scholarly journals Numerical Study Process Distribution of Contaminated Substances in the Atmosphere Taking Into Account the Physical and Mechanical Properties of Particles

2021 ◽  
pp. 10-15
Keyword(s):  
Numerical Study ◽  
Physical And Mechanical Properties ◽  
Software Tool ◽  
Industrial Emissions ◽  
Factors Affecting ◽  
Implicit Finite Difference Scheme ◽  
Implicit Finite Difference ◽  
Harmful Substances ◽  
Study Process ◽  
And Diffusion

The article deals with the numerical modeling of the processes of transfer and diffusion of air pollutants in the boundary layer of the atmosphere. A mathematical model of the spread of industrial emissions in the atmosphere was developed, taking into account the motion velocity of finely dispersed substances and a number of other factors affecting the change in the concentration of harmful substances in the atmosphere. The model is described by multidimensional partial differential equations with corresponding initial and boundary conditions. For the numerical integration of the problem, the method of splitting into physical processes (of transfer, diffusion and absorption) and an implicit finite-difference scheme of the second order of approximation in spatial variables and in time were used. A software tool was developed to conduct a computational experiment on a computer and to perform a comprehensive study of the processes of transfer and diffusion of harmful substances in the atmosphere

scholarly journals The process of distribution Computer modeling of hazardous substances in the atmosphere taking into account the terrain relief

2021 ◽  
Vol 264 ◽  
pp. 01037
Author(s):  
Daler Sharipov ◽  
Zafar Abdullaev ◽  
Otabek Khafizov
Keyword(s):  
Mathematical Model ◽  
Climatic Factors ◽  
Software Tool ◽  
Hazardous Substances ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Factors Affecting ◽  
Transport And Diffusion ◽  
Harmful Substances ◽  
And Diffusion

The paper considers a mathematical model for research, forecasting, and management decisions on the process of spreading harmful aerosol substances in the atmosphere. When deriving a mathematical model of the object, the main weather and climatic factors affecting the process of transport and diffusion of harmful substances and the terrain of the region under consideration are taken into account. Changes in wind direction and speed are calculated using the Navier-Stokes equation of stream function and vortex velocity variables. The proposed software was implemented as a software tool in the Borland C ++ Builder environment to carry out computational experiments. The results of the performed numerical calculations are shown in the form of graphical objects.

scholarly journals Numerical Study of the Performance of a Double-Insulated Barbecue Oven: Implication for Energy Savings and Thermal Comfort

2021 ◽  
pp. 5-18
Author(s):  
Serge Wendsida Igo ◽  
Gaël Lassina Sawadogo ◽  
Drissa Ouedraogo ◽  
Abdoulaye Compaoré ◽  
David Namoano ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Energy Balance ◽  
Thermal Comfort ◽  
Energy Savings ◽  
Numerical Study ◽  
Energy Losses ◽  
Nodal Method ◽  
Implicit Finite Difference Scheme ◽  
Transfer Equations ◽  
Implicit Finite Difference

This work is devoted to a numerical study of the performance of a double insulated barbecue oven using terracotta bricks and plywood. The numerical methodology is based on the nodal method and the heat transfer equations have been established by performing an energy balance on each node. The equations obtained were then discretized using an implicit finite difference scheme and solved by the Gauss algorithm. The numerical results validated by the experiment show that this double insulation considerably reduces the energy losses through the walls of the oven. However, the addition of plywood does not significantly change the energy savings compared to simple terracotta insulation but does drop the external wall temperatures. Thus, for 4 cm of thickness of terracotta bricks and 1 cm of plywood, the energy savings (compared to the non-insulated oven) are of the order of 70% and the temperature of the outer walls of the oven does not exceed not 60°C, which ensures better thermal comfort for users.

Starting vortex, separation bubbles and stall: a numerical study of laminar unsteady flow around an airfoil

1975 ◽  
Vol 67 (2) ◽  
pp. 227-256 ◽  
Author(s):  
Unmeel B. Mehta ◽  
Zalman Lavan
Keyword(s):  
Numerical Study ◽  
Separation Bubble ◽  
Governing Equations ◽  
Implicit Finite Difference Scheme ◽  
Vortex Separation ◽  
Initial Generation ◽  
Relaxation Procedure ◽  
Implicit Finite Difference ◽  
Incipient Separation ◽  
Successive Relaxation

