250 1500 1750 20000

10

20

30

40

50

60

70

80

90

100

Vgas=10 m/sVgas=5 m/sVgas=3 m/s

Stack height (m)

Nor

mal

ized

max

imum

plum

ehe

ight

(Zm

ax/H

)

10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7

D=3 mD=1.5 m

Stack height (m)

Nor

mal

ized

max

imum

plum

edi

stan

ce(X

max

/H)

10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

120

140

160

180

200

D=3 mD=1.5 m

Wind speed (m/s)

Nor

mal

ized

max

imum

plum

ehe

ight

(Zm

ax/H

)

0 2 4 6 8 10 12 14 16 18 200

1

2

3

4

5

6

Vgas=10 m/sVgas=7 m/sVgas=5 m/sVgas=2 m/s

W ind speed (m/s)

Nor

mal

ized

max

imum

plum

edi

stan

ce(X

max

/H)

0 2 4 6 8 10 12 14 16 18 200

10

20

30

40

50

60

70Vgas=10 m/sVgas=7 m/sVgas=5 m/sVgas=2 m/sPeak Point


15

Fig.14. Relation between wind speed and Fig.15. Relation between stack height and normalized maximum-plume-width for normalized maximum-plume-distance for different gas-exit speeds, H=50m, D=1.5m. different gas-exit speeds, Vwind=5m/s, D=1.5m. Fig.16. Relation between stack height and Fig.17. Relation between stack height and normalized maximum-plume-height for normalized maximum-plume-width for different gas-exit speeds, Vwind=5m/s,D=1.5m. different gas-exit speeds, Vwind=5m/s, D=1.5m. Fig. 18. Comparison between the normalized Fig. 19. Comparison between the normalized maximum-plume-distance for two stack maximum-plume-height for two stack diameters in a wide range of wind diameters in a wide range of wind speed, H=50 m, Vgas=5 m/s. speed, H=50 m, Vgas=5 m/s.

Stack height (m)

Nor

mal

ized

max

imum

plum

edi

stan

ce(X

max

/H)

10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

120

140

160


S tack height (m)

Nor

mal

ized

max

imum

plum

ehe

ight

(Zm

ax/H

)

10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7

8


S tack he ight (m )

Nor

mal

ized

max

imum

plum

ew

idth

(Ym

ax/D

)

10 20 30 40 50 60 70 80 90 1000

5

10

15

20

25

30

35

40

45

50

55

60

65

70

V gas= 1 0 m /sV gas= 7 m /sV gas= 5 m /sV gas= 2 m /s

W ind speed (m/s)

Nor

mal

ized

max

imum

plum

edi

stan

ce(X

max

/H)

0 2 4 6 8 10 12 14 16 18 200

5

10

15

20

25

30

35

40

D =2.5 mD =1.5 m

W ind speed (m/s)

Nor

mal

ized

max

imum

plum

ehe

ight

(Zm

ax/H

)

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

D =2.5 mD =1.5 m

W ind speed (m/s)

Nor

mal

ized

max

imum

plum

ew

idth

(Ym

ax/D

)

0 2 4 6 8 10 12 14 16 18 200

10

20

30

40

50

60Vgas=10 m/sVgas=7 m/sVgas=5 m/sVgas=2 m/sPeak Point


16

Fig. 20. Comparison between the normalized Fig. 21. Comparison between the normalized maximum-plume-width for two stack diameters maximum-plume-distance for two stack in a wide range of wind speed, diameters in a wide range of stack H=50 m, Vgas=5 m/s. height, Vwind=5 m/s, Vgas=5 m/s. Fig. 22. Comparison between the normalized Fig. 23. Comparison between the normalized maximum-plume-height for different diameters maximum-plume-width for different in a wide range of stack height, diameters in a wide range of stack height, Vwind=5 m/s, Vgas=5 m/s. Vwind=5 m/s, Vgas=5 m/s. .

Fig. 24. Trajectory of solid particles of different diameters; emitting from a stack of H=50 m, D=2.5 m & Vwind=5 m/s, Vgas=10 m/s.

