Axisymmetric Turbulent Methane Jet Propagation in a Co-Current Air Flow Under Combustion at a Finite Velocity

2021 ◽  
pp. 89-108
Author(s):  
I.K. Khujaev ◽  
M.M. Hamdamov
Keyword(s):  
Turbulence Model ◽  
Air Flow ◽  
Maximum Temperature ◽  
Order Of Accuracy ◽  
Total Enthalpy ◽  
Combustible Gas ◽  
Implicit Finite Difference Scheme ◽  
Fuel Nozzle ◽  
Implicit Finite Difference ◽  
Research Show

The paper introduces a numerical method for solving the problem of the axisymmetric methane jet propagation in an infinite co-current air flow. For modeling, we used the dimensionless equations of the turbulent boundary layer of reacting gases in the Mises coordinates. To close the Reynolds equation, a modified k - ε turbulence model was used. The k - ε model is considered a low Rhine turbulence model. Assuming that the intensities of convective and turbulent transfers of components are the same and using the stoichiometric ratios of the concentrations of components during combustion, we reduced five equations for the transfer and conservation of the mass of components to two equations for the relative excess concentration of the combustible gas. The concentrations of the components were determined from the solutions of these equations. By using relatively excessive velocities and total enthalpy, we reduced the boundary conditions for the three equations to a general form. To solve the problem in the Mises coordinates, we used a two-layer, six-point implicit finite-difference scheme, which provides the second order of accuracy of approximation in coordinates. The equations for the conservation and transfer of substances being non-linear, an iterative process was implemented. The influence of the radius of the fuel nozzle on the indices of the turbulent jet and flame was investigated. Findings of research show that in an endless co-current flow of fuel with a decrease in the radius of the nozzle, the rate of the chemical reaction and the maximum temperature in the calculation area decrease, and the amount of unburned part of the combustible gas increases

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.

scholarly journals Finite Difference Solution to a Nonlinear Time-Fractional Logistic Model

2021 ◽  
Vol 13 (2) ◽  
pp. 60
Author(s):  
Yuanyuan Yang ◽  
Gongsheng Li
Keyword(s):  
Finite Difference ◽  
Theoretical Analysis ◽  
Difference Scheme ◽  
Logistic Model ◽  
Stability And Convergence ◽  
Numerical Examples ◽  
Implicit Finite Difference Scheme ◽  
Finite Difference Solution ◽  
Implicit Finite Difference ◽  
Convergence Of The Scheme

We set forth a time-fractional logistic model and give an implicit finite difference scheme for solving of the model. The L^2 stability and convergence of the scheme are proved with the aids of discrete Gronwall inequality, and numerical examples are presented to support the theoretical analysis.

The Simulation of Natural Ventilation of Buildings With Different Location of Windows/Openings

2015 ◽  
Author(s):  
A. Idris ◽  
B. P. Huynh ◽  
Z. Abdullah
Keyword(s):  
Air Quality ◽  
Flow Pattern ◽  
Turbulence Model ◽  
Natural Ventilation ◽  
Air Flow ◽  
Building Design ◽  
Building Envelope ◽  
Navier Stokes ◽  
Computational Domain ◽  
Numerical Predictions

Ventilation is a process of changing air in an enclosed space. Air should continuously be withdrawn and replaced by fresh air from a clean external source to maintain internal good air quality, which may referred to air quality within and around the building structures. In natural ventilation the air flow is due through cracks in the building envelope or purposely installed openings. Its can save significant amount of fossil fuel based energy by reducing the needs for mechanical ventilation and air conditioning. Numerical predictions of air velocities and the flow patterns inside the building are determined. To achieve optimum efficiency of natural ventilation, the building design should start from the climatic conditions and orography of the construction to ensure the building permeability to the outside airflow to absorb heat from indoors to reduce temperatures. Effective ventilation in a building will affects the occupant health and productivity. In this work, computational simulation is performed on a real-sized box-room with dimensions 5 m × 5 m × 5 m. Single-sided ventilation is considered whereby openings are located only on the same wall. Two opening of the total area 4 m2 are differently arranged, resulting in 16 configurations to be investigated. A logarithmic wind profile upwind of the building is employed. A commercial Computational Fluid Dynamics (CFD) software package CFD-ACE of ESI group is used. A Reynolds Average Navier Stokes (RANS) turbulence model & LES turbulence model are used to predict the air’s flow rate and air flow pattern. The governing equations for large eddy motion were obtained by filtering the Navier-Stokes and continuity equations. The computational domain was constructed had a height of 4H, width of 9H and length of 13H (H=5m), sufficiently large to avoid disturbance of air flow around the building. From the overall results, the lowest and the highest ventilation rates were obtained with windward opening and leeward opening respectively. The location and arrangement of opening affects ventilation and air flow pattern.

Natural Convection in a Non-Uniformly Heated Vertical Annular Cavity

2017 ◽  
Vol 377 ◽  
pp. 189-199 ◽  
Author(s):  
M. Sankar ◽  
S. Kiran ◽  
G.K. Ramesh ◽  
Oluwole Daniel Makinde
Keyword(s):  
Natural Convection ◽  
Boundary Conditions ◽  
Outer Wall ◽  
Uniform Heating ◽  
Cylindrical Wall ◽  
Thermal Boundary Conditions ◽  
Nusselt Numbers ◽  
Implicit Finite Difference Scheme ◽  
Implicit Finite Difference ◽  
Model Equations

Natural convection from the linearly heated inner and/or outer walls of a vertical annular cavity has been numerically investigated. The bottom wall is uniformly heated and top cylindrical wall is thermally insulated. In this analysis, we considered two different thermal boundary conditions, namely case (I) and case (II) to understand the effect of non-uniform heating of inner and/or outer walls on the convective flow and subsequently the local and global heat transfer rate. For case (I), the inner and outer walls are heated linearly, while the linearly heated inner wall and cooled outer wall is considered in case (II). An implicit finite difference scheme is applied to solve the model equations of the problem. The numerical simulations in terms of streamlines and isotherms, local and global Nusselt numbers are presented to illustrate the effects of Rayleigh number and non-uniform thermal boundary conditions for a fixed Prandtl number of Pr = 0.7.

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