The stalling characteristics of an airfoil in laminar viscous incompressible fluid are investigated. The governing equations in terms of the vorticity and stream function are solved using an implicit finite-difference scheme and point successive relaxation procedure. The development of the impulsively started flow, the initial generation of circulation, and the behaviour of the forces at large times are studied.Following the impulsive start, the lift is at first very large and then it rapidly drops. The subsequent growth of circulation and lift is associated with the starting vortex. After incipient separation, the lift increases owing to enlargement of the separation bubble and intensification of the flow rotation in it. The extension of this bubble beyond the trailing edge causes it to rupture and brings about the stalling characteristics of the airfoil. Subsequently, new bubbles are formed near the upper surface of the airfoil and are swept away. The behaviour of the lift acting on the airfoil is explained in terms of the strength and sense of these bubbles. The lift increases when attached clockwise bubbles grow and when counterclockwise bubbles are swept away and vice versa.

scholarly journals A Numerical Study of the Effect of Particle Size on Particle Deposition on Turbine Vanes and Blades

2021 ◽  
Vol 13 (5) ◽  
pp. 168781402110178
Author(s):  
Zhengang Liu ◽  
Weinan Diao ◽  
Zhenxia Liu ◽  
Fei Zhang
Keyword(s):  
Particle Size ◽  
Particle Deposition ◽  
Numerical Study ◽  
Stokes Number ◽  
Capture Efficiency ◽  
Particle Capture ◽  
Factors Affecting ◽  
Pressure Surface ◽  
Deposition Area ◽  
Turbine Vanes

Particle deposition could decrease the aerodynamic performance and cooling efficiency of turbine vanes and blades. The particle motion in the flow and its temperature are two important factors affecting its deposition. The size of the particle influences both its motion and temperature. In this study, the motion of particles with the sizes from 1 to 20 μm in the first stage of a turbine are firstly numerically simulated with the steady method, then the particle deposition on the vanes and blades are numerically simulated with the unsteady method based on the critical viscosity model. It is discovered that the particle deposition on vanes mainly formed near the leading and trailing edge on the pressure surface, and the deposition area expands slowly to the whole pressure surface with the particle size increasing. For the particle deposition on blades, the deposition area moves from the entire pressure surface toward the tip with the particle size increasing due to the effect of rotation. For vanes, the particle capture efficiency increases with the particle size increasing since Stokes number and temperature of the particle both increase with its size. For blades, the particle capture efficiency increases firstly and then decreases with the particle size increasing.

scholarly journals Numerical Investigation into Emission, Depletion, and Thermal Decomposition in a Reacting Slab

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
O. D. Makinde ◽  
T. Chinyoka ◽  
R. S. Lebelo
Keyword(s):  
Thermal Decomposition ◽  
Fossil Fuels ◽  
Mitigation Strategies ◽  
Assessment Tools ◽  
Nonlinear Mathematical Model ◽  
Heat And Mass Exchange ◽  
Implicit Finite Difference Scheme ◽  
Oil And Natural Gas ◽  
Implicit Finite Difference ◽  
Thermal Stability Of

The emission of carbon dioxide (CO2) is closely associated with oxygen (O2) depletion, and thermal decomposition in a reacting stockpile of combustible materials like fossil fuels (e.g., coal, oil, and natural gas). Moreover, it is understood that proper assessment of the emission levels provides a crucial reference point for other assessment tools like climate change indicators and mitigation strategies. In this paper, a nonlinear mathematical model for estimating the CO2emission, O2depletion, and thermal stability of a reacting slab is presented and tackled numerically using a semi-implicit finite-difference scheme. It is assumed that the slab surface is subjected to a symmetrical convective heat and mass exchange with the ambient. Both numerical and graphical results are presented and discussed quantitatively with respect to various parameters embedded in the problem.

scholarly journals A robust numerical solution to a time-fractional Black–Scholes equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. M. Nuugulu ◽  
F. Gideon ◽  
K. C. Patidar
Keyword(s):  
Finite Difference ◽  
Stock Options ◽  
Stochastic Dynamics ◽  
European Options ◽  
Numerical Convergence ◽  
Put Option ◽  
Implicit Finite Difference Scheme ◽  
Black Scholes ◽  
Implicit Finite Difference ◽  
Rigorous Mathematical Analysis

AbstractDividend paying European stock options are modeled using a time-fractional Black–Scholes (tfBS) partial differential equation (PDE). The underlying fractional stochastic dynamics explored in this work are appropriate for capturing market fluctuations in which random fractional white noise has the potential to accurately estimate European put option premiums while providing a good numerical convergence. The aim of this paper is two fold: firstly, to construct a time-fractional (tfBS) PDE for pricing European options on continuous dividend paying stocks, and, secondly, to propose an implicit finite difference method for solving the constructed tfBS PDE. Through rigorous mathematical analysis it is established that the implicit finite difference scheme is unconditionally stable. To support these theoretical observations, two numerical examples are presented under the proposed fractional framework. Results indicate that the tfBS and its proposed numerical method are very effective mathematical tools for pricing European options.

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