W ind speed (m/s)

Nor

mal

ized

max

imum

plum

ew

idth

(Ym

ax/D

)

0 2 4 6 8 10 12 14 16 18 200

5

10

15

20

25

30

35

40

45

D=2.5 mD=1.5 m

Stack height (m)

Nor

mal

ized

max

imum

plum

edi

stan

ce(X

max

/H)

10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

120

140

D =2.5 mD =1.5 m

S ta ck he ight (m )

Nor

mal

ized

max

imum

plum

ehe

ight

(Zm

ax/H

)

1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 000

1

2

3

4

5

6

7

D = 2 .5 mD = 1 .5 m

S ta ck he ig h t (m )

Nor

mal

ized

max

imum

plum

ew

idth

(Ym

ax/D

)

1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 00

5

1 0

1 5

2 0

2 5

3 0

3 5

4 0

4 5

5 0

D = 2 .5 mD = 1 .5 m

X ( K m )

Z(m

)

0 3 6 9 1 2 1 5 1 8 2 1 2 40

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

D = 6 0 m i c r o - m e t e rD = 7 0 m i c r o - m e t e rD = 8 0 m i c r o - m e t e rD = 9 0 m i c r o - m e t e rD = 1 0 0 m i c r o - m e t e r


17

Fig. 24. (cont.)

(a) X=0.5 Km (b) X=1.0 Km (c) X=1.5 Km (d) X=2.0 Km Fig. 25. Distribution of solid particles at different plume cross-sections in the wind direction for a stack of H=50 m, D=2.5 m & Vwind=5 m/s, Vgas=10 m/s.

X ( K m )

Z(m

)

0 3 6 9 1 2 1 5 1 8 2 1 2 40

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

D = 1 0 m i c r o - m e t e rD = 2 0 m i c r o - m e t e rD = 3 0 m i c r o - m e t e rD = 4 0 m i c r o - m e t e rD = 5 0 m i c r o - m e t e r

X ( K m )

Z(m

)

0 3 6 9 1 2 1 5 1 8 2 1 2 40

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

D = 1 m i c r o - m e t e rD = 3 m i c r o - m e t e rD = 5 m i c r o - m e t e rD = 7 m i c r o - m e t e rD = 9 m i c r o - m e t e r

Y ( m )

Z(m

)

4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 4 0 1 5 00

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

D = 1 -5 m ic ro

D = 5 - 9 m ic ro

D = 9 - 1 0 m ic ro

D = 1 0 -3 0 m ic ro

D = 3 0 - 5 0 m ic ro

D = 5 0 - 6 0 m ic ro

D = 6 0 - 8 0 m ic ro

D = 8 0 - 1 0 0 m ic ro

Y ( m )

Z(m

)

4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 4 0 1 5 00

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

D = 1 - 5 m ic ro

D = 5 - 9 m ic ro

D = 9 - 1 0 m ic roD = 1 0 - 3 0 m ic ro

D = 3 0 - 5 0 m ic ro

D = 5 0 - 6 0 m ic ro

D = 6 0 - 8 0 m ic ro

D = 8 0 - 1 0 0 m ic ro

Y (m )

Z(m

)

4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 4 0 1 5 00

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

D = 1 -5 m icro

D = 5 - 9 m icro

D = 9 - 1 0 m icro

D = 1 0 -3 0 m icro

D = 3 0 - 5 0 m icro

D = 5 0 - 6 0 m icro

D = 6 0 - 7 0 m icro

D = 7 0 - 8 0 m icro

Y (m )

Z(m

)

4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 4 0 1 5 00

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

D = 1 -5 m icro

D = 5 - 9 m icro

D = 9 - 1 0 m icro

D = 1 0 -3 0 m icro

D = 3 0 - 5 0 m icro

D = 5 0 - 6 0 m icroD = 6 0 - 7 0 m icro


18

(e) X=3 Km (f) X=5 Km (g) X=9 Km (h) X=15 Km

Fig. 25. (cont.)

Fig. 26. Temperature distribution downwind the stack in two planes for

a stack of H=50 m, D=2.5 m & Vwind=5 m/s, Vgas=10 m/s, Tambient=300 K.

X ( m )

Y(m

)

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 00

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

1 3 0

1 4 0

1 5 0

T e m p e r a t u r e ( K )4 5 04 4 0 . 6 2 54 3 1 . 2 54 2 1 . 8 7 54 1 2 . 54 0 3 . 1 2 53 9 3 . 7 53 8 4 . 3 7 53 7 53 6 5 . 6 2 53 5 6 . 2 53 4 6 . 8 7 53 3 7 . 53 2 8 . 1 2 53 1 8 . 7 53 0 9 . 3 7 5

X ( m )

Z(m

)

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 00

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

1 3 0

1 4 0

1 5 0

T e m p e r a t u r e ( K )4 5 04 4 0 . 6 2 54 3 1 . 2 54 2 1 . 8 7 54 1 2 . 54 0 3 . 1 2 53 9 3 . 7 53 8 4 . 3 7 53 7 53 6 5 . 6 2 53 5 6 . 2 53 4 6 . 8 7 53 3 7 . 53 2 8 . 1 2 53 1 8 . 7 53 0 9 . 3 7 5

Y (m )

Z(m

)

4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 4 0 1 5 00

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

D = 1 -5 m ic ro

D = 5 - 9 m ic ro

D = 9 - 1 0 m icro

D = 1 0 -3 0 m icro

D = 3 0 - 4 0 m icro

D = 4 0 - 5 0 m icro

Y (m )

Z(m

)

4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 4 0 1 5 00

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

D = 1 -5 m icro

D = 5 - 9 m icro

D = 9 - 1 0 m icro

D = 2 0 -3 0 m ic ro

D = 3 0 - 4 0 m icro

D = 1 0 - 2 0 m ic ro

Y (m )

Z(m

)

4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 4 0 1 5 00

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

D = 1 -5 m icro

D = 5 - 9 m icro

D = 9 - 1 0 m icro

D = 2 0 -3 0 m icro

D = 1 0 - 2 0 m icro

Y (m )Z

(m)

4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 4 0 1 5 00

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

D = 1 -5 m icro

D = 5 - 9 m ic ro

D = 9 - 1 0 m icro

D = 1 0 - 2 0 m icro


19

Fig. 27. Concentration of different components of the emitted gas from a stack of H=50 m, D=2.5 m & Vwind=5 m/s, Vgas=10 m/s.

X ( m )

Y(m

)

0 3 0 0 0 6 0 0 0 9 0 0 0 1 2 0 0 0 1 5 0 0 00

3 0

6 0

9 0

1 2 0

1 5 0

1 8 0

2 1 0

2 4 0

2 7 0

3 0 0

C O 2 ( m g / m 3 )1 6 7 01 5 6 5 . 4 51 4 5 3 . 6 31 3 4 1 . 8 11 2 2 9 . 9 91 1 1 8 . 1 81 0 0 6 . 3 68 9 4 . 5 4 27 8 2 . 7 2 46 7 0 . 9 0 65 5 9 . 0 8 84 4 7 . 2 7 13 3 5 . 4 5 32 2 3 . 6 3 51 0 0

X ( m )

Y(m

)

0 3 0 0 0 6 0 0 0 9 0 0 0 1 2 0 0 0 1 5 0 0 00

3 0

6 0

9 0

1 2 0

1 5 0

1 8 0

2 1 0

2 4 0

2 7 0

3 0 0

C O ( m g / m 3 )1 6 01 5 1 . 0 5 21 4 0 . 2 6 31 2 9 . 4 7 31 1 8 . 6 8 41 0 7 . 8 9 49 7 . 1 0 4 88 6 . 3 1 5 47 5 . 5 2 66 4 . 7 3 6 55 3 . 9 4 7 14 3 . 1 5 7 73 2 . 3 6 8 32 1 . 5 7 8 81 0

X ( m )

Y(m

)

0 3 0 0 0 6 0 0 0 9 0 0 0 1 2 0 0 0 1 5 0 0 00

3 0

6 0

9 0

1 2 0

1 5 0

1 8 0

2 1 0

2 4 0

2 7 0

3 0 0

N O x ( m g / m 3 )2 3 5 . 4 0 62 1 9 . 7 1 22 0 4 . 0 1 81 8 8 . 3 2 41 7 2 . 6 3 11 5 6 . 9 3 71 4 1 . 2 4 31 2 5 . 5 51 0 9 . 8 5 69 4 . 1 6 2 27 8 . 4 6 8 56 2 . 7 7 4 84 7 . 0 8 1 13 1 . 3 8 7 41 5 . 6 9 3 7

X ( m )

Y(m

)

0 3 0 0 0 6 0 0 0 9 0 0 0 1 2 0 0 0 1 5 0 0 00

3 0

6 0

9 0

1 2 0

1 5 0

1 8 0

2 1 0

2 4 0

2 7 0

3 0 0

S O 2 ( m g / m 3 )3 3 8 . 3 9 63 1 5 . 8 3 62 9 3 . 2 7 62 7 0 . 7 1 62 4 8 . 1 5 72 2 5 . 5 9 72 0 3 . 0 3 71 8 0 . 4 7 81 5 7 . 9 1 81 3 5 . 3 5 81 1 2 . 7 9 99 0 . 2 3 8 86 7 . 6 7 9 14 5 . 1 1 9 42 2 . 5 5 9 7


20

Fig. 28. Comparison between normalized Fig. 29. Comparison between normalized maximum-plume-distance obtained from the two maximum-plume-height obtained from two computational models for a stack of H=50m, computational models for a stack of H=50m, D=1.5m, Vgas=3m/s for different wind speeds. D=1.5m,Vgas=3m/s for different wind speeds. Fig. 30. Comparison between normalized Fig. 31. Comparison between normalized maximum-plume-distance obtained from maximum-plume-height obtained from the the two computational models for a stack of two mathematical models for a stack of D=1.5m,Vwind=5m/s, Vgas=3m/s for D=1.5m, Vwind=5m/s, Vgas=3m/s for different stack heights. different stack heights. Fig.32. Comparison between present models Fig.33. Comparison between present models and experimental and numerical published and experimental and numerical published results [9] for normalized plume-temperature. results [9] for normalized plume-velocity.

W in d sp e e d (m /s)

Nor

mal

ized

max

imum

plum

edi

stan

ce(X

max

/H)

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 00

5

1 0

1 5

2 0

2 5

3 0

K -e p silo n m o d e lL a rg e E d d y S im u la tio n

W in d spe e d (m /s)

Nor

mal

ized

max

imum

plum

ehe

ight

(Zm

ax/H

)

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 00

0 .5

1

1 .5

2

2 .5

3

3 .5

4

4 .5

5

K -e p silo n m o d e lL a rg e E d d y S im u la tio n

S ta ck he igh t (m )

Nor

mal

ized

max

imum

plum

edi

stan

ce(X

max

/H)

1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 00

2 0

4 0

6 0

8 0

1 0 0

1 2 0

1 4 0

1 6 0

1 8 0

K -e p silo n m o de lL a rg e E d d y S im u la tio n

S ta ck h e ig h t (m )

Nor

mal

ized

max

imum

plum

ehe

ight

(Zm

ax/H

)

1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 00

1

2

3

4

5

6

K -e p s ilo n m o d e lL a rg e E d d y S im u la tio n

D ownwind distance (m )

Nor

mal

ized

plum

eve

loci

ty(U

/Ua)

0 200 400 600 800 1000 1200 14000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

E xperim enta l (Khan and Abbasi)N um erica l (Khan and Abbasi)K-epsilon m odelLarge E ddy S im ulation

D ownwind distance (m )

Nor

mal

ized

plum

ete

mpe

ratu

re(T

/Ta)

0 200 400 600 800 1000 1200 14000.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

E xperim enta l (Khan and Abbasi)N um erica l (Khan and Abassi)K-epsilon m odelLarge E ddy S im ulation


21

Fig. 34. Relative percentage error of k–ε Fig. 35. Relative percentage error of k–ε model and large eddy simulation to the model and large eddy simulation to the experimental published results [9] for plume experimental published results [9] for plume temperature. velocity. Fig. 36. Relative percentage error of k–ε Fig. 37. Relative percentage error of k–ε model and large eddy simulation to model and large eddy simulation to numerical numerical published results [9] for published results [9] for plume velocity. plume temperature.

D ownwind distance (m)

Vel

ocity

rela

tive

erro

r(%

)

0 200 400 600 800 1000 1200 1400

0

5

10

15

20

25

30

35

40

K- epsilonLarge Eddy Simulation


Vel

ocity

rela

tive

erro

r(%

)

0 200 400 600 800 1000 1200 1400

0

5

10

15

20

25

30

35

40



Tem

pera

ture

rela

tive

erro

r(%

)

0 200 400 600 800 1000 1200 1400-2

0

2

4

6

8

10

12

14

16

18

20

22

24


D ownwind distance (m)

Tem

pera

ture

rela

tive

erro

r(%

)

0 200 400 600 800 1000 1200 1400-2

0

2

4

6

8

10

12

14

16

18

20

22

24

K-epsilonLarge Eddy S imulation

Turbulent Modeling of the Plumes of a Single Stack

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